J . Phys. Chem. 1986,90,2168-2173
2168
Cr042-, MOO^^-, and W042-matches perfectly with the position of the SERS enhancement peak. The widths of the excitation profiles are about the same for each adsorbate. Thus, there is no evidence of any extra resonances for 0042-on silver that might be. associated with a dielectric layer of Ag2Cr04on top of the silver metal. The R R S excitation profile25of solid Ag2Cr04peaked at 676 nm, about 12000-cm-' red-shifted from its position in alkali metal salts of chromate. Also, the position of the q(Cr-0) Raman band was lowered to 812 cm-' in solid Ag2Cr04compared to its position30at 851 cm-I in solid K2Cr04. The most intense surface Raman band of chromate ion on colloidal silver showed a similar lowering to 800 cm-'; however, no lower energy component of v(Cr-0) at 777 cm-I as in Ag2Cr04was detected in the surface spectra. Thus, we conclude that Ag(1) complexes are not adsorbed on the colloidal silver surface in contrast to recent SERS evidence31 for the existence of such complexes on silver electrodes. Also, Raman spectra of solid Ag2Mo04show a similar lowRaman band position to 870 cm-' from e r i ~ of ~ the g ~ q(M0-0) ~ its position at 896 cm-I in solid Na2Mo04and show in addition a medium intensity u(Mo-0) Raman band at 759 cm-'. Mol(30) Carter, R. L.; Bricker, C. E. Spectrochim. Acta, Part A 1971, 27, 569. (31) Watanabe, T.; Kawanami, 0; Honda, K.; Pettinger, B. Chem. Phys. Lett. 1983, 102, 565. (32) Schwab, S. D.; McCreery, R. L.; Cummings, K. D. J . Appl. Phys. 1985, 58, 355.
ybdate ion chemisorbed on colloidal silver in the present work also shows a lowering of its most intense SERS band to 865 cm-] from 896 cm-I for the same band in aqueous solution. Finally, the position of RRS and SERS resonances for CrO,*on colloidal silver is reversed to be effective in promoting energy transfer from silver to the excited states of the dye on its surface. Though, if the energy difference between the Fermi level of the silver particles and an affinity level (LUMO) of the chromate molecule on the surface were to give a resonance,33we should have observed it in our excitation profiles. Acknowledgment. This work was supported by Army Research Office Grant DAAG-29-85-K-0102, by N I H Grant GM-30904, and by NSF Grant CHE-801144. Registry No. CrO.,-, 13907-45-4; Mood2-, 14259-85-9; WO>-, 1431 1-52-5; Ag, 7440-22-4. (33) Otto, A. Abstracts of Papers, 190th National Meeting of the American Chemical Society Chicago, IL; American Chemical Society, Washington, DC, 1985. (34) In this paper the periodic group notation in parenthesis is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups IA and IIA became groups 1 and 2. The d-transition elements comprise groups 3 through 12, and the p-block elements comprise groups 13 through 18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.g., 111-3 and 13.)
STATISTICAL MECHANICS AND THERMODYNAMICS Pressure Coefficients of Conductance and of Glass Transition Temperatures in Concentrated Aqueous LEI, LiI, and AICi, Solutions D. R. MacFarlane, Chemistry Department, Monash University, Clayton, Victoria 31 68,Australia
J. Scheirer, Chemistry Department, Albright College, Reading, Pennsylvania I9603
and S. I. Smedley* Chemistry Department, Victoria University of Wellington, Private Bag, Wellington, New Zealand (Received: September 25, 1985)
We have measured the conductance of LiC1-RH20,R = 4.5,7.0, and 8.75, solutions from -70 to 10 'C and AIC13.RH20, R = 2.4, 3, and 18, solutions from -10 to 10 "C from 1 bar to 4 kbar. Glass transition temperatures for LiC1.RH20 where R = 3.0,4.5, 8.5, and 10.0, LiI.RH20 where R = 6.0, 8.5, and A1C13.RH20where R = 18.0, 24.0, and 30.0 to 4 kbar were also measured. The maximum in conductance for LiCl cannot be explained by minimum TB,since all of these increase linearly with increasing pressure. Therefore, we attribute the conductance maxima in concentrated LiCl solutions to pressure-enhanced proton mobility, where the protons arise from the hydrolysis of the metal cation. Conductance maxima in dilute solutions are ascribed to the pressure-enhanced structure-breaking effects of the ions.
