J. Phys. Chem. 1986,90, 1230-1232
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of solvent in organized layers is conceptually a different phenomenon. This is a characteristic way to dissolve oil and water in a biological system as well as in a surfactant system. The senior author has systematized the properties of organized solutions (systems)15and has shown that with efficient surfactants, whose cmc-is small. The adsorbability is 1arger and the solvent property is greater. Surfactants such' as R16[oCHzCH(15) Shinoda, K. J . Phys. Chem. 1985,89, 2429.
(CH3)],SO4MI,, well satisfy the characteristics of organized solutions, e.g., (1) very small saturation concentrations of single dispersion, (2) liquid state of the solute in the presence of solvent, (3) a large or infinite solubility of water and/or oil in the solute phase, etc. Acknowledgment. We sincerely thank the Kao Corporation for synthesis of the surfactants, the Asahi Glass Foundation for Industrial Technology for financial support, and Mr. A. Shinohara for his cooperation.
Double-Layer Interaction In the Prlmitlve Model and the Correspondfng Poisson-Boltzmann DescrlRtlon Roland Kjellander* and Stjepan Marrelja Department of Applied Mathematics, Research School of Physical Sciences, Australian National University, Canberra, ACT 2601, Australia (Received: January 2. 1986)
Using the anisotropic hypernetted chain approximation, we obtain accurate evaluationsof the double-layerrepulsion or attraction within the primitive model of electrolyte solutions. Most of the results are different from the predictions of the nonlinear Poisson-Boltzmann (PB) theory. However, the effects of finite ion size and electrostatic ion-ion correlations counteract each other, ?nd, for large surface separations, one can bring the PB theory with a suitably chosen effective surface charge to fit the accurate calculations. The difference between the real and the effective surface charges can partly be considered as a nonspecific, electrostatic "adsorption" of ions to the surface.
Introduction Despite its well-known deficiencies, the nonlinear PoissonBoltzmann (PB) equation is still the most practical and widely used method of describing the electric double layers in aqueous ionic solutions. In colloid chemistry, electrochemistry, or biophysics, theories that are based on the Poisson-Boltzmann equation have mostly been successful; only in a limited number of examples has a behavior clearly inconsistent with the PB predictions been reported. From the theorist's point of view, the success of the PB approach must be explained: it is impossible that the perfect agreement2 between different measured physical variables and the PB predictions does not hide a more complicated situation. Why do the deficiencies inherent in the PB approach remain unnoticed, or do the errors made in the PB approximation compensate each other to some extent? In this Letter we present results which come some way toward answering the above questions. We show that the effects of the electrostatically induced ion-ion correlations and of the finite ion size, which are both neglected in the PB theory, tend to compensate each other in calculations of doubk-layer interactions. When deviations are still present, the repulsion a t larger separations can still be described by the Pp theory, but the apparent surface charge will be different from (mainly smaller than) the real charge. This apparent charge may erroneously be taken as a true surface charge, or if the latter is known from an independent measurement, one may try to explain the discrepancy as due to ion adsorption (or desorption for large ions) at the surface.
Model and Methods Our results are obtained by applying a recently developed general p r o c e d ~ r e designed ,~ for calculations of properties of (1) A. Khan, B. J6nsson. and H. Wennerstram, J. Phys. Chem., 89,5180 (1985). (2) See, e.g. R. M. Pashley and J. N. Israelachvili, J . Colloid Inferface Sci., 101,511 (1984). S . McLaughlin, N. Mulrine, T. Gresalfi, G. Vaio, and A. McLaughlin, J . Gen. Physiol., 77, 445 (1981).
