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Orts F, Ortega G, Garzón EM, Fuchs M, Puertas AM. Dynamics and friction of a large colloidal particle in a bath of hard spheres: Langevin dynamics simulations and hydrodynamic description. Phys Rev E 2020; 101:052607. [PMID: 32575230 DOI: 10.1103/physreve.101.052607] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2019] [Accepted: 04/29/2020] [Indexed: 06/11/2023]
Abstract
The analysis of the dynamics of tracer particles in a complex bath can provide valuable information about the microscopic behavior of the bath. In this work, we study the dynamics of a forced tracer in a colloidal bath by means of Langevin dynamics simulations and a theory model within continuum mechanics. In the simulations, the bath is comprised of quasihard spheres with a volume fraction of 50% immersed in a featureless quiescent solvent, and the tracer is pulled with a constant small force (within the linear regime). The theoretical analysis is based on the Navier-Stokes equation, where a term proportional to the velocity arises from coarse-graining the friction of the colloidal particles with the solvent. As a result, the final equation is similar to the Brinkman model, although the interpretation is different. A length scale appears in the model, k_{0}^{-1}, where the transverse momentum transport crosses over to friction with the solvent. The effective friction coefficient experienced by the tracer grows with the tracer size faster than the prediction from Stokes's law. Additionally, the velocity profiles in the bath decay faster than in a Newtonian fluid. The comparison between simulations and theory points to a boundary condition of effective partial slip at the tracer surface. We also study the fluctuations in the tracer position, showing that it reaches diffusion at long times, with a subdiffusive regime at intermediate times. The diffusion coefficient, obtained from the long-time slope of the mean-squared displacement, fulfills the Stokes-Einstein relation with the friction coefficient calculated from the steady tracer velocity, confirming the validity of the linear response formalism.
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Affiliation(s)
- F Orts
- Departamento de Informática, Campus de Excelencia Internacional Agroalimentario (ceiA3), Universidad de Almería, 04120 Almería, Spain
| | - G Ortega
- Departamento de Informática, Campus de Excelencia Internacional Agroalimentario (ceiA3), Universidad de Almería, 04120 Almería, Spain
| | - E M Garzón
- Departamento de Informática, Campus de Excelencia Internacional Agroalimentario (ceiA3), Universidad de Almería, 04120 Almería, Spain
| | - M Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - A M Puertas
- Departamento de Física Aplicada, Universidad de Almería, 04120 Almería, Spain
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2
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Gruber M, Puertas AM, Fuchs M. Critical force in active microrheology. Phys Rev E 2020; 101:012612. [PMID: 32069683 DOI: 10.1103/physreve.101.012612] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2019] [Indexed: 11/07/2022]
Abstract
Soft solids like colloidal glasses exhibit a yield stress, above which the system starts to flow. The microscopic analogon in microrheology is the untrapping or depinning of a tracer particle subject to an external force exceeding a threshold value in a glassy host. We characterize this delocalization transition based on a bifurcation analysis of the corresponding mode-coupling theory equations. A schematic model that allows analytical progress is presented first, and the full physical model is studied numerically next. This analysis yields a continuous dynamic transition with a critical power-law decay of the probe correlation functions with exponent -1/2. To compare with simulations with a limited duration, a finite-time analysis is performed, which yields reasonable results for not-too-small wave vectors. The theoretically predicted findings are verified by Langevin dynamics simulations. For small wave vectors we find anomalous behavior for the probe position correlation function, which can be traced back to a wave-vector divergence of the critical amplitude. In addition, we propose and test three methods to extract the critical force from experimental data, which provide the same value of the critical force when applied to the finite-time theory or simulations.