Introduction In OUT previous paper on this topic' we presented data which illustrated how the conductivity of LiCl and LiI solutions passed (1) S. I. Smedley and D. R. MacFarlane, J . Electroanul. Chem., 118,445 (1 98 1).
0022-3654/86/2090-2168$01 S O / O
through a maximum with increasing Dressure. For LiCl solutions the ratio Ap/Ai reached a maXin& of 1.06 that was only weakly dependent on composition and pressure for all solutions from 0.093 ( R = 57) to 2.34 ( R = 23) mol dm-3 LiCl at 20 OC. However, at'52.6 O C and aboce none of these solutions exhibited conductivity lEc&na. At 20 OC and concentrations above 2.34 mol dm-3 the conductivity maximum decreased rapidly and oc-
-
0 1986 American Chemical Society
Conductivity vs. Pressure for LiCl, LiI, and AlC13 curred at lower pressures, such that for a 12.41 mol dm-3 ( R = 3.85) solution the maximum was 1.003 at 780 bar; however, the maximum remained a t 53.9 OC but was absent a t 100 OC. The conductivity ratio APIA, for dilute LiI solutions behaved in a similar manner but the maximum was absent for 1.26 mol dm-3 solution a t 20 OC, and for all higher concentrations at any temperature from 20 to 100 "C. We interpreted the increases in conductivity in terms of two distinct mechanisms. In dilute solutions, where bulk water exists, we attributed the increase in conductivity with increasing pressure to the pressure-induced structure-breaking ability of the Li+ and C1- ions and the decrease in conductivity to the higher viscosity of water at high pressures. The diminution in the conductivity maximum at higher temperatures was explained by the fact that the water becomes much less structured at 50 OC and ionsolvent interactions become less significant. We postulated that the conductivity maximum in the concentrated solutions might arise from a minimum in Towith increasing pressure which, through the equation
"1
A = A exp[ T - To predicts a maximum in A. Equation 1 can be derived from the Adam and Gibbs2 theory of molecular transport which regards To as an ideal glass transition temperature a t which the configurational entropy of the liquid reaches zero, and hence ionic motion ceases. Therefore, if To ( P = 1) were the ideal glass transition temperature at 1 atm, and if an increase in pressure were to give rise to an increase in configurational entropy, and hence ionic motion, then a greater temperature interval would be required to reduce the configurational entropy to zero; hence To(P)would decrease with increasing pressure. Tois the glass transition temperature that would be obtained if the liquid was cooled infinitely slowly and is therefore usually somewhat below the experimentally determined glass transition temperature Tg. TBis usually determined at a cooling rate of 10 OC/min and at this rate the liquid cannot maintain internal equilibrium with the consequence that the liquid heat capacity usually falls to that of the solid phase a t a temperature that is -20 OC above To. Despite these differences TBgenerally follow^^-^ the same trends with increasing concentration and pressure as does the value of To determined via eq 1. Therefore, a good test of the proposition that it is the minimum in the ideal glass transition temperature which gives rise to the conductivity maximum would be to measure Tgas a function of pressure. The clear implication is that if Tgdoes pass through a minimum then the proposition is supported, but if it does not, then some other explanation must be sought for the observed phenomena. A further test of the applicability of eq 1 to these systems is to measure the conductivity to very low temperatures to determine if, as predicted, the conductivity maximum continues to increase with decreasing temperature. Thus, we have measured the conductance and glass transition temperatures of a range of concentrated LiCl and LiI solutions as well as for three AlCl, solutions. Aluminium chloride was included in this study because it is a salt that is known to hydrolize extensively in water. As discussed below, we consider that the conductivity maximum arises from the hydrolysis of concentrated LiCl solutions, and it seemed appropriate to test this concept by studying A1Cl3 solutions. Experimental Technique Solutions. Anhydrous LiCl from May and Baker was dried overnight in an oven at 200 OC. LiI from Fluka and AlC13 from BDH were hydrates and were not dried. Their composition was (2) G.Adam and J. H. Gibbs,J . Chem. Phys., 43, 139 (1965). (3) C. A. Angell, L. J. Pollard, and W. Straws, J . Solution Chem., 1, 517 (1972). (4) C. A. Angell, L.J. Pollard, and W. Straws, J. Chem. Phys., 50, 2694 ( 1969).
