MATHEMATICAL MODELS OF MACROMOLECULAR CONFORMATIONS AND THEIR APPLICATION

• 作 者: 吴让泉 程正迪 吴承训
• 机 构: China Textile University, Shanghai,China Textile University, Shanghai,China Textile University, Shan
• 出 处: Science in China,Ser.B
• 发表日期: 1986年09期
• 关键词: Brownian excluded probabilistic calculating stiffness chains hitting flexibility

In this paper we suggest that the mathematical model of 6-dimensional (or more generally, n-dimensional) Brownian motion can be used to simulate the conformations of a macromolecular chain with the short (or long) range interaction. The dimensional value n is a significant characteristic of the flexibility-stiffness of the polymer chain. Under the condition of the constant module of the end-to-end state vector, we derived the probabilistic expression for the continuous transition of polymer chains from flexibility to stiffness.These models are still valid if the excluded volume effect is considered. By using the concept of the first hitting-time, we obtained the analytical expression of the partial transfer probability density function q_B(n,x;y) and the formula for calculating the parameter of the excluded volume effect.

In this paper we suggest that the mathematical model of 6-dimensional (or more generally, n-dimensional) Brownian motion can be used to simulate the conformations of a macromolecular chain with the short (or long) range interaction. The dimensional value n is a significant characteristic of the flexibility-stiffness of the polymer chain. Under the condition of the constant module of the end-to-end state vector, we derived the probabilistic expression for the continuous transition of polymer chains from flexibility to stiffness. The models are still valid if the excluded volume effect is considered. By using the concept of the first hitting-time, we obtained the analytical expression of the partial transfer probability density function q_B (n, x; y) and the formula for calculating the parameter of the excluded volume effect.