Viscoelasticity and Stokes-Einstein relation in repulsive and attractive colloidal glasses

We report a numerical investigation of the viscoelastic behavior in models for steric repulsive and short-ranged attractive colloidal suspensions, along different paths in the attraction strength vs packing fraction plane. More specifically, we study the behavior of the viscosity (and its frequency dependence) on approaching the repulsive glass, the attractive glass, and in the reentrant region where viscosity shows a nonmonotonic behavior on increasing attraction strength. On approaching the glass lines, the increase of the viscosity is consistent with a power-law divergence with the same exponent and critical packing fraction previously obtained for the divergence of the density fluctuations. Based on mode-coupling calculations, we associate the increase of the viscosity with specific contributions from different length scales. We also show that the results are independent of the microscopic dynamics by comparing Newtonian and Brownian simulations for the same model. Finally, we evaluate the Stokes-Einstein relation approaching both glass transitions, finding a clear breakdown which is particularly strong for the case of the attractive glass.     

Rheological Properties of Silica Particle Suspensions in Mineral Oil

The rheological properties of particles suspended in a non‐polar mineral oil have been investigated as a function of volume fraction of particles, particle size, surface properties and shear rate. Three different types of particles were investigated; glass microspheres, monodisperse silica particles and fumed silica. The suspensions showed shear thinning behavior at higher volume fractions, and the viscosity increased with decreasing particle size. The hydrophobic particles display lass shear thinning effects. The relative viscosity of all the suspensions was well fitted to the Krieger and Dougherty model.     

Pressure dependence of viscosity

We reanalyze the pressure dependence of viscosity of liquids of constant composition under isothermal conditions. Based exclusively on very general considerations concerning the relationship between viscosity and "free volume," we show that, at moderate values of pressure, viscosity increases, as a rule, with increasing pressure, provided the liquid is in stable or metastable (undercooled) equilibrium states. However, even if the behavior of the viscosity is governed by free volume effects, deviations from a positive pressure dependence are possible, when the liquid's thermal expansion coefficient is negative. We derive an equation that allows one to quantitatively determine the pressure dependence of viscosity, which requires, in the simplest case, only the knowledge of the temperature dependence of viscosity at constant pressure, the thermal expansion coefficient, and the isothermal compressibility of the liquid. As an example, the negative pressure dependence of water in the range of temperatures 0-4 degrees C and of several silicate liquids, such as albite, jadeite, dacite, basalts, etc., could be explained in such a way. Other glass-forming liquids initially (for moderate pressures) show a positive pressure dependence of viscosity that changes to a negative one when subjected to high (approximately GPa) isostatic pressure. A detailed analysis of water and already mentioned silicate melts at GPa pressures shows that, in addition to free volume effects, other pressure induced structural transformations may have to be accounted for in a variety of cases. By this reason, the theoretical analysis is extended (i) in order to describe the pressure dependence of viscosity for systems that are in frozen-in thermodynamic nonequilibrium states (glasses, i.e., undercooled liquids below the glass transition temperature Tg) and (ii) to systems which undergo, in addition to variations of the free volume, pressure induced changes of other structural parameters. In such cases a decrease of viscosity with increasing pressure may occur, in principle, even if the thermal expansion coefficient is positive. In this way, the present analysis grants a general tool to estimate the pressure dependence of viscosity and supposedly settles the controversy in the current literature.     

Transport coefficients of square-well fluids

We analyze the analytical form of the velocity time correlation function of a hard sphere system obtained by employing generalized Langevin equation for a square-well fluid. The self-diffusion coefficient and shear viscosity have been calculated using this analytical form of velocity tcf for a square-well fluid. The addition of an attractive square-well potential in place of hard sphere leads to a substantial influence on transport coefficients. Unlike harmonic model diffusion coefficient no longer vanishes. A breakdown of the Stokes–Einstein relation is observed at low densities for a square-well fluid.     

Glass sintering with concurrent crystallization

We critically review and discuss the main glass-sintering models: Frenkel, Mackenzie–Shuttleworth, Scherer and the recently developed Clusters model, and focus on the problem of sintering with concurrent crystallization. The Clusters model is tested under various practical conditions. Isothermal tests are carried out on a widely polydispersed alumino-borosilicate (ABS) glass having jagged particles, which is stable against devitrification, and on a soda–lime–silica (SLS) glass with a narrow spherical particle distribution, which crystallizes easily. The algorithm for non-isothermal processes is also tested with two distinct systems: the same ABS glass and a narrow-sized cordierite glass, which is devitrification-prone. In addition to physical parameters such as viscosity, surface tension, particle-size distribution, crystal growth rate and number of nucleation sites, microscopic-particle-packing data are introduced into the model and it is demonstrated that the evolution of both density and pore size distribution can be reasonably predicted. All the results are discussed taking into account the assumptions made in the derivations and other complicating factors, such as irregular particle shape, compositional shifts due to crystallization, temperature gradients and degassing during sintering. Finally, we discuss the physical and processing parameters that determine whether sintering will be favorable over crystallization. We demonstrate that the Clusters model and related algorithm provide a powerful simulation tool to design the isothermal or non-isothermal densification of devitrifying or stable glass compacts with any particle-size distribution, thus minimizing the number of time-consuming laboratory experiments.     

