J, Phys. Chem. 1983, 87. 1385-1390
C12E8 system with 1%of the surfactant replaced by the ionic surfactant sodium dodecyl sulfate.46 This replacement increases the cloud point substantially, but the observed self-diffusion coefficients remained the same, within the accuracy of the method for a given (absolute) temperature. Aggregate Structure Conclusion. NMR self-diffusion and proton relaxation studies give insight into the structure of micellar solutions of nonionic poly(ethy1ene oxide) surfactants. Compared to ionic surfactant systems, the situation is very complex and the micelles are highly variable with temperature, concentration, polar head group size, etc. At low temperatures, there is a growth into large micelles with increasing concentration in the case of C12E5, while Cl2E8 micelles appear to remain small and roughly spherical up to the highest concentrations. Changes in micelle size and shape on increasing the temperature toward the cloud point are more difficult to establish with certainty. However, there is good evidence for a micellar growth with increasing temperature for C&6; simultaneously, there is an increased flexibility in the micellar surface. The micelles are much less affected by a temperature increase and seem to be rather small even at high temperatures. The self-diffusion data are, however, not inconsistent with a moderate growth in aggregate size with increasing temperature. For nonionic surfactants with (45) Nilsson, P.G.;Lindman, B., to be submitted for publication. (46) Note Added in Proof. Much more complete information on phase equilibria in these nonionic surfactant systems is provided by Mitchell et al. (Mitchell,D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J . Chem. SOC., Faraday Trans. I, in press).
1385
a large ratio of ethylene oxide chain length to hydrocarbon chain length, the micelles can be expected to be small even close to the cloud point. The ethylene oxide chains are, over wide concentrtion and temperature ranges, characterized by low-order parameters and an extensive coiling. By combination of the different observations, a coherent picture starts to emerge. From the nature of the phase equilibria, from the NMR diffusion and relaxation data, and from general theoretical principles, the following factors determine to a large extent the preferred aggregate structure: (a) The longer the ethylene oxide chain and the shorter the alkyl chain, the more preferred is the spherical micelle due to the packing constraints. (b) The higher the temperature, the less farovable is the ethylene oxide-water interaction and the more favorable is the ethylene oxideethylene oxide interaction. This results in a decreased repulsion between the ethylene oxide chains in the micelle at higher temperatures. This gives a decreased area per polar group at the micellar surface which will favor large aggregates. (c) For a given temperature, an increase in concentration leads to a preference for larger aggregates due to an entropy effect35and due to dehydration of the ethylene oxide chains. Acknowledgment. We thank Dr. Bengt Jonsson and Dr. Norman Mazer for helpful discussions. Dr. John Lang gave many useful comments on the manuscript. Grants have been obtained from Stiftelsen Bengt Lundquists Minne, the Swedish Natural Sciences Research Council, and the Swedish Board for Technical Development. Registry No. C12Es,3055-95-6; CIZEB, 3055-98-9.
Dielectric Properties and Molecular Structure of Amide Solutions. 1. N-Methylacetamide in Carbon Tetrachloride Krzysztof PrMat, Jan Jadiyn, and Stefania Balanicka Institute of Molecular Physics, Polish Academy of Sclences, Smoluchowskiego 17/19, 60-179 Poznafi, Poland (Received April 29, 1982; In Final Form: October 27, 1982)
The results of dielectric polarization and infrared absorption measurements for solutions of N-methylacetamide in carbon tetrachloride have been presented. Equilibrium constants for dimerization ( K z )and multimerization ( K ) were determined from spectroscopic measurements. The values of these constants were then used for the interpretation of the dielectric results. Possible conformations of multimer chains of N-methylacetamide have been closely discussed.