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Affiliation(s)
- M Gruber
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - A M Puertas
- Departamento de Física Aplicada, Universidad de Almería, 04.120 Almería, Spain
| | - M Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
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Puertas AM, Malgaretti P, Pagonabarraga I. Active microrheology in corrugated channels. J Chem Phys 2018; 149:174908. [DOI: 10.1063/1.5048343] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Antonio M. Puertas
- Department of Applied Physics, Universidad de Almería, 04120 Almería, Spain
| | - Paolo Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - Ignacio Pagonabarraga
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lasuanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
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Segovia-Gutiérrez JP, de Vicente J, Puertas AM, Hidalgo-Alvarez R. Describing magnetorheology under a colloidal glass approach. Phys Rev E 2017; 95:052601. [PMID: 28618613 DOI: 10.1103/physreve.95.052601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2017] [Indexed: 06/07/2023]
Abstract
The equilibrium structure and dynamics of magnetorheological (MR) fluids are studied in this work by simulations, where particles are modeled as dipoles with a quasihard spherical core. Upon increasing the interaction strength, controlled experimentally by the magnetic field, elongated clusters grow and, for intense fields, thick columns form, aligned with the field. The dynamics of the system is monitored by the mean-squared displacement and density correlation functions, which show an increasing slowing down with the attraction strength. The correlation function shows a two-step decay, with a separation between microscopic and long time dynamics, a typical hallmark of undercooled fluids. We have therefore analyzed the dynamics of this MR fluid using the typical concepts for undercooled fluids. Thus, the second decay of the density correlation function is fitted with a stretched exponential, and the wave-vector dependence of the fitting parameters studied. Both the amplitude and the time scale oscillate in phase with the structure factor. Our results support the idea that the magnetorheological effect is in fact the manifestation of a colloidal system approaching an attractive glass transition (or gel transition).
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Affiliation(s)
- J P Segovia-Gutiérrez
- Department of Applied Physics, Faculty of Sciences, University of Granada, Fuentenueva s/n, 18071-Granada, Spain
| | - J de Vicente
- Department of Applied Physics, Faculty of Sciences, University of Granada, Fuentenueva s/n, 18071-Granada, Spain
| | - Antonio M Puertas
- Group of Complex Fluids Physics, Department of Applied Physics, University of Almeria, 04120 Almería, Spain
| | - R Hidalgo-Alvarez
- Department of Applied Physics, Faculty of Sciences, University of Granada, Fuentenueva s/n, 18071-Granada, Spain
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5
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Gruber M, Abade GC, Puertas AM, Fuchs M. Active microrheology in a colloidal glass. Phys Rev E 2016; 94:042602. [PMID: 27841487 DOI: 10.1103/physreve.94.042602] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2016] [Indexed: 06/06/2023]
Abstract
We study the dynamics of a probe particle driven by a constant force through a colloidal glass of hard spheres. This nonequilibrium and anisotropic problem is investigated using a new implementation of the mode-coupling approximation with multiple relaxation channels and Langevin dynamics simulations. A force threshold is found, below which the probe remains localized, while above it the probe acquires a finite velocity. We focus on the localized regime, comparing theory and simulations concerning the dynamics in the length scale of the cage and the properties of the transition to the delocalized regime, such as the critical power-law decay of the probe correlation function. Probe van Hove functions predicted by the theory show exponential tails reminiscent of an intermittent dynamics of the probe. This scenario is microscopically supported by simulations.
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Affiliation(s)
- M Gruber
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - G C Abade
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - A M Puertas
- Departamento de Física Aplicada, Universidad de Almería, 04.120 Almería, Spain
| | - M Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
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6
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Cukier RI. Variance of a potential of mean force obtained using the weighted histogram analysis method. J Phys Chem B 2013; 117:14785-96. [PMID: 24175967 DOI: 10.1021/jp407956c] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A potential of mean force (PMF) that provides the free energy of a thermally driven system along some chosen reaction coordinate (RC) is a useful descriptor of systems characterized by complex, high dimensional potential energy surfaces. Umbrella sampling window simulations use potential energy restraints to provide more uniform sampling along a RC so that potential energy barriers that would otherwise make equilibrium sampling computationally difficult can be overcome. Combining the results from the different biased window trajectories can be accomplished using the Weighted Histogram Analysis Method (WHAM). Here, we provide an analysis of the variance of a PMF along the reaction coordinate. We assume that the potential restraints used for each window lead to Gaussian distributions for the window reaction coordinate densities and that the data sampling in each window is from an equilibrium ensemble sampled so that successive points are statistically independent. Also, we assume that neighbor window densities overlap, as required in WHAM, and that further-than-neighbor window density overlap is negligible. Then, an analytic expression for the variance of the PMF along the reaction coordinate at a desired level of spatial resolution can be generated. The variance separates into a sum over all windows with two kinds of contributions: One from the variance of the biased window density normalized by the total biased window density and the other from the variance of the local (for each window's coordinate range) PMF. Based on the desired spatial resolution of the PMF, the former variance can be minimized relative to that from the latter. The method is applied to a model system that has features of a complex energy landscape evocative of a protein with two conformational states separated by a free energy barrier along a collective reaction coordinate. The variance can be constructed from data that is already available from the WHAM PMF construction.
