Polydisperse Colloidal Suspensions Research Articles

Sedimentation path theory for mass-polydisperse colloidal systems.

Both polydispersity and the presence of a gravitational field are inherent to essentially any colloidal experiment. While several theoretical works have focused on the effect of polydispersity on the bulk phase behavior of a colloidal system, little is known about the effect of a gravitational field on a polydisperse colloidal suspension. We extend here the sedimentation path theory to study sedimentation-diffusion-equilibrium of a mass-polydisperse colloidal system: the particles possess different buoyant masses but they are otherwise identical. The model helps to understand the interplay between gravity and polydispersity on sedimentation experiments. Since the theory can be applied to any parent distribution of buoyant masses, it can also be used to study the sedimentation of monodisperse colloidal systems. We find that mass-polydispersity has a strong influence in colloidal systems near density matching for which the bare density of the colloidal particles equals the solvent density. To illustrate the theory, we study crystallization in sedimentation-diffusion-equilibrium of a suspension of mass-polydisperse hard spheres.

Orientation dynamics of anisotropic and polydisperse colloidal suspensions

Small-angle light scattering (SALS) is employed to determine in situ microstructural changes of polydisperse colloidal suspensions under capillary flow. Titanium dioxide (rod-like) bundles and kaolinite nanoclay (platelet) flake-like stacks of particles are suspended in a Newtonian fluid to explore the effects of shape anisotropy. Subjecting the systems to a startup test in a flow cell in Stokes's regime, the evolution of the anisotropy factor (AF), and the average orientation angle (χ) of particles vs strain is probed at different averaged Péclet (Pe¯) numbers. Dilute and semi-dilute concentration regimes are explored in a capillary flow. Moving in the vorticity direction, we show significant changes in χ due to the gradient in shear rate in the capillary flow, while no cross-sectional flow migration was exhibited. In these polydisperse colloidal suspensions, two characteristic stages are observed: initial particle alignment and subsequent orientational demixing. Probing the velocity–vorticity (xy) plane, an initial particle alignment in the flow direction at high Pe¯ (> 1) occurs, is demonstrated by an elliptical SALS pattern, and then, an increase in AF is observed due to particles' phase mixing. This behavior is then followed by a breakdown in structure and loss of particle alignment due to orientational demixing. The evolution of the average orientation angle of particles in the xy plane can be clearly observed through these two stages by the help of high-resolution SALS contours. These experimental findings provide novel insights into the flow–microstructure relationship of polydisperse colloidal suspensions for the optimization of many industrial processing schemes.

Model equations of light scattering properties and a characteristic time of light propagation for polydisperse colloidal suspensions at different volume fractions.

We developed model equations of light scattering properties and a characteristic time of light propagation for polydisperse colloidal suspensions at different volume fractions. By the model equations, we examined numerical results using the first-order (dependent) scattering theory (FST) and radiative transfer theory in 600-980 nm wavelength. The model equations efficiently treat the interference of electric fields scattered from colloidal particles by a single effective coefficient, providing fast computation. Meanwhile, the FST provides accurate but complicated treatment. We found the interference effects on the scattering properties and characteristic time depend linearly on wavelength. Dimensionless analysis showed a simple mechanism of the interference effects, independently of wavelength and source-detector distance.

Photon transport model for dense polydisperse colloidal suspensions using the radiative transfer equation combined with the dependent scattering theory.

In near-infrared imaging and spectroscopy, high-fidelity modeling of photon transport for dense polydisperse colloidal suspensions is crucial. We developed photon transport models using the radiative transfer equation (RTE) with the dependent scattering theory (DST) at volume fractions up to 20%. The polydispersity and interference effects strongly influence results of the scattering properties and the RTE in cases of small mean diameter and large variance of the particle size distribution. We compared the RTE-results for the Henyey-Greenstein (conventional) function with those for the phase function using the DST. The RTE-results differ between both functions at low volume fractions for forward scattering media, suggesting the limitation of the conventional function.

Size-Selective Optical Printing of Silicon Nanoparticles through Their Dipolar Magnetic Resonance

Silicon nanoparticles possess unique size-dependent optical properties due to their strong electric and magnetic resonances in the visible range. However, their widespread application has been limited, in comparison with other (e.g., metallic) nanoparticles, because their preparation on monodisperse colloids remains challenging. Exploiting the unique properties of Si nanoparticles in nano- and microdevices calls for methods able to sort and organize them from a colloidal suspension onto specific positions of solid substrates with nanometric precision. We demonstrate that surfactant-free silicon nanoparticles of a predefined and narrow (σ < 10 nm) size range can be selectively immobilized on a substrate by optical printing from a polydisperse colloidal suspension. The size selectivity is based on differential optical forces that can be applied on nanoparticles of different sizes by tuning the light wavelength to the size-dependent magnetic dipolar resonance of the nanoparticles.

