Lyotropic Mesomorphism of the Cesium Pentadecafluorooctanoate

evidence of chain branching, and a DSC thermogram indicated a high state of ..... signature of each kind of phase and is also a function of com- posit...
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J . Phys. Chem. 1987, 91, 4092-4105

Lyotropic Mesomorphism of the Cesium Pentadecafluorooctanoate/Water System: High-Resolution Phase Dlagram Neville Boden,* Simon A. Corne, and Kenneth W. Jolleyt Department of Physical Chemistry, University of Leeds, Leeds LS2 9JT, England (Received: November 19, 1986)

A high-resolution phase diagram for the cesium pentadecafluorooctanoate (CsPFO)/heavy water system has been determined. A variety of techniques have been used including 'H NMR spectroscopy, DSC, polarizing microscopy, and electrical conductivity.

The NMR method is the main technique, and the results obtained provide a model illustration of its utility for mapping phase diagrams and investigating mesophase transitions. The most interesting feature is the Occurrence of a micellar nematic phase of the type ND+over an unprecedented range of concentrations (0.225-0.632 weight fraction of CsPFO) and temperatures (285.29-35 1.23 K). This phase is intermediate to a micellar lamellar phase L D at lower temperatures/higher concentrations of CsPFO and an isotropic micellar solution phase I at higher temperatures/lower concentrationsof CsPFO. The 2H quadrupole splittings measured for 2H20in both the nematic and lamellar phases are shown to be consistent with a model which assumes the micelles are oblate ellipsoids. The nematic to isotropic transition is weakly first order. The temperature interval TIN-TNI between the upper and lower boundaries to the transition decreases markedly as the concentration decreases. For concentrations with weight fractions less than 0.35, TIN-TNIis proportional to weight fraction of CsPFO; that is, the transition becomes second order at infinite dilution! Values for the nematic order parameter along the nematic to isotropic transition line have been estimated and found to decrease with decreasing concentration of CsPFO, a result inconsistent with the predictions of the Maier-Saupe mean field theory. In contrast to the nematic to isotropic transition, the lamellar to nematic transition changes from first to second order on dilution at a finite concentration which is identified with a tricritical point Tcp (320.50 K, W A = 0.53).

I. Introduction The conventional water-soluble lyotropic amphiphilic mesogens such as the soaps and synthetic surfactants exhibit characteristic phase behavior. They form micelles] in dilute solutions and liquid crystals in more concentrated one^.^-^ Critical micelle concentrations (cmc) are typically to lo-' mol dm-3, while critical liquid crystal concentrations (clc) vary from 0.5 mol dm-3 upward. In micellar solutions, the amphiphilic aggregates are notionally either small spheres or prolate/oblate ellipsoids, while in the liquid crystals they are generally considered to be infinite in extent (e.g., infinitely long cylinders in hexagonal phases or infinitely extending bimolecular layers in lamellar phases). This discontinuity in the structure of the aggregates, together with the quite different physical properties of the two kinds of solution, has meant that studies of micellar solutions, on the one hand, and liquid crystals, on the other, have tended to evolve separately. However, the relatively recent discovery5 of nematic micellar solutions would seem to provide the necessary catalyst for the unification of these two endeavors. Nematic micellar solutions occur intermediate to isotropic micellar solutions and smectic phases (hexagonal or lamellar).6 They have been shown to be aqueous solutions of orientationally ordered discoid (ND) or columnar (N,) micelle^.^-'^ The existing tenet is that these mesophases only occur overy very restricted concentration and temperature intervals in complex mixtures of an ionic surfactant, water, a long-chain alcohol, and/or a simple inorganic salt."~11~'2 The alcohol or salt is considered to be essential in order to stabilize the nematic phase. In particular, it has been purported that their role is to stabilize small discrete micelles (the axial ratio is typically in the range 2-4 for columnar and 0.25-0.5 for discoid micelles) against "explosive" growth into infinite cylinders (hexagonal phases) or bilayers (lamellar phases). l 3 . I 4 But is has now been demonstrated that neither salt nor alcohol is essential. Nematic phases, stable over extensive concentration and temperature intervals (ca. 0.1-0.5 volume fraction of amphiphile and below 370 K), can be obtained in simple two-component systems of both ionic and nonionic amphiphiles.15-'8 Thus, the effect of the salt or alcohol is simply to modify the smectic phase behavior in such a manner as to bring the smectic to isotropic transition line into the temperature-composition domain where 'On leave from: Department of Chemistry, Biochemistry and Biophysics. Massey University, Palmerston North, New Zealand.

