COMMUNICATIONS TO THE EDITOR The results in Table I suggest two more specific conclusions : ( 8 ) the binding and transition energies of es- in the alcohols are determined by interaction of the electron with an optimum configuration of OH dipoles in a small solvation domain, perhaps a single shell; ( 2 ) the optimum configuration for e,- is affected by molecular structure of the alcohol. Comparison of E,,, for the normal alcohols (cf. Table I or Figure 1) sho~vsthaS the optimum configuration is little affected by the number of C2 atonis (particularly for Cq through &); thus, the linctar alkyl chains of OH groups bound by the electron appear to extend radially into the solution with n c g l ~ g ~ ~:steric l e hindrance. However, an effect of molecular s h c t u r e on the optimum configuration i s clearly evident in the lower values of .&"ax for the branched alcohols, for which steric hindrance apparen tly decreaseE the interaction between the OH groups and the electron. Our most recent experiments give B A, of at least 3500 nm for 3-methyl-3-pentanol -pentanol. A decrease in steric hindrance with increase iri disianee of the branch point from the
Present results and those of Brown, el al.,6 and Magnusson, et a1.,6indicate that an alcohol can be diluted with an alkane to a concentration at which D, is essentially indistinguishable from that of the neat alkane and yet from that of exhibit relatively Mtle or no shift of A,, the neat alcohol toward that of the neat alkane (for which Anlax > 2000 nmle). Clearly, such resulbs arc not compatible with dielectric cont'inuum models but are icompatible with the suggested predominance of the sole of a solvation domain. The transition euergy is {determined by composition of the solvation domain. 'The equilibrium composition of the solvation domaiii is determined by (1) composition of the hinary mixture, ( 2 ) relative strength of the attractive interactions of ewith the mixture components (reflected by E",, of the neat) components), arid (3) strength of the attractive interactions between the mixture components. For alcohol--aikane mixtures in which there is weak int)eraction between the components and a large difference in the strength of their interactions with e-, the solvation domain rcmains essentially saturated with alcohol own to very low concentrations. However, for binary mixtures in which the interaction between components is strong or the difference in strength of their interactions with e - is small or both, a different dependence of the solvation domain composition and, Lherefore, of E,,, on solution composition is to be expected.14 In the mixtureti studied, as in the neat alcohols, the
2933 e*- spectra are present within the 5-nsec pulse and do not change over a t least a 20-nsec period. Clusters of alcohol molecules exist in alkane solutions even a t 8.1 M alcoholl7 and provide a distribution of preexisting sites of diverse compositions for trapping (localization] of the thermalized electrons. Evidently, relaxation of such trapped electrons to the equilibrium composition and configuration of es- is complete xithin 5 nsec in the 0.1 M solutions of alcohol in cyclohexane. Such an observation ie in accord with recent calculations by h!Iozumderl* on t)he time dependence of electron solvation as a function of the concentration of single dipole molecules randomly dispersed in a nonpolar medium. For elucidation of the solvation ~ e c ~ ~ ~ n i s m in alcohol-alkane mixtures, the studierj are being extended to lower alcohol concentrations, Blkaaes of greater viscosity, lower temperatures, and shorter times (for which purpose we have deveioped new infrared picosecond pulse-radiolysis sgstcnn utilizing an injection laser diode).
DEPBR'TMENT O F CHEMISTRY A N D
T H E l%ADfATION LABORATORY
ROBERT R. HENTZ* GERALDINE KENNEY-NTa4LLACE
UNIVERSITI~ OF WOTRE DAME NOTRE D A M E , INDlANA
46556
RccsivEu MAY26, 1973
Calculation of
AHdO ( g )
- AHd'(1)
for Dissociating
Dimers wia the "Dissociation-Vaporization" Rule. The AHdo (1) of Trimethylaluminum Publication costs assisted b y the Ethyl Corporation
Sir: For dissociating dimers such as the aluminum alkyls, both the heat of dissociation in the liquid phase (AHd'(1)) and that in the gaseous phase ( A H d o ( g ) ) are of considerable interest. Since it i s often the case that one of these quantities is known, but not the other, a method of calculating one value from the other would be very useful. For example, the A N d o ( i ) for trimethylaiuminum (TMA), often needed for the interpretation of kinetic data, has not been determined experimentally. It would be very helpful if A H d o ( l ) could be derived from the experimental value for AHdo(g)(20.40 lical/mol of dimer'), (1) C. H. Henriclcson and D. P. Eyman, Inorg. Chenz., 5 , 1461 (1967). The JournaE of Physical Chemistry, Vol. 7 6 , N o . BO, l 9 7 e
