1
|
Douglass I, Mayger H, Hudson T, Harrowell P. The stabilization of tubular crystals in mixtures of spherical particles. SOFT MATTER 2017; 13:1344-1351. [PMID: 28106204 DOI: 10.1039/c6sm02636b] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Novel crystal structures in binary atomic mixtures arise when the attractive well is wide enough to allow double occupancy by small particles. The resulting crystals consist of ordered packings of self assembled linear structures comprised of a cylindrical tube of large particles enclosing a close packed core of small particles that corresponds to a stacking of overlapping icosahedra. We show that the stability of these structures depends on two essential features of the spherically symmetric pairwise interactions: (i) a radius ratio between 0.414 and 0.588, and (ii) a width w of the attractive well in the interaction between unlike particles that satisfies w > σSS where σSS is the diameter of the small particle.
Collapse
Affiliation(s)
- Ian Douglass
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia.
| | - Helen Mayger
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia.
| | - Toby Hudson
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia.
| | - Peter Harrowell
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia.
| |
Collapse
|
2
|
Wang Y, Latypov RF, Lomakin A, Meyer JA, Kerwin BA, Vunnum S, Benedek GB. Quantitative evaluation of colloidal stability of antibody solutions using PEG-induced liquid-liquid phase separation. Mol Pharm 2014; 11:1391-402. [PMID: 24679215 DOI: 10.1021/mp400521b] [Citation(s) in RCA: 54] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
Colloidal stability of antibody solutions, i.e., the propensity of the folded protein to precipitate, is an important consideration in formulation development of therapeutic monoclonal antibodies. In a protein solution, different pathways including crystallization, colloidal aggregation, and liquid-liquid phase separation (LLPS) can lead to the formation of precipitates. The kinetics of crystallization and aggregation are often slow and vary from protein to protein. Due to the diverse mechanisms of these protein condensation processes, it is a challenge to develop a standardized test for an early evaluation of the colloidal stability of antibody solutions. LLPS would normally occur in antibody solutions at sufficiently low temperature, provided that it is not preempted by freezing of the solution. Poly(ethylene glycol) (PEG) can be used to induce LLPS at temperatures above the freezing point. Here, we propose a colloidal stability test based on inducing LLPS in antibody solutions and measuring the antibody concentration of the dilute phase. We demonstrate experimentally that such a PEG-induced LLPS test can be used to compare colloidal stability of different antibodies in different solution conditions and can be readily applied to high-throughput screening. We have derived an equation for the effects of PEG concentration and molecular weight on the results of the LLPS test. Finally, this equation defines a binding energy in the condensed phase, which can be determined in the PEG-induced LLPS test. This binding energy is a measure of attractive interactions between antibody molecules and can be used for quantitative characterization of the colloidal stability of antibody solutions.
Collapse
Affiliation(s)
- Ying Wang
- Materials Processing Center, ∥Department of Physics, and ⊥Center for Materials Science and Engineering, Massachusetts Institute of Technology , 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | | | | | | | | | | | | |
Collapse
|
3
|
Shin H, Schweizer KS. Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres. J Chem Phys 2013; 138:084510. [DOI: 10.1063/1.4792440] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
4
|
Neuhaus T, Likos CN. Phonon dispersions of cluster crystals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:234112. [PMID: 21613703 DOI: 10.1088/0953-8984/23/23/234112] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We analyze the ground states and the elementary collective excitations (phonons) of a class of systems, which form cluster crystals in the absence of attractions. Whereas the regime of moderate-to-high temperatures in the phase diagram has been analyzed in detail by means of density functional considerations (Likos et al 2007 J. Chem. Phys. 126 224502), the present approach focuses on the complementary regime of low temperatures. We establish the existence of an infinite cascade of isostructural transitions between crystals with different lattice site occupancies at T = 0 and we quantitatively demonstrate that the thermodynamic instabilities are bracketed by mechanical instabilities arising from long-wavelength acoustical phonons. We further show that all optical modes are degenerate and flat, giving rise to almost perfect realizations of Einstein crystals. We calculate analytically the complete phonon spectrum for the whole class of models as well as the Helmholtz free energy of the systems. On the basis of the latter, we demonstrate that the aforementioned isostructural phase transitions must terminate at an infinity of critical points at low temperatures, brought about by the anharmonic contributions in the Hamiltonian and the hopping events in the crystals.
Collapse
Affiliation(s)
- Tim Neuhaus
- Institute of Theoretical Physics, Heinrich Heine University of Düssedorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | | |
Collapse
|
5
|
Vogel T, Bachmann M, Janke W. Freezing and collapse of flexible polymers on regular lattices in three dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:061803. [PMID: 18233861 DOI: 10.1103/physreve.76.061803] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2007] [Indexed: 05/25/2023]
Abstract
We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple-cubic and face-centered-cubic lattices by means of sophisticated chain-growth methods. In contrast to the bond-fluctuation polymer model in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here.
