Abstract: The growth of polymer crystals in a dilute solution is theoretically investigated in terms of secondary nucleation and growth. Effects of the finiteness of molecular chain length and the nucleation of cilia are considered on the basis of the kinetic theory studied by Seto and Frank. The dependence of the growth rate of polyethylene single crystals on concentration and supercooling is explained as regime II growth where the growth of lower molecular weight materials (M_w <2.5×10⁴) is controlled by the nucleation of solute molecules while that of higher ones (M_w > 8×10⁴) by the nucleation of cilia.

Abstract: The lateral growth of polyethylene single crystals has been investigated. The dependence of the linear growth rate G on concentration C and supercooling ΔT was studied with fractionated polyethylene of relatively low molecular weight (M_w = 1.1×10⁴ and M_w/M_n = 1.16). The crossover of concentration dependence of growth rate was clearly observed; the exponent y (G ∝ C^y) varies from 1/2 to 1 with decreasing concentration. The variation of growth with concentration and supercooling is discussed in terms of a kinetic theory taking into account finite molecular length. The analysis shows that the growth is in the mode of multi-nucleation growth (regime II).

Abstract: A Monte Carlo simulation of nucleation and growth processes on one-dimensional substrates of finite length is presented with the step-gas model and the solid-on-solid model. The number of growth steps on the substrate is obtained and compared with analytic solutions quantitatively. The analytic solution of Bennett et al, and Goldenfeld is shown to be accurate. That of Frank is shown to be slightly overestimated in the crossover region between regimes I and II. This disagreement is attributed to the mean-field approxiniation employed. The recently predicted growth mode controlled by cilia-nucleation has been confirmed by the simulation.

Abstract: A model of growth of polymer single crystals is presented, taking account of the effect of impurity on secondary nucleation and growth process. The impurity on growth steps interrupts further crystallization of molecules on the steps. This effect gives rise to rounded lateral habits for single crystals of poly(ethylene oxide), branched polyethylene and linear polyethylene. A once folded chain stem on extended chain crystal surface as well as small branch and adsorbed solvent have the effect of impurity, respectively. The effect on the growth mode and lateral habit is analytically derived by kinetic equations. The results are applied to supercooling dependence of growth rate and lateral habit of polyethylene single crystals grown from poorer solvents.

Abstract: The growth rate of polyethylene single crystals is investigated in n-octane and decalin solutions for a wide range of supercoolings and concentrations. Transitions in the dependence of growth rate on supercooiing and concentration are found to occur at relatively low supercooling. The transitions cannot be explained as transitions from regime II to regime I. They are discussed in terms of the effect of an impurity on the growth process; travelling steps are interrupted by an impurity on the steps. The origin of the impurity is discussed. A low molecular weight fraction segregated from the growth face or a small loop defect along the crystallizing chains will behave as an impurity. The lateral habit obtained in n-octane solution at lower supercoolings is somewhat rounded on the {100} face. The rounding of the habit is also discussed as an impurity effect.

Abstract: We have succeeded in obtaining the nucleation rate and velocity of the travelling of steps from the nucieation and growth processes of polymer crystallization, utilizing the enhanced growth at re-entrant corners of {110} twinned crystals of polyethylene. The supercooling dependence of nucleation rate is two times as strong as that of growth rate; this fact suggests that the growth is by multi-nucleation (regime II). The velocity of steps is proportional to the concentration of solution and nucleation rate is independent of the concentration over the usual concentration range. These relations suggest that the growth face is saturated with adsorbed polymer molecules and the travelling of steps is controlled by the volume diffusion of polymer in the solution. The method described can be applied to other systems which have the same type of reentrant corner.

Abstract: We have studied the growth kinetics of {110} twins and single crystals of polyethylene in dilute solution of tetrachloroethylene. In terrns of {110} twins, we succeeded in obtaining twins without {100} sectors, using a relatively high molecular weight fraction M_w > 10⁴. It is confirrned that the growth is enhanced at the reentrant corner of the twins, and the enhanced growth face inclines to the {110} face because of consecutive generation of steps at the comer. These facts are strong evidence for nucleation-controlled growth of single crystals. The growth rates and obliquity are measured at various supercoolings and concentrations. From consideration of kinetics of steps on the growth face, the following rates and velocity are independently determined from the experirnental data: nucleation rate on a fiat face, velocity of step propagation, and generation rate of steps at the reentrant corner. The supercoohng dependence strongly supports regime ll growth. The results on concentra}tion dependence show that the velocity of steps is proportional to concentration over the whole range examined, and the nucleation rate is independent of it in the usual range and becomes proportional to it in the lower range. This concentration dependence of nucleation rate is attributed to the density of adsorbed polymer on the growth face. From this evidence, it is suggested that the rate of travel of steps is lirnited by volume diffusion of solute polymer, whereas the growth face is saturated with adsorbed polymer at ordinary concentrations. This contradictory situation could be explained by the hypothesis that the saturation density is rather low and that surface diffusion of adsorbed polymer is much slower than volume diffusion of solute polymer. The lower limit of the rate of folding is also deterrnined for the first time from the velocity of step propagation. As regards the single crystals, it is found that the habit maintains a lozenge shape with sharpened points, even at very high supercooling (ΔT > 50ºC) if the concentration is very dilute. Diffusion-limited growth is verified for the first time at the higher supercoolings, where the growth rate is almost independent of supercooling. The growth rate becomes almost equivalent to the velocity of steps determined in the experiments with twins, and this fact will support the accuracy of the evaluation of the step velocity. The order of magnitude of the growth rate obtained agrees with the value which is calculated from the balance between the flux of solute polymer to the grbwth face and the rate of growth of single crystals.

Abstract: The nucleation rate and propagation rate of steps on the {100} faces of polyethylene crystals have been determined. For single crystals, under conditions where the width of the {100} sectors remains constant during growth, it is confirmed that the growth is in regime I or the crossover region between regime I and II. In {110} twinned crystals, the {100} sectors are well developed and the width increases linearly with time; therefore, the growth in the twins must be in regime II. It is shown that the differing growth regimes of {100} faces in single crystals and twins allow the independent determination of the nucleation rate and the propagation rate of steps. The nucleation rate and propagation rate of steps on the {100} faces were determined from measurements of the constant width of the {100} faces in shgle crystals and the growth rate of the {100} faces in single crystals and twins. The observed rates show abnormal dependence on supercooling and concentration. The results are attributed to a weaker dependence of the constant width of {100} sectors on supercooling and concentration than predicted.

Abstract: The lateral crystal habit of polyethylene has been studied experimentally and theoretically. When the fraction of low-molecular-weight polyethylene (M_w = 2090 and M_w/M_n = 1.1) is crystallized from n-hexacontane solution at high temperatures (T> 105ºC), most chains are extended in the crystals and the lateral shape of single crystals becomes lenticular. The longer axis of the lenticular profile is parallel to the b axis of crystals and the tip has an acute angle; the {110} growth face disappears in this habit. The curved outline of the lenticular habit has been analysed with the kinetic theory of Seto and Frank on the basis of nucleation-controlled growth. A moving boundary condition has been applied to the growth of the crystal sector, as was done by Mansfield. It is shown that the lenticular habit is expected for strongly retarded crystallization on the {100} growth face.

Abstract: The lateral crystal habits of n-alkanes (n-C_nH_2n+2) have been observed just below the melting points bv optical microscopy for n = 18, 19, 20, 22, 24, 34, 44, 50 and 65. The shape of the crystals depends on the crystal phase: circular in the rotator phase, lenticular in phase C, and diamond in the low-temperature phase. The rounding of the lateral shape can be explained in terms of thermal roughening of the lateral faces in the disordered phases at high temperature.

Abstract: New results from experiments on light scattering from spherulites of polyethylene and isotactic polystyrene have been obtained. It was found that HV scattering can be explained well by the sum of the scattering from a perfect spherulite, i.e, a polycrystalline aggregate with radial symmetry, and that from randomly oriented crystallites. The orientation-correlation function of the randomly oriented crystallites has a form of exp( -r/a), where a is the correlation length, which is about one-sixth of the radius of the spherulite.

Abstract: In situ observation of the growth of isotactic polystyrene has been carried out under a transmission electron microscope. Bundles of lamellar crystals first emerge from the melt, and then a planar crystal parallel to (001) grows out from one end of each bundle. The planar crystal assumes the shape of a hexagon faceted with {110} planes surrounding the bundle at the center. The thickness of the melt surrounding the crystal is smaller than that of the outer area.

Abstract: Using the technique of extraction, single crystals have been obtained from polyethylene fractions isothermally crystallized from the melt at atmospheric pressure. It has been found that the lateral habit of single crystals changes in the vicinity of the transition temperature of growth regime (regime 1–II): lenticular shape elongated in the direction of the b axis (type A) in the range of regime I and truncated lozenge with curved edges of {100} and {110} growth faces (type B) in that of regime II. The transition of lateral habit causes a drastic change in the width of {110} growth faces; {110} growth faces are well developed in type B crystals while they cannot be observed and must be very small in type-A crystals. It has been shown that the growth regime of the small {110} growth face of type-A crystals must be in regime I; hence, the regime I–II transition can be explained as the result of this change in lateral habit (width of the {110} growth face).

Abstract: Three-dimensional shape of polyethylene single crystals grown from the melt has been studied. Two distinct types of lateral habit have been obtained: lenticular shape (type A) and truncated lozenge (type B) in the range of regime I and II. Electron microscopy has revealed chair-like shape of type B crystal and reconfirrned the planar shape of type A crystal. In the type B crystal, spiral growth has occurred frequently in the {110} sectors and the sense of the handedness of spiral terraces has been maintained. It has been suggested that the frequent occurrence of spiral growth is responsible for a morphological change (axialite-spherulite) accompanying the regime I–II transition. The origin of the chair-like crystals has been discussed and a possible mechanism has been suggested for the formation of spiral terraces; the mechanism is based on a distortion caused by the three-dimensional shape of chair-like crystals. It has been found that the chairlike crystals are curved in the opposite way to S-shaped lamellae observed by Bassett and Hodge in banded spherulites. In fact, the present work has led to the recognition of further classes of crystal with curving cross-sections and of distinctions between them. In final analysis, a unifying thread has been identified between lateral habits, growth kinetics and three-dimensional shape of lamellae, in turn, leading to some rationalization of multilayer developments including twisting in banded spherulites, the latter based on existing suggestions in the literature.

Abstract: The stability of neck propagation and its oscillatory mode have been studied for the cold drawing of poly(ethylene terephthalate) films. On the basis of Barenblatt's model considering a temperature rise at the neck, the stability has been analysed for neck propagation at constant speed and at constant load. It is shown that the stability is directly connected to the sign of the slope of the stress-drawing rate plot; unstable neck propagation should be in the region of negative slope. It is argued that the unstable mode changes to an oscillatory neck propagation for drawing at constant speed, while the mode in drawing at constant load is transformed to the other stable region. Experimental study has confirmed the unstable drawing at constant load and the transition of neck propagation rate. Oscillatory neck propagation has also been examined by a numerical calculation of non-Iinear differential equations based on Barenblatt's model. The limits of Barenblatt's model are also discussed.

Abstract: Recent investigations on the crystal growth of polyethylene from dilute solution and from the melt are reviewed. 1) The supercooling dependence of growth rate suggests the growth controlled by surface nucleation for the crystallization both from dilute solution and from the melt. 2) For solution crystallization, the growth should be in regime II. The growth mode of regime II explains the concentration dependence of growth rate, taking account of the nucleation of cilia. Surface nucleation rate shows the same concentration dependence as the adsorption isotherm of Langmuir's type. This means that the growth face is saturated with the adsorbed polymer in the normal range of concentrations (10^-3 – 10^-1 wt%). 3) Modified Seto and Frank's model considering the slow propagation of steps explains the curved growth front of single crystals obtained at higher temperatures from dilute solutions and from the melt. 4) The. regime I–II transition proposed for the growth from the melt can be attributed to the change in the laterai hablts from lenticular shape to truncated lozenge in the course of the regime I–II transition.

Abstract: The growth kinetics and morphology of polyethylene single crystals of a narrow molecular mass fraction (M_w = 1.36×10⁴ and M_w/M_n = 1.19) have been studied. Single crystals extracted from the melt show two types of curved lateral habit: a lenticular shape elongated in the direction of the b-axis and a truncated lozenge with curved edges of the {110} growth faces. The change in the lateral habits occurs in the vicinity of a transition in the supercooling dependence of growth rate, which has been explained as a change of growth mode from mono-nucleation (regime I) to multi-nucleation (regime II) growth. It has been argued that the growth mode change can be explained as the result of the morphological change in lateral habits. Concerning the origin of the curved lateral habits, the necessary conditions, such as the slow propagation of steps, have been discussed and a theoretical approach based on Seto and Frank's kinetics has been undertaken. The experimental results obtained are very similar to the results obtained recently for a higher molecular weight fraction and hence the present results confirm the model presented previously.

Abstract: Atomic force microscopy (AFM) was applied to the precise thickness measurements of thin lameliae nm thick of polyethylene single crystals which were grown from dilute solutions and precipitated on cleaved mica. The obtained values agree well with the thickness determined by small angle X-ray scattering. Moreover, observation allowed determination of the thickness difference of several angstroms in the different growth sectors of small crystals about several μ m wide. From the measurements, it was concluded that the free energy of the fold surface in the {110} growth sector was 30% larger than the values in the {100} sector. The larger surface energy in the {110} sector means higher fold energy in the growth sector.

Abstract: This article aims to link the mainstream subject of chain-folded polymer crystallization with the rather speciality field of extended-chain crystallization, the latter typified by the crystallization of polyethylene (PE) under pressure. Issues of wider generality are also raised for crystal growth, and bevond for phase transformations. The underlying new experimental material comprises the prominent role of metastable phases, specifically the mobile hexagonal phase in polyethylene which can arise in preference to the orthorhombic phase in the phase regime where the latter is the stable regime, and the recognition of "thickening growth" as a primary growth process, as opposed to the traditionally considered secondary process of thickening. The scheme relies on considerations of crystal size as a thermodynamic variable, namely on melting-point depression. which is, in general, different for different polymorphs. It is shown that under specifiable conditions phase stabilities can invert with size; that is a phase which is metastable for infinite size can become the stable phase when the crystal is sufficiently small. As applied to crystal growth, it follows that a crystal can appear and grow in a phase that is different from that in its state of ultimate stability, maintaining this in a metastab]e form when it may or may not transform into the ultimate stable state in the course of growth according to circumstance. For polymers this intermediate initial state is one with high-chain mobility capable of "thickening growth" which in turn ceases (or slows down) upon transformation, when and if such occurs, thus "locking in" a finite lamellar thickness. The complete situation can be represented by a P-T-\ell(crystal thickness) phase-stability diagram which, coupled with kinetic considerations, embodies all recognized modes of crystallization including chain-folded and extended-chain type ones. The task that remains is to assess which applies under given conditions of P and T. A numerical assessment of the most widely explored case of crystallization of PE under atmospheric pressure indicates that there is a strong likelihood (critically dependent on the choice of input parameters) that crystallization may proceed via a metastable, mobile, hexagonal phase, which is transiently stable at the smallest size where the crystal first appears, with potentially profound consequences for the current picture of such crystallization. Crystallization of PE from solution, however, would, by such computations, proceed directly into the final stage of stability, upholding the validity of the existing treatments of chain-folded crystallization. The above treatment, in its wider applicability, provides a previously unsuspected thermodynamic foundation of Ostwald's rule of stages by stating that phase transformation will always start with the phase (polymorph) which is stable down to the smallest size, irrespective of whether this is stable or metastable when fully grown, In the case where the phase transformation is nucleation controlled, a ready connection between the kinetic and thermodynamic considerations presents itself, including previously invoked kinetic explanations of the stage rule. To justify the statement that the crystai size can control the transformation between two polymorphs, a recent result on 1-4-poly-trans-butadiene is invoked, Furthermore, phase-stability conditions for wedge-shaped geometries are considered, as raised by current experimental material on PE. It is found that inversion of phase stabilities (as compared to the conditions pertainfng for parallel-sided systems) can arise, with consequences for our scheme of polymer crystallization and with wider implications for phase transformations in tapering spaces in general. In addition, in two of the Appendices two themes of overall generality (arising from present considerations for polymers) are developed analytically; namely, the competition of nucleation-controlled phase growth of polymorphs as a function of input parameters, and the effect of phase size on the triple point in phase diagrams. The latter case leads, inter alia to the recognition of previously unsuspected singularities, with consequences which are yet to be assessed.

Abstract: It is shown that under speciflable circumstances stabilities of competing phases can invert with size: specifically, that a phase which is metastable when of inflnite size can become the stable one when of sufficiently small dimensions. It follows that phase development, crystal growth in particular, may start in a phase variant which becomes metastable when the new phase is fully developed. If it stays in this form Ostwald's rule of stages will seem to be obeyed, if it transforms into the phase of ultimate stability the past history of phase development becomes obliterated. In the special instance of flexible polymers, polyethylene in particular, there can be thickening growth while in the metastable 'mobile' phase (hexagonal phase in polyethylene), hence residence within this phase will determine the lamellar thickness, consequently also the final texture of the crystallizing material. Based on these considerations the two so far essentially disconnected areas of chain folded and extended chain type crystallization can be visualised within a unified frame work with new, broadened perspectives for the whole subject of polymer crystallization. In addition, the scheme creates a junction between thermodynamic (stability) and kinetic (rates) aspects of phase transitions in wider generality.

