Nonequilibrium master kinetic equation modeling of colloidal gelation

Dilute gel networks vs. clumpy gels in colloidal systems with a competition between repulsive and attractive interactions

Using Brownian dynamics simulations we study gel-forming colloidal systems. The focus of this article lies on the differences of dense and dilute gel networks in terms of structure formation both on a local and a global level. We apply reduction algorithms and observe that dilute networks and dense gels differ in the way structural properties like the thickness of strands emerge. We also analyze the percolation behavior and find that two different regimes of percolation exist which might be responsible for structural differences. In dilute networks we confirm that solidity is mainly a consequence of pentagonal bipyramids forming in the network. In dense gels, tetrahedral structures also influence solidity.

Variance and higher moments in the sigmoidal self-assembly of branched fibrils

Self-assembly of functional branched filaments, such as actin filaments and microtubules, or dysfunctional ones, such as amyloid fibrils, plays important roles in many biological processes. Here, based on the master equation approach, we study the kinetics of the formation of the branched fibrils. In our model, a branched fibril has one mother branch and several daughter branches. A daughter branch grows from the side of a pre-existing mother branch or daughter branch. In our model, we consider five basic processes for the self-assembly of the branched filaments, namely, the nucleation, the dissociation of the primary nucleus of fibrils, the elongation, the fragmentation, and the branching. The elongation of a mother branch from two ends and the elongation of a daughter branch from two ends can, in principle, occur with four different rate constants associated with the corresponding tips. This leads to a pronounced impact of the directionality of growth on the kinetics of the self-assembly. Here, we have unified and generalized our four previously presented models of branched fibrillogenesis in a single model. We have obtained a system of non-linear ordinary differential equations that give the time evolution of the polymer numbers and the mass concentrations along with the higher moments as observable quantities.

Impact of granular inclusions on the phase behavior of colloidal gels

Colloidal gels formed from small attractive particles are commonly used in formulations to keep larger components in suspension. Despite extensive work characterising unfilled gels, little is known about how the larger inclusions alter the phase behavior and microstructure of the colloidal system. Here we use numerical simulations to examine how larger 'granular' particles can alter the gel transition phase boundaries. We find two distinct regimes depending on both the filler size and native gel structure: a 'passive' regime where the filler fits into already-present voids, giving little change in the transition, and an 'active' regime where the filler no longer fits in these voids and instead perturbs the native structure. In this second regime the phase boundary is controlled by an effective colloidal volume fraction given by the available free volume.

Kinetics of inherent processes counteracting crystallization in supercooled monatomic liquid

Crystallization of supercooled liquids is mainly determined by two competing processes associated with the transition of particles (atoms) from liquid phase to crystalline one and, vice versa, with the return of particles from crystalline phase to liquid one. The quantitative characteristics of these processes are the so-called attachment rateg+and the detachment rateg-, which determine how particles change their belonging from one phase to another. In the present study, acorrespondence rulebetween the ratesg+andg-as functions of the sizeNof growing crystalline nuclei is defined for the first time. In contrast to the well-known detailed balance condition, which relatesg+(N)andg-(N)atN=nc(wheren_cis the critical nucleus size) and is satisfied only at the beginning of the nucleation regime, the foundcorrespondence ruleis fulfilled at all the main stages of crystallization kinetics (crystal nucleation, growth and coalescence). On the example of crystallizing supercooled Lennard-Jones liquid, the rateg-was calculated for the first time at different supercooling levels and for the wide range of nucleus sizesN∈[nc;40nc]. It was found that for the whole range of nucleus sizes, the detachment rateg-is only≈2% less than the attachment rateg+. This is direct evidence that the role of the processes that counteract crystallization remains significant at all the stages of crystallization. Based on the obtained results, a kinetic equation was formulated for the time-dependent distribution function of the nucleus sizes, that is an alternative to the well-known kinetic Becker-Döring-Zeldovich-Frenkel equation.

Stiffening colloidal gels by solid inclusions

The elastic properties of a soft matter material can be greatly altered by the presence of solid inclusions whose microscopic properties, such as their size and interactions, can have a dramatic effect. In order to shed light on these effects we use extensive rheology computer simulations to investigate colloidal gels with solid inclusions of different sizes. We show that the elastic properties vary in a highly non-trivial way as a consequence of the interactions between the gel backbone and the inclusions. In particular, we show that the key aspects are the presence of the gel backbone and its mechanical alteration originating from the inclusions. To confirm our observations and their generality, we performed experiments on an emulsion that presents strong analogies with colloidal gels and confirms the trends observed in the simulations.

Microscopic structural origin behind slowing down of colloidal phase separation approaching gelation

The gelation of colloidal particles interacting through a short-range attraction is widely recognized as a consequence of the dynamic arrest of phase separation into colloid-rich and solvent-rich phases. However, the microscopic origin behind the slowing down and dynamic arrest of phase separation remains elusive. In order to access microscopic structural changes through the entire process of gelation in a continuous fashion, we used core–shell fluorescent colloidal particles, laser scanning confocal microscopy, and a unique experimental protocol that allows us to initiate phase separation instantaneously and gently. Combining these enables us to track the trajectories of individual particles seamlessly during the whole phase-separation process from the early stage to the late arresting stage. We reveal that the enhancement of local packing and the resulting formation of locally stable rigid structures slow down the phase-separation process and arrest it to form a gel with an average coordination number of z = 6–7. This result supports a mechanical perspective on the dynamic arrest of sticky-sphere systems based on the microstructure, replacing conventional explanations based on the macroscopic vitrification of the colloid-rich phase. Our findings illuminate the microscopic mechanisms behind the dynamic arrest of colloidal phase separation, the emergence of mechanical rigidity, and the stability of colloidal gels.

