Light scattering and diffusion in suspensions of strongly charged particles at low volume fractions (original) (raw)
Related papers
Journal of Colloid and Interface Science, 1992
An appropriate mean force potential was utilized in Felderhof's Theory to derive simple analytical expressions for the concentration dependence of the collective and short time self diffusion coefficients, as well as for the sedimentation velocity of charged spherical particles. It is demonstrated theoretically that the osmotic viriat and the Oseen hydrodynamic terms play a dominant role. To check the theoretical model, the dependence of the collective diffusion coefficient on the volume fraction of latex particles was experimentally studied. Dynamic light scattering was used at several different concentrations of electrolyte. It turns out that our experimental results, as well as the results of other authors, are in very good agreement with the proposed theoretical model. The results show that the increase of the electrolyte concentration leads to increase of the particle charge, but almost does not change the particle surface potential. A minimum in the dependence of the diffusion coefficient of a single particle on the ionic strength was also obtained.
Soft Matter, 2015
We present an easy-to-use analytic toolbox for the calculation of short-time transport properties of concentrated suspensions of spherical colloidal particles with internal hydrodynamic structure, and direct interactions described by a hard-core or soft Hertz pair potential. The considered dynamic properties include self-diffusion and sedimentation coefficients, the wavenumber-dependent diffusion function determined in dynamic scattering experiments, and the high-frequency shear viscosity. The toolbox is based on the hydrodynamic radius model (HRM) wherein the internal particle structure is mapped on a hydrodynamic radius parameter for unchanged direct interactions, and on an existing simulation data base for solvent-permeable and spherical annulus particles. Useful scaling relations for the diffusion function and self-diffusion coefficient, known to be valid for hard-core interaction, are shown to apply also for soft pair potentials. We further discuss extensions of the toolbox to long-time transport properties including the low-shear zero-frequency viscosity and the long-time self-diffusion coefficient. The versatility of the toolbox is demonstrated by the analysis of a previous light scattering study of suspensions of non-ionic PNiPAM microgels [Eckert et al., J. Chem. Phys., 2008, 129, 124902] in which a detailed theoretical analysis of the dynamic data was left as an open task. By the comparison with Hertz potential based calculations, we show that the experimental data are consistently and accurately described using the Verlet-Weis corrected Percus-Yevick structure factor as input, and for a solvent penetration length equal to three percent of the excluded volume radius. This small solvent permeability of the microgel particles has a significant dynamic effect at larger concentrations.
Dynamics of permeable particles in concentrated suspensions
Physical Review E, 2010
We calculate short-time diffusion properties of suspensions of porous colloidal particles as a function of their permeability, for the full fluid-phase concentration range. The particles are modeled as spheres of uniform permeability with excluded volume interactions. Using a precise multipole method encoded in the HYDROMUL-TIPOLE program, results are presented for the hydrodynamic function, H͑q͒, sedimentation coefficient, and self-diffusion coefficients with a full account of many-body hydrodynamic interactions. While self-diffusion and sedimentation are strongly permeability dependent, the wave-number dependence of the hydrodynamic function can be reduced by appropriate shifting and scaling, to a single master curve, independent of permeability. Generic features of the permeable sphere model are discussed.
Short-time dynamics of permeable particles in concentrated suspensions
The Journal of Chemical Physics, 2010
We study short-time diffusion properties of colloidal suspensions of neutral permeable particles. An individual particle is modeled as a solvent-permeable sphere of interaction radius a and uniform permeability k, with the fluid flow inside the particle described by the Debye-Bueche-Brinkman equation, and outside by the Stokes equation. Using a precise multipole method and the corresponding numerical code HYDROMULTIPOLE that account for higher-order hydrodynamic multipole moments, numerical results are presented for the hydrodynamic function, H͑q͒, the short-time self-diffusion coefficient, D s , the sedimentation coefficient K, the collective diffusion coefficient, D c , and the principal peak value H͑q m ͒, associated with the short-time cage diffusion coefficient, as functions of porosity and volume fraction. Our results cover the full fluid phase regime. Generic features of the permeable sphere model are discussed. An approximate method by Pusey to determine D s is shown to agree well with our accurate results. It is found that for a given volume fraction, the wavenumber dependence of a reduced hydrodynamic function can be estimated by a single master curve, independent of the particle permeability, given by the hard-sphere model. The reduced form is obtained by an appropriate shift and rescaling of H͑q͒, parametrized by the self-diffusion and sedimentation coefficients. To improve precision, another reduced hydrodynamic function, h m ͑q͒, is also constructed, now with the self-diffusion coefficient and the peak value, H͑q m ͒, of the hydrodynamic function as the parameters. For wavenumbers qa Ͼ 2, this function is permeability independent to an excellent accuracy. The hydrodynamic function of permeable particles is thus well represented in its q-dependence by a permeability-independent master curve, and three coefficients, D s , K, and H͑q m ͒, that do depend on the permeability. The master curve and its coefficients are evaluated as functions of concentration and permeability.
