Pressure influence on the glass transition of polymers and polymer blends

Summary p-V-T measurements have been carried out on a broad series of polymers and polymer blends. The effect of pressure on the glass transition temperature, T_g, and on related properties-increments of the coefficients of expansion, , and compressibility, K, at T_g-has been evaluated critically. The results are discussed in terms of the free volume, the order parameter, and the statistical mechanical theory. It is concluded that neither the simple free volume theory, nor the order parameter theory in the one order assumption predict correctly the observed behaviour. A possible explanation of the phenomena observed is offered assuming an expansion of the free volume, which is independent of the nature of the polymer. For the blends binary contacts between the components are discussed, with respect to interaction energy and to conformational rearrangements.Dedicated to Prof. Dr. W. H. Stockmayer to his 80th birthday with the best wishes     

Molecular interpretation of T∥, the rubbery-viscous ‘transition’ temperature of amorphous polymers

Many physical and mechanical properties of amorphous polymers show anomalous behaviour at a temperature above T_g, designated T_∥, the ‘liquid-liquid transition temperature’. It is suggested here that T_∥ can be considered to be the rubbery-viscous ‘transition’ temperature of amorphous polymers, analogous to T_g, the glassy-rubbery transition temperature. At T_∥, the viscous dissipation goes through a maximum due to a shift in response of the molecules to stress from a coiling-uncoiling process (elastic rubbery region) to slippage between the molecules (viscous region). It is argued here that this maximum is responsible for the occurrence of a maximum in log(decrement) traces obtained by torsional braid analysis (t.b.a.) above T_g.     

Morphological effects on glass transition behavior in selected immiscible blends of amorphous and semicrystalline polymers

The effects uncompatibilized immiscible polymer blend compositions on the T_g of the amorphous polymer were studied in the systems polystyrene/polypropylene (PS/PP), polystyrene/high density polyethylene (PS/PE) and polycarbonate/high density polyethylene (PC/PE). In the two similar systems of PS/PP and PS/PE, the T_g of PS increased with decreasing PS percentage in the blends. This variation in glass transition is attributed to the polymer domain interactions resulting from the different morphologies of various blend compositions. Experiments were conducted to study these effects by preparing blends with various polymers that varied the relationship between the T_g of the amorphous polymer and the crystallization behavior of the semicrystalline polymer. Results show that the variation in amorphous component T_g with composition depends strongly on the physical state of the semicrystalline domains. Whereas the T_g of PS in PS/PE blends changed with composition, the T_g of PC in the PC/PE blend did not change with composition.     

Sorption and diffusion of alcohols in amorphous polymers

The effects of polymer composition and penetrant molecular size on the solubility and diffusivity of alcohol vapors in a series of well characterized isoprene-methyl methacrylate copolymers and their corresponding homopolymers has been investigated at room temperature. The rate of sorption behavior changes progressively from Fickian to non-Fickian, to Case II to “Super Case II” transport with increasing methyl methacrylate (MMA) content in the polymers. The equilibrium solubility of the alcohols increases linearly with increasing penetrant molecular size for polymers which are above their glass transition temperature and decreases for polymers which are below their T_g. The solubility also initially increases as an approximately linear function of MMA content in the copolymers. At about 55 mole percent MMA, the sorbed concentration either levels off or passes through a maximum depending on the size of the penetrant. The apparent “diffusion coefficients” (D) decrease with increasing molecular volume of the penetrants. An exponential dependence was found between these two variables for PMMA. These “diffusion coefficients” also decrease exponentially with increasing MMA content in these polymers. However, at 55 mole percent MMA the copolymer undergoes a rubber to glass transition at the temperature of the experiments. On this basis, it is suggested that the hindered chain segmental motion contributes to the sorption process in addition to strictly thermodynamic considerations. Free volume theory can be used to explain the mechanism of diffusion through the rubbery polymers while the “hole” theory can be applied to explain the transport of the penetrants through the glassy polymers.     