Collapse
Affiliation(s)
- Thomas Vogel
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany.
| | | | | |
Collapse
|
6
|
Greenall MJ, Voigtmann T. Glass transition in fullerenes: Mode-coupling theory predictions. J Chem Phys 2006; 125:194511. [PMID: 17129127 DOI: 10.1063/1.2390705] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report idealized mode-coupling theory results for the glass transition of ensembles of model fullerenes interacting via phenomenological two-body potentials. Transition lines are found for C60, C70, and C96 in the temperature-density plane. We argue that the observed glass transition behavior is indicative of kinetic arrest that is strongly driven by the interparticle attraction in addition to excluded-volume repulsion. In this respect, these systems differ from most standard glass-forming liquids. They feature arrest that occurs at lower densities and that is stronger than would be expected for repulsion-dominated hard-sphere-like or Lennard-Jones-type systems. The influence of attraction increases with increasing the number of carbon atoms per molecule. However, unrealistically large fullerenes would be needed to yield behavior reminiscent of recently investigated model colloids with strong short-ranged attraction (glass-glass transitions and logarithmic decay of time-correlation functions).
Collapse
Affiliation(s)
- M J Greenall
- SUPA, School of Physics, The University of Edinburgh, JCMB, The King's Buildings, Edinburgh EH9 3JZ, United Kingdom.
| | | |
Collapse
|
7
|
Serrano-Illán J, Navascués G, Velasco E. Noncompact crystalline solids in the square-well potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:011110. [PMID: 16486125 DOI: 10.1103/physreve.73.011110] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2005] [Revised: 08/25/2005] [Indexed: 05/06/2023]
Abstract
We reexamine the phase diagram of the square-well potential, using both theoretical and computer-simulation techniques, for not too short ranges of the potential. The phase diagram turns out to contain a variety of crystalline structures, both compact and, interestingly, also noncompact. The latter result from a large increase in negative energy when pairs of particles come at distances within the interaction range, which more than compensates the entropy loss associated with reduced packing. Transitions between these crystalline structures give rise to a surprisingly rich phase diagram.
Collapse
Affiliation(s)
- Juan Serrano-Illán
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | | | | |
Collapse
|
8
|
Schöll-Paschinger E, Benavides AL, Castañeda-Priego R. Vapor-liquid equilibrium and critical behavior of the square-well fluid of variable range: A theoretical study. J Chem Phys 2005; 123:234513. [PMID: 16392937 DOI: 10.1063/1.2137713] [Citation(s) in RCA: 85] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The vapor-liquid phase behavior and the critical behavior of the square-well (SW) fluid are investigated as a function of the interaction range, lambdain [1.25, 3], by means of the self-consistent Ornstein-Zernike approximation (SCOZA) and analytical equations of state based on a perturbation theory [A. L. Benavides and F. del Rio, Mol. Phys. 68, 983 (1989); A. Gil-Villegas, F. del Rio, and A. L. Benavides, Fluid Phase Equilib. 119, 97 (1996)]. For this purpose the SCOZA, which has been restricted up to now to a few model systems, has been generalized to hard-core systems with arbitrary interaction potentials requiring a fully numerical solution of an integro-partial differential equation. Both approaches, in general, describe well the liquid-vapor phase diagram of the square-well fluid when compared with simulation data. SCOZA yields very precise predictions for the coexistence curves in the case of long ranged SW interaction (lambda>1.5), and the perturbation theory is able to predict the binodal curves and the saturated pressures, for all interaction ranges considered if one stays away from the critical region. In all cases, the SCOZA gives very good predictions for the critical temperatures and the critical pressures, while the perturbation theory approach tends to slightly overestimate these quantities. Furthermore, we propose analytical expressions for the critical temperatures and pressures as a function of the square-well range.
Collapse
|
9
|
Liu H, Garde S, Kumar S. Direct determination of phase behavior of square-well fluids. J Chem Phys 2005; 123:174505. [PMID: 16375544 DOI: 10.1063/1.2085051] [Citation(s) in RCA: 89] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have combined Gibbs ensemble Monte Carlo simulations with the aggregation volume-biased method in conjunction with the Gibbs-Duhem method to provide the first direct estimates for the vapor-solid, vapor-liquid, and liquid-solid phase coexistences of square-well fluids with three different ranges of attraction. Our results are consistent with the previous simulations and verify the notion that the vapor-liquid coexistence behavior becomes metastable for cases where the attraction well becomes smaller than 1.25 times the particle diameter. In these cases no triple point is found.