Compositional relaxation on the approach to the glass transition in a model trehalose solution

Molecular dynamics simulation was used to study the temperature dependence of the mutual diffusion coefficient D_{m} and the intermediate scattering function of equilibrium and metastable aqueous solutions of the cryoprotectant molecule trehalose at very low (2.2 and 9wt.%) and very high (80 and 95wt.%) concentrations. The simulations were conducted over a range of temperatures approaching the glass transition temperature T_{g} for each concentration. Similar to a recent observation made on a glass-forming model polydisperse colloidal suspension [Hannam etal., Phys. Rev. E 96, 022609 (2017)2470-004510.1103/PhysRevE.96.022609], we confirmed by a set of independent computations that D_{m} is responsible for the long-time decay of the intermediate scattering function. We observed that D_{m} decreased on the approach to the glass transition temperature, resulting in an extremely slow long-time decay in the intermediate scattering function that culminated in the arrest of compositional fluctuations and a plateau in the intermediate scattering function at T_{g}. In both cases, crystallization requires a change in the composition of the solution, which is a process controlled by D_{m}. This transport coefficient can either increase or decrease as solidification is approached, because it depends on a product of thermodynamic and mobility factors. Our observations show that in both cases, for the glass-forming liquids, it is observed to decrease, while for a previously studied monodisperse colloidal suspension which crystallizes easily, it increases. The similarity in the behavior of these two very different glass-forming systems (the polydisperse colloidal suspension and the sugar solution) shows the importance of the mutual diffusion coefficient to our understanding of vitrification and suggests a possible distinction between between glass-forming and crystallizing solutions.

Dynamics of the floating nematic phase formation in platelet suspension with thickness polydispersity by sedimentation.

An inverted phase coexistence, where an ordered phase appears on top of a disordered phase, has been observed in polydisperse colloidal suspensions. Herein, we studied the dynamics of this phenomenon in a suspension of a mixture of two types of platelets, namely, thick and thin. We show that the thick platelets preferentially sediment first excluding the thin platelets, and create a region enriched with thin platelets at some place above the bottom, which eventually gives the inverted configuration. We show that such interplay between the sedimentation and the isotropic-nematic phase transition can cause a rich and complex sedimentation dynamic. Depending on the initial concentration and the gravity strength, the interface between the isotropic phase and the nematic phase can move up or down during the sedimentation, and a variety of final equilibrium structures can appear.

Stratification and Size Segregation of Ternary and Polydisperse Colloidal Suspensions during Drying.

We investigate the drying process of three-component and polydisperse colloidal suspensions using Brownian dynamics simulations. We have previously reported (Phys. Rev. Lett. 2016, 116, 118301) on the drying of binary mixtures. For binary mixtures, we found that a gradient of colloidal osmotic pressure develops during drying and that this leads to the final film being stratified with a layer of smaller particles on top of a layer of larger particles. Here, we find that stratification by size is very general and also occurs in ternary and polydisperse mixtures. We name the segregation effect colloidal diffusiophoresis. In particular, we show that by changing the composition of a ternary mixture, different stratification morphologies can be achieved and hence the film properties can be tuned. In polydisperse spheres, colloidal diffusiophoresis leads to enrichment in the large particles at the bottom part of the film, whereas the top part is enriched with smaller particles. This segregation means that in the final film, the particle size distribution depends on height. Thus, the properties of the film will then depend on height. We propose a model that predicts a power-law dependence of the phoretic velocity on particle size. Results from the model and simulation show a good agreement.

Dynamics of highly polydisperse colloidal suspensions as a model system for bacterial cytoplasm.

