ELECTRICAL CONDUCTIVITY OF SOLID AMMONIUM PERCHLORATE
trodes covered with adsorbed (organic) layers is invariably lower than for a clean electrode. This has led to wide beliefe,’ that subtracting the base electrolyte capacity leads to a significant “overcorrection” for double-layer charging in estimating adsorbate coverages by stripping. (2) It is shown that to avoid error, the charge must be integrated from the PZC of the solution containing the adsorbate to a potential where desorption is complete. Similarly, charge must be integrated from the PZC to the same potential for the base electrolyte. W h e n the latter is subtracted f r o m the former, there i s n o double-layer error. (3) I n practice, the PZC is not readily accessible for solid electrodes and charge integration must actually be carried out from the adsorption potential. This leads to a small “undercorrection” for double-layer
2843
effects, but since significant adsorption only usuallv occurs a t small rational potentials, the error is not large (generally 1-3%). (4) The double-layer effects can lead to significant errors in considering stripping kinetics. A novel experiment, involving the continuous measurement of the differential capacity during stripping, is suggested to distinguish charging from faradaic processes. ( 5 ) It is shown that it is satisfactory to measure the infinite frequency double-layer capacity for these corrections.
-
Acknowledgments. The author is pleased to thank Dr. Richard Payne and Dr. James X. Butler for some helpful discussions. This work was supported by the Office of Naval Research under Contract S00014-66(20210.
Electrical Conductivity of Solid Ammonium Perchlorate’
by Henry Wise Chemical Dynamics Department, Stanford Research Institute, Menlo P a r k , California (Received February I , 1967)
The electrical conductivity of solid ammonium perchlorate was measured over a temperature range from 500 to 600°K. From the variation of the ionic conductivity in an applied electric field as a function of temperature, the enthalpy of formation of lattice defects is found to be 24 kcal and the energy barrier for lattice-defect migration, 20 kcal. The relatively high electrical conductivity of ammonium perchlorate compared with alkali halides and the marked influence of gaseous ammonia on the conductivity are interpreted in terms of a mechanism of charge transfer by proton jump.
Introduction In the kinetics of decomposition of ammonium perchlorate (AP), . . the defect structure of the crystalline solid appears t o play a dominant part. The early work by BircumshaW and Neu’man2 had indicated the tion to be centered around nucleation sites. The phenomena associated with structure-sensitivc nucleation, according to which nuclei are formed in certain regions favored on the basis of energetic considerations,
have been encountered in a number of crystalline systems undergoing exothermic and endothermic deApplication of nucleat,ion theory t o (1) This work was sponsored by the Office of Naval Research, Department of the Navy, under Contract Nonr-3415(00), Authority NR 092-507. (2) L. R. Bircumshaw and B. H. Newman, Proc. Roy. SOC.(London), A227, 115 (1954). (3) w, E, Garner, Ed,, “Chemistry of the Solid state,,, Academic Press, New York, N. Y., 1955.
Volume 71, Sumher 9
August 1967
HENRY WISE
2844
the decomposition kinetics of ammonium perchlorate has recently been made and the observed autocatalytic nature of the reaction has been i n t e r ~ r e t e d . ~Although the origin of dislocation is not well understood, the generation of vacancies and interstitial ions a t dislocations may readily be associated with exothermic reactions of ionic crystal^.^ As a matter of fact, it may be involved in the process of nucleus growth which is found to be associated with the thermal decomposition of ammonium perchlorate.6 I n order to examine the energy requirements associated with lattice-defect formation, a series of experimental measurements were made of the electrical conductivity of ammonium perchlorate. On the basis of the properties of solid alkali halides it may be assumed that the conductivity of ammonium perchlorate is predominantly ionic in character. Recent measurements on pure and doped ammonium chloride' have been in accordance with such an assumption. Information on the energies required for lattice defect formation and migration may be obtained from a determination of the variation of ionic conductivity in an applied electric field as a function of temperature. For defects of the Schottky type, in which some of the anion and cation sites in the lattice are vacant, the specific electrical conductivity is given by8
x
=
+
xo exp - [(CO '/zWd/kTI
(1)
where xo contains terms related to the crystal properties, Wo is the enthalpy of formation of lattice defects, and U0is the activation energy for latticc-defect migration.
