Effect of water-soluble polymers, polyethylene glycol and poly(vinylpyrrolidone),on the gelation of aqueous micellar solutions of Pluronic copolymer F127

The micellization of F127 (E98P67E98) in dilute aqueous solutions of polyethylene glycol (PEG6000 and PEG35000) and poly(vinylpyrrolidone) (PVP K30 and PVP K90) is studied. The average hydrodynamic radius (rh,app) obtained from the dynamic light scattering technique increased with increase in PEG concentration but decreased on addition of PVP, results which are consistent with interaction of the micelles with PEG and the formation of micelles clusters, but no such interaction occurs with PVP. Tube inversion was used to determine the onset of gelation. The critical concentration of F127 for gelation increased on addition of PEG and of PVP K30 but decreased on addition of PVP K90. Small-angle X-ray scattering (SAXS) was used to show that the 30 wt% F127 gel structure (fcc) was independent of polymer type and concentration, as was the d-spacing and so the micelle hard-sphere radius. The maximum elastic modulus (G0 max) of 30 wt% F127 decreased from its value for water alone as PEG was added, but was little changed by adding PVP. These results are consistent with the packed-micelles in the 30 wt% F127 gel being effectively isolated from the polymer solution on the microscale while, especially for the PEG, being mixed on the macroscale.

Microwave-assisted hydrogel synthesis: a new method for crosslinking polymers in aqueous solutions

It has been found that hydrogels may be formed by microwave irradiation of aqueous solutions containing appropriate combinations of polymers. This new method of hydrogel synthesis yields sterile hydrogels without the use of monomers, eliminating the need for the removal of unreacted species from the final product. Results for two particularly successful combinations, poly(vinyl alcohol) with either poly(acrylic acid) or poly(methylvinylether-alt-maleic anhydride), are presented. Irradiation using temperatures of 100–150 °C was found to yield hydrogels with large equilibrium swelling degrees of 500–1000 g g−1. Material leached from both types of hydrogel shows little cytotoxicity towards HT29 cells.

A novel X-ray rheometer for in situ studies of polymer melts and solutions during shear flow

A novel X-ray rheometer based on a parallel plate geometry is described. This system allows time-resolved X-ray scattering intensity data to be obtained from polymeric samples subjected to shear flow. The range of quantitative structural parameters, such as molecular orientation and inter chain correlations, which can be obtained from the data is highlighted. Examples of the utility of X-ray scattering in examining optically opaque samples and the extraction of 〈P2〉 and 〈P4〉 orientation parameters are given using anisotropic hydroxypropylcellulose solutions as the sample.

Time-resolved in situ X-ray scattering studies of aqueous hydroxypropylcellulose solutions

The evolution of the global orientation parameter for a series of aqueous hydroxypropylcellulose solutions both during and following the cessation of a steady-state shear flow is reported. Time-resolved orientation measurements were made in situ through a novel X-ray rheometer coupled with a two-dimensional electronic X-ray camera, and using an intense X-ray source at the LURE synchrotron. After the cessation of flow, the global orientation decreases from the steady-state orientation level to zero following shear flow at low shear rate or to a small but finite value after flow at a high shear rate. The decrease of orientation with time shows different behaviour, dependent upon the previously applied shear rate.

Analytic Benchmark Solutions for Open-Channel Flows

An important test of the quality of a computational model is its ability to reproduce standard test cases or benchmarks. For steady open–channel flow based on the Saint Venant equations some benchmarks exist for simple geometries from the work of Bresse, Bakhmeteff and Chow but these are tabulated in the form of standard integrals. This paper provides benchmark solutions for a wider range of cases, which may have a nonprismatic cross section, nonuniform bed slope, and transitions between subcritical and supercritical flow. This makes it possible to assess the underlying quality of computational algorithms in more difficult cases, including those with hydraulic jumps. Several new test cases are given in detail and the performance of a commercial steady flow package is evaluated against two of them. The test cases may also be used as benchmarks for both steady flow models and unsteady flow models in the steady limit.

Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω 2 u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.