There are various kinds of macromolecules in bacterial cell cytoplasm. The size polydispersity of the macromolecules is so significant that the crystallization and the phase separation could be suppressed, thus stabilizing the liquid state of bacterial cytoplasm. On the other hand, recent experiments suggested that the macromolecules in bacterial cytoplasm should exhibit glassy dynamics, which should be also affected significantly by the size polydispersity of the macromolecules. In this work, we investigate the anomalous and slow dynamics of highly polydisperse colloidal suspensions, of which size distribution is chosen to mimic Escherichia coli cytoplasm. We find from our Langevin dynamics simulations that the diffusion coefficient (D_{tot}) and the displacement distribution functions (P(r,t)) averaged over all colloids of different sizes do not show anomalous and glassy dynamic behaviors until the system volume fraction ϕ is increased up to 0.82. This indicates that the intrinsic polydispersity of bacterial cytoplasm should suppress the glass transition and help maintain the liquid state of the cytoplasm. On the other hand, colloids of each kind show totally different dynamic behaviors depending on their size. The dynamics of colloids of different size becomes non-Gaussian at a different range of ϕ, which suggests that a multistep glass transition should occur. The largest colloids undergo the glass transition at ϕ=0.65, while the glass transition does not occur for smaller colloids in our simulations even at the highest value of ϕ. We also investigate the distribution (P(θ,t)) of the relative angles of displacement for macromolecules and find that macromolecules undergo directionally correlated motions in a sufficiently dense system.

Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions

In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics (SEASD), a novel computational method for dynamic simulations of polydisperse colloidal suspensions with full hydrodynamic interactions. SEASD is based on the framework of Stokesian Dynamics (SD) with extension to compressible solvents, and uses the Spectral Ewald (SE) method [Lindbo and Tornberg (2010) [29]] for the wave-space mobility computation. To meet the performance requirement of dynamic simulations, we use Graphic Processing Units (GPU) to evaluate the suspension mobility, and achieve an order of magnitude speedup compared to a CPU implementation. For further speedup, we develop a novel far-field block-diagonal preconditioner to reduce the far-field evaluations in the iterative solver, and SEASD-nf, a polydisperse extension of the mean-field Brownian approximation of Banchio and Brady (2003) [39]. We extensively discuss implementation and parameter selection strategies in SEASD, and demonstrate the spectral accuracy in the mobility evaluation and the overall O(Nlog⁡N) computation scaling. We present three computational examples to further validate SEASD and SEASD-nf in monodisperse and bidisperse suspensions: the short-time transport properties, the equilibrium osmotic pressure and viscoelastic moduli, and the steady shear Brownian rheology. Our validation results show that the agreement between SEASD and SEASD-nf is satisfactory over a wide range of parameters, and also provide significant insight into the dynamics of polydisperse colloidal suspensions.

Size is an essential parameter in governing the UVB-protective efficacy of silver nanoparticles in human keratinocytes.

BackgroundUltraviolet (UV) radiation from sun, particularly its UVB component (290–320 nm), is considered the major etiological cause of skin cancer that impacts over 2 million lives in the United States alone. Recently, we reported that polydisperse colloidal suspension of silver nanoparticles (AgNPs) protected the human keratinocytes (HaCaT) against UVB-induced damage, thus indicating their potential for prevention of skin carcinogenesis. Here we sought out to investigate if size controlled the chemopreventive efficacy of AgNPs against UVB-induced DNA damage and apoptosis.MethodsPercent cell viability was examined by WST-1 assay after treating the cells with various doses (1–10 μg/mL) of AgNPs of different sizes (10, 20, 40, 60 and 100 nm) for 12 and 24 h. For protection studies, cells were treated with AgNPs of different sizes at a uniform concentration of 1 μg/mL. After 3 h, cells were irradiated with UVB (40 mJ/cm2) and dot-blot analysis was performed to detect cyclobutane pyrimidine dimers (CPDs) as an indication of DNA damage. Apoptosis was analyzed by flow cytometry after staining the cells with 7-Amino-Actinomycin (7-AAD) and PE Annexin V. Immunoblot analysis was accomplished by processing the cells for protein extraction and Western blotting using specific antibodies against various proteins.ResultsThe data show that the pretreatment of HaCaT cells with AgNPs in the size range of 10–40 nm were effective in protecting the skin cells from UVB radiation-induced DNA damage as validated by reduced amounts of CPDs, whereas no protection was observed with AgNPs of larger sizes (60 and 100 nm). Similarly, only smaller size AgNPs (10–40 nm) were effective in protecting the skin cells from UV radiation-induced apoptosis. At the molecular level, UVB –irradiation of HaCaT cells led to marked increase in expression of pro-apoptotic protein (Bax) and decrease in anti-apoptotic proteins (Bcl-2 and Bcl-xL), while it remained largely unaffected in skin cells pretreated with smaller size AgNPs (10–40 nm).ConclusionsAltogether, these findings suggest that size is a critical determinant of the UVB-protective efficacy of AgNPs in human keratinocytes.

