ULTRASONIC ABSORPTION IN HYDRATED MELTS It seems very likely that, after the initial loss of one methyl group from the trimethylalumnium, the aluminum atom reacts further with nearby oxygen atoms of the silica, through a concerted 4-center reaction involving the unfilled fourth-coordinate position of the aluminum atom. This results in the breaking of two silicon-oxygen linkages and the formation of two silicon-methyl bonds, giving the observed adsorbed species. This assumption is also supported by the
921 observed16 reactions in the liquid state between trialkylaluminums and octamethylcyclotetrasiloxane in which the Si-0-Si bond can be cleaved. I n these reactions, the trialkylaluminum acts as an alkylation agent by transfer of one alkyl group to the silicon moiety. The alkylation action of trialkylaluminums has been well established.3' (31) H. Jenkner, Chem. Z., 8 6 , 527 (1962).
Ultrasonic Absorption in Hydrated Melts. I. Systems of Ca(N03)2.4Hz0and Its Mixtures with Water by G. S. Darbari and 5. Petrucci Polytechnic Institute of Brooklyn, Brooklyn, New York
11.201
(Received September 16, 1968)
Results of ultrasonic absorption measurements of Ca(N03)2.4Hz0melts and of 1:4.3, 1z4.7, and 1:5.0 Ca(NOa)2-HzO mixtures are presented. The temperature range 25-75' and the frequency range of 3-195 MHa have been investigated. A relaxation process at 20 A 5 MHa for Ca(NO3)2.4H2O,shifting to higher frequencies by addition of water, is reported. This relaxation tends to disappear by increasing the temperature. The volume viscosities are calculated in the frequency region below and above the observed relaxation region. The conclusion is drawn that two overlapping sources of the volume viscosities exist. A t frequencies below the relaxation region, structural and nonstructural molecular rearrangements contribute to the excess sound absorption over the classical Stokes value. The energy barrier of this over-all process is larger than the one for shear viscous flow as indicated by the decrease of the ratio qv/v. with temperature. A t frequencies larger than the observed relaxation region only the structural contributions to the sound absorption remain. The barrier of energy for the compression volume viscosity qp' is the same as the one for the shear viscosity q.. This indicates that all of the possible translation molecular rearrangements have been frozen out after the relaxation except the ones with a barrier of translational energy equal to the viscous flow.
Introduction Theories of equilibrium and mass transport properties of diluted electrolytic solutions are based on the classical Debye-Huckel model. Transport theories start a t infinite dilution and dissect a transport property like electrical conductance into the ionic components and calculate the ionic interactions a t nonzero concentration. The Fuoss-Onsager' and other similar theories, with all of the complexity of the mathematical derivation and sophistication in predicting the various interionic effects, are rarely valid a t C 2 10-2-10-1 M for a 1:l electrolyte in water a t room temperature. For concentrated solution the situation for transport theories has begun to improve in the past few years. As predicted a long time ago by FUOSS,~ the most promising development seems to be derived from the fused-salt end of the concentration scale. Angel13 has applied the free-volume theory of Cohen and Turnbul14with remarkable success to transport theories
of fused salts and glass-forming mixtures like the system Ca ( NO3)2-KN03,3to other fused salts,6 to highly concentrated glass-forming electrolyte solutions like Ca(N03)z.4Hz0 and Mg(NO3)z.nHzO ( n variable from 3 to 6 ) , and to mixtures of Ca(NO3)z.4H2OKNOa.637 According to the Cohen and Turnbull theory as well as to similar ones,* liquids that show a glass transition have an apparent energy of activation for shear flow that changes rapidly with temperature and (1) R . M. Fuoss and F. Accascina, "Electrolytic Conductance," Interscience Publishers, Inc., New York, N . Y., 1959: R. M . Fuoss and K.-L. Hsia, Proc. Natl. Acad. Sci. U.S., 57, 1550 (1967). ( 2 ) R . M . Fuoss. Chem. Rev., 17, 27 (1935). (3) C. A. Angell, J. Phys. Chem., 6 8 , 218 (1964); 6 8 , 1917 (1964). (4) M . H . Cohen and D. Turnbull, J. Chem. P h y s . . 31, 1164 (1959). (5) C. A. Angell. J. Phys. Chem., 6 9 , 399 (1965). (6) C. A. Angell, ibid., 6 9 , 2137 (1965). (7) C. A. Angell, J. Electrochem. Soc., 112, 1224 (1965). (8) A. Doolittle, J. A p p l . P h y s . , 22, 1471 (1951); 23, 238 (1951); M . Williams, R . Landel, and J. Ferry, J. Am. Chem. Soc., 77, 3701 (1955) ; J. Beuche, J . Chem. P h y s . , 3 0 , 748 (1959). Volume 73, Number 4 April 1969
