J . Phys. Chem. 1984, 88, 3923-3925 excitation fluorescence measurement: neither spectral shift nor lifetime variation of the T* fluorescence were observed. These results clearly support no excitation energy dependence of pF, suggesting that no process is capable of competing with the fast population of relaxed T* in methanol at room temperature. On the other hand, ’ p p ~may be no longer constant in the case that the rapid proton transfer, competing with internal conversion, takes place from specific excited states. Nishimoto and Forster” reported two one-photon-allowed transitions at 225 and 238 nm with the oscillator strengthsA2251 = 1.077 andA2381 = 0.614, estimated by an SCF MO calculation of 7-HQ, in the 210-250-nm region. The observed absorption spectrum shown in Figure 3 may be ascribed to these two onephoton-allowed transitions.I2 Further, they obtained the onephoton forbidden transition at 221 nm with f = 0.079. The observed main peak (218 nm) in the TPE spectrum seems to correspond to this forbidden transition, though the assignment of the shoulder (240 nm) is not obvious a t the present stage. It has been reported that pseudoparity (pairing) rules may be mutually exclusive for one- and two-photon transitions of the molecules (monoflu~robenzene,’~ ~ h e n a n t h r e n e , ’etc.) ~ without a center of symmetry. Thus, such an inversion correlation between one- and two-photon parameters of 7-HQ mentioned above suggests that the selection rules are still operative. The two-photon absorpton cross section was estimated to be 5.1 X cm4 s photon-’ molecule-’ at 440 nm by the method of Parma and O m e n e t t ~ .Therefore, ~ the TPE spectrum (A, = 218 nm) of the T* fluorescence may be assigned to the one-photon forbidden band (221 nm). This fact indicates that the two-photon-allowed ~~
~
~
(11) Nishimoto, K.; Forster, L. S . J . Phys. Chem. 1967, 71, 409. (12) The authors express their thanks to a reviewer for this assignment of
the electronic transitions. (13) Scott, T. W.; Callis, P. R.;Albrecht, A. C. Chem. Phys. Lett. 1982, 93, 111. (14) Dick, B.; Hohlneicher, G. Chem. Phys. Letr. 1983, 97, 324.
3923
state (218 nm) may be the reactive state for the rapid proton transfer (surpassing internal conversion to N*), which is responsible for the appearance of green T* fluorescence. A similar discussion has been made by Parma and OmenettoI5 for the different feature in the fluorescence spectrum of 7hydroxycoumarin (U) in ethanol when excitation of U proceeds via one- and two-photon absorption: One-photon excitation of U results in dual fluorescence (blue and green) due to U* and an “exciplex species”, [U- - -H+]*, while two-photon excitation of this solution affords only the blue florescence of U*. By assuming that states of different parity are reached by one- and two-photon excitations, they speculated that the state reached in the two-photon excitation does not undergo the energy transfer required for the formation of the “exciplex species”. However, it is more reasonable to assign the origin of the largely Stoke’s shifted green fluorescence as the excited-state tautomer16 rather than the exciplex species. Thus, it is noteworthy that two-photon-induced excited-state proton transfer is favorable for 7HQ/(MeOH)2 reported in the present paper and unfavorable for U/EtOH. It is probable that the driving force for such a rapid proton transfer is attributed to the significantly increased acidity of the phenol group and/or the increased basicity of the ring nitrogen atom of 7-HQ in the two-photon-allowed state. The TPE spectrum in the wavelengths of normal fluorescence cannot be examined by monitoring the fluorescence but by monitoring the largely Stoke’s shifted T* fluorescence. Therefore, the phenomenon of two-photon-induced proton transfer, reported in the present paper, may provide us with valuable information about several higher two-photon states of organic molecules. Acknowledgment. The authors are grateful to Tomoko Adachi for her valuable comments. (15) Parma, L.; Omenetto, N. Chem. Phys. Lett. 1978, 54, 544. (16) Yakatan, G. J.; Juneau, R. J.; Schulman, S. G. Anal. Chem. 1972, 44, 1044.
