Computer simulation of long polymers adsorbed on a surface. II. Critical behavior of a single self‐avoiding walk

The scanning simulation method is applied to a model of polymer adsorption in which a single self‐avoiding walk is terminally attached to an attracting impenetrable surface on a simple cubic lattice. Relatively long chains are studied, of up to 1000 steps, which enable us to obtain new estimates for the reciprocal transition temperature ‖e‖/kBTa=θa =0.291±0.001 (e is the interaction energy of a monomer with the surface), the crossover exponent φ=0.530±0.007 and the free energy exponents at Ta, γ1SB =1.304±0.006 and γ11SB =0.805±0.015. At T=∞ we obtain, γ1=0.687±0.005, γ11=−0.38±0.02, and the effective coordination number q=4.6839±0.0001, which are in good agreement with estimates obtained by other methods. At T>Ta we demonstrate the existence of strong correction to scaling for the perpendicular part of the mean‐square end‐to‐end distance 〈R2〉⊥ and for the monomer concentration profile ρ(z) (z is the distance from the surface). At T=∞ the leading correction to scaling term for 〈R2〉⊥ is c/Nψ, where c≊−0.9 ...

[1]  Kurt Kremer,et al.  Adsorption of polymer chains at surfaces: Scaling and Monte Carlo analyses , 1982 .

[2]  S. Edwards.  The statistical mechanics of polymers with excluded volume , 1965 .

[3]  Hagai Meirovitch,et al.  A new simulation of branched polymers , 1987 .

[4]  P. G. de Gennes,et al.  Polymer solutions near an interface. Adsorption and depletion layers , 1981 .

[5]  A. Bray,et al.  Critical behaviour of semi-infinite systems , 1977 .

[6]  A. Silberberg.  Adsorption of Flexible Macromolecules. IV. Effect of Solvent–Solute Interactions, Solute Concentration, and Molecular Weight , 1968 .

[7]  G. Torrie,et al.  Some tests of scaling theory for a self-avoiding walk attached to a surface , 1978 .

[8]  S. Dietrich,et al.  Field-theoretical approach to multicritical behavior near free surfaces , 1981 .

[9]  P. Gennes,et al.  Scaling theory of polymer adsorption : proximal exponent , 1983 .

[10]  J. Orban,et al.  On the conformational transition of a self‐avoiding walk adsorbed at an interface , 1981 .

[11]  K. Schmidt.  Using renormalization-group ideas in Monte Carlo sampling , 1983 .

[12]  A. Guttmann,et al.  Critical behaviour of the n-vector model with a free surface , 1980 .

[13]  P. Gennes.  Scaling theory of polymer adsorption , 1976 .

[14]  M. Lax.  A Direct Enumeration Study of Self-Avoiding Walks Terminally Attached to a Surface , 1974 .

[15]  P. Richmond,et al.  Effects of excluded volume on the conformation of adsorbed polymers , 1977 .

[16]  C. Croxton.  A Monte Carlo analysis of terminally attached self-avoiding polymer sequences in the vicinity of a rigid boundary , 1986 .

[17]  T. Ishinabe.  Critical exponents for surface interacting self‐avoiding lattice walks. II. The square lattice , 1982 .

[18]  K. Freed.  Excluded volume effects in polymers attached to surfaces: Chain conformational renormalization group , 1983 .

[19]  M. N. Barber.  Scaling Relations for Critical Exponents of Surface Properties of Magnets , 1973 .

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

[21]  S. Whittington,et al.  Exact enumeration of self‐avoiding walks on the cubic lattice terminally attached to an interface , 1976 .

[22]  A. Sokal,et al.  New Monte Carlo method for the self-avoiding walk , 1985 .

[23]  M. Lax,et al.  Surface Effects of the Four-Choice Cubic Lattice , 1975 .

[24]  M. Lax.  A Study of the Segmental Distribution of a Polymer Chain Terminally Attached to a Surface , 1975 .

[25]  K. Kremer.  Adsorption of a self-avoiding walk, a real space renormalisation group study of d=2,3 , 1983 .

[26]  G. Torrie,et al.  The surface susceptibility exponent for the polymer problem , 1980 .

[27]  Frank L. McCrackin,et al.  Configuration of Isolated Polymer Molecules Adsorbed on Solid Surfaces Studied by Monte‐Carlo Computer Simulation , 1967 .

[28]  P. G. de Gennes,et al.  Exponents for the excluded volume problem as derived by the Wilson method , 1972 .

[29]  G. J. Fleer,et al.  Statistical theory of the adsorption of interacting chain molecules. II. Train, loop, and tail size distribution , 1980 .

[30]  S. Whittington,et al.  Asymptotic Behavior of the Number of Self-Avoiding Walks Terminally Attached to a Surface to which They Never Return , 1977 .

[31]  P. G. de Gennes,et al.  Some conformation problems for long macromolecules , 1969 .

[32]  T. Lubensky,et al.  Critical phenomena in semi-infinite systems. I.εexpansion for positive extrapolation length , 1975 .

[33]  M. Watts.  The end-point distribution of self-avoiding walks on a crystal lattice. II. Loose-packed lattices , 1974 .

[34]  S. Dietrich,et al.  Scaling laws and surface exponents from renormalization group equations , 1980 .

[35]  S. Dietrich,et al.  Critical behaviour of the energy density in semi-infinite systems , 1981 .

[36]  G. Torrie,et al.  Self‐avoiding walks interacting with an interface , 1976 .

[37]  T. Ishinabe.  Critical exponents for surface interacting self-avoiding lattice walks. I. Three-dimensional lattices , 1982 .

[38]  Interaction of a polymer chain with an asymmetric liquid-liquid interface , 1986 .

[39]  J. Hammersley,et al.  Self-avoiding walks interacting with a surface , 1982 .

[40]  P. C. Hohenberg,et al.  Phase Transitions and Static Spin Correlations in Ising Models with Free Surfaces , 1972 .

[41]  H. Meirovitch,et al.  Computer simulation of long polymers adsorbed on a surface. I. Corrections to scaling in an ideal chain , 1988 .

[42]  P. Gennes.  Scaling Concepts in Polymer Physics , 1979 .

[43]  P. C. Hohenberg,et al.  Surface effects on magnetic phase transitions , 1974 .

[44]  H. Meirovitch,et al.  Scanning method as an unbiased simulation technique and its application to the study of self-attracting random walks. , 1985, Physical review. A, General physics.