Semi-dilute polymer solutions

Prediction of Rheological Behaviour of Semi-Dilute Polymer Solutions at Finite Rates of Deformation... 

Below a critical concentration, c, in a thermodynamically good solvent, r 0 can be standardised against the overlap parameter c [r)]. However, for c>c, and in the case of a 0-solvent for parameter c-[r ]>0.7, r 0 is a function of the Bueche parameter, cMw The critical concentration c is found to be Mw and solvent independent, as predicted by Graessley. In the case of semi-dilute polymer solutions the relaxation time and slope in the linear region of the flow are found to be strongly influenced by the nature of polymer-solvent interactions. Taking this into account, it is possible to predict the shear viscosity and the critical shear rate at which shear-induced degradation occurs as a function of Mw c and the solvent power. 

Shear-banded Flow in a Semi-dilute Polymer Solution - T2 Effects... 

Fig. 58a, b. Segmental diffusion in semi-dilute polymer solutions. Schematic view of the Q-dependence of the relaxation rates Q(Q) at a fixed concentration. a Good solvent conditions b -conditions. (Reprinted with permission from [168]. Copyright 1994... 

Fig. 59. Incomplete screening of hydrodynamic interactions in semi-dilute polymer solutions. Presentation of different regimes which are passed with increasing concentration. A,C Unscreened and screened Zimm relaxation, respectively, B enhanced Rouse relaxation. (Reprinted with permission from [12]. Copyright 1987 Vieweg and Sohn Verlagsgemeinschaft, Wiesbaden)...

Since the cross linking density of the gel is low enough, there are many contact points between polymer chains. The structure of the gel, therefore, is analogous to that of the semi-dilute polymer solution suggesting that the concentration dependence of the correlation length is explained by the following power law relationship [6]... 

Their explanations of these results adapted scaling law concepts originally developed for semi-dilute polymer solutions [61]. 

Admittedly, much of our interpretation of the kinetic behavior of responsive gels can be criticized as hand-waving . More work is required to prove that the interpretations we have presented here are valid. However, the analogies between semi-dilute polymer solutions and gels have been well established by others. The step we have made here has been to extend these concepts from perturbations from equilibrium to the macroscopic shifts of practical interest in responsive gel applications. While this extension is fraught with hazards, the qualitative connections which seem to persist remain helpful and point the way for future work on kinetics. 

Hess W (1986) Self-diffusion and reptation in semi-dilute polymer solutions. Macromolecules... 

The long decay time (T2 ) of the other component is typical of semi-diluted polymer solutions. The T2 value continuously increases with an increasing solvent content. This... 

Callaghan, P. T., and Coy, A. (1992). Evidence for reptational motion and the entanglement tube in semi-dilute polymer solutions. Phys. Rev. Lett. 68, 3176-3179. 

Low temperature The polymer is in a good solution state and possesses the shape of an expanded coil. At low concentration, the polymer molecule has no contact with other molecules (single polymer chain). If the diluted solution is irradiated, radicals were produced and some polymer chains react. Molecules with high molecular weight, mostly branched, are formed (Quemer et al. 2004). Irradiation of a higher-concentrated polymer solution (semi-diluted polymer solution with concentration above the overlap concentration ), results in a homogeneous macroscopic (bulky) gel. 

Adam, M., and Delsanti, M., Viscosity of semi-dilute polymer solutions, J. Phys. (Paris), 43, 549-557 (1982). 

Heo, Y., and Larson, R. G., The scaling of zero-shear viscosities of semi-dilute polymer solutions with concentration, J. RheoL, 49, 1117-1128 (2(X)5). 

What do we mean by a polymeric fluid It is a viscous liquid, made of heavily entangled polymer chains. In particular, it could be a polymer melt, a concentrated or a semi-dilute polymer solution. You can easily get a feel for what these are like. All you need to do is melt a piece of ordinary plastic, so that it starts flowing. Obviously the most significant reason why polymeric liquids are important is because they are encountered in all technological processes of plastic production. Polymeric fluids are quite peculiar. In many ways, they are nothing like water or any other ordinary fluid that we are used to. 

Summarizing these experimental studies, we see that s as a function of c becomes independent of M regardless of solvent quality when the solution enters the semi-dilute regime. This feature suggests that the unit of sedimentation in semi-dilute polymer solutions is not an individual polymer chain but its subchain. 

Comparing of (1.71) with the experimental data allows for measurements of the viscoelastic relaxation time 0 of dilute and semi-dilute polymer solutions. 

In ref. [48] an environment of a quenched configuration of a semi-dilute polymer solution is introduced as a special case of long-range correlated disorder for polymer dynamics. For the statics this environment is shown to be equivalent to an annealed one, i.e. without impact. 

Ghoniem, S. Chauveteau G. Moan, M. Wolff, C. Mechanical degradation of semi-dilute polymer solutions in laminar flows. Can. J. of Chem. Engng. 59 (1981) 450-454... 

Fig. 3.10. Crystallization process of a single chain on the growth front of a small crystallite traced by the molecular simulations of a semi-dilute polymer solution. The crystalline units are the bonds containing five or more parallel neighbors. In contrast, the crystallization process on a very large growth front exhibits a continuous rather than the stepwise increase of the crystalline units [49]...

Entangled chains in semi-dilute polymer solutions, discussed in Section 12.4, are still able to move relative to each other. As a consequence, the system behaves as a liquid, albeit a viscous liquid. 

What is expected with respect to colloidal stability of large R 3> < ) and tiny R semi-dilute polymer solution ... 

Odijk [131-134] published a relevant series of papers devoted to the protein limit R he considered semi-dilute polymer solutions where the eorrelation length seales as He first ealeulated the density profile of a small eoUoid in... 

We now consider the large -limit, which is the regime where along the binodals exceeds unity, so we have semi-dilute polymer solutions. The characteristic length scale in semi-dilute polymer solutions is which scales as (4.15), (j)p. For colloid-polymer mixtures this expression can be rewritten in... 

In a semi-dilute polymer solution, there is a certain mutual friction between the coils and the solvent. The dissipated energy (per cm ) is of the form... 

This chapter extends the survey of literature of dilute and semi-dilute polymer solution properties - both theoretical and experimental aspects - begun in Part I of this series, to include literature appearing in the years 1979 and 1980. Our brief, introduced only shortly here, is to examine those aspects of the above properties that depend on the shape and size of polymer molecules, but not specifically upon their chemical nature. Some of the topics examined here will, judging by experience gained with the first volume, also appear in other chapters of this volume. In particular, reference should be made to the chapters covering neutron scattering (11), polymer characterization (12), and computer applications (19). 

C. M. Marques and J. F. Joanny, Adsorption of semi-dilute polymer solutions on fractal colloidal grains, J. Phys. France) 49, 1103 (1988). 

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