2934 M A
1
M@---C:
e
(3)
(M2) hi
+
--
h H v ' t ~ 1 , ~ ) AHvo(~2,2ti0)
0.93 kcal Me
I
I
--C---Me
-+ 2Me---C==CZg.,
(4)
I
Me ~AH,O(IK,dE(n50)
AHvo(~)
= AHdC'(g,26")AW~O(D,W) (1)
Since A M d C ( g )and AHclo(l) are customarily taken as constants ( e ~ ~ ) ~ rdata ~ ~are ~ enot~ usually ~ t a ~accurate enough to eslabiiiih their temperature variation), thew valuer, wtll be :~ssumedto apply at 25". Equation 9 may then lbe .iirll teri ARdo(g) - h R i " ( ~ , bARV0(M,7.S~,-
aMovcu,2s9
(2)
It is eonveriied to refer t o eq 2 as the "DissociationVapo,*izaGion Pule," (It i s noted that similar rules can be written lor other cbxiensive properties such as entropy and free energy.) Determination OF 6~ for a particular monomer-dimer system consists of the evaluation of the "vaporization difference" for that system. It might be expected that the vaporization difference (and therefore the value of ~ n i d dhave about the same value for different ~ ~ ) n ~ ~systerr~. ~ e ~It -will- be ~ of' ~ in~ terest to test zhis expectation and to determine the range of SH value6 for a particular class of compounds, rlaixely, the a m i n i m alkyls. Since heats of vaporization of pure nxonomers and pure dimers are not available, ~e n u ~ fturn t o analogous compounds for v hich the nece;,sapy data are available. The branched aliphatic h ~ ~ ~ c ~ both c a ~saturated ~ o ~ ~and s olefinic, are well suri,ed t o this urpose. Like pure aluminum alkyl monomers and di ers, they are 6cnorma19'liqiids w h c h obey Trouton's rule. Individual hydrocarbons can bc selected whioh bear a close structural resemblancc t o particulap monomers and dimers. For example IT-P d i i n l-e the following equations simulating tEe di~o:,ialion OS TB'IA dimer into iyIonomer2 31e -\Tc, Ale--C
I 1
-CH-
Me
CH,-i\Ie
I
-+
l\/lc--C=CW2
I
+
,
(M1) T?se Jourral afPhgsicaZ Chemistry, Val. 76,No. $0,1972
8~ = 1.14 kcal
Me
Me
I I
I
Me-C--CH2-CH-Me Me
+ H&)
-+2Me
(53
8~ = 1.04 kcal (H2(g) disregarded in the calculation).
The close agreement of the three values for 6~ is noted. To obtain comparable values of ic~lfor a series of (simulated) aluminum alkyls, it is convenient t o write equations similar t o eq 5 and calculate the necessary values of AHv' (260) from ~ ~ o r ~ w ccorret~'~a lation of heats of vaporization of isomeric alkanes with molecular structure. The following values of SH in kcal/mol of dimer were derived in this manner: 0.99 for (simulated) Me3AI, 1.06 for XeaAIEt, 1.13 for MeAIEt?, 1.13 for Et& 1.28 for ~ ~ and 1.26 ~ A for EtAIPr,. The value of 8~ for the simulaked aluminum alkyls increases quite slowly with increasing molecular size and it would be expected that 8~ for the actual aluminum alkyls would do the same. ~ ~The r hydrocarbons simulating TiVIA diiner (or monomer) in eq 3, 4, and 5 boil about 15-30" lower than pure TMA dimer (or monornw). A s just shown, however, the value of SH is affected only slightly by ra moderate change in boiling point, It is coiicluded that 6~ for TMA is about 1.84 (average for q 3, 4, and, 5). TJ Eyman's' value of 20.40 Iical fo awdo(l)(l['&h!L) ANd*(g, - 613 19.4 lical/mol of dimer. I n an earlier paper,* based on heat oE dilution experiments, we reported the bWdo (I) of triethylaluminum (TEA) as 16.83 .I: 0.23 kcal/mol a i dimer. We have determined from heat of mixing ~ ~ ~on TIVIA~ r ~ TEA (to be described in a forthcoming paper) that a N d o ( n ) (ThSIQ) - AHd"(l,(TEA) =-- 2.47 0.05 (2) The thermochemical data were taken from F'. 33. Rossini, et al., "Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds," Carviegie Preas, Pittsburgh, Pa., 1953, and Supplements. (3) E. Morawetz, J . Chem. Thwmodyn., 4, 145 (1992). (4) M , B. Bmith, J . Phys. Chem., 71,364 (1967).
~
COMMUNICATIONS TO THE EDITOR kcal/mol of dimer at 25”. This leads to the experimental value 16.93 2.47 = 19.40 f 0.30 kcal/mol of dimer for A N d o ( , )of TMA, in excellent agreement with i,he value derived by hydrocarbon simulation. It is concluded that (1) the proposed general method of calculating 8H EEZ AHd”(p)- A N d O ( 1 ) for dissociating dimers is supported y experimental results in the case of the aluminum alkyls; (2) the method is readily extensible to other dissociating dimers (such as carboxylic acids) and t o other properties (such as entropy and free anergyj; ( 3 ) the value of 6~ is about LO4 kcal/mol of dimer. for ‘SMA and increases quite slowly with increasing molecular size; (4) the value of A \ N d o ( i ) f o r $MA is estabiislzed as 19.40 f 0.30 kcal/mol of dimer..
