Spinodal decomposition in a model colloid-polymer mixture in microgravity

Mechanical Slowing Down of Network-Forming Phase Separation of Polymer Solutions

Phase separation is a fundamental phenomenon leading to spatially heterogeneous material distribution, which is critical in nature, biology, material science, and industry. In ordinary phase separation, the minority phase always forms droplets. Contrary to this common belief, even the minority phase can form a network structure in viscoelastic phase separation (VPS). VPS can occur in any mixture with significant mobility differences between their components and is highly relevant to soft matter and biomatter. In contrast to classical phase separation, experiments have shown that VPS in polymer solutions lacks self-similar coarsening, resulting in the absence of a domain-coarsening scaling law. However, the underlying microscopic mechanism of this behavior remains unknown. To this end, we perform fluid particle dynamics simulations of bead-spring polymers, incorporating many-body hydrodynamic interactions between polymers through a solvent. We discover that polymers in the dense-network-forming phase are stretched and store elastic energy when the deformation speed exceeds the polymer dynamics. This self-generated viscoelastic stress mechanically interferes with phase separation and slows its dynamics, disrupting self-similar growth. We also highlight the essential role of many-body hydrodynamic interactions in VPS. The implications of our findings may hold importance in areas such as biological phase separation, porous material formation, and other fields where network structures play a pivotal role.

Hydrodynamic stability criterion for colloidal gelation under gravity

Attractive colloids diffuse and aggregate to form gels, solidlike particle networks suspended in a fluid. Gravity is known to strongly impact the stability of gels once they are formed. However, its effect on the process of gel formation has seldom been studied. Here, we simulate the effect of gravity on gelation using both Brownian dynamics and a lattice-Boltzmann algorithm that accounts for hydrodynamic interactions. We work in a confined geometry to capture macroscopic, buoyancy-induced flows driven by the density mismatch between fluid and colloids. These flows give rise to a stability criterion for network formation, based on an effective accelerated sedimentation of nascent clusters at low volume fractions that disrupts gelation. Above a critical volume fraction, mechanical strength in the forming gel network dominates the dynamics: the interface between the colloid-rich and colloid-poor region moves downward at an ever-decreasing rate. Finally, we analyze the asymptotic state, the colloidal gel-like sediment, which we find not to be appreciably impacted by the vigorous flows that can occur during the settling of the colloids. Our findings represent the first steps toward understanding how flow during formation affects the life span of colloidal gels.

Phonon transport properties of particulate physical gels

Particulate physical gels are sparse, low-density amorphous materials in which clusters of glasses are connected to form a heterogeneous network structure. This structure is characterized by two length scales, ξ s and ξ G: ξ s measures the length of heterogeneities in the network structure and ξ G is the size of glassy clusters. Accordingly, the vibrational states (eigenmodes) of such a material also exhibit a multiscale nature with two characteristic frequencies, [Formula: see text] and ω G, which are associated with ξ s and ξ G, respectively: (i) phonon-like vibrations in the homogeneous medium at [Formula: see text], (ii) phonon-like vibrations in the heterogeneous medium at [Formula: see text], and (iii) disordered vibrations in the glassy clusters at ω > ω G. Here, we demonstrate that the multiscale characteristics seen in the static structures and vibrational states also extend to the phonon transport properties. Phonon transport exhibits two distinct crossovers at frequencies ω* and ω G (or at wavenumbers of [Formula: see text] and [Formula: see text]). In particular, both transverse and longitudinal phonons cross over between Rayleigh scattering at [Formula: see text] and diffusive damping at [Formula: see text]. Remarkably, the Ioffe–Regel limit is located at the very low frequency of ω*. Thus, phonon transport is localized above ω*, even where phonon-like vibrational states persist. This markedly strong scattering behavior is caused by the sparse, porous structure of the gel.

Structure formation and coarsening kinetics of phase-separated spin-coated ethylcellulose/hydroxypropylcellulose films

