Comment on “Percus-Yevick theory for the system of hard spheres with a square-well attraction”

1978 ◽  
Vol 28 (9) ◽  
pp. 1059-1060
Author(s):  
T. Vicsek
Keyword(s):  
Hard Spheres ◽  
Square Well

Percus-Yevick theory for the system of hard spheres with a square-well attraction

1977 ◽  
Vol 27 (3) ◽  
pp. 247-254 ◽  
Author(s):  
I. Nezbeda
Keyword(s):  
Hard Spheres ◽  
Square Well

Perturbation theory for a mixture of hard spheres and square‐well molecules

1974 ◽  
Vol 61 (3) ◽  
pp. 926-931 ◽  
Author(s):  
Douglas Henderson
Keyword(s):  
Perturbation Theory ◽  
Hard Spheres ◽  
Square Well

Monte-Carlo integration for virial coefficients re-visited: hard convex bodies, spheres with a square-well potential and mixtures of hard spheres

2002 ◽  
Vol 100 (20) ◽  
pp. 3313-3324 ◽  
Author(s):  
A. YU. VLASOV ◽  
X.-M. YOU ◽  
A. J. MASTERS
Keyword(s):  
Monte Carlo ◽  
Hard Spheres ◽  
Convex Bodies ◽  
Virial Coefficients ◽  
Monte Carlo Integration ◽  
Square Well

Solvophobic Interaction between Hard Spheres in a Square-Well Fluid

2000 ◽  
Vol 69 (4) ◽  
pp. 1084-1092 ◽  
Author(s):  
Yosuke Yoshimura
Keyword(s):  
Hard Spheres ◽  
Square Well

STICKY SPHERES IN QUANTUM MECHANICS

1994 ◽  
Vol 06 (05a) ◽  
pp. 947-975 ◽  
Author(s):  
M. D. PENROSE ◽  
O. PENROSE ◽  
G. STELL
Keyword(s):  
Quantum Mechanics ◽  
Brownian Motion ◽  
Gaseous Phase ◽  
Virial Coefficient ◽  
Hard Spheres ◽  
Second Virial Coefficient ◽  
Dimensional System ◽  
3 Dimensional ◽  
Fermi Statistics ◽  
Square Well

For a 3-dimensional system of hard spheres of diameter D and mass m with an added attractive square-well two-body interaction of width a and depth ε, let BD, a denote the quantum second virial coefficient. Let BD denote the quantum second virial coefficient for hard spheres of diameter D without the added attractive interaction. We show that in the limit a → 0 at constant α: = ℰma2/(2ħ2) with α < π2/8, [Formula: see text] The result is true equally for Boltzmann, Bose and Fermi statistics. The method of proof uses the mathematics of Brownian motion. For α > π2/8, we argue that the gaseous phase disappears in the limit a → 0, so that the second virial coefficient becomes irrelevant.

scholarly journals Protein aggregation in salt solutions

2015 ◽  
Vol 112 (21) ◽  
pp. 6766-6770 ◽  
Author(s):  
Miha Kastelic ◽  
Yurij V. Kalyuzhnyi ◽  
Barbara Hribar-Lee ◽  
Ken A. Dill ◽  
Vojko Vlachy
Keyword(s):  
Protein Aggregation ◽  
Hard Spheres ◽  
Protein Crystallization ◽  
Virial Coefficients ◽  
Necessary Condition ◽  
Thermodynamic Perturbation Theory ◽  
Salt Solutions ◽  
Biological Drugs ◽  
Second Virial Coefficients ◽  
Square Well

Protein aggregation is broadly important in diseases and in formulations of biological drugs. Here, we develop a theoretical model for reversible protein–protein aggregation in salt solutions. We treat proteins as hard spheres having square-well-energy binding sites, using Wertheim’s thermodynamic perturbation theory. The necessary condition required for such modeling to be realistic is that proteins in solution during the experiment remain in their compact form. Within this limitation our model gives accurate liquid–liquid coexistence curves for lysozyme and γ IIIa-crystallin solutions in respective buffers. It provides good fits to the cloud-point curves of lysozyme in buffer–salt mixtures as a function of the type and concentration of salt. It than predicts full coexistence curves, osmotic compressibilities, and second virial coefficients under such conditions. This treatment may also be relevant to protein crystallization.

scholarly journals Crystal, Fivefold and Glass Formation in Clusters of Polymers Interacting with the Square Well Potential

Polymers ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1111
Author(s):  
Miguel Herranz ◽  
Manuel Santiago ◽  
Katerina Foteinopoulou ◽  
Nikos Ch. Karayiannis ◽  
Manuel Laso
Keyword(s):  
Local Density ◽  
Hard Spheres ◽  
Local Environment ◽  
Crystal Nucleation ◽  
Average Chain Length ◽  
Model Parameters ◽  
Face Centered Cubic ◽  
Polymer Systems ◽  
Hexagonal Close Packed ◽  
Square Well

We present results, from Monte Carlo (MC) simulations, on polymer systems of freely jointed chains with spherical monomers interacting through the square well potential. Starting from athermal packings of chains of tangent hard spheres, we activate the square well potential under constant volume and temperature corresponding effectively to instantaneous quenching. We investigate how the intensity and range of pair-wise interactions affected the final morphologies by fixing polymer characteristics such as average chain length and tolerance in bond gaps. Due to attraction chains are brought closer together and they form clusters with distinct morphologies. A wide variety of structures is obtained as the model parameters are systematically varied: weak interactions lead to purely amorphous clusters followed by well-ordered ones. The latter include the whole spectrum of crystal morphologies: from virtually perfect hexagonal close packed (HCP) and face centered cubic (FCC) crystals, to random hexagonal close packed layers of single stacking direction of alternating HCP and FCC layers, to structures of mixed HCP/FCC character with multiple stacking directions and defects in the form of twins. Once critical values of interaction are met, fivefold-rich glassy clusters are formed. We discuss the similarities and differences between energy-driven crystal nucleation in thermal polymer systems as opposed to entropy-driven phase transition in athermal polymer packings. We further calculate the local density of each site, its dependence on the distance from the center of the cluster and its correlation with the crystallographic characteristics of the local environment. The short- and long-range conformations of chains are analyzed as a function of the established cluster morphologies.

Monte Carlo Equation of State for Hard Spheres in an Attractive Square Well

1965 ◽  
Vol 43 (4) ◽  
pp. 1198-1201 ◽  
Author(s):  
A. Rotenberg
Keyword(s):  
Monte Carlo ◽  
Equation Of State ◽  
Hard Spheres ◽  
Square Well

scholarly journals The influence of bond rigidity and cluster diffusion on the self-diffusion of hard spheres with square well interaction

2008 ◽  
Vol 128 (20) ◽  
pp. 204504 ◽  
Author(s):  
Sujin Babu ◽  
Jean-Christophe Gimel ◽  
Taco Nicolai ◽  
Cristiano De Michele
Keyword(s):  
Hard Spheres ◽  
The Self ◽  
Self Diffusion ◽  
Square Well ◽  
Cluster Diffusion
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