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Rohrbach PB, Kobayashi H, Scheichl R, Wilding NB, Jack RL. Multilevel simulation of hard-sphere mixtures. J Chem Phys 2022; 157:124109. [DOI: 10.1063/5.0102875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a mixture of size-asymmetric hard spheres, in the grand canonical ensemble. A three-level version of the method is compared with a previously-studied two-level version. The extra level interpolates between the full mixture and a coarse-grained description where only the large particles are present -- this is achieved by restricting the small particles to regions close to the large ones. The three-level method improves the performance of the estimator, at fixed computational cost. We analyse the asymptotic variance of the estimator, and discuss the mechanisms for the improved performance.
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Affiliation(s)
- Paul B Rohrbach
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge Department of Applied Mathematics and Theoretical Physics, United Kingdom
| | | | | | - Nigel B. Wilding
- School of Physics, University of Bristol School of Physics, United Kingdom
| | - Robert L. Jack
- DAMTP, University of Cambridge Department of Applied Mathematics and Theoretical Physics, United Kingdom
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Kobayashi H, Rohrbach PB, Scheichl R, Wilding NB, Jack RL. Correction of coarse-graining errors by a two-level method: Application to the Asakura-Oosawa model. J Chem Phys 2019; 151:144108. [DOI: 10.1063/1.5120833] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Affiliation(s)
- Hideki Kobayashi
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Paul B. Rohrbach
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert Scheichl
- Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Nigel B. Wilding
- H.H. Wills Physics Laboratory, University of Bristol, Royal Fort, Bristol BS8 1TL, United Kingdom
| | - Robert L. Jack
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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Guo Z, Kindt JT. Gibbs ensemble Monte Carlo with solvent repacking: phase coexistence of size–asymmetrical binary Lennard-Jones mixtures. MOLECULAR SIMULATION 2017. [DOI: 10.1080/08927022.2017.1373192] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Ziwei Guo
- Department of Chemistry, Emory University, Atlanta, GA, USA
| | - James T. Kindt
- Department of Chemistry, Emory University, Atlanta, GA, USA
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Tasios N, Dijkstra M. From 2D to 3D: Critical Casimir interactions and phase behavior of colloidal hard spheres in a near-critical solvent. J Chem Phys 2017; 146:134903. [DOI: 10.1063/1.4979518] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nikos Tasios
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
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Tasios N, Edison JR, van Roij R, Evans R, Dijkstra M. Critical Casimir interactions and colloidal self-assembly in near-critical solvents. J Chem Phys 2016; 145:084902. [DOI: 10.1063/1.4961437] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nikos Tasios
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - John R. Edison
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
| | - René van Roij
- Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Robert Evans
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
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Kindt JT. Grand canonical Monte Carlo using solvent repacking: Application to phase behavior of hard disk mixtures. J Chem Phys 2015; 143:124109. [DOI: 10.1063/1.4931731] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- James T. Kindt
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
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Rovigatti L, Gnan N, Parola A, Zaccarelli E. How soft repulsion enhances the depletion mechanism. SOFT MATTER 2015; 11:692-700. [PMID: 25428843 DOI: 10.1039/c4sm02218a] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We investigate binary mixtures of large colloids interacting through soft potentials with small, ideal depletants. We show that softness has a dramatic effect on the resulting colloid-colloid effective potential when the depletant-to-colloid size ratio q is small, with significant consequences on the colloidal phase behaviour. We provide an exact relationship that allows us to obtain the effective pair potential for any type of colloid-depletant interaction in the case of ideal depletants, without having to rely on complicated and expensive full-mixture simulations. We also show that soft repulsion among depletants further enhances the tendency of colloids to aggregate. Our theoretical and numerical results demonstrate that--in the limit of small q--soft mixtures cannot be mapped onto hard systems and hence soft depletion is not a mere extension of the widely used Asakura-Oosawa potential.
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Affiliation(s)
- Lorenzo Rovigatti
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria.
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Edison JR, Tasios N, Belli S, Evans R, van Roij R, Dijkstra M. Critical casimir forces and colloidal phase transitions in a near-critical solvent: a simple model reveals a rich phase diagram. PHYSICAL REVIEW LETTERS 2015; 114:038301. [PMID: 25659025 DOI: 10.1103/physrevlett.114.038301] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2014] [Indexed: 06/04/2023]
Abstract
From experimental studies, it is well known that colloidal particles suspended in a near-critical binary solvent exhibit interesting aggregation phenomena, often associated with colloidal phase transitions and assumed to be driven by long-ranged solvent-mediated (SM) interactions (critical Casimir forces), set by the (diverging) correlation length of the solvent. We present the first simulation and theoretical study of an explicit model of a ternary mixture that mimics this situation. Both the effective SM pair interactions and the full ternary phase diagram are determined for Brownian disks suspended in an explicit two-dimensional supercritical binary liquid mixture. Gas-liquid and fluid-solid transitions are observed in a region that extends well away from criticality of the solvent reservoir. We discuss to what extent an effective pair-potential description can account for the phase behavior we observe. Our study provides a fresh perspective on how proximity to the critical point of the solvent reservoir might influence colloidal self-assembly.
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Affiliation(s)
- John R Edison
- Soft Condensed Matter, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
| | - Nikos Tasios
- Soft Condensed Matter, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
| | - Simone Belli
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, Netherlands
| | - Robert Evans
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - René van Roij
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
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Ashton DJ, Sánchez-Gil V, Wilding NB. Monte Carlo methods for estimating depletion potentials in highly size-asymmetrical hard sphere mixtures. J Chem Phys 2013; 139:144102. [DOI: 10.1063/1.4824137] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- D J Ashton
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
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Ashton DJ, Wilding NB, Roth R, Evans R. Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: comparison of simulation results with theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:061136. [PMID: 22304069 DOI: 10.1103/physreve.84.061136] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2011] [Indexed: 05/31/2023]
Abstract
We report a detailed study, using state-of-the-art simulation and theoretical methods, of the effective (depletion) potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres, the size disparity being measured by the ratio of diameters q ≡ σ(s)/σ(b). Small particles are treated grand canonically, their influence being parameterized in terms of their packing fraction in the reservoir η(s)(r). Two Monte Carlo simulation schemes--the geometrical cluster algorithm, and staged particle insertion--are deployed to obtain accurate depletion potentials for a number of combinations of q ≤ 0.1 and η(s)(r). After applying corrections for simulation finite-size effects, the depletion potentials are compared with the prediction of new density functional theory (DFT) calculations based on the insertion trick using the Rosenfeld functional and several subsequent modifications. While agreement between the DFT and simulation is generally good, significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods, namely, η(s)(r) = 0.35. These discrepancies are, however, small compared to those between simulation and the much poorer predictions of the Derjaguin approximation at this η(s)(r). The recently proposed morphometric approximation performs better than Derjaguin but is somewhat poorer than DFT for the size ratios and small-sphere packing fractions that we consider. The effective potentials from simulation, DFT, and the morphometric approximation were used to compute the second virial coefficient B(2) as a function of η(s)(r). Comparison of the results enables an assessment of the extent to which DFT can be expected to correctly predict the propensity toward fluid-fluid phase separation in additive binary hard-sphere mixtures with q ≤ 0.1. In all, the new simulation results provide a fully quantitative benchmark for assessing the relative accuracy of theoretical approaches for calculating depletion potentials in highly size-asymmetric mixtures.
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Affiliation(s)
- Douglas J Ashton
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
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