The Journal of Physical Chemistry, Vol. 90, No. 10, 1986 2169 determined by potentiometric titration against standardized A g N 0 3 and was found to be LiI.2.63H20 and A1Cl3-6.08H20. All solutions were prepared by weighing the appropriate amounts of the salt and doubly distilled water. Compositions are expressed in terms of the ratio R , with the number of moles of water to the number of moles of salt. Conductance Measurements. For conductance measurements the solutions were held in a Pyrex glass conductance cell 7 cm long made from two concentric thin-walled capillary tubes. The conductance measurement was made on the solution in the inner tube, using platinized platinum wire electrodes. The solution in the outer tube made contact with the hydraulic oil at its open end and with the measuring chamber through a small hole in the inner tube near the other end, thus preventing admission of oil to the conductance path. Pressurizing the sample simply moved the oil-solution boundary in the outer tube. The cell was held in a pressure vessel constructed from 3 16 stainless steel. Pressures up to 4 kbar were generated by pumping Shell Tellus 11 oil from a hydraulic handpump into a pressure intensifier and then into the pressure vessel. Pressures were measured by a Heise-bourden gauge calibrated in 10-bar divisions and accurate to f 5 bar. The pressure vessel was maintained at constant temperature by immersing it in a stirred ethanol bath held constant to f0.05 "C by a Hetotherm temperature controller. The bath temperature was measured with a chromel-alumel thermocouple with the cold junction in an ice bath, the emf being read from a Datron 1057a multimeter. When the conductance of a sample remained constant after a change in pressure or temperature, the cell was assumed to be in thermal equilibrium with the bath. Conductance was measured with a Hewlett-Packard Model 4192A L F impedance analyzer. The conductance of a sample was determined at 1 atm, then with increasing pressures up to about 4 kbar and with decreasing pressures back to l atm. No significant difference was seen between the initial and final 1-atm measurements or between measurements with pressure increasing and those with pressure decreasing. Glass Transition Temperature Measurements. Glass transition temperatures were measured by a differential thermal analysis procedure. One Inconel-sheathed chromel-alumel thermocouple 1 mm in diameter dipped into the sample in the bottom of a Pyrex glass tube 3 mm X 10 cm. A second identical thermocouple dipped into the pressurizing fluid, which was above the sample and served as a reference. This pressurizing fluid, a mixture of 90% isopentane and 10% Shell Tellus 11 oil by volume, was found to remain fluid at liquid air temperatures. The thermocouples were sealed into a standard Aminco pressure plug and the glass tube was held in position by a packing of Teflon tape. This assembly was screwed into a 18 mm X 18 cm pressure vessel made from stainless steel and connected to the pressure pumping system described above through a 4 cm X 35 cm stainless steel tube containing a moveable Teflon plug to separate the Shell Tellus 11 oil in the pump from the isopentane-oil mixture in the pressure vessel. This pressure vessel was placed into a close-fitting aluminum cylinder 5 cm X 15 cm high to ensure temperature uniformity in the sample area. The sample emf and differential emf from the thermocouples were recorded on a dual-pen recorder. The sample emf was also measured on a Daltron 1057a multimeter and recorded every 2 min on the chart paper, each time the differential emf pen crossed a line on the chart paper. By this procedure Tgvalues could be determined to an accuracy of about fl.O OC, the main uncertainty being in the interpretation of the TBtraces. In a run a syringe was used to place the sample in the bottom half of the glass tube. The tube was fixed in position around the thermocouples by Teflon tape. The rest of the tube was filled with the isopentane-oil mixture through a small hole near the top of the tube and the assembly was sealed into the pressure vessel, which was also filled with the isopentane-oil mixture. This pressure vessel, in its aluminum casing, was cooled rapidly by immersion in liquid air to at least 20 "C below its glass transition temperature. It was then attached to the pressure system, removed from the liquid air, and allowed to warm by heat from the room
2170
The Journal of Physical Chemistry, Vol. 90, No. 10, 1986
MacFarlane et al.
