存在粒子间相互作用时亚扩散粒子的孪生复合动力学
Kinetics of geminate recombination of subdiffusing particles in the presence of interparticle interaction
摘要：
利用非马尔可夫分数阶Smoluchowki方程（FSE），对相互作用粒子的成对亚扩散辅助反应（SDAR）动力学进行了详细分析。结果表明，粒子间相互作用势为势阱形状，反应性位于势阱内。研究了深井极限条件下的反应动力学，给出了FSE的解析解。这种解决方案使人们能够获得一个简单的分析形式的动力学。分析表达式表明，SDAR动力学相当大程度上取决于反应机制内的井。详细分析了亚扩散辅助活化速率模型和一级反应模型的动力学特性。开发的理论适用于解释的实验动力学的光致发光衰减在非晶$a$ -Si：H半导体所管辖的孪生重组的电子和空穴，最近发现进行subdiffusive相对运动。结果分析表明，亚扩散辅助的活化反应速率机制应用于非晶$a$ -Si：H半导体更接近实际。实验和理论动力学的比较允许获得一些动力学参数的研究中的系统：从井中逃逸的速率和参数表征的偏离subdiffusive运动从常规的。
英文摘要：
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 which 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 for obtaining 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.
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