Prewetting in Partially Miscible Liquids and the Structure and Thermodynamics of Transient Foams and Aerosols Jesis Gracia, Carmen Varea, and Alberto Robledo* Divisidn de Estudios de Posgrado, Facultad de Qulmica. Universidad Nacional Autdnoma de Mcxico. MZxico 0451 0, D.F. (Received: March 19, 1984; In Final Form: May 24, 1984)
We obtain, through a statistical-mechanical calculation for the nonuniform van der Waals binary mixture, the stable stationary states corresponding to transient foams and aerosols in partially miscible liquids. The structures responsible for enhanced foaminess are described by prewetting profiles that connect vapor to liquid film or droplet uniform regions. Model foam behavior is in agreement with the experimental evidence on foam stability of Ross and Nishioka. A distinct limit to this stability is the branch of the solubility curve where perfect wetting occurs. Global behavior is analyzed in the mixture interaction space, where regions of nonfoaming, normal foaming, and biliquid foaming mixtures are delineated.
Introduction The statistical-mechanical and thermodynamic background to foam and aerosol behavior is less well understood than desirable in view of their technological importance. The recent investigations on foamability in binary and ternary liquid mixtures by Ross and co-workers1,2have uncovered some of the common factors governing the stability of liquid film or droplet structures. Their work suggests that transient foaminess is a general phenomenon occurring in multicomponent systems even where the amphipatic molecular structure of the solute, or cosolvent, is not readily (1) S. Ross and G. Nishioka, J . Phys. Chem., 79, 1561 (1975); “Foams”, R. J. Akers, Ed., Academic Press, London, 1976. (2) S. Ross and R. E. Patterson, J . Phys. Chem., 83, 2226 (1979).
0022-3654/84/2088-3923$01.50/0
identified. They also pointed out that appreciable foam stability is only to be found at certain temperatures and compositions: those close to the critical solubility points. Highest foam stability appears at the homogeneous side of the solubility curve, where contours of equal stability (isaphroic lines) were determined for some systems.’ Nitrogen gas was bubbled through the solutions at measured rates G and the steady-state volume vo of foam recorded. The ratio Z = vo/G was found to be almost independent of G and was used as a measure of foaminess.’ For a binary system, represented in a temperature composition projection, the isaphroic lines center near the consolute end point as a maximum and decrease in value the farther they are from it.’ These lines are not symmetric around the critical composition but appear biased toward one side (see Figure la). The isothermal variation of foam 0 1984 American Chemical Society
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Letters
The Journal of Physical Chemistry, Vol. 88, No. 18, 1984 T
Figure 1. (a) Equal foam stability contours for a binary fluid mixture with an upper critical end point (UCEP). The highest stability appears close to the three-phase coexistence curve. (b) Isothermal variation of foam stability Z: for the same system for T I < TUCEP.
stability z1 with composition for the binary system is shown in Figure lb. The pure components, as it is a common experience, do not foam, but as the concentration of either component increases, foam with increasing stability can be maintained. But only at one side of the diagram high stability values are observed, and these apparently diverge when the immiscibility composition is reached; then, as the two-liquid region is entered, a complete defoaming action takes place. On the other hand, the low-stability branch of the diagram continues producing foams inside the two-liquid region, but they suffer a slow decline as the conjugate liquid separates out. No similar account on the behavior of aerosol structures as related to the phase diagram of their constituents seems to have appeared in the literature. Although a phenomenological rationale, significantly successful for the behavior patterns described above has been in terms of the high adsorption or segregation that occurs at interfaces near a consolute end point: a quantitative derivation from a first-principles model of these results helps to establish how the properties of the interfaces involved determine the mechanisms of foam stabilization and defoaming action. We briefly report the properties of stable stationary nonuniform structures belonging to the statistical-mechanical model that leads to the thermodynamic formulas of the van der Waals binary m i x t ~ r e . ~A. ~distinction between permanent and transient foams and dispersions must be emphasized. In the former case the addition of a suitable amphipatic surfactant decreases drastically the interfacial energies and favors the appearance of lamellar or micellar structures that provide enhanced stability to films and droplets.' However, mixtures lacking this kind of surfactant can produce foams made of thick liquid films if kept, for example, under agitation.' The structures studied are those consisting of a macroscopic liquid film, or droplet, surrounded by its equilibrium vapor. They constitute our model foam and aerosol systems. The surface energy of such a thick film is twice that of a simple liquid-vapor interface but is the minimum free energy arrangement under the chosen boundary conditions.
