The Journal of
Physical Chemistry
0 Copyright, 1988, by the American Chemical Society
VOLUME 92, NUMBER 21 OCTOBER 20, 1988
LETTERS Coupling of Acoustic Phonons in LiCl Aqueous Solutions to a Relaxation Mode of the Ionic Hydration Shell and Observation of Central Peaks in Inelastic Light Scattering N. J. Tao and S. M. Lindsay* Department of Physics, Arizona S t a t e University, Tempe, A r i z o n a 85287 (Received: June 3, 1988; In Final Form: August 17, 1988)
We have measured Brillouin spectra of LiCl aqueous solutions as a function of concentration. A classical model of phonons damped by a viscous loss process does not describe the spectra adequately. They are better described by a coupled mode system consisting of a phonon and a relaxation mode of water molecules in the ionic hydration shell. The hydration shell relaxation is well-described by a single relaxation time which, for example, is 24 ps at 36 mol % LiCI. The relaxation time and the coupling strength depend on the concentration, which indicates that the dynamic properties of the water molecules in the ionic hydration shell are affected by interionic interactions.
Introduction Brillouin scattering has long been used as a probe of structural relaxation at gigahertz frequencies. The normal approach has been to extract phonon line widths and frequency shifts and fit them using relaxation theory. Mountain has pointed out, using a hydrodynamic argument, that the coupling of the acoustic vibration to a loss process leads to a new (central) feature in the spectrum,’ experimentally first observed in CC14.2 A number of recent developments make a study of the full spectral. shape useful. A more general description of the scattering process is given by the coupled mode formalism which exploits the fluctuation-dissipation theorem to allow a line shape to be calculated from a phenomenological model. This approach encompasses the nonhydrodynamic case of an acoustic phonon coupled to a relaxing degree of f r e e d ~ m . We ~ have extended such calculations to apply
them to the case of a hydrated polyion! A second development is the use of a nine-pass tandem interferometerS which makes examination of central peaks much easier. This Letter describes coupled mode scattering in LiCl solutions where the relaxing degree of freedom is the ionic hydration shell relaxation. This system illustrates the success of the coupled mode formalism well. The resulting line shapes are not well-described by a sum of Lorentzians. Coupling gives non-Lorentzian central features that are well-described by coupled mode theory. Coupling effects reach a maximum when the relaxation rate is close to the frequency of the phonons (UT N 1). For pure water at rcom temperature, relaxation processes, such as the orientational and hydrogen bond breaking relaxations,6+’ are normally much faster than the vibrations of acoustic phonons of gigahertz frequencies, so, if there is coupling between the acoustic phonons
(1) Mountain, R. D. J. Res. Natl. Bur. Stand., Sect. A 1966, 70, 207. (2) Gornall, W. S.; Stegeman, G. I. A.; Stoicheff, B. P.; Stolen, R. H.; Volterra, V. Phys. Reu. Lett. 1966, 17, 297. (3) Fritz, I. J.; Reese, L. R.; Brody, E. M.; Wilson, C. M.; Cummins, H. 2. In Light Scattering in Solids; Balkanski, M., Ed.; Flammarion Siences: Paris. 1971.
(4) Tao, N. J.; Lindsay, S . M.; Rupprecht, A. Biopolymers, in press. (5) Lindsay, S. M.; Anderson, M. W.; Sandercock, J. R. Reo. Sci. Instrum. 1981, 52, 1478. ( 6 ) Montrose, C . J.; Bucaro, J. A.; Marshall-Coakley, J.; Litovitz, T. A. J. Chem. Phys. 1974, 12, 5025. (7) Aliotta, F.; Vasi, C.; Maisano, G.; Majolino, D.; Mallamace, F.; Migliardo, P. J . Chem. Phys. 1986, 84, 4731.
