Minimal conditions for solidification and thermal processing of colloidal gels.

Colloidal gelation is used to form processable soft solids from a wide range of functional materials. Although multiple gelation routes are known to create gels of different types, the microscopic processes during gelation that differentiate them remain murky. A fundamental question is how the thermodynamic quench influences the microscopic driving forces of gelation, and determines the threshold or minimal conditions where gels form. We present a method that predicts these conditions on a colloidal phase diagram, and mechanistically connects the quench path of attractive and thermal forces to the emergence of gelled states. Our method employs systematically varied quenches of a colloidal fluid over a range of volume fractions to identify minimal conditions for gel solidification. The method is applied to experimental and simulated systems to test its generality toward attractions with varied shapes. Using structural and rheological characterization, we show that all gels incorporate elements of percolation, phase separation, and glassy arrest, where the quench path sets their interplay and determines the shape of the gelation boundary. We find that the slope of the gelation boundary corresponds to the dominant gelation mechanism, and its location approximately scales with the equilibrium fluid critical point. These results are insensitive to potential shape, suggesting that this interplay of mechanisms is applicable to a wide range of colloidal systems. By resolving regions of the phase diagram where this interplay evolves in time, we elucidate how programmed quenches to the gelled state could be used to effectively tailor gel structure and mechanics.

Modeling colloidal interactions that predict equilibrium and non-equilibrium states.

Modulating the interaction potential between colloids suspended in a fluid can trigger equilibrium phase transitions as well as the formation of non-equilibrium "arrested states," such as gels and glasses. Faithful representation of such interactions is essential for using simulation to interrogate the microscopic details of non-equilibrium behavior and for extrapolating observations to new regions of phase space that are difficult to explore in experiments. Although the extended law of corresponding states predicts equilibrium phases for systems with short-ranged interactions, it proves inadequate for equilibrium predictions of systems with longer-ranged interactions and for predicting non-equilibrium phenomena in systems with either short- or long-ranged interactions. These shortcomings highlight the need for new approaches to represent and disambiguate interaction potentials that replicate both equilibrium and non-equilibrium phase behavior. In this work, we use experiments and simulations to study a system with long-ranged thermoresponsive colloidal interactions and explore whether a resolution to this challenge can be found in regions of the phase diagram where temporal effects influence material state. We demonstrate that the conditions for non-equilibrium arrest by colloidal gelation are sensitive to both the shape of the interaction potential and the thermal quench rate. We exploit this sensitivity to propose a kinetics-based algorithm to extract distinct arrest conditions for candidate potentials that accurately selects between potentials that differ in shape but share the same predicted equilibrium structure. The algorithm selects the candidate that best matches the non-equilibrium behavior between simulation and experiments. Because non-equilibrium behavior in simulation is encoded entirely by the interparticle potential, the results are agnostic to the particular mechanism(s) by which arrest occurs, and so we expect our method to apply to a range of arrested states, including gels and glasses. Beyond its utility in constructing models, the method reveals that each potential has a quantitatively distinct arrest line, providing insight into how the shape of longer-ranged potentials influences the conditions for colloidal gelation.

Correction: Phase mechanics of colloidal gels: osmotic pressure drives non-equilibrium phase separation.

Correction for 'Phase mechanics of colloidal gels: osmotic pressure drives non-equilibrium phase separation' by Lilian C. Johnson et al., Soft Matter, 2021, 17, 3784-3797, DOI: 10.1039/D0SM02180F.

Phase mechanics of colloidal gels: osmotic pressure drives non-equilibrium phase separation.

Although dense colloidal gels with interparticle bonds of order several kT are typically described as resulting from an arrest of phase separation, they continue to coarsen with age, owing to the dynamics of their temporary bonds. Here, k is Boltzmann's constant and T is the absolute temperature. Computational studies of gel aging reveal particle-scale dynamics reminiscent of condensation that suggests very slow but ongoing phase separation. Subsequent studies of delayed yield reveal structural changes consistent with re-initiation of phase separation. In the present study we interrogate the idea that mechanical yield is connected to a release from phase arrest. We study aging and yield of moderately concentrated to dense reversible colloidal gels and focus on two macroscopic hallmarks of phase separation: increases in surface-area to volume ratio that accompanies condensation, and minimization of free energy. The interplay between externally imposed fields, Brownian motion, and interparticle forces during aging or yield, changes the distribution of bond lengths throughout the gel, altering macroscopic potential energy. The gradient of the microscopic potential (the interparticle force) gives a natural connection of potential energy to stress. We find that the free energy decreases with age, but this slows down as bonds get held stretched by glassy frustration. External perturbations break just enough bonds to liberate negative osmotic pressure, which we show drives a cascade of bond relaxation and rapid reduction of the potential energy, consistent with renewed phase separation. Overall, we show that mechanical yield of reversible colloidal gels releases kinetic arrest and can be viewed as non-equilibrium phase separation.

