7678
J. Phys. Chem. 1993,97, 7678-7690
Phase Diagram of the Cesium Pentadecafluorooctanoate (CsPFO)/H20 System As Determined by 133CsNMR: Comparison with the CsPFO/D20 System Neville Boden,',? Kenneth W. Jolley,***and Mark H. Smith$ School of Chemistry, University of k e d s , k e d s LS2 9JT. U.K., and Department of Chemistry and Biochemistry, Massey University, Palmerston North, New Zealand Received: January 1 1 , 1993; In Final Form: May 3, I993
The high-resolution phase diagram of the cesium pentadecafluorooctanoate (CsPFO)/H20 system has been mapped out using mainly 133Cs+NMR spectroscopy. It is this system, rather than the CsPFO/D20 one whose phase diagram has earlier been established, which is often used in experimental studies of phase transitions. While the two diagrams are qualitatively similar, there are quantitative differences. Substituting H2O for D2O lowers both TNIand TNLat corresponding concentrations: at 9 = 0.15, T ~ l ( D 2 0 )- TNI(H~O) is 3.9 K and TNL(DzO)- TNL(H~O) is 4.3 K; these differences decrease with increasing 9 (temperature) and eventually vanish a t 4 = 0.41 (80 "C). This behavior arises from differences in micelle size: the micelles are a little larger in D20 than in H20 at corresponding concentrations and temperatures below 80 OC. This "isotope effect" on micelle size is attributed to tighter binding of Cs+ to surface carboxylate groups via bridging water molecules in the case of D2O. The cmc's occur at higher concentrations in D20, in contrast to the behavior of the sodium alkyl sulfates and alkyltrimethylammonium bromides which have lower cmc's in D2O. It is argued that this is because the PFO- monomer has a higher free energy in H2O than in D20, while for hydrocarbon surfactants the opposite applies. This contrasting behavior reveals fundamental differences in the interactions of hydrocarbon and perfluorocarbon chains with water. The free energy associated with creating a "cavity" in the solvent appears to be dominant in the case of perfluorocarbon chains, while for hydrocarbon chains it is the free energy associated with the chain-water intermolecular forces which dominates.
Introduction The self-assembly and self-organizationalbehaviors of shortchain fluorosurfactantsin aqueous solution are of current interest. This is because of their preference for discotic (disc-shaped) micelles which are stable over wide concentration and temperature intervals. This gives rise to generic phase behavior,1s4J quite different from that of conventional soaps and s~rfactants.6,~ The dominant feature of the phase diagrams of the latter is that the transition from one mesophase to the next is associated with a dramatic change in the topology of the aggregates. In contrast, in the case of the discotic micellar systems, these transitions are almost solely associated with changes in the orientational or translational orderingof the micelles. Typically,with increasing concentration, transitions to first a nematic phase of type ND* and, subsequently, a smectic lamellar phase of type LD are observed.9 The ND phase is characterized by long-range correlations in the orientation of the symmetry axes of the micelles, while in the LD phase the micelles are arranged on equidistant planes. Cesium pentadecafluorooctanoate (CsPFO) is the archetypal surfactant: this is because its phase diagram in water is the most amenable one for experimental study.l.10 The phase diagram for the CsPFO/D20 system' exhibits an Ng phase (+ denotes positive diamagnetic anisotropy) for mass fractions w between 0.225 (volume fraction 4 = 0.114) and 0.632 (4 = 0.426)and temperatures T between 285.3 and 351.2 K. The Ng-to-L, transition is second order to low concentrations but crosses over to first order at a tricritical point Tcp at w = 0.43 (4 = 0.25); T = 304.80 K.l0 The ammonium5 and rubidium11 salts exhibit similar phase behavior ( TNIat corresponding 4 are in order Cs+ > Rb+ > NH:), while the Na+ and K+ salts are not sufficiently soluble to form liquid crystals. The Li+ salt behaves more like a classical soap, exhibiting hexagonal and lamellar phases but no nematic phase,l2 and the parent acid exhibits possibly a classical University of Leeds. t Massey University. t
lamellar phase. l 3 The corresponding salts of heptadecafluorononanoic acid yield similar phase diagrams," with the corresponding transition temperatures about 25 K higher. A recent theoretical study14for a system of amphiphile monomers which self-assemble into polydisperse disc-shaped micelles which, in turn, interact via hard core forces yielded a calculated phase diagram qualitativelysimilar to that for the CsPFO/D20 system. Thus, the orderdisorder transitions in the CsPFO/D20 system appear to be primarily governed by hard core forces. Of course, the factors that govern the self-assembly of the micelles, that is the concentration and temperature dependence of their shape and size, are also instrumental in determining the form of the phase diagram. The stability of the LD phase stems from the translational entropy of the micelles which offsets the excess free energy of surfactant molecules in the rims of the micelles. The I-to-Ng-to-L, sequence of transitions is in many ways similar's to the isotropic liquid-nematic-smectic A sequence observed for thermotropic calamitic liquid crystals. However, there is a fundamental difference. In thermotropics, internal (molecular) degrees of freedom play a relatively minor role. In micellar systems, in contrast, restructing of the micelle, upon dilution or change in temperature, for example, may lead to coupling between internal (micellar) and external (order parameter) degrees of freedom. Such coupling creates a new situation where the nature of the transition can be drastically different. For this reason there is considerable interest in experimental studies of phase transitions in complex micellar liquid crystals, particularly in the CsPFO s y ~ t e m . ' , ~ ~ ~The J~J~35 published phase diagram is for the CsPFO/D20 system:' D20 is used rather than H2O because the phase diagram has been established by 2H NMR spectroscopy. However, the preference of many worker~22-24.~~-~~ to study the CsPFO/H20 system (as compared to the CsPFO/D20 system) can be confusing and has, in some instances,led to apparent inconsistences. It is, therefore, of some strategic importance to establish the high-resolutionphase
0022-365419312097-7678$04.00/0 0 1993 American Chemical Society
Phase Diagram of the (CsPFO)/H20 System diagram for CsPFO in ordinary water, one of the aims of this new study. A preliminary list of fixed points has already been published by us.I0 Another aim has been to exploit the effect on phase behavior and micellization of substituting Dz0 for HzO to learn more about the nature of the molecular interactions that govern the size and shape of the micelles. The notion is that DzO is a more "structured" (stronger hydrogen bonding) solvent than water36 and that this will modulate, for example, hydrophobic interactions. For the homologous series of sodium alkyl sulfates2 and alkyltrimethylammonium bromides3 substitution of DzO for H20 results in lower critical micelle concentrations (cmc's) and higher aggregation numbers (the effect is small and increases with alkyl chain length) but has no apparent effect on the fractional surface charge a. The isotope effect on micellizationhas, therefore, been entirely attributed to a more negative free energy of transfer of the alkyl chain from solution to micelle in the case of D20.3There are no reported studies of isotope effects for micellization of perfluorocarbon surfactants. However, studies of KPF03' and NaPF038-40 in H2O have established that they have lower cmc's, higher aggregation numbers, and larger changes in partial molar heat capacities and partial molar volumes compared to hydrocarbon surfactants. This has been attributed to the greater hydrophobicity of the fluorocarbon chain. We might therefore anticipate correspondinglylarger isotopeeffects for fluorocarbons compared to hydrocarbons. We have used 133Cs NMR to map the phase diagram for the CsPFO/HzO system. This has certain advantages compared to 2H NMR of heavy water, which we have previously employed in studies of the CsPFO/D20 ~ystem.'~4~9~2~ Hitherto, 133CsNMR has been fairly widely used in studies of lyotropic liquid crystals: 133Csquadrupole ~ p l i t t i n g s , ' chemical ~*~~ and chemical shift a n i ~ o t r o p i e s ~ 1have ~ ~ ~all 4 ~been used to provide detailed information about the binding of Cs+ ions in lyotropic liquid crystal systems. However, its deployment, as described herein, for the precise location and characterization of phase transitions, as a probe of micelle size and shape, and as a monitor of micellar orientational ordering, introduces new methods and these are therefore described in some detail. Experimental Methods NMR Spectroscopy. 133CsNMR spectra were measured with a JEOL GX270 spectrometer operating at 35.44 MHz and using a pulse width of 9 I.IS (45' pulse). Typically, the FID was sampled using 32K data points over a 32-kHz width giving a resolution after Fourier transformation of 2 Hz per data point. The sampletemperature-control system used in this study was designed46so as to minimize temperature gradients and to provide for accurate and precise control of the sample temperature. Electrical Conductivity. Critical micelle concentrations were obtained from electrical conductivity measurements made using a Phillips PW9512/61 conductivity cell attached to a Phillips PW9509 digital conductivity meter operating at a frequency of 2 kHz. Temperature control was achieved using the same temperature-control system as was used for the NMR measurements.4 DifferentialScanningCalorimetry (DSC). DSC thermograms were recorded using a Perkin-Elmer DSC-2 instrument which was interfaced with a Model 3600 thermal analysis data station. The instrument was calibrated using a standard indium sample. Thermograms were obtained on heating the samples at a rate of 5 K/min. Materials and Sample heparation. CsPFO was prepared by neutralizing an aqueous solution of pentadecafluorooctanoicacid (Aldrich Chemical Company, Inc.) with cesium carbonate (BDH, Ltd.). The neutralized solution was evaporated to dryness in an oven at 100 OC, and the salt was recrystallized twice from n-butanol. NMR measurements were made on samples in the concentration range w = 0.2-0.68. Samples were prepared by weighing
The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 7679
340 I I
320
e 300 280
260
'
0.0
Ice + K I
,
0.2
,
,
,
0.6
0.4
,
0.8
1.o
W
Figure 1. Phase diagram for the CsPFO/H20 system. Nomenclature: I, isotropicmicellar solutionphase (to the right of the line of cmc's (dashed vertical line)); N;, discotic nematic phase with positive diamagnetic susceptibility;LD,discotic lamellar phase; K, crystal; Tcp, the lamellarnematic tricritical point; Tp(ice,I,K), the ice-isotropic solution-crystal triple point; Tp(I,N,K), the isotropic micellar solution-nematic-crystal triple point; Tp(I,N,L),the isotropic micellar solution-nematic-lamellar triple point; Cep, the critical end point; Kp, the Krafft point.
