J. Phys. Chem. 1986, 90, 4465-4470
4465
Spin Relaxation, Local Order, and Solute Motion In Viscous Liquids Bonner C. Nishida,? Robert L. Vold, and Regitze R. Vold* Department of Chemistry, University of California, S a n Diego. La Jolla. California 92093 (Received: February 14, 1986)
Deuterium spin-lattice relaxation rates have been measured for chloroform-d and acetonitrile-d3 in dilute solutions with hexadecane, dibenzyl ether, diphenyl ether, p-nonylphenylpoly(oxyethy1ene ether) ( ( n) = 8.6), and N-(p-methoxymethoxybenzy1idene)-p-n-butylanilineat Larmor frequencies between 4.6 and 38.4 MHz and temperatures from 0 to 70 OC. I4N relaxation rates ( R , and R2)were measured at 18.1 MHz for the acetonitrile solutions over a similar range of temperatures. Correlation times 71 for reorientation of the solute C3 axis determined from these data as a function of temperature are analyzed in terms of their empirical relation to solvent viscosity 7. At high temperature and low viscosity ( ? / T C 0.05 cP/K) 71 is as usual a linear function of ?/T, although for some of the solutions the slope is noticeably smaller than predicted by rotational diffusion calculations with slip boundary conditions. At low temperature and high viscosity ( q / T > 3 cP/K) T~ is approximately constant, independent of q/ T, and the limiting value depends on the particular solute/solvent combination. At low temperatures ordering of solutes with respect to surrounding solvent is apparent, and translational diffusion of the solute through locally ordered regions is responsible for observed frequency dependence of the spin relaxation rates.
Introduction Numerous e~perimentsl-~ have demonstrated a surprisingly general linear relation between the rotational correlation time rR of a rigid solute molecule and 7,the coefficient of shear viscosity of the medium. A constant slope C = d ~ ~ / d ( ? / Tis)expected on the basis of purely hydrodynamic considerations, but it is clear that hydrodynamics does not provide a complete picture of the rotational motion of small solute molecules in dense fluids. The importance of extrahydrodynamic considerations such as relative solute/solvent size is illustrated by a growing body of evidence relating rRto isothermal compressibility4 or free v01ume.~ In addition, the dependence of C upon pres~ure,~.’ solute concentration,8 and the particular solute/solvent pairg provides support for the idea that events at the molecular level must be incorporated in more satisfactory theories of solute rotation. Rough sphere calculations of Hynes et a1.I0and a semiempirical model developed by Dote et al.” both include parameters that describe how angular momentum of the solute decays via transfer to solvent molecules, and both models work somewhat better than an early attempt by Gierer and WirtzIz to calculate a microviscosity correction to the Debye-Stokes-Einstein equations for a sphere rotating in a viscous continuum. Hu and Zwanzig’s sol u t i o ~to ~ ’the ~ rotational diffusion equation with slipping boundary conditions also often leads to calculated correlation times that agree with experimental values. Since all these models work about equally well even though they are based on rather different physical pictures, the essential molecular factors which govern solute rotation are not yet unambiguously identified. Fron an experimental point of view, further progress in elucidating the nature of solute reorientation is more likely to come from investigating breakdowns of the linear relation between 7R and 9 or v / T than from gathering additional data about the slope for particular solutions. The linear relation between 7 R and 9 or v / T is expected to fail at high viscosity because microscopic boundary layer effects dominate the transfer of angular momentum from solute to solvent as the latter becomes more rigid,IO but experimental data bearing on this question are relatively scarce.14 W e have therefore measured the 2H spin-lattice relaxation rates of chloroform-d and the *H and I4N relaxation rates of acetonitrile-d, in two solvents for which the viscosity could be varied over a wide range: p-nonylphenylpoly(oxyethy1eneether) ((n) = 8.6, “Triton”), where 22 < 9 < 316 CPbetween 20 and 75 “C) and N-(p-n-methoxybenzy1idene)-p-n-butylaniline (MMBBA), where 14 C 71 < 640 CP between 0 and 61 O C . ESR and N M R relaxation data for very viscous solutions cannot be interpreted exclusively in terms of solute rotation. Freed and Present address: IBM Instruments, Inc., Orchard Park, Danbury, CT 068 10.