Porous phase-separated ethylcellulose/hydroxypropylcellulose (EC/HPC) films are used to control drug transport from pharmaceutical pellets. The drug transport rate is determined by the structure of the porous films that are formed as water-soluble HPC leaches out. However, a detailed understanding of the evolution of the phase-separated structure in the films is lacking. In this work, we have investigated EC/HPC films produced by spin-coating, mimicking the industrial fluidized bed spraying. The aim was to investigate film structure evolution and coarsening kinetics during solvent evaporation. The structure evolution was characterized using confocal laser scanning microscopy and image analysis. The effect of the EC:HPC ratio (15 to 85 wt% HPC) on the structure evolution was determined. Bicontinuous structures were found for 30 to 40 wt% HPC. The growth of the characteristic length scale followed a power law, L(t) ∼ t⁽ⁿ⁾, with n ∼ 1 for bicontinuous structures, and n ∼ 0.45-0.75 for discontinuous structures. The characteristic length scale after kinetic trapping ranged between 3.0 and 6.0 μm for bicontinuous and between 0.6 and 1.6 μm for discontinuous structures. Two main coarsening mechanisms could be identified: interfacial tension-driven hydrodynamic growth for bicontinuous structures and diffusion-driven coalescence for discontinuous structures. The 2D in-plane interface curvature analysis showed that the mean curvature decreased as a function of time for bicontinuous structures, confirming that interfacial tension is driving the growth. The findings of this work provide a good understanding of the mechanisms responsible for morphology development and open for further tailoring of thin EC/HPC film structures for controlled drug release.

Pinhole mirror-based ultra-small angle light scattering setup for simultaneous measurement of scattering and transmission

An ultra-small angle light scattering setup with the ability of simultaneous registration of scattered light by a charge-coupled device camera and the transmitted direct beam by a pin photodiode was developed. A pinhole mirror was used to reflect the scattered light; the transmitted direct beam was focused and passed through the central pinhole with a diameter of 500 μm. Time-resolved static light scattering measurement was carried out over the angular range 0.2° ≤θ≤ 8.9° with a time resolution of ∼33 ms. The measured scattering pattern in the q-range between 5 × 10^-5 and 1.5 × 10^-3 nm^-1 enables investigating structures of few micrometers to submillimeter, where q is the scattering vector. A LabVIEW-based graphical user interface was developed, which integrates the data acquisition of the scattering pattern and the transmitted intensity. The Peltier temperature-controlled sample cells of varying thicknesses allow for a rapid temperature equilibration and minimization of multiple scattering. The spinodal decomposition for coacervation (phase separation) kinetics of an aqueous mixture of oppositely charged polyelectrolytes was demonstrated.

Structural, mechanical, and vibrational properties of particulate physical gels

Our lives are surrounded by a rich assortment of disordered materials. In particular, glasses are well known as dense, amorphous materials, whereas gels exist in low-density, disordered states. Recent progress has provided a significant step forward in understanding the material properties of glasses, such as mechanical, vibrational, and transport properties. In contrast, our understanding of particulate physical gels is still highly limited. Here, using molecular dynamics simulations, we study a simple model of particulate physical gels, the Lennard-Jones (LJ) gels, and provide a comprehensive understanding of their structural, mechanical, and vibrational properties, all of which are markedly different from those of LJ glasses. First, the LJ gels show sparse, heterogeneous structures, and the length scale ξ_s of the structures grows as the density is lowered. Second, the LJ gels are extremely soft, with both shear G and bulk K moduli being orders of magnitude smaller than those of LJ glasses. Third, many low-frequency vibrational modes are excited, which form a characteristic plateau with the onset frequency ω_* in the vibrational density of states. Structural, mechanical, and vibrational properties, characterized by ξ_s, G, K, and ω_*, respectively, show power-law scaling behaviors with the density, which establishes a close relationship between them. Throughout this work, we also reveal that LJ gels are multiscale, solid-state materials: (i) homogeneous elastic bodies at long lengths, (ii) heterogeneous elastic bodies with fractal structures at intermediate lengths, and (iii) amorphous structural bodies at short lengths.

Two-dimensional Cahn-Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures

The evolution of the microstructure due to spinodal decomposition in phase separated mixtures has a strong impact on the final material properties. In the late stage of coarsening, the system is characterized by the growth of a single characteristic length scale L ∼ Ct^α. To understand the structure-property relationship, the knowledge of the coarsening exponent α and the coarsening rate constant C is mandatory. Since the existing literature is not entirely consistent, we perform phase field simulations based on the Cahn-Hilliard equation. We restrict ourselves to binary mixtures using a symmetric Flory-Huggins free energy and a constant composition-independent mobility term and show that the coarsening for off-critical mixtures is slower than the expected t^1/3-growth. Instead, we find α to be dependent on the mixture composition and associate this with the observed morphologies. Finally, we propose a model to describe the complete coarsening kinetics including the rate constant C.

