Potential energy surface slits

The two adiabatic potential energy surfaces that we will use in the present calculations, are called a reactive double-slit model (RDSM) [59] where the first surface is the lower and the second is the upper surface, respectively,... 

Turner et al. [83] of the HI decomposition reaction, 2HI = H2 + I2, in carbon slit pores and carbon nanotubes. Large increases occurred (by up to a factor of 60) in the reaction rate, due to selective attraction of the transition state species to the pore walls. This selective attraction arises because the transition species is larger than other molecular species in the reaction mixture and has a stronger dispersion interaction with the carbon wall. More rigorous and complete calculations require the use of a dual scale approach, involving ab initio methods to determine the potential energy surface of the reaction, and atomistic molecular dynamics simulations to determine reaction rates [41]. 

Everett and Powl (1976) applied both the 9-3 and the 10-4 expressions in their theoretical treatment of potential energy profiles for the adsorption of small molecules in slit-like and cylindrical micropores. As one would expect, the two corresponding potential energy curves were of a similar shape, but the differences between them became greater as the pore size was reduced. Strictly, the replacement of the summation by integration is dependent on the distance between the molecule and the surface plane, becoming more accurate as the distance is increased (Steele, 1974). 

The energetic inhomogeneity of the surface along the x and y directions is not taken into account, but this is not expected to affect the results significantly at 308 and 333 K [39]. The cross interaction potential parameters between different sites were calculated according to the Lorentz-Berthelot rules Oap = aa + and eafi= ( The potential energy t/ due to the walls inside the slit pore model for each atom of the CO2 molecule is given by the expression C/ = + Uw(H-r where H is the distance between the carbon centers across... 

To obtain the film that is stabilized by itself, we have performed a number of MC simulation runs for the plane-parallel slit but of variable thickness (starting from the thickness, H/D = 10, shown in Fig. 7) in order to find the local minima in the configurational potential energy E per film particle. The transformation of the macroion layer structuring when the distance between confining surfaces, i.e. slit thickness becomes smaller, has been monitored during simulations with the thickness step AH/D equals to 1/10 of macroion... 

Consider now N particles confined to a slit-pore with metallic substrate surfaces. The total configurational potential energy of this system is then obtained from... 

Having understood the behaviour of the single lattice layer with sub-lattice layers, we now turn to the case where there are two lattice layers and sub-lattice layers underneath each of those layers. An atom or a molecule residing inside the slit pore has to interact with two surface layers including their sub-lattice layers. In this case, the potential energy of interaction is the sum of the potentials for each surface, that is... 

Figure 5.7 Scaled potential energy minima e /e within cylindrical and slit-shaped pores with varying radius R and slit size 2d, respectively, where eS is the minimum potential within the pore and e is the minimum potential with a single flat surface. Curves that go below the horizontal axis are the scaled potentials within the centre of the pore e(0)/e where the potential in the centre e(0) becomes less than the minimum potential with a single flat surface e, i.e. e(0)/e < 1, within larger pores. Reprinted with permission from Journal of the Chemical Society Faraday Transactions I, Adsorption in slit-like and cylindrical micropores in the Henry s law region. A model for the microporosity of carbons by D. H. Everett and J. C. Fowl, 72, 619-636, Copyright (1976) Royal Society of Chemistry...

Despite these findings it is still common to arbitrarily assume infinite pore wall thickness in using the slit pore model, and the associated pore size dependent Steele 10-4-3 potential [6] is then employed for estimatiiig the potential energy profile in a pore of any size. The inappropriateness of this assumption has recently been demonstrated in our laboratory, where it has been shown [5] that in typical nanoporous carbons having surface area in the range important for practical application (>800 m /gm) the pore walls must actually be rather thin, and comprised of only a very small number (2-3) of graphene layers. For such small wall thicknesses the adsorption potential is much weaker than that obtained for the infinitely thick wall, and the adsorbed amoimts can be lower by factors of 2 or more, particularly at low pressures where fluid-solid interactions dominate [5]. 

Calculations of the interaction energy in very fine pores are based on one or other of the standard expressions for the pair-wise interaction between atoms, already dealt with in Chapter 1. Anderson and Horlock, for example, used the Kirkwood-Miiller formulation in their calculations for argon adsorbed in slit-shaped pores of active magnesium oxide. They found that maximum enhancement of potential occurred in a pore of width 4-4 A, where its numerical value was 3-2kcalmol , as compared with 1-12, 1-0 and 1-07 kcal mol for positions over a cation, an anion and the centre of a lattice ceil, respectively, on a freely exposed (100) surface of magnesium oxide. 

Immersion calorimetry provides a very useful means of assessing the total surface area of a microporous carbon (Denoyel et al., 1993). The basic principle of this method is that there is a direct relation between the energy of immersion and the total area of the microporous material. Indeed, for the two model cases of slit-shaped and cylindrical micropores, the predicted maximum enhancement of the adsorption potential (as compared with that of the flat surface of same nature) is 2.0 and 3.68, respectively (Everett and Powl, 1976). These values are remarkably similar to the increased surface area occupied by a molecule in the narrowest possible slit-shaped and cylindrical pores (i.e. 2.0 in a slit and 3.63 in a cylinder). To apply the method we... 

This expression agrees rather well with the exact summation and gives the correct limiting form at large z which is an energy that varies as as calculated from the theory of dispersion interactions [10]. Although this potential is widely used in studies of structure in films adsorbed on a surface, it is even more popular in simulations of sorption in parallel-walled slit pores, some of which will be discussed below. 

Median radius of the analyzer Radius of analyzer internal hemisphere Radius of analyzer external hemisphere Factor accounting for surface roughness Irradiated area surface area Transmission function Average transmission function Electrical potential of the analyzer internal hemisphere Electrical potential of the analyzer external hemisphere Slit width displacement of energy levels upon the formation of a doubly ionized atom... 

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