Influence of the glass transition on solvent self-diffusion in amorphous polymers

The free-volume theory of diffusion is used to analyze the temperature dependence of solvent self-diffusion coefficients both above and below the glass transition temperature at concentrations removed from the pure polymer limit. The glass transition can have a pronounced effect on the temperature dependence of solvent self-diffusion coefficients at small solvent concentrations, but the theory predicts a decreased effect of the transition on the diffusion process with increasing solvent concentration.     

The glass transition

This work deals with a comparison of data obtained from differential scanning calorimetry (DSC) and thermally stimulated depolarization current (TSDC) investigations. Measurements were performed on various poly(ethylene terephthalate) films: a wholly amorphous, a thermally crystallized and drawn samples. For each specimen, the TSDC complex spectra, resolved into elementary ones, led to the determination of the classical compensation temperature (T _c ). The glass transition temperature (T _g) and the fictive equilibrium temperature (T _f) were determined by means of DSC. It appears thatT _c is different fromT _g and very close toT _f.     

Equilibrium nano-structures in poor solvent polymer solutions near glass transition temperature

Poor solvent polymer solutions near the glass transition temperature are considered on the basis of the nonlocal entropy model which allows the possibility of microphase separation transition. The dependence of the magnitude of nonlocal entropy and nonlocality radius on the temperature are explicitly taken into account. It is shown that accounting for nonlocal entropy can lead to i) the solubility enhancement in the vicinity of glass transition temperature, ii) microphase separation transition. Microphase separation transition is studied in the weak segregation limit. Phase diagrams containing the regions of stability of different microdomain structures, as well as the regions of macroscopic phase separation, are obtained.     

Effect of composition on the width of the calorimetric glass transition in polymer–solvent and solvent–solvent mixtures

The calorimetric glass‐transition temperature (T_g) and transition width were measured over the full composition range for solvent–solvent mixtures of o‐terphenyl with tricresyl phosphate and with dibutyl phthalate and for polymer–solvent mixtures of polystyrene with three dialkyl phthalates. T_g shifted smoothly to higher temperatures with the addition of the component with the higher T_g for both sets of solvent–solvent mixtures. The superposition of the differential scanning calorimetry traces showed almost no composition dependence for the width of the transition region. In contrast, the composition dependence of T_g in polymer–solvent mixtures was different at high and low polymer concentrations, and two distinct T_g's were observed at intermediate compositions. These results were interpreted in terms of the local length scale and associated local composition variations affecting T_g. The possible implications of these results for the dynamics of miscible polymer blends were examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1155–1163, 2004     

The glass transition temperature of polystyrene

A round robin test was performed to determine the reliability of values for the glass transition temperatureT _g as determined by DTA on polymers. Ten different instruments were involved. The test material was high molecular weight polystyrene. Values forT _g (midpoint) were reported in the range 107°C±2 K. The respective heat flow curves differed considerably in shape. In the literature aT _g of 100°C is often given for polystyrene. The discrepancy between this value and the value of 107°C found in the round robin test is due to three differences: the thermal history of the sample, the evaluation of the heat flow curves, and the effect of finite sample size.     

On the role of frustration on the glass transition and polyamorphism of mesoscopically heterophase liquids

The model of heterophase fluctuations is developed accounting frustration of the mesoscopic solidlike fluctuons. Within the framework of this model, the glass transition and polyamorphous transformations are considered. It is shown that the frustration increases the temperature range in which the heterophase liquid state exists. the upper and lower boundaries of this temperature range are determined. These boundaries separate different phase states-amorphous solid, heterophase liquid, and fluid phases. Polyamorphous liquid-liquid transitions in the liquid are investigated. Frustration can call forth continuous fluid-solid phase transformation avoiding the first- or second-order phase transition. Conditions under which the first-order phase transition fraction takes place are formulated. Two scenarios of the first-order liquid-liquid polyamorphous transformation are described. As an example the glacial phase formation and the first-order liquid-liquid phase transition in triphenyl phosphate are considered and discussed. Impact of frustration on the liquid crystallization and crystallinity of the glassy state is studied.     

