Evaluation of thermodynamic parameters for blends of polyethersulfone and poly(methyl methacrylate) or polystyrene in dimethylformamide

Determination of χ from liquid-liquid phase data in ternary polymer systems (solvent/polymer/polymer) with hydrogen bonding

“…Experimental compositions in equilibrium, φ i γ (i = 1, 2; γ = α, β), from the binodal curve and randomly generated, [17]. These diagrams have served to obtain all the phase compositions for each component through the tie-lines joining the two phases in equilibrium at the binodal or cloud-point isotherm as explained elsewhere [17,[20][21][22]. Next, following the methods and procedure described in the Theory section, the volume fractions φ i γ (i = 1, 2, 3; γ = α, β) have been determined for all the phases equilibria of the above TPS and are compiled in Table 1 …”

“…In the literature is possible to find g ij values as a function of temperature and composition according to Equation (22) [5,15]: (22) where α ij and c ij are constants for a given system and temperature interval, and D ij (T) (Equation (2)), being a and b parameters with entropic and enthalpic character, respectively [4]. According to Equation (18), the corresponding χ ij values are given by Equation (23): (23) and according to Equation (16) the corresponding ε ij should be as given by Equation (24): (24) There are other models describing the g dependences with temperature and composition for binary polymer systems.…”

“…Other models allow to express the g ij interaction parameters in BPS by using a less number of fitting parameters, according to Equation (27): (27) with D ij and c ij as defined in Equation (22). Now, the χ ij values attained are given by Equation (28): (28) This expression has been recently used to thermodynamically analyze the phase separation occurring during the polymerization of a thermoset epoxy system into a thermoplastic matrix [11,12,25].…”

“…Fortunately, there are more traditional and simple systems with well-known values of the interaction parameters that can be used to judge the validity of the approximations used in the more complex and actual systems. In this regard, in recent papers, dealing with compatibility between polystyrene copolymers and other polymers in solution via hydrogen bonding [17][18][19], the phase diagrams of the ternary polymer systems (TPS) have been obtained from experimental liquid chromatography data [20][21][22]. The achievement of χ values from liquid-liquid phase data has been considered a reliable method [16] and consists in solving the equations obtained by equating the chemical potentials in both phases in equilibrium, for all the components.…”

Ternary Polymer Solutions with Hydrogen Bonds, 2

“…After calibration, 50 mL of both phases were injected and from the calibration the weight percentage of every polymer was determined, as usual. [16,17] Phase diagrams have been limited to a global polymeric content below 30 wt.-%, because higher polymeric concentrations showed very high viscosities, which prevent adequate separation of the two phases in equilibrium and therefore the evaluation of their compositions.…”