Glass transition and phase state of organic compounds: dependency on molecular properties and implications for secondary organic aerosols in the atmosphere

Recently, it has been proposed that organic aerosol particles in the atmosphere can exist in an amorphous semi-solid or solid (i.e. glassy) state. In this perspective, we analyse and discuss the formation and properties of amorphous semi-solids and glasses from organic liquids. Based on a systematic survey of a wide range of organic compounds, we present estimates for the glass forming properties of atmospheric secondary organic aerosol (SOA). In particular we investigate the dependence of the glass transition temperature T(g) upon various molecular properties such as the compounds' melting temperature, their molar mass, and their atomic oxygen-to-carbon ratios (O:C ratios). Also the effects of mixing different compounds and the effects of hygroscopic water uptake depending on ambient relative humidity are investigated. In addition to the effects of temperature, we suggest that molar mass and water content are much more important than the O:C ratio for characterizing whether an organic aerosol particle is in a liquid, semi-solid, or glassy state. Moreover, we show how the viscosity in liquid, semi-solid and glassy states affect the diffusivity of those molecules constituting the organic matrix as well as that of guest molecules such as water or oxidants, and we discuss the implications for atmospheric multi-phase processes. Finally, we assess the current state of knowledge and the level of scientific understanding, and we propose avenues for future studies to resolve existing uncertainties.     

Radical‐mediated modification of polypropylene: Selective grafting via polyallyl coagents

Selective graft modifications of polypropylene (PP) are demonstrated in which desirable functionality is introduced without the degradation that accompanies conventional radical‐mediated processes. A range of modification strategies is presented, each exploiting triallyl trimellitate (TATM) or its derivatives to counteract the effects of macroradical fragmentation on the molecular weight. Model compound studies, as well as examinations of atactic PP reaction products, show that allylic ester activation occurs predominately by a radical‐addition/hydrogen‐transfer sequence, with a limited propensity for telomerization. The cografting of TATM and maleic anhydride leads to maleated PP of a high melt viscosity, whereas the apparent incompatibility of TATM with vinyltrimethoxysilane requires the use of TATM‐assisted thiol–ene addition and/or diallyl silane grafting to produce moisture‐curable PP derivatives. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4882–4893, 2005     

Use of a Cross-Sectional Model for Determining Rheology in Settling Slurries: Effect of Solvent,Particle Size,and Density

Transport models for partially settling slurries need accurate rheology correlations, particularly describing viscosity relationship to the particle concentration. A method is needed to untangle the effects of settling on apparent viscosity and the real effects of particle concentration on viscosity during rheology measurements. Our approach is based on model inversion of a cross-section model for the vertical particle concentration gradient and the local rheologies in the gap of a Couette type rheometer, established by a balance between gravitational particle settling and shear induced migration of the particles. The Krieger-Dougherty rheology correlation with adjustable parameters has been applied, where the parameters are determined by minimizing the difference between the measured viscosity data and those calculated by the model. Fairly mono-disperse silver coated polystyrene particles with two sizes and densities were used in both the aqueous and oil phase. In the raw data an apparent shear thinning tendency is observed. Through the model inversion process, this is accounted for by the shear dependent settling and the steep increase of viscosity with particle concentration. Maximum packing fraction was obtained through settling experiments. The difference between this value and the maximum packing fraction from the model inversion was less than 3% for oil-based suspensions. The larger difference was found for smaller particle size in water which is attributed to the larger effect of interparticle forces.     

On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glasses

We reformulate the interpretation of the mean-field glass transition scenario for finite dimensional systems, proposed by Kirkpatrick, Thirumalai, and Wolynes (KTW). This allows us to establish clearly a temperature dependent length xi( *) above which the mean-field glass transition picture has to be modified. We argue in favor of the mosaic state introduced by KTW, which leads to the Adam-Gibbs relation between the viscosity and configurational entropy of glass forming liquids. Our argument is a mixture of thermodynamics and kinetics, partly inspired by the random energy model: small clusters of particles are thermodynamically frozen in low energy states, whereas large clusters are kinetically frozen by large activation energies. The relevant relaxation time is that of the smallest "liquid" clusters. Some physical consequences are discussed.     

