Kinetic studies of the photopolymerisation of acrylamide in aqueous solution:effects of bromoform as a Chain transfer agent

The effects of adding bromoform (CHBr3) as a potential chain transfer agent in the photopolymerisation of acrylamide (AM) in aqueous solution have been studied both in terms of influencing the rate of polymerisation and the molecular weight of the polyacrylamide (PAM) formed. Using 4,4′-azo-bis(4-cyanopentanoic acid) (ACPA) as photoinitiator, two different CHBr3 concentrations as chain transfer agent were compared: 0.5 and 2.0 mol % (relative to AM), the higher of which was determined by the limit of CHBr3 water solubility. The results showed that CHBr3 was an effective chain transfer agent that could regulate the molecular weight of the PAM formed without seriously affecting the polymerisation rate. It is concluded that chain transfer to CHBr3occurs by both Br and H atom transfer although Br transfer is the more favoured due to the weaker C-Br bond. Furthermore, Br transfer leads to Br-terminated chains in which the terminal C-Br bond can re-dissociate leading to re-initiation and re-propagation of the same chain, thereby maintaining the polymerisation rate. Continuing studies into how this mechanism can be exploited in order to synthesize water-soluble block copolymers of potential biomedical importance are currently in progress.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett. 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.