A self-consistent theory of the effective interactions in charge-stabilized colloidal dispersions

Grimson, Malcolm J.; Silbert, M.

doi:10.1080/00268979100102311

Cited by 63 publications

(82 citation statements)

References 19 publications

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“…Both are mean-field theories in the sense that they ignore fluctuations in microion distributions. An advantage of linear response theory, however, is that it encompasses the volume energy, which can be important for describing phase behavior [18,21,23,24,25,26]. Moreover, response theory can be straightforwardly generalized to incorporate nonlinear response, which entails both many-body effective interactions and corrections to the pair potential and volume energy [27].…”

Section: Theorymentioning

confidence: 99%

“…Following the same general strategy as applied previously to charged colloids [18,21], we reduce the multi-component mixture to an equivalent onecomponent system governed by effective interactions, which are approximated via perturbation theory. For clarity of presentation, we initially ignore salt ions.…”

Section: Theorymentioning

confidence: 99%

“…It is first convenient to convert the counterion Hamiltonian to the Hamiltonian of a classical one-component plasma (OCP) of counterions by adding to H c , and subtracting from H mc , the energy of a uniform compensating negative background [22], E b = −N c n cvcc (0)/2, wherê v cc (0) is the k → 0 limit of the Fourier transform of v cc (r). Now regarding the macroions as an "external" potential for the OCP, we invoke perturbation theory [18,19,21] and write…”

Section: Theorymentioning

confidence: 99%

“…For example, for macroions of diameter σ = 100 nm, valence Z = 100, and volume fraction η = (π/6)n m σ 3 = 0.01, in water at room temperature (λ B = 0.714 nm), we find Γ ≃ 0.014. As for charged colloids [18,21], we adopt the random phase approximation (RPA), which is accurate for weakly-coupled plasmas. The RPA equates the two-particle direct correlation function of the OCP to its exact asymptotic limit: c (2) (r) = −βv cc (r).…”

Section: Theorymentioning

confidence: 99%

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Counterion penetration and effective electrostatic interactions in solutions of polyelectrolyte stars and microgels

Denton

2003

Phys. Rev. E

129

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Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modelling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pair interactions are Yukawa in form for separated macroions, but are softly repulsive and bounded for overlapping macroions. A one-body volume energy, which depends on the average macroion concentration, emerges naturally in the theory and contributes to the total free energy.

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Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

See 2 more Smart Citations

Counterion penetration and effective electrostatic interactions in solutions of polyelectrolyte stars and microgels

Denton

2003

Phys. Rev. E

129

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“…Three-body interactions can be derived in similar fashion [12]. However, the averaging over the microion degrees of freedom also leads to a structureindependent, but state-dependent volume term, part of which is associated with the self-energy of individual double-layers, and which is reminiscent of the volume term in metals [13,14]; this term has a profound effect on the phase diagram of charge-stabilized colloids [14,15].…”

Section: Introductionmentioning

confidence: 99%

Many-body interactions and correlations in coarse-grained descriptions of polymer solutions

2001

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We calculate the two, three, four, and five-body (state independent) effective potentials between the centers of mass (CM) of self avoiding walk polymers by Monte-Carlo simulations. For full overlap, these coarse-grained n-body interactions oscillate in sign as (−1) n , and decrease in absolute magnitude with increasing n. We find semi-quantitative agreement with a scaling theory, and use this to discuss how the coarse-grained free energy converges when expanded to arbitrary order in the many-body potentials. We also derive effective density dependent 2-body potentials which exactly reproduce the pair-correlations between the CM of the self avoiding walk polymers. The density dependence of these pair potentials can be largely understood from the effects of the density independent 3-body potential. Triplet correlations between the CM of the polymers are surprisingly well, but not exactly, described by our coarse-grained effective pair potential picture. In fact, we demonstrate that a pair-potential cannot simultaneously reproduce the two and three body correlations in a system with many-body interactions. However, the deviations that do occur in our system are very small, and can be explained by the direct influence of 3-body potentials.

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Effective Interactions between Macroions 2

Structure Formation in Solution

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A self-consistent theory of the effective interactions in charge-stabilized colloidal dispersions

Cited by 63 publications

References 19 publications

Counterion penetration and effective electrostatic interactions in solutions of polyelectrolyte stars and microgels

Counterion penetration and effective electrostatic interactions in solutions of polyelectrolyte stars and microgels

Many-body interactions and correlations in coarse-grained descriptions of polymer solutions

Effective Interactions between Macroions 2

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