2560
G. Brink, C. Campbell, and L. Glasser
Dielectric Studies of Molecular Association. Concentration Dependence of the Dipole Moment of 2,3,4-frimethyl-3-pentanol in Solution George Brlnk, Colin Campbell, and Leslie Glasser' Department of Chemistry, Rhodes University, Grahamstown, 6 140 South Africa (Received February 10, 1976) Publication costs assisted by Rhodes University
The permittivities a t 2 MHz and 25 "C for 2,3,4-trimethyl-3-pentanol in cyclohexane, carbon tetrachloride, and benzene solutions have been measured over the entire alcohol concentration range. By use of the Kirkwood-Frohlich equation the apparent dipole moments of the alcohol as a function of concentration have been evaluated; using the concentration dependence and infrared absorption results, the nature of the proposed associated species are considered. Monomer-dimer-trimer and monomer-dimer-tetramer equilibrium models have been fitted to the dipole moment data and to nuclear magnetic resonance chemical shift data over the whole concentration range.
Introduction We have previously discussed the permittivity data a t 25 "C for 1-octanol, 2-octanol, 3-octanol, and 4-octanol in the solvents cyclohexane, carbon tetrachloride, and benzene.1,2 The apparent dipole moments of the solutions were calculated from the measured permiltivities, using the KirkwoodFrohlich equation. The concentration dependence of the dipole moments, together with infrared absorption results, gives information on the molecular nature of the associated species which form as the solute concentration is increased. We have concluded that the least complex equilibrium description consists of monomer-small high dipole moment polymer-low dipole moment cyclic polymer-high dipole moment polymers. In benzene the formation of the cyclic polymer is repressed because the monomer and high dipole moment open polymers are stabilized by an interaction with the solvent. By contrast, the cyclic species is favored in cyclohexane solutions where the interaction of alcohol and solvent molecules is small. In the present study we consider the association behavior of 2,3,4-trimethyl-3-pentanol in cyclohexane, carbon tetrachloride, and benzene solutions over the whole concentration range. The hydroxyl group of this alcohol is sterically hindered and it is expected that the association behavior may differ from that of the simpler alcohols. A number of workers have studied the NMR chemical shifts of these sterically hindered alcohols because it was thought that the only associated species over the whole concentration range would be a dimer; this makes equilibrium constant determinations e a ~ i e rThis .~ idea seems to originate from infrared studies where it is found that the low frequency peak near 3350 cm-l, which is usually attributed to polymers larger than the dimer, is absent for some hindered alcohol^.^ However, a single associated species would result in wappP increasing or decreasing monotonously as a function of concentration, contrary to the observations presented here. Experimental Section and Results The purification of the alcohol (Fluka, purum grade) and solvents, and the permittivity and infrared absorption measurements have been described previous1y.l Infrared spectra shown in Figure 2 were recorded on a Beckman IR-8 spectrophotometer; frequencies are accurate to f 5 cm-l for the -OH stretching vibrations. Additional results described in the The Journal of Physical Chemistry, Vol. 80, No.23, 1976
text were recorded on a Perkin-Elmer Model 180 spectrophotometer and are accurate to fl cm-l. Low temperature spectra were obtained using a Beckman VLT-2 cell and TEM-2 controller. Chemical shift data were obtained using a Perkin-Elmer R12 nuclear magnetic resonance spectrometer; the sample temperature was 35 "C. Hydroxyl proton shifts were measured relative to a methyl resonance but the values we give are relative to TMS. The low-frequency (2 MHz) permittivities for 2,3,4-trimethyl-3-pentanol in cyclohexane, carbon tetrachloride, and benzene a t 25.0 "C are given in Supplementary Tables 1-111 (see paragraph at end of text regarding supplementary material). Dipole moments were calculated as beforel and are also given in the supplementary tables. Figure 1 shows the concentration dependence of gaPp2 for the alcohol in (a) cyclohexane, (b) carbon tetrachloride, and (c) benzene solution, with a logarithmic scale along the abscissa. The line through data points represents a least-squares fit for an equilibrium model as discussed below. The arrows indicate the concentrations at which the infrared spectra depicted in Figure 2 were recorded. Chemical shift data for the alcohol in carbon tetrachloride solutions over the whole concentration range at 35 "C are given in Supplementary Table IV. Figure 3 shows the concentration dependence of G(ppm) using the logarithm of solute mole fraction on the abscissa; the line through the data points represents a least-squares fit for an equilibrium model. The infrared spectra of 2,3,4-trimethyl-3-pentanolin n hexane at low temperatures is shown in Figure 4. The solution concentration was 0.03 M a t 25 "C. The solvent n-hexane was chosen because of its low freezing point. Discussion
