Viscosity of dilute solutions

For commercial purposes the molecular weight is usually characterised from measurements of the viscosity of dilute solutions. It has been shown that, for dilute solutions, the relation between the viscosity and the molecular weight (in this case the viscosity average molecular weight) may be given by the relationship... 

Huggins M.L. The Viscosity of Dilute Solutions of Long-Chain Molecules. IV. Dependence on Concentration. J. Am. Chem. Soc., 64,11 (1942) 2716-2718. 

We will now turn our attention from the viscosity of dilute solutions and look at the viscosity of melted polymers. The viscosity of melted polymers is important in transferring resins and in polymer processing such as determining the correct conditions to have a specific flow rate for injection processing and in determining the optimum conditions to get the necessary dimensions of extruded shapes. Fillers, plasticizers, temperature, solvents, and molecular weight are just some of the variables that influence the viscosity of polymer melts. Here we will look at the dependence of melt viscosity on polymer molecular weight. Polymer melts have viscosities on the order of 10,000 MPa (1 centipoise =0.001 Pa/sec). 

Huggins, M.L. 1942. The viscosity of dilute solutions of long-chain molecules. IV. Dependence on concentration. J. Amer. Chem. Soc., 64 2716. 

The properties of solutions of macromolecular substances depend on the solvent, the temperature, and the molecular weight of the chain molecules. Hence, the (average) molecular weight of polymers can be determined by measuring the solution properties such as the viscosity of dilute solutions. However, prior to this, some details have to be known about the solubility of the polymer to be analyzed. When the solubility of a polymer has to be determined, it is important to realize that macromolecules often show behavioral extremes they may be either infinitely soluble in a solvent, completely insoluble, or only swellable to a well-defined extent. Saturated solutions in contact with a nonswollen solid phase, as is normally observed with low-molecular-weight compounds, do not occur in the case of polymeric materials. The suitability of a solvent for a specific polymer, therefore, cannot be quantified in terms of a classic saturated solution. It is much better expressed in terms of the amount of a precipitant that must be added to the polymer solution to initiate precipitation (cloud point). A more exact measure for the quality of a solvent is the second virial coefficient of the osmotic pressure determined for the corresponding solution, or the viscosity numbers in different solvents. 

Viscosity of Dilute Solutions of Salts in Mixed Solvents... 

Pao,Y.-H. Dependence of intrinsic viscosity of dilute solutions of macromolecules on velocity gradient. J. Chem. Phys. 25,1294-1295 (1956). 

Considering the development of the theory of melt viscosity, one notices a similar kind of evolution as with the intrinsic viscosity of dilute solutions. In both cases starting points were formed by empirical relations describing the respective molecular weight dependencies. Only afterwards, the relations are interpreted on more fundamental grounds. 

Bawn, C. E. H. High polymer solutions. Part V. Effect of concentration on the viscosity of dilute solutions. Trans. Faraday Soc. 47, 97 (1951). 

Huggins, M. L. The viscosity of dilute solutions of long-chain molecules. 

For convenience, this chapter has been divided into three sections in which the viscosity of dilute solutions and dispersions, non-Newtonian flow, and the viscoelastic properties of semi-solid systems are discussed. 

Moore, W. R., Murphy, M., Viscosities of Dilute Solutions of Polyvinyl... 

Tn a previous symposium volume on this topic (7), we suggested that - the viscosity B coefficient for the solution of a salt in a mixed solvent could indicate preferential solvation of the ions by one solvent component over the other. This suggestion was supported by some measurements that were interpreted qualitatively as showing preference of potassium iodide for water over methanol, for example. As a start toward more systematic study of the effect, this chapter reports the measurement of the viscosities of dilute solutions of several salts in a single solvent pair, water-methanol. We also report a small step toward a quantitative interpretation. 

Physico-Chemical Properties of Salvarsan Solutions.— These solutions show the characteristic properties of colloids, dialysis through a parchment membrane showing but slight diffusion, w hiist in methyl alcohol solution diffusion takes place more readily. The disodium salt diffuses about four times as quickly as the free hydrochloride. Hie idscosity of aqueous solutions of Salvarsan increases from the moment of preparation until an approximately constant value is reached. This value is much higher than the initial value. As the concentration of the solution increases, the initial velocity of increase of scosity and the final value are affected, and the presence of acid or alkali also has a marked effect. With rise of temperature the viscosity more quickly attains its maximum value, but this value is diminished The viscosity of dilute solutions diminishes on keeping. The ps value of Salvarsan is 7-60 of the dihydrochloride, 2-41 of the monohydrochloride, 3-00 of the monosodium salt, 10-88 and of tlie disodium salt, 11 43. The presence of an isoelectric point at ps value about 3 4 is indicated. ... 