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inhomogeneous simple fluids, to describe primitive model electrolyte solutions between two planar walls. The model solution consists of charged hard spheres surrounded by a continuum solvent characterized only by its dielectric constant (e = 80). In the simplest case, which is considered here, only counterions are present in the solution. From the calculations, we obtain the structure of and the interactions between electric double layers on the same level of approximation as normally achieved in primitive model treatments of bulk electrolyte problems. In the present calculation we use the anisotropic hypernetted chain (HNC) approximation on the two-particle levei, and hence our treatmeqt differs from earlier integral equation theories of the double layer that have been formulated on the one-particle level. Consequently, we are able to correctly include the paircorrelational effects in the double-layer interactions. The HNC approximation provides a very accurate description of correlations due to long-range interactions, like the Coulomb interaction. In the present case, this is confirmed by the very good agreement of the double-layer interactions calculated for point charge ions4 with available Monte Carlo results' for identical systems. The accuracy of the HNC approximation in describing hard-core interactions is somewhat lower, in particular a t high densities or very large particle radii (cf. ref 6 which deals with bulk electrolyte solutions). Nevertheless, the ion density throughout most of the electric 'double layer is low enough for the H N C scheme to give reasonably accurate results.
Results and Discussion For moderately low ion concentrations and fairly small ionic radii, the ion-ion correlation can simply be described as a local (3) R. Kjellander and S . MarEelja, J . Chem. Phys., 82, 2122 (1985). (4) R. Kjellander and S . MarEelja, Chem. Phys Lett., 112, 49 (1984) [Errata. ibid.. 114. 124 (198511. (5) L. Guldbrand,B. hnsSb;l, H. Wennerstrbm, and P. Linse, J. Chem. Phys., 80, 2221 (1984). (6) J. C. Rasaiah, D. N. Card, and J. P. Valleau, J. Chem. Phys., 56,248 (1972). J. P. Valleau, L. K. Cohen, and D. N. Card, J. Chem. Phys., 72,5942 (1 980).
0 1986 American Chemical Society
Letters
The Journal of Physical Chemistry, Vol. 90, No. 7, 1986 1231
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Figure 1. The repulsion (log scale) between two uniformly charged walls (u = 0.224 C/m2) as a function of their separation in an aqueous solution of monovalent counterions of radius R = 0 (lower full curve) and R = 3 A (upper full curve), compared with the Poisson-Boltzmann predictions
for the same surface charge (dashed curve) and for a reduced surface charge, u = 0.062 C/m2 (dotted curve). If the dashed PB curve is shifted about 7 A to the left, it will practically coincide with the full R = 0 curve at separations above some 50 8,. The wall-wall separation is taken throughout as the distance between the points of closest approach of the ions to the two walls. The temperature is 300 K. reduction in the average ion density around each ion due to the electrostatic repulsion between them. One consequence of this is that compared to the PB theory prediction, more ions are allowed closer to the walls, since the region between each ion and the closest wall is, on the average, depleted of other ions. The gathering of ions closer to the walls leads to a lowering of the concentration at the midplane between the surfaces, and hence to a less repulsive, kinetic contribution to the interaction between the surfaces. Furthermore, the ion-ion correlations across the midplane lead to a local reduction in density at one side due to an ion at the other side. This results in an attractive, correlational contribution to the interaction between the two walls. In the presence of small divalent counterions, the net interaction may even become attractive at short wall-wall separation^.^^^ On the other hand, the finite size of the ions contributes a repulsive pressure term due to the ionic core-core interactions. This term becomes important in cases of severe crowding of ions, mostly when the ionic radius is sufficiently large and the surfaces are near each other. (Note that the results of ref 4, including Table I there, refer to pointcharge ions. It was only in the ion-wall interaction that an ion radius of 3 A was used, as stated in the text.) At larger separations we generally obtain a double-layer repulsion that, in the case of small ions, is reduced compared to the PB prediction. It can nevertheless be fitted to the PB force law by choosing other values of the parameters in the PB equation. A case of a monovalent electrolyte is illustrated in Figure 1. In the PB expression, one can either assume a lower surface charge density or take the point of closest approach of the ions to the walls further out (or, equivalently, increase the wall-wall distance), and then obtain a good fit with the proper interaction, as calculated by using the original parameters. This explains why the use of the PB force law at larger surface separations may lead to good agreement with the data, but, at the same time, it implies that the surface charge density obtained by the curve fitting is underestimated or the distance between the points of closest approach is overestimated. However, when the ionic radius is close to 3 A, the accurately calculated repulsion for the monovalent electrolyte agrees fairly well with the PB force law over quite a wide separation range, as seen in Figure 1. Here, the effects of the
100 150 200 SEPARATION I A I Figure 2. The pressure between two uniformly charged surfaces (a = 0.224 C m2)in a solution of divalent ions of various radii (R = 0, 3, 3.5, and 4 , respectively, full curves) compared with the PB prediction (dashed curve). The PB force curve for a surface charge of 0.0088 C/m2 is also shown (dotted curve). The pressure for surface separationsbelow some 10 8, for the case R = 3 8, is shown in Figure 3, and the corresponding continuation of the curve for R = 0 can be found in ref 7 .