Simulations and experiments of phase separation in binary dusty plasmas

Molecular dynamics simulations of binary dusty plasmas have been performed and their behavior with respect to the phase separation process has been analyzed. The simulated system was inspired by experimental research on phase separation in dusty plasmas under microgravity on parabolic flights. Despite vortex formation in the experiment and in the simulations the phase separation could be identified. From the simulations it is found that even the smallest charge disparities lead to phase separation. The separation is due to the force imbalance on the two species and the separation becomes weaker with increasing mean particle size. In comparison, experiments on the phase separation have been performed and analyzed in view of the separation dynamics. It is found that the experimental results are reproduced by the simulation regarding the dependency on the size disparity of the two particle species.

Power-law coarsening in network-forming phase separation governed by mechanical relaxation

A space-spanning network structure is a basic morphology in phase separation of soft and biomatter, alongside a droplet one. Despite its fundamental and industrial importance, the physical principle underlying such network-forming phase separation remains elusive. Here, we study the network coarsening during gas-liquid-type phase separation of colloidal suspensions and pure fluids, by hydrodynamic and molecular dynamics simulations, respectively. For both, the detailed analyses of the pore sizes and strain field reveal the self-similar network coarsening and the unconventional power-law growth more than a decade according to ℓ ∝ t1/2, where ℓ is the characteristic pore size and t is the elapsed time. We find that phase-separation dynamics is controlled by mechanical relaxation of the network-forming dense phase, whose limiting process is permeation flow of the solvent for colloidal suspensions and heat transport for pure fluids. This universal coarsening law would contribute to the fundamental physical understanding of network-forming phase separation.

An experimental setup for dip-coating of thin films for organic solar cells under microgravity conditions

We report the design and testing of a custom-built experimental setup for dip-coating from volatile solutions under microgravity conditions onboard an aircraft. Function and safety considerations for the equipment are described. The equipment proved to work well, both concerning the safety and the preparation of thin films. No leakage of the solvents, nor the solvent vapors, was detected, not even in a situation with a fluctuating gravitational field due to bad weather conditions. We have shown that the equipment can be used to prepare thin films of polymer blends, relevant for organic solar cells, from solution in a feasible procedure under microgravity conditions. The prepared films are similar to the corresponding films prepared under 1 g conditions, but with differences that can be related to the absence of a gravitational field during drying of the applied liquid coating. We report on some introductory results from the characterization of the thin films that show differences in film morphology and structure sizes.

Exploration of space to achieve scientific breakthroughs

Living organisms adapt to changing environments using their amazing flexibility to remodel themselves by a process called evolution. Environmental stress causes selective pressure and is associated with genetic and phenotypic shifts for better modifications, maintenance, and functioning of organismal systems. The natural evolution process can be used in complement to rational strain engineering for the development of desired traits or phenotypes as well as for the production of novel biomaterials through the imposition of one or more selective pressures. Space provides a unique environment of stressors (e.g., weightlessness and high radiation) that organisms have never experienced on Earth. Cells in the outer space reorganize and develop or activate a range of molecular responses that lead to changes in cellular properties. Exposure of cells to the outer space will lead to the development of novel variants more efficiently than on Earth. For instance, natural crop varieties can be generated with higher nutrition value, yield, and improved features, such as resistance against high and low temperatures, salt stress, and microbial and pest attacks. The review summarizes the literature on the parameters of outer space that affect the growth and behavior of cells and organisms as well as complex colloidal systems. We illustrate an understanding of gravity-related basic biological mechanisms and enlighten the possibility to explore the outer space environment for application-oriented aspects. This will stimulate biological research in the pursuit of innovative approaches for the future of agriculture and health on Earth.

Experimental investigation of phase separation in binary dusty plasmas under microgravity

Three-dimensionally extended dusty plasmas containing mixtures of two particle species of different size have been investigated under microgravity conditions. To distinguish the species even at small size disparities, one of the species is marked with a fluorescent dye, and a modified two-camera video microscopy setup is used for position determination and tracking. Phase separation is found even when the size disparity is below 5%. Particles are tracked to obtain the diffusion flux, and resulting diffusion coefficients are calculated to be about -10^{-6}mm^{2}/s, which is in the expected range for a phase separation process driven by plasma forces. Additionally, a measure for the strength of the phase separation is presented that allows us to quickly characterize measurements. There is a clear correlation between size disparity and phase separation strength.

