I. Studies of Some Absorption Spectra in the Photographic Infrared. II. Studies of the Hydrogen Bond. III. The Raman Spectra of CCl₂F-CClF₂ and CClF₂-CClF₂ Citation Rasmussen, Robert Severin (1941) I. Studies of Some Absorption Spectra in the Photographic Infrared. II. Studies of the Hydrogen Bond. III. The Raman Spectra of CCl₂F-CClF₂ and CClF₂-CClF₂. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/216h-k397. https://resolver.caltech.edu/CaltechTHESIS:03122025-214929725 Abstract Absorption of formaldehyde and difluoro-methane under low dispersion in the photographic infra-red region is described, and approximate vibrational assignments made. An attempt was made to study some of the bands of difluoro-methane under high dispersion, but does not yield much information. The C-H band of formic acid monomer photographed under high dispersion is discussed. It has the same rotational structure as the 0-E bands. The small moment of inertia is calculated. for the third C-H vibrational state, and the band origin located. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Badger, Richard McLean Thesis Committee: Unknown, Unknown Defense Date: 1941 Record Number: CaltechTHESIS:03122025-214929725 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:03122025-214929725 DOI: 10.7907/216h-k397 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17058 Collection: CaltechTHESIS Deposited By: Ben Maggio Deposited On: 13 Mar 2025 21:10 Last Modified: 13 Mar 2025 21:22 Thesis Files PDF - Final Version See Usage Policy. 18MB Repository Staff Only: item control page

PART I. STUDIES OF SOL'.E ABSORPTIO~T SPECTRA. IN '.i:HE PHWOGRJ\.P=nc C:FRA-RED. PART IL S'lUDIES OF TtIE h'YDl1OGE: 7 :BOl:D. p_t.ffiT III. TEE RA!.IA:.: SPECTRA OF CC1 2 F-CC1F 2 A?TD CClF 2 -CCD.':a• ~nesis by Robert S. Rasmussen, In Partial Fulfilment of the Requirements for t}1e Degree of Doctor of Philosophy. California Institu.te of Teclmology Pasadena, California TABLE OF COl~TENT S I. II. Studies of Some Absori_,?t ion Spectra in the Photogr aphic Infra-red. A·o stract. . 1 1. Forma ldehyde. . 2 2. Difluoro-methane. 3. Formic Acid . . . ....... 5 10 Studies of the Hydrog en :Bor..d. Abstract . . . . . . . . . . . 18 . 1. Freezing Point Depression of Etbyl Alcohol in Carbon Tetrachloride. . . . . . . . . . . . . . . . 19 2. Calculati ons on Quantitative Spectroscopic Meas1.u·ements and their Int erpretation . 28 Widths of Association Eer,.ds . . • . . 40 3. ........ " . . . . ~ ... ........ Su1:1mary of Thesis . . . . . . . . . . . . . . . 52 55 Acknov,ledgement s. . . . . . . . . . . . . . . Propositions . . . . . . . . . . . . , . . . • • • • • • • . 57 rnDEX OF FIG1JRES ...... 0 Figu.re 1. 11, 000 A. bands of CH 2 F2 . • . . • Figure 2. Vibrations and axes of inert ia of CH 2 F 2 molecule. . . . . .. . . .. 0 Figure 3. Trace of HCOOH band at 11,700 A. Figure 4. Freez inr; po int apparatus. Figure 5. Polymerization number vs. concentration, ethyl a lcohol in CC1 4 , -23°. . . . . .. 7 7 15 .... 20 24 Figure 6. Formal absorpt ion coeffic i ent, ethyl a lcoh ol in CC1 4 • • • • • • • • • Figure 7. Hal f -width vs. frequency shift of methyl alcohol . • . . . . • . . . 42 Energy level di2~g-.ram f or association of methyl a lcohol. . . . • . • . . . 46 Figure 8. PART I. STUDIES OF SCL':E ABS0RPTIClT SPEC'I'RA ET THE PHO]0GRAPRIC E'.FRA-R:EO. 1 A13STRACT Absorption of formaldehyde and difluoro-methane under low dispersion in the photographic infra-red regi on is described, and approximate vibrational assignments made. An attempt was made to study some of the bands of difluoro-methane under high dispersion, but does not yield much information. The C-H band of formic acid monomer photographed ~,nder high dispersion is discussed. the same rotational structure as the 0-E bands. It h a s The small moment of inertia is calculated. for the third C-H vibrational state, and the banc1 origin located. 2 STUDIES OF SOME A13S0BPTIOH SPECTRA IN THE PHOTOGRAPHIC rnFRA.-RED. 1. Formaldehyde. The spectru.m of formaldehyde vapor has heretofore never been photographed in the infra-red region. It was the purpose of this investigation to do this, and it was further hoped that the third harmonic C-H bands might be obtained Md photographed under high dispersion, thus possibly yielding data of interest regarding molecu.lar constants in the excited state. The third harmonic bands lie a 'c too long a wave length to accomplish this, however, as will be described below. The infra-red spectrum in the f1.mdamental region and son,e of , u lt ra-vio • 1 e~~ spec·rum t h ave b een obt ame • d un d er h.ig h d.ispersion • l t·De and analyzed. The fundamental C-H stretching frequencies are at 2675 cm. -l for the perpendicular vibration and 2780 cm. -l for the parallel. These a.re markedly low as compared with C-H frequencies in other molec·des, but if the anha.rmonicity constant were normal, it was thou.ght that the third harmonics might lie in the photographically attainable region. Experimental Procedure. The main concern in working with formaldehyde vapor is the prevention of polymerization to solid products on the walls and windows of the absorption tube. J3y having the walls very cleeJ1 and the for- (1) Infra-red: Ebers and Hielsen, J. Chem. Phys., 6, 311 (1938). Ultra-violet: Dieke and Kistiakowslcy, Phys. Rev.,~' 4 (1934). 3 mt:1,l<l.e}',_yde very pu.re, it is possible to keep the material for several , • hours without polymerizing. The procedure followed in preparing ') pure formaldehyde was tr,at of Spence and Wilde:... The absorption tube and preparation apparatus were well cleaned with cleaning solut ion before use, and baked out to remove o:xygen. The preparation system was sealed directly to the absorption tuoe, and no stopcocks were used. This treatment did prevent polymerization in the main part of the system, but where t}1e vapor came into contact with mercury, as in the manometer and 1 iquid air trap to the merc·ury pump, polymerization occurred. This was not ra-oid enough to cause any trouble, however. The pressure was regulated by the temperature of a cold acetone bath on the trap containing 1 iquid formaldehyde. exposure it was kept at fifty centimeters. was ten feet long. During the The absorption tube A Bausch and Lomb Littrow glass prism spectro0 graph having a dispersion of 70 A. per mm. in this region was used, with a slit of .1 mm., and Eastman 1 Z plates hypersensitized with arnrnonia solution. lamp. The source vms a 500 watt tungsten projection The wave-length calibration was obtained from lJa, K, Ca, and Ea arc lines, from the salts on a carbon arc. A background ex--po- sure using the empty absorption tube was taken along;side the absorption exposure. (2) Spence and Wil d. , J. Chem. Soc ., 338 (1 935). 4 Results. There was no absorption fo1Jnd in the third harmonic region strong enough to be seen, although the plate was darkened to abou.tll,900 i., the limit of its sensitivity. observed, at 10,355 pectively). l Two weak higher harmonic bands were and 9590 i. (9654 cm. -l and 10,425 cm. -1 , res- The latter of these had a doublet structure. Neither of these 'Wa-l' ' attempted with high dispersion; because of their weakness, a much longer absorption path would "be req_uired. Discussion. The dou"blet nature of the 10,425 cm.-l band is indicative of a parallel--type band; this "band is also in the correct region for a fourth harmonic C-E stretching vibration band. either the 411 11 or the 2\/11 + 2V..1. overtones. Hence, it may be Assu.ming it is 4v11 , _, one calculates an anharmonicity constant tu x e of 53 cm.... , which e is abnormally high corJ1iared with C-H vi"brations of other molecules, where it is 35 cm.-l on the averc3€e. This together with the low fundamental frequencies explains why the third harmonic falls at such a lor.€:: wave length that it could n'ot be found with the photographic technique; it would occm· at l~? ,500 i. Indeed, the absorption curves from 1 to 5 /A published by Patty and lifielsen 3 show a band (3) Patty and Nielsen, Phys. Rev., .3_2, 957 (1932). at 1. 25 p. , which is therefore one of tne third harmonic C-H stretching viorat ions. bt.nd Th.e 965~- cm. -l,.. is undoubtedly a combination of a third hartht , monic C-H stretching vibration with one of 1500-1700 cm.- .... fre/\ q_·nencies. 2. Difluoro-methane. This molecule was investigated. to determine its general absorption in the photographic region, and particularly to obtain the fine structure of the t>ird harmonic C-II bands, since the moments of inertia a.re sufficiently snall so that this might be accomplisheo.. It was not found possible to do this, however, because of thP overlappins of a strong atmospheric water absorption band. Ex:perimental Procedure~~ Results. A small cylinder of difluoro-methane was obtained through the courtesy of Dr. A. F. :Benning of the DY.Pont de Nemours Company. The boiling point was given as -51. 