Langmuir 1997, 13, 2665-2669
2665
Solvent Isotope Effect on the Self-Assembly and Liquid Crystalline Phase Behavior in Aqueous Solutions of Ammonium Pentadecafluorooctanoate P. J. B. Edwards, K. W. Jolley,* M. H. Smith, and S. J. Thomsen Department of Chemistry, Massey University, Palmerston North, New Zealand
N. Boden Centre for Self Organising Molecular Systems, The University, Leeds LS2 9JT, U.K. Received November 18, 1996X The partial high-resolution phase diagram of the ammonium pentadecafluorooctanoate (APFO)/H2O system (weight fraction of APFO from 0.350 to 0.630) has been established using 14N NMR to determine the liquid crystalline phase transition temperatures. Comparison between the APFO/H2O phase diagram and the previously published APFO/D2O one reveals that at comparable volume fractions the phase transition temperatures are lower in the APFO/H2O system, but the difference between these decreases with increasing volume fraction of surfactant (increasing temperature). This isotope effect on the phase behavior can be understood in terms of phase transitions which are driven by hard particle interactions together with changes in the micellar self-assembly attributed to a tighter binding of ammonium ions to surface carboxylate groups in the case of D2O, leading to larger micelles in D2O than in H2O at corresponding volume fractions and temperatures. The magnitude of the solvent isotope effect is similar to that previously determined in the closely related cesium pentadecafluorooctanoate (CsPFO)/water systems, an observation which is consistent with the presence of a counterion-surface interaction via bridging water molecules. Polynomials are presented, which give the liquid crystalline phase transition temperatures (to an accuracy of (0.3 K) as a function of weight fraction of surfactant, for both the APFO/H2O and APFO/D2O systems.
Introduction Salts of short chain perfluorocarboxylic acids form solutions of disklike micelles which are stable over wide concentration and temperature ranges.1-8 This stability gives rise to lyotropic liquid crystalline systems which exhibit exceptional and characteristic phase behavior. To date, high-resolution phase diagrams have been published for the cesium pentadecafluorooctanoate (CsPFO)/D2O,5 CsPFO/H2O,1 ammonium pentadecafluorooctanoate (APFO)/D2O,3 and tetramethylammonium heptadecafluorononanoate (TMAHFN)/D2O9 systems. Such phase diagrams are vital to an understanding of the origin and stability of disklike micelles and the nature of the partially ordered nematic and smectic phases which they form. In all these systems, with increasing concentration of surfactant, the disklike micelles undergo a sequence of disorder-order transitions from the isotropic phase I to form, first, a nematic ND phase and subsequently, a smectic lamellar L phase. This phase behavior has been explained in terms of phase transitions which are predominantly X
Abstract published in Advance ACS Abstracts, April 15, 1997.
(1) Boden, N.; Jolley, K. W.; Smith, M. H. J. Phys. Chem. 1993, 97, 7678. (2) Boden, N.; Edwards, P. J. B.; Jolley, K. W. Self-Assembly and Self-Organization in Micellar Liquid Crystals. In Structure and Dynamics in Supramolecular Aggregates and Strongly Interacting Colloids; Chen, S. H., Huang, J. S., Tartaglia, P., Eds.; Kluwer: Dordrecht, The Netherlands, 1992; pp 433. (3) Boden, N.; Clements, J.; Jolley, K. W.; Parker, D.; Smith, M. H. J. Chem. Phys. 1990, 93, 9096. (4) Boden, N.; Clements, J.; Dawson, K. A.; Jolley, K. W.; Parker, D. Phys. Rev. Lett. 1991, 66, 2883. (5) Boden, N.; Corne, S. A.; Jolley, K. W. J. Phys. Chem. 1987, 91, 4092. (6) Boden, N.; Bushby, R. J.; Jolley, K. W.; Holmes, M. C.; Sixl, F. Mol. Cryst. Liq. Cryst. 1987, 152, 37. (7) Boden, N.; Corne, S. A.; Holmes, M. C.; Jackson, P. H.; Parker, D.; Jolley, K. W. J. Phys. 1986, 47, 2135. (8) Boden, N.; Jolley, K. W.; Smith, M. H. Liq. Cryst. 1989, 6, 481. (9) Dombroski, J. P.; Edwards, P. J. B.; Jolley, K. W.; Boden, N. Liq. Cryst. 1995, 18, 51.