A theory for the diffusion of large molecules in amorphous polymers above Tg

A general theory of diffusion of large molecules in rubbery amorphous polymers is of interest for the scientific understanding and with regard to material design and process optimization. A broadly applicable model would be useful in developing controlled transport of plasticizers and other additives through polymeric substances. A diffusion model is presented which has been developed for large molecular penetrants above the T_g of the amorphous polymer allowing for required increase in redistribution of the free volume of the polymer structure, as well as the penetrant size and shape. Applicability of the model is demonstrated by comparing theoretically developed diffusion curves for DNOP and DNDP in PVC vs. their weight fractions at 82°C and 91°C. These theoretically derived plots are compared with experimental D vs. w₁ curves for these systems generated at lower temperature.     

Conformational transition characterization of glass transition behavior of polymers

The conformational transition behavior of polymer in the amorphous state has been investigated through molecular dynamics simulations across the glass transition temperature (T_g). We find that the conformational transition, a localized and short time dynamics feature, crosses over different barrier heights when the system transforms from the molten state into the glass state and the barrier height in the glass state is markedly lower than that above T_g. In addition to the overall transition behavior, the specific transitions between the rotational isomeric states (RIS) g⁺, t⁻, t⁺ and g⁻ are also investigated in detail. The populations of these specific transitions undergo considerable changes when the temperature decreases; meanwhile, the larger transition rates of the ending torsions get diminished. Besides the rate, the rotation degrees of the dihedrals during the transitions also change their distributions tremendously through T_g, below which most of the larger transition angles (50-100°) were inhibited remaining those sharply around 30°. This possibly explains why below T_g the conformational transition process has a lower effective barrier.     

A thermally stimulated depolarization current study of polymers in the glass transition region

The low‐frequency dielectric properties of a number of polymers, composites and blends have been studied using a thermally stimulated depolarization current (TSDC) apparatus that was designed and constructed in‐house. The TSDC technique can be used to determine the glass transition of a polymer sample. This TSDC glass transition temperature has been shown to be very similar to that obtained from differential scanning calorimetry (DSC). The actual difference between these two values depends on the heating rates used with each technique, however. TSDC data can also be combined with AC dielectric data to produce a data set, which possesses a very wide frequency range. Finally, individual TSDC relaxation peaks can be fit with the Williams‐Walts distribution function to obtain an estimate of their distributions. This is especially useful when studying polymer blends, but could also be utilized in the study of other systems.     

Influence of cohesive forces on the glass transition temperatures of polymers

The relationship between cohesive energy (c.e.) or cohesive energy density (c.e.d.) and the glass transition tenperature (T_g) of polymers has been re-examined on the basis of literature data. For polymers with T_g above 25°C., there is no correlation between published or calculated values of c.e. or c.e.d. and T_g. However, for the rest of the polymers there is a linear relationship between c.e.d. and T_g, and a broad relationship between c.e. and T_g. These results imply that c.e.d. is the regulating, though not the only, factor in determining T_g's up to values of approximately 25°C.     

The effect of confinement in nanoporous polymers on the glass transition temperature

The glass transition temperature (T_g) of nanoporous polyetherimide (PEI) and PEI thin films was investigated. The T_g decreased from its bulk value in both of these confined systems. Monte Carlo simulations were performed to calculate the nearest neighbor pore-to-pore distances in the nanoporous PEI. A quantitative analogy between the nanoporous PEI and PEI thin films is proposed through an equivalence of nearest neighbor pore-to-pore distances and thin film thickness. The effect of confinement is believed to be due to the interface regions, which possess higher chain mobility than the bulk. When these high mobility interface regions are sufficiently close together, the excess mobility at the interface region affects the dynamics of the system by restraining percolation of the slow domains resulting in the observed decrease in T_g.     

On free volume of polymers above the glass transition

The magnitude of the activation energy for diffusion, E_D is shown to be inversely dependent on the fractional free volume of the polymer above T_g. From the proportionality of E_D above and below T_g, the magnitude of E_D below T_g is also inversely dependent on the free volume in that temperature range. While this correlation holds very well for our determinations of fractional free volume above T_g it does not correlate with the Simha-Boyer fractional free volume below T_g, contrary to expectations.     

