Pair potential models soft-sphere

Instead of the hard-sphere model, the Lennard-Jones (LJ) interaction pair potential can be used to describe soft-core repulsion and dispersion forces. The LJ interaction potential is... 

In the present work we study binary soft-sphere mixtures with a core-size ratio mass ratio m2/m = 2.0 and an equimolar concentration (ij = 0.5) for both 3-d and 2-d systems. Using a constant-temperature MD technique and the peiodic boundary conditions, we have carried out MD simulations for the models. The pair potential, Eq. (1), was cut off over the distance rlnumber density wm kept constant, i.e. n" = 0.8 the temperature was varied to achieve a desired Teff. The microscopic time scale was chosen to... 

In 1924, Lennard-Jones [16] introduced a model for a soft-sphere pair potential of the form... 

As an example, we can point to the system of soft spheres studied by Agrawal and Kofke [42-43]. This model is defined by an inverse-power pair potential ... 

Figure 6 shows pair correlation functions from HNC calculations of an aqueous tetraalkyl-ammonium salt solution. In contrast to the MSA calculations, the HNC calculations yield g/y (r) functions that give a realistic picture of the solution structure. It can be inferred that no noticeable cation-anion association takes place, in agreement with chemical model calculations at lower concentrations. Also, no cation-cation association exists, which indicates that no hydrophobic interaction occurs between the large organic ions. Interpenetration of the cations is found, which can be reproduced because of the soft-sphere COR++(r) potential in Eq. (93). 

This tunable potential also describes a variety of similar haiiy-partide-like sj tems, such as star-like micelles, that is, block copolymer micelles with a very small core compared to the corona layer. On the other hand, for typical colloidal spheres grafted with small stabiB2ang layers or for micelles with a core occupying a significant fiacdon of the overall particle, this potential is inappropriate. V(r) of eqn [18] is one of the very few anal Uic forms of pair interaction potential, tuned with a single parameter, further justifying the choice of star polymers as model soft colloids. 

In reference [19], a systematic comparison between the predictions of the SCGLE theory and the corresponding computer simulation data for four idealized model systems was reported. The first two were two-dimensional systems with power law pair interaction, u(r) = Air", with n = 50 (i.e., strongly repulsive, almost hard-disk like) and with n = 3 (long-range dipole-dipole interaction). The third one was the three-dimensional weakly screened repulsive Yukawa potential (whose two-dimensional version had been studied in reference [18]). The last system considered involved short-ranged, soft-core repulsive interactions, whose dynamic equivalence with the strictly hard-sphere system allowed discussion of the properties of the latter reference system. For all these systems G(r, f) and/or F(k, f) were calculated from the self-consistent theory, and Brownian dynamics simulations (without hydrodynamic interactions) were performed to carry out extensive quantitative comparisons. In all those cases, the static structural information [i.e., g(r) and 5(A )] needed as an input in the dynamic theories was provided by the simnlations. The aim of that exercise was to... 

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