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Heyes DM, Dini D, Costigliola L, Dyre JC. Transport coefficients of the Lennard-Jones fluid close to the freezing line. J Chem Phys 2019; 151:204502. [DOI: 10.1063/1.5128707] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- D. M. Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D. Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - L. Costigliola
- “Glass and Time,” IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - J. C. Dyre
- “Glass and Time,” IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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Heyes DM. Translational and rotational diffusion of rod shaped molecules by molecular dynamics simulations. J Chem Phys 2019; 150:184503. [PMID: 31091888 DOI: 10.1063/1.5092958] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The results of molecular dynamics simulations of the dynamical evolution of assemblies of linear rigid rods of variable aspect ratio, a, and number density, ρ, in the isotropic phase are reported. The rods consist of m equally spaced sites interacting with the Weeks-Chandler-Andersen repulsive pair potential, where 2 < m < 16. With increasing m, features specific to long rods, such as anisotropic self-diffusion, become apparent. There is also an increasing separation between the characteristic relaxation times of the torque, angular velocity, and reorientational time correlation functions with increasing density. The latter is exponential at high densities even for dimers. The isotropic translational diffusion coefficient, Di, and rotational diffusion coefficient, Dr, are reported as a function of m and ρ or volume fraction, ξ. The mDi data scale with ξ throughout much of the simulated range, while the rotational diffusion coefficients scale approximately as m3Dr against ρ at low densities but as ∼m6Dr at high ρ, consistent with theories of colloidal and noncolloidal rod-containing liquids. The crossover density between the two regimes is parameterized in analytic form. The probability distribution functions for displacements and angular jumps in a given time show evidence of non-Gaussian behavior with increasing density. The shear viscosity and Di scale approximately as m and m-1, respectively, in the semidilute regime, which is consistent with a Stokes-Einstein-like relationship. At high concentrations, a frustrated or glassy structure formed in which the rods were randomly oriented.
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Affiliation(s)
- D M Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
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Truong PV, Shingleton S, Kammoun M, Black RL, Charendoff M, Willis C, Ardebili H, Stein GE. Structure and Properties of Sulfonated Pentablock Terpolymer Films as a Function of Wet–Dry Cycles. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b00194] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Stacy Shingleton
- Kraton Performance
Polymers, Inc., 16400 Park Row, Houston, Texas 77084, United States
| | | | - Rephayah L. Black
- Department of Chemical and Biomolecular Engineering, The University of Tennessee at Knoxville, Knoxville, Tennessee 37996, United States
| | - Marc Charendoff
- Kraton Performance
Polymers, Inc., 16400 Park Row, Houston, Texas 77084, United States
| | - Carl Willis
- Kraton Performance
Polymers, Inc., 16400 Park Row, Houston, Texas 77084, United States
| | | | - Gila E. Stein
- Department of Chemical and Biomolecular Engineering, The University of Tennessee at Knoxville, Knoxville, Tennessee 37996, United States
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Abstract
The location of the melting line (ML) of the Lennard-Jones (LJ) system and its associated physical properties are investigated using molecular dynamics computer simulation. The radial distribution function and the behavior of the repulsive and attractive parts of the potential energy indicate that the ML is not a single isomorph, but the isomorphic state evolves gradually with temperature, i.e., it is only "locally isomorphic." The state point dependence of the unitless isomorphic number, X̃, for a range of static and dynamical properties of the LJ system in the solid and fluid states, and for fluid argon, are also reported. The quantity X̃ typically varies most with state point in the vicinity of the triple point and approaches a plateau in the high density (temperature) limit along the ML.
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Affiliation(s)
- D M Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - A C Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
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Heyes DM, Turner P, English RJ, Williams R, Brańka AC. Second virial coefficient of rod-shaped molecules and molecular dynamics simulations of the isotropic phase. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042134. [PMID: 25974465 DOI: 10.1103/physreve.91.042134] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2015] [Indexed: 06/04/2023]
Abstract
The second virial coefficient, B(2) is computed of linear rigid rods composed of m equally spaced sites interacting with sites on other rods via the hard-sphere or Weeks-Chandler-Andersen (WCA) pair potentials. The dependence of B(2) on a wide range of separation distance between the sites L and m for both types of potential is computed. Molecular dynamics simulations were carried out of the thermodynamic, static, and percolation properties of the WCA rigid rods in the isotropic phase as a function of rod number density ρ. Simple scaling relationships are discovered between thermodynamic and other static properties as a function of ρ and m, which extend well into the semidilute density range. The percolation threshold distance (PTD) between the centers of mass of the rods complies well with a mean-field random orientation approximation from low density well into the semidilute regime. The corresponding site-site PTD proved more problematic to represent by simple functions, but at high rod density, scales better with the number of sites density rather than the rod number density.
