Dynamics of hard sphere suspensions using dynamic light scattering and X-ray photon correlation spectroscopy: Dynamics and scaling of the intermediate scattering function (original) (raw)
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Dynamic light scattering measurements in the activated regime of dense colloidal hard spheres
Journal of Statistical Mechanics: Theory and Experiment, 2009
We use dynamic light scattering and numerical simulations to study the approach to equilibrium and the equilibrium dynamics of systems of colloidal hard spheres over a broad range of densities, from dilute systems up to very concentrated suspensions undergoing glassy dynamics. We discuss several experimental issues (sedimentation, thermal control, non-equilibrium ageing effects, dynamic heterogeneity) arising when very large relaxation times are measured. When analyzed over more than seven decades in time, we find that the equilibrium relaxation time, τ α , of our system is described by the algebraic divergence predicted by mode-coupling theory over a window of about three decades. At higher density, τ α increases exponentially with distance to a critical volume fraction ϕ 0 , which is much larger than the mode-coupling singularity. This is reminiscent of the behavior of molecular glass-formers in the activated regime. We compare these results to previous work, carefully discussing crystallization and size polydispersity effects. Our results suggest the absence of a genuine algebraic divergence of τ α in colloidal hard spheres.
iii Pa'Mi Chaparrita Que siempre ilumina mi camino en la oscuridad v Abstract This thesis reports on a comprehensive experimental study of the collective dynamics of colloidal hard sphere suspensions. The main quantity measured is the coherent Intermediate Scattering Function (ISF) using a range of techniques based on Dynamic Light Scattering (DLS). The collective dynamics are measured as a function of scattering vector for volume fractions spanning from dilute samples, through the fluid phase and the metastable region, up until deep in the glass region. This work describes two major explorations: (i) the effect of volume of fraction on the q-dependency of the collective dynamics; and (ii) a study of the ageing processes in colloidal glasses. The present work is unique in the application of several advanced experimental techniques, and in the level of averaging that has been carried out, enabling a more sophisticated analysis than has previously been possible. This includes the characterization of non-Fickian processes and the determination of the current-current correlation function (CCCF) in the metastable fluid, and the quantitative characterization of the ageing process in the hard sphere glass. In addition, by combining aspects of the coherent and incoherent ISFs, this work also allows the expression of the collective dynamics in terms of the single particle displacement. The results show a dynamical change at the freezing point (φ f ), which exposes the incapacity of the system to dissipate thermal energy via diffusing momentum currents, i.e. viscous flow. The structural impediments responsible for this, associated with dynamical heterogeneities, begin at the structure factor peak, and spread to other spatial modes as the volume fraction increases. Above the glass transition (φ g ), structural relaxation becomes arrested at all spatial modes probed, i.e. flow is arrested. It is found that, following the quench, samples above the glass volume fraction approach some final "ideal" glass in an algebraic manner. However, although the long time dynamics exhibit ageing, the non-ergodicity factor, a measure of the average structure of the sample, does not show any significant ageing. This dynamical ageing process, decoupled from changes in the average structure, is identified with irreversible exchange of particles.
Physical Review E, 2000
X-ray photon correlation spectroscopy and small-angle x-ray scattering measurements are applied to characterize the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions between 2.7% and 52%. The static structures of the suspensions show essentially hard-sphere behavior. The short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient, which are based on a hard-sphere model ͓C. W. J. Beenakker and P. Mazur, Physica A 126, 349 ͑1984͔͒. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension ͓P. N. Segre and P. N. Pusey, Phys. Rev. Lett. 77, 771 ͑1996͔͒. Our measurements are parametrized in terms of a viscoelastic model for the intermediate scattering function ͓W. Hess and R. Klein, Adv. Phys. 32, 173 ͑1983͔͒. Within this framework, two relaxation modes are predicted to contribute to the decay of the dynamic structure factor, with mode amplitudes depending on both wave vector and volume fraction. Our measurements indicate that, for particle volume fractions smaller than about 0.30, the intermediate scattering function is well described in terms of single-exponential decays, whereas a double-mode structure becomes apparent for more concentrated systems.
