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DOI: 10.1063/1.445549

# Computer Simulation Of Self-avoiding Walks: Testing The Scanning Method

H. Meirovitch

Published 1983 · Chemistry

The scanning method is a computer simulation technique for macromolecules suggested recently. The method is described here in detail and its applicability (in contrast to other simulation techniques) to a wide range of chain models is discussed. It is argued that for most of these models the scanning method constitutes the most efficient tool for estimating the entropy. The method is applied to self‐avoiding walks (SAWs) (of N≤399 steps) on both a three‐choice square lattice and a five‐choice simple cubic lattice and the results for the entropy, the end‐to‐end distance, the radius of gyration, and other quantities of interest are found to be in very good agreement with the results obtained by other numerical techniques. In particular, our calculations support the law of divergence for the persistence length of SAWs on two‐dimensional lattices suggested recently by Grassberger. However, for the simple cubic lattice, the persistence length is found by us to be constant.

This paper references

10.1088/0305-4470/8/8/017

The shape of polymer chains and rings

D. Rapaport (1975)

10.1103/PHYSREVB.17.1365

Critical Indices from Perturbation Analysis of the Callan-Symanzik Equation

G. Baker (1978)

10.1063/1.1696437

Monte Carlo Generation of a Restricted Random Walk and the Excluded‐Volume Problem

S. Windwer (1965)

10.1088/0305-4470/11/8/008

Molecular dynamics simulation of polymer chains with excluded volume

D. Rapaport (1978)

10.1063/1.1678909

Mean square endpoint separation of off‐lattice self‐avoiding walks

R. Grishman (1973)

10.1063/1.433279

Self‐avoiding walks interacting with an interface

G. Torrie (1976)

10.2307/3610170

Symposium on Monte Carlo Methods

S. Vajda (1957)

10.1021/MA50006A065

COMPUTER SIMULATION OF THE STATIC AND DYNAMIC PROPERTIES OF A POLYMER CHAIN

D. Ceperley (1981)

10.1063/1.434297

Excluded volume effects in the stabilization of colloids by polymers

K. M. Middlemiss (1977)

10.1063/1.1733626

Excluded‐Volume Effect for Two‐ and Three‐Dimensional Lattice Models

C. Domb (1963)

10.1063/1.431357

Self‐avoiding walks terminally attached to an interface

S. Whittington (1975)

10.1103/PHYSREVB.21.3976

Critical exponents from field theory

J. L. Guillou (1980)

10.1021/MA60041A028

Polymer Adsorption on a Surface by an Exact Enumeration Study

P. Mark (1974)

10.1063/1.1670122

Monte Carlo Studies of Configurational and Thermodynamic Properties of Self‐Interacting Linear Polymer Chains

J. Mazur (1968)

10.1007/BF01012031

On the zero fluctuation of the “microscopic free energy” and its potential use

H. Meirovitch (1976)

10.1063/1.441836

Polymers confined to thin slabs: Scaling law

M. Lax (1981)

10.1063/1.1732301

Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution

P. H. Verdier (1962)

10.1088/0305-4470/8/1/012

Application of the method of Pade approximants to the excluded volume problem

M. Watts (1975)

10.1073/PNAS.75.5.2069

Statistics of self-avoiding walks confined to strips and capillaries.

F. Wall (1978)

10.1063/1.431268

Macromolecular dimensions obtained by an efficient Monte Carlo method without sample attrition

F. T. Wall (1975)

10.1063/1.1712225

Configuration of Isolated Polymer Molecules Adsorbed on Solid Surfaces Studied by Monte‐Carlo Computer Simulation

F. McCrackin (1967)

10.1088/0305-4470/2/2/001

The entropy of a confined polymer. I

S. Edwards (1969)

10.1007/BF01420588

The critical behaviour of two-dimensional self-avoiding random walks

P. Grassberger (1982)

10.1021/MA00236A018

Method for estimating the entropy of macromolecules with computer simulation. Chains with excluded volume