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Affiliation(s)
- D M Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 OEX, United Kingdom
| | - P Turner
- School of Engineering & the Built Environment, Edinburgh Napier University, Merchiston Campus, 10 Colinton Road, Edinburgh EH10 5DT, United Kingdom
| | - R J English
- School of Engineering & the Built Environment, Edinburgh Napier University, Merchiston Campus, 10 Colinton Road, Edinburgh EH10 5DT, United Kingdom
| | - R Williams
- School of Engineering & the Built Environment, Edinburgh Napier University, Merchiston Campus, 10 Colinton Road, Edinburgh EH10 5DT, United Kingdom
| | - A C Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
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Zhang CY, Jian XL, Lu W. Structure and percolation of one-patch spherocylinders. SOFT MATTER 2015; 11:1362-1368. [PMID: 25575168 DOI: 10.1039/c4sm02402h] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
When the volume fraction exceeds the threshold, the colloidal particles would form a spanning cluster to realize percolation, which is affected by the shape of the particles, interaction between particles, etc. In this paper, we use the Monte Carlo method to study the structure and percolation of a system of one-patch spherocylinders which have been fabricated recently [Chaudhary et al., J. Am. Chem. Soc., 2012, 134, 12901]. With strong adsorption, one-patch spherocylinders self-assemble into multipods which further make contact with each other to form a percolation network at a high volume fraction, while the percolation network is inhibited by the local structures in a system of one-patch spheres. The main multipods are dipods when the patch angle equals π/3, while they are tetrapods and pentapods when the patch angle equals 2π/3. With enhancing the adsorption, the bigger the patch angle, the more the percolation threshold drops. The orientational order parameter, the distribution of the relative orientation between the nearest neighbors and the probabilities of a spherocylinder owning n adsorbing neighbors have been calculated to analyze the formation and transition of the structures.
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Affiliation(s)
- Cheng-Yu Zhang
- College of Engineering, Nanjing Agricultural University, Nanjing 210031, China.
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Finney JL, Woodcock LV. Renaissance of Bernal's random close packing and hypercritical line in the theory of liquids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:463102. [PMID: 25335484 DOI: 10.1088/0953-8984/26/46/463102] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We review the scientific history of random close packing (RCP) of equal spheres, advocated by J D Bernal as a more plausible alternative to the non-ideal gas or imperfect crystal as a structural model of simple liquids. After decades of neglect, computer experiments are revealing a central role for RCP in the theory of liquids. These demonstrate that the RCP amorphous state of hard spheres can be well defined, is reproducible, and has the thermodynamic status of a metastable ground state. Further evidence from simulations of square-well model liquids indicates an extended role of RCP as an amorphous ground state that terminates a supercooled liquid coexistence line, suggesting likewise for real liquids. A phase diagram involving percolation boundaries has been proposed in which there is no merging of liquid and gas phases, and no critical singularity as assumed by van der Waals. Rather, the liquid phase continuously spans all temperatures, but above a critical dividing line on the Gibbs density surface, it is bounded by a percolation transition and separated from the gas phase by a colloidal supercritical mesophase. The colloidal-like inversion in the mesophase as it changes from gas-in-liquid to liquid-in-gas can be identified with the hypercritical line of Bernal. We therefore argue that the statistical theory of simple liquids should start from the RCP reference state rather than the ideal gas. Future experimental priorities are to (i) find evidence for an amorphous ground state in real supercooled liquids, (ii) explore the microscopic structures of the supercritical mesophase, and (iii) determine how these change from gas to liquid, especially across Bernal's hypercritical line. The theoretical priority is a statistical geometrical theory of RCP. Only then might we explain the coincident values of the RCP packing fraction with Buffon's constant, and the RCP residual entropy with Boltzmann's ideal gas constant.
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Affiliation(s)
- John L Finney
- Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, UK
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Godfrin PD, Castañeda-Priego R, Liu Y, Wagner NJ. Intermediate range order and structure in colloidal dispersions with competing interactions. J Chem Phys 2013; 139:154904. [DOI: 10.1063/1.4824487] [Citation(s) in RCA: 63] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Woodcock LV. Fluid phases of argon: A debate on the absence of van der Waals’ “critical point”. ACTA ACUST UNITED AC 2013. [DOI: 10.4236/ns.2013.52030] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Rickayzen G, Brańka AC, Pieprzyk S, Heyes DM. Single particle force distributions in simple fluids. J Chem Phys 2012; 137:094505. [PMID: 22957579 DOI: 10.1063/1.4748103] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The distribution function, W(F), of the magnitude of the net force, F, on particles in simple fluids is considered, which follows on from our previous publication [A. C. Brańka, D. M. Heyes, and G. Rickayzen, J. Chem. Phys. 135, 164507 (2011)] concerning the pair force, f, distribution function, P(f), which is expressible in terms of the radial distribution function. We begin by discussing the force on an impurity particle in an otherwise pure fluid but later specialize to the pure fluid, which is studied in more detail. An approximate formula, expected to be valid asymptotically, for W(F) referred to as, W(1)(F) is derived by taking into account only binary spatial correlations in the fluid. It is found that W(1)(F) = P(f). Molecular dynamics simulations of W for the inverse power (IP) and Lennard-Jones potential fluids show that, as expected, W(F) and P(f) agree well in the large force limit for a wide range of densities and potential forms. The force at which the maximum in W(F) occurs for the IP fluids follows a different algebraic dependence with density in low and high density domains of the equilibrium fluid. Other characteristic features in the force distribution functions also exhibit the same trends. An exact formula is derived relating W(F) to P(x)(F(x)), the distribution function of the x-cartesian components of the net force, F(x), on a particle. W(F) and P(x)(F(x)) have the same analytical forms (apart from constants) in the low and high force limits.
