Monte Carlo simulation spherical distribution

The electrostatic charges of surfactants seriously affect the localization of host molecules in the water pool. Monte Carlo simulation in which ionic reversed micelles are treated as spherical entities showed the presence of the electrical double layer in the interface of the water pool, and the distribution of counterions followed the Poisson-Boltzmann approximation [51]. Mancini and Schiavo [52] assumed recently, by the yield of halogenation, that the specific interactions between bromide or chloride ions and an ammonium head-group in cationic reversed micelles keep the ions in a defined position on the interface. 

Sorensen, T.S. and Sloth, P., Ion and potential distribution in charged and non-charged primitive spherical pores in equilibrium with primitive electrolyte solution calculated by grand canonical ensemble Monte Carlo simulation, J. Chem. Soc. Faraday Trans., 88 (4), 571-589, 1992. 

Abstract Results are presented from Monte Carlo simulations of a three-dimensional lattice model of a binary mixture of amphiphile and solvent. The amphiphiles are represented by connected chains on a simple cubic lattice and free self-assembly is allowed within the simulations. Earlier work on this model, for chains of length four, has shown that it exhibits a critical micelle concentration and a cluster size distribution which is consistent with those observed experimentally. The results presented in this paper use chains of length six, two of which are head segments and also include the effect of chain rigidity. It is found that the mean aggregation number is greater than that achieved with shorter chains and the cluster size distribution has a significantly enhanced minimum, with the micelles more spherical in... 

An important complication arises here because the intermolecular structure factor as introduced in Eq. (2.13) has now become a function of the form factor P(q), i.e., the distribution of polyions depends on their mutual orientation and their shape and vice versa. It is only in the case of spherical polyions that S(q) and P(q) are separable by the use of center-of-mass coordinates. For rod-like polyions the mutual orientation and the spatial distribution are correlated, and for flexible polyions the chain conformation and the spatial distribution of chains depend on each other. Assuming weak interactions, several approximations were introduced to separate form- and structure factor. However, for strong, long-range electrostatic interactions intra- and intermolecular correlations cannot yet be properly separated [28]. This is an important limitation to all current theories except for Monte Carlo simulations. 

In designing modules of mono- or multilamp immersion-type photochemical reactors, again the concept of convergence of light distribution and reactor geometries is followed, and knowledge of light penetration in a suspension of optimal photocatalyst concentration is therefore essential. Optimal thickness of annular irradiated reaction volume is best determined by a spherical probe under conditions where only absorption by the photocatalyst has to be taken into account [12, 78, 98, 99]. The radiant power P = f(r) within the limits of r and rR, respectively, has been simulated by the Monte Carlo method on the basis of... 

Our ability to understand the structure and properties of water in all its forms has been dramatically enhanced by the use of computer simulation. Early studies of the liquid used simple representations of the potential surface. These were often three or four point-charge distributions, adjusted to fit dipole and quadrupole moments, embedded in a simple spherical nonelectrostatic interaction. The simulations used classical Monte Carlo (MC) or molecular dynamic (MD) calculations, and the water molecules were assumed to be rigid. Recently, more advanced calculations have been based on quantum simulations, the introduction of intramolecular degrees of freedom, and accurate potential surfaces. As one side benefit... 

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