The Influence of Dimensionality on the Rate of Diffusive Escape From an Energy Well.
The Influence of Dimensionality on the Rate of Diffusive Escape From an Energy Well.
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维数对能量井扩散逃逸速率的影响。
DOI：
10.1115/1.4005895
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Freund,LB
中科院分区：
文献类型：
--
作者：
Freund,LB
当描述分子之间的化学键的分离时，通常使用的理想化是能量阱的理想化，其规定了分子之间的相互作用的能量在反应坐标方面的依赖性。要克服的峰和阱的根部之间的能量差是所谓的活化能，并且阱的总体形状通过关于传输的本构假设来决定分离的动力学。本说明书中隐含的一个假设是，当系统在随机热激发下探索其能量环境时，键的状态仅以单一自由度（反应坐标）演化。在本讨论中，我们将考虑由同一能量分布描述的几个键。这些情况的不同之处在于，在第一种情况下，能量分布沿着从阱的根部延伸的线变化，在第二种情况下，能量分布沿着从阱的根部延伸的平面中的任何径向线变化，并且在第三种情况下，能量分布沿着从阱的根部延伸的空间中的任何径向线变化。为了集中讨论，我们确定在每种情况下从阱中逃逸状态的统计速率，要求阱的轮廓在所有三种情况下都是相同的。它被发现，逃逸率每一个指数依赖于井的深度，但指数的系数随井的深度不同，在考虑的三种情况下。
A commonly used idealization when describing separation of a chemical bond between molecules is that of an energy well which prescribes the dependence of energy of interaction between the molecules in terms of a reaction coordinate. The energy difference between the peak to be overcome and the root of the well is the so-called activation energy, and the overall shape of the well dictates the kinetics of separation through a constitutive assumption concerning transport. An assumption tacit in this description is that the state of the bond evolves with only a single degree of freedom—the reaction coordinate—as the system explores its energy environment under random thermal excitation. In this discussion we will consider several bonds described by one and the same energy profile. The cases differ in that the energy profile varies along a line extending from the root of the well in the first case, along any radial line in a plane extending from the root of the well in a second case, and along any radial line in space extending from the root of the well in a third case. To focus the discussion we determine the statistical rate of escape of states from the well in each case, requiring that the profile of the well is the same in all three cases. It is found that the rates of escape each depend exponentially on the depth of the well but that the coefficients of the exponential vary with depth of the well differently in the three cases considered.