Physical Chemistry Chemical Physics, 2004
One of the fields where electroacoustic techniques (electrokinetic sonic amplitude, ESA, and colloid vibration current, CVI, are presently available) are expected to be most useful is concentrated suspensions. Here, other electrokinetic techniques, linked to the observation of individual particles, show great limitations. In spite of this, the problem of electroacoustics in concentrated suspensions is far from being fully resolved. In this work, the method considered is ESA, where the quantity of interest is the dynamic or ac mobility of the particles, u d *. Our aim is to compare in a systematic way two procedures for the calculation of u d * in concentrated suspensions: One is based upon the use of a cell model, often used in electrokinetics of concentrated systems, and the other is an analytical formula elaborated by O'Brien and coworkers taking explicitly into account particle-particle interactions. On the average both methods seem to describe properly the frequency dependence of u d *, at least up to volume fractions of solids of the order of 40%. Maxima and minima are sometimes found that can be explained through consideration of electrical double layer relaxations (alpha and, mainly, Maxwell-Wagner-O'Konski) affecting the strength of the dipole moment induced by the external field. As to the effect of ka (a: particle radius; k: reciprocal double layer thickness) on u d *, it is found that the analytical formula, in spite of being a '' large ka '' model can be used with confidence down to ka $ 10. The two methods can also predict the reduction in |u d *| upon increasing volume fraction, but only the cell model suggests that the phase angle of |u d *| goes to zero when the particle-to-particle distance is very much reduced (highest volume fractions). It appears that the phase angle can be very sensitive to the different ways in which the methods used account for the interactions between neighbouring particles, as no significant differences are found when the effect of the volume fraction (or the zeta potential) on |u d *| are estimated using any of the models.
2007
Sedimentation-diffusion equilibrium density profiles of suspensions of charge-stabilized colloids are calculated theoretically and by Monte Carlo simulation, both for a one-component model of colloidal particles interacting through pairwise screened-Coulomb repulsions and for a three-component model of colloids, cations, and anions with unscreened-Coulomb interactions. We focus on a state point for which experimental measurements are available [C.P. Royall et al., J. Phys.: Cond. Matt. 17, 2315 ]. Despite the apparently different picture that emerges from the one-and threecomponent model (repelling colloids pushing each other to high altitude in the former, versus a self-generated electric field that pushes the colloids up in the latter), we find similar colloidal density profiles for both models from theory as well as simulation, thereby suggesting that these pictures represent different view points of the same phenomenon. The sedimentation profiles obtained from an effective one-component model by MC simulations and theory, together with MC simulations of the multi-component primitive model are consistent among themselves, but differ quantitatively from the results of a theoretical multi-component description at the Poisson-Boltzmann level. We find that for small and moderate colloid charge the Poisson-Boltzmann theory gives profiles in excellent agreement with the effective one-component theory if a smaller effective charge is used. We attribute this discrepancy to the poor treatment of correlations in the Poisson-Boltzmann theory.
