NOTES
1432
interest, arid introduced an empirical correction factor. Schlag and Sandsmark' suggested a nonempirical finite series, which had a leading term identical with the single term expression given by Marcus and Rice.3 Further terms become important a t lower energies. Schlag and Sandsmark, however, had developed only the first three terms of their series. More recently, further terms in this series were developed by an inverse Laplace transform expansion technique.*, In particular, Thiele has given a general coefficient'O from which, as he has shown, the first four terms of the series of Schlag and Sandsmark can be generated by a multinomial formula. In view of the apparent usefulness of an exact and simple method for generating p(E), it was decided to generate the complete series for several molecules from this multinomial formula and compare this method of counting with a detailed combinatorial calculation.' This was programmed on a computer since the collation of terms becomes an impossible bookkeeping task. The general term in the series is generated by a proper collection of Thiele's specific terms. The number of terms in this series, when complete, is approximately half the nun~berof vibrational degrees of freedom. The complete series was computed for methyl chloride, cyclopropane, cyclopropane-&, CBr3C1,CClzO, CHBr3, C2H4,C4H2, and benzene." The typical computation time was about 1 min. to calculate a complete set of densities, p(E), for all E up to 250 kcal. When one compares the densities obtained from the complete series with exact combinatorial cal~ulations,~ one finds only small discrepancies for these molecules at 10 kcal. and above, at most lo%, the discrepancy being further reduced at higher energies (see Table I). Below this energy, the densities fluctuate more strongly about the average value given by the series. This causes no difficulty since it takes but a few seconds to compute the values up to 10 kcal. by the exact combinatorial n~ethod.' Hence, one can reduce the exact
Table I ,Molecule
Methyl chloride Cyclopropsne C yclopropane-ds CBrsCl CClZO CHBra
C2Ha C4Hl Benzene
-Discrepancy 10 kcal.
at (in %)-15 kcal. 20 kcal.
8.16 -9.45 3.70 -0.01 0.88 1.37 0.32 -3.80 3.86
-0.52
The Journal of Physical Chemtetry
-3.47 -0.33
-0.02 -0.19 -0.01 0.00 1.50 -1.93
-1.73 -2.00 -0.80 -0.01 0.04 -0.22 -1.42 -1.70
calculation of densities to a very high speed computer subroutine. For an arbitrary group of frequencies, the subroutine will generate the value for all densities, p(E), up to 250 kcal.12
Acknowledgment. The support of this work by a grant from the Petroleum Research Fund of the American Chemical Society is gratefully acknowledged. (7) E. W. Schlag and R. A. Sandsmark, J . Chem. Phys., 37, 168 (1962). (8) (a) P. C. Haarhoff, Mol. Phys., 6,337 (1963); (b) P. C. Haarhoff, ibid., 7, 101 (1963). (9) E. Thiele, J . Chem. Phys., 39, 3258 (1963). (10) It should be pointed out that these are only the coefficients for the expansion about the pole p = 0. The effect of higher poles can be shown to just lead to oscillations on top of this smoothed function, without changing its average value as a function of energy. The effect of these higher poles will only be important for the first few kcal./mole. Computationally, this is adequately handled by a simple direct count up to 10 kcal./mole (see below). The Dirichlet integral technique of Schlag and Sandsmark effectively also rejects these oscillatory terms when it replaces a multiple sum by a multiple integral. Since only the first 10 kcal./mole are involved, a direct count procedure is to be preferred to explicitly including quantum corrections in the series techniques. (11) Frequencies chosen were those listed in ref. 6. (12) A copy of the program written in IBM Fortran I V (IBSYS system) with instructions is available upon request.
