Molecular dynamics revealed from frequency dependent heat capacity

Temperature modulated DSC (TMDSC) measurements at reasonably high frequencies allow for the determination of baseline heat capacity. In this particular case vitrification and devitrification of the rigid amorphous fraction (RAF) can be directly observed. 0.01 Hz seems to be a reasonably high frequency for Bisphenol‐A Polycarbonate (PC). The RAF of PC is established during isothermal crystallization. Devitrification of the RAF seems to be related to the pre‐melting peak. For PC the melting of small crystals between the lamellae is thought to yield the pre‐melting peak.     

Linear Relations of Activation Energy in Non-isothermal Kinetics

Temperature-modulated DSC (TMDSC) measurements at reasonably high frequencies allow for the determination of base-line heat capacity. In this particular case vitrification and devitrification of the rigid amorphous fraction (RAF) can be directly observed. 0.01 Hz seems to be a reasonably high frequency for bisphenol-A polycarbonate (PC). The RAF of PC is established during isothermal crystallization. Devitrification of the RAF seems to be related to the lowest endotherm. For PC the melting of small crystals between the lamellae is expected to yield the lowest endotherm. This revised version was published online in July 2006 with corrections to the Cover Date.     

The amount of immobilized polymer in PMMA SiO2 nanocomposites determined from calorimetric data

For semicrystalline polymers there is an ongoing debate at what temperature the immobilized or rigid amorphous fraction (RAF) devitrifies (relaxes). The question if the polymer crystals are melting first and simultaneously the RAF devitrifies or the RAF devitrifies first and later on the crystals melt cannot be answered easily on the example of semicrystalline polymers. This is because the crystals, which are the reason for the immobilization of the polymer, often disappear (melt) in the same temperature range as the RAF. For polymer nanocomposites the situation is simpler. Silica nanoparticles do not melt or undergo other phase transitions altering the polymer-nanoparticle interaction in the temperature range where the polymer is thermally stable (does not degrade). The existence of an immobilized fraction in PMMA SiO₂ nanocomposites was shown on the basis of heat capacity measurements at the glass transition of the polymer. The results were verified by enthalpy relaxation experiments below the glass transition. The immobilized layer is about 2 nm thick at low filler content if agglomeration is not dominant. The thickness of the layer is similar to that found in semicrystalline polymers and independent from the shape of the nanoparticles. Nanocomposites therefore offer a unique opportunity to study the devitrification of the immobilized fraction (RAF) without interference of melting of crystals as in semicrystalline polymers. It was found that the interaction between the SiO₂ nanoparticles and the PMMA is so strong that no devitrification occurs before degradation of the polymer. No gradual increase of heat capacity or a broadening of the glass transition was found. The cooperatively rearranging regions (CRR) are either immobilized or mobile. No intermediate states are found. The results obtained for the polymer nanocomposites support the view that the reason for the restricted mobility must disappear before the RAF can devitrify. For semicrystalline polymers this means that rigid crystals must melt before the RAF can relax.     

Dielectric relaxation of poly(phenylene sulfide) containing a fraction of rigid amorphous phase

The dielectric relaxation behavior of poly(phenylene sulfide), PPS, has been investigated from room temperature to 180°C. This study was undertaken to examine the mobility of the amorphous phase through the glass transition region, to determine the contribution that rigid amorphous phase material makes to the relaxation process. Semicrystalline samples contain a fraction of the rigid amorphous phase, which was determined from the heat capacity increment at the glass transition, using degree of crystallinity determined from x-ray scattering. In the dielectric experiment, we measured the temperature and frequency dependence of the real and imaginary parts of the dielectric function. ε″ vs. ε′ was used to determine the dielectric relaxation intensity, δε = ε_s–ε∞, at temperatures above the glass transition. For amorphous PPS, δε decreases as temperature increases, while for all semicrystalline PPS, δε increases with temperature. The ratio of semicrystalline intensity to amorphous intensity determines the total fraction of dipoles which are already relaxed at a given temperature. Results indicate that more and more rigid amorphous phase material relaxes as the temperature is increased. This provides the first evidence that rigid amorphous phase material in PPS contains chains that possess different levels of molecular mobility. Finally, to the temperature of the loss peak maximum, at a given frequency, we assign the value of the dielectric T_g. For both melt and cold crystallization, the dielectric T_g systematically decreases as the crystallization temperature increases, and as the fraction of rigid amorphous phase decreases.     

