The Structure of CH3COOH-CBH,2 Mixtures
The Journal of Physical Chernistty, Vol. 82, No. 18, 1978 2029
An Investigation of the Structure of the Mixture Acetic Acid-Cyclohexane by the Nuclear Magnetic Relaxation Method A. L. Capparelll, H. G. Hertz,” and R. Tutsch Institut fur Physlkalische Chemie und Elektrochemie der Universitat Karlsruhe, Karlsruhe, West Germany (Received November 8, 1977; Revised Manuscript Received June 1.2, 1978)
Longitudinal relaxation times T1of the various protons in the system CH3COOH-C6H12have been measured as a function of mixture composition. From these data intramolecular relaxation rates and intermolecular proton relaxation rates arising from interactions among the proton-carrying groups are extracted. The experimental results have been evaluated to yield orientation dependent model molecular pair distribution functions involving pairs of acid molecules, pairs of cyclohexane molecules, and acid-cyclohexane pairs. 1. Introduction An extended study of mixtures of carboxylic acids in various solvents is in progress at this lab~ratoryl-~ and the present paper is another contribution to the investigation of some structural properties of acetic acid in polar and nonpolar solvents. Results regarding its mixture with water1 and CC1: have been previously reported and model pair distribution functions for pure acetic acid and for the moderately dilute state have been determined. In the present paper the pure liquid will only be treated briefly. Most remarkably, the chemical shift of the OH proton of acetic acid (and other acids) in an inert solvent mixture moves downfield as the acid concentration c2 is deThen, at fairly small CH3COOHconcentrations the shift goes through a minimum (maximum downfield shift) and becomes more and more positive as c2 0. This general behavior is common for the solvents CC14 and C6H,,. However, the position of this minimum in C6H12 is shifted toward smaller concentrations than in CCl, (x2 = 0.04 and 0.07, respectively; x2 is the mole fraction of acid).7 The monomer-dimer equilibrium constants are also reported in ref 7, Le., K = 2467 f 70 L/mol and K = 7515 f 225 L/mol at 29 “ C in the solvents CC14 and C6H12, respectively. The authors of that work concluded that CCl, is a “more polar” solvent than C6H12. Of course, it is of great interest to examine whether this difference in chemical shift behavior can be identified with direct structural particularities. In fact, study of the association of acetic acid in CC12 and of proponic acid in CC1: have revealed that at relatively low acid concentrations the cyclic dimer appears to be present in a more or less folded form which is evidenced by the existence of a distinct magnetic interaction between the methyl protons of different molecules. A similar pair configuration was also observed for the hydrocarbon chains of propionic and butyric acid dissolved in water.l Thus the question arises whether this folding of dimers is also present in a “more inert” solvent such as C&2 where polar bonds as in CCl, are not present. Thus it is the purpose of the present paper to study the dimer configurations of acetic acid in the solvent CeH12. At the same time, for comparison it seemed to be of interest to study CH&OOH-C6H12 pair configurations. There should be no association between these two components and consequently direct comparison of bonded and unbonded pair configurations should be instructive, in particular, also to demonstrate the ability of the nuclear magnetic relaxation method. 2. Experimental Section Proton relaxation times of samples containing only one type of proton and deuteron relaxation times were mea-
-
0022-365417812082-2023$01 .OO/O
sured with a 90°-90” pulse sequence at a resonance frequency of 25.56 MHz for protons and 12 MHz for deuterons. The pulse spectrometers are home-made and of conventional type (see, e.g., ref 9). Measurements were carried out at 25 f 0.1 “C; water at this temperature was pumped through a Colora ultrathermostat and the probe head. Measurements of systems where two nonequivalent protons are present were done with the adiabatic fast passage technique (AFP),loJ using a Varian HR 100 spectrometer. Measurements and evaluations were performed as described by Engelsmann et a1.12 The temperature for the AFP measurements was held constant at 25 f 0.5 “C by controlling the room temperature. Diffusion coefficients were measured at 25 f 0.1 “C with a 19.5-MHz spectrometer applying the pulsed field gradient technique.13J4 In all cases for a single experimental point obtained by pulse measurements the uncertainty is f5%. For AFP and diffusion measurements the uncertainty of a single experimental point is &lo%. Each experimental point given in the figures is the average of two to three measurements. Yet in certain cases the composition dependence of the relaxation rates is small and the statistics are such as to reduce the experimental error to f 5 % also for the AFP measurements. Sample tubes containing the mixtures were evacuated several times until they were completely free from air. Of course, during pumping the temperature of the sample was low enough to prevent changes in composition. Sample tubes were then sealed off. Distillation of the substances used was usually carried out before experiments.
