NOTES
2260
pentanone as compared to that of 2-pentanone4,5,5-d3. Since Z-pentanone has three H atoms in the y-position, while 2-pentanone-4,5,5-d3 has only one H atom and two more strongly bonded D atoms in this position, 2-pentanone would have a relatively higher probability of undergoing a molecular elimination than 2-pentanone-4,5,5-d8. TABLE I11 VAPORPHASEPHOTOLYSIS OF CH3COCH2CH2CH8. THE EFFECT OF OXYGENAT 3130 1. la
Ketone pressure = 26.5 mm. Poi, mm. T , OK.
...
1.57 X IO" quanta/cc./sec. *ethylem
1.4 6.4 56.5
from which decomposition occurs does, however, depend on the equilibrium temperature. It is ipteresting t o note that in the vapor phase at 3130 A. the effect of temperature on the ratio C2D3H/ CaHzDs is of the same order of magnitude. This is not surprising in view of the fact, as was pointed out before, that the ratios of the ethylenes in the two phases are comparable. TABLE IV LIQUIDPHASE PHOTOLYSIS OF CH2COCH2CHDCD2H A,
A.
3130 3130 3130 2537 3130
0.30 .25 .20 -13
305 306 303 305
Vol. 65
Liquid Phase.-In the liquid phase (Table IV) the ratio CzD3H/C2H2D2decreases with an increase in temperature. A plot of log CZD3H/ C2HsDz against 1/T yields a difference of 1.15 0.15 kcal./mole in the activation energy for the transfer of a D atom a2d an H atom. Since the point obtained a t 2537 A. lies on the same line of the Arrhenius plot, the ratio CzDsH/CzH2Dz is independent of wave length. It may indeed be expected that in the liquid phase, collisional deactivation is important. The mean energy level
*
T,OK.
198 214 273 296 343
Rethyleas X IO' (co./min.)
5.40 6.55 27.8
...
26.2
CzDaH/ChHzDi
6.40 5.37 3.44 2.76 2.12
The relative quantum yield of ethylene is within experimental error constant from 343 to 273OK. At temperatures below 273'K., however, there is a pronounced decrease in the yield of ethylene. Because ethylene can be formed only by a molecular elimination process, cage recombination cannot be invoked to explain the reduction in quantum yield. It is more likely that an activation energy of a few kcal./mole is required for the decomposition process.
NOTES THE ELECTRODE POTENTIALS OF GERMANIUM: SOME COMMENTS ON THE INTERPRETATION BY LOVRECEK AND BOCKRIS BY J. I. CARASSO, M. M. FAKTOR AND H. HOLLOWAY Post Ofice Research Stataon, DoEZzs H i l l , London N.W. 8, England Received March 80,1961
I n a recent paper' Lovrerek and Bockris have described measurements of the electrode potentials of germanium over a range of pH in deoxygenat,ed solutions. These potentials were interpreted as mixed potentials arising from the simultaneous occurrence of the two electrode reactions Ge
+ HzO +GeO + 2H+ + 2e2Hf + 2e- +Hz
(1) (2)
These authors showed that the resultant overall corrosion reaction Ge
+ H20 ---+ GeO + H2
(3)
would be thermodynamically feasible only in solutions which are in equilibrium with a low pressure of hydrogen. (The maximum hydrogen pressure for which the postulated process is possible depends upon the form of GeO involved, being about (1) B. LovreEek and J. O ' M . Bockris, J (1959).