CsPFO and water (deionized,doubly distilled)directly into 5-mm0.d. NMR tubes which were then flame sealed. Samples were stored at room temperature and gave consistent NMR measurements over several months, providing care was taken prior to each measurement to ensure a homogenous sample. This was accomplished by thoroughly shaking the sample at a temperature corresponding to an isotropic solution phase. DSC samples were prepared in the concentration range w = 0.2-0.90 by weighing directly into glass ampules, which were then flame sealed. For w > 0.7 samples, mixing was achieved by centrifugation of the lamellar phase up and down the tube until the sample appeared homogeneous when viewed through cross polarizers. Immediately prior to measurement the ampules were broken and the samples weighed into aluminum pans whose lids were sealed by crimping. The dilute samples required for the electrical conductivity measurements were prepared by weighing CsPFO and water into 10-cm3volumetric flasks. There was no difficulty in mixing these samples which were all in the isotropic solution phase at room temperature.
Results The Phase Diagram. The phase diagram for the CsPFO/ water system, shown in Figure 1, is qualitatively very similar to that for the CsPFO/heavy water system.' There are, however, quantitative differences, as can be seen from the comparison of the data for the various fixed points of the two systems in Table I. Essentially,changing from D20 to H2O lowers the temperatures of the L,-to-Ng and the Ng-to-I transitions by roughly 4 K at 4 0.1 and by 1 K at 4 0.4. Before discussing the implication of these isotopeeffects,aspects of the experimentsused to establish the various transition lines will be discussed. 1 Line of Critical Micelle Concentrations. The cmc's were obtained over the temperature range 5-90 OC from plots of electrical conductivity K versus mole fraction of surfactant x, as shown in Figure 2. The plots are seen to be linear both above and below the cmc. This provides for an objective estimate of the cmc's from the intersection of the best fit straight lines to the data. The effect on the cmc's of substituting H2O for D20 is shown in Figure 3. At all temperatures the cmc's of the heavy water system are higher than those in the water system, the opposite of the behavior of hydrocarbon/water systems3
-
I
Boden et al.
7680 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993
TABLE I: Fixed Points at Standard Pressure in the Phase Diagrams of the CsPFO/H20 and CsPFO/DzO Systems T/K w 6 c/moldm-3 x CsPFO/HzO Tp(I,N,L) 342.72 0.0527 1.821 0.628 0.398 isotropic 1.841 0.0538 0.634 0.404 nematic 1.898 0.0565 0.645 0.416 lamellar Tp(I,N,K) 281.31 0.496 0.00992 0.233 0.108 isotropic 0.501 0.0100 0.235 0.109 nematic Tp(Ice,I,K) 272.0 0.0003 0.009 0.0036 0.016 isotrodc 281.7 CeP 0.302 0.148 0.675 0.0141 nematic = lamellar 275.5 0.016 0.0065 0.030 0.00055 KP 273.15 Tr ice TCP 302.04 0.46 0.25 1.16 0.027 CsPFO/DzO Tp(I,N,L) 351.23 0.0578 1.946 0.626 0.425 isotropic 0.632 0.426 1.975 0.0592 nematic 2.054 0.0632 0.648 0.443 lamellar Tp(I,N,K) 285.3 isotropic 0.221 0.111 0.510 0.0103 nematic 0.225 0.114 0.520 0.0105 Tp(HI,I,K) 275.8 isotropic 0.011 0.0049 0.0224 0.00041 CeP 285.72 nematic = lamellar 0.287 0.151 0.691 0.0145 KO 280.0 0.016 0.0071 0.033 0.00060 T~HI 276.95 TCP 304.80 0.43 0.25 1.14 0.027
2. Solubility Curve TE. The solubility curve in the concentration interval w = 0.01-0.25 was established by electrical conductivity measurements. Samples were first cooled from the isotropic solution phase until a sharp discontinuity in the conductivity versus temperature curve indicated crystallization of the supercooled sample. The conductivity was then measured on heating, while shaking the sample, and the temperature at which the heating and cooling curves merged was taken to be TC.I In the concentration range w = 0.3-0.9, T, was determined from DSC measurements. Thermograms were recorded on heating, and dissolution of CsPFO was indicated by an endotherm with AH = 150 kJ mol-' of amphiphi1e.I Supercooling was generally observed on cooling. 3. Krafft Point Kp' The Krafft point is taken as theintersection of the line of cmc's with the solubility curve. 4 . Liquid Crystal Transition Lines. The L,-to-Ni and the N:-to-I transition lines have been precisely located solely by 133Cs N M R spectroscopy. This has involved measurements of both quadrupole splittings and chemical shifts. The relationship between these two quantities and the various experimental variables will be outlined as an introduction to their use to locate phase transition lines in lyotropic liquid crystal systems. Considering only the nuclear quadrupolselectricfield gradient interaction, to first order the NMR spectrum for a 133Csspin ( I = 7/2) in a macroscopically aligned uniaxial nematic or lamellar mesophase will consist of seven equally-spaced lines of relative intensities 7:12:15:16:15: 12:7. The relationship of thequadrupole splitting, the separation between the lines A;, to the micelle structure and orientational ordering of the micelles can beobtained by an extension of previous arguments1 for the quadrupole splittings of ZH in DzO in such mesophases. This leads to the following expression for the partially averaged quadrupole splitting10 1
A?(@) = r;iI4Js SJ'z(c0~
4)
(1)
In eq 1 the upper tilde denotes partially averaged quantities and
4 is the angle between the mesophase director n and the magnetic field B. S is an order parameter which represents the ensemble
0 " ' " " " " " " 0 2 4 6
8
1 0 1 2 1 4
1 0 ~ ~
Figure 2. Electrical conductivity K versus mole fraction x of CsPFO for the CsPFO/H20 (open circles) and CsPFO/D20 (closedcircles) systems at 303.15 K. The cmc's are obtained from the intersection of the best fit straight lines to the data above and below the cmc. The cmc's for the water and heavy water systemsat this temperature occur at mole fractions of CsPFO of 4.84 X 10-4 and 5.40 X 10-4, respectively.
-5B
7.0
1,
6.5
-
,
,
I
,
,
I
'
'
'
'
I
"
"
I
"
' ' 4 0 -
(0 *I
0
0
.
0 0 0
5.5
0
0 0 0
4.5
270
290
330
310
350
370
T/K
Figure 3. Dependence of the cmc on temperature in the CsPFO/H20 (open circles) and CsPFO/D20 systems (closed circles). average of the orientational fluctuations of the micellar axes M(k,l,m) with respect to the direction of n. 1Q& is the partially averaged component of the nuclear quadrupole-electric field gradient interaction tensor measured when B is parallel to n in a perfectly ordered mesophase and is given by
14,ls = C p , X n E c + %Ea -m / 3 1
(2)
n
In eq 2 the Si, are the elements of the Saupe ordering matrix for the principal axes (a, b, c) of the nuclear quadrupole interaction tensor at the nth site which has statistical weight pn,xn = (e2qQ/ h)" is the corresponding quadrupole coupling constant, and g, is the asymmetry parameter. In the general case the actual values for xnand gn may vary from site to site and will thus be determined by the detailed structure of the micelle. However for the case considered here, eq 2 can be considerably simplified along similar lines to that for ZH quadrupole splittings in the CsPFO/D20 system.l For Cs+ ions not bound to the surface IQZl.b = 0, so that the observation of a finite quadrupole splitting implies that for the fraction of ions B which are bound the hydration shells must be distorted from spherical symmetry. The nature of this distortion will be elaborated on later, but it transpires that a singlevalue for x is obtained irrespective of the particular binding site on the micelle surface. As this distortion will always be symmetrical about a normal to the surface, the effective order parameter S,, will be unity. We also need to allow for averaging of the quadrupole splitting arising from the diffusive motion of the Cs+ ion over surface sites. For a uniform distribution of the ions over the micelle surface, this averaging is given by (Pz(cos
Phase Diagram of the (CsPFO)/H20 System
The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 7681 A I
I
I
I
I
I
I
,
,
350
l
,
,
,
250
l
,
,
,
L
vmz
Figure 5. 133CsNMR spectra for the Zeeman transition in a CsPFO/ H20 (w = 0.549) sample in (a) the isotropic phase, I, (b) the isotropic/ nematic, I/N& biphasic region, (c) the nematic/lamellar, Ni/LD, biphasic region.