1 *26
1.24
1.22
1.20
1.18
1-16
K F 1 ' 1 4 1.12
1.10
$08 1.06
+ 04 1.01
1.00
.9E .96
.94 .92
.90
.8I
46
44
1
P K bar Figure 1. The conductivity ratio K ~ / K ,vs. pressure for various salt solutions, K~ and
to determine Tg a t 1 atm pressure. The heating rate was found to be about 4-5 OC/min in all measurements. As soon as Tghad been recorded, the pressure was increased and the pressure vessel was again immersed in liquid air to below its Tgvalue. It was removed and warmed to determine Tgat that pressure. Since the pressure changed slightly as the sample warmed, the pressure reading was recorded just after the glass transition was observed. Additional measurements of Tgwere then made at increasingly higher pressures up to about 4 kbar, and then at decreasing pressures back to 1 atm. Care was taken to avoid temperatures more than 20 OC above T in most samples to prevent crystallization, and the initial and h a 1 T i s at 1 atm were normally found to be reproducible to within 11.0 OC. Data obtained while increasing the pressure toward 4 kbar was indistinguishable from data obtained while decreasing the pressure toward 1 atm. For AlC13, R = 30, however, the solution crystallized just above Tg; hence it was necessary to warm the sample to room temperature to melt it after each Tg measurement. To determine the effect of imposing pressure below Tg rather than above Tg,all glasses in some runs were formed at 1 atm rather than under pressure, with no significant or systematic difference except for LiCl, R = 4.5. Tg traces for LiCl, R = 4.5,were found to be indistinct and nonreproducible when the glasses were formed under pressure, but they were quite distinct and reproducible when the glasses
are the conductivities at p and 1 bar, respectively. were formed at 1 atm; hence all T i s for this solution were obtained with glasses formed at 1 atm. K,
Results The conductivity results are displayed in Figure 1 and show that the conductivity ratio K , , J K ~ passes through a maximum for all but one of the AlCl, solutions, and that for the LiCl solutions and the remaining AlCI3 solutions the maximum increases with decreasing temperature at constant composition. The experimental glass transition data is shown in Figure 2. Tgincreases linearly with pressure from 1 bar to 4 kbar. LiC1, R = 4.5,solutions display two T i s over the pressure range of 0.5 to 1.5 kbar. The Tg vs. P. data for each solution were fit to a straight line by the method of least squares, and the resulting slopes and intercepts are shown in Table I. The intercepts from the LiCl and a1c13 solutions agree with the 1-atm data of Angell and Sare5 within about 2 OC, being generally higher. The dTJdP values are similar to those found for other ionic solutions by Williams and Angel16 who found for ionic liquids that dTg/dP lies in the range -0.6 to +11.0 K kbar-I. For LiCl, R = 4.5,the (5) C. A. Angell and E. J. Sare, J . Chem. Phys., 52, 1058 (1970). (6) E. Williams and C. A. Angell, J . Phys. Chem., 81, 232 (1977)
The Journal of Physical Chemistry, Vol. 90, No. 10, 1986 2171
Conductivity vs. Pressure for LiCl, LiI, and A1Cl3
- 95
J -95
-100
. -100
-105
- - 105
-110
. -110
-
-115
-120
-1 25
-115
-120
Y
R=6*0 -130 -135
I
- 80 - 85 - 95
-1 25
LiCI, R = 8 - 5 -130 -130
TL:
90
-120
1;
-125
-
-115
-130
. -120
-135
-
-125
-130
-
-130
-100
-105
-170
-110
'
-115
-115
/
-135
-110
1 -135
1 0
1
3
4
Figure 2. Glass transition temperatures of various salt solutions as a function of pressure.