+
Acknotdedgmenents. The helpful suggestions of Dr. M. E. Wiegand are gratefully acknowledged. B.SMITH CHEWCAL RESEARCH AND DEVELOPMENT MARTIN ETHYI~ CORPORA~~ON BATONRowaE, LOWIEIANA 70821 RECXIVED M A Y
30, 1972
2935 weight ratio of protein t o aqueous solvent changes from about loea to about 6 as collagen goes from dilute solution t o the solid state (ea. 15 wt% water), the question of the possible effect of water content on the conforniation of the helix also poses itself. To resolve these questions, wc consider the optical activity of a crystal as a second-rank tensor12
where ail are the components of the tensor and 1,,1, are the direction cosines of the light beam with respect to the molecular axes 1, 2 , and 3. Due t o the cylindrical symmetry of the collagen helix, all noiidiagonal components of the optical activity tensor of collagen are zero and, furthermore, a11 = aZ2. I n this notation, 0111 = a22 is the optical activity measured with the light beam perpendicular to the helicd axis, while is the optical activity measured parallel t o that axis. I n dilute solution, where the helical macromolecules interacting with the lighht beam are r a ~ ~ d ~ i oriented nly in the solvent, it can be easily shown that 20111 %ohtion =
Resolution of Components of the Optical Rotation T ~ ~ n of s oCollagen ~ Publieation costs assisted by the National Institutes of Health and the National Science Foundation
Sir.: The optical activity of collagen in dilute solution een studied (e.g., ref 1 and 2) and the results have reviewed comprehensi~ely.~?~ By contrast, the optical activity in the solid state has not received much attention although the early measurements of Smith,5 Robinson and Bott,* Robinson,’ Cohen, and Elliott8 on solid films of denatured collagen (gelatin) are noteworthy exceptions t o such paucity of interest. I n the solid state, collagen appears to possess much stronger optical activity than En solution. At the reference wavelength 365 mp, for example, the wellknown dilute solution value of the specific rotation is -130Q,9 whereas the specific rotation of a solid film cast ’from a dilute solution of rat tail collagen at room containing ea. 55 wt% collagen is as Early work1*5~6 with films of gelatin cast aL SOOM temperature or below (cold-cast gelatin) has shown that the specific rotation of this partly denatured form of collagen is also considerably higher in the solid state than in solution. No convincing explanation has been previously given for this phenomenon. The question immediately arises whether the triplehelical structure of the collagen molecule undergoes a significant change in its dimensions in going from a relatively unperturbed existence in dilute solution to the highly crowded solid state. Furthermore, since the
+ 3
Q83
(2)
A distinction between the optical activity in dilute solution and in the solid state can be drawn by measuring the individual componeizts ai%(i = 1,2,3) in solid specimens and then comparing their arithmetic average directly with the optical activity in dilute solution which, according t o eq 2 , is the arithmetic average of the tensorial components in that state also. We report here the results of such a comparison. Since there is a significant difference in refractive index between a dilute solution specimen and a solid specimen, the Lorentz correction factor13 has been applied to all values of specific rotation reported below; values of specific rotation [ a ] reduced in this manner are distinguished by the subscript 1; (e.q., [ Q I ] ~ ) ~ Even though the specific rotation was determirred over a (1) C. Cohen, J . Biophys. Biochem. Cytol., 1,203 (1955). (2) E. R. Blout, J. P. Carver, and J. Gross, J . Amer. C‘itena. Soc., 85, 644 (1963). (3) P. H. von Hippel, “Treatise on Collagen,” Vol. 1, G. N. Ramachandran, Ed., Academic Press, London, 1967, Chapter 6 . (4) J. P. Carver and E. R. Blout, ref 3, Chapter 9. (5) C. R. Smith, J . Amer. Chem. Soc., 41, 135 (193.9). (6) C, Robinson a n d M . J. Bott, Nature (London), 168,325 (1951). (7) C. Robinson, “Nature and Structure of Collagen,” J. T. Randall, Ed., Butterworths, London, 1953, p 96. (8) A . Elliott, “Recent Advances in Gelatin and Glue Research,” G. Stainsby. Ed., Pergamon Press, Elmsford, N. Y., 1958, p 267. (9) P. 5’. Davison a n d M . P. Drake, Biochemistry, 5, 313 (1966). (10) I. li, Yannas and C. Huang, MacromoZecu7es, 5,99 (1872). (11) I. V. Yannas, Rev. Macromol. Chem., C7(1),49 (1972). (12) J. E’. Nye, “Physical Properties of Crystais,” Oxford University Press, Oxford, 1957. (13) P. Urnes and P. Doty, Advan. Protein Chew., 16,401 (1961). The Journal of Physical Chemistry, Vol. 76, No. 90,1972
