Jan., 1962 the Warren scheme for the region of low alkali oxide content (< 15 mole %). At higher alkali contcnt, however, Warren assumes that some oxygens are bonded only to one boron, in which case the frartion of fourfold coordinated boron should be lcss than that given by the ratio S i (1- S). The dashed line in Fig. 1 indicates the values expected by Warren. I n order to investigate further the discrepancy between experimental and theoretical data we have repeated aiid extended some of Silver and Bray’s measurements. During this work we made the observation that there is a close agreement between the spectra of crystalline boron oxide and vitreous boron oxide, from which we infer that the similarity of the spectra is based on a corresponding similarity of the two states with regard tx, the boron coordination. These findings, on the other hand, suggest the existence of corresponding relationships between other crystalline and vitreous boron compounds. Sincc the crystalline compounds so far investigated all lie on the theoretical N4(S) curvc, the corresponding vitreous states are expected to yield Ne-values in the close vicinity of the theoretical line, an assumption which actually is borne out by experiment. I n particular, we may refer to a study of potassium borate glass a t room temperature. The samples were prepared by melting boric acid and potassium carbonate in a platinum crucible. After solidification, the samples were coated with a plastic to be protected against moisture. The cylinders prepared were 16 mm. in diameter and of 70 mm. length. The compositions were determined by analyses within 0.1%. Spectra were recorded with a Varian-4250 wide line spectrometer a t 13.0 Mc./ see. and three different settings of the radiofrequency field. Our recorded spectra were in agreement with those reported by Silver and Bray.2 A rigorous calculation of the fraction of fourfold coordinated boron based on a detailed analysis of the two lines would, however, require considerable work, while still yielding values of limited accuracy because of the poor signal-to-noise ratio of the recorded broad line spectrum. As the signal-tonoise ratio of the sharp line much exceeds that, of the broad one, we have therefore, to a first approximation, chosen to calculate only the area under the sharp absorption line as a measure of the changes in the amount of four-co6rdinated boron. The area is estimated to be of the magnitude y‘,.2’, where ylrll is the ordinate and zm the abscissa of the milximuni of the experimental sharp line derivative, taking the center of the line as origin. For absorp tiori curves of Gaussian or Lorentz line shapes, the area is proportional to this quantity. As y,’ and J,, refer to the criitral part of the sharp line, thp influence on these quantities from the superposition of the broad line could be neglected. The calculated absorption line area is taken to be proportional to the fraction of fourfold coordinated boron and l o the volume density of boron atoms in the sample. In this way it was possible to calculate the ratio between Nrvalues for samples of different, K20contcnt. The method, of course, does not allow an absolutc deterniination of N 4 . Our values, shown
NOTES
*
175
............ o
-e---
SILVER 8 BRAY PRESENT AUTHORS WARREN
...r 0
30 S % 0 10 20 Fig. I.-The fraction of fourfold cotirdinated boron atoms, Ai,, aa a function of the molar KzO coricentrstion S. The solid line represents the theoretical curve N , = S/(1 - S ) .
in Fig. 1 by open circles, therefore have been fitted to the theoretical line N4 = S/ (1 - 5)by the method of least squares, yielding a standard deviation from the theoretical value of 3y0. A significance test of the deviation indicates that the boron-oxygcn coordination in the potassium borate glass is in agreement with the Si(1 S)-rule, in cont,radict,ionto the results obtained by Silver and bra^.^.^
-
T H E KINETICS OF T H E HYDROLYSIS OF POLYETHYLENE TEREPHTHALATE FILM BY T. DAVIES,P. L. GOLDSMITH, D. A. S. RAVENSA N D I. M. WARD Reaaarch Deparfment, Imperial Chemical Industries Limited, Fibres Didnun, Hookstone Road, Harrogate, Yorkshire, England Received June 2031981
In a recent papcr,l Golike and Lasoski have reported results for the hydrolysis of polyethylene terephthalatc film. The problem of polyethylene terephthalate degradation has received considerablo attention in these Laboratories and a recent account As our conclusions of this work has been differ materially from those drawn by Golike and Lasoski, we feel that it, is worth considering the cxperimental evidence of both investigations. We shall show that although the experimental results of Golike and Lasoski are in good agreement with our own, a very different interpretation of these results can be obtained. The principal conclusion of Golike and Lasoski is that the reaction rate is controlled by diffusion of water into the sample. We (1) R. C.Golike and S. W . Lasoeki, J . Phya. Chem., 64, 895 (1960). (2) D. A. S. Ravens stid I. M. Ward, Trans. Furaday Soc., 67, 150 (1961).