Influence of Small-Scale Correlation on the Interface Evolution of Semiflexible Homopolymer Blends

Within the framework of a dynamic self-consistent field theory, we study the effect of the correlations in a small scale on polymer dynamics, adopting the semiflexible homopolymer blends as the model system. This is accomplished by taking the pair correlation function of ideal semiflexible chains as the Onsager coefficient and the Debye function as an approximation to the Onsager coefficient. Relying on the difference of the two pair correlation functions in the small-scale region, we can identify the effect of small-scale correlations. In the equilibrium state, with the chain length growing, the interface width has a continuous transition from the contour length to radius of gyration. The investigation of interfacial evolution and chain orientation reveals that strong small-scale correlations would accelerate the small-scale dynamic process. We also expect that such a small-scale effect should be highlighted in the process where microscopic phase separation happens.

Polymer nanocomposite capsules formed by droplet extraction: spontaneous stratification and tailored dissolution

We report the formation of polymeric and nanocomposite capsules via droplet solvent extraction, focusing on the interplay between solvent exchange and removal, demixing and directional solidification kinetics. We investigate a model system of sodium poly(styrene sulfonate), NaPSS and silica nanoparticles in aqueous solution, whose phase behaviour is experimentally measured, and examine a series of selective extraction solvents (toluene, butyl acetate, ethyl acetate and methyl ethyl ketone), ranging from 0.04 to 11% v/v water solubility. Tuning the rate of solvent exchange is shown to provide an effective means of decoupling demixing and solidification timescales, and thereby tunes the internal microstructure of the capsule, including hollow, microporous, core-shell, and bicontinuous morphologies. In turn, these determine the capsule dissolution mechanism and kinetics, ranging from single to pulsed release profiles of nanoparticle clusters (at intermediate solubilities), to minimal dissolution (at either extremes). These findings provide facile design and assembly strategies for functional capsules with time-varying release profiles.

Many-body interactions between charged particles in a polymer solution: the protein regime

We study the phase behavior of charged particles in electrolyte solutions wherein non-adsorbing polymers are added to provide an attractive depletion interaction. The polymer has a radius of gyration similar to that of the particle radius, which causes significant many-body effects in the effective polymer mediated interaction between particles. We use a recently developed analytical theory, which gives a closed expression for the full depletion interaction, accounting for all orders of many-body terms in the potential of mean force. We compare with simulations of an explicit polymer model and show that the potential of mean force provides an accurate and computationally efficient description for the charged particle/polymer mixture, over a range of electrolyte concentrations. Furthermore, we demonstrate that the usual pair potential approach is highly inaccurate for these systems. A simple simulation method is used to estimate the limits of stability of the mixture. The pair approximation is shown to predict a much greater region of instability compared with the many-body treatment, due to its overestimation of the polymer depletion effect.

Simple analysis of scattering data with the Ornstein-Zernike equation

In this paper we propose and explore a method of analysis of the scattering experimental data for uniform liquidlike systems. In our pragmatic approach we are not trying to introduce by hands an artificial small parameter to work out a perturbation theory with respect to the known results, e.g., for hard spheres or sticky hard spheres (all the more that in the agreement with the notorious Landau statement, there is no physical small parameter for liquids). Instead of it being guided by the experimental data we are solving the Ornstein-Zernike equation with a trial (variational) form of the interparticle interaction potential. To find all needed correlation functions this variational input is iterated numerically to satisfy the Ornstein-Zernike equation supplemented by a closure relation. Our method is developed for spherically symmetric scattering objects, and our numeric code is written for such a case. However, it can be extended (at the expense of more involved computations and a larger amount of required experimental input information) for nonspherical particles. What is important for our approach is that it is sufficient to know experimental data in a relatively narrow range of the scattering wave vectors (q) to compute the static structure factor in a much broader range of q. We illustrate by a few model and real experimental examples of the x-ray and neutron scattering data how the approach works.

Experimental investigations and phase-field simulations of triple-phase-separation kinetics within liquid ternary Co-Cu-Pb immiscible alloys

