Free energy of an inhomogeneous polymer‐polymer‐solvent system

Abstract

SynopsisThe free energy of an inhomogeneous polymer-polymer-solvent system has been obtained by extending Debye's approach for a polymer-solvent system. Our ternary result reduces to Debye's result for a binary polymer-solvent system and to McMaster's result for a binary polymer-polymer system at the appropriate limits. Like Debye's work, we neglect the entropic gradient contribution to free energy. Based on the ternary result we suggest a generalized expression for the free energy of multiple polymers dissolved in a common solvent. This expression is used to find the free energy of an inhomogeneous polydispersed polymer-solvent system. (2)Ks(polymer-polymer) = -__ 6 NlGl NzG2

Polystyrene Microstructured Foams Formed by Thermally Induced Phase Separation from Cyclohexanol Solution

“…Here we restrict ourselves to a comparison of characteristic sizes of produced morphologies. For a detailed investigation of the morphology type and controlling parameters see available literature …”

“…For a detailed investigation of the morphology type and controlling parameters see available literature. [6,27,28,[30][31][32][34][35][36][37][38]40,41,[47][48][49][50][51] Since the dynamics of the phase separation is influenced by the constitutive equations for the fluxes and by the value of diffusion coefficient, [6] we restrict ourselves to the comparison of final morphology profiles. This approach is also chosen by the fact that the kinetics of the spinodal decomposition is qualitatively well described by Cahn-Hilliard model but the lack of data about the diffusivities prohibits quantitative predictions of morphology evolution dynamics.…”

Spinodal Decomposition in Ternary Systems with Significantly Different Component Diffusivities

“…We assume a Flory‐Huggins form: where the N i are chain lengths and the χ are binary interaction parameters. The kappa in Equation (2) and (3) are gradient energy parameters that are known functions of the radius of gyration and the interaction parameters 16, 17. The composition and gradient dependent chemical potentials are given by: …”

Free energy of an inhomogeneous polymer–polymer–solvent system. II

“…We use ( 8 ) , ( l l ) , and where E , is the potential energy between a solvent molecule j and a polymer molecule i with centers of mass separated by distance r. Here, as Debye, lo we assumed that the average density of the monomers of the polymer coil can be represented by a Gaussian distribution. Thus, the number of monomers in an element of volume d~ at a distance r from the center of mass of the polymer coil is,10,12…”

“…A brief review of these coefficients has been provided in ref. 8. The binary and ternary theories for spinodal decomposition that start with eq.…”