Dynamics in dense hard-sphere colloidal suspensions
Physical Review E, 2012
The dynamic behavior of a hard-sphere colloidal suspension was studied by X-ray Photon Correlation Spectroscopy and Small Angle X-ray Scattering over a wide range of particle volume fractions. The short-time mobility of the particles was found to be smaller than that of free particles even at relatively low concentrations, showing the importance of indirect hydrodynamic interactions. Hydrodynamic functions were derived from the data and for moderate particle volume fractions (Φ ≤ 0.40) there is a good agreement with earlier many-body theory calculations by Beenakker and Mazur [C.W.J. Beenakker and P. Mazur, Physica A 120, 349 ]. Important discrepancies appear at higher concentrations, above Φ ≈ 0.40, where the hydrodynamic effects are overestimated by the Beenakker-Mazur theory, but predicted accurately by an accelerated Stokesian dynamics algorithm developed by Banchio and Brady [A.J. Banchio and J. F. Brady, J. Chem. Phys. 118, 10323 (2003)]. For the relaxation rates, good agreement was also found between the experimental data and a scaling form predicted by Mode Coupling Theory. In the high concentration range, with the fluid suspensions approaching the glass transition, the long-time diffusion coefficient was compared with the short-time collective diffusion coefficient to verify a scaling relation previously proposed by Segrè and Pusey [P.N. Segrè and P.N. Pusey, Phys. Rev. Lett. 77, 771 (1996)]. We discuss our results in view of previous experimental attempts to validate this scaling law [L. Lurio et al., Phys. Rev. Lett. 84, 785 (2000)].
Journal of Applied Crystallography, 2000
The dynamics of concentrated, charge-stabilized colloidal silica suspensions was studied over a wide range of wave-vectors. The short-time diffusion coefficient, D(Q), was measured for concentrated suspensions up to their solidification points by photon correlation spectroscopy with coherent X-rays and compared to free particle diffusion D 0 , studied by Dynamic Light Scattering (DLS) in the dilute case. Small angle X-ray scattering (SAXS) was used to determine the static structure factor S(Q). D 0 /D(Q) peaks for Q values corresponding to the maximum of the static structure factor showing that the mostly likely density fluctuations decay the slowest. The data allow one to estimate the diffusion coefficient D(Q) in the Q → 0 and Q → ∞ limits. Thus, hydrodynamic functions can be derived free from any modeling of the static or dynamic properties. The effects of hydrodynamic interactions on the diffusion coefficient in charge-stabilized suspensions are presented for volume fractions 0.075 < Φ < 0.28.
Probing Static Structure of Colloid–Polymer Suspensions with Multiply Scattered Light
Journal of Colloid and Interface Science, 1999
Time-dependent measurements of light propagation were conducted in aqueous dispersions of 523 nm diameter polystyrene at concentrations between 0.1 and 0.4 solids volume fraction in order to assess how particle correlation is influenced by depletion interactions arising from the addition of soluble polyethyleneoxide (PEO). In the absence of polymer, the transport scattering length can be predicted from Mie scattering theory and the Percus-Yevick (P-Y) model for static structure of a dense hard-sphere colloidal solution. Depletion forces arising from the addition of PEO of varying molecular weights influenced the spatial ordering of the dispersion and caused a further increase in the transport scattering length beyond that predicted by hard-sphere static structure factor but similar to that predicted by the mean sphere approximation (MSA) to the P-Y model described by Ye et al. (1996). Onset of flocculation occurred with increased PEO addition and correlated with PEO molecular weight. Phase separation was noted by no further change in the transport scattering length, except when flocculation was induced by the highest molecular weight PEO. The use of time-dependent measurements of light propagation in dense systems provides an alternative to smallangle light, neutron, and X-ray scattering characterization of interaction potentials in dense, multiply scattering samples and promises further fruitful investigation of colloidal particle interactions in suspensions.
