782
L a n g m u i r 1988,4, 782-784
exponent a was supposed equal to d - 2. The main purpose of this letter is to put eq 2 on mathematical grounds by using the topological framework of Pfeifer et al.4.5 This analysis will raise some intrinsic difficulties concerning the adsorption properties on a fractal surface with d = 3. This will be discussed in the last section in parallel with several other problems not properly handled by actual models.
111. Discussion As can be observed in the former paragraph, the case d = 3 plays a singular role in the adsorption process. First, the monolayer volume is null, as observed by Pfeifer et ai.: and it is not possible to define any f i factor. Second, the excluded volume Vexcl(r)is a constant, independent of the yardstick size. The pore size distribution (PSD), defined as3t4
11. Multilayer Adsorption and Pore Filling Efficiency In this section we will use the topological approach of Pfeifer et a L 4 p 5 to give a mathematical justification of eq 2. Let us define W(r),the neighboring volume, as the volume enclosed between-the surface of a corrugated solid, with a fractal dimension d, and an external hull a t distance r, with r standing as the size of the y a r d ~ t i c k .As ~ shown p r e v i ~ u s l y W(r) , ~ is expressed as
dVexcl(d PSD(r) = -= C ( d - 2)(3 - d)r2-d dr is also null. In this idealized asymptotic situation and for a yardstick size above the inner cutoff of the fractal regime, the adsorption takes place in the very external hull of the solid matrix. Most of the time one must come back to a classical picture of the adsorption process. The derivation of section I1 assumes some properties of the fractal surface. In particular, pores with a smaller wall-to-wall distance in the entrance than in the “center” (bottlenecks) must be excluded. The Manger sponge is a good illustration of the type of geometry which does not exhibit this type of problem and should be correctly described. The aperture of each pore has the same size of the pore itself, and necks are not observed.* When necks are present a t scales of different length, the monolayer volume defined by eq 4 overestimates the real monolayer capacity. An example of this situation was recently analyzed? Undoubtedly this particular class of fractals, with generation of pore necks, deserves further attention. The last remark we want to address deals with the respective role of multilayer adsorption and capillary condensation. This last process is certainly very active on a fractal corrugated surface where a broad pore size distribution exists (cf. eq 14). The cutoff between the formation of n adlayers and the onset of the capillary condensation is not obvious a t all and should be a function of the pore geometry. The wedge-shaped pore is an interesting example of this problem. In this case there is no characteristic pore size, and multilayer and condensation processes appear simultaneously. Actual models of adsorption based on a generalization of the BET theory are not yet appropriate to handle these difficulties and more specially to describe the high partial pressure part of the adsorption isotherm.
W(r)= ~ ~ a 9 - a
(3)
where L is the overall size of the object and C a shape factor. The monolayer volume, Vmono(r), is the volume of a set of points belonging to W(r),whose distance from the external boundary of W(r)is inferior to r. As proposed by Pfeifer et al.4 we can write (4)
which gives Vmono(r)= ~ ( -3d ) ~ d 9 - ~
(5)
The excluded volume, which cannot be occupied by yardsticks of size r, is defined as vexc10.) = W ( r )- Vmono(r) (6)
or
Vexcl(r)= ~ ( -d2 1 ~ 2 ~ 3 - 2
(7)
Let us now consider an i-layer adsorbed on this fractal surface. Its average thickness p can be expressed as p = ir (8) Then from eq 3 we have dW(p) = C(3 - d)Lap2-‘dp
(9)
d W(p)is the elementary volume between boundaries p and p + dp. This is the volume of the layer i assuming dp = r. The number of molecules in the layer i is
The number of molecules in the first layer in contact with the solid can be expressed from eq 5 as Vmono(r) = ~ ( -3 N, = r3
i2-2
(12)
This result can be easily generalized to the case of an embedding Euclidean space of dimension E fi
=
;E-1-2
Photoelectrochemistry in Particulate Systems. 8. Photochemistry of Colloidal Selenium Nada M. DimitrijeviE*v+and Prashant V. Kamat*
(11)
The factor fi can be computed when d is different from the dimension of the Euclidean embedding space. From eq 1 we get fi =
(8) Brochard, F. J. Physique. 1985, 46, 2117. (9) Van Damme, H.; Levitz, P.; Bergaya, F.; Alcover, J. F.; Gatineau, L.; Fripiat, J. J. J. Chem. Phys. 1986, 85, 616.