NOTES
176
Vol. 66
an over-all activation energy of 25 kcal. for hydrolysis, which compares reasonably well with 26 kcal. by McMahon6 and our own value2 of 27 kcal. The activation energy for d i f f u ~ i o nis~ ~14~ kcal. The evidence presented here would seem to confirm that diffusion does not control the hydrolysis rate. In conclusion, there are errors in the mathematics of the diffusion calculations.' The approximation tanh x/z = 1 x2/3 is only valid for x < a/2, i.e., dkm.1 < 1.57. Hence in Table 111' when m D is 625 or 740 the approximation cannot apply when 21 = 0.0075 - 0.0187 cm. and when d T D z i s 171 it cannot apply when 21 = 0.0187 cm. It follows that all the derived quantities a t GO" are$incorrect and, in general, errors ranging from 10-70% have been introduced by the use of this approximation. We have constructed curves for tanh ellel (where e = d k A / D ) for values of 0 from 50-1000 2.0 2.5 3.0 3.5 and compared them with the plots of cach row of 10S/T. k' in Table 11' against "E." Table I gives Fig. 1.-0, Golike and Lasoskil; 0, Ravens and Ward.* examples of this comparison for results where the believe that this is incorrect, for reasons set out in experimental curve is of similar shape to the theoretdetail below. First, it is incorrect to ignore the ical curve. Furthermore, thcre are some condireverse reaction of esterification at low vapor pres- tions where no value of 0 gives a good fit, e.g., 130' sures and secondly, at high vapor pressures it can at 100% r.h. and this leaves doubt as to the adebe shown that the diffusion rate is orders of magni- quacy of the theory. tude greater than the reaction rate. TABLE I From our resultq2 the rate of end group changes at 150" a t 100 arid 0.5'7, relative humidity (r.h.) Coli e a+ Estimated (Table 111') can be calculated. Thus e Con&tiom Lasoski
-
4:
where rp and r h are the rates of change of [COOH] for esterification and hydrolysis, respectively, and KO -h 12. An intrinsic viscosity of 0.56 is equivalent to a total end group concentration2 of 110 X 10" mole/g. of which for this sample3 [COOH] = 20 and [OH] = 90. Thus a t 100% r.h. Th 2 100 r, and hence esterification is negligible whereas ~at 0.5% r.h., r, = rh. We also have been able to comDare the half-life time ( t ~for ) the rcaction calculated from our results with the half-life time (&) for water diffusion using the unpublished results of Small.* Small's results also have been confirmed by measurement of the rate of deuteration of the end groups when polyethylene terephthalate is immersed in DzO, this rate also being diffusion controlled.6 At 149" under 100% r.h. ([HtO] in polymer = 400 X lo+ mole/ g.) 1~ = 5.4 X 104 sec. and from Small's results the diffusion constant Dld9 = 2.5 X 10" cm.2 sec.-', giving a value for to = 40 sec. for a film thickness of 0.045 cm. Further confirmation of our conclusions is shown by a direct comparison of Golike and Lasoski's results at 100% r.h. for 0.0025 cm. film with our results (recalculated using the intrinsic viscositymolecular weight relationship given') for 0.045 cm. film. This is shown in Fig. 1 and it can bc seen that although there is an 18-fold increase in film thickness the agreement is satisfactory. This gives (3)
R. C. Golike, private conimumcation.
(4)
K. W. Small, unpubliahed results.
( 5 ) I. M. Ward, unpublished resulta.
150" 18 mm. 100' 51%r.h. 80" 10070r.h. 80" 51% r.h.
112 132 131 155
90 170 90 70
I n view of the incorrect basis of the curves in Fig. I of the original paper it may seem surpriLcing that the plot of log k vs. 1/11' is a straight line. The reason for this is that the part of the argument which gives COprobably is valid. In addition, the extrapolation from the thinnest film to I = 0 is very short and provided that the derivative of the curve of 16' us. I is small a rcasonable value of kCo is given by the calculated values of 12' when I = 0.0025 cm. Thus the rate constants used in Ii'ig. 2l are almost holly derived from the thinnest film where, on thc theory of Golike and Lasoski, diffusion can be most nearly neglected. (6) €1. A. MoMahon, el al., Chem. En& Data Ser., 4, 57 (1059).
CONCERNING A SO-CALLED CHECK O S THE INITIAL DEVIATION FROM NEWTONIAN FLOW OF POLYh!EEIt SOLUTIONS BY JOHNF. VOEKS The Daw Chrmieal Company, Western Division, Pitlsburg, California Received J u l y 17, 1.981
The viscosity of a polymer solution or of a polymeric melt is, in general, non-Newtonian. As has been observed frequently (see for example Oldroyd'), the viscosity must be a positive even func-
