Phase Stability of Hydrogen-Bonded Polymer Mixtures. II. Mixtures of Intercomplexing Polymers

Equations for the second derivative of the Gibbs energy of mixing with respect to composition were derived on the basis of the Barker-Guggenheim theory of quasichemical equilibrium for mixtures of two polymers containing polar groups and a nonpolar rest. Using equations derived, conditions for the phase separation in mixtures of two strongly intercomplexing polymer components were evaluated. The phase instability appears when the components differ in their polar group contents (strictly speaking, in their surface fractions in respective macromolecules), or due to an unfavorable interaction between nonpolar groups of the components. The effect is conditioned by small affinity of polar to nonpolar groups and may be influenced by the difference in this affinity between both components; nevertheless, the latter factors are not sufficient for a phase instability to occur.

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Phase Stability of Hydrogen-Bonded Polymer Mixtures: Application of the Quasichemical Theory

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19951830 ◽

1995 ◽

Vol 60 (11) ◽

pp. 1830-1854

Author(s):

Julius Pouchlý ◽

Antonín Živný ◽

Antonín Sikora

Keyword(s):

Relative Size ◽

Molecular Surface ◽

Polymer Mixtures ◽

Main Attention ◽

Model Calculations ◽

Small Deviations ◽

Polar Groups ◽

Energy Of Mixing ◽

Gibbs Energy Of Mixing ◽

Random Mixing

Expressions for the second derivative of Gibbs energy of mixing with respect to composition and/or the corresponding Flory-Huggins interaction parameter are derived using the Barker-Guggenheim quasichemical theory. The calculation is performed first for a system of compounds with a homogeneous molecular surface, then for a binary mixture of molecules the surface of which consists of various kinds of contact sites. The result is expressed in terms of "indexes of nonrandomness", the factors which characterize deviations of individual types of contact pairs from random mixing at a given composition. Main attention is paid to a mixture of substances, each of which contains a different type of polar groups and a nonpolar residue which is similar for both components. Translucent relations are obtained in two limit cases, namely for small deviations from random mixing and for small attraction between polar and nonpolar groups. The effect of the relative size of the polar groups and of the affinity to formation of various heterocontacts is illustrated using the limit relations derived, as well as by means of model calculations.

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Phase Stability of Hydrogen-Bonded Polymer Mixtures. III. Spinodal Diagrams

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19990031 ◽

1999 ◽

Vol 64 (1) ◽

pp. 31-43 ◽

Cited By ~ 1

Author(s):

Julius Pouchlý ◽

Antonín Živný ◽

Antonín Sikora

Keyword(s):

Relative Content ◽

Strong Interactions ◽

Polar Group ◽

Polymer Mixtures ◽

Phase Instability ◽

Temperature Range ◽

Polar Groups ◽

Boltzmann Function ◽

Chain Lengths ◽

Two Temperature

Relations derived on the basis of the Barker-Guggenheim quasichemical theory were used for construction of spinodal diagrams (temperature versus composition) of a mixture of two polymers in which hydrogen bonds and other strong interactions exist. A function dependence of parameters of quasichemical equilibrium, η, was proposed, which has the form of the Boltzmann function at lower temperatures, but at higher temperatures corresponds to random mixing. The spinodal diagrams were constructed for several sets of dependences of η on temperature in a wide temperature range for different chain lengths, r, or for different values of the content of polar groups in one of the polymers. According to circumstances, the phase diagram shows one or two temperature regions of phase instability or the phase instability occurs in a certain range of composition at any temperature. Though the chain length was chosen equal for both polymers, the phase diagrams are asymmetric in the sense that the critical points are shifted towards that border of the diagram which corresponds to the component with a larger relative content of the polar group. The temperature range of phase instability is strongly influenced by small changes in the relative surface area of polar groups in the molecules.

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Activities of Components in the Ca2MgSi2O7-CaSiO3Molten System

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19960837 ◽

1996 ◽

Vol 61 (6) ◽

pp. 837-843

Author(s):

Ladislav Kosa ◽

Ivan Nerád ◽

Katarína Adamkovičová ◽

Jozef Strečko ◽

Ivo Proks

Keyword(s):

Gibbs Energy ◽

Molar Mass ◽

Excess Entropy ◽

Enthalpy Of Mixing ◽

Real Particle ◽

Entropy Of Mixing ◽

Energy Of Mixing ◽

Gibbs Energy Of Mixing

Activities of the components, the Gibbs energy of mixing, and the excess entropy of mixing have been calculated for the Ca2MgSi2O7-CaSiO3 system. The mole fractions of the components were calculated assuming that in the point of the formal component Ca2MgSi2O7, the molar mass of the quasi-real particle in the melt corresponds to its formula molar mass, whereas in the point of the formal component CaSiO3 the molar mass of the quasi-real particle in the melt is 8.5 times higher than as corresponds to its formula. The fact that the enthalpy of mixing is zero whereas the excess entropy of mixing is non-zero suggests that Ca2MgSi2O7-CaSiO3 melts behave as athermal solutions.

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