Viscosity of hard sphere suspensions

A simple functional representation of the concentration dependence of the low-shear viscosity eta of hard sphere suspensions is proposed. The representation, which agrees with published literature at all volume fractions phi, has a hitherto-unremarked transition in its functional form at phi approximately 0.42 identical with phi(t). phi(t) is definitely less than the volume fraction 0.49 of the hard sphere melting transition.     

Two-dimensional crystallization of hard sphere particles at a liquid–liquid interface

A method for studying crystallization of hard sphere like particles in two dimensions is presented. The method involves trapping the particles at the interface between two immiscible liquids. Particles at the interface undergo 2D Brownian motion, and at sufficiently high densities crystallization is observed. The pseudo hard sphere nature of the particle interactions under these conditions is maintained, as demonstrated by the area density at which crystallization occurs. In contrast to established techniques for studying crystallization in pseudo 2D hard spheres, the particles trapped at the interface undergo no vertical motion, so the system is in principle closer to a true 2D system. The method is therefore amenable to the study of the effects of polydispersity on crystallization behaviour. The advantages and disadvantages of the method are discussed.     

Phonons in suspensions of hard sphere colloids: volume fraction dependence

The propagation of sound waves in suspensions of hard sphere colloids is studied as a function of their volume fraction up to random close packing using Brillouin light scattering. The rich experimental phonon spectra of up to five phonon modes are successfully described by theoretical calculations based on the multiple scattering method. Two main types of phonon modes are revealed: Type A modes are acoustic excitations which set up deformations in both the solid (particles) and the liquid (solvent) phases; for type B modes the stress and strain are predominantly localized near the interface between the solid particles and the surrounding liquid (interface waves). While the former become harder (increase their effective sound velocity) as the particle volume fraction increases the latter become softer (the corresponding sound velocity decreases).     

Activated hopping and dynamical fluctuation effects in hard sphere suspensions and fluids

Single particle Brownian dynamics simulation methods are employed to establish the full trajectory level predictions of our nonlinear stochastic Langevin equation theory of activated hopping dynamics in glassy hard sphere suspensions and fluids. The consequences of thermal noise driven mobility fluctuations associated with the barrier hopping process are determined for various ensemble-averaged properties and their distributions. The predicted mean square displacements show classic signatures of transient trapping and anomalous diffusion on intermediate time and length scales. A crossover to a stronger volume fraction dependence of the apparent nondiffusive exponent occurs when the entropic barrier is of order the thermal energy. The volume fraction dependences of various mean relaxation times and rates can be fitted by empirical critical power laws with parameters consistent with ideal mode-coupling theory. However, the results of our divergence-free theory are largely a consequence of activated dynamics. The experimentally measurable alpha relaxation time is found to be very similar to the theoretically defined mean reaction time for escape from the barrier-dominated regime. Various measures of decoupling have been studied. For fluid states with small or nonexistent barriers, relaxation times obey a simple log-normal distribution, while for high volume fractions the relaxation time distributions become Poissonian. The product of the self-diffusion constant and mean alpha relaxation time increases roughly as a logarithmic function of the alpha relaxation time. The cage scale incoherent dynamic structure factor exhibits nonexponential decay with a modest degree of stretching. A nearly universal collapse of the different volume fraction results occurs if time is scaled by the mean alpha relaxation time. Hence, time-volume fraction superposition holds quite well, despite the presence of stretching and volume fraction dependent decoupling associated with the stochastic barrier hopping process. The relevance of other origins of dynamic heterogeneity (e.g., mesoscopic domains), and comparison of our results with experiments, simulations, and alternative theories, is discussed.     

On the influence of a patterned substrate on crystallization in suspensions of hard spheres

We present a computer simulation study on crystal nucleation and growth in supersaturated suspensions of mono-disperse hard spheres induced by a triangular lattice substrate. The main result is that compressed substrates are wet by the crystalline phase (the crystalline phase directly appears without any induction time), while for stretched substrates we observe heterogeneous nucleation. The shapes of the nucleated crystallites fluctuate strongly. In the case of homogeneous nucleation amorphous precursors have been observed [T. Schilling et al., Phys. Rev. Lett. 105(2), 025701 (2010)]. For heterogeneous nucleation we do not find such precursors. The fluid is directly transformed into highly ordered crystallites.     

Electrophoresis of ionic microgel particles: from charged hard spheres to polyelectrolyte-like behavior

We perform electrophoretic mobility measurements of ionic microgel particles in the deswollen and swollen phases. The results show that microgels behave as charged hard spheres in the first case and as free-draining spherical polyelectrolytes in the latter. A unified theory for the electrophoresis of polyelectrolyte-coated particles [H. Ohshima, Adv. Colloid Interface Sci. 62, 189 (1995)] is shown to contain the essential physics for describing the experiments, upon adequate consideration of the particles swelling behavior and network-solvent friction variations.     

