Specific viscosity, dilute polymer solutions

Owing to the coiled configurations of molecular chains, the viscosity r of dilute polymer solutions increases with respect to that of the solvent, rj. The difference q — is proportional to the radius of the coil and the number of coils per unit of volume is C/M)N, where C is the concentration of polymer in the solution, M is the molecular weight of the polymer, and is Avogadro s number. Since the radius of the coil can be expressed in terms of the mean square end-to-end distance, (r ), the specific increment of the viscosity of the solution due to the polymer can be written as... 

The opportunity to measure the dilute polymer solution viscosity in GPC came with the continuous capillary-type viscometers (single capillary or differential multicapillary detectors) coupled to the traditional chromatographic system before or after a concentration detector in series (see the entry Viscometric Detection in GPC-SEC). Because liquid continuously flows through the capillary tube, the detected pressure drop across the capillary provides the measure for the fluid viscosity according to the Poiseuille s equation for laminar flow of incompressible liquids [1], Most commercial on-line viscometers provide either relative or specific viscosities measured continuously across the entire polymer peak. These measurements produce a viscometry elution profile (chromatogram). Combined with a concentration-detector chromatogram (the concentration versus retention volume elution curve), this profile allows one to calculate the instantaneous intrinsic viscosity [17] of a polymer solution at each data point i (time slice) of a polymer distribution. Thus, if the differential refractometer is used as a concentration detector, then for each sample slice i. 

In Section 5.1.2 the effect of solute molecules and particles on viscosity is briefly discussed. It follows that the intrinsic viscosity [t/] is a measure of the extent to which a certain solute can increase viscosity. (Remember that t] equals specific viscosity — 1) divided by concentration for infinitesimally small concentration.) According to the Einstein equation (5.6) the specific viscosity of a dispersion of spheres is 2.5q>, where

volume fraction. This means that [t/] = 2.5

0, where c is concentration in units of mass per unit volume. For a very dilute polymer solution the effective volume fraction can be given as the number of molecules per unit volume N times (4/3)jir, where ty, is the hydrodynamic radius see Eq. (6.5). Furthermore, N = c- M/Nav- For the amylose mentioned in the question just discussed, rh x 25 nm and M = 106 Da. It follows that [//] would equal... 

A typical result of a calculation [127] of the complex viscosity rf(co) is shown in Fig. 11. The real part of the viscosity, / (w), which describes the dissipation of energy when the fluid is sheared, is approximately frequency-independent for small cu, i.e., the fluid behaves as a Newtonian fluid. There is a characteristic frequency co where f/ (o>) drops rapidly. The imaginary part of the viscosity, rf"(o)), which describes the elastic response of the fluid to an external perturbation, increases linearly for small co and reaches a maximum at CO = CO. This behavior is not specific to microemuisions but has been observed in other complex fluids as well, such as in suspensions of spherical colloidal particles [128,129] and in dilute polymer solutions [130]. 

Polymer solutions are never ideal since dissolved macromolecules influence each other even at very low concentration. On the other hand, a reliable correlation of solution viscosity and molecular weight is only possible if the dissolved macromolecules are not affected by mutual interactions they must be actually independent of each other. Therefore, the viscosity of polymer solutions should be determined at infinite dilution. However, such measurements are impossible in practice. So one works at an as low as possible polymer concentration and extrapolates the obtained values to zero concentration. To do so, the elution time measurements are not only carried out for one single polymer concentration but for varying polymer concentrations (e.g., 10, 5, 2.5, 1.25 g/1). For each solution, the value of the reduced specific viscosity is figured out (the data will make evident that this quantity is clearly concentration-dependent even at the lowest possible polymer... 

Experimentally, the viscosity of dilute polymer solutions is, in most cases, determined with glass capillary viscometers, making application of the Hagen-Poiseuille s law for laminar flow of liquids. The time required for a specific volume of a liquid to flow through a capillary of... 

Viscosimetric determinations. The Newtonian intrinsic viscosity of the xanthan molecule was determined by measuring the viscosities of several dilute polymer solutions with a Contraves Low-Shear viscometer. Extrapolation at zero polymer concentration of the reduced specific viscosity gave the value of the intrinsic viscosity, and the Huggins constant was calculated from the slope of the curve. 

For example, if we have two dilute polymer solutions at the same polymer concentration, but solution one contains polymer molecules having a molecular weight one-half that of the polymer in solution two, then the ratio of specific viscosity for the two solutions can be determined from equation (5),... 

For dilute polymer solutions a simple approximate expression for specific viscosity can be derived from Einstein s equation for a dilute suspension of hard (incompressible) spheres in a liquid. The viscosity of a suspension of N spheres, each with a hydrodynamic volume Ve in a total volume V of a liquid, is given by... 

In contrast to the later used specific viscosity, rjs is the viscosity of the diluted polymer solution and i/o is the viscosity of the pure solvent. With consideration of (20.24) Malkin developed a method to connect a measured viscosity diuing a polymerization with the kinetics of the reaction and called this method, rheokinetics [41]. The initial equation from 1980 is shown in (20.25). 