Toward a flow-dependent phase-stability criterion: Osmotic pressure in sticky flowing suspensions.

Equilibrium phase instability of colloids is robustly predicted by the Vliegenthart-Lekkerkerker (VL) critical value of the second virial efficient, but no such general criterion has been established for suspensions undergoing flow. A transition from positive to negative osmotic pressure is one mechanical hallmark of a change in phase stability in suspensions and provides a natural extension of the equilibrium osmotic pressure encoded in the second virial coefficient. Here, we propose to study the non-Newtonian rheology of an attractive colloidal suspension using the active microrheology framework as a model for focusing on the pair trajectories that underlie flow stability. We formulate and solve a Smoluchowski relation to understand the interplay between attractions, hydrodynamics, Brownian motion, and flow on particle microstructure in a semi-dilute suspension and utilize the results to study the viscosity and particle-phase osmotic pressure. We find that an interplay between attractions and hydrodynamics leads to dramatic changes in the nonequilibrium microstructure, which produces a two-stage flow-thinning of viscosity and leads to pronounced flow-induced negative osmotic pressure. We summarize these findings with an osmotic pressure heat map that predicts where hydrodynamic enhancement of attractive bonds encourages flow-induced aggregation or phase separation. We identify a critical isobar-a flow-induced critical pressure consistent with phase instability and a nonequilibrium extension of the VL criterion.

"Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics.

Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction φg,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of φg and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ φ ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for φ < 0.60. We observe similar relaxation dynamics up to φ = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion.

Yield of reversible colloidal gels during flow start-up: release from kinetic arrest.

Yield of colloidal gels during start-up of shear flow is characterized by an overshoot in shear stress that accompanies changes in network structure. Prior studies of yield of reversible colloidal gels undergoing strong flow model the overshoot as the point at which network rupture permits fluidization. However, yield under weak flow, which is of interest in many biological and industrial fluids shows no such disintegration. The mechanics of reversible gels are influenced by bond strength and durability, where ongoing rupture and re-formation impart aging that deepens kinetic arrest [Zia et al., J. Rheol., 2014, 58, 1121], suggesting that yield be viewed as release from kinetic arrest. To explore this idea, we study reversible colloidal gels during start-up of shear flow via dynamic simulation, connecting rheological yield to detailed measurements of structure, bond dynamics, and potential energy. We find that pre-yield stress grows temporally with the changing roles of microscopic transport processes: early time behavior is set by Brownian diffusion; later, advective displacements permit relative particle motion that stretches bonds and stores energy. Stress accumulates in stretched, oriented bonds until yield, which is a tipping point to energy release, and is passed with a fully intact network, where the loss of very few bonds enables relaxation of many, easing glassy arrest. This is immediately followed by a reversal to growth in potential energy during bulk plastic deformation and condensation into larger particle domains, supporting the view that yield is an activated release from kinetic arrest. The continued condensation of dense domains and shrinkage of network surfaces, along with a decrease in the potential energy, permit the gel to evolve toward more complete phase separation, supporting our view that yield of weakly sheared gels is a 'non-equilibrium phase transition'. Our findings may be particularly useful for industrial or other coatings, where weak, slow application via shear may lead to phase separation, inhibiting smooth distribution.

Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Stresslet and straining motion couplings.

