Effective interactions and volume energies in charged colloids: Linear response theory

Abstract

Interparticle interactions in charge-stabilized colloidal suspensions, of arbitrary salt concentration, are described at the level of effective interactions in an equivalent one-component system. Integrating out from the partition function the degrees of freedom of all microions, and assuming linear response to the macroion charges, general expressions are obtained for both an effective electrostatic pair interaction and an associated microion volume energy. For macroions with hard-sphere cores, the effective interaction is of the DLVO screened-Coulomb form, but with a modified screening constant that incorporates excluded volume effects. The volume energy -a natural consequence of the one-component reduction -contributes to the total free energy and can significantly influence thermodynamic properties in the limit of low-salt concentration. As illustrations, the osmotic pressure and bulk modulus are computed and compared with recent experimental measurements for deionized suspensions. For macroions of sufficient charge and concentration, it is shown that the counterions can act to soften or destabilize colloidal crystals.

Where the linearized Poisson–Boltzmann cell model fails: Spurious phase separation in charged colloidal suspensions

“…In the Donnan-equilibrium case, one should also take the microion-microion correlations in the infinite salt reservoir into account. However, the phase separation in deionized aqueous suspensions of charged colloids predicted by linearized theories 52,53,54,55,56,57,58,59 -which are claimed 52,53 to be driven by the state-independent volume terms 50, 51 -seems to be related to mathematical artifacts of the linearization itself and does not correspond thus to a real physical effect, as already pointed out in previous works 64,65 via the linearization of the PB functional for WS-cell models and revisited it here.…”

“…For example, they have been seen in Monte Carlo simulations in the presence of multivalent counterions 45,46,47 or when the low-temperature ordering of the discrete charges is taken into account. 48 Under the conditions described in the previous paragraph those controversial experimental findings are either attributed to the presence of long-range attractive electrostatic interactions between like-charged polyions 49 or by state-independent volume terms 50, 51 obtained by approximations that involve some kind of linearization: random-phase approximation, 52, 53, 54 DH pair-distribution functions augmented by a variational approach for the polyion-polyion interactions, 55 linear-response approximation, 56 extended DH theory for asymmetric electrolytes, 57 mean-spherical approximation (MSA) 58 and symmetric PB and MSA. 59 Even though it has been argued by Overbeek and others 60 that the Sogami-Ise attraction 49 is due to inconsistencies in their thermodynamic treatment, the question does not seem to be settled yet and discussion is still in progress.…”

Effect of glycerol and dimethyl sulfoxide on the phase behavior of lysozyme: Theory and experiments

“…The factor 1/(1 − φ) corrects for the volume occupied by proteins and thus takes into account the free volume accessible to the micro-ions, which cannot penetrate the protein. 35,36 We ignore here the small free volume corrections arising from the finite size of the microions. The van der Waals attraction is of the form 8…”

Short-time transport properties in dense suspensions: From neutral to charge-stabilized colloidal spheres

“…NaCl). The factor 1/(1 − φ) has been introduced to correct for the free volume accessible to the microions, owing to the presence of colloidal spheres [55]. It is of relevance for dense suspensions only.…”