316.023 h
v/kHz ' ' I 15 10 5 0 -5 -10 -15 Figure 4. l13CsNMR spectra of a CsPFO/H20 (w = 0.549) sample in (a) the isotropic phase, I, (b) the aligned nematic phase, N:, and (c) an unaligned lamellar phase, LD, prepared by cooling the sample from the isotropic phase into the LDphase outsidethe spectrometermagnetic field. In c, the maxima correspond to the singulatitiesof.Pake powder spectra; that is they arise from director orientations perpendicular to the direction of B,Le., 4 = 90'. Thus, the apparent quadyole splitting is given by Ai(90") = 1 / 28(9,L,S in contrast to Av(0') = 1 / 141&&S in spectrum 4b. The Zeeman transition line for the unaligned LD phase sample, shown in the insert of part c, has a uniaxial chemical shift tensor line shape reflecting the uniaxial symmetry of the mesophase. 1
"
'
I
"
'
I
"
'
I
"
'
l
"
'
~
/
a ) )= ~ (3/2c0s2 CY - 1 / 2 ) ~ , where a is the angle between the normal to the surface and the symmetry axis of the micelle and the angular brackets denote the average is taken over the surface. Equation 2 can in this case be simply expressed as 14,lS
= (P,(COS
4)SXS
(3)
Values of (P~(cos a ) )for ~ an oblate ellipsoid (discotic micelle) as a function of the axial ratio have been calculated.' However, a recent study of the NHJ'FO/water system has revealed that ammonium ions have a small preference for binding to sites of lowest surface curvature on discotic micelle^.^ This is in contrast to water molecules which appear to be uniformly distributed over the micelle surface. For counterions, such a uniform distribution cannot be assumed and the nature of the distribution must be taken into account in the calculation of (&(cos a))s. 133Cs spectra in various phases of a w = 0.549 sample are shown in Figure 4. In the isotropic micellar solution phase I (Figure 4a) the spectrum is a singlet, consistent with S = 0, while in the nematic Ng phase (Figure 4b) the spectrum is a septet, the characteristic signature of a macroscopically aligned mesophase. In this case the nematic director is uniformly aligned along the direction of the applied magnetic field B,that is, 4 = . ' 0 The spectrum in Figure 4c is seen to be far more complex: it corresponds to a LD phase sample prepared by cooling from the I into the LD phase in the absence of a magnetic field. If the sample had been cooled in the presence of the field, a macroscopically aligned LD phase would have been obtained and the spectrum would have been indistinguishable from that in Figure 4b. In the unaligned LD phase each of the principal doublets in
the spectrum of the aligned sample is replaced by a Pake powder pattern consistent with an isotropic distribution of director orientations. Only the Pake singularities, with separation corresponding to 4 = 90' in eq 1, Le., having half of the splitting of the aligned 4 = Oo spectrum, are clearly visible in Figure 4c. To first order, the Zeeman resonance line (m = +1/2 to is unaffected by the quadrupole interaction. However, it is seen, on expansion of the frequency scale, to have a uniaxial chemical shift tensor line shape (Figure 4c), reflecting the uniaxial symmetry of the mesophase. Similar chemical shift line shapes have previously been observed for l33Cs in classicalbilayer lamellar pha~es.~1*4'For the case of a macroscopically aligned (single domain sample) discotic micellar mesophase, the partially averaged chemical shift is given by 5zz(4)
= ai + 2/,Cpn[szci
I2
0
-350
-
-400
-
-450
L---u-J
a
0
0.0
0
2.5
1
8""
2'ol 1.5
1.0
2.0
3.0
4.0
5.0
6.0
,
7.0
10%
Figure 6. Isotropic shift ui - unf for CsPFO/H20 (open circles) and CsPFO/D20 (closed circles) solutions as a function of the mole fraction x of CsPFO. The shifts are measured relative to a 130Cs frequency corresponding to an infinitely dilute CsCl/H20 solution. This was obtained by measuring the absolute lS3Csresonance frequencies of a series of CsCl solutions in the concentration range 0.0024.05 m and extrapolating the resulting straight line plot to m = 0. The shift to high fields on substituting heavy water for water is roughly constant at 1.1 ppm at corresponding mole fractions.
(0.3 1 ppm) at the corresponding nematic-to-lamellar transition (Figure 5c): here the discontinuity in the 133Csshift (bzz(Oo)(LD)- bzz(Oo)(Ng))is small as a result of the small discontinuities in S,P2(cosCY), and @ across the weak first-order transition in this sample. Now, from the relationship between chemical shift and frequency uo = yBo( 1 - bzz),we see from Figure 5b that in both the nematic and lamellar phases (bzz(Oo)- ai) < 0. This implies that (all - U ~ ) Mis also negative, or ( u ~ ) M > ( 0 1 1 ) ~ . The concentration dependence of 01 for the two systems CsPFO/H20 and CsPFO/D20 is shown in Figure 6. The isotopeeffect q(D20) - ol(H20) is 1.1(1) ppm at corresponding mole fractions over the entire concentration range. It is of the same sign and magnitude as that in the corresponding cesium octanoate/water system42 and compares with the value 0.8 ppm for CsCl solutions. The magnitude of this isotopic shift is a measure of the extent of direct ion-water contact.42 Its invariance with concentration indicates no significant elimination of water of hydration on binding of the ion to the micelle. The chemical shifts arising from binding of the ion to the micelle can, therefore, be attributed solely to either a distortion of the symmetries of the hydration shell or the electronic configuration of the hydrating water molecules, or a combination of these effects. The shift to lower frequencieswith increasing concentration of CsPFO in both H2O and D2O solutions is consistent with an increasing fraction of bound ions and a bound-ion shift to lower frequency of that for the free ion (Le,, a b > a?. In contrast, in the cesium octanoate/ water system, the bound-ion shift is to higher frequency of that for the free i0n.4~The observe shift to lower frequencies arises from an increase in shielding as a result of a decrease in the overlap integral between the ion's outer orbitals and the oxygen of the hydrating water molecule. This overlaphas been predicted42 to decrease with an increase in the acid strength of the surfactant head group. Thus, the change in the Cs+ ion chemical shift to lower frequencieson substitutinga fluorocarbon for a hydrocarbon chain can be understood in terms of the accompanying increase in acid strength of the carboxylate anion. The temperature dependences of the normalized quantities Al/Al( TNI)and AC/Ab( TNI)are identical (FigFre 7). Thevalues for Ab used in this plot were calculated from azz(Oo)- ut (eq 6) and will be correct only if ui does not change appreciably over the temperature range of the experiment. That this was the case was confirmed by measuring AC from the powder pattern in the LD phase.48 The values for Ab obtained by the two techniques were identical within experimental error. The shape of the plot
1.o 320
322
324
I
326
328
330
1.0 332
TIK
Figure 7. Partially averaged I3'Cs quadrupole splittings A? (triangles) and chemical shift anisotropies A 5 (squares), normalized to their value at TNI,as a function of temperature for CsPFO/D20 (w = 0.550): TLN = 325.1 1 K,TNL= 325.80K,TNI= 330.02 K,and Tm = 330.61 K.The values for A? and A 5 at TNIare 1725 Hz and 3.95 ppm, respectively.
