Energetic and Entropic Forces Governing the Attraction between Polyelectrolyte-Grafted Colloids (original) (raw)
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Colloidal interactions mediated via polyelectrolytes
The Journal of Chemical Physics, 1995
Using Monte Carlo simulation, scaling, variational and mean-field arguments we investigate forces between charged spherical aggregates conferred by oppositely charged polymeric chains. Two types of polymer mediated attraction are found in this system, both of a bridging type but differing markedly in terms of the range. The entropic bridging force is of a range comparable to the average monomer-monomer separation in the chain. It is present whenever many chains have to compensate the charge on two macroions. The energetic bridging force has a range of the order of the length of the polymer chain and pertains to situations when a single chain has to compensate the charge on more than one macroion. In what follows we shall give a detailed analysis of both bridging interactions with a special regard for polycounterion versus simple counterion effects. The two types of bridging are in a certain sense complementary and should be present in polymer-surfactant systems at different regimes of the polymer-macroion concentration ratios.
Role of polyelectrolyte charge density in tuning colloidal forces
AIChE Journal, 2004
An atomic force microscope was used to study the effects of polymer charge density on surface interactions between similarly charged silica surfaces. Copolymers of acrylamide and acrylic acid of three different charge densities (f p ϭ 15, 40, and 70%) were used. The dynamic light-scattering technique was used to obtain the characteristic size of these polymers in solution. Flocculation tests were performed to complement force-distance measurement. At 20 mM KCl and pH ϳ 8.0, the low charge density copolymer (f p ϭ 15%) caused a purely repulsive force profile between silica surfaces irrespective of the added polymer concentration, suggesting a strong adsorption of the copolymer on the surface. The medium (f p ϭ 40%) and high (f p ϭ 70%) charge density copolymers, on the other hand, provided an adhesive bridging attraction at low polymer concentrations, but a purely repulsive force at higher polymer concentrations. The range of these repulsive forces, however, was significantly smaller than that measured for the low charge density polymer. The medium and high charge densities exhibit nearly an identical behavior in controlling the intersurface forces, although the forces are different with respect to magnitude. The flocculation tests follow the same trend as that of force-distance data, where a complete, a partial, and no flocculation observed with high, medium, and low charge density polymers, respectively. In all the cases, the range of surface interactions can be correlated with the polymer chain dimension corresponding to the fast diffusion process (individual chains) obtained from dynamic light-scattering measurements. Mean-field models proposed for charged polymers can qualitatively explain both the dependency of bridging interactions on polymer charge density and the dependency of force-distance profiles on added polymer concentrations. Finally, a mean-field model was used quantitatively to account for the measured electrosteric interactions and their dependency on polymer charge density.
The Journal of Chemical Physics, 2010
We study the effective interaction between differently charged polyelectrolyte-colloid complexes in electrolyte solutions via Monte Carlo simulations. These complexes are formed when short and flexible polyelectrolyte chains adsorb onto oppositely charged colloidal spheres, dispersed in an electrolyte solution. In our simulations the bending energy between adjacent monomers is small compared to the electrostatic energy, and the chains, once adsorbed, do not exchange with the solution, although they rearrange on the particles surface to accomodate further adsorbing chains or due to the electrostatic interaction with neighbor complexes. Rather unexpectedly, when two interacting particles approach each others, the rearrangement of the surface charge distribution invariably produces anti-parallel dipolar doublets, that invert their orientation at the isoelectric point. These findings clearly rule out a contribution of dipole-dipole interactions to the observed attractive interaction between the complexes, pointing out that such suspensions can not be considered dipolar fluids. On varying the ionic strength of the electrolyte, we find that a screening length κ −1 , short compared with the size of the colloidal particles, is required in order to observe the attraction between like charged complexes due to the non-uniform distribution of the electric charge on their surface ('patch attraction'). On the other hand, by changing the polyelectrolyte/particle charge ratio, ξ s , the interaction between like-charged polyelectrolyte-decorated (pd) particles, at short separations, evolves from purely repulsive to strongly attractive. Hence, the effective interaction between the complexes is characterized by a potential barrier, whose height depends on the net charge and on the non-uniformity of their surface charge distribution.
Chain Stiffness and Attachment-Dependent Attraction between Polyelectrolyte-Grafted Colloids
2010
We report here the effects of chain stiffness and surface attachment on the effective interactions between polyelectrolyte-grafted colloidal particles in monovalent salt obtained using Monte Carlo simulations. Our approach involves computation of the distance-dependent potential of mean force between two polyelectrolytegrafted colloidal particles treated at a coarse-grained resolution. Two chain stiffnesses, flexible and stiff, and two surface attachment modes, free and constrained, at low grafting densities are examined. PMF calculations across a range of surface and polyelectrolyte charge allows us to map out the strength and extent of the attractive and repulsive regime in the two-dimensional charge space. We observe striking differences in the effects of chain stiffness between the two modes of attachment. When the chains are freely attached, the stiff-chains colloids exhibit a marginal reduction in the attraction compared to their flexible-chain counterparts. In contrast, when the chains are attached in a constrained manner, the colloids with stiff chains exhibit a significantly stronger attraction and a broader attractive regime compared to flexible-chain colloids. These differences in the effects of stiffness between the two attachment modes are explained in terms of differences in the energetic and entropic forces balancing adsorption of chains at their own surface versus chain extension to mediate bridging interactions across two particles. Our results thus underscore the importance of surface attachment of chains and its proper accounting in computational and experimental studies and suggests the mode of chain attachment as an additional control parameter for modulating intercolloid interactions for applications such as stabilization of colloidal systems and bottom-up self-assembly of nanostructures.
