Session P18: Mechanics and Non-linear Rheology of Soft Gels II

Salt effects on the sol-gel transitions of aqueous peptide-amphiphile solutions

A hydrogel made of a peptide amphiphile (PA) is an interesting soft material especially in the biomedical fields due to its controllable nanoscale structures with excellent biocompatibility. To extend the practical use of PA, a comprehensive study of the sol-gel transitions of PA is necessary to be used as e.g. a biomedical material. The effects of the types of salts in our body or in medicinal agents on the physical properties of the PA solution are not fully understood. In this study, different types of salt with various negative ions were added to a PA (C16-W3K) solution. The salt effects on the rheological properties, the pH, and the zeta potentials of the PA solutions were studied. From the rheological testing, it was found that the C16-W3K solutions could not gelate in the presence of Na$_{\mathrm{2}}$CO$_{\mathrm{3}}$ or Na$_{\mathrm{3}}$PO$_{\mathrm{4}}$, which could be caused by the aggregation of the wormlike micelles made of C16-W3K. pH-wise, the sol-gel transitions could be observed only when the PA solutions were relatively acidic (the Zeta potential was positive) instead of basic (the Zeta potential was very negative) . It was therefore concluded that the sol-gel transitions of the PA solution could be effectively controlled by the types of salt.   

Effect of depletant dispersity on clustering and gelation of model charged colloids

Depletion interactions are commonly used to induce well-controlled attractions between colloids. The range and strength of this attraction are controlled by the size and concentration of the depletant, respectively. In earlier theoretical studies, both the range and strength of attraction could change dramatically when the depletant was not uniform in size, resulting in shifts in phase boundaries. Nonetheless, the role of dispersity on the phase behavior of colloidal suspensions remains poorly understood, with previous studies showing conflicting results. Here, we experimentally explore the effect of depletant dispersity on clustering and gelation of charged poly(methyl methacrylate) particles using unary and binary mixtures of polystyrene. When the concentration of polymer in mixtures was represented as a sum of the normalized concentrations of each polymer species, the non-equilibrium phase behavior was largely independent of polymer size and dispersity for short-ranged attractions. Disparities between sample sets with unary or binary mixtures of depletant were found near the transition from a fluid of clusters to a gel, and in a region of reentrant melting of repulsively caged particles due to short-ranged attractions.   

Swelling, Structure, and Phase Stability of Soft, Compressible Microgels

Microgels are soft colloidal particles that swell when dispersed in a solvent. The equilibrium particle size is governed by a delicate balance of osmotic pressures, which can be tuned by varying single-particle properties and externally controlled conditions, such as temperature, pH, ionic strength, and concentration. Because of their tunable size and ability to encapsulate dye or drug molecules, microgels have practical relevance for biosensing, drug delivery, carbon capture, and filtration. Using Monte Carlo simulation, we model suspensions of microgels that interact via Hertzian elastic interparticle forces and can expand or contract via trial size changes governed by the Flory–Rehner free energy of cross-linked polymer gels. We analyze the influence of particle compressibility and size fluctuations on bulk structural and thermal properties by computing swelling ratios, radial distribution functions, static structure factors, osmotic pressures, and freezing densities. With increasing density, microgels progressively deswell and their intrinsic polydispersity broadens, while compressibility acts to forestall crystallization*. \\[1ex] *M. Urich and A. R. Denton, {\it Soft Matter} {\bf 12}, 9086 (2016). \\A. R. Denton and Q. Tang, {\it J. Chem. Phys.} {\bf 145}, 164901 (2016).   

Modeling non-linear micromechanics of hydrogels using dissipative particle dynamics

In response to an appropriate external stimulus microgels are capable of undergoing large and reversible changes in volume (10-20 times) which has made them attractive as microscopic actuators and drug delivery agents. However, the mechanics of microgels is not well understood in part due to inhomogeneities within the network. Full-scale atomistic modeling of micrometer-sized gel networks is currently not possible due to the large length and time scales involved. We develop a mesoscale model based on dissipative particle dynamics to examine the mechanics of microgels in solvent. By varying the osmotic pressure of the gels we probe the changes in bulk modulus for different values of the Flory-Huggins parameter. We examine how the bulk modulus depends on inhomogeneities we introduce within the gel structure by altering the crosslink density and by embedding rigid nanoparticles.   

