Dynamics and Rheology of Soft Colloidal Glasses

Interfacial Pressure and Viscoelasticity of Antibodies and Their Correlation to Long-Term Stability in Formulation

Monoclonal antibodies (mAbs) form viscoelastic gel-like layers at the air-water interface due to their amphiphilic nature, and this same protein characteristic can lead to undesired aggregation of proteins in therapeutic formulations. We hypothesize that the interfacial viscoelasticity and surface pressure of mAbs at the air-water interface will correlate with their long-term stability. To test this hypothesis, the interfacial viscoelastic rheology and surface pressure of five different antibodies with varying visible particle counts from a three-year stability study were measured. We find that both the surface pressures and interfacial elastic moduli correlate well with the long-time mAb solution stability within a class of mAbs with the interfacial elastic moduli being particularly sensitive to discriminate between stable and unstable mAbs across a range of formulations. Furthermore, X-ray reflectivity was used to gain insight into the interfacial structure of mAbs at the air-water interface, providing a possible molecular mechanism to explain the relationship between interfacial elastic moduli and the long-term stability.

Interpenetration of fractal clusters drives elasticity in colloidal gels formed upon flow cessation

Colloidal gels are out-of-equilibrium soft solids composed of attractive Brownian particles that form a space-spanning network at low volume fractions. The elastic properties of these systems result from the network microstructure, which is very sensitive to shear history. Here, we take advantage of such sensitivity to tune the viscoelastic properties of a colloidal gel made of carbon black nanoparticles. Starting from a fluidized state at an applied shear rate ₀, we use an abrupt flow cessation to trigger a liquid-to-solid transition. We observe that the resulting gel is all the more elastic when the shear rate ₀ is low and that the viscoelastic spectra can be mapped on a master curve. Moreover, coupling rheometry to small angle X-ray scattering allows us to show that the gel microstructure is different from gels solely formed by thermal agitation where only two length scales are observed: the dimension of the colloidal and the dimension of the fractal aggregates. Competition between shear and thermal energy leads to gels with three characteristic length scales. Such gels structure in a percolated network of fractal clusters that interpenetrate each other. Experiments on gels prepared with various shear histories reveal that cluster interpenetration increases with decreasing values of the shear rate ₀ applied before flow cessation. These observations strongly suggest that cluster interpenetration drives the gel elasticity, which we confirm using a structural model. Our results, which are in stark contrast to previous literature, where gel elasticity was either linked to cluster connectivity or to bending modes, highlight a novel local parameter controlling the macroscopic viscoelastic properties of colloidal gels.

Rheological Response of Polylactic Acid Dispersions in Water with Xanthan Gum

In this work, the rheological behavior of stable poly(lactic acid) (PLA) dispersions in water, intended for coating applications, was investigated. The newly prepared dispersion consists of PLA particles with an average diameter of 222 ± 2 nm based on dynamic light scattering (DLS) and scanning electron microscopy (SEM) analyses, at concentrations varying in the 5-22 wt % range. Xanthan gum (XG), a bacterial polysaccharide, was used as a thickening agent to modulate the viscosity of the formulations. The rheological properties of the PLA dispersions with different XG and PLA contents were studied in steady shear, amplitude sweep, and frequency sweep experiments. Under steady shear conditions, the viscosity of all the formulations showed a shear-thinning behavior similar to XG solutions in the whole investigated 1-1000 s^-1 range, with values dependent on both PLA particles and XG concentrations. Amplitude and frequency sweep data revealed a weak-gel behavior except in the case of the most diluted sample, with moduli dependent on both PLA and XG contents. A unified scaling parameter was identified in the volume fraction (ϕ) of the PLA particles, calculated by considering the dependence of the continuous phase density on the XG concentration. Accordingly, a master curve at different volume fractions was built using the time-concentration-superposition approach. The master curve describes the rheological response of the system over a wider frequency window than the experimentally accessible one and reveals the presence of a superimposed β relaxation process in the high-frequency region.

Softness mapping of the concentration dependence of the dynamics in model soft colloidal systems

The dynamics of a series of soft colloids comprised of polystyrene cores with poly(N-isopropylacrylamide) (PNIPAM) coronas was investigated by diffusing wave spectroscopy (DWS). The modulus of the coronas was varied by changing the cross-link density and we were able to interpret the results within a hard-soft mapping framework. The soft, swellable particle properties were modeled using an extended Flory-Rehner theory and a Hertzian pair potential. Following volume fraction jumps, softness effects on the concentration dependence of dynamics were determined, with a 'soft colloids make strong glass-forming liquid'-type of behavior observed close to the nominal glass transition volume fraction, φ_g. Such behavior from the current systems cannot be fully explained by the osmotic deswelling model alone. However, inspired by the soft-hard mapping from Schmiedeberg et al, [Europhys. Lett. 2011, 96(3), 36010] we estimated effective hard-sphere diameters and achieved a successful mapping of the α-relaxation times to a master curve below φ_g. Above φ_g, the curves no longer collapse but show strong deviations from a Vogel-Fulcher type of divergence onto soft jamming plateaux. Our results provide evidence that osmotic deswelling itself cannot fully explain the observed dynamics. Softness also plays an important role in the dynamics of soft, concentrated colloids.