Accurate modeling of particle interactions arising from hydrodynamic, entropic, and other microscopic forces is essential to understanding and predicting particle motion and suspension behavior in complex and biological fluids. The long-range nature of hydrodynamic interactions can be particularly challenging to capture. In dilute dispersions, pair-level interactions are sufficient and can be modeled in detail by analytical relations derived by Jeffrey and Onishi [J. Fluid Mech. 139, 261-290 (1984)] and Jeffrey [Phys. Fluids A 4, 16-29 (1992)]. In more concentrated dispersions, analytical modeling of many-body hydrodynamic interactions quickly becomes intractable, leading to the development of simplified models. These include mean-field approaches that smear out particle-scale structure and essentially assume that long-range hydrodynamic interactions are screened by crowding, as particle mobility decays at high concentrations. Toward the development of an accurate and simplified model for the hydrodynamic interactions in concentrated suspensions, we recently computed a set of effective pair of hydrodynamic functions coupling particle motion to a hydrodynamic force and torque at volume fractions up to 50% utilizing accelerated Stokesian dynamics and a fast stochastic sampling technique [Zia et al., J. Chem. Phys. 143, 224901 (2015)]. We showed that the hydrodynamic mobility in suspensions of colloidal spheres is not screened, and the power law decay of the hydrodynamic functions persists at all concentrations studied. In the present work, we extend these mobility functions to include the couplings of particle motion and straining flow to the hydrodynamic stresslet. The couplings computed in these two articles constitute a set of orthogonal coupling functions that can be utilized to compute equilibrium properties in suspensions at arbitrary concentration and are readily applied to solve many-body hydrodynamic interactions analytically.

Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation.

The formulation of detailed models for the dynamics of condensed soft matter including colloidal suspensions and other complex fluids requires accurate description of the physical forces between microstructural constituents. In dilute suspensions, pair-level interactions are sufficient to capture hydrodynamic, interparticle, and thermodynamic forces. In dense suspensions, many-body interactions must be considered. Prior analytical approaches to capturing such interactions such as mean-field approaches replace detailed interactions with averaged approximations. However, long-range coupling and effects of concentration on local structure, which may play an important role in, e.g., phase transitions, are smeared out in such approaches. An alternative to such approximations is the detailed modeling of hydrodynamic interactions utilizing precise couplings between moments of the hydrodynamic traction on a suspended particle and the motion of that or other suspended particles. For two isolated spheres, a set of these functions was calculated by Jeffrey and Onishi [J. Fluid Mech. 139, 261-290 (1984)] and Jeffrey [J. Phys. Fluids 4, 16-29 (1992)]. Along with pioneering work by Batchelor, these are the touchstone for low-Reynolds-number hydrodynamic interactions and have been applied directly in the solution of many important problems related to the dynamics of dilute colloidal dispersions [G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 375-400 (1972) and G. K. Batchelor, J. Fluid Mech. 74, 1-29 (1976)]. Toward extension of these functions to concentrated systems, here we present a new stochastic sampling technique to rapidly calculate an analogous set of mobility functions describing the hydrodynamic interactions between two hard spheres immersed in a suspension of arbitrary concentration, utilizing accelerated Stokesian dynamics simulations. These mobility functions provide precise, radially dependent couplings of hydrodynamic force and torque to particle translation and rotation, for arbitrary colloid volume fraction ϕ. The pair mobilities (describing entrainment of one particle by the disturbance flow created by another) decay slowly with separation distance: as 1/r, for volume fractions 0.05 ≤ ϕ ≤ 0.5. For the relative mobility, we find an initially rapid growth as a pair separates, followed by a slow, 1/r growth. Up to ϕ ≤ 0.4, the relative mobility does not reached the far-field value even beyond separations of many particle sizes. In the case of ϕ = 0.5, the far-field asymptote is reached but only at a separation of eight radii and after a slow 1/r growth. At these higher concentrations, the coefficients also reveal liquid-like structural effects on pair mobility at close separations. These results confirm that long-range many-body hydrodynamic interactions are an essential part of the dynamics of concentrated systems and that care must be taken when applying renormalization schemes.

Macromolecular interactions and geometrical confinement determine the 3D diffusion of ribosome-sized particles in live Escherichia coli cells.

The crowded bacterial cytoplasm is comprised of biomolecules that span several orders of magnitude in size and electrical charge. This complexity has been proposed as the source of the rich spatial organization and apparent anomalous diffusion of intracellular components, although this has not been tested directly. Here, we use biplane microscopy to track the 3D motion of self-assembled bacterial Genetically Encoded Multimeric nanoparticles (bGEMs) with tunable size (20 to 50 nm) and charge (-2160 to +1800 e) in live Escherichia coli cells. To probe intermolecular details at spatial and temporal resolutions beyond experimental limits, we also developed a colloidal whole-cell model that explicitly represents the size and charge of cytoplasmic macromolecules and the porous structure of the bacterial nucleoid. Combining these techniques, we show that bGEMs spatially segregate by size, with small 20-nm particles enriched inside the nucleoid, and larger and/or positively charged particles excluded from this region. Localization is driven by entropic and electrostatic forces arising from cytoplasmic polydispersity, nucleoid structure, geometrical confinement, and interactions with other biomolecules including ribosomes and DNA. We observe that at the timescales of traditional single molecule tracking experiments, motion appears sub-diffusive for all particle sizes and charges. However, using computer simulations with higher temporal resolution, we find that the apparent anomalous exponents are governed by the region of the cell in which bGEMs are located. Molecular motion does not display anomalous diffusion on short time scales and the apparent sub-diffusion arises from geometrical confinement within the nucleoid and by the cell boundary.