A parallel implementation of the Stokesian Dynamics method applied to the simulation of colloidal suspensions

We present a strategy for the numerical simulation of polydisperse colloidal suspensions on supercomputers using distributed memory. In order to simulate large colloidal systems we have parallelized the Stokesian Dynamics method and combined it with DLVO theory. Through an efficient parallelization using the message passing system MPI we are able to reduce the computational costs of the problem from O(N2) to O(Pnp,max2), where N is the number of particles in the system, P the number of used processes and np,max=⌈NP⌉, respectively. This allows the simulation of large colloidal systems, as the computational time now not only depends on the number of particles, but also on the number of cores, through which the CPU time can be reduced dramatically.

Origins of Microstructural Transformations in Charged Vesicle Suspensions: The Crowding Hypothesis

It is observed that charged unilamellar vesicles in a suspension can spontaneously deflate and subsequently transition to form bilamellar vesicles, even in the absence of externally applied triggers such as salt or temperature gradients. We provide strong evidence that the driving force for this deflation-induced transition is the repulsive electrostatic pressure between charged vesicles in concentrated suspensions, above a critical effective volume fraction. We use volume fraction measurements and cryogenic transmission electron microscopy imaging to quantitatively follow both the macroscopic and microstructural time-evolution of cationic diC18:1 DEEDMAC vesicle suspensions at different surfactant and salt concentrations. A simple model is developed to estimate the extent of deflation of unilamellar vesicles caused by electrostatic interactions with neighboring vesicles. It is determined that when the effective volume fraction of the suspension exceeds a critical value, charged vesicles in a suspension can experience "crowding" due to overlap of their electrical double layers, which can result in deflation and subsequent microstructural transformations to reduce the effective volume fraction of the suspension. Ordinarily in polydisperse colloidal suspensions, particles interacting via a repulsive potential transform into a glassy state above a critical volume fraction. The behavior of charged vesicle suspensions reported in this paper thus represents a new mechanism for the relaxation of repulsive interactions in crowded situations.

A novel particle tracking method with individual particle size measurement and its application to ordering in glassy hard sphere colloids

Particle tracking is a key to single-particle-level confocal microscopy observation of colloidal suspensions, emulsions, and granular matter. The conventional tracking method has not been able to provide accurate information on the size of individual particle. Here we propose a novel method to localise spherical particles of arbitrary relative sizes from either 2D or 3D (confocal) images either in dilute or crowded environment. Moreover this method allows us to estimate the size of each particle reliably. We use this method to analyse local bond orientational ordering in a supercooled polydisperse colloidal suspension as well as the heterogeneous crystallisation induced by a substrate. For the former, we reveal non-trivial couplings of crystal-like bond orientational order and local icosahedral order with the spatial distribution of particle sizes: Crystal-like order tends to form in regions where very small particles are depleted and the slightly smaller size of the central particle stabilizes icosahedral order. For the latter, on the other hand, we found that very small particles are expelled from crystals and accumulated on the growth front of crystals. We emphasize that such information has not been accessible by conventional tracking methods.

An approach for the critical coagulation concentration estimation of polydisperse colloidal suspensions of soil and humus

The critical coagulation concentration (CCC) is considered as one of the most important parameters to evaluate the particles aggregation and sedimentation behaviors in the environment. Even though there are a few methods for its measurement, each method has its limitations especially as those methods to be applied to polydisperse systems like soil. Thus, the purpose of this research is to establish a new and more reliable method for its determination. Two types of polydisperse colloidal materials were adopted: soil and humus in the experimental studies. The dynamic light scattering technique was employed to determine the effective hydrodynamic diameter of the particles or aggregates changing with time under different pH and electrolyte concentrations of CaCl2 or KCl. In addition, the fractal dimension of aggregates was also detected with the static light scattering technique. A new aggregation rate total average aggregation rate (TAA rate) was defined firstly. We found the defined TAA rate increased linearly with the increase of electrolyte concentration at electrolyte concentrations lower than the CCC value, and the TAA rate stayed approximately constant at electrolyte concentrations higher than the CCC value; an intersection point of the two straight lines therefore could be observed, and the electrolyte concentration at the intersection point will theoretically be the CCC value. The experimental results for the two materials under different pH conditions indeed meet those theoretical predictions, which imply that the CCC value can be determined through the measurement of the TAA rate under different electrolyte concentrations. The comparison of the CCC values obtained between our new method and the widely applied stability ratio method showed that the new method was much better than the stability ratio method for the two polydisperse materials. In addition, the static light scattering measurements also showed that the variations of the fractal dimensions of the aggregates with electrolyte concentrations could be well explained by the CCC values obtained by the new method, which once again verified the applicability of the new method. A new theory and a corresponding new method for the CCC estimation, which can be applied to polydisperse colloidal suspensions, were developed, and the new method has been demonstrated to be much better than the widely applied method for polydisperse materials in environment.

