Margolin G, Barkai E
Department of Chemistry and Biochemistry, Notre Dame University, Notre Dame, Indiana 46556, USA.
J Chem Phys. 2004 Jul 15;121(3):1566-77. doi: 10.1063/1.1763136.
Following recent experiments on power law blinking behavior of single nanocrystals, we calculate two-time intensity correlation functions I(t)I(t+t') for these systems. We use a simple two state (on and off) stochastic model to describe the dynamics. We classify possible behaviors of the correlation function and show that aging, e.g., dependence of the correlation function on age of process t, is obtained for classes of the on time and off time distributions relevant to experimental situation. Analytical asymptotic scaling behaviors of the intensity correlation in the double time t and t' domain are obtained. In the scaling limit I(t)I(t+t('))-->h(x), where four classes of behaviors are found: (i) finite averaged on and off times x=t' (standard behavior); (ii) on and off times with identical power law behaviors x=t/t' (case relevant for capped nanocrystals); (iii) exponential on times and power law off times x=tt' (case relevant for uncapped nanocrystals); (iv) for defected off time distribution we also find x=t+t'. Origin of aging behavior is explained based on simple diffusion model. We argue that the diffusion controlled reaction A+B <==>AB, when followed on a single particle level exhibits aging behavior.
在最近关于单个纳米晶体幂律闪烁行为的实验之后，我们计算了这些系统的双时强度关联函数(I(t)I(t + t'))。我们使用一个简单的两态（开和关）随机模型来描述动力学。我们对关联函数的可能行为进行了分类，并表明对于与实验情况相关的开启时间和关闭时间分布类别，会出现老化现象，例如关联函数对过程时间(t)的依赖性。我们得到了双时(t)和(t')域中强度关联的解析渐近标度行为。在标度极限下(I(t)I(t + t('))\to h(x))，其中发现了四类行为：(i) 有限的平均开启和关闭时间(x = t')（标准行为）；(ii) 具有相同幂律行为的开启和关闭时间(x = t/t')（与 capped 纳米晶体相关的情况）；(iii) 指数开启时间和幂律关闭时间(x = tt')（与 uncapped 纳米晶体相关的情况）；(iv) 对于有缺陷的关闭时间分布，我们还发现(x = t + t')。基于简单扩散模型解释了老化行为的起源。我们认为，当在单个粒子水平上跟踪扩散控制反应(A + B \rightleftharpoons AB)时，会表现出老化行为。