Colloidal Physics Modeling Reveals How Per-Ribosome Productivity Increases with Growth Rate in Escherichia coli.

Faster-growing cells must synthesize proteins more quickly. Increased ribosome abundance only partly accounts for increases in total protein synthesis rates. The productivity of individual ribosomes must increase too, almost doubling by an unknown mechanism. Prior models point to diffusive transport as a limiting factor but raise a paradox: faster-growing cells are more crowded, yet crowding slows diffusion. We suspected that physical crowding, transport, and stoichiometry, considered together, might reveal a more nuanced explanation. To investigate, we built a first-principles physics-based model of Escherichia coli cytoplasm in which Brownian motion and diffusion arise directly from physical interactions between individual molecules of finite size, density, and physiological abundance. Using our microscopically detailed model, we predicted that physical transport of individual ternary complexes accounts for ~80% of translation elongation latency. We also found that volumetric crowding increases during faster growth even as cytoplasmic mass density remains relatively constant. Despite slowed diffusion, we predicted that improved proximity between ternary complexes and ribosomes wins out, illustrating a simple physics-based mechanism for how individual elongating ribosomes become more productive. We speculate that crowding imposes a physical limit on growth rate and undergirds cellular behavior more broadly. Unfitted colloidal-scale modeling offers systems biology a complementary "physics engine" for exploring how cellular-scale behaviors arise from physical transport and reactions among individual molecules. IMPORTANCE Ribosomes are the factories in cells that synthesize proteins. When cells grow faster, there are not enough ribosomes to keep up with the demand for faster protein synthesis without individual ribosomes becoming more productive. Yet, faster-growing cells are more crowded, seemingly making it harder for each ribosome to do its work. Our computational model of the physics of translation elongation reveals the underlying mechanism for how individual ribosomes become more productive: proximity and stoichiometry of translation molecules overcome crowding. Our model also suggests a universal physical limitation of cell growth rates.

The confined Generalized Stokes-Einstein relation and its consequence on intracellular two-point microrheology.

Two-point microrheology (TPM) is used to infer material properties of complex fluids from the correlated motion of hydrodynamically interacting probes embedded in the medium. The mechanistic connection between probe motion and material properties is propagation of disturbance flows, encoded in current TPM theory for unconfined materials. However, confined media e.g. biological cells and particle-laden droplets, require theory that encodes confinement into the flow propagator (Green's function). To test this idea, we use Confined Stokesian Dynamics simulations to explicitly represent many-body hydrodynamic couplings between colloids and with the enclosing cavity at arbitrary concentration and cavity size. We find that previous TPM theory breaks down in confinement, and we identify and replace the underlying key elements. We put forth a Confined Generalized Stokes-Einstein Relation and report the viscoelastic spectrum. We find that confinement alters particle dynamics and increases viscosity, owing to hydrodynamic and entropic coupling with the cavity. The new theory produces a master curve for all cavity sizes and concentrations and reveals that for colloids larger than 0.005 times the enclosure size, the new model is required.

Vitrification is a spontaneous non-equilibrium transition driven by osmotic pressure.

