Viscosity semidilute solutions

Dependencies of Viscosity and Modulus in Unentangled Dilute and Semidilute Solutions on c, N, and tn for Low and High Salt Conditions"... 

Therefore in this Rouse regime of unentangled semidilute solutions where hydrodynamic interaction is screened, both the reduced viscosity and reduced modulus decrease with increase in polymer concentration in salt free solutions... 

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. 

Figure 6.20 (a) Viscosity of solution of poly(y-benzyl-L-glutamate) (PBLG molecular weight 231,000), in m-cresol as a function of shear rate at 29 C for various mass percentages ranging from dilute ( 0.31%) to semidilute (0.31-2.5%) to concentrated isotropic (5-9.5%). The different symbols and lines refer to data taken on different instruments, (b) Zero-shear viscosity as a function of concentration, (reprinted with permission from Mead and Larson, Macromolecules 23 2524. Copyright 1990 American Chemical Society.)... 

It is expected that the same picture that gives a good account of the linear viscoelastic behavior of polymer melts should also hold for semidilute and concentrated solutions. In the case of semidilute solutions some conclusions can be drawn from sealing arguments (19,3, p. 235). In this way, concentration dependence of the maximum relaxation time tmax the zero shear rate viscosity r Q, and the plateau modulus G% can be obtained, where t is the viscosity of the solvent. The relevant parameters needed to obtain Xmax as a function of concentration are b, c, N, kgT, and Dimensional analysis shows that... 

However, polymer coils overlap and dominate most of the physical properties of semidilute solutions (such as viscosity). Thus, adding a very small amount of polymer to a solvent can create a liquid with drastically different properties than the solvent. This unique feature of polymer overlap is due to their open conformations. Linear polymers in solution are fractals with fractal dimension I) < 3. In semidilute solutions, both solvent and other chains are found in the pervaded volume of a given coil. The overlap parameter P is the average number of chains in a pervaded volume that is randomly placed in the solution ... 

This result can alternatively be obtained from a de Gennes scaling argument. At the overlap concentration 0 N the polymer contribution to viscosity is of the order of the solvent viscosity, and grows as a law in concentratioHrin semidilute solution -----------------------------... 

Concentration dependence of viscosity in semidilute solutions of polystyrene at 35 °C. (a) Solutions in the good solvent toluene have (pj(p reduce data for different molar masses to a universal curve, using data from M. Adam and... 

Consider a solution of polystyrene with molar mass M= 0°g moP in cyclohexane at 35 °C (0-solvent with viscosity ris = 7.6 x 10 Pa s). Estimate the relaxation time, plateau modulus, viscosity, and diffusion coefficient as functions of concentration in semidilute solution. 

Theoretical discussion of the concentration and molecular weight dependence of the viscosity of semidilute solutions of rigid-rod macromolecules has been reported. Doi and Edwards [1978] derived the well-known result... 

The success of the deGermes theory suggests that the viscosity in semidilute solutions can also be explained in terms of the universal length and the actual radius of gyration of the macromolecules. This theory is presented in Section 6.4. 

The viscosities of some semidilute solutions were measured by using a Brookfield cone/plate viscometer. All the measurements were performed at temperature 25 C. 

In good-solvent semidilute solutions (polystyrene-benzene), the viscosity q is proportional to that of the solvent and is a function of C/C. The relative viscosity = q/n can be described by a power law at 04C ... 

Fig. 3. Relative viscosity ( ) and longest relaxation time (o) in seconds as a function of molecular weight at a concentration of 5% in polystyrene cyclohexane semidilute solutions at 35 C. 

As the hydrodynamic interaction is screened in semidilute solutions, the molecular weight dependencies of the diffusion coefficient, the longest relaxation time, and the viscosity change in the semidilute solutions are exactly the same as in the Rouse model. However, since the Rouse model was originally designed for an isolated chain, the concentration dependencies of these quantities are not captured by the Rouse model. Nevertheless, we shall refer to the correct description of polymer dynamics in semidilute solutions as the Rouse regime. A summary of the main results for the Zimm model in dilute solutions... 

A. Jamieson and D. Telford. Newtonian viscosity of semidilute solutions of polystyrene in tetrahydrofuran. Macromolecules, 15 (1982), 1329-1332. 

C. E. loan, T. Aberle, and W. Burchard. Light scattering and viscosity behavior of dextran in semidilute solution. Macromolecules, 34 (2001), 326-336. 

The obviousness of this updating is confirmed by the reduction of the concentration dependences of the viscosity of solutions of different polymers to the generalized curves in the corresponding coordinates for the region of dilute and semidilute solutions (Fig. 9.1). The specific features of the chain structure... 

In semidilute solution and upon addition of salt (NaCl) an anti-poly-electrolyte effect was observed. That means that the viscosity ifacreased with the ionic strength and was several orders of magnitude higher than that measured in pure water [8-9]. 

The semidilute solution behavior of these materials was described elsewhere [9]. We want to mention here that in pure water and above a critical polymer concentration, Cp, the viscosity of the modified polymers rise sharply and can be several orders of magnitude higher than that of the precursor. The longer the alkyl chain and the higher the modification degree the lower the C value [9]. Above the C , the addition of small amounts of NaCl leads to a further enhancement of the viscosity. 

Surprisingly the sample modified with the shorter alkyl chain (3-C8) presents a slight increase in the viscosity ratio as the salt concentration increases. Obviously the octyl groups are too short to induce hydrophobic aggregation as was also put forward by the study of this polymer in semidilute solution [9]. The slight increase in viscosity is due to other effects which will be discussed in the last section of this paper. 

The rheological behavior of ionomer solutions in nonpolar solvents were extensively studied [16 -33]. Typical reduced viscosity-polymer concentration profiles of dilute and semidilute solutions of S-PS ionomers and of unmodified polymer are presented in Fig. 19.1. At low concentration the viscosity of ionomer solutions is lower than that of the reference polymer but increases much more... 

---