Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution

A method is described for simulating the dynamical behavior of a linear polymer in dilute solution, subject to random collision with solvent molecules. Equilibrium distributions of various chain dimensions may be obtained by periodic inspection of the chain. Relaxation phenomena in such chains may also be studied. Results are given for equilibrium distribution and relaxation behavior of the end‐to‐end length, for chains of 8, 16, 32, and 64 beads. The equilibrium chain dimensions are in satisfactory accord with the calculations of Wall and his collaborators, while the relaxation times are close to those predicted with the aid of the hydrodynamic theory of Rouse and Zimm.

[1]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion II , 1945 .

[2]  A. W. Rosenbluth,et al.  MONTE CARLO CALCULATION OF THE AVERAGE EXTENSION OF MOLECULAR CHAINS , 1955 .

[3]  F. T. Wall,et al.  Statistical Computation of Mean Dimensions of Polymer Molecules. IV , 1957 .

[4]  J. Kiefer,et al.  An Introduction to Stochastic Processes. , 1956 .

[5]  P. Flory.  Principles of polymer chemistry , 1953 .

[6]  L. Hiller,et al.  PROPERTIES OF MACROMOLECULES IN SOLUTION , 1954 .

[7]  B. Zimm.  Dynamics of Polymer Molecules in Dilute Solution: Viscoelasticity, Flow Birefringence and Dielectric Loss , 1956 .

[8]  Martin Greenberger,et al.  Microanalysis of Socioeconomic Systems: A Simulation Study , 1962 .

[9]  A. Roig,et al.  Excluded Volume Effect of Linear Polymer Molecules , 1960 .

[10]  A. Miyake.  General Theory of Relaxations in the Polymer Chain , 1959 .

[11]  N. Wax,et al.  Selected Papers on Noise and Stochastic Processes , 1955 .

[12]  F. T. Wall,et al.  New Method for the Statistical Computation of Polymer Dimensions , 1959 .

[13]  P. E. Rouse.  A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers , 1953 .

[14]  W. Stockmayer.  Problems of the statistical thermodynamics of dilute polymer solutions , 1960 .

[15]  Leonard M. Isaacson,et al.  Improved Statistical Method for Computing Mean Dimensions of Polymer Molecules , 1957 .

[16]  W. Kuhn,et al.  Über die Gestalt fadenförmiger Moleküle in Lösungen , 1934 .