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The Journal of Physical Chemistry, Vol. 92, No. 21, 1988
and a relaxational mode, it will not be important at room (or higher) temperatures unless the coupling is very strong. However, for the water molecules in the DNA primary hydration shell, the orientational relaxation time is almost an order of magnitude slower than that of bulk water at room temperature^,^^^ and we find that the acoustic phonons in hydrated DNA couple strongly with a relaxation mode of the water molecules in the DNA hydration ~ h e 1 1 .Since ~ ~ ~ DNA is a charged molecule, the strong Coloumb interaction breaks the tetrahedral hydrogen-bonding structure of the water molecules in the hydration shelli0and slows down their motion. The acoustic vibrations of a charged molecule give rise to a vibrating local electric field, and this field modulates the motion of the water molecules in the hydration shell. It is of interest to examine similar behavior in the much simpler case of a 1 : 1 electrolyte solution. Furthermore, such spectroscopy provides a sensitive probe of hydration shell dynamics. Surprisingly, such a simple system does not appear to have been examined in this way before (although conventional Brillouin"-iz and ultrasound13 studies have been carried out in many aqueous electrolytic solutions). According to the fluctuation-dissipation theorem, the Brillouin scattering is proportional to
where x,(w) is the susceptibility of the acoustic phonon coupled to a relaxing degree of freedom. (Here we assume that the relaxation mode does not scatter light directly.) There have been many different theoretical description^^^'"'^ for various systems, but the ideas are basically same. As explained in ref 8, the derivations of Brody et al." and of Fritz et aL3can be conveniently applied to hydrated ion systems, and it is also easy to compare with the familiar hydrodynamic approach of Mountain,' so we chose this approach. Accordingly, we have 1
xdw) =
22
lb
6
lb
FRQUENCY SHIFT(GHz1
Figure 1. Brillouin spectra (VV) of LiCl solutions at concentrations of 0, 15, 2 5 , and 36 mol % (from top to bottom). There are gaps in the spectra where instrumental ghosts have been removed. The instrumental width is -200 MHz (too small to be indicated easily on the these
spectra).
(2)
The first term of the denominator describes an uncoupled acoustic phonon which has a frequency wo = Voq. ( V , is the speed of a noncoupled acoustic phonon, and q is its wavevector, given by (47rn/X) sin ( 8 / 2 ) ,where n is the refractive index of the solution, X is the laser wavelength, and 0 is the scattering angle.) A damping term, y = Kq2 ( K is a constant), is included. The second term is due to coupling to a relaxational mode with a relaxation time T. For the coupling between an acoustic phonon of a hydrated molecular system and a relaxation mode of the hydration shell, we have shown4that 6 = tq,(Nw,,,,)'~2Aq,where tq, is the number of the ions per unit volume, Nwa,, is the number of water molecules in the ionic hydration shell, and A is a parameter that measures the average coupling strength between an ion and a water molecule in the ionic hydration shell.
Experiments Brillouin spectra were taken on a nine-pass tandem interferometer5 using about 150 mW of the 5145-A line of a SpectraPhysics 2020 argon ion laser. The instrumental full width at half-height was -200 MHz, which produces negligible broadening of the spectra. (We have extended the calculations of Lindsay (8) Tao, N. J.; Lindsay, S. M.; Rupprecht. A. Biopolymers 1987,26, 171. (91 Swamv. K. N.: Clementi. E. In Structure and Dvnamics of Nucleic Acid;, Proteik and Membranes; Clementi, E.; Chin, S., 'as.; Plenim: New York, 1987; p 219. (10) Tao, N. J.; Lindsay, S. M.; Rupprecht, A,, submitted for publication in Biopolymers. (11) Montrose. C. J.; Fritsch, K. J . Acoust. SOC.Am. 1970, 47, 786. (12) Hsich, S.-Y.; Gammon, R. W.; Macedo, P. B.; Montrose, C. J. J . Chem. Phys. 1972, 56, 1663. (13) Fritsch, K.; Montrose, C. J.; Hunter, J. L.; Dill, J. F. J . Chem. Phys. 1970, 52, 2242. (14) Barker, A. S.; Hopfield, J. J. Phys. Rev. A 1964, 135, 1732. ( I 5 ) Worlock, J. M.; Scott, J. F.; Fleury, P. A. In Light Scatrering Spectra ofsolids; Wright. G. B.. Eds.: SDringer: New York. 1969; D 689. (16) Desai,k. C.; Kapral, R. Phyi. Rev. A 1972, 6, 2377'. (17) Brody, E. M.; Herman, H. Z . Phys. Rev. Lett. 1968, 21, 1263.
