2044
The Journal of Physical Chemistry, Vol. 82,No. 18, 1978
E. McCafferty
Temperature Dependence of Dielectric Loss in Distinguishing between Maxwell-Wagner and Debye Processes in Adsorbed Layers E. McCafferty Naval Research Laboratory, Washington, D.C. 20375 (Received March 6, 1978) Publication costs asslsted by the Naval Research Laboratory
With adsorbed water on solid surfaces, an increase with temperature in the peak heights of dielectric loss-coverage curves at constant frequency has been attributed previously to system heterogeneity arising from the differences in conductivities of adsorbate and substrate (Maxwell-Wagner behavior). It is shown that this same effect can be produced by molecular relaxation processes (Debye behavior) having a distribution of relaxation times. The increase in peak heights depends on the temperature dependence of both the Cole-Cole distribution parameter and the area under the dielectric loss-log frequency curve. Thus, an increase with temperature in the maxima in dielectric loss isotherms is not sufficient evidence to differentiate between Maxwell-Wagner and Debye processes for surface adsorbed layers.
Introduction Dielectric relaxation methods have been used to study the vapor phase adsorption of various polar molecules on many different solid surfaces. Reviews have been given by McIntosh1 and BunzL2 One of the difficulties in such studies is in determining whether the observed dielectric relaxation is a Debye or Maxwell-Wagner process. In a Debye p r o c e ~ sthe , ~ dielectric dispersion is due to the rotation of dipolar molecules in the applied field and hence is characteristic of the molecular structure of the adsorbate. In contrast, Maxwell-Wagner p r o c e ~ s e sare ~ , ~caused by the inherent heterogeneity of the dielectric system and originate in the differences in conductivities of the adsorbate and substrate. Both processes give a similar dependence of the dielectric constant and loss on frequency. With adsorbed water films, it is particularly difficult to distinguish between these two processes because of the possibility of surface conductivity in the adsorbed due to protonic cond~ctivity~~’ or to dissolution of surface ions of the ~ u b s t r a t e . ~ ! ~ One method sometimes used to differentiate between these two processes involves the temperature variation of dielectric loss isotherrns.l0J1 The observation that the height of loss peaks increases with increasing temperature has been ascribed to Maxwell-Wagner dispersion. The purpose of this communication is to show that this behavior can also be caused by Debye processes having a distribution of relaxation times. Analysis In studies of adsorbed water on silica gel, Kamiyoshi and OdakelO and later Nair and Thorpel’ observed that maxima in dielectric loss isotherms ( E ” vs. amount adsorbed for a fixed frequency) increased with temperature. See Figure la. Following Morgan,12 these authors attributed this behavior to Maxwell-Wagner dispersion. The qualitative argument given was that conductance, which causes an ohmic loss of electrical energy as heat, increases with temperature, so that the value of emu’’ at a particular frequency within the dispersion range should also increase with temperature. In a discussion of Morgan’s original paper, S ~ m m e r m a nsuggested ~~ that the increase in emu’’ claimed to be characteristic of Maxwell-Wagner losses could also occur with Debye behavior and a distribution of relaxation times. Sommerman’s suggestion was necessarily qualiThis article not subject to
tative, because it was proposed before Cole and Cole14had modified the Debye equations to allow for a distribution of relaxation times. For ideal Debye b e h a v i ~ r ,the ~ ! ~complex dielectric constant is e*
= E,
+1 + iwr €8
E,
where E, is the static dielectric constant, e, the high-frequency limit, w the angular frequency, and T the relaxation time. Cole and Cole14modified eq 1for systems which do not exhibit a single relaxation time but instead are distributed around a mean value ro:
where a is a measure of the spread of the distribution (0 Ia I1). The quantities E,, E,, r0,and a are all functions of temperature T and may also vary with the amount adsorbed F. The imaginary part of eq 2 gives the loss factor for the Cole-Cole distribution
and is shown in Figure lb. Taking (at”/aw) = 0 shows that w r o = 1 at the maximum in E” vs. log w , or 1 1 (4) TO=-=urnax
2‘iTfchar
where urnaxis the angular frequency at which e’’ is a maximum, and fchar is the characteristic frequency. Dielectric loss data are usually presented as the Debye curves in Figure l b (e’’ vs. log w at fixed I?) rather than the dielectric loss isotherms in Figure l a (E” vs. r at fixed w). However, the two methods of presentation are related for Debye processes. To see this relationship, we examine the maxima in d’-r curves which have a Cole-Cole distribution. Taking (ad’/ar)= 0 (at constant temperature) in eq 3 gives
U S . Copyright. Published 1978 by the American Chemical Society
Temperature Dependence of Dielectric Loss in Adsorbed Layers
The Journal of Physical Chemistry, Vol. 82,No. 18, 1978 2045
(a) Constant Frequency a
30 -
2
- 0.