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Affiliation(s)
- Robert I Cukier
- Department of Chemistry Michigan State University , East Lansing, Michigan 48824-1322, United States
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Puertas AM. Fluctuation theorem for an optically trapped tracer in dense colloids. A simulation study. EPJ WEB OF CONFERENCES 2013. [DOI: 10.1051/epjconf/20134404001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Zhang M, Szamel G. Effective temperatures of a driven, strongly anisotropic Brownian system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061407. [PMID: 21797364 DOI: 10.1103/physreve.83.061407] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2011] [Indexed: 05/31/2023]
Abstract
We use Brownian dynamics computer simulations of a moderately dense colloidal system undergoing steady shear flow to investigate the uniqueness of the so-called effective temperature. We compare effective temperatures calculated from the fluctuation-dissipation ratios and from the linear response to a static, long-wavelength, external perturbation along two directions: the shear gradient direction and the vorticity direction. At high shear rates, when the system is strongly anisotropic, the fluctuation-dissipation-ratio-derived effective temperatures are approximately wave-vector independent, but the temperatures along the gradient direction are somewhat higher than those along the vorticity direction. The temperatures derived from the static linear response show the same dependence on the direction as those derived from the fluctuation-dissipation ratio. However, the former and the latter temperatures are different. Our results suggest that the presently used formulas for effective temperatures may not be applicable for strongly anisotropic, driven systems.
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Affiliation(s)
- Min Zhang
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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Weysser F, Puertas AM, Fuchs M, Voigtmann T. Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:011504. [PMID: 20866622 DOI: 10.1103/physreve.82.011504] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2010] [Revised: 06/26/2010] [Indexed: 05/29/2023]
Abstract
We analyze the slow glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory (MCT) of the glass transition. Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multicomponent calculation, but qualitative disagreement at small q when the system is treated as effectively monodisperse. The origin of the different small-q behavior is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantitative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behavior are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics.
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Affiliation(s)
- F Weysser
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
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10
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Puertas AM. Aging of a hard-sphere glass: effect of the microscopic dynamics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:104121. [PMID: 21389455 DOI: 10.1088/0953-8984/22/10/104121] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We present simulations of the aging of a quasi-hard-sphere glass, with Newtonian and Brownian microscopic dynamics. The system is equilibrated at the desired density (above the glass transition in hard spheres) with short-range attractions, which are removed at t = 0. The structural part of the decay of the density correlation function can be time rescaled to collapse onto a master function independent of the waiting time, t(w), and the timescale follows a power law with t(w), with exponent z ∼ 0.89; the non-ergodicity parameter is larger than that of the glass transition point (the localization length is smaller) and oscillates in harmony with S(q). The aging with both microscopic dynamics is identical, except for a scale factor from the age in Newtonian to the age in Brownian dynamics. This factor is approximately the same as that which scales the α-decay of the correlation function in fluids close to the glass transition.