922 becomes infinity a t a temperature TO. At this temperature the liquid assumes the characteristics of an amorphous solid or a glass. Generally TO> OOK while for To = OOK the non-Arrhenius character of the liquid disappears and the temperature dependence of the transport property resembles the one of an Arrhenius liquid. TOwas therefore defined as an ideal glass temperature where all of the translational movements disappear and the free-volume parameter goes to ze1-0.~ It is also clear that in terms of the transport properties of the glass-forming liquid it is the difference ( T - TO)that is characteristic of the ability of the liquid to sustain mass transport. For normal liquids T is the corresponding value (To = 0 ) . An alternate treatment relating TOto the temperature where the configurational entropy vanishes has been proposed.9 The following is not invalidated by this alternate thermodynamic approach. The general idea proposed by the Cohen-Turnbull theory4 is that “any liquid in principle would go through a glass transition if suflciently undercooled and if crystallization did not occur. The implication of the use of the Cohen and Turnbull theory to electrolyte solutions by Angell is to have tested a theoretical tool to explain the temperature and concentration dependencelo of transport properties, a problem unsolved by classical approaches in concentrated solutions. The major limitation to the general applicability of the above theory is the limited number of systems showing glass-forming properties, and therefore the limited possibility of verifying the generality of the above findings in all ionic liquids. Indeed to observe a glass transition temperature, it is necessary to cool a liquid to a temperature where the time scale of the experiment and the time scale of the mass transport molecular rearrangements become comparable. For ordinary mass transport experiments, therefore, one must cool the liquid close to To for glass-forming liquids. In general, many liquids crystallize before showing even a non-Arrhenius behavior, thus limiting the possibility of applying the above theory. This limitation can, in principle, be removed if one could study the glasslike properties of a liquid at temperatures higher than the glass transition temperatures. This can be achieved if the time scale of the experiment is so reduced that the time necessary for the molecular rearrangements becomes of the same order as the time necessary to respond to the applied stress. sec) are far beyond the range of These times ( < classical transport experiments but are within the range of ultrasonic techniques (where the applied stress corresponds to a high-frequency adiabatic compression). By using ultrasonic waves, a pseudo-glass transition may, in principle, be caused in normal liquids a t temperatures above their freezing temperatures.ll The Journal of Physical Chemialry
G. S. DARBARI AND S. PETRUCCI Litovitz applied ultrasonic absorption techniques to fused alkali nitrates and demonstrated the existence of a volume viscosity vv with ratios r]y/vs w 5-20.12 For the case of fused ZnC121ait was possible to measure the actual relaxation time and attribute it to a structural relaxation. The hydrated melt Ca(N0s)2.4H20,that, as stated above, is a glass-forming liquid , had been investigated in this laboratory in a pilot research.14 A relaxation appeared to exist. I n this paper a more extensive and precise series of measurements in a wider range of temperatures varying the salt-water composition is presented. A phenomenological interpretation of the sound absorption at frequencies below and above the relaxation region is proposed in terms of the volume viscosities. It is contended that if this interpretation is correct, ultrasonic absorption may become a tool for the study of mass transport properties of electrolyte solutions and fused salts. The enormous potentiality of this method is in its ability to “freeze out” progressively all of the possible translational molecular rearrangements by varying the frequency of the compressional wave.
Experimental Section Fisher reagent Ca(NOs) 2.4Hz0 was used without further purification. It was melted in a closed bottle without loss of water. This was checked by subsequent analysis by cation-exchange technique and acid titration by Tha111.l~~Addition of water by weight to Ca ( NOa) 2 .4H20 and subsequent analysis of the melt was performed in order to prepare the various mixtures investigated. The thermostat with a proportional Bailey thermoregulator was used and thus the temperature was maintained constant within 0.05’. A new ultrasonic stainless steel cell of improved design especially suitable for moderately high temperatures (below the Curie point of quartz) was used, It consists of a twin-crystal interferometric system. The upper crystal (sender) is a 1-in. diameter X-cut quartz crystal mounted on the top of a 7 in. long, 1-in. diameter fused-quartz delay line. The lower crystal (receiver), also a 1-in. diameter X-cut quartz crystal, is mounted on a circular stainless steel plate suspended from a stainless steel block by means of three rods placed 120’ apart. The metal block also holds the delay line. The metal plate holding (9) G. Adam and J. H. Gibbs, J . Chem. Phys., 4 3 , 139 (1965). (10) C. A. Angell, J . Phys. Chem., 7 0 , 3988 (1966). (11) T. A. Litovitz in “Physical Acoustics,” Vol. 2, Part A, W. P. Mason, Ed., Academic Press, 1965, (12) R. W. Higgs and T. A. Litovite, J. Acoust. Soc. A m . , 32, 1108 (1964). (13) G. T. Gruber and T. A. Litovite, J . Chem. Phys., 40, 13 (1964). (14) S. Petrucci and F. Fittipaldi, J . Acoust. SOC. A m . , 42, 517 (1967). (14a) L. Meites, “Handbook of Analytical Chemistry,” McGrawHill Book Co., Inc., New York, N. Y . , 1963, p 334.
