分形结构对CO催化氧化非线性动力学行为影响的理论研究

A Theoretical Study of Nonlinear Dynamics of COC atalytic Oxidatation on Fractal Surface*

在平均场近似下建立了包含分形上反常扩散在内的理论模型，描述了典型单分子－双分子反应：ＣＯ＋Ｏ２的非线性动力学规律，并着重考察了分形结构对振荡行为以及非平衡相变的影响。我们发现：①随分形维数ｄｆ的降低，振荡区向ＣＯ的低分压方向偏移并减小，甚至消失；同时，在相同的反应条件下，对二维规则表面不存在振荡行为的区域，有可能因分形上的受限扩散而诱导振荡。②在较高温度下，分形结构除了控制体系的非线性动力学行为，还能够改变ＣＯ从低覆盖度到高覆盖度不同状态之间的非平衡相变的类型：分维数降低，相变可由一级变为二级；而在低温下，分形结构对相变规律的影响作用并不十分显著，即只可能改变相变发生的位置，不足以改变相变类型。

A theoretical model was proposed under meanfield approximation,specially including abnormal diffusion on fractal surface,to describe behavior of nonlinear dynamics in a typical dimermonomer model∶CO+O2The Oscillatory behavior and kinetic phase transition were studied intensively(1)As decreasing of fractal dimension,the oscillatory regimes shift to lower CO pressure,shrink,and vanish finallyA kind of fractalinduced oscillation,resulted from limited diffusion,found(2)At higher temperature,fractal structure controls not only nonlinear dynamics behaviors but also kinetic phase transition from highcovered state to lowcovered state of COLower dimension structure may drive the transition from the first order to second oneBut this situation does not appear at low temperature,where fractal control only moves the critical point,but it is not enough to change the transition order