Abstract: The oscillatory behaviour of neck propagation during cold drawing of polymer films has been studied numericaily. Previous calculations based on Barenblatt's model considering the temperature rise at the neck have been refined by introducing heat diffusion and the consequent temperature distribution in the film. Period doubling of the oscillation and other phenomena that were observed experimentally and remained to be explained have been produced by the refined model.

Abstract: This lecture is aimed to link the "main stream" subject of chain folded polymer crystallization to the "speciality stream" of extended chain crystallization: the latter as typified by the crystallization of polyethylene under pressure. This is achieved through a scheme based on some new experimental material comprising the recognition of thickening growth as a primary growth process of lamellae and of the prominence of metastable phases, specifically of the mobile hexagonal phase in polyethylene. The scheme relies on the consideration of crystal size as a stability determining factor, namely on melting point depression, which in general is different for different polymorphs. It is shown that under specificable conditions phase stabilities can invert with size, i.e. a phase which is metastable fof infinite size can become the stable one when the phase is sufficiently small. When applying this condition to crystal growth it follows that a crystal in such a situation will appear and grow in a phase that is different from that in its state of ultimate stability, maintaining this state as a metastable one or transforming into the ultimate stable state during growth according to circumstances. The consequences of such deliberations, of potential significance to all phase transformations also beyond polymer crystallization, are being developed throughout the paper.

Abstract: The growth of isotactic polystyrene crystals from a thin melt film is examlnecl by atomic force microscopy. The crystals protrude from the film up to about 126 nm to form a hexagonal spira1 with a hollow screw dislocation at the center; the distance between neighboring steps of the growth spiral is discussed on the basis of the critical nucleus. The entire crystal has collapsed to the substrate. An amorphous layer a few nanometers thick covers the surface of the crystal. At the crystal-liquid interface, a concave region about 2 nm deep extends ca. 426 nm.

Abstract: The growth kinetics of single crystals of polyethylene from dilute solution have been studied. Special emphasis was placed on the role of adsorption of polyethylene chains on the growth face prior to the process of surface nucleation. It has been argued that an adsorption isotherm determines the concentration dependence of the growth rate and introduces a change in the dependence. The change in the concentration (C) dependence of the growth rate (G) is basically from G ∝ C^1/2 to G ∝ C with decreasing concentrations, The Langmuir adsorption isotherm explains the change as a transition from a dilute to a plateau regime correspondlng to the saturation of the growth face with adsorbed polymer. Experiments have been carried out with several molecular-weight fractions to examine the molecular-weight dependence of the crossover concentration of the solution. There is found to be an exponential decrease in crossover concentration with increasing molecular weight. This result agrees with the prediction derived from the models of Langmuir-type polymer adsorptlon and provides strong support for the above argument.

Abstract: The dependence of the lamellar thickness (\ell) of an extended-chain single crystal (ECSC) of polyethylene (PE) crystallized at various pressures below or at the triple-point pressure (P_tri = 0.5 GPa) on the degree of supercooling (ΔT) and the pressure have been studied. The value of \ell increased with the decrease in ΔT [i.e, increase in the crystallization temperature (T)] at a fixed pressure, similar to the well known ΔT dependence of \ell for a folded-chain single crystal (FCC). The observed maximum value of \ell, obtained at the lowest ΔT increased with increasing pressure and the crystal changed from FCC to an extended-chain crystal (ECC) at ca. 0.25 GPa. Application of the chain-sliding diffusion theory, previously proposed by one of the authors (M.H.), was found to explain well observed significant ΔT dependence of \ell and the pressure dependence. It was proposed that the value of \ell is determined by the cessation of lamellar thickening growth at the phase transition from metastable hexagonal to stable orthorhombic. The phase transition was also studied and it is suggested to be a nucleation-controlled process of the primary nucleus.

Abstract: Computer simulation was carried out to study the morphological change in the lateral habit of polyethylene single crystals grown from the melt. Monte Carlo simulation was utilized for modelling the processes of surface nucleation and step propagation on the growth faces of a two-dimensional crystal with hexagonal packing. Anisotropy of growth was introduced in the simulation by choosing different rates for these processes on the {110} and {100} faces. Depending on the ratio of the step propagation velocity to the rate of increasing width of the growth face, the computer simulation produced curved crystals of truncated lozenge or lenticular shape, both of which have been observed experimentally. The change in morphology has been analysed quantitatively.

Abstract: The melting point maximum against pressure is reported for poly(4-methyl-pentene-1): 270ºC at 1.5 kbar. X-ray diffraction at high pressures shows no transformation up to 15 kbar at room temperature; the long-range order in the crystal remains unchanged with pressure while disorder of the first kind increases to cause the increase of the internal energy of the crystal. The origin of the melting point maximum is discussed on the basis of the low packing coefficient of helical polymers with bulky side groups and the long-range order maintained up to the melting point at high pressures.

Abstract: A new method is presented to analyse endothermic or exothermic process with temperature modulated differential scanning calorimetry, utilizing the shift in phase lag between sample temperature and heat flow. It has been shown that the temperature coefficient of transformation rate, e,g. of crystal growth, is obtainable by the analysis, The method is applied to polymer crystallization and the validity has been examined with the experimental results of polyethylene crystallization.

Abstract: Crystal growth of isotactic polystyrene in thin amorphous films has been investigated by transmission electron microscopy (TEM) and atomic force microscopy (AFM) . The single crystals grown above 234ºC are hexagonal plates parallel to the (001) planes with {110} facets. The crystals become round due to a kinetic roughening transition at about 195ºC. At temperatures below 170ºC two dimensional spherulites grow. Crystals with spiral overgrowth terraces grow to be thicker than the original films. The amorphous parts surrounding the planar crystals are thin and are observed as 'bright haloes' in bright field images of TEM. In situ observations showed that the bundle of lamellae with a 'halo' grows first and the planar crystals grow from the end/ends of the bundle. AFM observation has shown that the crystals are covered with amorphous layers and have a hollow dislocation at the center. The growth rate of crystals in thin films is 70% and for the overgrowth terraces is 40% of that in the bulk.

Abstract: We have examined the applicability of a new analysing method of temperature modulated differential scanning calorimetry to the exothermic process of poly(ethylene terephthalate) crystallization. The method utilizes the change in the phase lag between modulation components of sample temperature and of heat flow, to introduce an apparent heat capacity of complex quantity. The phase lag showed a peak and a dip during the isothermal crystallization, above and below the temperature at which the growth rate of crystals becomes a maximum, respectively. The present method incorporates the change, and predicts negative and positive ternperature dependence ofcrystal growth rate, for the peak and dip in the phase lag, respectively. The temperature dependence of crystal growth rate agreed well with the literature values obtained from the direct measurements of growth rate of spherulites by optical microscopy.

Abstract: A new method is presented to analyse an exothermic or endothermic process with temperature modulated differential scanning calorimetry. The response of exo- or endo-thermic process against temperature modulation has been directly taken into account in an apparent heat capacity difference of complex quantity. Utilizing the shift in phase lag between sample temperature and heat fiow, the specific heat during the transfonnation process and the temperature coefficient of the transformation rate, e,g. crystal growth rate, are obtainable by the analysis under a reasonable assumption. The applicability of the present method has been examined with the experimental results of polyethylene crystallization.

Abstract: A dynamic heat capacity of poly(ethylene terephthalate) in the temperature range of glass transition has been examined by a new technique of temperature modulated differential scanning calorimetry. The shift of glass transition temperature caused by the desorption of water could be monitored by the change in the dynamic heat capacity. Under quasiisothermal condition, the increase in the glass transition temperature causes the decrease in the magnitude of the dynamic heat capacity and a negative or positive change in the phase, depending on temperature.

Abstract: The non-isothermal crystallization of poly(ethylene terephthalate) has been examined by temperature modulated differential scanning calorimetry (TMdsc). A new analytical model of TMdsc has been applied to the process, taking account of the response of exothermic heat flow to temperature modulation in an apparent heat capacity of complex quantity. By examining the frequency dependence of the apparent heat capacity, the applicability has been successfully examined for the non-isothermal process, The method is capable of determining the temperature dependence of crystal growth rate from TMdsc data analysis. The results agree well with the dependence determined from literature values of spherukite growth rate measured by optical microscopy.

Abstract: Molecular weight (M) dependence of lateral growth rate (V) of an extended chain single crystal (ECSC) of polyethylene (PE) crystallized at high pressure (P = 0.4GPa) was studied. We obtained a well-known relation that V = V₀ exp(- B/ΔT), where V₀ and B are constants related to a self-diffusion constant of molecules and free energy of forming a critical nucleus and ΔT is degree of supercooling. We showed that V₀ decreases with increasing M and B does not depend on M, which are similar to results reported by Hoffman et al, for a folded chain crystal (FCC) of PE. This indicates that M dependence of V is controlled by the self-diffusion process of molecules, while that is not done by the nucleation process. We obtained an experimental formula. V(M) ∝ D(M) ∝ M^H, where D is a self-diffusion constant and H is a constant, H = 0.7. A similar relation has been shown, reported by Hoffman et al. and by us in a separate paper. But the H given by us was larger, H = 1.8. It should be noted that the H of a FCC is much larger than that of an ECSC. We will propose a new mechanism from this significant difference on H in a separate paper, that M dependence of V is mainly controlled by the surface diffusion process of chain molecules on a surface of a crystal not by the self-diffusion process within the melt.

Abstract: The effect of tacticity on the formation of the most ordered form of α2 modification of crystals of isotactic polypropylene (iPP) during melt crystallization at atmospheric pressure has been investigated. It was found that melt crystallization of iPP with 99.5% isotacticity at 150ºC resulted in nearly 100% pure α2 form crystals, i.e. fraction of α2 = 1. At temperatures higher than 150ºC, f(α2) was found to decrease from unity. The present study on the two different molecular weight samples showed that molecular weight does not influence the α2 formation. The results are explained on the basis of the effect of chain mobility and thermal expansion on the regularity of interchain packing.

Abstract: Molecular weight (M) dependence of the lateral growth rate (V, of folded chain crystals (FCCs) of polyethylenes (PE) was investigated. This study was carried out on single (or single crystal-like) crystals using the equilibrium melting temperature determined by applying Gibbs-Thomson's equation. The well-known relation V =V₀ exp( - B/ΔT) was obtained where V₀ and B are constants and ΔT is a degree of supercooling. V₀ strongly decreased with increase of M, whereas B did not, which indicates that the self-diffusion process of polymer chains mainly controls the M dependence of V, whereas the nucleation one does not. Experimental formula that V ∝ V₀ ∝ D ∝ M^-H where D is self-diffusion constant and H is a constant; H = 1.7 was obtained. These results are similar to Hoffman et al.'s results but their H was rather smaller, H = 1–1.5. A similar study on extended-chain single crystals (ECSCs) reported in our previous' paper gave the same experimental formula but H was much smaller. H = 0.7. From the difference in H between FCCs and ECSCs, a new proposal that M dependence of V may be mainly controlled by the surface diffusion process of chain polymers on the growing crystal surface is discussed briefly.

Abstract: Irreversible melting of poly(ethylene terephthalate) crystals on heating has been examined by temperature modulated differential scanning calorimetry (t.m.d.s.c.). The apparent heat capacity of complex quantity obtained by t.m.d.s.c. showed a strong dependence on frequency and heating rate during the melting process. In order to explain this behavior, a kinetic modeling of melting has been presented. The modeling considers the melting of an assembly of fractions having a continuous distribution of non-equilibrium melting points. Three cases of the superheating dependence of melting rate coefficient have been examined: constant rate coefficient, linear dependence and exponential dependence. The modeling predicts frequency response functions similar to Debye's type with a characteristic time dependent on heating rate. The response function successfully explains the dependence on frequency and heating rate of the apparent heat capacity obtained experimentally. The characteristic time of melting of crystallites has been evaluated as a fitting parameter of the response function, and the superheating dependence of melting rate coefficient has been distinguished by the heating rate dependence of the characteristic time. Taking account of the relatively insensitive nature of crystallization to temperature modulation, it is further suggested that the 'reversing' heat flow is related to the pure endothermic heat flow of melting and the 'non-reversing ' heat flow corresponds to the exothermic heat flow of re-crystallization and reorganization when extrapolated to ω → 0. The behavior of the apparent heat capacity will be an important characteristic feature of the melting kinetics, and hence the modeling will develop a new applicability of t.m.d.s.c. to the melting of polymer crystals,

Abstract: Temperature modulated differential scanning calorimetry (TMDSC) has been applied to study the irreversible melting kinetics of polyethylene crystals on heating. The apparent heat capacity obtained by TMDSC showed strong dependences on the applied frequency (modulation period) and on the heating rate. Considering the details of the melting kinetics, the dependence has been explained by a frequency response function similar to Debye's type with a characteristic time representing the melting kinetics. From the analysis, it has been confirmed that the `reversing' heat flow extrapolated to ω → 0 is correspondent to the `total' heat flow, when re-crystallization and re-organization are not significant during the melting process. It is further suggested that the characteristic time is related to the superheating effect seen in the `total' heat flow. It is pointed out that the distribution of the melting points may be estimated by the deconvolution of the melting kinetics from the `total' heat flow.

Abstract: A new method is presented to analyze the irreversible melting kinetics of polymer crystals with a temperature modulated differential scanning calorimetry (TMDSC). The method is based on an expression of the apparent heat capacity, mc_p + (i/ω)F'_T, with the true heat capacity, mc_p, and the response of the kinetics, F'_T. The present paper experimentally examines the irreversible melting of nylon 6 crystals on heating. The real and imaginary parts of the apparent heat capacity showed a strong dependence on frequency and heating rate during the melting process. The dependence and the Cole-Cole plot could be fitted by the frequency response function of Debye's type with a characteristic time depending on heating rate. The characteristic time represents the time required for the melting of small crystallites which form the aggregates of polymer crystals. The heating rate dependence of the characteristic time differentiates the superheating dependence of the melting rate. Taking account of the relatively insensitive nature of crystallization to temperature modulation, it is argued that the 'reversing' heat flow extrapolated to ω → 0 is related to the endothermic heat flow of melting, and the corresponding 'non-reversing' heat flow represents the exothermic heat flow of re-crystallization and re-organization. The extrapolated 'reversing' and 'non-reversing' heat flow indicates the melting and re-crystallization and/or re-organization of nylon 6 crystals at much lower temperature than the melting peak seen in the total heat flow.

Abstract: The flow instability has been examined in a polymer liquid extruded from a die, especially periodic spurt, observed under constant piston moving. A stick-slip model of' a group of' microscopic springs has been presented to explain the macroscopic slip which is supposed to occur during the instability. The constitutive relationship of the slip velocity and the applied force has been derived and the coupling of' the slip dynamics and the compressibility of the melt in the reservoir has been considered. The steady state solution, the linear stability analysis, and the numerical calculation suggested the followings. 1) The flow curve is basically N-shaped. 2) The range of the negative slope in the flow curve can be unstable. 3) In the unstable range, limit cycle appears around an unstable steady state. 4) The controlling parameter of the stability is the melt depth in the reservoir, which determines the compliance of the whole system. Experimental examination of the periodic spurt of polyethylene has confirmed those theoretical predictions. The results clearly suggest that the instability should be treated as a bifurcation of the dynamical system.

Abstract: Computer simulation has been applied to the modeling of the melting kinetics of polymer crystals, which we have recently presented to predict the response of the kinetics to a sinusoidal modulation in temperature on heating. The frequency and heating-rate dependencies have been examined with a Gaussian or uniform distribution of the melting points. For both of the distributions, the details of the dependence have been examined on the basis of the analytical results of the modeling. It has also been confirmed that the response of the kinetics has higher harmonics as expected from the formulation of the modeling. This behavior corresponds to the experimental results of temperature-modulated DSC (T-MDSC) in the melting region of polymer crystals.

Abstract: Temperature-modulated differential scanning calorimetry (T-MDSC) has been applied to the isothermal crystallization of poly(vinylidene fluoride), isotactic polypropylene, syndiotactic polypropylene, poly(ethylene terephthalate), poly(caprolactam) and poly(ethylene succinate). It has been confirmed that the imaginary part of the apparent heat capacity determined by T-MDSC gives the temperature dependence of linear growth rate. The proper choice of the baseline for the phase angle of the complex heat capacity has been discussed and it is concluded that the change in the crystallinity evaluated from the integration of mean exothermic heat flow can be used as the baseline.