3. Results The proton and deuteron magnetic relaxation rates of the mixtures needed to perform a full structural analysis have been measured and the experimental relaxation rates are shown in Figures 1-6. We performed only a reduced number of measurements in mixtures of CHSCOOD-CBHDll or CD3COOH-C6HD11since the available amount of C6HD11was not sufficient for the whole program. The remainder of the corresponding measurements was carried out with C6H12. For study of the intermolecular relaxation rate of the cyclohexane protons caused by acid protons use of C6HDll is more advanteous than that of C&z because the intramolecular contribution to the relaxation rate is much smaller. Measurements of CH3 relaxation rates in the presence of nonequivalent protons were not performed because the relaxation effects were below the limits of experimental error of the AFP techniques. Figure 7 shows the self-diffusioncoefficients of acetic acid and cyclohexane in the mixture. 0 1978 American Chemical Society
2024
The Journal of Physical Chemistry, Vol. 82, No. 18, 1978
A. L. Capparelli, H. G. Hertz, and R. Tutsch
r-2s-1
1@-2s-1 P
l28
f 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
.O
0.9
Figure 1. Proton magnetic relaxation rate (total relaxation rate) (0), and proton intramolecular relaxation rate ( 0 )in the system CH,COOD-CBDI2. xz is the mole fraction of the acid. Deuteron magnetic relaxation rate of the system CH,COOD-C6Hlz (A, right-hand ordinate). The lowest curve shows the intermolecular CH, proton relaxation rate.
r = 25 OC.
Figure 4. Relaxation rates of italicized protons in the system CBHDll 4- CD&OOH (0)and C6Hl2 CD,COOH (A) as a function of the acid mole fraction x2. Proton relaxation rates in the systems C6HDl, CD,COOD ( 0 )and C&2 CD,COOD (A)as a function of the acid mole fraction xp. Intermolecular proton relaxation rate of C6HDil caused by proton of CD,COOH ( 0 )multiplied by 3/2. The dashed line shows the same quantity indicated as the difference between A and A. T = 25 OC.
+ +
1
16t
ai
,
a2
0.3 01
05
0.6
07
x2
0.8 09
+
-2 -1
Yo
i'o
Flgure 2. Proton relaxation rate of the system CD,COOH-C6Diz as a functlon of the acid mole fraction x z (0). Intermolecular OH proton relaxation rate caused by CH, proton, multiplied by a factor 3/2 (0). The lowest smooth curve shows the latter quantity after correction for OH CH, intramolecular contribution. T = 25 OC.
LC
+-
/
14t
t oc
/ /
l2 1
I
0.2
0.3
0.4 a5
a6
1
0.7 0.8 0.9
to
Figure 3. Proton relaxation rate (total relaxation rate) (0)and proton intramolecular relaxation rate (0)of the system C6H,,-CD3COOD; x i is the mole fraction of C&p The smooth curve without experimental points shows the proton intermdlecular relaxation rate in the system C6H12-CD&OOD. T = 25 OC.
Figure 5. Relaxation rate of italicized protons in the systems C8HD,, CH,COOD (0)and C&z 4- CH,COOD (A) as a function of acid mole fraction x2. Proton relaxation rates in the systems C~HDI, -k CD,COOD ( 0 )and C6H12 -k CD,COOD (A)as a function of acid mole fraction x z . Intermolecular proton relaxation rates ( X 3/2)of C6HDI1 (0)and of C&t12(A), both caused by CH, group of the acid. The intermolecular relaxation rates are the differences between the respective quantities indicated by the open and filled symbols. T = 25 OC.
