Note: Rigorous results for the partition function of a square-well chain in hard-sphere solvent

2017 ◽  
Vol 147 (16) ◽  
pp. 166101 ◽  
Author(s):  
Mark P. Taylor
Keyword(s):  
Partition Function ◽  
Hard Sphere ◽  
Rigorous Results ◽  
Square Well

The analytical evaluation of the first-order density cluster integral in the radial distribution function

1970 ◽  
Vol 320 (1542) ◽  
pp. 323-348 ◽  
Keyword(s):  
Hard Sphere ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Scattering Data ◽  
X Ray ◽  
Lennard Jones ◽  
X Ray Scattering ◽  
Cluster Integrals ◽  
Square Well ◽  
Three Body

It is shown how to evaluate the two-body, and three-body cluster integrals, ɳ 3 , ɳ * 3 , β 3 , β * 3 (equations (1.1) to (1.4)) for the hard-sphere, square-well and Lennard-Jones ( v :½ v ) potentials; the three-body potential used is the dipole-dipole-dipole potential of Axilrod & Teller. Explicit expressions are presented for the integrals ɳ * 3 , β * 3 using the above potentials; in the case of the first integral, its values for both small and large values of the separation distance are also given, for the Lennard-Jones ( v :½ v ) potential. Similar considerations have been carried out for ɳ 3 and β 3 , except that explicit expressions for the hard-sphere, and square-well potentials are not given, since these had been done before by other authors. The intermediate expressions for the four cluster integrals, are in terms of single integrals, and such expressions are valid for any continuous potential. Numerical results based on some of the expressions in this paper are compared with the results of numerical evaluation of the above integrals by other authors, and the agreement is seen to be good. Making use of the Mikolaj-Pings relation, the above results are used to obtain relationships between the second virial coefficient, and X-ray scattering data, as well as a means of deducing the pair potential at large separations, directly from a knowledge of X-ray scattering data, and the second virial coefficient.

The three body partition function for hard core square well clusters

1980 ◽  
Vol 73 (9) ◽  
pp. 4663-4667 ◽  
Author(s):  
W. H. Zurek ◽  
W. C. Schieve
Keyword(s):  
Partition Function ◽  
Hard Core ◽  
Square Well ◽  
Three Body

scholarly journals Self-assembly mechanism in colloids: perspectives from statistical physics

Open Physics ◽  
2012 ◽  
Vol 10 (3) ◽  
Author(s):  
Achille Giacometti
Keyword(s):  
Integral Equation ◽  
Self Assembly ◽  
Hard Sphere ◽  
Statistical Physics ◽  
Colloidal Particles ◽  
Building Blocks ◽  
Computational Effort ◽  
Spherical Particles ◽  
Square Well ◽  
Patchy Colloids

AbstractMotivated by recent experimental findings in chemical synthesis of colloidal particles, we draw an analogy between self-assembly processes occurring in biological systems (e.g. protein folding) and a new exciting possibility in the field of material science. We consider a self-assembly process whose elementary building blocks are decorated patchy colloids of various types, that spontaneously drive the system toward a unique and predetermined targeted macroscopic structure. To this aim, we discuss a simple theoretical model — the Kern-Frenkel model — describing a fluid of colloidal spherical particles with a pre-defined number and distribution of solvophobic and solvophilic regions on their surface. The solvophobic and solvophilic regions are described via a short-range square-well and a hard-sphere potentials, respectively. Integral equation and perturbation theories are presented to discuss structural and thermodynamical properties, with particular emphasis on the computation of the fluid-fluid (or gas-liquid) transition in the temperaturedensity plane. The model allows the description of both one and two attractive caps, as a function of the fraction of covered attractive surface, thus interpolating between a square-well and a hard-sphere fluid, upon changing the coverage. By comparison with Monte Carlo simulations, we assess the pros and the cons of both integral equation and perturbation theories in the present context of patchy colloids, where the computational effort for numerical simulations is rather demanding.

The hard-sphere and square-well models for the surface properties of liquid metals

1979 ◽  
Vol 67 (2-3) ◽  
pp. 397-398 ◽  
Author(s):  
P.K. Chakrabarti ◽  
T. Nammalvar ◽  
R.C. Sastri
Keyword(s):  
Surface Properties ◽  
Hard Sphere ◽  
Liquid Metals ◽  
Square Well ◽  
Well Models
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