The concentration behavior of haPp2of 2,3,4-trimethyl-3pentanol in the three solvents, as shown in Figure 1,is very similar to that of 1-,2-, 3-, and 4 - 0 c t a n o l s , ~the ~ ~high concentration region excepted. The association sequence, monomer-small high dipole moment polymer-low dipole moment cyclic polymer, readily accounts for the observed behavior. The initial flat region in cyclohexane solution can be interpreted as the consequence of the simultaneous formation of a small high dipole moment species and a cyclic species, as discussed before.1,2 As before, association is repressed in
2561
Dielectric Studies of Molecular Association
3.20
2.2
r
C
I
3.00.
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2.20
-
2.00
.
1.80
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-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
log (C/molI-1)
Figure 1. paPp2 vs. the logarithm of molar solute concentration for 2,3,4-trimethyl-3-pentanol in (a)cyclohexane, (b) carbon tetrachloride, and (c) benzene solutions at 25.0 "C.The lines through the data points represent the best least-squares fits: 1-2-3 model for cyclohexane solutions and 1-2-4 model for carbon tetrachloride and benzene solutions. The arrows indicate the concentrations at which the infrared spectra in Figure 2 were recorded.
'i
80
c
60
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-
3634
yy
It
bl
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Ill
t
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Figure 2. infrared spectra at 25 OC of 2,3,4-trimethyl-3-pentanol in (a) cyclohexane, (b) carbon tetrachloride, and (c) benzene at concentrations (I) 0.0107, (11) 0.0339, and (Ill) 0.0650 M, using a 1-mm sample cell and Beckman IR 8 spectrophotometer.
benzene solutions because of the stabilization of the monomer by the solvent. The absence of a rise in kapp2at high concentrations distinguishes this sterically hindered alcohol from others we have studied.'v2 We have previously suggested that the high dipole moment species, at high concentrations, involves an interconnection of chains so that end groups of one chain join along a neighboring chain at an acceptor atom which is already involved in hydrogen bonding.2 Space filling models show that it is not possible for two hydroxyl protons to bond
to a single hydroxyl oxygen acceptor in the sterically hindered 2,3,4-trimethyl-3-pentanol molecule. The solvent effect on polymer formation is well illustrated in the infrared absorption spectra in Figure 2. The peak in the 3500-cm-l region is most apparent in cyclohexane solutions, where monomers are not stabilized, and at these concentrations is virtually absent in benzene solution where there is significant solute-solvent interaction. An interesting feature of the infrared spectra is that no new polymer peak develops in any of these three solvents as the concentration is increased; in solutions of the other octanols studied another peak develops in the 3350-cm-l region and is linked with a decrease in kappa.However, for dilute 2,3,4-trimethyl-3-pentanol in carbon tetrachloride, the polymer peak occurs at 3518 cm-l a t 25 "C; for pure solute the peak occurs at 3490 cm-l. As the solute concentration is increased the peak shifts between these two limits but no new peak occurs. We are thus led to conclude that the dimer absorption (or small high dipole moment polymer) and the cyclic (low dipole moment) species absorptions overlap at room temperature. Presumably, because of steric hindrance, the hydrogen bonds in the cyclic species are not much stronger than in the dimer and much weaker than in the cyclic species in, e.g., 1-octanol. The effect of temperature on the absorption of a dilute solution of 2,3,4-trimethyl-3-pentanol in n-hexane is shown in Figure 4. Before considering the effect of temperature, the splitting of the monomer peak should be noted. The splitting is less obvious in the spectra presented in Figure 2 because of the low instrumental resolution. This splitting is not due to the end group of a dimer since it persists even at the lowest concentrations and the relative size of the two halves is quite insensitive to an increase in solute concentration. Its origins are not understood although it might represent two configuration of a rotational isomer or result from Fermi resonance with a combination band. As previously argued, the peak near 3500 cm-l, a t room temperature, consists of two overlapping polymer absorptions. As the temperature is lowered, both of these absorptions shift to lower frequencies, but the peak representing the cyclic species evidently moves to a greater extent. Splitting of the peaks is observed at about -55 "C and at lower temperatures The Journal of Physical Chemistry, Vol. 80, No. 23, 1976
G. Brink, C. Campbell, and L. Glasser
2582
2.20
.
