Langmuir 1987, 3, 304-306
304
100.0
0.0 00
200 0
400 0
600 0
REACTION TIME (hours) Figure 1. Cumulative amounts of H2and NH3 obtained from
photodissociation of H 2 0 and photoreduction of N2 by 20 mW of light of energy greater than 2.3 eV. The catalyst consists of aqueous suspensions of partially reduced particles of iron oxide. For comparison we indicate the amounts of H2 that would correspond to the stoichiometric oxidation of Fe(I1) by H20 in samples containing 100% and 5% Fe(I1). formation was 10 pmol/h.g of catalyst. We can roughly express the rate in terms of catalyst surface area. For our experimental conditions the result is 100 pmol/h.m2 (which would be equivalent to 0.5 pA/cm2), assuming that only half of the particles are illuminated on one side a t any given time. By using Ar instead of N2 as the circulating gas, ammonia production was less than the detection limit of the trichloramine method (2 X In the case of Ha,
the yield was unaffected by using Ar instead of N2 as the circulating gas. NH3 and H2 and O2 thus appear to be formed in parallel processes. The production of both H2 and NH, was only observed when the catalyst was illuminated with light of wavelength shorter than 540 nm. When the reaction was carried in the dark neither H2 nor NH, was observed. The formation of O2was demonstrated by using a pellet suspended in 3 mL of water labeled with I80 and detecting products of mass 36, 34, and 32 mass spectrometrically. The observed O2 to H2 ratios varied between 0.41 and 0.51 in four different measurements. The oxidation products formed in the NH, reaction are not known at present. The results of these experiments are presented in Figure 1. Our studies demonstrate that the catalyst remains active for production of both NH, and H2 for about 450 h. Assuming that the catalyst contained 5 atom % of Fe(I1) (in the form of Fe304),the yield of H2 obtained in about 450 h would be equivalent to 80 times the stoichiometric reducing capacity of the catalyst while the yield of NH, obtained in about 580 h of illumination would be equivalent to 20 times the stoichiometric reducing capacity of the catalyst. In fact, no significant consumption of Fe(I1) was detected either by X-ray diffraction or by oxidimetric measurements on samples of the used catalyst. It can be concluded that the observed reactions are catalytic. As can be seen in the figure, a significant decay of catalytic activity was observed after several hundred hours of illumination. The reasons for this decay are under investigation. A more detailed account of these and other experiments will be published in a forthcoming paper.
Acknowledgment. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract DE-AC03-76SF00098. M.M.K. thanks the Egyptian Ministry of Higher Education for the award of a support fellowship.
Geometric Formalism of the Thermodynamics of Adsorption at Interfaces between Two Fluid Phases Kinsi Motomura* and Makoto Aratono Department of Chemistry, Faculty of Science, Kyushu University 33, Fukuoka 812, Japan Received July 2, 1986 The adsorption of surface-active solutes at interfaces between two fluid phases has been shown to be analyzed thermodynamically by use of the equations derived by introducing two dividing planes chosen so as to make the excess numbers of moles of solvents of the phases with reference to them zero. The positions of the dividing planes have been related to the variation in the concentrations of the solvents. Finally, this geometric formalism of the thermodynamics of adsorption has been proven to be identical with the Hansen convention. Gibbs made it possible to investigate the adsorption at interfaces between two bulk phases thermodynamically by introducing the dividing surface.' This geometric formalism was extended by Guggenheim and Adam.2 Defay et aL3 and Adamson4 elucidated the connection of the (1) Gibbs, J. W. Collected Works; Dover: New York, 1961; Vol. 1. (2) Guggenheim, E. A.; Adam, N. K. Proc. R. SOC.London, A 1933, 139, 218.
0743-7463/87/2403-0304$01.50/0
location of dividing surface with the variation in the concentration of a component across the inhomogeneous region between the bulk phases. In 1962, Hansen5 devised the algebraic formalism which does not rely on any dividing (3) Defay, R.; Prigogine, I.; Bellemans, A. Surface Tension and Adsorption; Everett, D. H., Translator; Longmans: London, 1966; p 21. (4) Adamson, A. W. Physical Chemistry of Surfaces; Wiley-Interscience: New York, 1976. (5) Hansen, R. S. J.Phys. Chem. 1962, 66, 410.