7°, and the sample was sub st ant ially p,.,1.re. The sample was held in a trap in a dry ice-acetone bath, 2..nd the absor}?t ion tube was filled by warming the trap vnt i1 a suitable pressv.re was obtained. A low dispersion photograph was taken, with the gas at a press11re of fifty centimeters in a six meter absorption tv.be. The low dispersion spectrograph, photographic materials and wave length calibration were as described previously. Several bands were observed, whose wavE lengths and probable assignments are given in Table I. 6 The fom· third harmonic "bends were fairly strong; the two low frequency ones of these are in the lo\v sensitivity region of the plate, Table I. :Sands of CH2 F 2 in the photographic infra,-red region. Mi.) 1/(cm. -l) ho,-,ever. Assignment 11,790 11,620 11,LllO 11,250 s,4so s,610 8,760 3,890 10,350 10,200 10,080 9 ,740 9,660 9,300 9,920 10,270 Conio i nat ions of above with 1000-1300 cm.- 1 frequencies. 3,970 3, 390 11,140 ll,2Lf0 Fourth harmonics of C-H stretching Third harmonics of C-H stretc.riing 0 T"ne 11,410 A. band had a.n envelope of the p erpendicular ty:pe, wh ile the 11,250 1. band had one of the parallel tyPe, with a well-defined do1.,1_blet struct1.:--r e. Figure 1 shows the ,appearance of these envelopes, as idealized from a microphotorneter trace and vis1.1al inspection. The combination and fo1.1rth harmonic bands were extremely weak. Sever a l attempts were made to obtain high dispersion photographs of the 11,410 1. band. A six meter absorption tube was first used, with a 32-32 candle power headlight la!T!P as source. The spectra- meter used was the twenty-one foot grating spectrometer, having a '.3_ is::;iersi on of about 2 1. per mm. in this region. . 2 mrr. The slit width was Hypersensitized Eastman lZ p lat~s were employed. Third 7. Figure 1. Bands of CH2 F 2 , 11,000 A. to 12,001. Envelopes of two low freq_uency bands are not known. Min•r .l/¥iJ S ym mehi c Fi. ure 2. .Axes of inertia and CH stretch ing . ibrations for C:! 2 F 2 • s order iron arc Hnes were used for calibration. During absorption exposures, the slit was covered with a red glass filter to cut out higher orders than the first. With this ar~angement, twenty-four hour exposures gave fairly good pictures. The water band with origin at 11,360 A. overlies this whole region, however. The structure of the difluoro-methane ,;:: bands stands out so 1 ittle from the back:ground that the vrat er lines precluded any further analysis. There was a strong sharp Q, branch 0 observed, whose sharp edge lay at 11,247.7 .A. , just at the center of the band measured in low dispers,ion, and which converged rather unusually to the red. The only other structure that could be de- tected was an occasional weak line between the water lines. Efforts were made to improve the diflu oro=meth&~e absorption by ·using a 500 watt lamp an cl a seventy-five foot steel absorption tuoe. The inner surface of this had been corroded by previous use with acids, however, and not eno1.,1g,.'l li ght could be gotten thro·ugh to expose the plate sufficiently before fogging occurred. No attempts were made to photograph t he other bands under high dispersion, beca:u.se of their weakness or unfavorable sit uation. Discussion. If one accepts the assignments of the four bands in the 11,000 i. region as the four third harmonics of the syrn.rnetric and antisymmetric C-H stretching vibrations Vs and 'Va' then two of th e bands, 9 3 v s and 1) s + 2 1)a, will arise fro m electric moment chan 1,;es along t h e intermediate axis of inertia, and the other two, 2 -,.I s + 1) and a 3 V , will have electric moment chang es a long the axis of gre2,t est a inertia (see fig . 2). The fo!•mer two (intermediate moment) sh ould hav e no ~ branch, while the latter two (great est moment) sho1J.ld . 4 From this crite1·i on we would make the following frequ enc:-r assignments, on t h e basis of the presence of a Q, branch in the 11,250 t 0 3va 11,250 A. 2V a +v s 11,)-1.10 1. V +2y a b and: 0 s 11,620 A. 0 3 Vs 11,790 A. T:h is agrees with the rule that an ar1t isymmetric frequency is higher t han the corresponding sy m,.-netric one. Another argument for this as- signment is that the Q branch conve:cg es to the red, and the intensity distribution of the P and R branches indica'ces a similar converg ence for them. Thus the moments of inertia decrease in the upper state. For a symrn.etrical vibration, an increase would surely be expect ed. Look:i.ng a t the molecule as an a l most - symmetrical spindle rot at or, both of t h e types of vi brat ions involved here are perpendicular to t h e p seudo-syrnrJetry axis, and so should appear in (4) See in this conn ect i cn the envelopes g iven by :Badg er and Zumwa lt, J. Chem. Pby s . , _§, 711 (193s). 10 general li..1ce perpendicular - type band_s 5. This is not true for the 11,250 1. band, however; it has the parallel - ty-pe envelope. There is really no anomaly here, howeve1·; it is very probab]y a breakdovm of the approximation of considerin@ : the molecu.le to oe a sym,'.letric top . The interpretation of the four 10,000 i. "bands as como inat ions 6 follows from the Raman frequencies of the liquid ; there are fou1· frequencies there between lOOCJ encl 1300 cm. -l which might oe involved in such a combination. A partial analysis has been made of the rotational fine structure of the third and fourth harmonic 0-H bands of formic acid monomer 7 . In this work, the third harmonic C-H oa.nd was similarly investigated unde1· high dispersion. It was originally hoped in studying this ba.'ld that it would be lJOSsible to find the intensity of the "branch relative to its intensity in the 0-E bands. In the C-~I vi- "brat ion, the chan§~ e of electric moment is almost parallel to the intermediate axis of inertia, a...>1.d the llQ, branch should oe small. The 0- ri bands, on the other hai.'ld., involve a change of electric moment T'ne moment 19 of inertia calculated fro m a likely model are 92, 81 and 16•10- 40 g. cm. 2 Gloclcler and Leader, J. Chem. Phys., 1, 382 (1939). :Bauer ana_ :Badger, J. Chem. Phys. , .2, 852 (1937). Thompson, J. Chem. Phys., 1, 453 (1939). 11 with components along both intermediate and minor axes of inertia, and consequently have a noticeable ~Q branch. Because of background unevenness it was imoossible to decide to what extent a ~l branch was present in the C-H band, 'out it surely was not very prominent. Thompson7 had reported this band at 11, 70c persion photographs. A., from low dis- This was confirmed, and the rotational analysis described below shows it to belong to the monomer, so it is undoubtedly the third harmonic C-~ stretching vibration. Experimental Procedure and. Results. The formic acid used was Baker and .Adamson 1 s reagent grade. Distillation from a sodiurll formate -concentrated su.lfuric acid mixtu.re 8 in a one-foot column further removed water. The fraction used came over at 100.4 - 101.4° (u.ncorr.). The distillation system was lJrot ect ed from moisture by a P 2 0 5 tube. The formic acid was then trm1sferred to a trap on the absorption tube under conditions which excluded water. The absorption tube was of glass, ten feet long, surrounded with a heating coil of iron wire, and asbestos wrapped. Du.ring e:..'})osures the tube was kept at 110 - 120°, and the trap containing the acid at (S) Hamel, Cher.1. Zent., (I), 1701 (1905). 