Donnan equilibrium and the osmotic pressure of charged colloidal lattices

Tamashiro, M. N.; Levin, Yan; Barbosa, Márcia C.

doi:10.1007/s100510050192

Cited by 30 publications

(50 citation statements)

References 16 publications

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“…Work along these lines is in progress. [12,39]. Over this range of volume fractions, the screening constant increases from zero to κσ ≃ 4.…”

Section: Discussionmentioning

confidence: 93%

“…Future work will address influences of effective triplet interactions on the osmotic pressure [42]. It should be mentioned that the Poisson-Boltzmann cell model [12,39] (upper curve in Fig. 1) matches the experimental data well, especially at higher η.…”

Section: E Osmotic Pressure and Bulk Modulusmentioning

confidence: 93%

“…Tracing out from the partition function statistical degrees of freedom associated with all but a single component, the mixture is formally mapped onto an equivalent one-component system of "pseudoparticles" governed by an effective state-dependent interaction [9]. Effective interactions in charge-stabilized colloids have been modeled by a variety of techniques, including Poisson-Boltzmann cell models [10][11][12] density-functional theory [13][14][15][16][17][18], Monte Carlo and Molecular Dynamics simulation [19][20][21][22], and powerful ab initio methods [13,23].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

2000

Phys. Rev. E

112

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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.

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“…Work along these lines is in progress. [12,39]. Over this range of volume fractions, the screening constant increases from zero to κσ ≃ 4.…”

Section: Discussionmentioning

confidence: 93%

Section: E Osmotic Pressure and Bulk Modulusmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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

2000

Phys. Rev. E

112

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“…The equilibrium between the suspension and the salt reservoir is referred to as Donnan equilibrium [42,43,44]. The effective average salt concentration n s in the suspension is not the same as the reservoir salt concentration c s , but is a function of the physical parameters of the system and can be calculated, e.g., in the PB cell model [45,46,47]. Here, we can compute n s from the total number of microions, obtained by integrating the microionic density distribution, n + (r) + n − (r), over G. Since the actual salt concentration in the system, n s , is of no interest in the following considerations we dispense with quantifying it, but will instead specify just c s , or, equivalently, κa = (8π(λ B /a)c s a 3 ) 1/2 which for simplicity we will refer to as 'salt concentration'.…”

Section: Simulation Techniquementioning

confidence: 99%

Many-body interactions and the melting of colloidal crystals

Dobnikar

Chen

Rzehak

et al. 2003

The Journal of Chemical Physics

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We study the melting behavior of charged colloidal crystals, using a simulation technique that combines a continuous mean-field Poisson-Boltzmann description for the microscopic electrolyte ions with a Brownian-dynamics simulation for the mesoscopic colloids. This technique ensures that many-body interactions between the colloids are fully taken into account, and thus allows us to investigate how many-body interactions affect the solid-liquid phase behavior of charged colloids.Using the Lindemann criterion, we determine the melting line in a phase-diagram spanned by the colloidal charge and the salt concentration. We compare our results to predictions based on the established description of colloidal suspensions in terms of pairwise additive Yukawa potentials, and find good agreement at high-salt, but not at low-salt concentration. Analyzing the effective pairinteraction between two colloids in a crystalline environment, we demonstrate that the difference in the melting behavior observed at low salt is due to many-body interactions. If the salt concentration is high, we find configuration-independent pair-forces of perfect Yukawa form with effective charges and screening constants that are in good agreement with well-established theories. At low added salt, however, the pair-forces are Yukawa-like only at short distances with effective parameters that depend on the analyzed colloidal configuration. At larger distances, in contrast, the pair-forces decay to zero much faster than they would following a Yukawa force law. This is explained with a screening effect of the macroions. Based on these findings, we suggest a simple model potential for colloids in suspension which has the form of a Yukawa potential, truncated after the first coordination shell of a colloid in a crystal. Using this potential in a one-component simulation, we find a melting line that shows good agreement with the one derived from the full PoissonBoltzmann-Brownian-dynamics simulation.2

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“…However, as already pointed out previously in the literature, 2, 3 the linearization scheme yields artifacts in the low-temperature, high-surface charge or infinite-dilution (of polyions) limits for the Donnan equilibrium problem 4,5,6,7,8 in spherical geometry, which describes a suspension of spherical charged polyions in electrochemical equilibrium with an infinite salt reservoir. In these limits the linearized osmotic-pressure difference between the colloidal suspension and the salt reservoir becomes negative, in disagreement with the full nonlinear PB result, that always displays positive osmotic-pressure differences.…”

Section: Introductionmentioning

confidence: 94%

Where the linearized Poisson-Boltzmann cell model fails: The planar case as a prototype study

Tamashiro

Schiessel

2003

Phys. Rev. E

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The classical problem of two uniformly charged infinite planes in electrochemical equilibrium with an infinite monovalent salt reservoir is solved exactly at the mean-field nonlinear Poisson-Boltzmann (PB) level, including an explicit expression of the associated nonlinear electrostatic contribution to the semi-grand-canonical potential. A linearization of the nonlinear functional is presented that leads to Debye-Hückel-like equations agreeing asymptotically with the nonlinear PB results in the weak-coupling (high-temperature) and counterionic ideal-gas limits. This linearization scheme yields artifacts in the lowtemperature, large-separation or high-surface charge limits. In particular, the osmotic-pressure difference between the interplane region and the salt reservoir becomes negative in the above limits, in disagreement with the exact (at mean-field level) nonlinear PB solution. By using explicitly gauge-invariant forms of the electrostatic potential we show that these artifacts -although thermodynamically consistent with quadratic expansions of the nonlinear functional -can be traced back to the non-fulfillment of the underlying assumptions of the linearization. Explicit comparison between the analytical expressions of the exact nonlinear solution and the corresponding linearized equations allows us to show that the linearized results are asymptotically exact in the weak-coupling and counterionic ideal-gas limits, but always fail otherwise, predicting negative osmotic-pressure differences. By taking appropriate limits of the full nonlinear PB solution, we provide asymptotic expressions for the semi-grand-canonical potential and the osmotic-pressure difference that involve only elementary functions, which cover the complementary region where the linearized theory breaks down.

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Donnan equilibrium and the osmotic pressure of charged colloidal lattices

Cited by 30 publications

References 16 publications

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

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

Many-body interactions and the melting of colloidal crystals

Where the linearized Poisson-Boltzmann cell model fails: The planar case as a prototype study

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