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Ahmadi S, Schmidt M, Spiteri RJ, Bowles RK. The effect of soft repulsive interactions on the diffusion of particles in quasi-one-dimensional channels: A hopping time approach. J Chem Phys 2019; 150:224501. [PMID: 31202224 DOI: 10.1063/1.5100544] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
Fluids confined to quasi-one-dimensional channels exhibit a dynamic crossover from single file diffusion to normal diffusion as the channel becomes wide enough for particles to hop past each other. In the crossover regime, where hopping events are rare, the diffusion coefficient in the long time limit can be related to a hopping time that measures the average time it takes for a particle to escape the local cage formed by its neighbors. In this work, we show that a transition state theory (TST) that calculates the free energy barrier for two particles attempting to pass each other in the small system isobaric ensemble is able to quantitatively predict the hopping time in a system of two-dimensional soft repulsive disks [U(rij)=(σ/rij)α] confined to a hard walled channel over a range of channel radii and degrees of particle softness measured in terms of 1/α. The free energy barrier exhibits a maximum at intermediate values of α that moves to smaller values of 1/α (harder particles) as the channel becomes narrower. However, the presence of the maximum is only observed in the hopping times for wide channels because the interaction potential dependence of the kinetic prefactor plays an increasingly important role for narrower channels. We also begin to explore how our TST approach can be used to optimize and control dynamics in confined quasi-one-dimensional fluids.
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Affiliation(s)
- Sheida Ahmadi
- Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada
| | - Marina Schmidt
- Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada
| | - Raymond J Spiteri
- Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada
| | - Richard K Bowles
- Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada
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Ooshida T, Otsuki M. Two-tag correlations and nonequilibrium fluctuation-response relation in ageing single-file diffusion. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:374001. [PMID: 30027890 DOI: 10.1088/1361-648x/aad4cc] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Spatiotemporally correlated motions of interacting Brownian particles, confined in a narrow channel of infinite length, are studied in terms of statistical quantities involving two particles. A theoretical framework that allows analytical calculation of two-tag correlations is presented on the basis of the Dean-Kawasaki equation describing density fluctuations in colloidal systems. In the equilibrium case, the time-dependent Einstein relation holds between the two-tag displacement correlation and the response function corresponding to it, which is a manifestation of the fluctuation-dissipation theorem for the correlation of density fluctuations. While the standard procedure of closure approximation for nonlinear density fluctuations is known to be obstructed by inconsistency with the fluctuation-dissipation theorem, this difficulty is naturally avoided by switching from the standard Fourier representation of the density field to the label-based Fourier representation of the vacancy field. In the case of ageing dynamics started from equidistant lattice configuration, the time-dependent Einstein relation is violated, as the two-tag correlation depends on the waiting time for equilibration while the response function is not sensitive to it. Within linear approximation, however, there is a simple relation between the density (or vacancy) fluctuations and the corresponding response function, which is valid even if the system is out of equilibrium. This non-equilibrium fluctuation-response relation can be extended to the case of nonlinear fluctuations by means of closure approximation for the vacancy field.
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Affiliation(s)
- Takeshi Ooshida
- Department of Mechanical and Physical Engineering, Tottori University, Tottori 680-8552, Japan
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Ooshida T, Goto S, Otsuki M. Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking. ENTROPY 2018; 20:e20080565. [PMID: 33265659 PMCID: PMC7513090 DOI: 10.3390/e20080565] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/07/2018] [Revised: 07/16/2018] [Accepted: 07/16/2018] [Indexed: 11/16/2022]
Abstract
Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as the particles are constantly pushed back by their neighbors. Since this “cage effect” emerges from many-body dynamics involving spatiotemporally correlated motions, the slow diffusion should be understood not simply as a one-body problem but as a part of collective dynamics, described in terms of space–time correlations. Such collective dynamics are illustrated here by calculations of the two-particle displacement correlation in a system of repulsive Brownian particles confined in a (quasi-)one-dimensional channel, whose subdiffusive behavior is known as the single-file diffusion (SFD). The analytical calculation is formulated in terms of the Lagrangian correlation of density fluctuations. In addition, numerical solutions to the Langevin equation with large but finite interaction potential are studied to clarify the effect of overtaking. In the limiting case of the ideal SFD without overtaking, correlated motion with a diffusively growing length scale is observed. By allowing the particles to overtake each other, the short-range correlation is destroyed, but the long-range weak correlation remains almost intact. These results describe nested space–time structure of cages, whereby smaller cages are enclosed in larger cages with longer lifetimes.
