Image charges in spherical geometry: Application to colloidal systems

Journal of Chemical Physics

Volumn 117, Issue 24, 2002, Pages 11062-11074

  Messina, René ^a  

^a MAX PLANCK INSTITUTE FOR POLYMER RESEARCH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CHARGED COLLOID; ELECTRICAL DOUBLE LAYER; INDUCED SURFACE CHARGE; SELF-IMAGE INTERACTION;

COMPUTER SIMULATION; ELECTROSTATICS; HAMILTONIANS; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; MOLECULAR DYNAMICS; MOLECULAR STRUCTURE; MONTE CARLO METHODS; PERMITTIVITY; POLARIZATION; POLYNOMIALS;

COLLOIDS;

EID: 0037461481     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1521935     Document Type: Article

References (38)

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16. im = -qa/b located at u.
17. 1(x)dx=0.
18. -6 in the most severe case where b = 8 σ.
19. This holds when the microion q is sufficiently far away from the interface so that only the dipolar term matters (i.e., l = 1). However close to the colloidal surface one has to take all higher multipolar contributions to get the exact potential of interaction.
20. We have carefully checked the both methods [i.e., Eq. (10) and Eq. (12)] are numerically identical. However, at large a (typically a > 30 σ) the Legendre sum in Eq. (23) becomes numerically unstable.
21. im located at the center of the sphere.
22. Note that the two-image charge approximation also holds when the charge q is very far from the interface (i.e., b/a ≫ 1). Unfortunately, all the relavant effects of image forces in spherical geometry occur within the opposite limit b/a → 1.
23. Our simulations will show that, especially for micellar systems, the image forces in many-counterion systems become only relevant when the self-image interaction is dominant.
24. In the case of a charged plate, to be consistent, one has to think either of a large finite plate in the presence of a single microion, or equivalently of an infinite plate in the presence of a very dilute dispersion of microions.
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33. max = 100.
34. For the net fluid charge Q(r) one has an arbitrary resolution Δr.
35. This feature also shows how important it is to treat precisely the self-image interaction as done in the present study with a Legendre sum.
36. Using MC simulations, Torrie et al. (Ref. 1) also reported in the planar case the appearance of a maximum in the counterion density for low surface charge density and fairly small salt content. However, they did not make any comparison between the position of this maximum and the position of a single counterion (per simulation box) minimizing the plate-counterion potential of interaction.
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