Table 111. Polyester Prepolymer HPLC Analytical Results Lot No. 2 Component Lot No. 1 10.15 12.95 BHET‘ 14.52 16.55 Dimer X i0.35 i0.71 U 2.4% 4.3% RS D 13.30 14.46 Trimer X t0.63 i0.79 U 4.7% 5.5% RSD 10.42 9.14 Tetramer X t0.76 i1.02 U 7.3% 11.1% RSD 6.90 5.19 Peritamer X r0.59 t0.39 U 8.6% 7.5% RSD 5.00 3.47 Hexamer X i0.25 i0.15 U 5.0% 4.3% RSD Heptamer X 3.51 U i0.51 RSD 14.3% HPLC total (less BHET) 53.71 48.81 19.38 24.10 GC total 73.09 72.91 Total assay Number of determinations 5 4 a Results from GC analysis. HPLC methods. The GC results are listed in Table I1 and show less than 25% of the sample is determined; over 75% is unaccounted for. Table I11 lists the HPLC results with precision data for the two prepolymer samples. These results show the greatly increased assay of the prepolymer possible by using the HPLC method. The prepolymer chromatogram given as Figure 2 does show the presence of oligomers higher than heptamer which are not well enough resolved for quantitation. The HPLC procedure, like the TLC methods reported in the literature ( 3 , 4 ) ,is based on adsorption chromatography. The oligomers assayed by this HPLC method are of the G(TG), series, where G = ethylene glycol and T = terephthalic acid. Attempts to analyze MHET were unsuccessful, as no
peak eluted. Because of their higher polarity, carboxyl-ended oligomers based on MHET are retained on the column. Cyclic oligomers, if present, would elute rapidly because of their lack of free end groups. No cyclic oligomers were detected in any prepolymer samples; however, chloroform extracts of ground polyester resin did show a component which eluted shortly after the HPLC solvent front. Since commercial polyester contains approximately 1-2% cyclic trimer, the observed HPLC peak is most probably the cyclic trimer. Du Pont (5) has separated prepolymer oligomers through tetramer by steric exclusion chromatography (GPC), which is based solely upon molecular size separation. However, the resolution was poor and no oligomers above tetramer were even detected. The procedure described in this paper clearly resolves oligomers through heptamer with octamer and nonamer visible as shoulder peaks which are not quantifiable.
APPENDIX A The structures of the compounds discussed in this paper are as follows: 1. Ethylene glycol (EG): HOCH2CH20H. 2. Diethylene glycol (DEG): HOCH2CH20CH2CH20H. 3. Terephthalic acid (TA): 1,4-C6H4(COOH)2. 4. Mono(2-hydroxyethyl) terephthalate (MHET): 1,4-
CGH~(COOH)(COOCH~CH~OH). 5. For bis(2-hydroxyethyl) terephthalate and the higher oligomers, the following structure can be assigned: HO(CHzCHzOCO-1,4-C6H4COo),cH~CH2OH,where for n = 1, the compound is BHET; for n = 2, the compound is dimer; for n = 3, the compound is trimer, etc. (1) E. R.
LITERATURE CITED Atkinson and S. I. Caiouche, Anal. Chern., 43, 460 (1971).
(2) J. Yamanis, R. Vilenchlch, and M. Adelman, J . Chromatogr., 108, 79 (1975). (3) S.Mori, S. Iwasaki, M. Furusawa, and T. Takeuchi, J. Chromatogr.,62, 109 (1971). (4) K. Dimov and E. Terlemezyan, J . folym. Sci., 10, 3133 (1972). (5) R . C. Williams, Du Pont Instruments Applications Laboratory, private communication, July 9, 1971, “Analysis of Polyester Oligomers”.
RECEIVED for review March 9,1977.
Accepted April 22,1977.
Experimentally Measured Mass Absorption Coefficients in Quantitative X-ray Diffraction Analysis Stefan0 Battaglia and Leonard0 Leoni” Institute of Mineralogy and Petrology, University of Pisa, 56 100 Pisa, Italy
Experimental mass absorption coefflclents, determlned from the measured lntensltles of Ag K a Compton scattered radlatlon, were used to carry out a quantitative x-ray diffraction analysls of a crystalline powder. The analysls was performed on three series of binary mixtures: quatlz-hematlte, quartr-calclte, and hematlte-calcite.
One of the most powerful techniques to obtain a quantitative analysis of a crystalline mixture is the x-ray powder diffraction technique. The basic relation between the dif1168
ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
fraction intensity I,(hkl) of a crystalline component (i) contained in a sample and its concentration (Wt %) is given by:
x,
X. 1. = h 1.I 1 P
(1)
where is the total mass absorption coefficient of the sample at the diffracted wavelength and k , is a constant which depends on the characteristics of the apparatus and on the structure of component i. To correct for matrix effects (absorption), a constant and known quantity of a crystalline
~-
~~~
Table I. Diffracted Intensities and Values of the Computed and Theoretical Concentrations Series hematite-quartz Sample [hematite Hem. (wt %) Quartz (wt %) quartz 1
2 3 4 5 6 7
8 9 10 11
12 13 14 15
14820 13985 13604 12911 11721 10912 4715
1581 3468 7473 17528 38413 112268
Ihernatite
Icdcite
103.47b (99.12) 95.57 (95.19) 86.41 (90.15) 77.60 (80.00) 60 59.14 (59.06) 39.80 39.64 (39.01) 10.20 11.96 (10.45) Series hematite-calcite Hem. (wt %)
1720 2860 5793 9275 10676 12525 13025
160627 85529 75911 38728 21220 19640 10281 2732
0.90' 5.20 10.10 19.95 40.10 60.10 79.90 90
Icalcite
Iquartz
9ga 95 90 79.90
< 26
(0.86) 5.27 (5.28) 9.88 (10.28) 20.79 (20.36) 40.54 (40.47) 57.02 (60.22) 80.60 (79.42) 90.89 (89.42) Series calcite-quartz Calcite (wt %)
la
5 10 20.10 40 60.20 89.80