0
0
0
.
0
8
\v I
20-
VW 10 -
(b)
Constant Amount Adsorbed
> I
0 0
f I
0
0
2
5°C 15” c 35” c
3
4
5
NUMBER OF LAYERS O F WATER DEBYE BEHMOR
,., O > O coupled with > O if K, (dA/dT) > K ,(de/dT) < O coupled with < O if IK, (da/dT)i > IK, (dA/dT)i
where K1 and K z are positive quantities given by
K1 =
Kz =
( ~ / 4 ) ( -~ Esm ) 1 sin ( a ~ / 2 )
+
( 2 . 3 0 3 / ~cos ) (a7r/2) 1 + sin ( a ~ / 2 )
(12)
Equation 10 shows that the direction of change of emax” depends on the balance of two terms. Thus, ems," can increase with T, decrease with T, or remain constant, depending on the direction of change of d a / d T and dA/dT. Simple combinations which will produce an inwith increasing temperature are (1)d a / d T crease in E,=” < 0 with dA/dT 2 0, and ( 2 ) d a / d T = 0 with dA/dT > 0. Other possible ways to increase ”,E, are given in Table I. These increases in the maxima in Debye loss curves are equivalent to an increase in the maximum of the corresponding d’-I’ curve, according to Figure 4. Thus, an increase with temperature in the maximum of a dielectric isotherm is not unique to Maxwell-Wagner processes, as previously believed, but can be caused by a Debye relaxation having a distribution of relaxation times. Discussion Experimental verification of the increase in ernail with increasing temperature is provided by the work of Glazun and c o - w ~ r k e r on s ~ ~the dielectric relaxation of adsorbed water on zeolites. Values of a were observed to decrease with increasing temperature ( d a / d T < 0), while (E, - E,) was independent of temperature (for a water content of 30%), so that dA/dT = 0. These two trends combine in eq 10 to predict that emax” would increase with temperature, even though a molecular relaxation process is involved. In another study, Ono and co-workerslg have analyzed Cole-Cole arc plots at various temperatures for water in the Debye curves adsorbed on starch. The value of ”,E, increased with temperature. Also, d a / d T 0 and d(EBt,)/dT > 0. According to eq 10, E”for the dielectric loss isotherms must also increase with temperature. Few dielectric studies a t interfaces report the temperature dependence of both a and (E, - ern). However, elements of one or the other are sometimes given, so that there are reports where (for a fixed coverage) d a / d T is n e g a t i ~ e lor ~ * ~ ~ (also Figure 2). For certain experimental conditions, values of (E, - E,), and thus A, have or remain been observed to increase with temperature19,27r30 constantz9 (also Figure 3). These examples illustrate temperature dependencies of CY and (E, - E,) which will produce an increase in ”,E, with increasing temperature, per the first two cases in Table I. According to Table I, emax“ can increase with temperature for instances where dA/dT (or d(E, - trn)/dr)is either positive or negative. From eq 7 , ernail is proportional to (E, - E,). As an approximation, E”, 0: E, because often E, >> E,. FrohlichS1has pointed out that dE,/dT is related
f“ LOG FREQUENCY
Figure 5. Schematic representation of Debye loss curves for which
a decreases with increasing temperature with the total dispersion remaining constant.