Controlling stages of supramolecular crystallization in suspensions of monodispersed spherical silica particles

Supramolecular crystallization in alcohol suspensions of monodispersed spherical silica particles at pH ~ 7-7.8 is controlled by sedimentation of structural units. At pH ~ 7.8-10.5 or in the presence of indifferent (inert) electrolytes, the crystallization is controlled by the linear growth of supramolecular crystals. The peculiarities of crystallization and nucleation in both cases are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetics of supramolecular crystallization of concentrated suspensions of monodisperse spherical silica particles

The kinetics of supramolecular crystallization of concentrated suspensions is three-dimensional and follows the Avrami-Erofeev equation: A=1-exp[-(kt)^m], where m=4. The rate constant k is proportional to the probability of the appearance of a crystallization center in unit volume in unit time and the linear crystal growth rate, which is determined experimentally.     

Critical flux of hard sphere suspensions in crossflow filtration: Hydrodynamic force bias Monte Carlo simulations

A Monte Carlo method is developed for crossflow membrane filtration to determine the critical flux of hard sphere suspensions. Brownian and shear-induced diffusion are incorporated into an effective hydrodynamic force exerted on the hard spheres in a concentrated shear flow. Effects of shear rate and particle size on the critical flux are investigated using hydrodynamic force bias Monte Carlo simulations, providing a baseline of the critical flux.     

Thermal property changes of poly(N-isopropylacrylamide) microgel particles and block copolymers

Investigation of the thermo-reversible properties of different poly(N-isopropyl acrylamide) samples, including microgels and block copolymers, with a combination of methods such as electron microscopy, dynamic light scattering, analytical ultracentrifugation, electrophoresis and ultrasound resonator technology allows comprehensive characterisation of the phase transition. By the combination of methods, it was possible to show that the precipitated polymer phase contains at 40 °C between 40 and 50 vol.% of water. Besides free bulk water, there is also bound water that strongly adheres to the N-isopropyl acrylamide units (about 25 vol.%). Ultrasound resonator technology, which is a non-sizing characterisation method, revealed for the microgel particles two more temperatures (at about 35 and between 40 °C and 50 °C depending on the chemical nature) where characteristic changes in the ultrasound attenuation take place. Moreover, the experimental data suggest that the phase transition temperature is related to surface charge density of the precipitated particles.     

Effect of polydispersity on the crystallization kinetics of suspensions of colloidal hard spheres when approaching the glass transition

We present a comprehensive study of the solidification scenario in suspensions of colloidal hard spheres for three polydispersities between 4.8% and 5.8%, over a range of volume fractions from near freezing to near the glass transition. From these results, we identify four stages in the crystallization process: (i) an induction stage where large numbers of precursor structures are observed, (ii) a conversion stage as precursors are converted to close packed structures, (iii) a nucleation stage, and (iv) a ripening stage. It is found that the behavior is qualitatively different for volume fractions below or above the melting volume fraction. The main effect of increasing polydispersity is to increase the duration of the induction stage, due to the requirement for local fractionation of particles of larger or smaller than average size. Near the glass transition, the nucleation process is entirely frustrated, and the sample is locked into a compressed crystal precursor structure. Interestingly, neither polydispersity nor volume fraction significantly influences the precursor stage, suggesting that the crystal precursors are present in all solidifying samples. We speculate that these precursors are related to the dynamical heterogeneities observed in a number of dynamical studies.     

Anomalous electrophoretic mobility of microgel particles in buffer solutions

The electrophoretic mobility (μ) of tunable surface charge poly(N-isopropylacrylamide) microgel particles (PNIPAM) was measured vs pH, using different anionic buffers. Two minima, just at the buffers’ pK values, were found for the μ-pH curve. The preferential penetration of the small counterions into the soft-charged shell explains the electrokinetic charge reduction. For pH values higher than the pK, the charge screening leads to electrostatic repulsions among coions. It pushes them towards the particles; thus, balancing the global ionic distribution.     

Equation of state of the hard sphere liquid

Using the results of Monte Carlo simulation, equations of state of hard sphere liquids are calculated for 106 values of the fill factor η= 0.005–0.530 (step of 0.005). In the region of liquid phase stability the absolute accuracy of about 0.00001–0.00008 is reached. Correctness of the accuracy estimate is discussed. The results obtained are compared with reported equations of state of the hard sphere liquid.     

The temperature dependence of the hard sphere diameter

The temperature dependence of the equivalent hard sphere diameter is analyzed using statistical mechanics. The analysis shows that algebraic equations for the hard sphere diameter which were developed by previous workers are not consistent with the statistical mechanics at high temperature. An algebraic equation which is consistent with the statistical mechanics is developed.     