nematic phases are stable. Thus, to optimize nematic phases it is necessary, first, to bring the smectic to isotropic transition line into the above temperature-composition domain and, second, to control the generally complex phase behavior of conventional amphiphilic me~ogens.'~ The latter can be achieved by designing amphiphiles which exclusively form aggregates of a particular structure. Thus, to optimize the stability of Nc phases amphiphiles are required which can only assemble into columnar aggregates. Ideally, a discoid amphiphilic molecule is required. An example of such a mesogen is 2,3,6,7,10,1 I-hexakis( 1,4,7-trioxaoctyl)triphenylene (TP6E02M).I5-l7 This forms an Nc- phase (the superscript minus denotes that the mesophase has negative diamagnetic anisotropy) over the concentration interval 0.14-0.5 l weight fraction of TP6E02M and between 274.8 and 296.9 K. Similarly, ND phases are optimized by choosing amphiphiles which can only form discoid or bilayer aggregates. The amphiphilic mesogen cesium pentadecafluorooctanoate (CsPFO) satisfies these requirements. The CsPFO/water (2H20)system has been shown18 to exhibit an ND' phase over wide concentration (0.225-0.632 weight fraction of CsPFO) and temperature (285.29-351.23 K) (1) Lindman, B.; Wennerstrom, H. In Toprcs in Currenr Chemistry; Springer-Verlag: Berlin, 1980; Vol. 87, pp 1-84. (2) Ekwall, P. In Aduances in Liquid Crystals; Brown, G . H., Ed.; Academic: New York, 1975; Vol. 1, pp 1-142. (3) Tiddy, G. J. T. Phys. Rep. 1980, 57, 1-46. (4) Pershan, P. S. Phys. Today 1982, 35, 34-39. (5) Lawson, K. D.; Flautt, T. J. J. Am. Chem. SOC.1967,89, 5489. Black, P. J.; Lawson, K. D.; Flautt, T. J. Mol. Cryst. Liq. Cryst. 1969, 7 , 201. (6) Boden, N.; Radley, K.; Holmes, M. C. Mol. Phys. 1981, 42, 493. (7) Charvolin, J.; Levelut, A. M.; Samulski, E. T. J . Phys. Lett. 1979, 40, L-587. (8) Hendrikx, Y.; Charvolin, J.; Rawiso, M.; Liebert, L.; Holmes, M. C. J . Phys. Chem. 1983,87, 3991. (9) Holmes, M. C.; Charvolin, J. J . Phys. Chem. 1984, 88, 810. (10) Boden, N.; Holmes, M. C. Chem. Phys. Let[. 1984, 109, 76 ( 1 1) Forrest, B. J.; Reeves, L. W. Chem. Phys. 1981, 81, 1. (12) Saupe, A. Nuovo Cimento SOC.Ital. Fis., D 1984, 3, 16. (13) Gelbart, W. M.; McMullen, W. E.; Masters, A,; Ben-Shaul, A. Langmurr 1985, I , 101. (14) Gelbart, W. M.; McMullen, W. E.; Ben-Shaul, A. J. Phys (Les Ulis., Fr.) 1985. 46. 1137. (15) Boden, N.; Bushby, R. J.; Ferris, L.; Hardy, C.; Sixl, F. Liq. Cryst. 1986. 1. 109. (16)~Boden,N.; Bushby, R. J.; Hardy, C. J . Phys. Letr. 1985, 46, L-325. (17) Boden, N.; Bushby, R. J.; Hardy, C.; Sixl, F. Chem. Phys. Lett. 1986, 123, 359. (18) Boden, N.; Jackson, P. H.: McMullen, K.: Holmes, M.C.Chem. Phys. Lett. 1979, 65, 416. I

.

