J. Phys. Chem. 1982, 86, 2094-2097
2094
TABLE VIII: Equilibrium Distances between Alkali Ions Framework Oxygen Ion in Lennard-Jones 6-12 Potential, r o , and the Distance between Oxygen Ion and the Center of the 8-Ring distance between and
oxygen ion and the center of the
small term of the polarization energy and consider the potential CP'. 9' =
CC[q(v)/ri(v) + UO(v)((ro(v)/ri(v))'* - 2(~,(v)/ri(v))~lI I
Y
We have by aid of the Laplace equation (V2CPrh=
132CC[(Uo(v)/ri(~)l~((rg(~)/ri(v))~~ - (5/11) X I
CS-A Rb-A K-A Na-A a
2.42 1.40 0.83 0.179
4.09 3.89 3.13 3.41
4.66 4.44 4.25 3.96
3.64 3.41 3.32 3.09
3.29 3.18 3.13 3.31
3.62 3.69 3.11 3.64
5.32 5.21 5.21 5.29
r* = r0/2'I6,at which V,-,, = 0.
especially in the direction perpendicular to the 8-ring plane. It may be said that the result is semiquantitatively reliable, as the covalent force may not operate so much in the present geometrical situation. Now let us discuss the existence of the double minima in the CP-z curve. The barrier height between the two minima is very small, e.g., 0.0086 eV, which is smaller than the limit of the reliability of the model used and the thermal energy at room temperature. In the real situation, the ninth sodium ion, NaII, is located not a t the center of the sodalite unit but at another site with a lower symmetry. Then the CP-z curve is deformed to be asymmetric, and one of two minima becomes deeper than the other and the true potential bottom. Even in such a case, the CP-z curve may have a very gentle curvature, and Cs+ thermally vibrates with a large amplitude. Hence, at higher temperature, Cs+ is easily displaced to make a path for a visiting hydrogen molecule to pass through the Cs+-blocked window. Principally, the potential surface might be calculated for the window-passing process. In such a calculation, however, a contribution of covalent force must be taken into account, which is beyond the present scheme, and future work is desired. We now discuss a criterion for the occurrence of the potential minimum. For simplicity let us neglect a very
Y
( ~ o ( Y /) r i ( ~ ) ) ~(18) Il
The conditions for the occurrence of a minimum, CPxxr > 0, a;, > 0, and az; > 0, require that a t least (VZCPr),> 0. The term in the square bracket in eq 18 becomes positive, if r i b ) < 2.21/6ro(v)
(19)
The distance between the center of the 8-ring and the framework oxygen, ri(v),is tabulated in Table VIII. The values for ro(v),in the table, are calculated by aid of eq 13 and the polarizabilities of respective cations. As can be seen from the table, the inequality 19 is always satisfied for pairs of 01-cation and 011-cation but not for those of OIrcation. Thus, this necessary condition is too loose to check the occurrence of the floating cation. A more severe measure is whether a cation a t the origin experiences a repulsive V,,, potential or not, since (d2Ve,/dx2)0< 0. If the distance between the pair of cation-oxygen, d(C-0), is shorter than r* (=r0/2lI6),the repulsive potential operates. Values for r* are also tabulated in Table VIII. The larger the difference r* - ~(C-OI), the higher the possibility of the cation floating. Thus, the possibility sharply decreases from Rb-A to K-A and Na-A. This is in good agreement with X-ray structural results. Acknowledgment. The present work was financially supported by a Grant-in-Aid from the Ministry of Education of the Japanese Government, Contract No. 443001. H.H. sincerely thanks the Toso-Shogakukai for the scholarship which enabled him to carry out the present work.