(13)
This equation demonstrates the numerical conjecture of our former paper.l 0743-7463/88/2404-0782$01.50/0
Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556 Received September 1, 1987. In Final Form: November 10, 1987
Introduction Selenium which exists in both crystalline and amorphous forms is an n-type semiconductor (Eg 1.7 eV’) with a broad range of applications (e.g., selenium rectifiers, xe-
-
‘On leave from Faculty of Science, Belgrade University, Yugoslavia.
0 1988 American Chemical Society
Langmuir, Vol. 4, No. 3, 1988 783
Notes
' 0
---
'3&O14kO1 ~ o o ' 6 0 0 w
Dp
WAVELENGTH (nm)
(8)
Figure 1. Absorption spectra of 2 X
Figure 2. Particle size distribution of Se colloids prepared in
rography).2 Optical and photoelectrical properties of different forms of selenium have already been In our continuing efforts to probe the corrosion processes of metal chalcogenides we have recently reported the laser flash photolysis and pulse radiolysis study of CdSe and In2Sea colloids."8 A major product of photoanodic corrosion of these semiconductors is elemental Se, which could be identified by the changes in the absorption spectrum. Se formed during the anodic corrosion process either exists in the colloidal form or precipitates on the surface of colloidal CdSe and In2Se3. The presence of Se, which is also photoactive, can influence the photoelectrochemical behavior of colloidal metal selenides. In view of this we have prepared colloidal particles of red amorphous Se in aqueous solution, and its photochemical and photoelectrochemical behavior is described here.
Figure 3. Transient absorption spectra of Se colloids obtained immediately after 355-nm laser pulse excitation: (a) 0,4 mM Se in water; (b) 0,after dilution of sample a with acetonitrile (0.8 mM Se in 20 v/v% H20-80 v/v% CH,CN). Insert is an ab-
M selenium colloids in aqueous medium (a) before (-) and (b) after (- - -) 30 min of visible light (A > 400 nm) irradiation.
Experimental Section Colloidal red amorphous Se was prepared in aqueous solution by mixing an equimolar concentration of selenious acid (Aldrich) and hydrazine monohydrate (99-100% Baker) with 0.1% Nafion (Aldrich, 5% solution) as a stabilizer. The reaction mixture was allowed to stay overnight to complete reaction l.9
-
H2Se03+ NzH4
Se + 3Hz0 + Nz
(1)
Appearance of a red-brown color confirmed the formation of Se colloids. When prepared under these conditions Se particles are expected to contain an adsorbed layer of the reducing agent? Up to a concentration of lo4 M, diluted solutions of Se were found to obey Beer's law; this was confvmed by recording the absorption spectra at various concentrations of Se. The colloidal suspension was stable for only a few hours while the aqueous colloidal suspension was stable for few days when stored in the dark. Electron micrographs were taken with a Hitachi H600 transmission electron microscopy after a drop of colloidal suspension was applied to a copper grid (400 mesh). Absorption spectra were recorded with a Cary 219 spectrophotometer. Flash photolysis (1) (a) Henrion, W. Phys. Status Solidi 1966,12, K113. (b) Hartke, J. L.; Regensburger, P. J. Phys. Rev. 1966, 139, A970. (2) Selenium; Zingaro, R. A., Cooper, W. C., Eds.; Van Nostrand Reinhold: New York, 1974. (3) (a) Hartke, J. L.; Regensburder, P. J. J. Appl. Phys. 1963,34, 1730. (b) Gilleo, M.A. J. Chem. Phys. 1961,19, 1291. (4) (a) Cherkasov, Yu. A,; Zakharova, N. B. Russ. Chem. Rev. 1977,46, 2240. (b) Stuke, J. In ref 2, 174-297. ( 5 ) Dimitrijevic, N.M. J. Chem. SOC.,Faraday Trans. 1 1987,83,1193. (6) Dimitrijevic, N. M.; Kamat, P. V. J . Phys. Chem. 1987,91, 2096. (7) Dimitrijevic, N. M.;Kamat, P. V. Langmuir 1987, 3, 1004-1009. (8) Dimitrijevic, N. M.;Kamat, P. V. Radiat. Phys. Chem. 1988, in press. (9) De Brouchere, L.; Watillon, A.; Van Grunderbuck, F. Nature (London) 1966, 178, 589.
