The Journal of
Physical Chemistry
0 Copyright 1995 by the American Chemical Society
VOLUME 99, NUMBER 45, NOVEMBER 9,1995
LETTERS Molecular Clusters in Liquid tert-Butyl Alcohol at Room Temperature A. K. Karmakar, S. Sarkar, and R. N. Joarder* Department of Physics, Jadavpur University, Calcutta 700 032, India Received: March 22, 1995; In Final Form: May 16, I995@
The hexamer ring clusters for the average intermolecular structure of hydrogen-bonded alcohols, methanol, and ethanol at room temperature were proposed earlier. This average structure is shown to be true for liquid tert-butyl alcohol also through the analysis of available diffraction data.
Introduction In our previous communications',2 we have made systematic studies of the intermolecular structures of liquid hydrogenbonded alcohols, e.g., methanol and ethanol, through a combined analysis of available X-ray and neutron diffraction data at room temperature. This analysis showed that in monohydric alcohols there is a possibility of the presence of hexamer closed chains due to intermolecular hydrogen bonding. In this letter, we briefly report the case for liquid tert-butyl alcohol, and it is shown that at room temperature at least, the X-ray diffraction data on liquid tert-butyl alcohol3strongly suggest the formation of hexamer ring clusters in a distinct and dominant form. The possibility of a linear tetramer chain suggested earlier by Magini et aL4 for liquid methanol is not ruled out but surely appears less convincing as per our diffraction data analysis. A recent computer simulationSindicates the possibility of a linear chain having an average 10-12 monomers in parallel alignment. The study of the intermolecular structure of liquid tert-butyl alcohol is important in the sense that it brings out the effect of replacement of one methyl group by one hydroxyl group (neopentane tert-butyl alcohol) on the intermolecular structureS3Like neopentane, the tert-butyl alcohol molecule is a big molecule almost spherically symmetric except some asymmetry introduced by the hydroxyl group. In liquid neopentane the diffraction data could be explained satisfactorily on the basis of a hard-sphere center structure and Apollo type orientational
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Abstract published in Advance ACS Abstracts, July 1, 1995.
0022-3654/95/2099-16501$09.00/0
correlation between neighboring molecules.6 It therefore appears that for liquid tert-butyl alcohol also the center structure should be almost hard-sphere (HS) like3 and the molecular structure factors should be calculable in terms of specific intermolecular structural units.
Intermolecular Structure In the following paragraphs we compute the tert-butyl alcohol intermolecular structure on the following assumptions: (i) the monomers in the liquid state at room-temperature form distinct model clusters, and the clusters are orientationally uncorrelated;'-* (ii) there is a well-defined geometric center of the molecule, and the center structure is well approximated by a HS model. From assumption (i) we can construct an intermolecular cluster structure function H,(k)I,* and compare the same with the experimentally available distinct structure function H ~ ( / c ) , ~ containing intermolecular informations. If the assumed cluster model is correct, then &(k) H,(k)for moderate and large k values.',2 In this method the X-ray results are preferred over the neutron results as the former simplify the intermolecular picture better in terms of the specific groups of scattering units.'s2 We consider the hexamer ring clusters as the probable average intermolecular structural association for tert-butyl alcohol monomers in liquid state. In the hexamer ring cluster (Figure la) all 0-H's with an H bond are in one plane and R-C-0 (R CH3) in a molecule rotates in a perpendicular plane about the 0 - H axis of that molecule. The intermolecular 0-0
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0 1995 American Chemical Society
Letters
16502 J. Phys. Chem., Vol. 99, No. 45, 1995
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Figure 1. (a) Hexamer ring cluster of liquid rerr-butyl alcohol. (b) Tetramer open chain cluster of liquid rut-butyl alcohol.