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FREQUENCY SHIFT(GHz)
Figure 2. Brillouin spectra (VV) of 36 mol % LiCl solution with scattering angles of 120°, 90°, 60°, and 30° (from top to bottom). The dots are experimental spectra, and the solid lines are calculated spectra.
et a1.lS to the nine-pass tandem interferometer.) LiCl was purchased from J.T. Baker Chemical Co. (purer than 99 wt %), and solutions were sealed in glass tubes. The spectra were taken at various scattering angles from 30° to 150'.
Results VV polarized Brillouin spectra (vertically polarized incident light and vertically polarized scattered light) at 90' scattering angle are shown as a function of concentration in Figure 1. From top to bottom, the spectra are of pure water and 15, 25, and 36 mol % solutions. As LiCl concentration increases, the width of the acoustic phonon broadens, and a central mode grows. This behavior is typical for a phonon coupling to a relaxation mode. (18) Lindsay, S. M.; Burgess, S.; Shepherd, I. W. Appl. Opt. 1977, 16, 1404.
The Journal of Physical Chemistry, Vol. 92, No. 21, 1988 5857
Letters
rise to depolarized scattering, but the corresponding central feature would be q dependent (characteristic of translational diffusion). The VH spectral line width is independent of q. Furthermore, substitution of D 2 0 for H 2 0 narrows the line width by 25%, implying that the mode involves orientational motion of water
2
5
0
2
5
FREQUENCY SHIFT(GHz1
Figure 3. Depolarized spectra (VH) of LiCl solutions at concentrations of 14, 26, and 36 mol % (from bottom to top). The dots are experimental spectra, and the solid lines are single-Lorentzianfits. The arrows point to a little leaked VV scattering (due to imperfect polarizers). A small asymmetry (right-hand side is a little more intense) is instrumental in
origin. Figure 2 shows VV Brillouin spectra of 36 mol % LiCl as a function of scattering angle, 8. The dots are the experimental spectra, and the solid lines are the spectra calculated via eq 1 and 2. We have fitted the spectra at four different angles by choosing Vo,6 , ~y,, and an intensity scaling parameter. Since q = (4~n/X) sin (8/2), y = Kq2, and 6 = Cq (C = nion(Nwatcr)1/2A), we need only eight parameters to fit four spectra. The spectra are fitted very well by the simple model of an acoustic phonon coupled to a single relaxation mode. The coupling constant, A , is 1.4 X s-I m-2, and the relaxation time is 24 ps, which is close to the orientational relaxation time of water molecules in the ionic hydration shell obtained from the computer s i m ~ l a t i o n sand ~~ NMR.*O In a fit to any one spectrum, combinations of these parameters may be adjusted by up to 20% without increasing xZ much. However, in a fit to all four spectra, the parameters ( K , V,, C, and 7)are much more restricted, so that the uncertainties in these parameters are less than 10%. W e have also attempted to fit our spectra by using three Lorentzians and find that the spectra cannot be fitted satisfactorily. The inside of the phonon peak is fitted well, but the tail from the central Lorentzian makes the calculated line higher than the experimental data, even if the background counts are taken to be zero. In the coupled-mode fit, the high-frequency tail of the phonon peaks is steeper due to interference between the two modes. Note, also, that a simple sum of Lorentzians requires many more parameters to fit all the data, since the parameters must be readjusted for each scattering angle. Although the fits shown in Figure 2 appear to be excellent, some asymmetry in the instrumental scan results in a x2 value of -4 for the best fit to a given spectrum. This value is increased considerably (to 12 for the best fit) when simple Lorentzians are used, despite the greater number of fitting parameters in the Lorentzian fit. VH spectra (vertically polarized incident light and horizontally polarized collected light) are shown in Figure 3 for (top to bottom) 36,26, and 14 mol % solutions in a 90” scattering geometry. They are broad Lorentzian-like central modes. The intensity of the mode is concentration dependent, and it is at least 100 times weaker than that of the VV spectrum. The dots are experimental data, and the solid lines are single-Lorentzian fits. The width at 36 mol % concentration corresponds to a decay time of 16 ps, which is somewhat shorter than the relaxation time of the relaxation mode that couples to the LA phonons. This broad mode is depolarized, so an anisotropic polarizability is involved in the scattering process, and this implies that it is a mode of water molecules (because the ions are isotropic). Ion collisions can give
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(19) Okada, I.; Kitsuno, Y.; Lee, H.; Ohtaki, H. In Ions and Molecules in Solution; Tanaka, N., Ohtaki, H., Tamamushi, R., Eds.; Elsevier: New York, 1983; p 81. (20) Hertz, H. G. In Water: A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 3, p 301.