Phya. Chem.. 68, 1368
atm. for brown GeO and about atm. for yellow GeO.) Such low hydrogen pressures might well have been attained in the solutions which LovreEek and Bockris swept with helium. However, replacement of the atmosphere of helium by one of hydrogen would render the postulated corrosion reaction 3 impossible. Yet the authors have reported that the measured potentials were unaffected by sweeping with hydrogen. The only possible conclusion appears to be that at least one of the two postulated electrode reactions 1, 2 does not contribute to the measured Potentials, and that, if corrosion does occur in deoxygenated solutions, it does so by a process other than the postulated corrosion reaction 3. A further objection to the interpretation by LovreEek and Bockris concerns their claim that the difference between the measured mixed potentials and the reversible potentials for the anodic reaction is not more than 20 mv. This result was derived from the assumption that the corrosion current in deoxygenated solutions and the exchange current for the anodic reaction are both about 2 X amp. cm.-2. The value assumed for the corrosion current was derived from the results of Brattain and Garrett? who do not appear to have deoxygenated (2) W. H. Brattain and C. G. B. Garrett, Phys. Rev., 94, 750 (1954): BelZ System Tech. J . , Sl. 129 (1956).
NOTES
Dee., 1961 their solutions. Harvey and Gatosa have found that the rate of dissolution of germanium in oxygenated aqueous solutions at 35’ is about 1 pg. cm.-%r.- which corresponds to a corrosion current of about amp. More recently an investigation of the polarized germanium electrode by Paleolog, Tomashov and Fedotova4 has shown directly that the corrosion current in air saturated solutions is about 10-6 amp. at 25’. Harvey and Gatos3 found that in deoxygenated solutions the corrosion rate was much less than 1 pg. cm.-2 hr.-l and this implies that the value of the coramp. assumed by rosion current (2 X LovreEek and Bockris is much too high. The value of the exchange current for germanium oxidation quoted by LovreEek and Bockris was stated to be “extrapolated from Turner.”6 In fact, the reference quoted does not imply a value for this exchange current. Turner’s paper gives the slope of the Tafel line for germanium dissolution and, less accurately, its position. In order to derive a value for the exchange current one also must know either the position and slope of the Tafel line for the reverse reaction (deposition of germanium from solution) or the reversible potential for the anodic reaction. Neither of these pieces of information is given by LovreEek and Bockris so that the source of their value for the exchange current is a matter for conjecture. There is the further point that Turner’s Tafel slope applies a t current densities where germanium has been shown to be oxidized to the quadrivalent state6 and a different Tafel slope might apply to the postulated oxidation to the divalent state. In the absence of any information about the relative magnitudes of the corrosion current and the exchange current, consideration must be given to the possibility that the mixed potential which is measured is very different from the reversible anodic potential. Thus, if the corrosion current is one or two orders of magnitude greater than the anodic exchange current, the reversible anodic potential may be 120 to 240 mv. more negative than the mixed potential. This would admit the possibility that the anodic reaction is oxidation of germanium to the quadrivalent state, for example Ge 2H20 -+ GeOz 4H+ 1- 4e- or Ge
-++ + ~ H z O+ HnGeOa + 4H+ + 4e-
Our conclusions are: 1. the potential of the germanium electrode in deoxygenated solutions is not determined by the corrosion reaction which has been postulated by LovreEek and Bockris. 2 . LovreEek and Bockris’ statement that the corrosion current and the exchange current for the anodic reaction are of comparable magnitude appears to be quite unjustified. Therefore the proximity of the ~ ~ e a s u r epotentials d to reversible potentials calculated for the reaction. .( :e
+ H,O
GeO
+ 2H+ + 2e-
(3) W. W. Harvey and H. C. Gatos, J. Electrochem. SOC.,106, 654 (1958). (4) E. N. Paleolog, N. D. Tomoshov and A. 2. Fedotova, Zhur. K z . Khim., 34, 1027 (1960). (5) D. R. Turner, J . Electrochem. Sac., 103, 252 (1956). (6) F. Jirsa, L.anorg u allgem Chem., 568, 84 (1952).
