Measuring structure and interactions in colloidal fluids using test-particle insertion
<p>We use the Potential Distribution Theorem to evaluate distribution functions from equilibrium configurations using test-particle insertion. We use this methodology to determine the contact value of the pair distribution function in hard-disk systems: in contrast with the conventional distan...
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| Format: | Thesis |
| Language: | English |
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2020
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| _version_ | 1817931907898277888 |
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| author | Stones, AE |
| author2 | Dullens, R |
| author_facet | Dullens, R Stones, AE |
| author_sort | Stones, AE |
| collection | OXFORD |
| description | <p>We use the Potential Distribution Theorem to evaluate distribution functions from equilibrium configurations using test-particle insertion. We use this methodology to determine the contact value of the pair distribution function in hard-disk systems: in contrast with the conventional distance-histogram method, the insertion measurement is exact and does not require an approximate extrapolation. The resulting equations of state in both simulations and a hard-disk colloidal model system agree well with the predictions of Scaled Particle Theory. We also provide the first experimental measurement of the cavity distribution function y<sup>(2)</sup>(r) inside the hard core.</p>
<p>We next develop a model-free technique for measuring the pair potential u<sup>(2)</sup>(r) in pairwise-additive fluids, by matching the insertion and distance-histogram measurements of g<sup>(2)</sup>(r) using an iterative predictor-corrector scheme. We test the method extensively in simulation, before applying it successfully in a fluid of superparamagnetic colloidal particles, obtaining the anticipated form of u<sup>(2)</sup>(r) and the correct dependence on the applied magnetic field. We then extend the scheme to measure the full set of pair potentials in multicomponent fluids, demonstrating its efficacy in a three-component simulation.</p>
<p>We show that a given n-body distribution function g<sup>(n)</sup> (n>2) can be measured using n different insertion routes, which correspond to simultaneous insertion of between 1 and n test particles. We use these methods to measure g<sup>(3)</sup> in simulation: while the noise depends strongly on the number of simultaneous insertions, the resolution is superior to that of the distance-histogram method. Finally, we consider systems with three-body interactions. We show that matching g<sup>(2)</sup>(r) alone gives an effective pair potential which is unable to reproduce g<sup>(3)</sup> in pairwise-additive simulations. We therefore extend the predictor-corrector scheme to measure the three-body interaction u<sup>(3)</sup> by matching g<sup>(3)</sup>, and test it in simulation. The scheme broadly recovers the correct u<sup>(3)</sup>, but requires further development to reduce the noise.</p> |
| first_indexed | 2024-03-06T18:43:54Z |
| format | Thesis |
| id | oxford-uuid:0dd7bbdc-f7a2-4151-9d4b-e69df8536b7c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:29:29Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | oxford-uuid:0dd7bbdc-f7a2-4151-9d4b-e69df8536b7c2024-12-01T12:12:31ZMeasuring structure and interactions in colloidal fluids using test-particle insertionThesishttp://purl.org/coar/resource_type/c_db06uuid:0dd7bbdc-f7a2-4151-9d4b-e69df8536b7cPhysical ChemistryChemical PhysicsEnglishHyrax Deposit2020Stones, AEDullens, RAarts, DDoye, Jvan Roij, R<p>We use the Potential Distribution Theorem to evaluate distribution functions from equilibrium configurations using test-particle insertion. We use this methodology to determine the contact value of the pair distribution function in hard-disk systems: in contrast with the conventional distance-histogram method, the insertion measurement is exact and does not require an approximate extrapolation. The resulting equations of state in both simulations and a hard-disk colloidal model system agree well with the predictions of Scaled Particle Theory. We also provide the first experimental measurement of the cavity distribution function y<sup>(2)</sup>(r) inside the hard core.</p> <p>We next develop a model-free technique for measuring the pair potential u<sup>(2)</sup>(r) in pairwise-additive fluids, by matching the insertion and distance-histogram measurements of g<sup>(2)</sup>(r) using an iterative predictor-corrector scheme. We test the method extensively in simulation, before applying it successfully in a fluid of superparamagnetic colloidal particles, obtaining the anticipated form of u<sup>(2)</sup>(r) and the correct dependence on the applied magnetic field. We then extend the scheme to measure the full set of pair potentials in multicomponent fluids, demonstrating its efficacy in a three-component simulation.</p> <p>We show that a given n-body distribution function g<sup>(n)</sup> (n>2) can be measured using n different insertion routes, which correspond to simultaneous insertion of between 1 and n test particles. We use these methods to measure g<sup>(3)</sup> in simulation: while the noise depends strongly on the number of simultaneous insertions, the resolution is superior to that of the distance-histogram method. Finally, we consider systems with three-body interactions. We show that matching g<sup>(2)</sup>(r) alone gives an effective pair potential which is unable to reproduce g<sup>(3)</sup> in pairwise-additive simulations. We therefore extend the predictor-corrector scheme to measure the three-body interaction u<sup>(3)</sup> by matching g<sup>(3)</sup>, and test it in simulation. The scheme broadly recovers the correct u<sup>(3)</sup>, but requires further development to reduce the noise.</p> |
| spellingShingle | Physical Chemistry Chemical Physics Stones, AE Measuring structure and interactions in colloidal fluids using test-particle insertion |
| title | Measuring structure and interactions in colloidal fluids using test-particle insertion |
| title_full | Measuring structure and interactions in colloidal fluids using test-particle insertion |
| title_fullStr | Measuring structure and interactions in colloidal fluids using test-particle insertion |
| title_full_unstemmed | Measuring structure and interactions in colloidal fluids using test-particle insertion |
| title_short | Measuring structure and interactions in colloidal fluids using test-particle insertion |
| title_sort | measuring structure and interactions in colloidal fluids using test particle insertion |
| topic | Physical Chemistry Chemical Physics |
| work_keys_str_mv | AT stonesae measuringstructureandinteractionsincolloidalfluidsusingtestparticleinsertion |