12 95 - 105°. T:i.is gave about one at mosphere of pressure (normal boiling point is 101.3°). Under these conditions, the formic acid monomer pressure is about 400 mm. 9. A 500 watt tungsten projection la.mp was the light source. The twenty-one foot grati!lf; spectrometer was used, with slit at .2 mm., and other experimental details as described previom ly. :Because the b?..11d occurs in a very insensitive wave length region of the plate, it was found t hat plates fogged before being sufficiently exposed. Recourse was had to t h e use of a plano - convex cylindric lens which had been obtained and mo~u1ted for this purpose by Professor :Badger. ).1 r· r . '.) This has a focus of 25 cm., an aperture of cm. , and is six inch es long , eno1¥-;h to cover the reg ion of inT'ne i~e is cor..pressed vertically by a factor of three or 1wre by t~-ds lens, allowing correspondin.gly shorter exposure p eriods. The lens ,vas placed with the plane side towards the grating. It was adjusted perpendicular to the beam from grating to plate by interposing a srr.all mirror between the grating and lens, and setting the lens so t hat t h e light reflected from t h e plane surface ca.me back toward the grating. The cylindric axis of t h e lens wa s adjusted paral- lel to the plane of dispersion by tilting until the yellow mercury a.re lines as viewed from the plate position were vertical. (9) Coolidg e, J. Arn. Chem. Soc., .2Q, 2166 (1 928). The 13 focus of the grating is not greatly changed by the introduction of the lens. The focus was adjusted by trial, the grating carriage being moved until a focus plat e of iron lines showed sharp focus. When finally adjusted, the iron lines were vertical, and selfreversal could be clearly seen. T'ne lines were slightly broaclened, the result of an aberration introduced by the cylindric lens 10 . T'ne abel.Tction is negligible compared to the slit width used here. Since the cylindric lens made it impossible to place an iron arc reference spectrum alongside the absorption spectrum, calibration was effected in the following way. Some sharp atmospheric water lines which were off to one side and had not gone through the lens were used as references, and absorption maxima of the formic acid band measured relative to these on the cor:~arator. A plate was taken of atmospheric absorption, using the cylindric lens, and an iron arc superposed on t h is. The arc lines that had gone thraugh tlie lens and lay in the sar::e region as the formic acic, band were also measured relative to the same water lines, and the calibration thus accor:~l ished. Several formic acid plates were talcen with the cylindric lens, of which two were sufficiently good to show some band structu.re, (10) Eowen, Astrop~zys. J. , 88 (2), 113 (1933) • 14 na..'Tiely, several Pel and RQ, branch maxima. q1..ired were about 13 hours. 0 The exposure times re- Unfortunately, the bac..u;:grounds vre:c e extremely irregular, which made it diffici:.lt to m.easure the maxima accurately and irrr9os s ible to tel 1 about the presence or absence of a ~ branc.1-i. Fi 6..u-e 3 shows the microp:hotometer trace of the bMd, obtained by superpos ing the two plates exactl~r and running t hem through the microphot or.iet er. This removes some of the background irregularity and 6-rain. Discuss ion. The formic acid monomer is almost a symmetrical top molecule, t h e tv/0 larg est moments of inertia being nearlj,- equal and rrmch Thus the levels might be fitted by the er eat er t han the sma ll. • expression: w he = SJ(J + 1) + (r-S) X2 1-i Y= _;_~ g fT C • ..l. -c; where A and B are t l-:.e large moments of inertia and C the small one. Th is expression was fou11d by :Bauer and :Sad.ger 7 to fit the 0-II ba."lds very well, for K sitior s >3. AK= +l vrith -1 wit h AJ The Rn..,;,, AJ = 0, = 0 resp ectively . _,,., ma.xuna • . 1.-l, an d p n""' b ranw, are t'ne -i;ra...'1- (L ~K = 0 with A.J = 0, and AK= 0) qi ,._ . <Y II.. 0~ 0 0 r-- In rl rl It- +> "I Cl: 'D ,.0 " 0 ' :::r:: ... .., ... 0 'I: § " lo ti 0 <t-1 0 (i) (.) ro 1-t +> co ;.., .... 0 .µ • Q) 0 0) µ ~ ~... P, ., '!lo: ,. 0 (.) ·r/ r-, \ CJ > ., . ' 16 Q Since a "Q branch could;t)bt be picked out, there wou.ld oe aJ:1big cdty in the mwbering of the maxima accord.ing to K values in the lower state. The assignment of K was therefore made by choosing that numbering which gave the best a.greement of )"- S for the gr01.ind state as determined in the more accurate Q.;..H bm1d analyses. This is most consistent, furthermore, with the intensity distribution. The constants for the ground and upper stat es are cal cul at ed fro □ the combination relations, 1' - yll where single and dou."ble primes refe1· to upper and lower stat es respectively. The quaritities S I and S II ca'YJ. only be evaluated from P or R branches, i.e. , where transit ions A J = +l occD.r. Since these have not been resolved in tl:is ba."YJ.d, we can again use the fact _, that for the 0-E band, S 1 = S 11 = 0. 34S cm . .,_ Then we obtain y 11 = 2.51.n (cf:. 2.559 of :Bauer and Badger7 ) and Y1 = 2.509, f;iving small moments of inertia of 11.02·10 -40 • (_ ·, g. cm. 2 and Ul.lu±~O •10-40 g. cm. 2 is the ground and third C-H vibrational stat es respect i vel~r. The band• origin is at s507. 7 cm. -1 17 Tao le IL Freq-,1.encie:-;; m,d comoinat ions of maxima in formic acid oond at 8507.7 crn.-l K 0 1 2 3 ~r:j .,,. t) 7 s 9 10 ~ RQ -" s509. 9s 8513.67 8518.29 7') o:JLC....• 8525.89 8529. 77 3535.06 s53s. 66 8542,43 g5l_~6. 30 8550.04 Q'C')') G. RQ,(K) - P,~- (r) A 4K s504.s1 3501.30 3495.62 2.215 2.124 2.253 2.126 2.123 2.186 2.183 2.169 8491.87 8437. 22 3432.59 3477.53 3473. 07 3463.63 I -- RQ,(K-1) - PQ(K+J) 4K 2.170 2.256 2.202 2.219 2.165 2.177 2.214 2.urn 2.171 avg. 1' - s for K>3 = 2. 161 avg. dev. . 022 avg. t" - 6 for K>3 = 2.193 avg. dev. . 019 The values are "believed to be better than the average deviations indicate, since the deviations are less for the more accurately measureaole higher K maxima. PART II. STUDIES OF TEE HYDROGEti BOHD. 18 Abstract Experiments on the freezing poin t depression of soh.t ions of etr:;,-1 alcohol in carbon tetrachloride are described, and the association data derived therefro~ are compared with spectroscopic measurements by others. It is concluded that the narrow O-H band in dilute solutions is due to monomers only. i n the polymer are discv.ssed. The O-H frequencies Monomer-dimer eq_uilibrium constants fo r et hyl alcohol, benzyl alcohol, ancl phenol axe CO!npaJ.'ed. Widths of association bands of hydro:xyl comp ot nds cU'e discussed, and the temperature effect on the frequency of a ssociation bands described . .An elementary theory is gi vaYJ. to explain these features of the ass ociation bands. 19 STUDIES OF THE RYDRCG EN J3 OND Although the phenomenon of hydrogen bonding has been recognized for several years and the spectroscopic study of it has brought forth a large number of papers, there are several quest,ions concerning it about which little is known. The work described below is e.n attempt to further elucidate the quest ions of int eJ'.'.nal ruid free energy of hydrogen bond formation, and the interpretation of some of the spectr.oscopic details. 1. Freezing !'~ Depress ion of Soh,t ions of ~tbyl .Alcohol in Carbon Tetrachloride. lih:i.ch work has been done on the study of hydrogen bonding by physical means (freezing point depression, distribution coefficients, etc.). It has generally been done with complicated molecules, how- ever, and almost invariably in solvents such as benzene, vrhere there is a large interaction with the solvent. This makes interpretation difficult, . if qne is interested in hydrogen bonds themselves. It was undertakeil by Professor R. M. :Badger and reyself to measure the freezing point depression of solutions of etl1yl alcohol in carbon tetrachloride, since here the results should be much less ambig1:1,ous~ 2.0 rubber cyl,inder Fig'U.X'e 4. Freezing point apparatus . 21 E:x:perimental Proced:r¥'e· Commercial absoluxe ethyl alcohol was used, and fuither dried for several days over anhydrous sodium sulfat_e. chloride was reagent grade. A The carbon tetra- one-tenth normal stock solution was made up, and dilutions of this used in the runs. Dewar flask was used as container. A c~pper-coated A large diameter test tube for holding the solution was supported through a hole in a rubber stopper which fitted over the mouth of the Dewar, and the.Beckmann thermometer and stirring rod introduced. through another stopper into the test tube. tried. Different methods of stirring and cooling were originally The technique descrioed below was finally ad.opted as giving a good rate of cooling and efficient stirring. The stirring rod entered the apparatus through a glass sleeve; water vapor was prevented from entering by fastening a cylinder of. sheet rubber to the sleeve and to the stirring rod (see figure 4). The stirrer was driven in a reciprocating motion by an eccentric attachment to a small motor. In mak:i.ng a run, the solution was cooled almost to the freezing point, and the Dewar separately cooled with cold acetone from a dry ice bath. The Dewar was emptied, and the tube containing the solu- tion and thermometer placed in it. This resulted in a cooling rate which was sufficiently slow to give a good cooling curve. The tem- perature was read after 15 sec. intervals, using a telescope and 22 reading to . 001 degree. Cooling curves were constructed from the readings, and the freezing point read fron these. Supercooling of about one-tenth degree was observed in nearly every case. Results. The res,).lt s are given in Table III. Those on pure carbon tetrac.t1.loride and the dilute solutions are more discordant than the concentrated solutions, probably because the stirrer stuck due to the formation of larger crystals in the former case. The freezing point values are averages of from two to four good r-ons. The errors are estimated from the deviations. The value of the freezing point lowering constant for non-as- • t.ing mo 1 ecu1 es is • t rucen ' f·rom o·. th er sources ll , since • 't canno t socia 1· be obtained with any certainty here by extrapolation. This quantity divided by the observed lo,vering per unit concJp.tration gives the polymerization number, n, i.e. , the average number of C2 H5 0H groups per molec-c,. le. FiE:,"1.ll'e 5 shows the experimental values of n plotted against the formal concentration Q,, with the estimated limits of error, and a smooth curve drawn throl,gh to represent the dependence. Discuss ion. dn It is readily shown that the limiting slope aq: is equal to the equilibrium constant of the reaction, 0.1) Beckmann and 1.!a11tig, Z. .Anorg. u all.gem. Chem., §I, 17 (1910). 