Thermodynamics of the glass transition

A thermodynamic analysis of the glass transition in polymers is presented, which predicts, with a minimum of assumptions, three of the four inequalities which have consistently been observed experimentally: i.e., that specific heat and isothermal compressibility of the glass are lower than those of the rubber, and that the Prigogine-Defay ratio is larger than unity. The analysis cannot predict the fact that the thermal expansion coefficient of the glass is also lower than that of the rubber, and indeed the converse situation is not a thermodynamic impossibility.     

The relation between the microphase separation transition and the glass transition in diblock copolymers

The microphase separation transition (MST) has been studied for short chain diblock copolymers poly(styrene-b-isoprene) and poly(styrene-b-mma). A detailed analysis of small-angle x-ray scattering (SAXS) profiles in the homogeneous phase allows determination of the interaction parameter and the spinodal temperature T_s of the MST. T_s for the PS/PI diblocks is found to be lower than the glass transition temperature of their hard blocks. This results in a coupling of the MST and the glass transition. Using both structural (SAXS) and thermal differential scanning calorimetry (DSC) methods it is shown that an endothermal peak found in the DSC diagrams is related to the combined effect of the MST and the glass transition. © 1992 John Wiley & Sons, Inc.     

The glass transition in polymer melts

This paper presents some results of a Monte Carlo simulation for the glass transition in two- and three-dimensional polymer melts. The melt was simulated by the bond-fluctuation model on a d-dimensional cubic lattice which was combined with a two-level hamiltonian favouring long bonds in order to generate a competition between the energetic and topological constraints in the system. This competition prevents crystallization and makes the melt freeze in an amorphous structure as soon as the internal relaxation times match the observation time of the simulation set by the cooling rate. The freezing point of the melt, i.e the glass transition temperature T_g, thus depends upon the cooling rate and additionally upon the chain length of the polymers. The dependence of the glass transition temperature on the cooling rate was closely analysed in three and that on the chain length in both two and three dimensions, resulting in a non-linear relationship between T_g and the logarithm of the cooling rate and a linear relationship between T_g and the inverse chain length, respectively. In addition to this behaviour of the melt during the cooling process an example for the relaxational properties of the three-dimensional model is provided by a quantitative analysis of the incoherent intermediate scattering function in the framework of the idealized mode coupling theory.     

Effect of solvent on glass transition temperature in chemically modified polyvinyl chloride (PVC)

Polyvinylchloride has been chemically modified with sodium benzene thiolate at different temperatures, in solvents promoting the formation of polymer gels, in solvents favoring light polymer interactions and in the absence of solvent, that is, in the melt. From the¹³C-NMR results it is shown that the substitution reactions on PVC, in all media and temperatures studied, are stereospecific and the nature of substituted chlorines the same.The glass transition temperature of modified polymers has been studied by differential scanning calorimetry. The glass transition temperature of the modified polymers in the absence of solvent decreases linearly with degree of substitution. When the reaction is carried out in solvents containing carbonyl groups, such as diethyl malonate, cyclohexanone and 2-butanone, the evolution of the glass transition up to about 25% substitution does not follow the above behavior. At higher levels of substitution the evolution ofT _g is similar to that in the melt. For the ether-containing solvents, such as tetrahydrofurane and dioxane, the evolution lies between the two previous curves.When the reactions of PVC with sodium benzene thiolate are carried out in cyclohexanone at different temperatures, between 15–90°C, the evolution of the glass transition temperature with conversion is different for each temperature, and if the reaction temperature increases, the slope of the initial part moves to that in the absence of solvent.These results are related to the formation of PVC gels or interactions. As the nature and percentage of substituted chlorine for a given chemical composition are the same in all the solvents and conditions studied, we propose that Cl-atoms of isotactic and/or heterotactic configurations are implied in the formation of PVC gels or interactions.     

