J. Phys. Chem. 1981, 85,3244-3247
3244
1
8.01
2
4
6
8
IO
minutes at 0.2 A/cm2
Figure 10. The free energy of adsorption of oxygen on Pt as measured by the “shift” parameter as a function of the duration of polarization.
in the reduction potential of surface oxygen as a result of highly anodic polarization would demonstrate the required variability of the strength of oxygen binding. Voltammetry on Pb02 to determine an oxygen reduction potential is impossible due to the masking effect of the reduction of Pb02 itself. Therefore, the Pt surface was chosen for such an experiment. Cyclic voltammetry was performed from 1.8 to 0.0 V vs. SHE in 2 M H2SO4 at 200 mV/s. The steady-state potential of the “oxide” reduction peak of 0.65 V was then used as the point of reference for the subsequent excursions to the ozone-evolving region. Figure 9 illustrates the steady-state voltammogram obtained by repeated cycling and defines the shift parameter used to calculate a change in the free energy with which oxide oxygen and adsorbed oxygen is bound to Pt. The heavier trace in the particular instance of Figure 9 represents the descent from 3 min of galvanostatic control at 0.20 A/cm2 (2.2-2.45 V vs. SHE): The potential and peak current of the oxide reduction peak are sensitive to scan rate; however, the “shift” parameter, being a difference, was seen to be much less
sensitive. From this shift, a free energy difference resulting from the intensity and duration of anodic polarization can be calculated by assuming a two-electron reduction. Figure 10 plots the free-energy differences obtained at a scan rate of 200 mV/s when a Pt electrode is polarized for increasing lengths of time in 2 M H2S04at 200 mA/cm2 (2.2-2.45 V vs. SHE) vs. cycling to 1.80 V. Though subject to some uncertainty, average values of up to 6 kcal/mol are found in the case of Figure 10. Such free-energy differences also increase with the current density of the hold. It is clear that the strength with which surface oxygen is held is, indeed, a polarization-dependent variable as our interpretations of the ozone evolution reaction require. Perhaps of significance,the rise to a steady-state value seen in Figure 10 is typical of that required for the ozone evolution reaction to reach a steady-state current efficiency in 2 M H2S04(here PbOz anodes exhibit 90-min risetimes). Thus, we believe it will be of interest to refine such studies, possibly extending them to more directly correlate oxygen binding, anion coverage, and ozone current efficiency.
Conclusions The investigation of several puzzling phenomena observed in studies of ozone current efficiency in sulfuric and phosphoric acids has led to an apparently consistent hypothesis as to the fundamental factors which control the selectivity of the anodic process for either oxygen or ozone. It is hoped that the conclusions developed can lead to the optimization of the reaction in the fluoro anion electrolytes, tetrafluoboric acid, or hexafluorophosphoric acid, already known to be capable of producing substantially higher current efficiencies.6s6 Acknowledgment. The authors are grateful to the Board of Patents of the University of California, Ametek Corporation, and the Department of Chemical Engineering, University of California, Berkeley, for their partial support of this work.
Transitions in the Sign of the Diamagnetic Anisotropy of a Lyotropic Mesophase without a Phase Change. Type 0 Disk Micelle Systems Bruce J. Forrest, Leonard W. Reeves,’ and Carol J. Roblnson Chemistry Depaftment, University of Waterloo, Waterloo, Ontarlo, Canada N2L 301 (Received: May 4, 198 1; In Flnal Form: Ju& 6, 108 I )
The diamagnetic anisotropy of magnetically aligning disk micelle lyotropic liquid crystals has been reversed by the inclusion of aromatic amphiphiles. This reversal occurs without a phase change and at the point of transition a nonaligning type 0 disk micelle mesophase is formed. Different host mesophases have been taken through the change in sign of the diamagnetic anisotropy, and the effects of temperature variation investigated. The rate of alignment of the type I disk micelle mesophases is a linear function of aromatic amphiphile concentration.
Introduction For a number of years we have studied a new series of lyotropic liquid cryst& which gain orientational order of the component disklike or rodlike micelles when placed into magnetic fields.12 These micelles, however, possess
little or no positional order of their centers of g r a ~ i t y . ~ The rod micelle mesophases have been named type I CM (cylindrical micelle), indicating positive diamagnetic SUSceptibility (Ax > 0))while the smmd has been m r ~ ~ tYPe ed I1 DM, indicating disk micelles with negative diamagnetic
(1) F. Y. Fujiwara, L. W. Reeves, M. Suzuki, and J. A. Vanin in “Solution Chemistry of Surfactants”,K. L. Mittal, Ed., Plenum Press, New York, Vol. 1, 1979, p 63.
