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基于缩放二阶直接相关函数的聚合物密度泛函理论方法。

Polymer density functional theory approach based on scaling second-order direct correlation function.

作者信息

Zhou Shiqi

机构信息

Institute of Modern Statistical Mechanics, Zhuzhou Institute of Technology, Wenhua Road, Zhuzhou City 412008, People's Republic of China.

出版信息

J Colloid Interface Sci. 2006 Jun 1;298(1):31-8. doi: 10.1016/j.jcis.2005.11.069. Epub 2006 Jan 5.

Abstract

A second-order direct correlation function (DCF) from solving the polymer-RISM integral equation is scaled up or down by an equation of state for bulk polymer, the resultant scaling second-order DCF is in better agreement with corresponding simulation results than the un-scaling second-order DCF. When the scaling second-order DCF is imported into a recently proposed LTDFA-based polymer DFT approach, an originally associated adjustable but mathematically meaningless parameter now becomes mathematically meaningful, i.e., the numerical value lies now between 0 and 1. When the adjustable parameter-free version of the LTDFA is used instead of the LTDFA, i.e., the adjustable parameter is fixed at 0.5, the resultant parameter-free version of the scaling LTDFA-based polymer DFT is also in good agreement with the corresponding simulation data for density profiles. The parameter-free version of the scaling LTDFA-based polymer DFT is employed to investigate the density profiles of a freely jointed tangent hard sphere chain near a variable sized central hard sphere, again the predictions reproduce accurately the simulational results. Importance of the present adjustable parameter-free version lies in its combination with a recently proposed universal theoretical way, in the resultant formalism, the contact theorem is still met by the adjustable parameter associated with the theoretical way.

摘要

通过求解聚合物 - RISM积分方程得到的二阶直接相关函数(DCF),利用本体聚合物的状态方程进行放大或缩小,所得的缩放后的二阶DCF比未缩放的二阶DCF与相应的模拟结果更吻合。当将缩放后的二阶DCF引入最近提出的基于LTDFA的聚合物DFT方法时,一个原本相关的可调但数学上无意义的参数现在变得在数学上有意义,即其数值现在介于0和1之间。当使用LTDFA的无可调参数版本而非LTDFA时,即可调参数固定为0.5,所得的基于缩放LTDFA的聚合物DFT的无参数版本也与密度分布的相应模拟数据吻合良好。基于缩放LTDFA的聚合物DFT的无参数版本被用于研究可变大小的中心硬球附近自由连接的切向硬球链的密度分布,其预测再次准确地再现了模拟结果。当前无可调参数版本的重要性在于它与最近提出的通用理论方法相结合,在所得的形式体系中,与该理论方法相关的可调参数仍然满足接触定理。

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