effect are shown in Figures 2 and 3. These are the expanded scale spectra in the methyl regions of hydroxypropyl cellulose and poly(propy1ene glycol), respectively. I n the latter, a methyl doublet a t lower field (80.4 Hz from TMS) grows in intensity and reaches a constant value as the concentration of isocyanate added increased. This can be assigned to end methyl protons. Figure 4 shows a plot of the ratio of the intensity of the low field doublet to that of the one at high field, 6s. the weight ratio of isocyanate to poly(propy1ene glycol). This is a typical titration plot, with two straight lines intersecting at the end point, a t which all the hydroxyls in the polymer chains are reacted. Goodlett ( I / ) found that trichloroacetylisocyanate reacted very rapidly with a variety of types of hydroxyl groups. I n our work, it appeared that the reaction was complete by the time the first NMR spectrum of the sample could be run, since n o change in the spectra was observed on standing for longer reaction times. Furthermore, addition of excess reagent to the sample caused no additional change in the spectrum. Therefore, the ratio of terminal methyls (END) to internal methyls (IN) in the polymer chain can be readily obtained and used t o calculate the number average molecular weight through : IN M - -__ X 116 134 (3) - END
(an)
+
A value of M , of 762 on the PPG sample was obtained’ which compares favorably with 790 from the supplier’s data and with 771 determined by a n independent N M R procedure (IO). However, because of the slight spectral overlapping of the upfield peak of the low field doublet with the low field peak of the high field doublet, and because of the fact that slight variations in the small value of E N D can cause a large error on it was more accurate to measure the E N D value by doubling the integrated area of the peak at lowest field, which is clearly resolved from spectral interferences. The resolution of end groups in PPG achieved by using this derivatizing reagent is greater than that reported using a solvent system of pyridine-HC1 (12). In the case of hydroxypropyl cellulose, a similar change in the methyl region was observed, as seen in Figure 2. The doublet a t lower field can be assigned t o terminal methyl groups. However, the spectral lines are broader than those observed in Figure 3, due t o the high viscosity of the sample solution and the fact that the methyls of hydroxypropyl cellulose are in slightly different structural environments in the more complex cellulose polymer. Because of this line broadening and overlap, only the resonance intensities from No. 1 (at 63.8 H z from TMS) and No. 4 (at 81.6 Hz) were measured. The ratio of intensities of these two lines was plotted against the weight ratio of isocyanate over hydroxypropyl cellulose sample in Figure 5 . Again, this is a typical titration plot, where N M R is used to follow the progress of titration. These data can be used to calculate MS and DS and the treatment of data is shown below. Treatment of Titration Data. M S VALUEFROM THE XAXIS. The amaunt of isocyanate reagent required per gram of sample is found from the X-axis in Figure 5 to be 1.400 grams. This can be used to calculate the moles of hydroxyls and therefore moles of the cellulose unit per gram of sample from the expression
mn,
Wt isocyanate __ - 1.400 3 X mol wt of isocyanate 188.4 X 3
=
2.48
x
10-3 (4)
(12) T. F. Page, Jr., and W. F. Bresler, ANAL.CHEM., 36,1981 (1964).
since each cellulosic unit carries 3 hydroxyls, regardless of size and extent of hydroxypropyl substitutions. The average molar weight of a unit is therefore Wt of sample l.Oo0 2.48 X No of moles of cellulose unit
=
4.04
x
102 (5)
This is a weight combination of hydroxypropyls (molar weight of 58) and a n anhydroglucose unit (molar weight of 162). Therefore, the average number of hydroxypropyl substituents per anhydroglucose unit or MS is : (Total wt) - (Wt cellulose) - 404 -162 Wt of hydroxypropyl 58
=
4.2
(6)
This value compares favorably with a value of 4.2 f 0.2 from the independent “direct ratio” method discussed earlier. DS VALUE FROM Y-AXIS. From an extension of the horizontal line in the titration plot in Figure 5 , one finds a ratio of peak No. 4/No. 1 of 1.53, which is a measure of the relative amount of terminal methyls and internal methyls, or END/IN
=
1.53
(7)
This together with a M S of 4.2 found earlier, or END
+ IN = 4.2
(8)
gives a value of 2.6 for END. This is the average number of terminal methyls per anhydroglucose unit and therefore is the average number of hydroxyl groups substituted, the DS. Because of the use of line intensity rather than the more accurate integrated area, and the uncertainty involved in measurements, the precision of DS is estimated at 5-10z. The accuracy of the DS determination cannot a t present be tested, since no referee method is available, and samples of known DS cannot be prepared. However, the determination of M , in the polypropylene glycol system can be used as a test of the quantitative accuracy of the procedure for end group analysis. As described previously, good agreement with other techniques was obtained. The precision of the special titration procedure for the determination of M S is comparable t o that of the direct ratio procedure, so that the more complex titration procedure is preferable only when a measurement of DS is required. The results of MS of 4.2 =t0.2 and DS of 2.6 f 0.2 on a Klucel E sample are approximately depicted by the idealized structure shown in Structure I. ACKNOWLEDGMENT
The authors thank E. D. Klug for helpful discussions and C. A. Lewis for the C-methyl analysis.
RECEIVED for review June 1,1971. Accepted August 23,1971.
Correct ion Separation of Uranium from Seawater by Adsorbing Colloid Flotation I n this article by Y. S. Kim and Harry Zeitlin [ANAL. CHEM.43, 1390 (1970)], there is an error in the abstract. Line 5 should read, “At pH 5.7 f 0.1 , , . ”.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
181