(2) B. J. Forrest and L. W. Reeves, C h e n . Reu., 81, 1 (1981). (3)L.Q.Amaral and M. R. Tavares, Mol. Cryst. Liq. Cryst. Lett., 56, 203 (1980).
0022-3654/81/2085-3244$01.25/0
0 1981 American Chemical Society
The Journal of Physical Chemistry, Vol.
Diamagnetic Anisotropy of Aligned Micelles ALIGNMENT RATE VS. AROMATIC CONTENT TYPE 0 DM TYPE II DM
f
TYPE I DM
d
Ij
0'
1
I
/ I
16
20
18 [KHB]/[KHB
+ SLS]
22
X 100
Flgure 1. Alignment rate constant, k, vs. aromatic content of the mesophase. At 17.75% KHB, a type 0 DM phase is obtained. M o w this concentration, the mesophase is type I1 DM, while above this concentration, it is type I DM. The sign of the diamagnetic anisotropy of the liquid crystal is changed, without an accompanying change of phase.
anisotropy (Ax < There are genuine phase transitions between these two types of structure^,^^^ and, in certain cases, an extremely narrow range of coexistence has been found.7 The origin of the diamagnetic susceptibility anisotropy can be traced to that of the pseudo-extended hydrocarbon chains in the bilayer structures that make up the large micelle^.^^^ This anisotropy is negative and hence the cooperative motion of parallel or radial chains in individual micelles is carried cooperatively by the orientational order of the liquid crystal such that the chains align perpendicular to an applied magnetic field.' In the case of cylindrical micelles, the symmetry axes of the rods oscillate about the director of the mesophase, which is aligned a t equilibrium along the magnetic field axis.5 For disk micelles, the alignment of chains perpendicular to the field is associated with the disk symmetry axes (the bilayer normals) becoming perpendicular to the field.g (See ref 9, Figure 1.) While this general argument based on the diamagnetic anisotropy of hydrocarbon chains has no experimental e ~ c e p t i o nit, ~is in principle possible to reverse the constituent diamagnetic anisotropy of the micelles by inclusion of aromatic rings anchored in the micelle such that the para axis is perpendicular to the interface. Given the much higher magnitude and opposite sign of the diamagnetic anisotropy of a benzene ring as compared to a hydrocarbon chain, such a procedure should create a disk micelle mesophase with positive diamagnetic anisotropy or type I properties. In order to show that this has been achieved, we must be able to add the aromatic detergent to a known type I1 DM phase and observe the transition in Ax to a type I DM system unambiguously. This same aromatic detergent, if solubilized in sufficient amount, should provoke a change in the sign of Ax in all type I1 DM mesophases, assuming little tilting of the aromatic ring from the normal direction to the bilayer plane. In addition, the O).436
(4) K. Radley, L. W. Reeves, and A. S. 'Ikacey, J.Phys. Chem., 80,174 (1976). (5)F. Y.Fujiwara and L. W. Reeves, J.Phys. Chem., 84,653 (1980). (6) D. M. Chen, F. Y. Fujiwara, and L. W. Reeves, Can. J. Chem., 55, 2396 (1977). (7)B. J. Forrest and L. W. Reeves, J. Am. Chem. SOC.,103, 1641 (1981). (8)B.J. Forrest and L. W. Reeves, Mol. Cryst. Liq. Cryst., 58, 233 (1980). (9)B.J. Forrest, F. Y. Fujiwara, and L. W. Reeves, J. Phys. Chem., 84,662 (1980).
85,No. 22, 1981 3245
velocity of alignment should be proportional to the concentration of the incorporated aromatic species.
