54
Langmuir 1989,5, 54-58
to quenching inertness at higher octanol amounts. This behavior is most likely associated with the above (opposing) phenomena, i.e., the DEA displacement effect becoming progressively predominant as the amount of octanol increases. An analogous formulation of the same mechanism may invoke a preferential extraction of DEA (or Py) from the surface vicinity upon pore fill up with octanol. As to the exciplex parameters A, and & (see Table 11), it is indicated that the presence of l-octanol partially releases the restrictions imposed on the generation of the exciplex on Si-60. Again, the plausible explanation is that Py is partially displaced by the alcohol into larger pores, values closer to those observed in, e.g., Si-200. leading to
Conclusions The capability of an aromatic amine such as DEA to serve as an effective electron donor in charge-transfer processes on silica surface drops virtually to zero by the strong adsorption interactions with the acidic silanol groups. An effective CT process is observed only when an excess of free (nonadsorbed) DEA molecules becomes available above monolayer coverage. The process is then markedly affected by the average pore size of the silica, most likely due to the nonhomogeneous distribution of the added DEA in the porous adsorbent. However, the details of the quenching mechanism are still unclear. Thus,
preliminary fluorescence lifetime measurements indicate that the population of quenched ‘Py* is heterogeneous. In the case of Si-100 most of the excited pyrene molecules react with DEA on a 50-200-ns time scale. However, with the other silicas considerable fractions are quenched over much shorter time scales which are below the resolution of our measurements (-10 ns). Further work, with subnanosecond time resolution, should be carried out for a quantitative classification of the pyrene populations participating in the DEA quenching process. Finally, it became evident that the course of the reaction of the surface is not governed simply by polarity effects as in the case of the same process in homogeneous solutions. Considerable steric restrictions on exciplex generation are clearly evident in the case of Si-60 which are completely absent in the case of Si-1O00. The effects are most likely associated with the details of the surface geometry, namely its porosity and irregularity. Further studies are in progress for elucidating the exact role of the surface fractal dimension and of the pore size distribution in controlling the course of the CT reactions.
Acknowledgment. Supported by the US-Israel Binational Fund and by the E. Berman Solar Energy Research Foundation. Registry No. Py, 129-00-0; DEA, 91-66-7; SiOz, 111-87-5; 1-octanol,7631-86-9.
Application of the Kirkwood-Buff Theory of Solutions to the Surface Phase between the Water-Ethanol Binary Liquid Mixture and Its Vapor E. Tronel-Peyroz,* J. M. Douillard, R. Bennes, and M. Privat Laboratoire de Physico-Chimie des Systcmes Polyphas6s, CNRS U A 330, Route de Mende, BP 5051, 34033 Montpellier, France Received January 29, 1988. In Final Form: August 2, 1988 From experimental data concerning adsorption at the liquid-vapor interface and a rough model for the transition layer, the Kirkwood-Buff integrals, Giju,have been calculated for the surface-phase mixture by using Ben-Naim’s procedure. The superficial local mole fractions were then calculated. Results obtained for the water-ethanol surface mixture are compared with those for the water-ethanol bulk mixture. It is shown that usual theoretical models offer no possibility of predicting the surface properties.
I. Introduction The classical method used for interpreting adsorption mechanisms combines both thermodynamic and nonthermodynamic pr0cedures.l Thus, starting from Gibbs’ equation and a determination of the adsorption isotherm, information concerning the orientation of the adsorbed molecules can be obtained by employing phenomenological models. One can go further with regards to the microscopic interpretation of these results by using the various molecular adsorption models, of which the adjustable parameters can be calculated as a function of the molecular properties of the adsorbed layers. Unfortunately, none of these models furnishes at the present time a satisfactory description of the structure of the superficial layer, and (1) Rangarajan,S . K.In Specialist Periodical Reports, Electrochemistry; Thorsk, H. R., Ed.; The Chemical Society: London, 1980; Vol. 7.
this is partly (as Nikitas has pointed out in his critical review) because “the various models have the same basic features. They idealize the adsorbed region to a monolayer for which an a priori lattice structure is assumed”.2 This relative failure is also due to the general difficulties encountered in explaining molecular interactions, the starting point of any microscopic model. In the exact theory of solutions developed by Kirkwood and BufP the essential parameter is the radial distribution function (rdf) gij(r),which is a measure of the importance of the correlation between the position and the orientation of i j pairs. This can be determined by classical scattering methods in a pure liquid but is difficult to determine in mixtures. (2) Nikitas, P. Electrochem. Acta 1985, 30, 1513. (3) Kirkwood, J. G.; Buff, F. P.J. Chem. Phys. 1951, 19, 774.
