Thermodynamic and Interfacial Analysis of Polypropylene Glycol: Dependence of the Gradient Energy Coefficient on Molecular Weight Using Simha–Somcynsky and Cahn–Hilliard Theories

Salwa Hatm Shukur; Saygin  Kuzeci

doi:10.51699/cajmns.v7i1.3102

Authors

Salwa Hatm Shukur Department of Physics, College of Education for Pure Science, Kirkuk University, Iraq
Saygin Kuzeci Department of Physics, College of Education for Pure Science, Kirkuk University, Iraq

DOI:

https://doi.org/10.51699/cajmns.v7i1.3102

Keywords:

Polymer Thermodynamics, Interfacial Properties, Phase Separation, Modified Cell Theory, Thermal Expansion

Abstract

This study presents a theoretical analysis of the thermophysical and interfacial properties of polypropylene glycol with different molecular weights using a combined Simha–Somcynsky equation of state and Cahn–Hilliard diffuse-interface framework. Properties including gradient energy coefficient, surface tension, density, specific volume, hole fraction, and occupied volume fraction were evaluated over 313–473 K and 0.1–150 MPa. Results show that increasing molecular weight reduces specific volume and density but increases surface tension and gradient energy coefficient, while increasing temperature produces opposite trends. Numerical accuracy was assessed through volume deviation measures. The approach reliably captures molecular-weight-dependent interfacial behavior relevant to PPG material design applications.

References

khalid a a and kuzeci s 2024 studying the gradient energy coefficient s as function of molecular weights. Math. Appl. 13

Nuri S M 2017 Extracting the density gradient profile of polyethylene glycol from bulk to surface Kirkuk Univ. Journal-Scientific Stud. 12 338–51

Lodge, T. P Lodge, T. P., & Hillmyer, M. A. (2000). Thermodynamics of polymer blends. Physics Today, 53(5), 36–41.

Paul, D. R., & Barlow, J. W. (1980). Polymer blends. Journal of Macromolecular Science, Part C: Polymer Reviews, 18(1), 109–168.

Maiti, P., & Okamoto, M. (2006). Crystallization and morphology of biodegradable poly(L-lactide)/clay nanocomposites. Polymer, 47(1), 472–480.

Tanaka, H. (2000). Viscoelastic phase separation. Journal of Physics: Condensed Matter, 12(15), R207–R264.

Fredrickson, G. H. (2006). The Equilibrium Theory of Inhomogeneous Polymers. Oxford University Press.

Cahn, J. W., & Hilliard, J. E. (1958). Free energy of a nonuniform system. I. Interfacial free energy. The Journal of Chemical Physics, 28(2), 258–267.

Cahn, J. W. (1961). On spinodal decomposition. Acta Metallurgica, 9(9), 795–801.

Elliott, C. M. (1989). The Cahn–Hilliard model for the kinetics of phase separation. In Mathematics of Phase Transitions (pp. 35–73). Springer.

Gurtin, M. E. (1996). Generalized Ginzburg–Landau and Cahn–Hilliard equations based on a microforce balance. Physica D: Nonlinear Phenomena, 92(3–4), 178–192.

Karma, A., & Rappel, W. J. (1998). Quantitative phase-field modeling of dendritic growth in two and three dimensions. Physical Review E, 57(4), 4323–4349.

Novick-Cohen, A. (1988). On the viscous Cahn–Hilliard equation. Materials Science and Engineering: A, 112, 267–276.

Rowlinson, J. S., & Widom, B. (2013). Molecular theory of capillarity. Courier Corporation.

Widom, B. (1978). Structure of the interface of coexisting phases. The Journal of Chemical Physics, 68(10), 3878–3884.

Zhong, C., Wang, W., & Lu, H. (1993). Simplified hole theory equation of state for polymer liquids. Fluid Phase Equilibria, 86, 137–146.