Screening of charged spheroidal colloidal particles

Alvarez, Carlos Eduardo Mendez; Téllez, Gabriel

doi:10.1063/1.3486558

Cited by 24 publications

(32 citation statements)

References 27 publications

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“…Such an effective potential can be derived within Poisson-Boltzmann formalism where we consider thin uniformly charged disks of density Q s and a continuous charge density profile for the ions. The far-field behavior of the electrostatic potential for highly charged disks (valid in relatively dilute colloidal suspensions) is exactly the same as the one obtained within the linearized PB theory provided that the boundary condition of constant surface potential is imposed on the surface of the colloid [24,25,29]. The value of the surface potential on the disk depends on its charge density Q s and ionic strength, that sets κ = (4πλ B i n i z 2 i ) 1/2 , where λ B = e 2 /(εk B T ) is the Bjerrum length [24].…”

Section: Effective Interactions For Charged Disks: Anisotropic Yumentioning

confidence: 53%

“…Our effective pair potential, obtained within non-linear Poisson-Boltzmann formalism and therefore repulsive, has the form of a screened Coulomb potential (Yukawa) multiplied by an angular function of the orientations of the two disks, which embodies the anisotropy of the interactions [24,25]. This anisotropy function depends on the ionic strength.…”

Section: Introductionmentioning

confidence: 99%

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Interplay of anisotropy in shape and interactions in charged platelet suspensions

Jabbari-Farouji

Weis

Levitz

et al. 2014

The Journal of Chemical Physics

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Motivated by the intriguing phase behavior of charged colloidal platelets, we investigate the structure and dynamics of charged repulsive disks by means of Monte-Carlo simulations. The electrostatic interactions are taken into account through an effective two-body potential, obtained within the nonlinear Poisson-Boltzmann formalism, which has the form of anisotropic screened Coulomb potential. Recently, we showed that the original intrinsic anisotropy of the electrostatic potential in competition with excluded volume effects leads to a rich phase behavior that not only includes various liquid-crsytalline phases but also predicts the existence of novel structures composed of alternating nematic-antinematic sheets. Here, we examine the structural and dynamical signatures of each of the observed structures for both translational and rotational degrees of freedom. Finally, we discuss the influence of effective charge value and our results in relation to experimental findings on charged platelet suspensions.

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Section: Effective Interactions For Charged Disks: Anisotropic Yumentioning

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Interplay of anisotropy in shape and interactions in charged platelet suspensions

Jabbari-Farouji

Weis

Levitz

et al. 2014

The Journal of Chemical Physics

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“…Series expansions to the Debye−Huckel equation exists for ellipsoidal, constant surface potential geometries. 25 It would also be interesting to study whether the quasi-equipotential approximation holds for more general geometries. …”

Section: Lettermentioning

confidence: 99%

Charge Renormalization for Ellipsoidal Macroions

2015

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We study the problem of counterion condensation for ellipsoidal macroions, a geometry well-suited for modeling liquid crystals, anisotropic vesicles, and polymers. We find that the ions within an ellipsoid's condensation layer are relatively unrestricted in their motions, and consequently work to establish a quasiequipotential at its surface. This simplifies the application of Alexander et al.'s procedure, enabling us to obtain accurate analytic estimates for the critical valence of a general ellipsoid in the weak screening limit. Interestingly, we find that the critical valence of an eccentric ellipsoid is always larger than that of the sphere of equal volume, implying that counterion condensation provides a force resisting the deformation of spherical macroions. This contrasts with a recent study of flexible spherical macroions, which observed a preference for deformation into flattened shapes when considering only linear effects. Our work suggests that the balance of these competing forces might alter the nature of the transition.T he behavior of weakly charged macroions in biological and soft materials is well described by the DLVO theory, which assumes very weak variations of the electrostatic potential, less than k B T, over scales comparable to the screening length. 1 In this limit, the counterions (or salt ions) within one screening length of a macroion are not bound to its surface, but are free to move. This approximation breaks down near highly charged macroions, where the counterions are bound to the surface and form a condensation layer. 2 The distribution and behavior of the counterions within this layer are not wellcharacterized by mean field analysis. Instead, they are highly localized, and can be considered part of a macroion-condensed counterion composite, which moves about as a single entity. 2−7 Considering the averaged field of this composite, one can construct a generalized DLVO theory based on the effective, renormalized charge. 8−10The degree of charge renormalization depends upon the shape of a macroion. As explained by Zimm and Le Bret, in the zero salt concentration limit, no condensation occurs for an isolated spherical macroion, because the attractive energy gained through condensation onto such a macroion is always less than the entropy associated with ion liberation. 11 In contrast, a finite fraction and complete counterion condensation occurs for cylindrical and planar macroions, respectively, in the same limit. 12,13 Counterion condensation is expected for all geometries under finite salt concentration conditions. 4,14−19 The most drastic, qualitative change occurs for the spherical geometry, for which a finite fraction of counterions now condense. This was first explained by Alexander et al., who obtained the condensation fraction by simply requiring the surface potential to equate to the free ion entropy. 2 These behaviors are of interest in that various experimental measures relating to macromolecule solutions, including the osmotic pressure, structure factor, and compressibilit...

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“…In this light, we view the above results as qualitative. Quantitative results that address many of the aforesaid simplifications can be obtained by employing approaches based on the solution of the Poisson-Boltzmann equation for spheroidal geometry [19].…”

Section: Charge Renormalization In Spheroidal Shellsmentioning

confidence: 99%

Coulomb energy of uniformly charged spheroidal shell systems

et al. 2015

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We provide exact expressions for the electrostatic energy of uniformly-charged prolate and oblate spheroidal shells. We find that uniformly-charged prolate spheroids of eccentricity greater than 0.9 have lower Coulomb energy than a sphere of the same area. For the volume-constrained case, we find that a sphere has the highest Coulomb energy among all spheroidal shells. Further, we derive the change in the Coulomb energy of a uniformly-charged shell due to small, area-conserving perturbations on the spherical shape. Our perturbation calculations show that buckling-type deformations on a sphere can lower the Coulomb energy. Finally, we consider the possibility of counterion condensation on the spheroidal shell surface. We employ a Manning-Oosawa two-state model approximation to evaluate the renormalized charge and analyze the behavior of the equilibrium free energy as a function of the shell's aspect ratio for both area-constrained and volume-constrained cases. Counterion condensation is seen to favor the formation of spheroidal structures over a sphere of equal area for high values of shell volume fractions.

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Screening of charged spheroidal colloidal particles

Cited by 24 publications

References 27 publications

Interplay of anisotropy in shape and interactions in charged platelet suspensions

Interplay of anisotropy in shape and interactions in charged platelet suspensions

Charge Renormalization for Ellipsoidal Macroions

Coulomb energy of uniformly charged spheroidal shell systems

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