0 1987 American Chemical Society

Lyotropic Mesomorphism of the CsPFO/Water System ranges. This is found between an isotropic micellar solution to higher temperatures and a lamellar phase to lower temperatures. Only aggregates with a bilayer structure are formed over the entire concentration range. This is a consequence of the rigidity and hydrophobicity of the fluorocarbon chain which, in combination with the low hydration energy of the cesium ion, promote the stability of bilayer aggregates as opposed to cylindrical ones. Very recently, a novel rod-shaped nonionic mesogen has been shown to form an ND+ phase over the range of weight fractions of 0.32-0.40. The CsPFO/water system is, arguably, the most attractive ND mesophase currently available for experimental study. There are four principal reasons for this. Firstly, fluorinated amphiphiles are more stable, both thermally and chemically, than their hydrocarbon counterparts. Secondly, it is a simple two-component sytem. Thirdly, the nematic phase is stable over an unprecedented range of concentrations and temperatures. Fourthly, the nematic phase is diamagnetically positive (ND'), which means that macroscopically aligned samples of nematic and lamellar phases can quite simply be obtained by cooling from the isotropic/nematic phase in a magnetic field with strength in excess of approximately 0.2 T. For mainly these reasons, this system has begun to attract the attention of liquid crsytal scientists.'0s20-28 Recently, it has been shown2*that the fundamental mesogenic aggregates are discrete discoid micelles in all of the three phases. Significantly, the lamellar phase consists of planar arrays of discoid micelles, not the classical infinite bimolecular layers. The nematic to lamellar transition is, therefore, quite analogous to the thermotropic nematic to smectic A transition. The transition has been shown to change from a first- to a second-order one at a tricritical point which occurs at a weight fraction of roughly 0.5.18 This behavior has been modeled by using molecular field theory.IO Clearly, this is an interesting transition, but it has k e n little studied to date. The only reported study thus far is one which has shown that where the transition is second order the rotational viscosity coefficient XI of the nematic phase diverges on approaching the smectic A like lamellar phase. The isotropic to nematic transition has been far more extensively s t ~ d i e d . ~ ~In- ~particular, ' studies of the pretransitional behavior have shown that TIN-T* (TINis the temperature corresponding to the onset of phase separation, and T* is the supercooling limit of the isotropic phase) decreases with decreasing amphiphile concentration and becomes of the order of 20 mK at a weight fraction of CsPFO of 0.30.23,26This is much smaller than is usually observed for thermotropic liquid crystals, indicating the transition is much weaker. In contrast to thermotropics, the mesogenic particles, that is, the micelles, are relatively loosely packed. This has implications for many of the properties of the nematic phase. For example, it has recently been demonstrated that the individual orientational fluctuations of the micelles are essentially decoupled from the collective director fluctuations.28 For a solution with weight fraction 0.55, the nematic order parameter is 0.35 at TNIand 0.72 at TNLand the respectively contributions from director fluctuations have been estimated as 29% and 8%. This large contribution close to the nematic to isotropic transition is quite consistent with the unusually soft elastic forces of these systems.2s The variation of the nematic order parameter with temperature has been shown to be far stronger than that which is characteristic of thermotropic nematics; this is a consequence of a growth of the diameter of the micelles on cooling.2s Indeed, many of the physical properties are de(19) Luhamm, B.; Finkelmann, H. Colloid Polym. Sei. 1986, 264, 189. (20) Boden, N.; McMullen, K.; Holmes, M. C. In Magnetic Resonance in Colloid and Interface Science; Fraissard, J. P., Resing, H. A,, Eds.; Reidel: Dordrecht, 1980; pp 667-673. (21) Boden, N.; Corne, S . A,; Jolley, K. W. Chem. Phys. Lett. 1984, 105, 99.

