1
|
Bond JE, Yeh AJ, Edison JR, Bevan MA. Diffusion, density, and defects on spheres. SOFT MATTER 2024; 20:6371-6383. [PMID: 39081122 DOI: 10.1039/d4sm00746h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/15/2024]
Abstract
We simulate and model diffusion of spherical colloids of radius, a, on spherical surfaces of radius, R, as a function of relative size and surface concentration. Using Brownian dynamics simulations, we quantify diffusion and microstructure at different concentrations ranging from single particles to dense crystalline states. Self-diffusion and structural metrics (pair distribution, local density, and topological charge) are indistinguishable between spheres and planes for all concentrations up to dense liquid states. For concentrations approaching and greater than the freezing transition, smaller spheres with higher curvature show increased diffusivities and nonuniform density/topological defect distributions, which differ qualitatively from planar surfaces. The total topological charge varies quadratically with sphere radius for dense liquid states and linearly with sphere radius for dense crystals with icosahedrally organized grain scars. Between the dense liquid and dense crystal states on spherical surfaces is a regime of fluctuating and interacting defect clusters. We show local density governs self-diffusion in dense liquids on flat and spherical surfaces via the pair distribution. In contrast, dynamic topological defects couple to finite diffusivities through freezing and in low density crystal states on spherical surfaces, where neither exist on flat surfaces.
Collapse
Affiliation(s)
- John E Bond
- Chemical & Biomolecular Engr., Johns Hopkins Univ, Baltimore, MD 21218, USA.
| | - Alex J Yeh
- Chemical & Biomolecular Engr., Johns Hopkins Univ, Baltimore, MD 21218, USA.
| | - John R Edison
- Chemical & Biomolecular Engr., Johns Hopkins Univ, Baltimore, MD 21218, USA.
| | - Michael A Bevan
- Chemical & Biomolecular Engr., Johns Hopkins Univ, Baltimore, MD 21218, USA.
| |
Collapse
|
2
|
King DA. Dynamics of wire frame glasses in two dimensions. J Chem Phys 2023; 159:094903. [PMID: 37668250 DOI: 10.1063/5.0164438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 08/11/2023] [Indexed: 09/06/2023] Open
Abstract
The dynamics of wire frame particles in concentrated suspension are studied by means of a 2D model and compared to those of rod-like particles. The wire frames have bent or branched structures constructed from infinitely thin, rigid rods. In the model, a particle is surrounded by diffusing points that it cannot cross. We derive a formal expression for the mean squared displacement (MSD) and, by using a self-consistent approximation, we find markedly different dynamics for wire frames and rods. For wire frames, there exists a critical concentration of points above which they become frozen with the long time MSD reaching a plateau. Rods, on the other hand, always diffuse by reptation. We also study the rheology through the elastic stress, and more striking differences are found: the initial magnitude of the stress for wire frames is much larger than for rods, scaling such as the square of the point concentration, and above the critical concentration, the stress for wire frames appears to persist indefinitely while for rods it always decays.
Collapse
Affiliation(s)
- David A King
- Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd St., Philadelphia, Pennsylvania 19104, USA
| |
Collapse
|
3
|
Pihlajamaa I, de Bruijn R, van der Schoot P. Geometric percolation of hard-sphere dispersions in shear flow. SOFT MATTER 2022; 18:4167-4177. [PMID: 35593227 PMCID: PMC9157507 DOI: 10.1039/d2sm00375a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Accepted: 05/16/2022] [Indexed: 06/15/2023]
Abstract
We combine a heuristic theory of geometric percolation and the Smoluchowski theory of colloid dynamics to predict the impact of shear flow on the percolation threshold of hard spherical colloidal particles, and verify our findings by means of molecular dynamics simulations. It appears that the impact of shear flow is subtle and highly non-trivial, even in the absence of hydrodynamic interactions between the particles. The presence of shear flow can both increase and decrease the percolation threshold, depending on the criterion used for determining whether or not two particles are connected and on the Péclet number. Our approach opens up a route to quantitatively predict the percolation threshold in nanocomposite materials that, as a rule, are produced under non-equilibrium conditions, making comparison with equilibrium percolation theory tenuous. Our theory can be adapted straightforwardly for application in other types of flow field, and particles of different shape or interacting via other than hard-core potentials.
Collapse
Affiliation(s)
- Ilian Pihlajamaa
- Group of Soft Matter and Biological Physics, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands.
| | - René de Bruijn
- Group of Soft Matter and Biological Physics, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands.
| | - Paul van der Schoot
- Group of Soft Matter and Biological Physics, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands.
| |
Collapse
|
4
|
Szamel G. An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids. J Chem Phys 2022; 156:191102. [PMID: 35597637 DOI: 10.1063/5.0091385] [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 propose an alternative theory for the relaxation of density fluctuations in glass-forming fluids. We derive an equation of motion for the density correlation function that is local in time and is similar in spirit to the equation of motion for the average non-uniform density profile derived within the dynamic density functional theory. We identify the Franz-Parisi free energy functional as the non-equilibrium free energy for the evolution of the density correlation function. An appearance of a local minimum of this functional leads to a dynamic arrest. Thus, the ergodicity breaking transition predicted by our theory coincides with the dynamic transition of the static approach based on the same non-equilibrium free energy functional.
