SOFT CONDENSED MATTER
HIGHLIGHTS 2006 37 ESRF M. Montani (b), and O. Francescangeli (c), Appl. Phys.
Lett.88, 073901 (2006).
(a) Dipartimento di Scienze dei Materiali e della Terra, Università Politecnica delle Marche, Ancona (Italy) (b) Dipartimento di Biologia Molecolare, Cellulare e Animale, Università di Camerino (Italy)
(c) Dipartimento di Fisica e Ingegneria dei Materiali e del Territorio, Università Politecnica delle Marche, Ancona (Italy)
Diffusion and hydrodynamic interactions in charge-
stabilised colloidal suspensions
Charge-stabilised suspensions are ubiquitously found in chemical and waste-treatment industries, and in medical and biological products. These systems are composed of meso-scaled colloidal particles dispersed in a low- molecular polar solvent like water. Examples include proteins and viruses, paint and clay particles, and well- characterised model systems consisting of spherical latex spheres. Diffusion properties of charge-stabilised colloids are determined by a subtle interplay of electro- steric and hydrodynamic inter-particle forces.
Hydrodynamic interactions (HI) are transmitted by a complicated solvent flow pattern created by the moving particles. The inherent many-body character of the long- range HI causes challenging problems in theoretical and computer simulation studies of particle diffusion.
A salient measure of the strength of HI with regard to diffusion is given by the hydrodynamic function H(q). It can be determined by a combination of static and dynamic small-angle X-ray scattering experiments.
Without HI, H(q) is equal to one. Any variation in its dependence on the wavenumber q is a hallmark of HI. At large q, H(q) becomes proportional to the short-time self- diffusion coefficient DS. In earlier work [1], it was concluded that HI between charged colloidal particles are screened in the important case of a low-salt suspension. This conclusion was based on the observation of experimentally extracted values of H(q) and DSthat are smaller than for a suspension of neutral hard colloidal spheres at the same concentration. The interpretation of the strong hydrodynamic hindrance in terms of hydrodynamic screening caused a controversy since, according to theory, HI screening should not occur for liquid-state suspensions of mobile particles.
In a recent article [2], we show that, in fact, there is no hydrodynamic screening present in low-salinity systems.
This important result has been obtained from combining
SAXS and XPCS measurements of H(q), and of the static structure factor S(q), for aqueous suspensions of fluorinated latex spheres, with dynamic computer simulations and predictions of a modified hydrodynamic many-body theory. The XPCS experiments on aqueous suspensions of fluorinated latex spheres of radius a = 82.5 nm, with well-defined amounts of NaCl added, have been done at the ESRF’s Troika beamline, ID10A.
The simulations were performed using a novel accelerated Stokesian Dynamics (ASD) method. Our simulation results for H(q) are the only ones available so far for charge-stabilised suspensions with significant many-body HI. All our experimental data on H(q), and on the collective diffusion function D(q) = D0 H(q)/S(q), where D0 is the diffusion coefficient of an isolated sphere, can be quantitatively described by the simulations, and by the modified hydrodynamic theory.
In particular, the behaviour of H(q) for deionised dense suspensions can be explained by many-body HI effects, without the need to conjecture hydrodynamic screening.
In addition, boundaries are provided in our study for the maximum of H(q), and for DS, over the entire range of salt concentrations. Experimental, theoretical and computer simulation results for the H(q), D(q) and static structure factor S(q) of a low-salt system are included in Figure 44.
These data are compared to the simulation prediction for a suspension of neutral hard spheres of the same size Fig. 44:Diffusion functions H(q) and D(q), and
structure factor S(q), of a low-salt suspension.
Experimental results (open squares) vs. ASD simulation (red lines) and theory (black lines) are shown. Green lines: simulation data for neutral hard spheres at same concentration.
SOFT CONDENSED MATTER
HIGHLIGHTS 2006 ESRF 38
and volume fraction. Figure 45displays upper and lower boundaries for the principal peak height, H(qm), of H(q).