Transport properties of the rough hard sphere fluid

Results are presented of a systematic study of the transport properties of the rough hard sphere fluid. The rough hard sphere fluid is a simple model consisting of spherical particles that exchange linear and angular momenta, and energy upon collision. This allows a study of the sole effect of particle rotation upon fluid properties. Molecular dynamics simulations have been used to conduct extensive benchmark calculations of self-diffusion, shear and bulk viscosity, and thermal conductivity coefficients. As well, the validity of several kinetic theory equations have been examined at various levels of approximation as a function of density and translational-rotational coupling. In particular, expressions from Enskog theory using different numbers of basis sets in the representation of the distribution function were tested. Generally Enskog theory performs well at low density but deviates at larger densities, as expected. The dependence of these expressions upon translational-rotational coupling was also examined. Interestingly, even at low densities, the agreement with simulation results was sometimes not even qualitatively correct. Compared with smooth hard sphere behaviour, the transport coefficients can change significantly due to translational-rotational coupling and this effect becomes stronger the greater the coupling. Overall, the rough hard sphere fluid provides an excellent model for understanding the effects of translational-rotational coupling upon transport coefficients.     

Phase diagram of the adhesive hard sphere fluid

The phase behavior of the Baxter adhesive hard sphere fluid has been determined using specialized Monte Carlo simulations. We give a detailed account of the techniques used and present data for the fluid-fluid coexistence curve as well as parametrized fits for the supercritical equation of state and the percolation threshold. These properties are compared with the existing results of Percus-Yevick theory for this system.     

On the structure of poly(N-isopropylacrylamide) microgel particles

This investigation presents a study of the internal structure of poly(NIPAM/xBA) microgel particles (NIPAM and BA are N-isopropylacrylamide and N,N'-methylene bisacrylamide, respectively). In this study, x is the wt % of BA used during microgel synthesis. Two values of x were used to prepare the microgels, 1 and 10. The microgel dispersions were investigated using photon correlation spectroscopy (PCS) and small-angle neutron scattering (SANS). These measurements were made as a function of temperature in the range 30-50 degrees C. Scattering maxima were observed for the microgels when the dispersion temperatures were less than their volume phase transition temperatures. The SANS data were fitted using a model which consisted of Porod and Ornstein-Zernike form factors. The analysis showed that the macroscopic hydrodynamic diameter of the microgel particles and the submicroscopic mesh size of the network are linearly related. This is the first study to demonstrate affine swelling for poly(NIPAM/xBA) microgels. Furthermore, the mesh size does not appear to be strongly affected by x. The data suggest that the swollen particles have a mostly homogeneous structure, although evidence for a thin, low segment density shell is presented. The study confirms that poly(NIPAM/xBA) microgel particles have a core-shell structure. The shell has an average thickness of approximately 20 nm for poly(NIPAM/1BA) particles which appears to be independent of temperature over the range studied. The analysis suggests that the particles contained approximately 50 vol % water at 50 degrees C. The molar mass of the poly(NIPAM/1BA) microgel particles was estimated as 6 x 10(9) g mol(-1).     

Microscopic investigations of homogeneous nucleation in charged sphere suspensions

We studied the homogeneous nucleation kinetics of an aqueous suspension of charged colloidal spheres under de-ionized conditions. Samples of equilibrium crystalline structure were shear molten and the metastable melt left to solidify after cessation of shear. At low particle number densities n, corresponding to low metastability of the melt, nucleation was monitored directly via video microscopy. We determined the nucleation rates gamma(t) by counting the number of newly appearing crystals in the observation volume per unit time. Using a suitable discrete adaptation of Avrami's [J. Chem. Phys. 7, 1003 (1939); ibid.8, 212 (1940); ibid.9, 177 (1941)] model for solidification via homogeneous nucleation and subsequent growth, we calculate the remaining free volume VF(t) to obtain the rate densities J(t) = gamma(t)/VF(t). We observe J(t) to rise steeply, display a plateau at a maximum rate density Jmax, and to decrease again. With increased n the plateau duration shrinks while Jmax increases. At low to moderate number densities fully solidified samples were analyzed by microscopy to obtain the grain-size distribution and the average crystallite size angle brackets(L). Under the assumption of stationarity, we obtained the nucleation rate density J(Avr), which increased strongly with increasing n. Interestingly, J(Avr) agrees quantitatively to Jmax and to J(Avr) as obtained previously from scattering data taken on the same sample at large n. Thus, by combination of different methods, reliable nucleation rate densities are now available over roughly one order of magnitude in n and eight orders of magnitude in J.     

Swelling behavior of poly- N-isopropylacrylamide microgel particles in alcoholic solutions

 It has been shown that the swelling of poly-N-isopropyl-acrylamide (poly-NIPAM) microgel particles can be controlled by the addition of alcohols, in addition to the previously observed effect of temperature. The degree of swelling is also controlled by the amount of cross-linker within the microgel particles. At 25 ^°C, poly-NIPAM microgel particles collapse upon the addition of MeOH, EtOH and 2-PrOH to a minimum size and then, reswell again as the alcohol-rich region is approached. This trend was also observed for poly-NIPAM microgel particles dispersed in 2-PrOH/water mixtures upon heating to 50 ^°C. The particles, dispersed in either water or alcohol/water mixtures were found to be stable to flocculation between 25 ^°C and 50 ^°C. Received: 27 February 1997 Accepted: 5 August 1997