Sept., 1959
MOLECULAR INTERACTIONS ON N.M.R. REFERENCE COMPOUNDS
1379
THE EFFECT OF MOLECULAR INTERACTIONS ON N.M.R. REFERENCE COMPOUNDS BY EDWIN D. BECKER National Institutes of Health, Bethesda, Maryland Received January 8,1069
A study has been made of the effect of molecular interactions on the proton magnetic resonance (p.m.r.) frequencies of cyclohexane and tetramethylsilane, two compounds that are frequently used as internal references for p.m.r. investigations. I n most of the cases studied the resonance frequencies of these compounds shifted 1-4 C.P.S. (at 40 mc.p.s.) when the com&osition of solutions containing the compounds was varied over a wide concentration range. The presence of hydrogen onding molecules did not cause appreciably larger interaction effects than were found for hydrocarbon-CCL solutions, but benzene at high concentration caused interaction shifts of 15-17 c.p.5.
Nuclear magnetic resonance, especially proton resonance (p.m.r.), is being used increasingly to distinguish between similar structural features in complex molecules’ and to study weak molecular interactions, particularly hydrogen bonding.2 Since these phenomena sometimes result in p.m.r. frequency shifts of only a few parts in lo8, the frequency of the proton of interest must be measured accurately with respect to a proton in a reference molecule that is either dissolved in the same solution as the molecule of interest (an “internal reference”) or placed in a separate capillary or coaxial tube (an “external reference”). The relative merits of the two types of reference have been discussed extensively by Bothner-By and Glick3and by Zimmerman and Fostere4 The physical separation of an external reference is desirable in preventing interaction between the sample and reference substances, but its use requires that a correction be made for the effect of the bulk magnetic susceptibility of the sample. Bothner-By and Glick3 made the susceptibility correction by replacing the theoretical “shape factor” for a solution in a cylinder, 27r/3, by an empirical factor averaging about 25y0 larger, but varying from system to system. Stephen5 has shown theoretically that the presence of an electrically or magnetically anisotropic molecule in a solution can cause molecular interactions that will affect the n.m.r. frequencies of other molecules, even though they are isotropic. He attributes the apparent departures in shape factor reported by Bothner-By and Glicka to the effect of such interactions. Recently tetramethylsilane has been proposed as an internal reference and has been shown to offer several distinct advantages, including magnetic and electric isotropy,6 which might be expected to reduce but not necessarily eliminate interactions that would alter its p.m.r. frequency. The present work is designed to evaluate the effects of molecular (1) See, for example, (a) R. U.Lemieux, R. K. Kullnig, H. J. Bernstein and W. G. Schneider, J . A m . Chenz. SGC.,79, 1005 (1957); (b) J. N. Shoolery and M. T . Rogers, ibid., 80, 5121 (1958). (2) See, for example, (a) C. &.I.Huggins, C . C. Pimento1 and J. N. Slioolery, THISJOURNAL, 60, 1311 (1956); (b) A. D. Cohen and C. Itrid, J . Chem. Phys.. 26, 790 (1956); (c) L. W. Reeves and W. G. flohneider, Canadian J . Chem.. 86, 251 (1957); (d) E. D.Becker, U. Liddel and J. N . Shoolery, J . Mol. Spectroscopy, 2, 1 (1958): (e) C. M. Huggins and D. R. Carpenter, THIBJOURNAL, 63, 238 (1959). (3) A. A. Bothner-By and R. E. Glick. J . Chem. Phys., 26, 1647 (1957). (4) J. R. Zimmerman and M. R. Foster, THISJOURNAL,61, 282 (1957). (5) h4. J. Stephen, MoEecular Physics. 1, 223 (1958). ( 0 ) C . , V . D.Tiers. THISJOURNAL, 62, 1151 (1058).
interactions on two p.m.r. reference compounds, tetramethylsilane and cyclohexane. Particular attention is given to systems containing hydrogen bonding molecules. The formation of a hydrogen bond generally causes a pronounced change in the p.m.r. frequency of the bonded proton and might also influence the frequency of an internal reference compound.
