Polyelectrolytes |
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Page 31
... Poisson - Boltzmann equation and calculate the free energy and also the osmotic coefficient . The Poisson - Boltzmann equation can be solved exactly only in a special case , i.e. , for a rodlike macroion with counter ions in a ...
... Poisson - Boltzmann equation and calculate the free energy and also the osmotic coefficient . The Poisson - Boltzmann equation can be solved exactly only in a special case , i.e. , for a rodlike macroion with counter ions in a ...
Page 40
... Poisson - Boltzmann equation for a rigid spherical macroion in a spherical free volume , for comparison with the case of the rigid rod . The Poisson - Boltzmann equation is written where and ΔΥ A = - = — ( 4ñе 。/ ɛ 。) А exp ( −e。/kT ) ...
... Poisson - Boltzmann equation for a rigid spherical macroion in a spherical free volume , for comparison with the case of the rigid rod . The Poisson - Boltzmann equation is written where and ΔΥ A = - = — ( 4ñе 。/ ɛ 。) А exp ( −e。/kT ) ...
Page 114
... Poisson - Boltzmann equation can be written as ( d2þ / dx2 ) + ( 1 / x ) ( @ p / dx ) + ( 1 / x2 ) ( d2 þ / d02 ) = A exp ( − p ) A = ( 4л2nе2 / εolkТ ) / § § exp ( − p ) x dx do ( 180 ) where the relative spatial coordinate x = r / a ...
... Poisson - Boltzmann equation can be written as ( d2þ / dx2 ) + ( 1 / x ) ( @ p / dx ) + ( 1 / x2 ) ( d2 þ / d02 ) = A exp ( − p ) A = ( 4л2nе2 / εolkТ ) / § § exp ( − p ) x dx do ( 180 ) where the relative spatial coordinate x = r / a ...
Contents
Preface | 1 |
theoretically understandable Idealized treatment based on the simplest | 5 |
Electrical Potential Around the Macroion | 9 |
Copyright | |
19 other sections not shown
Common terms and phrases
activity coefficient additivity law alkali apparent charge bound counter ions chain Chapter charge density charged groups chemical potential coefficient of counter concentration of counter concentration of free concentration of macroions copolymer coulomb counter ion condensation critical value cylindrical macroion cylindrical model decreases degree of dissociation degree of neutralization derived dielectric constant dielectric increment electric free energy entropy equilibrium experimental extensive force fluctuation free counter ions free energy free volume hydrogen ions increase interaction ionic atmosphere ionized groups kinds of counter larger than unity logarithm monomers number of charges number of counter number of free osmotic coefficient osmotic pressure Poisson-Boltzmann equation polyacids polyacrylic acid polyelectrolytes Polymer polyvalent counter ions potential trough potential valley proportional radius random coil ratio refractive index region relation repulsion result rodlike macroion salt concentration shown in Fig simple salt smaller than unity sodium ions spherical macroion total number valence water structure