2672
C. E. Vallet and J. Braunstein
Application of the Quasilattice Model to Association in Dilute Reciprocal Molten Salt Mixtures. The System Silver Sulfate-Potassium Nitrate' 6.E. Vallet** and J. Braunstein Reactor Chemistry Division. Oak Ridge National Laboratory. Oak Ridge, Tennessee
(Received M a y 70, '1973)
Pubiication costs assisted by Oak Ridge Nationai Laboratory
New emf measurements of the molten salt concentration cell Ag[KN03,AgN03(ref)jKN03,Ag1\;03, KZS04JAg were carried out over a wide range of silver nitrate concentrations ( 2 x to mole ratio) and with a new temperature cycling procedure. Experimental results are conipared with previous data and analyzed in terms of conventional association constants and the generalized quasilattice model. The pair association energy corresponding to the equilibrium constant K1 of (AgS04)-, MI, is found temperature dependent with - ( d A A l / d T ) 2.5 X 10-3 kcal/K. The dinuclear association constant K12 and association energy, AAIZ for Ag-S04-Ag, are found to be significant in this molten reciprocal system.
-
Introduction Measurements of association equilibria in dilute reciprocal molten salt mixtures ( i e . , dilute solutions of at least one foreign cation and one foreign anion in a molten salt solvent) provide valuable test.s of physical models such as the quasilattice model of molten salt^.^.^ The system silver sulfate-potassium nitrate is of particular interest for a number of reasons, as indicated by previous investigations by means of emf m e a ~ u r e m e n t s 5and . ~ phase diagrams.7 First, it is one of few systems in which a temperature dependence of the association energy has been r e p ~ r t e d , ~ but this temperature dependence has been questioned in a more recent study.6 Second, systems of mixed charge type offer a number of problems connected with the Temkin activities of various charged and neutral species and the counting of sites on the q ~ a s i l a t t i c e . ~ sS Third, the phase diagram investigation? provided a confirmation of the applicability of conformal ionic solution theory9 to the concentrated solution region of AgzS04 in molten K N 0 3 . Data in the dilute solution region, where a quasilattice correction term becomes important,1° appeared to be more consistent with a temperature-dependent association energy5 rather than with a more recent report of a constant association energy.6 It therefore seemed worthwhile to carry out a careful reinvestigation of the possible temperature dependence. Finally, the previous investigations were carried out over only a limited range of silver concentrations, making it impossible to analyze the data for higher order associations than the pairwise association s4
Ag' + SO4'+ T--t AgSO,-; K , In most dilute reciprocal molten salt systems in which further association has been observed, it has been found that the association h\.lX':-l'+ +
x-
?--)
MXE''-''+. , K ?
is considerably stronger than dinuclear association Mx'-'"
+
lcI'+
*
M,X~2:-"f.
, K,? where M is Ag or Cd. In the case of Cd, Klz is found to be negligible, probably by virtue of the high charge of the cation. It therefore seemed reasonable to design new exThe Journal of Physicai Chemistry, Voi 77. No. 22. 1973
AgNO:;AgK03 A g KSO:,
1 KKO,j ; K2SQ
Ag
(A)
2673
Silver Sulfate Associations in Molten K N 0 3 TABLE I: Reproducibility of Emf Data Obtained in a Temperature Cycle
Time. hr
R2(Ag)
R*(S04)
0 2.6
x
Emf at 622 K , mV
Emf at 663 K,mV
...
-32.14
10-3 -33.05
2.5 4.5 5.5 2.6
x
10-3
5.6
x
-37.34
-38.53
...
10-3
...
6.75 7.75 8.5
10.0 2.6
x
...
...
-37.17
-38.52 -42.01
...
...
-40.58
...
-40.95
...