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Figure 3. Different physical contributions to the total pressure between two uniformly charged surfaces (u = 0.224 C/m2) in a solution of divalent ions of radius R = 3 A.
ionic size and the electrostatic pair correlation effectively cancel. The effect of ionic size on the wall-wall interaction is particularly interesting in the case of divalent electrolytes, as illustrated in Figure 2. Generally, an increase in ion size leads to an increased contribution from the core-core repulsions. The qualitative features of the force between the walls do not change much below an ionic radius of around 3 A, and the curve retains an attractive portion a t separations smaller than about 15 A. For larger ion sizes the attraction disappears and the force is always repulsive,
J. Phys. Chem. 1986, 90, 1232-1234
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but even for a radius of 4 8, the repulsion is smaller than the PB prediction. In this case, the reduced repulsion can be fitted to the PB force law by choosing an effective surface charge of 0.0088 C/m2, while the real value is 0.224 C/m2. Most of this large reduction can be described as a nonspecific “adsorption” of the ions to the surfaces caused by the electrostatic pair-correlational effect. The relationship between the reduced repulsion and the correlationally induced increase in density of the ions close to the walls is also illustrated in our study of fully adsorbed, but laterally mobile, ions on two surfaces.’ W e found that the attractive part of the force curve for pointlike divalent ions is similar whether all ions are fully adsorbed on the surfaces or free to dissociate and form a diffuse double layer (as they are in this study). This holds down to a separation of about 5 A, where, in the latter case, the double layers start to overlap strongly, making the force below 2 A turn repulsive again. A detail of the pressure calculation for the ion radius of 3 A is shown in Figure 3 as an illustration of the behavior of the different contributions to the pressure between the surfaces. The repulsive kinetic term RTp(midpoint) is the only term considered in the PB theory (but with a much higher value of the concentration than obtained here). The electrostatic pair-correlation contribution is always attractive and becomes dominant in a range of separations between about 2 and 19 A. The hard-core repulsion term (core-core contact across the midplane) becomes significant relatively suddenly and then, as the surfaces approach each other, it becomes smaller again because the total momentum transfer between the ions is increasingly taking place in the direction along ~
~~
(7) R. Kjellander and S MarEelja, Chem. Scr., 25, 112 (1985).
