Syneresis of Colloidal Gels: Endogenous Stress and Interfacial Mobility Drive Compaction.

Colloidal gels may experience syneresis, an increase in volume fraction through expulsion of the continuous phase. This poroelastic process occurs when adhesion to the container is weak compared to endogenous stresses which develop during gelation. In this work, we measure the magnitude of syneresis, ΔV/V_{0}, for gels composed of solid, rubber, and liquid particles. Surprisingly, despite a constant thermoresponsive interparticle potential, gels composed of liquid and elastic particles synerese to a far greater extent. We conclude that this magnitude difference arises from contrasting modes of stress relaxation within the colloidal gel during syneresis either by bending or stretching of interparticle bonds.

Development of a multi-position indentation setup: Mapping soft and patternable heterogeneously crosslinked polymer networks.

We present the development of a multi-position indentation setup capable of spatially mapping mechanically heterogeneous materials. A detailed description of the indentation instrumentation is first provided, emphasizing force sensitivity, noise reduction, and signal fidelity. We first present indentation experiments on soft hydrogels that are submerged in water and show how the large contributions to the measured force due to the air-water surface tension can be avoided. The displacement field of the indented hydrogel is visualized using fluorescently coated microspheres embedded in the hydrogel, allowing simultaneous mapping of the stress and strain fields for a soft polymer network. We then fabricate a polymer network with patterned elasticity using halftone UV lithography and map the elastic modulus with the multi-position indentation instrument. The applied UV pattern is found back in the measured elastic modulus map, showing the capability of the multi-position indentation setup to map mechanically heterogeneous polymer networks.

Self-assembly of oppositely charged polyelectrolyte block copolymers containing short thermoresponsive blocks.

The assembly of oppositely charged block copolymers, containing small thermoresponsive moieties, was investigated as a function of salt concentration and temperature. Aqueous solutions of poly-[N-isopropylacrylamide]-b-poly[dimethylaminoethyl methacrylate] (NIPAM44-b-DMAEMA216) and PNIPAM-b-poly[acrylic acid]-b-PNIPAM (NIPAM35-b-AA200-b-NIPAM35) were mixed in equal charge stoichiometry, and analysed by light scattering (LS), NMR spectroscopy and small angle X-ray scattering (SAXS). At room temperature, two different micelle morphologies were found at different salt concentrations. At NaCl concentrations below 0.75 M, complex coacervate core micelles (C3M) with a PNIPAM corona were formed as a result of interpolyelectrolyte complexation. At NaCl concentrations exceeding 0.75 M, the C3M micelles inverted into PNIPAM cored micelles (PCM), containing a water soluble polyelectrolyte corona. This behavior is ascribed to the salt concentration dependence of both the lower critical solution temperature (LCST) of PNIPAM, and the complex coacervation. Above 0.75 M NaCl, the PNIPAM blocks are insoluble in water at room temperature, while complexation between the polyelectrolytes is prevented because of charge screening by the salt. Upon increasing the temperature, both types of micelles display a cloud point temperature (T cp), despite the small thermoresponsive blocks, and aggregate into hydrogels. These hydrogels consist of a complexed polyelectrolyte matrix with microphase separated PNIPAM domains. Controlling the morphology and aggregation of temperature sensitive polyelectrolytes can be an important tool for drug delivery systems, or the application and hardening of underwater glues.

A Hybrid Monte Carlo Self-Consistent Field Model of Physical Gels of Telechelic Polymers.

We developed a hybrid Monte Carlo self-consistent field technique to model physical gels composed of ABA triblock copolymers and gain insight into the structure and interactions in such gels. The associative A blocks of the polymers are confined to small volumes called nodes, while the B block can move freely as long as it is connected to the A blocks. A Monte Carlo algorithm is used to sample the node configurations on a lattice, and Scheutjens-Fleer self-consistent field (SF-SCF) equations are used to determine the change in free energy. The advantage of this approach over more coarse grained methods is that we do not need to predefine an interaction potential between the nodes. Using this MC-SCF hybrid simulation, we determined the radial distribution functions of the nodes and structure factors and osmotic compressibilities of the gels. For a high number of polymers per node and a solvent-B Flory-Huggins interaction parameter of 0.5, phase separation is predicted. Because of limitations in the simulation volume, we did however not establish the full phase diagram. For comparison, we performed some coarse-grained MC simulations in which the nodes are modeled as single particles with pair potentials extracted from SF-SCF calculations. At intermediate concentrations, these simulations gave qualitatively similar results as the MC-SCF hybrid. However, at relatively low and high polymer volume fractions, the structure of the coarse-grained gels is significantly different because higher-order interactions between the nodes are not accounted for. Finally, we compare the predictions of the MC-SCF simulations with experimental and modeling data on telechelic polymer networks from literature.

Hydrodynamically Coupled Brownian Dynamics: A coarse-grain particle-based Brownian dynamics technique with hydrodynamic interactions for modeling self-developing flow of polymer solutions.