+
deuteron is caused by electric quadrupole interaction. The constant L was taken from the work of Zeidler et al. without further examination. The corresponding numerical values are LcHS= 4.85' and L C H = 13.3315for acetic acid and cyclohexane, respectively. +he intermolecular relaxation rates have been obtained from the relation
The CH, and CH, intramolecular relaxation rates shown in Figures 1 and 3 were obtained from the relation The contribution of the proton relaxation rate caused by the dipole-dipole interaction with the deuterons was taken into account using the equationl0J' which implies that the proton intramolecular relaxation rate is proportional to the deuteron relaxation rate of the CD, deuterons. The nuclear magnetic relaxation of the
The Journal of Physical Chemistry, Vol. 82, No. 18, 1978 2025
The Structure of CH3COOH-C6H12Mixtures
acid we estimate a suitable correlation time as being the mean between the OH (13 ps) and the CH3correlation time (3 psl). The composition dependence of this correlation time is then given by the curve connecting the filled circles and triangles in Figure 1. 4. Evaluation of Experimental Data
4.1. Dynamical Information. In a similar way as in the mixture CH3COOH-CC4 the rotational correlation time T , as a function of the composition does not show any maximum as the concentration changes (see Figure 1). Such a behavior was observed for the aqueous solution. T, is given by the relation (l/Tl)hka= FT,, F is a constant.1° Thus again, the maximum of T, is a typical property of the solvent water. We can evaluate 7,for the OD group from the following expressionlo
0.5
Flgure 6. Relaxation rate of italicized proton in the systems CD,COOH HDllCa (0)and CD,COOH+ HIP& (A) as a function of acid mole fraction x p . The curve without experimental points shows proton relaxation rate of the system CD,COOH 4- C6D12,it is the same curve as given by symbols (0)in Figure 2. Intermolecular proton relaxation rates (X 3/2)of CD,COOH caused by HD,& (0)and by C6Hl, (A), however, the latter quantity divided by 12 (giving the effect of only one proton on C&,). = 25 OC.
(1/ T1)OD= 3/27r2Kq2~q
+
r
- 5 2 -1 D,10 cm s 2-
‘
0.1 0.9
0.2
03
0.8
0.7
0.4 06
0.6
0.7
0.8 0.9
05 oh
0.3
a2
05
0.1
,
7.0 x2
o
x
Figure 7. Selfdiffusion coefficients of CH,COOH (0)and of C6HIP (0) as a function of the acid mole fraction x p . T = 25 OC.
In all our figures the intermolecular relaxation rates obtained from AFP measurements have been multiplied by 3/2 in order to convert the results to equal spin values.1° In Figure 2 the lower experimental curve (filled sympols) represents the relaxation rate of the OH protons of acetic acid which is caused by the methyl protons of the acid (converted to the equal spin value by multiplying it by 3/2). Part of this relaxation rate is of an intramolecular nature. Due to proton exchange of the OH group, CH3COOD as the “relaxation producing” and CD3COOH as the relaxing species cannot be observed separately, we always get a contribution from the species CH3COOH,too. The lowest smooth curve in Figure 2 gives the CD3COOH H3CCOOD relaxation rate (converted to the equal spin value) when the intramolecular contribution caused by the methyl protons has been subtracted. Two OH methylproton distances were taken to be 3.5 A, that to the third proton was taken as 4.1 A. This implies that the OH group is “cis” with respect to the CO group. The corresponding trans conformation can be excluded, it would lead to a relaxation effect much stronger than the observed one. The correlation time for the CH3-OH interaction is not easily accessible which is due to the presence of internal rotation within the acid molecule. The methyl group rotates around the C-C bond; this causes an additional modulation of the proton-proton interaction. For the pure
-
(1)
Here 7, = T~ = TOD because the correlation time T~ characteristics the fluctuation of the electrical field gradient at the deuteron. Kq is the quadrupole coupling constant and is defined as Kq = eqQ/h.1° If we estimate Kq = 200 kHz,16then we find 7oD = 13 ps for the pure acid. From Figure 1 we obtain the extrapolation value of (1/ Tl)intra as c2 0, l/Tl = 0.097 s-l, which yields TOD = 8.2 ps. This is a rather typical value for the dimeric state and thus, as from other methods, we obtain evidence that at the lowest concentrations accessible to our method we have exclusively dimers. The difference between the two values of 7 0 D at x 2 = 1 and x 2 = 0.1 is almost the same as that reported for the system CH3COOD-CC14.2 The only particular feature is that in the present system the increase of the correlation time at mole fractions x 2 I0.5 is almost zero, whereas in the mixture with CCll the increase of T , is nearly linear over the entire composition range; for CH3COOH-C6H12there is even a slight maximum of the self-diffusion coefficient. D characterizes the translational diffusive motion of the acid molecule. Of course, increase of the rotational correlation time (and decrease of the translational diffusion coefficient D ) always is an indication for an enhanced degree of coupling between molecules. Yet, in view of the rearrangements of intermolecular configurations which occur in the range 0 I x 2 I 1, e.g., formation of new H bonds, the change of the quantities describing rotational and translational diffusive motion appears to be small. The rotational correlation time of C6H12in pure cyclohexane at 25 “C is 1.7 X s.15 We mentioned that the (translational) self-diffusion coefficients go through a flat maximum as the mixture composition is varied. In the same way the rotational correlation time of C6H12 goes through a minimum. This may be recognized from Figure 3 if one keeps in mind that the intramolecular relaxation rate is proportional to the rotational correlation time. Starting from pure C6H12 with increasing acid concentration flexible acid dimers are added which are smaller than C6H12 molecules. This causes acceleration of rotational motion. Then, at high acid concentration obviously the H-bonded networks again cause retardation. 