Melvin Lax

A Monte Carlo off‐lattice method: The slithering snake in a continuum

An off‐lattice Monte Carlo simulation of a polymer chain using the slithering snake method is introduced. The mean square end‐to‐end distance is calculated and compared with previous studies. Results indicate that small angular deviations from the tetrahedral lattice models produce large conformational change in the polymer chain.

Self‐avoiding walks with span limitations. I. The mean square end‐to‐end distance

Self‐avoiding walks on the simple cubic lattice of lengths up to 11 steps were exactly enumerated. The mean square end‐to‐end distance and its mean square components were recorded as a function of the span separation along one principle Cartesian axis. The molecular weight dependence for narrow spans (thin slabs—up to two lattice spacings) obeys that of a two‐dimensional walk as conjectured by Wall et al. As the slab thickness increases, one encounters a dimensionality transition in the behavior of the mean separations which is compared with similar transitions observed for the self‐avoiding walk in the presence of one interacting barrier. For thick slabs the behavior is three dimensional.

Monte Carlo lattice simulation of a simple electrolyte

Monte Carlo simulations are reported for the primitive electrolyte model of Card and Valleau [Ref.4(a)]. (AIP)

Polymers confined to thin slabs: Scaling law

A scaling method is applied to a polymer in a thin slab of thickness L. The results indicate that the component of the mean square end‐to‐end distance, in the direction parallel to the slab plane, <R2y(L)≳, behaves asymptotically as <R2y(L)≳∼L−1/4 N3/2. Results from data on self‐avoiding walks generated on the SC and FCC lattices verify the scaling law.

Span of an adsorbed polymer chain

Abstract Span data for a self-avoiding walk model of a polymer chain near a barrier is analyzed. Empirical expressions are obtained for the molecular weight dependence of the first and second moments of the span of such chains. Limiting estimates for the reduced moments of the distribution function of the span are also reported.

Segmental distribution properties of a polymer chain near an interacting barrier

Abstract The exact distribution of segments for self-avoiding walks of lengths N=4–14 bonds in the presence of an interacting barrier on the diamond lattice has been obtained by the method of direct enumeration. Behavior for the infinite chain was estimated and compared with Rubins results for the normal random walk. It is shown that the onset of a well defined transition for the self-avoiding walk coincides with the location predicted for the normal random walk. It was found that for a self-avoiding walk a plot of θ2 (the fraction of segments in level z) versus the interaction parameter φ is shifted to the right (higher φ), for all z, as compared with a similar plot for the normal random walk. Conditional probabilities for a self-avoiding walk having its t th segment in level z (when φ=0) are reported.

Span components for adsorbed polymer chains

An analysis is made of the molecular weight dependence of the span of surface restricted self‐avoiding walks. Results for the normal as well as parallel components of the span for some cubic lattices are reported.

Self‐avoiding walks with span limitations. II. The mean square radius of gyration

Results are reported on the average radius of gyration <S2N(L)≳L for self‐avoiding walks of size N steps having span L generated on the simple cubic lattice. Limiting behavior was fitted to expressions of the form <S2N(L)≳L∼ANγ(L) where γ(L) was found to vary from γ(O)∼1.50 to γ(N)∼1.20. In addition, the limiting ratio <S2N(L)≳L/<R2N(L)≳L was investigated. It was found that <S2N(O)≳L/<R2N(O)≳L →0.136, whereas <S2N(N)≳L/<R2N(N)≳L →0.155. In the interval O⩽L⩽N, γ(L)→1.0, and <S2N(L)≳L/<R2N(L)≳L →0.167, indicating a conformational change in the chains to a more compact randomlike configuration.