The phase-separation kinetics and microstructure evolution mechanisms of liquid ternary Co_{43}Cu_{40}Pb_{17} immiscible alloys are investigated by both the drop tube technique and phase-field method. Two successive phase separations take place during droplet falling and lead to the formation of a three-phase three-layer core-shell structure composed of a Co-rich core, a Cu-rich middle layer, and a Pb-rich shell. The Pb-rich shell becomes more and more conspicuous as droplet diameter decreases. Meanwhile, the Co-rich core center gradually moves away from the core-shell center. Theoretical analyses show that a larger temperature gradient inside a smaller alloy droplet induces the accelerated growth of the surface segregation shell during triple-phase separation. The residual Stokes motion and the asymmetric Marangoni convection result in the appearance of an eccentric Co-rich core and the core deviation degree is closely related to the droplet size and initial velocity. A three-dimensional phase-field model of ternary immiscible alloys, which considers the successive phase separations under the combined effects of Marangoni convection and surface segregation, is proposed to explore the formation mechanisms of three-phase core-shell structures. The simulated core-shell morphologies are consistent with the experimental observations, which verifies the model's validity in reproducing the core-shell dynamic evolution. Numerical results reveal that the development of three-phase three-layer core-shell structures can be attributed to the primary and then secondary phase separations dominated simultaneously by Marangoni convection and surface segregation. Furthermore, the effects of droplet temperature gradient on the growth kinetics of the surface segregation shell are analyzed in the light of phase-field theory.

Phase diagram and aggregation dynamics of a monolayer of paramagnetic colloids

We have developed a tunable colloidal system and a corresponding theoretical model for studying the phase behavior of particles assembling under the influence of long-range magnetic interactions. A monolayer of paramagnetic particles is subjected to a spatially uniform magnetic field with a static perpendicular component and a rapidly rotating in-plane component. The sign and strength of the interactions vary with the tilt angle θ of the rotating magnetic field. For a purely in-plane field, θ=90^{∘}, interactions are attractive and the experimental results agree well with both equilibrium and out-of-equilibrium predictions based on a two-body interaction model. For tilt angles 50^{∘}≲θ≲55^{∘}, the two-body interaction gives a short-range attractive and long-range repulsive interaction, which predicts the formation of equilibrium microphases. In experiments, however, a different type of assembly is observed. Inclusion of three-body (and higher-order) terms in the model does not resolve the discrepancy. We further characterize the anomalous regime by measuring the time-dependent cluster size distribution.

Kinetics of fluid demixing in complex plasmas: Domain growth analysis using Minkowski tensors

A molecular dynamics simulation of the demixing process of a binary complex plasma is analyzed and the role of distinct interaction potentials is discussed by using morphological Minkowski tensor analysis of the minority phase domain growth in a demixing simulated binary complex plasma. These Minkowski tensor methods are compared with previous results that utilized a power spectrum method based on the time-dependent average structure factor. It is shown that the Minkowski tensor methods are superior to the previously used power-spectrum method in the sense of higher sensitivity to changes in domain size. By analysis of the slope of the temporal evolution of Minkowski tensor measures, qualitative differences between the case of particle interaction with a single length scale compared to particle interactions with two different length scales (dominating long-range interaction) are revealed. After proper scaling the graphs for the two length scale scenarios coincide, pointing toward universal behavior. The qualitative difference in demixing scenarios is evidenced by distinct demixing behavior: in the long-range dominated cases demixing occurs in two stages. At first, neighboring particles agglomerate, then domains start to merge in cascades. However, in the case of only one interaction length scale only agglomeration but no merging of domains can be observed. Thus, Minkowski tensor analysis is likely to become a useful tool for further investigation of this (and other) demixing processes. It is capable to reveal (nonlinear) local topological properties, probing deeper than (linear) global power-spectrum analysis, however, still providing easily interpretable results founded on a solid mathematical framework.

Exploring the dynamics of phase separation in colloid-polymer mixtures with long range attraction

We have studied the kinetics of phase separation and gel formation in a low-dispersity colloid - non-adsorbing polymer system with long range attraction using small-angle light scattering. This system exhibits two-phase and three-phase coexistence of gas, liquid and crystal phases when the strength of attraction is between 2 and 4kBT and gel phases when the strength of attraction is increased. For those samples that undergo macroscopic phase separation, whether to gas-crystal, gas-liquid or gas-liquid-crystal coexistence, we observe dynamic scaling of the structure factor and growth of a characteristic length scale that behaves as expected for phase separation in fluids. In samples that gel, the power law associated with the growth of the dominant length scale is not equal to 1/3, but appears to depend mainly on the strength of attraction, decreasing from 1/3 for samples near the coexistence region to 1/27 at 8kBT, over a wide range of colloid and polymer concentrations.

Phase Separation of Binary Charged Particle Systems with Small Size Disparities using a Dusty Plasma

The phase separation in binary mixtures of charged particles has been investigated in a dusty plasma under microgravity on parabolic flights. A method based on the use of fluorescent dust particles was developed that allows us to distinguish between particles of slightly different size. A clear trend towards phase separation even for smallest size (charge) disparities is observed. The diffusion flux is directly measured from the experiment and uphill diffusion coefficients have been determined.

