Statistical mechanics of surfaces
<p>The equilibrium properties of a spherical drop are investigated using the penetrable-sphere model of a fluid. To estimate the surface tension, a new statistical mechanical formula, the extension of the Triezenberg-Zwanzig result for a planar surface, is derived. The density profiles for us...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
1982
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| _version_ | 1797103912328626176 |
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| author | Hemingway, S Hemingway, Stephen |
| author2 | Rowlinson, J |
| author_facet | Rowlinson, J Hemingway, S Hemingway, Stephen |
| author_sort | Hemingway, S |
| collection | OXFORD |
| description | <p>The equilibrium properties of a spherical drop are investigated using the penetrable-sphere model of a fluid. To estimate the surface tension, a new statistical mechanical formula, the extension of the Triezenberg-Zwanzig result for a planar surface, is derived. The density profiles for use in this are obtained from an integral equation expressing the constancy of chemical potential through the interface. Numerical solutions can be obtained and from these numerical estimates for the surface tension. They are in good agreement with estimates from an independent thermodynamic route. These routes, as well as a further, zero-temperature, exact, analytic one, show that the surface tension of this model increases with decreasing drop size.</p> <p>The planar surface of the model is also briefly investigated using a well-known integrodifferential equation. Two approximations are made for the direct correlation function, one a systematic improvement on the other. They yield solutions for the density profile of a limited range of temperatures below the critical point. When the direct correlation function of a Lennard-Jones fluid is approximated the resulting equation for the profile resists numerical solution.</p> |
| first_indexed | 2024-03-07T06:26:46Z |
| format | Thesis |
| id | oxford-uuid:f4913459-32d4-42a6-a6ec-fc6e33d0b69e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:26:46Z |
| publishDate | 1982 |
| record_format | dspace |
| spelling | oxford-uuid:f4913459-32d4-42a6-a6ec-fc6e33d0b69e2022-03-27T12:20:48ZStatistical mechanics of surfacesThesishttp://purl.org/coar/resource_type/c_db06uuid:f4913459-32d4-42a6-a6ec-fc6e33d0b69eStatistical mechanicsSolid-liquid equilibriumSurface energyEnglishPolonsky Theses Digitisation Project1982Hemingway, SHemingway, StephenRowlinson, JRowlinson, J<p>The equilibrium properties of a spherical drop are investigated using the penetrable-sphere model of a fluid. To estimate the surface tension, a new statistical mechanical formula, the extension of the Triezenberg-Zwanzig result for a planar surface, is derived. The density profiles for use in this are obtained from an integral equation expressing the constancy of chemical potential through the interface. Numerical solutions can be obtained and from these numerical estimates for the surface tension. They are in good agreement with estimates from an independent thermodynamic route. These routes, as well as a further, zero-temperature, exact, analytic one, show that the surface tension of this model increases with decreasing drop size.</p> <p>The planar surface of the model is also briefly investigated using a well-known integrodifferential equation. Two approximations are made for the direct correlation function, one a systematic improvement on the other. They yield solutions for the density profile of a limited range of temperatures below the critical point. When the direct correlation function of a Lennard-Jones fluid is approximated the resulting equation for the profile resists numerical solution.</p> |
| spellingShingle | Statistical mechanics Solid-liquid equilibrium Surface energy Hemingway, S Hemingway, Stephen Statistical mechanics of surfaces |
| title | Statistical mechanics of surfaces |
| title_full | Statistical mechanics of surfaces |
| title_fullStr | Statistical mechanics of surfaces |
| title_full_unstemmed | Statistical mechanics of surfaces |
| title_short | Statistical mechanics of surfaces |
| title_sort | statistical mechanics of surfaces |
| topic | Statistical mechanics Solid-liquid equilibrium Surface energy |
| work_keys_str_mv | AT hemingways statisticalmechanicsofsurfaces AT hemingwaystephen statisticalmechanicsofsurfaces |