Grid computing solutions for distributed repositories of protein folding and unfolding simulations

The P-found protein folding and unfolding simulation repository is designed to allow scientists to perform analyses across large, distributed simulation data sets. There are two storage components in P-found: a primary repository of simulation data and a data warehouse. Here we demonstrate how grid technologies can support multiple, distributed P-found installations. In particular we look at two aspects, first how grid data management technologies can be used to access the distributed data warehouses; and secondly, how the grid can be used to transfer analysis programs to the primary repositories --- this is an important and challenging aspect of P-found because the data volumes involved are too large to be centralised. The grid technologies we are developing with the P-found system will allow new large data sets of protein folding simulations to be accessed and analysed in novel ways, with significant potential for enabling new scientific discoveries.

Complex formation in solutions of oppositely charged polyelectrolytes at different polyion compositions and salt content

The formation of complexes in solutions containing positively charged polyions (polycations) and a variable amount of negatively charged polyions (polyanions) has been investigated by Monte Carlo simulations. The polyions were described as flexible chains of charged hard spheres interacting through a screened Coulomb potential. The systems were analyzed in terms of cluster compositions, structure factors, and radial distribution functions. At 50% charge equivalence or less, complexes involving two polycations and one polyanion were frequent, while closer to charge equivalence, larger clusters were formed. Small and neutral complexes dominated the solution at charge equivalence in a monodisperse system, while larger clusters again dominated the solution when the polyions were made polydisperse. The cluster composition and solution structure were also examined as functions of added salt by varying the electrostatic screening length. The observed formation of clusters could be rationalized by a few simple rules.

A Monte Carlo study of solutions of oppositely charged polyelectrolytes

The formation of complexes appearing in solutions containing oppositely charged polyelectrolytes has been investigated by Monte Carlo simulations using two different models. The polyions are described as flexible chains of 20 connected charged hard spheres immersed in a homogenous dielectric background representing water. The small ions are either explicitly included or their effect described by using a screened Coulomb potential. The simulated solutions contained 10 positively charged polyions with 0, 2, or 5 negatively charged polyions and the respective counterions. Two different linear charge densities were considered, and structure factors, radial distribution functions, and polyion extensions were determined. A redistribution of positively charged polyions involving strong complexes formed between the oppositely charged polyions appeared as the number of negatively charged polyions was increased. The nature of the complexes was found to depend on the linear charge density of the chains. The simplified model involving the screened Coulomb potential gave qualitatively similar results as the model with explicit small ions. Finally, owing to the complex formation, the sampling in configurational space is nontrivial, and the efficiency of different trial moves was examined.

Stability of stationary solutions of the forced Navier-Stokes equations on the two-torus

We study the linear and nonlinear stability of stationary solutions of the forced two-dimensional Navier-Stokes equations on the domain [0,2π]x[0,2π/α], where α ϵ(0,1], with doubly periodic boundary conditions. For the linear problem we employ the classical energy{enstrophy argument to derive some fundamental properties of unstable eigenmodes. From this it is shown that forces of pure χ2-modes having wavelengths greater than 2π do not give rise to linear instability of the corresponding primary stationary solutions. For the nonlinear problem, we prove the equivalence of nonlinear stability with respect to the energy and enstrophy norms. This equivalence is then applied to derive optimal conditions for nonlinear stability, including both the high-and low-Reynolds-number limits.

Chapter 16: Electrospinning of polymer solutions

Electrospinning is a technique that involves the production of nanoscale to microscale sized polymer fibres through the application of an electric field to a droplet of polymer solution passed through a spinneret tip. This chapter considers the optimisisation of the electrospinning process and in particular the variation with solution concentration. We show the strong connection between overlapping chains and the successful spinning of fibres. We use small-angle neutron scattering to evaluate the molecular conformations in the solutions and in the fibres.

Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

A theoretical investigation of a-Fe2O3–Cr2O3 solid solutions

We have examined the thermodynamic stability of a-Fe2O3–Cr2O3 solid solutions as a function of temperature and composition, using a combination of statistical mechanics with atomistic simulation techniques based on classical interatomic potentials, and the addition of a model magnetic interaction Hamiltonian. Our calculations show that the segregation of the Fe and Cr cations is marginally favourable in energy compared to any other cation distribution, and in fact the energy of any cation configuration of the mixed system is always slightly higher than the combined energies of equivalent amounts of the pure oxides separately. However, the positive enthalpy of mixing is small enough to allow the stabilisation of highly disordered solid solutions at temperatures of B400 K or higher. We have investigated the degree of cation disorder and the effective cell parameters of the mixed oxide as functions of temperature and composition, and we discuss the effect of magnetic interactions and lattice vibrations on the stability of the solid solution.