Intrinsic viscosity ratios

Relationships between dilute solution viscosity and MW have been determined for many hyperbranched systems and the Mark-Houwink constant typically varies between 0.5 and 0.2, depending on the DB. In contrast, the exponent is typically in the region of 0.6-0.8 for linear homopolymers in a good solvent with a random coil conformation. The contraction factors [84], g=< g >branched/ <-Rg >iinear. =[ l]branched/[ l]iinear. are another Way of cxprcssing the compact structure of branched polymers. Experimentally, g is computed from the intrinsic viscosity ratio at constant MW. The contraction factor can be expressed as the averaged value over the MWD or as a continuous fraction of MW. 

Much the most usual method of estimating branching is from the intrinsic viscosity ratio g1, defined in Eq. (4.2). In addition to the intrinsic viscosity of the sample, its (viscosity-average) MW must also be known, so that the denominator of the fraction (4.2) can be found. It is usual to use the light scattering technique for this, assuming that Afw = or if any information on the MWD is available, a correction may be applied to M . Recently it has become common to combine GPC measurements with those of viscosity see Subsection 9.2.4. 

The solution viscosity of cyclic polymers is lower than those of their linear analogues. The viscosity of cyclic and linear PS was preferentially studied and compared in cyclohexane, a theta solvent. Quite similar intrinsic viscosity ratios, [>/]c/[>/]i/ were determined by several research groups for this system for instance, values of 0.64-0.70 depending on the molar mass, of 0.67, and of 0.65 are reported. However, at high molar masses (>20 000gmor ), the ratio of intrinsic viscosities was found to approach unity.A similar tendency was reported also for cyclic and linear poly(2-vinylpyridine) and polybutadiene. For cyclic and linear PDMS, the ratio of intrinsic viscosities, [r ]cl[h] i under 0-conditions in bromohex-ane at 18 °C, was found to be equal to 0.66. ... 

Simha equation), where a/b is the length/diameter ratio of these cigarshaped particles. Doty et al.t measure the intrinsic viscosity of poly(7-benzyl glutamate) in a chloroform-formamide solution and obtained (approximately) the following results ... 

Based on these ideas, the intrinsic viscosity (in 0 concentration units) has been evaluated for ellipsoids of revolution. Figure 9.3 shows [77] versus a/b for oblate and prolate ellipsoids according to the Simha theory. Note that the intrinsic viscosity of serum albumin from Example 9.1-3.7(1.34) = 4.96 in volume fraction units-is also consistent with, say, a nonsolvated oblate ellipsoid of axial ratio about 5. 

Figure 9.3 Intrinsic viscosity according to the Simha theory in terms of the axial ratio for prolate and oblate ellipsoids of revolution.

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. 

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 dilute solution properties of copolymers are similar to those of the homopolymer. The intrinsic viscosity—molecular weight relationship for a VDC—AN copolymer (9 wt % AN) is [77] = 1.06 x 10 (83). The characteristic ratio is 8.8 for this copolymer. 

The significance of knowing the K and a values of fully hydrolyzed PVA is that molecular weight distribution data can be directly calculated using two methodologies. The first is the Mark-Houwink method, which requires prior knowledge of K and a values for fully hydrolyzed PVA and calibration standards such as PEG, PEO, or PSC. The second method is the intrinsic viscosity method. This method utilizes a simple ratio of the concentration signal to the specific... 

The simplest indicator of conformation comes not from but the sedimentation concentration dependence coefficient, ks. Wales and Van Holde [106] were the first to show that the ratio of fcs to the intrinsic viscosity, [/ ] was a measure of particle conformation. It was shown empirically by Creeth and Knight [107] that this has a value of 1.6 for compact spheres and non-draining coils, and adopted lower values for more extended structures. Rowe [36,37] subsequently provided a derivation for rigid particles, a derivation later supported by Lavrenko and coworkers [10]. The Rowe theory assumed there were no free-draining effects and also that the solvent had suf-... 

If the intrinsic viscosity is large (i.e., greater than about 4 deciliters per gram), the viscosity is likely to be appreciably dependent on the rate of shear in the range of operation of the usual capillary viscometer. Measurements in a viscometer permitting operation at a series of rates of shear extending to very low rates are then required in order to extrapolate nsp/c to its limiting value at a shear rate of zero. Extrapolation to infinite dilution does not eliminate the effect on this ratio of a dependence on shear rate. 

According to the interpretation given above, the intrinsic viscosity is considered to be proportional to the ratio of the effective volume of the molecule in solution divided by its molecular weight. In particular (see Eq. 23), this effective volume is represented as being proportional to the cube of a linear dimension of the randomly coiled polymer chain,... 

However, the quantity which is frequently discussed and related to specific branching models is the ratio of intrinsic viscosities at constant molecular weight )... 

At an equimolar ratio of the starting monomers the polymers formed have the highest intrinsic viscosity. 

In their seminal work in 1949, Zimm and Stockmayer [69] defined the ratio of the mean square radii of gyration of a branched and a linear polymer of equal molecular weight as the parameter g and is related to the parameter g, which is the ratio of the intrinsic viscosities of a branched and a linear polymer [65-69]. 

Figure 12. Variation of trans-i,4 content and intrinsic viscosity of polybutadiene with molar ratio of Bd to butylethylmagnesium (BEM). Conditions solvent, cyclohexane Mg-Al-Ba, 1.0/0.2/0.2 60°C.

Copolymer Feed Ratio Incorporated Intrinsic Viscosity (dL/g)... 

In addition, data on the size, shape and solvation of the polymer particles in aqueous solutions at temperatures below and above the transition phenomena registered by HS-DSC have been obtained [42]. Table 2 shows the results of capillary viscometry and light scattering experiments for the fractions p and s of poly(NVCl-co-NVIAz) synthesized at 65 °C from the feed with the initial molar comonomer ratio equal to 85 15. Since fraction p precipitates from the aqueous solution at temperatures > 34 °C, its intrinsic viscosity can be determined only at 20 °C, whereas for the fraction s such measurements were possible above and below the temperatures of the HS-DSC-registered conformational transition. 

Fig. 11. Variation of Qv/Q°° ratio ( ) and the reduced intrinsic viscosity of microgels [ird/frilo (O) with the DVB content in the monomer mixture. Experimental data points were taken from Hoffmann [70]. The dotted horizontal line represents the critical Qv/Q°° value for the onset of a phase separation.

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