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Affiliation(s)
- G Rickayzen
- School of Physical Sciences, University of Kent, Canterbury, Kent CT2 7NH, United Kingdom.
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Affiliation(s)
- Leslie V. Woodcock
- Manchester Interdisciplinary Biocentre, University of Manchester, Manchester M1 7DN, United Kingdom
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Nigro B, Grimaldi C, Ryser P. Tunneling and percolation transport regimes in segregated composites. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011137. [PMID: 22400542 DOI: 10.1103/physreve.85.011137] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2011] [Revised: 12/20/2011] [Indexed: 05/31/2023]
Abstract
We consider the problem of electron transport in segregated conductor-insulator composites in which the conducting particles are connected to all others via tunneling conductances, thus forming a global tunneling-connected resistor network. Segregation is induced by the presence of large insulating particles, which forbid the much smaller conducting fillers from occupying uniformly the three-dimensional volume of the composite. By considering both colloidal-like and granular-like dispersions of the conducting phase, modeled respectively by dispersions in the continuum and in the lattice, we evaluate by Monte Carlo simulations the effect of segregation on the composite conductivity σ, and show that an effective-medium theory applied to the tunneling network reproduces accurately the Monte Carlo results. The theory clarifies that the main effect of segregation in the continuum is that of reducing the mean interparticle distances, leading to a strong enhancement of the conductivity. In the lattice-segregation case the conductivity enhancement is instead given by the lowering of the percolation thresholds for first and beyond-first nearest neighbors. Our results generalize to segregated composites the tunneling-based description of both the percolation and hopping regimes introduced previously for homogeneous disordered systems.
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Affiliation(s)
- B Nigro
- LPM, Ecole Polytechnique Fédérale de Lausanne, Station 17, CP-1015 Lausanne, Switzerland.
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Johner N, Grimaldi C, Maeder T, Ryser P. Optimal percolation of disordered segregated composites. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:020104. [PMID: 19391696 DOI: 10.1103/physreve.79.020104] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2008] [Revised: 12/19/2008] [Indexed: 05/27/2023]
Abstract
We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modeled by hardcore spherical particles surrounded by penetrable shells, to occupy large regions inside the composite. We find that the percolation threshold is generally a nonmonotonous function of segregation, and that an optimal (i.e., minimum) critical concentration exists well before maximum segregation is reached. We interpret this feature as originating from a competition between reduced available volume effects and enhanced concentrations needed to ensure percolation in the highly segregated regime. The relevance with existing segregated materials is discussed.
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Affiliation(s)
- Niklaus Johner
- LPM, Ecole Polytechnique Fédérale de Lausanne, Station 17, CH-1015 Lausanne, Switzerland.
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Ambrosetti G, Johner N, Grimaldi C, Danani A, Ryser P. Percolative properties of hard oblate ellipsoids of revolution with a soft shell. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:061126. [PMID: 19256821 DOI: 10.1103/physreve.78.061126] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2008] [Revised: 07/31/2008] [Indexed: 05/27/2023]
Abstract
We present an in-depth analysis of the geometrical percolation behavior in the continuum of random assemblies of hard oblate ellipsoids of revolution. Simulations were carried out by considering a broad range of aspect ratios, from spheres up to aspect-ratio-100 platelike objects, and with various limiting two-particle interaction distances, from 0.05 times the major axis up to 4.0 times the major axis. We confirm the widely reported trend of a consistent lowering of the hard particle critical volume fraction with increase of the aspect ratio. Moreover, by assimilating the limiting interaction distance to a shell of constant thickness surrounding the ellipsoids, we propose a simple relation based on the total excluded volume of these objects which allows us to estimate the critical concentration from a quantity that is quasi-invariant over a large spectrum of limiting interaction distances. Excluded volume and volume quantities are derived explicitly.
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Affiliation(s)
- Gianluca Ambrosetti
- LPM, Ecole Polytechnique Fédérale de Lausanne, Station 17, CH-1015 Lausanne, Switzerland.
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