Conductivity Studies in Search of Liquid-Liquid Phase Separation by Solutions of Lithium In Methylamine R. Hagedorn and M. J. Slenko" Baker Laboratory of Chemistry, Cornell University, Ithaca, New Ywk 14853 (Received: September 9, 1981; In Final Form: December 1 1, 198 1)
The ac electric conductivity as a function of temperature has been measured on a series of lithium-methylamine solutions spanning the metal-nonmetal transition. Ten solutions in the range 3.5-17.4 MPM (mole percent metal) were investigated between 180 and 230 K. No breaks in the resistivity vs. temperature curves signaling liquid-liquid phase separation were observed, even for the most concentrated solutions. All the data could be fitted to functions of the type u = uo exp(-hE/kT). AE showed a maximum value of 0.16 eV at 11 MPM. The analogous maximum in lithium-ammonia solutions has a value of 0.15 eV for AE and occurs at 4 MPM. Introduction A characteristic feature of metal-ammonia solutions (except for cesium) is the separation on cooling into two coexisting liquid phases.' Pitzer, in 1958, suggested that (1) For an excellent review, see J. C. Thompson, 'Electrons in Liquid Ammonia", Clarendon Press, Oxford, 1976, Chapter 5. 0022-3654/82/ 2086-2094$0 1.2510
this separation into two liquid phases is a "liquid-vapor phase separation of the sodium within the ammonia solvent",2thus connecting it to the metal-nonmetal transition that is also characteristic of these systems. In the case of lithium, the miscibility gap occurs at 210 K and (2) K. S. Pitzer, J. Am. Chem. SOC.,80, 5046 (1958).
0 1982 American Chemical Society
Conductivity Studies of Li-CH,NH,
4.5 MPM;3 the metal-nonmetal transition, though somewhat dependent on the property change used to define it, occurs in the range 2-8 MPM.4 Recently, in an effort to understand better the role of the solvent in fixing the electronic properties of these solutions, extensive studies were undertaken of the electron- and nuclear-spin-lattice relaxation in lithium-methylamine solutions.5 Preliminary studies indicated that the sign of dTl,/dT (where TI, is the electron spin-lattice relaxation time) passes from positive to negative at the nonmetal-to-metal transition. Subsequent work placed the transition in the range 13.4-15.6 mol % lithium.6 In a detailed study of the ESR as a function of temperature for a range of lithium-methylamine solutions from 6.5 to 21.1 MPM, Buntaine' found curious kinks in the line width vs. temperature curves for two of the compositions, 15.6 and 18.0 MPM. As explanation of these kinks, which occurred between 180 and 220 K, and two visual sightings at 188 K of color boundaries in 16.4 and 18.0 MPM samples just taken out of an ultrasonic homogenizer, it was proposed that liquid-liquid phase separation was occurring in the lithiummethylamine systems just as in other M-NH3 solutions. The suggested consolute point was placed at 12-13 MPM and 200 K.* Because the phase diagram for Li-CH3NH2, as determined by Hagedorn and Lelieurg from DTA and vapor pressure studies, showed no miscibility gap, this investigation was undertaken to see if evidence for phase separation could be obtained from conductivity studies. Kraus and Lucasse'O had shown very early that one of the easiest methods for tracing the liquid-liquid phase separation in Na-NH3 solutions is to measure the conductivity of the solutions as a function of decreasing temperature in a U-shaped cell. When phase separation occurs, the more dilute, dense phase collects in the bottom of the U and raises the resistivity of the cell, thus producing a kink in the resistance vs. temperature curve at the temperature of phase separation. Experimental Section Starting materials were 99.99% lithium from Lithium Corporation of America and 98% methylamine from Matheson Co. Impurities in the methylamine were 0.0% ammonia, 0.8% (maximum) dimethylamine, 0.6% (maximum)trimethylamine, and 0.8% (maximum) water. The methylamine was stored over freshly cut lithium metal at -188 K for a minimum of 48 h before use. Subsequent mass spectrometric analysis showed no NH3 or H20. The lithium metal was cut and weighed in an evacuable DriLab under helium containing less than 1ppm of oxygen or nitrogen. The conductance cell was similar in design to one used previously in this 1aboratory.l' Two tungsten electrodes were sealed into glass tubes which were connected by a U-shaped capillary. The electrical resistance measured depended on the length and diameter of the capillary; three cells with different tube diameters of 0.1,0.3, and 0.5 cm (3) D. E. Loeffler, Ph.D. Thesis, Stanford University, 1949. (4)G. Lepoutre and J.-P. Lelieur in 'Metal-Ammonia Solutions, Colloque Weyl 11", J. J. Lagowski and M. J. Sienko, Ed., Butterworth, New York, 1970,p 271. (5)P.P. Ewards, J. R. Buntaine, and M. J. Sienko, Phys. Reu. B, 19, 5835 (1979). (6)J. R. Buntaine, M. J. Sienko, and P. P. Edwards, J. Phys. Chem., 84,1230(1980). (7)J. R. Buntaine, Ph.D. Thesis, Cornel1 University, 1980. (8)J. R.Buntaine and M. J. Sienko, J. Phys., 41C8,36 (1980). (9)R. Huedom and J.-P. Lelieur. J. Phvs. Chem.. 84.3652 (1980). (lo)C. A-Kraus and W. W. Luckse, J.-Am. Cheh. Am., 44. 1949 (1922). (11)M. J. Sienko, J . Am. Chem. SOC.,71,2707 (1949).