Results The density profiles of the two components that we find to provide enhanced stability to these stationary states are those associated with the phenomenon of prewetting:8-12 Le., an (3) S. Ross, Chem. Ind. (London), 47 (1981). (4) J. W. Cahn, J . Chem. Phys., 66, 3667 (1977). (5) C. Varea, A. Valderrama, and A. Robledo, J . Chem. Phys., 73,6265 (1980). (6) D. E. Sullivan, J . Chem. Phys., 77, 2632 (1982). (7) P. G. de Gennes and C. Taupin, J. Phys. Chem., 86, 2294 (1982). (8) H. Nakanishi and M. E. Fisher, Phys. Rev.Lett., 49, 1565 (1982). (9) D. E. Sullivan, Phys. Rev. E : Condens. Matter, 20, 3991 (1979); J . Chem. Phys., 74, 2604 (1981); R. Pandit and M. Wortis, Phys. Rev. B: Condensahon Matter, 25, 3226 (1982); G. Teletzke, L. E. Scriven, and H. T. Davis, J . Colloid Interface Sci., 87, 558 (1982). (10) M. E. Costas, C. Varea, and A. Robledo, Phys. Rev. Lett., 51, 2394 (1983).
0 Prewetting
I
Figure 2. (a) Wetting properties of the binary model mixture mapped
on a temperature-compositionprojection: UCEP (upper critical end point), ICP (interfacial critical point). (b) Density profiles for the nonwetting, prewetting, and macroscopic liquid-film (with prewetting) interfaces. APw is the prewetting layer thickness.
equilibrium structure of the LIV interface (where L, is a liquid and V a vapor phase) that contains a microscopic (or finite in molecular lengths) film resembling an L, metastable liquid phase. Prewetting occurs a t two-phase states close to equilibrium perfect-wetting three-phase states. The thickness of the L, film increases logarithmically as perfect wetting is approached where it becomes macroscopic, indicating a second-order interfacial t r a n ~ i t i o n .Provided ~ ~ ~ ~ ~that ~ along the three-phase states occurs a partial-to-perfect wetting transition of the first order, prewetting states also terminate at another but first-order interfacial transition b ~ u n d a r y . ~See , ~ Figure 2. The background to these transitions is the possibility of two different structures for the density profiles that describe the L I V interface. Both structures correspond to local minima of the free energy. We studied the model mixture for the range of values of the parameters A and { employed in the classification of van Konynenburg and Scott13 for which the equal-diameter mixture exhibits three-phase equilibria terminating at only one (upper) critical end point (UCEP). A and {provide respectively a measure of heat of mixing and critical point separation of the pure components. In a previous paperlo it was reported that for most mixtures all ({,A) points in the region t2 (A - 1)2 < 1 (A < 1 and { # 0) exhibit a first-order interfacial transition along their three-phase states. In that study there were also found mixtures, but with only one degree of freedom in ({, A) space, exhibiting second order or no transitions, with either perfect or partial wetting along all the three-phase line.I0 A calculation that treats nonuniformities exactly5 begins with the consideration of Kac-type interactions (in the infinite range limit) between like and unlike pairs and leads to the following (nonlocal) expression for the thermodynamic potential:
+
where
P C
i j - I ,2
kipi
P =
PI
+ PZ
and where the pi are the density profiles, aij are the interaction parameters, u is the molecular diameter of both types of molecules, pi are the chemical potentials, and P is the inverse temperature. In terms of the aij we have that A = (al1+ a,, - 2a12)/(a11 + (11) References 8 and 9 discuss prewetting in one-component systems bounded by a wall, while ref 10 studies the analogous states at fluid-fluid interfaces in binary mixtures. Prewetting states were first discussed phenomenologically by Cahn and Widom (ref 4 and 12). (12) B. Widom, J . Chem. Phys., 68, 3878 (1978). (13) R. L. Scott and P. H. van Konynenburg, Discuss. Faraday Soc., 49, 81 (1970); P. H. van Konynenburg and R. L. Scott, Phiios. Trans. R. SOC. London, Ser. A, No. 298, 495 (1980).