Structure and dynamics of colloidal suspensions studied by means of XPCS
Structure and dynamics of suspensions of charged colloidal spheres in water were studied by means of small-angle X-ray scattering and X-ray photon correlation spectroscopy using synchrotron radiation. Experimentally obtained dependences on the scattering vector q of the structure factor S(q), short-time collective diffusion coefficient D(q) and hydrodynamic function H(q) were in good agreement with theoretical predictions. No effect of screening of the hydrodynamic interactions, suggested in the literature, was found. The conditions are discussed at which the maximum of the hydrodynamic function peak value H(qm) can be obtained experimentally.
Dynamics of crystallization in hard-sphere suspensions
Physical Review E, 1996
Density fluctuations are monitored by small-angle light scattering during the crystallization of 0.22m-radius, hard colloidal spheres. Measured structure factors show an intensity maximum at finite-scattering vectors. The shape of the intensity distribution scales at early times during nucleation and growth and again at large times during ripening. At intermediate times there is a crossover region where scaling ceases to be valid. Both the amplitude and the position of the maximum intensity show quasi-power law behavior in time. The values of the observed exponents are within the range expected for classical growth models. The breadth of the intensity distribution increases with increasing volume fraction, suggesting greater crystal polydispersity with increasing volume fraction. The lower volume fraction intensity distributions suggest that crystals have a compound or internal structure, while the observed decrease in characteristic length in the crossover time regime may indicate breakup of crystals to this smaller internal structure. The results of measurements are compared with results calculated for nucleation and growth of crystals in suspensions of hard spheres. Results also are compared with earlier measurements made on samples containing 0.50-m radius spheres. Differences in the two systems are discussed in terms of interparticle potential, polydispersity, and gravitational effects. ͓S1063-651X͑96͒09610-9͔
Investigation of Static Structure Factor in Dense Suspensions by Use of Multiply Scattered Light
Applied Optics, 1999
Near-infrared, frequency-domain photon migration measurements of phase shift are used to derive accurate values of isotropic scattering coefficients in concentrated, interacting suspensions of aqueous polystyrene microspheres with volume concentrations ranging from 1% to 45% by solids and mean diameters ranging from 135 to 500 nm. Under conditions of high ionic strength, the isotropic scattering coefficient can be quantitatively predicted by the Percus-Yevick model for hard-sphere interactions and Mie theory. In addition, the attractive interactions between scatterers arising from the addition of soluble poly͑ethylene glycol͒ with molecular weights of 100 and 600 K cause hindered scattering. The increases in static structure and decreases in isotropic scattering coefficient agree with that predicted by Mie theory and the depletion interaction model developed by Asakura and Oosawa ͓J. Chem. Phys. 22, 1255 ͑1954͔͒. These results demonstrate the success of monitoring interaction between particles by use of multiple-scattered light and the necessity of incorporating models for these interactions when predicting scattering of dense, concentrated suspensions.
In Situ Characterization of Colloidal Spheres by Synchrotron Small-Angle X-ray Scattering
Langmuir, 1997
We have performed small-angle X-ray scattering with a synchrotron source on dilute suspensions of colloidal spheres of polystyrene latex, Stöber silica, and microemulsion-grown silica. Many interference fringes are observed of the monodisperse particles over a large range of scattering vectors and more than 5 orders of magnitude in intensity. We present a straightforward method to deduce the radii, the size polydispersity, and the interface thickness of the particles from a Porod plot of one and the same in situ measurement. The radii agree very well with static light-scattering data. The radii are larger than the electron microscopy data of dry spheres and smaller than the hydrodynamic radii from dynamic lightscattering data. The size polydispersities are smaller than those obtained by electron microscopy, which is well explained by the intrinsic random errors of electron microscopy. We find that nearly all the particles have a homogeneous internal density and a sharp interface with the suspending medium of less than 1 nm wide. In one case of a stepwise synthesized particle, we have discerned a dense core and a less-dense shell, without contrast matching with the suspending liquid. It is concluded that synchrotron small-angle X-ray scattering is a very powerful technique for the in situ study of colloidal systems.