Intrinsic viscosity (rj) is the viscosity of an infinitely diluted polymer solution. It is a measure of the hydrodynamic volume occupied by a macromolecule, which is closely related to the size and conformation of the chain, but is independent of concentration of macromolecule. In dilute solutions, by definition, the polymer chains are separated and there is negligible interaction between them. Therefore, the (rj) of polymer in solution depends only on the dimension and the molecular weight of polymer chain. Experimentally determined values of the relative and specific polymer viscosities were used to calculate it, according to Huggins [53] and Kraemer [64] equations given by... 

The most widely used molecular weight characterization method has been GPC, which separates compounds based on hydrodynamic volume. State-of-the-art GPC instruments are equipped with a concentration detector (e.g., differential refractometer, UV, and/or IR) in combination with viscosity or light scattering. A viscosity detector provides in-line solution viscosity data at each elution volume, which in combination with a concentration measurement can be converted to specific viscosity. Since the polymer concentration at each elution volume is quite dilute, the specific viscosity is considered a reasonable approximation for the dilute solution s intrinsic viscosity. The plot of log[r]]M versus elution volume (where [) ] is the intrinsic viscosity) provides a universal calibration curve from which absolute molecular weights of a variety of polymers can be obtained. Unfortunately, many reported analyses for phenolic oligomers and resins are simply based on polystyrene standards and only provide relative molecular weights instead of absolute numbers. 

ISO 1628-4 1999 Plastics - Determination of the viscosity of polymers in dilute solution using capillary viscometers - Part 4 Polycarbonate (PC) moulding and extrusion materials ISO 7391-1 1996 Plastics - Polycarbonate (PC) moulding and extrusion materials - Part 1 Designation system and basis for specifications ISO 7391-2 1996 Plastics - Polycarbonate (PC) moulding and extrusion materials - Part 2 Preparation of test specimens and determination of properties ISO 11963 1995 Plastics - Polycarbonate sheets - Types, dimensions and characteristics. 

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). 

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. 

Figure 8 illustrates the relationship between inherent viscosity (IV) and concentration for PBI/PAr/NMP solutions. It is interesting to note that the IV of all solution blends exhibited normal polymer solution characteristics. At a fixed concentration (0.5%), it was noted that the IV of the solution blends exceeded the rule of mixtures (see Fig. 9) suggesting that PBI and PAr exhibit specific interactions in a dilute solution, such that the resulting hydrodynamic sizes of the blends were greater than that of the calculated averages based on each component. 

Intrinsic Viscosity. The intrinsic viscosities, [rf], of some of the crosslinked polymers (copolymer 2.2 mole % HEM A) were measured by successive dilution on the reacted solutions. Figure 12 shows that the change in [ry] at 25 °C. was, within the experimental error, related directly to the change in specific viscosity at 80°C. As Figure 13 shows, cross-linking reduced the intrinsic viscosity of the polymer solution and also altered the slopes of the lines for both rj/c and log (1 -f- rj)/c against c. 

Many foods contain high-molecular weight polymers, such as proteins, pectins, and others. Often, they contribute significantly to the structure and viscosity of foods. In dilute solutions, the polymer chains are separate and the intrinsic viscosity, denoted as [ ], of a polymer in solution depends only on the dimensions of the polymer chain. Because [ ] indicates the hydrodynamic volume of the polymer molecule and is related to the molecular weight and to the radius of gyration, it reflects important molecular characteristics of a biopolymer. The concentrations of polymers used should be such that the relative viscosities of the dispersions are from about 1.2 to 2.0 to assure good accuracy and linearity of extrapolation to zero concentration (Morris and Ross-Murphy, 1981 da Silva and Rao, 1992). Intrinsic viscosity can be determined from dilute solution viscosity data as the zero concentration-limit of specific viscosity (ijsp) divided by concentration (c) ... 

The intrinsic viscosity of a polymer is obtained from the viscosities 17 and no of solution and solvent, respectively, through the following transformations. The relative viscosity is the ratio nrei = v Vo- By assuming that the viscosity n of a dilute solution is given by the sum of viscosities from solvent and solute molecules, the specific viscosity, Tjsp, represents the polymer contribution to viscosity ... 

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,... 

Viscosity measurements of the polymer solutions are carried out with an Ubbelodhe viscometer. The viscosities are measured in dilute aqueous solution in neutral pH. The time of flow for solutions is measured at four different concentrations (i.e. 0.1%, 0.05%, 0.025% and 0.0125%). From the time of flow of polymer solutions (t) and that of the solvent (t, for distilled water), relative viscosity(Ti, ), specific viscosity (tj p), reduced viscosity (t ) and inherent viscosity(Tij jj) are obtained by the following 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). 

Only a very limited range of measiuements of physical properties has been made, and for dilute and moderately concentrated aqueous solutions of commonly used polymers including carboxymethyl cellulose, polyethylene oxide, carbopol, polyacrylamide, density, specific heat, thermal conductivity, coefficient of thermal expansion and surface tension differ from the values for water by no more than 5-10% [Porter, 1971 Cho and Hartnett, 1982 Irvine, Jr. et al., 1987]. Thermal conductivity might be expected to be shear rate dependent, because both apparent viscosity and thermal conductivity are dependent on structure. Although limited measmements [Loulou et al., 1992] on carbopol solutions confirm this, the effect is small. For engineering design calculations, there will be little error in assuming that all the above physical properties of aqueous polymer solutions, except apparent viscosity, are eqnal to the values for water. 

The limiting value (at infinite dilution) of the ratio of specific viscosity of the polymer solution to concentration. 

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