S0743-7463(96)02009-4 CCC: $14.00
driven by hard particle interactions between disklike micelles, i.e. the isotropic-to-nematic transition occurs when the surfactant volume fraction φ reaches a critical value of the axial ratio of the micelle.2,10 Changes in the phase behavior may, therefore, be brought about by perturbing the self-assembly of the micelles. For example, we have previously shown that at a given temperature an increase in the length of the fluorocarbon chain leads to a displacement of both the I-to-ND and the ND-to-L phase transitions to lower φ as a consequence of a concomitant increase in micelle size while at any given φ the transition is shifted to higher temperatures since the micelles become smaller as the temperature is increased.10 Changes in the counterion also affect the self-assembly to a significant degree with consequent large changes in the phase transition temperatures.2,8,9 The addition of salt shifts the phase transitions to higher temperatures11-15 as does the addition of perfluoroethanol as a cosurfactant,16 while the addition of cosolvent has been shown to have the opposite effect.17,18 Thus, the electrostatic repulsion between charged head groups, the curvature dependence of the fluorocarbon chain packing, and the interfacial energy of the micelle all influence the size and shape of the micelles.2,10,19 (10) Boden, N.; Harding, R.; Gelbart, W. M.; Ohara, P.; Jolley, K. W.; Heerdegen, A. P.; Parbhu, A. N. J. Chem. Phys. 1995. (11) Cull, B.; Heino, M.; Lee, S. H.; Keast, S. S.; Neubert, M. E. Liq. Cryst. 1994, 17, 507. (12) Holmes, M. C.; Sotta, P.; Hendrikx, Y.; Deloche, B. J. Phys. 2 Fr. 1993, 3, 1735. (13) Holmes, M. C.; Smith, A. M.; Leaver, M. S. J. Phys. 2 Fr. 1993, 3, 1357. (14) Holmes, M. C.; Smith, A. M.; Leaver, M. S. J. Phys. 4 1993, 3, 177. (15) Rosenblatt, C.; Zolty, N. J. Phys. Lett. 1985, 46, L. (16) Rosenblatt, C. J. Phys. Chem. 1987, 91, 3830. (17) Boden, N.; Harding, R.; Jolley, K. W.; Thomsen, S. J. Mol. Cryst. Liq. Cryst 1997, in press. (18) Li, Z.; Rosenblatt, C. J. Chem. Phys. 1988, 89, 5033. (19) McMullen, W. E.; Ben-Shaul, A.; Gelbart, W. M. J. Colloid Interface Sci. 1984, 98, 523.
© 1997 American Chemical Society
2666 Langmuir, Vol. 13, No. 10, 1997
Changes in head group electrostatic repulsion and interfacial energy can be accomplished by changing the solvent. Thus, in a recent study,1 it was shown that the substitution of D2O by H2O in aqueous solutions of CsPFO leads to the formation of smaller micelles at any given temperature and concentration which results in a displacement of the liquid crystal phase transitions to lower temperatures. This result is in conflict with the expectation, based on self-assembly theory,19 that the higher interfacial tension and relative permittivity of H2O will produce larger micelles. In order to account for the experimental observations, it was necessary to propose a specific counterion-carboxylate interaction which leads to a more effective screening of the head group electrostatic repulsion by the counterion in the CsPFO/D2O system1sbonding to the surface carboxylate groups is via a bridging water molecule, substitution of D2O for H2O will result in a stronger hydrogen bond20 and a shorter Cs+CO2- distance. Such an explanation suggests that the solvent isotope effect will be largely independent of the nature of any hydrated counterion, and we might expect a similar change in the phase transition temperatures on substituting D2O for H2O in aqueous solutions of APFO. In these solutions the ammonium ions (predominantly ND4+ in APFO/D2O solutions) will be fully hydrated and will interact with the surface carboxylate groups via a bridging water molecule. To test this prediction we have investigating the subtle changes in the micellar selfassembly that result from substituting H2O for D2O in the APFO/water systems through the effect of this substitution on the phase behavior (i.e. a decrease in micelle size at any given φ will be revealed by a decrease in the I-to-ND phase transition temperature and vice versa.). Accordingly, 14N NMR has been used to map the