TABLE I: Least-Squares Fit for T,-Pressure Data
solution LiCI, R = 10 LiCI, R = 8.5 LiCI, R = 4.5,low temp LiCI, R = 4.5,high temp LiCI, R = 3 LII, R = 8.5 LiI, R = 6.0 AlCI3, R = 30 AlCl,, R = 24
AlC13, R = 18
dT,JdP, deg/kbar (*O.l)
intercept (fl.O)
4.0 4.2 4.4 5.5 5.6 3.1 3.6 5.0 4.8 4.0
-132.0 -132.8 -126.7 -123.1 -108.7 -132.7 -130.6 -130.2 -124.2 -111.2
T~'(Ioc
-134 -1 34 -1 28 -111 -132 -132 -124 -111
'At 1 atm, Augell and Sare.
intercept from the lower temperature T, line is consistent with the 1-atm data. Discussion The results of the curve fitting for the Tgdata are displayed in Table I. dT,/dP for LiCl increases with increasing concen-
tration from 4.0 K kbar-I for R = 10 to 5.6 K kbar-I for R = 3. A similar increase in dT,/dP is seen for LiI where the slope increases from 3.1 K kbar-I for R = 8.5 to 3.6 K kbar-I for R = 6.0, although dTg/dP for LiI is less than that for LiCl for the same concentration. For A1Cl3 d T,/dP decreases with increasing concentration, from 5.0 K kbar-' for R = 30 to 4.0 K kbar-' for R = 18. LiCl solutions with R = 4.5 display a behavior more complex than that of any of the other solutions in this study, since they show two distinct glass-transition-like heat capacity changes, ACp, in the pressure range from 0.5 to 1.5 kbar. As the pressure is increased in this range the lower temperature ACp gradually becomes smaller while the higher temperature C, gradually becomes larger. The single Tg observed at pressures above 1.5 kbar is significantly larger than the single T, found below 0.5 kbar and is very well-defined. The slope, dT,/dP, of the lower temperature Tgis 4.4 K kbar-I, very close to the value of 4.2 K kbar-I for R = 8.5, while that of the higher temperature Tg compares closely with that of the R = 3 line. The least-squares intercept of the lower temperature T, line is -126.7 OC,in good agreement with the 1-atm T, of -128 O C 5 It appears that the application of pressure to LiCl, R = 4.5, in the glass state causes a liquid-liquid
2172 The Journal of Physical Chemistry, Vol. PO, No. I O . 1986 phase separation as the glass is warmed through Tg,the LiCI-rich phase being of higher glass transition and hence returning to a glassy state. Thus as the temperature is raised further a second glass transition is observed. Phase separation in concentrated LiCl solution at 1 atm was proposed by Angell and Sare' to explain the odd behavior of Tgtraces for R = 9 to 11, although it seems likely that their observations were caused by homogeneous nucleation of ice crystals.* Ice formation cannot explain our LiCI, R = 4.5, results since. the Tgtraces were found to be reproducible in terms of pen deflection at Tgfor many cooling and heating cycles without raising the temperature more than 20 OC above the glass transition temperature. Hsich et aL8 found evidence for phase separation for LiCl solutions at low temperatures from light scattering, but with a critical point at about 12 mol % ( R 7.3) and T, only about 2 OC above Tg. We assume that the effect of pressure is to shift the upper consolute point to higher concentration and temperature with increasing pressure. The important and obvious conclusion from Figure 2 with respect to the Ap/Al maxima of Figure 1 is that there is clearly no minimum in T,(P) as would be required in To(P)if eq 1 is to adequately describe the conductivity data. We proceed therefore to discuss some alternative origins for this phenomenon. The densities of solutions examined in this work were not obtainable by the previous method because of the limited range of operation of the mercury column technique; hence it is difficult to compare the present results with those, of ref 1. However, it is possible to obtain an estimate of (Ap/Al)maxby extrapolating the density data from ref 11. In order to do this we have plotted ( c ~ / c ~ vs. ) concentration ~ ~ ~ ~ , ~to, obtain ~ ( c O / C I ) ~ ~ ~ Cfor , ~ .R R = 57, 11.4, 5.6,4.96, and 3.85, and P = 1500, 2000, 2500, and 3000 ,~ of temperature to within bar. Since ( c , / c , ) ~ ,is~independent the limits of experimental precision, this graph enabled us to interpolate the C J C , ratio corresponding to the maxima in K ~ / K ~ The estimates of (Ap/A,),,,ax obtained from this information are displayed in Figure 1 and indicate that there is a very small maximum for the R = 4.5 solution which is almost independent of temperature and that the maximum for the other solutions increases with both decreasing temperature and concentration. These trends follow those observed in our earlier work, the effect becoming much more pronounced at the lower temperatures and showing little sign of diminution at still lower temperatures. In order to discuss the possible origin of these phenomena