Experimental Section p-Heptyloxybenzoic acid was purchased from Frinton Laboratories and the potassium salt prepared by neutralization with a slight excess of ethanolic KOH. The product was recrystallized from EtOAc/EtOH. All other detergents were prepared and purified as reported prev i o ~ s l y . ~ JStandard ~ samples were made up with the following composition by weight: (A) potassium laurate: KC1:decanol:DzO '= 853:66:161:1891; (B) sodium lauroyl sarcosinate:NazS04:decanol:Dz0 = 610: 116:111:1102. Mixed phases were prepared by the substitution of potassium heptyloxybenzoate on a mole basis for potassium laurate or sodium lauroyl sarcosinate. Most 2H NMR spectra were recorded at 31 "C on a Bruker WP-80 at 12.28 MHz. Some were recorded at 25 "C on a Bruker WH-400 operating at 61.4 MHz. From 1 to 10 transients were routinely required. The magnetic type of each sample was determined by obtaining a spectrum immediately after the sample was placed in the field. As the mesophase aligns, either the main peaks (type 11)or the wings (type I) of the three-dimensional powder pattern grow with time, eventually producing a mesophase in which the director is either parallel (type I) or perpendicular (type 11) to the applied magnetic field. Rates of alignment of the type I samples were determined as described previously.ll Results and Discussion Potassium p-heptyloxybenzoate (KHB) was incorporated into a variety of known type I1 disk micelle systems. Hexadecyltrimethylammonium bromide and decylammonium chloride mesophases could not solubilize enought KHB within the disk micelles to reverse the sign of the diamagnetic anisotropy without provoking a phase change. However, both sodium lauroyl sarcosinate (SLS) which could be replaced by up to 26 mol % KHB and potassium laurate (KC12) which could be replaced by up to 40% on a mole basis by KHB proved to be satisfactory host mesophases. A change in the sign of the diamagnetic anisotropy of a mesophase without an accompanying phase change may be verified by 2HNMR of water bound to the surface of the micelles. Interstitial water tumbles isotropically, but on the NMR time scale, the water gains order on the time average due to fast exchange between free and bound water molecules. The change in quadrupole splitting, Av, of a deuterium NMR spectrum upon going from Ax < 0 to Ax > 0 will be exactly a factor of -2. The quadrupole splitting is given by AV = v~S,,(1/2)(3cos2 D - 1) ( 1) where S, is the degree of order of the electric field gradient axis (tensor assumed to be cylindrically symmetric), VQ is the quadrupole coupling constant, and 0 is the angle between the mesophase director and the applied magnetic field. Since D changes from 90 to 0" at the Ax transition, Av should change by a factor of -2 from immediately before to immediately following the point at which Ax = 0. In all the genuine phase transitions so far observed, the factor has never been found to be -2 within experimental e r r ~ r . ~ J At 31 "C, the A x transition for the potassium laurate system was found to occur between 29 and 30% KHB. Both samples were very slow in alignment. For example, (10)B. J. Forrest, L. Hecker de Carvalho, L. W. Reeves, and C. Rodgers, J.Am. Chem. SOC.,103,245 (1981). (11) F. Y. Fujiwara and L. W. Reeves, Can. J. Chem., 56,2178(1978).
I
3248
The Journal of Physical Chemistry, Vol. 85, No. 22, 198 1
the 30% sample was not completely aligned after 17 h in a magnetic field of 1.88 T. A more detailed study of the A x transition was carried out by replacing the host of a sodium lauroyl sarcosinate type I1 DM system with varying amounts of KHB. At the phase transition, the diamagnetic anisotropy generated by the benzoate ring currents will exactly balance the diamagnetic anisotropy of the hydrocarbon chains of all other micelle components, namely, SLS, the neutral amphiphile, 1-decanol, as well as the heptyl chain of KHB, itself. At the point where A x is exactly equal to zero, any alignment must be due to wall effects of the sample container. In addition, the rate of alignment in the post-transition region must be a linear function of the concentration of the added aromatic. The velocity of alignment depends upon the magnitude of A x , the magnetic field strength, and a viscosity term, XI, In tan D = -kt
+ In tan 0,
(2)
where D is the angle of the director with respect to the magnetic field at time t , !dois the initial angle of rotation of a prealigned sample at the beginning of the experiment, and k = A x P / X l where H i s the magnetic field strength. The viscosity characteristics near the change in A x are not greatly varying because intermicellar forces determine viscosity, and since the change in composition of the mesophase is small. Type I DM samples were prealigried for approximately 18 h in a magnetic field of 1.88 T, and subsequently rotated through an angle of about 25". The splitting of the D 2 0 quadrupole was monitored as a function of time, and the instantaneous angle D calculated by use of eq 1. Plots of -In tan D vs. time were straight lines (see, for example, Figure 2, ref 11) and the slopes yielded values of the rate constant, k. Due to the nature of the '/2 (3 cos2 D - 1) function which determines the observed quadrupole splitting, it is possible to determine if a homogeneous prealignment of the directors has taken place. If a distribution of directors were present, rotation through an angle of -25" would result in line broadening of the DzOdeuterium water doublet.'* No broadening of the signals was observed after prealignment for 18 h, except in the case of the 18.06% sample which was left to align for a further 48 h before the kinetic experiments were carried out. The rate constants are plotted vs. increasing concentrations of KHB in Figure 1. The straight line obtained confirms that the change in sign of diamagnetic anisotropy of the phase is due to the added aromatic. The x intercept predicts A x = 0 behavior when KHB replaces 17.75% of the host detergent on a mole basis. Immediately preceeding this point, at 17.49%, the mesophase is type I1 DM and aligns extremely slowly, although the rate constant cannot be measured with the present techniques. The quadrupole splitting of the deuterium water doublet of this fully aligned mesophase was 428 Hz. Immediately after the change in A x , at 18.06%, the aligned DzO splitting of the type I DM mesophase was 856 Hz, or exactly double the type I1 value, indicating a change in the sign of the diamagnetic anisotropy without a phase change. The effect on water binding over such an extremely small concentration range is, of course, negligible. The mesophase which possesses KHB as 17.75 mol % of its deter(12) F. M. Leslie, G. R. Luckhurst, and H. J. Smith, Chem. Phys. Lett.,
13, 368 (1972).
