Light scattering studies of hypersonic relaxations in ionic solutions

Volume 73, number I

LIGHT SCATTERING KG.

BREITSCHWERDT

hlsrlhtr

Jiir

Rccewed

1 July 1980

CHEMICAL PHYSICS LKI-TIIRS

STUDIES OF HYPERSONIC

RELAXATIONS

IN IONIC SOLUTIONS

and E. POLKE

Ange~tarzdtc Pl~ys~h. Linn crsltit Herdelbcrg, Hetdclberg. West Germany

10 Xl.~rch 1980

Thhr Jttenuatlon of llyprrson~c waves and the hypersomc vcloctty have been measured m rather ous soWIons ot hthwm chlorldc m the tempcrnture range 100-300 K by BrdIoum hght-snttermp sIon observed at trequcnctcs around 10 GHz may be explamed wth a ample rate process at higher vls.coclastlL behnwor below 250 K

1. Introduction

Hypersomc and ultrasomc relaxation expenments on hqulds yield mfonnatlon concermng the tmie scale snd mechanisms of structural rearrangements Usually the frequency dependence of the velocity and absorption of longltudmal waves IS studled usmg Brdloum hght scnttermg [I] and ultrasomc techmques [2--51 For lontc solutions [6-131 these mvestlgatlons have shown that compresslonal and shear relaxanon phenomena [ 141 generally cannot be described by a sunple rate process Instead, a sum of such processes [ 15- 191 or a contmuous spectrum of relaxation tunes has to be considered [ 11,14]_ The direct frequencydependent measurement of the hypersomc dlsperslon due to structural relaxatlon processes m dilute aqueous soluttons of smgly charged Ions 1s usually beyond the reach of hypersome medsurmg techniques However, the rates of density and composition fluctuations are reduced m the vlcmlty of Ions of sufficiently high charge denslty [20-221 , and relaxation processes are found tn the ultrasonic frequency range [23] _ Furthermore, pronounced vlscoelastic relaxation effects at ultrasome frequencies are generally observed m ltqutds when the shear vlscoslty g, attams values of 10 P or greater. In cases where the structural rearrangement process must be described by a broad dlstnbutlon of relaxation times, viscoelastlc effects may be found at vlscosltles as low as 1 P. In supercooled highly 186

concentrated techmques temperatures

(8 Xl) aqueTbc dtsperand htth

concentrated aqueous ionic solutions the viscosities approach 1 P, and the begmnmg of a vlscoelastlc relaxation can be detected m the ultrasonic frequency range [IO- 131. No detaded frequencydependent mvestlgatlon of the absorptton and the sound velocity has been carried out at hypersomc frequencies between 3 and 20 GHz so far. Among aqueous solutions of alkali hahdes. hthmm chloride solutions are good candidates to look for the dlsperslon region m the GHz range. The analysts of ultrasomc absorption measurements in aqueous solutlons of alkali halides at lower frequencies on the basis of a model where the water molecules are consldered to be m different iomc envxonments has shown [ 15-191 that Ll+ ions considerably reduce the fluctuation rates. Simdar results have been obtamed with nuclear magnetic relaxation [24], dlelectric relaxation [25,26] , and melastlc neutron scattermg [27] techniques. The ability of the hthmm chlonde solutions to wlthstand considerable supercoohng for long periods of time w&out crystalhzmg allows one to obtain data extendmg from the temperature region of high ffuldlty (vs = 10-t P) down to the glass transition region (Q = lot3 P).

2. Experimental

The expenrnental apparatus consisted of a smglefrequency tunable argon ion laser, a temperature

Volume 73, number 1

controlled scattering cell with an octagonal cross section m an evacuated box, a piezoelectrically scanned Fabry-P&rot interferometer with triple pass, a Peltiercooled photomultipher tube, and a lock-m amphfier. The free spectral range of the Fabry-P&rot interferometer vaned between 12 and 55 GHz with a medrum finesse of 60. The solutions were prepared from pure chemicals and membrane filtered with a selection hmrt at molecular weight 1000. The refractive index values of the sample were measured for each temperature with an Abbe refractometer_ The spectra were taken for three different scattering angles, 4?, 90”, and 135O and deconvoluted as discussed m the hterature [28] . By varying the scattering angle and the wavelength of the laser light a relatively wrde frequency range can be covered depending on the sound velocity and thus on type, concentratton, and temperature of the ionic solutions.