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(whereϕ_RCP≈ 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 <ϕ_g⩽ 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.

Signatures of Overaging in an Aqueous Dispersion of Carbopol

In this work, we study the effect of the deformation field on the physical aging behavior of an aqueous Carbopol dispersion. It is composed of soft swollen particles of gel that get deformed and acquire a polygonal shape, with flat interfaces rendering the dispersion a soft solid-like consistency as filled volume fraction approaches unity. It has been proposed that owing to release of stored elastic energy in the deformed particles, Carbopol dispersion undergoes microstructural evolution that is reminiscent of physical aging in soft glassy materials. We observe that application of moderate magnitude of oscillatory strain to Carbopol dispersion slows down its relaxation dynamics, thereby showing characteristics of overaging. On the other hand, the sufficiently high magnitude of strain makes the relaxation dynamics faster, causing rejuvenation. We also solve the soft glassy rheology model, which, when subjected to the same flow field, corroborates with experimental observations on the Carbopol dispersion. This behavior, therefore, suggests that in a system of jammed soft particles of Carbopol, the particles occupying shallow energy wells upon application of moderate strain field adjust themselves in such a manner that they predominantly occupy the deeper energy wells leading to observe the overaging dynamics.

Observation of soft glassy behavior in a magnetic colloid exposed to an external magnetic field

We provide the first experimental evidence for soft glassy behavior in a sterically stabilized magnetic colloid (ferrofluid) of relatively low volume fraction (φ = 0.037) when a uniform magnetic field is applied at a sufficiently high rate (fast quench). Fast magnetic-field quenches favor structural arrest of field-induced aggregates, owing to insufficient time to settle into lower energy states, thereby pushing the system to a frustrated metastable configuration like a repulsive glass. Brownian dynamics simulations are used to show that the polydisperse ferrofluid (as in experiments) forms thick ropes aligned along the field direction, while a monodisperse ferrofluid does not. The simulations show that there is practically no ordering of the thin, monodisperse chains, while the thick, polydisperse ropes show positional ordering with a typical center-center separation between the particles in different ropes of about 0.39 μm. As a consequence of structural arrest, the ferrofluid exhibits aging with broken time-translational invariance, a hallmark of glassy dynamics. The superposition of strain and creep compliance curves obtained from rheological measurements at different waiting times in the effective time domain corroborates the soft glassy behavior when exposed to a magnetic field applied at a fast ramp rate.

Correlation of droplet elasticity and volume fraction effects on emulsion dynamics

The rheological properties of emulsions are of considerable importance in a diverse range of scenarios. Here we describe a superposition of the effects of droplet elasticity and volume fraction on the dynamics of emulsions. The superposition is governed by physical interactions between droplets, and provides a new mechanism for modifying the flow behavior of emulsions, by controlling the elasticity of the dispersed phase. We investigate the properties of suspensions of emulsified wormlike micelles (WLM). Dense suspensions of the emulsified WLM droplets exhibit thermally responsive properties in which the viscoelastic moduli decrease by an order of magnitude over a temperature range of 0 °C to 25 °C. Surprisingly, the dependence of modulus on volume fraction is independent of droplet stiffness. Instead, the emulsion modulus scales as a power-law with volume fraction with a constant exponent across all temperatures even as the droplet properties change from elastic to viscous. Nevertheless, the underlying droplet dynamics depend strongly on temperature. From stress relaxation experiments, we quantify droplet dynamics across the cage breaking time scale below which the droplets are locally caged by neighbors and above which the droplets escape their cages to fully relax. For elastic droplets and high volume fractions, droplets relax less stress on short time scales and the terminal relaxations are slower than for viscous droplets and lower volume fractions. Characteristic measures of the short and long-time dynamics are highly correlated for variations in both temperature and emulsion concentration, suggesting that thermal and volume fraction effects represent independent parameters to control emulsion properties.