Microdynamics and arrest of coarsening during spinodal decomposition in thermoreversible colloidal gels

Coarsening and kinetic arrest of colloidal systems undergoing spinodal decomposition (SD) is a conserved motif for forming hierarchical, bicontinuous structures. Although the thermodynamic origins of SD in colloids are widely known, the microstructural processes responsible for its coarsening and associated dynamics en route to arrest remain elusive. To better elucidate the underlying large-scale microdynamical processes, we study a colloidal system with moderate-range attractions which displays characteristic features of arrested SD, and study its dynamics during coarsening through a combination of differential dynamic microscopy and real-space tracking. Using these recently developed imaging techniques, we reveal directly that the coarsening arises from collective dynamics of dense domains, which undergo slow, intermittent, and ballistic motion. These collective motions indicate interfacial effects to be the driving force of coarsening. The nature of the gelation enables control of the arrested length scale of coarsening by the depths of quenching into the spinodal regime, which we demonstrate to provide an effective means to control the elasticity of colloidal gels.

A many-body Hamiltonian for nanoparticles immersed in a polymer solution

We developed an analytical theory for the many-body potential of mean force (POMF) between N spheres immersed in a continuum chain fluid. The theory is almost exact for a Θ polymer solution in the protein limit (small particles, long polymers), where N-body effects are important. Polydispersity in polymer length according to a Schulz-Flory distribution emerges naturally from our analysis, as does the transition to the monodisperse limit. The analytical expression for the POMF allows for computer simulations employing the complete N-body potential (i.e., without n-body truncation; n < N). These are compared with simulations of an explicit particle/polymer mixture. We show that the theory produces fluid structure in excellent agreement with the explicit model simulations even when the system is strongly fluctuating, e.g., at or near the spinodal region. We also demonstrate that other commonly used theoretical approaches, such as truncation of the POMF at the pair level or the Asakura Oosawa model, are extremely inaccurate for these systems.

Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions, with rather well-characterized pair interactions and minimized external influences. In complementary approaches experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Over the last decade, both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity have been addressed in a quantitative way. Key parameters of crystallization have been derived and compared to those of metal systems. These systematic investigations significantly contributed to an enhanced understanding of the crystallization processes in general. Further, new fundamental questions have arisen and (partially) been solved over the last decade: including, for example, a two-step nucleation mechanism in homogeneous nucleation, choice of the crystallization pathway, or the subtle interplay of boundary conditions in heterogeneous nucleation. On the other hand, via the application of both gradients and external fields the competition between different nucleation and growth modes can be controlled and the resulting microstructure be influenced. The present review attempts to cover the interesting developments that have occurred since the turn of the millennium and to identify important novel trends, with particular focus on experimental aspects.

Homogeneous percolation versus arrested phase separation in attractively-driven nanoemulsion colloidal gels

We elucidate mechanisms for colloidal gelation of attractive nanoemulsions depending on the volume fraction (ϕ) of the colloid. Combining detailed neutron scattering, cryo-transmission electron microscopy and rheological measurements, we demonstrate that gelation proceeds by either of two distinct pathways. For ϕ sufficiently lower than 0.23, gels exhibit homogeneous fractal microstructure, with a broad gel transition resulting from the formation and subsequent percolation of droplet-droplet clusters. In these cases, the gel point measured by rheology corresponds precisely to arrest of the fractal microstructure, and the nonlinear rheology of the gel is characterized by a single yielding process. By contrast, gelation for ϕ sufficiently higher than 0.23 is characterized by an abrupt transition from dispersed droplets to dense clusters with significant long-range correlations well-described by a model for phase separation. The latter phenomenon manifests itself as micron-scale "pores" within the droplet network, and the nonlinear rheology is characterized by a broad yielding transition. Our studies reinforce the similarity of nanoemulsions to solid particulates, and identify important qualitative differences between the microstructure and viscoelastic properties of colloidal gels formed by homogeneous percolation and those formed by phase separation.

Texture analysis microscopy: quantifying structure in low-fidelity images of dense fluids

Optical images are often corrupted by noise, low contrast, uneven illumination and artefacts, which may pose significant challenges to image analysis, particularly for dense fluids. Traditionally, noise removal and contrast enhancement are achieved by global arithmetic operations on the image as a whole, and/or by image convolution with various kernels. However, these methods work under very limited conditions and can compromise detail within the image. Here, we develop a new technique, texture analysis microscopy (TAM), to overcome these challenges based on the method of image correlation. TAM recasts an image by the statistical similarities between a raw image and a template feature (e.g. a Gaussian) that best approximates features in the image. We demonstrate the superiority of TAM by applying it to low-fidelity images under conditions where traditional methods fail or have deteriorative performance, for analyses including structural correlations, particle identification and sizing.