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TABLE 1: Intermolecular Cluster Parameters (Hexamer) 0-0 bond 0-0 vibrational length (A) factor (AY
2.78 (2.74)
0.1 13 (0.08)
rotation angle (deg) of C's about OH axes R's about CO axes
(C1)273.2 (C2)13.4 (R1)334.5 (R2)216.1 (C3)346.0 (C4)1.2 (R3)0.9 (R4)124.9 (C5)219.6 (C6)315.0 (R5)354.8 (R6)11.6
Root-mean-squaredeviation of atom-atom distance; values in the parentheses are from ref 3. distance, the rotation angles of C's,and twist angles of R's are determined by the method of x2 fitting between kHc(k) and experimental k&(k) from moderate to large k values. The vibrational factors are assumed proportional to the mean-square amplitude of displacement and the constant of proportionality (no) also determined by x2 fitting. It is however to be noted that we have redefined the intramolecular structure of tert-butyl alcohol by considering separately the H site associated with the OH bond just as we did in our earlier works with methanol and ethanol',* and recalculated the molecular structure function Hm(k). The OH bond length and COH bond angle are 1.09 8, and 125", respectively, which are in reasonable agreement with the values obtained for methanol and ethanol. The experimental &(k) function was then obtained by subtracting redefined Hm(k) function from the experimental total structure function H(k). The intermolecular parameters for hexamer model are depicted in Table 1. In Figure 2a we show the kHc(k) function of hexamer model against the experimental kHd(k) function. The agreement is quite convincing. We have also considered the linear tetramer open-chain cluster (Figure lb) for tert-butyl alcohol monomers that was suggested by Magini et al. for liquid methanol at room temperature4 and also somewhat endorsed recently by computer simulation work.5 The model is exactly similar to that for methanol used by Magini et al. with methyl groups in tetrahedral locations around carbon atoms without any twist. The corresponding agreement of kHC(k)function with k&(k) function (Figure 2a) is much less convincing. The difference between k&(k) and kHc(k) functions in the low and intermediate k region is due clearly to the intercluster interactions. To test the model structure further, we resort to assumption (ii) above. We take the center of the molecule at the central carbon atom and take the center structure given by the HS model
Figure 2. (a) (.* *) Experimental kH&).3 (-) kH,(k) of hexamer ring model. (- - -) kH,(k) of tetramer open-chain model. (b) Experimental H(k).3 (-) H ( k ) of hexamer ring model. (- - -) H ( k ) of tetramer open-chain model.
e-.)
of approximate core diameter. The distinct structure function, Hd(k), is given by',2 Hd(k)
= Hc(k)
+ F*"(k)[Sc(k)
- F,(k) - l1
(l)
where Sc(k) is the center structure function and in the present case it is that due to HS model on Percus-Yevick (PY) theory' with core diameter 4.95 8,; F2,(k) and F3(k) are respectively the uncorrelated intermolecular form factor and the structure factor of molecular center pairs within the cluster. The total structure function, H(k), is given by
H(k) = Hm(k)
+ Hd(k)
(2)
In Figure 2b we show the calculated H(k)'s for hexamer closedring and linear tetramer open-chain cluster models along with Narten's H(k) data.3 The agreement with the hexamer cluster is evidently better. Both the models approximately produce the inner peak (-0.8 though its position is better obtained in the hexamer ring cluster model. The more convincing comparison is made by taking the real space version of eq 1. Thus, the radial distribution function, Gd(r), is given by Gd(r) = 1
+ (2x@r)-'hmkHd(k)Sin(kr) dk
(3)
where e is the density of liquid tert-butyl alcohol. The calculated Gd(r)'S for two cluster models are compared with the expenmental data3 (Figure 3). The function Gd(i) mainly identifies the peak locations of the dominant site-site correlations. It is clear that the hexamer ring cluster represents a better approximation to reality. It is however true that the linear tetramer open-chain cluster also produces the general features of Gd(r) curve but neither the peak heights nor the peak positions are produced well. General Remarks Thus using Narten's X-ray data, we have shown that in the liquid state at room temperature the tert-butyl alcohol monomers
J. Phys. Chem., Vol. 99,No. 45, 1995 16503
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Figure 3. (.**) Experimental Gd(r).3 (-) Gd(r)of hexamer ring model. (- - -) Gd(r1)of tetramer open-chain model.
