Single-chain-in-mean-field simulations of weak polyelectrolyte brushes.

Structural properties of brushes which are composed of weak acidic and basic polyelectrolytes are studied in the framework of a particle-based approach that implicitly accounts for the solvent quality. Using a semi-grandcanonical partition function in the framework of the Single-Chain-in-Mean-Field (SCMF) algorithm, the weak polyelectrolyte is conceived as a supramolecular mixture of polymers in different dissociation states, which are explicitly treated in the partition function and sampled by the SCMF procedure. One obtains a local expression for the equilibrium acid-base reaction responsible for the regulation of the charged groups that is also incorporated to the SCMF sampling. Coupled to a simultaneous treatment of the electrostatics, the approach is shown to capture the main features of weak polyelectrolyte brushes as a function of the bulk pH in the solution, the salt concentration, and the grafting density. Results are compared to experimental and theoretical works from the literature using coarse-grained representations of poly(acrylic acid) (PAA) and poly(2-vinyl pyridine) (P2VP) polymer-based brushes. As the Born self-energy of ions can be straightforwardly included in the numerical approach, we also study its effect on the local charge regulation mechanism of the brush. We find that its effect becomes significant when the brush is dense and exposed to high salt concentrations. The numerical methodology is then applied (1) to the study of the kinetics of collapse/swelling of a P2VP brush and (2) to the ability of an applied voltage to induce collapse/swelling of a PAA brush in a pH range close to the pKa value of the polymer.

Statics of polymer droplets on deformable surfaces.

The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer chains onto a flat solid substrate. We tune the softness of the surface by varying the grafting density. Droplets are comprised of bead-spring polymers of various chain lengths. First, both systems, brush and polymer liquid, are studied independently in order to determine their static and dynamic properties. In particular, using a numerical implementation of an AFM experiment, we measure the shear modulus of the brush surface and compare the results to theoretical predictions. Then, we study the wetting behavior of polymer droplets with different surface/drop compatibility and on substrates that differ in softness. Density profiles reveal, under certain conditions, the formation of a wetting ridge beneath the three-phase contact line. Cap-shaped droplets and cylindrical droplets are also compared to estimate the effect of the line tension with respect to the droplet size. Finally, the results of the simulations are compared to a phenomenological free-energy calculation that accounts for the surface tensions and the compliance of the soft substrate. Depending on the surface/drop compatibility, surface softness, and drop size, a transition between two regimes is observed: from one where the drop surface energy balances the adhesion with the surface, which is the classical Young-Dupré wetting regime, to another one where a coupling occurs between adhesion, droplet and surface elastic energies.

Molecular transport and flow past hard and soft surfaces: computer simulation of model systems.

The equilibrium and flow of polymer films and drops past a surface are characterized by the interface and surface tensions, viscosity, slip length and hydrodynamic boundary position. These parameters of the continuum description are extracted from molecular simulations of coarse-grained models. Hard, corrugated substrates are modelled by a Lennard-Jones solid while polymer brushes are studied as prototypes of soft, deformable surfaces. Four observations are discussed. (i) If the surface becomes strongly attractive or is coated with a brush, the Navier boundary condition fails to describe the effect of the surface independently of the strength and type of the flow. This failure stems from the formation of a boundary layer with an effective, higher viscosity. (ii) In the case of brush-coated surfaces, flow induces a cyclic, tumbling motion of the tethered chain molecules. Their collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations. The flow past a polymer brush cannot be described by Brinkman's equation. (iii) The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. Their steady-state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface. (iv) On a soft, deformable substrate like a polymer brush, we observe a lifting-up of the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters for maximizing the deformation at the three-phase contact.

Evolution of entanglements during the response to a uniaxial deformation of lamellar triblock copolymers and polymer glasses.

Using coarse-grained molecular-dynamics simulations, a generic styrene-block-butadiene-block-styrene triblock copolymer under lamellar conformation is used in order to investigate the mutual entanglement evolution when a structure of alternating glassy (S)/rubbery (B) layers is submitted to an imposed deformation. By varying the amount of loop chains between each phase, i.e., noncrossing chains, it is possible to generate different types of S/B interface definitions. A specific boundary driven tensile strain protocol has been developed in order to mimic "real" experiments and measure the stress-strain curve. The same protocol is also applied to a reference state consisting in a directed glassy homopolymers, as well as to an isotropic glassy polymer. The evolution of initial mutual entanglements from the undeformed samples during the whole deformation process is monitored. It is shown for all considered systems that initial entanglements mostly participate to the preyield regime of the stress-strain curve and that this network is debonded during the strain-hardening regime. For triblocks with a non-null amount of crossing chains, the lower the amount is, the longer the memory effect of the initial entanglement network in the postyield regime is. On the fly distributions of entanglements, which depart from the postyield regime, depict memory effects and long-time correlations during the strain-hardening regime. For triblocks, loop chains reinforce these effects.

On the study of local-stress rearrangements during quasi-static plastic shear of a model glass: do local-stress components contain enough information?

We present a numerical study of the mechanical response of a 2D Lennard-Jones amorphous solid under steady quasi-static and athermal shear. We focus here on the evolution of local stress components. While the local stress is usually taken as an order parameter in the description of the rheological behaviour of complex fluids, and for plasticity in glasses, we show here that the knowledge of local stresses is not sufficient for a complete description of the plastic behaviour of our system. The distribution of local stresses can be approximately described as resulting from the sum of localized quadrupolar events with an exponential distribution of amplitudes. However, we show that the position of the center of the quadrupoles is not related to any special evolution of the local stress, but must be described by another variable.

Inhomogeneous elastic response of silica glass.

Using large scale molecular dynamics simulations we investigate the properties of the nonaffine displacement field induced by macroscopic uniaxial deformation of amorphous silica, a strong glass according to Angell's classification. We demonstrate the existence of a length scale xi characterizing the correlations of this field (corresponding to a volume of about 1000 atoms), and compare its structure to the one observed in a standard fragile model glass. The "boson-peak" anomaly of the density of states can be traced back in both cases to elastic inhomogeneities on wavelengths smaller than xi where classical continuum elasticity becomes simply unapplicable.

Plastic response of a 2D Lennard-Jones amorphous solid: detailed analysis of the local rearrangements at very slow strain rate.

We analyze in detail the atomistic response of a model amorphous material submitted to plastic shear in the athermal, quasi-static limit. After a linear stress-strain behavior, the system undergoes a noisy plastic flow. We show that the plastic flow is spatially heterogeneous. Two kinds of plastic events occur in the system: quadrupolar localized rearrangements, and shear bands. The analysis of the individual motion of a particle shows also two regimes: a hyper-diffusive regime followed by a diffusive regime, even at zero temperature.