Pressure effects revealed by small angle neutron scattering on block copolymer gels

We study the effects of hydrostatic pressure (P) on aqueous solutions and gels of the block copolymer B20E610 (E, oxyethylene; B, oxybutylene; subscripts, number of repeats), by performing simultaneous small angle neutron scattering/pressure experiments. Micellar cubic gels were studied for 9.5 and 4.5 wt% B20E610 at T = 20-80 and 35-55 degrees C, respectively, while micellar isotropic solutions where Studied for 4.5 wt% B20E610 at T > 55 degrees C. We observed that the interplanar distance d(110) (cubic unit cell parameter a = root 2d(110)) decreases while the correlation length of the Cubic order (delta) increases, upon increasing P at a fixed T for 9.5 wt% B20E610. The construction of master Curves for d(110) and delta corresponding to 9.5 wt% B20E610 proved the correlation between changes in T and P. Neither d(110) and delta nor the cubic-isotropic phase transition temperature was affected by the applied pressure for 4.5 wt% B20E610. The dramatic contrast between the pressure-induced behavior observed for 9.5 and 4.5 wt% B20E610 suggests that pressure induced effects might be more effectively transmitted through samples that present wider domains of cubic structure order (9.5 wt% compared to 4.5 wt% B20E610).

Modelling small angle neutron scattering data from electrospun fibres

Electrospinning is a technique employed to produce nanoscale to microscale sized fibres by the application of a high voltage to a spinneret containing a polymer solution. Here we examine how small angle neutron scattering data can be modelled to analyse the polymer chain conformation. We prepared 1:1 blends of deuterated and hydrogenated atactic-polystyrene fibres from solutions in N, N-Dimethylformamide and Methyl Ethyl Ketone. The fibres themselves often contain pores or voiding within the internal structure on the length scales that can interfere with scattering experiments. A model to fit the scattering data in order to obtain values for the radius of gyration of the polymer molecules within the fibres has been developed, that includes in the scattering from the voids. Using this model we find that the radius of gyration is 20% larger than in the bulk state and the chains are slightly extended parallel to the fibre axis.

SANS/WANS time-resolving neutron scattering studies of polymer phase transitions using NIMROD

We use new neutron scattering instrumentation to follow in a single quantitative time-resolving experiment, the three key scales of structural development which accompany the crystallisation of synthetic polymers. These length scales span 3 orders of magnitude of the scattering vector. The study of polymer crystallisation dates back to the pioneering experiments of Keller and others who discovered the chain-folded nature of the thin lamellae crystals which are normally found in synthetic polymers. The inherent connectivity of polymers makes their crystallisation a multiscale transformation. Much understanding has developed over the intervening fifty years but the process has remained something of a mystery. There are three key length scales. The chain folded lamellar thickness is ~ 10nm, the crystal unit cell is ~ 1nm and the detail of the chain conformation is ~ 0.1nm. In previous work these length scales have been addressed using different instrumention or were coupled using compromised geometries. More recently researchers have attempted to exploit coupled time-resolved small-angle and wide-angle x-ray experiments. These turned out to be challenging experiments much related to the challenge of placing the scattering intensity on an absolute scale. However, they did stimulate the possibility of new phenomena in the very early stages of crystallisation. Although there is now considerable doubt on such experiments, they drew attention to the basic question as to the process of crystallisation in long chain molecules. We have used NIMROD on the second target station at ISIS to follow all three length scales in a time-resolving manner for poly(e-caprolactone). The technique can provide a single set of data from 0.01 to 100Å-1 on the same vertical scale. We present the results using a multiple scale model of the crystallisation process in polymers to analyse the results.

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.