2261
is not evidence that the latter reaction has any potential determining significance. Acknowledgment is due to the Engineer-in-Chief of the British Post Office for permission to publish. T H E REACTIVITY OF HYDROGEN ATOMS I N T H E LIQUID PHASE: T H E LACK OF EFFECT OF LINEAR ENERGY TRANSFER IN T H E RADIOLYSIS OF HYDROCARBONS BY W. G.BURNS Chemzstry Dimsion, Atomic Energy Reaeareh Eetablishment, Harwell, Didcot, Berkahire, England Received M a y 29, 1961
An encouraging trend in the radiation chemistry of alkane hydrocarbons has been the explanation of some features of the product yields in terms of the reaction behavior of atoms and radicals determined in the gas phase when generated by means other than radiation.lv2 Hardwick3 has recently attempted to show that the collision yields of many paraffin, which occur in reactions of the type H. the radiolysis of the liquids, are roughly the same as found in the gas phase (Le., -lo-’), the reason for high rate constants in the liquid phase being the large frequencies (-10’4 see.-’ molecule-’) for solute-solvent collision^.^ The atoms considered are scavengeable, and not “hot.” If the kinetic interpretation 5 v 6 of the decrease in radiolytic hydrogen yield with scavengers present is correct, there are two characteristics of the hydrogen yields from pure cyclohexane and pure n-hexane which seem to require explanation. They are: 1. The apparent lack of contribution to the H. -+ HZfor hydrogen yield by the reaction H. radiation of low LET3; 2. The invariance of the yields with changing LET of the In the reaction scheme
+
+
+
H. He +Hz ki (1) H. GH12 +HP CSHii. ICs (2) we have kz = 6.6 X lo9 cc. mole-’ see.-‘ (ref. 3), and if we take kl = 6 X 10l2 cc. mole-’ set.-',
+
+
the value used for H atoms in v ~ a t e r ,reaction ~.~~ 1 can provide effective competition for reaction 2 if [H.] approaches (k&) [C~HIZ], i e . , -lo-’ M . Such concentrations of hydrogen atoms might be exceeded in the center of the track left by a densely ionizing particle if they were formed very near the center of the track. For example, in a column of 10 A. radius in which G(H,) -4 (the value for cyclohexane)6r11for radiation of LET 5 e.v./,&., the concentration of H atoms is 1.1M . To reduce the recombination to negligible proportions this concen(1) J. H. Futrell, J. A m Chem. Soc., 81, 5921 (1959). (2) T. J. Hardwick, J . Phys. Chem.. 64, 1623 (1960). (3) T. J. Hardwick. zbzd., 61, 101 (1961). (4) E. -4. Moelwyn-Hughes, J . Chem. Sac., 95 (1932). (5) G E. Adams, J. H. Baxendale and R. D. Sedgwiek, J . Phys. Chem., 63, 854 (1959). (6) J. G. Burr and J. D. Strong, Abstracts of the 137th National Meeting of the A.C.S. p. 43-R. (7) R. H. Schuler and .4.0. Allen, J . Am. Chem. Soc., 7 7 , 507 (1955). (8) H. A. Dewhurst and R. H. Schiiler, zbid., Si, 3210 (1959). (9) A. K. Gangulyand J. L. Magee, J . Chem. Phys., 25, 129 (1996). (10) P. J. Dyne and J. M. Kennedy, Can. J . Chem., 38, 61 (1960). (11) P. J. Dyne and W. M. Jenkinson, zbid., 38, 539 (1960).