The Journal of Physical Chemistry, Vol. 86,No. 11, 1982 2095
Li -CH3NH2
to
2.51
9.4 M P M
\
\ O\ 0,
" I I .5
O'O
\
I I0O
220
200
T [KI
Flgure 1. Resistivity of lithium-methylamine solution as a function of temperature at a concentration of 9.4 MPM.
were used. Cell constants were determined with standard KCl solutions, using specific conductance values taken from standard tables.I2 So that decomposition problems were minimized, the cells were thoroughly cleaned prior to each use. The electrodes were cleaned by electrolytic action on concentrated KOH solutions, rinsed with distilled water, then rinsed quickly with a HF/HN03 mixture, rerinsed with water, and finally dried at 100 "C. Lithium was introduced into the cell through a side arm, and the cell was pumped for about 12 h to a pressure of less than 5 X lo* mmHg. A known amount of methylamine, which was dried and stored over lithium, was condensed from a calibrated bulb into the cell at liquid nitrogen temperature. When the condensation was complete, the cell was disconnected from the line and the solution made by introducing the cell into a dry iceethanol bath. The cell was allowed to warm to about -40 "C to facilitate complete dissolution and homogenization. By proper manipulation of stopcocks on the two arms of the U, the solution could be forced back and forth through the capillary until mixing was complete. The homogenization process turned out to be quite long for the more concentrated solutions. For the electrical measurements, the cells were introduced into a thermostatted bath, the temperature of which was monitored by an Oxford Instruments temperature controller with an accuracy of 0.1 "C. The resistance was measured with an ac bridge connected with copper wires to the tungsten electrodes. Each run was performed at least twice to ensure reproducibility. An inhomogeneous solution showed up by giving lower resistance values from one run to the next. After a measurement was completed, the cell was reconnected to the vacuum line, the solution frozen with liquid nitrogen, and checked for possible decomposition by measurement of residual hydrogen pressure. Measurements where decomposition occurred were discarded. In this way, samples between 3.5 and 17.5 MPM and in a temperature range between 180 and 230 K were measured. The error of the measurements is believed to be *2%. (12)A. Weissenberger and B. W. Rossiter, Ed., 'Physical Methods of Chemistry", Wiley-Interscience, New York, 1971,Vol. I, part IIA, p 178.
The Journal of Physical Chemistry, Vol. 86, No. 11, 1982
2096
Hagedorn and Sienko
TABLE I: Resistivity Constants for Lithium-Methylamine Solutions
t
log R = C,
concn, MPM 3.5 5.4 9.4 10.6 11.4 11.9 13.3 15.4 16.1 17.4
h
3
‘0
[ L i -
4 t
..
