Dilute polymer solutions Intrinsic viscosity

Anotlier simple way to obtain the molecular weight consists of measuring tire viscosity of a dilute polymer solution. The intrinsic viscosity [q] is defined as tire excess viscosity of tire solution compared to tliat of tire pure solvent at tire vanishing weight concentration of tire polymer [40] ... 

Dilute Polymer Solutions. The measurement of dilute solution viscosities of polymers is widely used for polymer characterization. Very low concentrations reduce intermolecular interactions and allow measurement of polymer—solvent interactions. These measurements ate usually made in capillary viscometers, some of which have provisions for direct dilution of the polymer solution. The key viscosity parameter for polymer characterization is the limiting viscosity number or intrinsic viscosity, [Tj]. It is calculated by extrapolation of the viscosity number (reduced viscosity) or the logarithmic viscosity number (inherent viscosity) to zero concentration. 

The number average molecular weight is required. This is obtained directly from measurements of a colligative property, such as the osmotic pressure, of dilute polymer solutions (see Chap. VII). It is often more convenient to establish an empirical correlation between the osmotic molecular weight and the dilute solution viscosity, i.e., the so-called intrinsic viscosity, and then to estimate molecular weights from measurements of the latter quantity on the products of polymerization. 

We attempt here to develop a mathematical expression for the dependence of the dilute solution intrinsic viscosity of multispecies polymers on both molecular weight and polymer composition with some broad degree of generality and to particularize the result for the specific cases of copolymers and terpolymers such as SAN and S/MA/MM. The details of the derivation are specific to polymers resulting from addition polymerization across a single double bond in each monomer unit. In principle the approach may be expanded to other schemes of polymerization so long as... 

Shape effect of PFPE molecules or magnetic particles in suspension, including agglomeration phenomena at low concentration, interaction among these particles, and effects of floes can be examined via solution viscosity (r ) measurement. For a very dilute polymer solution [108], there is no interaction among polymer molecules, and the solution viscosity results from the contribution of the solvent plus the contribution of the individual polymer molecules. The intrinsic viscosity, therefore, is a measure of the hydrodynamic volume of a polymer molecule as well as the particle aspect ratio. Figure 1.24 shows the determination of the intrinsic viscosity for Zdol4000 in three different solvents. 

Theory (Odijk et al., 1977/79, Mandel et al., 1983/86) predicts that in the dilute state (c < c ) most of the parameters of the solution (intrinsic viscosity, diffusivity, relaxation times) will be functions of the molar mass, but not of the polymer concentration. In the so-called semi-diluted solution state the influence of the polymer concentration (and that of the dissolved salts) becomes very important, whereas that of the molar mass is nearly absent. Experiments have confirmed this prediction. 

For spheres, [t)] = 2.5. An exponential dependence on has been found for the relaxation time of flexible polymer molecules in the crossover regime from dilute to concentrated solutions (Amelar et al. 1991). [For polymers, the intrinsic viscosity is a dimensional quantity see Eq. (3-5).]... 

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. 

The intrinsic viscosity depends on the average molecular weight of the polymer by a power law behavior. It is given by Equation 12.7 for a dilute polymer solution under 0 conditions. 

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... 

Dilute Solution Properties. The rheology of dilute polymer solutions has been used extensively to gain insight into the structure and conformation of polymers in solution (11). The intrinsic viscosity provides a measure of the molecular weight of a polymer through a relationship such as the Mark-Houwink-Sakurada equation. Earlier studies of polyacrylamide (PAM) systems and details of the complexity of the characterization of high-molecular-weight water-soluble systems can be found in references 9, 13, and 14. 

Let us consider further simple technique of determination of fractal dimension -D of macromolecular coil in diluted polymer solution, within the framework of which the Eq. (11) was obtained. The determination of value is the first stage of macromolecular coils study within the framework of fractal analysis (see chapter 1) and the similar estimations are performed by measurement of the exponents in Mark-Kuhn-Hou-wink t5q)e equations, linking intrinsic viscosity [r ] (the Eq. (1)), translational diffrisivity or rate sedimentation coefficient with pol5mers molecular weight MM [3] ... 

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. 

Kraemer equation For dilute polymer solutions, an equation relating the inherent viscosity to intrinsic viscosity and concentration. It is... 

Viscosity-Average Moiecuiar Weight. The viscosity of dilute polymer solutions may be related to the molecular weight of the polymer by the appropriate calibration (see Viscometry). The polymer is usually separated into narrow molecular weight distribution fractions, which are characterized by absolute molecular weight methods. The molecular weight is related to the intrinsic viscosity [ j] by the Mark-Houwink relationship (eq. 6). 

In the case of dilute polymer solution, rj is the intrinsic viscosity a 0.7 and K depends on temperature and solvent nature. In contrast, in the case... 

Polymer surfactant, poly(Na-acrylamidoalkanoate)s [73] at a low concentration, was observed to increase its viscosity with dilution. Moreover, the intrinsic viscosity is strongly influenced by the presence of electrolytes. The viscosity of this polymerized surfactant decreased markedly with the addition of NaCl, indicating that the electrostatic repulsions between the charged head are suppressed, which causes a contraction of the polymer chain in the solution. The mixture of this surfactant with alum [74] was found to show coagulant properties in the same manner as cationic polyamines. 

The intrinsic viscosity ( /] is obtained by extrapolation of reduced viscosity of the dilute polymer solution (q-qs)lcqs> to zero polymer concentration, c—>0 (here rj is the viscosity of the polymer solution and the viscosity of pure solvent). In the nondraining limit of large N, the coils behave in a shear flow as impermeable for the solvent particles of effertive radius J ,. In dilute-solution limit, the Einstein equation i/ = i/s[l+ (5/2) ] applies, where is the volume fraction of particles in the solution. Hence, the intrinsic viscosity [i/] measures the (inverse) average intramolecular concenttation of the monomer units assuming that they are confined within a sphere of radius J ,. 

FOX Fox, T.G., Properties of dilute polymer solutions 111. Intrinsic viscosity/tempeiature relationships for conventional poly methyl methacrylate. Polymer, 3, 111, 1962. 

---