Discreteness-of-Charge Effect and the Stability Theory of Colloids

Levine, S.; Calvert, D.; Bell, Gail S.

doi:10.1038/191699a0

Cited by 15 publications

(9 citation statements)

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“…If JkA(us)l << 1, then ra becoilles the radius ro of the disc whose area is equal to the average area available to an adsorbed ion, and so This is the Grahame cut-off approximation, used in the previous papers by the authors (6)(7)(8)(9)(10)(11)(12). The following interpretation of kA(us), which is proved in Appendix A, suggests that kA(us) is small a t large up.…”

Section: T H E Cut-off Disc Model and T H E Condition O F Electrical mentioning

confidence: 99%

“…We need only replace eo, K , and qd respectively by Zeo, ZK, and Zqd and also the Grahame relation [2.9] by provided za is redefined as f 1, according as the adsorbed counter-ion is positive or negative. In the previous papers (6)(7)(8) on the relation between the discrete-ion effect and colloid stability, we compared the coagulating powers of 1-1,2-2, and 3-3 electrolytes and assume g , = d/p for all three valency types. Choosing the same value of g, we also treated a mixture of 1-1 and 2-2 electrolytes and showed that the phenomenon of mutual antagonism can be obtained on the basis of the discrete-ion effect.…”

Section: And(o 0 )mentioning

confidence: 99%

“…Two anomalous stability properties found for example with silver halide sols are (i) a decrease in concentration of coagulatiilg electrolyte (i.e. a decrease in stability) with increase in the surface density of potential-determining ions (6,7,8,16), particularly with polyvalent coagulating ions and (ii) the phenomenon of mutual antagonism in the presence of mixed coagulating electrolytes (17). All these properties find a common explanation in the discrete-ion effect.…”

mentioning

confidence: 99%

“…by a regular hexagonal array and this model has very recently been examined by Barlow and Rilacdonald (IS) (see also Stigter (38)). In the second method, which has been developed by the present authors (6)(7)(8)(9)(10)(11)(12), the discrete-ion effect for the adsorbed counter-ions is described in terms of a lateral repulsion between neighboring counter-ions in the case where these are all of the same sign. Consequently in the adsorption plane each counter-ion is surrounded by an area in which the mean surface charge distribution is strongly depleted.…”

mentioning

confidence: 99%

“…Following Grahame (19) we imagine that each (fully charged) adsorbed ion is situated at the center of a disc which is free of adsorbed charge and has an area equal to the average area per adsorbed counter-ion. This method, which we shall call the 'Grahame cut-off' approximation, has been used in the earlier papers by us (6)(7)(8)(9)(10)(11)(12). In this paper, investigations of this model by statistical mechanics show that the radius of the Grahame disc, which is to be free of adsorbed charge, is too large, particularly a t small densities of adsorbed ions; we shall refer to the model of the appropriate smaller disc as the 'revised cut-off' approximation.…”

mentioning

confidence: 99%

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The Diffuse Layer Correction to the Discrete-Ion Effect in Electric Double Layer Theory

Levine¹,

Mingins²,

Bell³

1965

Can. J. Chem.

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The screening effect of the diffuse layer on the self-atmosphere (or discrete-ion) potential of a counter-ion adsorbed from aqueous electrolyte on to a plane charged interface is investigated. A theory based on Fourier-Bessel integrals and the approximate method of Loeb and Williams for treating the potential distribution in the diffuse layer is presented. The distribution of counter-ions in the adsorption plane surrounding a specified ion adsorbed in the plane is expressed in terms of a two-dimensional grand canonical ensemble and this is approximated by a 'revised cut-off model'. The 'Grahame cut-off model' is an approximation to the adsorbed counter-ion distribution based on a canonical ensemble and me present arguments t o show that this interpretation is incorrect. We also show that the radius of the revised disc is, in general, smaller than that of the Grahame disc but approaches it a t large charge densities (ro) of counter-ions in the Stern inner region. Colnparison is made with an alternative approach to this discrete-ion effect by Buff and Stillinger, who also applied a Fourier-Bessel technique to the mercury -aqueous electrolyte system. Their results provide a lower estimate to the magnitude of the self-atmosphere potential, whereas our revised cut-off model gives an upper estimate. A third method, which assumes the adsorbed ions to be situated on a hexagonal lattice, is also discussed and is found to give a potential larger than the upper estimate of the --. . revised cut-off approach.It is shown that the effect of the diffuse laver is to diminish the discrete-ion potential a t the adsorbed ion. When the electrolyte concentGtion tends to zero the results wit'h the Grahame model reduce to those derived in a n earlier paper from the method of multiple electrostatic images. Calculations on the discrete-ion potential a t a n adsorbed counter-ion are given for metallic and dielectric surfaces in contact with a n aqueous 1-1 electrolyte solution and the parameters of the inner region are chosen to be consistent with known data on mercury and silver iodide systems. I t is shown in both cases that on dilute salt solutions ( 5 1M/100) the diffuse layer screening is small compared to the unscreened term except a t small charge densities of counter-ions in the inner region.

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