Intrinsic viscosity number

Intrinsic viscosity is frequently used for linear macromolecular characterization, and intrinsic viscosity number values can be used to determine the molecular weight [15]. The intrinsic viscosity number is the... 

Table 9.3 lists the intrinsic viscosity for a number of poly(caprolactam) samples of different molecular weight. The M values listed are number average figures based on both end group analysis and osmotic pressure experiments. Tlie values of [r ] were measured in w-cresol at 25°C. In the following example we consider the evaluation of the Mark-Houwink coefficients from these data. 

All that can be concluded from the data given in the preceding example is that the particle is not an unsolvated sphere. However, when an appropriate display of contours is examined for f/fo (e.g.. Ref. 2), the latter is found to be consistent with an unsolvated particle of axial ratio about 4 1 or with a spherical particle hydrated to the extent of about 0.48 g water (g polymer). Of course, there are a number of combinations of these variables which are also possible, and some additional experimental data—such as the intrinsic viscosity—are needed to select that combination which is consistent with all experimental observations. 

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 viscosity ratio or relative viscosity, Tj p is the ratio of the viscosity of the polymer solution to the viscosity of the pure solvent. In capillary viscometer measurements, the relative viscosity (dimensionless) is the ratio of the flow time for the solution t to the flow time for the solvent /q (Table 2). The specific (sp) viscosity (dimensionless) is also defined in Table 2, as is the viscosity number or reduced (red) viscosity, which has the units of cubic meters per kilogram (m /kg) or deciUters per gram (dL/g). The logarithmic viscosity number or inherent (inh) viscosity likewise has the units m /kg or dL/g. For Tj g and Tj p, the concentration of polymer, is expressed in convenient units, traditionally g/100 cm but kg/m in SI units. The viscosity number and logarithmic viscosity number vary with concentration, but each can be extrapolated (Fig. 9) to zero concentration to give the limiting viscosity number (intrinsic viscosity) (Table 2). 

The relative viscosity of a dilute dispersion of rigid spherical particles is given by = 1 + ft0, where a is equal to [Tj], the limiting viscosity number (intrinsic viscosity) in terms of volume concentration, and ( ) is the volume fraction. Einstein has shown that, provided that the particle concentration is low enough and certain other conditions are met, [77] = 2.5, and the viscosity equation is then = 1 + 2.50. This expression is usually called the Einstein equation. 

The number-average molecular weight of dimethylsiloxane can also be determined from the intrinsic viscosity [Tj, dL/g] (extrapolated to zero viscosity) ia toluene or methyl ethyl ketone according to the foUowiag equatioa (339,340) ... 

Viscosity, intrinsic Also called limiting viscosity number. For a plastic, it is the limiting value of an infinite dilution. It is the ratio of the specific viscosity of the plastic solution to its concentration in moles per liter. 

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. 

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. 

Values obtained for and a for a number of polymer-solvent pairs are given in Table XXX. It will be observed that the exponent a varies with both the polymer and the solvent. It does not fall below 0.50 in any case and seldom exceeds about 0.80. Once K and a have been established for a given polymer series in a given solvent at a specified temperature, molecular weights may be computed from intrinsic viscosities of subsequent samples without recourse to a more laborious absolute method. 

We, therefore, propose an indirect method for obtaining the variation of the intrinsic viscosity and number average molecular weight across the chromatogram. First the intrinsic viscosity-molecular weight relationship for a polymer with long chain branching (LCB) is assumed to be expressable in a form similar to that used by Ram and Milts (6),... 

Since our indirect method produces both the linear (b=0) and branched intrinsic viscosities across the chromatogram, it is possible to estimate several LCB parameters as a function of elution volume or number average molecular weight. The branching factor G(V) can be written as... 

Intrinsic viscosity measurements were done with a large number of solvents varying in pH, ionic strength, etc., using Cannon-Ubbelohde semimicro dilution viscometers. This was done to provide information on the effect of mobile phase composition on the size of a polymer molecule in solution and thus to facilitate the interpretation of GPC behavior. 

The intrinsic viscosities and Mn (from vapour pressure osmometry) of a number of chemically modified polymers are listed in Table I. Figure 11 shows a plot of intrinsic viscosity versus... 

Figure 2. Relation between the intrinsic viscosity and the number-averaged molecular weight of trimethylsilylated alkoxide polymeric particles for Si(0C2H5) solutions with different r values. (Reproduced with permission from Ref. 3. Copyright 1984 North Holland Physics Publishing.)...

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