Hydrodynamic mechanisms of spinodal decomposition in confined colloid-polymer mixtures: a multiparticle collision dynamics study

A multiscale model for a colloid-polymer mixture is developed. The colloids are described as point particles interacting with each other and with the polymers with strongly repulsive potentials, while polymers interact with each other with a softer potential. The fluid in the suspension is taken into account by the multiparticle collision dynamics method (MPC). Considering a slit geometry where the suspension is confined between parallel repulsive walls, different possibilities for the hydrodynamic boundary conditions (b.c.) at the walls (slip versus stick) are treated. Quenching experiments are considered, where the system volume is suddenly reduced (keeping the density of the solvent fluid constant, while the colloid and polymer particle numbers are kept constant) and thus an initially homogeneous system is quenched deeply into the miscibility gap, where it is unstable. For various relative concentrations of colloids and polymers, the time evolution of the growing colloid-rich and polymer-rich domains are studied by molecular dynamics simulation, taking hydrodynamic effects mediated by the solvent into account via MPC. It is found that the domain size [script-l](d)(t) grows with time t as [script-l](d)(t) [proportionality] t(1/3) for stick and (at late stages) as [script-l](d)(t) [proportionality] t(2/3) for slip b.c., while break-up of percolating structures can cause a transient "arrest" of growth. While these findings apply for films that are 5-10 colloid diameters wide, for ultrathin films (1.5 colloid diameters wide) a regime with [script-l](d)(t) [proportionality] t(1/2) is also identified for rather shallow quenches.

Spatial ordering of colloids in a drying aqueous polymer droplet

We explore the role of polymer chains on deposition of colloidal particles at solid surfaces from drying aqueous drops and show that the kinetics of phase separation of colloids and polymers can be explained by spinodal decomposition of binary systems. Concentrations of polymer solutions and polymer chain lengths were varied to understand the aggregation dynamics of colloidal particles via a polymer bridging mechanism. We show that when polymer concentration in the droplet is increased, particles spatially order upon drying due to a combination of the phase separation of highly bridged particles and the Marangoni flow effect. The demonstrated effect of particle-adsorbing, water-soluble polymers on the coffee-ring formation opens up new ways of creating highly ordered, long-range patterned surfaces using a facile, template-free approach.

Crystal-arrested phase separation

We have studied the interplay between phase separation and crystallization in a colloid-polymer mixture along one kinetic pathway in samples which exhibit three-phase equilibrium coexistence. In analogy with atomic systems, the range of the effective attractive interaction between colloids is sufficiently long to allow for a stable liquid phase. By direct imaging in microgravity on the International Space Station, we observe a unique structure, a "crystal gel," that occurs when gas-liquid phase separation arrests due to crystallites within the liquid domain spanning the cell. From the initial onset of spinodal decomposition until arrest caused by this structure, the kinetics of phase separation remain largely unaffected by the formation of the third phase. This dynamic arrest appears to result from the stiffness of the crystalline strands exceeding the liquid-gas interfacial tension.

Multi-scale kinetics of a field-directed colloidal phase transition

Polarizable colloids are expected to form crystalline equilibrium phases when exposed to a steady, uniform field. However, when colloids become localized this field-induced phase transition arrests and the suspension persists indefinitely as a kinetically trapped, percolated structure. We anneal such gels formed from magneto-rheological fluids by toggling the field strength at varied frequencies. This processing allows the arrested structure to relax periodically to equilibrium--colloid-rich, cylindrical columns. Two distinct growth regimes are observed: one in which particle domains ripen through diffusive relaxation of the gel, and the other where the system-spanning structure collapses and columnar domains coalesce apparently through field-driven interactions. There is a stark boundary as a function of magnetic field strength and toggle frequency distinguishing the two regimes. These results demonstrate how kinetic barriers to a colloidal phase transition are subverted through measured, periodic variation of driving forces. Such directed assembly may be harnessed to create unique materials from dispersions of colloids.