Introduction In a previous paper' we presented the dielectric investigation of the self-association of a cyclic amide (ybutyrolactam), in which, for steric reasons, the peptide group -NHCO- has a cis configuration. In this case, association by the N-H-.O=C hydrogen bond leads mainly to the formation of nonpolar cyclic (1) J. Jadiyn, J. Malecki, and Cz.Jadkyn, J. Phys. Chem., 82, 2128 (1978). (2) P. Kedziora and J. Malecki, Adu. Mol. Relaxation Interac. Pocesses, 17, 141 (1980). (3) H. Lumbroso and C. Liggois, Adu. Mol. Relaxation Interac. Processes, 16, l(1980). 0022-3654/ 83/ 2087-1385$0 1.50/0
In N-monosubstituted aliphatic amides, owing to their spacial structure, the peptide group has a trans configuration that makes multistep chain association possible and creates a much more complicated situation then in case of cis lactams. The elucidation of the structure of the trans-amide chains and energy of their formation is quite important, since the peptide unit in the protein has the same trans configuration and these amides seem to form a good, simple model for biological systems. N-Methylacetamide (NMA) is the most frequently used model compound for the peptide unit in proteins. How(4) L. Hellemans and L. De Maeyer, J. Chem. Phys., 63,3490 (1975).
0 1983 American Chemical Society
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The Journal of Physical Chemistty, Vol. 87, No. 8, 1983
ever, available data"14 on the thermodynamic parameters of self-association of NMA are divergent, and there is practically no information about the structure of the multimers formed. These multimers are undoubtedly highly polar and of the chain type. This can be easily conclused from the high value of electric permittivity for pure secondary amides15J6and from the rise of the apparent dipole moment observed while increasing the concentration in nonpolar s01vents.l~ The shape of hydrogen-bonded multimers is not widely discussed in literature. Bass and co-workersl8 have proposed a multimer model for pure liquid amides. We will refer to this model in the next part of the paper. In this paper we discuss the results of dielectric polarization measurements assuming various models for NMA multimers. IR spectroscopy enabled us to eliminate the complex problem of self-associationequilibrium constants.
Experimental Section Materials. N-Methylacetamide (Fluka) was dried with calcium sulfate and twice distilled at 10 mmHg (bp 110 "C). Carbon tetrachloride (Poch) was dried with Pz05, distilled (bp = 76.5 "C), and then kept over molecular seives 4A. Chemicals were stored in a drying chamber in which all solutions were prepared. Apparatus. Quantitative spectroscopic investigations in the IR region were carried out on a Perkin-Elmer 577 spectrophotometer using 4.6-mm NaCl cells for amide concentrations less than 0.02 M, and 1-mm cells for higher amide concentrations. The electric permittivity c was measured with a DM 01 Dipolmeter (WTW) a t a measuring frequency 2 MHz, with an accuracy of f 2 X Density was measured with a hydrostatic den~itometer'~ to within f 2 X g/cm3. Results The experimental dependence of the apparent dipole moment of the amide on its concentration in CCll is determined by the real concentrations of successive multimers (these can be expressed by equilibrium constants) and their dipole moments:
For systems with multistep chain association one deals with too many parameters to achieve a unique fitting of the experimental and theoretical c w e s . One of the drastic but still reasonable approximation concerns the value of (5)J. M. Klotz and J. S. Franzen, J. Am. Chem. Soc., 84,3461 (1962). (6)K. R.Bhaskar and C. N. R. Rao, Biochim. Biophys. Acta, 136,561 (1967). (7)R. 0.Grigsby, S. D. Christian, and H. E. Affsprung, J . Phys. Chem., 72,2465 (1968). (8) J. Ahlf and D. Platthaus, Ber. Bumenges. Phys. Chem., 74,204 (1970). (9)H. Lowenstein, H. Lassen, and A. Hvidt, Acta Chem. Scand., 24, 1687 (1970). (10)L. L. Graham and C. Y. Chang, J. Phys. Chem., 75,776 (1971). (11)M. Lindheimer, G. Etienne, and B. Brun, J. Chim. Phys., 69,829 (1972). (12)J. N. Spencer, R. C. Garrett, F. J. Mayer, J. E. Merkle, C. R. Powell, M. T. Tran, and S. K. Berger, Can. J. Chem., 58,1372 (1980). (13)M.Davies and D. K. Thomas, J . Phys. Chem., 60,763 (1956). (14)M. T.Mussetta and N. Q.Trinh, C. R.Acad. Sci. Paris, Ser. C., 289,13 (1979). (15)G. R. Leader and J. F. Gromley, J. Am. Chem. Soc., 73,5731 (1951). (16)J. W.Vaughn and P. G. Sears, J. Phys. Chem., 62, 183 (1958). (17) S.Mizushima, T. Simanouti, S. Nagakura, K. Kuratani, M. Tsuboi, H. Baba, and 0. Fujioka, J. Am. Chem. Soc., 72,3490 (1950). (18) S.J. Bass,W. J. Nathan, R. M. Meighan, and R. H. Cole, J . Phys. Chem., 68,509 (1964). (19)J. Jadiyn and J. Malecki, Rocz. Chem., 48,531 (1974).