We present a novel coarse-grain particle-based simulation technique for modeling self-developing flow of dilute and semi-dilute polymer solutions. The central idea in this paper is the two-way coupling between a mesoscopic polymer model and a phenomenological fluid model. As our polymer model, we choose Responsive Particle Dynamics (RaPiD), a Brownian dynamics method, which formulates the so-called "conservative" and "transient" pair-potentials through which the polymers interact besides experiencing random forces in accordance with the fluctuation dissipation theorem. In addition to these interactions, our polymer blobs are also influenced by the background solvent velocity field, which we calculate by solving the Navier-Stokes equation discretized on a moving grid of fluid blobs using the Smoothed Particle Hydrodynamics (SPH) technique. While the polymers experience this frictional force opposing their motion relative to the background flow field, our fluid blobs also in turn are influenced by the motion of the polymers through an interaction term. This makes our technique a two-way coupling algorithm. We have constructed this interaction term in such a way that momentum is conserved locally, thereby preserving long range hydrodynamics. Furthermore, we have derived pairwise fluctuation terms for the velocities of the fluid blobs using the Fokker-Planck equation, which have been alternatively derived using the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) approach in Smoothed Dissipative Particle Dynamics (SDPD) literature. These velocity fluctuations for the fluid may be incorporated into the velocity updates for our fluid blobs to obtain a thermodynamically consistent distribution of velocities. In cases where these fluctuations are insignificant, however, these additional terms may well be dropped out as they are in a standard SPH simulation. We have applied our technique to study the rheology of two different concentrations of our model linear polymer solutions. The results show that the polymers and the fluid are coupled very well with each other, showing no lag between their velocities. Furthermore, our results show non-Newtonian shear thinning and the characteristic flattening of the Poiseuille flow profile typically observed for polymer solutions.

Coarse-grained simulations for flow of complex soft matter fluids in the bulk and in the presence of solid interfaces.

We present a coarse-grained particle-based simulation technique for modeling flow of complex soft matter fluids such as polymer solutions in the presence of solid interfaces. In our coarse-grained description of the system, we track the motion of polymer molecules using their centers-of-mass as our coarse-grain co-ordinates and also keep track of another set of variables that describe the background flow field. The coarse-grain motion is thus influenced not only by the interactions based on appropriate potentials used to model the particular polymer system of interest and the random kicks associated with thermal fluctuations, but also by the motion of the background fluid. In order to couple the motion of the coarse-grain co-ordinates with the background fluid motion, we use a Galilean invariant, first order Brownian dynamics algorithm developed by Padding and Briels [J. Chem. Phys. 141, 244108 (2014)], which on the one hand draws inspiration from smoothed particle hydrodynamics in a way that the motion of the background fluid is efficiently calculated based on a discretization of the Navier-Stokes equation at the positions of the coarse-grain coordinates where it is actually needed, but also differs from it because of the inclusion of thermal fluctuations by having momentum-conserving pairwise stochastic updates. In this paper, we make a few modifications to this algorithm and introduce a new parameter, viz., a friction coefficient associated with the background fluid, and analyze the relationship of the model parameters with the dynamic properties of the system. We also test this algorithm for flow in the presence of solid interfaces to show that appropriate boundary conditions can be imposed at solid-fluid interfaces by using artificial particles embedded in the solid walls which offer friction to the real fluid particles in the vicinity of the wall. We have tested our method using a model system of a star polymer solution at the overlap concentration.

Multiple relaxation modes in associative polymer networks with varying connectivity.

The dynamics and mechanics of networks depend sensitively on their spatial connectivity. To explore the effect of connectivity on local network dynamics, we prepare transient polymer networks in which we systematically cut connecting bonds. We do this by creating networks formed from hydrophobically modified difunctionalized polyethylene glycol chains. These form physical gels, consisting of flowerlike micelles that are transiently cross-linked by connecting bridges. By introducing monofunctionalized chains, we can systematically reduce the number of bonds between micelles and thus lower the network connectivity, which strongly reduces the network elasticity and relaxation time. Dynamic light scattering reveals a complex relaxation dynamics that are not apparent in bulk rheology. We observe three distinct relaxation modes. First we find a fast diffusive mode that does not depend on the number of bridges and is attributed to the diffusion of micelles within a cage formed by neighboring micelles. A second, intermediate mode depends strongly on network connectivity but surprisingly is independent of the scattering vector q. We attribute this viscoelastic mode to fluctuations in local connectivity of the network. The third, slowest mode is also diffusive and is attributed to the diffusion of micelle clusters through the viscoelastic matrix. These results shed light on the microscopic dynamics in weakly interconnected transient networks.

Interactions between nodes in a physical gel network of telechelic polymers; self-consistent field calculations beyond the cell model.