Abstract: Molecular weight (M) dependence of the primary nucleation rate (I) of an extended chain single crystal of polyethylene crystallized at high pressure (P=0.4 GPa) was studied. We obtained for the first time an experimental formula that I∝M⁻¹ which we named "power law of primary nucleation". We showed a well-known experimental formula that I=I₀exp(−κ⁄ΔT²), where I₀ is a constant proportional to the diffusion constant of molecules (D), κ is related to the activation free energy for forming a critical nucleus (ΔG^*) and ΔT is the degree of supercooling. We showed that only I₀∝D decreases with increase in M and κ does not depend on M. From this results we concluded that M dependence of I is mainly controlled by the "chain sliding diffusion" process not by the formation process of a critical nucleus, that is, I(M)∝D(M)∝P_s(M) and ΔG^*=const. Here D can be regarded as an "expanded diffusion constant" and P_s is a survival probability defined in "chain sliding diffusion" theory presented before by one of authors (MH). Based on these results we proposed a "chain sliding diffusion theory of primary nucleation" that the primary nucleation is a process of “chain sliding diffusion” within the nucleus which requires disentanglement of molecular chains within the interface between the nucleus and the melt. The theory explained well the observed power law.

Abstract: The response of a chemical reaction to temperature modulation has been examined experimentally in an epoxy thermosetting system. The kinetic response appears in the imaginary part of the complex heat capacity determined by TMDSC. From the imaginary part and the 'non-reversing' heat flow of reaction, the activation energy has been determined. The value of the activation energy obtained is in good agreement with the value determined from Kissinger's plot utilizing the peak temperatures of the exothermic reaction with different heating rates.

Abstract: Complex heat capacity obtained in melting region of polymer crystals by temperature-modulated differential scanning calorimetry of heat flux type has been calibrated with a method based on a model proposed by Hatta. The calibration method corrects for the effect of thermal conductivity of the DSC apparatus on the magnitude and phase angle of the heat capacity. The validity of the correction has been confirmed by examining the reversible melting and crystallization of indium under quasi-isothermal conditions. For the irreversible melting of polymer crystals analyzed with an additional underlying heating rate, the calibrated heat capacity becomes a complex quantity with a frequency dependence roughly approximated by Debye's type, the characteristic time of which depends on the underlying heating rate. This behavior qualitatively agrees with the previous results obtained by the calibration of baseline-subtraction from the phase angle. The applicability of the "baseline-subtraction" has also been discussed.

Abstract: We present a new method to analyze irreversible transformation kinetics of melting in polymer crystals with temperature modulated differential scanning calorimetry (TMDSC). In the melting region of several polymers, the apparent heat capacity obtained with TMDSC can be expressed as C_s + |F_melt/β|/(1 + i ω τ(β)). with the true heat capacity, C_s, the endothermic heat flow of melting, F_melt, the angular frequency of temperature modulation, ω, and the mean time of melting of each crystallite, τ, depending on the underlying linear heating rate, β. In the case of isotactic polypropylene, the frequency dependence cannot be approximated by this formula. The dependence suggests the possibility of the retardation in the melting kinetics to follow temperature modulatfon.

Abstract: Crystallization behavior of isotactic polypropylene (iPP) with extremely high isotacticity has been studied over a very wide range of crystallization temperature T_c (145ºC < T_c < 166ºC). Optical polarized microscopy observation reveals that morphologies obtained before and after T_c=157.0ºC are different in nature. Differential scanning calorimetric measurement shows that the melting temperature (T_m) increases significantly with increase of both T_c and crystallization time t. A sudden jump in the slope of T_m versus log t plot is observed at T_c=157.0ºC, which suggests a kind of order-disorder transition taking place at high T_c (>157.0ºC) to allow better chain sliding diffusion. Such a disordering has been confirmed by means of X-ray measurements and will be reported in another paper of this series. It was also convinced that annealing at high temperature subsequent to lower temperature crystallization promotes much more rapid lamellar thickening than crystallization alone does at the same high temperature. The lamellar thickness is determined by transmission electron microscopy and also shows a discontinuous upward shift at T_c=157.0ºC. The lamella with the thickness up to 66 nm is reported for the first time.

Abstract: We have examined the morphology of poly(vinylidene fluoride) (PVDF) single crystals grown from melt and from blends with poly(ethyl acrylate) (PEA), PVDF/PEA . 0.5/99.5 and 30/70 by weight. The single crystals, of relatively higher molecular weight, were grown isothermally in the temperature range where banded spherulites are formed with sufficient crystallization time. The crystals were extracted by dissolving amorphous PEA and PVDF crystals formed on quenching. The three-dimensional morphology of the single crystals was examined by transmission electron microscopy (bright field, dark field and diffraction) with a tilting stage. For all cases, the tilting of chains (25–27degrees) to the fold surface has been confirmed. The three-dimensional shape of all the crystals was chair type for the 30/70 blend and pure PVDF. In chair crystals, spiral terraces keep the handedness in each growth direction. From this evidence, it is proposed that the chair crystals with consecutive creation of spiral terraces of the same sense are responsible for the twisting relationship between crystallites in the radial direction of the banded spherulites.

Abstract: An extension of the modeling proposed previously has been examined for the irreversible melting kinetics of polymer crystals on heating with response to temperature modulation. The previous modeling has been successful in the explanation of the frequency dependence of the apparent heat capacity obtained with temperature modulated DSC in the melting region of poly(ethylene terephthalate), polyethylene and poly(caprolactam). In the present work this modeling was extended to explain an unusual behavior reported by Schawe et al. for poly(e-caprolactone) and syndiotactic polypropylene, in which the latent heat gave a subtractive effect to the real part of the apparent heat capacity. A retardation of the melting rate coefficient in response to temperature change has been considered. The retardation implies an activation process in the melting kinetics of polymer crystals.

Abstract: The number-average molecular weight (M_n) dependence of the primary nucleation rate (I) of polyethylene (PE) folded-chain single crystals was studied in the ordered phase. We observed that the M_n dependence of I is mainly controlled by the diffusion process of polymer chains within the interface between a nucleus and the melt and/ or within the nucleus. The results show that I decreases with increasing M_n and follows a power law I ∝ M_n^-2.3 for the ordered phase. It is named the power law of the nucleation rate. In a previous article we showed that for the disordered phase I ∝ M_n^-1 . In this article, we concluded that I decreases with increasing M_n and follows a universal power law, I ∝ M_n^-H for both ordered and disordered phases. The power H depends on the degree of order of the crystalline phase, which is related to the morphology.

Abstract: The method of "modulated driving force" has been applied to the kinetics of ferroelectric - paraelectric transition in copolymers of vinylidene fluoride (VDF) with trifluoroethylene (TrFE). The method examines the response of transition kinetics to a periodically modulated driving force, e.g., supercooling or superheating. The response to the modulation in temperature appears in the apparent heat capacity obtained by a temperature-modulated differential scanning calorimeter. By examining the frequency dispersion and its dependence on underlying linear heating (or cooling) rate, the mean time required for the completion of transition in each crystallite and the dependence of transition rate on superheating (or supercooling) are obtainable. In VDF/TrFE copolymers, it is known that the transition behavior undergoes a drastic change from reversible transition with low VDF content to nucleation-controlled transition with higher content. Several types of compositions VDF/TrFE= 47/53, 52/48, 59/41, 65/35, 69/31 and 73/27 by mol%! have been examined experimentally with this method in terms of the crossover of transition behaviors.

Abstract: The application of a periodically modulated driving force has been examined in the melting and crystallization kinetics of ice crystals confined in a porous media. The kinetic response of transformation gives the real and imaginary parts of the 'apparent' heat capacity obtained with a temperature modulated differential scanning calorimetry (TMDSC). Based on a modeling of the kinetics, the detailed examination of the frequency dispersion and its dependence on underlying heating/cooling rate enables us to evaluate the transformation rate and the dependence of the rate coefficient on the driving force, i,e. the degree of supercooling or superheating. The experimental results indicate that the transformation processes are limited by heat diffusion from the growth interface of each crystallite to surroundings.

Abstract: The flow instability in a polymer liquid extruded from a die has been discussed on its temperature dependence, based on a modeling of the behavior by a statistical stick-slip model of a group of springs. The present experimental results of polyethylene melt showed the shift of an N-shaped flow curve to lower shear rate with decreasing temperature, which approaches the melting point of polyethylene crystals. This result is consistent with the microscopic modeling of the flow instability with the disentanglement of the chain in the bulk under high shear rate. The shift of flow curve with temperature explains the existence of the temperature window with minimum applied pressure under constant speed found by Keller et al.

Abstract: The self-excited oscillation of neck propagation during cold drawing of polymer films has been examined experimentally. On the basis of Barenblatt's model considering a thermo-mechanical coupling at the neck, the temperature rise at the neck has been studied with an infrared camera. The temperature began to rise in a range showing a negative velocity dependence of the applied load. The behavior is consistent with the view of thermo-mechanical coupling. The temperature rise was up to 80ºC (>T_g) and explains the occurrence of crystallization for faster drawing rates. It has also been confirmed that the temperature rise follows the oscillation of stress due to the coupling.

Abstract: Melting kinetics of polymer crystals has been examined experimentally by calorimetric methods utilizing the combination of a conventional differential scanning calorimetry of heat flux type (CDSC-HF) and a temperature-modulated DSC (TMDSC). The superheating effect in the kinetics has been discussed based on a modeling of the melting kinetics. For low-density polyethylene and linear polyethylene, the melting rate showed nearly linear dependence on the degree of superheating, which indicates the kinetics controlled by heat diffusion or by surface kinetics on rough interface. For isotactic polypropylene, poly(ethylene terephthalate) and poly(ε-caprolactone), the dependence is non-linear and close to the limiting case of exponential dependence, which indicates nucleation-controlled kinetics of melting. A possible mechanism of the activation process in the melting kinetics has been discussed in consideration of the specific feature of polymer crystals far from its most stable state. The consistency of the results of CDSC-HF and TMDSC has been confirmed by this analysis with a calibration of peak temperature for the instrumental thermal delay in CDSC-HF.

Abstract: The method of "periodically modulated driving force" has been applied to the kinetics of polymer crystallization examined by a dynamic visco-elastic measurement with temperature modulation. The dynamic elasticity obtained by the measurement shows a strong nonlinearity in its dependence on the degree of crystallinity, and hence the simple time derivative does not represent the rate of crystallization. With the application of periodic modulation in temperature and the examination of the response of crystallization kinetics appearing in the modulation in the elasticity, it has been shown that the temperature dependence of growth rate can be determined even with the nonlinear dependence of this quantity. The method is applied to the crystallization of polyethylene, poly(vinylidene fluoride) and isotactic polypropylene. The agreement with the results from the direct measurement of growth rate by optical microscopy is satisfactory.

Abstract: An experimental formula of the nucleation rate I of polyethylene as a function of number density of entanglement ν_e within the melt was obtained as I(ν_e) ∝ exp(- γ ν_e); where γ is a constant. In order to obtain a functional form of I(ν_e), I is determined by changing ν_e within the melt. The ν_e within the melt can be changed when crystals with different lamellar thickness \ell are melted. It is shown that the ν_e within the melt just after melting is related to \ell before melting. The ν_e of folded chain crystals (FCCs) is large, while that of extended chain single crystals (ECSCs) is very small. Therefore, strictly speaking, the experimental formula is a kind of 'semi-experimental' one. Because it is obtained by combining an experimental formula of I as a function of \ell before melting I(\ell) and a formula between \ell and ν_e based on the most probable model. It was found that the ν_e dependence of I is mainly controlled by the topological diffusion process within the interface between the melt and a nucleus and/or within the nucleus not by the forming process of a critical nucleus. The slope of the plots of log I against ΔT² was constant, irrespective of morphologies, FCCs and ECSCs, where ΔT is the degree of supercooling. From this fact, it was concluded that the fold type nucleus are formed from the melt of ECSCs as well as from the melt of FCCs. In our previous study, we found that I decreases exponentially with increase of annealing time Δt at a temperature above the melting temperature. From these results, we proposed a 'two-stage melt relaxation', i.e. fast conformational and slow topological relaxations. When the ECSCs are melted, extended chains within ECSCs are rapidly changed to random coiled chain conformation and then chains gradually entangle each other. We also proposed a formula, ν_e(Δt) ∝ - ln {Const. + A exp(-Δt/τ_m)}, where A is a constant and τ_m is the 'melt relaxation' time.

Abstract: A second-order phase transition of α2 form isotactic polypropylene (iPP) is found at high annealing temperature (T_a = 159.3ºC) by means of X-ray diffraction method. Although the lattice shape and the space group keep the same as those of the α2 form, i.e. monoclinic and P2₁/c, with increase of T_a it has been revealed that there are discontinuous increases in the slopes of the lattice constants a and b against T_a Plots, while the c and the p keep almost constant. As a result, the slope of the unit cell volume V versus T_a Plot also shows a discontinuous increase at T_a = 159.3ºC, indicating the occurrence of the second-order phase transition. In order to distinguish the two phases, the phase above the transition temperature is named α2' phase and the transition temperature is denoted T_α-α2'. These facts suggested that the α2' form is a mobile phase where the molecular chains would become loosely packed and mobile, promoting the better chain sliding diffusion. A fast lamellar thickening process has been confirmed in the higher temperature region than T_α-α2', which was reported in the precedent paper. General significance is proposed that mobile phases possibly exist at high temperature, close to the melting temperature and accelerate lamellar thickening, which improves physical properties of polymers.

Abstract: We experimentally investigated the dynamical behavior of adhesive tape in peeling with emphasis on the emergence of slow and fast peeling motions. The dynamical morphological phase diagram for peeled adhesive tape as a function of peel speed and spring constant was obtained. The spatiotemporal patterns of peeled adhesive were classified into four types: low-speed pattern, high-speed pattern, oscillatory pattern, and spatiotemporal intermittent pattern.

Abstract: The molecular weight (M_n) dependence of the primary nucleation rate (I) of folded chain single crystals (FCSCs) of polyethylene (PE) was studied. A power law for the nucleation rate, I ∝ M_n^-2.4 was found. The FCSCs were formed by isothermal crystallization from the melt into an ordered phase (=Orthorhombie phase). A new experimental method was established to obtain reliable I, which has been difficult in the case of heterogeneous nucleation for long years. The degree of supercooling (ΔT) dependence of I fits well with the theoretical I given by classical nucleation theory, I = I₀ exp(-ΔG*/kT) = D exp(-C/ΔT²), where l₀ is proportional to the topological diffusion coefficient of polymer chains (D), ΔG* is the free energy for forming a critical nucleus, k is the Boltzmann constant, T is temperature, and C is a constant. It is found that ΔG* (∝ C) does not depend on M_n, while I₀ decreases with increase of M_n, from which it is concluded that formation of a critical nucleus is not controlled by M_n while only topological diffusion of polymers is controlled by M_n, i.e., I ∝ D(M_n). Similar power laws of PE were already found by the present authors on I of extended chain single crystals (ECSCs), i.e., I ∝ M_n^-1.0, and on the lateral growth rates (V) of ECSCs and FCSCs, V ∝ M_n^-0.7 and V ∝ M_n^-1.7, respectively. ECSCs were formed by isothermal crystallization from the melt into a disordered phase (=hexagonal phase). Therefore, it is concluded that a common power law, I, V ∝ D(M_n) ∝ M_n^-H of PE is confirmed, irrespective of nucleation or growth and irrespective of crystalline phases, ordered or disordered phases. It is to be noted that the power H depends on the degree of order of the crystalline phase, from which it is concluded that both nucleation and growth are controlled by the topological diffusion of polymer chains within interface between a nucleus (or crystal) and the melt and/or within the nucleus. The topological diffusion is related to chain sliding diffusion and disentanglements.

Abstract: The numerical solution of a rate equation proposed by Sadler and Gilmer for the pinning of polymer crystallization has been examined to discuss the supercooling dependence of the kinetic barrier in comparison with that of surface nucleation postulated in the standard model. The entropy and free energy of the stems in the pinning region with the fluctuation of stem length have been evaluated from the stationary solution with the expression of conditional entropy of a finite Markov chain. The results have confirmed that the pinning stems form a local minimum in the free energy landscape and the rate-determining process is the detachment of the whole pinning region. The dependence on supercooling of the kinetic barrier is smaller than that of nucleation but not negligible for the parameters of polyethylene crystallization.

Abstract: Effect of the shear flow (\dot{γ}=0.5–5 s^-1) on the nucleation and on the morphology of polyethylene (PE) during crystallization from the melt was studied by means of polarizing optical microscopy and small angle X-ray scattering. In order to analyze the results by the nucleation theory, we observed the effect of shear flow on the equilibrium melting temperature (T_m⁰). The T_m⁰ under shear flow and that under quiescent state are almost the same, T_m⁰=140.2–140.3ºC. Therefore, the shear flow does not affect the T_m⁰. The "heterogeneous" primary nucleation rate (I) and the induction onset time of nucleation (τ_onset) of the isolated crystals under shear flow are also almost the same as those under quiescent state. The heterogeneous primary nucleation means that isolated nuclei are sporadically generating from the melt with the aid of heterogeneities such as nucleating agents. After the generation of primary nuclei, the "shish" were generated independent of the primary nucleation. We found that the shish were formed by the chain elongation caused by the velocity difference between polymer chains and dust particles, etc. After that, we observed that the "kebabs" were formed on the shish. It was found that the nucleation from the melt after melting of the "shish-kebabs" (at melt annealing temperature T_max = 160ºC for 5 min) was accelerated compared with the ordinary melt crystallization after melting of folded chain crystals. This indicates that the "solid memory effect" of the former solid is significant. This is because of the low entanglement density within the melt of shish kebabs.