(13) R. Casini, S. Faetti, M. Martinelli, and S. Santucci, J . Mug. Reson., 26, 201 (1977). (14) J. W. Emsley, J. C. Lindon, G. R. Luckhurst, and D. Shaw, Chem. Phys. Lett., 19, 345 (1973).
Forrest et al.
ID
Flgure 2. Diagramatic depiction of the disk micelle, director D, and magnetic field Ho for (A) Ax < 0 and (B) A x > 0. The location of a hydrocarbon chain axis at the right in (A) corresponds to its orientation in the disk micelle. The all-trans form is drawn but kinks, jogs, and single gauche rotations are present in the real situation. The alignment of the aromatic amphiphile component of the disk bilayer in (B) is also shown. The micelles have freedom of motion about the dlrector axis of the mesophase and this is not shown.
gent possesses a net diamagnetic anisotropy of zero, and in accordance with previous nomenclature such lyotropics are now named type 0 DM (disk micelle). Figure 2 illustrates diagramatically the alignment of the mean position of the finite micelles with respect to the magnetic field and mesophase director. A qualitative study of the A x transition was also carried out at 25 "C in a much higher magnetic field, 9.40 T, where alignment times are approximately 25 times faster than at 1.88 T. Because of the different geometry of superconducting magnets, the alignment processes could not be quantitated in the manner possible with iron-core magnets, but it was found that, at this lower temperature, the transition in A x was shifted to higher concentrations of KHB. At 18.06% KHB, the mesophase was type I1 DM while that of 19.00% was clearly type I. A sample of 18.50% KHB aligned the most slowly, although after 15 min in the magnetic field (equivalent to over 6 h at a field of 1.88 T), it became apparent that the mesophase would eventually align as a type I1 and thus still possessed slightly negative diamagnetic anisotropy. The effect of temperature was more marked in the case of potassium laurate system where type 0 DM was found to occur between 29 and 30% KHB, while a t 25 "C, mesophases of 30% and even 35% KHB were still type 11. The temperature sensitivity of the A x transition is not surprising because each chemically distinct amphiphile is anchored differently at the hydrophobic-hydrophilic interface and these independent anchorings are expected to be affected by different amounts by temperature variations.2 Conclusion It has been shown possible to vary the sign of the diamagnetic anisotropy of lyotropic liquid crystals which spontaneously align in magnetic fields, thereby producing transitions from type 11 DM to type 0 DM and subsequently to type I DM. Further studies will involve a more complete investigation of the effect of temperature and will yield comparisons of the relative magnitudes of the diamagnetic anisotropies of hydrocarbon chains and aromatic rings. In addition, the very slow orientation of a type 0
3247
J. Phys. Chem. 1901, 85, 3247-3250
DM due to wall effects should be dependent upon the shape of the container. Acknowledgment. This work was supported by the National Science and Engineering Research Council of Canada through operating grants to L. W. Reeves. Some of the deuterium NMR spectra were obtained through the
South West Ontario NMR facility at the Guelph-Waterloo Centre funded by a Major Installation Grant from NSERC. Sodium lauroyl sarcosinate was the generous gift of Colgate-Palmolive Ltd., Toronto, Canada. L. W. Reeves also thanks Joel H. Hildebrand for the lifelong scientific influence he has had, especially in trying to see the simplifying aspects of complex chemical problems.
