Electrostatistics of counter-ions at and between planar charged walls: From Poisson-Boltzmann to the strong-coupling theory

European Physical Journal E

Volumn 5, Issue 5, 2001, Pages 557-574

  Netz, R R ^a  

^a MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001552389     PISSN: 12928941     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101890170039     Document Type: Article

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59. -2). In a final expansion in inverse powers of Ξ the logarithmic cofactor would therefore give rise to analytic behavior at higher order. This shows that an analytic expansion should be possible at all orders, but it also shows that agreement of higher-order terms with for example numerical results would be rather poor because the logarithmic behavior involves resummation of higher-order terms in our expansion scheme.
60. The canonical method for avoiding divergencies at all intermediate steps in the calculation is by regularizing the interaction υ(r) for example by adding an arbitrary exponential prefactor which cuts off the interaction at some distance and then taking the limit where this distance goes to infinity at the very end. As we checked explicitly, this leads to the same final density distribution as obtained by our direct fugacity renormalization.
61. The careful reader notices that the criteria used for obtaining the limits of validity for PB and SC theories, equations (71) and (112), respectively, are slightly different since in the case of the SC estimate we excluded the term of unity in the expression (110), while for the PB estimate we did not separate off this constant. In both cases, we chose the option which results in the more conservative estimate.
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