Experimental The experiments were conducted with a Varian V-4300-2 high resolution n.m.r. spectrometer o erating at 40 mc./sec., and a Varian 12” magnet with fielt trimmer and flux stabilizer. Frequency differences were measured by the sideband superposition technique.? Each reported value is the average of three independent measurements and is accurate to about A0.4 C.P.S. All studies were made with solutions in precision concentric tubes,‘ with either benzene or dioxane in the annulus as an external reference. Measurements were made a t room temperature, 28 f 2‘. Chemicals were high purity reagent grades which were further purified by appropriate standard procedures.88,b Tetramethylsilane (Dow-Corning) was supplied by Dr . C. M . Huggins of the General Electric Company and was vacuum distilled by him. The compound showed no spurious p.m.r. lines. The solutions were prepared by weighing all components except the tetramethylsilsne. The total volume of the former components was made u p to 10 ml. in a volumetric flask and 0.5 ml. of tetramethylsilane was added to the solution juFit before u6e.B This procedure minimized evaporation of the volatile tetramethylsilane and ensured that all solutions contained identical volume fractions ( N 0.05) of tetramethylsilane. The susceptibility correction for tetramethylsilane was thereby held constant for all experiments and did not affect the determination of frequency shifts. No attempt was made to degas the samples. The presence of atmospheric oxygen in the solutions is likely to cause only a Rmall alteration of the p.m.r. frequency ( w 0.5 c.p.s.),l0 which will be approximately the same for all thc solutions studied herein.
Results and Discussion Each set of experiments consisted of the measurement of p.m.r. frequencies as a function of the mole fraction of one of the components in a binary, ternary or quaternary solution. The systems studied are listed in the second column of Table I. Several of these particular combinations of substances were chosen so that the volume magnetic susceptibility of the solutions remained constant as the relative concentrations of two of the components were varied. The magnetic susceptibility (7) J. T. Arnold and M. E. Packard. J . Chem. Phys., 19, 1608 (1951). (8) (a) A. Weissberger. et al., “Organic Solvents,” Interscience Publ., New York. N . Y.,1955. (b) L. F. Fieser, “Experiments in Organic Chemistry.” D. C. Heath Co., New York, N. Y.,1941. (9) Tetramethylsilane was stored below room temperature and its volume measured at approximately 15’. (10) D.F. Evans, Chemistry and Indugfry. 520 (1958).
EDWIND. BECKER
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Si ICH,), ,E---/-
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Vol. 63
is not dependent on the extent of hydrogen bonding. The specific susceptibility of such a solution can therefore be calculated in the usual way, as the weighted arithmetic mean of the specific susceptibilities of the components. The departures from additivity in density found by Venkateswarlu and Sriraman12 are not large enough to be significant in the present work. TABLE I1 VOLUMEMAQNETICSUSCEPTIBILITIES Compound
Used in this work
R X 106 (0.g.s. units) Other values
Benzene 0.617" 0.617,b0 . 617,t 0. 616d I I I I I I Cyclohexane .611d . 631e 0 .2 4 .6 .a 1.0 1-Butanol . 611d VOLUME FRACTION n-DECANE. . 613d ,614" Fig. 1.-P.m.r. frequencies of tetramethylsilane and n- %-Decane .596d decane, measured with respect to benzene as an external 2,2,4-Trimethylpentane reference: - - - -, observed data; , corrected for Cyclohexanol . 694d bulk magnetic susceptibility changes. Carbon tetrachloride .692* .G91d Chloroform .740* . 731e data used in this work are given in Table 11. .530d 529' Since there are wide discrepancies among many Methanol a V. C. G. Trew, Trans. Faraday SOC., 49, 604 (1953). C. M. French and V. C. G. Trew, ibid., 41, 439 (1945). TABLE I C. M. French, ibid., 43, 356 (1947). S. Broersma, J . FREQUENCY SHIFTS OF P.M.R. REFERENCECOMPOUNDSChem. Phys., 17, 873 (1949). e Value used in references 2c. Frequency shiftb f D. B. Woodbridge, Phys. Rev., 48,672 (1935).
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Expt.
Compounds'
Obsd.