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Affiliation(s)
- Takeshi Ooshida
- Department of Mechanical and Physical Engineering, Tottori University, Tottori 680-8552, Japan
- Correspondence:
| | - Susumu Goto
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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Ahmadi S, Bowles RK. Diffusion in quasi-one-dimensional channels: A small system n, p, T, transition state theory for hopping times. J Chem Phys 2017; 146:154505. [PMID: 28433039 DOI: 10.1063/1.4981010] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Particles confined to a single file, in a narrow quasi-one-dimensional channel, exhibit a dynamic crossover from single file diffusion to Fickian diffusion as the channel radius increases and the particles begin to pass each other. The long time diffusion coefficient for a system in the crossover regime can be described in terms of a hopping time, which measures the time it takes for a particle to escape the cage formed by its neighbours. In this paper, we develop a transition state theory approach to the calculation of the hopping time, using the small system isobaric-isothermal ensemble to rigorously account for the volume fluctuations associated with the size of the cage. We also describe a Monte Carlo simulation scheme that can be used to calculate the free energy barrier for particle hopping. The theory and simulation method correctly predict the hopping times for a two-dimensional confined ideal gas system and a system of confined hard discs over a range of channel radii, but the method breaks down for wide channels in the hard discs' case, underestimating the height of the hopping barrier due to the neglect of interactions between the small system and its surroundings.
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Affiliation(s)
- Sheida Ahmadi
- Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada
| | - Richard K Bowles
- Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada
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Revuelta F, Bartsch T, Garcia-Muller PL, Hernandez R, Benito RM, Borondo F. Transition state theory for solvated reactions beyond recrossing-free dividing surfaces. Phys Rev E 2016; 93:062304. [PMID: 27415277 DOI: 10.1103/physreve.93.062304] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2015] [Indexed: 11/07/2022]
Abstract
The accuracy of rate constants calculated using transition state theory depends crucially on the correct identification of a recrossing-free dividing surface. We show here that it is possible to define such optimal dividing surface in systems with non-Markovian friction. However, a more direct approach to rate calculation is based on invariant manifolds and avoids the use of a dividing surface altogether, Using that method we obtain an explicit expression for the rate of crossing an anharmonic potential barrier. The excellent performance of our method is illustrated with an application to a realistic model for LiNC⇌LiCN isomerization.
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Affiliation(s)
- F Revuelta
- Grupo de Sistemas Complejos, Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, Universidad Politécnica de Madrid, Avda. Complutense s/n 28040 Madrid, Spain.,Instituto de Ciencias Matemáticas (ICMAT), Cantoblanco, 28049 Madrid, Spain
| | - Thomas Bartsch
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - P L Garcia-Muller
- Centro de Investigaciones Energéticas Medioambientales y Tecnológicas, Avda. Complutense 40, 28040 Madrid, Spain
| | - Rigoberto Hernandez
- Center for Computational Molecular Sciences and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
| | - R M Benito
- Grupo de Sistemas Complejos, Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, Universidad Politécnica de Madrid, Avda. Complutense s/n 28040 Madrid, Spain
| | - F Borondo
- Instituto de Ciencias Matemáticas (ICMAT), Cantoblanco, 28049 Madrid, Spain.,Departamento de Química, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
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Ooshida T, Goto S, Matsumoto T, Otsuki M. Insights from Single-File Diffusion into Cooperativity in Higher Dimensions. ACTA ACUST UNITED AC 2016. [DOI: 10.1142/s1793048015400019] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Diffusion in colloidal suspensions can be very slow due to the cage effect, which confines each particle within a short radius on one hand, and involves large-scale cooperative motions on the other. In search of insight into this cooperativity, here the authors develop a formalism to calculate the displacement correlation in colloidal systems, mainly in the two-dimensional (2D) case. To clarify the idea for it, studies are reviewed on cooperativity among the particles in the one-dimensional (1D) case, i.e. the single-file diffusion (SFD). As an improvement over the celebrated formula by Alexander and Pincus on the mean-square displacement (MSD) in SFD, it is shown that the displacement correlation in SFD can be calculated from Lagrangian correlation of the particle interval in the one-dimensional case, and also that the formula can be extended to higher dimensions. The improved formula becomes exact for large systems. By combining the formula with a nonlinear theory for correlation, a correction to the asymptotic law for the MSD in SFD is obtained. In the 2D case, the linear theory gives description of vortical cooperative motion.