water.
sorption profile recorded at 430 nm (sample a).
experiments were performed with a 355-nm laser pulse (pulse width 6 na) from Quanta-RayND:YAG laser system. Steady-state photolysis was performed by using a collimated and filtered (400-nm cutoff) light beam from a 600-W tungsten halogen lamp. All experiments were performed at room temperature (-22 "C).
Results and Discussion Absorption Characteristics. The absorption spectrum of Se colloids prepared in aqueous solution (Figure 1) exhibits an onset of absorption around 800 nm that matches well with the previously reported absorption characteristics of red amorphous ~ e l e n i u m . While ~ the absorption a t higher energy (A < 550 nm) is due to interband transitions, the absorption at longer wavelength is considered to be nonphotoconductive. It has been established earlier that a gap of -0.6 eV exists between the optical absorption edge and the photoconductive edge.'O The absorption a t longer wavelengths, which is nonphotoconductive, has been attributed to intrinsic exciton transitions.'l Continuous irradiation with the visible light (A > 400 nm) led to its degradation as observed from the absorption spectra (Figure 1). Such a photocorrosion was similar to the one observed for other short bandgap semiconductor colloids such as CdSe.6 The particle size distribution of Se colloids prepared in aqueous medium is shown in Figure 2. Particle size distributions were obtained by measuring the particle diameter from the electron micrograph. These particles were (10) Cooper, W. C.; Westbury, R. A. In ref 2, 794-805. (11) (a) Siemsen, K. J.; Fenton, E. W. Phys. Reu. 1967,161,632. (b) Tabak, M.D.; Water, P. J., Jr. Phys. Reu. 1968,173,899. (c) Pai, D. M.; Ing. S. W. Phys. Reu. 1968, 173, 729.
784 Langmuir, Vol. 4, No. 3, 1988
Notes
'
W
'3&'44b0'&6b0'
-O0l0'
7"ebo'
WAVELENGTH (nm)
Figure 4. Changes in the absorption spectrum of deaerated aqueous solution containing colloidal Se (2 mM) and ZV (- lo4 M) after 15 min of visible light (A > 400 nm) irradiation.
spherical, with the particle diameter ranging from 600 nm) confirmed the participation of excitonic states in trapping of charge carriers. Photoelectrochemical Reduction. Viologen compounds have proved to be excellent probes to study the interfacial charge-transfer processes in colloidal semiconductor systems. When a suspension of colloidal selenium containing zwitterionic viologen was subjected to visible light irradiation (A > 400 nm), the reduction of ZV was found to occur: e-(Se) + ZV ZV(4) The difference spectrum obtained from the absorption spectra before and after the steady-state photolysis is shown in Figure 4. This absorption spectrum, which exhibits absorption maxima at 395 and 600 nm,c o n f i i e d the formation of ZV'-. The yield of ZV- observed with laser pulse excitation was very low (4 < 0.01). Transient absorption due to ZV'- could not be directly observed in laser flash photolysis experiments as the photobleaching dominated the transient absorption spectrum. Though colloidal Se possesses photoelectrochemical properties like other semiconductor colloids, it exhibits very low efficiency for the charge-transfer process. As observed with colloidal Si,16 Se colloids also undergo extensive photocorrosion. Better understanding of the structure and properties of Se colloids, varying the method of preparation, and retardation of the corrosion processes are necessary before these semiconductor colloids are considered for the photoelectrochemical systems. +
Acknowledgment. The research described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is Document No. NDRG3015 from the Notre Dame Radiation Laboratory. Registry No. Se, 1182-49-2. (17)Alfasei, 2.;Bahnemann, D.; Henglein, A. J. Phys. Chem. 1982,86, 4656. (18)Fojtik, A.;Weller, H.; Fiechter, S.; Henglein, A. Chen. Phys. Lett. 1987,134,477.