high-resolution phase diagram for the APFO/H2O system so that this can be compared with the existing APFO/D2O one.3 The phase diagram for the APFO/H2O system currently available11 was obtained from optical microscopy measurements, mapped only the I-to-ND and ND-to-L phase transition lines, and is of insufficient quality to serve as a basis for a detailed comparison of the solvent isotope effect on the phase behavior and self-assembly in APFO solutions. The high-resolution phase diagram presented here adds to the list of those that are currently available in the literature1,3,5,8,9 for these unique systems. It accurately and precisely delineates the I-to-ND and NDto-L phase transition lines (polynomials are presented which give the liquid crystal phase transition temperatures as a function of weight fraction w of APFO for both the APFO/H2O and APFO/D2O systems) and establishes the location of various fixed points. Experimental Methods and Materials Materials. APFO was prepared by neutralizing an aqueous solution of pentadecafluorooctanoic acid (Riedel de Hae¨n) with ammonium hydroxide. The neutralized solution was freeze dried and the salt was recrystallized twice from a 10:1 (v/v)n-hexane/ n-butanol solution. The recrystallized salt was placed in a vacuum desiccator for several days to remove all traces of the recrystallizing solvent. NMR Spectroscopy. 14N NMR spectra were measured with a JEOL GX270 spectrometer operating at 19.38 MHz. The 14N free induction decays were sampled using 64 K data points over a frequency range of 64 kHz giving a resolution after Fourier transformation of 2 Hz per data point. The sample temperatures were controlled using a computer-controlled double-pass waterflow control system21 designed so as to minimize temperature gradients and with an accuracy, precision and settability of (20) Nemethy, G.; Scheraga, H. A. J. Chem. Phys. 1964, 41, 680. (21) Boden, N.; Corne, S. A.; Halford-Maw, P.; Fogarty, D.; Jolley, K. W. J. Magn. Reson. 1992, 98, 92.
Edwards et al.
Figure 1. Partial phase diagram for the APFO/H2O system. Nomenclature: I, isotropic micellar solution phase; N+ D, nematic phase with disklike micelles and positive diamagnetic susceptibility; L, lamellar phase; K, crystal; Tp(I,N,L), the isotropic micellar solution-nematic-lamellar triple point; Tp(I,N,K), the isotropic micellar solution-nematic-crystal triple point; Cep, the critical end point; Tcp, the lamellar-nematic tricritical point; Tc, the solubility curve. No supercooling or super heating effects are observed at the L-to-ND and ND-to-I transition since the enthalpy change at these transitions is very small.29 The heat of solution is large, however,5 and supercooling is readily achieved by cooling across Tc, which enables liquid crystalline phase transitions below the solubility curve to be accessed. The polynomials for the liquid crystal phase transition lines, representing the best-fits through the data points (open circles), are given in Table 1, and the precise location of the fixed points are given in Table 2. (0.005 K. Measurements were made on 12 samples in a weight fraction APFO w range from 0.350 to 0.630. The samples were prepared by weighing APFO and water (deionized and doubly distilled) directly into 5-mm o.d. NMR tubes, which were then flame sealed. Samples were stored at room temperature and gave consistent NMR measurements over the period of the study (3 months) providing care was taken to ensure a homogeneous sample. This was done by thoroughly mixing the samples in the isotropic phase just prior to carrying out an experimental measurement. Electrical Conductivity Measurements. These were made using a Phillips PW9512/61 conductivity cell attached to a Hewlett Packard HP 4192A impedance analyzer operating at a frequency of 25 kHz. The sample cell was surrounded by a double-pass water-flow jacket. Temperature control was achieved using the same system as was used for the NMR measurements.21 Conductivity samples were made up immediately prior to use and made homogeneous by mixing in the isotropic phase before being transfered to the conductivity cell.