23 Tab le III. Fre ezing p oint dep r ess ion measux ements on s oluti on s of ethyl a lc ohol in carb on tetrachloride. formal c one . _ _y,_ 0 f r eezing po int** 3. 760_:!:. 012 - -= -~AT T .6 T 0 n Kr./,* AT (18 .7)* 1.00 . 0103 3 . 607_±.014 . 153_±. 026 14. 8 1.26 . 0253 3 .425_:!:.010 • 335.±• 022 13 . 0 I. Ll4 . 0517 3 . 292_±. 004 . 4 63+. 016 9. 05 2 . 03 .1033 3 . 02 3_±. 001 • 732_±. 013 7. 03 2 . 64 * Va l u e f or K., t :0. e lower ;-,, e; cm, s t a.nt for non- ass oc i at i ng mol ecu les , from refer ence 11. **Fr e ezing po i nt on t h e aro i t ra.r? s c a le of t h e Beckma..11n t her raon et er; t h e t rue f r eezing p oint of }Yo.re caroon t etr a ch lor i d e is - 22 . 9°c. Tab le I V. Some of the a ss oc iation eqr il ibr..\:µm cons t ant s for C2 H5 0H i n CC1 4 , as calc1;.l ated by La ss ettr e 1 s method . - 23 0 K;a 29 . 5 +20° E = 6ooocal. +20 ° E = 1 000 c a l. 4. 99 3. 7 2 K3 L 006 23 . 3 16. 00 K4 37, 000 178 .7 74. o ~ ": i • n ,.o 1-3 /.fo ,.q 2.2 0 2 3 + s ,01Q ' Fir !i 7 alcohol in CC1 4 8 q /0 ,, ~ l'l Evaluation of this slope leads to a value of 23 :!:_ 4 for the constant,. making allowance for the uncertainty in the curve. One can go further and calculate a whole set of equilibrium constants for the cm:1tinued association, using the method of Lassettre 12 . This method is based upon the fact that if the poly- merization number can be expressed in the form, (1) n == 1 + a;. Q, + ~N, where N(-Q,) is the true total concentration of all polymeric species, n then the equilibrium constants Kt can be expressed as functions of a. and i3. Here, is the constant for the particular association, and Ct is the concentration of the polymer ( C2 H5 0H) t. Over the range of concentrations studied here, n can be approximately fitted by an e~ression like (1) above with a. == 9.10 and ~ == 20. 4. It is of course to be recognized that many other sets of equilibrium constants will represent the data to within the experimental error; the individual constants obtained from this treatme.nt may not have much validity in (12) Lassettro, Chem. Rev., 20, 281 (1937). 26 themselves, but taken all together they very likely give a fair re:presentat ion of the process of CO;"ltinued association. Unfortunately the res,!.lts of the freezing point measurements can not be directly compared with data obtained from other types of measurement made at room temperature. A correct j_on of the equili- brium constants to room temperatu.re has conseq_uently been made as follows. We make the very reasonable assumptions that the association is conr_pletely due to by"drogen bond forma·l;ion, and that the 1zydrogen bond ener@ is constant, irrespective of polymer size. do not have a precise value for this energy. However, we Estimates have been made from the heats of va:_porization and sublimation of liquid ethyl alcohol, giving about 6800 ca lJries per mole13 . In solution in an inert solvent, we might expect about the same. Hydroxyl groups are capable of forming vreak by"drogen bo.1ds with carbon tetrachloride molecu.les, however, so in this solvent the energy should be reduced . .Another estimate of the energy in solution can be obtained from the spectroscopic transmission curves published by Errera, Gaspart and 14. Sack Curves are given for etciyl alcohol solutions in carbon tetrachloride at 20° and at 55°c. 13y finding a concentration at one temperature which has the sa.r:1e absorption curve o.s another concen- (13) :Sadger and :Sauer, J. Chem. Phys., .2, 851 (1937). Pauling, 11Kature of the Chemical 3ond, 11 Cornell University Press (1939), p. 284. (11+) Errera, Gaspart a111i Sack, J. Chem. Phys.,.§., 63 (194o). 27 trat ion at the other teffii'.lerature, the ratio of eq_uil ibriurn constants, and hence the energy, is approximately given by the ratio of these concentrations. The energy calcule-ted in this way is "between 6000 e.nd 7000 calories. In Table IV are given some of the association constants as calculated from Lassettre 1 s ffiethod, at -23° and also as corrected to +20°, assuming energy (heat content) values of 6000 a..rid 7000 calories per mole. From these constants, curves have been , calcula.t ed. giving the monomer concentration versus formal concentration at +20° for each energy, and also true total concentration, N, versus f orr.1al concentration for each energy value. These curves are u.sed lat er in the interpretati on of spectroscopic results. The estimation of the monomer-dimer constant from the limiting slope is va.lio., and makes no ass-c.nptions about the rest of the coi1stant s. The Lassettre treatment gives a somewhat different value for this constant because of the approximat ior1s inherent in it. Correcting the true cor:.stant fro::: -230 to +20° using an energy of 6000 calories, we get 3.9 as the monomer-dimer constant at room ternperature, with a large error possible due mainly to the lack of precise lmov.1ledge of the energy of the bond. If one could measure the association by non-spectroscopic means at room temperature, one could obtain in:·ormation aoout the energy quantities, and also have res"l.'.lts that would be directl;y cor::parable 2S ,7ith spectroscopic observations. .'i. method is being developed to ac- complish this b:r mea.s·urin6 deviations from Henry's law, but so far no res1..'.lt s have been obtained. It is to be expected that for aliphatic alcohols, association as measm·ed by physico-chemical a..r1d. by spectroscopic methods should be identical. For phenoJ.s, however, this might not necessarily be the case, since other types of association than by byd,rog en "to.1ds might occur. 2. Calculations -2!~ ~uarititative §.r:...1c:;__ctroscopic Measurements §lli! Thaj£ Int erpretaticn. Perhaps the n:ost direct a.'1d useful we.y to study the energy relations of hydrogen bonds is that of infra-red spectroscopy. In order to obtain reliable data by this method, it is necessary to be able to make acc1.1.rate qua.'1titative intensity measurements, to have good resolving povver if narrov, bands are being measure; and to go clown to ver-J low concentrations. Such measurements should ;( iVe equilibrium constants at one te~0eratu:re, and if carried out over a temperature range, should yield the energies of formation of the bonds. Only a very few papers have appeared in whic}'!. nany of these conditions are fulfilled. The lower aliphatic acids in the vapor phase have been studied over a temperature range by Hofstadter, F Herr12n and co-workers .) , and the monon,er-climer energies determined. (15) Herman, J. Chem. Pbys., _§, 252 (191.~o). 29 ,,_ 11l.1 , ph eno 116,17,18 On so 1u t ions, t h ere have appeared :pa.p ers on et -iW 1 a l co110 and benzyl alcoho1 19 , all in carbon tetrachloride. Co92a.rison of Freezing Point_ ~ S12ectroscopic ~ . In default of b eing able to malce exa ct absorption inten sity meas·1.u:-ements on ethyl alcoh ol in carbon tetra chlorid e to compare with the freezing point data, some of the p ublished transmission curves 1 u of Errera, Gaspa.rt anr Sac}:- · in the 3 fA region hnve been used for t h is p urpose. Thes e curves seem adequ ate for a ro1.1.6 h quantit ative treatment, a lthough t h ey were not so used o y the authors. t h e frequency ra."YJ.g e 3100 to 3750 cm. .125 to 3 volume per cent. -1 T':: ey cover , and concentration r ang e from They sh ow t he usual narrow band at 3640 cm. which is attributed to free 1'.ydro:C"Jl groups and t h e very broad b and extending from 3100 to 3600 cm.-l wh ich is characteristic of the hydrog en bonded hydroxyl. In dilute solutions the na rrow band is stronger, while in concentrated ones it is weaker than the broad association band. The calculations presented below a re on the narrow 3640 cm. band in dilute soluti ons at 20°C. -1 The c_~ ange of t h is band ~ith concentration is compared with a s soci at ion· data derived in the last (16) Fox and I,artin, Proc. Roy. Soc. (London), AJ.62, 419 (1937). (17) Kempter and f'iiecke, lfaturwiss., n_, 583 (1939). (lS) Wulf and Jones, J. Chem. Ph:;s. , 3, 745 (1940). (19) Fox a nd Martin, Trans. Faraday Soc. I ~6. 