Abstract: Molecular weight (M) dependence of the equilibrium melting temperature T_m⁰ of isotactic polypropylene (iPP) with high tacticity ([mmmm]= 99.6%) was studied. Four fractionated iPPs with M_n = 23, 64, 94 and 263 × 10³ were used. T_m⁰ was obtained by using an improved method based on the Gibbs-Thomson plot proposed in previous papers. The effect of "melting kinetics" on melting temperature (T_m) was eliminated by observing isothermal melting of spherulites. The effect of lamellar thickening on T_m during T_m measurement at high temperature was also eliminated by observing thick lamellae formed at high crystallization temperatures (T_c= 148–166ºC). With increase of M, T_m⁰ increased significantly. The empirical equation, T_m⁰ = 119.5 + 23.6 × log M - 2.0 × (log M)² (ºC), was obtained. The molecular weight dependence of the α2-α2' transition was observed. The transition temperature (T_α2-α2') also increased with increase of M. The ΔT dependence of lamellar thickness was concluded to be controlled by that of lamellar thickening.

Abstract: We examined the free surface of a banded spherulite of poly (vinylidene fluoride) (PVDF) by atomic force microscopy. The directions of the slope of multilayer terraces of lamellar crystals are retained in each half of a banded spherulite; this evidence confirms the macroscopic selection of one-handedness in the formation of spiral terraces in each growth direction of the sheaf at the center of banded spherulite of PVDF. In a previous paper, it was confirmed that the three-dimensional morphology of all single crystals of PVDF grown from the melt is of chair-type, and hence, it is most probable that the stress in the chair crystal is responsible for the formation of spiral dislocations and terraces keeping the same handedness in each growth direction. The chair-type morphology is created because of the chain tilting to the fold surface, which can introduce symmetry breaking and, consequently, the selection of handedness in nonchiral polymers such as PVDF.

Abstract: Direct evidence that nuclei are formed during the induction period of crystallization is obtained for the first time by means of small-angle X-ray scattering (SAXS). Polyethylene (PE) was used as a model crystalline polymer. The nucleating agent was mixed with PE in order to increase the scattering intensity I_x from nuclei as large as 10⁴ times bigger than usual. I_x increased soon after quenching to the crystallization temperature from the melt and saturated after some time. A new theory is proposed to estimate the size of the nuclei N, the number density distribution of nuclei with N at time t, f(t,N), and the induction time τ_i, by analyzing the SAXS scattering intensity. The volume-averaged size of the nuclei was nearly the same as that of critical nuclei and does not change so much with time during the induction period. Lamellae start stacking much later than nuclei start forming.

Abstract: At high supercoolings, isotactic polystyrene and polybutene-1 have a rounded crystal shape, suggesting kinetic roughening. Still, the growth rates of these polymer crystals show the supercooling dependence derived for nucleation controlled growth. On the other hand, isotactic poly-4-methylpentene-1 1,4 trans-polybutadiene at higher crystallization temperatures and polyethylene at high pressures show a rounded crystal shape: thermal roughening. Again, the growth rate is described by the nucleation theory. On the basis of these observations, we propose a crystallization kinetics taking account of the entropic barrier that was originally proposed by Sadler.

Abstract: A new method to determine the correct Gibbs-Thomson plot and equilibrium melting temperature (T_m⁰) of polymers was proposed. The Gibbs-Thomson plot method is reliable, because the Gibbs-Thomson equation is directly derived from thermodynamical relations. In this method, the heating rate dependence of melting temperature (T_m) was omitted by applying the theory of the "melting kinetics", and the effect of lamellar thickening on T_m was also omitted by observing thick lamellae. A differential scanning calorimeter (DSC) was used for observation of T_m as a conventional method. Transmission electron microscope (TEM) was used to observe a distribution of lamellar thickness (\ell). It was shown theoretically that peak temperature of melting endotherm (T_m(DSC)) corresponded to averaged reciprocal \ell (<\ell^-1>) for the case of sharp distributions of T_m and \ell^-1. The Gibbs-Thomson plot, T_m(DSC) vs <\ell^-1>, was carried out. A reliable Gibbs-Thomson plot and T_m⁰ ) 186.2ºC were obtained for a fraction of isotactic polypropylene (iPP) with high tacticity ([mmmm]=99.6%, M_n=64×10³ and M_w/M_n=2.4). It was shown that DSC double melting endotherm corresponded to the number-distribution of \ell^-1, when lamellar thickening did not occur.

Abstract: In part 1 of this series, we proposed a new method to determine the correct equilibrium melting temperature (T_m⁰). Effects of the "melting kinetics" and lamellar thickening were omitted from T_m. The correct T_m⁰ of isotactic polypropylene (iPP) ([mmmm]=99.6%, M_n=64×10³ and M_w/M_n=2.4) was observed to be 186.1ºC. In this paper, the rigorous Gibbs-Thomson plot was obtained by using the direct correspondence between maximum melting temperature (T_m,max) and maximum lamellar thickness (\ell_max). T_m,max and \ell_max were observed by means of optical microscope and transmission electron microscope (TEM), respectively. The validity of the Gibbs-Thomson plot obtained by means of a differential scanning calorimeter (DSC) (part 1 of this series) was confirmed by comparing it with the rigorous Gibbs-Thomson plot in this paper. The Hoffman-Weeks plot is widely used as one of the methods to obtain T_m⁰. It was shown that the Hoffman-Weeks plot is correct only when \ell ∝ 1/ΔT, where ΔT is the degree of supercooling, is satisfied. However, in the case of iPP, the condition is not satisfied, and so the result obtained by the Gibbs-Thomson plot is not equivalent to that obtained by the Hoffman-Weeks plot. The existence of α2' phase was confirmed again by breakings in slopes of \ell and T_m against T_c at 159ºC. Furthermore, the broad bimodal distribution of \ell was caused by the difference between the lamellar thickening growth rate of isolated mother lamellae and the lamellae thickening rate of stacked daughter lamellae.

Abstract: The three-dimensional morphology of polyethylene single crystals grown from dilute solution has been examined by atomic force microscopy. Single crystals were deposited on a soft ground of aqueous solution of poly(vinyl alcohol) (PVA) to avoid the collapse of thin lamellar crystals with thickness of 10 nm. The observation of single crystals on dried PVA clarifies the morphology of a chair type crystal as well as well-known hollow pyramidal type. It has been confirmed that the screw dislocations in the chair type follow a selection rule of the handedness in a manner to relieve the distortion in the chair type.

Abstract: A simple model for the peeling process of pressure-sensitive adhesive tape is presented. The model consists of linear springs and dashpots and can be solved analytically. Based on the modeling, the curved profile of the peeling tape is spontaneously determined in terms of viscoelastic properties of adhesives. Using this model, two experimental results are discussed: critical peel rates in the peel force and the peel rate dependence of the detachment process of adhesive from the substrate.

Abstract: We investigated (i) the relationship between the spatiotemporal pattern of a deformed adhesive and peel load during peeling, and (ii) the dependence of the pattern formation on peel speed in the hard spring limit case. In the hard spring limit case, it is found that elastic and viscous peeling states coexist. It is also found that the occupation ratio of tunnel structures in a separation front is determined by the peel speed and is a monotonically decreasing function of peel speed. We experimentally confirmed that the value of peel load has a linear dependence on the occupation ratio of tunnel structures. An explanation of dynamical behavior is also given on the basis of the creation-annihilation dynamics of tunnel structures.

Abstract: The method of "periodically modulated driving force" with temperature modulated differential scanning calorimetry has been applied to the transition kinetics in Ti_x Ni_100-x, x ∼ 50at.%. The alloy presents two different types of solid-solid phase transitions. The details of the transition kinetics especially of the ΔT dependence of transition rate have been examined by the present analysis.

Abstract: A new method of full deconvolution of the instrumental coefficients in scanning calorimeter of heat flux type has been proposed, including reasonable determination method of the thermal contact resistance between the sample pan and its stage. The determination utilizes the response of dynamic heat capacity obtained by temperature-modulated (T-M) mode of a commercial differential scanning calorimeter used as a single calorimeter. By taking into account of the contribution of heat exchange with purge gas, an extension of standard modeling has been proposed for the evaluation of the instrumental coefficients. An alternative method bypassing the full deconvolution is also proposed.

Abstract: We have solved the molecular mechanism of the formation of shish of isotactic-polypropylene (iPP) and polyethylene (PE) from the sheared melt based on kinetic study by means of polarizing optical microscope. We found that the rate determining process for the formation of shish is a nucleation process in the most range of degree of supercooling (ΔT) except for large ΔT of PE. We have shown a direct evidence of the formation of bundle nucleus from the oriented melt, which is consisted of elongated chains caused by artificial pins. For polymers, a universal mechanism of nucleation from the isotropic or oriented melt was proposed. We also found that there is a critical shear rate for the formation of shish. This experimental fact indicates that the shish will be formed when the elongation of chains will overcome the conformational relaxation of chains and chain conformation within the oriented melt is kept liquid crystal like one.

Abstract: In part 1 of this series of paper, we have solved the formation mechanism of shish from the oriented melt based on the kinetic observation. In this work, we have shown for the first time the molecular mechanism of the growth of shish by kinetic study. We found that there are two different type of the growth of shish against the flow direction. The growth rate along the flow direction (U) is proportional to ΔT, where ΔT is the degree of supercooling. This indicates that U is mainly controlled by the rearrangement process of the chain near the end surface of the shish. On the other hand, the growth rate perpendicular to the flow direction (V) obeyed a well-known equation V ∝ exp(-B/ΔT), where B is a constant proportional to the free energy necessary for forming a critical secondary nucleus ΔG*. This indicates that V is mainly controlled by the secondary nucleation process on the side surface of shish. Moreover, we also found that there is a critical shear rate \dot{γ}* for the growth of shish. Below \dot{γ}*, U and V approached to zero and the growth rate of spherulite, respectively. From this experimental fact, we proposed that the chain conformation near the interface between the melt and shish, i.e. near the end and side surface of shish is elongated and oriented by the shear flow above \dot{γ}*.

Abstract: Three-dimensional morphology of polyethylene single crystals grown from dilute solutions and from the melt has been examined by atomic force microscopy. The observation of single crystals clarifies the morphology of chair-type as well as hollow pyramidal type for solution crystallization. From the melt, only chair-type was obtained. It has been confirmed that the screw dislocations in the chair-type follow a selection rule of the handedness in a manner to relieve the distortion in the chair-type. The meaning of the selection is discussed in connection with the twisting correlation in the banded spherulites grown from the melt of non-chiral polymers, such as polyethylene.

Abstract: In order to investigate the detailed structure of a banded spherulite observed by polarized light microscopy, we develop a new image processing technique that can visualize defects (band defects) in the concentric bands and determine the growing directions of crystals everywhere in a spherulite. This technique is applied to a banded spherulite of poly(vinylidene fluoride) and reveals that the spherulite has many defects (colliding defects), on which crystals collide with neighboring ones. It is found that the band defects are included in the colliding defects. The number of colliding defects increases linearly with the radius to give a constant density. Between the defects, the orientations of crystals are well correlated to form a coherent area. On the basis of these findings, a mechanism of the formation of the coherent band pattern is discussed.

Abstract: The crystallization process from supercooled melt results in the formation of nanosize nuclei in the earlier stage (induction period) through subsequent attachment or detachment of repeating unit to nuclei. The size distribution of nucleus f(N_j,t) in the induction period of nucleation process from the melts has not been experimentally confirmed yet by direct observation. The reason is that the number density of nuclei ν is too small to be detected experimentally. In our previous work, we showed the direct evidence of nucleation experimentally by means of small angle x-ray scattering (SAXS) technique. Further we have succeeded to observe the nucleation and f(N_j,t) of polymer crystallization from the melts by SAXS using synchrotron radiation. We increased ν by adding a nucleating agent to a polymer (polyethylene). The time evolution of f(N_j,t) was observed for the first time.

Abstract: As a typical example of higher-order structures of crystalline polymers, the formation mechanism of polymer spherulites has been reviewed with the emphasis on the concentric ring pattern seen in many polymers. The ring pattern originates from a twisting correlation of lamellar crystallites in the radial direction. The origins of twisting stress, the pitch determination mechanism, and the coordination of twisting phase along the tangential direction have been discussed.

Abstract: Isothermal crystallization of three-dimensional (3D) spherulites from the bulky melt under low shear rate flow was studied based on new in situ observation along a direction perpendicular to the flow velocity gradient plane (XZ plane) by means of optical microscope, where X- and Z-axes are perpendicular and parallel to the flow direction, respectively. Spherulites are rotating. A novel "spiral pattern" was found on the surface of the rotating "half-spherulite" near the surface of the melt for the first time. The half-spherulite is named "spiralite" which enabled us to have a visible image of the rotation of spherulite. Hence, we could detect the growth rate around the Z-axis V(Z) and that around the X-axis V(X) by using the spiral pattern. We could experimentally obtain V(Z) > V(X) in this study. From kinetic viewpoint, this fact indicates that free energy for formation of a critical nucleus around the Z-axis is smaller than that around the X-axis. From this, it is concluded that the "oriented melt" is formed around the Z-axis. We proved it theoretically by showing that micro shear rate (Z) on the interface around the Z-axis significantly increases and chains will be elongated even when macro is low ( < 10 s^-1). With increase of (Z), the chain elongation will overcome the entropic relaxation, that results in formation of the "oriented melt". Crystallization mechanism under low shear flow is proposed that the growth rate of spherulite or shish is accelerated around interface, due to formation of the "oriented melt". Finally, we proposed a possible relationship between melt structure and crystallization under anisotropic and isotropic external fields.

Abstract: We examined various spatiotemporal patterns evolving in deformed adhesives during peeling. The patterns are regarded as a spatiotemporal distribution of a tunnel structure formed by the deformed adhesive, and are classified into the following four types: (A) uniform pattern with tunnel structure, (B) uniform pattern without tunnel structure, (C) striped pattern alternating between A and B in time, and (D) spatiotemporal pattern made by the coexistence of two regions with and without the tunnel structure. We are able to reproduce these patterns and the mechanical and statistical behaviors by constructing a model with a state variable representing the stability of the tunnel structure. The essential factor of the pattern formation is the competition between a local asymmetric interaction and a global coupling of the state variables.

Abstract: Molecular weight (M) dependence of the lateral growth rate (V) of a form crystal of isotactic polypropylene (iPP) was studied. Reliable equilibrium melting temperature determined in our previous study was used for the analysis of supercooling dependence of V. A power law of M of V, V ∝ M_n^-H, was obtained, where H is a small constant (H = 0.7). The small H, which is similar to that of the hexagonal phase of polyethylene (H = 0.7) in comparison with the value of H = 1.7 for the orthorhombic phase of polyethylene, confirmed our prediction of smaller H for "rod like" chain polymers because of easier chain sliding within the interface between the crystalline phase and the melt. Thus, the universality of the important role of topological nature in polymer crystallization was confirmed. Lateral surface free energy (σ) of the a form of iPP was obtained as σ ≅ 1.59×10^-6J/cm².

Abstract: "How do chain molecules spontaneously entangle from completely disentangled polymer melt?" remains the most interesting unsolved problem. In order to solve this problem, we used the concept that the melt of "nascent" polymer crystallized during polymerization just after melting does not include any entanglements. We succeeded in detecting the increase of entanglement density ν_e with the increase of annealing time Δt above the equilibrium melting temperature before isothermal crystallization. The increase of ν_e was detected by observing the decrease of nucleation rate I  from the melt of nascent polymer with different Δt s. I  is a very sensitive detector of entanglements because the nucleation is a rearrangement process of chains to the crystalline lattice through the disentanglement. Therefore, I  is significantly suppressed with the increase of ne. We found a two-step decrease of I  with an increase of Δt for the first time. This should correspond to a two-step increase of ν_e with an increase of Δt. This indicates that simple entanglements such as twist or knot with lower order (one time knot) were formed within short time and then the complicated ones such as knot with higher order (two or three times knots) or loops (entanglements by loop conformation) were formed.

Abstract: Crystallization of isotactic polystyrene (it-PS) from dilute solution at high supercooling has been investigated by dynamic light scattering (DLS). We successfully obtained simultaneously, in situ in solutions, the time developments of both random coils of it-PS molecules and the growing crystals. The size of coils remains constant during growth, while the crystals pass through two stages, that is, an induction period at the early stage with very slow growth rates and a subsequent linear growth stage. It is confirmed that the temperature dependence of the linear growth rates, determined by DLS, agree well with that determined by electron microscopy. The temperature dependences of the growth rate and the inverse of induction time are dependent on the viscosity of solvent, which indicates that all dynamics are dominated by the segmental motion of polymer chains in solution at high supercoolings (low temperatures). Two possibilities are proposed for the induction period.

Abstract: The growth rate and morphology of isotactic polystyrene crystals grown in ultrathin films have been examined experimentally in terms of the dependences both on the film thickness and on the crystallization temperature. We have found that the thickness dependence of growth rate, G , shows a crossover change when the film thickness becomes comparable with the lamellar thickness of the polymer crystals, irrespective of the temperatures. The morphology of crystals grown in ultrathin films shows a branching typical of dendrites, the growth of which is supposed to be controlled by a diffusion field. The change in the tip width of the dendrites with crystallization temperature follows the expected dependence of the Mullins-Sekerka stability length, I_MS ∝ (D/G)^1/2, determined by the diffusion coefficient, D , and the growth rate. The results confirm that a diffusion field plays an essential role in the evolution of the structure.

