Dynamic viscosity dilute solution

Glowinkowski S, Gisser DJ, Ediger MD (1990) C-13 nuclear-magnetic-resonance measurements of local segmental dynamics of polyisoprene in dilute-solution— nonlinear viscosity dependence. Macromolecules 23(14) 3520-3530. doi 10.1021/ma00216a021... 

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

Fluorescence is measured in dilute solution of model compounds for polymers of 2,6-naphthalene dicarboxylic acid and eight different glycols. The ratio of excimer to monomer emission depends on the glycol used. Studies as functions of temperature and solvent show that, in contrast with the analogous polyesters in which the naphthalene moiety is replaced with a benzene ring, there can be a substantial dynamic component to the excimer emission. Extrapolation to media of infinite viscosity shows that in the absence of rotational isomerism during the lifetime of the singlet excited state, there is an odd-even effect In the series in which the flexible spacers differ in the number of methylene units, but not in the series in which the flexible spacers differ in the number of oxyethylene units. 

Note once again that equations (9.6) and (9.7) determines the stresses for the completely idealised macromolecules (without internal viscosity, hydro-dynamic interaction and volume effects) in dilute solutions. To remedy the unrealistic behaviour of constitutive equations (9.6) and (9.7), some modifications were proposed (Rallison and Hinch 1988 Hinch 1994). 

In the simplest case, at N = 1, the considered subchain model of a macromolecule reduces to the dumbbell model consisting of two Brownian particles connected with an elastic force. It can be called relaxator as well. The re-laxator is the simplest model of a macromolecule. Moreover, the dynamics of a macromolecule in normal co-ordinates is equivalent to the dynamics of a set of independent relaxators with various coefficients of elasticity and internal viscosity. In this way, one can consider a dilute solution of polymer as a suspension of independent relaxators which can be considered here to be identical for simplicity. The latter model is especially convenient for the qualitative analysis of the effects in polymer solutions under motion. 

Cooke BJ, Matheson AJ (1976) Dynamic viscosity of dilute polymer solutions at high frequencies of alternating shear stress. J Chem Soc Faraday Trans II 72(3) 679-685 Curtiss CF, Bird RB (1981a) A kinetic theory for polymer melts. I The equation for the single-link orientational distribution function. J Chem Phys 74 2016—2025 Curtiss CF, Bird RB (1981b) A kinetic theory for polymer melts. II The stress tensor and the rheological equation of state. J Chem Phys 74(3) 2026—2033 Daoud M, de Gennes PG (1979) Some remarks on the dynamics of polymer melts. J Polym Sci Polym Phys Ed 17 1971-1981... 

Rabin Y, Ottinger HCh (1990) Dilute polymer solutions internal viscosity, dynamic scaling, shear thinning, and frequency-dependent viscosity. Europhys Lett 13(5) 423—428 Rallison JM, Hinch EJ (1988) Do we understand the physics in the constitutive equation J Non-Newton Fluid Mech 29(l) 37-55... 

The still faster ( nsec) dynamics of local motions of polymer molecules in dilute solutions have been investigated by Ediger and coworkers (Zhu and Ediger 1995, 1997). They find that the rates of these local motions of a few bonds are not proportional to the solvent viscosity, unless the solvent reorientation rate is fast compared to the polymer local motion. Thus, for local motions (such as bond reorientations) of polymer molecules, Stokes law of drag does not always hold. 

Figure 6.17 Normalized intrinsic viscosity [r ]/[)7]o for a dilute solution of poly(y-benzyl-L-glutamate) (PBLG) = 208,000) in m-cresol. The line is a calculation for the rigid-dumbbell model, with the relaxation time t = lj6Dro adjusted to the value 10- sec to obtain a fit. The stress tensor for a suspension of rigid dumbbells is given by Eq. (6-36) with Cstr replaced by k T/Dro-(From Bird et al. 1987 data from Yang 1958, Dynamics of Polymeric Liquids, VoL 2, Copyright 1987. Reprinted by permission of John Wiley Sons, Inc.)...

Rheology is a powerful method for the characterization of HA properties. In particular, rotational rheometers are particularly suitable in studying the rheological properties of HA. In such rheometers, different geometries (cone/plate, plate/plate, and concentric cylinders) are applied to concentrated, semi-diluted, and diluted solutions. A typical rheometric test performed on a HA solution is the so-called "flow curve". In such a test, the dynamic viscosity (q) is measured as a function of the shear rate (7) at constant strain (shear rate or stress sweep). From the flow curve, the Newtonian dynamic viscosity (qo), first plateau, and the critical shear rate ( 7 c), onset of non-Newtonian flow, could be determined. 

It can be shown that for most dilute solutions there exists a simple correlation between dynamic and steady state flow characteristics (16). For most detergent solutions the magnitude of the complex viscosity 1 n I at a certain angular frequency CO coincides with the steady state viscosity n, at the corresponding shear rate "f (12, 17). 

In Figures 3 d, 3 e, and 3 f are shown the data on the dynamic properties of several dilute solutions. The quantities plotted there are the real and imaginary parts of the intrinsic complex viscosity ... 

Irradiation of solutions of concentration higher than 3% results in the formation of an insoluble gel because of intermolecular radical recombination similar to (4). In dilute solutions, however, intramolecular radical recombination occurs leading to cyclization. Decrease in the hydro-dynamic volume of the molecule is responsible for the decrease in the intrinsic viscosity of the solution. 

For polymeric fiuids, early Idnetic-theory workers (40) attempted to calculate the zero-shear-rate viscosity of dilute solutions by modeling the polymer molecules as elastic dumbbells. Later the constants in the Rivlin-Ericksen (17) expansion were obtained for dumbbells (41, 42) and other more complex models and only recently have the kernel functions in the memory integral expansions been obtained (43), This rapidly expanding field has been summarized recently in a monograph (44) here, too, molecular dynamics simulation may prove fhiitful (45),... 

Some questions arise from experimental facts pertaining to the relative viscosity, of certain dilute aqueous solutions, where r] is the dynamic viscosity of the solution and ) w that of water at the same temperature. Jones and Stauffer (1936) reported that for 0.09966 Mofcesium iodide at 25 = 0.98910, i.e., it is <1. 

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