Comparison of Water Sorption and Deuterium-Hydrogen Exchange Sites in Poly -L-valine l a
by W. W. Brandt and R. S. BudrysIb Department of Chemistry, Illinois Institutc of TechnoEogy, Chicago, Illinois 60616 (Received November SO, 1964)
Measurements of deuterium-hydrogen (D-H) exchange capacities and rates on dissolved polypeptides or proteins have become one of the standard methods to determine the chain conformations of these macromolecules.2 H atoms which are readily exchanged are usually assumed to be easily accessible. In solid polymers, on the other hand, D-H exchange capacities may (1) (a) This work was supported by PHS Grant AM-4324. Material supplementary to this article has been deposited as Document No. 8130 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy may be secured by citing the document number and by remitting $2.50 for photoprints, or $1.75 for 35 mm. microfilm. Advance payment is required. Make checks or money orders payable to: Chief, Photoduplication Service, Library of Congress. (b) Abstrated in part from the work of R. S. B. to be submitted in partial fulfillment of the research requirements for the Ph.D. degree in the Department of Chemistry, Illinois Institute of Technology. ( 2 ) H. A. Scheraga, "Protein Structure," Academic Press, Inc., New York, N. Y.,1961.
NOTES
likewise yield a measure of the accessibility of amide groups, provided diffusion to or from the neighborhood of the polymer exchange site is relatively fast and not rate controlling. A second possible measure of the accessibility of polar groups is the “monolayer area,” derived from sorption isotherm data using B.E.T. theory. Various polypeptide-sorbate systems have been treated in this fashion.3-5 There is considerable doubt whether the two measures of sorption site accessibility mentioned above should agree. Hnojewyj and Reyerson found that sorption and exchange sites in poly- g glutamic acid are not identical, while earlier studies on proteins seemed to indicate their equivalence.6 More recent work of Ehrlich and Bettelheim’ showed that sorption and exchange sites in mucopolysaccharides are probably different. In view of these findings, one may suspect that a number of sorption and exchange sites are in fact identical, but that some are not. To test this idea, D-H exchange experiments were carried out on two poly-aamino acids for which sorption isotherm data are already available 3 b , 4
1433
Interestingly, the number of D atoms introduced into PV is distinctly larger than what corresponds to complete exchange a t the polymer chain end groups only. The converse is true for PL.
1
a( moles gas/moles monomer)
0.5
0.4
0.3
0.2
0.I
Experimental The poly-L-valine (PV) and poly->leucine (PL) used in the present work are the ones described earlier.3bj4 One of the two PV samples used had previously been exposed to TFA (trifluoroacetic acid). The exchange experiments were carried out using a quartz balance of conventional design. The samples were degassed, exposed to D 2 0vapor, and after a definite time the DzO vapor was quickly removed and replaced by a new batch of undiluted vapor. The procedure was repeated until there was no further change in the sample weight. The results are plotted as the number of moles of D exchanged per polymer repeat unit against the cumulative time of exposure. Results and Discussion From Figure 1 one notes that the PV used has a much higher exchange capacity than PL. Thus, there is a definite correlation to the sorption uptake for HC1 and TFA on fresh samples of the two polymers. A nunierical agreement of the number of exchange sites and of sorption sites cannot be tested because the isotherms do not permit an umambiguous estimate of the sorption L‘m~n~layer.’’ The relatively high exchange and sorptive capacity of PV are in accord with the low quality of its /3 structure, as judged from X-ray diffraction patterns.
20
40 time(hrs.)
60
80
100
Figure 1. Deuterium-hydrogen exchange capacities a t 75.2”: 0, poly-L-leucine; 0, poly-r,-valine in original form; and A, poly-Lvaline after prolonged exposure to trifluoroacetic acid. Dotted lines indicate approximate D-H exchange expected if only chain ends are involved; upper line, poly-L-valine; lower line, poly-L-leucine.
Aside from the gross correlation of sorptive and exchange capacities, there is an interesting discrepancy : the P V sample which was previously exposed to TFA takes up much less of this sorbate, compared to the original sample.3b This is in accord with the iinprovement in the polymer secondary structure, seen in the X-ray diffraction patterns.3b On the other hand, the D-exchange capacity is markedly increased. We conclude that the accessibility, measured as the D-H (3) (a) L. Pauling, J . A m . Chem. SOC.,6 7 , 555 (1945); (b) W. W. Brandt and It. S. Budrys, J . Biol. Chem., 239, 1442 (1964). (4) W. W. Brandt and R. 5. Budrys, J . Phys. Chem., 6 9 , 600 (1965). (5) L. H. Reyerson and W. 5. Hnojewyj, ibid., 6 7 , 1945 (1963), and references cited there. (6) W. S. Hnojewyj and L. H. Reyerson, ibid., 6 7 , 711 (1963). (7) S. H. Ehrlich and F. A. Bettelheim, ibid., 6 7 , 1954 (1963).