Results and Discussion Phase Diagram for the APFO/H2O System. The phase diagram for the APFO/H2O system is shown in Figure 1. The liquid crystal phase transition lines shown in this figure were delineated from the temperature dependence of the 14N quadrupole splittings as described previously in detail for the tetramethylammonium heptadecafluorononanoate/D2O system.9 For 14N (I ) 1) nuclei in ammonium ions in a macroscopically aligned uniaxial nematic or lamellar mesophase, the NMR spectrum consists of a doublet with separation ∆ν˜ , referred to as the partially averaged quadrupole splitting, given by5
∆ν˜ (φ) ) 3/2|q˜ zz|sSP2(cos φ),
(1)
where here φ is the angle between the director n and the
Solvent Isotope Effects in APFO/Water Systems
Langmuir, Vol. 13, No. 10, 1997 2667 Table 1. Coefficients of the Polynomials (T/K ) aw3 + bw2 + cw + d) Used To Construct the Liquid Crystalline Phase Transition Lines for the APFO/H2O System (Figure 1) and the APFO/D2O Phase Diagram,3 the Phase Transition Temperatures Calculated from These Polynomials Agree to within (0.3 K with the Experimental Values transition
Figure 2. Temperature dependence of the partially averaged 14N quadrupole splittings ∆ν ˜ for the APFO/H2O (w ) 0.574) sample together with representative spectra from the single and phase coexistence regions. The phase transition temperatures TNI, TNL, and TLN are readily identified from the discontinuities in the ∆ν˜ vs temperature curves. TNI is determined from the first appearance of the nematic doublet on cooling the sample from the I into the I/N+ D phase coexistence region.9 Below the lamellar-nematic tricritical point Tcp (see Figure 1) the transition is apparently second order in that no 14N NMR; i.e., N+ D/L coexistence regime can be detected by there is no discontinuity in the quadrupole splittings at this transition. For samples with w < 0.49, the location of TNL is located from the discontinuity in the temperature dependence of ∆ν˜ .1,3,5,8,9
magnetic field B, S is the second-rank orientational order parameter representing the ensemble average of the orientational fluctuations of the micellar axes with respect to n, and |q˜ zz|s is the partially averaged component of the nuclear quadrupole-electric field gradient interaction tensor measured parallel to n in a perfectly ordered mesophase, given by
|q˜ zz|s ) 〈P2(cos R)〉sχNβ,
(2)
where χN is the quadrupole coupling constant for the ammonium ion, and β is the fraction of ions which are bound to the micelle surface. 14 N spectra of a w ) 0.574 sample are shown in Figure 2 together with the temperature dependence of the 14N quadrupole splittings. In the isotropic micellar solution phase the spectrum is a singlet, consistent with S ) 0 (eq 1). When the sample is cooled below TIN, the upper boundary to the I-to-ND transition, a symmetrical doublet from the ammonium ions in the nematic phase is superimposed on the isotropic singlet. With further cooling the doublet intensity increases as the singlet intensity decreases until below TNI, the lower boundary to the I-to-ND transition, only the nematic doublet is observed, the splitting of which increases with decreasing temperature largely due to a concomitant increase in the orientational order parameter S. When the sample is cooled below TNL, the upper boundary to the ND-to-L transition, a second doublet appears symmetrically disposed with respect to the nematic doublet. The discontinuity in the quadrupole splitting is characteristic of a first order ND-to-L transition. When the sample is cooled below the lower boundary to the transition TLN the nematic doublet vanishes and only the lamellar doublet is observed, the splitting of which increases with increasing temper-
w range
a
b
c
d
TIL/TIN TNI TNL TLN
APFO/H2O 0.35-0.63 1207.465 -1280.664 603.6692 0.35-0.62 951.9714 -988.0944 494.8753 0.49-0.62 3194.927 -4092.260 1914.160 0.38-0.63 1342.446 -1505.424 720.0366
TIL/TIN TNI TNL TLN
APFO/D2O 0.39-0.64 2885.833 -3688.073 1759.865 -5.189191 0.39-0.59 866.8651 -814.8514 402.6325 207.0486 0.49-0.59 9290.991 13747.57 7043.466 939.6626 0.44-0.66 1675.910 -1930.771 911.5742 123.9360
173.2450 186.0265 -34.37367 147.7156