The Journal of Physical Chemistry, Vol. 88, No. 18, 1984 3925
Letters 1 and ~ {~ =) ( a 2 2- al1)/(aI1 + ~ 2 ~ The ~ ) .associated equations for the profiles are solved under the conditions when phase equilibrium is possible. The interfacial tensions are subsequently determined as the excess free energy. We can visualize how Q provides two different sets of profiles for the LIV interface in the following way. The nonuniform minima of D are a compromise between the first term in eq 1, which favors the system to stay in a uniform stationary state, and the second term, which is minimized by the smoothing of the profiles. Q exhibits a third uniform (metastable L2) minimum along the LIV equilibrium states at temperature (TI only between (in (pl,p 2 ) space) the three-phase point and the intersection with the spinodal curve branch for L2. Thus, depending on how many uniform minima are employed in the minimization of Q,one obtains one of the two types of profiles. The nonwetting interface exists for all LIV states, but prewetting profiles appear only as the L2 minimum persists. Prewetting profiles become equilibrium structures only for that interface that experiences perfect wetting at three-phase coexistence. We shall present elsewhere detailed results obtained for P , , ~ ( Zas ) generated by the numerical solution of the EulerLagrange equations obtained from (1). Here it is more appropriate to discuss analytically the behavior near perfect wetting in terms of the approximate profiles ~
V
p;,z a22)so that prewetting occurs only for the LIV states. From the density expansion of eq 1 and 2 we find that at the prewetting-to-perfect wetting transition d2AQ/dA2lpw 0 while d 2 A Q / ( d p > 8 p F ) IPw m. Our numerical calculations are consistent with this behavior. Summing up, the equilibrium interfacial tension AD, suffers a discontinuity in its first derivative at the prewetting transition, signaling the onset of enhanced adsorption. This regime becomes saturated at the conditions of threephase coexistence; there, monolayer (or few layer) adsorption becomes unstable, the adsorption coefficient r2diverges as Ape does, and the liquid L2 appears in bulk at the interface.
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Discussion Liquid films could not be formed without thermodynamic stability. Also, their mechanical stability against external stresses (as those imposed by gravity or capillary forces and responsible for drainage and rupture) is provided by restoration mechanisms (like the Marangoni effect') that depend upon thermodynamic stability. Some features in Figures 1 and 2 can now be related. The lack of symmetry with respect to the critical composition in Figure 1, and in particular the divergence of 8, is a reflection of the fact that prewetting states only occur at one branch of the three two-phase possible equilibria, at the L,V interface. The question of why foams lose their stability at the second-order prewetting-to-perfect wetting transition is answered by the fact that there d2Q/dA2 IPw 0, indicating no resistance of the interface against thickening. However, since d2Q/(dpf2dp?) IPw m in the vincinity of liquid-liquid immiscibility, liquid films and droplets are best maintained due to the increased stiffness of their interfaces toward further adsorption. By contrast, the other extreme in composition, that of the L2V equilibrium, could only show poor or moderate foam and aerosol stability for there are no singularities there in the curvatures that measure interfacial stability. The slow decay shown in Figure l b in the immisibility region occurs because as bulk liquid L1 develops, the LIV interface captures the available liquid L2 to produce its perfect-wetting structure. L, acts as a defoamer of L2 foam, but the more stable L1 foams are destroyed by the instability of their interfaces against multilayer formation. Adsorption at film interfaces, with the ensuing decrement of surface tension, leads to appreciable foaminess. Thus, the prewetting boundary in Figure 2a does not indicate the onset of foamability; it would only appear as a finite discontinuity in the B vs. x isotherms. This may be experimentally observable, but the available data' are insufficient for this purpose. Prewetting can be studied throughout the interaction space ({,A). We can conclude on the ground of the known1° wetting behavior of the model mixture the following: Mixtures with a negative heat of mixing, A < 0, are basically nonfoamable. Also, the symmetric mixtures (A > 0 and { = 0) should produce poor foams, for their three-phase states are always partial wetting. On the contrary, the best foams should be formed in mixtures for which the geometric-mean combining rule l2+ ( A - 1)2 = 1 is a good approximation. In this case prewetting endures at low temperatures because all three-phase states are perfect wetting and all two-phase LIV states are prewetting. Other mixtures featuring high foamability may be those approaching perfect immiscibility. This requires that, say, a l l >> a22,so that A N 1 and { 1, but the ratio of the two other parameters remains undetermined. This is the system that maps into Sullivan's mode19J0 of the solid-fluid interface. For these mixtures the wetting transition along the three-phase states is second order and there is no prewetting transition? Finally, when the heat of mixing is large and positive (A 1) and the difference in critical points of the pure components is small ({ 0), the critical interface at the UCEP is of the liquid-vapor type13and the interface that experiences the wetting transitions is of the liquid-liquid type since it is this that has the highest interfacial tension.I0 Prewetting in this circumstance favors the stabilization of biliquid foams.I4
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Acknowledgment. We acknowledge financial support by Consejo Nacional de Ciencia y Tecnologia de Mixico. (14)
F.Sebba, J . Colloid Interface Sci., 40, 468
(1972).