‘1 1
1
/
1
/
180
1
1
/
I
l
l
1
+
(CJT)
C,
C,
- 1.40
610.3 657.2 763.4 843.4 832.6 813.6 749.9 576.8 380.1 199.5
- 1.87
3.21 -4.07 -4.11 - 4.08 -4.45 -4.36 -3.28 - 2.69 --
t
,
2 20
200
[KI
T
t
Figure 2. Resistivity as a function of temperature at a concentration of 17.4 MPM.
t
W Q
0.08
0.04
0.6.
1
6
\\
/
I
I
1
4 -I
0 . ”
1
I
I
12
8
I
I
I
.
16
MPM
P’
-
I
I l
l
l
l
l
l
l
l
l
.
Figure 4. Apparent “activation energy“ hE for conductivity expressed as u = no exp(-A€lkT). The solid line represents Li-CH,NH, (this investigation); the dashed line represents Li-NH, (after ref 16).
MPM
with increasing concentration, suggests that there would indeed be sufficient difference in density between coexisting phases (anticipated to be 9.3 and 16 MPM at 160 Ks) that the concentrated phase would easily rise to the top of the cell. Viscosity, nevertheless, could impede this; unlike the case of metal-ammonia, where viscosity deResults and Discussion creases with metal concentration, it is known that conFigures 1 and 2 display the resistivity vs. temperature centrated solutions of lithium in methylamine are conresults from two different concentration regions. The run at 9.4 MPM (Figure 1)is, according to the ESR eviden~e,~ siderably more viscous than dilute ones.15 Still, it must be admitted, we observed no time effects in our experion the nonmetallic side and the run at 17.4 MPM (Figure ments. Hence, on the basis of these experiments, it ap2) is on the metallic side of the metal-nonmetal transition. pears that in the observed temperature and concentration Neither curve shows any obvious breaks or kinks. The range for Li-CH3NH2 there is no liquid-liquid phase runs displayed are typical of the whole series of measeparation. surements. Between the two concentrations represented in Figures Interpolation of our data to 208 K allows comparison 1 and 2 there is a drop of more than two orders of magwith the results of Toma, Nakamura, and Shimoji.13 nitude in the resistivity, and the temperature dependence These workers had previously investigated the electrical is strongly diminished (note the change of scale for ordiconductivity and thermoelectric power of concentrated nates of Figures 1and 2). It is possible to fit the observed lithium-methylamine solutions from 200 to 213 K but it data in the nonmetallic regime to a function of the form was thought they may not have gone low enough in temperature to detect phase separation. Figure 3 shows a log R = C, + (C,/T) comparison between our results interpolated to 208 K and which reflects an Arrhenius-type function corresponding those reported by Toma, Nakamura, and Shimoji. As can to a thermally activated conduction mechanism. Surbe seen the results are in good agreement. prisingly, this fit turned out to be the best over the whole I t should be noted that, for this technique to detect concentration range observed. Table I gives for the various liquid-liquid phase separation, there must be a physical lithium-methylamine solutions the values of the constants separation of the two coexisting solutions into different C1 and C2 from which the experimental curves can be parts of the measuring cell. Densities of lithium-methylreconstructed. It should be noted that, for the higher amine solutions have not been measured below 223 K nor concentrations (above 15 MPM), the data can be fitted for solution more concentrated than 10 MPM. However, equally well by using a simple power law. extrapolation of the results of Yamamoto, Nakamura, and Shimoji,14which show a pronounced decrease of density Figure 3. Semlkgarithmic plot of conductivlty as a function of concentration for lithium-methylamine solutions at 208 K. Circles indicate measurements from this investigation: the solld curve is constructed after ref 13.
(13) T. Toma, Y. Nakamura, and M. Shimoji, Phil. Mag., 33, 181
(1976).
(14) M. Yamamoto, Y. Nakamura, and M. Shimoji, Faraday SOC., Trans.,67, 2292 (1971). (15) M. Yamamoto, Y. Nakamura, and M. Shimoji, J . Chem. SOC., Faraday Trans. I, 68, 135 (1972).
