Department of Chemistry, University of Delhi, Delhi-110007, India.
Phys Chem Chem Phys. 2013 Dec 14;15(46):20294-302. doi: 10.1039/c3cp53864h.
The orientational relaxation dynamics of semiflexible dendrimers are theoretically calculated within the framework of optimized Rouse-Zimm formalism. Semiflexibility is modeled through appropriate restrictions in the direction and orientation of the respective bond vectors, while the hydrodynamic interactions are included via the preaveraged Oseen tensor. The time autocorrelation function M(i)(1)(t) and the second order orientational autocorrelation function P(i)(2)(t) are analyzed as a function of the branch-point functionality and the degree of semiflexibility. Our approach of calculating M(i)(1)(t) is completely different from that of the earlier studies (A. Perico and M. Guenza J. Chem. Phys., 1985, 83, 3103; J. Chem. Phys., 1986, 84, 510), where the expression of M(i)(1)(t) obtained from earlier studies does not demarcate the flexible dendrimers from the semiflexible ones. The component of global motion of the time autocorrelation function exhibits a strong dependence on both degree of semiflexibility and branch-point functionality, while the component of pulsation motion depends only on the degree of semiflexibility. But it is difficult to distinguish the difference in the extent of pulsation motion among the compressed (0 < φ < π/2) and expanded (π/2 < φ < π) conformations of semiflexible dendrimers. The qualitative behavior of P(i)(2)(t) obtained from our calculations closely matches with the expression for P(exact)(2)(t) in the earlier studies. Theoretically calculated spectral density, J(ω), is found to depend on the degree of semiflexibility and the branch-point functionality for the compressed and expanded conformations of semiflexible dendrimers as a function of frequency, especially in the high frequency regime, where J(ω) decays with frequency for both compressed and expanded conformations of semiflexible dendrimers. This decay of the spectral density occurs after displaying a cross-over behavior with the variation in the degree of semiflexibility in the intermediate frequency regime. The characteristic area increases with the increase in the semiflexibility parameter, where the expanded conformations of semiflexible dendrimers record the maximum characteristic area. For the compressed conformations the relative increment of this area is considerably lower than that of the expanded conformations of semiflexible dendrimers.
半刚性树状大分子的取向弛豫动力学是在优化的罗瑟-齐姆公式框架内理论计算的。半刚性通过对各个键矢量的方向和取向的适当限制来建模，而水动力相互作用则通过预平均的奥森张量来包含。分析了作为支化点功能和半刚性程度函数的时间自相关函数 M(i)(1)(t)和二阶取向自相关函数 P(i)(2)(t)。我们计算 M(i)(1)(t)的方法与早期研究完全不同（A. Perico 和 M. Guenza J. Chem. Phys.，1985，83，3103；J. Chem. Phys.，1986，84，510），其中早期研究中获得的 M(i)(1)(t)表达式并不能将柔性树状大分子与半刚性树状大分子区分开来。时间自相关函数的全局运动分量强烈依赖于半刚性程度和支化点功能，而脉动运动分量仅取决于半刚性程度。但是，很难区分半刚性树状大分子的压缩（0 < φ < π/2）和扩展（π/2 < φ < π）构象之间脉动运动程度的差异。从我们的计算中得到的 P(i)(2)(t)的定性行为与早期研究中 P(exact)(2)(t)的表达式非常吻合。理论计算的光谱密度 J(ω)被发现取决于半刚性程度和支化点功能，以及作为频率函数的半刚性树状大分子的压缩和扩展构象，特别是在高频区，其中 J(ω)在半刚性树状大分子的压缩和扩展构象中随频率衰减。这种光谱密度的衰减在中间频率范围内随着半刚性程度的变化表现出交叉行为后发生。特征区域随着半刚性参数的增加而增加，其中半刚性树状大分子的扩展构象记录最大特征区域。对于压缩构象，该区域的相对增量明显低于半刚性树状大分子的扩展构象。