Persistent dynamics in colloidal glasses suggest the existence of a non-equilibrium driving force for structural relaxation during glassy aging. But the implicit assumption in the literature that colloidal glasses form within the metastable state bypasses the search for a driving force for vitrification and glassy aging and its connection with a metastable state. The natural relation of osmotic pressure to number-density gradients motivates us to investigate the osmotic pressure as this driving force. We use dynamic simulation to quench a polydisperse hard-sphere colloidal liquid into the putative glass region while monitoring structural relaxation and osmotic pressure. Following quenches to various depths in volume fractionϕ(whereϕRCP≈ 0.678 for 7% polydispersity), the osmotic pressure overshoots its metastable value, then decreases with age toward the metastable pressure, driving redistribution of coordination number and interparticle voids that smooths structural heterogeneity with age. For quenches to 0.56 ⩽ϕ⩽ 0.58, accessible post-quench volume redistributes with age, allowing the glass to relax into a strong supercooled liquid and easily reach a metastable state. At higher volume fractions, 0.59 ⩽ϕ< 0.64, this redistribution encounters a barrier that is subsequently overcome by osmotic pressure, allowing the system to relax toward the metastable state. But forϕ⩾ 0.64, the overshoot is small compared to the high metastable pressure; redistribution of volume stops as particles acquire contacts and get stuck, freezing the system far from the metastable state. Overall, the osmotic pressure drives structural rearrangements responsible for both vitrification and glassy age-relaxation. The connection of energy, pressure, and structure identifies the glass transition, 0.63 <ϕg⩽ 0.64. We leverage the connection of osmotic pressure to energy density to put forth the mechanistic view that relaxation of structural heterogeneity in colloidal glasses occurs via individual particle motion driven by osmotic pressure, and is a spontaneous energy minimization process that drives the glass off and back to the metastable state.

Sticky-probe active microrheology: Part 2. The influence of attractions on non-Newtonian flow.

We derive a theoretical framework for the non-Newtonian viscosity of a sticky, attractive colloidal dispersion via active microrheology by modeling detailed microscopic attractive and Brownian forces between particles. Actively forcing a probe distorts the surrounding arrangement of particles from equilibrium; the degree of this distortion is characterized by the Péclet number, Pe≡Fext/(2kT/a), where kT is the thermal energy and a the probe size. Similarly, the strength of attractive interactions relative to Brownian motion is captured by the second virial coefficient, B2. We formulate a Smoluchowski equation governing the pair configuration as it evolves with external and attractive forces. The microviscosity is then computed via non-equilibrium statistical mechanics. For active probe forcing, the familiar hard-sphere boundary-layer and wake structures emerge as Pe grows strong, but attractions alter its shape: changes in relative probe motion arising from its attraction to the bath particles can lead to a high-Pe, strong-attraction flipping of the microstructure, where an upstream depletion boundary layer forms, along with a downstream accumulation wake. This highly distorted structure is analyzed at the micro-mechanical level, where changes in the time spent upstream or downstream from a bath particle lead to hypo- and hyper-viscosity. When attractions are strong, separating the interparticle microviscosity into contributions from attractions and repulsions reveals an attractive undershoot and a repulsive overshoot, as advection grows strong enough to break interparticle bonds downstream and drain the wake. In contrast to linear-response rheology that is predictable entirely by B2 for short-ranged attractions, here the non-Newtonian viscosity is not, owing to the additional length scale introduced by the boundary layer. The ratio of external to attractive forces eventually supersedes B2 as the relevant predictor of structure and rheology. This behavior may provide interesting connections to active motion in biological systems where attractive forces are present.

Toward a nonequilibrium Stokes-Einstein relation via active microrheology of hydrodynamically interacting colloidal dispersions.

We derive a theoretical model for the nonequilibrium stress in a flowing colloidal suspension by tracking the motion of a single embedded probe. While Stokes-Einstein relations connect passive, observable diffusion of a colloidal particle to properties of the suspending medium, they are limited to linear response. Actively forcing a probe through a suspension produces nonequilibrium stress that at steady state can be related directly to observable probe motion utilizing an equation of motion rather than an equation of state, giving a nonequilibrium Stokes-Einstein relation [J. Rheol., 2012, 56, 1175-1208]. Here that freely-draining theory is expanded to account for hydrodynamic interactions. To do so, we construct an effective hydrodynamic resistance tensor, through which the particle flux is projected to give the advective and diffusive components of a Cauchy momentum balance. The resultant phenomenological relation between suspension stress, viscosity and diffusivity is a generalized nonequilibrium Stokes-Einstein relation. The phenomenological model is compared with the statistical mechanics theory for dilute suspensions as well as dynamic simulation at finite concentration which show good agreement, indicating that the suspension stress, viscosity, and force-induced diffusion in a flowing colloidal dispersion can be obtained simply by tracking the motion of a single Brownian probe.

Sticky, active microrheology: Part 1. Linear-response.

