Electrostatic model, zeolite

What is the simplest adsorption model that can adequately define sorption in the system of interest for purposes of our study The simpler the model, the less information is needed to parameterize it. The distribution coefficient model requires only entry of the mass of sorbent in contact with a volume of water and a value for K,. Pesticide adsorption can often be modeled adequately using a simple K ) approach (cf. Lyman et al. 1982). For smectite and ver-miculite clays and zeolites that have dominantly pH-independent surface charge, ion-exchange or power-exchange models may accurately reproduce adsorption of the alkaline earths and alkali metals. If the system of interest experiences a wide range of pH and solution concentrations, and adsorption is of multivalent species by metal oxyhydroxides, then an electrostatic model may be most appropriate. 

Jacobs et al. [724] introduced the FTIR measurement of the shift of the OH stretching band upon benzene adsorption as a measure of the acid strength of the hydroxy groups. Jacobs [725] also provided a theoretical reasoning for this effect. Similarly, O Malley [794] developed an electrostatic model for predicting the shift of typical IR bands upon adsorption of aromatics on the respective zeolitic OH groups. 

Two methods for including explicit electrostatic interactions are proposed. In the first, and more difficult approach, one would need to conduct extensive quantum mechanical calculations of the potential energy variation between a model surface and one adjacent water molecule using thousands of different geometrical orientations. This approach has been used in a limited fashion to study the interaction potential between water and surface Si-OH groups on aluminosilicates, silicates and zeolites (37-39). 

A number of techniques have been employed to model the framework structure of silica and zeolites (Catlow Cormack, 1987). Early attempts at calculating the lattice energy of a silicate assumed only electrostatic interactions. These calculations were of limited use since the short-range interactions had been ignored. The short-range terms are generally modelled in terms of the Buckingham potential,... 

Of course, concerns about periodicity only relate to systems that are not periodic. The discussion above pertains primarily to the simulations of liquids, or solutes in liquid solutions, where PBCs are a useful approximation that helps to model solvation phenomena more realistically than would be the case for a small cluster. If the system truly is periodic, e.g., a zeolite crystal, tlien PBCs are integral to the model. Moreover, imposing PBCs can provide certain advantages in a simulation. For instance, Ewald summation, which accounts for electrostatic interactions to infinite length as discussed in Chapter 2, can only be carried out within the context of PBCs. 

Benzene-benzene interactions were modeled with a Buckingham potential that was shown to yield reasonable predictions of the properties of liquid and solid benzene. Benzene-zeolite interactions were modeled by a short-range Lennard-Jones term and a long-range electrostatic term. In total, 16 benzene molecules were simulated in a unit cell of zeolite Y, corresponding to a concentration of 2 molecules per supercage. Calculations ran for 24 ps (after an initial 24-ps equilibration time) for diffusion at 300 K. 

Hope et al. (116) presented a combined volumetric sorption and theoretical study of the sorption of Kr in silicalite. The theoretical calculation was based on a potential model related to that of Sanders et al. (117), which includes electrostatic terms and a simple bond-bending formalism for the portion of the framework (120 atoms) that is allowed to relax during the simulations. In contrast to the potential developed by Sanders et al., these calculations employed hard, unpolarizable oxygen ions. Polarizability was, however, included in the description of the Kr atoms. Intermolecular potential terms accounting for the interaction of Kr atoms with the zeolite oxygen atoms were derived from fitting experimental results characterizing the interatomic potentials of rare gas mixtures. In contrast to the situation for hydrocarbons, there are few direct empirical data to aid parameterization, but the use of Ne-Kr potentials is reasonable, because Ne is isoelectronic with O2-. 

Adsorption isotherms of methane in silicalite have also been predicted in a number of calculation studies (62, 155, 156). Goodbody et al. (62) predicted a heat of adsorption of 18 kJ/mol and simulated the adsorption isotherm up to 650 bar. From the adsorption isotherm, they found that the sinusoidal pore volume contains more methane molecules at all pressures. Snurr et al. (155) performed GC-MC and MD simulations over a wide range of occupancies at several temperatures. The intermolecular zeolite-methane potential parameters were taken from previous MD studies (11, 87) and the methane-methane parameters from MD simulations were adjusted to fit experimental results for liquid methane (157). Electrostatic contributions were neglected on account of the all-silica framework, and methane was represented by a rigid, five-center model. 

Snurr et al. (192) used biased GC-MC simulations to predict isotherms, isosteric heats of adsorption, and locations of benzene and p-xylene at various concentrations. The suitability of a bias method is clear, at low coverages to prevent trial insertions overlapping with the zeolite walls and at high coverages to prevent overlap with other sorbate molecules. (Slightly different bias schemes were used for the two extremes of concentrations.) Interactions between sorbates and zeolites—both of which were considered to be rigid—were modeled with parameters from the literature (79, 87). Electrostatic interactions were included to account for the quadrupole moment of the sorbates. Sorbate-sorbate interaction parameters were taken from Shi and Bartell (194) for benzene and from Jorgensen et al. (195) for p-xylene. 

The question of methanol protonation was revisited by Shah et al. (237, 238), who used first-principles calculations to study the adsorption of methanol in chabazite and sodalite. The computational demands of this technique are such that only the most symmetrical zeolite lattices are accessible at present, but this limitation is sure to change in the future. Pseudopotentials were used to model the core electrons, verified by reproduction of the lattice parameter of a-quartz and the gas-phase geometry of methanol. In chabazite, methanol was found to be adsorbed in the 8-ring channel of the structure. The optimized structure corresponds to the ion-paired complex, previously designated as a saddle point on the basis of cluster calculations. No stable minimum was found corresponding to the neutral complex. Shah et al. (237) concluded that any barrier to protonation is more than compensated for by the electrostatic potential within the 8-ring. 

The zeolite framework was described by a specific force field developed by van Santen et al. [11] while the hydrocarbon molecules and their interaction among themselves and with the zeolite lattice were described by the generic force field Drdding n [12]. All the internal coordinates of the alkane molecules were allowed to fully relax. The nonbonded interactions (electrostatic and van der Waals) were computed for aU atoms within a cutoff-radius of 12A. Periodic boundary conditions were imposed along the three axes of the zeolite model to simulate an infinite crystal. 

Quantitative indications on the strength of Sn cations were obtained by Pickert et al., who calculated the electrostatic field along the three-fold cubic axis in the zeolite cavity near a surface cation at Sn for a particular fully ionic model at a Y zeolite with Si/Al = 2. Further calculations were later made by E. Dempsey ... 

Table III shoves the comparison of the calculated potential energy of neopentane on NaX zeolite with the experimental value of the heat of adsorption (O. M. Dzhigit, A. V. Kiselev, L. G. Ryabukhina, Zh. Fix. Khim. 1970, 44, 1790). Two models, 1 and II (Figure 3), of the distribution of the force centers in zeolite NaX and two orientations, (1) and (2), of the neopentane molecule at site Sn (Figure 4) were used. The calculations show that for approximate evaluation of potential energy, it is only necessary to take into consideration about 50 nearest charged oxygen atoms and 4 cations. In model II, the influence of other cations (which are situated in sites Sn of the supercage) were taken into consideration. The other cations, which are distributed more randomly, do not influence seriously the electrostatic fleld in the space occupied by the neopentane molecule near one of the Sn sites (calculations by L. G. Ryabukhina and A. A. Lopatkin).

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