Collapse
Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| |
Collapse
|
5
|
Szamel G. Dynamics of interacting Brownian particles: A diagrammatic formulation. J Chem Phys 2007; 127:084515. [PMID: 17764277 DOI: 10.1063/1.2759487] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion, we introduce a basis that consists of orthogonalized many-particle density fluctuations. We obtain an exact hierarchy of equations of motion for time-dependent correlations of orthogonalized density fluctuations. To simplify this hierarchy we neglect contributions to the vertices from higher-order cluster expansion terms. An iterative solution of the resulting equations can be represented by diagrams with three- and four-leg vertices. We analyze the structure of the diagrammatic series for the time-dependent density correlation function and obtain a diagrammatic interpretation of reducible and irreducible memory functions. The one-loop self-consistent approximation for the latter function coincides with mode-coupling approximation for Brownian systems that was derived previously using a projection operator approach.
Collapse
Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80525, USA
| |
Collapse
|
6
|
Lionberger RA, Russel WB. Microscopic Theories of the Rheology of Stable Colloidal Dispersions. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141700.ch3] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
|
7
|
Dean DS, Lefèvre A. Self-diffusion in a system of interacting Langevin particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061111. [PMID: 15244544 DOI: 10.1103/physreve.69.061111] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2004] [Indexed: 05/24/2023]
Abstract
The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature beta and the particle density rho. The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small beta and rhobeta constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.
Collapse
Affiliation(s)
- D S Dean
- DAMTP, CMS, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | | |
Collapse
|
8
|
Yeomans-Reyna L, Medina-Noyola M. Self-consistent generalized Langevin equation for colloid dynamics. PHYSICAL REVIEW E 2001; 64:066114. [PMID: 11736243 DOI: 10.1103/physreve.64.066114] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2001] [Indexed: 11/07/2022]
Abstract
We present a general self-consistent theory of colloid dynamics which, for a system without hydrodynamic interactions, allows us to calculate F(k,t), and its self-diffusion counterpart F(S)(k,t), given the effective interaction pair potential u(r) between colloidal particles, and the corresponding equilibrium static structural properties. This theory is build upon the exact results for F(k,t) and F(S)(k,t) in terms of a hierarchy of memory functions, derived from the application of the generalized Langevin equation formalism, plus the proposal of Vineyard-like connections between F(k,t) and F(S)(k,t) through their respective memory functions, and a closure relation between these memory functions and the time-dependent friction function Delta zeta(t). As an illustrative application, we present and analyze a selection of numerical results of this theory in the short- and intermediate-time regimes, as applied to a two-dimensional repulsive Yukawa Brownian fluid. For this system, we find that our theory accurately describes the dynamic properties contained in F(k,t) in a wide range of conditions, including strongly correlated systems, at the longest times available from our computer simulations.
Collapse
Affiliation(s)
- L Yeomans-Reyna
- Instituto de Física Manuel Sandoval Vallarta, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64 78000, San Luis Potosí, SLP, Mexico
| | | |
Collapse
|
9
|
Szamel G. Nonequilibrium structure and rheology of concentrated colloidal suspensions: Linear response. J Chem Phys 2001. [DOI: 10.1063/1.1366335] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
10
|
Yeomans-Reyna L, Medina-Noyola M. Overdamped van hove function of colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:3382-3394. [PMID: 11088839 DOI: 10.1103/physreve.62.3382] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2000] [Indexed: 05/23/2023]
Abstract
The generalized-hydrodynamic theory for collective diffusion of a monodisperse colloidal suspension is developed in the framework of the Onsager-Machlup theory of time-dependent fluctuations. The time evolution of the intermediate scattering function F(k,t) is derived as a contraction of the description involving the instantaneous particle number concentration, the particle current, and the stress tensor of the Brownian fluid as state variables. We show that the proper overdamped limit of this equation requires the explicit separation of the stress tensor in its mutually orthogonal kinetic and configurational contributions. Analogous results also follow for the self-intermediate scattering function F(s)(k,t). We show that neglecting the non-Markovian part of the configurational stress tensor memory, one recovers the single exponential memory approximation (based on sum rules derived from the Smoluchowski equation) for both F(s)(k,t) and F(k,t). We suggest simple approximate manners to relate the collective and the self-memory functions, leading to Vineyard-like approximate relations between F(s)(k,t) and F(k,t).
Collapse
Affiliation(s)
- L Yeomans-Reyna
- Instituto de Fisica "Manuel Sandoval Vallarta," Universidad Autonoma de San Luis Potosi, Alvaro Obregon 64, 78000 San Luis Potosi, SLP, Mexico
| | | |
Collapse
|
11
|
Szamel G. Tagged chain diffusion equation and effective friction tensor in dense polymer solutions. J Chem Phys 1998. [DOI: 10.1063/1.475384] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
12
|
Lionberger RA, Russel WB. Effectiveness of nonequilibrium closures for the many body forces in concentrated colloidal dispersions. J Chem Phys 1997. [DOI: 10.1063/1.473029] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
13
|
Löwen H. Brownian dynamics of hard spherocylinders. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:1232-1242. [PMID: 9962084 DOI: 10.1103/physreve.50.1232] [Citation(s) in RCA: 113] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
14
|
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]
|
15
|
Szamel G, Schweizer KS. Reptation as a dynamic mean‐field theory: Self and tracer diffusion in a simple model of rodlike polymers. J Chem Phys 1994. [DOI: 10.1063/1.466403] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
16
|
Szamel G. Reptation as a dynamic mean-field theory: Study of a simple model of rodlike polymers. PHYSICAL REVIEW LETTERS 1993; 70:3744-3747. [PMID: 10053951 DOI: 10.1103/physrevlett.70.3744] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
17
|
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]
|