These boundaries are approached at very small and large amounts of added salt, respectively.
In conclusion, by a concerted experimental-theoretical effort, we could explain and quantify the influence of many-body HI on diffusion properties of charge- stabilised colloidal spheres. A consistent understanding of the micro-hydrodynamics of charge-stabilised spheres is important to gain improved insight into transport properties of more complex colloidal particles of interest for industry and biology.
References
[1] D.O. Riese, G.H. Wegdam, W.L. Vos, R. Sprik, D. Fenistein, J.H.H. Bongaerts and G. Grübel, Phys. Rev.
Lett.,85, 5460 (2000).
[2] A.J. Banchio, J. Gapinski, A. Patkowski, W. Häußler, A. Fluerasu, S. Sacanna, P. Holmqvist, G. Meier, M.P. Lettinga and G. Nägele, Phys. Rev. Lett.,96, 138303 (2006).
[3] Härtl et al., J. Chem. Phys. 110, 7070 (1999) and Segreet al.,Phys. Rev. E52, 5070 (1995).
Principal Publication and Authors
A.J. Banchio (a), J. Gapinski (b), A. Patkowski (b), W. Häußler (c), A. Fluerasu (d), S. Sacanna (e), P. Holmqvist (f), G. Meier (f), M.P. Lettinga (f) and G. Nägele (f), Phys. Rev. Lett.,96, 138303 (2006).
(a) Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba (Argentina)
(b) Institute of Physics, A. Mickiewicz University, Poznan (Poland)
(c) FRM-II, Technische Universität München (Germany) (d) ESRF
(e) Van’t Hoff Laboratory, University of Utrecht (The Netherlands)
(f) Institut für Festkörperforschung, Forschungszentrum Jülich (Germany)
Dynamics of a lamellar phase studied by XPCS and dynamic light scattering
X-ray photon correlation spectroscopy (XPCS) is a relatively new technique, successfully used to study the dynamics of soft-matter systems. Conceptually, it is rather similar to the traditional dynamic light scattering (DLS) technique, but its main advantages with respect to DLS are the potential for reaching much higher scattering wave vectors and the fact that it is less affected by multiple scattering.
Smectic phases are amenable for study by XPCS, since their high degree of order confines the scattered signal in the vicinity of the Bragg peaks. In the present work we used XPCS to measure the dispersion relation of fluctuations in bulk samples of a lamellar lyotropic phase (exhibiting smectic symmetry) and compared the results with DLS measurements.
XPCS had never been applied to lamellar lyotropic phases. Although the symmetry is the same for thermotropic smectics, there are notable differences due to the two-component character of the lyotropic phase (leading to additional hydrodynamic modes), to its lower elastic moduli, which influence both the relaxation rates and the ‘spread’ of the diffuse scattering around the Bragg position (thus limiting the accessible wave vector range). The relaxation rate of the fluctuations is described by the elasticity of the phase and the associated dissipation coefficients (viscosities). We should therefore be able to determine these material constants, compare them with the values obtained by other methods and (as a next step) test the validity of the elasticity theory at high wave vectors.
The samples were prepared in flat glass capillaries and oriented by thermal cycling between the lamellar and the isotropic phases, resulting in very good homeotropic anchoring. The experiments were performed at ID10A using an X-ray energy of 13 keV, in the uniform filling mode of the storage ring. The scattered signal was detected by a fast avalanche photodiode (APD) and the output signal was processed online by a FLEX autocorrelator.
It is well known that bulk lamellar phases exhibit the Landau-Peierls instability, leading to a characteristic Fig. 45:Simulation and theoretical predictions for
H(qm) versus volume fraction φ. Red lines: prediction for charged spheres at zero salinity, with near-field HI disregarded; black line: hard spheres. The filled black triangles and red squares are our XPCS/SAXS data.
Earlier experimental data [3] are included for comparison.
