Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

Theories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Pressure‐volume‐temperature and glass transition behavior of silica/polystyrene nanocomposite

The pressure‐volume‐temperature (PVT) behavior and glass transition behavior of a 10 wt % silica nanoparticle‐filled polystyrene (PS) nanocomposite sample are measured using a custom‐built pressurizable dilatometer. The PVT data are fitted to the Tait equation in both liquid and glassy states; the coefficient of thermal expansion α, bulk modulus K, and thermal pressure coefficient γ are examined as a function of pressure and compared to the values of neat PS. The glass transition temperature (T_g) is reported as a function of pressure, and the limiting fictive temperature (T_f′) from calorimetric measurements is reported as a function of cooling rate. Comparison with data for neat PS indicates that the nanocomposite has a slightly higher T_g at elevated pressures, higher bulk moduli at all pressures studied, and its relaxation dynamics are more sensitive to volume. The results for the glassy γ values suggest that thermal residual stresses would not be reduced for the nanocomposite sample studied. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1131–1138     

Influence of matrix glass transition temperature on the memory effect of polymer‐dispersed liquid crystals

In this article, macroinitiators with different glass transition temperature (T_g) were synthesized by reversible additional‐fragmental chain transfer polymerization, and used to prepare polymer‐dispersed liquid crystals (PDLCs) with methyl acrylate. The memory effect of these PDLCs was investigated. The results showed that remarkable memory effect exhibit only in PDLCs with high and low T_g block chain. The possible mechanism responsible for the behavior is sketched. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 729–732, 2010     

Extension of the chain‐end,free‐volume theory for predicting glass temperature as a function of conversion in hyperbranched polymers obtained through one‐pot approaches

Compared with linear polymers, more factors may affect the glass‐transition temperature (T_g) of a hyperbranched structure, for instance, the contents of end groups, the chemical properties of end groups, branching junctions, and the compactness of a hyperbranched structure. T_g's decrease with increasing content of end‐group free volumes, whereas they increase with increasing polarity of end groups, junction density, or compactness of a hyperbranched structure. However, end‐group free volumes are often a prevailing factor according to the literature. In this work, chain‐end, free‐volume theory was extended for predicting the relations of T_g to conversion (X) and molecular weight (M) in hyperbranched polymers obtained through one‐pot approaches of either polycondensation or self‐condensing vinyl polymerization. The theoretical relations of polymerization degrees to monomer conversions in developing processes of hyperbranched structures reported in the literature were applied in the extended model, and some interesting results were obtained. T_g's of hyperbranched polymers showed a nonlinear relation to reciprocal molecular weight, which differed from the linear relation observed in linear polymers. T_g values decreased with increasing molecular weight in the low‐molecular‐weight range; however, they increased with increasing molecular weight in the high‐molecular‐weight range. T_g values decreased with increasing log M and then turned to a constant value in the high‐molecular‐weight range. The plot of T_g versus 1/M or log M for hyperbranched polymers may exhibit intersecting straight‐line behaviors. The intersection or transition does not result from entanglements that account for such intersections in linear polymers but from a nonlinear feature in hyperbranched polymers according to chain‐end, free‐volume theory. However, the conclusions obtained in this work cannot be extended to dendrimers because after the third generation, the end‐group extents of a dendrimer decrease with molecular weight. Thus, it is very possible for a dendrimer that T_g increases with 1/M before the third generation; however, it decreases with 1/M after the third generation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1235–1242, 2004     

A calorimetric study of the glass transition kinetics in polyisoprene

The connection between the dielectric and calorimetric relaxation behaviours of synthetic polyisoprene Cariflex IR 305 is studied. A similar comparison of dielectric and dilatometric results was described in [1]. The heat capacity was measured during heating of samples prepared with different thermal history. Experimental results were compared with the heat capacity curves calculated for a model based on the multiparameter theory of Kovacs et al. [4]. The model considers the relaxation system as being composed of a set of subsystems characterized by different relaxation times. The distribution of relaxation times and their temperature dependence were taken from the diclectric measurement. The relaxation time of a subsystem from posed to depend, not only on the actual, temperature of the sample, but also on the deviation of this subsystem from equilibrium, or alternatively, on the deviation of the system as a whole. The comparison between the measured and modeled curves shows that both influences must be taken into account in order to explain the experimental results.Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday.     