Physical aging and compressed exponential behaviors in a model soft colloidal system

Diffusing wave spectroscopy (DWS)-based micro-rheology has been used in different optical geometries (backscattering and transmission) as well as different sample thicknesses in order to probe system dynamics at different length scales [D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer. J. Phys., 1990, 51(18), 2101-2127]. Previous study from this lab [Q. Li, X. Peng, G. B. McKenna. Soft Matter, 2017, 13(7), 1396-1404] indicates the DWS-based micro-rheology observes the system non-equilibrium behaviors differently from macro-rheology. The object of the present work was to further explore the non-equilibrium dynamics and to address the range of utility of DWS as a micro-rheological method. A thermo-sensitive core-shell colloidal system was investigated both during aging and subsequent to aging into a metastable equilibrium state using temperature-jump induced volume fraction-jump experiments. We find that in the non-equilibrium state, significant differences in the measured dynamics are observed for the different geometries and length scales. Compressed exponential relaxations for the autocorrelation function g2(t) were observed for large length scales. However, upon converting the g2(t) data to the mean square displacement (MSD), such differences with length scale diminished and the long-time MSD behavior was consistent with diffusive behavior. These observations in the non-equilibrium behaviors for different length scales leads to questioning of some interpretations in the current field of light scattering-based micro-rheology and provides a possibility to interrogate the aging mechanisms in colloidal glasses from a broader perspective than normally considered in measurements of g2(t) using DWS-based micro-rheology.

Segmental and secondary dynamics of nanoparticle-grafted oligomers

The local segmental and secondary dynamics of tetramethylene oxide oligomer grafted to silica nanoparticles (NPs) were investigated as a function of grafting density and molecular weight. Grafting slows the segmental (α) dynamics, but gives rise to faster secondary (β) motions. Interestingly, the magnitude of these effects decreases with the extent of grafting (i.e., surface coverage), as well as with oligomer molecular weight. The disparity in dynamical effects reflects the decoupling of the segmental and more local β dynamics, the former is associated with stronger dynamic correlations that extend over a greater spatial range. This results in greater sensitivity to interactions, including tethering of the chains to the NP surface.

Long-term aging behaviors in a model soft colloidal system

Colloidal and molecular systems share similar behaviors near to the glass transition volume fraction or temperature. Here, aging behaviors after volume fraction up-jump (induced by performing temperature down-jumps) conditions for a PS-PNIPAM/AA soft colloidal system were investigated using light scattering (diffusing wave spectroscopy, DWS). Both aging responses and equilibrium dynamics were investigated. For the aging responses, long-term experiments (100 000 s) were performed, and both equilibrium and non-equilibrium behaviors of the system were obtained. In the equilibrium state, as effective volume fraction increases (or temperature decreases), the colloidal dispersion displays a transition from the liquid to a glassy state. The equilibrium α-relaxation dynamics strongly depend on both the effective volume fraction and the initial mass concentration for the studied colloidal systems. Compared with prior results from our lab [X. Di, X. Peng and G. B. McKenna, J. Chem. Phys., 2014, 140, 054903], the effective volume fractions investigated spanned a wider range, to deeper into the glassy domain. The results show that the α-relaxation time τ_α of the samples aged into equilibrium deviate from the classical Vogel-Fulcher-Tammann (VFT)-type expectations and the super-Arrhenius signature disappears above the glass transition volume fraction. The non-equilibrium aging response shows that the time for the structural evolution into equilibrium and the α-relaxation time are decoupled. The DWS investigation of the aging behavior after different volume fraction jumps reveals a different non-equilibrium or aging behavior for the considered colloidal systems compared with either molecular glasses or the macroscopic rheology of a similar colloidal dispersions.

Interfacial Particle Dynamics: One and Two Step Yielding in Colloidal Glass

The yielding behavior of silica nanoparticles partitioned at an air-aqueous interface is reported. Linear viscoelasticity of the particle-laden interface can be retrieved via a time-dependent and electrolyte-dependent superposition, and the applicability of the "soft glassy rheology" (SGR) model is confirmed. With increasing electrolyte concentration (φ^elect) in the aqueous subphase, a nonergodic state is achieved with particle dynamics arrested first from attraction induced bonding bridges and then from the cage effect of particle jamming, manifesting in a two-step yielding process under large amplitude oscillation strain (LAOS). The Lissajous curves disclose a shear-induced in-cage particle redisplacement within oscillation cycles between the two yielding steps, exhibiting a "strain softening" transitioning to "strain stiffening" as the interparticle attraction increases. By varying φ^elect and the particle spreading concentration, φ^SiO₂, a variety of phase transitions from fluid- to gel- and glass-like can be unified to construct a state diagram mapping the yielding behaviors from one-step to two-step before finally exhibiting one-step yielding at high φ^elect and φ^SiO₂.