Erythrocyte Sedimentation: Collapse of a High-Volume-Fraction Soft-Particle Gel

The erythrocyte sedimentation rate is one of the oldest medical diagnostic methods whose physical mechanisms remain debatable today. Using both light microscopy and mesoscale cell-level simulations, we show that erythrocytes form a soft-particle gel. Furthermore, the high volume fraction of erythrocytes, their deformability, and weak attraction lead to unusual properties of this gel. A theoretical model for the gravitational collapse is developed, whose predictions are in agreement with detailed macroscopic measurements of the interface velocity.

Erythrocyte sedimentation: Effect of aggregation energy on gel structure during collapse

The erythrocyte (or red blood cell) sedimentation rate (ESR) is commonly interpreted as a measure of cell aggregation and as a biomarker of inflammation. It is well known that an increase of fibrinogen concentration, an aggregation-inducing protein for erythrocytes, leads to an increase of the sedimentation rate of erythrocytes, which is generally explained through the formation and faster settling of large disjoint aggregates. However, many aspects of erythrocyte sedimentation conform well with the collapse of a particle gel rather than with the sedimentation of disjoint aggregates. Using experiments and cell-level numerical simulations, we systematically investigate the dependence of ESR on fibrinogen concentration and its relation to the microstructure of the gel-like erythrocyte suspension. We show that for physiological aggregation interactions, an increase in the attraction strength between cells results in a cell network with larger void spaces. This geometrical change in the network structure occurs due to anisotropic shape and deformability of erythrocytes and leads to an increased gel permeability and faster sedimentation. Our results provide a comprehensive relation between the ESR and the cell-level structure of erythrocyte suspensions and support the gel hypothesis in the interpretation of blood sedimentation.

Real space analysis of colloidal gels: triumphs, challenges and future directions

Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such as an increase in strength prior to catastrophic failure. Remarkably, such complex phenomena are faithfully captured by an extremely simple model-'sticky spheres'. Here we review progress in our understanding of colloidal gels made through the use of real space analysis and particle resolved studies. We consider the challenges of obtaining a suitable experimental system where the refractive index and density of the colloidal particles is matched to that of the solvent. We review work to obtain a particle-level mechanism for rigidity in gels and the evolution of our understanding of time-dependent behaviour, from early-time aggregation to ageing, before considering the response of colloidal gels to deformation and then move on to more complex systems of anisotropic particles and mixtures. Finally we note some more exotic materials with similar properties.

Structural and dynamical properties of dilute gel networks in colloid-polymer mixtures

The competition of short-ranged depletion attraction and long-ranged repulsion between colloidal particles in colloid-polymer mixtures leads to the formation of heterogeneous gel-like structures. Our special focus will be on the states where the colloids arrange in thin strands that span the whole system and that we will refer to as dilute gel networks. These states occur at low packing fractions for attractions that are stronger than those at both the binodal line of the equilibrium gas-liquid phase separation and the directed percolation transition line. By using Brownian dynamics simulations, we explore the formation, structure, and aging dynamics of dilute gel networks. The essential connections in a dilute gel network are determined by constructing reduced networks. We compare the observed properties to those of clumpy gels or cluster fluids. Our results demonstrate that both the structure and the (often slow) dynamics of the stable or meta-stable heterogeneous states in colloid-polymer mixtures possess distinct features on various length and time scales and thus are richly diverse.

Colloidal density control with Bessel-Gauss beams

Optical manipulation of colloidal systems is of high interest for both fundamental studies and practical applications. It has been shown that optically induced thermophoresis and nonlinear interactions can significantly affect the properties of dense colloidal media. However, macroscopic scale phenomena can also be generated at thermal equilibrium. Here, we demonstrate that steady-state variations of particle density can be created over large, three-dimensional regions by appropriately structured external optical fields. We prove analytically and experimentally that an optical vortex beam can dynamically control the spatial density of microscopic particles along the direction of its propagation. We show that these artificial steady-states can be generated at will and can be maintained indefinitely, which can be beneficial for applications such as path clearing and mass transportation.

Directionality of growth and kinetics of branched fibril formation

The self-assembly of fibrils is a subject of intense interest, primarily due to its relevance to the formation of pathological structures. Some fibrils develop branches via the so-called secondary nucleation. In this paper, we use the master equation approach to model the kinetics of formation of branched fibrils. In our model, a branched fibril consists of one mother branch and several daughter branches. We consider five basic processes of fibril formation, namely, nucleation, elongation, branching, fragmentation, and dissociation of the primary nucleus of fibrils into free monomers. Our main focus is on the effect of the directionality of growth on the kinetics of fibril formation. We consider several cases. At first, the mother branch may elongate from one or from both ends, while the daughter branch elongates only from one end. We also study the case of branched fibrils with bidirectionally growing daughter branches, tangentially to the main stem, which resembles the intertwining process. We derive a set of ordinary differential equations for the moments of the number concentration of fibrils, which can be solved numerically. Assuming that the primary nucleus of fibrils dissociates with the fragmentation rate, in the limit of the zero branching rate, our model reproduces the results of a previous model that considers only the three basic processes of nucleation, elongation, and fragmentation. We also use the experimental parameters for the fibril formation of Huntingtin fragments to investigate the effect of unidirectional vs bidirectional elongation of the filaments on the kinetics of fibrillogenesis.