Pralat et al.
TABLE I: Thermodynamic Parameters of NMA Self-Association in CCl, t,
K,, dm3/mol
"C 20 30 40 50
5.3 t 4.0 i 3.1 2 2.9 *
K, dm3/mol
0.8 0.8 0.8 0.8
40t 1 31 25 20
i i
i
1 1 1
- A H , = 18 t 3 kJ/mol - A H = 19 i 1 kJ/mol - A S , = 25 t 8 J/(deg.mol) -AS = 1 5 t 4 J/(deg,mol)
1.0
1 I . ~
09 0.8
0.7 0.6
05
,0 2 0
004
008
012
1 - 7 2 016 c.M
Flgure 1. Dependence of (3 = tmax/t,mx on N-methylacetamide concentration in CCI,. Solid lines represent the theoretical dependences obtained from numerical solution of eq 9.
equilibrium constants. Namely, one assumes that all but the first equilibrium constant K2,describing dimerization, are the same:20
A,
+ Al 2Az Kz
#
K , = K4
A,
+ A,..1 5 A,
... = K , = K
(2)
The above assumption reduces the large number of K , parameters to only two: K z and K . Such a simplified model is used in most of the cited papers."14 The values of equilibrium constants K 2 and K were determined by IR spectroscopy, which seems to be, in case of chain association, the most reliable method.
IR Studies IR spectra of NMA solutions in CC14were recorded in 3600-3300-cm-' region, i.e., in the region of the N-H group stretching vibration, at 20, 30, 40, and 50 "C. Both equilibrium constants were determined from the experimental dependence of molar extinction coefficients c- for band of the free N-H group situated at 3480 cm-' (monomers and end groups in multimers) on the amide concentration. As was showed p r e v i ~ u s l y for " ~ the ~ ~ model ~ ~ considered with the two association constants one achieves the following relation:
(20)N. D. Coggeshall and E. L. Saier, J . Am. Chem. Soc., 73,5414 (1951). (21)N.A. Kuzniecow and A. L. Smolansky, Zh. Prikl. Spectrosc., 15, 92 (1971).
The Journal of Physical Chemistry, Vol. 87, No. 8, 1983 1387
NMA in CCI, .2
"
-2,
30y, 20
0
, , , , , ,
02
04
06
!
H
0
,c,j:::
H
0.8
Figure 2. Experimental dependence of the apparent dipole moment of N-methyiacetamide on its concentration In CCI,.
where c denotes the molar concentration of the amide, while = emax/emmar expresses the fraction of non-hydrogen bonded N-H groups. emmax is the value of molar extinction coefficient extrapolated to infinite amide dilution. The values of emmar from our measurement were 293,280,267, and 254 dm3 mol-l cm-' at 20, 30,40, and 50 OC, respectively. Equation 3, describing the relation between and the amide concentration, predicts a linear dependence of (1 - /3)1/2/(2/3- 1 ) ~ on '/~ P[(1- P ) c ] ~ / ~ /-( 1). ~ P For the NMA + CC14system we achieved, within the experimental error, such a linear dependence for all temperatures. The values of equilibrium constants obtained from these dependences are presented in Table I. In Figure 1 solid lines represent the theoretical dependences of P(c) obtained from numerical solution of eq 3 with the values of K 2 and K from Table I. As can be seen, eq 3 well describes our experimental results.