NOTES
2262
Vol. 65
method of ref. 12) and with kl increased by a factor 10. The effect of an increase in toby a factor 100 is shown in curves 2A and 2B from which it is clear that the conditions for densely ionizing radiation are not so sensitive to changes in D and kl as those a t low LET, but that a value of to = 10-8 sec. is sufficient to reduce the dependence of S on the radiation type to about the required limits. Further increases of t o will cause the drop in 2(1 S) to occur a t higher values of 2. The lack of dependence of the G-values of alkane decompositions on radiation type is remarkable when it appears that we can calculate kz and show that there is the possibility of effective competition between the bimolecular and unimolecular reaction increasing L E T A . Fig. 1.-Expected G(H2)from cyclohexane due to atomic of hydrogen atoms. Even in the case of benwhere the G-values for gas production abstraction and recombination, for different values of ~ene,’~J5 track radius: 1A: D = 2 X lo-’ cm.*/sec.; kl = 9 X show a decided dependence on LET (possibly ex1012 cc. mole-’ sec.-l; t o = 1.25 x 10-10 sec.; r = 10 R.; plained on an excited molecule basis), the simplic1B: D = 2 X lo-‘ cm.2/sec.; k, = 9 X 10” oc. mole-l ity of the gas products, consisting only of hydrogen sec.-l; to = 1.25 x 10-10 sec.; r = 30 R.; 2A: D = 2 X and acetylene, even at a linear energy deposition 10-6 cm.*sec.; k, = 9 X 10’2 cc. mole-’ set.-'; t o = 1.25 X 10-8 sec.; r = 100 A.; 2B: D = cm.*/sec.; k, = rate of -26 e.v./A. is striking. 9 X 1013 cc. mole-’ see.-’; t o = 1.25 X 10-8 sec.; r = It is suggested that a possible explanation of 300 23. these effects is that the initial decomposition, e.g. to hydrogen atoms, occurs a t larger distances (pertration would need to be reduced by a factor be- haps 100-300 A.) from the position of energy tween lo2and los, ie., the “initial” radius T of the deposition than is sometimes supposed in models track increased by a factor between 10 and 32. for the radiation chemistry of water (-10 A.). In a more quantitative approach, values of S , This may be the result of an intermolecular disthe total fraction of radicals which react with persal of energy, or a diffusion of molecules withscavenger, have been calculated using the model out decomposition (or possibly the latter following of Ganguly and Magees for various values of the the former). parameters kl, q = k2Csto, and 2 = 1/(2 - 7) (14) W. G. Burne. W. Wild and T. F. Williams. Proc. Snd Intern. (-dB/dz)o in 100 e.v. per cm., where 77 is the mean Peaceful Uses Atomic Energy, 39, 266, 1958. LET/initial LET. The parameter 2 depends on Conf. (15) W. G. Burns, “Rassegna Internationale Elettronica and Nuthe radiation type and is designed to take account cleare, Sezione Nuoleare,” Vol. VI, Rome, 1959, p. 99. of the increasing LET with penetration for a given particle; it has a value of for fast electrons, 1.8 X lo6, 5.6 X lo6, and 1.3 X lo7 (100 e.v.) cm.-l for 20 M.e.v. deuterons, 40 and 10 M.e.v. THE RELATIONSHIP OF BOND DISSOCIAa-particles. With the following constants: D = TION ENERGIES, METHYL AFFINITIES 2 X cm.2/sec., to = 1.25 X sec., Le., TO AND RADICAL REACTIVITIES = 10 A., kl = 9 X 10l2cc. mole-’ set.-', number BY L. A. ERREDE of radicals per spur of 100 e.v. = 4,kz = 6.6 X lo9 Contribution No. 804 from the Central Research Labordories of the cc. mole-’ set.-', C, = 9.3 X mole cc.-1 (the Minnesota Mining and Manufacturing Company, St. Paul, Minn. last three values appropriate to cyclohexane), Received June it,lB8l values of G(H) (1 S)/2 have been found and are It was reported in a previous publication’ that given in Fig. 1 curve 1A as a function of 2. This represents the expected G(H2) since reaction 2 the energv (D) required to dissociate an organic results in abstraction, and the expected G-value is molecule R i - R j into its radical fragments R,. and seen to decrease with increasing LET. The addi- Rj., can be calculated by means of equation 1 tional G(K) due to unimolecular processes is conD = 7leiej (1) sidered not to vary with radiation type. where ci and ej are the characteristic binding coThe diffusion constant is that used for H atoms efficients for the groups forming the bond in yuesin and is appropriate for the interdiffusion For monovalent atoms H, F, C1, Br and I, of medium sized molecules12such as benzene’’3 but tion. c is given approximately by equation 2 for hydrogen atoms in cyclohexane this value may ex = E‘/s/r (2) be too low. However S will not be very dependent on D since reaction 1 is thought to be diffusion con- where E is Pauling’s electronegativity2 of the atom trolled, and any increase in S on increasing D and r is the corresponding C-X bond length (in caused by favoring reaction 2 will be partly offset Angstrom units). by the increase in k l , proportional to D. Curve 1B The eg of a group RIRIR&- can be calculated by was calculated with D = 2 x 10-4 cm.2/sec. (ob- equation 3 provided that the groups (or atoms) R1, tained for H atoms in cyclohexane by using the (1) L. A. Errede, J . Phya. Chem., 64, 1031 (1960). The rvalue for
+
+
(12) 8. Glawtone, K. J. Laidler and E. Eyring, “The Theory of Rate Processes,” New York, N. Y., 1941. (13) K. Graupner and E. R. S. Winter, J . Chem. Soc., 1445 (1952).
