Matches in SemOpenAlex for { <https://semopenalex.org/work/W2137630369> ?p ?o ?g. }
- W2137630369 endingPage "639" @default.
- W2137630369 startingPage "619" @default.
- W2137630369 abstract "An analytical approximation to the nonlinear Poisson-Boltzmann (PB) equation is applied to charged macromolecules that possess one-dimensional symmetry and can be modeled by a plane, infinite cylinder, or sphere. A functional substitution allows the nonlinear PB equation subject to linear boundary conditions to be transformed into an approximate linear (Debye-Hückel-type) equation subject to nonlinear boundary conditions. A simple analytical result for the surface potential of such polyelectrolytes follows, leading to expressions for the amount of condensed (or renormalized) charge and the electrostatic Helmholtz energy for polyelectrolytes. Analytical high-charge/low-salt and low-charge/high-salt limits are shown to be similar to results obtained by others based on PB or counterion condensation theory. Several important general observations concerning polyelectrolytes treated within the context of PB theory can be made including: (1) all charged surfaces display some counterion condensation for finite electrolyte concentration, (2) the effect of surface geometry is described primarily by the sum of the Debye constant and the mean curvature of the surface, (3) two surfaces with the same surface charge density and mean curvature condense approximately identical fractions of counterions, (4) the amount of condensation is not determined by a predefined condensation distance although such a distance can be determined uniquely from it, and (5) substantial condensation occurs if the Debye constant of the electrolyte is much less than the mean curvature of a highly charged polyelectrolyte." @default.
- W2137630369 created "2016-06-24" @default.
- W2137630369 creator A5053859669 @default.
- W2137630369 creator A5059385141 @default.
- W2137630369 date "2010-03-08" @default.
- W2137630369 modified "2023-10-14" @default.
- W2137630369 title "Counterion condensation and shape within Poisson-Boltzmann theory" @default.
- W2137630369 cites W117731420 @default.
- W2137630369 cites W1526091498 @default.
- W2137630369 cites W1529844403 @default.
- W2137630369 cites W1543654345 @default.
- W2137630369 cites W1581138409 @default.
- W2137630369 cites W1651667742 @default.
- W2137630369 cites W1964944707 @default.
- W2137630369 cites W1965113234 @default.
- W2137630369 cites W1966439065 @default.
- W2137630369 cites W1966511631 @default.
- W2137630369 cites W1967682967 @default.
- W2137630369 cites W1967845469 @default.
- W2137630369 cites W1968551656 @default.
- W2137630369 cites W1968763142 @default.
- W2137630369 cites W1970043733 @default.
- W2137630369 cites W1970434645 @default.
- W2137630369 cites W1970650374 @default.
- W2137630369 cites W1971306482 @default.
- W2137630369 cites W1971392714 @default.
- W2137630369 cites W1972321784 @default.
- W2137630369 cites W1972326506 @default.
- W2137630369 cites W1972362244 @default.
- W2137630369 cites W1974267568 @default.
- W2137630369 cites W1975384601 @default.
- W2137630369 cites W1977362259 @default.
- W2137630369 cites W1977727653 @default.
- W2137630369 cites W1978682980 @default.
- W2137630369 cites W1978931963 @default.
- W2137630369 cites W1979436289 @default.
- W2137630369 cites W1979587445 @default.
- W2137630369 cites W1981240943 @default.
- W2137630369 cites W1981749461 @default.
- W2137630369 cites W1982220284 @default.
- W2137630369 cites W1982483258 @default.
- W2137630369 cites W1982865641 @default.
- W2137630369 cites W1983889948 @default.
- W2137630369 cites W1986035736 @default.
- W2137630369 cites W1988674273 @default.
- W2137630369 cites W1988999732 @default.
- W2137630369 cites W1991967648 @default.
- W2137630369 cites W1992267299 @default.
- W2137630369 cites W1992578344 @default.
- W2137630369 cites W1994985503 @default.
- W2137630369 cites W1995277545 @default.
- W2137630369 cites W1995598255 @default.
- W2137630369 cites W1996681847 @default.
- W2137630369 cites W1996923773 @default.
- W2137630369 cites W1998677820 @default.
- W2137630369 cites W2002013329 @default.
- W2137630369 cites W2003234896 @default.
- W2137630369 cites W2003496571 @default.
- W2137630369 cites W2005121547 @default.
- W2137630369 cites W2005731797 @default.
- W2137630369 cites W2006661569 @default.
- W2137630369 cites W2006858059 @default.
- W2137630369 cites W2008179820 @default.
- W2137630369 cites W2008289821 @default.
- W2137630369 cites W2009085431 @default.
- W2137630369 cites W2010239071 @default.
- W2137630369 cites W2010541858 @default.
- W2137630369 cites W2011408439 @default.
- W2137630369 cites W2013004673 @default.
- W2137630369 cites W2013148093 @default.
- W2137630369 cites W2014119798 @default.
- W2137630369 cites W2018487771 @default.
- W2137630369 cites W2020183368 @default.
- W2137630369 cites W2020746144 @default.
- W2137630369 cites W2021137846 @default.
- W2137630369 cites W2021431226 @default.
- W2137630369 cites W2021594503 @default.
- W2137630369 cites W2023681445 @default.
- W2137630369 cites W2024031237 @default.
- W2137630369 cites W2024059620 @default.
- W2137630369 cites W2025042628 @default.
- W2137630369 cites W2025507661 @default.
- W2137630369 cites W2026452359 @default.
- W2137630369 cites W2026518463 @default.
- W2137630369 cites W2026884660 @default.
- W2137630369 cites W2027914810 @default.
- W2137630369 cites W2029454802 @default.
- W2137630369 cites W2029576036 @default.
- W2137630369 cites W2029582401 @default.
- W2137630369 cites W2029788853 @default.
- W2137630369 cites W2030189109 @default.
- W2137630369 cites W2032326831 @default.
- W2137630369 cites W2032549034 @default.
- W2137630369 cites W2033036426 @default.
- W2137630369 cites W2033062721 @default.
- W2137630369 cites W2034320525 @default.
- W2137630369 cites W2034605243 @default.
- W2137630369 cites W2035901183 @default.