Semidilute solutions intramolecular

Semidilute Viscometrics. Solution viscometrics at concentrations above the overlap concentration (C ) indicated dramatic effects caused by the associative nature of the hydrophobic groups in the polymer. As shown by the reduced viscosity-concentration profiles of Figure 3, the introduction of only 1.0 mol % N-n-octylacrylamide to polyacrylamide can increase the viscosification efficiency dramatically. Increasing the hydrophobe level to 1.25 mol % further increased solution viscosity. At 2000 ppm, the presence of the hydrophobe caused a greater that 10-fold increase in viscosity. This result was in contrast to the behavior of these polymers in dilute solution see the box in Figure 3). The presence of hydrophobic functionality on the polymer resulted in a decrease in the reduced viscosity at concentrations below C. In dilute solution, intramolecular hydrophobic associations decreased the hydrodynamic radii of the polymer coils and thus reduced the... 

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. 

The first theories that implemented a proper balance of intramolecular interactions and conformational elasticity of the branches were developed by Daoud and Cotton [21] and by Zhulina and Birshtein [22-24]. These theories use scaling concepts (the blob model), originally developed by de Gennes and Alexander to describe the structure of semidilute polymer solutions [64] and planar polymer brushes [65, 66]. Here, the monomer-monomer interactions were incorporated on the level of binary or ternary contacts (corresponding to good and theta-solvent conditions, respectively), and both dilute and semidilute solutions of star polymers were considered. Depending on the solvent quality and the intrinsic stiffness of the arms, the branches of a star could be locally swollen, or exhibit Gaussian statistics [22-24]. 

The scaling concept was applied for the analysis of chain conformations and static properties of the semidilute polymer solutions. The unique characteristic length scale in dilute solution imposes a unique characteristic concentration of the solution, which coincides with the intramolecular concentration c in an isolated coil. All the properties of the semidilute solution can be derived from those of the dilute solution by scaling procedure with the aid of proper crossover functions of a single dimensionless variable c/c. These crossover functions are universal, that is, independent of any details of chemical stmcture of the chains, and exhibit power-law asymptotic behavior at c/c 1. 

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... 

On the other hand, the crossover from dilute to semidilute regime in solutions of randomly branched polymers is strongly affected by size and shape polydispersity. In particular, at moderate concentrations, large dusters are overlapped, whereas the smaller ones still behave as in the dilute regime, penetrate the larger ones, and contribute to screening of the intramolecular exduded-volume repulsions. The concentration effects in semidilute solutions of polydisperse randomly branched polymers were analyzed in detail in Reference 158. 

Hence, no forces arise and the polymer chain does not expand. In the literature one often finds a particular formulation for addressing this effect. As the concentration gradient given for an isolated chain is compensated for by the presence of monomers from the other chains, one says that the latter ones screen the intramolecular excluded volume interactions. Here we leave it at this short remark. Further comments on this picture and the origin of the saying will follow at a later stage when we discuss the properties of semidilute solutions. 

In the previous chapter, we considered the structures of single chains in the dilute regime. Now we may inquire how these become altered in semidilute solutions. Discussions can be based on the pair distribution function of the individual chains, thereby focussing on the structure of single chains in states where chains overlap and interpenetrate. We choose for this intramolecular pair correlation function a symbol with a hat, g(r), to distinguish it from the general pair distribution function g(r), which includes monomers from all chains. 

Star-branched polymers upon the increase in star concentration, occurs only in the semidilute regime, i.e., when the average polymer concentration in the solution exceeds the intramolecular concentration in an isolated star [24]. 

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