it is convenient to consider the LiCl solutions as falling into one of two categories, those below 2 mol dm - 3 as dilute solutions. and those above as concentrated solutions or molten salts. Dilute Solutions. From 0.092 ( R = 57) to 2.34 mol dm-' ( R = 23) (Ap/Al)maxis approximately constant and occurs approximately at the same pressure at 20 " C . We ascribe the maximum to pressure-enhanced increases in the mobility of Li+ and CI- ions.9 Since the increases in the mobility of the 1 2 and CI- ions with increasing pressure are attributed to pressure-induced rupturing or distortion of hydrogen bonds, then one would anticipate that at some higher pressure the rate of bond disruption would not be sufficient to overcome the effects of increased viscous drag on the mobility of the ions and the conductivity would begin to decrease with increasing pressure. Clearly, the relative rates at which the mobility initially increases with pressure because of bond disruption, and that at which it subsequently decreases with pressure, will determine the height and position of the maximum in AP/Al. The fact that the maximum is nearly the same for solutions within this range of concentration supports the contention that the phenomenon arises from the independent properties of each ionic cosphere. Above -2 M ( R = 26) the conductivity maximum diminishes as the concentration increases, a.nd this can be explained as arising from the overlap of cospheres at this concentration. However,
-
-(7) C. A. Angell and E. J. Sare, J . Chem. Phys., 49, 4713 (1968). (8) S.-Y. Hsich, R. W. Gammon, P. B. Macedo, and C. .I. Montrose, J . Chem. Phys., 56, 1663 (1972). (9) S. 1. Smedley, The Interpretation of Ionic Conducriuiry in Liquids, Plenum Press, New York, 1980. (IO) Y. Lee and J. Jonas, J . Magn. Reson., 5 . 267 (1971).
.
MacFarlane et al. at some concentration not far above 2 M, the concept of a cosphere becomes untenable as each ion will be within the cosphere of its neighbors and another explanation must be postulated for the conductivity maximum. Concentrated Solutions or Molten Salts. The low-temperature results from this work confirm the prediction of eq 1 when To is taken from the table in ref 1, i.e. the maximum becomes more pronounced for a given concentration as the temperature approaches To. This behavior is, however, completely contradictory to that predicted from eq 1 when To is given the values of Tg as measured in this work. Under these circumstances a conductivity maximum is not predicted. Now if the conductivity maximum arose from the pressureenhanced mobility of the I,i+ and/or CI- ions which, as we have observed, extends down to very low temperatures, then it is reasonable to expect that this effect would give rise to a minimum in 7g. This is because in the liquid at the glass transition temperature at 1 bar, an increase in pressure which gives rise to an increase in ion mobility will increase the translational entropy of the Li' and/or CI- ions. Therefore a lower temperature is required to reduce the translational entropy of those ions to zero; thus Tg would decrease with increasing pressure. If we take the experimental evidence at face value, we can conclude that either eq 1 is not applicable to LiCl solutions or some other means of ionic charge transport becomes important in concentrated LiCl solutions that does not affect the pressure dependence of Tg. A clue to what this mechanism might be is given by the work of Harman and Sutter."~'* They claim on the basis of their spin-lattice measurements" of LiCl in H 2 0 and D 2 0 that the activation energy for diffusion of water with respect to Li' is such that the water molecules do not undergo a loss of configurational entropy on going through the glass transition. In a later paperI2 they claim that the spin-lattice relaxation times for H 2 0in LiCl arise from the reorientation of hydrated water molecules by rotation about the dipolar axis, and by jumps from one hydration sphere to another. It is possible, therefore, that the conductivity maximum could be related to the mobility of water molecules in the system. Now if a water molecule, when sandwiched between a Li+ and a CI- ion in a concentrated solution, underwent hydrolysis then the proton vacancy so created could move rapidly around the Li+ ion, i n the direction of the electric field, by exchange from one water of hydration to the next and be passed from one hydration sphere to the next. This latter step would also be rapid since in concentrated solutions the hydration spheres are in contact. The mobility of a proton or proton vacancy in dilute aqueous solutions is about ten times that of the Li' or CI- ion. The excess proton mobility probably arises from the Eigen-DeMaeyer