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Affiliation(s)
- Takeshi Ooshida
- Department of Mechanical and Aerospace Engineering, Tottori University, Tottori 680-8552, Japan
| | - Susumu Goto
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Takeshi Matsumoto
- Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Michio Otsuki
- Department of Materials Science, Shimane University, Matsue 690-8504, Japan
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Cuetos A, Patti A. Equivalence of Brownian dynamics and dynamic Monte Carlo simulations in multicomponent colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022302. [PMID: 26382401 DOI: 10.1103/physreve.92.022302] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2015] [Indexed: 06/05/2023]
Abstract
We propose a simple but powerful theoretical framework to quantitatively compare Brownian dynamics (BD) and dynamic Monte Carlo (DMC) simulations of multicomponent colloidal suspensions. By extending our previous study focusing on monodisperse systems of rodlike colloids, here we generalize the formalism described there to multicomponent colloidal mixtures and validate it by investigating the dynamics in isotropic and liquid crystalline phases containing spherical and rodlike particles. In order to investigate the dynamics of multicomponent colloidal systems by DMC simulations, it is key to determine the elementary time step of each species and establish a unique timescale. This is crucial to consistently study the dynamics of colloidal particles with different geometry. By analyzing the mean-square displacement, the orientation autocorrelation functions, and the self part of the van Hove correlation functions, we show that DMC simulation is a very convenient and reliable technique to describe the stochastic dynamics of any multicomponent colloidal system. Our theoretical formalism can be easily extended to any colloidal system containing size and/or shape polydisperse particles.
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Affiliation(s)
- Alejandro Cuetos
- Department of Physical, Chemical and Natural Systems, Universidad Pablo Olavide, 41013 Sevilla, Spain
| | - Alessandro Patti
- School of Chemical Engineering and Analytical Science, The University of Manchester, Sackville Street, Manchester M13 9PL, United Kingdom
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Horsch M, Hasse H. Molecular Modeling and Simulation in Fluid Process Engineering. CHEMBIOENG REVIEWS 2015. [DOI: 10.1002/cben.201500010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Dutta AR, Sekar P, Dvoyashkin M, Bowers CR, Ziegler KJ, Vasenkov S. Relationship between single-file diffusion of mixed and pure gases in dipeptide nanochannels by high field diffusion NMR. Chem Commun (Camb) 2015; 51:13346-9. [DOI: 10.1039/c5cc04960a] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Under single-file confinement, the relationship between diffusion rates of mixed and pure gases is studied experimentally for the first time and observed to differ from that for normal diffusion.
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Affiliation(s)
- Akshita R. Dutta
- Department of Chemical Engineering
- University of Florida
- Gainesville
- USA
| | - Poorvajan Sekar
- Department of Chemical Engineering
- University of Florida
- Gainesville
- USA
| | | | | | - Kirk J. Ziegler
- Department of Chemical Engineering
- University of Florida
- Gainesville
- USA
| | - Sergey Vasenkov
- Department of Chemical Engineering
- University of Florida
- Gainesville
- USA
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Horsch M, Hasse H. Molekulare Modellierung und Simulation in der Fluidverfahrenstechnik. CHEM-ING-TECH 2014. [DOI: 10.1002/cite.201400036] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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