4.2. Structural Information. 4.2.1. Calculation of Closest Distances of Approach. Let us denote the representative spin for the methyl proton as I, the spin of the carboxyl proton as S, and the spin of the methylene protons in C6H12 as T. The evaluation of the experimental results has been performed using the model atomic distribution function proposed in previous work of this lab~ratory.l-~J~ In this treatment the radial distribution
-
2020
The Journal of Physical Chemistry, Voi. 82, No. 18, 1978
2t
’t
b -
’I
, , , x27 0.4 06 0.8 .O Flgure 8. (a) Intermolecular closest distances of approach between OH protons (ass),CH3 protons (aII),and between OH and CH, (aIs) in the mixture acetic acid-cyclohexane as a function of the acld mole fraction. (b) Intermolecular closest distances of approach between (effective single) protons on C&l1? molecules (a,) and closest distances of approach between CeHl, and CH, (alT) and OH (aST)in the same mixture. For further details see text. , 0.2
function is given essentially as a three-parameter function which occurs as a factor leading to a quantity g(n,k,1)19920 in the formula for the intermolecular relaxation rate (see also eq 14 of ref 18)
where y is the gyromagnetic ratio of the proton; n, is the first coordination number of the relaxing proton with respect to the surrounding protons, for all intermolecular spin separations >b a uniform atom (i.e., spin) distribution is valid; c2is the number density of protons; a is the closest intermolecular distance of approach between the interacting protons; and K = 312 if magnetic dipole-dipole interaction occurs between like spins,1° K = 1 otherwise. k and 1 are two geometric parameters, and n characterizes the steepness of the effective intermolecular potential between the atoms or molecular groups. For the hydroxyl proton we set g = 1 corresponding to n L 6, Le., we assumed that the intermolecular potential which represents the H bond is sufficiently well described by a 6 function. There should be a fairly flat distribution between the methyl groups and between the protons on different C&12 molecules and we chose n = 1,which gives g(n,h,Z)= 0.25. The same value was applied for the C6Hl,-acid and C6HD11-acid distribution function, however, for the CH3-OH interaction we assumed a slightly sharper distribution function, that is, we took n = 2. From geometrical considerations we chose the outer radius of the first coordination sphere of the reference molecule to be b = 7 A. Since the volume of the cyclohexane molecule is greater for the C6H12-C6H12and C6H12-acid intermolecular relaxation rates we have set b = 9 A and b = 8 A, respectively. In Figure 8a aII, ass, and aIs, the closest distances of approach between 1-1, S-S, and I-S protons, respectively,
A. L. Capparelli, H. G. Hertz, and R. Tutsch
are shown. These data have been calculated from the intermolecular relaxation rates given in Figures 1 and 2 and the acid self-diffusion coefficients shown in Figure 7 using eq 2. The calculation of these closest distances of approach involves the formation of a twofold difference. Therefore a consideration of the error introduced is needed. Starting from an experimental error of &5% connected with the original measurements, at high and low acid concentration (x2= 0.2) this introduces an uncertainty in the intermolecular relaxation rate of f20 and &30%, respectively. The “translational” part of the intermolecular relaxation rate which is due to all molecules with . the error involved distance Z b , amount to ~ 5 0 % Thus in the short range contribution is A40 and f60% at high and low concentrations, respectively. The latter contriSince at low concentrations the a values butions is 0: are more likely to come out too small we estimate the uncertainty of the closest distances of approach to be &8% at high and +16, -6% at low concentrations, respectively. The first coordination numbers for the methyl-methyl and the methyl OH interactions have been assumed as follows: n, = 1 + 2x2 (3)
-
and for OH-OH we assumed n, = 1 + x 2
(4) ( x 2 is the mole fraction of acetic acid). The value 1 is due to the presence of the H-bonded partner. Of course strictly n, 0 as x2 0, however dissociation of the dimers occurs at a very low concentration, in the range where our method is effective there is always at least one partner molecule H bonded to a given reference molecule. For the CH3-CH3 intermolecular relaxation rate the iteration procedure implied in eq 2 with n = 1and n, as given by eq 3 no longer converges for x2 C 0.4, therefore aII in that range has been drawn as a dashed curve. The dotted curve represents the aII which one obtains if only the “translational” formula for the intermolecular relaxation rate (i-e.,the second term on the right-hand side of eq 2) is applied. +