the surfaces. Note that the ionic radius affects all three terms via the distribution functions. Therefore, we have a size effect also at larger separations, where the core-core contact term is vanishingly small. The repulsive core-core contribution quickly becomes larger with increasing ion radius, e.g. for a 3.5-A radius it has a maximum value of approximately 5.5RT at the separation of 5 A. The sudden change in slope of the corresponding force curve in Figure 2 at the separation 13 A is due to the onset of this contribution for smaller distances. For even larger radii the core term in the pressure dominates for moderate to small wall separations. The examples discussed above show that, for primitive model electrolytes, the PB theory can often provide a remarkably good fit to the accurately calculated double-layer repulsion. However, the fitted parameters in the PB force law will not always be the real physical parameters of the system. If we restrict ourselves to larger separations, the overlap of the two double layers is small and the interaction between the surfaces is transmitted via a dilute ionic solution. Then, the PB theory constitutes a valid limiting law provided the situation near the surfaces, where the PB description breaks down, is taken into account by changing, e.g., the real surface charge to a different, “effective” charge. The surface adsorption of ions deduced on the basis of the PB theory may then partly correspond to the increase in ion density near the surfaces caused by the electrostatic ion-ion correlations rather than by some specific ion-surface interaction. Note Added in Proof. We have now extended the study to the corresponding system in equilibrium with a bulk electrolyte solution (work to be published). We found that the same mechanisms are operative in both cases, leading to the same general picture at least for moderate surface separations.
Locking of Dephasing and Energy Redistribution in Molecular Systems by Multiple-Pulse Laser Excitation Edward T. Sleva, Max Glasbeek, and Ahmed H. Zewail* Arthur Amos Noyes Laboratory of Chemical Physics,+California Institute of Technology, Pasadena, California 91 125 (Received: January 23, 1986)
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In this paper, we report experimental results on the locking of dephasing of molecules in the gas phase. The locking of inhomogeneous dephasing of the B X transition of iodine is achieved by using multiple-pulse and phase-coherent laser excitation, instead of a single-pulse excitation. We detect the locking using echo techniques. The locking concept is extended to the problem of intramolecular dephasing, emphasizing the potential for controlling selectivity in laser chemistry.
Introduction Experimentally, it is now established that there ensues upon coherent excitation a coherent evolution of vibrational/rotational motion in large polyatomic molecules. This has been demonstrated for several large molecules on a single excited-state potential energy surface.’ Knowledge about the time scale for this coherent evolution and intramolecular vibrational energy redistribution (IVR) has suggested several schemes for controlling selectivity and “eliminating” IVR which is the source of energy scrambling and dephasing in molecules. The theoretical ideas involved in these schemes include: (a) excitation of vibrational states on a time scale shorter than the time of IVR, Le., before energy is completely randomized and coherence is lost;2 (b) the use of phase-coherent pulse sequences; e.g., by using multiple phase-coherent pulse sequences as suggested by US,^^^ or by using two-photon spec‘Contribution No. 7360.
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troscopy as suggested by Tannor and Rice;4or (c) the use of strong resonant laser excitation as suggested by Yeh et al.5 and by Mukamel and Sham6 Experimentally, it is therefore important to develop methods for “inhibiting” dephasing by intra- or intermolecular effects. In this paper, we present a new experimental approach for the locking of dephasing (energy scrambling) in molecular systems. The approach is based on the use of multiple phase-coherent laser pulses (instead of one pulse) to excite the sample. Basically, a ~~~
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(1) Felker, P. M.; Zewail, A. H. Chem. Phys. Lett. 1983,
J02,113. Felker,
P.M.; Zewail, A. H. Phys. Reu. Let?. 1984,53, 501. Felker, P. M.; Zewail, A. H. J. Chem. Phys. 1985,82,2961, 2975, 2994, 3003. (2) Zewail, A. H. Phys. Today 1980, 33,27. Bloembergen, N.;Zewail, A. H. J . Phys. Chem. 1984.88,5459. ( 3 ) Warren, W. S.; Zewail, A. H. J . Chem. Phys. 1983,78, 3583. (4) Tannor, D. J.; Rice, S.A. J. Chem. Phys. 1985,83,5013. (5) Yeh, J. J.; Bowden, C. M.; Eberly, J. H. J . Chem. Phys. 1982,76. 5936. (6) Mukamel, S.; Shan, K. Chem. Phjs. Let?. 1985,I 1 7 , 489
0 1986 American Chemical Society