in Figure 7 is well understood:l.5 the behavior in the Ng phase is dominated by the temperature dependence of S,while in the LD phase it is (P2(cos CY))^ and @c,which are dominant. For both the CsPFO/H20 and CsPFO/D20 systems, the ratio Ai(Oo)/Abhas a magnitude of 436(2) Hz which is independent of both temperature and composition. This result is consistent with the field gradient at the 133Csnucleus also arising from distortion of the first hydration shell of the ion. The observed proportionality between A? and Ab for hydrated 133Csions in the vicinity of a charged surface is, therefore, qualitatively understandable. A similar proportionality between sgCOchemical shift anisotropies and quadrupole couplings has been demonstrated for a series of octahedral cobalt complexes49and explained in terms of polarization of electrons in the 3d and 4p orbitals as being the common dominating factor in determining the magnitude of both the electric field gradient at the nucleus and the componentsofthechemicalshift shieldingtensor. Theobservation of a constant Al(Oo)/A? ratio does not, therefore, necessarily imply that both quantities are temperature independent. However, we have recently shown that in the APFO/D20 system, the temperature variation in the 2H quadrupole splittings of heavy water can be explained solely in terms of changes in S and (P2(cos CY))^ with a temperature- and concentration-independent deuterium quadrupolecouplingconstant.5 In addition,in lyotropic liquid crystal systemswhich consistof "classicallamellar bilayers", in which neither the lamellar structure nor the order parameter vary with temperature, it has beendemonstrated that theobserved quadrupole splittings of counterions are temperature independent.41.m It is likely, therefore, that x and thus (a11- U * ) M are independent of temperature and concentration over the range covered in this study. This being so, variations in A.3(Oo),bu( O O ) , or Ab can be considered to solely arise from changes in the micellestructure ((&(cos CY))^), micellar ordering (S), or boundion fraction (@), or indeed any combination of the three. We will demonstrate how quadrupole splitting measurements can be used to expose these properties later. First, we will illustrate how measurements of quadrupole splittings and shift anisotropiescan be used to precisely locate phase transition temperatures.1JO ( i ) Nematic-to-Isotropic Transition Line. The sequence of spectra observed for the Zeeman transition for a w = 0.350 sample on cooling from the isotropic into the nematic phase are shown in Figure 8. The line width of the isotropic-phase Zeeman peak increases slowly with decreasing temperature until, at a temperature slightly greater than that of the upper boundary TINto the isotropic-to-nematic transition, a rapid increase occurs. For thew = 0.35sample, the width increases from 5 Hz at TNI+ 0.5 K to 25 Hz at T N I 0.1 K (Figure Sa). This broadening is due to unresolved fine structure which, on further cooling, is revealed as two broad peaks with line widths of about 150 Hzsymmetrically
+
Phase Diagram of the (CsPFO)/HzO System
The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 7683 3.5
h j
TIK
294.087
3.0 (a)
2.5
g
h
2.0
N
I5a
%
v
1.5
E 0
1.o
0.5
293.958
0.0
293.94
293.98
294.02
TIK
Figure 9. Plots of the field-inducedquadrupolesplittingsAF (open circles) and their inverse (closedcircles)versus temperature for I3Cscounterions in the isotropic phase, I, and the isotropic/nematic, I/N& biphasic region of CsPFO/H30 (w = 0.35). The discontinuityin the temperature dependenceoftheA d identifies TIN(293.977(1)K),andits extrapolation to zero gives T5(293.960(1) K) (see e~ 8).
n
J i
293.887 /
400
~
'
'
200
I
'
'
,
0
1
'
,
-200
'
,
~
VIHZ "
-400
I
I
Figure 8. Sequence of lS3Csspcctra observed on cooling a sample with w = 0.350 from the isotropic phase, I, (a and b) into the isotropic/ nematic, I/N:, biphasic region (c-e), through to the nematic, Ng, phase, f.
disposed about the central singlet (Figure 8b). The separation of these peaks increasesrapidly in magnitude until the temperature of the transition to the nematic phase is reached, after which it is essentially invariant. This temperature T I Nis signified by the appearance of the small nematic Zeeman peak to high frequencies of the isotropic Zeeman peak (Figure 8c). As the temperature is lowered further, the relative amount of the nematic phase increases (Figure 8c-e) until at the temperature of the lower boundary to the transition TNI the system is entirely nematic (Figure 8f). The change in the appearance of the isotropic phase signal on approaching TINis due to orientational ordering of the micelles induced by the magnetic field.20 It arises from the magnetic torque acting on the micelles, a torque which is enhanced by the buildup in the angular correlationsof the micellesas the transition is approached. This unquenches the l33Cs quadrupole splittings. Only the m = 1/2(-1/2) to 3/2(J/z) transitions are easily seen, theouter satellite peaks arising from transitionsbetweenthe higher levels are very broad and tend to disappear into the spectral noise. The magnitude of the splitting is related to the degree of orientational ordering of the micelles, as defined by their orientational order parameter (Pz(cosb ) ) , where j3 is the angle between the magnetic field B and the micellar symmetry axis,
where xa is the anisotropy in the magnetic susceptibility of a micelle and T1 is the extrapolated supercooling limit of the isotropic phase. Over the narrow temperature interval for which quadrupole splittings can be measured, the values of and xs are to a good approximation constant. Thus the splitting is predicted to depend on B2 and to diverge at T1 consistent with the plot of A F 1 versus temperature given in Figure 9. Precise values of both TINand T1 can be obtained from this plot. The
valuefor T~~-TS0f0.017Kforthew=0.35sample(~=0.177) compares well with a value of 0.016 K obtained for a CsPFO/ DzO (w = 0.302; 4 = 0.160) sample obtained from 2H NMR measurements.20 At the field strength of this study the field-induced splittings become too small to accurately measure for samples with mass fractions greater than about 0.4. For these samples it is possible to obtain an accurate value of T I Nby looking for the first appearance of the nematic Zeeman peak (see Figure 8c) which is preceded by pretransitional broadening of the isotropic peak. This is a much better method than looking for the first appearance of the quadrupole coupled peaks, which tend to be broad and more difficult to detect when the proportion of nematic phase is small. Of course, the appearance of the Ng phase peak, which can be located to a temperature precision of fO.O1 K,indicates that the sample is already in the mixed-phase region. The maximum error in TINas a result of this depends on the sensitivity of detection of the Ng phase peak and the temperature range of the mixed-phase region. The line width of the Zeeman transition for the nematic phase is only about 4 Hz, and it is easy to detect this peak at a I-t0-N: peak intensity ratio of *1:50. For the w = 0.55 sample, the temperature range of the I/N: coexistence regime is 0.400 K,so from the lever rule we would expect the Ng peak to be readily observable at " ( T I N- 0.008) K. For sampleswith concentrationsw of less than 0.55,the corresponding systematic error will be even smaller, since the width of the coexistence regime decreases with decreasing w.1JO The best method to determine TNI,the lower boundary to the isotropic-to-nematic transition, makes use of the discontinuity in the temperature dependence of the magnitude of the quadrupole splitting Ai(Oo)at this phaseboundary (Figure 10). In themixedphase region, the nematic splitting changes little with temperature as a consequence of the value of S being essentially constant along the Ng-to-I transition line.lJo At TNIthe isotropic phase disappears and there is a rapid increase in the value of S and consequently the nematic quadrupole splitting with decreasing temperature. Thesharpdiscontinuity in AP(Oo) at T N I ~aSprecise indication of this temperature. The 133Csquadrupole splittings are much larger than the corresponding 2H splittings,1° and complications due to chemical exchange' of Cs+ ions between coexisting phases are seldom seen. In practice, it is important to determine T N Iby measuring the quadrupole splittings on heating from a nematic phase produced by rapid cooling across the I/N: coexistence regime. Slow cooling through this region leads to phase separation and a consequent concentration gradient within the sample. Such a situation is easily detected by L33Cs NMR from the persistence
Boden et al.
7684 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 2.2,
,
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Figure 10. Partially averaged lo3Csquadrupole splittings A; as observed on heating CsPFO/H2O (w = 0.350) from the Ng into the Ng/I biphasic regime. The lower temperature to the transition TJI (293.880(5) K) is readily identified from the discontinuity in the Av versus temperature plot.
