Configurationally biased Monte Carlo simulations

Table 1.1 Configurationally biased Monte Carlo simulations of the adsorption enthalpies of hydrocarbons for two zeolites.

C. Configurationally Biased Monte Carlo Simulation (CBMC)... 

Configurationally biased Monte Carlo techniques [63-65] have made it possible to compute adsorption isotherms for linear and branched hydrocarbons in the micropores of a siliceous zeolite framework. Apart from Monte Carlo techniques, docking techniques [69] have also been implemented in some available computer codes. Docking techniques are convenient techniques that determine, by simulated annealing and subsequent freezing techniques, local energy minima of adsorbed molecules based on Lennard-Jones-or Buckingham-type interaction potentials. 

The importance of the entropy of adsorption is illustrated by experimental and calculated adsorption free energies for hexane in the 12-ring one-dimensional channel mordenite (MOR) and 10-ring one-dimensional channel of ferrierite (TON). Table 4.4 compares the simulated values for the heats of adsorption from configurationally biased Monte Carlo calculations valid at low micropore filling. The corresponding adsorption equilibrium constants are also compared in Table 4.4. One notes the increase in the energy of adsorption for the narrow-pore zeolite. However, at the temperature of reaction, the equilibrium adsorption constant is also a factor 10 lower for the narrow-pore zeolite. 

There are basically two different computer simulation techniques known as molecular dynamics (MD) and Monte Carlo (MC) simulation. In MD molecular trajectories are computed by solving an equation of motion for equilibrium or nonequilibrium situations. Since the MD time scale is a physical one, this method permits investigations of time-dependent phenomena like, for example, transport processes [25,61-63]. In MC, on the other hand, trajectories are generated by a (biased) random walk in configuration space and, therefore, do not per se permit investigations of processes on a physical time scale (with the dynamics of spin lattices as an exception [64]). However, MC has the advantage that it can easily be applied to virtually all statistical-physical ensembles, which is of particular interest in the context of this chapter. On account of limitations of space and because excellent texts exist for the MD method [25,61-63,65], the present discussion will be restricted to the MC technique with particular emphasis on mixed stress-strain ensembles. 

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