CsHa listed in Table I should read 1.18 instead of 1.11. (2) L. Pauling, “The Nature of the Chemical Bond,” 2nd Ed., Cornell University Press, Ithaca, N. Y.,1948, p. 68.
NOTES
Dee., 1961
2263
2
104 8
6 4
2 h
f
10’
3 s v .d
3
6
4
4
c.l
h
.f! 8 m
2
!i
k 102
m
8 6 4
2
10
8 6 4
2 1 0.50
0.60
0.70 0.80 0.90 1.oo Calculated c for resultant adduct radical. Fig. 1.
1.10
1.20
R: and Rs do not have a center of unsaturation a means of equation 3, since e ’ ~for X - A can be deduced from the value determined experimentally to one of the central carbon atoms. and then used in conjunction with el and e2 to cal‘0 = 0.43 + 0.162(~+ 4 f BQ) (3) culate the eg of any other homolog. The eg of radicals such as CHSCeH5, .CH(CeH5)2 The basic +values that could be deduced from and CH2-CH=CHa cannot be calculated by eq. available bond dissociation energy data3-6 are 3, but rather must be determined experimentally.’ collected in Table I of reference 1. Although these However, once the e-value is determined for one (3) M. Szwaro, Chem. Revs., 47, 75 (1950). member of a homologous series such as CRIR,A (4) A. H. Sehon and M. Szwarc, Ann. Reo. Phys. Chem.. 8, 439 (or CRIA1A2),where A is a group with a center of (1957). unsaturation a to the central atom, the E for all (5) T. L. Cottrell, “The Strengths of Chemical Bonds,” 2nd Ed., other members of that series can be calculated by Butterworth’e Scientifio Publiaations, London, 1958.
NOTES
2264
VALUES
FOR
Vol. 65
TABLE^ I HYDR~CARBON RADICALS CALCULATED FROM SZWARC’S METHYL AFFINITY DATA
Olefin
kdki
Ref.
Radical (R)
Calcd. B.D.E. in kcal. for R-CHs
c
R-H
0.53 .52 .5l .57 .69
50 49 48 53 65
41 40 39 44 53
.68
64
52
-66
62
51
.93
87
71
0-0 Y Ra H H
CH3
H CHs CHI
20,000 2 900 300
7 7 7
2,000
7
f
Et a-Pr t-Bu
H CsHaCHCH=CHCH2CH3 CHSCHZ
-/
2,375
ili
9
\CH2.
3 288
9
datala now can be used to calculate the bond dissociation energy of a large number of bonds not yet determined experimentally, there are still many
0 //
classes of bonds such as X-CR2A, where A is C-
CHs
I
6 I
CHzCH
Et0
A
94 kcal.
H CH3 H
0 ll
OR, -CR, CN, SOtR, etc., for which the key experimental bond dissociation energy data to find the respective EA’ are lacking. It has been pointed out by Wallings that the methyl affinities, as determined by Sewarc’ and his students, can be used to calculate the dissociation energy of C-H bonds a to some of these centers of unsaturation. Szwarc’s data are given in the form of kz/kl ratios that indicate the rate of addition of methyl radicals to olefins (kz) relative to the rate of hydrogen abstraction from isooctane (kJ. CHZ. CH3.
kz +M+ CHEM.
