Session F37: Clustering and Gelation with Competing Interactions I

Inverse design of voids: clusters of nothing

Much work has been done to find and characterize potentials (both pair and many-body) that result in interesting fluid architectures, particularly with respect to clustered fluids. In this work, we inverse design a pair potential possessing competitive attractions and repulsions that forms voids—“clusters” of empty space. We show that these voids are relatively spherical and reasonably monodisperse in size. We study the behavior of this potential with respect to modulating system density and temperature and we find that, like clusters of particles, these voids are capable of self-assembling into columns, lamellar sheets, as well as a bicontinuous structure. Moreover, we find that this potential can form both clusters and voids, depending on the state point, demonstrating a correspondence between the competitive interactions that are suitable to form these two structural motifs.   

Inverse Design of Equilibrium Cluster Fluids

Equilibrium cluster fluids have garnered much recent attention, but the types of interparticle forces that can lead to self-assembly of such entities have not been systematically explored. As a step towards addressing this, we leverage powerful inverse design tools to fabricate a fluid of monodisperse, spherical, liquid-droplet-like clusters of a desired size and good center of mass mobility. The inverse designed pair potential possesses a broad attractive well and narrow repulsive barrier at larger separations—a qualitatively different form as compared to the so-called SALR potential [short-range attractive (SA) and long-range repulsive (LR)] often associated with equilibrium cluster formation in colloids. Such differences suggest alternative mechanisms for cluster formation—leading to structured fluids with qualitatively different static and dynamic properties. Lastly, we explore the representability of our inverse designed potentials through simple parametrized forms.   

Decoding the pair correlations and properties of equilibrium microscopic cluster phases

Due to competing interactions acting between particles, dispersed colloidal suspensions can reversibly transition to phases comprising aggregate clusters. Cluster phases have been reported for both ‘model’ colloidal particles and complex monomers (e.g., proteins); however, many questions remain regarding how to detect and characterize cluster phases given only pair structural correlations (the information most accessible across diverse systems) and how to relate clustering susceptibility and behavior to underlying monomer-monomer interactions. Using molecular simulations and liquid-state theory across a wide survey of conditions, we decode the widely-observed intermediate range order pre-peak in the structure factor by: (1) validating a physically-intuitive rule for detecting clustering based on the pre-peak thermal correlation length; and (2) relating pre-peak position to cluster size and bulk monomer density. We further demonstrate how clustering transitions and resultant properties relate to monomer interactions along coordinates tunable in experiments. These trends are suitable for comparing against clustering systems that can be directly visualized (via, e.g., confocal microscopy), which should aid in assessing the realism of commonly-adopted monomer interaction potentials.   

Multiscale modeling of the thixotropic behavior of aggregating soft colloidal particle suspensions

A multiscale model is presented that incorporates microscopic information at the soft, aggregating, colloidal particle level to a macroscopic description of a thixotropic suspension with a yield stress. This is accomplished by incorporating the relevant physics describing aggregation and breakage at the particle level into a population balance microscopic framework. A moment approach is followed to allow for model coarsening and its incorporation into a macroscopic description. Furthermore, to describe the aggregate dynamics under flow, it is necessary to include an additional description of the aggregate deformation. The yielding behavior of gel networks observed in thixotropic suspensions is modeled by adapting micromechanical models of emulsions and pastes to describe aggregate deformation under flow. A key outcome of this work is the recognition of the important role of competition between orthokinetic and perikinetic aggregation on polydispersity and dynamical behavior. Comparison to rheological experiments on a model thixotropic suspension will also be presented to validate the model developed.   

Elasto-hydrodynamic network analysis of colloidal gels

Colloidal gels formed at low particle volume fractions result from a competition between two rate processes: aggregation of colloids and compaction of pre-gel aggregates. Recent work has shown that the former process is highly sensitive to the nature of the hydrodynamic interactions between suspended colloids. This same sensitivity to hydrodynamic flows within the gel leads to pronounced differences in the spectrum of relaxation times and response to deformation of the gel. This talk explores those differences and their consequences through computational simulations and the framework of elasto-hydrodynamic network analysis. We demonstrate a significant impact of hydrodynamic interactions between gelled colloids on macroscopic gel dynamics and rheology as well as the effect of hydrodynamic screening in gelled materials.   

Shape mismatch in self assembly leads to fiber-like aggregates

Aggregating proteins tend to form fibers, often for the worse - think of Alzheimer's disease. Could this propensity to form fibers be a generic physical property of irregular aggregating objects, rather than something specific to protein chemistry? We investigate the aggregation of simple ill-fitting, deformable objects and find that geometrical frustration can lead to self-assembly into slender aggregates.   

Gelation And Mechanical Response of Patchy Rods.

