Tongchuan Suo

Doubly self-consistent field theory of grafted polymers under simple shear in steady state

We present a generalization of the numerical self-consistent mean-field theory of polymers to the case of grafted polymers under simple shear. The general theoretical framework is presented, and then applied to three different chain models: rods, Gaussian chains, and finitely extensible nonlinear elastic (FENE) chains. The approach is self-consistent at two levels. First, for any flow field, the polymer density profile and effective potential are calculated self-consistently in a manner similar to the usual self-consistent field theory of polymers, except that the calculation is inherently two-dimensional even for a laterally homogeneous system. Second, through the use of a modified Brinkman equation, the flow field and the polymer profile are made self-consistent with respect to each other. For all chain models, we find that reasonable levels of shear cause the chains to tilt, but it has very little effect on the overall thickness of the polymer layer, causing a small decrease for rods, and an increase of no more than a few percent for the Gaussian and FENE chains. Using the FENE model, we also probe the individual bond lengths, bond correlations, and bond angles along the chains, the effects of the shear on them, and the solvent and bonded stress profiles. We find that the approximations needed within the theory for the Brinkman equation affect the bonded stress, but none of the other quantities.

Grafted polymers inside cylindrical tubes: Chain stretching vs layer thickness

We present a study of the detailed structure of grafted polymer chains and the layers they form inside cylindrical tubes, using the finitely extensible nonlinear elastic chain model and numerical self-consistent field theory. For very large tube radius, the chain stretching and layer thicknesses are the same as for polymers grafted to a planar surface. For decreasing radius, our calculations indicate that the layer almost always gets thinner, although there can be situations where it is very slightly thicker. However, we find that this thinning is not necessarily due to changes to the polymers: in fact, the root-mean-squared layer thickness would decrease even if the polymers themselves are completely unchanged. Furthermore, we find that the polymer stretching can increase at the same time that the layer thickness decreases. These apparent paradoxes are resolved by analyzing and distinguishing between the volume fraction profiles and monomer number distributions in these systems, including how they change and why. We also find that, in a given system, parts of each polymer move towards the curved surface and parts away from it, and that these differences are key to understanding the behavior.

End-anchored polymers in good solvents from the single chain limit to high anchoring densities

An increasing number of applications utilize grafted polymer layers to alter the interfacial properties of solid substrates, motivating refinement in our theoretical understanding of such layers. To assess existing theoretical models of them, we have investigated end-anchored polymer layers over a wide range of grafting densities, σ, ranging from a single chain to high anchoring density limits, chain lengths ranging over two orders of magnitude, for very good and marginally good solvent conditions. We compare Monte Carlo and molecular dynamics simulations, numerical self-consistent field calculations, and experimental measurements of the average layer thickness, h, with renormalization group theory, the Alexander-de Gennes mushroom theory, and the classical brush theory. Our simulations clearly indicate that appreciable inter-chain interactions exist at all simulated areal anchoring densities so that there is no mushroom regime in which the layer thickness is independent of σ. Moreover, we find that there is no high coverage regime in which h follows the predicted scaling, h ∼ Nσ1/3, for classical polymer brushes either. Given that no completely adequate analytic theory seems to exist that spans wide ranges of N and σ, we applied scaling arguments for h as a function of a suitably defined reduced anchoring density, defined in terms of the solution radius of gyration of the polymer chains and N. We find that such a scaling approach enables a smooth, unified description of h in very good solvents over the full range of anchoring density and chain lengths, although this type of data reduction does not apply to marginal solvent quality conditions.

Multiple transitions between various ordered and disordered states of a helical polymer under stretching

Using coarse-grained molecular dynamic simulations, we systematically investigate the conformational transitions of a helical polymer chain under tension. While a typical helix-coil transition is derived by our simulation with the absence of the stretching and varying temperature, the chain behaviors become more interesting and complicated when the force is applied. Specifically, when the temperature is low enough relative to the chain rigidity, the polymer is solid-like and displays a series of stepwise conformational transitions on the force-extension curve. We introduce a chain disorder parameter to capture the essence of these transitions. Detailed investigation indicates that the first few transitions correspond to the breaking of the helices, while the last one denotes a transition from a fully disordered state to an all-trans ordered conformation. By increasing the temperature, the thermal fluctuation makes the chain enter a liquid-like state, in which the initial weak stretching induces extra helix formation, followed by the force-induced helix breaking and the transition to the all-trans state. In contrast to the solid-like state, the liquid-like chain always adopts a mixed conformation with both helical and disordered regions. Further increasing the temperature makes the chain fully flexible and thus no helices can form at such a gas-like stage. We further study the relaxation behaviors of the polymer by decreasing the force and find hysteresis for the solid-like cases. Finally, we compare our simulation results with experiments in a semi-quantitative fashion and get quite good agreement.