2.00. 1-60.
1
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8
1.00
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LOG RLCOHOL MOLE FRRCTION
Flgure 3. Proton magnetic resonance chemical shifts vs. the logarithm of solute mole fraction for the hydroxyl proton of 2,3,4-trimethyl-3-pentanol in carbon tetrachlorlde solution at 35 O C . The line through the data represents the least-squares fit for a 1-2-3 model: K2 = 7.80 f 3.23,K3 = 20.54f 9.85, 6, = 0.622f 0.005,82 = 0.789 f 0.167, 8 3 = 5.234f 0.379, standard deviation = 0,0089. 100
1
however, unlikely in view of the studies of Johari and Dannhauser5 who have shown that the dipole moments of undiluted, sterically hindered alcohols, for example, 3,4dimethyl-3-hexanol, decrease as the temperature is lowered to -100 O C . By contrast, the dipole moments of most unhindered alcohols increase as the temperature decrease^.^ As we have suggested? the end groups of these high dipole moment species are stabilized by interconnection of chains, resulting in some hydroxyl oxygen groups aceepting two hydroxyl protons. Evidently this form of bonding is not possible in the sterically hindered alcohols and the end groups are consequently not stabilized; the species dominant a t high concentrations (or low temperatures) is therefore of low dipole moment, probably cyclic. Thus, to account for the low temperature infrared spectra in Figure 4 it may be necessary to assume significant concentrations of more than one cyclic species. In order to test our model of monomer-high dipole moment species-low dipole moment species being the only important associated species over the whole concentration range of this hindered alcohol, we apply the general equation used beforel-2
and Wavmumbar/cm-l
Figure 4. Infrared spectra of 2,3,4-trimethyl-3-pentanol in +hexane (0.03 M at 25 "C) at various temperatures using a 1-mm sample cell and Perkin-Elmer Model 180 spectrophotometer.
the low frequency peak dominates the absorption. Another interpretation is that a low frequency peak develops at low temperatures independently of the overlapping peaks which occur a t room temperature. This new peak would then represent either another cyclic, low dipole moment species, or a high dipole moment species as normally occurs in nonhindered alcohols. The existence of this high dipole moment species is, The Journal of Physical Chemistry, Vol. 80, No. 23, 1976
where i refers to the ith species, Ki the ith equilibrium constant, and c the total concentration. Table I gives the results of least-squares curve fitting for 1-2-3 and 1-2-4 models; the best curves are drawn through the experimental data in Figure 1. In some cases the Newton-Raphson iterative procedure2 did not converge and the parameters given are not necessarily the best; these parameters are enclosed in parentheses. The error on each parameter is given to one standard deviation. The standard deviations of the fits, u, show that the 1-2-4 model fits best for carbon tetrachloride. In benzene and cyclohexane solutions the situation is less clear; in each case the
Dielectric Studies of Molecular Association
2563
TABLE I: Parameters from Least-Squares Fit for Two Models for 2,3,4-Trimethyl-3-pentanolin Solution at 25 "C Solvent Cyclolhexane Carbon tetrachloride
K2' K3
gz ab
@12
Kz K4
gz U
Monomer-Open Dimer-Closed Trimer 2.185 f 0.02d 2.325 f 0.018 1.339 f 0.538 4.292f 2.013 1.856 f 0.803 5.427 f 3.486 1.204f 0.033 1.617 f 0.115 0.064 0.027
Benzene 0) (2.162)c (0.018) (0.104) (11.4) (0.047)
(g3 =
Monomer-Open Dimer-Closed Tetramer (g4 = 0) (2.102)c 2.261 ic 0.022 2.171 & 0.012 (249.9) 27.59 f 9.93 0.113f 0.069 (14335) 206.2 f 138.0 0.0381 f 0.018 (1.09) 1.176 f 0.013 2.126 f 0.475 (0.039) 0.023 0.039
a Equilibrium constants based on units of moles per liter. Standard deviation of fit calculated from pcalcd2 and fiobsdz. Convergence not achieved.