(4)
kl
+ HS +CH4 + S.
(5)
Walling6 reported that log kz/kl is related to the bond dissociation energy of the bond CHZM-H according t.o the equation log kz/ki
11.36
- 0.104[Rn + D(R-H)]
(6)
where R, is the “resonance energy” of the olefin M and D(R-H) is the B.D.E. of the bond CHZM-H. Unfortunately, only a few R, values are known and consequently only a few new D(R-H) were calculated by Walling. These are given here in kcal. directly above the bond in question.s (6) C. Walling, J . Phys. Chem., 64, 166 (1960). (7) M. Szwarc and J. H. Binks. Theoretical Organic Chemistry,” The Kekule Meeting, London, 1958; Butterworth’s Scientific Publications, London, 1959.
94 kcale
C&oCH3-C
8 1
H
74 kcal.
H
CH3
The magnitude of the R, term in equation 6, however, is relatively small (usually < 4 kcal.) and actually it often falls within the experimental error for determination of many B.D.E. values. An equivalent straight line relationship with a slightly less negative slope also is obtained if one ignores R, and simply plots log k2/kl as a function of D(R-H), or as a function of ER, since D(R-H) = 7 1 e ~ e ~ In . Fig. 1, Sewarc’s methyl of olefinic hydrocarbons are plotted as a function of the eg value calculated for the corresponding radical adduct. RI CHs.
+
R3
\
/
/
\
C=C
R2
R4
Ri R3
bI -4. ‘/
+CH3
(7)
R2 R4
It is noted that the three straight lines representing addition of methyl radicals to CHFC splitting by 50 to 70%, so that the rate is roughly (39 mole yopurity) was used throughout. The methylcyclo- proportional to the 0.2 power of the methylcyclopentane and hydrogen were dried to less than 5 p.p.m. by pressure. weight of water, using procedures described p r e v i o u ~ l y . ~ *pentane ~ The ratio of paraffins to olefins in the reaction The catalyst used in this work was v-alumina,6 prepared by calcining p-alumina trihydrate, obtained from Davison product was found to increase markedly with in(2) hl. N. Dojarenko, Ber., 69, 2933 (1926). (3) J. H. Sinfelt, H. Hurwita and J. C. Rohrer, J. Phys. Chem., 64, 892 (19fiO). (4) J. 11. Ginfelt, I€. Hurwits and R. A . Shulman. ibid., 64, 1559 (19(jOj.
( 5 ) €1. C. Stunipf. A . S. Russell, J. W. Neamine a n d C. .\I Tucker, . I u d . E n y . Cherrt.. 42, 1398 (l'J50).
creasing hydrogen pressure, as shown in Table I. In the case of C3 and C4 products, the ratio of paraffin to olefin increased by about 40-fold when the hydrogen pressure was increased from 2 to 20 atm., while the ratio of hexanes to hexenes increased by 10 to 12-fold. However. in no caw
NOTES
2274
did the ratio approach the equilibrium value. For example, the equilibrium value of propane/ propylene a t 20 atm. hydrogen pressure is about 100 times as high as the value found in this work.6 Typical isomeric distributions of some of the products are given in Table 11. I n the case of the olefins, only the distribution of the butenes is given, since the distributions of the higher molecular weight olefins mere not well determined by the chromatographic analyses. For the butenes, the distribution is roughly in accord with that a t equilibrium. In the case of the butanes and pentanes, the isoparaffins predominate in the products. For the butanes, the distribution is the inverse of the equilibrium distribution. The distribution of the hexanes which were observed in the product was not far different from that a t equilibrium. However, essentially no dimethylbutanes were observed, whereas a t equilibrium there should be about 28% present. TABLE I1 TYPICAL ISOMERIC DISTRIBUTIONS OF PRODUCTS mole %-Eq:ilibriumk
-Composition, -0bsd.0471'
499'
471
naceous residues arising from side reactions involving extensive dehydrogenation and polymerization. It is also conceivable that increasing hydrogen pressure may increase the concentration of acidic sites (protons) on the surface, which in turn may be important in the initial formation of carbonium ion type intermediates. The small effect of methylcyclopentane pressure on the rate of the ring splitting reaction suggests that the active catalyst sites are well covered with hydrocarbon intermediates over the range of pressures studied. The apparent activation energy of the reaction is about 30 kcal./mole. It is significant that the predominant reaction of methylcyclopentane over alumina is ring splitting with essentially no isomerization to cyclohexane, whereas over platinum supported on the same alumina appreciable isomerization-dehydroisomerization to cyclohexane and benzene is o b ~ e r v e d . ~ This suggests that the intermediates involved in these reactions are different in detail, although both are presumably of the carbonium ion type. (9) J. H. Sinfelt and J.