Determination of the pressure coefficient and pressure effects in capillary flow

General expressions for determining the pressure coefficient and axial distribution of the viscosity and pressure in capillary flow are derived for Newtonian and shear-thinning fluids. The pressure-dependent viscosity model is obtained from the WLF equation as derived from Doolittle's free volume theory. The model has also been derived from Eyring's hole theory for viscosity. Poiseuille's equation is modified to correct for the pressure effect on viscosity. A Newtonian, low-molecular-weight polystyrene and a shear-thinning, high-molecular-weight polystyrene were tested in an Instron capillary rheometer. The axial velocity distribution was found to be negligibly affected by pressure whereas the viscosity was shown to increase markedly with a decrease in volume. The resulting pressure effects on the viscosity of both samples were analyzed by using the derived expressions.     

Self-diffusion coefficients and shear viscosity of inverse power fluids: from hard- to soft-spheres

Molecular dynamics computer simulation has been used to compute the self-diffusion coefficient, D, and shear viscosity, eta(s), of soft-sphere fluids, in which the particles interact through the soft-sphere or inverse power pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The simulations were carried out on monodisperse systems for a range of n values from the hard-sphere (n --> infinity) limit down to n = 4, and up to densities in excess of the fluid-solid co-existence value. A new analytical procedure is proposed which reproduces the transport coefficients at high densities, and can be used to extrapolate the data to densities higher than accurately accessible by simulation or experiment, and tending to the glass transition. This formula, DX(c-1) proportional, variant A/X + B, where c is an adjustable parameter, and X is either the packing fraction or the pressure, is a development of one proposed by Dymond. In the expression, -A/B is the value of X at the ideal glass transition (i.e., where D and eta(s)(-1) --> 0). Estimated values are presented for the packing fraction and the pressure at the glass transition for n values between the hard and soft particle limits. The above expression is also shown to reproduce the high density viscosity data of supercritical argon, krypton and nitrogen. Fits to the soft-sphere simulation transport coefficients close to solid-fluid co-existence are also made using the analytic form, ln(D) = alpha(X)X, and n-dependence of the alpha(X) is presented (X is either the packing fraction or the pressure).     

Effect of soluble polymer binder on particle distribution in a drying particulate coating

Soluble polymer is frequently added to inorganic particle suspensions to provide mechanical strength and adhesiveness to particulate coatings. To engineer coating microstructure, it is essential to understand how drying conditions and dispersion composition influence particle and polymer distribution in a drying coating. Here, a 1D model revealing the transient concentration profiles of particles and soluble polymer in a drying suspension is proposed. Sedimentation, evaporation and diffusion govern particle movement with the presence of soluble polymer influencing the evaporation rate and solution viscosity. Results are summarized in drying regime maps that predict particle accumulation at the free surface or near the substrate as conditions vary. Calculations and experiments based on a model system of poly(vinyl alcohol) (PVA), silica particles and water reveal that the addition of PVA slows the sedimentation and diffusion of the particles during drying such that accumulation of particles at the free surface is more likely.     

Simple statistical thermodynamic model of the heteroaggregation and gelation of dispersions and emulsions

The heteroaggregation behaviour of mixtures of equal-sized particles (type A+type B) exhibiting short-ranged attractive interactions is investigated using the sticky hard-sphere model. The average cluster size is calculated as a function of the total particle volume fraction, the binary mixture composition, and the A-B stickiness interaction parameter τ(AB)(-1). We show that a value of τ(AB)(-1)=10(2), equivalent to an attractive well depth of ～5kT in a realistic continuous pair potential, leads to a state of heteroaggregation just below the gelation threshold of the equimolar mixture of volume fraction 0.1. We discuss the conditions under which the assumptions of this statistical thermodynamic model are satisfied experimentally, with particular reference to recent data on the heteroaggregation behaviour of protein-stabilized emulsions and latex particle dispersions.     

Effect of depletion interactions on transport of colloidal particles in porous media

The influence of depletion interactions on the transport of micrometer-sized, negatively charged polystyrene latex particles through porous media was studied by analysis of particle breakthrough curves as a response to short-pulse particle injections to the inlet of a packed column of glass beads. The column outlet latex particle concentration profiles and the total amount of particles exiting the column were determined as a function of the concentration of small, silica nanoparticles in the solution and the bulk flow rate. Because of similar charges, the silica particles do not adsorb to either the latex particles or glass beads and thus induce an attractive depletion force between the latex particles and glass bead collectors. The total column outlet latex particle amount was calculated by integrating the measured breakthrough concentration curve and compared to the known amount of injected particles at the column inlet. It was found that the particle recovery was a decreasing function of the silica nanoparticle concentration and the carrier fluid residence time, and an increasing function of the velocity in the bed. In addition, removing the silica nanoparticles from the flowing solution caused a second outlet peak to appear, suggesting that some of the polystyrene particles were captured in secondary energy wells. The experimental data were interpreted using the predicted potential energy profile between a single particle and a glass bead, which was assumed to consist of electrostatic, van der Waals, and depletion components. The results indicate that secondary energy wells significantly affect particle transport behavior through porous media.     