I O x 10-3
10-3
22.0 23.5
-42.14
, . .
perature was controlled by means of a chromel-alumel thermocouple in the aluminum block, its hot junction being at the same level as the middle of the liquid in the cell, connected to a Leeds and Northrup D.A.T. controller and Speedomax H recorder. The temperature of the melt, measured with a second chromel-alumel thermocouple dipping in the cell, was found constant to k0.2" over the runs. The temperature of the melt was recorded continuously with a Honeywell potentiometric recorder. Cell and Electrodes. The reference compartments were of Pyrex tubing (8 mm 0.d.) with an asbestos fiber sealed into the bottom as described previously.12 They contained 4 molten (K-Ag)N03 solutions (mole ratio Rl(AgX03) x 10-3) with a silver wire electrode dipped in the melt. The measuring compartment was a 250-ml Pyrex beaker into which was dipped a bare silver wire electrode. The melt ( K N O S - A ~ N O ~ - K ~ S ~ ~ ) ( R z~( (SA 0 4~) ) , in the beaker was vigorously stirred and sparged with oxygen-free argon in each experiment. The emf's obtained were mostly in the range -50 to +50 mV. The quantities of K N 0 3 employed in the beaker as solvent were approximately 1 mol. Emf measurements were made with a Keithley dc differential voltmeter. Electrode Behavior. ( a ) Potassium ,Vitrate-Siluer LWtrate M e l t . Previously,13 similar cells have been used extensively and it was shown they follow well Nernst's law
-
RT
E = -F
x2(XgNO J In x,(AgNO,)
discrepancy through a run of 5 X 10-2 mV. The emf's were unchanged if measured relative to different silver electrodes in the beaker. In this way, random errors arising from variations of bulk melt composition or temperature variation are separated from errors associated with the reference electrodes. When we operated at 663 and 622 K in a run, we checked the reproducibility of the emf measurements on returning to the initial temperature. An emf measurement was taken first a t temperature T , and then the temperature was fixed a t T' and another emf measurement made; the temperature was then returned to T and a new measurement was made, followed by another at T'. Table I gives results of one such cycle (this one being the worst case in terms of Kernst behavior before adding sulfate). The relative variation in measured emf changes is less than 1%at the lower temperature and less than 5% at the higher temperature. The Evaluation of Association Constants and Quasilattice Parameters from Emf Measurements
Calculation of Conventional Constants K1, K12. The emf change upon K & 0 4 addition to compartment 2 of cell A is given by
where Z(Ag) and f(NO3) are ionic fractions before the
KzS04 addition and y(AgNO3) is the activity coefficient of silver nitrate. In terms of ionic and mole ratios R, the activity coefficient may be expanded in power series for dilute solutions in AgNO3 and K2S04.14
where Kl's are the conventional association constants
Equation 2 can be rewritten in terms of the mole ratios R, since the experiments are most conveniently carried out a t constant mole ratios of silver nitrate rather than at constant mole fractions of silver nitrate. The resulting expression for the emf change is
where 1 refers to the reference compartment, xj(AgN03) being t)he mole fraction of AgN03 in compartment i. First, we checked our electrodes for comparison with Nernst's law by isothermal runs; we found very good agreement, better than 0.1 mV. Furthermore, runs carried RT out at two temperatures provided a test of Nernst behavAE=X F ior of the electrodes by means of the difference [(T'/ ?')E(T)- E(1")j. The average deviation was found less than 0.1 mV for ten runs and three electrodes. Although we observed after two working weeks a shift of the Nernst line, the E cs. In RZ(AgN03) relation was still a linear one during a run. ( b ) Potassium rVitrate-Siiluer Nitrate-Potassium Sulfate Melt. An estimation of the errors was provided by simulFor experiments