Correlated rigidity percolation and gelation of colloidal particles

Rigidity percolation on a lattice with sites or bonds randomly diluted is controlled by the isostatic point, where the degrees of freedom and constraints balance, and the system is at the verge of mechanical instability. In the case of triangular lattice rigidity percolation occurs very close to $p=2/3$ as predicted from isostaticity. Interestingly, we found that when the site dilution is correlated, this transition occurs at a lower $p$, meaning that less “material” is needed for rigidity in the disordered structure. This correlation may be seen as a consequence of short range attraction between the particles which makes them cluster. We characterized critical scaling associated with the site correlation parameter, and will discuss implication to understand experimental systems such as gelation of colloidal particles.   

Nonlinear viscoelasticity and generalized failure criterion for polymer gels

Polymer gels display a multiscale microstructure that is responsible for their solid-like properties. Upon external deformation, these soft viscoelastic solids exhibit a generic nonlinear mechanical response characterized by pronounced stress- or strain-stiffening prior to irreversible damage and failure, most often through macroscopic fractures. Here we show on an acid-induced protein gel that the nonlinear viscoelastic properties of the gel can be described in terms of a ``damping function" which predicts the gel mechanical response quantitatively up to the onset of macroscopic failure. Using a nonlinear integral constitutive equation built upon the experimentally-measured damping function in conjunction with power-law linear viscoelastic response, we derive the form of the stress growth in the gel following the start up of steady shear. We further couple the shear stress response with Bailey's durability criteria for brittle solids in order to predict the critical values of the stress $\sigma_c$ and strain $\gamma_c$ for failure of the gel, and how they scale with the applied shear rate. Our work provides a consistent framework to describe the failure of polymer gels in a range of different deformation histories explored under external applied shear rate or shear stress.   

Understanding the mechanical properties of cement in terms of its early-stage gelation

Despite the nearly ubiquitous use of concrete as a construction material, cement hydration is still poorly understood. The variety of hydration products, the non-uniform rate of reaction, and the changing chemical background all contribute to making this a complex process. Recently, a novel statistical physics approach combining Grand Canonical Monte Carlo with molecular dynamics has achieved remarkable correspondence with experimental data. It treats the main hydration product, Calcium Silicate Hydrates (C-S-H), as colloidal particles with a simple effective interaction that varies with the degree of hydration---due to changing ph, ion concentration, etc. Working with this model, I investigate the percolation of the gel structure and the onset of mechanical properties in the early stages of hydration, which end up affecting the material properties at much later times. In particular, I have studied how the tendency of C-S-H to form at the surface of cement grains may affect the gel morphology, its structural heterogeneity, and ultimately its mechanical strength. By varying the effective interaction potential between C-S-H particles, I can rationalize the interplay between the evolution of the gel morphology and the changing physicochemical environment in which the gel forms.   

Failure of cement hydrates: freeze-thaw and fracture

Mechanical and viscoelastic behavior of concrete crucially depends on cement hydrates, the ``glue'' of cement. Even more than the atomistic structure, the mesoscale amorphous texture of cement hydrates over hundreds of nanometers plays a crucial role for material properties. We use simulations that combine information of the nano-scale building units of cement hydrates and on their effective interactions, obtained from atomistic simulations and experiments, into a statistical physics framework for aggregating nanoparticles.Our mesoscale model was able to reconcile different experimental results ranging from small-angle neutron scattering, SEM, adsorption/desorption of N$_{2}$, and water to nanoindentation and gain the new fundamental insights into the microscopic origin of the properties measured [1]. Our results suggest that heterogeneities developed during the early stages of hydration persist in the structure of C-S-H, impacting the rheological and mechanical performance of the hardened cement paste. In this talk I discuss recent investigation on failure mechanism at the mesoscale of hardened cement paste such as freeze-thaw and fracture. Using correlations between local volume fractions and local stress we provide a link between structural and mechanical heterogeneities during the failure mechanisms. 1. Ioannidou K. et al, The mesoscale texture of cement hydrates, Proceedings of National Academy of Science USA, 113 (8), 2029-2034 (2016)   

Surface Friction of Polyacrylamide Hydrogel Particles

Polyacrylamide hydrogel particles have recently become a popular system for modeling low-friction, granular materials near the jamming transition. Because a gel consists of a polymer network filled with solvent, its frictional behavior is often explained using a combination of hydrodynamic lubrication and polymer-surface interactions. As a result, the frictional coefficient can vary between 0.001 and 0.03 depending on several factors such as contact area, sliding velocity, normal force, and the gel surface chemistry. Most tribological measurements of hydrogels utilize two flat surfaces, where the contact area is not well-defined. We have built a custom, low-force tribometer to measure the single-contact frictional properties of spherical hydrogel particles on flat hydrogel surfaces under a variety of measurement conditions. At high velocities ($\textgreater$ 1 cm/s), the friction coefficient depends linearly on velocity, but does not tend to zero at zero velocity. We also compare our measurements to solid particles (steel, glass, etc.) on hydrogel surfaces, which exhibit larger frictional forces, and show less dependence on velocity. A physical model for the friction which includes the lubrication layer between the deformed surfaces will be discussed.   