Dielectric Studies Figure 2 shows the experimental dependence of the apparent square of the dipole moment pap: of Nmethylacetamide on its concentration in CC14as calculated from the Onsager f o r m ~ l a .The ~ ~very ~ ~ strong ~ increase in the dipole moment from 15 to 70 D2 observed in a relatively small NMA concentration range (to ca. 0.4 mol/dm3) indicates a rapid expansion in self-association leading to the formation of highly polar multimers. The scale of correlation factor g = pap:/p12, where pl denotes the dipole moment of the NMA monomer, is also shown in this figure. Due to the strong dependence of pap< on NMA concentration, the determination of p1 requires very precise measurements of the electric permittivity and density in very dilute solutions. We performed such measurements at 20 "C for NMA solutions in carbon tetrachloride and benzene; in latter solvent paPp2is not so sensitive to concentration. In both solvents the values of p1 are, within the limits of experimental error (f0.07 D), the same, 3.87 and 3.85 D in CC14and C6H6,respectively. This result is in agreement with the value of 3.82 D obtained by Meighan and Cole,u and the value of 3.85 D obtained by Lumbroso25 in benzene. The value of 4.39 D obtained by Mizushima" is too high, while the value of 3.53 D obtained by us26is too low. For the highest studied concentration of NMA (0.8 mol/dm3) the correlation factor g reaches a high value of (22)L.Onsager, J . Am. Chem. SOC.,58, 1486 (1936). (23)J. Malecki, W a d . Chem., 24, 751 (1970). (24)M. Meighan and R. H. Cole, J. Phys. Chem., 68, 503 (1964). (25)H. Lumbroso and C. Pigenot, C. R.Acad. Sci. Paris, Ser. C , 266, 735 (1968). (26)K. Pralat, J . Jadiyn, and J. Malecki, Pol. J . Chem., 52, 1571 (1978).
H
+
Figure 3. Geometrical model of N-methylacetamide N,Ndimethylacetamide (R = CH,) complex and N-methylacetamide (R = H) dimer.
c-H 3
Figure 4. Model of rigid linear multimers of NMA.
about 5 (at 20 OC). For pure NMA the value of g is only slightly higher than 5.18 This fact clearly emphasizes the significance of NMA self-association studies in dilute solutions.
Dimer and Trimer Dipole Moment of N-Methylacetamide In a previous paper2' we presented a dielectric titration study for N-methylacetamide (acid) + N,N-dimethylacetamide (base) in nonpolar solvent systems. From these measurements we derived the dipole moment of the NMA + DMA (1:l)complex in CC4. It amounts to 7.25 D. By analogy, we recognized the dipole moment of this complex as the dipole moment of the NMA dimer. Molecules of NMA and DMA have the same geometry and dipole moment,24p28also the hydrogen-bonded complex NMA + DMA and the (NMA)2 dimer have the same geometry (Figure 3). The dipole moment calculations for the dimer, carried out with the geometric presented in Figure 3 under the assumption of free rotation around the hydrogen bond and with the polarity of hydrogen bond as Ap = 0.3 D, gave the value of 7.25 D. This is typical polarity for weak hydrogen bond^.^',^^ Thus,the value of 7.25 D seems to be correct for the NMA dimer. (27)K. Pralat and J. Jadiyn, Pol. J. Chem., in press. (28)R. J. Kurland and E. B. Wilson, Jr., J . Chem. Phys., 27, 585 (1957). (29)H. E. Hallam and C. M. Jones, J. Mol. S t r u t . , 5, 1 (1970). (30)M. Kitano, T.Fukuyama, and K. Kuchitsu, Bull. Chem. SOC. Jpn., 46, 384 (1973). (31)H. Ratajczak and L. Sobczyk, J. Chem. Phys., 50, 556 (1969). (32)L. Sobczyk and Z. Pawelka, J. Chem. SOC.,Faraday Tram. 1 , 7 0 , 832 (1974).
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,D 80
Pralat et al.
8, 1983
c I
-
0 0 3
Figure 5. Dependence of /mer dipole moment on the number of molecules in a chain, calculated for various models of NMA mukimers.
The dipole moment of the NMA trimer, p3 = 9.95 D, was calculated in a similar way by taking into account the rotation of both end molecules.
Dipole Moment of Higher Chain Multimers of NMA Increasing the number of molecules raises the number of possible chain conformations and makes the structure of the multimer more complicated. Let us consider two extreme models: 1. One model proposes rigid linear multimers (Figure 4). Such linear chains are formed in crystalline Nmethyla~etamide.~~ The dipole moment dependence on the number of elements in the multimer chain is shown in Figure 5. The calculations were performed for the geometry shown in Figure 3 and under the assumption of free rotation of both utmost molecules. 2. A second model assumes free rotation about all hydrogen bonds in the multimers, which means all possible conformations has the same probability of existence. The dipole moment of successive multimers can in this case be calculated from Eyring's formula.34 Bass and co-workerslaproposed in the interpretation of their dielectric studies of pure N-alkylamides in intermediate model. In this model one assumes free rotation of the dipole moments of the individual chain elements and the same angle 3 between vectors of the dipole moments and the axis of chain. Thus, in this model of "elongated" multimers, the projection of the dipole moment of any molecule on the axis of chain amounts to pi cos 3 while the dipole moment of the imer can be calculated from the following formula: pi = pl(i[l
+ (i - 1) COS'
S])1/2
(4)
The dependence of pLon i calculated for 3 = 55' is presented in Figure 5. In next part we will use all three geometric models for interpretation of the dielectric results.