+
In Figure 8b the closest distances of approach between the cyclohexane molecules (spin T) and between C6H12 and the two groups of acetic acid are shown. As always, these are closest distances between the “representative” spins on the molecules. In the methyl group the location of the representative spin should be close to the nucleus of the carbon atom. The cyclohexane molecule is roughly a sphere of 3.2 A radius containing another sphere of =2 A radius over which 12 protons are uniformly distributed. It is a reasonable estimate to locate the effective spin on a sphere which is defined by the mean intramolecular positions of the carbon nuclei. The distances uTT have been obtained from the experimental results shown in Figure 3. In pure liquid C6H12 the first coordination number of C6H12 with respect to itself has been taken to be n, = 3; the decrease of n, as xl, the mole fraction of C6H12, decreases was taken to be proportional to the C6H12 concentration. UIT, the closest distance of approach between the methyl group and cyclohexane, was derived from the experimental results shown in Figure 5. The relaxation rate of the C6H12 protons in the limit x1 0, caused by the methyl protons, s-l (after multiplication by 312). Here the first is 3.5 X loM2 coordination number of C6H12 with respect to CH3 was +
The Journal of Physical Chemistry, Vol. 82, No. 18, 1978 2027
The Structure of CH3COOH-CBHj2 Mixtures
taken to be n, = 4. We were not able to measure in the reverse situation and thus to obtain the relaxation rate of the methyl protons on one single acid molecule ( x 2 0 ) caused by the protons of C6H12. From the concentration dependence of the experimental relaxation rate (1/ T1)IT given in Figure 5 we cannot detect any pecularities which would suggest that uIT varies strongly with mixture composition. Therefore in Figure 8a we have assumed that uIT is constant over the entire composition range. Next we turn to the discussion of U S T , i.e., the closest distance between OH and C6HIz. We begin with the limiting situation xz 0; this means we have one single acid molecule surrounded only by C6H12 molecules. The corresponding experimental relaxation rates are shown in Figure 6 and the two extrapolation values of the intermolecular relaxation rates (0 and A) should be the same. For our evaluation we take the mean value (l/Tl)ST= 1.5 X s-l (after multiplication by 3/2). With n, = 3 this yields asT = 3.25 A, which is a comparatively small distance. Assuming that the distribution function is sharper, e.g., n = 2 instead of n = 1, yields asT = 4.1 8. On the other end of the composition range, x2 1, the experimental data are taken from Figure 4. Now we have one single C6H12 molecule surrounded only by acid mols ecules, From Figure 3 we read (l/T1)ST= 1.5 X (after multiplication by 3/2). With n, = 4 this gives a fairly large separation, aST = 6-6.5 A. It is interesting to remark that the closest distance of approach between CH3and OH a t x2 1was also found to be very large (see Figure 8a). Thus, obviously, there is a strong tendency for the polar part of the acid molecule in the pure acid to repel1 any nonpolar constituent. The line in Figure 8b connecting the two limiting values of asT represents a freely drawn linear interpolation. 4.2.2. Discussion of the Quantity A i n Acetic AcidCyclohexane Mixtures. In Figure 9a we have plotted the quantity
-
"}
\OH-OH
~
\
30t
-
-
-
for the OH protons and the methyl protons vs. c i , where c i is the number density of the protons (particles/cm3). As has been explained elsewhere1~2~21~22 the variation of the quantity A with concentration represents a general criterion for the presence of association. If one has A = constant then the local solute concentration around a given solute molecule is the same as the mean solute concentration. In this event association is absent. On the hand, if A > Ao as c i decreases, where Ao = (1/Tl)inter(Dl/c20/) correspondingto the pure liquid of the component denoted as the solute, then the local solute concentration around the reference solute molecule is greater than the mean solute concentration; this means we have association between solute particles. The increase of A for the OH protons is obvious (Figure 9) and is in agreement with the presence of the H-bonded dimer in solution (as shown, for example, in ref 2). A for the methyl group is constant within the limits of experimental error. Thus association with respect to the methyl groups is absent. The CH3 group belonging to the Hbonded dimer pair partner has a distance from the reference methyl group large enough so that the fluctuating local field from those protons does not contribute to the relaxation process. In contrast to this finding, in the system CH30D-CC142 an increase of A for the methyl protons as the acid concentration decreases has been observed; thus in that mixture association exists also with respect to the methyl groups. Changing the mode of
'
0:6
Ok
O(L
0;
0:2
0:I
b C; ,lo-22
Flgure Q, Association parameter A for the various groups and molecules as a function of the proton concentration (protons/crn3) in the mixture CH3COOH-C8HI2. For further details see text.
