Universal Equation of State for Flexible Polymers Beyond the Semidilute Regime.

We reconsider the isothermal equation of state (EOS) for linear homopolymers in good solvents, p=p(c,T), which relates the osmotic pressure p of polymers with the bulk concentration c and the temperature T. The classical scaling theory predicts the EOS in dilute and semidilute regimes. We suggest a generalized EOS that extends the universal behavior of polymer solutions up to the highly concentrated state and confirm it by molecular dynamics simulations and available experimental data. Our conjecture implies that properties of polymer chains dominate the EOS in the presence of many-body interactions. Our theoretical approach is based on a viral expansion in terms of concentration blobs leading to a superposition of two power laws in the regime of concentrated solutions.

Hierarchical excluded volume screening in solutions of bottlebrush polymers.

Polymer bottlebrushes provide intriguing features being relevant both in nature and in synthetic systems. While their presence in the articular cartilage optimizes synovial joint lubrication, bottlebrushes offer pathways for fascinating applications, such as within super-soft elastomers or for drug delivery. However, the current theoretical understanding lacks completeness, primarily due to the complicated interplay of many length scales. Herein, we develop an analytical model that demonstrates how structural properties of bottlebrushes depend on the concentration, ranging from dilute solutions to highly concentrated melts. The validity of our model is supported by data from extensive molecular dynamics simulations. We demonstrate that the hierarchical structure of bottlebrushes dictates a sequence of conformational changes as the solution concentration increases. The effect is mediated by screening of excluded volume interactions at subsequent structural parts of the bottlebrushes. Our findings provide important insights that should enable improved customization of novel materials based on the architectural design of polymer bottlebrushes.

Diblock-copolymer thin films under shear.

The behavior of lamellae forming diblock-copolymer melts confined by two non-selective substrates under shear is studied by means of molecular dynamics simulations. Since the substrate/copolymer preferential interaction is absent, the vertically oriented lamellae (L⊥) are formed. The response of L⊥ phase under transverse and perpendicular modes of shear is studied for a wide range of shear rates, γ̇. In particular, shear deformation and reorientation transition, flow behavior, and difference in the macroscopic response under the two modes of shear are discussed. We show that an inclined lamellae state observed for transverse shear below a critical shear rate γ̇* is stabilized by a cyclic motion of chains close to the substrates. The value of γ̇*, at which lamellae dissolve and reorient along the flow field during transverse shear, coincides with the onset of shear-thinning. For γ̇<γ̇*, the shear viscosity for transverse shear is much larger compared to that observed in perpendicular shear, while there is no difference for γ̇>γ̇*.

Polymer brushes under high load.

Polymer coatings are frequently used to provide repulsive forces between surfaces in solution. After 25 years of design and study, a quantitative model to explain and predict repulsion under strong compression is still lacking. Here, we combine experiments, simulations, and theory to study polymer coatings under high loads and demonstrate a validated model for the repulsive forces, proposing that this universal behavior can be predicted from the polymer solution properties.