0743-7463/89/2405-0054$01.50/0 0 1989 American Chemical Society
Langmuir, Vol. 5, No. 1, 1989 55
Kirkwood-Buff Integrals for Water-Ethanol However, the theory links the thermodynamic properties to the Kirkwood-Buff integrals Gia defined in eq 2. These parameters can be calculated foliowing inversion of the Kirkwood-Buff theory as described by Ben-Naim from experimental value^.^ As they are directly linked to the rdf, they are very sensitive to molecular interaction^.^ The aim of this paper is to show how Ben-Naim's procedure can be applied to surface phases, by using a crude model for the interface. In section IV, we give the preliminary resulta obtained for a simple binary liquid mixture (water-ethanol) at the liquid-vapor interface. This new procedure used to extract some structural information from the experimental data should enable the microscopic study of surface layers to progress. 11. Kirkwood-Buff Parameters in the Surface
Phase From the classical work performed by Guggenheim,6 Eriksson,' and Mohilner,e the surface layer constituting the interphase between two bulk phases may be thermodynamically analyzed as an autonomous phase. In the adjacent phases, all the thermodynamic variables fluctuate around their mean values. The same can be said for the thermodynamic variables that characterize the surface phase,9 For example, the surface composition fluctuations in the adsorbed layer of a binary liquid in equilibrium with its vapor are given by the classical expression F2"
X1" (8 In a2'/dx2')T,P,nl.
111. Determination of the Composition of the
Surface Mixture 1. Useful Relationships. The superficial phase is defined as the phase which contains the entire heterogeneity of the composition. We define this by choosing the surface of separation at the limit where this phase presents the same composition as the bulk so1ution.l' Chosen in this way, the composition of the surface mixture is given by Xi" e -*
ri
Ciri' i = 1, 2
(1)
where xiu are the molar fractions and aiuis the activity of the adsorbed molecules in the surface phase CT (2 is the constituent with the smallest surface tension). According to the Kirkwood-Buff theory, the isothermal compressibility (XT"),the partial volume of i (vi"), and the composition fluctuation (P) can be expressed in terms of Gij", which is defined as
Gij" = ~ + m ( s i-j 1") ( 4 d ) dr
Numerous studies have shown that the u phase is much closer to a liquid than to a gaseous state.1° Therefore, it can be considered that XT" is close to XTa and that RTXT" is negligible in respect to the other terms in eq 3-5 (the exponent a indicates the bulk phase). To evaluate the G f term in the surface phase, it is therefore necessary to calculate the composition of the surface mixture.
(2)
The physical meaning of this term is easily understandable if one considers the product piuGijuwhere pi0 is the number density of i molecules. In fact, piugjj"(47rP)is the mean number of i molecules in a volume between two spheres of radius r and r + dr situated at a distance r from a central particle j , whereas p:(47rr2) is the same number in the same volume but with the molecules randomly located in the superficial mixture. The product piuGijuis therefore an excess value measuring the mean number of i molecules around a j molecule, and Gijuis the same term by density units. The relationships between Gi."and the thermodynamic variables are well-known4and iead us to note the following for a binary surface mixture:
(4) Ben-Naim, A. J. Chem. Phys. 1977,67,4884. (5) Ben-Naim, A. Water And AqueouP Solutions;Plenum: New York, 1974. (6) Guggenheim, E. A.; Adam, N. K. h o c . R. SOC.London Ser. A . 1933,139, 218. (7) Eriksson, J. C. Arch. Kemi. 1966,21, 31; 1966, 25, 343; 1966, 26, 49. (8) Nakadomari, H.; Mohilner, D. M.; Mohilner, P. R. J.Phys. Chem. 1976, 80, 1761. (9) Bennes, R.; Douillard, J. M.; Privat, M.; Tronel-Peyroz, E. J. Colloid Interface Sci. 1987,117, 574.