(22) (23) (24) (25) (26) (27)

Larson, B. D.; Litster, J . D. Mol. Cryst. Liq. Cryst. 1984, 113, 13. Rosenblatt, C.; Kumar, S.;Litster, J. D. Phys. Reu. A 1984, 29, 1010. Holmes, M. C.; Boden, N. Mol. Cryst. Liq. Cryst. 1985, 124, 1 3 1 . Rosenblatt, C. Phys. Rev. A 1985, 32, 1 1 15. Rosenblatt, C. Phys. Reu. A 1985, 32, 1924. Rosenblatt, C. J . Phys. Lett. 1985, 46, L-1191. (28) Boden, N.; Corne, S. A,; Holmes, M. C.; Jackson, P. H.; Parker, D.; Jolley, K. W. J . Phys. (Les Ulis, Fr.) 1986, 47, 2135.

The Journal of Physical Chemistry, Vol. 91, No. 15, 1987

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pendent upon the size of the micelles. This exhibits a complex variation with concentration. The diameter, after initially increasing with concentration, passes through a maximum at ca. 0.45 weight fraction of CsPFO and then decreases.29 The CsPFO/water mesophases are undoubtedly rich in phenomena for investigation. For this purpose, and also because of its intrinsic information content, a precise "high-resolution" phase diagram is required. The only one currently available is restricted to the ND phase, and its immediate surroundings, and its precision is also somewhat limited.18 In this paper we describe the determination of a precise, high-resolution phase diagram. N M R spectroscopy, polarizing microscopy, DSC, and electrical conductivity measurements are all used. N M R measurements of the quadrupole splitting of deuterium in labeled water is the technique which is mainly used and is described in some detail. The results obtained for the CsPFO/water system provide a beautiful illustration of the utility of this method for studying phase behavior of lyotropic amphiphilic mesophases. An important feature of our experiments is the careful control of the temperature and composition of the sample. 11. Experimental Methods Materials. Pentadecafluorooctanoic acid (Pure) was obtained from Fluorochem. Ltd., England, and was used without further purification. The I9F N M R spectrum of the acid showed no evidence of chain branching, and a DSC thermogram indicated a high state of purity (>99%). CsPFO was prepared by dissolving the acid in water and titrating with an aqueous solution of cesium hydroxide to a pH of 7.0. The salt solution was evaporated to dryness in an oven and recrystallized twice from a 5050 (v/v) solution of n-hexane and 1-butanol. The crystals so obtained were white and glossy, indicative of a high state of purity. A check on the purity by DSC was not possible since the crystalline salt decomposed at 495 K. The 'H N M R spectrum in CDCI, confirmed that all of the solvent had been removed. Nuclear magnetic resonance samples were prepared by weighing the salt and the 2H20(Sigma U.S.A., 99.8 atom% *H) directly into 5-mm-0.d. N M R tubes which were then flame-sealed. Since any CsPFO in the vicinity of the flame would undergo decompositon, the salt was introduced into the N M R tube through a glass funnel which extended to within roughly 10 mm of the base of the tube. The 2H20was introduced by means of a hypodermic syringe fitted with a long 22 gauge needle. At low amphiphile concentrations, homogeneous solutions were obtained simply by heating the samples into the isotropic micellar phase and shaking. For amphiphile concentrations greater than weight fractions of 0.6, the samples were mixed by centrifugation and thermostating at temperatures above the liquid crystal-isotropic transition temperature. This process was continued until the sample appeared to be homogeneous as viewed by the naked eye and between crossed polarizers. Samples for optical microscopy, DSC, and electrical conductivity measurements were similarly prepared in ampules. The ampules were opened immediately prior to use, and precautions were taken to minimize concentration changes by evaporation in the transfer of samples to the measuring apparatus. Microscopy. A Vickers M17 polarizing microscope (York, England) with a home-built hot stage replacing the standard specimen stage was used. Polarizer and analyzer were inclined at angles of 45' to the direction of a static magnetic field of 0.48 T provided by a small electromagnet (Oxford Instruments, England) with pole diameter 2.5 cm and gap 1.5 cm. Samples were studied in rectangular optical capillaries with an optical path length of 200 wm (CAM LAB, Cambridge, England), unless otherwise stated. N M R Spectroscopy. Deuterium spectra of 2 H 2 0were measured with a Brucker HFX-90 spectrometer operating at 13.82 MHz in the pulse Fourier transform mode. The conditions of (29) Holmes, M. C.; Reynolds, D. J.; Boden, N. Mol. Cryst. Liq. Cryst., in press; J . Phys. Chem., in press.