Binary Langmuir and Freundlich Isotherms for Ideal Adsorbed Solutions M. Douglas Levant and Theodore Vermeulen’ Department of Chemical Engineering, University of California, Berkeley, California 94720 (Received May 5, 198 1)
Explicit isotherms are derived for the adsorption of two components, both of which as pure components obey either the Langmuir or Freundlich equation. These isotherms, in the form of rapidly converging series expansions, are based on analytic expressions for the spreading pressure and thus satisfy the Gibbs adsorption isotherm as required by the ideal adsorbed solution theory. For equal Langmuir monolayer capacities or equal Freundlich exponents, the isotherms reduce to forms obtained previously by other investigators. The expressions contain only parameters appearing in the single-componentequations, and can be considered to give “maximally probable” predictions of binary behavior.
Introduction The ability to characterize adsorption equilibria accurately is important in a number of chemical processes, ranging from the study of adsorption at fluid interfaces to the design of heterogeneous chemical reactors. For multicomponent systems, the description of adsorption equilibria can be quite difficult, as evidenced by the large body of literature in this field published over many decades. It is often most convenient if adsorption equilibria are represented by explicit equations. Several two- and three-parameter isotherms are used routinely for this purpose. For multicomponent adsorption, isotherms containing only parameters that appear in the singlecomponent isotherm equations are preferred, at least for those cases in which such a form can be shown to be both realistic and theoretically valid, since it is not necessary in this case to measure experimentally any multicomponent parameters. The ideal adsorbed solution theory, proposed by Myers and Prausnitz,l provides a link between single-component and multicomponent adsorption. Based on the Gibbs adsorption isotherm, a general thermodynamic criterion for interfacial systems, the theory allows prediction of multicomponent equilibria from single-component isotherms alone. In this paper, honoring Joel Hildebrand’s consistent reliance on fundamental physical and thermodynamic realities, the ideal adsorbed solution theory is used to derive explicit and thermodynamically consistent binary Langmuir and Freundlich isotherms. This is accomplished for cases of moderate numerical difference between parameters appearing in the single-component equations. The results are in the form of series expansions, and provide correction terms to existing isotherm equations. Thermodynamic consistency, used here in the familiar t Department of Chemical Engineering, University of Virginia, Charlottesville, VA 22901.
0022-3654/81/2085-3247$01.25/0
context. means that the Gibbs adsorption isotherm is satisfied. The single-component Langmuir and Freundlich isotherms are the most popula; two-parameter isotherm equations. The Langmuir isotherm is written here as QKP (1) q=-P where Q is the molar monolayer capacity. The Freundlich isotherm is q = K’P” (2) Conventionally, the Langmuir or the Freundlich isotherm (when appropriate) is applied as a convenient empirical representation of experimental data, without implying the inherent validity of any particular physical model which may underlie a derivation of the respective isotherm. There have been several previous efforts to extend these isotherms to binary adsorption. For the Langmuir isotherm, Butler and Ockrent2 and Markham and B e n t ~ n , ~ on the basis of kinetic considerations alone, obtained QiWi
qi = 1
+ KIPl + K2P2
(i = 1 or 2)
(3)
This isotherm has been criticized4p5because it is thermodynamically inconsistent with the Gibbs adsorption isotherm for an ideal adsorbed solution, unless the molar monolayer capacities Q1 and Q2 are equal. Recently, two studies have appeared concerned with a multicomponent Freundlich isotherm. Digiano et al.6 used the ideal adsorbed solution theory to obtain such an isotherm in the case that all components have the same (1)A. L. Myers and J. M. Prausnitz, AIChE J., 11, 121 (1965). (2) J. A. V. Butler and C. Ockrent, J.Phys. Chem., 34,2841(1930). (3)E. C. Markham and A. F. Benton, J. Am. Chem. Soc., 63,497
(1931). (4)C. Kemball, E.K. Rideal, and E. A. Guggenheim, Trans. Faraday Soc., 44, 948 (1948). ( 5 ) D. B. Broughton, Ind. Eng. Chem., 40,1506 (1948). (6)F. A. Digiano, G. Baldauf, B. Frick, and H. Sontheimer, Chem. Eng. Sci., 33, 1667 (1978).
0 1981 American Chemical Society