least-squares fit of one of the two models used failed to converge. However, the relative values of the equilibrium constants for the alcohol association in the three solvents reflect the qualitative behavior of the papp2curves: association is hindered in benzene solutions, less so in carbon tetrachloride solutions, and occurs readily in cyclohexane solutions. The chemical shift data in C C 4 solution shown in Figure 3 and taken from Supplementary Table IV may be analyzed in much the same way as the dipole moment data, using the Gutowsky-Saika equationq6 The relevant equations are then
and c = C iKi(cl)i
where 6 is the observed chemical shift and 6, the chemical shift of the ith species. Because the results were obtained at 35 "C (the temperature a t which the permanent magnet of the spectrometer is thermostatted) the concentrations are given in mole fraction units rather than in moles per liter and consequently the quantitative results cannot be directly compared with the dipole moment data. A good fit was achieved
for the 1-2-3 model and the best calculated curve is drawn through the experimental data in Figure 3. We were, however, unable to achieve convergence with the 1-2-4 model, even though this was the preferred model for C C 4 solutions from the dipole moment results. We may attribute this either to the inherent uncertainties of curve fitting or to the possibility that both trimers and tetramers exist at high solute concentrations but that the trimer is the favored species a t higher temperatures. Least-squares fits for simple 1-2,1-3, and 1-4 models gave significantly poorer fits as expected. The parameters for the best 1-2-3 fit are given in the figure caption of Figure 3. Even though the chemical shift data are of high quality, the uncertainties in the values of K2, K3, 62, and 63 are substantial; this can be expected to be a usual feature of the generally unstructured chemical shift data. Conclusions The study of a sterically hindered alcohol has been rewarding in view of the relative simplicity of its self-association behavior at room temperature. We have shown that the dipole moment and NMR data are well represented, over the whole concentration range by a monomer-open dimer-cyclic polymer model. The main difference between this and structurally simpler alcohols is its inability to form high dipole moment associated species a t high concentrations. We consider this to be due to the inability of chains to form interconnected networks and thereby stabilize the end group. Acknowledgments. We wish to acknowledge the assistance of the South African Council for Scientific and Industrial Research in the purchase of equipment used in this work, and to the South African Coal, Oil and Gas Corp. Ltd. (S.A.S.O.L.) for support of the research upon which this paper is based. Supplementary Material Available: four tables containing dielectric data for 2,3,4-trimethyl-3-pentanol in the solvents cyclohexane, carbon tetrachloride, and benzene at 25.0 "C and chemical shift data for the same alcohol in carbon tetrachloride a t 35 "C (4pages). Ordering information is available on any current masthead page. References a n d Notes (1) C. Campbell, G. Brink, and L. Glasser, J. Phys. Chem., 79, 660 (1975). (2) C. Campbell, G. Brink, and L. Glasser, J. Phys. Chem., 80,686 (1976). (3)J. C.Davis and K. K. Deb, Adv. Magn. Reson., 4,201 (1970). (4)F. A. Smith and E. C. Creitz, J. Res. Nati. Bur. Stand., 45, 145 (1951). (5)G. P. Johari and W. Dannhauser, J. Phys. Chem., 72, 3273 (1968). (6)H. S.Gutowsky and A. Saika, J. Chem. Phys., 21, 1688 (1953).
The Journal of Physical Chemistry, Vol. 80, No. 23, 1976