Conductivity Studies of LI-CH,NH,
To yield an “activation energy” for the conduction process, the resistivity data were converted to conductivity data and expressed as u = uo exp(-AB/kT) The values so obtained for A E are displayed in Figure 4. They are compared there with the results found for lithium-ammonia solutions. Nasby and Thompson16investigated the Hall voltage and conductivity of Li-NH, over the range 1.2-14 MPM and found they too were able to fit their data with a similar equation indicative of a thermally activated process. The Li-NH, system is considered to be metallic above 8 MPM, and the data for the metallic solutions can be equally fitted by a power law. Comparison between the ammonia and methylamine systems (Figure 4) shows similarity in that the activation energies are about the same and both systems show a peak in the activation energy at the point where the metalnonmetal transition begins. The subsequent drop in the activation energy can be interpreted as the closing of a pseudogap in the Mott sense.” This occurs at a higher concentration in methylamine than in ammonia: the surface tensions are about the same, the dielectric constant of CH3NH2is less than that of NH,, hence, the solvated electron is more confined in CH3NH2than it is in NH,. (In H20, the solvated electron is even more confined because extraordinarily high surface tension favors a smaller cavity despite a large dielectric constant.) The concentration dependence of conductivity in the metallic range for lithium-ammonia solutions has been quantitatively accounted for by Ashcroft and RussakofflB by modifying the approach of Faber and Ziman19for binary mixtures. The lithium-ammonia solutions are considered as binary mixtures containing two scatterers with different scattering length; one scatterer is the free ammonia, viewed as a point dipole, and the other is the solvated Lit cation. Since they view the free ammonia dipole to be the stronger (16)R.D.Nasby and J. C. Thompson, J. Chem. Phys., 53,109(1970). (17)N.F. Mott, Phil. Mag., 19,835 (1969). (18)N. W.Ashcroft and G. Russakoff, Phys. Rev. A , 1, 39 (1970). (19)T. Faber and J. M. Ziman, Phil. Mug., 11, 153 (1965).
The Journal of Physical Chemistry, Vol. 86, No. 11, 1982
2097
scatterer and since its concentration is rapidly depleted as more Lit is added to be solvated, they are able to explain the unexpectedly strong concentration dependence of the conductivity in the lithium-ammonia solutions in the metallic regime. Although the lithium-methylamine solutions roughly follow the same general trend, it is not possible to use directly the Ashcroft-Russakoff approach for our solutions. Methylamine is a somewhat weaker dipole than ammonia and, if the electrons are scattered principally by the long-ranged dipole forces, we would expect the resistivity to diminish on going from Li-NH, to Li-CH3NH2. The opposite is the case. Ashcroft and Russakoff regarded the NH, molecule as a point dipole and neglected the scattering power of the ammonia central potential. It may be that the central potential of the methylamine molecule is a more important factor because the molecule is larger. The actual calculation, however, of the scattering of the electrons by the central potential of the methylamine is rather difficult. Another complication is that, even in the most concentrated solutions, the Li-CH3NH2 solutions may not yet have reached true metallic behavior. At saturation (approximately 22 MPM) the electrical conductivity13is approximately 400 (Q cm)-’, a factor of approximately 40 below the corresponding value for saturated Li-NH, solutions, and very close to the predicted minimum metallic conductivity20 uCrit 100-300 ( Q cm)-’. There is also independent evidence from ESR experimentsz1that concentrated Li-CH3NH2solutions are in the strong scattering regime where the transport is more diffusion-like. Acknowledgment. This investigation was sponsored by the National Science Foundation under grant No. DMR 78-12238 and was supported in part by the Air Force Office of Scientific Research and the Materials Science Center a t Cornel1 University. R.H. thanks DFG (Deutscheforschungsgemeinschaft)for travel support. (20)N.F. Mott, “Metal-Insulator Transitions”, Taylor and Francis, London, 1974. (21)P.P.Edwards, A. R. Lusis, and M. J. Sienko, J. Chem. Phys., 72, 3103 (1980).
