We focus here on the thermodynamic properties of adsorbates formed by two-species $A+B \to \oslash$ reactions on a one-dimensional infinite lattice with heterogeneous "catalytic" properties. In our model hard-core $A$ and $B$ particles undergo continuous exchanges with their reservoirs and react when dissimilar species appear at neighboring lattice sites in presence of a "catalyst." The latter is modeled by supposing either that randomly chosen bonds in the lattice promote reactions (Model I) or that reactions are activated by randomly chosen lattice sites (Model II). In the case of annealed disorder in spatial distribution of a catalyst we calculate the pressure of the adsorbate by solving three-site (Model I) or four-site (Model II) recursions obeyed by the corresponding averaged grand-canonical partition functions. In the case of quenched disorder, we use two complementary approaches to find $\textit{exact}$ expressions for the pressure. The first approach is based on direct combinatorial arguments. In the second approach, we frame the model in terms of random matrices; the pressure is then represented as an averaged logarithm of the trace of a product of random $3 \times 3$ matrices -- either uncorrelated (Model I) or sequentially correlated (Model II).
Catalytic reactions with bulk-mediated excursions: Mixing fails to restore chemical equilibrium
本文分析了在催化平面（CP）与液相接触的体系中，活性组分的体介导漂移（BME）对催化类Langmuir-Hinshelwood A + B \to 0反应的长时间行为的影响。这种BME是由于颗粒从CP上反复解吸，随后在液相中扩散，并最终在CP上重新吸附而远离初始分离点。这一过程导致沿CP的有效超扩散输运。我们认为这两个“批”反应，其中所有的活性物质的颗粒最初吸附到CP上，和反应后的颗粒稳定流入CP上。我们发现，“批”反应的BME提供了一个有效的混合通道，在这里出现的平均场型行为。相反，对于反应后的粒子稳定流入，我们观察到基本偏离的平均场行为，并发现BME的混合效应是不足以恢复化学平衡。我们发现，一个稳定的状态被建立为t \to \infty，其中的CP的平均覆盖率的极限值取决于颗粒在本体液相中的扩散系数和吸附颗粒的空间分布是强烈相关的。此外，我们表明，这样一个稳定状态的放松所描述的幂律函数的时间，在相反的指数时间依赖性描述的方法，在完美的搅拌系统的平衡。
We study equilibrium properties of catalytically-activated $A + A \to \oslash$ reactions taking place on a lattice of adsorption sites. The particles undergo continuous exchanges with a reservoir maintained at a constant chemical potential $μ$ and react when they appear at the neighbouring sites, provided that some reactive conditions are fulfilled. We model the latter in two different ways: In the Model I some fraction $p$ of the {\em bonds} connecting neighbouring sites possesses special catalytic properties such that any two $A$s appearing on the sites connected by such a bond instantaneous…
Exactly Solvable Model of Monomer-Monomer Reactions on a Two-Dimensional Random Catalytic Substrate
我们提出了一个\textit{exactly solvable}模型的单体-单体$A + B \to \emptyset$反应的二维非均匀，催化基板和研究的平衡性质的两个物种的吸附。该基板包含随机放置的催化键的平均密度$q$连接相邻的吸附位点。相互作用的$A$和$B$（单体）物质与相应的相邻气体储存器进行连续交换。如果$A$和$B$颗粒占据通过催化键连接的吸附位点，则反应$A + B \to \emptyset$瞬间发生。我们发现，对于\textit{annealed}无序的情况下，在催化键的位置的反应模型研究可以映射到一般的自旋$S = 1$（GS 1）模型。在这里，我们集中在一个特定的情况下，该模型减少到一个精确可解的布卢姆-埃默里-格里菲斯（BEG）模型（T。Horiguchi，Phys. Lett. A { \bf 113}，425（1986）; F.Y. Wu，Phys. Lett. A，{ \bf 116}，245（1986）），并推导出两种吸附物的无序平均平衡压力的精确表达式。我们发现，在相等的部分蒸汽压的$A$和$B$物种，该系统表现出二阶相变，反映了一个自发对称性破缺与大的波动和渐进的覆盖整个衬底的任何一个物种。
A new lattice Boltzmann model (LBM) for chemically reactive mixtures is presented. The approach capitalizes on the recently introduced thermodynamically consistent LBM for multicomponent mixtures of ideal gases. Similar to the non-reactive case, the present LBM features Stefan--Maxwell diffusion of chemical species and a fully on-lattice mean-field realization of the momentum and energy of the flow. Besides introducing the reaction mechanism into the kinetic equations for the species, the proposed LBM also features a new realization of the compressible flow by using a concept of extended equil…
