No abstract

No abstract

Small‐angle neutron scattering has been successfully used since the 1970s. As a general rule, methods to extract the useful signal from that received by the detector are well known and give good results. At the Laboratoire Léon Brillouin, for example, these methods have been employed for a long time. However, the data reduction software has been changed for the following reasons. Problems are encountered if the container of the sample gives a spurious signal or if the scattering angle is so large that its cosine cannot be approximated by 1. In the present paper, generalizations of formulas are made in order to account for these difficulties. The decrease of scattered intensity delivered by an incoherent sample that is often observed at large angles is shown to be only due to a geometrical effect. The consequent modifications of the relations used for the normalization of cells of position‐sensitive detectors and for the absolute calibration are given. As for the inherent background of the sample, the contribution of density fluctuations is usually neglected. This contribution is formally given as a function of the contrast lengths and of the isothermal compressibility of the sample. This new result allows numerical evaluations of the different terms of the inherent sample background. Practical examples are given. Finally, several methods, developed at the Laboratoire Léon Brillouin, are given to determine the background properly. They are based on systematic measurements of transmissions and background levels of suitably prepared blank samples.

No abstract

DNA and synthetic poly(styrenesulfonate) (PSS) solutions without excess simple salt were investigated with small-angle neutron scattering. For both polyelectrolytes, the transition from the rod to the coil regime was covered by an appropriate choice of molecular weights. The polymer, polymer−counterion, and counterion partial structure functions were obtained using contrast variation. For PSS, the single-chain scattering (form function) was observed from samples with zero-average polyion scattering length density contrast. The PSS polymer structure can be described by a locally rodlike configuration, but the projected monomer repeat distance 0.17 nm is smaller than the value expected for a fully stretched (trans) conformation. The PSS persistence length is of order 10 nm and does not agree with any theoretical analysis based on either the bending rigidity of a wormlike chain or modern variational results. The interpolymer structure was derived and compared with results based on the random-phase approximation. Poor agreement was observed, due to the high linear polyion charge density and, hence, strong electrostatic coupling. For highly charged linear polyelectrolytes, it was shown that from the full set of partial structure functions information on the radial counterion profile can be obtained without resorting to a model describing chain correlations. For PSS and DNA, the data agree with the counterion distribution obtained from the classical Poisson−Boltzmann theory and the cylindrical cell model, if the momentum transfer is far greater than the inverse persistence length.

Abstract:We have studied salt free semi dilute polyelectrolyte solutions by small angle neutron scattering. Specific labelling associated with an extrapolation method has allowed the separation of the form factor of a single polyelectrolyte chain Sl(q) and the structure factor S2(q). Two lengths are deduced from these two factors: the persistence length bt which characterizes the electrostatic interactions along the chain by a fitting of Sl(q) with calculation of the scattering function for a wormlike chain, and from S2(q), qm 1 which characterizes the interactions between chains. These two lengths vary in the same way with the concentration ofpolyions (bt o: cp 1/2, qm 1 oc r 1/2) and a constant relation exists between them: only one length is then necessary to describe the structure of polyelectrolyte soltuion on this semidilute concentration range.

No abstract

In this paper measurements of the radius of gyration of a polyion in salt free semi-dilute polyelectrolyte solutions are presented. We have used neutron scattering to extract the form factor of a single polyelectrolyte chain from the total correlation function by using a specific labelling associated with an extrapolation method. Assuming that the wormlike chain model takes into account the local flexibility of the chain due to electrostatic interactions along the chain, we have extracted, from the radii of gyration, values for the persistence length bt. Both Rg and bt decrease with increasing polyion concentration, c p. We can distinguish two concentration régimes : at low concentration, Rg decreases as cp-½ and bt as c p-1 and at high concentration R g decreases as cp-¼ and bt , as cp-½. These two régimes for the variation of bt with cp are well described by a calculation of Le Bret for the electrostatic contribution to the persistence length of the polyion