to the entropy of the system and that E, may either increase or decrease with T depending on the effect of an applied field on the order in the system. If the adsorbate is liquidlike, an external field would create order so that E, would decrease with increasing T. On the other hand, the adsorbate may be ordered or “structured”, as is the case with hydroxylated o ~ i d e swhere l ~ ~ ~for~ certain coverages adsorbed water is organized through extensive hydrogen bonding. For such instances, E, could increase with T, because the external field increases the disorder. Figure 5 shows schematically one type of temperature dependence of Debye loss curves which will generate an increase in peak height of the dielectric loss isotherms. For a given temperature, the curve shapes and areas are the same for each coverage so that (aa/aI’)Tand (aA/aI’)T are zero, as in the treatment of eq 5 and 6. The peaks are also located so that the characteristic frequencv increases with With increasing temperature, the curves become more like ideal Debye behavior ( d a / d T is negative), and the total dispersion remains constant (dA/dT = 0), but with the peak height increasing. The peak heights in the Debye curves in Figure 5 a t a fixed frequency off* correspond to the peak heights in the €’’-I’curves in Figure 6, according to the present analysis. The relaxation time is given by T~ = 1 / ( 2 ~ f , = ) , which follows from ( a ~ ” / a w ) ~ , T= 0, or (aE”/aI’),,T = 0. Thus, in Figure 6, the frequency f* is the characteristic frequency for the coverages rl.(at T3), rZ (at Tz),and r3(at TI). Moreover, these points also satisfy the characteristic frequency-coverage curves in Figure 6. Such increases in fchar with increasing temperature (at a fixed coverage) have been observed experimentally for a number of systems, including water on ~x-Fe203;~~ water, ethanol, and acetone on kaolinite,26 and water on hemoglobin.’I Concluding Remarks An increase with temperature in the maxima in dielectric loss-coverage curves (at a fixed frequency) is not unique
The Journal of Physical Chemistry, Vol. 82, No. 18, 1978 2047
Communications to the Editor
References and Notes
f*
i i i
A M O U N ~ADSORBED
Figure 6. Dielectric loss isotherms and characteristic frequency curves corresponding to the Debye loss curves in Figure 5.
to Maxwell-Wagner processes. This same effect can be caused by a Debye process having a distribution of relaxation times. Thus, this particular temperature dependence of the dielectric loss is not a sufficient criterion to distinguish between Maxwell-Wagner and Debye dielectric processes in adsorbed layers. Other approaches should be used to distinguish between the two mechanisms. Surface conductivity could be measured using direct current techniq~es~J’1~~ or by noting the appearance of “tails” superimposed on Cole-Cole arc plots at low f r e q u e n c i e ~ l ~due J ~ ?to~ ~ increased dielectric loss and capacitance arising from Maxwell-Wagner eff e c t ~ . ~Supporting ~?~~ evidence for Debye relaxation processes could be obtained from determination and analysis of enthalpies or entropies of a d ~ o r p t i o n . ~ J ~ ? ~ ~
R. L. McIntosh, “Dielectric Behavior of Physically Adsorbed Gases”, Marcel Dekker, New York, N.Y., 1966. L. Sobczyk, H. Engelhardt, and K. Bunzl in “The Hydrogen Bond”, P. Schuster, G. Zundel, and C. Sandorfy, Ed., Vol. 111, North Holland Publishing Co., Amsterdam, 1976, p 937. P. Debye, “Polar Molecules”, The Chemical Catalog Co., New York, N.Y., 1929, p 89. C. P. Smyth, ”Dielectric Behavior and Structure”, McGraw-Hill, New York, N.Y., 1955. C. G. Koops, Phys. Rev., 83, 121 (1951). J. H. Anderson and 0. A. Parks, J . Phys. Chem., 72, 3662 (1968). J. J. Friplat, A. Jelll, G. Ponceiet, and J. AndrB, J . Phys. Chem., 