397 (1 940). - -1 30 section. The spectral slit width was about one third of the half- width of the band, so tha.t there should. not be much falsification of the value of minimwn transmission. curves are given in Table V. The measurements made from the The transmission coefficients f or several frequencies vrere taken, and the formal absorption coefficients a calcc,Ja ted from the usu2.l relation 1 a. = - ~R, where Q is as before the formal concentration and. R, is the path length in centimeters. The absorption coefficients were plotted, a.~d small background correction£ estimated.. Since the shape of this ban d_ does not change noticeably with concentration, it is sufficient to take the maximum absorption coefficient minus the background correction as a measure of the strength of absorption, rather tl12n the integrated area under the whole band. Fox and rtart ir.19 have investigated this procedl;.re in detail for the sharp benzyl alcohol band_, and four1d_ it to be valid. The values of corrected a. r:iax. so calculated. are given in t h e next to last column of' Table V. Errera et al. gave two sets of curves covering the con cent rat ion ran,c: e of interest here: one set using a 1 :,an. cell for t~1e more concentrated solutions, and o::,e set using a 5 wm. cell for the dilute solutions. One solution, . 5 volu1ne per cent, was run in both cel l s and there is a discre~ancy between the two values of a. max. which is too large to be accounted for oy errors in transmission measurements. It is in all probabilit;i due to errors in measuring 31 Table V. Calcu.lation of absorption coefficients of ma.xinrurn of 36LfO cm. -l band, ethyl alcohol in carbon tetrachloride (from transmission curves of Errera, Gaspart and 63 (194-o).) Sack, J. Chem. Phys.,~. volvme 12ercent .125 . 25 .5 . ~.) .75 1.0 formal cone. '<l . 0214 . 0427 . 0854 . 0854 .1282 .1709 * transmission T 1/ro = R, . 238 .110 .0275 . Lf25 . .321 .1 . 276 .1 i=" .) .5 . r, .) .1 _JL ~ ex.** 58.2 44.s 56 Lf 3 3l.f. 5 41.5 36. 5 30.5 56 43 3)_,r • .)i:- 3co.:.,;~: 1f3. 5 38.5 32.7 Corrected for "background ** Corrected for cell discrepancy 34.5 30.5 25.5 32 the cell lengths; indeed, correcting the a max. values for the 1 mm. cell oy a multiplicative factor so that the .5 volume per cent solutions match makes all the a. max. values fall on a fairly smooth curve ( see last column of Table V). The a max. so calcu lated is not constant, as it would be for suostances which do not associE:,,te, but is related to the concentration of aosoroing gro1.,'{)s, C, thus: a C (2) a. = a Clo max. ~ where Clo is the true aosorpt ion coefficient of absoroing groups, and is a constant independent of cone entrat j on (ass uming the LambertBeer law, of cou.:cse). As to the identification of t h e absorbing groups, two wa;/s of interpret in6 the 36L~o cm. -l band have been suggest ed. Either it is due to all the bydroxyl gro'l~.p s whic l-, have not acted as the donor of a hydrogen bond (free b;ydro:xyl groups), of yrh ic1.-:. there are one per polymer irrespective of size: free bydroxyl group ~ ••• E-H· •• i-H· ••• rH or else it is due to the monomers only, the freq·uency of the free hydro:xyl groups on the polymers being changed simply because the OX'Jgen has 'become the acceptor of a hydrogen bond. In the first case, the quantity Ca in (2) is N, the total concentration of all polymers; in the second case, Ca is C1 , the monomer concentration. 33 Now by c.>i.oosing an appropriate value for 0.0 and ki1owing the dependence of H and C1 on le(, from the freezing point data, we ca."l match the spectroscopic data. In fig·ure 6 are plotted the five spectro- scopically .measuxed points that fall in the concentration range cove1·ed by the free:7,ing ::;:,oint neasurements. There are also shown calculated curves, which were constructed f:ro.rn the curves mentioned on p. l.7 giving the dep-ena_ence of C1 and H on Q, assuming the two values for AE. An a.0 was chosen in each case to give the -t; est fit. Two of the curves shown are 0:.1 the assu.r:r_pt ion that only monomers absorb, and two that o.11 p ol r:1ers absorb. It is seen that no one of the curves fits well, although the 6000 calorie one fits best; the inaccuracy in the spectroscopic points is one or two units of a, so too good a fit is not to "be expected. It seems reasonably clear, however, that the ass,·mpt i :)::1 t:1A,t all :9 01?:Jei·s absorb gives t c- CJ f l .?. '.; e, c1.u:ve t o Zit the points; i.e., the rate of falHng off of absorbing gro1.lps with inc:cease in concentrat icn is too slow if we assur::e all polymers absorb. Hence Yre can co:r,clude tha t the nari·ow 3640 cr.1. band is due to monomers 011ly. In all three papers on -ohenol referred to a b ove 16,17 ,18 , t "k He authors made the asS"\:unption of regardin g the absorption at the n8.rrow band as due to monomers only, and fitted their data fairly well by chaos ing appropriate: equilibrh1m constants and absorption coefficients. The procedure described above, however, ,;:rhich u ses eq_uili- ; • 20 1° 0 Fig1;.re 6. ,o'Q JO ,s Fr:, pl ',__,::;orpt ion coefficient vs. concentration, ethyl alcohol .:..1 Cvl 4 • • - experimental 1 - calculated, absorption by monomers , ~E = 6000 cal. II II II II SE = 7000 cal. 2 II II II polymer s, 6E = 6000 cal. 3 II II II II l'..E = 7000 cal. L~ s 2 3 ... o.) -t::- 35 briurn constants derived from non-spectroscopic measurements, removes the gratuitous char act er of this assurrrot ion. Frequencies of the Polymef..S· The question naturally arises as to what becomes of the free hydroxy-1 frequency of the polymer. One explanation would be that there are no such free groups, the polymers closing u.p in rings. This would require the dimer to be sor::ething of the tYPe, This hypothesis has in its favor firstly the fact that it explains the absence of free hydroxy-I group polymer absorption from the region of monomer absorption, and secondly that if such dimers as (3) occur, the hydrogen bonds in them might be somewhat weaker because of steric conditions. Now the association band is actually found to be composite,l5,l 6 ,l9 havi:r~ a moderately broad band (A band) ~ t au~ auou 3500 cm. -l w.h ich is • s t ronger in • very d.l i u t e (< . 1 mo 1 ar ) 0 -1 solution than a very broa,d bend (J3 ba.nd ) at about 3350 cm. . J3 bend increases rapidly in higher concentrations ( swamps out the A band. The >.1 molar), and From this behavior, the various a1..1.thors have postulated. that the A band is clue to dimers, and the J3 to higher polymers. If one uses the relation between frequency shift and energy suggested by Eadger 20 , then the energy of the dimer oond w ·rnld (20) J3ad 6 er, J. Chem. Phys.,_§, 288 (194o). monomer :b :md Ethyl alcohol (Errera , Gas:9art and Sac..1<: association -------- A bands B 3640 cr.n . -1 3525 3325 3470 3370 3490 3350 3610 • ) 3620 :Senzyl alcohol (Fox and 1"·, iar t in 36~-0 Phenol (Fox and Martin ) be less by a fact or of about one-half than that for higher polyme1·s, as would be expected. for the v,eal--:er bonds of a dimer suc.11 a s (3). The presence of two su.ch bonds :per dimer would, however, make the total energ/ of dimerizat ion a'oout the same as that of a.'1 ordinary bond, i.e., abo1xc 6000 cal. Regarding t h is hyp othesis of the c;ycl ization of ]) Olymers, however, one is a little inclined to question the stability of such cor:Ip lexes as (:;), and, on gr01111d.sof entro:JY, the stability of larger cy clic p olymers. However , so~ne apparently very strong evidence i n favor of dimers of t h e form of (3) can be aclduced ._ from dipole moment calculations made by Wiison 21 on ethyl alcohol in n-hexane solu.t ion, fro m t h e da ta of Seyt he and St oops 22 . It is fo·und. tha t wh en }' 2 / µ g 2 is plotted against concentrati 01'- , ,rhe:r e ' fl-/ I" g is the ratio of dipole moments in solution and in vap or, the curve first decreases, going dO\'iD fro:n unity at zero concentration - -- - - - - -- (21) Wilso:1 , Chem. Rev., .?_2, 400 (1939). (22) Smythe and Stoops, ,T. Ar'.!. Chem. Soc., .21:, 3312 (1 929 ). 37 to 0. 6 at 0. 4 molar, and then rises uniformly to the very high values characteristic of the large polymers. The initial decrease indicates that the dimers have a smaller electric moment than the monomers. If one assumes that the monomer moment is icl.ent ical with that of the vapor and the d.ime1· moment is zero (as Wilson suggest ed.) 1 and uses the equilibrium constant 3. 9 of mono□ er-dimer association of ethyl alcohol in caroon tetrachloride, then a curve of p?