We perform Brownian Dynamics simulations to study the gelation of suspensions of attractive, rod-like particles. We show that details of the particle-particle interactions can dramatically affect the dynamics of gelation and the structure and mechanics of the networks that form.~If the attraction between the rods is perfectly smooth along their length, they will collapse into compact bundles. If the attraction is sufficiently corrugated or patchy, over time, a rigid space spanning network forms. We study the structure and mechanical properties of the networks that form as a function of the fraction of the surface that is allowed to bind. Surprisingly, the structural and mechanical properties are non-monotonic in the surface coverage. At low coverage, there are not a sufficient number of cross-linking sites to form networks. At high coverage, rods bundle and form disconnected clusters. At intermediate coverage, robust networks form. The elastic modulus and yield stress are both non-monotonic in the surface coverage. The stiffest and strongest networks show an essentially homogeneous deformation under strain with rods re-orienting along the extensional axis. Weaker, clumpy networks at high surface coverage exhibit relatively little re-orienting with strong non-affine deformation. These results suggest design strategies for tailoring surface interactions between rods to yield rigid networks with optimal properties.   

Protein gelation kinetics near the overlap concentration

Proteins can be crosslinked to form gel networks either as a tool to study biological problems or as a method for creating novel materials. The bulk mechanical properties of protein gels in steady state are a manifestation of the gel structure, but the polymerization kinetics are often disregarded. Using the gelation of an aqueous denatured silk protein solution as a model polymer system, we probe the gelation kinetics (modulus vs. time) and find two regimes that depend on whether the initial protein concentration $(c)$ is near or below the overlap concentration $(c*)$. We find that systems with $c/c*\sim 1$ exhibit immediate and single-mode modulus growth until the completion of polymerization that can be scaled onto a characteristic polymerization curve. However, systems with $c/c* < 1$ display delayed modulus development followed by two-stage modulus growth that can be normalized onto a separate distinctive polymerization curve. These two regimes are probed by changing both the initial concentration and the overlap concentration separately, emphasizing the importance of the overlap concentration on the assembly of polymeric/complex fluids.   

Coupled diffusion processes and 2D affinities of adhesion molecules at synthetic membrane junctions

A more complete understanding of the physically intrinsic mechanisms underlying protein mobility at cellular interfaces will provide additional insights into processes driving adhesion and organization in signalling junctions such as the immunological synapse. We observed diffusional slowing of structurally diverse binding proteins at synthetic interfaces formed by giant unilamellar vesicles (GUVs) on supported lipid bilayers (SLBs) that shows size dependence not accounted for by existing models. To model the effects of size and intermembrane spacing on interfacial reaction-diffusion processes, we describe a multistate diffusion model incorporating entropic effects of constrained binding. This can be merged with hydrodynamic theories of receptor-ligand diffusion and coupling to thermal membrane roughness. A novel synthetic membrane adhesion assay based on reversible and irreversible DNA-mediated interactions between GUVs and SLBs is used to precisely vary length, affinity, and flexibility, and also provides a platform to examine these effects on the dynamics of processes such as size-based segregation of binding and non-binding species.   

Enhanced gel formation in binary mixtures of nanocolloids with tunable short-range attraction

We report a combined experimental, theoretical, and simulation study of the phase behavior and microstructural dynamics of concentrated binary mixtures of spherical nanocolloids with a size ratio near two and with a tunable, intrinsic short-range attraction. In the absence of the attraction, the suspensions behave as well mixed, hard-sphere liquids. For sufficiently strong attraction, the suspensions undergo a gel transition. Rheometry measurements show that the fluid-gel boundary of the mixtures does not follow an ideal mixing law, but rather the gel state is stable at weaker interparticle attraction in the mixtures than in the corresponding monodisperse suspensions. X-ray photon correlation spectroscopy measurements reveal that, in contrast with depletion-driven gelation at larger size ratio, gel formation in the mixtures coincides with dynamic arrest of the smaller colloids while the larger colloids remain mobile. Molecular dynamics simulations indicate the arrest results from microphase separation that is caused by a subtle interplay of entropic and enthalpic effects and that drives the smaller particles to form dense regions.   

Gelation of calcium-silicate-hydrate in cement~

The calcium-silicate-hydrate (C-S-H) gel forms and densifies via precipitation and aggregation of nano-scale hydrates within a couple of hours during cement hydration and it is the main responsible for cement strength. We have investigated equilibrium and arrested states representative of the effective interactions between the nano-scale C-S-H at different stages of the hydration. The inter-hydrate interactions are due to ion correlation forces arising from strong surface charge heterogeneities and change from repulsive to strongly attractive during the early stages of cement hydration, according to the ionic concentration. We analyze the cluster size distributions, the morphology, the local packing and the free energy of aggregates and crystalline phases, using molecular dynamics and Monte Carlo simulations. We compare the results of equilibrium calculations with non-equilibrium simulations that capture the main features of the hydration kinetics. The emerging picture is that the evolving effective interactions provide a thermodynamic driving for the growth of the gel and for its continuous densification that is crucial to cement strength. ~   

