Computational Mathematicsematics

Computational Methods in Surface and Colloid Science by Malgorzata Borowko

By Malgorzata Borowko

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90) affects UFFthrough the a ~ ~ u ~ e n t f rF1 := lri - I for a fluidmolecule 90) yields three terms ~rouped an located at con~gurationintegral as [75] pplying Leibniz’s rule for the di~erentiationof a parameter integral 1761, it follows from Eqs. (89) and (95) that =O because U becomes infinitely large if z1 = S, on account of the divergence of at this point. In Eq. (96), g 2 is defined analogously to gl in Eq. (95) and the above argument may be repeated N -l times, to obtain finally +t where F:”] := -8Z$~/8~,is the total force exerted by the film on substratek.

In other words, an addition is attempted witha preferred orientation of the molecule determined by the macroscopic director rl of the entire simulation cell. The position of the center of mass of the molecule is again ~ ldetailed e balance the probchosen randomly. According to the ~ r i ~ c of ability for a realization of an addition attempt is given by [73] whereas for a removal attempt, where rf is given in Eq. (80). However, B has to be replaced by B' defined analogously as (linear molecules only) where I is the moment of inertia.

For the free energy of the ideal gas under these premises. where the atomic partition function is given by A is the thermal de where Z1is the single-atom configurational integral, and roglie wavelength. Thefarright side of Eq. (31) follows immediately because the potential energy of a molecule in the present two-dimensional ideal gas does not depend on its y coordinate (see Fig. 3). The configuration integral depends on S , in a piecewise fashion. For S, in the nth period of the potential, that is for (n -l)E

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