ature primarily as a result of an increase in the micelle size (increase in 〈P2(cos R)〉s). Below the concentration of Tcp (Figure 1) the transition is apparently second order in that there is no discontinuity in the quadrupole splittings at the transition. There is, however, a discontinuity in the temperature dependence of the quadrupole splitting which enables TLN to be precisely located.1,5,8 The polynomials for the liquid crystalline phase transition lines in both the APFO/H2O and the APFO/D2O3 systems are given in Table 1. 14 N NMR measurements not only provide a precise technique for the determination of the liquid crystal phase transition temperatures, they also enable the singular points Tcp and Tp(I,N,L) to be accurately located. The temperature of Tp(I,N,L) is determined from observation of the spectral changes which occur on cooling a w ) 0.620 sample (i.e. a sample with a concentration between the nematic and lamellar concentrations at Tp(I,N,L) (Figure 1)) from the isotropic phase. At this concentration a lamellar doublet first appears on cooling below TIL, the upper boundary to the I/L phase coexistence region. The intensity of this doublet grows with respect to the isotropic singlet with decreasing temperature. When further cooling below Tp(I,N,L) takes place, a nematic doublet appears inside the lamellar one.5,9 The temperature at which the nematic doublet is first seen is taken as the temperature of Tp(I,N,L). The compositions of the isotropic, nematic, and lamellar phases were obtained from the abscissas of the respective curves at this triple point temperature. Tcp is estimated as the point at which TNL - TLN becomes zero.1,8,9 The location of Tcp is significant only in that it represents an estimated point at which a mixed nematic/lamellar phase can no longer be resolved by 14N NMR measurements. For a w ) 0.500 sample the width of the L/ND phase coexistence regime is only 20 mK; i.e., the transition is very weakly first order. For samples below this weight fraction separate signals from L and ND phases are not observed in the 14N spectra. It is, however, probable that this transition is always first order.1,22,23 The solubility curve Tc shown in Figure 1 was determined from electrical conductivity measurements on seven samples covering the concentration range w ) 0.350 to 0.650. Samples were first cooled in decrements of 1 K from about 10 K above Tc, waiting 5 min at each temperature before recording the conductivity, until (22) Halperin, B. I.; Lubensky, T. C.; Ma, S. K. Phys. Rev. Lett. 1974, 32, 292. (23) Anisimov, M. A.; Cladis, P. E.; Gorodetskii, E. E.; Huse, D. A.; Taratuta, V. G.; van Saarloos, W.; Voronov, V. P. Phys. Rev. A 1990, 41, 6749.
2668 Langmuir, Vol. 13, No. 10, 1997
Edwards et al.
Figure 3. Temperature dependence of the electrical conductivity κ of a APFO/H2O (w ) 0.350) sample on cooling (closed circles) from above Tc into the I + K phase coexistence region (see Figure 1) and then heating (open circles) to above Tc. Cooling was carried out in decrements of 1 K, waiting 5 min at each temperature before taking a conductivity reading, until crystallization of APFO was indicated by a rapid fall in the conductivity. Heating was carried out in increments of 0.25 K, waiting 20 min at each temperature before taking a conductivity reading to enable thermodynamic equilibrium between the K and I phases to be established. Tc is located as the temperature at which the cooling and heating curves merge. Table 2. Fixed Points at Standard Pressure in the Phase Diagrams of the APFO/H2O and APFO/D2O3 Systems T/K
w
Tp(I,N,L) isotropic nematic lamellar Tp(I,N,K) isotropic nematic Cep nematic ) lamellar Tcp
APFO/H2O 337.5(1) 0.602(2) 0.612(2) 0.622(2) 289.6(2) 0.413(4) 0.415(4) 289.9(2) 0.453(4) 297 0.49
Tp(I,N,L) isotropic nematic lamellar Tp(I,N,K) isotropic nematic Cep nematic ) lamellar Tcp
APFO/D2O 338.1(1) 0.581(2) 0.589(2) 0.604(2) 292.1(3) 0.393(5) 0.395(5) 292.4(3) 0.430(5) 304 0.49
φ
x
0.443(2) 0.453(2) 0.464(2)
0.0594 0.0618 0.0643
0.273(4) 0.275(4)
0.0286 0.0288
0.307(4) 0.339(4)
0.0334 0.0386
0.446(2) 0.455(2) 0.470(2)
0.0605 0.0627 0.0662
0.277(5) 0.278(5)
0.0292 0.0294
0.308(5) 0.362(5)
0.0339 0.0427
crystallization of the supercooled sample occured. The conductivity was then measured on heating in 0.25 K temperature increments, waiting 20 min at each temperature and thoroughly shaking the sample prior to measurement. The longer time was necessary on heating to enable thermodynamic equilibrium between I and K phases to be established. The temperature dependence of the electrical conductivity on carrying out this procedure on the w ) 0.350 sample is shown in Figure 3. The point at which the heating and cooling curves coincide defines Tc. The fixed points Cep and Tp(I,N,K) (Figure 1) were obtained from the interception of the solubility curve with the liquid crystal phase transition lines. A summary of all the fixed points in both the APFO/H2O and APFO/ D2O3 systems is presented in Table 2. The phase diagram for the APFO/H2O system shown in Figure 1 is qualitatively similar to the low-resolution phase diagrams previously determined for this system that used a cross-polarizing microscope to detect the phase boundary
Figure 4. Plot of the 14N ∆ν˜ values along the nematic-toisotropic transition line TNI and the lamellar-to-nematic transition line TLN vs volume fraction φ of APFO for the APFO/H2O (open circles) and the APFO/D2O (closed circles) systems. Volume fractions were calculated using the appropriate H2O and D2O densities at TNI and a value for the molar volume3 of APFO of 230.5 cm3.