carried out in dilute solutions, i.e.. taneous emf measurements with two reference electrodes R(KZS04) and R(AgN03) loo), these numerical factors are negligible. The silver-sulfate association constants, however, have values about 13 and hence the numerical factor 3 in eq 7b cannot be ignored. The factor 3 in eq 7b is not an approximation but results from the evaluation of the limit. Because the measurements in this study were carried out over a wide range of silver contents and extrapolated to zero silver concentration, eq 7b gives an evaluation of K1 that is independent of the quasilattice model. In previous investigations of this system only a very limited range of silver concentration was investigated, and it had therefore been necessary to employ the quasilattice model in the evaluation of the association constants. Our wide range of silver concentration also made possible the evaluation of Klz from eq 7c, which was not possible with earlier investigations. Q u a d a t t u x Model Calculations. With the quasilattice model,l5 the association constants obtained from the above relations are related to energy parameters for nonrandom mixing on the quasilattice. In the present case, ions of differing charge type are present in the melt; hence the asymmetric approximation16 for a single kind of ligThe Journal of Physical Chemistry, Vol. 77, No. 22, 7973
Results
Emf Measurements. Since previous investigators536 reported very small emf changes in cell A on potassium sulfate additions and a discrepancy in the temperature dependence of the association energy, we carried out a rather large number of experiments 1 8 in order to resolve the discrepancy conclusively. We made measurements mainly at 349 and 390", the higher temperature being below 400" to avoid salt decomposition, mentioned as a possibility in the discussion of results in ref 6. A few measurements were made also at 430". Calculations. Determination of Association Constants from t h e Emf Measurements. In the KzSO4 concentration range studied, 0 < Rz(KzSO4) < we found a linear dependence of the emf changes on the potassium sulfate mole ratio. From the experimental data, [aAE/ ~ R Z ( K ~ S O ~ ) J) Rwas ~ C derived A ~ N ~ with ~ a least-squares eq 7b and 7c, values of ( 8 ) = [ ~ ~ E / ~ R z ( K z S ~ ~ ) ] R , , A ~ N are plotted against the mole ratio of silver nitrate tions were employed to reduce the subjectivity of the results.) The data scattering being very small, the leastsquares lines are very close t o each experimental result; a t Rz(KzS04) = 0, for example, the zero shift, [LE(, is always found to be less than 0.1 mV. The least-squares fits to the data are shown in Table 11.
2675
Silver Sulfate Associations in Molten KN03 at )Rz(KzS04) TABLE I I : Least-Squares Limiting Slopes (s) = [ ~ ~ E / ~ R ~ ( K ~ S O ~ ] R , , . ~= ~0 Fitted ~ ~ ~ to the Emf Measurements
r = 622 K
-
-
r = 663 K
_ _ _ _ _ _ _ _ I
Rz(AgN9) x 100.207 0.486a 0.96 1.43 1.43 2.6b 2.66c 6.96d 8.3 8.7e
(S),
v
Zero shift, vxio-5
Rz(AgN23)
x 10-
v
vx
(SI,
0.1 7
-3.9 -5.6 3.2 3 4 3.9 -2.5 5.3 -5.8 -0.8584 -0.7952
Zero shift,
RZ(AgN9)
x io-
10-5
3.87 4.4 4.77 4.77 6.96d 7.38 7.77 8,7e
-4.5 -2.4
0.38 0.481~ 0.759 0.89 2.2 2.6b 2,66e
(S)
-19 -6 -1.5 -0.8
-11 -4.3
Zero shift,
v
vx
10-5
-5.8 -1.5 -1.4 -0.74 2 0.17 -1.3 -0.4
-0.9100 -0.9090 -0.9225 -0.9340 -0.9794 -0.947 -0.901 -0.9064
-1.4 -14
a-e Values obtained in temperature cycles
"
I In order to obtain the association constants as given by eq 7b and 7c, values of (s) = [ ~ ~ E ~ R Z ( K ~ S O ~ ) ] R , ( ~ \ ~ N ~ ~ ) are plotted against the mole ratio of silver nitrate Rz(AgN03) a t both temperatures, 622 and 663 K, as shown in Figure 1. The least-squares equations of these lines are: for 10 silver concentrations a t 622 K
_!
..
u)
'
8
!T=663K
- 0.7 2
0
4
8
6
(x~o-~)
RZ(AgN031
and for 16silver concentrations a t 663 K
Figure 1. Least-squares extrapolation of limiting slopes (s) to zero silver nitrate mole ratio.
