T. C. B. McLeish

Hierarchical self-assembly of chiral rod-like molecules as a model for peptide β-sheet tapes, ribbons, fibrils, and fibers

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, P11-I and P11-II, is illustrative of the proposed scheme. P11-I and P11-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 kBT), and sufficiently rigid (persistence length l̃fibril ≈ 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.

Molecular constitutive equations for a class of branched polymers: The pom-pom polymer

Polymer melts with long-chain side branches and more than one junction point, such as commercial low density polyethylene (LDPE), have extensional rheology characterized by extreme strain hardening, while the shear rheology is very shear thinning, much like that of unbranched polymers. Working with the tube model for entangled polymer melts, we propose a molecular constitutive equation for an idealized polymer architecture, which, like LDPE, has multiple branch points per molecule. The idealized molecule, called a “pom-pom,” has a single backbone with multiple branches emerging from each end. Because these branches are entangled with the surrounding molecules, the backbone can readily be stretched in an extensional flow, producing strain hardening. In start-up of shear, however, the backbone stretches only temporarily, and eventually collapses as the molecule is aligned, producing strain softening. Here we develop a differential/integral constitutive equation for this architecture, and show that it predicts rheology in both shear and extension that is qualitatively like that of LDPE, much more so than is possible with, for example, the K-BKZ integral constitutive equation.

Preparation of Hierarchical Hollow CaCO3 Particles and the Application as Anticancer Drug Carrier

One-pot approach to couple the crystallization of CaCO(3) nanoparticles and the in situ symmetry-breaking assembly of these crystallites into hollow spherical shells was developed under the templating effect of a soluble starch. Further functional study using HP-a as an anticancer drug carrier (DOX) demonstrated its advantages for localizing drug release by the pH value-sensitive structure and enhancing cytotoxicity by increasing cellular uptake, perinuclear accumulation, and nuclear entry.

Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release

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.

Spinodal-assisted crystallization in polymer melts

Recent experiments in some polymer melts quenched below the melting temperature have reported spinodal kinetics in small-angle x-ray scattering before the emergence of a crystalline structure. To explain these observations we propose that the coupling between density and chain conformation induces a liquid-liquid binodal within the equilibrium liquid-crystalline solid coexistence region. A simple phenomenological theory is developed to illustrate this idea, and several experimentally testable consequences are discussed. Shear is shown to enhance the kinetic role of the hidden binodal.

Predicting low density polyethylene melt rheology in elongational and shear flows with “pom-pom” constitutive equations

A recent constitutive equation derived from molecular considerations on a model architecture containing two branch points a “pom-pom” captures the qualitative rheological behavior of low density polyethylene (LDPE) in shear and extension for the first time [, J. Rheol. 42, 82 (1998)]. We use a hypothetical melt of pom-poms with different numbers of arms to model the behavior of LDPE. The linear relaxation spectra for various LDPE samples are mapped to the backbone relaxation times of the pom-pom modes. Data from start-up flow in uniaxial extension fixes the nonlinear parameters of each mode giving predictions for shear and planar extension with no free parameters. This process was carried out for data in the literature and for our own measurements. We find that multimode versions of the pom-pom equation, with physically reasonable distributions of branching, are able to account quantitatively for LDPE rheology over four decades in the deformation rate in three different geometries of flows. The method sug...

Computational linear rheology of general branch-on-branch polymers

We present a general algorithm for predicting the linear rheology of branched polymers. While the method draws heavily on existing theoretical understanding of the relaxation processes in entangled polymer melts, a number of new concepts are developed to handle diverse polymer architectures including branch-on-branch structures. We validate the algorithm with experimental examples from model polymer architectures to fix the parameters of the model. We use experimentally determined parameters to generate a numerical ensemble of branched metallocene-catalyzed polyethylene resins. Application of our algorithm shows the importance of branch-on-branch chains in the system and predicts the linear rheology with good quantitative agreement over a wide range of branching density and molecular weight.

Definitions of entanglement spacing and time constants in the tube model

Numerous papers have recently appeared in the literature presenting quantitative comparisons of experimental linear viscoelastic data to the most recent versions of “tube” models for entangled polymer melts and solutions. Since these tube models are now being used for quantitative, rather than just qualitative, predictions, it has become important that numerical prefactors for the time constants that appear in these theories be evaluated correctly using literature data for the parameters (i.e., density, plateau modulus, etc.) that go into the theories. However, in the literature two definitions of the entanglement spacing in terms of plateau modulus have been presented, and confusion between these has produced numerous errors in the recent literature. In addition, two different definitions of the “equilibration time,” a fundamental time constant, have also appeared, creating additional potential for confusion. We therefore, carefully review the alternative definitions and clarify the values of the prefactors that must be used for the different definitions, in the hope of helping future authors to avoid such errors.

Molecular drag–strain coupling in branched polymer melts

The “pom-pom” model of McLeish and Larson [J. Rheol. 42, 81–110 (1998)] provides a simple molecular theory for the nonlinear rheology of long chain branched polymer melts. A feature of this model is a maximum stretch for the branched molecules. Sharp transitions were predicted in the extensional viscosity at this maximum stretch. We introduce a simple treatment of the coupling between relaxed and unrelaxed polymer segments at branch points. The branch point is allowed to move in a quadratic localizing potential of unknown strength. Taking account of this effect smoothes the sharp transitions of the model and accounts for the extensional viscosity of “pom-pom” model polymers at their maximum stretch. The result is an improved multimode pom-pom fit for low-density polyethylene rheology. By fitting the nonlinear extensional viscosity, quantitative predictions are made for the nonlinear steady shear viscosity and transient first normal stress difference in shear.

Entangled Dynamics and Melt Flow of Branched Polymers

One of the most puzzling properties of branched polymers is their unusual viscoelasticity in the melt state. We review the challenges set by both non-linear experiments in extension and shear of polydisperse branched melts, and by the growing corpus of data on well-characterised melts of star-, comb- and H-molecules. The remarkably successful extension of the de Gennes/Doi-Edwards tube model to branched polymers is treated in some detail in the case of star polymers for which it is quantitatively accurate. We then apply it to more complex architectures and to blends of star-star and star-linear composition. Treating linear polymers as “2-arm stars” for the early fluctuation-dominated stages of their stress-relaxation successfully accounts for the relaxation spectrum and “3.4-law” viscosity-molecular weight relationship. The model may be generalised to strong flows in the form of molecular constitutive equations of a structure not found in the phenomenological literature. A model case study, the “pom-pom” polymer, exhibits strong simultaneous extension hardening and shear softening, akin to commercial branched polymers. Computation with such a constitutive equation in a viscoelastic flow-solver reproduces the large corner vortices in contraction flows characteristic of branched melts and suggests possible future applications of the modelling tools developed to date.