H. Meirovitch (1983)

10.1103/PHYSREVLETT.50.736

Self-Avoiding Walks of Continuous Spatial Dimensionality

Z. Alexandrowicz (1983)

10.1021/MA60042A022

On the Osmotic Second Viral Coefficient of Athermal Polymer Solutions

A. Bellemans (1974)

10.1063/1.1841242

Probability of Initial Ring Closure for Self‐Avoiding Walks on the Face‐Centered Cubic and Triangular Lattices

J. L. Martin (1967)

10.1063/1.1672034

Monte Carlo of Chains with Excluded Volume: a Way to Evade Sample Attrition

Z. Alexandrowicz (1969)

10.1063/1.1741967

MONTE CARLO CALCULATION OF THE AVERAGE EXTENSION OF MOLECULAR CHAINS

M. Rosenbluth (1955)

10.1063/1.432523

Monte Carlo study of systems of linear oligomers in two‐dimensional spaces

H. Okamoto (1976)

10.1063/1.435311

Simulation of polymers by self‐avoiding, nonintersecting random chains at various concentrations

F. T. Wall (1977)

10.1088/0305-4470/7/4/012

The end-point distribution of self-avoiding walks on a crystal lattice. II. Loose-packed lattices

M. Watts (1974)

10.1063/1.1681416

Numerical results on the radius of gyration of surface interacting self‐avoiding walks

M. Lax (1974)

10.1063/1.1730022

Statistical Computation of Radii of Gyration and Mean Internal Dimensions of Polymer Molecules

F. T. Wall (1959)

10.5860/choice.33-2140

Principles of polymer chemistry

P. J. Flory (1953)

10.1021/MA60036A016

Monte Carlo Studies of Self-Interacting Polymer Chains with Excluded Volume. II. Shape of a Chain

J. Mazur (1973)

10.1007/BF01293328

Self-avoiding-walks (SAW's) on diluted lattices, a Monte Carlo analysis

K. Kremer (1981)

Modern Theory of Polymer Solutions

H. Yamakawa (1971)

10.1063/1.433381

Self‐avoiding random walks subject to external spatial constraints

F. T. Wall (1976)

10.1088/0305-4470/2/2/002

The entropy of a confined polymer. II

R. Collins (1969)

10.1063/1.438608

Monte Carlo studies on the freely jointed polymer chain with excluded volume interaction

A. Baumgaertner (1979)

10.1103/PHYSREVLETT.49.1062

Exact Critical Point and Critical Exponents of O ( n ) Models in Two Dimensions

B. Nienhuis (1982)

10.1063/1.432498

Computer simulation of multiple chain systems—equation of state of hard sphere chains

J. Curro (1976)

10.1063/1.1743664

Improved Statistical Method for Computing Mean Dimensions of Polymer Molecules

F. T. Wall (1957)

10.1088/0305-4470/15/12/014

A new method for simulation of real chains: scanning future steps

H. Meirovitch (1982)

10.1088/0305-4470/14/1/002

Phenomenological renormalisation of the self avoiding walk in two dimensions

B. Derrida (1981)

10.1063/1.433423

The configurational statistics of a polymeric chain confined by impenetrable barriers

R. Gaylord (1976)

10.1063/1.1672277

Mean‐Square Intrachain Distances in a Self‐Avoiding Walk

C. Domb (1969)

This paper is referenced by

10.1016/S0032-3861(02)00240-9

Energetic analysis of the two PMMA chain tacticities and PMA through molecular dynamics simulations

A. Soldera (2002)

10.1109/ESTC.2006.280098

Diffusion of Water in Amorphous Polymers at Different Temperatures Using Molecular Dynamics Simulation

E. Dermitzaki (2006)

10.1088/0305-4470/19/9/015

On the correction-to-scaling exponent of linear polymers in two dimensions

D. Hunter (1986)

10.1016/0166-1280(95)04433-7

A model of solvation of polypeptide side chains. Application to angiotensin II

O. Collet (1996)

Chapter 2 Preparation of the PVME Cells

J. C. Berthet (2005)

10.1016/J.COMMATSCI.2016.04.006

A criterion for the normal properties of graphene/polymer interface

Zeshuai Yuan (2016)