Tuning the demixing of colloid-polymer systems through the dispersing solvent

We report measurements on fluid-fluid phase separation in a colloid-polymer mixture by means of confocal scanning laser microscopy and we show that we can access the various coarsening regimes by tuning the properties of the solvent. By increasing the viscosity of the solvent we are able to access the diffusive hydrodynamic regime of spinodal decomposition. By matching the density of the solvent and colloids we are able to grow structures to large length scales before they are destroyed by buoyancy forces. Tuning the solvent's density furthermore gives control over which phase flows up and down, illustrating the flexibility of this particular system.

Kinetics of fluid demixing in complex plasmas: role of two-scale interactions

Using experiments and combining theory and computer simulations, we show that binary complex plasmas are particularly good model systems to study the kinetics of fluid-fluid demixing at the "atomistic" (individual particle) level. The essential parameters of interparticle interactions in complex plasmas, such as the interaction range(s) and degree of nonadditivity, can be varied significantly, which allows systematic investigations of different demixing regimes. The critical role of competition between long-range and short-range interactions at the initial stage of the spinodal decomposition is discussed.

Optical experiments on a crystallizing hard-sphere-polymer mixture at coexistence

We report on the crystallization kinetics in an entropically attractive colloidal system using a combination of time resolved scattering methods and microscopy. Hard sphere particles are polystyrene microgels swollen in a good solvent (radius a=380 nm, starting volume fraction 0.534) with the short ranged attractions induced by the presence of short polymer chains (radius of gyration r g=3 nm, starting volume fraction 0.0224). After crystallization, stacking faulted face centered cubic crystals coexist with about 5% of melt remaining in the grain boundaries. From the Bragg scattering signal we infer the amount of crystalline material, the average crystallite size and the number density of crystals as a function of time. This allows to discriminate an early stage of conversion, followed by an extended coarsening stage. The small angle scattering (SALS) appears only long after completed conversion and exhibits Furukawa scaling for all times. Additional microscopic experiments reveal that the grain boundaries have a reduced Bragg scattering power but possess an increased refractive index. Fits of the Furukawa function indicate that the dimensionality of the scatterers decreases from 2.25 at short times to 1.65 at late times and the characteristic length scale is slightly larger than the average crystallite size. Together this suggests the SALS signal is due scattering from a foam like grain boundary network as a whole.

The role of polymer polydispersity in phase separation and gelation in colloid-polymer mixtures

Mixtures of nonadsorbing polymer and colloidal particles exhibit a range of different morphologies depending on the particle and polymer concentrations and their relative size ratios. These can be very important for technological applications, where gelation can produce a weak solidlike structure that can help reduce phase separation, extending product shelf life. However, industrial products are typically formulated with polydisperse polymers, and the consequences of this on the phase behavior of the mixture are not known. We investigate the role of polymer polydispersity and show that a small amount of larger polymer in a distribution of nominally much smaller polymer can drastically modify the behavior. It can induce formation of a solidlike gel structure, abetted by the small polymer, but still allow further evolution of the phase separation process, as is seen with a monodisperse distribution of larger polymer. This coarsening ultimately leads to gravitational collapse. We describe the full phase behavior for polydisperse polymer mixtures and account for the origin of the behavior through measurements of the structure and dynamics and by comparing to the behavior with monodisperse polymers.

Phase behaviour of deionized binary mixtures of charged colloidal spheres

We review recent work on the phase behaviour of binary charged sphere mixtures as a function of particle concentration and composition. Both size ratios Γ and charge ratios Λ are varied over a wide range. Unlike the case for hard spheres, the long-ranged Coulomb interaction stabilizes the crystal phase at low particle concentrations and shifts the occurrence of amorphous solids to particle concentrations considerably larger than the freezing concentration. Depending on Γ and Λ, we observe upper azeotrope, spindle, lower azeotrope and eutectic types of phase diagrams, all known well from metal systems. Most solids are of body centred cubic structure. Occasionally stoichiometric compounds are formed at large particle concentrations. For very low Γ, entropic effects dominate and induce a fluid-fluid phase separation. Since for charged spheres the charge ratio Λ is also decisive for the type of phase diagram, future experiments with charge variable silica spheres are suggested.

Unusual crystallization kinetics in a hard sphere colloid-polymer mixture

We investigated the crystallization kinetics of a hard sphere colloid-polymer mixture at conditions where about 95% of solid coexists with about 5% of fluid. From time resolved Bragg and small angle light scattering, we find that the crystallite size increases with a power law of exponent alpha approximately 1/3 during both the conversion and the coarsening stage. This observation points to a single conserved order parameter for both stages and cannot be explained if the mixture is regarded as an effective one-component system. We alternatively suggest that--based on local geometric demixing--the polymer density takes the role of the conserved order parameter.