Charged colloids and polyelectrolytes: from statics to electrokinetics
Journal of Physics: Conference Series, 2005
A review is given on recent studies of charged colloidal suspensions and polyelectrolytes both in static and non-equilibrium situations. As far as static equilibrium situations are concerned, we discuss three different problems: 1) Sedimentation density profiles in charged suspensions are shown to exhibit a stretched non-bariometric wing at large heights and binary suspensions under gravity can exhibit an analog of the brazil-nut effect known from granular matter, i.e. the heavier particles settle on top of the lighter ones. 2) Soft polyelectrolyte systems like polyelectrolyte stars and microgels show an ultra-soft effective interaction and this results into an unusual equilibrium phase diagram including reentrant melting transitions and stable open crystalline lattices. 3) The freezing transition in bilayers of confined charged suspensions is discussed and a reentrant behaviour is obtained. As far as nonequilibrium problems are concerned, we discuss an interface instability in oppositely driven colloidal mixtures and discuss possible approaches to simulate electrokinetic effects in charged suspensions.
Interaction between charged anisotropic macromolecules: Application to rod-like polyelectrolytes
The Journal of Chemical Physics, 2004
In this paper we propose a framework allowing one to compute the effective interactions between two anisotropic macromolecules, thereby generalizing the Derjaguin, Landau, Verwey, and Overbeek theory [E. J. W. Verwey and J. T. G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948)] to nonspherical finite size colloids. We show in particular that the effective interaction potential remains anisotropic at all distances and provide an expression for the anisotropy factor. We then apply this framework to the case of finite rod-like polyelectrolytes. The calculation of the interaction energy requires the numerical computation of the surface charge profiles, which result here from a constant surface potential on the rod-like colloids. However, a simplified analytical description is proposed, leading to an excellent agreement with the full numerical solution. Conclusions on the phase properties of rod-like colloids are proposed in this context.
Interactions between Charged Surfaces Immersed in a Polyelectrolyte Solution
Langmuir, 2007
With grand canonical simulations invoking a configurationally weighted scheme, we have calculated interactions between charged surfaces immersed in a polyelectrolyte solution. In contrast to previous simulations of such systems, we have imposed full equilibrium conditions (i.e., we have included diffusive equilibrium with a bulk solution). This has a profound impact on the resulting interactions: even at modest surface charge densities, oppositely charged chains will, at sufficiently large separations, adsorb strongly enough to overcompensate for the nominal surface charge. This phenomenon, known as charge inversion, generates a double-layer repulsion and a free-energy barrier. Simpler canonical approaches, where the chains are assumed to neutralize the surfaces perfectly, will not capture this stabilizing barrier. The barrier height increases with the length of the polyions. Interestingly enough, the separation at which the repulsion becomes attractive is independent of chain length. The short chains here are unable to reach across from one surface to the other. We therefore conclude that the transition to an attractive regime is not provided by the formation of such "intersurface'' bridges. With long chains and at large separations, charge inversion displays decaying oscillatory behavior (i.e., the apparent surface charge switches sign once again). This is due to polyion packing effects. We have also investigated responses to salt addition and changes in polyelectrolyte concentration. Our results are in qualitative and semiquantitative agreement with experimental findings, although it should be noted that our chains are comparatively short, and the experimental surface charge density is poorly established.
Le Journal de Physique IV, 2000
The paper summarizes recent theoretical work on the effective interactions between charge-stabilized, spherical colloidal particles. Despite the purely repulsive nature of the effective pair potential, fluid-fluid phase separation is shown to occur at very low salt concentrations, due to a frequently forgotten "volume" term. A longrange attractive component to the pair interaction is predicted when the colloidal particles are confined by charged surfaces (e.g. in slit or pore geometries), in agreement with recent experimental findings. The importance of excluded volume and solvent effects is briefly discussed.
Energetics of Colloids: Do Oppositely Charged Particles Necessarily Attract Each Other?
The Journal of Physical Chemistry, 1995
The electrostatic free energy of two oppositely charged macroions, suspended in ionic solution is calculated for different distances between the macroions. This is done by using a lattice field theory formulation of the statistical mechanics of Coulomb gas particles of finite size interacting with a fixed charge distribution (J. Chem. Phys. 1995, 102,4584). In many cases, it is found that, regardless of the size of the mobile ions, the minimum of the free energy is at a separation between the macroions corresponding to a noncontact configuration. Illustrative examples, which emphasize the source of the repulsion at near-touching configurations are presented and discussed.
Like-charge colloid–polyelectrolyte complexation
The Journal of Chemical Physics, 2002
We investigate the complexation of a highly charged sphere with a long flexible polyelectrolyte, both negatively charged in salt free environment. Electroneutrality is insured by the presence of divalent counterions. Using molecular dynamics (MD) within the framework of the primitive model, we consider different Coulomb coupling regimes. At strong Coulomb coupling we find that the adsorbed chain is always confined to the colloidal surface but forms different conformations that depend on the linear charge density of the chain. A mechanism involving the polyelectrolyte overcharging is proposed to explain these structures. At intermediate Coulomb coupling, the chain conformation starts to become three-dimensional, and we observe multilayering of the highly charged chain while for lower charge density the chain wraps around the colloid. At weak Coulomb coupling, corresponding to an aqueous solvent, we still find like-charge complexation. In this latter case the chain conformation exhibits loops.