0 1987 American Chemical Society
Langmuir, Vol. 3, No. 2, 1987 305
Letters
I
A
Figure 1. Schematic illustration of the system.
surface. Moreover, he proposed a new convention in which the chemical potentials of two components are eliminated from the independent variables instead of the pressure and chemical potential of one component as in the case of the Gibbs convention. I t was indicated, though not proved, by Motomura6y7that the algebraic method of Hansen is identical with a geometric one which specifies two dividing planes in the neighborhood of the inhomogeneous region. denied this indication without giving any mathematical reasons. Therefore, it is required to argue a geometric formalism of the Hansen convention. Let us consider a system consisting of two fluid phases, in equilibrium with each other, separated by a plane interface. The interface is not a definite geometrical plane but an inhomogeneous region of which the physical properties are different from those of the phases and merge gradually into them. The interfacial phenomena must be described in terms of thermodynamic properties assigned to the inhomogeneous region. By introduction of two planes which divide the system into three regions, viz., two homogeneous fluid phases denoted by A and B and an inhomogeneous interfacial region, the total volume V is expressed in the form = VA V" VB (1) where VA, v",and are the volumes attributed to phase A, the interfacial region, and phase B, respectively. Since the system is assumed, without loss of generality, to be confined to a rectangular parallelepiped vessel of which the xy plane is parallel to the interface and the z axis is perpendicular to it, the following equation is obtained by dividing eq 1by the interfacial area u and then substituting the thicknesses lA and lB of phases A and B and the distance T between the two dividing planes (Figure 1): v / U = LA + 7 lB (2)
v
+ +
+
We should notice that the positions of the dividing planes cannot be determined with great precision. Now it may be appropriate to define the interfacial excess number of moles of component i in the unit area of the interfacial region with reference to these dividing planes: riu= n i / u - lAciA - lBctB (3) where ni is the total number of moles of component i in the system and ciAand ciB are the numbers of moles of component i per unit volume in the homogeneous interiors of the phases A and B. Suppose that the system under consideration is composed of k + 2 components; the components a and b are the solvents of the phases A and B, respectively, and the components 1, ..., k are surface-active solutes. In general, ~~~~~~
J. Colloid Interface Sci. 1978, 64, 348. J. Colloid Interface Sci. 1986, 110, 294. (8) Good, R.J. J. Colloid Interface Sci. 1982, 85, 128. (9) Good, R.J. J. Colloid Interface Sci. 1986, 110, 298. (6) Motomura, K.
(7) Motomura, K.
C.3
cb
Figure 2. Schematic illustration of the relation between the variation in the concentrations of solvents a and b and the location of dividing planes.
we are mainly concerned with the adsorption behavior of surface-active solutes relative to the solvents. We write eq 3 for the components a, b, and i:
rau= na/u - lAcaA- lBc,B
(4)
- lACbA - lBCbB
(5)
ri"= ni/g - lACiA - 1Bc.B
(6)
rb"
=
nb/g
Elimination of lA and lB among eq 4-6 and rearrangement result in the relation
ri"- r a u ( C t C b B ni/U
- CbAC?) - CiACaB)/(CaACbB - CbACaB) =
- CbACiB)/(CaACbB
rb'(CaACiB
- (na/(r)(CiACbB
- CbAC?)/(CaACbB
(nb/6)(CaAC?
- CbACaB) -
- CiAC?)/(CaACbB
- CbAC?)
(7)
It is seen that all the quantities on the right side depend on the state of the system and are independent of the location chosen for the dividing planes. This fact indicates that the interfacial excess number of moles of component i per unit area expressed by the left side of eq 7 is invariant with respect to movement of the dividing planes and accordingly is the quantity inherent in the adsorption of component i. Therefore, it may be called the interfacial density of solute i relative to the solvents denoted by riH: riH=
ri"- ra"(CiACbB - CbACiB) / (CaACbB rb'(CaACiB
- CbACaB) - CbAC?)