C0r.C
1 1-Butanol .... ... 2 Cyclohexane .... ... 3 Tetramethylsilane -1.3 -1.3 1 Cyclohexanol .... B ... 2 Carbon tetrachloride .... ... 3 Tetramethylsilane 1.8 1.8 C 1 Methanol .... ... 2 Carbon tetrachloride .... ... 3 Cyclohexane 16.8 3.0 4 Tetramethylsilane 17.4 3.6 D 1 2,2,4-Trimethylpentane 11.3 3.8 2 Carbon tetrachloride .... ... 3 Tetramethylsilane 11.5 3.7 E 8.2 1 n-Decane 1.5 2 Carbon tetrachloride .... ... 3 Tetramethylsilane 2.5 9.2 18.3 17.7 F' 1 Benzene 2 Cyclohexane 16.9 16.4 15.3 14.7 3 Tetramethylsilane -9.1 G 1 Chloroform -19.9 2 Cyclohexane -1.9 -12.2 0. Solutions contained components 1 and 2 a t volume fractions vl, v2 of 0 to 0.95, and components 3 and 4 a t vg,u p = 0.05. Shift' in resonance frequency (c.P.R.)as VI increases from 0 to 1.0. A positive number indicates a shift to higher field (greater number of c.p.5. from benzene) with increasing v,. c Frequency shift corrected for change in magnetic susceptibility of solution. Correction made using theoretical shape factor 2?r/3. For details of calculation see references 2c, 3 and 4.
A
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published susceptibility data, we attempted wherever possible to select compounds for which two or more literature values are in agreement." Venkateswarlu and Sriraman12 have shown for a number of hydrogen bonding systems that the magnetic susceptibility per gram (specific susceptibility) (11) An error in susceptibility of 0.012 X 1 0 - 8 c.g.8. units is equival e n t t o an n.m.r. frequency change of 1.0 c.p.8 (12) K. Venkateswarlu and S. Sriraman, Bull. Chem. SOC.Japan, 81, 211 (1958).
Plots of typical data are given in Fig. 1. The frequencies are expressed relative to benzene as an external reference. A summary of the results is presented in Table I. I n each experiment the proportions of components 1 and 2 were varied over wide ranges, while components 3 and 4 were present in small and constant volume fractions. The figures in the table give the total frequency shift of the line due to the indicated component as the mole fraction N 1 of component 1 is varied from 0 to 1. (It was necessary to make a small extrapolation to obtain results a t N 1 = 0 and 1.0.) A positive number indicates a shift toward higher field (greater number of C.P.S. from benzene) with increasing N1. Experiments A, B and C demonstrate the behavior of the tetramethylsilane resonance in solutions containing varying proportions of a hydrogen bonding molecule and a relatively inert, nonpolar molecule. The shifts of 1-3 C.P.S.probably arise from variations in the molecular interactions between tetramethylsilane and its changing environment. The shift in C, which includes a substantial susceptibility correction, is not noticeably different from A and B, where no correction was needed. In experiments D and E (with only non-polar. molecules) the frequency shifts of both tetramethylsilane and the hydrocarbon are not significantly different from those in A-C, where alcohols were present. All three molecules present in D are isotropic or nearly isotropic and would be expected theoretically6 to undergo little or no magnetic interaction. The observed 4 C.P.S.shift might be due to perturbations not included in Stephen's treatment or possibly to errors in susceptibility measurement or isomeric composition of the hydrocarbon. The large shifts observed in F, where practically no susceptibility correction is needed, must be
Sept., 1959
PHENOMENOLOGICAL THEORY OF ION SOLVATION
attributed to the effect of molecular interactions, probably arising from the large magnetic anisotropy of b e r ~ z e n e . ~ -It l ~ is noteworthy that the teframethylsilane and cyclohexane frequencies shift nearly as much as that of benzene. Although Tiers6 has commented on the discrepancies to be found in aromatic systems, his figures do not indicate the extent of the interaction effect or the degree to which tetramethylsilane must be regarded as suspect when used as an internal reference in solutions containing aromaCic components in high concentration. In G our experimental result on the frequency shift of chloroform, which is probably self-associated through weak hydrogen bonds, is in excellent agreement with that of Reeves and Schneider.z The corrected shift of 9 C.P.S.differs from the reported 11 c.P.s.~ because of a different choice of susceptibility data. The 2 C.P.S. shift of the cyclohexane frequency is in accord with the results of A-E. The origin of the small frequency shifts (1-4 c.P.s.) observed in most of these experiments is far from clear. Although the treatment by Stephen6 suggests some of the types of interaction that can cause such effects, the theory is not sufficiently refined to permit a meaningful calculation of the magnitude of these small shifts. When the data of Bothner-By and Glick3,l3 are analyzed in terms of frequency shifts not accounted for by the classical susceptibility correction, rather than in terms of an empirical shape (13) A. A. Bothner-By and R. E. Click, J . Ckem. P h y s . . 26, 1051 (1957).
