Light scattering by cooperative diffusion in semi-dilute polymer solutions

2014 We report measurements of relaxation times of the autocorrelation function for the Rayleigh line of light scattered by semi-dilute polymer solutions. LE JOURNAL DE PHYSIQUE LETTRES TOME 37, MARS 1976 Classification Physics Abstracts 7.146-7.221-7.610-5.660 Recent observations of polymer diffusive motions by light scattering have dealt with two extreme situations : the very dilute solution [1, 2], in which chains perform, as entities, diffusive motion, and the network [3] with fixed density of cross links. Here the deformation of the structure spreads out as a diffusive motion. From a systematic study of the effect of average molecular weight M in between cross links, a remarkable property of this motion [3] was established in swollen networks : the diffusion coefficient Ds, which is the ratio of elastic modulus to friction coefficient is inversely proportional to the power law of M as found in the diffusion coefficient Do in very dilute solution. This suggests that the relevant quantity for the M dependance of Ds is the average distance between cross links. The semi dilute solution is an intermediate situation which has been considered by several authors [4, 5], as networks with a finite lifetime. Viscoelastic properties [4, 6] have been interpreted in this way. However, the situation was described as purely random, i.e. with total loss of hydrodynamic as well as excluded volume effects, so that the distance between neighbour cross links would scale in a trivial manner with concentration. De Gennes [7] has shown on the contrary that this distance reflects basic long chain properties and that the dynamical correlations in semi-dilute solutions are of fundamental interest. We shall try to present his arguments as follows : 1) There is a characteristic frequency 7~, above which the solution can be considered as a network and below which it is seen as individual diffusive motions of the chains ; TR depends upon molecular weight and concentration of the polymers. The range of values taken by TR is well suited to an experiment on light scattering by diffusive network deformation. 2) As in the permanent network, the diffusion coefficient associated with deformation, D~, depends upon the average distance between adjacent cross links. However, this length does not depend upon molecular weight of the chains. It is only a function of concentration where kB is the Boltzman constant, T the temperature, ilo the viscosity of the solvent and ~ the dynamical screening length, identical to the static characteristic correlation length [8] where v is the excluded volume exponent (v = -1 in three dimensions) and d the dimension of space. De Gennes [7] established this result as a consequence of two non trivial identifications : first, the elastic modulus of the network scales with concentration like the osmotic pressure ; second, the hydrodynamic screening length scales like the excluded volume screening [8] length ~ (eq. (2)). Evidence for this dynamical correlation is determined from the time dependence of the observed autocorrelation function for the Rayleigh line in a light scattering experiment. The experimental set up is the same as described before in reference [1]. Since the network deformation corresponds to a well defined range of frequencies, it is important that the experiment be carried out in the proper momentum transfer k = (4 7c/~) sin (0/2) domain. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:0197600370305300 L-54 JOURNAL DE PHYSIQUE LETTRES Following reference [7] the smallest momentum kmin is directly obtained form TR