3. Results and discussion

-65

.

.

,” ,” u1 300N

-x\ -LOT’ \

July

1980

LI Cl 8m .

\

\

\

0

5

6 7 8 10 12 f IGHZ)

Frg. 1. Absorption coeffiaent versus frequency for an 8 X1 LrCl solution. Sohd Imes. best tits to expenmenti data; dashed

hnes:

mterpolatlon

to ultrasomc

data of refs. [29,3OJ_

The light scattermg data are analyzed quantitative!y using a complex reciprocal longitudinal modulus [2], whrch corresponds to a complex compresstbili-

From the frequency shift 5 fB of the Brilloum hnes one obtains an approxrmate value of the hrghfrequency sound velocity c = fB X/2a sin (e/2),

I

CHEMICAL PHYSICS LETTERS

(1)

where tz is the refractive index of the sample for the incoming laser lure of wavelength X, and 0 is the angle between the mcrdent and scattered beams. The sound absorption crff 2 IS frequency mdependent at frequenciesf well below and above a relaxation region. It may be wntten m the followmg way:

(y/f2 = ~~fJCIg2 9

(2)

where

SfB IS the Bnlloum linewidth. As an example, the absorptron a/f2 of an 8 M LiCl solution at four drfferent temperatures is shown rn fig. 1. The frequency dependence of a/f 2 indicates the existence of a relaxation region. The sohd curves are best fits to the expenmental points, the dashed curves are interpolations to the ultrasonic data at lower frequencies [29,30]. As can be seen, the relaxatron strength increases with decreasing temperature whrle the dominant relaxation frequency shifts to lower values. The correspondmg dispersion in the sound velocity IS shown in fig. 2.

Fig 2. Sound velocity versus frequency for an 8 M LiCZ soluhon. Solid lines: best fits to experimental data, dashed Lines: interpolation to ultrasonic data of refs. [2930] _

Volume

73

number

ty for purely

CHEMICAL

1

compresslonal

PHYSICS

(3)

where p IS the density and w the angular frequency. For a rate process with a discrete relaxation time rd the sound velocity may be wrltten c=

[I/CL +(c$-

&/(I

+o*T~)+&J*]-~‘2,

(4) where co and c, are the sound velocity at very low and at very high frequencies, respectively. The absorption is

Lr/f2 = 27&p

- c--y)c7d/( 1 + J&

(5)

The curves given by the expressions for the sound velocity, cq. (4), and the absorption, eq. (S), are in reasonable agreement with the best fit curves of fig 2 and fig. 1, respectively The dlsperslon and the absorption data yield relaxation tunes which differ only slightly from each other. Both relaxation times may be consldered to be identical wlthm the accuracy of the measurements m the temperature range be-

[21

(6) where the relaxational modulus hi, = 122, - ?lfo, MO the low-frequency modulus, hl, the high-frequency modulus, 7L the longltudmal stress relaxation time, and g(-rL) the dlstnbutlon function for the relaxation tunes. The average longitudmal relaxation tune (TV) =

1oclo: aoo-

300 -

zoozW 150-

&Ir(rL) = K,$>

100: 80ogoLO3020-

15-

3.5

LO

L5

50

55 103/T (K-‘I

Fig. 3. Rekratlon tunes versus reciprocal temperature. XXX values obtamed from absorption data, 000: values obtamed from

188

veloaty

ITS

dTL

(7)

IS related to the average structural or volume relaxatlon time (TV) and the average shear relaxation time (7s) by

s 2

10: 8-

r 0

%LClO-

0 -

1980

tween +20 and -40°C (fig. 3), if the l&t scattenng data are transferred into the acoustic regime [3 11. The relaxation time obtamed for the 8 M LlCl solutlon is 7 = 8.5 X lo-‘* s at 20°C. The temperature depyidence of the relaxation time between +20 and -40°C yieIds an activation energy of We,,, = 0.175 eV for the relaxation process. With the precedmg analysis the relaxation times differ more strongly at temperatures below -40°C. Thus is the temperature range where the viscosity of the solution approaches 1 P [ 13 ] , and data analysis on the basis of the vlscoelastlc model with a dlstribuhon of relaxation times IS more appropnate. The complex longltudmal modulus may be characterized by

stress

p/h1 = ( I/c - m/w)‘,

1 July

LETTERS

data.