Effects of moisture on glass transition and microstructure of glycerol-plasticized soy protein

The glass transition behavior of the glycerol-plasticized soy protein sheets (SL series) at various relative humidity (RH) was investigated by using differential scanning calorimetry with the aluminum pan and O-ring-sealed stainless steel capsule, and the microstructure of these sheets was detected on small-angle X-ray scattering. The results revealed that there were three glass transitions (Tg1, Tg2 and Tg3), corresponding to glycerol-rich, protein-rich and protein-water domains, in the protein-glycerol-water ternary system. The Tg1 values of the SL-series sheets at 75% RH decreased from -49.3 to -83.8 degrees C with an increase of glycerol content from 10 to 50 wt.-%, whereas Tg2 and Tg3 were almost invariable at about 60 degrees C and 3 degrees C, respectively. In addition, the Tg1, Tg2 and Tg3 values of the SL-25 containing 25 wt.-% glycerol at 0%, 35%, 58%, 75% and 98% RH were in the range of -12.7 - -83.2 degrees C, 65.8 - 53.1 degrees C and 3.5 - 1.9 degrees C, respectively. The result from small-angle X-ray scattering indicated that the radii of gyration (Rg) of protein-rich domain were in the range of 60-63 nm; this suggested the existence of protein macromolecules as aggregates in the stable protein-rich and protein-water domains. With an increase of RH, the tensile strength and Tg values of the SL-series sheets decreased, but the elongation at break increased. In view of the results above, the moisture in ambient environment significantly influenced the Tg values and microstructures of the glycerol-plasticized soy protein sheets, leading to the changes of the mechanical and thermal properties.     

Intermolecular forces and the glass transition

Random first-order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random first-order transition theory, is used to treat individual glassy configurations, whereas the liquid phase is treated using common liquid-state approximations. Free energies are calculated using liquid-state perturbation theory. The transition temperature, T*A, the temperature where the onset of activated behavior is predicted by mean field theory; the lower crossover temperature, T*C, where barrierless motions actually occur through fractal or stringy motions (corresponding to the phenomenological mode coupling transition temperature); and T*K, the Kauzmann temperature (corresponding to an extrapolated entropy crisis), are calculated in addition to T*g, the glass transition temperature that corresponds to laboratory cooling rates. Relationships between these quantities agree well with existing experimental and simulation data on van der Waals liquids. Both the isobaric and isochoric behavior in the supercooled regime are studied, providing results for DeltaCV and DeltaCp that can be used to calculate the fragility as a function of density and pressure, respectively. The predicted variations in the alpha-relaxation time with temperature and density conform to the empirical density-temperature scaling relations found by Casalini and Roland. We thereby demonstrate the microscopic origin of their observations. Finally, the relationship first suggested by Sastry between the spinodal temperature and the Kauzmann temperatures, as a function of density, is examined. The present microscopic calculations support the existence of an intersection of these two temperatures at sufficiently low temperatures.     

The ideal glass transition of hard spheres

We use the replica method to study the ideal glass transition of a liquid of identical hard spheres. We obtain estimates of the configurational entropy in the liquid phase, of the Kauzmann packing fraction phi(K), in the range of 0.58-0.62, and of the random close packing density phi(c), in the range of 0.64-0.67, depending on the approximation we use for the equation of state of the liquid. We also compute the pair-correlation function in the glassy states (i.e., dense amorphous packings) and we find that the mean coordination number at phi(c) is equal to 6. All these results compare well with numerical simulations and with other existing theories.     

The glass transition temperature of polymer melts

We develop an analytic theory to estimate the glass transition temperature T(g) of polymer melts as a function of the relative rigidities of the chain backbone and side groups, the monomer structure, pressure, and polymer mass. Our computations are based on an extension of the semiempirical Lindemann criterion of melting to locate T(g) and on the use of the advanced mean field lattice cluster theory (LCT) for treating the thermodynamics of systems containing structured monomer, semiflexible polymer chains. The Lindemann criterion is translated into a condition for T(g) by expressing this relation in terms of the specific volume, and this free volume condition is used to calculate T(g) from our thermodynamic theory. The mass dependence of T(g) is compared to that of other characteristic temperatures of glass-formation. These additional characteristic temperatures are determined from the temperature variation of the LCT configurational entropy, in conjunction with the Adam-Gibbs model for long wavelength structural relaxation. Our theory explains generally observed trends in the variation of T(g) with polymer microstructure, and we find that T(g) can be tuned either upward or downward by increasing the length of the side chains, depending on the relative rigidities of the side groups and the chain backbone. The elucidation of the molecular origins of T(g) in polymer liquids should be useful in designing and processing new synthetic materials and for understanding the dynamics and controlling the preservation of biological substances.     

