Diffusion coefficient in a semi-dilute solution measured by concentration gradient technique and compared to quasielastic light scattering results

2014 We show experimentally that the translational diffusion coefficient of a semi-dilute solution does not depend on the time scale over which the measurement is made. As a consequence isothermal and adiabatic compressibilities are identical in semi-dilute solutions, and this diffusion coefficient can be viewed either as a cooperative diffusion coefficient in the pseudo-gel model, or as a diffusion coefficient of a coil without hydrodynamic interactions between its elements. LE JOURNAL DE PHYSIQUE LETTRES TOME 40, ler SEPTEMBRE 1979, Classification Physics Abstracts 05.40 61.40 66.90 82.90 A semi-dilute solution is characterized by an interpenetration of the coils, when the monomer concentration c is bigger than the overlap concentration c* [1] ] (c* = M/7~, where M is the mass and R the radius of gyration of the coil). One can define an average distance ~ between contact points which depends only on concentration (~ ~ c 0.75). One can also define an average life time TR of the contact points which is identical to the time necessary for a semi-dilute coil to change its conformation [2] ; TR is called the reptation time. , If one observes the relaxation properties of a semi-dilute solution resulting from a constraint such as a stress : a viscoelastic response is observed if the observation is made in a time interval smaller than TR, whereas the response is purely viscous if the observation is made in an interval greater than TR [3]. However, when the constraint is a concentration gradient we find that the relaxation process, i.e. the translational diffusion coefficient, is independent of the time interval. (*) Centre de Recherche sur les Macromolec~les, 67083 Strasbourg Cedex, France. The diffusion coefficient is defined as the ratio of the rate of transfer of a diffusion substance, per unit area, to the concentration gradient. . It can be expressed as [4] : where f and M are respectively the frictional coefficient and the mass of the moving species, and 7c the osmotic pressure of the solution. The diffusion coefficient in a time interval shorter than TR has been calculated [1] as follows : the semidilute solution is considered as a gel of mesh size ~, the diffusion coefficient is equal to the ratio [5] where E is the elastic modulus of the transient network, and 9 the friction of the solvent through one unit volume of gel. If E and 9 are expressed as a function of ~, the diffusion coefficient is found to be equal to [6] Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019790040017043500 L-436 JOURNAL DE PHYSIQtJE -~ LETTRES where f (~) is the frictional coefficient of one element of size ~ called a blob. The semi-dilute solution can also be considered as a non interacting assembly of blobs, then D is independent of molecular weight and scales with concentration as a power law. The quasi-elastic light scattering technique has been widely used [7] in order to measure the diffusion coefficient at a time scale much shorter than TR. This technique allows us to determine the characteristic decay time i of spontaneous concentration fluctuations on a space scale k-1 (k is the transfer vector). It has been found for the polystyrene benzene system, at room temperature that T = (Dk~)-1 and D = 5.63 x 10-6 CO.67 cm2 s -1 [8]. The characteristic time r