Estimation of solvent diffusion coefficient in amorphous polymers using the Sanchez-Lacombe equation-of-state

A modified free-volume model was proposed to predict the solvent diffusion coefficient in rubbery polymers without knowledge of any diffusion data. With the introduction of the Sanchez-Lacombe (SL) equation-of-state (EOS) into the Vrentas-Duda model, this model is an attempt to bridge the gap between the thermodynamic and transport properties of polymer solutions. The free volume provided by polymers for solvent diffusion can be estimated solely using the parameters of the SL EOS characteristics and the polymer glass transition temperature; thus the proposed model avoids the need to use polymer viscoelastic data in determination of polymer free-volume parameters. The other parameters in the Vrentas-Duda model remain applicable. Calculated results of solvent self- and mutual-diffusion coefficients of four common solvents in two polymers indicated that the modified model can give reliable predictions. In addition, it can reflect the effect of pressure on solvent diffusivity for concentrated polymer solutions.     

A comparative study of the kinetic theories of the glass transition phenomenon in high polymers

The effect of thermal history on the glass transition temperature (T_g) of poly(vinyl chloride) was studied. The parameters like the hole energy (E_h), the activation energy for the disappearance of holes (E_j), the activation enthalpy for the structural relaxation (Δh1* and Δh2*) and the activation energy for the glass transition process (E) were calculated. The increase of E_h value with the increase in T_g value shows that there exists a holesize distribution. The E_j (26.9 ± 0.5 kcal/mol) value calculated according to Wunderlich's treatment, the Δh1* (27.8 ± 0.6 kcal/mol) value obtained by Moynihan's procedure and the E (35.3 kcal/mol) value from Barton-Critchley's method agree well with one another in the poly(vinyl chloride) system. The Δh2* quantity, obtained through Moynihan's formulations, increase as the rate of heating was increased, a result similar to the variation of E_h value with the rate of heating.     

The effect of disperse dyes on the glass transition temperature of polymers

The lowering of the glass transition temperature (T_g) of a polymer produced by the incorporating various concentrations of azo disperse dyes has been investigated, and the effects of the structure and concentrations of the dyes were examined. The T_g values were lowered with increasing dye concentrations in the polymer, and the lowering of T_g produced by the dyes was influenced not only by the molecular structure of the dyes but also the dye-polymer interactions.     

Gruneisen parameter and fluctuation volume of amorphous polymers and glass

The Gruneisen parameter of glassy polymers and inorganic glass is a linear function of the fraction of the fluctuation volume that is frozen at the glass transition temperature. The nature of an interrelation between linear and nonlinear properties of solids, in particular, between the Gruneisen parameter and Poisson’s ratio is discussed.     

Ductile and brittle behavior of amorphous polymers. Relationship with activation energy for glass transition and mechanical fracture

An equation correlating the activation energy for the glass transition with T_R, a characteristic reference temperature, the fractional free volume, and the rate of change of the fractional free volume was developed. The resultant activation energies for about 30 polymers are given and favorably compare with the literature. The relationship between the activation energy and the bond-rupture energy indicates whether a polymer will fail in a ductile or brittle fashion. More accurate results are shown to be dependent on the stress, the stress concentration, molecular orientation, frequency of load application, and temperature. Equations correlating all these with the activation energies are given. These results are in agreement with the molecular domain model. Experimental observations from the literature seem to corroborate the suggestion that the molecular domain model holds in the amorphous solid, too.     

Ratio of the glass transition temperature to the melting point in polymers

A study of the ratio of the glass temperature to the melting point of 132 polymers is described. Contrary to some other workers' observations on smaller numbers of polymers there is no sharp division between the ratios observed for symmetrical and unsymmetrical polymers. The arithmetic mean of the ratio is 0·63 and 0·69 respectively, but the combined standard deviation is 0·11. There is no correlation between the ratios and the crystalline forms of polymers.     

Role of electrostatic forces in the glass transition temperatures of ionic polymers

The glass transition temperatures of ionic polymers have been correlated with cohesive energy densities (CED). The CEDs of ionic polymers, such as ionene polymers, polyphosphates, and polyacrylates were calculated under the assumption that they could be approximated to the electrostatic energy of the system. The T_gs of ionic polymers could be conveniently expressed by the equation $\text{T}{}_{\mathrm{g}}\text{= K}{}_1\text{(CED)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ in which K₁ took a different value for each polymer system. This paper discusses the influence on T_g of the change in both the cohesive energy and the degree of freedom of segmental motion caused by the introduction of ionic characteristics in polymeric chains.