Effects on gelation transition by tuning the interaction of solvent-solute molecules in a bridging system

A mixed suspension of large hard spheres and small soft microgels with well-defined bridging interaction is used to construct a new short-range attractive system. Soft poly (N-isopropylacrylamide) microgels ($R_{\mathrm{\thinspace }}=$ 80 nm) are absorbable to the surface of hard polystyrene spheres ($R_{\mathrm{\thinspace }}=$ 960 nm) in aqueous solution. For a constant volume fraction of hard spheres ($\Phi _{\mathrm{MS}})$, gradually increasing amount of microgels ($\Phi _{\mathrm{MG}})$ leads to a liquid-gel-liquid transitions through bridging and steric stabilized mechanisms. Rheological measurements were performed on suspensions with $\Phi_{\mathrm{MS}}$ ranging up to 0.35 to carefully identify the transition boundaries between liquid-like and solid-like behaviors triggered by $\Phi_{\mathrm{MG.\thinspace }}$Meanwhile, neutron scattering technique with Baxter's sticky hard-sphere potential fit was used to investigate the effective interparticle potential at and around the gelation boundaries. By exhibiting a set of experimental results from this explicit model system and comparing with the theoretical data, we try to clarify a debate issue about the relative position of the gel line and the liquid-gas coexistence line in the potential $U -\Phi $ plane.   

Gelation of anisotropic silica colloids with thermoreversible short-range interactions

Colloidal suspensions containing anisotropic particles are widely used in particle-based technologies including pharmaceuticals, consumer products, and coatings. The rheological properties of colloidal suspensions are known to be affected by particle shape; however, the combined influence of particle shape and attraction strength is not quantitatively understood for dynamic arrest transitions such as gelation. A model system of anisotropic silica colloids with thermoreversible, short-range attractions was developed to quantify the effect of particle shape and attractions on the gelation behavior. This tunable model system aims to map a fundamental state diagram for anisotropic particle suspensions as a function of particle shape, volume fraction, and interaction strength. Macroscopic rheological properties of thermoreversible gels were explored to determine the influence of particle shape on the gel transition. Neutron and x-ray scattering methods further probed the underlying fluid and gel microstructure at various temperatures, volume fractions, and aspect ratios. Linking these fundamental macroscopic and microscopic measurements will provide practical insight into particle technologies and manufacturing processes containing anisotropic colloidal suspensions.   

Colloidal interactions: bridging the gap from atomistic-scale descriptions to the mesoscale Primitive Model and introducing the Explicit Solvent Primitive Model approach

We investigated the interactions responsible for the cohesion of colloidal materials such as clays, cement... The swelling/cohesive properties of these (lamellar) materials depend both on the nature of the (interlayer) cations and on the surface charge of the layers. The overall goal of this work is determining the right level of modelling complexity required to capture the cohesive behaviour of charged materials immersed in an electrolyte. In addition to the analytical mean-field DLVO theory, we used various numerical modelling approaches of increasing complexity from the so-called Primitive Model to full-atomistic description. In particular, we introduced the Explicit Solvent Primitive Model (ESPM), in which ions are modelled as charged hard spheres and solvent molecules as soft spheres with embedded point dipoles. We showed that taking explicitly into account the solvent in such a Primitive Model description, significantly impacts the cohesion. Ionic correlation interactions are always present between charged objects immersed in an electrolyte and always play an important role, even in the case of system carrying a low surface charge balanced by monovalent counter-ions.   

Coupling of gelation and glass transition in a biphasic colloidal mixture---from gel-to-defective gel-toglass

The state transition from gel to glass is studied in a biphasic mixture of polystyrene core/poly ($N$-isopropylacrylamide) shell (CS) microgels and sulfonated polystyrene (PSS) particles. At 35 °C, the interaction between CS is due to short-range Van der Waals attraction while that between PSS is from long-range electrostatic repulsion. During variation of the relative ratio of the two species at a fixed apparent total volume fraction, the mixture exhibits a gel-to-defective gel-to-glass transition. When small amounts of PSS are introduced into the CS gel network, some of them are kinetically trapped, causing a change in its fractal structure, and act as defects to weaken the macroscopic gel strength. An increase of PSS content in the mixture promotes the switch from gel to defective gel, $e.g.$, the typical two-step yielding gel merges into one-step yielding. This phenomenon is an indication that inter-cluster bond breakage coincides with intra-cluster bond fracture. As the relative volume fraction of PSS exceeds a critical threshold, the gel network can no longer be formed; hence, the mixture exhibits characteristics of glass. A state diagram of the biphasic mixture is constructed, and the landscape of the different transitions will be described in future studies