lines.11 However, this is the first time that the mixed phase regimes have been delimited and the various fixed points located. The high accuracy and precision to which these and the phase transition lines have been located enable a detailed comparison of this phase diagram to be made with that of the corresponding APFO/D2O system so as to reveal any possible solvent isotope effects. Comparison with Phase Behavior in the APFO/ D2O System. Within experimental error, with the exception of Tcp, the fixed points in the APFO/H2O system occur at identical volume fractions but at lower temperatures than they do in the APFO/D2O system (Table 2). In addition, at comparable volume fractions, the phase transition temperatures are lower in the APFO/H2O system than in the APFO/D2O system3 (Table 1) as is the location of the solubility curve. The difference between the liquid crystal phase transitions does, however, decrease with increasing volume fraction of surfactant (increasing temperature). At a volume fraction of 0.261 the TNI transition temperatures for the APFO/D2O and APFO/H2O systems are respectively 289.5 and 286.5 K, while at a volume fraction of 0.420 the corresponding values are 327.2 and 326.4 K. The apparently lower volume fraction for Tcp in the APFO/H2O system is a consequence of the higher resolving power of 14N NMR measurements compared with that available from the 2H measurements used to establish Tcp in the APFO/D2O system.3 As mentioned before, Tcp has no significance other than that it represents the lower limit at which separate ND and L signals can be resolved. To understand the above observations we need to consider the effect of the solvents on micelle sizes in the two systems. The concentration dependence of the 14N quadrupole splittings along the TNI and TLN transition lines is shown in Figure 4. The observation that at any given volume fraction the quadrupole splittings at both TNI and TLN are the same in the two systems argues strongly for a constant micelle size at the transition,1,10 consistent with phase transitions driven by repulsive interactions between micelles. X-ray measurements show that the micelle axial ratio increases (micelles get smaller) with increasing temperature,3,17 and so at any given volume fraction the micelles in H2O must be smaller than those in D2O; i.e., substitution of H2O for D2O affects the self-assembly in such a way as to produce smaller micelles, and in order to recover the critical axial ratio for the I-toND transition, it is necessary to go to lower temperatures.
Solvent Isotope Effects in APFO/Water Systems
In the absence of specific counterion-carboxylate interactions, changes in the micelle self-assembly on substituting D2O for H2O would be expected to result from changes in the surface energy of the micelles as a result of changes in the interfacial tension γ at the fluorocarbon/ solvent interface and/or differences in the relative permittivities of the two solvents. Self-assembly theory19 qualitatively predicts larger micelles in the H2O system at any given temperature and composition rather than smaller ones as demanded by the experimental observations.1 To estimate the magnitude of this predicted change in micelle size on substituting D2O for H2O, we can consider a first-order model based on the self-assembly theory of McMullen et al.,19 which assumes that the mean area per head group ao is solely determined by a balance of opposing attractive (γfc/wa) and repulsive (c/a) contributions. γfc/w is the interfacial tension between the water and fluorocarbon surfactant, and the magnitude of the constant c is determined by the sum of the ionic interaction terms between the negatively charged head groups and these will depend upon the relative permittivity of the solvent (c ∝ -1). The average chemical potential of a surfactant with head group area a in an aggregate consisting of n surfactant molecules can thus be written as µ˜ n° ) γa + c/a + g,1 where g represents the ‘bulk’ free energy associated with packing of hydrophobic chains and ao ∝ (γ)-1/2 is the value of a which minimizes µ˜ n°. Assuming the micelle to consist of an oblate rightcircular cylinder (body) enclosed by a half-toroidal rim ao can be obtained from the expression,10 ao ) nrimarim + (n - nrim )abody, where arim and abody are the areas per molecule in the rim and body respectively and n and nrim are the micelle aggregation number and the number of molecules in the rim respectively. Providing n can be determined experimentally, the remaining quantities on the right hand side of the above expression can be calculated from the length L of the fluorocarbon chain and its volume vs.10 For the PFO- chain we use values for L and vs of 14.4 nm10 and 0.363 nm3,3 respectively. For a APFO/H2O (w ) 0.500) sample at 311 K, the micelle volume vm obtained from a small-angle X-ray scattering experiment17 is 38.6 nm3, giving a micelle aggregation number n () vm/vs) of 106 and a value for ao of 0.54 nm2. To estimate the micelle volume in a APFO/D2O sample of the same mole fraction x of surfactant (0.0401), we need the interfacial tensions between fluorocarbon and solvent and the relative permittivities of the solvents. At 311 K the r values are 73.96 and 73.41 in water and heavy water, respectively.24 Interfacial tensions can be calculated from the equation25 d d γfc/w ) γw/a + γfc/a - 2xγfc/a γw/a
where γd represents the dispersive contributions to the surface tensions. Values for the water/air surface tensions γw/a were taken from the published data for H2O24 and D2O26 (69.9 and 68.7 mN m-1 respectively at 311 K). The (24) Weast, R. C. Handbook of Chemistry and Physics, 52nd ed.; The Chemical Rubber Co.: Cleveland, OH, 1971. (25) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press Ltd.: London, 1991. (26) Horvath, A. L. Physical Properties of Inorganic Compounds; Edward Arnold: London, 1975.