923
ULTRASONIC ABSORPTIONIN HYDRATED MELTS the lower crystal can be oriented with respect to the lower face of the delay line by means of the micrometers driving the three 120° apart rods holding the lower plate. The upper crystal and the attached delay line can be moved vertically with respect to the lower metal plate and crystal by means of a micrometer that could read up to 5 X 10-4in. The assembly incorporates coaxial electrical connectors for the two crystals, the electrical line connecting the lower crystal (receiver) being insulated from contact with the liquid by a stainless steel tubing. The entire assembly is dipped in a Pyrex cell containing the melt so that only the lower plate and the crystal and part of the delay line are immersed in the melt. An O-ring seal between the Pyrex cell and the metal assembly keeps the melt completely sealed. The advantage of this "dip" cell is that the melt can be purified if necessary (by vacuum, dry Nz, filtration) before using the ultrasonic cell directly in the Pyrex cell. In such cases a Pyrex apparatus with O-ring vacuum connections and stopcocks is connected t o the Pyrex cell. All of the drying procedure precedes the melting of the salt, and then the upper glass apparatus is removed and substituted with the ultrasonic cell. The ultrasonic cell compartment above the melt can also be blanketed by dry nitrogen when necessary.
Q 3OoC
0 35OC 0 4OoC
0 45oc
1200
*oo} I
I
I
5
IO
20 f(MHZ),
I
50
I
100
I
I
200
50
Figure 2. Plot of a/fz (om-' secz) vs. the frequency (MHz) for Ca(N0a)z. 4.3H20 at various temperatures.
The above assures the flexibility for working in anhydrous fused salts. X-cut quartz crystals of 3, 5, and 10MHz (fundamental) were used. The electronic equipment consisted of a Chesapeake U-100 pulser (frequency range 1-210 MHz) , an Arenberg WA-600-E receiver (frequency range 3-65 MHz), and a Matec 560 receiver (frequency range 5-320 MHz) . A 608A HewlettPackard standard signal generator and a Tektronix 535 scope completed the assembly. The mounting of this instrumentation and its detailed use have been discussed elsewhere.16
tX(N03)24.0H20 26001 cp 36OC 0 35oc 0 4OoC
0 45OC 0 60°C
8 75oc
2000~
Results
I800
a (cm-1) as a/f" (cm-l se?) a t various frequencies f
In Table I the results for the absorption coefficient (MHz) and temperatures ("C) are reported for the compositions investigated. The sound velocities measured a t 10MHz are also reported. No definite trend within the sensitivity of the method (&20 m/sec) was observed in the case of Ca(NOa)z.4.7H2O and Ca(N0,)2*5Hzo. In Figures 1 4 the quantlities 101'(a/f2) are reported us. the frequency f. For Ca(N03)z. 4Hz0 a t 75' a straight line indicates the absence of a relaxation (within the sensitivity of the data) in the frequency range investigated. For the other temperatures and compositions, the data have been fitted to the function for a single relaxation
1600
t" E
{ 1400
In 0
600
400 200
0
f(MH2)
Figure 1. Plot of a / f e (cm-1sec2) vs. the frequency (MHz) for
Ca(NOa)z.4Hz0 at various temperatures.
where B is the high-frequency value of a / f z , A is a (15) 9. Petrucci, J . P h y s . Chem., 71, 1174 (1967); 9. Petrucci and M. Battistini, dbtd., 7 1 , 1181 (1967). Volume YS, Number 4 April 1069
G. S. DARBARI AND S. PETRUCCI
924
Table I: Data of Sound Absorption a / f aand Frequency f for Various Temperatures and Compositions Investigated
-t
--t
=300-----. 1017 (01
= 350-
If 9,
(ff
cm-1 sect
f , MHz
f , MHz
7 - t
= 40°-
-t
=450--
1017
1017
If 2).