Abstract: Recent development of the analyzing method of DSC of heat flux type has been reviewed. In the DSC of heat flux type, sample temperature and heat flux are determined from the time-series data of experimentally available temperatures at the sample stage and furnace. For the determination, the instrumental coefficients such as thermal contact resistance between the sample pan and its stage are required. The following methods are discussed for determining the instrumental coefficients: the methods based on the analytical solutions of the melting of indium, on a standard material with known heat capacity, and on the response of complex heat capacity obtained by T-M DSC. Sample temperature and heat flow under non-steady condition can be evaluated by this method. The methods also provide reasonable calibration of the dynamic heat capacity of T-M DSC.

Abstract: The role of "epitaxy" of nucleating agent (NA) in nucleation mechanism of polymers was studied to formulate the nucleation rate (I ) as a function of concentration of NA (C_NA) in mixture of polymer and NA and lateral size of a NA crystal (a_NA), I ∝C_NA/a_NA. It is proved that the epitaxy of NA controls nucleation mechanism by confirming above formula experimentally by observing nucleation by means of optical microscopy. We also clarified that heterogeneous nucleation is a probabilistic phenomenon by confirming that "induction time of nucleation (τ_i)" did not depend on CNA. We established a method to obtain reliable I and ti by adding NAwhich has been a difficult problem in polymer science.

Abstract: Nucleation mechanism of polymers was studied by means of small angle X-ray scattering (SAXS) by improving our two previous studies. The first one showed first direct SAXS observation of nucleation of polyethylene (PE). The second one reported how "size distribution f(N,t)" of nuclei of nano-meter size (nano-nuclei) evolves with time (t ), where N is number of "repeating unit" in a nucleus. Unfortunately the f(N,t) was obtained by incorrect analysis of SAXS intensity (I_X), i.e., too simple one-dimensional (1D) nucleus was assumed to analyze the I_X. In this paper, we determined simultaneously correct f(N,t) and "two-dimensional (2D) shape" of nano-nucleus. From this it is clarified that nano-nucleus shows significant fluctuation in size and shape and repeats frequent generation and disappearance, which corresponds to the conclusion that the end surface free energy of the nano-nucleus (σ_e(nano)) is 1/5 times as large as that of macroscopic crystal (σ_e(macro)). f(N,t) decreased with increase of N. f(N,t) increased and saturated with increase of t.

Abstract: Degree of supercooling (ΔT ) dependence of nano-nucleation was studied by means of small angle X-ray scattering (SAXS) and a new nucleation theory was proposed. We obtained the ΔT dependence of size distribution f(N,t) directly, where N is number of particle and t is time, which concluded that the "induction period" of crystallization is not controlled by so called "spinodal decomposition" but by nucleation one. It clarified that the critical nano-nucleation mainly controls not only the steady nano-nucleation but also macro-crystallization experimentally as the zero-th approximation by using the newly obtained ΔT dependence of f(N,t) and nucleation rate (I ) of macroscopic crystal obtained by means of optical microscope (OM). Time evolution of total free energy of nucleation of a huge closed system δG(t) was obtained experimentally for the first time, which clearly confirmed that nano-nucleation is the process where δG(t) passes through an activation barrier and reaches the most stable state by completion of melt-solid (crystal) phase transition due to well known "Ostwald ripening". We proposed a new nucleation theory by introducing a "mass distribution function Q(N,t) ∝ N f(N,t) ". We proposed a new basic equation of the mass conservation law, ∂Q(N,t)/∂t = - ∂j(N,t)/∂N , where j(N,t) is net flow. This solved the serious problem in classical nucleation theory (CNT), where so called "fundamental kinetic equation" does not satisfy the mass conservation law. The coupling of our "real image" and correct theory will enable us to realize the ultimate structure and physical properties of materials, which should be a very interesting "fruit".

Abstract: Role of nucleating agent (NA) in nucleation mechanism of polymers was solved based on kinetic study. Theoretical prediction in our previous study that I ∝ C_NAa_NA^-1 (1) was experimentally confirmed by changing C_NA and a_NA, where I is nucleation rate of polymers, C_NA is a concentration of NA in the mixture of NA and a polymer and a_NA is lateral size of a NA crystal. As the eq 1 is formulated by assuming an important role of epitaxy between NA and polymer crystals, the confirmation of eq 1 confirmed the essential role of the epitaxy in acceleration mechanism of nucleation of polymers. a_NA was decreased from the order of μm to nm and narrow distribution of a_NA (f(a_NA)) was obtained by improving "bottom up" method. We have an important conclusion in polymer science and industries that decreasing a_NA from the order of μm to nm and narrowing f(a_NA) are the most effective methods to improve the performance of NA.

Abstract: The melting behaviors of polyethylene and poly(vinylidene fluoride) have been experimentally examined by thermal analysis, optical microscopy, and atomic force microscopy. The melting velocity is found to show a nonlinear dependence on the degree of effective superheating. The dependence clearly suggests the existence of an activation barrier, though crystal melting is generally supposed to proceed without any barriers. The behavior has been reproduced by a Monte Carlo simulation of the entropic barrier of pinning proposed by Sadler and Gilmer for chain-folded crystallization of polymers.

Abstract: The formation mechanism of non-banded polymer spherulites has been examined experimentally for isotactic poly(butene-1) grown from the melt by optical, atomic force, and transmission electron microscopies associated with quenching and chemical etching. At the growth front of the spherulites, the maximum width of lamellar crystals, &lambda_m, showed a square-root dependence on the growth rate. The dependence suggests an instability-driven branching. In terms of the correlation of lamellar orientation in the spherulites, an auto-correlation function has been determined from the image taken by polarizing optical microscopy. The correlation showed an exponential decay along the radial direction, and the correlation length was in proportion to &lambda_m. Those experimental evidences suggest that the structure is formed by the coupling of the branching instability and the random re-orientation of lamellar crystals on the occasion of branching in the non-banded spherulites of poly(butene-1).

Abstract: Due to twisting correlation of crystallites along the radial direction, polyethylene spherulites are known to develop concentric band pattern. Mechanism of branching and re-orientation of lamellar crystallites in the banded spherulites has been examined experimentally by optical and atomic force microscopies associated with quenching and chemical etching. The microscopic observation suggests a branching instability of lamellar crystals at the growth front of the spherulite. We propose a mechanism of consecutive branching and twisting re-orientation of branches regulated by the inherent torsional stress expected for the banded spherulites and the branching instability. We have experimentally examined the relationships among the growth rate, the maximum lateral width of crystals at the growth front, and the period of bands for three different molecular weight fractions of polyethylene. The predicted relationship among them holds for the fractions.

Abstract: The formation mechanism of banded spherulites of poly(vinylidene fluoride) has been examined experimentally by optical and atomic force microscopies. We have confirmed the proportional relationship between the band spacing and the maximum lateral width of lamellar crystals at the growth front, and the square root dependence of the maximum width and the band spacing on the growth rate. The square root dependence suggests a splaying instability of the growth front regulated by a gradient of free energy in the liquid side, and the proportional dependence suggests the dominant effect of torsional re-orientation on the occasion of splaying in the period determination of band spacing.

Abstract: We have studied the crystallization of blended poly(ethylene terephthalate) (PET) and poly(butylene terephthalate) (PBT). The effect of transesterification in the blend on crystallization has been examined by thermal analysis and optical microscopy. At higher temperatures above 200ºC, the crystallization of one of the component (PBT) was enhanced by the existence of the crystals of another component (PET) for the intermediate degree of transesterification. The results indicate the importance of the details of the transesterification at molecular scale.

Abstract: The mechanism of instability-driven branching of lamellar crystallites in the formation of polymer spherulites has been examined experimentally for polyethylene-banded spherulites in terms of the molecular weight dependence by optical and atomic force microscopies associated with quenching and chemical etching. The possibility of instability-driven branching has been suggested by the experimental results of our previous work in terms of the temperature dependences of the band spacing, the lamellar width at the growth front, and the growth rate. The examination of the dependences on the average and distribution of molecular weights enables us to differentiate possible origins of the instability, e.g., compositional gradient with the diffusion of uncrystallized fractions and pressure gradient caused by the density difference between the crystal and the melt. The experimental results suggest the instability driven by the pressure gradient in the melt ahead of the growth front.

Abstract: Mechanical and thermal properties of a hot-melt adhesive made from the styrenic triblock copolymer of polystyrene-block-poly(ethylene-co-propylene)-block-polystyrene, tackifier, and plasticizer oil were examined in terms of the effect of addition of a homopolymer, poly(2,6-dimethyl-1,4-phenylene ether) (PPE). PPE is miscible with the styrene component of the triblock copolymer and has glass transition temperature, T_g, higher than that of the styrene component. The properties were examined by shear adhesion failure temperature test, 180º peel test, dynamic mechanical analysis, and temperature-modulated differential scanning calorimetry. It has been shown that the adhesive properties depend on T_g of the styrene domains, which linearly increases with the content of added PPE. The broader glass transition that resulted from the addition of PPE indicated inhomogeneous distribution of PPE in the styrene domains. Thermal resistance of the adhesive is sustained by physical crosslinks comprising the glassy styrene domains, which are finally broken above T_g of the PPE-rich part of the styrene domains.

Abstract: Effect of epitaxy of nucleating agent (NA) on nucleation of polymers was investigated based on kinetic study. Nucleation rate (I ) of polymers is given by I = I₀ exp(-ΔG^*/kT_c )  (1), where I₀ is prefactor, ΔG^* is free energy for forming critical nucleus, k is Boltzmann constant and T_c is crystallization temperature.  We reported in the previous paper that decreasing the size of NA is important for increasing I₀, i.e., I.  In this study we focus on ΔG^* dependence of I.  In the case of heterogeneous nucleation, ΔG^* is a function of interfacial free energy between NA and nucleus (Δσ).  Δσσ varies between 0 and 1 where σ is lateral surface free energy of nucleus.  Δσσ of isotactic polypropylene (iPP) mixed with three NAs were between 0.13 and 0.23, which were evaluated by the fit of eq 1 to the experimental data of I.  I  increased by 38 orders of magnitude for ΔT=30 K with decreasing Δσσ from 1 to 0.  In the case of NA, I  increased by 60 times for ΔT=30 K with decreasing Δσσ from 0.23 to 0.13.  I  significantly depends on Δσ.  Therefore we concluded that ΔG^*(Δσ ) is essentially important for acceleration of nucleation.

Abstract: The phase behaviors of aqueous polymer solutions are known to be affected by the presence of ions even if the polymer itself does not have any charges. We studied the effect of salt (sodium chloride) on the eutectic phase behavior of non-ionic polymer, poly(ethylene glycol) (PEG) in aqueous solutions using differential scanning calorimetry. We observed that the addition of NaCl increased the liquidus temperature of PEG and decreased that of water. As a result, a steep rise (or fall) is induced in the liquidus around the eutectic point. A simple Flory-Huggins lattice model for the mixture (PEG-water-NaCl) was applied to the experimental results. The model quantitatively reproduced the change in the liquidus both with and without NaCl. The obtained interaction parameters suggest that the increase of the PEG melting temperature by NaCl can be understood as the depletion of NaCl around PEG, possibly due to the image charge repulsion.

Abstract: Signals obtained from a differential scanning calorimeter (DSC) include instrumental effects of time lag due to slow thermal conductance. The dynamic response of samples is influenced by the effects, especially on the occasion of phase transitions. A deconvolution method calibrating the instrumental effects for the heat-flux DSC is reviewed and applied to the eutectic mixtures of aqueous solutions of NaCl and glycerol to determine the phase behaviors without ambiguity in the interpretation of the peak profile. The method is useful for the measurements with fast heating runs, which inevitably have larger time lag but is required for e.g. polymeric systems to reduce reorganization on heating. The results of the deconvolution are well agreed with the data in the literature.

Abstract: The orientation of lamellar crystals in non-banded spherulites of it-polystyrene and it-poly(butene-1) was investigated by microbeam X-ray diffraction. The two-dimensional intensity map of diffraction enables us to examine the local orientation of lamellar crystallites in the non-banded spherulites. The obtained results indicated the re-orientation of crystallites in non-banded spherulites and confirmed our previous observation on the anisotropic birefringence of a group of crystal stacks by polarizing optical microscopy.

Abstract: Based on our recent proposal for the formation mechanism of polymer spherulites, the correlation between the morphology and crystallization kinetics has been examined for it-polystyrene (itPS) spherulites grown from the melt down to temperatures near the glass transition, T_g. The inner structure of the nonbanded spherulites of itPS has been characterized by the persistence length of the patchy pattern observed by polarizing optical microscopy. The persistence length was in proportion to the width of lamellar crystals at the growth front, which was observed by atomic force microscopy. The result reconfirms our suggestion that the inner structure of spherulites is determined by the size of the building blocks. For the determination mechanism of the width of lamellae, the possibility of instability-driven branching has been examined by the correlation between the characteristic lengths and the growth rate in terms of the temperature dependence near T_g. The correlation followed the dependence predicted for the two cases of the instability caused by the compositional gradient and by the pressure gradient. The compositional gradient is determined by the self-diffusion of polymer chains and the pressure gradient by the melt viscosity. Near T_g, owing to the development of spatial heterogeneity, the decoupling of self-diffusion from the melt viscosity can be expected. By examining the possible decoupling, the cases were dismissed for the influence of self-diffusion of portions of polymer chain on crystallization at the growth front and for the compositional gradient formed by small uncrystallized molecules.

Abstract: Kinetics of the solid-solid II-I phase transition of isotactic polybutene-1 was investigated. The fraction W_I of phase I as a function of time t_tr during the phase transition was measured by X-ray diffraction at various temperatures T_tr. The Avrami indices n of the W_I-t_tr plots are approximately unity for T_tr > 288 K. A bell-shaped temperature dependence of the transition rate V with the maximum transition rate at 285 K was obtained. The V-T_tr curve and the Avrami index n = 1 suggest that the rate-determining process is primary nucleation. The dependence of V on T_tr for T_tr < 283 K is described by the William-Landel-Ferry (WLF) equation, which shows that the glass transition affects the transition rate. The Avrami index decreases to n < 1 for T_tr < 283 K, indicating a broadened distribution of the transition rate caused by the spatial heterogeneity of the amorphous state at low temperatures near the glass transition. Those evidences at low temperature clearly suggest that the solid-solid phase transition is influenced by the mobility of chain folding, tie chains and cilia in the amorphous between the stacks of lamellar crystals.

Abstract: We report dynamic Monte Carlo simulations of lattice polymers melting from a metastable chain-folded lamellar single crystal. The single crystal was raised and then melted in an ultrathin film of polymers wetting on a solid substrate, mimicking the melting observations made by using Atomic Force Microscopy. We observed that the thickness distribution of the single crystal appears quite inhomogeneous and the thickness increases gradually from facetted edges to the center. Therefore, at low melting temperatures, melting stops at a certain crystal thickness, and melting-recrystallization occurs when allowing crystal thickening; at intermediate temperatures, melting maintains the crystal shape and exhibits different speeds in two stages; at high temperatures, fast melting makes a melting hole in the thinnest region, as well as a saw-tooth-like pattern at the crystal edges. In addition, the linear melting rates at low temperatures align on the curve extrapolated from the linear crystal growth rates. The temperature dependence of the melting rates exhibits a regime transition similar to crystal growth. Such kinetic symmetry persists in the melting rates with variable frictional barriers for c-slip diffusion in the crystal as well as with variable chain lengths. Visual inspections revealed highly frequent reversals upon melting of single chains at the wedge-shaped lateral front of the lamellar crystal. We concluded that the melting kinetics is dominated by the reverse process of intramolecular secondary crystal nucleation of polymers.

Abstract: Isolated single crystals of isotactic polypropylene (iPP) grown from the melt were studied by optical microscopy and atomic force microscopy (AFM). The single crystals had a well-known rectangular shape when crystallized at high temperatures (T_c) above 155ºC. The width increased with decreasing T_c, and the shape became hexagonal below 130ºC. The single crystals were sectored with thickness difference between them. The growth rate along the a*-axis, G_a*, agreed well with the growth rate of spherulites, as expected. G_a* had two inflection points on the plots against (TΔT)^-1. The lower temperature inflection corresponds to the regime II-III transition, and the higher temperature one is accompanied by an inflection of the growth rate in the b-axis direction, G_b, which has been measured for the first time. The inflection of G_b at the lower inflection temperature of G_a* was much smaller than that of G_a* and may not exist. The crystals are basically surrounded with flat surfaces and no indications of kinetic roughening in the regime III were recognized in the AFM images. The inflections of G_a* and G_b caused a complicated shape change of the aspect ratio, having a minimum at around 135ºC.