description somewhet we may say that in the mixture acetic acid-carbou tetrachloride we have a folded dimer whereas in the more inert solvent cyclohexane the dimers are not folded, or, what is certainly more correct, the degree of folding is less. One comment is necessary here. In fact, the quantity A is a criterion for the presence of association in an exact and well-defined sense. However, as may be seen from a comparison of the intermolecular relaxation rate shown in Figure 1 with the corresponding total and intramolecular relaxation rates, the experimental error connected with the determination of A usually is appreciable. Thus, at a concentration c i = 0.3 X cmW3the quantity A given in Figure 9a may well be by a factor 2 larger than shown, and, on the other hand, the A value at the same concentration in Figure 7 of ref 2 may only be half as great. Still, there is strong evidence that the more inert solvent C6H12has the effect that the bending of the dimer is less. Finally, it may be seen from Figure 9b that there is no self-association observable for C6H12. 4.2.3. Pair Configurations of Maximum Occurrence Probability. If we consider the intramolecular vector connecting (representative)spin I with spin S, then we may say that in a simplifying model approach the acetic acid molecule is represented by a rod. Spins I and S are sitting on the ends of this rod. Now the closest distances of approach U I T , ais, and ass can be transcribed to give a rod-rod model pair distribution function. In a first step such model pair distribution functions only describe planar pair configurations, however, nonplanar configurations have also been treated previ~usly.~ In the present study we confine ourselves to planar configurations. The shape of the atomic pair distribution function p(r) is such that in the neighborhood of the closest distance of approach the function increases very strongly and reaches its maximum value. For the atomic model pair distribution we very often U S ~ ~ the ~ ~slope ~ J of~ p(r) J ~at r = a as infinite, so that the maximum of the model pair distribution function is at r = a. Then the construction of a
2028
The Journal of Physical Chemistw, Vol. 82,No. 18, 1978
A.
L. Capparelli, H. G. Hertz, and R. Tutsch
Le., am = 2.5 8,which seems unrealistic. On the other hand, strict agreement with the expected “classical” position m, i.e., an atomic pair distribution would demand n function between OH and CH3which is a 6 function. This would lead us to a rigid dimer molecule which, however, is conflicting with another observation. We are now going to explain this argument. In the classical cyclic dimer the OH-OH proton-proton separation is known to be x2.6 A. With the experimental OH-OH intermolecular relaxation rate this gives 7, = 15 ps. However, from the OD relaxation rate we had derived 7, = 8.2 ps (see section 4.1). Thus, both correlation times differ by about a factor 2. Moreover, they differ in the wrong sense, because the OH vector has the same directioh as the axis of the hypothetical rigid dimer. A vector in this direction should have the longest correlation time and for all other directions the correlation time should be equal or shorter, and, in particular, the intermolecular OH-OH proton-proton direction is perpendicular to the axis of the dimer. Now, the quadrupole coupling constant, which we had estimated to be 200 kHz, may be smaller, this would make the correlation time longer (see eq 1). However, we feel that this cannot account for the total effect. Therefore we conclude that there is a fairly fast bending or folding motion within the dimer. The hinge is approximately given by the OH-OH proton-proton axis, however, there should also be a certain degree of gliding of the OH hydrogen atom on the surface of a sphere represented by the oxygen of the CO group. Such a motion controls the reorientational movement of the OD vector fairly strongly and thus causes a shortening of the effective correlation time, which enters in eq 1,but it almost does not control the motion of the intermolecular OH-OH vector. This model is also in agreement with our finding for the system CH3COOH-C1,; wd have a folding of the dimer in both cases, however the degree of folding is less in the present system. The approach of the CH3 groups toward one another is not close enough as to produce a contribution to the intermolecular CH3-CH3 relaxation rate. This lesser degree of bending is also reflected by the chemical shift of the OH proton which is more downfield in the solvent CGH12 than observed in the system CH3COOH-CC14 We have included in Figure 8a the dotted line for a11in order to demonstrate the effect of the form of the solute-solute pair distribution functions. As already mentioned, this dotted curve corresponds to the uniform distribution with spin density ci. It should be remembered that there is indeed a certain contribution to the total methyl-methyl distribution which is probably essentially uniform. These are the methyl groups of those molecules which do not belong to the H-bonded pair partner. According to eq 3 the part of the first coordination number corresponding to these molecules is 0.2 and x2 = 0.1. The closest distance of approach of these CH3 groups toward the reference CH3 group should be similar to the figures given by the dotted curve in Figure 8a. However in the routine process of evaluation the presence of these particles has been neglected. Finally, in Figure 11 we show two configurations of maximum occurrence probability for the pair C6Hlz-acid. Now the model pair distribution function is a point-rod distribution function, no longer a rod-rod distribution function, As already mentioned, in the pure acid, x2 1,the polar group points away from the “dielectric hole” represented by the C d l 2 molecule (hatched area), whereas in the almost pure hydrocarbon (xz 0) this is not the case. In both cases we have shown one representative rod molecule, one of the other equivalent configurations has
-
I%-
\
\
/
Figure 10. Pair configuration of maximum occurrence probability for acetic acid in C6HI2 at mole fraction x2 = 0.1 as obtained from a suitably chosen model molecular pair distribution function: S = HO, I = CH,. The heavily drawn arrows represent our final result, the circles have radii equal to the closest distances of approach.