Attractive colloidal-scale forces between macromolecules in biological fluids are suspected to play a role in important system dynamics, including association times, spatially heterogeneous viscosity, and anomalous diffusion. Passive and active microrheology provide a natural connection between observable particle motion and viscosity in such systems via generalized Stokes-Einstein and Stokes' drag law relations. While such models are robust for purely repulsive colloidal-scale interactions, no such theory exists to model the effects of attractive forces. Here we present such a model for the linear-response regime, where a Brownian probe particle is driven gently through a complex fluid by an external force that weakly augments thermal fluctuations. As the probe moves through the bath, hard-sphere repulsion results in an accumulation of particles on its upstream face and a trailing depletion zone, producing particle drag that slows the probe. Linear-response viscosity can be inferred constitutively from this speed reduction. One expects attractive forces to make the suspension more viscous, but surprisingly, weak attractions exerted by upstream particles actively pull the probe forward, giving it a "hypoviscous" environment through which it slides more easily. As attractions grow stronger, particles join to the probe in a long-lasting doublet, extracting particles from the upstream region and depositing them behind the probe. At a critical value of the second virial coefficient common to all potentials we studied, the distorted structure reverses direction, and continued growth of attraction strength causes the probe to drag a cluster of density along, dramatically increasing viscosity. But at this transition, the structure is neutral under the balance of attraction and repulsion, allowing the probe to "cloak" itself and move through the bath undetected and unhindered relative to hard-sphere dispersions. This poses an intriguing mechanism by which proteins or other macromolecules may change their surface chemistry in order to alter the viscosity of the surrounding medium to speed their own motion, or simply to pass undetected through a cell.

Physical biology of the cancer cell glycocalyx.

The glycocalyx coating the outside of most cells is a polymer meshwork comprising proteins and complex sugar chains called glycans. From a physical perspective, the glycocalyx has long been considered a simple 'slime' that protects cells from mechanical disruption or against pathogen interactions, but the great complexity of the structure argues for the evolution of more advanced functionality: the glycocalyx serves as the complex physical environment within which cell-surface receptors reside and operate. Recent studies have demonstrated that the glycocalyx can exert thermodynamic and kinetic control over cell signalling by serving as the local medium within which receptors diffuse, assemble and function. The composition and structure of the glycocalyx change markedly with changes in cell state, including transformation. Notably, cancer-specific changes fuel the synthesis of monomeric building blocks and machinery for production of long-chain polymers that alter the physical and chemical structure of the glycocalyx. In this Review, we discuss these changes and their physical consequences on receptor function and emergent cell behaviours.

The impact of probe size on measurements of diffusion in active microrheology.

We present a framework to elucidate the influence of polydispersity on flow-induced diffusion in active microrheology. A colloidal probe particle is driven through a suspension of hydrodynamically interacting background particles, where the probe may be larger or smaller than the bath particles. The thermodynamic size of the particles may be greater than their hydrodynamic size; the hydrodynamic sizes can be identical with thermodynamic sizes that differ, or vice versa, or a combination of both. The diffusive behavior is set entirely and dually by the proximity with which two particles can approach one another, and by the extent to which this minimum approach distance is occupied by the hydrodynamic size of the forced particle. We find that reducing the size of the probe reduces flow-induced diffusion when hydrodynamic interactions are weak but increases flow-induced diffusion when hydrodynamic interactions are strong-regardless of the strength of external forcing. This behavior owes its origins to a rich evolution of the dominance of hydrodynamic and entropic forces with changes in the relative hydrodynamic and thermodynamic sizes of the particles.

Far-from-equilibrium sheared colloidal liquids: disentangling relaxation, advection, and shear-induced diffusion.

Using high-speed confocal microscopy, we measure the particle positions in a colloidal suspension under large-amplitude oscillatory shear. Using the particle positions, we quantify the in situ anisotropy of the pair-correlation function, a measure of the Brownian stress. From these data we find two distinct types of responses as the system crosses over from equilibrium to far-from-equilibrium states. The first is a nonlinear amplitude saturation that arises from shear-induced advection, while the second is a linear frequency saturation due to competition between suspension relaxation and shear rate. In spite of their different underlying mechanisms, we show that all the data can be scaled onto a master curve that spans the equilibrium and far-from-equilibrium regimes, linking small-amplitude oscillatory to continuous shear. This observation illustrates a colloidal analog of the Cox-Merz rule and its microscopic underpinning. Brownian dynamics simulations show that interparticle interactions are sufficient for generating both experimentally observed saturations.