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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Double layer forces ： ウィキペディア英語版 Double layer forces Double layer forces occur between charged objects across liquids, typically water. This force acts over distances that are comparable to the Debye length, which is on the order of one to a few tenths of nanometers. The strength of these forces increases with the magnitude of the surface charge density (or the electrical surface potential). For two similarly charged objects, this force is repulsive and decays exponentially at larger distances, see figure. For unequally charged objects and eventually at shorted distances, these forces may also be attractive. The theory due to Derjaguin, Landau, Verwey, and Overbeek (DLVO) combines such double layer forces together with Van der Waals forces in order to estimate the actual interaction potential between colloidal particles.〔W. B. Russel, D. A. Saville, W. R. Schowalter, Colloidal Dispersions. Cambridge University Press: Cambridge, 1989.〕 An electrical double layer develops near charged surfaces (or another charged objects) in aqueous solutions. Within this double layer, the first layer corresponds to the charged surface. These charges may originate from tightly adsorbed ions, dissociated surface groups, or substituted ions within the crystal lattice. The second layer corresponds to the diffuse layer, which contains the neutralizing charge consisting of accumulated counterions and depleted coions. The resulting potential profile between these two objects leads to differences in the ionic concentrations within the gap between these objects with respect to the bulk solution. These differences generate an osmotic pressure, which generates a force between these objects. These forces are easily experienced when hands are washed with soap. Adsorbing soap molecules make the skin negatively charged, and the slippery feeling is caused by the strongly repulsive double layer forces. These forces are further relevant in many colloidal or biological systems, and may be responsible for their stability, formation of colloidal crystals, or their rheological properties. ==Poisson–Boltzmann model== The most popular model to describe the electrical double layer is the Poisson-Boltzmann (PB) model. This model can be equally used to evaluate double layer forces. Let us discuss this model in the case of planar geometry as shown in the figure on the left. In this case, the electrical potential profile ''ψ''(''z'') near an charged interface will only depend on the position ''z''. The corresponding Poisson's equation reads in SI units : $$ \frac = - \frac where ''ρ'' is the charge density per unit volume, ''ε''0 the dielectric permittivity of the vacuum, and ''ε'' the dielectric constant of the liquid. For a symmetric electrolyte consisting of cations and anions having a charge ±''q'', the charge density can be expressed as : $$ \rho = q (c_+ - c_-) where ''c''± = ''N''±/''V'' are the concentrations of the cations and anions, where ''N''± are their numbers and ''V'' the sample volume. These profiles can be related to the electrical potential by considering the fact that the chemical potential of the ions is constant. For both ions, this relation can be written as : $$ \mu_\pm = \mu_+^ + kT \ln c_\pm \pm q \psi where $\backslash mu\_\backslash pm^$ is the reference chemical potential, ''T'' the absolute temperature, and ''k'' the Boltzmann constant. The reference chemical potential can be eliminated by applying the same equation far away from the surface where the potential is assumed to vanish and concentrations attain the bulk concentration ''c''B. The concentration profiles thus become : $$ c_\pm = c_ e^ where ''β'' = 1/(''kT''). This relation reflects the Boltzmann distribution of the ions with the energy ±''qψ''. Inserting these relations into the Poisson equation one obtains the PB equation〔J. Israelachvili, Intermolecular and Surface Forces. Academic Press: London, 1992.〕 : $$ \frac = \frac (Gibbs–Duhem relation for a two component system at constant temperature〔 : $$ -V d\Pi + N_+ d\mu_+ + N_- d\mu_- = 0 Introducing the concentrations ''c''± and using the expressions of the chemical potentials ''μ''± given above one finds : $$ d\Pi = kT(dc_+ + dc_-) + q(c_+ - c_-) d \psi The concentration difference can be eliminated with the Poisson equation and the resulting equation can be integrated from infinite separation of the plates to the actual separation ''h'' by realizing that : $2\; (d^2\; \backslash psi\; /\; dz^2)\; d\backslash psi\; =\; d\; (d\backslash psi\; /\; dz)^2$ Expressing the concentration profiles in terms of the potential profiles one obtains : $$ \Pi = kT c_(e^ + e^ - 2) - \frac \left(\frac \right)^2 From a known electrical potential profile ''ψ''(''z'') one can calculate the disjoining pressure from this equation at any suitable position ''z''. Alternative derivation of the same relation for disjoining pressure involves the stress tensor.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Double layer forces」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.