modeli3and is dependent on the reorientational correlation time for water. Our model for excess proton mobility in LiCl solutions would depend on the time for anisotropic reorientation of water about its dipolar axis which is ten times faster than the reorientational correlation time in dilute solutions.I2 In addition, the mobility of Lif and CI . ions in say 12 M solutions is about ten times less than in dilute solutions.' Thus we argue that the excess proton mobility in 12 M LiCl is about lo3 times that of the Li+ and CI- ions. Therefore, in order to produce the conductivity maxima that we observe, the concentration of proton vacancies would be such as to require the Now for hydrolysis constant of Li(H20)4+to be k, = 1 X Li+ in dilute solution kh = 1 X lO-I9,l4but this can be expected to increase considerably in very concentrated solutions where the 0-H bond is strongly polarized under the combined influence of a Li+ and a CI- ion. Indeed, NMR studiesI5 illustrate that the downfield shift of the proton resonance frequency (or the deshielding effect) in lithium halide solutions increases with increasing concentration and anion basicity. Furthermore, at E. J. Sutter and J. F. Harmon, J . Phys. Chem., 79, 1958 (1975). J. F. Harmon and E. J. Sutter, J . Phys. Chem., 82, 1938 (1978). Proc. R . SOC.London. Ser. A . 247. 505. 533 (1958). F. Bas010 and R. G. Pearson, 'Mechanisms of'lnorganic Reactions, Wiley, New York, 1958. (1 5) E. J. Sare, C. T. Moynihan, and C. A. Angell, J . Phys. Chem., 77, (11) (12) (13) (14j
1869-1876 (1973).
Conductivity vs. Pressure for LiCl, LiI, and A1Cl3 concentrations of R = 4 the shift for LiN03 and C a N 0 , are very similar, indicating that kh for both these solutions are comparable. The hydrolysis constant for Ca2+in dilute solutions is thus it is conceivable that kh for LiC1.4H20 could reach a value close to 10-8. The effect of pressure on the conductivity of LiCb4H20, according to the above scheme, would depend on (i) the pressure dependence of the Li(H20)4+and C1- mobilities, (ii) the pressure dependence of the hydrolysis constant, and (iii) the effect of pressure on the proton vacancy transfer mechanism. The activation volumes AV = -(RT a In h/dP), for Li(H20)4+and C1are positive in this region of concentration and become larger with decreasing temperature and increasing concentration. This fact accounts for the drop in conductivity at higher pressures, the hydrolysis constant being probably insensitive to pressure since the process involves the partial neutralization of two ions in solution. However, the proton vacancy mechanism would probably give rise to an increase in conductivity with increasing pressure. If the rate-determining process of the vacancy mechanism is the rotation of a hydration molecule about the dipolar axis, then hydrogen bonding of a water molecule in the hydration layer to another water molecule outside that layer, say in LiC1.5H20, would hinder the rotation. However, compression of the system would rupture some of these bonds and give rise to a drop in the rotational correlation times and an increase in the conductivity. Since hydrogen bonds are more likely to form at lower temperatures where the kinetic energy of molecules is reduced, then the effect of pressure on the conductivity will be enhanced as the temperature is lowered. According to the mechanism outlined above, the composition of LiCI.4H20 would have a zero or negative pressure coefficient of conductivity. This is because the vacancy mechanism would be unaffected by pressure, since there are very few water molecules outside the coordination layer of the Li+, and AVLi(Hp)4+and AVclwill be greatest. As R increases, the number of hydrogen bonds between hydration water molecules and those in the second layer will increase and give rise to a greater positive pressure dependence of conductivity; furthermore, AVLi(Hp)4+and AVcl- will be smaller and the maximum will move to higher pressures, as observed. However, at a concentration when Li(H20)4+and C1- are separated on average by two or three water molecules, hydrolysis probably becomes insignificant and the mechanism described for dilute solutions will become the prevalent cause of the conductivity maximum. On the basis of the above discussion it might be expected that many other ionically conducting systems would exhibit a conductivity maximum. For example, CaZf ions have a pressureenhanced structure-breaking effect in 4.5 M CaBr, solutions, and Ca2+ would hydrolyze water more strongly than Li+, but CaC12/H20solutions do not exhibit a conductivity maximum, at least for R = 6.0. The A1Cl3/H20 solutions studied in this work exhibit little or no conductivity maximum, yet the Al(H20)63f ion is extensively hydrolyzed in solution, and might therefore be expected to exhibit a conductivity maximum. We explain these observations by noting that the increase in conductivity with increasing pressure is ascribed to the decrease in rotational correlation time of a hydration water molecule about its dipolar axis and not to the magnitude, or the pressure dependence, of the hydrolysis constant, and that the decrease in conductivity is a result of the effect of pressure on the mobility of the ions. Thus for AlC13/H20 the pressure coefficient of conductivity would be given by
