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Wani YM, Kovakas PG, Nikoubashman A, Howard MP. Diffusion and sedimentation in colloidal suspensions using multiparticle collision dynamics with a discrete particle model. J Chem Phys 2022; 156:024901. [PMID: 35032985 DOI: 10.1063/5.0075002] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study self-diffusion and sedimentation in colloidal suspensions of nearly hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to experimental data and Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne-Prager-Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the solvent at short times. However, the long-time self-diffusion coefficient in MD+MPCD is comparable to that in experiments, and the sedimentation coefficient in MD+MPCD is in good agreement with that in experiments and BD+RPY, suggesting that MD+MPCD gives a reasonable description of hydrodynamic interactions in colloidal suspensions. The discrete-particle MD+MPCD approach is convenient and readily extended to more complex shapes, and we determine the long-time self-diffusion coefficient in suspensions of nearly hard cubes to demonstrate its generality.
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Affiliation(s)
- Yashraj M Wani
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | | | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Michael P Howard
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, USA
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Härtl W, Versmold H, Zhang-Heider X. Tracer Particle Diffusion in Crystal- and Fluid-like Ordered Colloidal Suspensions. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19910950930] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Juárez-Maldonado R, Medina-Noyola M. Theory of dynamic arrest in colloidal mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051503. [PMID: 18643070 DOI: 10.1103/physreve.77.051503] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2007] [Revised: 02/18/2008] [Indexed: 05/26/2023]
Abstract
We present a first-principles theory of dynamic arrest in colloidal mixtures based on the multicomponent self-consistent generalized Langevin equation theory of colloid dynamics [M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E 72, 031107 (2005); M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E76, 039902 (2007)]. We illustrate its application with a description of dynamic arrest in two simple model colloidal mixtures: namely, hard-sphere and repulsive Yukawa binary mixtures. Our results include observation of the two patterns of dynamic arrest, one in which both species become simultaneously arrested and the other involving the sequential arrest of the two species. The latter case gives rise to mixed states in which one species is arrested while the other species remains mobile. We also derive the ("bifurcation" or fixed-point") equations for the nonergodic parameters of the system, which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species. The solution of this system of equations indicates unambiguously which species is arrested (finite localization length) and which species remains ergodic (infinite localization length). As a result, we are able to draw the entire ergodic-nonergodic phase diagram of the binary hard-sphere mixture.
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Affiliation(s)
- R Juárez-Maldonado
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, SLP, México
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Guevara-Rodríguez FDJ, Medina-Noyola M. Dynamic equivalence between soft- and hard-core Brownian fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:011405. [PMID: 12935141 DOI: 10.1103/physreve.68.011405] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2002] [Indexed: 05/24/2023]
Abstract
In this work, we demonstrate the dynamic equivalence between the members of the family of Brownian fluids whose particles interact through strongly repulsive radially symmetric soft-core potentials. We specifically consider pair potentials proportional to inverse powers of (r/sigma). This equivalence is the dynamic extension of the static equivalence between all these pair potentials and the hard-sphere fluid, assumed in the treatment of soft-core reference potentials in the classical (Weeks-Chandler-Andersen or Barker-Henderson) perturbation theories of simple liquids. In contrast with the strict hard-sphere Brownian system, in the case of soft-sphere potentials the conventional Brownian dynamics algorithm is indeed well defined. We find that, except for small values of nu, and/or very short times, the dynamic properties of all these systems collapse into a single universal curve, upon a well-defined rescaling of the time and distance variables. This family of systems includes the hard-sphere limit. This observation permits a conceptually simple, new, and accurate Brownian dynamics algorithm to simulate the dynamic properties of the hard-sphere model dispersion without hydrodynamic interactions. Such an algorithm consists of the straightforward rescaling of the Brownian-dynamics simulated properties of any of the dynamically equivalent soft-sphere systems.
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Affiliation(s)
- F de J Guevara-Rodríguez
- Instituto Mexicano del Petróleo, Programa de Ingeniería Molecular, Eje Central Lázaro Cárdenas 152, 07730 México, Distrito Federal, Mexico.