Cooperativity length evolution during crystallization of poly(lactic acid)

Effects of stereoregularity and crystallization mode on the amorphous phase dynamics are investigated for poly(lactic acid) PLA. An isothermal crystallization from the melt and a cold crystallization are imposed. For each PLA, the cold crystallization leads to the appearance of a less perfect crystalline phase and to an important rigid amorphous fraction RAF content (35%), although only 10% of RAF is generated after crystallization from the melt. Temperature Modulated Differential Scanning Calorimetry is used to determine the Cooperative Rearranging Regions (CRR) size at the glass transition temperature in the mobile amorphous phase MAP. It is shown that the CRR size in the MAP is not modified by the appearance and the spherulite growth. For the intra-spherulite MAP, a confining effect is evidenced, causing an amorphous phase thickness decrease during crystallization, and inducing a drastic CRR size reduction.     

Rigid amorphous fraction in poly(ethylene terephthalate) determined by dilatometry

Volumetric thermal analysis of semicrystalline poly(ethylene terephthalate), PET, with different content of crystalline phase was carried out using mercury-in-glass dilatometry. The effect of crystals on the thermal properties of amorphous phase (glass transition temperature, T _g, thermal expansion coefficients, α) were determined. At cold-crystallization (106°C, up to 4 h), crystalline content of 2.4–25.3 vol.% was achieved. Increasing content of crystalline phase broadens the glass transition region and increases T _g. The change of thermal expansion coefficient during glass transition is lower than that predicted by the two-phase model, which indicates the presence of a third fraction — rigid amorphous fraction (RAF), whose content steadily increases during crystallization. However, its relative portion (specific RAF) is significantly reduced. Further significant decrease in specific RAF appears after annealing at a higher temperature.     

Dielectric relaxation study of atactic poly(epichlorohydrin)/poly(3-hydroxybutyrate) blends

Binary blends of atactic poly(epichlorohydrin) (aPECH) and poly(3-hydroxybutyrate) (PHB) were investigated as a function of blend composition and crystallization conditions by dielectric relaxation spectroscopy. The quenched samples were found to be miscible in the whole composition range by detecting only one glass transition relaxation, for each composition, which could be closely described by the Gorden-Taylor equation. The cold-crystallized blends displayed two glass transition relaxations at all blend ratios indicating the coexisting of two amorphous populations: a pure aPECH phase dispersed mainly in the interfibrillar zones and a mixed amorphous phase held between crystal lamellae. The interlamellar trapping of aPECH was small and decreases with increasing the overall PHB content in the blend. At high crystallization temperatures the aPECH molecules was found to reside mainly in the interfibrillar regions due to its high mobility relative to the crystal growth rate of PHB. Our results suggest that because the intersegmental interaction in aPECH/PHB blends is weak, the mobility of the amorphous component at a given crystallization temperature decides diluent segregation.     

Structural evolution in microbial polyesters

The crystallization behavior of microbially synthesized poly(3-hydroxybutyrate) (PHB) and its copolymers [P(HB-co-HHx)] containing 2.5, 3.4, and 12 mol % 3-hydroxyhexanoate (HHx) comonomer and the melting of the resultant crystals were studied in detail using time-resolved small-angle X-ray scattering and differential scanning calorimetry. The polyesters were found to undergo primary crystallization as well as secondary crystallization. In the primary crystallization, the thicknesses of the lamellar crystals were sensitive to the crystallization temperature, but no thickening was observed throughout the entire crystallization at a given temperature. The thickness of the lamellar crystals in the PHB homopolymer was always larger than that of the amorphous layers. In the copolymers, by contrast, the randomly distributed HHx comonomer units were found to be excluded from the lamellar crystals into the amorphous regions during the isothermal crystallization process. This interrupted the crystallization of the copolymer chains, resulting in the formation of lamellar crystals with thicknesses smaller than those of the amorphous layers. The lamellar crystals in the copolymers had lower electron densities compared to those formed in the PHB homopolymer. On the other hand, secondary crystallization favorably occurred during the later stage of isothermal crystallization in competition with the continuous primary crystallization, forming secondary crystals in amorphous regions, in particular in the amorphous layers between the primarily formed lamellar crystal stacks. Compared to the primarily formed lamellar crystals, the secondary crystals had short-range-ordered structures of smaller size, a broader size distribution, and a lower electron density.     