of a small isotropic signal at temperatures where the quadrupole splitting changes rapidly with temperature. By spending as little time as practicable in the mixed-phase region, phase separation problems are, at best, avoided or, at least, minimized. (ii) Lamellar-to-Isotropic Transition Line. Phase separation is particularly rapid in the I/LD phase coexistence regions due to both the larger density differences between the phases and the lower viscosities at the high temperatures characteristic of this region of the phase diagram. It is, therefore, particularly important to approach the upper TILand lower TLItemperature boundaries of the mixed-phase regime from the pure-phase regions: i.e., T I Lis obtained by cooling from the isotropic phase and TLIby heating from the lamellar phase. The best way to determine TILis from the first appearance of the lamellar Zeeman peak on cooling from the isotropic phase (cf. determination of TIN in previous section). To determine TLIthe sample is first cooled rapidly from the homogeneous isotropic phase into the lamellar phase by immersion of the NMR tube in a beaker of water at an appropriate temperature. This is necessary since the width of the I/LD mixed-phase region is typically 6 K and during the time it takes to cool across this region using the sample temperature control system (- 10 min), macroscopic phase separation occurs in the sample tube and an interface is visible between an upper isotropic and a lower lamellar phase. Rapid cooling outside the field results in samples homogeneous in concentration but having an isotropic distribution of directors. The appearance of the Zeeman peak for a w = 0.65 sample, following the above preparation scheme, is shown in Figure 1l a and is consistent with an isotropic directordistribution for a sample with ( u ~ ) M > ( ~ 1 1 ) (see ~ eq 5). On heating the sample in the magnet, the director rotates into alignment along the direction of the magnetic field (Figure 11b-e) for (TLI- T) < 0.5 K. This phenomenon, which occurs over the full concentration range of the lamellar phase at temperatures close to TLI(and TLN),was not observed at the lower field strengths used in our earlier study on the CsPFO/D20 system.' On further heating of the aligned sample (Figure 1le), the presence of the mixed-phase region is indicated by the appearance of the isotropic-phaseresonance line (Figure 1If). However, precisevaluesfor T ~ ~ a r e b edetermined st from plots of the quadrupole splittings of the ordered sample against temperature across the phase boundary. The plots so obtained show a discontinuityin the temperature dependence at TLI,similar to that at TLNfor samples exhibiting a first-order lamellar-to-nematic transition (see Figure 13). (iii) Nematic-to-Lamellar Transition Line and Location of the Tricritical Point Tcp. Theappearanceofthespectraobserved on cooling from the nematic into the lamellar phase depends on the CsPFO concentration of the sample. At CsPFO mass fractions
(f)
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Figure 11. Io3CsZecman transition in CsPFO/H20 (w = 0.650) in its lamellar LDphase (a-e) and the I/LD biphasic region (f and g). The unaligned sample in a was prepared by rapid cooling from the isotropic phase into the lamellar phase outside the spectrometer magnetic field. The sequence of spectra from b to e, taken at 20-min intervals, illustrates the slow realignment of the lamellar director in the spectrometer field (6.3 T). The I/LDbiphasic region is indicated by the appearance of the &man transitionfor the isotropicphase (f),the intensity of which grows at the expense of the %man transition for the ordered LOphase as the temperature is raised (g), in accordance with the lever rule.
of 0.5, and above, separate signals for the nematic and lamellar phases are readily observed correspondingto the nematic/lamellar coexistence region. The spectra obtained for a w = 0.550 sample are shown in Figure 12. The quadrupole splittings in the mixedphase region can be precisely measured enabling TNLand TLN, the upper and lower temperature boundaries to the mixed-phase region, respectively, to be determined from the discontinuitiesin the quadrupole splittings (see Figure 13). As the CsPFO mass fraction decreases, the width of the mixed-phase region also decreases making it more difficult to locate TNLand TLN,At w = 0.48, the gap TNL- TLNis only 20 mK, which is the limit of experimental resolution. Therefore, for samples with w < 0.48 no discontinuity in the quadrupole splitting is observed. The discontinuity in the temperature dependence of the quadrupole splitting (Figure 13) is now identified with TLN,and this transition is now represented by the dashed curve in Figure 1. The concentration at which the transition appears to cross over from first to second order was taken as that at which the gap TNLTLNextrapolates to zero (Figure 14) and identified to a tricritical point Tcp. We followed a similar procedure in the case of the CsPFO/D20 system.1° It is clear, however, from Figure 14 that TNL- TLNappears to become asymptotic to the w axis as w decreases. Indeed, Halperin, Lubensky, and Ma51 have predicted that the nematic-to-lamellar transition of pure thermotropicliquid crystals and their mixtures should always be at least weakly first order as a consequence of coupling between director fluctuations and the smectic order parameter. This coupling gives rise to a cubic term in the Landau free energy expression for the transition that drives the transition first order. Support for this prediction was recently reported by Anisimov et al. who performed precise measurementson binary thermotropicliquid crystal systems using adiabatic scanning calorimetry.52 It was shown that there is a crossover from classical Landau theory behavior at a solute concentration roughly identified as that of the Landau tricritical
Phase Diagram of the (CsPFO)/H20 System
The Journal of Physical Chemistry,Vol. 97,No. 29, 1993 7685
I TIK
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Figure 14. Plot of the transition gap TNL TLNas a function of the concentrationof CsPFOin the system CsPFO/H20. Tm TLNappears to go to zero in the vicinity of I$= 0.25 (w = 0.46) which is taken to be
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the location of an apparent tricritical point Tcp. 350
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Figure 13. Partiallyaveraged 133Cs quadrupolesplittings A; as observed oncooliigsamplesofCsPFO/H20 (w = 0.500),lowertrace,andCsPFO/ H2O (w = 0.45), upper trace, from the N i into the LDphase. For the w = 0.500 sample,separate signals for the N; and LDphasesare observed in the biphasic region enabling both T N L(=308.435(5) K) and TLN
(=308.380(5) K) to be clearly identified from the discontinuitiesin the quadrupolesplittings. For thew = 0.450 sample,no biphasicspectra are evident and TLN(=300.74(1) K) is identified as the discontinuity in the temperature dependence of the quadrupole splittings. point. Above this concentration the entropy change for the transition is strongly dependent on solute concentration while below the point the concentration dependence is weak, but more importantly, the entropy change is always positive, Le., the transition is first order along the whole of the nematic-to-lamellar transition line. This conclusion was also supported by dynamical measurements on propagating interfaces. Assuming that TNLTLNis proportional to the strength of the transition, the general appearance of Figure 14 suggests that this may also be the case for the NA-to-L, transition in the CsPFO/water system. The tricritical point as identified here is therefore likely to only have the empirical significance ascribed to it. (iu) Location of the Triple Point T,(I,N,L). This was determined from observation of the Zeeman transition on cooling a w = 0.640 sample from the isotropic solution phase along the
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Figure 15. (b) NMR spectra for the Zeeman transition on cooling CsPFO/H20 (w = 0.64) along the isopleth shown in a. The Occurrence
of a lamellar phase Zeeman peak to high frequency of an isotropicphase peak at T = 345.01 K shows the sampleto be in the I/LD biphasicregion. On further cooling the lamellar peak increasesin intensity and a nematic phase Zeeman peak, between the I and LOsignals, first appears at T = 342.49 K, indicating that the sample has been cooled below Tp(I,N,L) and is in the Ni/LDbiphasic region. Over a period of about 5 min (the lower three spectra were taken at 2-min intervals) thermodynamic equilibriumis reestablished as the I phase signal is seen to disappear and peaks for the N; and LD phases remain in roughly the proportions predicted by the lever rule. The unsymmetricalappearance of the highfrequency (LOphase) peak is due to concentration gradients induced in the sample by phase separation during the experiment. isopleth of Figure 1Sa. The lamellar-phasespectrum first appears a t T < T,Land grows a t the expense of the isotropic solution spectrum as the temperature is lowered. At T,(I,N,L), a peak, from a nematic phase, is observed. The formation of this peak is accompanied by the rapid disappearance ( - 5 min) of the isotropic-phase signal corresponding to the passage from the isotropic-lamellar to the nematic-lamellar coexistence regime at T,(I,N,L). Of course, phase separation occurs during the
~
Boden et al.
7686 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 measurement, but this is not a problem because T,(I,N,L) is really a line of points over a concentration range as indicated in Figure 15a. The triple point concentrations of the isotropic, nematic, and lamellar phases are given, respectively, by the abscissae of the isotropic, nematic, and lamellar phase boundary curves at the triple point temperature.
Discussion
350 330
5 310 290
Solvent Isotope Effect at the cmc. For CsPFO solutions, substitution of D20 for H2O results in higher cmc's (Figures 2 and 3). In contrast, for homologousseriesof sodium alkyl sulfates2 and alkyltrimethylammonium bromides3 substitution of D20 for H 2 0 results in lower critical micelle concentrations. To understand the origin of the contrasting isotope effects on micellization of fluorocarbon and hydrocarbon surfactants, we need to consider the equilibrium between surfactant ion monomers S-, counterions Cs+, and monodisperse micelles:
nS- + pes+ = s,,cs,'where z is the charge on the micelle, andp = n - z is the number of counterions associated with the micelle. Neglecting activity coefficients,the free energy of micellization per monomer can be expressed as3
where @ = p / n . For large n, the first term in brackets in eq 9 is often ignored and the free energy of micellization written as AGO RT(1 8) In cmc, where the further simplifying assumption that, at thecmc, [S-]= [Cs+] = cmc has beenapplied. The aggregation number of the perfluorinated micelles in the NaPFO/H20 system at thecmc has been estimated from neutron scattering experiments38 to have a value of 23, while a lower value of 15 has beenestimated fromNMR mea~urements.~~ These values are close to the value of 18 estimated for a classical spherical micelle of PFO- anions.' Ignoring the first term in eq 9 will lead to a small error of up to 3% depending on the value for 8, in the absolute values for the free energy of micellization. Values for @ have been determined from the ratio of the slopes of the K versus x plots (see Figure 2) below and above the c ~ c . ' ~ , Over ' ~ the temperature range 20-90 OC, @ changes from 0.62(3) to 0.51(5) with no significant difference between the values in light and heavy water. For hydrocarbon surfactants, too, there are no significant changes in @ on substituting D2O for H202.3and a decrease in @ with increasing temperature has been observed in alkyltrimethylammonium bromide micellar solutions.54We are thus led to attribute the increase in the cmc of CsPFO solutions on substituting D2O for H20 to a more negative value of AGO in H 2 0 . This result is precisely the opposite of that obtained for hydrocarbon surfactant^.^^^ Now, since neither n nor @ is significantly different at the cmc, it follows that the free energy of the surfactant ion monomer in a micelle is unchanged on substituting D20 for H20. We must, therefore, conclude that the PFO- monomer has a higher free energy in H2O than in D20, while for hydrocarbon surfactant ions the converse is obtained. The difference in the behavior of the hydrocarbon and perfluorocarbon surfactants is attributable to the difference in the interactions of their respective hydrocarbon and perfluorocarbon chains with the solvent. This can be understood by considering the free energy change A p Y associated with the work of creating a cavity in the solvent large enough to accommodate the solute (surfactant) and that A& associated with the attractive Lennard-Jones solute-solvent intermolecular i n t e r a c t i ~ n .On ~ ~substituting D2O for H20 the number density p of solvent molecules decreases which results in a corresponding decrease in A$" (it becomes less positive) and an increase in Apit (becomes less negative). Thus, for hydrocarbon surfactants, the change in must dominate that for A p Y , resulting
+
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E 290
0.0
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0.2
0.3
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@ Figure 16. Comparison of (a) the isotropic-to-nematic transition and (b) the nematic-to-lamellar transition tempertemperatures, TNI, atures, TNL,versus volume fraction 4 of CsPFO for the CsPFO/HzO (open circles) and CsPFO/DzO (closed circles) systems.