- CiACaB)/(CaACbB
(8)
Taking into account that Fau, r b " , and riU depend on the choice of the dividing planes and that there exist the equality relations o = ~ ~ A c a- A ( c i A c bB - C b A C ? ) / ( C 2 C b B CbA(CaAC?
- CbACaB)
- CtC?)/(CaACbB
-
- CbAC?)
(9)
and 0=
CiB
- CaB(CiACbB - CbAC?)/(CaACbB - CbACaB) CbB(CaACp - C$CaB)/(CaACbB - CbAC?)
(10)
it is found, since the dividing planes can be shifted so as to make ra"and r b " vanish, that riHis identical with the interfacial excess number of moles of component i per unit area with reference to the two mathematical dividing planes chosen so that na/g
- I A PCaA - 1B3CaB = 0
(11)
and
nb/g cb A - l B P C b B = 0 (12) Now we can relate the positions of the two dividing planes to the variation in the concentrations of solvents a and b across the interfacial region between two fluid
306 Langmuir, Vol. 3, No. 2, 1987
Letters where yAand yBare the quantities per unit volume in the phases A and B, respectively. Finally it is necessary to make sure that the interfacial excess thermodynamic quantities defined above are identical with those defined by Hansen. According to Hansen? the specific surface excess quantities $, r,,and 9 are given by the expressions
....... .......
rs =
v/o - @/a
r, = n , / a - (A*/&,"
- AB/.
(14)
- (xB/u)c,B
(15)
and C,
Figure 3. Schematic illustration of the mterfad density of solute i relative to the solvents.
phases A and B. In Figure 2, a picture of how the concentrations vary across the interfacial region is illustrated schematically on an enlarged scale. The dividing planes are drawn so that eq 11and 12 are satisfied simultaneously; that is, the area shaded with vertical strokes is equal to the area shaded with horizontal strokes for each solvent. It is understood, therefore, that the interfacial density of solute i relative to the solvents, riH, corresponds to its interfacial excess number of moles per unit area represented by the area shaded with cross strokes in Figure 3. For an extensive quantity Y of the system, the corresponding interfacial excess quantity per unit area with reference t o the dividing planes, yH.can be defined in an analogous manner: YH
= y/,, - p , , A - p . H y B
(13)
ys = Y / . - (AA/a),,A - ( X B / u ) y B
where XA and AB are chosen so that r, = rz= o
(16) (17)
Supposing that components 1 and 2 are the solvents, comparison of eq 14-17 with eq 2,3, and 11-13 leads us to the conclusion that the quantities $, r,,and ys are the same BS the quantities r", r,H,and yH,respectively, because the relations A A / ~ = 1A.H
(18)
= 1B.H
(19)
and xBio
hold for the system shown in Figure 1. Therefore, we can conclude that the geometric formalism based on the specification of two dividing planes is identical with the Hansen convention.
PAUL BILOEN, 1939-1986 It is with much sadness that we report the death of a member of the Langmuir Advisory Board, Paul Biloen, on Oct. 28, 1986, at the age of 47. Paul will be missed aa a researcher in the field of catalysis, a member of the Langmuir family, and a warm human being. Born in Holland at the outbreak of World War 11, his philosophy of life was tempered by his experiences as a child caught up in the Holocaust. After completing his studies in chemistry and chemical engineering a t the University of Amsterdam, culminating in a doctoral thesis with Professor G. Jan Hoytink, Biloen joined the research staff of the Koninklyke/Shell Laboratories in 1968, where he remained until 1982. From 1976 to 1982, he was Head of the Physical Chemism and Heterogeneous Catalysis section of Shell Laboratories. His contributions to his chosen field were recognized in 1982 with an appointment BS Professor of Chemical and Petroleum Engineering at the University of Pittsburgh, where he remained until his death. He is survived by his wife Ansje and his two sons David, 18, and Peter, 16.