cm-1 sect
f , MHz
@/fa), cm-1 secz
3 2522 10 2225 15 2040 21 1900 27 1850 30 1840 33 1780 39 1720 45 1720 51 1670 75 1580 81 1570 u = 1915 f 20 m/sec
10 1573 5 1300 15 1180 15 1500 21 1349 21 1095 25 1110 27 1313 30 1360 30 1010 33 1254 35 1020 39 1232 45 970 45 1236 50 968 50 1200 55 960 51 1207 69 915 57 1181 75 902 70 1183 87 890 81 1174 105 868 87 1179 110 857 u = 1905 f 20 m/sec u = 1888 f 20 m/eec
--t
--t
= GO0-
-1
1017
1017
If , cm-1 secs
(a/f 9,
(aif 9 , cm-1 sect
(ff 2 )
f , MHz
I, MHz
3 1000 10 956 15 800 21 760 27 755 30 775 33 700 35 737 39 690 45 695 57 690 69 695 81 642 u 87 640 90 638 99 645 105 645 110 640 u = 1848 f20 m/sec
cm-1 secp
f , MHz
10 424 15 410 25 380 30 352 35 395 50 331 57 335 70 355 90 340 110 364 130 334 150 353 = 1830 f 20 m/sec
Ca(NO&. 4.3H20 e300---
= 350---
1017
(ffIf9, f,
cm - 1 seca
MHz
f , MHz
= 40°----1
---t
1017
1017
(ffIf93 cm-1 sec2
(a/f 2 ) *
15 1020 1450 25 980 25 1440 35 965 45 1310 55 1290 45 948 75 1235 65 910 85 888 85 1210 125 838 95 1150 135 815 105 1190 u = 1874 i 20 m/sec u = 1862 f 20 m/sec
15
f , MHz
cm-1 sect
15 750 25 748 740 35 45 738 65 700 673 75 695 85 95 658 105 675 115 655 u = 1860 i20 m/sec
-t
P
45”1017
(a:/f 2)
f.MHz
15 25 35 75 85 95 105
9
cm-1 sect
135
575 565 565 555 545 538 520 520 527
155
500
115
u = 1854 f20 m/sec
Ca(NOa)v4.7H20, u = 1856 f 20 m/sec = 250----.
-t
et
If 2 ) cm-1 seca
f, MHz
15 25 33 39 45 55 65 95 125 135
-~
945 885 868 880 835 825 795 795 750 740
= 30°--
= 35’-7
(ff
9
f , MHz
15 35 45 65 75 85 95 105 115 125
650 625 615 600 580 575 575 565 560 550
~~
The Jouvnal of Physical Chemistry
(aIf 2) *
If 9,
cm-1 sec2
=4O0-1017
---t
1017
1017
1017 (ff
t-
f, MHz
cm-1 seca
15 25 35 45 55 75 85 95 105 115 125 135 145 155
470 480 475 478 475 468 468 470 458 460 460 455 445 435
f , MHz
5 15 25 36 45 65 75 85 95 125 135 145
= 750-
-1
1017
(fflf?, cm-1 seca
415 395 390 385 370 378 348 348 355 340 345 330
= 4 6 O - 7
-t
1017
f, MHz
/fa) cm-1 sec*
15 25 35 45 55 65 75 85 95 105 115 125 135
275 275 285 295 295 285 285 280 280 280 275 265 265
(ff
1
5 259 16 200 25 200 35 218 45 210 55 214 65 221 75 181 90 180 110 196 130 179 150 192 170 189 u = 1820 f 20 m/sec
925
ULTRASONIC ABSORPTIONIN HYDRATED MELTS Table I (Continued) Ca(NOJz-5Hz0, u = 1847 ---t
(01/f?. cm-1 secz
15 25 45
f , MHz
75 85 95 105 115 135
505 495 478 485 475 478 473 455 428 435 418 408 410
15 25 35 45 55 75 85 90 105 115 125 135 165
660 643 653 643 600 600 575 550 560 540
55
if9 cm-1 secz
(01
20 m/sec
---t
E
409---
1017
1017
1017
f,M H s
= 350-------.
(01
cm-1
secz
f , MHz
15
constant, and fr is the relaxation frequency. Equation 1 has been fitted to the data as a three-parameter equation in A , B , and fr. The solid lines in Figures 1-4 represent eq 1, except for the melt Ca(NOa)2-4Hz0 a t 75’ where the best estimate of the value of a / f z is 10-17(200f 10) cm-l sec2. The results of the above calculations are given in Table 11. The A and B values are precise within &lo%.
