The Journal of
Physical Chemistry
~
Registered in US.Patent Office
0 Copyright, 1981, by the American Chemical Society
VOLUME 85, NUMBER 5
MARCH 5,1981
LETTERS ‘H and *H NMR Study of Isopropylbenzene Ring Motions in the Supercooled Liquid State E. Arndt and J. Jonas* Department of Chemlstry, School of Chemical Sciences, Unlverslty of Illlnois. Urbana, Illinois 6 180 1 (Received: November 24, 1980; In Flnal Form: January 19, 1981)
The temperature dependence of the proton spin-lattice relaxation times, TI, of the ring nuclei of isopropylbenzene-d7has been measured as a function of isotopic dilution in perdeuterated isopropylbenzene in the supercooled liquid region. The shear viscosity increases by a factor of 2 X lo4 over the temperature interval from -65 to -132 “C. The intramolecular and intermolecular contributions to the proton T I of the ring nuclei have been separated. The finding that the molecules lose the rotational freedom at a much slower rate than their translational mobility provides information about the nature of the anomalous behavior of the viscosity of isopropylbenzene in the supercooled liquid state.
As a part of our systematic investigation of the transport and relaxation processes in liquids,l we have started a series of studies aimed at improving our understanding of the dynamic structure of viscous liquids2l3(7 I1P).With this long-term goal in mind, we present a study of ring motions in isopropylbenzene in the supercooled liquid region. The finding of a discontinuity in the viscosity behavior4 in supercooled isopropylbenzene provided the main motivation for the present experiments. In their studies of viscosity behavior of supercooled liquids, Barlow et al.4 have noted deviations from the Fulcher equation6 (1)J. Jonas in “Proceedings of the NATO ASI, High Pressure Chemistry”, H. Kelm, Ed., D. Reidel, Dordrecht, 1978,pp 65-110. (2)J. Jonas and E. Arndt, J. Magn. Reson., 32, 297 (1978). (3)M. Wolfe and J. Jonas, J . Chem. Phys., 71,3252 (1979). (4)A. Barlow, J. Lamb, and A. Matheson, Proc. R. SOC.London, Ser. A , 292,322 (1966). 0022-3654/81/2085-0463$01.25/0
In 7 = A
+ B / ( T - To)
(1)
where A , B , and Toare constants. For some molecules, including isopropylbenzene, a discontinuity a t the temperature Tk was found in their viscosity behavior. Below Tk,eq 1fits the viscosity data with one set of constants, whereas above Tk,a different set of constants must be used. For example, the Tkis 171 K for isopropylbenzene. This deviation was initially interpreted as a clustering phenomenon. A later paper by Davies and Matheson: however, presented an analysis based on rotational motions, using the principles of the free volume theorya7 They described the transition from the high- to the low-ternperature viscosity behavior as a complete quenching of free (5)G.Fulcher, J. Am. Ceram. SOC.,8, 339 (1925). (6)D. Davies and A. Matheson, J. Chem. Phys., 46, IO00 (1966). (7)M. Cohen and D. Turnbull, J. Chem. Phys., 31,1164(1959).
@ 1981 American Chemical Society
464
The Journal of Physical Chemlstry, Vol. 85, No. 5, 1981
Letters
: 5.0
1°-4,5 ‘“4,5
5,O
5.5
6,O 6,5 1 0 ~( O K1) ~
7.0
7,5
Flgure 1. The proton spin-lattice relaxation time, T , , of isopropylbenzene-d, Is given by A. The symbol 0 denotes the T , of 0.25 mole fraction of isopropylbenzene-d, in perdeuterated isopropylbenzene. The dotted line represents the intermolecular contribution; the full llne represents the intramolecular contribution to the proton relaxation rate. T, indicates temperature for the discontinuity‘ In the temperature behavior of viscosity.