in them having a higher free energy and consequently a lower solubility in D20. This behavior is the opposite of that of CH4 and C2H6, which are found to be more soluble in However, similar behavior has been observed for the solubilizationof larger hydrocarbons such as benzene.57 For PFO- we have established that transfer from H2O to D20 results in a decrease in monomer free energy, that is, it is more soluble in D2O. Thus, in this case the change in A $ " must dominate that in A&'. This result is quite in keeping with the larger molecular volumes and consequently larger values of A p T of perfluorocarbon chains. It is also likely that Apt' is less favorable, that is, less negative. (Fluorocarbon-fluorocarbon interactions are weak in comparison to hydrocarbon-hydrocarbon interactions5*suggesting weaker van der Waals chain-water attractions Apt' for perfluorocarbon than for hydrocarbon surfactants.) The lower solubilities of fluorocarbon gases in water59,a and the lower cmc values of perfluorocarbon surfactants61 can be reconciled in the same manner. The observed convergence of the cmc values in water and heavy water with increasing temperature (Figure 3) is in keeping with the decrease in the relative number density pH20/ pDzOs5with increasing temperature. Comparison witb Phase Behavior in Heavy Water. A comparison of the liquid crystal phase transition temperatures TNI and TNLin the water and heavy water systems is given in Figure 16. It is clear from this figure that the effect of substituting H20 for D2O at a fixed volume fraction of amphiphile is to lower both T N Iand TNL:at q5 = 0.15, TNI(D~O) - TNI(H~O)is 3.9 K and TNL(DzO)- TNL(H~O) is 4.3 K;the corresponding values at q5 = 0.25 are 3.2 and 3.5 K. The differences continue to decrease with increasing 4 and eventually disappear at a volume fraction of about 0.41 (T= 80 "C), which is also roughly the volume fraction at the isotropic-nematic-lamellar triple point Tp( I,N,L) in the two systems.lJ0 Since the order-disorder transitions in both the CsPFO and APFO/D20 systems appear to be primarily governed by hard core forces,'4,62 we might anticipate that the shift in the phase transition temperatures arises predominantly from the effect of substituting water for heavy water on the self-assembly behavior. This hypothesiscan be tested by comparing the 133Csquadrupole splittings at corresponding q5. Such splittings are a sensitive function of the micelle aggregation number through the (Pz(cos
The Journal of Physical Chemistry, Vol. 97, NO.29, 1993 7687
Phase Diagram of the (CsPFO)/H20 System
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@ Figure 17. Plot of the 133Csquadrupolesplittings A I measured along (a) and (b) the lamellar-tothe isotropic-to-nematic transition line, TNI, versus volume fraction Q of CsPFO for the nematic transition line, TLN, CsPFO/H20 (open circles) and CsPFO/DzO (closed circles) systems. CY)) term in eq 1. (The small angle X-ray diffraction technique previously used to investigate the self-assembly of CsPFO micelles19is not sufficiently accurate to detect the small changes of aggregation number involved here.) The 133Cs quadrupole splittings at TNIand TLNare shown as a function of volume fraction of surfactant for the water and heavy water systems in Figure 17. The decrease in Ai, at TLNwith increasing 4 (Figure 17b) is predominantly due to decreases in both (P~(cosa))1J9 and 8 6 3 with increasingsurfactant concentration, Le., the order parameter is essentially constant (S = 0.755) at TLN.The coincidence of the AI versus 4 along the N/L curve suggests at least a "corresponding states" kind of behavior, that is, the transition occurs when the micelles attain a given size at a particular 4.14 We can therefore estimate the sizes of the micelles in H20 from those measured previously in D2019by comparing the TLNvalues for the two systems and the rate of change in aggregation number with temperature in the isotropic phase.I9 In DzO at 4 = 0.25 (wm 0.45), for example, the number average aggregation number of the micelles fi at TLN(307.8 K for the w = 0.45 sample) is about 200 and the value of dA/dT in the isotropic phase just above T N Iis -3. Assuming that A has the same value in the 4 = 0.25 water sample at its TLN(m3.5 K below that of the heavy water sample) and that dfi/dT for the water sample is the same as that for the heavy water sample, then at the heavy water TLN the aggregation number for the micelle in water will about 190, i.e., about 5% lower. The 133Cs quadrupole splittings along T N Ido not coincide (Figure 17a), in contrast to the situation along TLN.At all volume fractions, Ai, for the D2O system are greater than those for the H20 system, although they do appear to be converging at high 4 (high temperatures). At this transition, then, there is evidence for an isotope effect on Ai, which corresponds with a greater nematic phase width (AT) for H20 solutions. The difference AT(H20) - AT(D20) is, however, small compared with the shift in the phase transition temperatures. At 4 = 0.15, for example, it has a value of 0.4 K compared with values of 3.9 and 4.3 K for T N I ( D ~-~ T ) ~ l ( H 2 0 )and TLN(&O) - TLN(H~O).The corresponding quantities at 4 = 0.25 are 0.3, 3.2, and 3.5 K, respectively. The major effect of substitution of DzO for H20
at this transition is to increase the size of the micelles, and this is the origin of the shifts in the transition temperatures, as was the caseat the lamellar-to-nematic transition. There is, however, a direct, though small, isotope effect at the nematic-to-isotropic transition. It is not clear to us at the present time why the nematicto-lamellar transition is not similarly affected. The actual shift involved, 0.4 K at 4 = 0.15, is much greater than the width 0.08 K of the biphasic region, Le., TIN- TNI.That is, both of the transition lines are significantly shifted. In summary, at any given volume fraction and temperature, the aggregates are apparently larger in the CsPFO/D20 system. Since the micelle sizes are essentially the same at the transition temperatures, these are greater for the heavy water system. It is this difference in micelle size for a given thermodynamic state of the system that is responsible for the observed isotope effect on the phase transition lines. To identify the origin of the increase in micelle size on substitution of D2O for H20, we have investigated the effects of the concomitant changes in the various properties of water on the self-assembly of discotic micelles within the framework of the model of McMullen et u1.@ The micelle is taken to be an oblate right-circular cylinder (body) closed by a half-torroidal rim. The chemical potential of a surfactant molecule will clearly be different in the "body" than in the "rim". It has been shown that only small discotic micelles can be stable, and this requires that the chemical potential of the surfactant in the rim be only slightly greater than that in the body so that the entropy of mixing suppresses their explosive growth into infinite bilayers. The chemical potential for a surfactant in environment i (body or rim) with head group area (I,can be written $ ( a ) = hi(a) + gi(a)
(10)
where hi(u)represents contributions from interfacial free energy (7.) and electrostatic repulsion (c/u), and gi(u) represents the "bulk" free energy associated with packing of hydrophobic chains in the micelle. The latter depends not only on the head group area u but also on the compressional and splay elasticity of the chains, which is dependent on the thickness and curvature of the surfactant "film". The average chemical potential of a surfactant in an aggregate consisting of n surfactants will, therefore, depend in a complicated way on the number of molecules in the rim with respect to the bcdy so that eq 10 can be written64
= p$ +f(n)CY(n)kT
(1 1)
where the fraction of surfactant molecules in the rimfin) and the difference in their chemical potentials in the rim and the body + ) W a r e both functions of n, and the latter quantity is also a function of the average a0 of the optimum head group areas a!) in the body and rim. The u t ) can, in principle, be calculated by minimizing hi(u) + gi(u) (eq 10) with respect to (I,but since little is known about the actual elasticity effects, a phenomenological approach was adopted and a parameter y (0 I y I2) defined such that a0 = u( 1 y)/l, where D is the volume of the surfactant molecule and I may be thought of as a mean of the lengths of the surfactant molecules (film thickness) in the body and rim. Using the ii: calculated in this way, the micelle size distribution can be obtained from
+
x, = nxy exp[n(py - # ) / k ~ ]
(12)