The Journal of Physical Chemistry, Vol. 90, No. 10, 1986 2173 it is for this reason that we believe the conductivities of CaCl, and AlCl, solutions do not pass through a maximum. For AICI,, 3. Lithium iodide solutions do show a small conductivity maximum, but only in dilute solutions up to 0.824 mol dm-3 and at 20 OC. Since the I- ion has a negative pressure coefficient of conductance, we attribute the maximum to the positive pressure-dependent mechanism for conductivity of Li+ as described for dilute solutions. The absence of a maximum is concentrated LiI solutions is best explained by the large negative pressure coefficient of conductivity expected from the large I- ion, and the probable absence of hydrolysis because of the lower anion basicity of this ion. Ichikawa et and Copestake et al.I7 have shown from neutron-scattering experiments that, for LiCb2.02H20 and LiC1.3.72H20, chloride ions penetrate into the Lif ion hydration sphere. Direct Li+-Cl- correlations are observed. Copeland and others compare the nature of the contact between the cation and anion as being similar to those in molten LiCl; indeed the first peak in their experimentally established chloride-chloride pair correlation function for LiC1.3.72H20 occurs at 3.75 A compared to 3.8 A from X-ray and computer-modeling experiments of pure LiCl. These experiments also indicate that in LiCb3.72H20 roughly equal numbers of water molecules and chloride ions are in direct contact with the Li', i.e. three of each, since the Li+ tends to sixfold coordination. The possibility exists therefore that the contact between Lif and C1- ions may produce a form of ion pair whose degree of association decreases with increasing pressure and has been observed in numerous molten salt systems. At low temperatures close to the melting point these systems contain multivalent cations or anions; however, ion pairs can also form at higher temperatures and at low densities in univalent-univalent systems. Both types of system show a greater positive pressure coefficient of conductance as the temperature is raised, because the system becomes more compressible at higher temperatures, giving rise to a greater change in the degree of association. This is not observed for the systems studied in this work where the opposite effect occurs. It is unlikely that the close contact between Lif and C1- ions in these hydrate systems leads to any significant form of ion pair formation whose lifetime is sufficient to affect the conductivity of the system. As far as conductivity measurements are able to determine, the degree of ion pairing in molten LiCl in the proximity of the melting point is insignificant, and the introduction of water to the system is unlikely to change this, especially in the case where at least two C1- ions can penetrate the hydration sheath, so that the Li ion is shared equally between the two.
x=
Conclusion
The condutance maximum observed in dilute LiCl solutions (below R = 23) arises from pressure-enhanced structural effects in the bulk solvent that give rise to increases in the mobility of the Li+ and C1- ions. At higher pressures these effects are overwhelmed by the viscous drag of the compressed solvent and the conductance decreases. For concentrated solutions, since Tg increases monatonically with pressure the conductance maximum cannot be accounted for by the VTF equation. Instead, it is postulated that pressure-enhanced proton mobility gives rise to the increase in conductivity with the protons arising from the hydrolysis of the metal cation. At higher pressures the conductivity decreases because of the viscous drag on the hydrated ions. Registry No. LiCI, 7447-41-8; AICl,, 7446-70-0; LiI, 10377-51-2; HzO, 7732-18-5.
where U is the single ion mobility and F Faraday's constant. Here the first term is negative and the second positive, and we assume that kh (term 3) is independent of pressure. Clearly, the greater the value of X the more likely that d h / d P will be negative, and
(16) K. Ichikawa, Y . Kameda, T. Matsumoto, and M. Misawa, J . Phys. C, 17, 725-729 (1984). (17) A. P. Copestake, G. W. Neilson, and J. E. Enderby, J . Phys. C,18, 4211 (1985).