Volume 69, Number
4
April 1966
COMMUNICATIONS TO THE EDITOR
1434
exchange capacity, depends on the polymer secondary structure in a way not yet understood, and that a t least some of the exchange - sites are not functioning as sorption sites. an sorptioll data reported earlier8 show D20 to be sorbed more extensively than
HzO, confirming the findings of Hnojewyj and Reyerson on similar ~ y s t e m s . ~ (8) W. W. Brandt and R. S. Budrys, ADI, Library of Congress, Document No. 8130. (9) W. S. Hnojewyj and L. H. Reyerson, J . Phys. Chem., 65, 1694 (1961).
C O M M U N I C A T I O N S TO T H E E D I T O R
The Importance of Xenon Fluorides in the Xenon-Photosensitized Reactions of the Perfluoroalkanes
Sir: No work has been reported on the xenon-photosensitized reactions of perfluoroalkanes since the work of Dacey and Hodgins in 1950.' They found that CF4 was decomposed into a solid polymer and fluorine by Xe(3P1) with unit quantum efficiency although a product balance was not obtained. We are of the opinion that the xenon fluorides play a major role in this and other xenon-photosensitized reactions of the perfluoroalkanes. Following the development of a suitable all-quartz resonance lamp of improved design, we investigated the reactions of cZF6, C3F8, and c-C4F8. Most of our work was done with the latter compound; hence, we will confine our discussion to it. The products resulting from the xenon-photosensitized reaction of c-C4Fs were CF4, CtF6, C3F8, and a larger amount of a higher molecular weight flluorocarbon probably comprised mostly of C8 compounds. Small amounts of CzF4 and traces of c-CsF6 and C3F6 were found by vapor phase chromatographic analysis. XeFz was identified among the products by the absorption bands 549 and 564 cm.-le3 The higher molecular weight fluorocarbons were not positively identified. With a reaction cell volume of 142 cc. and a constant lamp intensity of 2 x l O I 5 quanta/sec. (determined by photolysis of COz), the reaction proceeds with a pressure drop that is linear with time (Figure 1 ) . To explain these results, the following mechanism is proposed. The Xe(3P1) may either abstract two fluorilles from I he fluorocarbon or pass its energy to the fluorocarbon without reaction. I t is assumed that the The Journal 0jPhysical Chemistry
+ c-C4FS Xe* + c-C4Fs
Xe*
+
+ C-C4F6* Xe + c-C4FS*
XeFz
+
(1)
(2)
energy-rich c-C4F8*from reaction 2 decomposes in one of the two ways known to occur with its thermal dec-C~F~ + * 2CzF4 c-C4Fs* + C3F6
+ CFt
(3) (4)
composition. 4-6 The quantities of energy required for these reactions are 74 and 87 kcal., respectively. The products of reactions 3 and 4 are fluorinated by the XeFz formed by reaction 1, thus accounting for all the low molecular weight fluorocarbons found except the tjrace of c-C3F6, which is assumed to be formed when reaction 4 occurs. It is known that! XeFz is a fluorinat-
+ XeFt CFz + XeFz C3F6 + XeFz
C2F4
+
-
+
CZF6
+ Xe
CF4
+ Xe
C3Fs
+ Xe
(7)
ing agent, although Chernick, et al., have found that it is slow to react with perfluoroolefins at room temperat ~ r e . Near ~ the thin quartz window separating the xenon discharge from the reaction space, the tempera(1) J. R. Dacey and J. W. Hodgins, Can. J . Res., 28B, 173 (1950). (2) G. H . Miller, and J. R. Dacey, Rev. Sci. Instr., in press. (3) D. E. Milligan and D. R. Sears, J . A m . Chem. SOC., 85,823 (1963). (4) B. Atkinson, and A. B. Trenwith, J . Chem. Soc., 2082 (1953). (5) J. N. Butler, J . A m . Chem. Soc., 84, 1393 (1962). (6) A. Lifshitz, H. Carroll, and 9. Bauer, J . Chem. Phys., 39, 1661 (1963). (7) T. C . Shieh, N . C. Yang, and C. L. Chernick, J . A m . Chem. SOC., 8 6 , 5021 (1964).
