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.

Figure 1

Normalized sticking coefficient for Ising kinetics with $\gamma =-1$ and different values of the lateral interaction. Top to bottom: $\beta V=-4,-2,-1,0,1,2,4,20$.

Figure 2

Thermal desorption spectra using Ising kinetics with $\gamma =-1$ for different lateral interactions: (a) attractive case: left to right, mobile (line) $V\left(\text{kcal}/\text{mol}\right)=-2,-4$ and immobile (dash) $V\left(\text{kcal}/\text{mol}\right)=-2,-4$; (b) repulsive case: left to right, mobile (line) $V\left(\text{kcal}/\text{mol}\right)=4,2$, and immobile (dash) $V\left(\text{kcal}/\text{mol}\right)=4,2$. The case of null interaction is also included in both figures.

Figure 3

Schematic picture of the transition barrier in the symmetric Butler-Volmer approximation, used to calculate the TDA and OSD transition rates. After Ref. [46].

Figure 4

Normalized sticking coefficient for TDA with different values of parameter $U$. (a) Attractive $\left(\beta V=-4\right)$ and (b) repulsive $\left(\beta V=4\right)$ lateral interactions. In both figures, $\beta U=0,2,4,10$ from top to bottom at $\theta =0.6$. The sticking coefficient for $V=0$ (dash) is also included.

Figure 5

Mobile (line) and immobile (dash) TPD spectra using TDA for repulsive lateral interaction, $V=2\text{kcal}/\text{mol}$ and two different values of parameter $U$: $U<2\text{kcal}/\text{mol}$ (left) and $U=20\text{kcal}/\text{mol}$ (right).

Figure 6

Normalized sticking coefficients for interaction kinetics with $\gamma =-1$ and different values of the lateral interaction.

Figure 7

Thermal desorption spectra using interaction kinetics with $\gamma =-1$ for repulsive lateral interaction. $V=0$ (dot), immobile (dash) TPD spectra $V=3\text{kcal}/\text{mol}$ and mobile (solid) TPD spectra $V=3$, 10 kcal/mol.

Figure 8

Normalized sticking coefficients for TST with Brönsted-Polanyi relations for different values of the lateral interaction.

Figure 9

Thermal desorption spectra using TST for attractive lateral interaction $V=2\text{kcal}/\text{mol}$ and different values of the lateral interaction in activated state. The case $V=0$ (dot) is also included. Immobile (dash) TPD spectra: left to right ${ϵ}_1^{\ast }=V,V/2,0$; and mobile (solid) TPD spectra: left to right ${ϵ}_1^{\ast }=V,V/2,0$. Here ${ϵ}_2^{\ast }=2{ϵ}_1^{\ast }$ is considered

Figure 10

Normalized sticking coefficients for soft Glauber dynamics for different values of the lateral interaction.

Figure 11

Immobile (dash) and mobile (solid) thermal desorption spectra using soft Glauber dynamics for repulsive and non-interacting lateral interaction. Left to right $V\left(\text{kcal}/\text{mol}\right)=10,1,0$.

Figure 12

Normalized sticking coefficient for Inverse relation where different values of lateral interaction are considered. The sticking coefficient for $V=0$ (dash) is also included.

Figure 13

Thermal desorption spectra using inverse relation for different values of the attractive and null lateral interaction. Immobile (dash) TPD spectra: left to right $V\left(\text{kcal}/\text{mol}\right)=0,-2,-6$; and mobile (solid) TPD spectra: left to right $V\left(\text{kcal}/\text{mol}\right)=0,-2,-6$.

Figure 14

Thermal desorption spectra using OSD for different values of the parameter $U$. (a) attractive $V=-2\text{kcal}/\text{mol}$ lateral interaction, immobile (dash) and mobile (solid) TPD spectra: left to right $U\left(\text{kcal}/\text{mol}\right)=10,5,2,0$; (b) repulsive $V=2\text{kcal}/\text{mol}$ lateral interaction, immobile (dash) and mobile (solid) TPD spectra: $U\left(\text{kcal}/\text{mol}\right)=0$ (left), 10 (right). In both figures $V=0$ (dot) is also included.