are seen to form hexamer ring clusters in abundance in preference to linear tetramer chain clusters. This was shown to be true for other monohydric alcohols also.'%2This cluster formation is of course an average one. Large local and instantaneous deviations from this average configuration are not ruled out. We have used Narten's data to test the cluster model. These are old data but to our knowledge quite reliable. The recent X-ray diffraction works on the mixture of tert-butyl alcohol and water is available. The data with pure tert-butyl alcohol agrees quite well with the data of Narten. Dore et aL9 did not publish results of a neutron diffraction study. To our knowledge no neutron diffraction work has been reported so far. The reference interaction site model (RISM) calculations'0 with the van der Waals model fail to reproduce the experimental data. Calculations for hydrogen-bonded liquids' I have yet to be extended to liquid tert-butyl alcohol. The results of computer simulations'* are also not available for pure rert-butyl alcohol. So a direct comparison of our cluster model results with results of statistical mechanical calculations is not possible. The computer simulation of a highly dilute mixture of rertbutyl alcohol and water (3 mol %) has been reported'* but not of pure liquid tert-butyl alcohol. In this low concentration, out of 216 molecules only 7 were tert-butyl alcohol molecules. The interaction potential between tert-butyl alcohol dimers was assumed to be that from molecular orbital (MO) calculations. The atom-atom radial distribution functions and also the pair interaction distribution functions show that there is no hydrogen bonding between rert-butyl alcohol molecules. This result is in contradiction with diffraction analysis results of pure liquid. The results for seven tert-butyl alcohol molecules at so low
concentration is likely to be different. The potential model for tert-butyl alcohol dimers where hydrophobic group is so dominating is also expected to be quite complex, more complex than that for methanol etc. The essential requirement of the computer simulation with pure liquid tert-butyl alcohol is therefore modeling the interaction potential accurately. A recent computer simulation on liquid methanol, however, gives little evidence to support a planar assembly of oxygen sites or the formation of hexamer rings.5 This is of course quite surprising in view of the results deduced here from diffraction analysis. We however recall that a similar situation exists in the case of liquid hydrogen fluoride. The neutron diffraction data on liquid hydrogen f l u ~ r i d e ~give , ' ~ quite good indications of the formation of hexamers, but such structures are never shown in computer simulation work.I4 The hexamer rings are evidently present in gaseous state.I5 The various physical arguments which we had put forward in favor of hexamer ring clusters in liquid methanol' are also true for liquid tert-butyl alcohol structure. Anyway, we believe that the intermolecular association for liquid tert-butyl alcohol deduced here is quite significant and could serve as useful guide for mixtures and other studies.
Acknowledgment. The authors gratefully acknowledge the financial support by CSIR and DST,Government of India. References and Notes (1) Sarkar, S.; Joarder, R. N. J . Chem. Phys. 1993, 99, 2032. (2) Sarkar, S.; Joarder, R. N. J . Chem. Phys. 1994, 100, 5118. (3) Narten, A. H.; Sandler, S. I. J . Chem. Phys. 1979, 71, 2069. (4) Magini, M.; Paschina, G.; Piccaluga, G. J . Chem. Phys. 1982, 77, 205 1. (5) Svishchev, I. M.; Kusalik, P. G. J . Chem. Phys. 1994, 100, 5165. (6) Rao, R. V. G.; Joarder, R. N. J . Phys. C: Solid State 1981, 14, 4745. (7) Wertheim, M. S. Phys. Rev. Lett. 1963, 10, 321; J . Math. Phys. 1964, 8, 927. ( 8 ) Nishikawa, K.; Iijima, T. J . Chem. Phys. 1990, 94, 6227. (9) Dore, J. C. J. Mol. Struct. 1991, 250, 193. (10) Narten, A. H.; Sandler, S. I.; Rensi, T. Faraday Discuss. Chem. SOC.1978, 66, 39. (11) Bausenwein, T.; Bertagnolli, H.; David, A,; Goller, K.; Zweier, H.; Todheide, K.; Chieux, P. J . Chem. Phys. 1994, 101, 672. (12) Tanaka, H.; Nakanishi, K.; Touhara, H. J . Chem. Phys. 1984, 81, 4065. (13) Deraman, M.; Dore, J. C.; Powles, J. G.; Holloway, J. H.; Chieux, P. Mol. Phys. 1985, 55, 1351. (14) Klein, M. L.; McDonald, I. R. J . Chem. Phys. 1979, 71, 298. Coumoyer, M. E.,; Jorgensen, W. L. Mol. Phys. 1984, 51, 119. (15) Jantzen, J.; Bartell, L. S. J . Chem. Phys. 1968, 50, 3611. Jp9508315