Collapse
Affiliation(s)
- Hongjun Liu
- Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
| | | | | |
Collapse
|
10
|
Abstract
Various Monte Carlo techniques are used to determine the complete phase diagrams of the square-well model for the attractive ranges lambda = 1.15 and lambda = 1.25. The results for the latter case are in agreement with earlier Monte Carlo simulations for the fluid-fluid coexistence curve and yield new results for the liquidus-solidus lines. Our results for lambda = 1.15 are new. We find that the fluid-fluid critical point is metastable for both cases, with the case lambda = 1.25 being just below the threshold value for metastability. We compare our results with prior studies and with experimental results for the gamma(II)-crystallin.
Collapse
Affiliation(s)
- D L Pagan
- Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015, USA.
| | | |
Collapse
|
11
|
Lomakin A, Asherie N, Benedek GB. Liquid-solid transition in nuclei of protein crystals. Proc Natl Acad Sci U S A 2003; 100:10254-7. [PMID: 12925745 PMCID: PMC193547 DOI: 10.1073/pnas.1334069100] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
It is generally assumed that crystallization begins with a small, crystalline nucleus. For proteins this paradigm may not be valid. Our numerical simulations show that under conditions typically used to produce protein crystals, small clusters of model proteins (particles with short-range, attractive interactions) cannot maintain a crystalline structure. Protein crystal nucleation is therefore an indirect, two-step process. A nucleus first forms and grows as a disordered, liquid-like aggregate. Once the aggregate grows beyond a critical size (about a few hundred particles) crystal nucleation becomes possible.
Collapse
Affiliation(s)
- Aleksey Lomakin
- Department of Physics, Center for Materials Science and Engineering and Material Processing Center, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA
| | | | | |
Collapse
|
12
|
Malherbe JG, Regnaut C, Amokrane S. Attractive forces in sterically stabilized colloidal suspensions: from the effective potential to the phase diagram. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:061404. [PMID: 12513282 DOI: 10.1103/physreve.66.061404] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2002] [Indexed: 05/24/2023]
Abstract
The potential of mean force for macroparticles at infinite dilution is computed for several models of solvent-solvent and solvent-macroparticle interactions by using the reference hypernetted chain (RHNC) integral equations with Rosenfeld's density functional theory bridge functions. The phase diagram of the associated effective fluid is obtained from the RHNC free energy for the fluid branch and the perturbation theory for the solid one. The computation of the effective potential and of the fluid branch is tested by comparison with Monte Carlo simulation. The important modifications with respect to the pure hard spheres that were previously reported are confirmed. The possibility of inverting the relative stability of the fluid-fluid and the fluid-solid transitions by appropriate combination of the interaction parameters is shown. The importance of a fine description of the interactions is illustrated in the example of the role of the range of the solvent-solvent interaction potential.
Collapse
Affiliation(s)
- J G Malherbe
- Groupe de Physique des Milieux Denses, Faculté des Sciences et de Technologie, Université Paris XII-Val de Marne, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France.
| | | | | |
Collapse
|
13
|
Mederos L, Navascués G, Velasco E. Self-consistent nonperturbative theory for classical systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:016131. [PMID: 11800760 DOI: 10.1103/physreve.65.016131] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2001] [Indexed: 05/23/2023]
Abstract
We construct a self-consistent nonperturbative theory for the structure and thermodynamics of a classical system of particles that goes beyond the usual approaches based on perturbation theory. Our theory, which gives accurate predictions for the phase diagram, is based on two ingredients: first, use is made of an exact expression for the free energy of a many-body system in terms of a reference system and a coupling integral connecting the latter to the final system; second, correlation functions may be very accurately approximated using a number of sum rules relating the radial distribution function with thermodynamic quantities. Consistency between the coupling integral expression and the sum rules may be achieved by means of a self-consistent process.
Collapse
Affiliation(s)
- L Mederos
- Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, E-28049 Madrid, Spain
| | | | | |
Collapse
|
14
|
Noro MG, Frenkel D. Extended corresponding-states behavior for particles with variable range attractions. J Chem Phys 2000. [DOI: 10.1063/1.1288684] [Citation(s) in RCA: 367] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
15
|
Serrano-Illán J, Velasco E, Navascués G, Mederos L. Two-body correlations in two-dimensional classical solids and their role in first-order perturbation theories. J Chem Phys 2000. [DOI: 10.1063/1.481510] [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
|
16
|
Clement-Cottuz J, Amokrane S, Regnaut C. Phase diagram of highly asymmetric binary mixtures: A study of the role of attractive forces from the effective one-component approach. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:1692-1702. [PMID: 11046454 DOI: 10.1103/physreve.61.1692] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/1999] [Indexed: 05/23/2023]
Abstract
The phase diagram of an asymmetric solute-solvent mixture is investigated at the level of the effective one-component fluid. The solvent is taken into account by computing the potential of mean force between solute particles at infinite dilution for different models of solvent-solvent and solute-solvent short range interactions. Fluid-fluid and fluid-solid coexistence lines are determined from the free energy in the reference hypernetted chain theory for the fluid branch and from a variational perturbation theory for the solid one. The phase boundaries so determined compare well with recently published Monte Carlo data for mixtures of pure hard spheres. The influence of solute-solvent and solvent-solvent short range attractive forces is then investigated. When compared with pure hard core interactions, these forces are found to produce dramatic changes in the phase diagram, especially on the solvent packing fractions at which a dense fluid of solutes can be stable and on the separation of the fluid-fluid and fluid-solid coexistence lines. Finally, the connection of these results with the behavior of some colloidal suspensions is emphasized.