Interpretation of the Dielectric Polarization Results The value of papp,determined from measurement of the electric permittivity, density, and refractive index of solution, denotes the apparent value of dipole moment for an individual amide molecule. In the ideal case, i.e., for solutions of noninteracting molecules, this value should be equal to the dipole moment of the free molecule (monomer) and the factor g = pap;/pl2 should be equal to l , independent of the solution concentration. The above is (33) J. L. Katz and B. Post, Acta Crystallogr., 13, 624 (1960). (34) H. Eying, Phys. Reu., 39, 746 (1932).
strictly true only for spherical molecules. As was shown by Bonnet and BarrioP5 for solutions of a slightly polar solute in a nonpolar solvent the deviation of the g value from 1 can be explained by the anisotropy of the polar molecules. For solutions in which one observes chain association, the geometrical anisotropy of the multimers cannot be neglected. Equation 1 becomes more complicated than for the mixture of spherical molecules and new parameters describing the anisotropy of multimers must be taken into account. The equilibrium constants for association were determined by an independent method in order to be able to discuss this anisotropy. Let us consider the solution of NMA in CC14 as a mixture of spherical solvent molecules and elipsoidal multime n with axes ai,bi,ci, where the permanent dipole moment pi is directed along ai. Then, using Scholte's theory36as developed by Weaver and Parry,37 one can easily derive the following relation between the pappzof the amide determined from Onsager's formula and the molecular properties of successive multimers: 3(2t pap:
=
(2t
+ n:)'
+ l)(na2 + 2)'
X
where t denotes the electric permittivity of the solution, and n, is the refractive index of pure amide. xi is the fraction of imer defined as Xi
iNi =ENj
i = 1, 2, 3 , ...
1
where Ni denotes the number of particles of imer, while CiiNidenotes the total number of amide molecules. With the mass law the fraction of monomers can be calculated from the following equation:38 (7) where c denotes the nominal molar concentration of the amide. Fractions of dimers and higher imers can be calculated from the equations x2 =
i xi = -Kxlcxi_, 1-1
2K2x12c i = 3 , 4, ...
(8)
Coefficients of molecular shape A,. contained in eq 5 are given by the following formulae:
For the rotatory ellipsoid a # b = c evaluation of the integral in eq 9 is easy and one obtains eq 10.
(35) P. Bonnet and J. Barriol. J. Chim. Phys., 74, 600 (1977). (36) T. G. Scholte, Physica, 15, 437, 450 (1949). (37) J. R. Weaver and R. W. Parry, Inorg. Chem., 5, 703 (1966). (38) L. A. La Planche, H. B. Thompson, and M. T. Rogers, J . Phys. Chem., 69, 1482 (1965).
The Journal of Physical Chemistry, Vol. 87, No. 8, 1983
NMA in CCI,
100
L
c
/
1389
(sphericol)
80
60
40
To calculate the value of the coefficients A for a particular multimers one must make some assumptions concerning ai and bi. For the first three terms of the sum in eq 5, i.e., for monomers, dimers, and trimers, the dipole moments of which were determined experimentally or calculated without special model assumptions, we assumed spherical symmetry (a = b = c ) , Le., Aal = Aa2 = A,, = lI3. For multimers containing more than three molecules one can consider t.he following cases: (i) In the model with the same probability of occurrence for all possible multimer conformations there is no preferred direction and therefore the assumption that the “average” multimer has spherical symmetry seems reasonable. Then, the coefficients A& = 113 and eq 5 simplify to the form
There are no arbitrary parameters in this model. (ii) In the model of rigid linear multimers and in the model of “elongated” multimers we assume bi = ci = qa, (q Il),where q denotes a “thickening” of the association chain in comparison with the chain in which spheres with a radius of al (representing monomers) are set side by side on a straight line (in this case q = 1). Then, we assume that the volume of the ellipsoid representing the imer is equal to the i multiplicity of the volume of the sphere representing the monomer. From this assumption one obtains ai
1
= -a1 q2
Thus, in the model of linear multimers only one parameter q appears, while in the model of “elongated” multimers there are two parameters q and 9, both variable in course of fitting the theoretical and experimental dependence of yaPp2 to the concentration. Theoretical calculation of papp2from eq 5 requires the summation from i = 1 to infinity. In practice, one must find a reasonable limit. We stop the summation when the value of a successive term was lower then the sum of all previous terms multiplied by 0.0005. Even if the sum of neglected terms is about ten times higher then the last term taken, this procedure still should give us the value of yap: with an accuracy better than 0.5%. Our calculations were taken for concentrations lower than 0.14 M; in such dilute solutions summation of the first 50 terms in eq 5 gives sufficiently good accuracy. For higher concentrations the calculations become not only time consuming, but also their reality is doubtful due to the necessity of dipole moment calculations for very large multimers. Results of the model calculations are shown in Figure 6.