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Affiliation(s)
- Antonio M Puertas
- Group of Complex Fluids Physics, Department of Applied Physics, University of Almeria, 04120 Almeria, Andalucía, Spain
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11
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Lange E, Caballero JB, Puertas AM, Fuchs M. Comparison of structure and transport properties of concentrated hard and soft sphere fluids. J Chem Phys 2009; 130:174903. [PMID: 19425812 DOI: 10.1063/1.3124182] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using Newtonian and Brownian dynamics simulations, the structural and transport properties of hard and soft spheres have been studied. The soft spheres were modeled using inverse power potentials (V approximately r(-n), with 1n the potential softness). Although, at constant density, the pressure, diffusion coefficient, and viscosity depend on the particle softness up to extremely high values of n, we show that scaling the density with the freezing point for every system effectively collapses these parameters for n > or = 18 (including hard spheres) for large densities. At the freezing points, the long range structure of all systems is identical, when length is measured in units of the interparticle distance, but differences appear at short distances (due to the different shapes of the interaction potential). This translates into differences at short times in the velocity and stress autocorrelation functions, although they concur to give the same value of the corresponding transport coefficient (for the same density to freezing ratio); the microscopic dynamics also affects the short time behavior of the correlation functions and absolute values of the transport coefficients, but the same scaling with the freezing density works for Newtonian or Brownian dynamics. For hard spheres, the short time behavior of the stress autocorrelation function has been studied in detail, confirming quantitatively the theoretical forms derived for it.
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Affiliation(s)
- Erik Lange
- University of Konstanz, D-78457 Konstanz, Germany
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12
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Determining the Glass Transition in Polymer Melts. REVIEWS IN COMPUTATIONAL CHEMISTRY 2007. [DOI: 10.1002/9780470189078.ch1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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13
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Puertas AM, Odriozola G. Linking Phase Behavior and Reversible Colloidal Aggregation at Low Concentrations: Simulations and Stochastic Mean Field Theory. J Phys Chem B 2007; 111:5564-72. [PMID: 17461568 DOI: 10.1021/jp068698b] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We have studied the link between the kinetics of clustering and the phase behavior of dilute colloids with short range attractions of moderate strength. This was done by means of computer simulations and a theoretical kinetic model originally developed to deal with reversible colloidal aggregation. Three different regions of the phase diagram were accessed. For weak attractions, a gas phase of small clusters in equilibrium forms in the system. For intermediate attractions, the system undergoes liquid-gas separation, which is signatured by the formation of a few large droplike aggregates, a gas phase of small clusters, and an overall kinetics where a few seeds succeed in explosively growing at long times, after a lag time. Finally, for very strong attractions, fractal unbreakable clusters form and grow following DLCA-like (diffusion limited cluster aggregation) kinetics; liquid-gas separation is prevented by the strength of the bonds, which do not allow restructuration. Good qualitative and quantitative agreement is found between the dynamic simulations and the kinetic model in all the three regions.
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Affiliation(s)
- Antonio M Puertas
- Grupo de Física de Fluidos Complejos, Departamento de Física Aplicada, Universidad de Almería, 04120 Andalucía, Spain
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Puertas AM, Fernández-Barbero A, de Las Nieves FJ. Structure factor scaling in colloidal charge heteroaggregation. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2005; 18:335-41. [PMID: 16283089 DOI: 10.1140/epje/e2005-00036-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2005] [Indexed: 05/05/2023]
Abstract
The structure factor, S(q), of a system composed of a 1:1 mixture of oppositely charged colloids undergoing heteroaggregation is studied by Browninan dynamics simulations. A peak develops in S(q) at low wave vectors, which can be scaled for different times to overlap using the scaling of spinodal decomposition, as shown for DLCA. The same master function is obtained for different interaction ranges. The origin of the peak can be traced back to a depletion layer of clusters surrounding every aggregate. At those long distances, cluster-cluster interaction is negligible and the aggregation is diffusion limitted, as deduced from the evolution of peak position, and the S(q) scaling at different interaction ranges. The interaction is, nevertheless, strong enough to affect the internal cluster structure.
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Affiliation(s)
- A M Puertas
- Group of Complex Fluids Physics, Department of Applied Physics, University of Almeria, 04120, Almeria, Spain.