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factor, it is seen that the only shifts significantly larger than those found in the present work are for aromatic systems and for molecules containing highly polarizable iodine atoms (CHIS and CH&. In both instances interactions are predicted to be large and can be accounted for in order of magnit ~ d e . In ~ the present study there is apparently no dependence of interaction shift on susceptibility change. Thus there seems to be little or no justification for using an arbitrarily averaged empirical factor in externally referenced systems. With regard to internal references, the present study shows that the strong perturbations involved in hydrogen bonding do not exert a measurable influence on the resonance frequency of an “inert” reference compound such as cyclohexane or tetramethylsilane. This behavior is in marked cont,rast to the frequency shift of the hydrogen bonded proton, which frequently amounts to 200 C.P.S. or more (at 40 mc.p.s.) for a moderately strong hydrogen bonds2 In the study of such strong bonds a 2-3 C.P.S. shift of the reference frequency is likely to be negligible; but with weak hydrogen bonds, where the total shift may be less than 10 c.p.s.,14it is apparent that measurements made with an internal reference can be seriously in error. It is clear, too, from our results that an internal reference should be avoided whenever possible in a system containing aromatics a t high concentration. Acknowledgment.-We would like to thank Mr. Robert B. Bradley for collaborating in this investigaticin. (14) C/. experiment G and references 2c,e.
PHENOMENOLOGICAL THEORY OF ION SOLVATION. EFFECTIVE RADII OF HYDRATED IONS BY E. R. NIGHTINGALE, JR. Depa,,linent of Chemistry, University of Nebraska, Lincoln 8, Nebruska Received J a n u a r y 10, 1060
The empirical correction to Stokes’ law proposed by Robinson and Stokes has beeii extended for small ioiis to provide a concordant !et of radii for the hydrated ions. Ions with a crystal ionic radius of about 2 A. exhibit a minimum hydrated radius of 3.3 A. corresponding to the maximum in the equivalent conductance. The internal consistency of the set of radii is demonstrated by correlation with the temperature coefficient of equivalent conductance, the viscosity B-coefficient and the partial molar ionic entropy. Except for the small monatomic ions with the minimum hydrated radius, the hydrated ionic radius a t 25” is demonstrated to be a linear function of the viscosity B-coefficient. The significance of this relation is discussed in terms of the structural modification rendered by the ions to water.
Introduction The interpretation of ionic processes in solution, particularly in water, has been the subject of many discussions. The recent monographs by Harned and Owen,l and Robinson and Stokes2 summarize well the present status of the field. One of the most difficult problems encountered in studying electrolyte solutions is that concerning the nature of the ion-solvent interaction, and the interpretation of thermodynamic and transport processes in terms of appropriate parameters such as the effec(1) H. 5. Harned and B. B. Owen, ”Physical Chemiatry of Electrolyte Solutions,” Reinbold Publ. Gorp., 3rd ed., New York, N . Y., 1957. (2) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,’ Academic Picas. Inc.. New York, N. Y.. 195.5.
tive radii of solvated ions. Much of the difficulty arises because the applicability of a single model to represent the various phemonena has never been demonstrated and, in fact, is not to be expected, for solvation as measured by irreversible transport phenomena is quite different from that inferred from thermodynamic measurements. Thermodynamic interpretations require a priori :L suitable theory of ionic interaction and solvation. Hence it is probable that transport processes can provide the most appropriate information concerning the ion-solvent interaction since theee processes supply information concerning the nature of the kinetic entities. The present discussion concerns the derivation of LL consist8entset of radii
