Thermodynamic properties of quasi-one-dimensional fluids
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914857069051904 |
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| author | Franosch, Thomas Schilling, Rolf |
| author_facet | Franosch, Thomas Schilling, Rolf |
| contents | We calculate thermodynamic and structural quantities of a fluid of hard spheres of diameter $σ$ in a quasi-one-dimensional pore with accessible pore width $W $ smaller than $σ$ by applying a perturbative method worked out earlier for a confined fluid in a slit pore [Phys. Rev. Lett. \textbf{109}, 240601 (2012)]. In a first step, we prove that the thermodynamic and a certain class of structural quantities of the hard-sphere fluid in the pore can be obtained from a purely one-dimensional fluid of rods of length $ σ$ with a central hard core of size $σ_W =\sqrt{σ^2 - W^2}$ and a soft part at both ends of length $(σ-σ_W)/2$. These rods interact via effective $k$-body potentials $v^{(k)}_\text{eff}$ ($k \geq 2$) . The two- and the three-body potential will be calculated explicitly. In a second step, the free energy of this effective one-dimensional fluid is calculated up to leading order in $ (W/σ)^2$. Explicit results for, e.g. the perpendicular pressure, surface tension, and the density profile as a function of density, temperature, and pore width are presented presented and partly compared with results from Monte-Carlo simulations and standard virial expansions. Despite the perturbative character of our approach it encompasses the singularity of the thermodynamic quantities at the jamming transition point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19946 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thermodynamic properties of quasi-one-dimensional fluids Franosch, Thomas Schilling, Rolf Soft Condensed Matter Statistical Mechanics We calculate thermodynamic and structural quantities of a fluid of hard spheres of diameter $σ$ in a quasi-one-dimensional pore with accessible pore width $W $ smaller than $σ$ by applying a perturbative method worked out earlier for a confined fluid in a slit pore [Phys. Rev. Lett. \textbf{109}, 240601 (2012)]. In a first step, we prove that the thermodynamic and a certain class of structural quantities of the hard-sphere fluid in the pore can be obtained from a purely one-dimensional fluid of rods of length $ σ$ with a central hard core of size $σ_W =\sqrt{σ^2 - W^2}$ and a soft part at both ends of length $(σ-σ_W)/2$. These rods interact via effective $k$-body potentials $v^{(k)}_\text{eff}$ ($k \geq 2$) . The two- and the three-body potential will be calculated explicitly. In a second step, the free energy of this effective one-dimensional fluid is calculated up to leading order in $ (W/σ)^2$. Explicit results for, e.g. the perpendicular pressure, surface tension, and the density profile as a function of density, temperature, and pore width are presented presented and partly compared with results from Monte-Carlo simulations and standard virial expansions. Despite the perturbative character of our approach it encompasses the singularity of the thermodynamic quantities at the jamming transition point. |
| title | Thermodynamic properties of quasi-one-dimensional fluids |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2406.19946 |