rotation. Thus, in the low-temperature region, rotation could take place only as a result of translation. Since a translation step may or may not lead to a rotation step, the situation can be described by 7 D 5 78, where TD is the diffusion correlation time and 7 8 is the reorientation correlation time. Since the NMR relaxation experiments allow us to obtain information about motions at the molecular level, we thought it worthwhile to investigate the rotational and translational motions of the isopropylbenzene molecules, focusing specifically on the motion of the ring. To our best knowledge, this is the first isotopic dilution study in a supercooled nonassociative liquid. Selectively deuterated samples of isopropylbenzene-d7 (deuterated chain), isopropylbenzene-d5(deuterated ring), and perdeuterated isopropylbenzene were prepared by the syntheses given in ref 8-10. The isopropylbenzene-d, proton spin-lattice relaxation times were measured at 60 MHz over a temperature range of -65 to -132 “C at 0.25, 0.50,0.75, and 1.0 mole fraction of isopropylbenzene-d7in perdeuterated isopropylbenzene. The relaxation rates were extrapolated to infinite dilution, with the intra- and intermolecular contributions being separated by use of the method of Powles and Figgins-l’ The results are given in Figure 1. For clarity sake, only the experimental proton TI data for the 1.0 and 0.25 mole fractions are shown in Figure 1 because the experimental T1 values for the intermediate 0.5 and 0.75 mole fractions parallel the Tl values given. The gap in the experimental data around 161 K reflects problems with crystalization. This instability region, which is very much a function of purity, has been observed and discussed in detail by Kishimoto et al.12 in their calorimetric study of isopropylbenzene. However, we are confident that our low-temperature measurements are accurate because samples with different thermal history still yield T1 values reproducible to within &5%. A qualitative inspection of Figure 1 reveals several interesting features. First, the “discontinuity” temperature Tk is approximately at the minimum of T1 (UT N l ) , in(8) E. Kline, B. Campbell, and E. Spaeth, J. Org. Chem., 24, 1781 (1959). (9)R.Zawadzki and H. Kwart, Bol. Znst. Quim. Univ. Nac. Auton. Mez., 21,259 (1969). (10)W . Bissinger and F. Kung, J. Am. Chem. SOC.,69, 2158 (1947). (11)J. Powles and R. Figgins, Mol. Phys., 10, 155 (1966). (12)K. Kishimoto, H.Suga, and S. Seki, Bull. Chem. SOC.Jpn., 46, 3020 (1973).
5,5
6,O
1 0 ~(OK) 1 ~
Figure 2. The T , data for the ring deuterons in lsopropylbenzene-d, as a function of temperature. The full line representsthe fit obtained by using the Cole-Davidson distrlbutlon of correlation times.
dicating motions occurring with a correlation time of -2 X lo4 s. Secondly, and most significant, below Tk the intermolecular contribution to the ring proton relaxation rapidly decreases in comparison to the intramolecular contribution. Although the dependence of Tl on correlation time is mechanism dependent and the motions are anisotropic, we may safely assume that a separation of this magnitude reflects a real difference in the correlation times. Thus, at the lower temperatures, 7~ > r8. Indeed, the proton relaxation is very rapidly dominated by the intramolecular interaction. This appears to contradict the predicted behavior6based on the viscosity results (i.e., rD I
In order to describe the proton intramolecular relaxation behavior, we had to assume a distribution of correlation times. Because it results in a closed expression for Tl, the Cole-Da~idson’~ distribution has proven convenient for describing NMR relaxation data. The solid line in Figure 2 represents such a fit to the intramolecular Tl values. The distribution
=o
7 > 7 0
is characterized by the maximum cutoff time, T ~and , the distribution width parameter, P. It is applied to NMR experiments through the Kubo-Tomita formalism14
T1-l = C [
1
-TG(T)d T 1 + W2T2
where C is the interaction constant, and is equal to (3/40). (e2qQ/h)2 for deuterium (asymmetry parameter taken to be zero), and (3/10)y4h2/r6for proton. Performing the integrals in eq 3 gives15
c
Tl-l = CtJ
[
3
sin (/3 arctan w0) 2 sin (/3 arctan 2 w 0 ) (1 + W2T02)fl/2 (1 + 402T02)s/2 (4)
+
is taken to be the average correlation time given by 7 8 = pro. As with other supercooled liquids? it is possible to fit the relaxation data with a simple Arrhenius temperature 78
~
~
~~~~~
(13)D.Davidson and R. Cole, J. Chem. Phys., 19, 1484 (1951). (14)R. Kubo and K. Tomita, J.Phys. SOC.Jpn., 9,888 (1964). (15)S.Roeder, E.Stejskal,and W. Vaughan, J.Chem. Phys., 43,1317 (1965).