In the model of linear multimers the best possible agreement between theoretical and experimental data can
20
0.04
0
0.12
0.08
c, F
0.16
Flgure 6. Comparison of the values of hap: calculated for various multimer models with the experimental results at 20 ‘C.
10:
0
’
1
004
1
’ 008
1
)
012
’
2
c,M
Figure 7. Comparison of the results obtained from the model of elongated multimers (q = 2.0, 9 = 51’) with the experimental results at various temperatures. The summation in eq 5 was executed up to ,i = 54, 47, 42, and 34 at 20, 30, 40, and 50 OC, respectively.
be achieved for q = 1. However, as can be seen in Figure 6, neither the model of linear multimers, nor the model with all possible conformations, are in agreement with experimental data. If, in the case of rigid linear multimers we expected this, then for the latter model we predict the better agreement. We expected that in dilute solutions of NMA in a nonpolar solvent multimers of all conformations can be easily formed, since the dense packing as the main argument for elongationla seemed to be not so significant in dilute solutions. The fitting achieved for the model of “elongated” multimers is quite good and this result agrees with the conclusion of Bass and co-workers.18 We obtained the following values of fitted parameters: q = 2.0, 9 = 51’. Despite the fact that our model contains two fitted parameters, its results are for us quite convincing because it correctly describes the dependence of pap on temperature. With the values of q and 19 as at 20 we achieved in a natural way, i.e., changing only the values of the equilibrium constants (Table I), very good reproduction of the pa p2 dependence on concentration at 30,40, and 50 “C (soli3 lines in Figure 7). Of course, all above attempts for a model description of NMA association can be simplified by assuming spherical symmetry of all multimers, disregarding the model used for the calculations of their dipole moments. Then, in the model of elongated multimers 9 remains as the only fitted parameter. In this case, the best agreement is again reached for elongated multimers, but it is not as
‘8
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J. P h p . Chem. 1983,87,1390-1396
good a fitting as for ellipsoidal symmetry, and the experimental temperature dependence of pap: cannot be reproduced by the change of equilibrium constants only. Good fitting at various temperatures can be achieved by a considerable change in the value of IJ (about Z O O ) . Thus, the assumption concerning the geometry of multimers is essential and strongly modifies the dependence of pap: on concentration. This is illustrated in Figure 6 for the model of linear multimers. Conclusions This paper presents an example of fruitful common interpretation of spectroscopic and dielectric measurements. Spectroscopic determination of equilibrium constants for self-association enabled us to discuss the conformation of chain multimers of N-methylacetamide. This discussion shows that neither the model of rigid chains (like in crystalline amide) nor the model in which the
formation of all conformers is equally probable described the results of dielectric studies. However, the model of “elongated” multimers, proposed by Bass and co-workers for the interpretation of dielectric properties of pure liquid amides, appears to work also for dilute NMA solutions. This is a quite simple model, but nevertheless it takes into account the most important properties of multimers, their shape and the dependence of dipole moment on the number of elements in the association chain. Our consideration also showed the strong influence of assumptions concerning the geometry of multimers on the theoretical dependence of pap: on concentration.
Acknowledgment. This work was supported by the Polish Academy of Sciences within the framework of Project MR-1.9. Registry No. N-Methylacetamide, 79-16-3; carbon tetrachloride, 56-23-5.