:

+ 2 G&’

= tlv +$ qs,

(8)

where K, IS the relaxational part of the bulk modulus, G, the high-frequency shear modulus, and ov the volume or bulk vlscoslty. It IS reasonable to assume that the average shear and longrtudmal relaxation times are comparable m magmtude. Indeed, the average longrtudinal relaxation times obtained from the absorption data (fig. 3) and the average shear relaxation times (TJ obtamed from shear impedance measurements at 88 MHz [ 131 below -100°C agree wlthm an order of magnitude at -100°C. At - 100°C the activation energy for the relaxation process is considerably kugher than it is at room temperature. At temperatures below -50°C the velocity data

Volume 73, number 1

CHEMICAL

PHYSICS

LETTERS

Table 1 Enthalp~es (eV), actwatlon enthalplcs (eVj, and relaxation ttmes at 20°C

H2O

LI+ Cl-

L

1980

(IO-'*s)for LiCl-Hz0

t

AH12

AH23

42

AH23

‘VCZ.UP

rtheor

Texp

0.10

-0 04 -0 04 -0.04

0.20

0 075 0.17 0 13

0.175

3.6 7.9 2.9

8.5

could not be analyzed because the limitmg low-frequency and high-frequency values are lackmg. In the temperature range between -100 and -170°C the expenrnentally determmed relaxation tunes are less accurate Here the dominant part of the drspersron region IS below the frequency range accessible with Brrllouin hght scattermg techmques. The miscibrhty gap in the phase diagram of the LiCl-Hz0 system [32] drd not show up m the l&t scattenng measurements if the measunng temperature was approached from higher temperature values. The experrmental data at hrgher temperatures are compared with the relaxation time and the activation enthalpy found for the inner sphere of the Lf ran rf the ultrasonic absorptron measured at lower frequencies IS analyzed according to the n-state model [17-191. In the dynamic rz-state model no specified structuraI forms are postulated to exist in the liquid because the assumptrons may be mcomplete or inadequate Instead, the excess ultrasonic absorption at frequencies below the relaxatron region IS ascribed to structural relaxations between states MIk, ii = 1,2, , tz, which represent drfferent structural forms k m drfferent ionic envrronments z. The states are characterized by their free enthalpies and molar volumes as well as by the free actrvatron enthalpies between them. A set of these quantrtres is obtamed by a leastsquares fit to the ultrasonic absorptron as a function of temperature and pressure. The temperatureand pressuredependent values of the total molar volume, the thermal expansron coefficient, the compressrbrlity, and the specific heat act as constramts in the analysis. The non-relaxatronal or mstantaneous contnbutrons of the thermal expansion coefficient, the compressrbrhty, and the specific heat cannot be calculated mdependently because the mtermolecular potentials [33] arenot well known. Therefore these values are taken from the numerical analysis_ The numbers 2 of solvent molecules in the different ionic environments are also obtained from the computer analysis.

ldy

In order to descnbe the structural relaxation of LiCI solutions correctly for concentrations higher than about 6 M it has to be assumed that the influence of the ionic environment with the longer relaxation time, i.e., the Lf environment, dominates when the Inner spheres overlap. Then essentially a single relaxation time should prevarl. Temperature-independent enthalpies AH and activation enthalpies & for unperturbed water and for the inner spheres of Li+ and Cl- are given in table 1 together with the corresponding relaxation times for LLtemperature of 20°C [18,19] _The relaxation time 7tieor = 7.9 X IO-I2 s for the Li+ environment is in good agreement wrth the expenmental value at room temperature. The actrvation enthalpy AHzS = 0.17 eV for the Inner Lif sphere also agrees welI with the measured actrvation energy We.+. This indicates that at temperatures down to 40°C the structural rearrangement m the solution essentially consists of molecular rate processes which are governed by the interaction with the Lf ions. At lower temperatures the vtscoelastic processes dominate.

