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 (SBS) 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.Comment: 10 pages, 11 figure

Inhomogeneous elastic response of silica glass

Using large scale molecular dynamics simulations we investigate the properties of the {\em non-affine} 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

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 contact angles 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-Dupr\'e wetting regime, to another one where a coupling occurs between adhesion, droplet and surface elastic energies.Comment: 13 pages, 11 figure

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

The properties of polymer liquids on hard and soft substrates are investigated by molecular dynamics simulation of a coarse-grained bead-spring model and dynamic single-chain-in-mean-field (SCMF) simulations of a soft, coarse-grained polymer model. Hard, corrugated substrates are modelled by an FCC Lennard-Jones solid while polymer brushes are investigated as a prototypical example of a soft, deformable surface. From the molecular simulation we extract the coarse-grained parameters that characterise the equilibrium and flow properties of the liquid in contact with the substrate: the surface and interface tensions, and the parameters of the hydrodynamic boundary condition. The so-determined parameters enter a continuum description like the Stokes equation or the lubrication approximation.Comment: 41 pages, 13 figure

Dynamic and elastic heterogeneities in a 2D model glass

A generic soft-glass prototype is considered, as the glass transition is approached. Using standard methods, and by means of Molecular Dynamics simulation, a growing critical length scale (DH) is extracted upon cooling. On the other hand, this glass is also well characterized in the low-temperature limit, from which it has been shown that its elastic response under applied deformation involves some correlated particle displacements called elastic heterogeneities (EH). We then first aim to address the connection between both lengths. As EH appear to involve some structural rearrangements, this problem then also address either the structural nature of DH or the suitability of DH to capture EH's formation. It is shown that standard methods upon cooling fail to capture the birth of EH, but mainly capture, for the lowest temperatures, fluctuations around an effective theory of elasticity for amorphous materials, in which the medium can be considered as continuous above a length scale of the order of DH. We then test a recently proposed theory of the critical slowing-down of supercooled liquids, which predicts some scaling laws for DH. Such scalings are recovered for our soft model glass