Rheology of a reversible supramolecular polymer studied by comparison of the effects of temperature and chain stoppers

The rheology of a reversible supramolecular polymer is studied by comparing the effects of an increase in temperature and the addition of chain stoppers. The dependence of the zero-shear viscosity and the terminal relaxation time on temperature is exponential, and the activation energy for viscous flow can be calculated. Above a critical stopper fraction, power laws describe the stopper dependence of the viscosity and relaxation time. A simple model for the effect of the addition of chain stoppers on the average degree of polymerization adequately describes the results. A comparison of flow curves at several temperatures and stopper fractions reveals considerable differences between solutions with the same zero-shear viscosity. These are mainly associated with differences in the terminal relaxation time. A mechanism of shear-induced alignment and subsequent elongation of chains is proposed, with which the experimental results are consistent.     

Influence of interparticle interaction effects on the rheological properties of low density polyethylene filled with glass beads

The rheological properties of Low-density polyethylene (LDPE) compounds with different fractions of glass beads have been investigated by means of high pressure capillary rheometry. The purpose of this study is to find a functional approach for describing the flow behaviour of suspensions as a function of the volumetric filler content and the applied shear stress or shear rate, respectively. The flow behaviour of suspensions is influenced by interaction effects, which are dependent on the filler particle, its volume content and particle size. While small glass beads exhibit pronounced interparticle interaction effects even at low volumetric filler concentrations, large glass beads show a plateau of negligibly interactions up to approx. 20% volumetric filler content. With introducing a generalized interaction function the flow behaviour of the tested suspensions could be described with reasonable accuracy in consideration of the transition from negligible to pronounced interactions.     

PVT and oscillatory tests to analyze pressure effects on polypropylene/Rodrun LC3000 blends: Determination of the pressure dependency of the viscosity

A combined analysis of Pressure-Volume-Temperature (PVT), Dynamic Mechanical Thermal Analysis (DMTA) and oscillatory flow measurements for blends of a polypropylene (PP) with a commercial liquid crystalline polymer (Rodrun LC3000) is presented. This analysis allows the determination of the pressure-viscosity coefficient b = ∂lnη₀/∂P. This coefficient depends on the Rodrun LC3000 content, increasing with it and is of the same order of magnitude as values reported for several commercial polymers showing a similar dependence of the viscosity on pressure. The analysis of the pressure dependence of Tg (related to b) leads to the conclusion that the number of segments involved in the glass transition of PP increases with the Rodrun LC3000 content, thus demonstrating that the polymers are not totally immiscible. As far as the authors know, this is the first time that the dependence of the viscosity on the pressure has been reported for thermoplastic/liquid crystalline polymer blends.     

Transport Coefficients of Two-temperature Lithium Plasma for Space Propulsion Applications

Lithium has been proposed as an attractive metal propellant for advanced electric propulsion. In our current work, transport coefficients including the viscosity, thermal conductivity, and electrical conductivity of lithium plasma under both the equilibrium and non-equilibrium conditions are calculated based on a two-temperature model. The collision integrals used in calculating the transport coefficients are significantly more accurate than values used in previous theoretical studies, resulting in more reliable values of the transport coefficients. Results are computed for different degrees of thermal non-equilibrium, i.e. the ratio of electron to heavy particle temperatures, from 1 to 15, with the electron temperature ranging from 300 to 60,000 K in a wide pressure range from 0.0001 to 100 atm. We compare our calculated results with existing published results and discrepancies are found and explained.     

Particles driven up the wall by bursting bubbles

The phenomenon of particles being "driven up the wall" of a vessel by bursting bubbles at an air-water interface covered with hydrophobic nanoparticles is reported. Experiments have shown that the bubbles bursting at the interface give rise to the local surface pressure gradient, which pushes the particles to climb and coat the walls of the vessel. A theoretical model based on the lubrication approach to estimate the height and speed at which the particle layers climb up the walls yields values that are in fair agreement with the experimental measurements. The effects of the liquid viscosity, electrolyte strength, and particle wettability are also examined.