89, 2185 (1965). A. Soffer and M. Folman, Trans. Faraday Soc., 82, 3559 (1966). B. J. Goldsmith and J. Muir, Trans. Faraday Soc., 58, 1656 (1960). K. Kamiyoshl and T. Odake, J . Chem. Phys., 21, 1295 (1953). N. K. Nair and J. M. Thorpe, Trans. Faraday Soc., 61, 974 (1965). S. 0. Morgan, Trans. Nectrochem. Soc., 85, 109 (1934). G. M. L. Sommerman, Trans. Electrochem. Soc., 65, 116 (1934). K. S. Cole and R. H. Cole, J . Chem. Phys., 9, 341 (1941). E. McCafferty, V. Pravdic, and A. C. Zettlemoyer, Trans. Faraday Soc., 88, 1720 (1970). E. McCafferty and A. C. Zettlemoyer, Discuss. Faraday Soc., 52, 239 (1971). P. G. Hall and G. K. Kowarellii, Trans. Faraday Soc., 84, 1940 (1968). K. Umeya and T. Kanno, Bull. Chem. Soc. Jpn., 46, 1660 (1973). S. Ono, T. Kuge, and N. Koizumi, Bull. Chem. Soc. Jpn., 31, 40 (1958). J. E. Algle, J . Text. Inst., 82, 696 (1971). B. Morris, J . Phys. Chem. Sollds, 30, 73, 89, 103 (1969). R. M. Fwss and J. G. Kirkwood, J. Am. Chem. Soc., 63,385 (1941). C. J. F. Bottcher, “Theory of Electric Polarisation”, Elsevier, Amsterdam, 1952, p 372. S. Takashima, J. Po/ymer Scl., 82, 233 (1962). S. Takashima and H. P. Schwan, J. Phys. Chem., 69,4176 (1965). S. M. Nelson, H. H. Huang, and L. E. Sutton, Trans. Faraday Soc., 65, 225 (1969). 0. Brausse, A. Mayer, T. Nedetzka, P. Schlecht, and H. Vogel, J . Phys. Chem., 72, 3098 (1969). C. J. F. Bottcher, ref 23, p 367. B. A. Glazun, M. M. Dubinin, I. V. Zhilenkov, and M. F. Rakityanskaya, Bull. Acad. Sci. USSR, Div. Chem. Sci., 1156 (1967). S. C. Harvey and P. Hoekstra, J . Phys. Chem., 76, 2987 (1972). H. Frohllch, “Theory of Dielectrics”, Clarendon Press, Oxford, 1958, p 12. M. L. Hair and W. Hertl, J . Phys. Chem., 73, 4269 (1969). K. Kawasaki and N. Hackerman, Jpn. J. Appl. phys., 6, 1184 (1967). R. P. Auty and R. H. Cole, J . Chem. Phys., 20, 1309 (1952). B. V. Hamon, Austr. J . Phys., 8, 304 (1953).
COMMUNICATIONS TO THE EDITOR Effect of Laser Radiation on the Catalytic Decomposition of Formic Acid on Platinum fublicatlon costs assisted by the Naval Research Laboratory
Sir: In our program of investigation into laser promoted chemical reactions we have found that laser excitation of molecular, gas-phase species can influence both the rates of reaction of such species on surfaces and also the relative amounts of various products formed. To our knowledge, this is the first observation of such an effect. The system we wish to report is the catalytic decomposition of HCOOH over Pt. Formic acid is known to decompose on Pt by two reaction paths HCOOH C02 H2 ( 1)
-
-+
+ CO + H 2 0
(2)
with (1)being predominant.1,2The relative amount of the This article not subject to US. Copyright.
two products depends upon the condition of the surface and its temperature. In this study it was found that irradiation with a laser line that is strongly absorbed by HCOOH causes a decrease in the rate of formation of both C 0 2 and CO or selectivity inhibits CO formation, depending upon the condition of the Pt surface. The experimental apparatus used is illustrated in Figure 1. The output of the continuous wave (CW) C02 laser, capable of single line operation with a power output of about 10 W, was directed through the axis of a spirally wound Pt filament in a reaction flask equipped with KC1 windows. The filament was electrically heated and was in a circuit in which its resistance could be measured precisely. Its temperature was determined from literature data for the change of resistance of Pt with temperature3 and could be maintained constant within 1-2 “C. Typically, the flask was charged with HCOOH, either pure or diluted in He. The filament was then turned on and its resistance maintained constant a t a value corre-
Published 1978 by the American Chemical Society