(s) = -0.9170(&0.0200)
The corresponding value of the association constant for the equilibrium Ag+
+ SO,'- P (AgSOJ-;
Ki
calculated by means of eq 7b is a t 622K: K I = 13.232 f 0.321 a t 663 K: K , = 13.051 f0.350 Since the evaluation of K12 involves both the intercept and the less accurate slope of the least-squares line, the accuracy of Kl2 will depend on the relative magnitudes of the second and third terms on the right-hand side of eq 7c. Since
vs. mole
[dAE/dR,(K?SO,)],?:,,,,,:
lim RnK.sO?,
- 1.3915(&4.3463)R,(AgXO3)
=0
ratio of silver nitrate at 622 ( 0 )and
663 K ( 0 )
Table 111, the disagreement between these authors is greatest a t the highest temperature (440"). Our measurements a t 430" were in excellent agreement with Watt and Blander's result a t this temperature as seen in Figure 2. In further calculations we omitted the discordant result arising probably from a systematic error. Assuming a linear variation of pair formation energy with temperature, and taking 2 = 5 ! we found the following results for least-squares fits. By taking all the data
AA1/ kea1 = 0.3345 (f3.3 x IO-') 3.01 X (,t2.5 x 10-')T/K
(Fit I)
and by taking only our data
AA1/kcal
compared to about 13 for K1, the uncertainty of K I Z will be greater than that of K1. From the larger set of data (16 points) a t 663 K we find for the equilibrium (AgS0,)-
+ Ag'
Ag-SO,-Ag;
K12
K!i = 7.6 f 3.0; T = 663K'O Comparison with t h e Quasilattice Model. (AgS04)Association Energy. In either the asymmetric, symmetric, or generalized approximations, the association energy (Ml) .of the (AgS04)- grouping is given by eq 8a. Watt and Blander5 found an unexpected temperature dependence for MI; more recently, Sacchetto, e t C Z ~ .conclud,~ ed that Ai41 was temperature independent. As shown in
-0.2873(='~1.9X lo-') 2.11 x (rt9.05 x 10-%'/K (Fit 11) These lines are drawn in Figure 2 along with the experimental results. The data from ref 5 are given without error estimation, but from the scattering of the emf measurements we believe this error may be in the range of 100 cal. In order to compare the results of this investigation with a previous estimate of the (AgS04)- association energy from the K,Ag/NOs,S04 phase diagram,7 we calculated MI a t 607 K, the melting point of KN03 Fit I: AAl/kcal = -1.493 f 0.029 Fit 11: M l l k c a l = -1.568 f 0.018 The range of values of .1A1 estimated from the liquidus =
The Journal of Physical Chemistry, Vol. 77,
No. 22, 1973
C. E. Vallet
2676
TABLE I l l : Temperature Dependence of (AgSOI)- Pair Formation Energy (U,) Assuming 2 = 5
62C
640
T (K: 66C
680 700 _______________
,
1
1
and J . Braunstein
Lt
~
622 622 636 646
663 680
68 1 703 706 71 5 722
i,
6
1.55 i 0.05 1.599 f 0.023
Our wolk
1.53 1.61 -1: 0.05
5 6 Our work
1.691 k 0.026 1.63 k 0.05 1.69 1.77 f 0.05
l6
1
4
+
I
ii
.,.3 $ 0% WORK
WITH ESTIMATED ERR02 FROM MEASUREMENTS 3F 'WATT AN9 BLANDER WITH EST8NATECl EQ90R !195C!
11
FROM M E M J E E M E ~ T S OF SAC:HET E t 01 WITH ESTIMATE3 ERROR !197? OMITTED 'ROM THE LEAS- SQUARES CALCULATION I = LINEAR FIT CF ALL XTi\
rn
* LALUE
6
5 Our work 5
1.80 1 . 5 2 f 0.05a
6
1.90
5
Value omitted from least sauares calculation
__ -_____
TABLE I V : (AgSQd)-and (Ag-SQ4-Ag) Association Energies Calculated Assuming 2 = 5 T'K 622 663
L A - 'kcal -1.599 k 0 . 0 2 2 -1.691 jz 0.026
AA12/kcala -1.97
f 0.29
1A,2/kcalh
-3.8
*
0.29
From ey 9, random orientation for second A g + and with experimental results taken at 663 i< From eq 10 fixed (e g linear) orientation for second Ag' and with experimental results taken at 663 K
measurements,' -1.5 to -1.2 kcal, overlaps the values obtained from the emf investigations. It may be concluded that all the experimental results, including those of Sacchetto. e t al , 6 if one omits their highest temperature result. are in accord with a temperature dependence of the (AgSOe)- pair formation energy, the small temperature coefficient being in the range of -2 to -3 X 10-3 kcal/K between 622 and 722 K . Temperature Coefficient of S A 1 from Temperature Cscles. From the results of cycles such as that illustrated in Table I, the limiting slopes