Dynamics of suspensions of hydrodynamically structured particles: Analytic theory and experiment
2015
We present an easy-to-use analytic toolbox for the calculation of short-time transport properties of concentrated suspensions of spherical colloidal particles with internal hydrodynamic structure, and direct interactions described by a hard-core or soft Hertz pair potential. The considered dynamic properties include self-diffusion and sedimentation coefficients, the wavenumber-dependent diffusion function determined in dynamic scattering experiments, and the high-frequency shear viscosity. The toolbox is based on the hydrodynamic radius model (HRM) wherein the internal particle structure is mapped on a hydrodynamic radius parameter for unchanged direct interactions, and on an existing simulation data base for solvent-permeable and spherical annulus particles. Useful scaling relations for the diffusion function and self-diffusion coefficient, known to be valid for hard-core interaction, are shown to apply also for soft pair potentials. We further discuss extensions of the toolbox to long-time transport properties including the low-shear zero-frequency viscosity and the long-time self-diffusion coefficient. The versatility of the toolbox is demonstrated by the analysis of a previous light scattering study of suspensions of non-ionic PNiPAM microgels [Eckert et al., J. Chem. Phys., 2008, 129, 124902] in which a detailed theoretical analysis of the dynamic data was left as an open task. By the comparison with Hertz potential based calculations, we show that the experimental data are consistently and accurately described using the Verlet-Weis corrected Percus-Yevick structure factor as input, and for a solvent penetration length equal to three percent of the excluded volume radius. This small solvent permeability of the microgel particles has a significant dynamic effect at larger concentrations.
Sedimentation of charged colloids: The primitive model and the effective one-component approach
Physical Review E, 2007
Sedimentation-diffusion equilibrium density profiles of suspensions of charge-stabilized colloids are calculated theoretically and by Monte Carlo ͑MC͒ simulations, both for a one-component model of colloidal particles interacting through pairwise screened-Coulomb repulsions and for a three-component model of colloids, cations, and anions with unscreened-Coulomb interactions. We focus on a state point for which experimental measurements are available ͓C. P. Royall et al., J. Phys.: Condens Matter 17, 2315 ͑2005͔͒. Despite the apparently different picture that emerges from the one-and three-component models ͑repelling colloids pushing each other to high altitude in the former, versus a self-generated electric field that pushes the colloids up in the latter͒, we find similar colloidal density profiles for both models from theory as well as simulation, thereby suggesting that these pictures represent different viewpoints of the same phenomenon. The sedimentation profiles obtained from an effective one-component model by MC simulations and theory, together with MC simulations of the multicomponent primitive model are consistent among themselves, but differ quantitatively from the results of a theoretical multicomponent description at the Poisson-Boltzmann level. We find that for small and moderate colloid charge the Poisson-Boltzmann theory gives profiles in excellent agreement with the effective one-component theory if a smaller effective charge is used. We attribute this discrepancy to the poor treatment of correlations in the Poisson-Boltzmann theory.
Physics of Fluids, 2011
For suspensions of permeable particles, the short-time translational and rotational self-diffusion coefficients, and collective diffusion and sedimentation coefficients are evaluated theoretically. An individual particle is modeled as a uniformly permeable sphere of a given permeability, with the internal solvent flow described by the Debye-Bueche-Brinkman equation. The particles are assumed to interact non-hydrodynamically by their excluded volumes. The virial expansion of the transport properties in powers of the volume fraction is performed up to the two-particle level. The first-order virial coefficients corresponding to two-body hydrodynamic interactions are evaluated with very high accuracy by the series expansion in inverse powers of the inter-particle distance. Results are obtained and discussed for a wide range of the ratio, x, of the particle radius to the hydrodynamic screening length inside a permeable sphere. It is shown that for x & 10, the virial coefficients of the transport properties are well-approximated by the hydrodynamic radius (annulus) model developed by us earlier for the effective viscosity of porous-particle suspensions.
Light scattering study of the diffusion of interacting particles
Journal of the Chemical Society, Faraday Transactions 2, 1980
The diffusion coefficient of a water-in-oil microemulsion has been measured as a function of the concentration of the suspended particles using photon correlation techniques. The data have been analysed using an extension of the thermo-hydrodynamic theory of G. K. Batchelor to the case of a potential of mean force between particles which consists of a hard-core repulsion and an attractive part. The parameters for this potential are consistent with those obtained from the osmotic compressibility as determined by static light scattering.