Statistical thermodynamics evaluation of polymer–polymer miscibility

Abstract

The Simha and Somcynsky (S–S) statistical thermodynamics theory was used to compute the solubility parameters as a function of temperature and pressure [δ = δ(T, P)], for a series of polymer melts. The characteristic scaling parameters required for this task, P*, T*, and V*, were extracted from the pressure–temperature–volume (PVT) data. To determine the potential polymer–polymer miscibility, the dependence of δ versus T (at ambient pressure) was computed for 17 polymers. Close proximity of the δ versus T curves for four miscible polymer pairs: PPE/PS, PS/PVME, and PC/PMMA signaled the usefulness of this approach. It is noteworthy, that the tabulated solubility parameters (derived from the solution data under ambient conditions) propounded the immiscibility of the PVC/PVAc pair. The computed values of δ also suggested miscibility for polymer pairs of unknown miscibility, namely PPE/PVC, PPE/PVAc, and PET/PSF. In recognizing the limitations of the solubility parameter approach (the omission of several thermodynamic contributions), these preliminary results are auspicious because they indicate a new route for estimating the miscibility of any polymeric material at a given temperature and pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2909–2915, 2004

Pressure–volume–temperature dependencies of polystyrenes

“…During the last two decades the simultaneous least-squares (lsq) fit of all data to S-S eos has been employed, Thus for example, Scientiste from MicroMath has been used [14][15][16][17][18][19][20]. Rapid convergence is obtained in two-steps: (1) fitting data to the polynomial expression [16],Ṽ ZṼðP;TÞ, provides the initial values of P*, T*, and V*, and then (2) fitting the data to the coupled Eqs.…”

“…The S-S theory has been used to provide description of the cohesive energy density [14,15], internal pressure, PVT behavior [16][17][18][19][20], etc. The great advantage of the S-S derivation is direct incorporation of the free volume parameter, h, which in turn may be used to interpret variety of dynamic properties, e.g.…”

Rheology of Polymer Blends

“…(2.30) suggests that minimization of the enthalpic term might provide the necessary condition for miscibility [190]. The required characteristic scaling parameters, , and , are readily extracted from the , data.…”

“…A theoretical derivation based on Eq. (2.29) indicated that solvent may increase the macromolecular mobility equivalent to that found at a temperature about 300 C higher than the glass transition temperature, that is, at g 300 [190].…”

Equations of State and Free‐Volume Content

“…The discrepancy originates in the solubility method used to determine the δ value of high polymers. The extra free volume introduced by solvents increases the polymer free volume, equivalent to heating it to T ≥ T g + 300 K [Utracki, 2004a;Utracki and Simha, 2004] FIGURE 6.2 Compressibility parameter for PS; monotonic increase of κ with T is observed only at T > 1.2T g,P=0 . The transitory behavior at T g ≤ T ≤ 1.2T g is invisible in Figure 6.1.…”