Abstract: Molecular weight dependence of growth and morphology of spherulites of isotactic poly(butene-1), iPB-1, and those of the mixtures with atactic poly(butene-1), aPB-1, were examined by atomic force microscopy (AFM) and polarizing optical microscopy (POM) in order to examine the mechanism of the structural evolution by the branching and re-orientation of lamellar crystals at the growth front. The width of lamellar crystals and the characteristic size of the inner structure of spherulites decreased with increasing molecular weight. The result suggests that the mobility of the melt determines the sizes in spherulites and supports the growth front instability induced by a gradient triggering the branching. The sizes in the mixtures also decreased with increasing weight-averaged molecular weight, M_w. The size dependence in low M_w region, however, was too strong and that in high M_w was too weak in comparison with the predicted dependence for the prepared M_w. It has been concluded that the peculiar behaviors should be discussed with effective M_w influenced by the occurrence of separation and exclusion of non-crystallizing aPB-1 at the growth front.

Abstract: Unlike inorganic and organic molecules, in semicrystalline polymers melting gets complicated because of the requirement of conformational transformation of the chain segments, where part of the same chain resides in crystal and also in the amorphous phase. The chain segment residing in the amorphous part can be constrained, either due to adjacent or nonadjacent reentry leading to different nature of chain folding, and arising differences in local chain mobility due to differences in topological constraints. Thus different conformational possibilities in the amorphous region of the semicrystalline polymer has implications on melting temperature and the processes involved in the order to the disorder phase transformation. With a series of experiments on Ultra High Molecular Weight Polyethylene, where the topological constraints are tailored by adopting different synthesis route, it is shown that melting behaviour cannot be fully explained by GibbsThomson equation only. Nonlinearity in melting temperature on heating rate invokes kinetics in melting process, where depending on the heating rate melting can occur either via successive detachment of chains and their reeling in the melt, or by cluster melting. The role of superheating on melting process is also addressed.

Abstract: Crystallization of it-Polybutene-1 (iPB-1) from thin films of several tens nm thick evolves a cellular structure composed of single-layered lamellar crystals. The dependences on thickness and crystallization temperature of the structure, namely of the cell width corresponding to the lamellar width, have been examined quantitatively. Temperature dependence of the cell width well agrees with the width of lamellar crystals grown from bulk melt, for the thin films with thickness in the same order in magnitude as the long spacing of crystal-melt stacks in the bulk melt. Crystallization from thin films is self-evidently controlled by mass transport under possible influence of compositions. The correspondence of the growth structures from thin films and from bulk melt therefore suggests the essential role of the gradient field of mass transport for lamellar branching in bulk melt, which eventually evolves polymer spherulites. The dependence of cell width on film thickness reflects the facility of mass transport in thicker melt films and the overgrowth on the single-layered lamellar crystals.

Abstract: We investigated the phase separation phenomena in dilute surfactant pentaethylene glycol monodedecyl ether (C₁₂E₅) solutions focusing on the growth law of separated domains. The solutions confined between two glass plates were found to exhibit the phase inversion, characteristic of the viscoelastic phase separation; the majority phase (water-rich phase) nucleated as droplets and the minority phase (micelle-rich phase) formed a network temporarily, then they collapsed into an usual sea-island pattern where minority phase formed islands. We found from the real-space microscopic imaging that the dynamic scaling hypothesis did not hold throughout the coarsening process. The power law growth of the domains with the exponent close to 1/3 was observed even though the coarsening was induced mainly by hydrodynamic flow, which was explained by Darcy's law of laminar flow.

Abstract: In order to clarify the formation mechanism of polymer spherulites, we have experimentally examined the effect of externally applied gradient field of temperature on the structural evolution of polymer crystallization, especially on the characteristic length scales of the inner structures of nonbanded crystallization of isotactic poly(butene-1) and of banded crystallization of poly(vinylidene fluoride) and polyethylene. The inner structures were strongly influenced by the temperature gradient and suggested the important role of the gradient field of temperature, i.e., of chemical potential in general, at the growth front in the bulk melt. The results are in accordance with our proposal and experimental confirmation on the formation of polymer spherulites based on the instability-driven branching promoted by a self-induced gradient field in the bulk melt.

Abstract: For the banded spherulites of poly(ε-caprolactone), PCL, grown from the blends with miscible polymers of polyvinyl butyral and poly(styrene-co-acrylonitrile), the effects of blended amorphous polymers on the band spacing have been examined experimentally. The results reconfirmed the strong influence of the second components even with small amount (c.a. 0.09wt%). For the crystallization under the strong influence of the second components probably on the lamellar surface, we have examined the applicability of our modeling of spherulitic growth and its limit. Important findings in this paper are the followings: 1) On the confirmation of the applicability of the modeling for the amount of the second component small enough and the band spacing long enough. 2) On the violation of the predicted relationship of the modeling with increasing amount of the second component, which caused sharp decrease in the band spacing. 3) On the observation of the lower bound of the band spacing, to which the band spacing approached with the increase in the second component. With approaching the lower bound, the band spacing eventually became independent of other growth conditions such as crystallization temperature.

Abstract: We propose the rule "254" cellular automaton model with a probabilistic global rule. The global rule regulates the proportion of total cell states. The model reproduces spatiotemporal patterns obtained by an experiment of peeling an adhesive tape. The statistical properties of the spatiotemporal patterns are characterized from the fractal point of view.

Abstract: Melting kinetics of it-polypropylene crystals has been examined over wide heating rates of 0.6 K min^-1–10⁴ K s^-1 using a standard DSC and a fast-scan DSC. With fast-scan DSC, we have an access to the melting of crystals obtained at low temperatures, which are susceptible to re-organization at the heating rates applicable with standard DSC. It is clearly discernible that the appearance and disappearance of multiple melting peaks are strongly influenced by the applied heating rates and dependent on the crystallization temperatures. By examining the heating rate dependence of superheating of melting, we have determined the melting points of as-grown crystals formed under wide crystallization temperatures.

Abstract: Analysis methods are discussed for the thermal transition kinetics of the 1st-order phase transitions (e.g. crystallization, melting, and solid-solid phase transformation) and chemical reaction by thermal analysis using differential scanning calorimetry, DSC, with constant rate of heating (cooling) and periodic modulation in temperature. The analysis examines the heating rate dependences of the peak temperature obtained by a constant heating (cooling) of DSC and of the characteristics time of the frequency dispersion of an effective dynamic heat capacity determined by Temperature-Modulated DSC. Those dependences are from kinetic response of the transformation processes, so that shares common valuable information on the kinetics. The following transition kinetics has been examined, and the applicability of the methods has been confirmed: polymer crystallization, polymer crystal melting, isotropization transition of a nematic polymer, an epoxy thermosetting system, martensitic transformation of TiNi alloy, melting and crystallization of ice/water confined in a porous silica gel, ferroelectric transformations of P(VDF-TrFE) copolymers. The emphasis is on the application to the complex systems having broad transition region with fast kinetics: a typical example is the melting of polymer crystals.

Abstract: There exists a threshold-sensitive dynamical transition between uniform and periodic growth modes in the domain growth of ascorbic acid crystals from its aqueous supersaturated solution film. The crystal growth induces solution flow. Humidity controls the fluidity of the solution. The solution flow varies the film thickness. The threshold exists in the thickness of the solution film. If the thickness becomes lower than the threshold, the solution flow and the crystal growth almost stop.

Abstract: Melting behaviors of linear polyethylene (PE) have been experimentally examined by fast-scan and conventional differential scanning calorimetry (DSC). By fast-scan heating up to 10⁴ K s^-1, the melting peak temperature, T_peak, is free from the influences of re-organization and re-crystallization and follows the shift only with superheating, which has been evaluated by a power-law behavior. The melting point, T_M, of the chain-folded crystals has been determined as T_peak extrapolated to zero heating rate without the influences of non-equilibrium effects. The Hoffman-Weeks plot of T_M against crystallization temperature, T_c, suggests the equilibrium melting point T_M⁰=141.1°C of the linear PE having M_w=52.0x10³ and the doubling of lamellar thickness concluded from the linear relationship between T_M and T_c with the slope close to 1/2. While the lamellar doubling is a well-known behavior of PE crystallized from the melt, the present results with T_c down to ∼100°C suggest the doubling completed in a quite short time interval. The value of T_M⁰=140.4°C has also been obtained by the Gibbs-Thomson plot of T_M against the inverse of lamellar thickness, (d_c)^-1, determined by small angle X-ray scattering. The agreement of the results within ±1°C suggests the Hoffman-Weeks plot as an appropriate method for the melting point determination with fast-scan heating, only with which the determination procedure is free from re-organization and re-crystallization. The consistent behavior has also been confirmed in terms of the end-surface free energy, σ_e, determined by the Gibbs-Thomson plot and by the growth kinetics of crystallization.

Abstract: A quantitative evaluation has been tried on the thermal lags of a fast-scan (≤10⁴ K s^-1) microchip differential scanning nanocalorimeter (DSC). A thin layer (∼0.2 μm thick) of a standard material of Tin was vapor deposited on a thin film of polyethylene (PE) sample (∼1-10 μm thick), and the thermal lags have been examined by the dependences on the applied heating rate, film mass, and film thickness of the melting onset temperature of Tin on the bottom and top surfaces of PE films put on the sensor stage of nanocalorimeter. Thermal lags are comprised of the instrumental thermal resistance and the temperature gradient in the film. The instrumental thermal lag was detected by the melting of Tin on the bottom of PE films and well explained by the reported value of the thermal resistance of sensor. The temperature gradient in the film was detected by the melting of Tin on the top surface of PE films, and showed the dependence predicted by the modeling of heat transfer in the thickness direction. The influences of thermal lags have also been examined in terms of the heating rate, β, dependence of the shift in melting peak temperature of PE crystals. The power of β^z characterizing the β dependence of the shift became larger with increasing film mass and thickness, i.e. with introducing larger thermal lags. When the power is utilized as a fitting parameter, the influence of thermal lags on the melting point extrapolated to zero heating rate could be kept at small level (±1°C) even for thick films (∼10 μm). Those behaviors have been validated by numerical calculations based on the modeling of fast-scan microchip DSC.

Abstract: We studied the power-law heating-rate dependence of superheating for the melting of alpha- and beta-crystals of isotactic polypropylene by means of chip-calorimeter, and expanded our parallel observation to higher heating rates by means of molecular simulations. We observed that, at low heating rates, the melting of lamellar crystals after thickened via melting-recrystallization exhibits no power-law-dependent superheating; at medium heating rates, the melting of crystals after thickened via chain-sliding diffusion exhibits the power-law-dependent superheating with the power indexes sensitive to chain mobility in the crystals; while at high heating rates, the zero-entropy-production melting of crystals without further thickening maintains the power-law-dependent superheating but with the power indexes uniform at an upper-limit 0.375. We attributed the index 0.375 to a result combining local intramolecular nucleation and global roughening growth at the lateral surface of lamellar crystals, which dominate the kinetics of crystal growth and melting of polymer crystals at high temperatures.

Abstract: The most common higher order structure of crystalline polymers is called spherulite. A spherulite is a polycrystalline aggregate densely filled with thin lamellar crystals and formed by consecutive lamellar branching and reorientation of those crystals in non-crystallographic directions. Polymer spherulites have inner structures characterized by periodic banding or patchy patterns that are created by the reorientation with correlated twisting or in random directions, respectively. The specific reorientation is related to the unbalance of surface stresses caused by the chain folding on the upper and lower basal planes of the lamellar crystals. The branching mechanism is related to the fingering instability of the growth front caused by a gradient in chemical potential ahead of the growth front. The dynamical coupling of the branching and reorientation evolves the spherulitic growth in crystalline polymers.

Abstract: Crystal melting behavior of indium and isotactic polypropylene has been examined by differential scanning calorimetry of heat flux type in terms of the heating rate, β, dependence. The melting shows the dependence characterized by a power, z, of the shift in peak temperature in proportion to β^z. The power, z, differentiates the melting with and without superheating. For polymer crystal melting, intrinsic nature of the broad melting region with a fractional power, z≤1/2, due to superheating of melting kinetics has been reconfirmed experimentally. On the other hand, the crystal melting of indium, which is supposed to proceed with negligible superheating, showed the shift in peak temperature with the power in the range of 1/2≤z≤1, depending on sample mass, which is due to instrumental thermal lag predicted by the Mraw's model consisting of lumped elements. The β dependence is influenced by the thermal lag determined by the thermal contact resistance between the sample pan and the stage, the effect of which has been examined in terms of the dependence on sample mass and the application of silicone grease between the sample pan and the stage. The influence of two different types of the definition of heat flow has also been examined; the simplified one without the time derivative of temperature difference showed an apparent shift in peak temperature at faster scan rates in a similar way as that of thermal lag.

Abstract: The lamellar thickness distribution (LTD) of not-reorganized linear polyethylene was calculated on the basis of the melting point distribution using fast scanning calorimetry (FSC) by applying the following precautions. First, by taking sufficiently small sample mass and thickness, the influence of thermal lag during fast-heating is thought to be negligible. Second, by fast-heating, reorganization and cold crystallization are strongly hindered or even suppressed. Third, the influence of superheating has been accounted for and corrected by deconvolution of the FSC curve using the calculated melting kinetics of single-sized lamellae consisting of folded-chain crystal. Under such precautions, the resulting FSC heating curve reflects the melting point distribution of metastable-but-not-reorganized folded-chain crystals. Finally, the Gibbs-Thomson equation was applied to calculate the LTD from the melting point distribution. The average lamellar thickness calculated was in good agreement with that determined by small-angle X-ray scattering and low-frequency Raman spectroscopy.

Abstract: Fast scanning chip calorimetry in its non-adiabatic version allows for heating and cooling at rates up to 10⁶ K/s, covering all polymer processing relevant rates. Furthermore it allows for systematic studies of nucleation, crystallization, melting and reorganization for a large number of polymers. After an introduction, open problems and the need for further investigation of polymer crystallization are explained, followed by a brief description of the novel technique of fast scanning chip calorimetry and its capability to shed further light on fundamental details of the polymer-crystallization process. In the fourth part, specific examples of non-isothermal and isothermal crystallization studies are provided, including the discussion of the effect of nucleating agents. The possibility to investigate homogeneous nucleation and its kinetics is highlighted too. The fifth part focuses on the analysis of the melting kinetics and the determination of the zero-entropy-production melting temperature.

Abstract: The multiple melting peaks of isothermally crystallized poly(ether ether ketone) were investigated by fast-scanning chip calorimetry over a wide range of heating rates from 500 to 60,000 K s^-1. The analysis of heating rate dependence of melting temperatures revealed that there are two crystal populations with distinct melting kinetics for the samples prepared at different crystallization temperatures, 170°C ≤ T_iso ≤ 270°C. For each T_iso, the two melting temperatures of the metastable crystals without prior reorganization or superheating (i.e. zero-entropy-production melting temperatures) were constantly 20 K and 30 K, respectively, higher than T_iso. We first discuss this behavior quantitatively based on the Lauritzen-Hoffman nucleation approach. Finally we conclude that these increases in temperature are linked to the number of stems which construct the secondary surface nuclei. The existence of two crystal populations can be caused by differences in the stability of the crystal or "local" differences in the free energy of the surrounding melt.

Abstract: Differential scanning calorimetry and fast scanning chip calorimetry heating experiments were carried out in a wide range of rates of temperature change from 0.2 to 60,000 K s^-1 for isothermally crystallized polyamide 6. Multiple melting peaks were observed. With increasing heating rate, the highest-temperature endotherm shifts toward lower temperatures and finally disappears due to suppression of the reorganization. The critical heating rate to suppress reorganization was 15-50 times higher than the critical cooling rate to cause complete vitrification. On heating at rates higher than the critical heating rate to suppress reorganization, there were observed two melting processes of different kinetics. Four possible assignments were considered regarding the two crystal populations. These are (i) crystals grown during primary and secondary crystallization, (ii) crystals grown in the bulk and nucleated at the surface/substrate, (iii) crystals, which are subjected to different local stress originating from heterogeneities in interlamellar regions, and (iv) the crystal/mesophase polymorphism.

Abstract: Melting of original crystals and their recrystallization during heating were successfully separated for isothermally crystallized poly(butylene terephthalate) (PBT). The corresponding kinetics was determined and quantitatively discussed for a wide range of heating rates (0.1−100,000 K s^-1) using fast-scanning chip calorimetry (FSC) and differential scanning calorimetry (DSC). The double melting peaks observed on the FSC curves are assigned to the melting of original crystals (low-temperature peak) and recrystallized and/or reorganized crystals (high-temperature peak). Heating rate dependence of the degree of recrystallization has been evaluated and the kinetics was discussed on the basis of Ozawa's method. Compared with the melt-crystallization and cold-crystallization, recrystallization kinetics is the fastest process. This is because many crystal remnants, which do not transform into the isotropic melt, act as athermal nuclei, and accelerate recrystallization.

Abstract: Crystallization kinetics of poly (butylene terephthalate) (non-talc-PBT) and its 0.1 wt% talc composites (talc-PBT) was determined for a wide range of cooling rates and isothermal temperatures. The critical cooling rate to suppress crystallization is 2,000 K ^-11 for non-talc-PBT and 7,000 K ^-1 for talc-PBT. The cooling rate dependence of the total enthalpy change and heating rate dependence of enthalpy of cold crystallization are quantitatively discussed on the basis of the Ozawa's method. For isothermal crystallization, the annealing-temperature (T_iso) dependence of crystallization half-time (t_1/2) shows a bimodal curve with two minima. Talc shortens the t_1/2 at T_iso above 340 K and acts as a heterogeneous nucleation agent. Tammann's approach revealed that the t_1/2 is shortened by pre-nucleation for non-talc-PBT but not for talc-PBT.