0022-3654/86/2090-4465$0 1.50/0
c o - ~ o r k e r s ~ ~have - ” developed a model of “slowly relaxing local structures” (SRLS) which accounts for their ESR data in terms of rapid, but restricted, solute reorientation in a locally ordered environment followed by much slower relaxation of the local order. This formulation also accounts for nuclear spin relaxation measurements on solutes in the isotropic phase of thermotropic nematic liquid crystals, and we thought it of interest to determine whether the onset of local structure relaxation is connected with breakdown of the linear relation between 7 R and solution viscosity. Our choice of MMBBA for the present investigation was motivated by its similarity to the well-characterized liquid crystal MBBA. Triton, with viscosity somewhat greater than that of MMBBA, represents nonionic amphiphilic molecules which are known to form large structures in water, but it does not form thermotropic mesophases. The solutes chloroform and acetonitrile are both capable of specific association with these solvents, chloroform by virture of weak hydrogen bonds and acetonitrile by virtue of its large dipole moment. Accordingly, as a means of reference, we measured the relaxation behavior of both solutes in less viscous solvents with related functional groups (diphenyl and dibenzyl ether) as well as in a viscous inert hydrocarbon (n-hexadecane).
(1) Kivelson, D.; Madden, P. Annu. ReL;. Phys. Chem. 1980, 31, 523. (2) Alms, G. R.; Bauer, D. R.; Brauman, J. I.; Pecora, R. J. Chem. Phys. 1974, 61, 2255. (3) Whittenburg, S . L.; Wang, C. H. J. Chem. Phys. 1977, 66, 4255. (4) Vold, R. R.; Vold, R. L.; Szeverenyi, N. M. J . Chem. Phys. 1979, 70, 5213. (5) Tiffon, B.; Ancian, B.; Dubois, J. E. J . Chem. Phys. 1981, 74, 6981. (6) Zager, S. A.; Freed, J. H. J. Chem. Phys. 1982, 77, 3360. (7) Wilbur, D. J.; Jonas, J. J . Chem. Phys. 1975, 62, 2800. (8) Tiffon, B.; Ancian, B. J . Chem. Phys. 1982, 76, 1212. (9) Zager, S. A.; Freed, J. H. J. Chem. Phys. 1982, 77, 3344. (IO) Hynes, J. T.; Kapral, R.; Weinberg, M. J . Chem. Phys. 1978, 69, 2723. (1 1) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J. Phys. Chem. 1981, 85, 2 169. (12) Gierer, A.; Wirtz, K. Z. Naturforsch., A: Astrophys., Phys. Phys. Chem. 1953,8A, 532. (13) Hu, C.-M.; Zwanzig, R. J. Chem. Phys. 1974, 60, 4354. (14) Magee, M. D. J. Chem. Soc., Faraday Trans. 2 1974, 929. (15) Polnaszek, C. F.; Freed, J. H. J . Phys. Chem. 1975, 79, 2283. (16) Freed, J. H. J. Chem. Phys. 1977, 66, 4183. (17) Lin, W.-J; Freed, J. H. J. Phys. Chem. 1979, 83, 379. (18) Vold, R. R.; Kobrin, P. H.; Vold, R. L. J . Chem. Phys. 1978, 69, 3430. (19) Poupko, R.; Vold, R. L.; Vold, R. R. J . Phys. Chem. 1980,84, 3444. (20) Vold, R. L.; Vold, R. R. Isr. J . Chem. 1983, 23, 315.
0 1986 American Chemical Society
Nishida et al.
