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Register a new userIon size effects on the electric double layer of a spherical particle in a realistic salt-free concentrated suspension
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Authors
Rafael Roa n Fisica Aplicada I
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A new modified Poisson-Boltzmann equation accounting for the finite size of the ions valid for realistic salt-free concentrated suspensions has been derived, extending the formalism developed for pure salt-free suspensions [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960-3968] to real experimental conditions. These realistic suspensions include water dissociation ions and those generated by atmospheric carbon dioxide contamination, in addition to the added counterions released by the particles to the solution. The electric potential at the particle surface will be calculated for different ion sizes and compared with classical Poisson-Boltzmann predictions for point-like ions, as a function of particle charge and volume fraction. The realistic predictions turn out to be essential to achieve a closer picture of real salt-free suspensions, and even more important when ionic size effects are incorporated to the electric double layer description. We think that both corrections have to be taken into account when developing new realistic electrokinetic models, and surely will help in the comparison with experiments for low-salt or realistic salt-free systems.
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We study the electrophoretic mobility of spherical particles and the electrical conductivity in salt-free concentrated suspensions including finite ion size effects. An ideal salt-free suspension is composed of just charged colloidal particles and the added counterions that counterbalance their surface charge. In a very recent paper [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960- 3968] we presented a model for the equilibrium electric double layer for this kind of suspensions considering the size of the counterions, and now we extend this work to analyze the response of the suspension under a static external electric field. The numerical results show the high importance of such corrections for moderate to high particle charges, especially when a region of closest approach of the counterions to the particle surface is considered. The present work sets the basis for further theoretical models with finite ion size corrections, concerning particularly the ac electrokinetics and rheology of such systems.
We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution, that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell-Wagner-OKonski process associated with the counterions condensation layer, is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.
A simple non-local theoretical model is developed considering concentrated ionic surfactant solutions as regular ones. Their thermodynamics is described by the Cahn-Hilliard theory coupled with electrostatics. It is discovered that unstable solutions possess two critical temperatures, where the temperature coefficients of all characteristic lengths are discontinuous. At temperatures below the lower critical temperature ionic surfactant solutions separate into thin layers of oppositely charged liquids spread across the whole system and the electric potential is strictly periodic. At temperatures between the two critical temperatures separation can occur only near the solution surface thus leading to an oscillatory-decaying electric double layer. At temperatures above the higher critical temperature as well as in stable solutions there is no separation and the electric potential decays exponentially.
The electrostatic potential profile of a spherical soft particle is derived by solving the Poisson-Boltzmann equations on a spherical system both numerically and analytically. The soft particle is assumed to consist of an ion-permeable charged outer layer and a non-permeable charged core with constant charged density. The contribution of the core to the potential profile is calculated for different charges and dielectric constants. Our results show that the charged core heavily influences the local potential within the soft particle. In contrast, the potential distribution outside the particle in the salt solution is found to be weakly dependent on the core features. These findings are consistent with previous experiments showing the minor impact of the core of the MS2 virus on its overall electrical properties. Our studies also indicate that while a change in temperature from 290 K to 310 K only slightly varies the potential, the ionic strength in the range of 1-600 mM has a significant effect on the potential profile. Our studies would provide good understanding for experimental research in the field of biophysics and nanomedicine.
A concentrated, vertical monolayer of identical spherical squirmers, which may be bottom-heavy, and which are subjected to a linear shear flow, is modelled computationally by two different methods: Stokesian dynamics, and a lubrication-theory-based method. Inertia is negligible. The aim is to compute the effective shear viscosity and, where possible, the normal stress differences as functions of the areal fraction of spheres $phi$, the squirming parameter $beta$ (proportional to the ratio of a squirmers active stresslet to its swimming speed), the ratio $Sq$ of swimming speed to a typical speed of the shear flow, the bottom-heaviness parameter $G_{bh}$, the angle $alpha$ that the shear flow makes with the horizontal, and two parameters that define the repulsive force that is required computationally to prevent the squirmers from overlapping when their distance apart is less than a critical value $epsilon a$, where $epsilon$ is very small and $a$ is the sphere radius. The Stokesian dynamics method allows the rheological quantities to be computed for values of $phi$ up to $0.75$; the lubrication-theory method can be used for $phi> 0.5$. A major finding of this work is that, despite very different assumptions, the two methods of computation give overlapping results for viscosity as a function of $phi$ in the range $0.5 < phi < 0.75$. This suggests that lubrication theory, based on near-field interactions alone, contains most of the relevant physics, and that taking account of interactions with more distant particles than the nearest is not essential to describe the dominant physics.
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