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Lahtinen JM, Mašı́n M, Laurila T, Ala-Nissila T, Chvoj Z. Many-particle diffusion in continuum: Influence of a periodic surface potential. J Chem Phys 2002. [DOI: 10.1063/1.1467908] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ohshima YN, Hatakeyam KE, Satake M, Homma Y, Washidzu R, Nishio I. Cross-correlation functions in two-dimensional and three-dimensional colloidal crystals. J Chem Phys 2001. [DOI: 10.1063/1.1417506] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lahtinen JM, Hjelt T, Ala-Nissila T, Chvoj Z. Diffusion of hard disks and rodlike molecules on surfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:021204. [PMID: 11497569 DOI: 10.1103/physreve.64.021204] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2001] [Indexed: 05/23/2023]
Abstract
We study the submonolayer diffusion of hard disks and rodlike molecules on smooth surfaces through numerical simulations and theoretical arguments. We concentrate on the behavior of the various diffusion coefficients as a function of the two-dimensional (2D) number density rho in the case where there are no explicit surface-particle interactions. For the hard disk case, we find that while the tracer diffusion coefficient D(T)(rho) decreases monotonically up to the freezing transition, the collective diffusion coefficient D(C)(rho) is wholly determined by the inverse compressibility which increases rapidly on approaching freezing. We also study memory effects associated with tracer diffusion, and present theoretical estimates of D(T)(rho) from the mode-mode coupling approximation. In the case of rigid rods with short-range repulsion and no orientational ordering, we find behavior very similar to the case of disks with the same repulsive interaction. Both D(T)(rho) and the angular diffusion coefficient D(R)(rho) decrease with rho. Also in this case D(C)(rho) is determined by inverse compressibility and increases rapidly close to freezing. This is in contrast to the case of flexible chainlike molecules in the lattice-gas limit, where D(C)(rho) first increases and then decreases as a function of the density due to the interplay between compressibility and mobility.
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Affiliation(s)
- J M Lahtinen
- Helsinki Institute of Physics and Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Espoo, Finland
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Ohshima YN, Nishio I. Colloidal crystal: bead–spring lattice immersed in viscous media. J Chem Phys 2001. [DOI: 10.1063/1.1366640] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Banchio AJ, Nägele G, Bergenholtz J. Collective diffusion, self-diffusion and freezing criteria of colloidal suspensions. J Chem Phys 2000. [DOI: 10.1063/1.1286964] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Brands A, Versmold H, van Megen W. Tracer particle diffusion in crystal-like ordered colloidal suspensions. J Chem Phys 1999. [DOI: 10.1063/1.478181] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Indrani AV, Ramaswamy S. Universal self-diffusion and subdiffusion in colloids at freezing. PHYSICAL REVIEW LETTERS 1994; 73:360-363. [PMID: 10057150 DOI: 10.1103/physrevlett.73.360] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Cichocki B, Felderhof BU. Dynamic scattering function of a semidilute suspension of hard spheres. J Chem Phys 1993. [DOI: 10.1063/1.464523] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Härtl W, Versmold H, Wittig U, Linse P. Structure and dynamics of polymer colloid suspensions from dynamic light scattering and Brownian dynamics simulation. J Chem Phys 1992. [DOI: 10.1063/1.463448] [Citation(s) in RCA: 30] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Leegwater JA, Szamel G. Dynamical properties of hard-sphere suspensions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:4999-5011. [PMID: 9908719 DOI: 10.1103/physreva.46.4999] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Szamel G, Leegwater JA. Long-time self-diffusion coefficients of suspensions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:5012-5019. [PMID: 9908720 DOI: 10.1103/physreva.46.5012] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Szamel G, Blawzdziewicz J, Leegwater JA. Self-diffusion in sheared suspensions: Violation of the Einstein relation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:2173-2176. [PMID: 9907233 DOI: 10.1103/physreva.45.r2173] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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