Rheological and tribological study of complex soft gels containing polymer, phospholipids, oil, and water

Oil-in-water emulsions with polymers are widely used for personal care products. Since the accumulation of traditional surfactants on the skin can promote irritation, an alternative is the use of hydrogenated phosphatidylcholine (HPC), a phospholipid that can form a lamellar structure similar to the skin barrier. This research aims to investigate the effect of composition on the rheological and tribological characteristics in complex systems containing HPC. For tribology experiments we used a soft model contacts made of polydimethylsiloxane (PDMS), while for bulk rheology studies we used dynamic and steady shear experiments. We examine how the addition of polymer, HPC and oil affects friction coefficients, lubrication regimes, viscoelasticity, yield stress, and gel formation. The bulk rheology shows that the studied systems are shear thinning and have gel-like behavior. The effect of each component was investigated by going from simple to more complex systems. The Stribeck curves obtained are related to the bulk rheology results to obtain physical insights into these complex systems. The results suggest that the polymer and phospholipids are being adsorbed onto the PDMS surface, reducing the friction coefficient at lower entrainment speeds.   

Effect of Geometry on Cavitation in Polymeric Gels

Pressurization of a defect in a soft elastic network results in elastic instability or cavitation. This phenomenon has been harnessed in developing cavitation rheology technique for probing local mechanical properties of soft polymeric gels. The Finite Element Analysis (FEA) of the cavitation process both in bulk sample and in cavitation geometry is presented here. The critical pressure for cavitation as a function of the elastocapillary number (ECN), which relates the elastic modulus of the material, the dimension of the initial flaw, and surface energy, have been captured. The system boundary has an effect on the cavitation and the critical pressure increases significantly for a confined geometry, i.e., for the case where the boundary is closer to the initial crack. Effect of solvent diffusion on the cavitation phenomena will also be presented. The modeling results will be compared with that obtained experimentally for pluronic gels.   

Embedding memories in colloidal gels though oscillatory shear

While gels are ubiquitous in applications from food products to filtration, their mechanical properties are usually determined by self-assembly. We use oscillatory shear to train colloidal gels, embedding memories of the training protocol in rheological responses such as the yield strain and the gel network structures. When our gels undergo shear, the particles are forced to rearrange until they organize into structures that can locally undergo reversible shear cycles. We utilize a high-speed confocal microscope and a shear cell to image a colloidal gel while simultaneously straining the gel and measuring its shear stresses. By comparing stroboscopic images of the gel, we quantify the decrease in particle rearrangement as the gel develops reversible structures. We analyze and construct a model for the rates at which different regions in the gel approach reversible configurations. Through characterizing the gel network, we determine the structural origins of these shear training memories in gels. These results may allow us to use shear training protocols to produce gels with controllable yield strains and to better understand changes in the microstructure and rheology of gels that undergo repeated shear through mixing or flowing.   

Theory of the Thermal Diffusion of Microgel Particles in Highly Compressed Suspensions

One amazing property of microgel colloids is the ability of the particles to thermally diffuse, even when they are compressed to a volume well below their swollen state volume, despite the fact that they are surrounded by and pressed against other particles. A glass transition is expected to occur when the colloid is sufficiently compressed for diffusion to cease. It is proposed that the diffusion is due to the ability of the highly compressed particles to change shape with little cost in free energy. It will be shown that most of the free energy required to compress microgel particles is due to osmotic pressure resulting from either counterions or monomers inside of the gel, which depends on the particle's volume. There is still, however, a cost in free energy due to polymer elasticity when particles undergo the distortions necessary for them to move around each other as they diffuse through the compressed colloid, even if it occurs at constant volume. Using a scaling theory based on simple models for the linking of polymers belonging to the microgel particles, we examine the conditions under which the cost in free energy needed for a particle to diffuse is smaller than or comparable to thermal energy, which is a necessary condition for particle diffusion. Based on our scaling theory, we predict that thermally activated diffusion should be possible when the mean number of links along the axis along which a distortion occurs is much larger than $N^{1/5}$, where $N $is the mean number of monomers in a polymer chain connecting two links in the gel.$^{\, \, }$