POISSON-BOLTZMANN EQUATION AND ITS APPLICATION TO POLYELECTROLYTES

被引:324
作者
FIXMAN, M
机构
[1] Department of Chemistry, Yale University, New Haven
关键词
D O I
10.1063/1.437340
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
The validity of the Poisson-Boltzmann (PB) equation is reconsidered on the basis of functional expansion techniques supplemented by the mean spherical approximation. In the application of greatest interest a strong Coulomb potential originating in an external source, such as a polyelectrolyte molecule, acts on a salt solution of small mobile ions. Where the local charge density of mobile ions is high, substantial errors may occur in the PB approximation that relates charge density to mean potential. However, the solution to the PB equation is nevertheless a good approximation in the indicated application because a quite small percentage change in the electrostatic potential can compensate large errors in the Boltzmann distribution. An application to DNA illustrates this compensation, and also its impending failure at bulk salt concentrations in excess of 0.1 M. A two phase (or condensation) model is derived as an approximation to the PB equation and retains fair accuracy even at substantial salt concentrations, where the limiting laws lose theoretical validity. © 1979 American Institute of Physics.
引用
收藏
页码:4995 / 5005
页数:11
相关论文
共 28 条
[1]   THE COUNTERION DISTRIBUTION IN SOLUTIONS OF ROD-SHAPED POLYELECTROLYTES [J].
ALFREY, T ;
BERG, PW ;
MORAWETZ, H .
JOURNAL OF POLYMER SCIENCE, 1951, 7 (05) :543-547
[2]  
BELL GM, 1966, CHEM PHYSICS IONIC S, P409
[3]   STATISTICAL MECHANICAL THEORY OF DOUBLE-LAYER STRUCTURE AND PROPERTIES [J].
Buff, FP ;
Stillinger, FH .
JOURNAL OF CHEMICAL PHYSICS, 1963, 39 (08) :1911-+
[4]   POLYELECTROLYTE EXCLUDED VOLUME PARADOX [J].
FIXMAN, M ;
SKOLNICK, J .
MACROMOLECULES, 1978, 11 (05) :863-867
[5]   THE POTENTIAL OF AN INFINITE ROD-LIKE MOLECULE AND THE DISTRIBUTION OF THE COUNTER IONS [J].
FUOSS, RM ;
KATCHALSKY, A ;
LIFSON, S .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1951, 37 (09) :579-589
[6]   SOME EXACT RESULTS AND APPLICATION OF MEAN SPHERICAL APPROXIMATION TO CHARGED HARD SPHERES NEAR A CHARGED HARD WALL [J].
HENDERSON, D ;
BLUM, L .
JOURNAL OF CHEMICAL PHYSICS, 1978, 69 (12) :5441-5449
[7]   CONTRIBUTION OF HIGHER-ORDER CLUSTER TERMS TO ACTIVITY-COEFFICIENTS OF SMALL IONS IN POLYELECTROLYTE SOLUTIONS [J].
IWASA, K ;
KWAK, JCT .
JOURNAL OF PHYSICAL CHEMISTRY, 1977, 81 (05) :408-412
[8]   EXAMINATION OF LIMITING LAWS OF POLYELECTROLYTES AND COUNTERION CONDENSATION [J].
IWASA, K .
JOURNAL OF PHYSICAL CHEMISTRY, 1977, 81 (19) :1829-1833
[9]  
Katchalsky A., 1971, PURE APPL CHEM, V26, P327, DOI DOI 10.1351/PAC197126030327