A mean field approach to the structure of polyelectrolytes

We describe a variational mean field study of polyelectrolyte expansion based on the application of the Gibbs–Bogoliubov inequality and a generalized Gaussian trial Hamiltonian. The screened electrostatic interactions among the charged beads on the polyion are approximated by a pairwise additive Yukawa potential while we treat the excluded volume effects in terms of the Dirac δ function in the way usual in studies of neutral polymers. Expressing the Hamiltonian in terms of Fourier components, the variational procedure yields a set of Euler equations that are analyzed by the method of dominant balance to study the scaling regimes in various limiting situations. The method predicts correct scaling laws for weakly screened polyelectrolytes, dominated by long‐ranged Coulombic repulsions. At strong screening or low degrees of ionization, when the polymer resembles a self‐avoiding walk, the calculations overestimate the scaling exponent, the value of ∼4/3 replacing the Flory value, a deficiency known from earli...

[1]  C. Woodward,et al.  Mean-field Monte Carlo technique for studies of electric double layers and flexible polyelectrolytes , 1992 .

[2]  W. Reed,et al.  Monte Carlo study of titration of linear polyelectrolytes , 1992 .

[3]  R. Podgornik.  Self-consistent-field theory for confined polyelectrolyte chains , 1992 .

[4]  H. Orland,et al.  Scaling behavior of polyelectrolytes and polyampholytes: Simulation by an ensemble growth method , 1991 .

[5]  B. Jönsson,et al.  Monte Carlo and mean field studies of a polyelectrolyte in salt solution , 1991 .

[6]  A. Teŕamoto,et al.  Perturbation theory of isotropic-liquid-crystal phase equilibria in polyelectrolyte solutions , 1991 .

[7]  J. Victor.  Poisson-Boltzmann integral equation for polyelectrolyte solutions , 1991 .

[8]  J. D. Cloizeaux,et al.  Polymers in Solution: Their Modelling and Structure , 2010 .

[9]  P. Higgs,et al.  Conformation changes of a polyelectrolyte chain in a poor solvent , 1991 .

[10]  S. Carnie,et al.  Computer simulations of polyelectrolyte chains in salt solution , 1990 .

[11]  J. Valleau.  Flexible polyelectrolyte in ionic solution: A Monte Carlo study , 1989 .

[12]  A. Kholodenko,et al.  Conformational statistics of random polyelectrolyte chain in theta region and transition to collapse: Qualitative study , 1988 .

[13]  S. Edwards,et al.  The size of a polymer in random media , 1988 .

[14]  Rajiv K. Kalia,et al.  Condensed Matter Theories , 1988 .

[15]  M. Muthukumar.  Adsorption of a polyelectrolyte chain to a charged surface , 1987 .

[16]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[17]  M. Bawendi,et al.  Renormalization group treatment of excluded volume effects in a polyelectrolyte chain in the weak electrostatic coupling limit. II. Decomposition of interactions and calculation of properties , 1986 .

[18]  Harold L. Friedman.  A Course in Statistical Mechanics , 1985 .

[19]  D. Bratko,et al.  Monte Carlo studies of polyelectrolyte solutions. Effect of polyelectrolyte charge density , 1985 .

[20]  H. Mark,et al.  Encyclopedia of polymer science and engineering , 1985 .

[21]  H. Friedman,et al.  HNC solution for the central force model for liquid water , 1983 .

[22]  M. Fixman.  The flexibility of polyelectrolyte molecules , 1982 .

[23]  M. Lax,et al.  Monte Carlo lattice simulation of a simple electrolyte , 1981 .

[24]  Sam F. Edwards,et al.  Size of a polymer molecule in solution. Part 1.—Excluded volume problem , 1979 .

[25]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[26]  J. Skolnick,et al.  Polyelectrolyte Excluded Volume Paradox , 1978 .

[27]  T. Odijk,et al.  On the theory of the excluded‐volume effect of a polyelectrolyte in a 1‐1 electrolyte solution , 1978 .

[28]  J. Skolnick,et al.  Electrostatic Persistence Length of a Wormlike Polyelectrolyte , 1977 .

[29]  J. Bailey.  An Asymptotic Self-Consistent Field Theory of Polyelectrolyte Expansion , 1977 .

[30]  T. Odijk.  Polyelectrolytes near the rod limit , 1977 .

[31]  Rosa María Velasco,et al.  Remarks on polyelectrolyte conformation , 1976 .

[32]  J. D. Cloizeaux.  The statistics of long chains with non-Markovian repulsive interactions and the minimal gaussian approximation , 1970 .

[33]  G. Felsenfeld,et al.  Conformation of polyribouridylic acid in solution. , 1970, Journal of molecular biology.

[34]  Jacqueline I. Kroschwitz,et al.  Encyclopedia of Polymer Science and Technology , 1970 .

[35]  Gerald S. Manning,et al.  Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties , 1969 .

[36]  H. Reiss.  Variation Principle Treatment of the Excluded‐Volume Problem , 1967 .

[37]  Charles Tanford,et al.  Physical Chemistry of Macromolecules , 1961 .

[38]  M. Nagasawa,et al.  Colligative properties of polyelectrolyte solutions. V. Activity coefficients of counter‐ and by‐ions , 1959 .

[39]  P. Doty,et al.  Macro-ions. II. Polymethacrylic Acid , 1952 .

[40]  Paul J. Flory,et al.  The Configuration of Real Polymer Chains , 1949 .

[41]  A. Katchalsky,et al.  Verhalten polyvalenter Fadenmolekelionen in Lösung , 1948 .