(7)
where r i are the superficial excesses, which are the real populations in the surface phase. They are related to F2,1, the relative surface excess, by the classical relationship
where d r is the decrease in the surface tension, dpZuthe variation of the bulk chemical potential of species 2, and xZa the bulk concentration. As stated by Prigogine, the area of 1 mol of mixture in the surface phase, A", is an homogeneous first-degree function of the surface concentrati0n.l' Using eq 7 and the definition A" = 1/(Fl r2), we obtain the relationship
+
Al"I'l+
AzT2
=1
(9)
where Ai" describes the partial molar area of constituent i in the u phase. From eq 8 and 9 (given the values of Ai"), it is not difficult to evaluate rl and r2and thus xiu. 2. Evaluation of Ai". As is generally done and as a first approximation, we shall first assume that the partial molar areas and partial molar volumes of species i in the surface phase are independent of the composition.' Thus, Ai" E Aiuaand viu N viuo with, by definition, vf = AiUodi, where di is the thickness of the transition layer at the liquidvapor interface of the pure liquid i. As we know that the density of this transition layer is less than the corresponding bulk density,1° the ratio t = vi"'/vi"", which describes the average density shift inside the surface phase, is less than 1. The ratio ti and the thickness di are not independent; they are roughly related to the ellipticity coefficient of pure liquid substances.12 A (10) Conway, B. E. Adu. Colloid Interface Sci. 1977, 8, 91. (11) Defay, R.; Prigogine, I. Surface Tension And Adsorption; Longmans: London, 1966; p 161. (12) Tronel-Peyroz, E.; Bennes, R.; Douillard, J. M.; Privat, M. C. R. S8ances Acad. Sci., SQr.2 1984,299, 1313.
Tronel-Peyroz et al.
56 Langmuir, Vol. 5, No. 1, 1989 Table I. Parameters Used To Calculate the Superficial Composition ti di, A uiUo,cms.mol-' Aiso,cm2.mol-' 3.7 x 108 6.0 22.3 water 0.81 4.4 x 108 15.7 69.0 ethanol 0.85
t Fl
Figure 1. Adsorption isotherm for the water-ethanol mixture (25 "C). reasonable value for ti for water (tl N 0.81) corresponds to an equivalent thickness of two layers of water at the pure liquid water-vapor interface; Le., dl = 6 A. The magnitude of t i for ethanol (component 2) may be evaluated from the relationship given by Eyring13 i/t,1/3 = 1
+ f(i- T/T,)
(10)
which is the same for both components. f is a constant, T the temperature, and T,the critical temperature. Using eq 10 for water and for ethanol and taking the ratio, we obtain t 2 9 0.85 for tl 9 0.81, T,= 647.3 "C (for water), and T,= 513.9 "C (for ethanol). With these values we can now evaluate d2 and therefore A2uo. The values of the different parameters used to calculate the surface composition 3cZu are given in Table I (see also ref 14). Of course, there are some approximations in this procedure, the most important being the partial molar volumes being independent of the composition. However, it seems to us less hypothetical than the hypothesis of the constant-thickness monolayer, which is incompatible with ellipticity results over the whole concentration range.
IV. Results and Discussion All measurements were made at 25 "C. The ethanol used was a commercial product obtained from Merck, ita purity being controlled by chromatography. The water was purified by reverse osmosis and distilled twice (once on acidified potassium permanganate). Experimental data (surface tension, activity coefficients of ethanol in the bulk mixture, ellipticity coefficients, etc.) have been published in ref 14 and give the adsorption isotherm shown in Figure 1with the parameters defined in section 111. 2. To calculate the activities of species 1 and 2 in the superficial phase (aiu),we use the relationship ,uiu= giu, which expresses the thermodynamic equilibrium between the chemical potentials. If piu is expressed in the surface phase, as performed by Eriksson,' this equilibrium leads to the relationship aiu= a: exp[Aiu'(y - y i 0 ) / R T l
(11)
where aiais activity of constituent i in the bulk phase and yio is the surface tension of constituent i. Hence, the (13) Lu, W. C.; Jhon, M. S.; Ree, T.; Eyring, H. T. J. Chem. Phys. 1967,46, 1075.
Figure 2. Variation of the surface concentration fluctuation versus the surface molar fraction for the water-ethanol mixture: ( 0 )experimental points, (-) calculated values for the associated complex model (ref 14);(- - -) theoretical value for an ideal binary mixture.
(14)Tronel-Peyroz, E.; Douillard, J. M.; Tenebre, L.; Bennes, R.; Privat, M.Langmuir 1987, 3, 1027.
/
0.5
Xl
Figure 3. Variation of Gll versus the molar fraction: (- - -) bulk Glia versus the bulk molar fraction x$; (-) surface GllUversus the surface molar fraction x2u.
1,
G11((m3m o l i ' ) ,
,
,0:5
3
Figure 4. Variation of Gzzversus the molar fraction: (- - -) bulk GZ2"versus the bulk molar fraction xzu; (-) surface G22uversus the surface molar fraction x2
