Calculation of intrinsic viscosity

The size exclusion chromatography for this study was done in the routine manner execept for the inclusion of an online viscosity detector called a Differential Viscometer <3> (Viscotek Corp., Porter, Texas, USAl. This instrument together with an RI concentration detector permits the calculation of intrinsic viscosities across the chromatogram. An IBM PC data system with software is also provided (5). The software acquires data from both detectors, and performs calculations of intrinsic viscosity and molecular weight distributions using the Universal Calibration Method. 

The extremely simple expressions for intrinsic viscosity at zero gradient and sedimentation coefficient containing in the denominator the square root of molecular weight agree very well with experimental data of theta solutions in the whole range from fully drained to impermeable coil. They turned out to be very good approximations of the more complicated expressions derived by Kirkwood-Riseman and Debye-Bueche ° and hence were used for the calculation of intrinsic viscosity of polydisperse samples. 

All values were calculated for intrinsic viscosity of gelatin B solutions to 37.4°C and compared against the value of Huggins, normally used as standard. It is noteworthy that each method has a relative error percentage and low for methods of more than four pair s values (Er% > 0.30). 

Since the measurements most commonly used as an index of long branching are those of intrinsic viscosities, whereas the most readily calculable theoretical measures of branching are the purely geometrical quantities or g0, and since the theoretical problem of relating these is not completely solved (Section 4), one of the applications of model branched polymers is to test proposed relationships. 

Calculate the intrinsic viscosity for these two polymers. The Mark-Houwink constants for this system are known to be a = 0.72 and k = 11 x 10 4 dl g-1 calculate the molecular weights of the two nylon fractions. 

EXAMPLE 13.5 Determination of the Thickness of Adsorbed Polymer Layer from the Intrinsic Viscosity of the Dispersion. An adsorbed layer of thickness 8RS on the surface of spherical particles of radius R increases the volume fraction occupied by the spheres and therefore makes the intrinsic viscosity of the dispersion greater than predicted by the Einstein theory. Derive an expression that allows the thickness of the adsorbed layer to be calculated from experimental values of intrinsic viscosity. 

The intrinsic viscosity [17] (dl/g or ml/g) is an important physico-chemical constant of polymers estimated by extrapolation to an infinite dilution, that is to a zero concentration of the polymer. (For the Fikentscher function k — Eigenviscositat — see p. 278). If the intrinsic viscosity were in fact a measure of the length of the polymer chain molecules, then it would be expected not to vary as a result of changing the solvent. Dobry [59] has determined the viscosities of 0.04% solutions of nitrocellulose (11.4% N) in different solvents and calculated the intrinsic viscosity by means of extrapolation. The results are collected in Table 43. The changes in the... 

The Mw values are in better agreements than MN9s. They are in the range 40,000-48,000. The Mw calculated from intrinsic viscosity favors equation for fractions rather than that for whole polymers. The best estimates of MW/MN ratios are 2.0-3.5. 

While the data of Figures 1, 2, and 3 are plotted in terms of M, the parameter actually measured in gel permeation experiments is Re. The Re of a random coil can be calculated from intrinsic viscosity data using the expression... 

From the adsorbance of dimethylsiloxane blocks, the mean separation y between adjacent dimethylsiloxane chains was calculated and found to be almost equal to the radius of gyration (s2)1,2 of the dimethylsiloxane chain calculated from intrinsic viscosity. 

An example illustrating the application of Eq. (2.4) for calculating Mn is shown in Fig. 2.2. The position of the line at 45° reflects the exact equality of the Mn values calculated from the concentration of active centers and those determined by measurement of intrinsic viscosity, [r ]. Bearing in mind possible experimental errors and the accuracy of the equation relating [tj] and Mn, we can conclude that the correspondence between the two series of Mn values is satisfactory. 

The irradiation dose was 12 Mrad/h from a source of total activity of 8000 Ci. The gels were prepared from 5% starch suspensions. Calculated from intrinsic-viscosity data determined in 90% aq. Me2SO. 

By calculating the intrinsic viscosity of a macromolecule using Equation (4.2) we can determine how the viscosity is affected. For instance, the shape of the red blood cell influences the viscosity of blood. If the shape of the red blood cell changes from a disc to a prolate ellipsoid the viscosity of the blood will increase as will the energy required to pump blood through the capillaries. This occurs in sickle cell anemia when the disclike red blood cell changes in shape as a result blood flow and oxygen absorption are impaired. 

Figure 4.2. Determination of intrinsic viscosity. Intrinsic viscosity is determined by extrapolation of the reduced specific viscosity (r sr) to zero concentration. The reduced specific viscosity is calculated by taking the difference between the flow time in a capillary for polymer in a solvent and that of the pure solvent and dividing the difference by the flow time of the pure solvent times the polymer weight concentration. Data are shown for hyaluronan for various fractions isolated from bovine vitreous.

Pepper (7) has shown that for a DP calculated on the basis of intrinsic viscosity and yielding a DPvis 5 X 102, DPn 1 X 102. Taking this latter value and using Equation 9... 

Calculated from the rate expression Rp = fcP[NVC][C7H7+SbCl6 ]. b Estimated from measurements of intrinsic viscosity in benzene at 25°C. (38). 

The procedure to determine the molecular weight of a branched polymer is as follows. If for a certain GPC column the universal calibration curve is measured with the aid of a series of monodisperse linear polymers of known molecular weight, the next step is to determine the elution volume and the intrinsic viscosity of the unknown branched fraction. Then the product [rj]M corresponding to the mean elution volume of a branched fraction is read from the universal calibration curve this value divided by the determined intrinsic viscosity gives the molar mass of the fraction. At the same molar mass one can also calculate the intrinsic viscosity of the linear polymer by using the Mark-Houwink equation. 

The value of the intrinsic viscosity of the sample calculated in this fashion, [77], can then be compared to that obtained experimentally for the whole sample, [77]. But you need a value of A to do these calculations. So what you actually do is first calculate the intrinsic viscosity for the sample as if it were linear, i.e., A = 0. Then, if the cal-... 

Calculate the intrinsic viscosity of the polymer and explain why there are such marked differences between these two sets of data. Because this is real data the results may be equivocal. You will be expected to comment on your conclusions and be critical in your answer ... 

Note that this procedure need not be restricted to determination of MHS constants in the GPC solvent alone [221. The ratio of intrinsic viscosities in Eq. (3-76) can be measured in any solvent of choice as long as the w, and Jj values for the two polymer samples of interest are available from GPC in a common, other solvent. The first step in the procedure is the calculation of K and a in the GPC solvent as outlined in the preceding paragraph. The intrinsic viscosities of the same two polymers are also measured in a common other solvent. The data pertaining to this second solvent will be designated with prime superscripts to distinguish them from values in the GPC solvent. In the second solvent,... 

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