Thermodynamics of the Glassy Polymer State: Equilibrium and Non-Equilibrium Aspects

Abstract

This work examines, first, the non-equilibrium character of the glassy state of polymer systems and its significance in the development of novel materials for important technological applications. Subsequently, it summarizes the essentials of the generalized lattice fluid approach for the description of this highly complex non-equilibrium behavior with an approximate and simple, yet analytically powerful formalism. The working equations are derived in a straightforward and consistent manner by clearly defining the universal and specific variables needed to describe the discussed properties. The role of the non-random distribution of molecular species and free volume in the glassy system is also examined, as is the role of strong specific interactions, such as hydrogen-bonding networks. This work also reports examples of applications in a variety of representative systems, including glass densification, retrograde vitrification, increase in glass-transition temperature in hydrogen-bonded polymer mixtures, and hysteresis phenomena in sorption-desorption from glassy polymer matrices.

Keywords: glass densification; glass transition; lattice-fluid; penetrant sorption; polymer swelling; statistical thermodynamics.

Figure 1

Experimental PVT data for poly(vinyl acetate) (PVAc) at the glass transition region [6]. The straight lines are drawn to show the change in slope at the glass transition and the definition of Tg at the intersection. The thick green line passing through the intersections shows the variation in Tg with pressure.

Figure 2

Schematic illustration of the role of formation history on the density of the final glassy state. States I and C are obtained from the same isobars (same constant pressure, atmospheric) at different cooling rates. State G, shown at the same final temperature T₁, is obtained by first pressurizing the melt to a high pressure, P₂, and then cooling isobarically to temperature T₁, at which point isothermal depressurization takes place until atmospheric pressure is reached.

Figure 3

The four types of T_g behavior as a function of pressure, as predicted by the LF model. Reprinted with permission from ref. [13].

Figure 4

Glass transition temperatures of a SVPh60/PIBMA mixture. Filled rectangles represent experimental data [20]. The equation of the solid line was calculated from the LFHB model. The dashed line represents the non-hydrogen bonding LF contribution to T_g. Reproduced with permission from reference [20].

Figure 5

Experimental [37] (symbols) and calculated (lines) gas solubilities of CO₂ in unconditioned (a) and conditioned (b) PC at 35 °C, obtained by considering the excess volume to be known. Reproduced, with permission, from reference [36].

Figure 6

Experimental [37] (symbols) and calculated (lines) gas solubilities on unconditioned and conditioned PC samples, considering volume changes to be known (a) and volume changes in the same sample calculated by considering gas solubilities to be known (b). Reproduced with permission from [36].

Figure 7

NRHB model fitting of PVT data [40] to obtain the scaling constants for PC.

Figure 8

Changes in PC-CO₂ volume during sorption and desorption at 35 °C, ρ₂ = 1.200 g/cm³ or V₀ = 0.8333 cm³/g [38].

Figure 9

Comparison of CO₂ sorption/desorption data [38] in PC at 35 °C with NE-LFHB (solid lines) (correlation of only sorption data with ξ = 1.1533) and NETGP-NRHB (dashed lines) (correlation of only sorption data with ξ = 1.1444). In both models, the values of the mixture volume are taken from Figure 8.

Figure 10

Comparison of H₂O sorption data [43] in 6FDA_6FpDA at 30 °C by NE-LFHB (correlation of sorption data with ξ = 0.8211 and G₁₂ = −12,773 J mol⁻¹) and NETGP-NRHB (correlation of sorption data with ξ = 0.869 and G₁₂ = −12,100 J mol⁻¹).

Figure 11

The swelling constant as a function of pressure in the CO₂-PC system, as obtained from Equation (51) and the experimental ΔV/V₀ data [37] at 35 °C. The line is obtained from the correlated ΔV/V₀ data.