If 2)
(ff /fa) *
9
cm-1
f. MHz
385 378 365 370 368 342 348 348 328 325 305
25 35 45 55 65 85 95 115 135 165
1017
1017
(olif2).
I
15 25 35 45 55 75 85 95 105 125 135 145 155 165 175 195
cm-1
sece
f, MRs
sec2
304 300 290 292 305 295 288 280 285 275 280 280 275 270 265 250
15 25 35 45 55 65 75 85 95 105 115 125 135 165
255 230 225 240 238 245 240 240 222 225 230 228 235 218
70 0
600
-- 500 ‘E
0 N
3
400
v)
Discussion According to Litovitz’l and Lamb,le the ratio a/$ exceeds the classical Stokes value for most liquids, the excess being due to a volume viscosity contribution to the energy loss. The total loss is
+ + ( y - 1)
a! 2n2 4 - = -[ - % q v
f”
PU3
3
‘1
(2)
CP
0 25‘C 30°C 0 35OC
a
Figure 4. Plot of a/f2 (cm-l see2) 2)s. the frequency (MHs) for Ca(NO& 5H20 at various temperatures,
with u the sound velocity, p the density (g/cm3), y = c,/cv, c, and cv the specific heats a t constant pressure and volume, respectively, .x the coefficient of thermal conductivity, qB the shear viscosity coefficient, and T~ the volume viscosity coefficient. The classical Stokes expression on the other hand is
’ooo 40%
45*c
fu;
loot
800
f(MH2)
Figure 3. Plot of a/fa (0rn-I seta) vs. the frequency (MHs) for Ca(NO&4.7HzO at various temperatures.
For almost all liquids (except liquid metals and liquid helium) the term due to the thermal conductivity is smallllJ* compared with the term due to shear viscosity. For the present data the aolaR8/f” (calculated on the basis of eq 3 omitting the thermal conductivity term) is lower than the B value in eq 1 as it can be seen from (16) J. Lamb, ref 11, pp 203-209. Volume 73,Number 4 April 1083
926
G. S. DARBARI AND S. PETRUCCI
Table 11: Densities, Shear Viscosities, A , B, andf, Parameters (a,,lasa/f2)and Ratios qv/qa and the Various Temperatures and Compositions Investigated
q v ’ / q B for
Temp, ‘C
p. g/cmr
?Ea
1011 A , cm-1 sec*
p
1017 B, c m - 1 seta
LO”(~8bokedfz) cm-1 secz 9
f r , MHz
%/%
tlp.’/~m = R
Ca(N0&4H20 30 35 40 45 60 75
1.743 1.738 1.734 1.730 1.717 1.704
2.014 1.392 1.062 0.835 0.427 0.234
1050 620 480 350 90
30 35 40 45
1.721 1.717 1.712 1.710
1.175 0.832 0.661 0.501
400 250 140 80
25 30 35 40 45
1.694 1.690 1.688 1.681 1.678
1.123 0.832 0.589 0.468 0.363
250 130 60 70 50
25 30 35 40 45
1.673 1.672 1.671 1.663 1.657
0.813 0.602 0.468 0.355 0.279
200 140 110 100 50
...
1500 1100 850 650 350 200
18 f 3 20 f 3 20 f 3 20 f 3 20 f 5
...
433 304 239 201 107 60
6.5 6.2 6.1 5.3 4.1 3.2
3.3 3.5 3.4 3.0 3.0 3.1
45 f 5 50 f 5 60 rf 10 70 f 10
272 197 157 121
6.0 5.8 5.3 5.0
4.0 4.1 4.1 4.2
272 202 143 114 89
3.3 3.0 3.1 3.2 3.0
2.2 2.2 2.4 2.4 2.3
201 151 110 89 70
3.3 3.2 3.5 3.4 3.2
2.0 2.0 2.2 2.0 2.3
Ca(NOJ2. 4.3H20 1100 800 640 500
Ca (NO&*4.7H20 720 520 400 320 240
60 f 10 70 f 10 100 f 10 100 f 20 120 f 20
Ca(NO& 5.0Hz0 500 380 290 220 190
Table 11. This suggests that contributions to qv from other relaxation processes with relaxation frequency higher than the one observed exist. The ratio v V / q s can be calculated rearranging eq 2 and 3 (dropping the thermal conductivity terms) into
(4) The value of a in eq 4 can be considered either below the observed relaxation frequency region or above it. I n both cases the ratio a / f z is constant with frequency. From eq 1 for f