Comparisons of the predictions of the FENE dumbbell model with measurements of the extensional viscosity of dilute solutions have been fairly encouraging. Figure 3-2 compares the Trouton ratio predicted by a multimode FENE dumbbell model with experimental data for a Roger fluid Good agreement is obtained if one uses a value of the... 

Because of the polyelectroly tic nature, pectin solutions need to be made in excess of salt, usually in 0.05 0.1 M sodium chloride or phosphate, and use the same solvent for dilution (isoionic dilution) (Pals and Hermans, 1952). This is because, unlike neutrol polymers, the viscosity of dilute solution of polyelectrolytes displays unique dependence on concentration. As shown in Figure 9.5, the qsp of sodium pectate exhibits a maximum in pure water and low concentration of salt, a phenomenon caused by the so-called electroviscous effect. When the salt concentration is... 

An especially appealing aspect of the use of equations 11.25 and 13.8 to estimate Mcr is that Equation 11.25 was developed [11] by using data on rubbery polymers. It therefore relates more directly to the zero-shear viscosity of a polymer melt than does an extrapolation from data on the viscosities of dilute solutions under theta conditions. We have found that the use of equations 11.25 and 13.8 is generally preferable to the use of Equation 13.7 in calculating Mcr. The correlation developed for Vw in Section 3.B has allowed the much more general use of Equation 11.25 than was previously possible by using group contributions. 

Owing to the compact nature of globular proteins, their intrinsic viscosity is generally markedly lower than that of synthetic polymer having similar or higher molecular weight. In consistency with that, the specific viscosity of dilute solutions was found to be much more sensitive to the concentration of the polymer than to the presence of protein. In the limit of high dilutions,... 

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),... 

Capillary Viscometry. The viscosity of dilute solutions of the polymer was determined with a Canon-Fenske capillary viscometer set in a thermostat bath at 25 0.05 C. A stock solution of 0.15 g dL was prepared in distilled water, stored at 4 C for 2 days, and then filtered through a No. 1 sinter glass funnel to remove fibers and detritus from the preparation of the cellulose ether. Nine other solutions were prepared from this stock by dilution with filtered distilled water. All these solutions were then stored at 4 C for a further 24 h to ensure that all the solutions had the same temperature history, as this factor has been shown to be important in producing reproducible solutions of cellulose ethers (4, 5). The concentration range prepared was 0.015-0.15 g dL" and the flow times ranged from 294 to 1609 s. 

Since some of the solvents used on this study are mixed solvents, with both components having a high vapor pressure, it was necessary to study the viscosity of dilute solutions with sealed viscometers. Commercially available suspended level Cannon viscometers constructed to permit sealing under vacuum were used. The solution was filtered into the viscometer and degassed by successive freeze-thaw cycles, and the viscometer was sealed under vacuum. In use, the viscometer was mounted on a holder in a constant temperature bath to permit the rotation of the viscometer to the horizontal to fill the bulb, and rotation to the vertical for determination of the efflux time. 

Intrinsic Viscosity. Viscosities of dilute solutions determined with capillary viscometers were analyzed by the usual relations... 

Viscosity of dilute solutions. A capillary viscometer (Cannon-Manning semimicro, No. 100) was used for determination of the intrinsic viscosity and for study of enzymatic degradation. Measurements were carried at 37 C. For the latter study specific fluidities, the reciprocal of specific viscosity, were plotted against reaction time. With random degradation of a chain polymer a straight line is obtained by this plotting, and the slope of the line is proportional to the reaction rate constant (4). 

Besides, let s add to this analysis the characteristic times of the segmental motion, estimated based on coefficient of the frictional component of viscosity of diluted solution ), concentrated solution and melt ( ). 

Simha, R., Effect of shape and interaction on the viscosity of dilute solutions. Proceedings of the International Congress on Rheology, Holland (1948), Interscience Publishers, New York (1949). 

Simha, R., Remarks on the viscosity of dilute solutions of polymers and related phenomena. Part 111. Paper 2, in High-Polymer Physics, Robinson, H.A., Ed., Chemical Publishing Co., Inc., New York (1948). 

---