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 cylindrical ...
... 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 cylindrical ...
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 Δψ = - — ( 4ñe 。/ 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 Δψ = - — ( 4ñe 。/ 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 | |
17 other sections not shown
Common terms and phrases
absence of salt activity coefficient activity of counter addition of salt additivity law alkali apparent charge average bound counter ions chain Chapter charge density charged groups chemical potential coefficient of counter concentration of counter concentration of free concentration of macroions copolymer counter ion condensation critical value cylindrical macroion decreases degree of dissociation degree of neutralization density Q derived dielectric constant dielectric increment electric free energy electric potential entropy equilibrium experimental extensive force fluctuation free counter ions free energy free volume hydrogen ions increase interaction ionized groups kinds of counter macromolecules monomers monovalent number of charged number of counter number of free osmotic coefficient osmotic pressure Poisson-Boltzmann equation polyacids polyacrylic acid polyelectrolytes polyvalent counter ions proportional radius random coil ratio refractive index region relation result rodlike macroions rods salt concentration salt solution shown in Fig simple salt small ions sodium ions spherical macroion total number valence