The glass transition temperature of natural rubber

In view of the lack of precise experimental data in the literature concerning the determination of a definedTg value for natural rubber (NR) and the differences when such data are given, a reference definition ofTg(Vo) is offered and a procedure for obtaining it described in detail. It is proposed that the value obtained for uncured NR of 200.5 K be used as a low temperature standard in the study of other polymerTg's which occur in this region.     

Testing the role of solvent surface tension in protein ionization by electrospray

This work was aimed at probing the influence of solvent surface tension on protein ionization by electrospray. In particular, we were interested in testing the previously suggested hypothesis that the charge-state distributions (CSDs) of proteins in electrospray ionization mass spectrometry (ESI-MS) are controlled by the surface tension of the least volatile solvent component. In the attempt to minimize uncontrolled conformational effects, we used acid-sensitive proteins (cytochrome c and myoglobin) at low pH or highly stable proteins (ubiquitin and lysozyme) in the presence of low concentrations of organic solvents. A first set of experiments compared the effect of 1- and 2-propanol. These two alcohols have similar chemico-physical properties but values of vapor pressure below and above that of water, respectively. Both compounds have much lower surface tension than water. The solvents employed allowed testing of the influence of surface tension on protein spectra obtained from similarly denaturing solutions. The compared solvent conditions gave rise to very similar spectra for each tested protein. We then investigated the effect of the addition of dimethyl sulfoxide to acid-unfolded proteins. We observed enhanced ionization in the presence of acetic or formic acid, consistent with the previously described supercharging effect, but almost no shift of the CSD in the presence of HCl. Finally, we analyzed thermally denatured cytochrome c, to obtain reference spectra of the unfolded protein in high-surface-tension solutions. Also in this case, the CSD of the unfolded protein was shifted towards lower m/z values relative to low-surface-tension systems. In contrast to the other results reported here, this effect is consistent with an influence of solvent surface tension on CSD. The magnitude of the effect, however, is much smaller than predicted by the Rayleigh equation. The results presented here are not easy to reconcile with the hypothesis that the maximum charge state exhibited by proteins in ESI-MS reflects the Rayleigh-limit charge of the precursor droplet. The data are discussed with reference to models for the mechanism of electrospray ionization.     

The glass transition and crystallization of ball milled cellulose

Samples of ball milled cellulose were prepared by ball milling pulps from eucalyptus and softwood (spruce/pine). Water sorption isotherms were obtained by both dynamic vapor sorption and equilibration over saturated salt solutions, in the water content range of 5–42% db (db = dry basis; water as a % age of total solids). Dynamic mechanical analysis using a pocket technique showed a water content dependent thermal transition occurring at the same temperature for the two pulp samples, which was interpreted as a glass transition. Fitting the data to a Couchman–Karasz relationship predicted a value for T _g of the dry cellulose of approximately 478 K, which was similar to values previously reported for other dry polysaccharides. No clear glass transition could be observed calorimetrically, although an endotherm at approximately 333 K was measured, which in polymers is normally attributed to enthalpic relaxation, however the lack of dependence of this endotherm on water content suggests that the melting of some weak associations, such as residual hydrogen bonds, could be a more credible explanation. An exotherm was also observed on heating, which was dependent on water content and which was attributed to partial crystallization of the cellulose. This was confirmed by Wide angle X-ray diffraction and cross polarization magic angle spinning ¹³C NMR (CPMAS NMR). The recrystallisation was predominantly to form I of cellulose. This was thought to be caused by a small amount of residual form I (probably less than 5%) acting as a template for the crystallizing material. Differential scanning calorimetry reheat curves showed the appearance of freezable water for water contents higher than 20%, as a result of a transfer of water to the amorphous phase following crystallization. The increase in cellulose rigidity following crystallization was also confirmed by CPMAS NMR relaxation. Low resolution proton NMR T ₂ relaxation suggested the presence of proton water/cellulose exchange, which was active at water contents of 20% and above.     

Determination of the glass transition temperature

The definition of the glass transition temperature, T _g, is recalled and its experimental determination by various techniques is reviewed. The diversity of values of T _g obtained by the different methods is discussed, with particular attention being paid to Differential Scanning Calorimetry (DSC) and to dynamic techniques such as Dynamic Mechanical Thermal Analysis (DMTA) and Temperature Modulated DSC (TMDSC). This last technique, TMDSC, in particular, is considered in respect of ways in which the heterogeneity of the glass transformation process can be quantified.