Discussion For DNA, we found that the relaxation time does not depend on the concentration of DNA, and the coupling strength is simply proportional to the number of water molecules in the primary hydration shell. For a system like LiCl solution, the situation is more complicated. When we tried to fit the spectra at various concentrations using the relaxation time and coupling strength we obtained for the 36 mol % sample, we have to invoke an unusual concentration dependence for y. This implies that the coupling strength and the relaxation time are concentration dependent. VH spectra show clearly that the half-width of the central mode decreases as the concentration increases, which also means that the dynamic properties of the ionic hydration shell are affected by the neighboring ions. This is consistent with neutron-scattering dataZZwhich show that the diffusion coefficient of the water molecules in the Li’ hydration shell is concentration dependent. We may understand the difference between the hydrated D N A and LiCl in this way; for DNA, only about a tenth of the phosphate groups of a double helix interact strongly with the phosphates of a neighboring double helix,23so only the few water molecules that bind on these phosphates are influenced strongly by the interhelical interactions, and therefore the dynamics and structure of DNA primary hydration shell are not very sensitive to DNA concentration. In fact, it has been foundlo that the number of water molecules in the primary hydration shell does not depend on DNA concentration much, while the hydration number of Li’ does change as the concentration changes.22 (It increases from 3.3 at 9.95 m to 5.5 at 3.57 m . ) For LiCl, the hydrated ions are basically spherical, leaving no space for water molecules to “hide”. We have shown that the acoustic phonons of LiCl solutions couple to a relaxational mode, but its origin is not clear. For a weak coupling, it has been shown24 that only bulk viscosity is related to the coupling of the acoustic phonons and a relaxation mode; however, it is not straightforward to identify the process at a microscopic level, and we leave such discussion for a future publication,21 although we note the similarity of the structural relaxation time and the water reorientation time (determined by the depolarized spectra). Conclusions We have taken Brillouin polarized (VV) and depolarized (VH) light scattering spectra of LiCl aqueous solutions as a function of concentration and scattering angle. The Brillouin spectra indicate that the acoustic phonons in the solutions couple to a relaxational mode of the water molecules in the ionic hydration shell. The relaxation time and the coupling constant are cons-l centration dependent, having values of 24 ps and 1.4 X m-2, respectively, at 36 mol %. The depolarized spectrum can be fitted by a single Lorentzian, which may be due to an orientational motion of the water molecules in the ionic hydration shell. The corresponding relaxation time is also concentration dependent, and it is 16 ps at 36 mol %. Both VV and VH spectra show that the dynamic properties of the water molecules in the hydration shells are strongly influenced by interionic interactions. This is consistent with the structural data and other measurements.
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Acknowledgment. We thank C. A. Angell, M. D. Soumpasis, and A. Garcia for helpful discussions. This work has been supported in part by the N S F (BBS 8615653) and O N R (N00014-84-0487). N.J.T. acknowledges a research assistantship from the ASU graduate college. (21) Tao, N. J.; Lindsay, S. M., to be published. (22) Enderby, J. E. Sci. Prog. (Oxford) 1981, 67, 553. (23) Lindsay, S. M.; Lee, S. A.; Powell, J. W.; Weidlich, T.; DeMarco, C.; Lewen, G. D.; Tao, N. J.; Rupprecht, A. Biopolymers 1988, 27, 1015. (24) Zwanzig, R. J . Chem. Phys. 1965, 43, 714.