rod-rod model pair distribution function from the closest distance of approach yields pair configurations of maximum occurrence probability. These configurations are obtained from the aL,values (i,j= IS) with suitable circle constructions as has been explained elsewhere.ls The information consisting of three closest distances of approach between atoms (or representative groups) is then converted to the following three quantities: vector connecting centers of two rods (orientation and length) and S (dithe angle between this vector and the vector I rection of the rod) in the pair partner molecule. In this paper we shall not discuss the pair configuration of maximum occurrence probabilities for pure acetic acid. This has been done previously.2 As already briefly mentioned the pair configurations of maximum occurrence probability according to our findings are characterized by a fairly large OH-CH3 separation. The inert methyl groups tend to keep away as much as possible from the polar region formed by H-bonded acid molecules. These configurations may be considered as a link of extended chains, however statements concerning chains are outside the domain of the present method which only gives information in the language of pair distribution functions. The classical cyclic dimer of acetic acid was found not to play a dominant role in pure liquid acetic acid. In Figure 10 the circle construction is shown together with the resulting pair configuration of maximum occurrence probability. The figure is valid for an acid mole fraction x2 = 0.1. The closest distances of approach used are those shown in Figure 8a; aU corresponds to the dashed curve. From the geometry of the molecule we have an intramolecular IS separation rIs = 3.3 A. Two pair partner S vectors are drawn representing the molecule (the I rod). These two configurations are equivalent, they have the same occurrence probability because the pair distribution function must be self-consistent.lg Arrangements according to the two dotted arrows in principle also should occur with the same probability. However for other physical reasons, namely, the existence of special H-bonded structures, these configurations can be rejected as being dominant ones. In Figure 10 apart from the I S rod we have indicated the heavy atoms (C and 0) of the acid molecule by small circles. With dashed lines a pair partner in the classical cyclic H-bonded configuration with an oxygen-oxygen (C-O-H.-O=C) separation of 2.7 A has been drawn. One sees that there is fairly good agreement between the expected and the observed arrangement of the I S vector relative to the reference molecule. We find the OH proton to be closer to the methyl group than expected from the classical configuration. Our UIS was obtained with a steepness parameter n = 2; had we taken n = 1then the aIs separation would come out still smaller,
-
-
+
-
+
+
The Journal of Physical Chemistry, Vol. 82, No. 18, 1978 2029
’H-I3C Coupling Constants in Complexed CHCI, OH Y C H 3 ,
‘sH12 X2’1
OH
CgH12 X*ZO.l
Figure 11. Pair configurations of maximum occurrence probability between a cyclohexane (T) and an acid molecule in the limit of infinite dilution of CBHIP in the acid and in a state of moderate dilution of the acid.
been indicated by a rod which is interrupted. Acknowledgment. We thank Professor Seelmann-Eggebert for supplying us with a sample of C6H1Dl1. One of the authors (A. L. Capparelli) expresses his gratitude to the organizers of the “9. Internationales Seminar fur Forschung und Lehre in Verfahrenstechnik, Technischer und Physikalischer Chemie an der Universitat Karlsruhe” for the award of a fellowship. Financial silpport by the “Fonds der Chemischen Industrie” is gratefully acknowledged. References and Notes (1) H. G. Hertz and R. Tutsch, Ber. Bunsenges. Phys. Chem., 80, 1269 (1976).