where x, is the mole fraction of surfactant in nmers, and XI and p! are, respectively, the mole fraction and the chemical potential of the monomers. The isotropic-to-nematic phase transition is determined by the number average micelle size A = C:~,,,x,,/~,",,(x,/n), where m is the minimum micelle size
(-4uP/3v). The input parameters for the model are XI,1, u, y(uo), p!, and y. For the CsPFO/water system, the (eq 11) were calculated using values for u and 1 for the PFO- moiety of 0.364 nm3 and
7688 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 1.1 nm, respectively.5 The isolated monomer chemical potential in H20 was taken to be 15.0kTW and the interfacial tension y set a t 0.025 J m-2, a value which is roughly half of that for the perfluorohexanewater interface (0.0565 J m-2)58as suggested by T a n f ~ r and d ~ ~J6nsson.66 A value for y of 0.42 was chosen to be consistent with a region of discotic micelle stabilityaa4For the purposes of this discussion the actual values chosen are not critical, rather it is the effect that substitution of D20 for H2O will have on py, y, and a&) and the consequences of these changes for the micelle size distribution. This was determined from eq 12 for any given x1and the total surfactant concentration X calculated as xI Cnb,,,xn. Comparisons were made at a constant X of 1 X 10-3. From thecmc results, we concluded that thechemical potential of the monomer p i in D2O is less than its value in H20. To determine the effect that this would have on the micelle size distribution, pp was changed from 15.0kT to 14.9kT and x1 readjusted to give the same total amphiphile concentration X of 1 X 10-3 as described above. The value of x1 increased from 1.25 X 1 W (py = 15.0kT) to 1.38 X 1 W (py = 14.9kT), a result which is consistent with the higher cmc value for the surfactant in heavy water, but ft was unchanged at 142 in each case. Thus, as other workers have also discovered, the precise value for py determines the critical micelle concentration but the distribution is not affected.67~68 To significantly alter the size distribution at a fixed X it is necessary to change the value of a0 (Le., y ) . For example, increasing y from 0.42 to 0.43 results in a higher xl(l.30 X 1 W ) as a result of the increase in p: and, more importantly, a decrease in f , from 142 to 115. Thus, larger micelles are associated with smaller values of a0 and vice versa, Le., a t constant X,a0 for a fluorocarbon surfactant in a micelle in D2O must be smaller than the corresponding value in H20. Changes in a0 will follow from changes in either hi(a),gi(a),or both (eq 10). However, in the present study the origin of the change must lie in changes in h,(a),since there is no reason to suspect any direct changes in the configurational entropy of the fluorocarbon chains on substituting D2O for H20. Thus, while changes in hi(a) will lead to changes in gi(a),the latter will be the “effect” rather than the “cause” of the change. We will, therefore, only consider changes in hi(a) so as to simplify the argument. That is eq 10 is rewritten ji: = ya + c/a g, and a0 0: (c/y)l/2 becomes the value of a which minimizes ji:. To our knowledge, there are no data for the temperature dependence of the interfacial tension for fluorocarbon/water. However, we can expect this to vary similarly to the liquid/vapor surface tension. The surface tension of D2O is about 0.1% lower than that of H2O at 25 “C and falls faster than that for H2O with increasing temperature.69~~0Thus, if change in the interfacial tension were the significant factor in determining the micelle size variation between D2O and H20 we would expect the micelles in H2O to be bigger than those in D2O at any given temperature and concentration and the difference in micelle sizes to increase with increasing temperature. The opposite is actually observed, so we may conclude that the probable very small change in the interfacial tension, on substituting D2O for H20, has a negligible effect on the micelle size. The magnitude of the constant c is determined by the sum of the ionic interaction terms. Considering the electrostatic repulsions between the negatively charged head groups, these will depend on the relative permittivity of the aqueous phase. The relative permittivity t of D2071 is slightly smaller than that of H2072at the same temperature over the temperature range4-100 “C. The difference between the two does, however, decrease with increasing temperature. At 4 OC, t for H20 and D2O are 85.86 and 84.48, respectively, while at 80 OC, the values are 60.70 and 60.56. The lower t for D2O means stronger head group repulsions, Le., a larger value for c, and hence smaller micelles in D2O than in H20, a prediction at odds with observation. Thus, py
+
+
Boden et al. the observed behavior cannot be accounted for in terms of the changes in either y or e. The electrostatic repulsion between neighboring C02- head groups will, however, be modulated by the binding of counterions to the micelle surface, and it is this effect which we next exDlore. The 133Cs chemical shift measurements have established that the counterion is a fully hydrated Cs+ ion which binds to the micelle surface, and thus it is plausible that at least one of the water molecules in the hydration sphere of the Cs+ cation forms a hydrogen bond to a C02Now, at corresponding temperatures, D20 in heavy water forms intrinsically stronger hydrogen bonds than H20,36 as a consequence of the isotope effect on the zero-point vibration energies. Similar isotope effects can be expected to affect the binding of the Cs+ cation to the C02- anion via its effect on the bridging water molecule. Substitution of DzO for H20 will result in a stronger hydrogen bond, a shorter Cs+-C02- distance, and consequently, a more effective screening by the Cs+of the electrostatic repulsion between neighboring C02- headgroups. This will lead to a decrease in c and, consequently, ao, which will result in a larger micelle in D2O. Though the effects may be small, they are detectable. In contrast, the size of the micelle decreases appreciably as the temperature is raised and this behavior may be similarly accounted for in terms of bonding through a bridging water molecule. On raising the temperature, the hydrogen bond will weaken, that is, the Cs+-C02- distance will increase and the screening of the repulsive force will be reduced. Thus, c and consequently a0 will increase resulting in a smaller micelle. Of course, the values of both y and e will also decrease and contribute to the increase in ao. While we are unable to separate the various contributions at the present time, the effects of temperatureon counterion binding does provide a unique interpretation of both the isotope effect and the temperature dependence of the micelle size. The decrease in the bound-ion fraction with increasing temperature observed in both the C~PFO/water6~ and APFO/ water5 systems is best considered as an effect of, rather than the cause of, the decrease in micelle size with increasing temperature. Ion binding is brought about by ion condensation which, in turn, is determined by surface charge d e n ~ i t y . ~ So 3 . ~on~both accounts we can expect ion condensation to be greater on the body than on the rim of the micelle. It will be demonstrated in the next section that this is indeed the case. The value of the parameter c will, therefore, in reality, be greater for molecules in the rim than in the body of the micelle. Within the model, this difference is accommodated in the same way as the differences in the bend and splay free energies of the chains. In summary,the stability of the discotic micelles in the CsPFO/ water system would seem to stem from the elastic properties (chain rigidity) of the perfluorocarbon chains, which govern the inhomogeneity of the surface curvature 0, parameter), on the one hand, and the binding of the Cs+ counterions to the surface (a0 parameter), on the other. I3WsQuadrupole Splittings. It has previously been shown for the APFO/D20 system5 that the temperature dependence of the 2H quadrupole splittings of heavy water can be ascribed to changes in just S and (&(cos a ) )with ~ temperature. That this is the case for the CsPFO/D20 system, too, is shown by the excellent agreement between the reduced 2H quadrupole splittings and the reduced S(P2(cos a)) S values63for a CsPFO/D20 ( w = 0.508) sample demonstrated in Figure 18a. The agreement is excellent, not only through the nematic phase but deep into the lamellar phase as well. Thus, as for the APFO/D20 system, water molecules appear to be uniformly distributed over the micelle surface and the interaction of the water molecules with the surface is not substantially altered by changes in the fraction of bound counterions.