·J p. g 2 can "be calcub.ted which fits the Wilson curve fairly well in the region of small concentration, where trimeI's and higher pol;yme1·s are unimportant. The deviations from perfect fit are s1)ch that if one used a larger cmrntant, as would. be anticipated in :passing from caroon tetrachloride, vrl-1ich bonds slightly to the hydroxyl group, to hexane, which has ver;/ little interaction with the alcohol, then t:1e fit would be better. There are other J)Ossiole explanations for the A and 13 bands, however. Fo1· insta:r1ee, the A band might be the shifted. free hydroxyl frequency of the polymers, assuming they do not form rings, while the :B band is due to the h;:rdrogen bonded hya;coxyls in the poly,ner. A priori, we would e:;.'I)ect these free hydroxyls of the polymers, if they have their frequency shifted at an, to have it shifted to lower ')'"' frequencyc..) This ex)la.'lat ion of the A and 13 ba:ods suf f ers from (23) The ba.rid in aliphatic alcohol and acid liq-0.ids and concentrated. solutions at ca. 9100 1 (to the high frequency side of the third h2.rr0onic mor.omer brn1d) found. "by J3adger and Eau.er, er. Che,:1. Phys., 2 , s39 (J_937), mv.st "be attributed to some sort of an overtone in the l1 i ,7.;her polymers and is not the shifted. free hJdroxJl frequency as assu1neo. oy Paul int:, 11lTJ,tu.:ce of U.:.e Chemical 3ond, 11 1, . 307. lTo such b?.l1cl has beer. re.:iort ed in the fundarnental or second harnonic regions. 38 the disadvantage that from the great deal of work that has been done on intra-molecular hydrogen bonds it is knovm t hat t he accept or oxygen does not have its hydroX'Jl frequency changed 24 . This might conceivably be due to some difference between inter- and intr a-molec-c.lar bonds. In any case, it should be yi ossible to distinguish experimentall~r between these two hY}_)Otheses, since the A ba.'ld is in the first case due to dimers , a.nd in the second. to all :polymers. Caref-c,.l spectroscopic mea sm·ements migh t decide whether it increases with concentrat ion as the dimer ,:loes, or as a ll t}1e polymers. lfone of t h e work so far published is adequate to make a decision in t h is ma..~n er, however. It seems most probable t h at t he true state of affairs is between the two extremes of cor:iplet e cycl izat ion or none. The explana- tion of the A band as due to t he dimer in the form (3) seems to fit all the facts and does not contradict t h e evidence from intra-molecula.1· "bonds, as an open dimer would. In t he higher polymers, there ct-e probaoly both chain and rin g configurations, with the nurnoer of free hydroxyls fro m p oly mers co 1:-iparat ively small so t hat in dilute solution they are negligible co;-:1:9ared to the monomer. (24) e. g ., compare the curves for catechol and phenol i'!ul f ,md Liddel, J . .Am. Chem. Soc., 5J.., 1L1-6L~ (1 93 5) . g iven by 39 It is of interest to compare the known eq_uilibriwn constants of monomer-dimer association. Vro.lf and Jones 18 obtained a value of 1. 7 for the association const ant of the phenol react io n , at 25°C. Correcting this to 20°, using an energ;,,r of 6000 calories, we obtain 2.0. Kempter a:ad Mecke 17 found this constant to be 2.3 at an unspecified room t emoerat-c .re. 1 10 Fror:i Fox and l,'.artin 1 s work on benzyl alcohol 7 , the consta.'1t for t h is monomer-dimer eq_u.ilibrium has been calculated from the pu.blished values ·of a max. of the A b and. Usin;: t h is band as a measu.re of dimer concent1·a t :i_.~-n, which is valid in dilute solution re ~~a:rdless of whether this oana_ has contrHmtions from higher polymers at higher concentrat i •-~ns or not, the equilib1·ium constant can be obtained fro m the limit in§: first and second derivatives of the for mal absorption intensity a. ma,"'{• with respect to concentration. The rela tions are, = a0 K (d~ax-) ~ =0 2 d a.max.) ( = 3 a0 K d~2 Q,=0 2 40 where 0.0 is the true absorption coefficient of the dimer at the maximum of the A band, and K is as usual the ccnstant for the association, K The value obtained in this manner for benzyl alcohol is .46. Tabulating the value::,. (for monomer-dimer constants in carbon tetrachloride) that have been ootained so far: K(CCl4. solution) .AF 0 of association Ethyl alcohol 3.9 -800 cal. Phenol 2.0 -410 Benzyl alcohol . 46 +450 The inaccuracies in the constants are not believed great enough to change the order. If the energies of the "bonds are about the same in the three cases, then the free energies follow the order one would ex-pect from the relative entropies: the larger the radical, the greater the probability of dissociatu1g the dimer. l· Wi~ of Association ~ One of the most stril~ing features of the infra-red absorption "band associated with the hydrogen bond is its great width as compared with other vibrational oa11ds. The band of methyl alcohol in liquid or concentrated solution in the third harmonic, for example, has a }ialf-width (width at half of maxim·c,m intensity) of around 700 cm. -1 Two rough empirical generalizations concerning the width of association bru1ds have l)ecor:ie evident from some studies made by the 41 author and froE1 absorption curves published b;y others. One of these is that the width of the association band formed by a given molecule bonding itself to various other molecules is roughly proportional to the frequency shift. Figure 7 illustrates this on methyl alcohol in the third harmonic region. Methyl alcohol monomers form weak hydrogen bonds with carbon tetrachloride, as mentioned previously; this is indicated by a shift of the monomer frequency of 25 cm. 7 -.1. in this solvent from its frequency in the relatively inert solvent petroleum ether 25 . This shift is accon~anied by a slight broadening, as indicated in figure 7. Furthermore, dilute methyl alcohol solu- t ions in benzene show the hydroxyl band to be shifted very considerably and corresponding;l;/ broadened. This rather large effect is undoubtedly due to the high polarizability of the aromatic ring. These two cases together _with the liquid alcohol bend are shown in figure 7, and indicate the trend of the width with the frequency shift. A second generalization which cart be made regarding the width of association bands is that the width increases by a factor of two or more in the second harmonic and of three or more in the third (25) This frequency shift mi[pt be explained in other words as due to the increased electrostatic interact ion of the hydrox-yl dipole with the more polarizable chlorine over the less polariza:ble h;:rdrocarbon molec1.·les. This is ,just what we understand as a h:rdrogen bond. in cases where the interactim, is more pronounced, however, so it seems not unjustified to call t ,is a. weok hydrocen ·bond. - ¼':r- I t 100 200 300 lfOO 500 6oo 'J"O 300 ... I •- "!'----fy 1.;,~- · - , ; ~, ..c, 02 Figure 7. [ ' .1 -v-:,,--.- .aoo .4,, 4oo benzene, solution . 1 iquid nethyl alcohol 4. 3. CC1 4 sol~tion 2. petroleum etl er sold ion 1. vapor Half- widths of C33 0H third harmonic OH ba.~d vs . frequency shift . 100 0~ 24 l'J -{::: 43 over that in the fundamental. Table VI shows the available data on a few molecules. It will be noticed that the data given are rather meager; this is because the dispersion used in most of the published hydrogen bond work is too low to obtain reliable estimates of band widths. lJever- theless, • the figures given indicate roughly the relation between width and harmonic given above. A simple theory to explain the widths of these bands can be basecJ_ on the idea, sur;gested by Professor :Badger, that the bruids are due to transitions from excited states of the very low frequency bencling and torsional motions between tvro molecules (or clusters of molecules) which are held. together by a hydrogen bond. . Assuming there are m of these vi·,:,rat ions, and the frequencies are so low tnat we can treat them classically, the distribution of the systems over the energy in these m degrees of freedom is, E (L~) dn = cr-l e-x:'t' dE. At a certain value of energy corresponding to dissociation of the gro·ups held together by the bond, the distribution is cut off. For each of the upper 0-H vibrational levels there will be a similar set of low frequency levels, and a dissociation limit. diagrar:1 would appear as shown in figure 8. An energy level An association band is now to be understood as d_ue to transitions from the whole group of lower levels to a gro1,-q;i of upper ones. If we neglect any variation 44 Taole VI. Half-widths of sor.1e association bands , (half-widths in cm.-.,_) Fundamental ~armonic 3rd harEJonic Methyl alcohol Ethyl alcohol 8 Phenol 310 Benzyl Alcohol 2201 a Buswell, Deitz and Rodebu.sh , J. Chem. Phys., 5_, 501 (1937). bBadger and :Bauer, J. Cher::. Phys., S,, 839 (1937). cErrera, Gaspart and Sack, J. Chem. Piws., ~. d. 63 (1940). Errera and Sack, Trans. Faraday Soc., ~. 728 (1938). eFox and. Martin, Proc. Roy. Soc. (London), AJ.62, 419 (1937). 1 Fox a.VJ.cl I/art in, Trans. Fe.rada;y Soc., J..