Sorption in disordered porous media

The lattice-gas model of sorption in disordered porous media is studied for a variety of settings, using existing, updated and newly developed numerical techniques. Firstly, we construct an efficient algorithm to calculate the exact partition function for small lattice-gas systems. The exact partition function is used for detailed analysis of the core features exhibited by such systems. We proceed to develop an interactive Monte Carlo (MC) simulation engine, that simulates sorption in a porous media sample and provides real-time visual data of the state space projection and the 3d view of the sample among other parameters of interest, as the external fields are manipulated. The use of such tool provides a more intuitive understanding of the system behaviour. The MC simulations are employed to study sorption in several porous solids: silica aerogel, Vycor glass and soil. We investigate how the phenomena depend on the microstructure of the original samples, how the behaviour varies with the external conditions, and how it is reflected in the paths that the system takes across its state space. Secondly, we develop two methods for estimation of the relative degeneracy (the number of microstates that have the same value of some macroscopic variables) in the systems that are too large to be handled exactly. The methods, based on a restricted infinite temperature sampling, obtain equidegenerate surfaces and the degeneracy gradient across the state space. Combined with the knowledge of an internal energy of a microstate, it enables us to construct the free energy map and thus the equilibrium probability distribution for the studied projection of the state space. Thirdly, the jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-ergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for large parallel processing systems. The updated algorithm is tested on the Ising model and applied to the lattice-gas model for sorption in aerogel and Vycor glass at low temperatures, when dynamics of the system is significantly slowed down. It is demonstrated that the updated jump-walking simulations are able to produce equilibrium isotherms which are typically hidden by the hysteresis effect characteristic of the standard single-flip simulations. As a result, we answer the long standing question about the existence of the first-order phase transitions in Vycor. Finally, we investigate sorption in several distinct topology network representations of soil and aerogel samples and demonstrate that the recently developed analytical techniques for random networks can be used to achieve a qualitative understanding of the phenomena in real materials.EPSR