On the thermodynamics of curved interfaces and the nucleation of hard spheres in a finite system

Total energy calculations of three- and four-atomic silver clusters have been performed by the spin-polarized version of the CNDO/2 method to get the most stable equilibrium geometries, atomization energies, and charge and spin distribution on the atoms for three different basis sets: {s}, {sp}, and {spd}. When viewed from the equilateral triangle and square geometries, the last electronic configuration, i.e. the {spd} one, appears to be most stable with respect to the geometrical deformations considered. In this case, the behaviour of the atoms of both clusters resembles that of hard spheres (i.e. close-packing).

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Excess entropy of the systems of molecules differing in size and shape

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19830192 ◽

1983 ◽

Vol 48 (1) ◽

pp. 192-198 ◽

Cited By ~ 5

Author(s):

Tomáš Boublík

Keyword(s):

Equation Of State ◽

Hard Spheres ◽

Excess Entropy ◽

Convex Bodies ◽

Pure Substance ◽

Liquid Equilibrium ◽

Simple Rules ◽

Different Shapes ◽

The Mean

The excess entropy of mixing of mixtures of hard spheres and spherocylinders is determined from an equation of state of hard convex bodies. The obtained dependence of excess entropy on composition was used to find the accuracy of determining ΔSE from relations employed for the correlation and prediction of vapour-liquid equilibrium. Simple rules were proposed for establishing the mean parameter of nonsphericity for mixtures of hard bodies of different shapes allowing to describe the P-V-T behaviour of solutions in terms of the equation of state fo pure substance. The determination of ΔSE by means of these rules is discussed.

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Study of Sedimentation Velocity of Block Copolymer Micelles

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19930071 ◽

1993 ◽

Vol 58 (1) ◽

pp. 71-76 ◽

Cited By ~ 3

Author(s):

Minmin Tian ◽

C. Ramireddy ◽

Stephen E. Webber ◽

Petr Munk

Keyword(s):

Block Copolymer ◽

Methacrylic Acid ◽

Mixed Solvent ◽

Hard Spheres ◽

Sedimentation Velocity ◽

Hydrodynamic Coefficient ◽

Block Copolymer Micelles ◽

Copolymer Micelles ◽

Size Heterogeneity ◽

Good Agreement

No anomalies were observed during the measurement of sedimentation coefficients of block copolymer micelles formed by copolymers of styrene and methacrylic acid in a mixed solvent; 80 vol.% of dioxane and 20 vol.% of water. The shapes of the sedimenting boundaries suggest that the size heterogeneity of the micelles is small. Linear relations between 1/s and c were obtained. The value of the hydrodynamic coefficient κ was between 2 and 4 in a good agreement with the value 2.75 or 2.86 that was obtained by combining Burgers' or Fixman's values of the coefficient of the concentration dependence kvs for hard spheres with Einstein's value of [η] for spheres.

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Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc2009510 ◽

2010 ◽

Vol 75 (3) ◽

pp. 359-369 ◽

Cited By ~ 6

Author(s):

Mariano López De Haro ◽

Anatol Malijevský ◽

Stanislav Labík

Keyword(s):

Equation Of State ◽

Binary Mixtures ◽

Hard Sphere ◽

Hard Spheres ◽

Virial Coefficients ◽

Fluid Mixture ◽

Binary Fluid ◽

Virial Series ◽

Consolute Point ◽

Critical Constants

Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

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A Concretization of an Approximation Method for Non-Affine Fractal Interpolation Functions

Mathematics ◽

10.3390/math9070767 ◽

2021 ◽

Vol 9 (7) ◽

pp. 767

Author(s):

Alexandra Băicoianu ◽

Cristina Maria Păcurar ◽

Marius Păun

Keyword(s):

Approximation Method ◽

Finite System ◽

Countable System ◽

Fractal Interpolation ◽

Interpolation Function ◽

Finite Systems ◽

Fractal Interpolation Function ◽

Fractal Interpolation Functions ◽

Finite Set ◽

Interpolation Functions

The present paper concretizes the models proposed by S. Ri and N. Secelean. S. Ri proposed the construction of the fractal interpolation function(FIF) considering finite systems consisting of Rakotch contractions, but produced no concretization of the model. N. Secelean considered countable systems of Banach contractions to produce the fractal interpolation function. Based on the abovementioned results, in this paper, we propose two different algorithms to produce the fractal interpolation functions both in the affine and non-affine cases. The theoretical context we were working in suppose a countable set of starting points and a countable system of Rakotch contractions. Due to the computational restrictions, the algorithms constructed in the applications have the weakness that they use a finite set of starting points and a finite system of Rakotch contractions. In this respect, the attractor obtained is a two-step approximation. The large number of points used in the computations and the graphical results lead us to the conclusion that the attractor obtained is a good approximation of the fractal interpolation function in both cases, affine and non-affine FIFs. In this way, we also provide a concretization of the scheme presented by C.M. Păcurar .

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