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Thermodynamics of hard-sphere fluids in polydisperse random porous media: Extended scaled particle theory

T. Hvozd, M. Hvozd, M. Holovko

Abstract

Accurate descriptions of reference systems are a central task in liquid-state theories for the study of more complex systems. Using scaled particle theory (SPT), we derive a fully analytical description of the thermodynamic properties of a hard-sphere (HS) fluid confined in size-polydisperse HS random porous media, extending the existing approaches to higher matrix packing fractions. We calculate chemical potentials for a wide range of porous-matrix parameters, including the matrix packing fraction, degree of polydispersity, and particle-size distributions. Within the proposed framework, our results show excellent agreement with available Monte Carlo simulations and previous integral-equation theories over a broad range of matrix packing fractions, $0.1 \leqslant η_0 \leqslant 0.3$, and degrees of polydispersity.

Thermodynamics of hard-sphere fluids in polydisperse random porous media: Extended scaled particle theory

Abstract

Accurate descriptions of reference systems are a central task in liquid-state theories for the study of more complex systems. Using scaled particle theory (SPT), we derive a fully analytical description of the thermodynamic properties of a hard-sphere (HS) fluid confined in size-polydisperse HS random porous media, extending the existing approaches to higher matrix packing fractions. We calculate chemical potentials for a wide range of porous-matrix parameters, including the matrix packing fraction, degree of polydispersity, and particle-size distributions. Within the proposed framework, our results show excellent agreement with available Monte Carlo simulations and previous integral-equation theories over a broad range of matrix packing fractions, , and degrees of polydispersity.
Paper Structure (4 sections, 37 equations, 4 figures)

This paper contains 4 sections, 37 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Generalization of the SPT2 approach to HS fluids in size-polydisperse disordered HS matrices
  3. Results and discussion
  4. Conclusions

Figures (4)

  • Figure 1: (Colour online) Dependence of the fluid density on the chemical potential, calculated in this work using the SPT2a (dashed lines), SPT2b1 (dotted lines), and SPT2b3* (solid lines) approximations, and compared against MC simulation data from reference Leon2006 (symbols), at fixed matrix packing fraction $\eta_0=0.2$ and for various widths of the rectangular size distribution: (a) $\sigma_0 = 1$, (b) $0.9 \leqslant \sigma_0 \leqslant 1.1$, and (c) $0.6 \leqslant \sigma_0 \leqslant 1.4$. (d) Same as in panels (a)--(c), but the solid lines correspond to the new SPT2b3** approach.
  • Figure 2: (Colour online) Dependence of the fluid density on the chemical potential, calculated in this work using (a) the SPT2a (dashed lines), SPT2b1 (dotted lines), and SPT2b3* (solid lines) approximations, and compared against MC simulation data from reference Leon2006 (symbols), at fixed width of the rectangular size distribution, $0.6 \leqslant \sigma_0 \leqslant 1.4$, and for various matrix packing fractions: $\eta_0=0.1$ (red lines and filled circles), and $\eta_0=0.2$ (blue lines and filled triangles). (b) Same as in panel (a), but the solid lines correspond to the new SPT2b3** approach.
  • Figure 3: (Colour online) Dependence of the fluid density on the chemical potential, calculated in this work using the SPT2a (dashed lines), SPT2b1 (dotted lines), and SPT2b3* (solid lines) approximations, and compared against MC simulation data from reference Leon2006 (symbols), for: (a) $\eta_0 = 0.25$ and $0.6 \leqslant \sigma_0 \leqslant 1.4$; (b) $\eta_0 = 0.3$ and $0.6 \leqslant \sigma_0 \leqslant 1.4$; and (c) $\eta_0 = 0.3$ and $0.9 \leqslant \sigma_0 \leqslant 1.1$. (d) Same as in panels (a)--(c), but the solid lines correspond to the new SPT2b3** approach.
  • Figure 4: (Colour online) Dependence of the fluid density on the chemical potential (a) and on the pressure (b), obtained within the SPT2b3** approximation for a Schultz--Zimm distribution at matrix packing fraction $\eta_0 = 0.2$ and various degrees of polydispersity: $\gamma = 99$ (solid lines), $\gamma = 24$ (dashed lines), and $\gamma = 8$ (dotted lines). Panels (c) and (d) show the corresponding results for $\eta_0 = 0.25$.