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The Journal of Physical Chemistry, Vol. 91, No. 15, 1987

TABLE I: Uncertainties in Phase Transition Temperatures

RWIA

03

2CO 100

50

30 20

Boden et al.

10

5

0

w A range 0.0-0.30 0.0-0.30 0.30-0.65 0.30-0.53 0.53-0.65 0.65-1.00 0.65-1.00

42 0 4 00

transition I-I/K, I-N'J I/K-HI/K' I-N, I-L" N-La N-La

io.10

f0.04 il.0 f0.S

I-L-HI/K' I-Ld

" NMR. Electrical conductivity. e

error in tempe f0.04 fl.O f0.04

DSC. dPolarizing microscopy.

In kelvin. WIA

120100 80 7 0 60

I

0

0.5

1

1

I

I

1.0

flA

Figure 1. Phase diagram for the CSPFO/~H~O system. Nomenclature: K, crystal; L,, lamellar phase; NDt, nematic phase with positive dia-

magnetic anisotropy and discoid micelles; I, isotropic micellar solution; HI, heavy ice; Tcp, the lamellar-nematic tricritical point; Tp(I,N,L), the isotropic micellar solution-nematic-lamellar triple point; Tp*(N,L,K), the apparent nematic-lamellar-crystal "triple" point; Tp(I,N,K), the isotropic micellar solution-nematic-crystal triple point; Tp(HI,I,K), the heavy ice-isotropic micellar solution-xystal triple point; Kp, the Krafft point; T,, the solubility curve for CsPFO.

280

2 70

, I--*-*-

15

.-.

.20

~

25

30

4

35

WA

Figure 2. Expanded portion of the phase diagram showing the triple points Tp(I,N,K) and Tp*(N,L,K) and supercooling of the isotropic

micellar solution phase below the T, curve. measurement were determined by the concentration of 'H20 in the sample. Typically, for samples with a weight fraction of 2 H t 0 of 0.7, some 10 signals were averaged at a repetition rate of 2.5 , for a H z into 8K of storage with a dwell time of 50 ~ swhile sample with a weight fraction of 0.4, 100 signals were averaged at a repetition rate of 2.5 H z into 2K of storage. To provide precise control and homogeneity of the temperature of the sample, sample tubes were mounted inside the cryostat shown in Figure S1 (supplementary material). This was constructed from a standard 10-mm-0.d. N M R tube and is readily loaded into a standard N M R probe. The temperature of the sample was controlled to within k0.005 K by water pumped from a cryostat (Colora WK 3, West Germany) and was measured to the same precision and accuracy by using a copper-constantan thermocouple calibrated at the Standards Laboratory, Harwell, England. Sample rotation was provided by connecting the sample tube, via a watertight bearing, to a stepping motor driven by the spectrometer computer. Electrical Conductivity. Electrical conductivity measurements were made using an apparatus designed to determine the conductivities of macroscopically aligned liquid crystalline mesophases and which has been described elsewhere." The simple conductivity measurements employed to define the solubility curve in dilute solutions do not require this level of sophistication and any commercially available conductivity meter could be used, but proper control of sample temperature is essential. Differential Scanning Calorimetry (DSC). DSC thermograms were recorded on a DuPont 900 instrument. Samples were weighed into aluminum pans which were then sealed by the normal lid-crimping procedure. Supercooling below the solubility curve occurs readily in the CsPFO/*H20 system, and so the thermograms were always obtained by heating the sample. The thermograms were always found to be reproducible over several days. 111. Results