The Journal of Physical Chemistty, Vol. 85, No. 5, 1981 405
Letters
to the intermolecular proton Tl data. For comparison, we
also include the reorientational correlation time rR(A) 10calculated by using the viscosity modified Debye equa-
-
10-6
t-
,0-li5
I 5.0
I 5.5
I 6.0
I
I
6.5
7.0
1J
75
1 0 ~( O K1) ~
Figure 3. The temperature dependence of the correlation times: TO (full line), obtained from proton Intramolecular T i data: rt (dashed line), obtained from the Intermolecular proton T i data. The symbols A represent rRcalculated by uslng a modified Debye equation with parameter K = 0.2 (for details, see the text). TMrepresentsthe melting point.
dependence of re, even in the high-temperature region. Consequently, we use a function of the form re = A exp[B/(T - To)] (5) where A, B, and ro are constants. The intramolecular proton Tl data are well described in terms of eq 4 by using the distribution width = 0.9. In order to provide an independent check that the isotopic dilution technique can be applied in this specific study, we also present the deuteron Tldata at 9.2 MHz of isopropylbenzene-d6in Figure 2. The ring deuteron relaxation times reflect only the reorientational motions of the ring with no contribution due to the side-chain motion. We realize that proton Tl and deuteron Tlreflect to a different extent the anisotropy of the ring motion but for the qualitative discussion, we may neglect such a difference. It is satisfying to find that the deuteron T1 can also be described by the ColeDavidson distribution of correlation times by using the same parameters as for the intramolecular proton T1 data. The solid line in Figure 2 represents such a fit. We realize that calculation of the correlation times for the reorientational and translational motion of the isopropylbenzene molecule from the present NMR data involves a number of assumptions. However, for the purpose of a general discussion of the nature of the viscosity behavior in supercooled isopropylbenzene, we present Figure 3 which gives the reorientational correlation time re,which is the average correlation time (eq 4), as obtained from the intramolecular proton Tldata. The translational (diffusion) correlation time, rt, is calculated by applying Torrey’s isotropic jump diffusion modells in the large jump limit
tion1’J8 with the parameter K = 0.2. The viscosity values as given by Barlow et al.4 were used in the calculation. The value of the parameter K , which reflects the coupling between the rotational and translational motions, is estimated on the basis of those K values obtained for a series of monosubstituted benzenes as studied previously in our lab~ratory.’~ At higher temperatures, the agreement between T R and re is very good. At low temperatures T < Tk,it appears that re < rR, reflecting possibly a “rattling” motion of the isopropylbenzene molecule at viscosities at which the diffusional motions are significantly slowed down. With the caveat of the underlying assumptions, we may conclude that ro < rt at temperatures below Tk and that the discontinuity in the viscosity behavior may be related to a rapid slowdown of the translational motions and continued reorientational motions. If one uses the usual hydrodynamic equations and calculates the diffusional correlation time, rD, one finds that TD has, of course, . the same temperature dependence as T R and r~ 1 r ~ The reason why rt is shorter than rR or TD at temperatures slightly below Tkis not clear. Obviously, the applicability of simple hydrodynamic equations in the highly viscous region is open to question and needs further systematic experiments. The low-temperature activation energies obtained by assuming a constant distribution parameter for the intra and isotropic jump diffusion for the inter &e., as shown in the correlation time plot) are 5.2 and 18 kcal/mol, respectively. It is interesting to make a qualitative observation that &(intra) and &(inter) compare favorably to the values of the activation energies for the p (5.7 kcal/mol) and a (30 kcal/mol) relaxation as calculated from their dielectric data for isopropylbenzene as obtained by Johari and Goldstein.20 This qualitative comparison indicates the possibility of a connection between the 0 relaxation and reorientational motions of the molecule. On the basis of present data, one can only speculate on the detailed nature of the motions involved. Further experiments with additional model compounds may elucidate the interesting dynamics of molecules in the supercooled liquid state. Acknowledgment. We gratefully acknowledge the assistance of Dr. Peter Beak for his suggestions regarding the synthesis of the isopropylbenzene compounds, and the Air Force Office of Scientific research for funding under the grant AFOSR 77-3185. (16)H.Torrey, Phys. Reu., 92, 962 (1953). (17)R. E. D. McClung- and D. Kivelson, J. Chem. Phvs., 49. 3380 (1968). (18)M. Fury and J. Jonas, J. Chem. Phys., 65,2206(1976). (19)R. A. Assink, J. DeZwaan, and J. Jonas, J. Chem. Phys., 56,4976 (1972). (20)G. Johari and M. Goldstein, J. Chem. Phys., 63, 2372 (1970).
