Scattering semidilute solutions

Fang, L Brown, W, Decay Time Distributions from Dynamic Light Scattering for Aqueous Poly(vinyl alcohol) Gels and Semidilute Solutions, Macromolecules 23, 3284, 1990. 

The scattering function g k) is a function of static correlation length as given by Eqs. (225)-(227). For semidilute solutions at high salt concentrations, Dc follows from Eqs. (226) and (282) in the —> 0 limit. 

This study addresses two questions 1) Is polymer aggregation in solutions directly related to solvent quality 2) If not, does solvent quality exert an effect on the viscosity of semidilute solutions separate from the effect of aggregation The copolymer poly(vinylbutyral) (PVB) was chosen for this investigation. PVB is known to aggregate in several solvents (IS). Light scattering and intrinsic viscosity measurements were used to assess solvent quality. Viscosities were measured at one concentration in three solvents and temperatures from 25 to 55 C. 

The single-chain structure factors calculated in the previous sections correspond to the infinite dilution limit. This limit also corresponds to zero scattering intensity and is not useful so that concentration effects have to be included in the modeling of polymer solutions. First, Zimm s single-contact approximation [5] is reviewed for dilute polymer solutions then, a slight extension of that formula which applies to semidilute solutions, is discussed. 

A semidilute solution [42] of high molecular weight deuterated polystyrene (Mw = 1.95 x 106 g/mole, Mw/M = 1.64) in dioctyl phthalate (DOP) at a volume fraction of 2.83% of polystyrene was measured by SANS at room temperature. A characteristic intensity behavior I(Q) was obtained after data correction (solvent incoherent scattering, empty cell scattering and usual background corrections, etc.) and was circularly averaged. The reduced I(Q) data was then fitted to the following form ... 

Figure 5.12 compares Eq. (5.75) (l/i>= 1.7) with SANS data on a semidilute solution of polystyrene in carbon disulphide. Since the solvent contains no protons, no deuterium labelling is necessary for good scattering contrast. Fitting Eq. (5.75) with the good solvent value of l/i> = 1.7 to the data yields =5.5nm and provides an excellent description of the data. 

Small-angle neutron scattering data for a semidilute solution of polystyrene (M = 1 100000 gmol ) in CS2 with i" = 0.025g/mr 2.5c. The curve is... 

Dynamic modes of semidilute solutions can also be studied using dynamic scattering. The dynamic structure factors S(q, t) of these more complicated systems still have a simple diffusive behaviour at low values of... 

FIG. 2 Relaxation times of dynamic modes observed in polyelectrolyte solutions and mixtures over a broad range of experimental conditions 0 diffusion of low molecular weight salt diffusion of polyions or polyion segments in semidilute solutions 3 interaction mode in polyelectrolyte mixtures and diffusion of polyelectrolyte domains (clusters). The data are based mostly on the work on linear flexible polyelectrolytes. Relaxation times correspond to scattering at 90°. See text for more details. 

Sedlak M, Konak , Stepanek P, Jakes J. Semidilute solutions of poly-(methacrylic acid) in the absence of salt dynamic light scattering study. Polymer 1987 28 873-880. 

The dynamic behavior of linear charged polyelectrolytes in aqueous solution is not yet understood. The interpretation of dynamic light scattering (DLS) of aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) is particularly complicated. The intensity correlation function shows a bimodal shape with two characteristic decay rates, differing sometimes by two or three orders of magnitude, termed fast and slow modes. The hrst observations in low salt concentration or salt free solution were reported by Lin et al. [31] for aqueous solutions of poly(L-lysine). Their results are described in terms of an extraordinary-ordinary phase transition. An identical behavior was hrst observed by M. Drifford et al. in NaPSS [32], Extensive studies on this bimodal decay on NaPSS in salt-free solution, or solutions where the salt concentration is increased slowly, have been reported [33-36]. The fast mode has been attributed to different origins such as the coupled diffusion of polyions and counterions [34,37,38] or to cooperative fluctuations of polyelectrolyte network [33,39] in the semidilute solutions. 

The existence of a bimodal linewidth distribution may be attributed to several factors. When a polymer is large, interference between segments of the same chain will give rise to an intramolecular scattering contribution to the linewidth. We have ruled out this possibility since K has a maximum value of 1.2 and is often much less than one in our experiments. Thus, our experiments cannot observe the contributions due to internal motions and they amount to, at most, one to two percent of the total scattered intensity.(lO) We have also made other studies whereby a second faster peak can be attributed to a pseudo-gel motion in semidilute solutions (l ). This explanation is unreasonable because the concentrations of our solutions are very small. We should not have reached the semidilute regime. 

Only at a sufficiently high polymer concentration, when the dimensions of the arms approach those of individual linear chains in a semidilute solution at the same concentration, do the star coronae become fully interpenetrated and the correlation peak in the scattering curves disappears. In this concentration regime, the thermodynamic properties of the solution of branched macromolecules become similar to those of linear chains. 

This prediction on the shrinkage of the polymer chains in semidilute solution was confirmed by neutron scattering. ... 

Scattering from semidilute solutions of star polymers 64... 

Remarkably, as follows from eqn [43], the size of an individual chain in semidilute solution decreases as a function of the average solution concentration. This is explained by progressively enhancing screening of the intramolecular repulsions. The predicted by eqn [43] concentration dependence of the individual chain dimension has been confirmed in neutron scattering experiments with labeled chains. At c c, individual chains in semidilute solution are strongly overlapped and interpenetrate the average concentration of... 

The intensity of radiation scattered by semidilute solution of star polymers can be decomposed into two contributions ... 

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