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     

Effect of copolymer composition and conversion on the glass transition of methyl acrylate–methyl methacrylate copolymers

The glass transition of methyl methacrylate methyl acrylate copolymers over a wide range of conversion and sequence distribution have been analyzed with the only purpose of predicting the change in the glass transition in copolymers as a function of conversion and consequently of comonomer sequence distribution. © 1994 John Wiley & Sons, Inc.     

Effect of glass transition temperature of polymeric binders on properties ceramic materials

In the paper are presented the studies of the effect of glass transition temperature of new water-thinnable polymeric binders on the properties of ceramic materials obtained by die pressing. The parameters of ceramic samples comprising polymeric binders have been compared with those of samples comprising poly(vinyl alcohol) (PVA) — water-soluble binder. When using poly(acrylic-styrene) (AS), poly(acrylic-allyl) (AA) and poly(vinyl-allyl) (VA) water-thinnable binders, materials of greater density and mechanical strength were obtained in the green state as well as after sintering than those in the case of using PVA. The dependence of the chemical structure of the binders applied on the properties of samples such as the glass transition temperature and hydrophobic-hydrophilic balance of the copolymers has been discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Self‐diffusion of small molecules into rubbery polymers: A lattice free‐volume theory

In the framework of the free‐volume (FV) theory, a new equation was derived for the evaluation of self‐diffusion coefficients of small molecules in polymers above the mixture glass transition temperature. The derivation of the equation turned out to be straightforward once the equivalence between the free volume and the unoccupied volume given by thermodynamic lattice theories is assumed. A parameter evaluation scheme is proposed, which is substantially simpler compared with the conventional Vrentas–Duda approach, even without losing generality. The key assumption is discussed, and its consistency is verified from a numerical viewpoint. A comparison with experimental solvent self‐diffusion coefficients for several solvent/polymer binary systems confirmed that the proposed theory presents good correlative ability over wide temperature and composition ranges. Moreover, the introduced thermodynamic foundation allows one to easily include the pressure effect too. In the frame of the proposed lattice free volume theory, the sizes of the polymer jumping units decrease with temperature and increase with pressure. Such behavior converges with theoretical expectations and opens the way for a predictive FV theory. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 529–540, 2010     

Effect of dopant structure on refractive index and glass transition temperature of polymeric fiber‐optic materials

Graded‐index plastic optical fibers, composed of doped polymers, have advantages over conventional glass optical fibers, but need to be developed further for practical application. Here, a variety of aromatic sulfide dopants were synthesized, and their effects on the refractive indexes and glass transition temperatures (T_g) of poly(methyl methacrylate) and methyl 2‐chloroacrylate/2,2,2‐trichloroethyl methacrylate copolymers were studied. While polymers containing large dopants exhibited relatively high refractive indices, their T_g values were low, making these materials unsuitable for graded‐index plastic optical fiber applications. Six dopants yielded polymers that exhibited higher T_g values than the conventionally used (diphenyl sulfide)‐doped polymer. The dopant dibenzothiophene, in particular, yielded polymers with the highest refractive indexes and T_g values, and polymers containing (phenylthio)benzene dopants also performed well. Copyright © 2013 John Wiley & Sons, Ltd.     

On the glass transition temperature of styrene-n-butyl methacrylate copolymers in dependence on chemical composition,molecular weight,and mixtures

For statistic copolymers of styrene and n-butyl methacrylate, the relation between the glass transition temperature and the chemical composition or molecular weight of the copolymers has been determined. Further, the dependence of the glass transition temperature on the composition of binary and ternary blends from statistical poly (styrene-co-n-butyl methacrylates) of a nearly equal chemical composition but a very different molecular weight has been studied. Among several equations considered for the correlation between glass transition temperature and composition of the mentioned copolymers with relatively low molecular weights, the Gordon/Taylor and Couchman equations gave the best agreement with the experimental results. For the glass transition temperature of poly(styrene-co-n-butyl methacrylate) with an n-butyl methacrylate content of about 30 wt % in dependence on the molecular weight, the Kanig-Ueberreiter and Fox-Flory equations proved to be useful for the examined molecular weight range. The glass transition temperatures of the polymer blends have been studied for a low/high-molecular component system, a system of two low-molecular components, as well as for systems with a third component. The glass transition temperatures of the mixtures frequently exceeded those of their individual components. © 1994 John Wiley & Sons, Inc.     