§, 897 (1940). in transition probabilitJ a;nong the group of lower levels, then the band intensity distribution will be entirely determined oy the population distribution in the lower group. To discuss the transitions, it is necessary to know how the two sets of levels interact, i.e., how a level corresponding to a certain set of quantu.m members of the low frequency vibrations changes as we change the 0-H vibrational q_uanhun number. From the fact that the bends do get wider as we go to successively higher harmonics, we can say that the low frequency levels must spread apart in the upper 0-H vibrational stat es, the more so the higher the state. This is illustrated by the transitions shown in figure 8. Be- cause of the spreading apart of the levels in the third 0-H vibrational level, the absorption a.rising from molecules in the energy regions indicated at the bottom of the transition arrows occurs at different frequencies; hence the association band is broad, since it inclu.des contributions from the whole lower group of levels. The main part of the intensity will undoubtedly come from transitions in which the low frequency vibration q_ua..11tum numbers do not change; contributions to the intensity from transitions in which these change also will not affect the main argument, but will result in som~ additional broadening. This spreading apart of the levels must increase with harmonic, as remarked above, to explain t},e increase in width with harmonic. In order to rneke rouf;h nu..rnerical calcc:.l2,tions, it will lJe necessary 1 0-: vl1 )r<'· • oral levtls :o ~scoci2ted ole~ ·ler ·s 0-R vibrational J "" ...·~•er • e levels , di ssoc iat e:J ---------~;..;..;l~s;;....___-..,~~ - ~- ~ - - molec1les 0 ,2,Uo 3 - - - - - - - - - - - - - - - - - - T 10,'fS0 l T A~ -- 7,7,0 - - - - - - - - - - - - - - - -- --- _..,.._,.__+-_ l T 4:4<>0 '( ---- - --------------- 5,730 _.,__+--1--- , 3;5o -+---1-----+-~ T -- '1/00 - - - - - -- - - - - - - - - - - - - ~ - 0 0 c- • 1 .'V 1 ct fopram for as sociat • c: of methyl alcohol. ----------------- to int1·oduce furt11er sim.91 ifying assur:rot ions. We assune that the spreading apart of the levels is linear, and is governed by the difference in levels represented by the D 11 of figure 3; i.e. , a given level in the lower group ,rhose energy at)OVe the ground is a certain fr act ion of the dissociation ener&1' of the lower group, D0 , will occur in ru1 u.pper group witl:. an energy above the upper gr01.tp which is the same fr act ion of the D • n 11 11 grou.nd. 11 of the dissociat ion energy 11 , This ass1;.mption leads to a lfr.ea1· rel a tion bet·ween frequ.~ncy shift from boncled. to non-bonded. molecules and energy required to dissociate the bonded molec1,;les, and we know that this re lat ion is only very roughly true. This assumption mentioned in the ab ove paragraph was used in constructing figure 3 from the data on methyl alcohol 27 , since experimentally t h e only fre c~uenc~' t}-"at we can measure about the polymers is that of. tne absorption maxi rrvm. Assuming that the maxir.aur.1 population in the lowe1· group occ1.1rs at 5kT = 1020cm. -1 above the grou..."ld (as would 'oe true if all six degrees of freed.om 1 (27) The frequencies used are (cm.- ): fundamental polymer 3 ,330a r.1onomer 3, 630a - 2nd harmonic 3rd harmoniG_ 9,930d 10 ,l\l.~Od 8:Busvrell, Deitz a."rlcl Rodehush, J. Che r.-:. Pbys., 3., 501 (1937). bCalc·o.lat ed fror:i quad.rat ic term value expression cWulf a.YJ.cl Lidclel, J. Ar::. Cher:1. Soc., 5]_, 1Li-6L( (193 5, ). ~e.dger &"ld :Sauer, ~T. Chem. Ph;ys., _2, 839 (1937). in the bond. were of low eno1_,1t;r, frequency to be classically excited.), a.rid taking the dissociation energy in the ground state as 6000 cal. 2100 cm. -1 = , we can construct the polymer levels co1: b ining with the 0 level of rna.xinmm populat ton in the lower group from the knovrn polymer frequencies. The 11 These are the levels 4400, T(lO, and 10,950 cm. -l gro1md 11 of each upper group is then calculated from the relative positions in the lowest gro1-7.p. Wow if we assune, as mentioned before, that molecu.les in levels of energy E in the lovrnst group make transitions principally to levels in the upper grou_ns of the same low frequency vibration quantum members, then the principal absorption for these molecu.les will occur at a frequency, (5) 1) = 3150 + D1-.P-.0. E in the fundamental, Do V = 6290 + Dz-D.o. E in the second harmonic, etc. Do Further- more, molecv.les in the lower group vrhich are separated by an energy AE give rise to absorption frequencies to an upper g:coup whicr are separated oy a frequency difference, AE Since ,1e assume intensity is governed only by the lower group popuDn -Do lat ion, this means tli..at the quantity, , which we obtain from f1·equ.ency data only, should be a meast.u-e of the relative widths of Ve ha:cmonics. 'I'he calculated relative widths tu.rn ou.t to be, fundamental 4:"~0 2nd harmonic 820 3rd harmonic 2: 90 Cor:ip aring tr1is wit}1 Table VI it is seen to give an increase of on ly two fro m the t h ird haxmonic to the f1.:mda.rnental, against the exuerimental fact or of more than t h ree. T'11e fact t hat a large change is predict eel is sat i si'ying ; c ons ider in; · th e assurrmt ions made, not rrmch better agre erne::1t coul d b e e::-..'ye cted. ':'he t h eor;,r a lso acco-unts <l_"L,ali'ca tively for the relation between fre qu.en c/ shif t of one t y~)e of molec1.:i. l e bonrlinc: t o var ious ot her t~0es, and widt h of b and . In ter ms of figure g, t h is mea.YJ.s tlmt t h e intervals betwe e:1 levels of the dissoci2.ted molecul es rema i n constimt fro:-:1 one bo,1d a ccepto r to ru:.other , but t ::.ose of t he associated molec-c,les move closer toget her t he stronger t he bond. f ormed, cau.sing tne quantities Dn to becoi;1e lar 6 e , a1;.d. co,:.s equentl;,,· produce a v1id e bru1d. A,-:ot :~ er effect vr:1ich t he t h eor~, ac counts for , roughl;\' is t hat of t b.e i ncreas e of freq_uency of rnaximrn:: ab s orption of t he association . According to t he Jli ct -o.re given above, ..., -."llS is due to t he chm1;. ·e in T) O rnlati on d ist ributio::1 i n t he lov-:est group of levels. The frequenc;_r of maxi rrmt:1 aosorpt ion in th e t h ird b.armonic is ,_:c;iven, 2.c cor dtng t o (5 ), by , 50 TTe have teJ::en E to be 5kT, so th:1,t D.a:x:. , dv dT D.,,-D - -.,,,--=.c. - D0 -.1. ""' rn '.)K.i. -- 1 . .::;_,, cm. clegree TDis ca:, be coc1_Pared with the experimental val c,e of 1 cm. -1 per degree, o"btained fros i")hotogra:"Jhs taken in this laboratorJ over a tem,")erature rm.12:e of -30° to +7io C. .Again, considerin[, the ass1-.1.8D- tions, the agreer:ient seer:1s to oe satisfactory . .fu1 atterrr.:-it has been maa./ 6 to explain the oreadtn of association bands as due s i0[Jly to a S1-.1:_")81'J)OSi t ion of co,:10 inat ion om1ds from lov1-lyfr.g states of low freo.uenc~' viorations to an ,-1.p:per gro-..:.:p of s-c1c?l states. The brea,dth is presur:.nbl;y due to the combination fre- quencies only; this however, does not explain the change in v.ridth with harmonic, or the temperature shift. The necessary thing is the interaction between the 0-:-i: vibrational levels and the low freq_"Lienc;/ levels, so tlL,.t the !iL'fei?e'B:i; spacings in the lower and UJrper ~;rou.ps of levels is different an:1 thus accounts for the 'breadth. In conclusion, it r,1ir~1t be worthwhile to suramarize the nresent Etat"l:s of o-o.r knowled e re[;;?.rding h;/drogen bonds. For t:--ie cor.1- po-i.mds that have 'been stu.died ,:1ost exhaustively, namely the hydrcxy-1- (26) Davies and Sutherland, .T. Chem. Phys., _§_, 755 (1933). 51 c ontai n ing molecu les, a r ather g ood qualit at ive idea can be h ad of the process of hydror; en bond fo:cmation anc!. the spectrosc op ic changes associated wit }, it. noticeably lacking . Preci se qua.ntitative dat a are , however, K:no\'lleclr; e about bonds fo1· med by ot l1er t han hydrox-y l gr oups is s till in a r a th er emp irical stage; in t he ca.s e of bondin{; by &"nino grour)s, whi ch is of pr i me i mportanc e , t h is is due to the increased complexity h :h·oduced 'by the presence of two lT- E bonds. PART III. T:IE RAl.~AH SPEC'l1RA OF CC1 2 F-CC1F 2 .AHD CClF2-CClF2. 52 THE RAl.'1.AN SPECTRA OF CC1 2 F - CClF2 .AND CClF2 - CC1F 2 . In connect i on with the quest ion of t h e configu.rat ion of ethane-like molecules, some information might be expected to come from the Rame.n spectra of halo6 en su:bstituted ethanes. of these spectra have been published 28 . Several Flu.orine derivatives have not "been studied so extensively, because of the~r unavailability rath er 1 a t e 1y. "\..1.n t i 1 have appeared. Th e spec t ra o f C.-:.3 · T - 30 CF 3 29 and cc1 ""...F - CCI-"' 2"' T:iis series h a s nov; "been further extended by the a"l.1thor and V.r. R. A. Spurr to include CC1 2F - CC1F 2 and CC1F 2 CC1F 2 • A. Th e cor:1j)OU11ds were obtained throl,!Gll the courtesy of Dr. F. :Benn ine'; of the DuPont de i:Jemours Company. without a.TlJ' f urtr1e1· rrnrificat i on. 3. 