4466 The Journal of Physical Chemistry, Vol. 90, No. 18, 1986 Theoretical Background All of the spin-lattice relaxation rates discussed in this paper are related to spectral densities of motion by the familiar expression
R I = (37z/2)(eZqQ/h)2[J~(w~) + 4J2(2u0)l
(1)
where ezqQ/h is the quadrupole coupling constant for ZHor 14N, wo is the Larmor frequency, and where, by virture of the symmetry of the phase, the two spectral densities J1and J2 differ only in terms of the frequency at which they are evaluated. For symmetric top molecules, the spectral density, JM(u)can quite generally be written.z'-23 JM(w) = 74(3 COS'
p - I)'JMO(w)
+ 7 4 sin2 2p J M I ( w ) +
'14 sin4 @ JMZ(W) (2) p is the angle between the relaxation vector of interest, here the
z axis in the principal axis system of a symmetric electric field gradient tensor and the molecular symmetry axis, while the second subscript on J refers to projection onto this axis. For chloroform deuterons p is zero and only JMO is relevant. According to the SRLS this spectral density is de, describes relaxation of termined by three parameters: T ~ which the symmetry axis to an equilibrium distribution of orientations , describes slower relaxation relative to the local structure; T ~ which of the local structure to a macroscopically uniform distribution; and a local order parameter SL (SLz)l/z, which is defined as an ensemble average quantity. Thus we may write JMo(w) = (1 -SLz)71/(l + w271z) + S~'7,/(1 + w2Tx2) (3)
Polnaszek and Freed's original derivation15 was restricted to the was replaced by unity) limit of weak local order (so that (1 - SL2) and included a cross term between slow and fast motions which we have omitted from eq 3. It is interesting to note in this regard that the term - S L z ~ l / ( l + W ~ T , ~ which ) , we include in eq 3, is almost identical with Freed's cross term16 and renders eq 3 formally identical with the double Lorentzian spectral densities proposed by Ahlnas et aLz4and Lipari and S z a b ~ .The ~ ~ latter authors emphasize that the validity of eq 3 actually transcends many of the assumptions needed to derive it. For acetonitrile deuterons, whose principal field gradient axis makes an angle = 109" with the C3axis, we assume that the fast motion about the C3 axis is not affected by the surrounding structure. JMo is then still given by eq 3, while the spectral densities JM1and J M 2are unmodified from the original calculations of Woessner,26 Shimizu,22and Huntressz7 5JMI(U)
=
7b/(l
+ (w7b)')
(4a)
5 J d w ) = 7J(l +(~7~)')
(4b)
= 67l711/(7~.+ 57,1)
(4c)
= 6 7 ~ 7 1 1 / ( 4+7 2711) ~
(44
where 7b 7,
In the limit of no local order eq 2-4 reduce to the ordinary expressionszz~26~z7 for rotational diffusion of a symmetric top. In the opposite limit of perfect local order one expects intuitively that the molecular symmetry axis should not move relative to the local structure. This does not imply that 7, in eq 2-4 must go to infinity, but rather that the existence of a strong local ordering potential should make all terms involving T~ unimportant. The limiting behavior of eq 3 as SL 1 is satisfactory in this regard, but eq 4a-d are not. A more exact treatment of the local ordering potential, similar to that used for long-range order in liquid crystals,16sz8would replace both eq 3 and 4 with infinite sums of
-
(21) Woessner, D. E. J . Chem. Phys. 1962, 37, 647. (22) Shimizu, H. J. Chem. Phys. 1964, 40, 754. (23) Huntress, W. T., Jr. Ado. Magn. Reson. 1970, 4, 1. Hjelm, C.: Lindman, B. J . Phys. Chem. (24) Ahlnas, T.; Soderman, 0.; 1983, 87, 822. (25) Lipari, G.; Szabo, A. J . Am. Chem. SOC.1982, 104, 4546. (26) Woessner, D. E.; Snowden, B. S., Jr.; Strom, E. T. Mol. Phys. 1968, 14. 265. (27) Huntress, W. T. Jr. J . Phys. Chem. 1969, 73, 103.
TABLE I: Sample Composition and Relaxtion Measurements" solute/solvent CDC121n-hexadecane CDC1;)dibenzyl ether CDCl,/diphenyl ether CDCI3/Triton CDCI,/MMBBA CD$N/n-hexadecane CD3CN/dibenzyl ether
mol % solute 10 7.7 10 8.1 10.3 4.4 11
CD,CN/diphenyl ether CD$N/Triton
9.9 9.6
CD,CN/MMBBA
8.0
measurements R, ('H, 9.2, 38.4) R; i2H, 9.2, 30.7) R1(2H, 9.2) R, ('H, 4.6, 9.2, 30.7, 38.4) Rl (2H, 4.6, 9.2, 30.7, 38.4) R1 (I4N); R,(*H, 4.6, 9.2, 38.4) R , (I4N);R1(2H,9.2, 30.7, 38.4) RI (I4N); Rl(2H, 9.2, 38.4) RI (I4N); R2(I4N);Rl(2H, 4.6, 9.2, 30.7, 38.4) R , (I4N);R2(I4N);R,(*H, 4.6, 9.2, 30.7, 38.4)
Spin-lattice relaxation rates R1 and spin-spin relaxation rates R 2 were measured at the indicated Larmor frequencies (MHz) for *H and at 18.1 MHz for I4N.
Lorentzian functions, whose rate constants depend on the degree of local order. The number of experimentally accessible relaxation parameters does not warrant such an extension, but eq 2-4 should nevertheless be regarded with caution if SLis large. It is worth noting that if T~~