Abstract: Ivanov et al., Euro. Polym. J. 81 (2016) 598-606, conclude that "the phenomenon of the double (or multiple) melting behavior [in poly(trimethylene terephthalate) (PTT)] is not necessarily coupled to the melting-recrystallization processes and can be observed even in the absence of any recrystallization". To further clarify this long standing issue, the multiple-melting behavior of isothermally crystallized PTT was examined using differential scanning calorimetry (DSC) and fast scanning chip calorimetry (FSC) in a wide range of heating rates (0.1 K s^-1−60,000 K s^-1). The critical heating rate to suppress recrystallization, β_critical, was determined as 2000 K s^-1 from the analysis of heating rate dependence of melting temperature. Melting peaks observed below β_critical are due to the melting of recrystallized crystals, which are formed during slow heating. On the other hand, above β_critical, a single endothermic peak originated from the melting of initially formed crystals is observed. The result of thermal analysis strongly suggests that a single population of crystals is formed during isothermal crystallization of PTT. The heating rate of 1000 K s^-1, as used by Ivanov et al., was therefore not fast enough to suppress recrystallization.

Abstract: Kinetics of "melting" of sucrose crystals has been examined by conventional differential scanning calorimetry (DSC) and fast-scan calorimetry in terms of the possibility of a clear distinction between physical melting and chemical decomposition processes by fast scan up to 10,000 K s^-1. On the basis of a modeling of the crystal melting kinetics with superheating and the possible influence of thermal lag, the heating rate dependence of "melting" was carefully examined. The equilibrium melting point T_M of sucrose crystals at a zero heating rate was estimated to be T_M=188.9±1.2°C by fast-scan calorimetry, and the heat of fusion of 46 kJ mol^-1 was determined by conventional DSC, which is in agreement with the reported values in the literature. The Kissinger plot of the peak temperatures by heating runs and the plot of characteristic times of isothermal runs against the inverse of absolute temperature suggested a kinetic diagram, in which the "melting" behaviors above and below T_M are qualitatively different with purely physical melting above T_M and "melting" initiated by chemical decomposition at active sites below T_M.

Abstract: Unique behavior of superheated melting kinetics of polymer crystals has been examined in terms of the metastable nature of thin polymer crystals with chain folding. The superheated melting kinetics was characterized by the heating rate dependence of the melting peak in thermogram. By examining the behaviors of polyethylene molar mass fractions, its homolog, hexacontane, and indium, it has been experimentally confirmed that the metastability of crystals with chain folding has an essential role in the superheated melting kinetics; i.e. stable extended-chain crystals of hexacontane melts in the same way as indium without superheating, and metastable chain-folded crystals of higher molar mass polyethylene needs to overcome larger kinetic barrier for melting.

Abstract: Fast scanning chip calorimetry (FSC) experiments are reviewed in terms of the melting of semi-crystalline polymers examined over a wide range of heating rates. The analysis method of melting kinetics is summarized and it is shown that the heating rate dependence of melting temperatures revealed that there are two crystal populations with distinct melting kinetics for isothermally crystallized PA6 and PEEK. Some semi-crystalline polymers showed the following relation between the melting peak temperature, T_m, and the crystallization temperature, T_iso; T_m = T_iso + δT with a constant δT. Quantitative consideration of this issue is discussed on the basis of the Lauritzen-Hoffman standard model of polymer crystallization. We also discuss a method for obtaining the lamellar thickness distribution (LTD) of linear PE by using FSC.

Abstract: Fast scanning calorimetry (FSC) has been used to investigate the kinetics of nonisothermal crystallization, isothermal crystallization, and melting for semicrystalline polymers (ie, poly(butylene terephthalate, polyphenylene sulfide, and isotactic polypropylene). The scanning rate dependence of enthalpy of melt-crystallization, cold-crystallization, and re-crystallization obtained from FSC are quantitatively explained on the basis of Ozawa's method. For isothermal kinetics, FSC allows to obtain the annealing-temperature dependence of crystallization half-time in a wide range of the supercooling without any unwanted nucleation or crystallization during cooling. The effect of additives for nonisothermal or isothermal crystallization was also considered in this article. In addition, hyphenated technique of FSC and polarized optical microscopy clearly shows the differences in crystallization kinetics and morphologies.

Abstract: Crystallization and melting behaviors of chain-folded polymer crystals have been examined by fast-scan calorimetry (FSC) combined with small angle X-ray scattering (SAXS) and wide angle X-ray diffraction (WAXD) for poly(vinylidene fluoride). The melting point of lamellar crystals formed isothermally at T_c was measured by FSC in terms of the heating rate dependence and calibrated on the basis of the modeling of melting kinetics for the determination of the melting point at zero heating rate T_M. The Hoffman-Weeks (H-W) plot of T_M against T_c was on a linear straight line over T_c range broader than 30 K, and suggested the equilibrium melting point T_M⁰≅200°C of chain-extended infinite-size crystals of the α form. On the other hand, utilizing crystalline lamellar thickness dc determined by SAXS, both of the Melting and Crystallization lines in the Gibbs-Thomson (G-T) plots of T_M and T_c against (d_c)^-1, respectively, were found to seriously deviate from linear straight lines. By examining the secondary stage of crystallization on long time isothermal annealing at Tc in terms of the changes in T_M and the specific heat of fusion Δh_fs by FSC, a newly proposed thermal G-T plot of T_M against (Δh_fs)^-1 has confirmed the reliability of T_M⁰ of the α form determined by the H-W plot and the Tc dependent folding surface free energy σ_e, which brings the curved Melting and Crystallization lines in the G-T plots. In addition, on long time isothermal annealing, the changes in dc by SAXS and in crystallite size by WAXD have confirmed the molecular origin of the increase in T_M and Δh_fs in the secondary stage with thickening and perfecting of metastable chain-folded polymer crystals.

Abstract: Crystallization and melting behaviors of polyethylene (PE) crystals were examined by fast-scan chip sensor calorimetry (FSC) and small-angle X-ray scattering (SAXS). The melting point T_M of chain-folded thin lamellar crystals of PE was determined by utilizing FSC, and the crystalline lamellar thickness d_c by SAXS. The range of crystallization temperature T_c of SAXS as well as FSC was extended much broader than before by examining those samples prepared on a chip sensor of FSC and applied deep temperature jump for crystallization under large supercooling ΔT_c. While re-confirming the equilibrium melting point T_M⁰ with linear relationship of the Melting and Crystallization lines in the Gibbs-Thomson (G-T) plots of T_M and T_c against (d_c)^-1, respectively, and the Hoffman-Weeks (H-W) plot of T_M against T_c under relatively small ΔT_c, those G-T and H-W plots seriously deviated from linear straight lines under large ΔT_c. The origin of the curved G-T plots was ascribed to the T_c dependent folding surface free energy σ_e. The T_M⁰ and T_c dependent σ_e were convinced by a newly proposed Thermal G-T plot of T_M against the inverse of specific heat of fusion Δh_fs in terms of the increase during the secondary stage of crystallization on long time isothermal annealing at T_c of chain-folded PE crystals transforming to more stable states by lamellar thickening and crystal perfecting. The deviation from linear H-W plot under large ΔT_c was then ascribed to the crystal reorganization on heating of those less stable crystals formed under large ΔT_c even with fast heating. Application of fast heating and cooling by FSC plays an essential role in the confirmation of those thermodynamic behaviors of metastable polymer crystals with chain folding.

Abstract: Melting behaviors of polyethylene (PE) crystals on heating were examined in terms of the heating rate β dependence by fast-scan chip-sensor calorimetry. PE crystals were prepared under broad ranges of crystallization temperature T_c and isothermal holding time Δt, including Δt shorter than completion time of primary crystallization. On the basis of a modeling of melting kinetics with a rate coefficient determined by the degree of superheating ΔT and the careful examination of the influence of thermal lags, the detailed analysis confirmed a systematic change in the melting kinetics depending on the crystal stability; i.e. less stable crystals, which were formed at low T_c with short ΔT, experience lower kinetic barrier for melting. Melting peak of those less stable PE crystals showed linear β dependence, which exceeds the acceptable limit of the β dependence predicted from ΔT dependent melting rate in the modeling. The melting behavior approaches to that of indium, a standard material for melting, and suggests that the melting of those less stable PE crystals is nearly instantaneous without appreciable superheating, the confirmation of which becomes realized only by utilizing fast-scan calorimetry.

Abstract: The recrystallization behavior of poly(ethylene terephthalate), PET, in the melting region was examined by Fast-Scan and Temperature-Modulated Calorimetry. In addition to the prior results of Fast-Scan Calorimetry, FSC, evidence that recrystallization caused double PET melting peaks was obtained. An exothermic recrystallization peak was directly observed in the second heating run of FSC after the lower-temperature melting peak was eliminated through rapid heating and cooling. FSC was then performed with a temperature protocol of a periodic step-wise jump in temperature, a mode of temperature modulated FSC, T-M FSC. A broad and large peak of the effective dynamic heat capacity of complex quantity was observed in the melting region during T-M FSC analysis, which proved that melting occurred in the temperature range between the double melting peaks. A broad negative peak in the phase angle of the dynamic heat capacity was observed in the melting region at a low underlying heating rate with long modulation periods, which indicated that recrystallization and melting occurred simultaneously.

Abstract: In this paper, we report the molecular weight dependence of the crystal growth of isotactic polystyrene from 10 nm ultrathin films. The growth rate and characteristic length of the branching morphology of a crystal grown in 10 nm ultrathin films change depending on the molecular weight of the sample. Analysis of the molecular weight dependence according to the theory of growth front instability reveals that the diffusion coefficient of molecular chains in ultrathin films around branching crystals scales with the molecular weight as M_w^-1.4 for samples with weights higher than the critical molecular weight for the entanglement of polystyrene. This result indicates that the polymer chains in the depletion zone around the crystals diffuse in quasi-two dimensions through the reptational motion modified on an attractive substrate.

Abstract: The crystallization and melting behaviors of poly(butylene terephthalate) (PBT) and poly(ethylene terephthalate) (PET) were examined by Hoffman-Weeks (H-W), Gibbs-Thomson (G-T), and thermal Gibbs-Thomson (t-G-T) plots constructed by using fast-scan calorimetry and small-angle X-ray scattering. With PBT and PET, neither an H-W nor a G-T plot could be utilized for the determination of the equilibrium melting point (T_M⁰) of chain-extended infinite-size crystals. The thermal Gibbs-Thomson plot utilizes the change in the melting point and the heat of fusion of chain-folded crystals during the secondary stage of isothermal crystallization. T_M⁰ was determined from a t-G-T plot, and the results were in good agreement with the literature values for PBT and PET. G-T and t-G-T plots suggested a temperature-dependent folding surface free energy (σ_e), as has been proposed by Hoffman et al. The σ_e values obtained with G-T and t-G-T plots support the consistency of the analysis.

Abstract: Fast scanning calorimetry (FSC) measurements were carried out for multi-step, isothermal, crystallized poly (butylene terephthalate) to quantify the effect of single-step to triple-step annealing above T_g (40°C interval below the previous annealing temperature) on the crystallization/melting kinetics. In the case of double-step annealing, two endothermic peaks were observed on the FSC curves due to the melting of the crystal formed during the 1st step (base crystal; BC) and 2nd step (thermal history crystal; THC). The crystallization rate of the THC decreased due to the spatial restriction of the pre-existing BC. The melting kinetics of the THC were not affected by the time of 1st step crystallization. If the sample was re-heated to the 1st step temperature (T_c1) after multiple annealing, the thermal history of the previous annealing was completely erased. Moreover, in the re-annealing process at T_c1, secondary crystallization showed the same behavior as that expected from the result of single-step annealing.

Abstract: Analysis methods are discussed for polymer crystallization and melting with three different types of plots constructed by using fast-scan calorimetry and small angle X-ray scattering for the determination of the melting point T_M, heat of fusion ΔH_f and crystalline lamellar thickness d_c. Two of those plots are the well-known Hoffman-Weeks plot of T_M against crystallization temperature T_c and the Gibbs-Thomson (G-T) plot of T_M against 1/d_c in terms of the data-sets obtained in the primary stage of polymer crystallization. The third plot is a newly proposed Thermal G-T plot of T_M against 1/ΔH_f, both of which shows a logarithmic time evolution in the secondary stage with reorganization, i.e. lamellar thickening and crystal perfecting, of existing crystals formed in the primary stage. By utilizing those plots, the zero-entropy-production melting point T_M⁰, folding surface free energy σ_e, and a thickening coefficient γ can be evaluated. Obtained results are self-consistent and agreed with prior literature values. Temperature dependent σ_e suggests curved melting and crystallization lines of the G-T plot. Application of fast heating is essential for the quantitative analysis of the melting behavior of chain-folded lamellar crystals in a metastable state.

Abstract: An analysis method using small-angle X-ray scattering (SAXS) of the lamellar stacks of crystalline polymers was examined. The scattering profile was expressed by a fitting function on the basis of a paracrystalline stacking model of finite sequence of parallel lamellae in a stack with border zones continuously connecting to the mean density in spherulites. The SAXS pattern of poly(butylene terephthalate) was able to be fitted to both the conventional model with infinite number of parallel lamellae in a stack and the present model with finite number. The SAXS pattern of polyethylene could not be fitted by the conventional model supposing an infinite sequence, and it was necessary to suppose a lower finite number; the best fit result was obtained with two crystalline layers. A lower number of parallel lamellae in a stack is consistent with the fact that polyethylene lamellar crystals are twisted in three-dimensional space, and cannot form an infinite sequence of simple stacked structure of lamellae oriented parallel to each other. For the finite sequence with lower number, the determination of crystalline lamellar thickness requires the consideration of border zones. It was also confirmed that an alternative method using triangular shape of a one-dimensional autocorrelation function could be acceptable with better level of agreement for narrower distributions of thickness.

Abstract: The melting and recrystallization behaviors of poly(butylene terephthalate) (PBT) were investigated using temperature-modulated scanning calorimetry in both fast- and conventional slow-scan modes. With this method, the response of multiple transition kinetics, such as melting and recrystallization, can be differentiated by utilizing the difference in the time constants of the kinetics. In addition to the previous result of temperature-modulated fast-scan calorimetry of polyethylene terephthalate (PET), the supporting evidence of another aromatic polyester, PBT, confirmed the behavior of the exothermic process of recrystallization, which proceeds simultaneously with melting on heating scan in the temperature range of double melting peaks starting just above the crystallization temperature up to the main melting peak. Because the crystallization of PBT is much more pronounced than that of PET, similar behavior of recrystallization was obtained by the conventional temperature-modulated differential scanning calorimetry at a slow-scan rate.

Abstract: The crystallization behavior of the metastable α form of triacylglycerols (TAGs) plays a critical role as a precursor for the crystallization of more stable β′ and β forms for various applications in food and pharmaceutical products. However, precise analysis of the crystallization kinetics of α has not been performed, likely due to its rapid and complex behavior. This paper presents the observation results of the initial stages of the isothermal crystallization kinetics of α forms of 1,3-dipalmitoyl-2-oleoyl-glycerol (POP), 1,2-dipalmitoyl-3-oleoyl-rac-glycerol (rac-PPO), and molecular compound (MC) crystals of a POP/rac-PPO (1/1) mixture (MCPOP/PPO) using synchrotron radiation time-resolved X-ray diffraction and polarized optical microscopy. In all the TAGs, α crystals with a worm-like morphology started to grow rapidly in the first stage. Then, the α crystals slowly transformed into more stable forms in different manners for different TAG samples. In POP, the conversion was simple, as the α-2 form transformed into γ-3, whereas in rac-PPO, the lamellar distance values of the α-2 form continuously decreased with time and changed into the α-3 form. In the MCPOP/PPO crystals, in contrast, separate crystallization of α-2 of a rac-PPO fraction initially occurred, followed by the crystallization of α-2 of POP, and the two α forms merged into α-2 of MCPOP/PPO. This separate crystallization was caused by large differences in the crystallization kinetics of the α forms of POP and rac-PPO.

Abstract: Crystallization of poly(butylene succinate) (PBS) at 100°C, about 30 K below the equilibrium melting temperature, allowed the preparation of crystals, which were analyzed regarding their zero-entropy-production melting temperature. Irreversible melting occurs in a rather narrow temperature window of only around 8 K, between 101 and 109°C, revealing a narrow distribution of the thickness of isothermally formed lamellae and a rather low thickening/stabilization factor of less than 1.4. Quasi-isothermal temperature-modulated differential scanning calorimetry suggests significant reversible melting and crystallization during and after crystallization, proving the existence of a large fraction of crystalline phase being at the stability limit at the crystallization temperature. Heating of crystals formed at 100°C to above their zero-entropy-production melting temperature, followed by isothermal annealing, permitted the analysis of the kinetics of irreversible melting, yielding superheating-dependent rate constants of the order of magnitude of 10² s^-1 5−10 K above the zero-entropy-production melting temperature. The advanced analysis of the melting behavior of polymer crystals isothermally grown at low melt supercooling allows one to draw conclusions about their (inherently) low thermodynamic stability.