Collapse
Affiliation(s)
- J Clement-Cottuz
- Groupe de Physique des Milieux Denses, Faculte des Sciences et de Technologie, Universite Paris XII Val de Marne, 61 Avenue du General de Gaulle, 94010, Creteil Cedex, France
| | | | | |
Collapse
|
17
|
Velasco E, Navascués G, Mederos L. Phase behavior of binary hard-sphere mixtures from perturbation theory. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:3158-64. [PMID: 11970123 DOI: 10.1103/physreve.60.3158] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/1999] [Indexed: 04/18/2023]
Abstract
Using a first-order perturbation theory, we have studied the phase diagram of a binary mixture of hard spheres for different values of the size ratio. Recent models for the two-body depletion potential between large spheres are used to take into account the role of the small spheres. The theory predicts a complex phase diagram including a fluid-solid transition at high packing fraction of small spheres, metastability of fluid-fluid demixing, an isostructural solid-solid transition at high packing fraction of the large spheres for sufficiently small values of the size ratio q of the spheres, and the tendency to sticky-sphere behavior in the limit q-->0. The agreement with recent simulation results is quite good. We also show that this phenomenology was already implicit in the pioneering work of Asakura and Oosawa.
Collapse
Affiliation(s)
- E Velasco
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid E-28049, Spain
| | | | | |
Collapse
|
18
|
Abstract
Protein crystallization, aggregation, liquid-liquid phase separation, and self-assembly are important in protein structure determination in the industrial processing of proteins and in the inhibition of protein condensation diseases. To fully describe such phase transformations in globular protein solutions, it is necessary to account for the strong spatial variation of the interactions on the protein surface. One difficulty is that each globular protein has its own unique surface, which is crucial for its biological function. However, the similarities amongst the macroscopic properties of different protein solutions suggest that there may exist a generic model that is capable of describing the nonuniform interactions between globular proteins. In this paper we present such a model, which includes the short-range interactions that vary from place to place on the surface of the protein. We show that this aeolotopic model [from the Greek aiolos ("variable") and topos ("place")] describes the phase diagram of globular proteins and provides insight into protein aggregation and crystallization.
Collapse
Affiliation(s)
- A Lomakin
- Department of Physics, Center for Materials Science and Engineering, and Materials Processing Center, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA
| | | | | |
Collapse
|
19
|
|
20
|
Hasegawa M. Variational perturbation calculations for the phase diagram of systems with short-ranged interactions. J Chem Phys 1998. [DOI: 10.1063/1.475392] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
21
|
Bors̆tnik B, Jesudason CG, Stell G. Anomalous clustering and equation-of-state behavior as the adhesive-disk limit is approached. J Chem Phys 1997. [DOI: 10.1063/1.473865] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
22
|
Rascón C, Velasco E, Mederos L, Navascués G. Phase diagrams of systems of particles interacting via repulsive potentials. J Chem Phys 1997. [DOI: 10.1063/1.473666] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
23
|
Pourgheysar P, Mansoori GA, Modarress H. A single‐theory approach to the prediction of solid–liquid and liquid–vapor phase transitions. J Chem Phys 1996. [DOI: 10.1063/1.472790] [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
|
24
|
Rascón C, Mederos L, Navascués G. Perturbation Theory for Classical Solids. PHYSICAL REVIEW LETTERS 1996; 77:2249-2252. [PMID: 10061896 DOI: 10.1103/physrevlett.77.2249] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
25
|
Rascón C, Mederos L, Navascués G. Equation of state of the hard-sphere crystal. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:5698-5703. [PMID: 9964926 DOI: 10.1103/physreve.53.5698] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
26
|
Rascón C, Mederos L, Navascués G. Solid‐to‐solid isostructural transition in the hard sphere/attractive Yukawa system. J Chem Phys 1995. [DOI: 10.1063/1.469944] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|