Shushin A I
Institute of Chemical Physics, Russian Academy of Sciences, GSP-1, Kosygin str. 4, 117977 Moscow, Russia.
J Chem Phys. 2008 Sep 21;129(11):114509. doi: 10.1063/1.2978176.
The kinetics of geminate subdiffusion-assisted reactions (SDARs) of interacting particles is analyzed in detail with the use of the non-Markovian fractional Smoluchowki equation (FSE). It is suggested that the interparticle interaction potential is of the shape of potential well and reactivity is located within the well. The reaction kinetics is studied in the limit of deep well, in which the FSE can be solved analytically. This solution enables one to obtain the kinetics in a simple analytical form. The analytical expression shows that the SDAR kinetics fairly substantially depends on the mechanism of reactivity within the well. Specific features of the kinetics are thoroughly analyzed in two models of reactivity: the subdiffusion assisted activated rate model and the first order reaction model. The theory developed is applied to the interpretation of experimental kinetics of photoluminescence decay in amorphous a-Si:H semiconductors governed by geminate recombination of electrons and holes that are recently found to undergo subdiffusive relative motion. Analysis of results demonstrates that the subdiffusion assisted activated rate mechanism of reaction is closer to reality as applied to amorphous a-Si:H semiconductors. Comparison of experimental and theoretical kinetics allowed us to obtain some kinetic parameters of the systems under study: the rate of escaping from the well and the parameter characterizing the deviation of the subdiffusive motion from the conventional one.
利用非马尔可夫分数阶斯莫卢霍夫斯基方程（FSE）详细分析了相互作用粒子的双生亚扩散辅助反应（SDARs）的动力学。研究表明，粒子间相互作用势呈势阱形状，反应活性位于势阱内。在深势阱极限下研究反应动力学，此时FSE可解析求解。该解使人们能够以简单的解析形式得到动力学。解析表达式表明，SDAR动力学相当程度上取决于势阱内的反应活性机制。在两种反应活性模型中对动力学的具体特征进行了深入分析：亚扩散辅助活化速率模型和一级反应模型。所发展的理论被应用于解释非晶a-Si:H半导体中光致发光衰减的实验动力学，该动力学由电子和空穴的双生复合控制，最近发现它们经历亚扩散相对运动。结果分析表明，反应的亚扩散辅助活化速率机制应用于非晶a-Si:H半导体时更接近实际情况。通过比较实验和理论动力学，我们得到了所研究系统的一些动力学参数：从势阱逃逸的速率以及表征亚扩散运动与传统运动偏差的参数。
