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Effect of thick fixed-charge layers on electrostatic interaction — a theoretical approach

  • Colloid Science
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Abstract

The electrostatic interaction pressure of charged surface layers is considered qualitatively and quantitatively. In the case of mutual penetration of the surface layers in addition to Maxwell stress and osmotic resp. hydrostatic pressure an isotropic stress on the fixed charges carrying molecules of the surface layers has to be taken into account. The derivation of the pressure-distance equations is given starting from both thermodynamic/electrostatic and hydrostatic/electrostatic principles. A possible biological significance of the additional stress is discussed emphasizing its role in modifying the structure of surface layer molecules.

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Abbreviations

e 0 :

elementary charge

k :

Boltzmann constant

n i :

concentration of theith ionic species in the bulk solution

P :

hydrostatic pressure

P ∞ :

hydrostatic pressure in the bulk volume (× → ∞)

P h :

integration constant, independent on ×:P h=P(h)

T :

absolute temperature

Z i :

electrovalence of theith ionic species

δ :

thickness of the surface layer

ε, ε 0 :

relative and absolute permittivities

II(×) :

osmotic pressure at position ×

II ∞ :

osmotic pressure in the bulk solution (× → ∞)

\(\Pi ^{h_0 }\) :

osmotic pressure in the symmetry plane of interacting identical surface layers (electric field strength equals zero)

\(\Pi ^{h_1 }\) :

integration constant, independent on ×:\(x:\Pi ^{h_1 } = \Pi (h)\)

Π h e :

electrostatic component of the disjoining pressureΠ h e =Π e (h)

ϱ(×) :

mobile charge density profile (cations and anions of the electrolyte)

ϱ′(×) :

fixed charge density profile

ϱ t(x):

total charge density profile (ϱ t=ϱ′ +ϱ)

ϱ 1(x):

fixed charge density profile of one of the two surface layers (ϱ 1(×)≠ 0 for 0≦×≦δ)

Ψ(×) :

electric potential profile

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Author notes

  1. A. Voigt

    Present address: Zentralinstitut für Organische Chemie, Bereich Grenzflächenaktive Stoffe, Akademie der Wissenschaften der DDR, Berlin, G.D.R.

Authors and Affiliations

  1. Sektion Biologie, Bereich Biophysik, Humboldt-Universität zu Berlin, Berlin, G.D.R.

    E. Donath

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Donath, E., Voigt, A. Effect of thick fixed-charge layers on electrostatic interaction — a theoretical approach. Colloid & Polymer Sci 266, 1024–1030 (1988). https://doi.org/10.1007/BF01428812

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  • DOI: https://doi.org/10.1007/BF01428812

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