Phase Diagram of the (CsPFO)/HzO System
,
4.0
The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 7689
TABLE II: Quadrupole Splittings and Structural Parameters along the Lamellar-to-Nematic Transition Line for the
I
(a)
CsPFO/D20 System A?/kHz
3.0
0.55 325.10 0.50 315.63 0.45 307.80 0.40 300.70 0.35 294.63 0.30 289.00
2.0
in
1.o
3.0
2.0
0.0448 0.0366 0.0300 0.0244 0.0197 0.0157
0.33 0.28 0.26 0.25 0.24 0.23
0.612 0.688 0.710 0.723 0.731 0.752
0.47 0.44 0.45 0.45 0.48 0.50
4.0
(ScP2(cosa)>s)~(ScP2(cosa)> ) S Tm
-4
6.0,
,
,
,
,
,
,
,
0.700 0.595 0.511 0.430 0.362 0.300
4.920 5.470 6.170 6.800 7.550 8.200
/ J
1
0.8
5.0
4.0 0.6
3.0 2.0 1.o
0.4
1.o
2.0 3.0 4.0 5.0 IS~P2(cosa)>sP)~(Ssp)TNI
FigureJ8. Plots of reduced 2H (a) and 133Cs(b) quadrupole splittings A Y T / A Y Tagainst ~, the reduced quantities (S(P2(cos a))~)~/(S(P2(cos ~))s)T,,,and (S(P2(cos a))sfl)~/(S(P2(cos ~))sL?)T,.,,, respectively, for a CsPFO/D20 (w = 0.508) sample. The 2Hand laaCsquadrupole splittings at TNI(321.93 K) are 192 and 1600 Hz, respectively. The re and phase transition temperatures TIN,TNL,and T ~ ~ a322.26,316.59, 316.40 K, respectively. In each case the straight line has a slope of 1 and
1.6
1.4
an intercept of 0 appropriate to a uniform distribution of binding sites. The increasingly positive deviation of the reduced Ia3Csvalues with decreasing temperature(c.f. the reduced 2H values) is due to preferential binding of Cs+ ions to sites with low surface curvature. Similarly, we obtain from eqs 1 and 3 A3,/A?TNI = (S(P,(COS 4)SP)T/(S(P2(COS
.))Sb)TNI
(13) and we may use values for j3 obtained from X-ray and conductivity measurement^^^ to test the model for the 133Csquadrupole splittings. Reduced 133Csquadrupole splittings are plotted against reduced S(P2(cos a))sj3values (Le., the right- and left-hand sides of eq 13) for the CsPFO/D20 ( w = 0.508) sample in Figure 18b. Here, there is good agreement between the two quantities in the nematic phase, but a positive departure from the behavior predicted assuming a uniform distribution of binding sites is revealed in the lamellar phase. This positive deviation is consistent with Cs+ ions being preferentially adsorbed on the “planar” caps rather than the “curved” rims of the micelles, Le., on sites with a smaller radius of curvature and consequently having the higher charge densities.5 This would result in an effective increase in (Pz(cos a))S with decreasing temperature, i.e., with an increase in micelle size. A similar situation is obtained along the nematic-to-lamellar transition line where the orientational order parameter is expected to be constant at - 0 . 7 5 . 5 ~ ~The variations in the 2H and 133Cs quadrupole splittings will be a consequence of changes in (&(cos ~ ) ) S X A / X D (XA and XD are the mole fractions of amphiphile and D20,respectively)’ and (Pz(c0s a))&, respectively. Values for 2H and I33Cs quadrupole splittings at TLN,together with the corresponding values of (&(cos a))s,IJ9XA/XD, and $3 are given in Table 11. For the 2H quadrupole splittings at TLNwe may
1.2
1.o 1.o
1.2
1.4
1.6
1.8
(cPz(cosa)>sP)d(cP2(cosa)>s~)~.~5 Figure 19. Plots of (a) eq 14 and (b) eq 15. In each case the straight line has a slope of 1 and an intercept of 0 appropriate to a uniform
distribution of Cs+ binding sites. The positive departure from eq 15 is due to preferential bindingof Cs+ions to sites with low surfacecurvature. write A?w/A?o.55 = {(P2(COS.))S(X*/~D)~w/~(p2(cos.>)S(X*IXD))0.55 (14) while for the 133Cssplittings the corresponding expression is A3w/A30.55
= {(P2(c0s a))Ssk/{(p~(cOs
)Sfl)0.55
( l5,
For uniform distribution of binding sites, plots of the quantity on left-hand side against the quantity on right-hand side of both eqs 14 and 15 should give straight lines with a slope of 1. Such plots constructed from the data in Table 11, are shown in Figure 19. For the 2Hsplittings (Figure 19a) the assertion of uniform binding sites is once again upheld. The strong positive deviation (Figure 19b) in the case of the I 3 T s splittings is once again consistent with an inhomogeneous distribution of sites and a preference for those with a smaller radius of curvature. Precisely the same results are obtained when the corresponding data are compared along the nematic-to-isotropic transition line. Thus, 133Csquadrupole splittings, in contrast to the 2H ones, cannot be used to probe changes in micelle size and orientational ordering of micelles. There are, however, certain advantages for mapping phase behavior.lO
Conclusions The effect of substituting H20 for D2O on the phase diagram for the CsPFO/water system has been studied. The most significant findings can be summarized as follows:
7690 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 1. The phase diagram of the CsPFO/H20 system is qualitatively similar to that for the CsPFO/D20 system.' There are, however, quantitative differences. Substituting HzO for DzO at a fixed volume fraction of surfactant lowers both TNIand TLN. At 4 = 0.15, TNI(D~O) - T ~ l ( H z 0 )is 3.9 K and T L N ( & ~-) TLN(HzO)is 4.3 K. The differencesdecrease with increasing 4 (temperature) and eventually vanish at 4 = 0.41 (80 "C)when thermal effects dominate any isotope effects. 2. The increase of the transition temperatures on substituting DzO for H20 is attributed to concomitant changes in micelle size. Since the micelle sizes must be essentially the same at TNI( TLN)at corresponding concentrations and they are also known todecreaseas the temperatureis raised, it followsthat the micelles must be larger in DzO than in H20 at corresponding concentrations and temperatures below 80 "C. 3. This "isotope effect" on micelle size is attributed to the "tighter binding" of Cs+ to the surface carboxylate groups via bridging water molecules in the case of D20. 4. The cmc's occur to higher concentrations in D20. This is because the PFO- monomers have a higher free energy in H20 than in D2O. This is contrary to the behavior of hydrocarbon surfactants which have higher cmc's in HzO.
Acknowledgment. We wish to thank the Science and Engineering Research Council (UK) for project grants to N.B. and for a visiting fellowship to K.W.J. We also thank the University Grants Committee (NZ) for an equipment grant to K.W.J. and a studentship to M.H.S. The Royal Society of London and the British Council (NZ) are also thanked for travel grants to, respectively, N.B. and K.W.J. We also acknowledge helpful discussions with Dr. G. R. Hedwig, Massey University, about isotope effects of heavy water. References and Notes (1) Boden, N.; Corne, S.A,; Jolley, K. W. J . Phys. Chem. 1987,91,4092. (2) Chang, J. N.; Kaler, E. W. J. Phys. Chem. 1985,89, 2996. (3) Berr, S.S.J . Phys. Chem. 1987, 91, 4760. (4) Boden, N.; Jackson, P. H.; McMullen, K.; Holmes, M. C. Chem. Phvs. Lett. 1979. 65. 476. ' (5) Boden, N.;Clements, J.; Jolley, K. W.; Parker, D.; Smith, M. H. J. Chem. Phys. 1990,93,9096. (6) Ekwall, P. In Advances in Liquid Crystals; Brown, G. H., Ed.; Academic: New York. 1975;Vol. 1, DD 1-142. (7) Luzzati, V. In Biological Membranes; Chapman, D., Ed.; Academic: London and New York, 1986; Vol. 1, p 71. (8) Boden, N.; Radley, K.; Holmes, M. C. Mol. Phys. 1981, 42, 493. (9) Boden, N.; Corne, S.A,; Holmes, M. C.; Jackson, P. H.; Parker, D.; Jolley, K. W. J. Phys. 1986, 47, 2135. (10) Boden, N.; Jolley, K. W.; Smith, M. H. Liq. Cryst. 1989, 6, 481. (1 1) Reizlein, K.; Hoffmann, H. Prog. Colloid Polym. Sci. 1984,69,83. (12) Everiss, E.; Tiddy, G. J. T.; Wheeler, B. A. J. Chem. SOC.,Faraday Trans. I 1976, 72, 1747. (13) Fontell, K.; Lindman, B. J. Phys. Chem. 1983, 87, 3289. (14) Taylor, M. P.; Herzfeld, J. Phys. Rev. A 1991, 43, 1892. (15) Boden, N.; Holmes, M. C. Chem. Phys. Lett. 1984, 109,76. (16) Boden, N.; McMullen, K.; Holmes, M. C. In Magneric Resonances in Colloid and Interface Science; Fraissard, J. P., Resing, H. A., Eds.; Reidel: Dortrecht, 1980; pp 667673. (17) Boden, N.; Come, S. A.; Jolley, K. W. Chem. Phys. Lett. 1984,105, 99. (18) Boden,N.;Bushby,R. J.; Jolley, K.W.;Holmes,M.C.;Sixl, F. Mol. cryst. uq.cryst. 1987, 152, 37. (19) Holmes, M. C.; Reynolds, D. J.; Boden, N. J . Phys. Chem. 1987.91, 5257. (20) Jolley, K.W.;Smith, M. H.; Boden, N. Chem. Phys. Lett. 1989,162, 152.
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