Nanofiller effect on the glass transition of a polyurethane

The effect of silicananofiller on the glass transition of a polyurethane was studied by DSC. Thepristine polymer exhibits a single glass transition at about –10°C.Uniform SiO2 spheres with different average sizes and narrow size distributionswere synthesized in solution by the Stöber method [1]. Both the effectsof silica content within the polymer and particle size were investigated,as well as two different surface treatments. Scanning electron microscopy(SEM) clearly confirms the presence of the particles within the polymer matrix,showing uniform distribution and no agglomeration. While shifting of the glasstransition has been reported by many authors, we have not seen any noticeableshift in this polymer. Surprisingly, we found no relevant effects when eitherincreasing the filler content or changing the particle size. Different amountsof particles with average diameters of 175, 395 and 730 nm did not affectthe glass transition temperature of the pristine polymer.     

Pressure–volume–temperature properties and free volume parameters of PEO/PMMA blends

Melt-miscible polymer blends of poly(ethylene oxide)/atactic poly(methyl methacrylate (PEO/a-PMMA)) were prepared by melt-mixing and characterized by pressure–volume–temperature (PVT) dilatometry in the pressure and temperature range of 0 to 200 MPa and 20 to 200°C, respectively. The PVT data were analyzed in terms of two equations of state (EOS). The empirical Tait EOS was applied in the glassy, semicrystalline, and equilibrium melt state, and the Simha-Somcynsky EOS theory was applied in the equilibrium melt and glassy state. The Simha-Somcynsky EOS theory contains a free volume function. The temperature, pressure, and composition dependence of the free volume fraction h calculated from the Simha-Somcynsky EOS theory was studied. As a function of blend composition we observe that the free volume fraction, thermal expansivity, and compressibility all deviate mainly positively from linearity while the specific volume deviates mainly negatively from linearity. These findings are reconciled with composition-dependent free volume parameters, the free volume and cell volume as well as with self- and cross-interaction parameters derived from the Simha-Somcynsky EOS theory as applied to polymer mixtures. Moreover, the pressure dependence of glass and melting transitions as well as crystallization kinetics have been investigated. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1061–1080, 1998     

Effect of chain structure on the glass transition temperature and viscoelastic property of cis‐1,4‐polybutadiene via molecular simulation

In this work, by adopting the united atom model of cis‐1,4‐poly(butadiene) (PB), we systemically investigate the effect of the chain structure on the glass transition temperature (T_g) and the viscoelastic property of PB system. First, we analyze the atom translational mobility, bond reorientation dynamics, torsional dynamics, conformational transition rate, and dynamic heterogeneity of the PB chains with different chain structures in detail by determining the corresponding T_g. In addition, our results clearly indicate that with the decrease of the amount of the free end atoms of PB via the end‐linking method, the mobility of the PB chains quickly decreases. As a result, the T_g of the PB chains gradually increases. Depending on the chain structure and the calculation method, the T_g of the PB chains varies from 154 to 240 K. In addition, the temperature dependence of the dynamic properties has different Arrhenius behaviors above and below T_g. The calculated activation energy varies from 7.37 to 16.37 KJ/mol for different chain structures above T_g, which can be compared with those for other polymers. In addition, through the end‐linking approach the strong interaction between the PB chains improves the storage modulus G′ and the loss modulus . Meanwhile, the immobility of the free end atoms effectively reduces the friction loss of the chains under the shear field, which is reflected by the low loss factor . In summary, this work can further help to understand the effect of the chain structure on the dynamic properties of the PB chains. Meanwhile, it provides an effective approach to reduce the energy loss during the dynamic periodic deformation, which can cut the fuel consumption via the end‐linking method. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1005–1016     

The relevance of glass transition temperature for the process of tablet formation

The aim was to determine the relevance of the glass transition temperature (T_g) on the compressibility and compactibility of different excipients as celluloses, cellulose derivatives, lactoses, starch, maltodextrin and carrageenan. Their T_g was determined, they were tableted on an instrumented eccentric tableting machine and crushing force was analyzed. Using force, time and displacement tableting behavior was analyzed by 3D modeling. The parameters obtained, d (time plasticity), e (pressure plasticity) and w (fast elastic decompression), show different deformation mechanisms for the materials in relation to their T_g. Further, if the T_g can be reversibly exceeded during tableting, crushing force is high, otherwise crushing force is lower. This revised version was published online in July 2006 with corrections to the Cover Date.     