Stochastic description of the light scattered by a polydisperse colloidal suspension: Simulation and experiment

In this work, the stochastic properties of the detected signal in dynamic light scattering experiments are examined in light of Doob's theorem. For Markovian observations of the Brownian particle position, we prove from this theorem that the electric field scattered by a polydisperse suspension can be accounted for by a linear combination of Ornstein-Uhlenbeck processes. A new algorithm for generating the fluctuating field scattered by a polydisperse system is proposed from this alternative formalism. The statistics of our synthetic data is compared satisfactorily with that resulting from the experimental signal scattered by a binary suspension of polystyrene microspheres.

Effective interactions in polydisperse colloidal suspensions investigated using Ornstein–Zernike integral equations

We present a mean of calculating the effective interactions in polydisperse colloidal suspension from liquid state integral equation theory. The method is based on Lado’s expansion of correlation functions in a suitable set of orthogonal polynomials. The outlined approach is subsequently used to investigate the effects of polydispersity on the effective potentials for model systems with attractive and repulsive bare interactions. The dominant effect of polydispersity of the smaller species is to weaken the effective potentials between big colloidal particles. This can be exploited as another way of tuning the interactions in colloidal suspensions to match the desired properties.

Magnetooptical phenomena in disperse systems in uniform linearly oriented magnetic fields

The theory of magnetooptical phenomena in disperse systems subjected to constant magnetic fields is outlined. A magnetooptical method is proposed for determining the magnetic characteristics and size distribution of particles in polydisperse colloidal solutions and suspensions. The magnetooptical properties of aqueous colloids of anisaldazine and acetoxybenzalazine are studied and the size distribution functions of dispersed particles are determined.

Phase behaviour of polydisperse sticky hard spheres: analytical solutions and perturbation theory

We discuss the phase coexistence of polydisperse colloidal suspensions in the presence of adhesion forces. The combined effect of polydispersity and Baxter's sticky-hard-sphere (SHS) potential, describing hard spheres interacting via strong and very short-ranged attractive forces, give rise, within the Percus–Yevick (PY) approximation, to a system of coupled quadratic equations which, in general, cannot be solved either analytically or numerically. We review and compare two recent alternative proposals that have attempted to by-pass this difficulty. In the first, truncating the density expansion of the direct correlation functions, we have considered approximations simpler than the PY one. These Cn approximations can be systematically improved. We have been able to provide a complete analytical description of polydisperse SHS fluids using the simplest two orders C 0 and C 1. Such a simplification comes at the price of a lower accuracy in the phase diagram, but has the advantage of providing an analytical description of various new phenomena associated with the onset of polydispersity in phase equilibria (e.g., fractionation). The second approach is based on a perturbative expansion of the polydisperse PY solution around its monodisperse counterpart. This approach provides a sound approximation to the real phase behaviour, at the cost of considering only weak polydispersity. Although a final determination of the soundness of the latter method would require numerical simulations for the polydisperse Baxter model, we argue that this approach is expected to correctly take into account the effects of polydispersity, at least qualitatively.

Van Hove function of colloidal mixtures: Exact results

A general theory for the collective diffusion of a polydisperse colloidal suspension is developed in the framework of the generalized Langevin equation formalism of time-dependent fluctuations. The time-evolution of the intermediate scattering functions, F α β ( k , t ) , is derived as a contraction of the description involving the instantaneous particle number concentration, the particle current, and the kinetic and the configurational components of the stress tensor of the Brownian species as state variables. Analogous results also follow for the self-intermediate scattering functions, F α s ( k , t ) . We show that neglecting the non-markovian part of the configurational stress tensors memory, one obtains the multicomponent generalization of the single exponential memory approximation (SEXP), based on sum rules derived from the Smoluchowski equation, for both, F α s ( k , t ) and F α β ( k , t ) . As an illustrative example, the SEXP is applied to a simple model binary mixture of colloidal particles interacting through repulsive Yukawa pair potentials. The results are compared with Brownian dynamics simulations.