The rigid amorphous fraction in semicrystalline macromolecules

The first experimental evidence of the existence of the rigid amorphous fraction (RAF) was reported by Menczel and Wunderlich for several semicrystalline polymers. It was observed that the hysteresis peak at the glass transition was absent when these polymers were heated much faster than they had previously been cooled. In the glass transition behavior of poly(ethylene terephthalate) (PET), the hysteresis peak gradually disappeared as the crystallinity increased. At the same time, it was noted that the ΔC _p of higher crystallinity PET samples was much smaller than could be expected on the basis of the crystallinity calculated from the heat of fusion. It was also observed that this behavior was not unique to PET only, but is characteristic of most semicrystalline polymers: the sum of the crystallinity calculated from the heat of fusion and the amorphous content calculated from the ΔC _p at the glass transition is much less than 100% (a typical difference is ~20–30%). This 20–30% difference was attributed to the existence of the “RAF”. The presence of the RAF also affected the unfreezing behavior of the “mobile (or traditional) amorphous fraction.” As a consequence, the phenomenon of the enthalpy relaxation diminished with increasing rigid amorphous content. It was suggested that the disappearance of the enthalpy relaxation was caused by the disappearance or drastic decrease of the time dependence of the glass transition. To check the validity of this suggestion, the glass transition had to be also measured on cooling in order to overlay it on the DSC curves measured on heating. However, before this overlaying work could be accomplished, the exact temperatures on cooling had to be determined since the temperature of the DSC instruments that time could not be calibrated on cooling using the usual low molecular weight standards due to the common phenomenon of supercooling. Therefore, a temperature calibration method needed to be developed for cooling DSC experiments utilizing high purity liquid crystals using the isotropic → nematic, the isotropic → cholesteric, and other liquid crystal → liquid crystal transitions. After the cooling calibration was accomplished, the cooling glass transition experiments indicated that the glass transition in semicrystalline polymers is not completely time independent, because its width depends on the ramp rate. However, it was shown that the time dependence is drastically reduced, and the midpoint of the glass transition seems to be constant which can explain the absence of the enthalpy relaxation. The work presented here has led to a number of studies showing the universality of the rigid amorphous phase for semicrystalline polymers as well as an ASTM standard for DSC cooling calibration.     

Effect of Decoupling of Molecular Segments,Microscopic Stress‐Transfer and Confinement of the Nanophases in Semicrystalline Polymers

Summary: Semi‐crystalline macromolecules are globally metastable, multi‐phase systems with phase dimensions ranging from micrometers to nanometers. The polymer molecules, being usually longer than one micrometer, cross the boundaries and decouple at the interfaces. This decoupling is often not complete and different degrees of influence are extended across the interfaces. Thermodynamically, crystals can be characterized by their melting behavior and non‐crystalline phases by their glass transition. On weak coupling, the non‐crystalline segments only show a broadening of the glass transition to higher temperature. With stronger coupling, non‐crystalline material may remain solid at the transition of the bulk‐amorphous phase and form a separate, rigid‐amorphous nanophase, or rigid amorphous fraction, RAF. The RAF undergoes its glass transition either below, at, or even above, the melting temperature. In the presence of a RAF, the semi‐crystalline polymers may be a system of three or more types of phases with different relaxation effects due to the coupling between the phases. This and other examples of decoupling are discussed here and a general concept is developed. This applies to positional decoupling at positions of chemical changes within the molecule, such as in copolymers, and to physical changes, such as in entanglements, and is not limited to decoupling at interfaces. Finally, it is pointed out that there is also the possibility of a temporal decoupling of thermodynamically simultaneous changes, which on sufficiently slow kinetics in one may change to consecutive changes. Many of these aspects of decoupling on a molecular scale influence the macroscopic properties and must be considered for the analysis and application of modern materials.

Illustration of reversible melting of folded chain crystals.     

Melt-crystallization, glass transition and morphology of a (R)-3-hydroxybutyrate pentamer