Phase Diagram. This is given in Figure 1. The ordinate gives the temperature and the abscissa the concentration. The latter is given as the weight fraction of amphiphile (CsPFO) W , on the lower axis and as the mole ratio of water ('H20) to amphiphile (CsPFO) R W , A on the upper axis. The concentrations are con-

sidered to be accurate to within 0.1%; the absolute errors in the temperatures of the phase boundaries are summarized in Table I. Table I1 gives the coordinates for the various fixed points. The diagram is unusually simple when compared with those of other amphiphile/water mixture^^,^ and shows a number of unique and interesting features. There are only three homogeneous single-phase regions, apart from the pure compounds. These are the isotropic micellar solution phase I (simple molecular solution of amphiphile in water for concentrations less than the cmc), the nematic phase ND', and lamellar phase LD. All of the other areas are two-phase regions in which the system separates into two phases with compositions given by the intersection of horizontal lines (tie lines) with the phase boundary curves and with proportions given by the lever rule.30 The crystalline CsPFO (K) and heavy ice (HI) are completely immiscible, and there is a triple point (eutectic point) Tp(HI,I,K). The curve labeled T, is the solubility curve for the crystalline amphiphile. The solubility curve meets the cmc line at the Krafft point (Kp). At higher concentrations, first nematic and then lamellar mesophases are formed. The lamellar phase is unusual for a simple ionic amphiphile in that it occurs over an unusually wide interval of concentrations. The nematic phase is intermediate to the isotropic micellar solution phase and lamellar phase. This is also stable over an extensive concentration interval (wA = 0.225-0.632). This is, to our knowledge, far greater than for any other amphiphile/water system known to date. The separation of the upper ( T I N and ) lower ( TNI)boundaries to the nematic to isotropic transition is seen to decrease with decreasing concentration of CsPFO. For example, it decreases from 350 mK at W , = 0.5 to 60 mK a t wA = 0.15 where the nematic phase is metastable with respect to the isotropic micellar solution crystalline CsPFO (Figure 2). In fact, solutions with concentrations less than that of Tp(I,N,K) are readily supercooled below the solubility curve and undergo reversible isotropic to nematic and nematic to lamellar transitions. This supercooling phenomenon will be discussed later. Returning to the nematic

+

(30) Oonk, H. A. J. Phase Theory: The Thermodynamics of Heferogeneous Equilibra; Elsevier: Amsterdam, 1981.

The Journal of Physical Chemistry, Vol. 91, No. 15, I987 4095

Lyotropic Mesomorphism of the CsPFO/ Water System

TABLE lk Tempentpres and Compositions of Fixed Points on tbe Wise Diagram (Figure 1) TIK

WA ~~

Tp(I,N,L) isotropic nematic lamellar Tp( I ,N ,K) isotropic nematic Tp(H 1.W) isotropic Tp*(N,L,K) nematic = lamellar TCP KP TI (heavy ice)

QA

XA

cA/mol dm'3

~

351.23 (4) 0.626 0.632 0.648

0.0578 0.0592 0.0632

0.425 0.43 1 0.448

1.946 1.975 2.054

0.22 1 0.225

0.0103 0.0105

0.1 11 0.1 14

0.510 0.520

0.01 1

0.000407

0.00489

0.0224

0.287 0.530 0.012

0.0145 0.0397 o.Ooo445

0.151 0.332 0.00533

0.69 1 1.522 0.0244

285.29 (4)