V. Berg, H. G. Hertz, and R. Tutsch, Ber. Bunsenges. Phys. Chem., 80, 1278 (1976). A. Kratochwill and H. G. Hertz, J. Chim. Phys., 74, 814 (1977). H. J. Bender and H. G. Hertz, Ber. Bunsenges. Phys. Chem., 81, 468 (1977). L. W. Reeves and W. G. Schneider, Trans. Faraday Soc., 54,314 (1958). F. Conti and C . Franconi, Ber. Bunsenges. Phys. Chem., 71, 146 (1967). U. Jentschuva and E. Lippert, Ber. Bunsenges. Phys. Chem., 75, 782, 556 (1971). N. Tatsumoto, T. Sano, and T. Yasunaga, Bull. Chem. SOC.Jpn., 45, 3096 (1972). E. v. Goldammer and M. D. Zeidler, Ber. Bunsenges. Phys. Chem., 73, 4 (1969). A. Abragam, “The Principles of Nuclear Magnetism”, Oxford University Press, London, 1961. T. C. Farrar and E. D. Becker, ”Pulse and Fourier Transform NMR”, Academic Press, New York, N.Y., 1971. K. Engelsmann, H. G. Hertz, and M. D. Zeidler, 2. Phys. Chem. (Frankfurt am Main), 89, 134 (1974). 0. W. McCall, D. C. Douglas, and E. W. Anderson, Ber. Bunsenges. Phys. Chem., 67, 336 (1963). E. 0. StaiJskaland J. E. Tanner, J . Chem. Phys., 42, 288 (1965). M. D. Zeidler, Ber. Bunsenges. Phys. Chem., 69, 659 (1965). H. G. Hertz and M. D. Zeidler, “The Hydrogen Bond”, Vol. 111, P. Schuster, G. Zundel, and C. Sandorfy, Ed., North Holland Publishing Co., Amsterdam, 1976, p 1027. M. Gruner and H. G. Hertz, Adv. Mol. Relaxation Processes, 3, 75 ( 1972). H. G. Hertz, Ber. Bunsenges. Phys. Chem., 80, 950 (1976). H. G. Hertz and C. Radle, Ber. Bunsenges. Phys. Chem., 77, 521 (1973). M. Contreras and H. G. Hertz, Faraday Discuss., 64, 33 (1977). H. G. Hertz, B. Kwatra, and R. Tutsch, Z. Phys. Chem. (Frankfurt am Main), 103, 259 (1976). A. L. Capparelli, H. G. Hertz, B. Kwatra, and R. Tutsch, Z. Phys. Chem. (Frankfurt am Main), 103, 279 (1976).
Proton-Carbon 13 Coupling Constant in Complexed Chloroform J. P. Meille,+ J. C. Duplan, A. Brlguet, and J. Delmau” Laboratolre de Chimie Analytique I and Laboratoire de Spectroscopie et Luminescence, Universit6 Claude Bernard Lyon I, F 69627 Villeurbanne, France (Received November IO, 1977;Revised Manuscript Received April 14, 1978) Publication costs assisted by Universit6 de Lyon
The JlSC-lH variations of chloroform complexed by hexamethylphosphoric triamide (HMPT) are considered vs. the mole fraction of complexed chloroform. These data are determined by the usual method of chemical shift evolution with HMPT concentration and lead to the coupling constant value for the molecular edifice CHCl,/HMPT.
Introduction When chloroform is diluted in various solvents. medium effects alter the proton and carbon-13 chemical shifts1p2 and the coupling constant between these two Chemical shift and coupling constant changes are caused by the molecular associations which occur during the exchange and the observed values are averaged over molecular fractions of the free and complexed forms. Since the molecular fraction of the complexed state can be measured in the case of bimolecular association, it is possible to correlate the coupling constant with the equilibrium constant and we shall try to explain its Laboratoire de Chimie Analytique I. *Author to whom correspondence should be addressed at Laboratoire de Spectroscopie et Luminescence. 0022-3654/78/2082-2029$01 .OO/O
modifications through variations of the molecular structure of the ComPlexed molecule. Experimental Section A typical NMR study of complexes is given for the mixture of chloroform with hexamethylphosphoric triamide (HMPT).5 The equilibrium constant K can be obtained from the proton chemical shift evolution as a function of the concentration of HMPT. As an example, adding HMPT to a 5 X M solution of CHC13 in CS2 leads to K = 6.6 L/mol at 31 “C. Conversely knowledge of the equilibrium constant and the proton chemical shift permits calculation of the mole fraction PA of the complexed acceptor. In Figure 1are reported variations of pA (mole fraction of complexed chloroform) vs. 6H when the HMPT concentration varies as follows: (A) dilute solutions @ 1978 American Chemical Society