10.1016/J.MOLLIQ.2018.09.048

Component compatibility study of poly(dimethyl siloxane) with poly(vinyl acetate) of varying hydrolysis content: An atomistic and mesoscale simulation approach

S. K. Sethi (2018)

10.1016/J.MEMSCI.2016.05.021

Effect of type of poly(ethylene glycol) (PEG) based amphiphilic copolymer on antifouling properties of copolymer/poly(vinylidene fluoride) (PVDF) blend membranes

W. Ma (2016)

10.1002/POLB.21808

Using vibrational mode analysis for predicting the coefficient of thermal expansion of amorphous polymers

S. Shenogin (2009)

10.1080/08927022.2016.1241397

Mechanical equilibrium, a prerequisite to unveil auxetic properties in molecular compounds

F. Porzio (2017)

10.1038/s41598-019-45933-2

Local dynamics within the glass transition domain

F. Godey (2019)

10.1063/1.470345

On the equation of state for thermal polymer solutions and melts

M. Wolfgardt (1995)

10.1088/0305-4470/25/4/013

The Ising model on a SAW

M. Aertsens (1992)

10.1002/jcc.10316

Development and validation of COMPASS force field parameters for molecules with aliphatic azide chains

M. McQuaid (2004)

10.1016/J.MEMSCI.2018.07.016

Experimental and modeling study of blended membranes for direct methanol fuel cells

D. J. Kim (2018)

10.1021/am200264r

Adsorption and association of a symmetric PEO-PPO-PEO triblock copolymer on polypropylene, polyethylene, and cellulose surfaces.

Y. Li (2011)

10.1080/08927020601059901

Computation of densities, bulk moduli and glass transition temperatures of vinylic polymers from atomistic simulation

N. Metatla (2006)

10.1007/s10965-016-1174-3

Molecular simulation and experimental studies of the miscibility of polylactic acid/polyethylene glycol blends

Adisak Takhulee (2016)

Study of the Glass Transition Temperatures of Stereoregular PMMAs Using Different Force Fields

B. Press (2005)

10.1002/jcc.25069

The extent of the glass transition from molecular simulation revealing an overcrank effect

F. Godey (2018)

10.1016/J.SOLMAT.2017.06.016

Multiscale design and optimization of polymer-based photonic crystals for solar shielding

M. Bensaid (2017)

10.1016/J.POLYMER.2010.03.003

Heat capacities of both PMMA stereomers: Comparison between atomistic simulation and experimental data

A. Soldera (2010)

10.1109/HPCMP-UGC.2007.17

Combustion Chamber Fluid Dynamics and Hypergolic Gel Propellant Chemistry Simulations for Selectable Thrust Rocket Engines

M.J. Nusca (2006)

10.1002/adma.201403361

Chemically Specific Multiscale Modeling of Clay–Polymer Nanocomposites Reveals Intercalation Dynamics, Tactoid Self-Assembly and Emergent Materials Properties

J. Suter (2015)

10.1002/MASY.19981330105

Comparison between the glass transition temperatures of the two PMMA tacticities : A molecular dynamics simulation point of view

A. Soldera (1998)

10.1088/0964-1726/16/5/011

Molecular dynamics simulations of the shape-memory behaviour of polyisoprene

J. Diani (2007)

10.1016/J.POLYMER.2003.04.005

Molecular modelling of the uniaxial deformation of amorphous polyethylene terephthalate

M. Roberge (2004)

10.1039/c9cp04276h

How to characterize interfacial load transfer in spiral carbon-based nanostructure-reinforced nanocomposites: is this a geometry-dependent process?

A. Sharifian (2019)

10.1016/B978-0-32-346240-2.00007-8

Thermal Conductivity of Diamond Nanothread

H. Zhan (2017)

An Information Theoretic Study of the Ising Antiferromagnet with Quenched Dilution on a Triangular Lattice

M. D. Robinson (2003)

10.1002/APP.28005

Molecular dynamics simulations on the blends of poly(vinyl pyrrolidone) and poly(bisphenol‐A‐ether sulfone)

Sheetal S. Jawalkar (2008)

10.1002/APP.36977

Molecular simulation on relationship between composition and microstructure of PP/PC blend

Shanshan Dai (2012)

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