The role of cooling rate in crystallization-driven block copolymer self-assembly

Self-assembly of crystalline-coil block copolymers (BCPs) in selective solvents is often carried out by heating the mixture until the sample appears to dissolve and then allowing the solution to cool back to room temperature. In self-seeding experiments, some crystallites persist during sample annealing and nucleate the growth of core-crystalline micelles upon cooling. There is evidence in the literature that the nature of the self-assembled structures formed is independent of the annealing time at a particular temperature. There are, however, no systematic studies of how the rate of cooling affects self-assembly. We examine three systems based upon poly(ferrocenyldimethylsilane) BCPs that generated uniform micelles under typical conditions where cooling took pace on the 1–2 h time scale. For example, several of the systems generated elongated 1D micelles of uniform length under these slow cooling conditions. When subjected to rapid cooling (on the time scale of a few minutes or faster), branched structures were obtained. Variation of the cooling rate led to a variation in the size and degree of branching of some of the structures examined. These changes can be explained in terms of the high degree of supersaturation that occurs when unimer solutions at high temperature are suddenly cooled. Enhanced nucleation, seed aggregation, and selective growth of the species of lowest solubility contribute to branching. Cooling rate becomes another tool for manipulating crystallization-driven self-assembly and controlling micelle morphologies.

In the self-assembly of crystalline-coil block copolymers in solution, heating followed by different cooling rates can lead to different structures.     

Recent developments in the science and technology of high modulus flexible polymers

Recent progress in basic science and technological innovation is described for three areas of research in the IRC at Leeds University; melt spun high modulus polyethylene fibres, hydrostatic extrusion and die drawing.     

Free radical entry in emulsion polymerizations

Measurements of the rate coefficients characterising the entry of free radicals into seed particles in styrene emulsion polymerizations has allowed the rate determining step for entry to be identified. This was found to be the rate of production of oligomeric species in the aqueous phase by monomer addition to the primary free radicals. Once formed the subsequent diffusion of these species to the latex particles (and their incorporation within these particles) is relatively fast, contrary to the assumptions of the previous diffusion controlled theories. The experimental results imply that the entering free radicals contain only two or three monomer units. Thermodynamic considerations show that such species should be both water soluble and surface active. Similar conclusions have been reached for other sparingly water soluble monomers, such as butyl acrylate and butyl methacrylate.     

Simplified spectral phase interferometry for direct electric-field reconstruction by using a thick nonlinear crystal

We propose and demonstrate a novel implementation of spectral-shearing interferometry (SSI) for reconstructing the electric field of ultrashort pulses by utilizing asymmetric group velocity matching in a long nonlinear crystal. The proposed configuration eliminates the requirement for a linearly chirped auxiliary pulse that is in common in all existing SSI methods, relying on nonlinear conversion to produce a spectral shear.     

Frobenius manifolds and Frobenius algebra-valued integrable systems

The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a central role in ensuring integrability is preserved. In this paper, a new theory of Frobenius algebra-valued integrable systems is developed. This is achieved for systems derived from Frobenius manifolds by utilizing the theory of tensor products for such manifolds, as developed by Kaufmann (Int Math Res Not 19:929–952, 1996), Kontsevich and Manin (Inv Math 124: 313–339, 1996). By specializing this construction, using a fixed Frobenius algebra \({\mathcal {A}},\) one can arrive at such a theory. More generally, one can apply the same idea to construct an \({\mathcal {A}}\)-valued topological quantum field theory. The Hamiltonian properties of two classes of integrable evolution equations are then studied: dispersionless and dispersive evolution equations. Application of these ideas are discussed, and as an example, an \({\mathcal {A}}\)-valued modified Camassa–Holm equation is constructed.