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fluorocarbon/air interfacial tension γfc/a was assumed to be completely dispersive with a value25 of 19.0 mN m-1, and the dispersive contribution to the surface tension of d was taken to be27,28 20.0 mN m-1. H2O and D2O γw/a Using the above values and assuming the dispersive contributions to be independent of temperature γfc/H2O and γfc/D2O are calculated as 49.9 and 48.7 mN m-1 respectively. The predicted ao for the corresponding APFO/D2O sample (x ) 0.0401; w ) 0.473) is thus 0.55 nm2, which corresponds to a micelle volume of 35.9 nm3 (n ) 99). The volume fractions of these heavy water and water samples are practically the same (0.346 and 0.347, respectively) and the predicted smaller micelle size in the APFO/D2O sample at this volume fraction would result in a displacement of the I-to-ND transition to lower temperature by about 2 K compared with the APFO/H2O sample.3 Thus, the predicted decrease in the phase transition temperature on substituting D2O for H2O is small, and we could easily envisage small changes in the specific counterioncarboxylate interaction which lead to a greater shielding of the electrostatic head group repulsion as being primarily responsible for the observed isotope effect. Comparison with Solvent Isotope Effect in the CsPFO/H2O and CsPFO/D2O Systems. In the CsPFO systems the difference TNI(D2O) - TNI(H2O) is 3.9 K at φ ) 0.15 and eventually vanishes at φ ≈ 0.41 at a temperature which is about 25 K higher than that in the APFO/ water systems. In the CsPFO systems the counterion is fully hydrated,1 and the bonding to the surface carboxylate ions is via a bridging water molecule. Since, at corresponding temperatures, D2O in heavy water forms intrinsically stronger hydrogen bonds than H2O in water,20 as a consequence of the isotope effect on the zero-point vibrational energies, then substitution of D2O for H2O will result in a stronger hydrogen bond, a shorter Cs+CO2- distance, and, consequently, a more effective screening by the counterion of the electrostatic repulsion between the head groups. This will cause a decrease in the constant c and hence in ao, which will lead to larger micelles. The hydrogen-bonding effect must outweigh the predicted small increase in ao in the absence of any change in the specific counterion-carboxylate interaction. The solvent isotope effect observed in the APFO systems is similar to that observed in the CsPFO systems. Thus, while the identity of the counterion is important in determining the micelle self-assembly (the phase transition temperatures in the CsPFO systems are about 22 K higher than they are in the APFO systems) the changes in c on substitution of D2O for H2O are about the same in both systems, which suggests that the interaction between ammonium and carboxylate ions is also via bridging water molecules. Thus, the similarity in the solvent isotope effect in the APFO/water and CsPFO water systems is totally consistent with the notion that it is the intrinsically stronger hydrogen bonds in D2O solutions which result in a greater shielding of the head group repulsions by hydrated counterions. Acknowledgment. We wish to thank Massey University for the award of a Post Doctoral Fellowship to P.J.B.E. LA962009D (27) Good, R. J.; Elbing, E. Ind. Eng. Chem. 1970, 62, 54. (28) Fowkes, F. F. Ind. Eng. Chem. 1964, 56, 40. (29) Chin, S. T.; Kumar, S. Phys. Rev. Lett. 1991, 66, 1062.
