Viscosity experimental considerations

We must be careful in assessing the experimental results on the viscosity of branched polymers. If we compare two polymers of identical molecular weight, one branched and the other unbranched, it is possible that the branched one would show lower viscosity. Two considerations enter the picture here. First, since the side chains contribute to the molecular weight, the backbone chain... 

Experimental considerations For the measurement typically several concentrations are prepared and the specific viscosity t]sp or reduced viscosity f)red — r jr 0 are extrapolated to zero concentration. In the literature three different approaches are used to obtain the intrinsic viscosity and, with known [f)]-M relation, the molar mass. 

By way of example, the experimental results of Meissner (1971) on low-density polyethylene have been represented in Fig. 15.22, by plotting rie/))eo against t/x0 with as a parameter. For low values of all points lie on a single curve, which shows some correspondence to the curves of Fig. 15.16 for rj/rj0 against yxQ. If e > 1, however, the extensional viscosity increases considerably with increasing extension. 

It has been a common practice to measure the viscosities in a multigradient viscometer. The relative viscosities at each concentration are then plotted against the rates of shear, followed by extrapolation to zero rate of shear and the intrinsic viscosity is calculated from these intercepts for various concentrations in the customary Huggins plot. From both theoretical and experimental considerations, however, the shearing stress rather than the rate of shear should be preferred, although tradition has emphasized the latter (Section IV, C). 

Staudlnger (1932) on the basis of experimental considerations had given an empirical equation relating viscosity to the molecular weight of a macromolecular solute as... 

Empirical observations [9] indicate that smaller fiber diameters are obtained using low flows of material. Experimental considerations show that the viscosity greatly affects the diameter of the fibers. With increasing viscosity, the drop of material to be submitted to the electric field changes from a semi-spherical shape to a conical shape, and the length of the jet increases to a steady/laminar flow. The diameter of the fibers increases with increased viscosity, proportionally to the length of the jet. 

Surface Tension. Interfacial surface tension between fluid and filter media is considered to play a role in the adhesion of blood cells to synthetic fibers. Interfacial tension is a result of the interaction between the surface tension of the fluid and the filter media. Direct experimental evidence has shown that varying this interfacial tension influences the adhesion of blood cells to biomaterials. The viscosity of the blood product is important in the shear forces of the fluid to the attached cells viscosity of a red cell concentrate is at least 500 times that of a platelet concentrate. This has a considerable effect on the shear and flow rates through the filter. The surface stickiness plays a role in the critical shear force for detachment of adhered blood cells. 

Viscosity—Concentration Relationship for Dilute Dispersions. The viscosities of dilute dispersions have received considerable theoretical and experimental treatment, partly because of the similarity between polymer solutions and small particle dispersions at low concentration. Nondeformable spherical particles are usually assumed in the cases of molecules and particles. The key viscosity quantity for dispersions is the relative viscosity or viscosity ratio,... 

The authors of [40] used L. L. Blyler s and T. K. Kwei s formula to process experimental data [41, 8] and obtained good correlation between theory and experiment. In all the processed experiments viscosity was established in accordance with pressure at channel input. To describe data presented by C. J. Ma and C. D. Han [2-5], who1 studied freon-containing polymer melts, the same paper supposed that the entire volume of gas is expended in part on the increase of the free volume of the composition, and that the occupied volume also changes in its presence. This consideration made it possible for the authors of [40] to attain fair correlation between theory and practice. This makes, in our opinion, the ideas expressed in [39, 40] worthy of the most serious attention, however critical the following evaluation of these works may appear to the reader. 

Perrin model and the Johansson and Elvingston model fall above the experimental data. Also shown in this figure is the prediction from the Stokes-Einstein-Smoluchowski expression, whereby the Stokes-Einstein expression is modified with the inclusion of the Ein-stein-Smoluchowski expression for the effect of solute on viscosity. Penke et al. [290] found that the Mackie-Meares equation fit the water diffusion data however, upon consideration of water interactions with the polymer gel, through measurements of longitudinal relaxation, adsorption interactions incorporated within the volume averaging theory also well described the experimental results. The volume averaging theory had the advantage that it could describe the effect of Bis on the relaxation within the same framework as the description of the diffusion coefficient. 

The estimation of f from Stokes law when the bead is similar in size to a solvent molecule represents a dubious application of a classical equation derived for a continuous medium to a molecular phenomenon. The value used for f above could be considerably in error. Hence the real test of whether or not it is justifiable to neglect the second term in Eq. (19) is to be sought in experiment. It should be remarked also that the Kirkwood-Riseman theory, including their theory of viscosity to be discussed below, has been developed on the assumption that the hydrodynamics of the molecule, like its thermodynamic interactions, are equivalent to those of a cloud distribution of independent beads. A better approximation to the actual molecule would consist of a cylinder of roughly uniform cross section bent irregularly into a random, tortuous configuration. The accuracy with which the cloud model represents the behavior of the real polymer chain can be decided at present only from analysis of experimental data. 

Experimental measurements must be interpreted in connection with all external influences, including fluid flow, bulk viscosity, and pH of the system. Consideration must be given to whether the mass transport is occurring in one or more dimensions and whether mass transport is affected by pressure gradients and/or osmotic pressure gradients. 

T divided by the viscosity of the solvent r s. For n-octane this number is 837 K/cP at T = 323 K. The results of the fitting process are all below this theoretical value. This is not surprising, since even in the case of dilute solutions of unattached linear chains, the theoretical values are never reached (see Sect. 5.1.2). In addition the experimental T/r s values differ considerably for the different labelling conditions and the different partial structure factors. Nevertheless, it is interesting to note that T/r s for the fully labelled stars is within experimental error the arithmetic mean of the corresponding core and shell values. 

The dynamic surface tension of a monolayer may be defined as the response of a film in an initial state of static quasi-equilibrium to a sudden change in surface area. If the area of the film-covered interface is altered at a rapid rate, the monolayer may not readjust to its original conformation quickly enough to maintain the quasi-equilibrium surface pressure. It is for this reason that properly reported II/A isotherms for most monolayers are repeated at several compression/expansion rates. The reasons for this lag in equilibration time are complex combinations of shear and dilational viscosities, elasticity, and isothermal compressibility (Manheimer and Schechter, 1970 Margoni, 1871 Lucassen-Reynders et al., 1974). Furthermore, consideration of dynamic surface tension in insoluble monolayers assumes that the monolayer is indeed insoluble and stable throughout the perturbation if not, a myriad of contributions from monolayer collapse to monomer dissolution may complicate the situation further. Although theoretical models of dynamic surface tension effects have been presented, there have been very few attempts at experimental investigation of these time-dependent phenomena in spread monolayer films. 

The reader is cautioned that there is often a considerable divergence in the literature for values of rate constants [Buback et al., 1988, 2002], One needs to examine the experimental details of literature reports to choose appropriately the values to be used for any needed calculations. Apparently different values of a rate constant may be a consequence of experimental error, experimental conditions (e.g., differences in conversion, solvent viscosity), or method of calculation (e.g., different workers using different literature values of kd for calculating Rt, which is subsequently used to calculate kp/kXJ2 from an experimental determination of Rp). 

---