a t differing silver nitrate concentrations always exhibited a more negative value for the higher temperature, the average difference being 5622 - s663 = 0.070 (*0.052) V. This difference between the slopes at 622 and 663 K corresponds t o a difference of the association energy AA1(622) - AA1(663) = 0.127 (+0.061) kcal. The small variation of the limiting slope with R(AgNO3) is neglected in this estimate, whose purpose was to verify the sign and magnitude of the difference of -?,.AI at the two temperatures. The above differences of slope and of U1 obtained from the series of temperature cycles in a single cell may be compared with the corresponding differences obtained from the series of isothermal measurements in different cells reported in the previous section: s 6 2 2 - 8663 = 0.047 (+0.038) V and AA1(622) - AA1(663) = 0.092 (+0.049) kcal. rlg-SO4-Ag Association Energy. Our results were sufficiently accurate to allow a determination of K l z a t 663 K with eq 7b and 7c. The association energy A A 1 2 was calculated from eq 9 and 10 of the generalized quasilattice model and assuming either random or fixed orientation of the Ag-SO4-Ag groupings. The results are given in Table The Journal of Physical Chemistry, Vol. 77, No 22 1973
330
350
390 I i"C)
37C
410
4 30
450
Figure 2. Temperature dependence of (Ag-S04)- pair association energy A , data from ref 5, a, data from ref 6, *, omitted value in least squares calculations, 0 , our work Fit I is obtained from all these data Fit I I I S obtained from our results
IV. Although the uncertainty of AAlz does not permit a determination of whether it too, like hrll, is temperature dependent, it is clear that this second association is significant and may have a higher stability than the first association.20 A more negative association energy for the second (dinuclear) association than for the pair-wise association has been reportedz1 for the association of Ag+ and I- ions in molten KNO3. The association energy corresponding to a fixed ( e . g . , linear) grouping would indicate an unusually high degree of stabilization for addition of the second Ag+ which seems highly unlikely.
Conclusions We have reported new emf measurements for the dilute charge unsymmetric reciprocal molten salt system K.Ag/ NO3,SO4 (dilute in Ag+ and sO4'-). lnvestigations over a wide range of silver nitrate concentrations permitted an evaluation for the first time of the (Ag-SO4-Ag) triplet association energy. The (Ag-SQ4-Ag) groupings probably do not have fixed orientation (e.g., linear) since such an assumption would lead t o unusually high stabilization for addition of the second .4g+. Even with unrestricted orientation of the (Ag-SO4-Ag) groupings, the dinuclear association energy is comparable to and may be more negative than for the (AgSQ4)- pair. Our study confirms the increased stability of (AgsO4)pairs with increasing temperature.5 This dependence is in the same direction as observed for AgCN pairsz2 and for the charge unsymmetric C d X t (X = Br- or I - ) pairs.z3 In the quasilattice calculations only configurational entropy is taken into account; the variation of ,1A1 with the 2.5 x 10-3 kcal/K, may be temperature, [ - a A A l / a T ] understood as the "specific entropy of association" characterizing a change in the internal degrees of freedom of the SO4'- ion.
-
Acknouledgment. C,. E. V. is pleased to acknowledge a grant from the Ministere des Affaires Etrangeres Francais during the academic year 1972-1973.
Photoconductive Properties of Arylethynylcopper Polymers
Supplementar) Material Available. Detailed tables of data will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 2OX reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C . 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number JPC-73-2672. References and Notes Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. On leave from the Laboratoire de Thermodynamique, associe au C.N.R.S.. Universite de Provence, Marseille, France, under a research grant from the Ministere des Affaires Etrangeres Francais (1972-1973). M. Blander in "Molten Salt Chemistry," M. Blander, Ed., Interscience, New York, N. Y., 1964, p 221 J . Braunstein in "Ionic Interactions," Vol. I , S. Petrucci. Ed., Academic Press, New York, N. Y., 1971, p 179. W. J. Watt and M . Blander, J. Phys. Chem.. 64, 729 (1960). G. A. Sacchetto, C. Macca, and G . G. Bombi, d. Eiectroanai.