The melt-crystallization of an oligo[(R)-3-hydroxybutyrate] with five repeating units has been analyzed using standard and temperature-modulated calorimetry, optical microscopy, and atomic force microscopy. Specimens of different crystallinity and supermolecular structure were generated by variation of the rate of cooling of a quiescent melt, or by variation of the temperature of isothermal crystallization. Completely amorphous samples can be obtained by cooling of the melt at a rate of 40 K min⁻¹, or faster, to a temperature lower than the glass transition. The crystallinity depends on the crystallization temperature. The maximum enthalpy-based crystallinity of about 40-45% is obtained by crystallization at temperatures lower than the temperature of the maximum crystallization rate, which is between 310 and 320 K. Analysis of the apparent heat capacity in metastable structural equilibrium reveals reversible melting at temperatures between 320 and 370 K by observation of an excess heat capacity above the level of the vibrational heat capacity, i.e., in the temperature range of irreversible reorganization and melting. The reversible melting is discussed in the context of coupling of the crystalline and amorphous phases, and compared to earlier studies on oligoethylene and oligo(oxyethylene). The presence of crystals causes formation of a rigid amorphous fraction of about 30% at a crystallinity of 40%. Optical and atomic force microscopy reveal spherulitic crystallization. At relatively high crystallization temperature, and in the early stage of the crystallization process, dendrites are observed which finally yield spherulites of decreased perfection. Larger spherulites of higher perfection grow at relatively low crystallization temperature, as deduced from the appearance of the Maltese cross, and the regularity of banding. The band spacing is less than 5 μm, as is accurately determined by atomic force microscopy. The temperature dependence of the spherulitic growth rate is in accord with the calorimetric analysis of the crystallization rate.     

Recent developments in thermal analysis of polymers: Calorimetry in the limit of slow and fast heating rates

This review focuses on new insights into the crystal melting transition and the amorphous glass transition of polymers that have been gained through recent advances in thermoanalytical methods. The specific heat capacity can now be studied under two extreme limits, that is, under quasi‐isothermal conditions (limit of zero heating rate) and, at the other end of the scale, under rapid heating conditions (heating rates on the order of thousands of degrees per second), made possible through nanocalorimetry. The reversible melting, and multiple reversible melting, of semicrystalline polymers is explored using quasi‐isothermal temperature modulated differential scanning calorimetry, TMDSC. The excess reversing heat capacity, above the baseline, measured under nearly isothermal conditions is attributed to locally reversible surface melting and crystallization processes that do not require molecular nucleation. Observations of double reversible melting endotherms in isotactic polystyrene suggest existence of two distinct populations of crystals, each showing locally reversible surface melting. The second subject of the review, nanocalorimetry, is utilized to study samples of small mass under conditions of very fast heating and cooling. The glass transition properties of thin amorphous polymer films are observed under adiabatic conditions. The glass transition temperature appears to be independent of film thickness, and is observed even in ultra‐thin films. Recrystallization and reorganization during rapid heating are studied by nanocalorimetry of semicrystalline polymers. The uppermost endotherm seen under normal DSC scanning of poly(ethylene terephthalate) is caused by reorganization, and vanishes under the rapid heating conditions (3000K/s) provided by nanocalorimetry. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 629–636, 2005     

Calorimetric study and modeling of molecular mobility in amorphous organic pharmaceutical compounds using a modified Adam-Gibbs approach

The purpose of this study is to provide a quantitative characterization of the thermal behavior of amorphous organic pharmaceutical compounds across their glass transition temperature, and to assess their molecular mobility as a function of temperature and time by combining theoretical simulations with experimental measurements using differential scanning calorimetry. A computational approach built on the Boltzmann superposition principle of nonexponential decay and the Adam-Gibbs theory of entropic-dependent structural relaxation is presented. The heat capacities of the crystalline and amorphous forms are incorporated into the simulation in order to accurately assess the entropic fictive temperature as functions of temperature and time under any arbitrary set of experimental conditions. Using this method, we evaluated properties of the glass former, D and T0, and the nonexponentiality index beta, for amorphous salicin, felodipine, and nifedipine, by fitting the simulated glass transition profile with the experimentally determined heat capacity across the glass transition region. From this fit, the evolution of the relaxation time of the model compounds following any thermal cycle, including heating, cooling, and isothermal holds can then be estimated a priori. This study reveals the profound and inextricable effect of thermal history on the molecular mobility of the amorphous materials, and the ability of the glass to undergo fast changes in its molecular motions over an aging process even at low temperatures.     

Relationship between melting behavior and morphological changes of semicrystalline polymers

The present study on the case of poly(hexamethylene succinate) is to provide a basis for a better understanding of the subtle relationship between melting behavior and morphological changes of semicrystalline polymers. The melting behavior and morphological changes of poly(hexamethylene succinate) during both isothermal secondary crystallization and annealing processes were investigated by DSC and SAXS. DSC results showed that, with increasing crystallization time or annealing time, the melting endotherm continuously shifted to higher temperature, which suggested that some minor structural or morphological changes must occur. However, almost no changes at all on the crystal thickness were observed from SAXS measurements. The observed evidence confirmed that the increase in the melting temperature is not attributed to crystal thickening but crystal perfection. More exactly, the rearrangement and smoothing of tie molecules at the folding surface result in the reduction of the fold surface free energy, which dominantly contributes to the increase in the melting peak temperature. The origin of the new endothermic peak observed after annealing at elevated temperature was also discussed. TMDSC results indicated that the annealing peak resulted from the enthalpy relaxation and devitrification transition of rigid amorphous fraction formed by the driving force of thermodynamic nonequilibrium, rather than usually regarded as the melting of thin lamellae or imperfect crystals formed by annealing secondary crystallization.     