Free‐volume change during the volume phase transition of polyacrylamide gel studied by positron annihilation: Solvent‐composition dependence

Changes in the free‐volume parameters of polyacrylamide (PAAm) gels during the volume phase transition (VPT) were studied with the positron annihilation lifetime technique. The VPT was induced through the variation of the solvent composition in a mixture of acetone and water. The PAAm gels containing 0 and 4 mol % carboxyl groups in their polymer chains were adapted to compare the effect of the presence of ionic groups on the microscopic environment. The change of the free‐volume property is discussed on a nanoscopic scale, with attention paid to the interactions between the polymer chains and the solvent molecules. It is proven that the variations of the free‐volume parameters correlate significantly with the VPT phenomenon. The results of the free volume for both gels are well‐explained when an interaction parameter, ε_g, is assumed. The interpretation suggests that the state of the interactions among the components (the polymer chain, acetone, and water molecules) plays an important role in the change of the free volume of PAAm gels during the VPT. An increase of the dispersion of the free‐volume size near the VPT point was observed for the ionized PAAm gel. The broadened size distribution of the free volume of the ionized PAAm gel around the VPT point lay between those of pure water and the corresponding mixed solvent, suggesting that a local minimum of the average free‐volume size at the VPT point is caused by the increase of a specific interaction, hydrogen bonding. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 922–933, 2000     

A new formula for the entropy of mixing in polymer systems and free volume

The famous equations of Flory-Huggins for the entropy of mixing with one highmolecular component are of great importance for polymer physics. But Gujrati stated in 1980 [12] that these equations cannot be exact. This is why we derived a new formula for the dependence of the entropy from the fraction of vacant sites in a quasi-lattice. It differs significantly from that of Huggins and still more from that of Flory in the case of low free volume. The equations of Flory-Huggins are correct with reference to low polymer content only.If our formula for entropy is used instead of that of Huggins an important result of the theory of Gibbs-DiMarzio is called in question. The increase of thermal expansion at the glass transition cannot be explained by an increase of vacant sites. A growth of the number of unoccupied sites according to the thermodynamic equilibrium condition would bring about a far too great thermal expansion coefficient. From estimations of the energy of interaction between polymer molecules, which can be found in literature, it follows that the increase of entropy is far too small to enable the formation of vacant sites above the glass transition. It is unambiguously shown that the free volume, commonly regarded to be the decisive quantity with respect to glass transition, cannot consist of holes as considered in the quasi-lattice model and in many theoretical treatments.     

Temperature and pressure dependence of the free volume in the perfluorinated polymer glass CYTOP: A positron lifetime and pressure‐volume‐temperature study

The microstructure of the free volume was studied for an amorphous perfluorinated polymer (T_g = 378 K). To this aim we employed pressure–volume–temperature experiments (PVT) and positron annihilation lifetime spectroscopy (PALS). Using the Simha‐Somcynsky equation of state the hole free volume fraction h and the specific free and occupied volumes, V_f = hV and V_occ = (1 ? h)V, were determined. Their expansivities and compressibilities were calculated from fits of the Tait equation to the volume data. It was found that in the glass V_occ has a particular high compressibility, while the compressibility of V_f is rather low, although h (300 K) = 0.108 is large. In the rubbery state the free volume dominates the total compressibility. From the PALS spectra the hole size distribution, its mean, 〈v_h〉, and mean dispersion, σ_h, were calculated. From a comparison of 〈v_h〉 with V_f a constant hole density of N_h′ = 0.25 × 10²¹ g^?1 was estimated. The volume of the smallest representative freely fluctuating subsystem, 〈V_SV〉 ∝ 1/σ_h², is unusually small. This was explained by an inherent topologic disorder of this polymer. 〈v_h〉 and σ_h show an exponential‐like decrease with increasing pressure P at 298 K. The hole density, calculated from N_h′ = V_f/〈v_h〉, seems to show an increase with P which is unexpected. This was explained by the compression of holes in the glass in two, rather than three, dimensions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2519–2534, 2007