author={Marshall N. Rosenbluth and Arianna W. Rosenbluth},
  journal={Journal of Chemical Physics},
The behavior of chains of very many molecules is investigated by solving a restricted random walk problem on a cubic lattice in three dimensions and a square lattice in two dimensions. In the Monte Carlo calculation a large number of chains are generated at random, subject to the restrictions of no crossing or doubling back, to give the average extension of the chain 〈R2〉Av as a function of N, the number of links in the chain. A system of weights is used in order that all possible allowed… 

Figures and Tables from this paper

Statistics of confined chains. III: Hamiltonian paths

The entropy of self-avoiding walks embedded in a square lattice has been Monte Carlo estimated inside plane squares of various side sizes R. The length of the walks ranged from one to steps, the

Excluded Volume Effect in Polymer Chains. II. Properties of Restricted Chains on a Diamond Lattice

A study has been made of nonintersecting chains of N bonds on a diamond lattice by exact enumeration for small N and extrapolation of the results to large N. For the number of configurations, an

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

Excluded Volume Effect in Polymer Chains

A new Monte Carlo method for the statistical study of the polymer chain excluded volume problem is presented. Random chains which are not allowed to have closed loops of fewer than R links are

Configurational bias Monte Carlo: a new sampling scheme for flexible chains

A new type of Monte Carlo move is introduced that makes it possible to carry out large scale conformational changes of the chain molecule in a single trial move in a novel approach that allows efficient numerical simulation of systems consisting of flexible chain molecules.

Monte Carlo simulation of the conformational entropy of polymer chains

A Monte Carlo method, namely, the ‘‘statistical counting method’’ (SCM) has been proposed for simulating the conformational entropy of a single free or confined linear self‐avoiding random walk

Enumeration of cubic lattice walks by contact class

Self-avoiding walks on a three-dimensional (3D) simple cubic lattice are often used to model polymers, especially proteins. The Hamiltonian is generally taken to be a function of contacts between

Monte Carlo studies of two measures of polymer chain size as a function of temperature

Monte Carlo simulations of single polymer chains with both excluded volume and nearest-neighbor interaction energies are discussed. Two measures of chain size are obtained in the simulation, the


Über die Gestalt fadenförmiger Moleküle in Lösungen

ZusammenfassungEs werden statistische Betrachtungen angestellt betreffend die Form, welche kettenförmig gebaute Moleküle, welche in einer Lösung (oder im Gasraum) suspendiert sind, infolge der