不同结晶度的乙二醇及其水溶液玻璃化转变与焓松弛

为了考察晶体成分对无定形成分玻璃化转变和结构松弛行为的影响,利用差示扫描量热法(DSC),结合低温显微技术,研究了乙二醇(EG)及其50％水溶液在不同结晶度时的玻璃化转变和焓松弛行为.采用等温结晶方法控制骤冷的部分结晶玻璃体中的晶体份额.DSC结果表明,对于部分结晶的EG,只有单一的玻璃化转变过程,而对于50％EG,当结晶度不同时,不同程度地表现出两次玻璃化转变（无定形相Ⅰ和无定形相Ⅱ）.相Ⅰ的玻璃化转变温度和完全无定形态的含水EG的玻璃化转变温度相一致;相Ⅱ的玻璃化转变温度要比此温度约高6 ℃.低温显微观察结果印证了DSC实验结果.DSC等温退火的实验和KWW(Kohlrausch-Williams-Watts)衰变函数分析结果表明,EG无定形和50％EG中的两种无定形有不同的焓松弛行为.     

The thermal properties of poly(oxy-1,4-benzoyl), poly(oxy-2,6-naphthoyl), and its copolymers

The thermal properties, i.e., heat capacity, enthalpy, entropy, and Gibbs function, and the transition behavior of the copolymer system of 4-hydroxybenzoic acid and 2,6-hydroxynaphthoic acid have been studied based on differential scanning calorimetry. The heat capacities of the glass, crystal, and anisotropic melt are shown to be largely additive on a molar basis. Additivity is lost in the two transition regions, glass transition and disordering transition. Isothermal crystallization experiments on the copolymers revealed the existence of two types of crystals which melt at high temperature (fast-grown crystals) and low temperature (slowly grown crystals). The ATHAS computation method is used to bring heat capacities of the solid state into agreement with approximate frequency spectra. The changes in heat capacity at the glass transitions occur at 434°K for the poly(oxy-1,4-benzoyl) [33.2 J/(K mol)] and at 420°K for poly(oxy-2,6-naphthoyl) [46.5 J/(K mol)]. The copolymers have a transition range of above 100°K. The anisotropic melt is linked to the well-known condis state of poly(oxy-1,4-benzoyl) by a continuous changes in disorder and mobility without an additional first-order transition.     

Melting and crystallization of poly(butylene terephthalate) by temperature‐modulated and superfast calorimetry

Quantitative temperature‐modulated differential scanning calorimetry (TMDSC) and superfast thin‐film chip calorimetry (SFCC) are applied to poly(butylene terephthalate)s (PBT) of different thermal histories. The data are compared with those of earlier measured heat capacities of semicrystalline PBT by adiabatic calorimetry and standard DSC. The solid and liquid heat capacities, which were linked to the vibrational and conformational molecular motion, serve as references for the quantitative analyses. Using TMDSC, the thermodynamic and kinetic responses are separated between glass and melting temperature. The changes in crystallinity are evaluated, along with the mobile–amorphous and rigid–amorphous fractions with glass transitions centered at 314 and 375 K. The SFCC showed a surprising bimodal change in crystallization rates with temperature, which stretches down to 300 K. The earlier reported thermal activity at about 248 K was followed by SFCC and TMDSC and could be shown to be an irreversible endotherm and is not caused by a glass transition and rigid–amorphous fraction, as assumed earlier. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1364–1377, 2006     

Enthalpy relaxation of rigid poly(vinyl chloride)

The changes which take place on annealing rigid PVC in the vicinity of the glass transition have been followed by differential scanning calorimetry. The changes appear as an increase in the glass-transition temperature and a decrease in the enthalpy with time of annealing. For annealing at 75°C, the enthalpy after 50–100 hr approaches the value characteristic of the equilibrium liquid state. The results obtained for annealing at 65°C and 75°C are in accord with those expected for the relaxation of an amorphous material, and are at variance with those expected on the basis of crystallization taking place on annealing. The enthalpy relaxation process is characterized by a distribution of activation energies centered about 18.8 kcal mole^?1, and seems to reflect a multiplicity of molecular processes.