Experimental Details The electrical conductivity of ammonium perchlorate was determined in a conductivity cell composed of a quartz U-tube containing electrodes in the form of graphite rods (Grade ATJ Union Carbide Corp., Carbon Products Division), between which the ammonium perchlorate sample was held in place. The entire unit was housed in a furnace whose temperature was controlled at the desired level. To minimize polarization effects associated with dc conductivity measurements, the polarity of the electrical potential applied across the sample was alternated (frequency ranged froni 0.1 to 40 cps). The same apparatus had previously been employed for determining the specific conductivity of some alkali halide crystals. Since ammonium perchlorate reacts with carbon, the graphite electrodes were coated with a film of ~. silver, applied as a silver paint (Engelhard Industries, East Sewark' s'J*) and baked at 65001' for hr' Subsequently, a thin layer of colloidal gold (also from The Journal of Physical Chemistry
Engelhard Industries) was similarly applied. A small flow of nitrogen was passed through the cell during the electrical measurements. Both single crystals and pressed pellets of ammonium perchlorate were employed in the conductivity measurements. The single crystals n-ere grown from aqueous solution using ammonium perchlorate of high chemical purity (Reagent grade, Matheson Coleman and Bell). Small single orthorhombic crystals could be obtained by slow growth over a period of several weeks a t room temperature. The surfaces of the crystals were polished with a wet chamois cloth and painted with a colloidal gold suspension (Engelhard Industries). The gold was baked on the solid surface a t a temperature of about 400°K. The pellets were pressed from ammonium perchlorate particles (less than 43 p in diameter) at 8.75 X lo3 kg/cm2 to a density corresponding to 98% of that of a crystal. The die containing the ammonium perchlorate powder was evacuated before pressing. The pellets iyere 1.25 cm in diameter and from 0.05 to 0.10 cm in thickness. The single crystals were 0.5 cm long, 0.4 cm wide, and 0.2 cm high.
Results 3lost of the electrical conductivity measurements were carried out a t temperatures above the crystal transition temperature (l313"K). As shown in F'g '1 ure 1, the conductivity varied from 10-lo to lo-' (ohm cm)-l in the temperature region from 500 to 600°K. The conductivity did not show any discontinuity in going from the orthorhombic to the cubic crystal structure. During the short periods of time required for the measurements, the amount of thermal decomposition and sublimation of ammonium perchlorate was found to be small a t temperatures less than 575"K, as evaluated from changes in total mass of material. In several experiments ammonia was added to the carrier gas nitrogen to inhibit sublimationg and to explore the influence of ammonia on conductivity. The results indicated that the conductivity increased in the presence of ammonia (Figure 1) and depended on (4) S. H . Inami, W. 4. Rosser, and H. Wise, Trans. Faraday Soc , 62, 723 (1966). (5) F. Seitz, Phus. Rev., 80, 239 (1950). (6) A. V. Raevskii and G. B. Manelis, Dokl. A k a d . S a u l ; S S S R (Consultants Bureau Translation, Physical Chemistry Section), 151, 686 (1963); 160, 158 (1966). (7) T. M. Herrington and L. A. K. Staveley, Phys. Chem. Solids, 25, 921 (1964). (8) N. F. Mott and R. W. Gurney, "Electronic Processes in Ionic Crystals," Oxford University Press, Oxford, Fhgland, 1948. (9) W. A. Rosser, S. H. Inami, and H. Wise, J . Phys. Chem., 67, 1753 (1963).
ELECTRICAL CONDUCTIVITY OF SOLID AMMONIUM PERCHLORATE
2845
Table I : Variation in Electrical Conductivity with Partial Pressure of Ammonia (T, 503’K; Carrier Gas, N1) Ammonia (mole fraction)
Relative change in conductivity
0 0.18 0.42 0.61 0.80 1.00
1.00 2.6 4.5 6.0 10.8 12.5
~~~~~
Table I1 : Electrical Conductivity of Single Crystal Ammonium Perchlorate Temp, OK
\
A NH3 (mole fraction = 10-1I
1.6
1.7
1.8
1.9
( I / T ) X I O3
2.0
520 544 556 2.1
2.2
--Electrical Single crystal
conductivity, (ohm cm) -1Pressed pellet
1 . 1 x 10-9 0 . 5 x 10-8 0 . 9 x 10-8
0.8 X 0.3x 0 . 6 X lod8
2.3
OKA‘
Figure 1. Electrical conductivity of ammonium perchlorate as a function of temperature.
the partial pressure of ammonia in the carrier gas (Table I). It is of interest to note that the measurements carried out with single crystals of ammonium perchlorate are in satisfactory agreement with those obtained from the pressed pellets of ammonium perchlorate (Table 11). These results suggest therefore that such factors as surface conductivity, particle-toparticle contact resistance, and grain boundaries are of little influence on the conductivity measurements within the precision of our data. A similar conclusion may be reached from the observation that the electrical currents measured for a given applied voltage exhibited no frequency-dependent conductance.1° At all times the samples, both pressed pellet and single crystal, followed Ohm’s law.
