Modelling Networks in Varying Dimensions

Network materials may be usefully defined as systems in which significant connectivity may be identified and preserved even in relatively disordered states (such as liquids and glasses). Considering material structure in terms of an underlying network can be traced to Zachariasen [1] who sketched a two-dimensional representation of a network formed from a mixture of two- and three-coordinate sites. The network connectivity may result from the percolation of relatively simple, well-defined units (such as the triangles in Zachariasen s image or the tetrahedral Si04 coordination 

Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford 0X1 3QZ, UK e-mail mark.wilson chem.ox.ac.uk 

In molecular dynamics (MD) simulation atoms are moved in space along their lines of force (which are determined from the first derivative of the potential energy function) using finite difference methods [27, 28]. At each time step the evolution of the energy and forces allow the accelerations on each atom to be determined, in turn allowing the atom changes in velocities and positions to be evaluated and hence allows the system clock to move forward, typically in time steps of the order of a few fs. Bulk system properties such as temperature and pressure are easily determined from the atom positions and velocities. As a result simulations can be readily performed at constant temperature and volume (NVT ensemble) or constant temperature and pressure (NpT ensemble). The constant temperature and pressure constraints can be imposed using thermostats and barostat [29-31] in which additional variables are coupled to the system which act to modify the equations of motion. 

The interaction between atoms in the condensed phase may be expressed as a cluster expansion 

In this chapter we explore a range of networks by considering two (on the face of it relatively simple) systems C and Si02. These two systems present different modelling problems and hence require different approaches. 

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On this basis the porosity and surface composition of a number of silicas and zeolites were varied systematically to maximize retention of the isothizolinone structures. For the sake of clarity, data is represented here for only four silicas (Table 1) and three zeolites (Table 2). Silicas 1 and 3 differ in their pore dimensions, these being ca. 20 A and 180 A respectively. Silicas 2 and 4, their counterparts, have been calcined to optimise the number and distribution of isolated silanol sites. Zeolites 1 and 2 are the Na- and H- forms of zeolite-Y respectively. Zeolite 3 is the H-Y zeolite after subjecting to steam calcination, thereby substantially increasing the proportion of Si Al in the structure. The minimum pore dimensions of these materials were around 15 A, selected on the basis that energy-minimized structures obtained by molecular modelling predict the widest dimension of the bulkiest biocide (OIT) to be ca. 13 A, thereby allowing entry to the pore network. 

With the mesopore model, it is tacitly assumed that it behaves as a tube with solid walls. A more accurate model would be that of a convoluted tube, with of varying dimension, with other porosities leading from the so-called walls of the cylinder. It is therefore unlikely that processes of independent condensation and evaporation occur in the pores of such complex three-dimensional porous networks. 

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