C. Rohrer, ibid., 66, 978 (1961).
4990
Butanes 36 38 67 68 n-Butane 33 32 64 62 Isobutane Pentanes 31 32 33 25 n-Pentane 67 75 68 67 Isopentane Hexanesb 35 35 n-Hexane 30 30 40 39 44 45 2-Methylpentane 25 26 26 25 3-Mcthylpentane Butenes 56 56 64 61 Butene-IC Isobutenec( 25 25 20 24 trans-Butene-2 16 1- 5_ 18 19 -_ cis-Butene2 a Hg pressure = 20.0 atm., methylcyclopentane pressure = 1.0 atm., l0-12% conversion. Less than 1%. dimethylbutanes observed in hexanes fraction; comparison with equilibrium data based only on the three isomers shown. Butene-1 and isobutene not resolved.
1
-
Vol. 65
1
Discussion The observed hydrogenation activity of alumina in this work is in line with the observations of other workers mho found that alumina was active for hydrogenation of ethylene a t about the same temperatures as were used in the present Hydrogen transfer reactions also occur to some extent, :is evidenced by the fact that some hexanes are observed in the reaction products even when the reaction is carried out in the absence of hydrogen. The promotional effect of hydrogen pressure on the rate of the ring splitting reaction could conceivably be due to several factors. One possibility is that hydrogen increases the rate of desorption of products via hydrogenation. Another is that hydrogen serves to keep the surface free of carbo(6) "Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds," A P I Research Project 44, Carnegie Press. Inc. New York, N. E., 1953. (7) V. C. F. Holm and R. W . Blue, Ind. Enp. Chem., 43, 501 (1951). (8) S. W. Weller and 5. G. Hindin, J . Phys. Chem.. 60, 1501 (1956).
INFLUFKCE OF MOLECULAR WEIGHT DISTRIBUTION ON VISCOELASTIC PROPERTIES OF POLYMERS AS EXPRESSED BY THE ROUSE AND ZIMM THEORIES BY STUART E. LOVELLA N D JOHN D. FERRY Department of Chemistry, L'ninerszty of Wisconsin, iWadison, Wisconsan Received J u l y 34, 1961
-4t very low frequencies, the limiting value of the storage compliance of an uncross-linked polymeric system with any arbitrary distribution of molecular weight can be derived' from the Rouse theory2 in terms of certain molecular weight averages. The calculation assumes that the effective monomeric friction coefficient is the same for all modes of motion which perceptibly influence the viscoelastic behavior a t very low frequencies. If one compares the steady-state compliance of a homogeneous polymer (J&)with that of a sample with molecular weight distribution having the same number-average molecular weight (Jen), the result is J e n / J e b= iPz+iAVz/L'iTw-Vn
(1)
where the various molecular weight averages have their usual symbols. Somewhat similar calculations have now been made for other viscoelastic functions based on the same assumptions. At very low frequencies, the storage and loss moduli G' and G" are proportional to ~2 and W , respectively. The constants of proportionality can be formulated in terms of molecular weight averages by either the Rouse or the Zimm3 theory. For example, the Rouse theory provides for a homogeneous polymer when w 2 n 2
