Kinetic lattice gas model: Langmuir, Ising and interaction kinetics

Analysis of Temperature-Programmed Desorption via Equilibrium Thermodynamics

Temperature-programmed desorption (TPD) experiments in surface science are usually analyzed using the Polanyi-Wigner equation and/or transition-state theory. These methods are far from straightforward, and the determination of the pre-exponential factor is often problematic. We present a different method based on equilibrium thermodynamics, which builds on an approach previously used for TPD by Kreuzer et al. (Surf. Sci. 1988). Equations for the desorption rate are presented for three different types of surface-adsorbate interactions: (i) a 2D ideal hard-sphere gas with a negligible diffusion barrier, (ii) an ideal lattice gas, that is, fixed adsorption sites without interaction between the adsorbates, and (iii) a lattice gas with a distribution of (site-dependent) adsorption energies. We show that the coverage dependence of the sticking coefficient for adsorption at the desorption temperature determines whether the desorption process can be described by first- or second-order kinetics. The sticking coefficient at the desorption temperature must also be known for a quantitative determination of the adsorption energy, but it has a rather weak influence (like the pre-exponential factor in a traditional TPD analysis). Quantitative analysis is also influenced by the vibrational contributions to the energy and entropy. For the case of a single adsorption energy, we provide equations to directly convert peak temperatures into adsorption energies. These equations also provide an approximation of the desorption energy in cases that cannot be described by a fixed pre-exponential factor. For the case of a distribution of adsorption energies, the desorption spectra cannot be considered a superposition of desorption spectra corresponding to the different energies. Nevertheless, we present a method to extract the distribution of adsorption energies from TPD spectra, and we rationalize the energy resolution of TPD experiments. The analytical results are complemented by a program for simulation and analysis of TPD data.

Structural evolution of two-dimensional silicates using a "bond-switching" algorithm

Silicates are the most abundant materials in the earth's crust. In recent years, two-dimensional (2D) versions of them grown on metal supports (known as bilayer silicates) have allowed their study in detail down to the atomic scale. These structures are self-containing. They are not covalently bound to the metal support but interact with it through van der Waals forces. Like their three-dimensional counterparts, the 2D-silicates can form both crystalline and vitreous structures. Furthermore, the interconversion between vitreous to crystalline structures has been experimentally observed at the nanoscale. While theoretical work has been carried out to try to understand these transformations, a limitation for ab initio methods, and even molecular dynamics methods, is the computational cost of studying large systems and long timescales. In this work, we present a simple and computationally inexpensive approach, that can be used to represent the evolution of bilayer silicates using a bond-switching algorithm. This approach allows reaching equilibrium ring size distributions as a function of a parameter that can be related to the ratio between temperature and the energy required for the bond-switching event. The ring size distributions are compared to experimental data available in the literature.

Equivalence of on-Lattice Stochastic Chemical Kinetics with the Well-Mixed Chemical Master Equation in the Limit of Fast Diffusion

Well-mixed and lattice-based descriptions of stochastic chemical kinetics have been extensively used in the literature. Realizations of the corresponding stochastic processes are obtained by the Gillespie stochastic simulation algorithm and lattice kinetic Monte Carlo algorithms, respectively. However, the two frameworks have remained disconnected. We show the equivalence of these frameworks whereby the stochastic lattice kinetics reduces to effective well-mixed kinetics in the limit of fast diffusion. In the latter, the lattice structure appears implicitly, as the lumped rate of bimolecular reactions depends on the number of neighbors of a site on the lattice. Moreover, we propose a mapping between the stochastic propensities and the deterministic rates of the well-mixed vessel and lattice dynamics that illustrates the hierarchy of models and the key parameters that enable model reduction.

Hard versus soft dynamics for adsorption-desorption kinetics: Exact results in one-dimension

The adsorption-desorption kinetics is discussed in the framework of the kinetic lattice-gas model. The master equation formalism has been introduced to describe the evolution of the system, where the transition probabilities are written as an expansion of the occupation configurations of all neighboring sites. Since the detailed balance principle determines half of the coefficients that arise from the expansion, it is necessary to introduce ad hoc, a dynamic scheme to get the rest of them. Three schemes of the so-called hard dynamics, in which the probability of transition from single site cannot be factored into a part which depends only on the interaction energy and one that only depends on the field energy, and five schemes of the so-called soft dynamics, in which this factorization is possible, were introduced for this purpose. It is observed that for the hard dynamic schemes, the equilibrium and nonequilibrium observables, such as adsorption isotherms, sticking coefficients, and thermal desorption spectra, have a normal or physical sustainable behavior. While for the soft dynamics schemes, with the exception of the transition state theory, the equilibrium and nonequilibrium observables have several problems. Some of them can be regarded as abnormal behavior.

Additional constraints in adsorption-desorption kinetics

In this work, the adsorption-desorption kinetic in the framework of the lattice gas model is analyzed. The transition probabilities are written as an expansion of the occupation configurations. Due to that, the detail balance principle determine half of the adsorption A{i} and desorption D{i} coefficients, consequently, different functional relations between them are proposed. Introducing additional constrains, it is demonstrated that when those coefficients are linearly related through a parameter gamma , there are values of lateral interaction V , that lead to anomalous behavior in the adsorption isotherms, the sticking coefficient and the thermal programmed desorption spectra. Diagrams for the allowed values of V and gamma are also shown. Alternatively, a more reliable formulation for the adsorption desorption kinetic based on the transition state theory is introduced. In such way the equilibrium and non equilibrium observables do not present anomalous or inconsistent behavior.

Theoretical Approaches to Surface Kinetics: A Perspective

In this paper I outline the scope and success of the theory of equilibrium and nonequilibrium properties of surfaces and adsorbates Basic issues such as time and length scales lead to various levels of sophistication provided the proper assumptions are implimented successfully leading to a hierarchy of theories from the macroscopic level of nonequilibrium thermodynamics to Markov processes at the mesoscopic level and ultimately to a fully quantum mechanical description. Special ttention will be given to the role of detailed balance in sticking and desorption via direct and precursor-dominated channels.