2677 Chem., 36, 319 (1972). (7) M. L. Saboungi. C. E. Vallet. and Y. Doucet, J. Phys. Chem. 77, 1699 (1973). (8) J. Braunstein, H. Braunstein, R. E. Hagman. and A. S. Minano, Inorg. Chem., 12, 1407 (1973). (9) M. Blander and S, Yosim, J. Chem. Phys.. 3 9 , 2610 (1963). ( l o ) M. Blander and L. E.Topoi, Electrochim. Acta, 10, 1161 11965). (11) D. E. LaValle, Analytical Chemistry Division, ORNL. (12) J. Braunstein, J. Chem. Educ.. 44, 223 (1967). (13) M. Blander, F. F. Blankenship. and R. F. Newton, J. Phys. Chem 63, 1259 (1959). (14) Reference 4, p 228. (15) M. Blander, J. Chem. Phys., 34, 432 (1961): M. Blander and J. Braunstein. Ann. N. Y. Acad. Sci.. 79, 838 (1960) 1161 M. Blander. J. Phvs. Chem.. 6 3 . 1262 (19591 (17) Reference 4, p 233. (18) See paragraph at end of paper regarding supplementary material. (19) The value calculated from the smaller set of data (10 points) at the lower temperature, K , 2 = 3.6 rt 2.9 i s considered less reliable and, unlike the results at 663 K , the slope was more sensitive to the omission or retention of any one of the data points. (20) The results at 622 K indicate a less negative, but still significant second association energy -1.4 f 0.45 kcaijmoi, if ali the lowtemperature data are retained. However. i f the point at the highest silver concentration is discarded the iow temperature resuit is more consistent with the high-temperature result, -1.64 k 0.26 k c a l l mol. (21) A. Alvarez-Funes, J. Braunstein. and M . Blander, J. Amer. Chem. Soc., 84, 1538 (1962). (22) D. L. Manning and M. Blander. inorg. Chem , 1. 594 (1962). (23) J. Braunstein and R . M. Lindgren. J. Amer. Chem. SOC.. 8 4 . 1531 (1962).
Photoconductive Properties of Arylethynylcopper Polymers. Effects of Structure and Oxygen Yoshiyuki O k a m o t o " ' and S a m a r K . Kundu Research Division, Department of Chemicai Engineering. New York University. University Heights. New York. (Received August 3, 7973)
New York 70453
Eleven selected arylethynylcopper compounds were synthesized from their corresponding acetylenic compounds with cuprous salt. The dark resistivities of the compounds were in the range of 107-1011 12 cm. Under illumination by a tungsten light (100 W), the resistivities dropped t o 105-109 12 cm. The dark conductivities were increased when electron-donating groups were introduced on the aromatic ring. The conductivities were also enhanced if the size of aryl groups were increased. More conductive compounds were generally smaller in their photoconductive responses. The photocurrents of the copper compounds on surface cells tended to be considerably lower when measured under vacuum, compared with those under dry air. This phenomenon was attributed to the fact that oxygen in air reduced the recombination rate of the carrier, z e., oxygen traps the electron and increases the hole conductivity. However, these results contradicted Myl'nikov's observation that the photocurrent of phenylethynylcopper was increased when measured under vacuum. The photocurrent-intensity dependence and the Seebeck effect of these compounds were measured under vacuum and dry air. These results confirmed our observations.
Introduction Arylethynylcopper compounds (R-C=C-Cu) are coordination polymers having substantial back coordination from filled metal d orbitals to antibonding orbitals of acetylene groups toward the metal as shown in Figure 1.2a The coordination bondings were not affected by adding various electron-donating substances such as pyridine. bipyridyl, and triethylamine. However, we have found recently that the electrical conductivities of arylethynylcopper compounds were greatly increased by adding a small
amount of nitrocellulose.*b This was attributed to formation of a charge-transfer complex between the copper compounds and nitrocellulose. Recently, Myl'nikov and Terenin have reported interesting electrical properties for phenylethynyl~opper.~ The dark and photoconductivities of the copper compound were found to be depressed by oxygen and water vapor.* These phenomena accounted for the fact that the oxygen forms new effective recombination centers, thus diminishing the whole carrier lifetime. However, we have found The Journal of Physicai Chemistry, Voi. 77. No. 22, 7973