A Hydrogen-2 Nuclear Magnetic Resonance Study of Conformational and Dynamic Characteristics of Cyclohexane While Trapped within Thiourea Inclusion-Compound Channels Eva Meirovitch,’ Tamar Krant, and Shimon Vega The Weizrnann Institute of Science, Isotope Department, 76 100 Rehovot, Israel (Received: July 16, 1982; In Final Form: November 2, 1982)
We report on 2HNMR spectra from a polycrystalline powder of the thiourea-cyclohexane-dI2inclusion compound within the temperature range 134-345 K. Drastic changes in these spectra as a function of temperature are interpreted in terms of cyclohexane becoming engaged gradually in various uncoupled dynamic modes and undergoing several conformational alterations. At the lowest temperatures, chair-form conformers with a geometry consistent with minimal energy calculations (mec) prevail; the cyclohexane rings are in an upright position within the channels, with the triad axis z’lying parallel to the channel axis d, about which they spin rapidly. At 137 K the guest molecules tip over suddenly so that z’ becomes tilted at an average angle a relative to d with a concomitant onset of nonuniform reorientation about d. Over the next 125 K the average intrachannel orientation of cyclohexane changes gradually with a determined to an accuracy of f1.5’. We also find that at 159 K the motion about d becomes uniform and detect an increase of about 2’ in the angle between the axial and equatorial C-D bonds. At approximately 240 K, onset of rapid ring inversion is observed.
Introduction In isotropic liquids molecules reorient basically as individual entities, as described by the Stokes-Einstein and Debye equations, with rates governed by activation energies which are characteristic for the particular solvent used. In ordered solvents, such as the various liquid crystalline phases, molecules reorient in the presence of local ordering potentials but otherwise the main features of the reorientation process are conserved. Among many other techniques, nuclear magnetic relaxation has been used extensively to study molecular motion in isotropic fluids’ and recently in ordered fluids as ell.^^^ Can one infer from these studies the dynamic behavior of molecules in the solid state? (1)L. M. Jackman and F. A. Cotton, Ed., ‘Dynamic Nuclear Magnetic Resonance Spectroscopy”, Academic Press, New York, 1975. (2)(a) Z. Luz, R. Naor, and E. Meirovitch, J. Chem. Phys., 74,6621 (1981);(b) R. Poupko and Z. Luz, ibid., 75,1975 (1981). (3)R.R. Vold, R. L. Vold, and N. M. Szeverenyi, J . Phys. Chem., 85, 1934 (1981)
This question has been addressed in the past with nuclear magnetic resonance (NMR) spectroscopy using broad-line NMR, relaxation-time measurement^,^^^ and, very recently, complete line shape analysis6-10which became practical due to the development of the high-resolution solid-state NMR techniques. However, the number of studies focussing on the dynamics of molecules in solids (4)H.S.Gutowsky and G. E. Pake, J. Chem. Phys., 18,162(1950). (5)E.R. Andrew, J. Chem. Phys., 18,607 (1950). (6)(a) R. G. Griffin, L. Powers, and P. S. Pershan, Biochemistry, 17, 2718 (1978);(b) G.M. Gall, J. A. Verdi, and S. J. Opella, J. Am. Chem. SOC.,103,5039 (1981). (7)(a) D.E. Wemmer, D. J. Reuben, and A. Pines, J. Am. Chem. Soc., 103,28 (1981);(b) A. D. English and A. J. Vega, Macromolecules,12,353, 3 (1979). (8)H.W. Spiess, Chem. Phys., 6,217(1974);H.W Spiess, R. Grosescu, and U.Haeberlen, ibid., 6, 226 (1974);H.W. Spiess and H.Sillescu, J . Magn. Reson, 42,381 (1981). (9)(a) S.Alexander, A. Baram, and Z. Luz, Mol. Phys., 27,441 (1974); (b) A. Baram, Z. Luz, and S. Alexaner, J. Chem. Phys., 64,4321 (1976). (IO) (a) R. F. Campbell, E. Meirovitch, and J. H. Freed, J . Phys. Chem., 83,525 (1979);(b) E. Meirovitch and J . H. Freed, Chem. Phys. Lett., 64,311 (1979).
0022-3654/83/2087-1390$01.50/00 1983 American Chemical Society
