Long time tail in the diffusion of a spherical polymer

✍ Scribed by R.B. Jones

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 700 KB
• Volume: 101
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(80)90184-3

✦ Synopsis

We study the velocity autocorrelation function for the diffusion of a spherical macromolecule in solution. The diffusion is described by a generalized Langevin equation with memory character derived previously from fluctuation theory applied to the Debye-Bueche-Brinkman equation which describes the polymer-fluid interaction. The long time behaviour of the velocity autocorrelation function is obtained by establishing a low frequency expansion for the drag coefficient ~'(to). To derive this expansion we prove a number of analyticity properties of ~'(to). The longest lived contribution to the velocity autocorrelation function goes as t -3/2 as first discovered by Alder and Wainwright. We also obtain the first correction term of order t -s/2 which depends explicitly on the polymer structure. By use of a generalization of the Lorentz reciprocity theorem we show that the coefficient of this t -5/2 term is given in terms of the polymer mass and the two structure dependent coefficients that enter the static Fax6n theorem for the total force on the polymer.