A generic statistical mechanical model is presented for the self-assembly of chiral rod-like units, such as β-sheet-forming peptides, into helical tapes, which with increasing concentration associate into twisted ribbons (double tapes), fibrils (twisted stacks of ribbons), and fibers (entwined fibrils). The finite fibril width and helicity is shown to stem from a competition between the free energy gain from attraction between ribbons and the penalty because of elastic distortion of the intrinsically twisted ribbons on incorporation into a growing fibril. Fibers are stabilized similarly. The behavior of two rationally designed 11-aa residue peptides, P ₁₁ -I and P ₁₁ -II, is illustrative of the proposed scheme. P ₁₁ -I and P ₁₁ -II are designed to adopt the β-strand conformation and to self-assemble in one dimension to form antiparallel β-sheet tapes, ribbons, fibrils, and fibers in well-defined solution conditions. The energetic parameters governing self-assembly have been estimated from the experimental data using the model. The 8-nm-wide fibrils consist of eight tapes, are extremely robust (scission energy ≈200 k _B T ), and sufficiently rigid (persistence length l̃ _fibril ≈ 20–70 μm) to form nematic solutions at peptide concentration c ≈ 0.9 mM (volume fraction ≈0.0009 vol/vol), which convert to self-supporting nematic gels at c > 4 mM. More generally, these observations provide a new insight into the generic self-assembling properties of β-sheet-forming peptides and shed new light on the factors governing the structures and stability of pathological amyloid fibrils in vivo . The model also provides a prescription of routes to novel macromolecules based on a variety of self-assembling chiral units, and protocols for extraction of the associated energy changes.

The dynamics of entangled flexible polymers is dominated by physics general to many chemical systems. It is an appealing interdisciplinary field where experimental and theoretical physics can work closely with chemistry and chemical engineering. The role of topological interactions is particularly important, and has given rise to a successful theoretical framework: the 'tube model'. Progress over the last 30 years is reviewed in the light of specially-synthesized model materials, an increasing palette of experimental techniques, simulation and both linear and nonlinear rheological response. Our current understanding of a series of processes in entangled dynamics: 'reptation', 'contour length fluctuation' and 'constraint-release' are set in the context of remaining serious challenges. Especial attention is paid to the phenomena associated with polymers of complex topology or 'long chain branching'.

A refined version of the Doi and Edwards tube model for entangled polymer liquids is presented. The model is intended to cover linear chains in the full range of deformation rates from linear to strongly nonlinear flows. The effects of reptation, chain stretch, and convective constraint release are derived from a microscopic stochastic partial differential equation that describes the dynamics of the chain contour down to the length scale of the tube diameter. Contour length fluctuations are also included in an approximate manner. Predictions of mechanical stresses as well as the single chain structure factor under flow are shown. A comparison with experimental data is made in which all model parameters are fixed at universal values or are obtained from linear oscillatory shear measurements. With no parameter modification the model produces good agreement over a wide range of rheological data for entangled polymer solutions, including both nonlinear shear and extension. © 1993 The Society of Rheology. @DOI: 10.1122/1.1595099#