Discussion The experimental results obtained for the electrical conductivity of’ ammonium perchlorate suggest a model for ion transport which bears an interesting relationship to the mechanism of thermal decomposition of this material. Two experimental observations are of primary concern in formulating the model: (1) the relatively high conductivity of ammonium perchlorate compared with alkali halides, and (2) the marked influence of gaseous ammonia on the conductivity. It is
tempting to suggest that these characteristics of ammonium perchlorate are due to a charge-transfer process involving protons, similar in principle to the Grotthus mechanism of ionic conduction in the liquid In the case of ammonium perchlorate, the proposed mechanism of protonic charge transport involves movement of a proton from an ammonium ion in the lattice structure to an ammonia molecule located at a lattice vacancy or a t an interstitial position. The neutral ammonia molecule thus formed a t a lattice site may now become the recipient of a proton from an adjacent cation in the lattice. By this means charge transport may be greatly facilitated over that associated with ammonium ion migration zia Schottky or Frenkel defects. Based on some preliminary estimates, proton transfer in the [110] and [111] directions of the cubic lattice appears reasonable on energetic grounds.13 Such a model appears to explain the increase in electrical conductivity encountered in the presence of ammonia. In addition, the results obtained may be employed to obtain some measure of the energy require(10) D. P. Snowden, H. Saltsburg, and J. H. Perene, Phus. Chem. solids, 25, 1099 (1964). (11) S. Glasstone, “Electrochemistry,” D. Van Nostrand Co., New York, N. Y., 1942. (12) H. Danneel, Z . Elektrochem., 11, 249 (1905). (13) We are indebted to Dr. M.L. Huggins of this laboratory for initiating calculations of the energy requirements for prototropic change in the cubic structure of ammonium perchlorate.
Volume 71 ,%-umber 9 Auoust 1967 ~
WILLIAMH. ORTTUNG AND RICHARD W. ARMOUR
2846
ments for defect formation and proton transfer. As shown in eq 1, the exponential term in the conductivitytemperature relationship contains the sum of two terms, the activation energy for charge migration (U,) plus half the enthalpy for formation of defects (Wo). The activation energy deduced from the measurements of specific conductivity in the presence of ammonia is most likely associated with the activation energy for charge migration. The experimental value E2 = 20 kcal represents, therefore, the energy barrier for proton transfer (LT0). In the absence of ammonia, the exponential term in the conductivity relationship is found to be El = (1/2)Wo = 32 kcal which upon substitution yields 24 kcal for the enthalpy of defect formation. Further evidence for proton transfer between adjacent ion pairs is suggested by two thermodynamic
+
properties of ammonium perchlorate. Similar to the behavior of ammonium chloride, the ~ u b l i m a t i o n ~ ~ of ammonium perchlorate proceeds by a mechanism involving neutral molecules of ammonia and perchloric acid. It is indicative of the existence of a significant number of such molecules in the lattice and a corresponding number of lattice defects. In addition, experimental measurements of the heat capacity of ammonium perchlorate have demonstrated a relatively large endothermic enthalpy of crystal t r a n ~ i t i o n , ' ~ which may be indicative of vacancy formation enhanced by proton transfer in accordance with the model described. (14) S. H. Inami, W. A. Rosser, and H. n'ise, J . P h y s . Chem., 67, 1077 (1963).
(15) M. W. Evans, 40, 2431 (1964).
K. B. Buyer, and L. McCully, J . Chem. Phys.,
Polarizability Anisotropy from Crystal Refractive Indices.
I.
Lorentz
Internal Field Approximation with Application to Amino Acid Datal
by William H. Orttung and Richard W. Armour Department of Chemistry, Unizersity of California, Riaerside, California (Received February 8 , 1967)
The principal refractive index values and orientations have been measured for CY-, p-, and y-glycine and for dl-alanine and a-aminoisobutyric acid crystals. The three glycine crystals provided ten experimental parameters for evaluation of the six molecular polarizability components. The calculations were based on the Lorentz internal field approximation for each principal index direction. Qualitative agreement was obtained with predictions from the assumed additivity of bond polarizability tensors. Desirable refinements in the analysis are discussed.
Introduction Knowledge of the optical anisotropy of a molecule is valuable for interpretation of Kerr effect and related experiments and the purpose of our investigation is to find out whether optical polarizability tensors of organic molecules can be evaluated from crystal refractive indices. The key to such an analysis lies in the The Journal of Physical Chemistry
successful consideration of internal field and other environmental effects associated with the crystalline state. Bragg2 carried out molecular analyses of crystal optical data many years ago and Bunn and Daubeny3 (1) This investigation was supported in part by Public Health Service Research Grant GM11683 from the Division of General Medical Sciences.