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Chatterji A, Horbach J. Combining molecular dynamics with Lattice Boltzmann: A hybrid method for the simulation of (charged) colloidal systems. J Chem Phys 2005; 122:184903. [PMID: 15918761 DOI: 10.1063/1.1890905] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a hybrid method for the simulation of colloidal systems that combines molecular dynamics (MD) with the Lattice Boltzmann (LB) scheme. The LB method is used as a model for the solvent in order to take into account the hydrodynamic mass and momentum transport through the solvent. The colloidal particles are propagated via MD and they are coupled to the LB fluid by viscous forces. With respect to the LB fluid, the colloids are represented by uniformly distributed points on a sphere. Each such point [with a velocity V(r) at any off-lattice position r] is interacting with the neighboring eight LB nodes by a frictional force F = xi0(V(r)-u(r)), with xi0 being a friction coefficient and u(r) being the velocity of the fluid at the position r. Thermal fluctuations are introduced in the framework of fluctuating hydrodynamics. This coupling scheme has been proposed recently for polymer systems by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We investigate several properties of a single colloidal particle in a LB fluid, namely, the effective Stokes friction and long-time tails in the autocorrelation functions for the translational and rotational velocity. Moreover, a charged colloidal system is considered consisting of a macroion, counterions, and coions that are coupled to a LB fluid. We study the behavior of the ions in a constant electric field. In particular, an estimate of the effective charge of the macroion is yielded from the number of counterions that move with the macroion in the direction of the electric field.
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Affiliation(s)
- Apratim Chatterji
- Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
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16
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Voigtmann T, Puertas AM, Fuchs M. Tagged-particle dynamics in a hard-sphere system: mode-coupling theory analysis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:061506. [PMID: 15697373 DOI: 10.1103/physreve.70.061506] [Citation(s) in RCA: 72] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2004] [Indexed: 05/24/2023]
Abstract
The predictions of the mode-coupling theory of the glass transition (MCT) for the tagged-particle density-correlation functions and the mean-squared displacement curves are compared quantitatively and in detail to results from Newtonian- and Brownian-dynamics simulations of a polydisperse quasi-hard-sphere system close to the glass transition. After correcting for a 17% error in the dynamical length scale and for a smaller error in the transition density, good agreement is found over a wide range of wave numbers and up to five orders of magnitude in time. Deviations are found at the highest densities studied, and for small wave vectors and the mean-squared displacement. Possible error sources not related to MCT are discussed in detail, thereby identifying more clearly the issues arising from the MCT approximation itself. The range of applicability of MCT for the different types of short-time dynamics is established through asymptotic analyses of the relaxation curves, examining the wave-number and density-dependent characteristic parameters. Approximations made in the description of the equilibrium static structure are shown to have a remarkable effect on the predicted numerical value for the glass-transition density. Effects of small polydispersity are also investigated, and shown to be negligible.
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Affiliation(s)
- Th Voigtmann
- University of Edinburgh, School of Physics, JCMB The Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland
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17
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Mannella R. Quasisymplectic integrators for stochastic differential equations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:041107. [PMID: 15169008 DOI: 10.1103/physreve.69.041107] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2003] [Indexed: 05/24/2023]
Abstract
Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits and reproduce the equilibrium distributions to some higher order in the integration time step. Comparisons with other existing integration schemes are carried out both for static and dynamical quantities.
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Affiliation(s)
- R Mannella
- Dipartimento di Fisica and INFM, UdR Pisa, Università degli Studi di Pisa, Via Buonarroti 2, 56100 Pisa, Italy
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18
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Sergi A. Generalized bracket formulation of constrained dynamics in phase space. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:021109. [PMID: 14995429 DOI: 10.1103/physreve.69.021109] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2003] [Indexed: 05/24/2023]
Abstract
A generalized bracket formalism is used to define the phase space flow of constrained systems. The generalized bracket naturally subsumes the approach to constrained dynamics given by Dirac some time ago. The dynamical invariant measure and the linear response of systems subjected to holonomic constraints are explicitly derived. In light of previous results, it is shown that generalized brackets provide a simple and unified view of the statistical mechanics of non-Hamiltonian phase space flows with a conserved energy.
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Affiliation(s)
- Alessandro Sergi
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 3H6.
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19
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Paul W, Smith GD, Yoon DY. Static and Dynamic Properties of a n-C100H202 Melt from Molecular Dynamics Simulations. Macromolecules 1997. [DOI: 10.1021/ma971184d] [Citation(s) in RCA: 137] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- W. Paul
- Institut für Physik, Johannes−Gutenberg Universität, 55099 Mainz
| | - Grant D. Smith
- Department of Materials Science and Engineering and Department of Chemical and Fuels Engineering University of Utah, Salt Lake City, Utah 84112
| | - Do Y. Yoon
- IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, California 95120-6099
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