Acknowledgement

This work was supported Forschungsgemeinschaft.

in part by the Deutsche

References

111 BJ. Beme and R. Pecora. Dynamic h&t scattering (Wley, New York, 1976). 121 T.A. Lltovltz and CM. Da-, in: Phyacal acoustics,

Vol. 2A, ed. W-P. Mason (Academic Press, New York, 1965). Absorption and dk131 K.F. Henfeld and T.A. Lltovitz, persion of ultrasonic waves (Acadermc Press, New York, 1959). t41 A B. Bhatla. Ultraso~c absorption (Oxford Univ_ Press, London, 1967).

I89

Volume 73 number

151AJ hlathcson,

I

CHEMICAL

PHYSICS LEnERS

Xlolecular acoustrcs (Wiley, New York, 1971) 161S-H Chen,C C La1 and J. Rouch, J Chem Phys 67 (1977) 5080. 171 Xl. Gross, J Azoulay and D Gerhch, J Chem Phys 58 (1973) 5812 181 A R Mare: and E Ycager, J. Chcm. Phys 59 (1973) 206 191 J Stone, J Opt. Sot Am. 56 (1966) 1136 [lOI G S Darbarr. Xl R Rrchelson and S Petruccr. J. Chem Phys 55 (1971) 4351. 1111 J H. Ambrus. H. Dardy and C T hloynthan, J Phys Chem. 76 (1972) 3495 [121 S -Y. Hstch, R W Gammon, P B hlacedo and C J blontrose, J. Chem Phys 56 (1972) 1663 Il31 C.T Xloynrhan, N. Bahtactac, L Boone and T.A Lrtovrtz, J. Chcm. Phys 55 (1971) 3013 Il4l CJ. hlontrose and T A Lrtovrtz. J Acoust Sot Am 47 (1970) 1250. Phys Letters 6 (1970) 587 I151 Ii G. Brcrtschnerdt,Chem Ber Bunsenpcs Physrk Chem 75 [161 K G. Brertschwerdt, (1971) 319 [171 K G Brertschwerdt and H. Krstenmachcr. J Chem Phys 56 (1972) 4800 [181 K G Brertschwcrdt and H Wolz, Ber. Bunsenges Physrk Chem 77 (1973) 1000.

190

1191K G. Brettschwerdt,

1 July 1980

tn: Structure of water and aqueous solutrons, ed. W. Luck (Physrk Verlag, Wemheim, 1974) WI hl Ergen and K Tamm, Z. Elektrochem. 66 (1962) 93, 107. 1211 K G. Brertschwerdt, Chem. Phys Letters 1 (1967) 481. Ber Bunsenges. Physrk Chem 72 1221 K.G. Brertschwerdt. (1968) 1046. r231 A Bechtfer, K G Brertschwerdt and K Tamm, J. Chem Phys. 52 (1970) 2975 1241 H Langer and H G Hertz, Ber Bunsenges. Physrk. Chem. 81 (1977) 478. [25 I K. Grese, U. Kaatzc and R Pottel. J Phys. Chem. 74 (1970) 3718. Physrk Chem 76 (1972) 495 1261 K Geese, Ber. Bunsenges [271 GJ Safford, P S. Leung, A.W Naumann and PC. Schaffer, J Chem. Phys 50 (1969) 4444. H W Lerdecker and J.T. la hlacchra, J Acoust Sot Am WI 43 (1968) 143 WI G Kasper, T~CSIS, University of Herdelberg (1979) [301 K D. Schwalbach, prrvate communrcatron. I311 P. Deguent and J.P. Boon, J Chcm. Phys. 54 (1971) 4443 1321 C A. Angetl and E J Sare, J. Chem Phys. 49 (1968) 4713.52 (1970) 1058 I331 K.G Brertschwcrdt and H Krstenmacher, Chem. Phys Letters 14 (1972) 288