Triblock copolymers, with associative end-groups and a soluble middle block, form flower-like micelles in dilute solutions and a physical gel at higher concentrations. In a gel the middle blocks form bridges between domains/nodes that contain the ends. We combine the self-consistent field theory with a simple molecular model to evaluate the pair potential between the nodes. In this model the end-groups are forced to remain in nodes and the soluble middle blocks are in solution. When the distance between the centres of the nodes is approximately the corona diameter, loops can transform into bridges, and the pair potential is attractive. Due to steric hindrance, the interaction is repulsive at smaller distances. Till now a cell-model has been used wherein a central node interacts through reflecting boundary conditions with its images in a spherical geometry. This artificial approach to estimate pair potentials is here complemented by more realistic three-gradient SCF models. We consider the pair interactions for (i) two isolated nodes, (ii) nodes positioned on a line (iii) a central node surrounded by its neighbours in simple cubic ordering, and (iv) a central node in a face centred cubic configuration of its neighbours. Qualitatively, the cell model is in line with the more refined models, but quantitative differences are significant. We also notice qualitative differences for the pair potentials in the specified geometries, which we interpret as a breakdown of the pairwise additivity of the pair potential. This implies that for course grained Monte Carlo or molecular dynamics simulations the best choice for the pair potentials depends on the expected node density.

Hybrid Monte Carlo self-consistent field approach to model a thin layer of a polyelectrolyte gel near an adsorbing surface.

The use of thin layers of a surface bound (polyelectrolyte) hydrogels for measuring the concentration of metal ions from electrolyte solutions is our motivation for modeling such hydrogels. The gels are composed of polymeric species with conformational degrees of freedom on the nanometer scale. The polymer conformations are affected by the presence of cross-links in the gel on a five to ten times larger length scale, and the repulsive interactions generated by the charges along the chains. Here we present a hybrid computational Monte Carlo Self-consistent field (MC-SCF) approach to model such hydrogels. The SCF formalism is used to evaluate the conformational properties of the chains, implementing a freely jointed chain model, in between featureless cross-links. The Monte Carlo simulation method is used to sample the (restricted) translational degrees of freedom of the cross-links in the gel. We consider the case that the polymers in the gel have an affinity for surface positioned at the edge of the simulation volume. The polymer density decays as a power-law from the surface to the gel-density with an exponent close to -4/3. The gel features relatively large density fluctuations which is natural for a gel with a low density (φ ≈ 0.035), a low degree of cross-linking (average of three chainparts per cross-link), and relatively large chains (N = 50) in between the cross-links. Some parts of the gel can break loose from the gel and sample the adjoining volume. Representative snapshots exemplify large density fluctuations, which explain the large pore size distribution observed in experimental counterparts.

Shear banding and rheochaos in associative polymer networks.

We present experimental evidence of an instability in the shear flow of transient networks formed by telechelic associative polymers. Velocimetry experiments show the formation of shear bands, following a complex pattern upon increasing the overall shear rate. The chaotic nature of the stress response in transient flow is indicative of spatiotemporal fluctuations of the banded structure. This is supported by time-resolved velocimetry measurements.

Multiple shear-banding transitions in a supramolecular polymer solution.

We report on the nonlinear rheology of a reversible supramolecular polymer based on hydrogen bonding. The coupling between the flow-induced chain alignment and breakage and recombination of bonds between monomers leads to a very unusual flow behavior. Measured velocity profiles indicate three different shear-banding regimes upon increasing shear rate, each with different characteristics. While the first of these regimes has features of a mechanical instability, the second shear-banding regime is related to a shear-induced phase separation and the appearance of birefringent textures. The shear-induced phase itself becomes unstable at very high shear rates, giving rise to a third banding regime.

Brownian particles in supramolecular polymer solutions.

The Brownian motion of colloidal particles embedded in solutions of hydrogen-bonded supramolecular polymers has been studied using dynamic light scattering. At short times, the motion of the probe particles is diffusive with a diffusion coefficient equal to that in pure solvent. At intermediate time scales the particles are slowed down as a result of trapping in elastic cages formed by the polymer chains, while at longer times the motion is diffusive again, but with a much smaller diffusion coefficient. The influence of particle size and polymer concentration was investigated. The experimental data are compared to a theoretical expression for the mean-square displacement of an embedded particle in a viscoelastic medium, in which the solvent is explicitly taken into account. Differences between the friction and elastic forces experienced by the particle and the macroscopic viscosity and elasticity are explained by the inhomogeneity of the medium on the length scale of the particle size.

Statistical thermodynamics of equilibrium polymers at interfaces.

The behavior of a solution of equilibrium polymers (or living polymers) at an interface is studied, using a Bethe-Guggenheim lattice model for molecules with orientation dependent interactions. The density profile of polymers and the chain length distribution are calculated. For equilibrium polymers at a nonadsorbing surface it is found that the depletion layer thickness has a maximum. In dilute solutions it is proportional to the average radius of gyration of the polymers, which increases with increasing concentration. Above the overlap concentration it corresponds to the bulk correlation length, which decreases with increasing concentration. Furthermore, it is found that the surface region is predominantly occupied by the shorter chains. Both in dilute solutions and in a melt of equilibrium polymers, a very simple relation is found between the surface excess of a component and the chain length.