55° respectively. T'.ney were usea. The boiling points are 47. 7° and For the hi g!1-"boiling compou.nd, the liquid. was poured into the Raman tube, in which it wa s kept fro m evap orating simply by a cork. R 2...r:12-'1 The low-ooilin6 one was dj_stillecl into the trbe, and the tube sealed off. The spectrometer used had a dispersion of 7 mm. between the 0 4oL~6 and 4353 A. mercu:cy 1 ines. water cooled. The mercury arc was of glass, and Eastm::m D-C ort h o plat es were used. Exposure times (c~) See the bibliography given by 3:ibben, 11 The Rmncm Effect and its Chumica l ~):)licat ions, 11 Am. Cner:: . Soc. Monograph Series, Reinhold (193 9 ). (Z9 ) Yost and Hatcher, J. Chem. Phys., 2,, 992 (1937). r30) Gloclder and Sage, J. Chert . Fnys., ~. 291 (1 91~0). 53 we:ie of the orcler of 13 to 24 hm,x s . '.'.::C1 e s:9ectra were calforated from an iron arc reference spectrum, employing a q_uadrat ic dispersion eq_1,1ation and a corr-ection chart. Wave lengths are acc1.i.rate to better tha.'1 on ,c. kgstrom. For the CC1 2 F - CC1F 2 , no filters were used; this was t h e fi1·st compound nm and showed no decomposition on exposure. was measured from all three mercury E "tes, Scattering 4046, 4077, and 4358 1. So r:1e suosequent compounds, however, were decomposed, so on the CC1F 2 - CC1F 2 a saturatecl sodiuJn nitrite sohtion was used as filte1·. C This cut out nearly all of the 4046 ancl 4077 A. mercury lines, so that the only scattering line used was tl'ie 4358. The plates showed very little backgrouna_. The observed frequencies are given in Table VII. We have available severa l other fluorine and mixed chlorinefluorine derivatives of etl1a."le, which will be clo ,,e in t h e future. So far no a."l a lysis has been m2_de of the spectra obtaj_ned. ~l.-1- Table VII. Ra.~a.n frequencies of CC1 2 F - CC1F 2 and CC1F 2 CC.!?!__- CCl~2 CQIFz ..!_ (cm. -l) int ensit_;y_ 171 203 243 290 313 352 394 443 461 503 vwb vvw w w w vw 532 654 902 1043 1102 w s w vvw 1112 1211 w - CClF2 V'v'l m m w wb vw excit int; l i ~ 9,I I C a' I C a, a', b, C, c' a, a', c, c' a, al I b, C a, C a, b, C a, b a, b a, b, C a, b, a, b, a, b, a, b, a, C C C C C a, b a, C (all excited by 435s) 170 255 314 327 359 w ill ill L1 VVYv 403 ~-43 ..,I=; oo 5l.~7 679 vvw 702 105s 1117 1170 1250 s w w m m Abbreviations: anti anti s m w s a.11.t i b (under intensity)= broad 0 a scattered from 404~ ¾• b scattered from 407 7 A. c scattered from 435g 1. prime - anti-Stokes line measured. anti- anti-Stokes line measured. - CC1F 2 • 55 SUI.il:IARY OF T}IESIS In Part I, the absorption of formaldehyd e and difluoro-methane in the photograph ic infrar-red region is described and. d.iscu,ssed, and the t h ird har □ onic C-H band of formic acid under high dispersion is described and partially analyzed , yielding the small moment of inertia and the band orig in. In Part II, a stud.y of tl'- e associat i on of et n;yl alcohol in carbon tetrachloride solution b;;7 the freezfo e-; point met h od is 1,resented. T'.11e results are corr:pared with :pu-b lished s1Ject roscopic work, and co1:.clusions dra,vD as to the interpretatj_on of the spectra. Eq_·uili'brium constants of monomer-d.imer association are presented and cor:ruared. Widths of association b ands and the t emperat1.J.re shift of t r ese bands are described and. interpreted. Part III g ives the Raman spectra of CC1 2 F-CC1F 2 and CC1F 2 CC1F 2 • .A.CIC OWLEDG EEEl:T S I wish to expres s rrv v er y g reat i ndebt ednes s to Prof e s sor Richar d. l.:. :Ba dg er for hi s h elp f·d i nt er est. ad vice and as s i st an c e , and con stant I am al s o gr a t efr.l t o Doctors Lloy d Zumwalt and Eug ene Eyster for help ful discuss i on , to Doctor Chia- Si Lu for as s i stanc e i n dr awing t h e f i g1.J.res , and t o J,:i s t er Rob ert A. Spurr for h is col1a·b or ation on t he Raman work . 57 1. Dry r;elatin saturated wit J, heavJ wa ter will excnang e its ~ h ydro,::; en for deuterium in a peri od. of ~-3 hours 2.t ro ,::;r.1 t er:r'_) erature. '.i:::is leads t c dou'ot about tl1e i :1te1--preta.tion o:!' inf r r1,-red. b ands of ge:'..2.t in +D2 0 given b:,T Ellis and. Bat h , J. Che~:1. Pl-i;-o s., _§., 727 (193s ). 2. 3:1 solutions of KCl, IGC3 a.---iJ. KC:. ~s i:1 water d o not have 8.l1Y effect r.iea.s1.u-able b:r plrnt op'a~,n ic methods on t he frequency or intensity 0 of t h e water 02.nd at 9700 A. This behavior is different from that reported f or so;,1e oth er bnnds. 3. A :p osdbl e way of r.1::'i:.: :i.nf; correlations between force constants a!1d i::.1ternuclear distances for diatomic nolecules □ ", ght oe to ass'l1l-:-ie a simple :::,otentia.l f unction with onl;,r a few con sta.nts, to calculate t h ese con st ar!t s for a large number o: kno,:m. molecules, n.nd to look for reg\.J.larit ies in t :::.e Wff; / the co::-.stants change wi t }1 the cm: sti t -.:,ent ato,;1s. Su ch con stants would h a ve more ph y sical sig:1 ificance t '!1an t h e cm-i stru.:ts of el:lpir i cal rela tions such as 13adger 1 s rule, a ~,d mi &:ht lend themselves more readily to use with polyatomic molecules. 4. 'Z.1.e t l'..e or/ of s;,rmr'.let 1·~, groups can be ·used to obtain r a ther s i c-rply so:!!e of the i nf ra-reel rotationa l select i on rules fol' r.1olecular s::,ectrr. . . For examp l e , i t i nd ica tes t he abse:::ice o: a •~ branch i n pcrallel vibrati ons of li:lear □o lec-u.les. S• Laue photogral)hs of phenol cr?s t als sh ovr tha t t he;y are mm~ o::lin i.c , and not orth orl10!'J bi c, as stat ed. o:: Groth , 11 Kr:,rstallogra::phie, 11 ''/ . El1f; elmann , Lei:::izii::; (1917) , Vol. 4, p. 72. Chemisch e In view of tne fact that no monohycl.rox;,· alcol:ols have oeen d.one, this crystal should have its cormlete str,J.ct"lu·e worked out. The results will have an ir~ortant oearing on the theories of hydrogen oond.i:1.g , on the e):planation of d i e lectric :yroi-i erties of alcohols, a..-ric. on entropy calc·ulo..t ions on a lcoh ols fror.1 calorL:ietric data. 6. The vapor aosori)t ion spectrum of trimethylene glycol (C~I 2 0!:-C~I 2 -CH 2 0H) in the photographic infra-red shows that it does not form a.11 :ima-rciolecular hydrogen bond, whereas et l,;ylen e p;lycol 7. A great deal of evidence has a ccur:rulat ed. showing th a t molecules with permanent di:poles, or even molecules with no l)ermanent di)ole but with high polarizability, interact strongly and form corrrplexes with aromatic rings. Therefore the contim' ed use of "ben z en e as a solvent in associat i on studies, spectroscop ic work, kinetics studies, etc., seer.is ill considered, si::.1ce it makes the problem of theo1·etical interpretation more difficult. tetrachloride, or oetter a . S. Carbon saturated hydrocarbon, is preferaole. Sor:ie confusion has existed in the literature regarding the definition of the energy of a 1-i;:,· drogen bond (e.g., s ee Fox and l,artin, Trans, Faradey Soc., .l§, :)03 (1940).). T'nis is unwarra.'1ted., since tl1e e:1err:r is no.tur:c.lly defined as that req'\.!.irecl to pull two bonded rnolec'\.1les apart from their position of rnininrur:: energ to infinity: t h e relatio-_ri of this en ergy to ot l,er ener,c;;,- q1;antiti r.; s of the s~rstem 59 is clearl~r sliovm if an energ'l su.rface is dr2.wn, using as coordinates the distance of the hydrogen from the atom to which it is chemically bond.e el, and its distance from the atom to which it is hydrogen bonded. 9. A simple theory of hydrogen "bond format ion can "be "based on the assu.rrn_)tion that the attractive potential between a b;:_rd.rogen at or:1 on one molecule and a polarizable group on another molecule l..L follows an R-' law (which is the law for a free charg;e and a :polarizable body). The dependence of the frequenc,/ shift ~11 on the bond energy E then comes out, .3. AV= kE 2 fo1· bonds to atoms of the SEtme pol2rizaoility. This is very closely the shape of the empirical curve given by Badger, J. Chern. Phys., 10. In the scheme of correlation of statistical and thermodynamic quantities :proposed by Tol:nan, 11 The Princi:ples of Statistical I.Iechanics, 11 Oxford. d.938), ch. XIV, the three correlations made are, statistical th er2nodynar:1ic E avg. E A w}1ere E , avg. t , and 0 are the statistical qua,'1.tities of a Gibbs canonical ensemble; E, A, ru1d T are the the1·modynamic internal energr, v,orlc f"\_,mction and ter~erature respectively; and k is the Boltzmann constant. It is sufficient, however, onl;\r to make the first two. 60 It then follows t hat, e = CT, where C is a flJ.nction of vo l U'Tle sat is fy i nt:: a ce1·t ain differential e quation . pa:r t ic·c·l :=tr soluti on of t h is equati on . C = k is a