Calculation of phase diagrams not requiring the derivatives of the Gibbs energy demonstrated for a mixture of two homopolymers with the corresponding copolymer

Abstract

SUMMARY:A method is presented which allows the calculation of phase diagrams (spinodal, binodal and tie lines) on the basis of the Gibbs energy of mixing AG. No derivatives of AG with respect to the composition variables are required. This method is particularly useful in cases where the composition dependence of AG is very complex and no analytical representation of the derivatives can be given. The method is applied to a ternary mixture of two homopolymers with a copolymer consisting of the same monomers. The sequence distribution of the copolymer is kept constant between random and purely alternating, and phase diagrams are calculated for different chemical compositions of the copolymer. The complex phase separation behavior resulting for a 1 : 1 copolymer becomes much simpler as one monomeric unit starts to predominate in the copolymer.

Pressure Effects on Thermodynamics of Polymer Containing Systems

“…In the contrast, for a carefully selected system with chemically similar monomers, where  is positive but small, there exists a possibility for m V  < 0. These predictions are consistent with the work of Foreman and Freed using the lattice cluster model (Horst, 1995;Horst & Wolf, 1992). According to figure 27b and equation 35, we can qualitatively predict the pressure effect on this ternary system, i.e., the pressure effects on m V  in this system; at the same time, we also get the information on the pressure effects on  parameter for this system, i.e., with the increasing of TL in this system,  parameter increases from small to large.…”

“…According to our previous calculations An & wolf, 1998)  . In this paper, the spinodals and binodals for the systems TD/PS are calculated by means of a new method without the derivatives of Gibbs energy (Horst, 1995;Horst & Wolf, 1992). On the basis of the FH lattice model (Flory, 1953) …”

“…Like the spinodals and binodals of ternary and quaternary polymer blends were calculated with the method (Horst 1995;Horst & Wolf, 1992) (the knowledge of the first and second derivatives of G  with respect to the composition variables is not required), the spinodals and the binodals of the PEO/P(EO-b-DMS) system were calculated with the SL theory under different pressures. Figure 15 shows the calculated results of the spinodals and the binodals compared with the experimental data as showed in Figure 14.…”

Insights into photovoltaic properties of ternary organic solar cells from phase diagrams

“…We followed a computational less challenging approach described by Horst [59]. The impact of the dissociated counterions was modeled by adding an entropy term to the Flory-Huggins model as suggested by Hellebust et al The Flory-Huggins parameters were taken as fitting parameters, with the intention to reproduce the phase diagrams shown in Figure 6(b) and 6(c) by varying only the degree of ion dissociation.…”

“…Taking into account the estimated size of the components and their interaction parameters, the free energy at every point is calculated following the Flory-Huggins model [58]. The spinodal regions were found by comparing the energy of a point with the average energy of all pairs of opposite direct neighbors [59]. If the energy of one of those pairs is lower than the one of the point of interest, the total energy of the system can be lowered by a spontaneous separation into the neighboring compositions and therefore, the point is marked as unstable.…”