Abstract: Crystallization kinetics of poly(butylene terephthalate) under high supercooling was examined by Temperature-Modulated Fast Scanning Calorimetry (TM-FSC). By using temperature modulation for isothermal crystallization, we can determine the temperature dependence of crystal growth rate. The positive/negative dependence brings the negative/positive sign of the phase angle of dynamic heat capacity, respectively. The obtained dependence was compared with that of peak time of heat flow on isothermal crystallization. The isothermal peak time is inversely proportional to the crystallization rate and showed a double peak, corresponding to the crystal-growth- and nucleation-dominant temperature ranges. The result of TM-FSC over the entire temperature range including the nucleation-dominant lower temperature range was in agreement with the temperature derivative of the fitting curve of the crystal-growth-dominant higher-temperature peak. Hence, the present analysis confirmed that TM-FSC detected the change in crystal growth rate but not in nucleation rate. The crystal growth rate was practically determined by a mobility factor near the glass transition.

Abstract: When polymer crystallization is initiated by an instantaneous athermal nucleation and controlled by two-dimensional secondary nucleation on the growth face, for crystallization from the melt upon cooling at a constant scan rate β, an analysis based on the Avrami model reveals that a plot of β/(∆T_peak)²=β/(T_M⁰−T_peak)², in which T_peak represents the peak temperature of crystallization rate and T_M⁰ the equilibrium melting point, is nearly equivalent to that of the inverse of crystallization half-time τ_1/2 and peak time τ_peak, which are obtained from isothermal crystallization and used as a measure of crystal growth rate. Therefore, a plot of β/(∆T_peak)² against T_peak at different scan rates can be utilized to examine the temperature dependence of the crystal growth rate in the same way as that of τ_1/2 and τ_peak obtained under isothermal conditions at different temperatures. The applicability was confirmed via numerical calculations and experiments using poly(vinylidene fluoride) and poly(butylene terephthalate). The agreement of the temperature dependence estimated by the plot of β/(∆T_peak)² was much better than that of β/(T_peak)² used in the well-known Kissinger plot.

Abstract: Annealing of poly (L-lactic acid) (PLLA) at temperatures lower than the temperature of primary melt-crystallization leads to appearance of distinct low-temperature annealing peaks in subsequently recorded calorimeter heating scans. Reason is continuation of crystallization by growth of crystals of lower stability as formed during primary crystallization. The assignment of low-temperature annealing peaks to crystallization is based on a robust analysis of the decrease of the heat capacity of the semicrystalline structure slightly above the glass transition temperature and its correlation with the corresponding enthalpy of crystallization. Comparison of the form of annealing peaks with classical enthalpy-recovery peaks obtained on devitrification of the glassy amorphous phase of semicrystalline PLLA supports the interpretation regarding the origin of annealing peaks.

Abstract: Crystallization behaviors on two-step isothermal crystallization at T_c1 and T_c2 (<T_c1) were examined by fast scanning calorimetry for poly(butylene terephthalate) in order to identify the dominant process during the secondary stage of crystallization at T_c1 after the completion of spherulitic growth under isothermal condition. From the difference between the melting peaks obtained before and after the lowtemperature crystallization step at T_c2, the distinction of the following two processes became realizable: the growth of crystals formed at T_c2 and the stabilization of crystals formed at T_c1. The dependences on T_c2 and the duration of times Δt_c1 and Δt_c2 revealed the following: The formation and growth of new crystals are controlled by thermodynamic driving force determined by supercooling, and hence are suppressed at T_c1 higher than T_c2. The crystal stabilization is controlled by the mobility of polymer chains, and became more pronounced at T_c1. Therefore, the dominant process of the secondary crystallization under isothermal condition at T_c1 should be the stabilization of crystals formed in the primary stage and the formation of new crystals will only have a secondary effect.

Abstract: Quantitative analyses of the melting kinetics of superheated polymer crystals, including the isothermal analysis of the time dependence of melting and nonisothermal analysis of the heating-rate dependence of melting, were carried out by fast scanning calorimetry on linear polyethylene that has a narrow melting temperature region. The time evolution of the decrease in the total crystallinity during melting was modeled using a first-order kinetic equation with a rate coefficient, which defines a characteristic melting time under isothermal conditions. A superheating-dependent rate coefficient characterizes the heating-rate dependence of the nonisothermal melting. The obtained results of both analyses consistently suggest the presence of a superheating-dependent melting kinetics unique to initially metastable long-chain polymer crystals with the melting rate nonlinearly dependent on superheating. The dependence is exponential at least in a certain range of superheating. Examinations of the dependence on crystallization temperature, which controls the thickness of lamellar crystals, suggest an activated process of detaching a whole crystalline stem. A possible mechanism of the activation barrier is discussed in connection with distinct types of chain folding.

Abstract: A reinterpreted analysis method of the Ozawa model is presented for the nonisothermal kinetics of the nucleation and growth processes of polymer spherulites. The Ozawa model is based on the Avrami model which is valid for an isotropic crystallization with randomly dispersed nuclei and with growth rate dependent only on temperature. The crystallinity φ for the non-isothermal kinetics is expressed using a term of the form (β(T)/β_i)ⁿ with the applied scan rates of cooling β_i (i = 1 − N) and a function β(T) dependent only on the temperature T. The reinterpretation involves writing this term as (β_half(T)/β_i)ⁿln(2), where β_half(T) is regarded as an inverse function of T_half(β), i.e., the temperature T_half of φ=1/2 at a fixed scan rate β. The temperature-dependent β_half(T) is given by the fitting curve of T_half measured at the various cooling rates β_i. The original Ozawa plot shows φ as a function of a finite number of data points β_i (i = 1 − N) at a certain fixed temperature T. The reinterpreted Ozawa plot is a continuous curve of φ as a function of the T-dependent β_half(T) at a fixed cooling rate β, and can be utilized for a more reliable determination of the Ozawa index n. Moreover, β_half(T) can be replaced by β_peak(T), which is an inverse function of the peak temperature T_peak at a fixed cooling rate β. The applicability of the reinterpreted Ozawa model was experimentally examined for the spherulitic crystallization of poly(vinylidene fluoride) and by numerical calculations.

Abstract: The historically renowned original treatments of Avrami predicted the continuous change in the Avrami index between 3 and 4 with a time-dependent effective nucleation rate I for the nucleation and subsequent linear growth process of spherical domains under isothermal conditions. The nucleation rate I is determined by the number density N₀ of tiny germ-nuclei at t=0 and the transformation rate r of a germ-nucleus to the active nucleus. This model was applied to the crystallization of poly(butylene terephthalate) PBT, which revealed a continuous change in the Avrami index with temperature when a nucleating agent (NA) talc is added. In particular, for crystallization with NA, N₀ corresponds to the number density of NA particles, and the rate r represents the formation rate of active nucleus from an NA particle. The product of N₀ and crystal growth rate G, i.e., N₀^1/3G, and the rate r were independently evaluated from the time-dependent behavior of crystallization with the Avrami index between 3 and 4. The efficiency of NA is evaluated from the rate r and its temperature dependence, which is determined by the thermal activation barrier for the transformation and is characterized by an excess surface free energy Δσ evaluable using the current analysis method. The dispersibility of NA is assessed by the relative increase of N_na/N_wo in N₀, with the addition of NAs N_na from the number density without agents N_wo. The applicability and usability of the analysis method were confirmed for PBT crystallization with talc, using fast scanning calorimetry. The evaluated rate r exhibited a stronger temperature dependence than the crystal growth rate G, and the relative increase N_na/N_wo was more than 100 times in the sample with well-dispersed talc.

Abstract: The influence of crystallization on the amorphous phase of low isotacticity polypropylene (LT-PP) was studied by analyzing the enthalpy relaxation behavior using fast scanning calorimetry (FSC) and temperature modulated FSC. The high temperature shift of the enthalpy recovery peak and the glass transition temperature during crystallization was interpreted as a transformation of the unconstrained amorphous (UCA) to constrained amorphous (CA) phase. Enthalpy relaxation approach had the same result as the conventional heat capacity analysis of mobile amorphous (MA) phase as proposed by Wunderlich. Our study revealed that successive glass transition of rigid amorphous (RA) phase in a three-phase model and the gradual increase in the heat capacity of the MA phase in a two-phase model are experimentally indistinguishable above the crystallization temperature.

Abstract: On the kinetics of non-isothermal crystallization of polymers, the reinterpreted Ozawa method proposed in a previous report is studied further to generate valuable information. The Ozawa method is used to investigate the crystallization kinetics with constant temperature scanning rates β and is concerned with the basic formula for apparent crystallinity, from which the true crystallinity is derived using the concept of an extended volume of the Kolmogorov–Johnson–Mehl–Avrami model. The formula is expressed by the temperature scanning rate β and a function of temperature T, β_Oz(T). This study investigates the temperature derivative of β_Oz(T), which represents the crystal growth rate in the presence of athermal nucleation from foreign heterogeneities including nucleating agents; this case is applicable to most polymer crystallization processes. The validity of this relationship was verified by comparing it directly to the crystal growth rate in numerical simulations and by comparing it to the crystallization peak and half times of isothermal crystallization for experimental results of poly(butylene terephthalate). This evaluation provides basic information on the crystal growth rate, which is necessary for understanding polymer crystallization. As is well known, the temperature derivative of β_Oz(T) also corresponds to the function required to derive Nakamura et al. model’s suggested equation for polymer processing.

Abstract: Modulated temperature differential scanning calorimetry (MTDSC) is one of the periodic temperature modulation methods in thermal analysis. MTDSC applies a small periodic modulation to temperature scan and analyzes the response that appears in the heat flow. This method is implemented as one measurement mode of conventional DSC and thus is the most commonly used method among periodic temperature modulation methods. As a unique feature of MTDSC, not only the heat flow response to the periodic modulation but also the response to the temperature scan at a constant rate are obtained simultaneously. Namely, MTDSC is a method that combines the measurements of both the conventional DSC and the periodic temperature modulation. By utilizing this feature, useful and important analyses are performed not only for the glass transition that appears as a change in heat capacity, but also for the kinetics of chemical reaction and of the first-order phase transitions such as crystallization, melting, and recrystallization. This section describes the principles, features, and advantages of MTDSC.

Abstract: An analyzing method using periodic temperature modulation is applied to the kinetics of enthalpy recovery that occurs when an amorphous material in the glassy state devitrifies during heating. In particular, this study demonstrates that an analytical expression of the kinetic response can be formulated by assuming temperature modulation with a periodic temperature jump and isothermal holding. This analysis provides a reasonable interpretation for the well-known fact that the magnitude of the dynamic heat capacity of complex quantity obtained by temperature modulation does not exhibit a large peak corresponding to the enthalpy recovery peak. Furthermore, it is demonstrated that the phase angle peak of the dynamic heat capacity was affected by the kinetics. Its quantitative evaluation provides useful information on the relaxation time during glass transition. Numerical simulations and experimental results of atactic polystyrene examined by conventional differential scanning calorimetry and fast scanning calorimetry confirm these findings.

Abstract: The recent progress in the understanding of the melting kinetics of polymer crystals was reviewed. The melting behavior of folded-chain crystals (FCC) of polymers becomes seriously complicated due to the metastability of FCC causing melting-recrystallization cycles and reorganization of crystals. Conventional calorimetry of the melting under constant rate of heating suggested a heating rate dependence of melting peak temperature, which is understood as a superheated melting kinetics. A morphological observation of melting of single crystals supported this behavior. Recent progress of chip-sensor fast scanning calorimetry (FSC) also confirmed the behavior and enabled the examination of isothermal melting kinetics. The results suggested an exponential dependence of melting rate on superheating, which can be interpreted as a consequence of inhomogeneous stability of crystalline stems derived from broad variations of chain-folding conformations. As a further application of FSC to organic crystals, melting kinetics of sucrose is also reviewed.

Abstract: The kinetics of enthalpy relaxation of atactic polystyrene after temperature jump-down and jump-up in the glass state is studied using temperature-modulated fast scanning calorimetry (T-M FSC). During the isothermal relaxation, the dynamic heat capacity obtained by T-M FSC underwent a systematic change suggesting a shift of relaxation time. The relaxation time in the nonequilibrium glass state is dependent on the sample’s actual temperature T and the nonequilibrium structure that has been indexed by a fictive temperature T_f. The changes in the magnitude and phase angle of the dynamic heat capacity on relaxation prove the influence of the nonequilibrium structure. The influence is indexed by an effective temperature T_eff, which is derived from the obtained dynamic heat capacity compared with its temperature dispersion in the liquid state. T_eff also corresponds to the mean temperature of the actual and fictive temperatures and can be expressed by T_eff≅xT+(1-x)T_f with the nonlinearity parameter x of the Tool–Narayanaswamy–Moynihan model that partitions the activation factor of relaxation into the contributions of T and T_f. Evaluation of T_f and T_eff will provide valuable insights into the relaxation time in glass state, which plays an essential role in the glass transition behaviors of amorphous materials.

Abstract: Fast scanning calorimetric experiments were carried out on low-isotacticity polypropylene (LT-PP) to evaluate the effect of pre-nucleation below the glass transition temperature (also known as Tammann’s crystal nuclei development method) on the kinetics of crystallization and melting. The melting kinetics of secondary crystallized LT-PP was not affected by the presence of crystal nuclei, although the isothermal crystallization rate of LT-PP was accelerated by increasing the amount of crystal nuclei. The maximum primary crystallization decreased with increasing amounts of crystal nuclei. This behavior can be explained by the formation of uncrystallizable defects between the crystalline domains.

Abstract: The isothermal crystallization kinetics of poly(butylene terephthalate) at low temperatures near the glass transition was investigated by using chip-sensor fast scanning calorimetry. The Avrami analysis revealed that the Avrami index underwent a systematic change from 4 to less than 2 in the low-temperature peak of the crystallization rate, and significantly low crystallinity was achieved in the primary stage near the glass transition temperature. The mechanism was ascribed to the inhibition of the crystal growth by the rigid amorphous fraction (RAF) that is constrained by crystals, as proposed by Schawe for other crystalline polymers. A mobile amorphous fraction (MAF) as opposed to RAF can be evaluated by temperature-modulated fast scanning calorimetry. Near the glass transition temperature, MAF was confirmed to transform into RAF with the progress of crystallization, and all amorphous fractions became rigid.

Abstract: The relationship between the changes in the crystallization kinetics and the crystal domains of poly(butylene terephthalate) was examined under isothermal conditions. In the target range of the crystallization temperature T_c across the double peak of the crystallization rate, the Avrami exponent n characterizing the nucleation and growth kinetics of the crystal domains exhibited a continuous change in the range of 3≤n≤4. This was in correspondence to the change in the nucleation mode for spherical domains, such as spherulites and nodules, between nucleation from foreign heterogeneities and that from the homogenous melt. We identified the morphology of the crystal domains responsible for this change, that is, whether spherulites or 10-nm-scale granular nodules are involved in the change in the crystallization kinetics. Isothermally crystallized samples were prepared by applying a temperature jump using chip-sensor-based fast-scanning calorimetry. Optical microscopy and atomic force microscopy revealed a continuous change in the size of spherulites around a 1 μm scale across the T_c range of the crossover change because of the higher nuclei density at lower T_c. This behavior confirms that the Avrami exponent n=4 is attained by the kinetics of crystal domains of sub-micrometer scale spherulites initiated by nucleation from the homogeneous melt in the low-temperature peak; spherulites of this scale were confirmed by the addition of talc as a nucleating agent in the high-temperature peak. As a limiting case of the continuous change, the extremely high nuclei density at low T_c and the corresponding reduction in the size of spherulites resulted in the formation of 10-nm-scale granular nodules, which did not coalesce because of the rigid amorphous fraction formed around them near the glass transition temperature.

Abstract: This study aimed to clarify the secondary crystallization process of low-isotacticity polypropylene (LT-PP). LT-PP demonstrates an exceptionally low crystallization rate at room temperature, which is approximately 1/5000 lower than that of isotactic PP (iPP). During the secondary crystallization of LT-PP at 30 ºC, the thickness of lamellar (c-axis) and a- and b-axes of crystallite size remained constant. In addition, no significant change was observed in the C-C-C bending vibration. It seems that the direction of the C-C-C molecular order is similar to the thickness direction. This vibration mode may be associated with changes in the thickness of the lamellae. To explain the log(t) dependence of crystallinity, the Seto–Frank model was employed.

Abstract: The effects of crystal nuclei or crystallization on the isothermal crystallization behavior of isotactic polypropylene homopolymer are examined using fast scanning calorimetry (FSC) and wide-angle X-ray scattering (WAXD). During crystalline nucleation below the glass transition temperature as described by Tammann’s two-stage nucleation approach, an increased crystallization rate is observed, regardless of whether the mesophase structures formed in the low-temperature region or α-crystals formed in the high-temperature region. No increase in isothermal crystallization rate is detected following self-nucleation just above the melting point. Additionally, the influence of the pre-existing crystals on the subsequent crystallization behavior is investigated by combining crystallization time and temperature profiles, whereby crystallization at high temperatures is followed by slight crystallization at low temperatures, and in reverse order. Surprisingly, it is confirmed that the presence of pre-existing crystals do not affect the subsequent crystallization rate. The crystallization rate of iPP is influenced only by low-temperature pre-annealing that enhances the pre-nucleation.