275.8 (2) 285.72 (4) 320.50 (4) 280.0 (1) 276.95

Figure 3. Photomicrograph showing the sequence of textures observed in a thin film of CsPFO in water with concentration decreasing from left to right (magnification X100). The concentration gradient was established by allowing water to penetrate into an array of crystals placed on a glass slide and covered with a cover slip. Nomenclature: K, crystal; LD,lamellar phase; ND nematic phase; I, isotropic micellar solution phase.

to isotropic transition, it is clear that this transition remains first order but weakens significantlyas the concentration is lowered. In contrast, the separation of the upper (TNL) and lower (TLN) boundares of the lamellar to nematic transition decreases rapidly with decreasing amphiphile concentration and vanishes for concentrations less than wA = 0.53. That is, the transition changes from first to second order at this concentration which corresponds to a tricritical point T~p.3'3~ The line of second-order transitions is represented by a broken line. Cesium pentadecafluorooctanoateundergoes thermal decomposition at 495 K,and this imposes an upper temperature limit to the accessible phase behavior. Microscopy. The micrographic textures of thin films of solution observed under the polarizing microscope can be used for the identification of the mesophase. The photomicrograph in Figure 3 show the sequences of phases obtained at room temperature for a film with a concentration gradient established by allowing water to penetrate into an array of crystals placed on a glass slide and covered with a cover slip. A nematic phase is seen to occur between an isotropic micellar solution phase and a lamellar phase. The nematic phase is identifiable by its mobility and Schlieren texture and the lamellar phase by its mosaic texture. A welldefined nematicisotropic biphasic region is seen, while the lamellar/nematic phase boundary is less distinct. Since the nematic phase is intermediateto an isotropic micellar solution phase at lower concentrations/higher temperatures and

a lamellar phase at higher concentrations/lower temperatures, the nematogenic unit in the nematic phase must, by inference, be 4 discoid micelle. This is confirmed by the pseudoisotropic texture which is observed for an annealed sample of nematic phase in an optical capillary. When a magnetic field was suddenlv applied in a direction parallel to the plane of the homeotropic layer, a striated texture was observed; this is caused by back-flow associated with a homeotropic-to-planar Friedericks transition of a mesophase with positive diamagnetic susceptibility ( A x = x I Thus, the nematic phase behaves as type ND+,a result which has been confirmed by X-ray diffraction.'0*28 Microscopy has been used to characterize the mesophase occurring at a given concentration and temperature and to obtain approximate values for the lamellar to isotropic/nematic and nematic to isotropic transition temperatures. The method does not, however, have sufficient resolution to accurately define the temperature widths of mixed-phase regions, particularly for the nematic to lamellar transitions, nor does it give the relative amounts of the coexisting phases. N M R Spectroscopy. NMR measurementsof the quadrupole splitting of 2H in labeled water is unparalleled as an experimental method for mapping phase diagrams and for studying the mechanism of phase transitions in lyotropic amphiphilic liquid crystals. This is because the quadrupole splitting is a characteristic signature of each kind of phase and is also a function of composition and temperature. It can, therefore, provide detailed information about the uniformity of composition and temperature in bulk samples. This is particularly useful information when traversing phase coexistence regions as in most instances it enables the relative amounts of the coexisting phases to be monitored. It can also be used to monitor the orientational distribution of the mesophase director and to distinguish between uniaxial and biaxial mesophases. The results of the CsPFO/water system provide a pedagogical illustration of the utility of the method, and for this reason they are presented in some detail. This description will, it is hoped, be particularly useful to liquid crystal scientists who are not NMR specialists and will also act as a standard reference for our future work on phase behavior. The spectrum for a *Hspin (I = 1) in labeled water in a macroscopically aligned uniaxial mesophase (nematic, lamellar, or hexagonal) is always a symmetrical doublet whose separation (quadrupole splitting) is, to first order, given by34 where the upper tilde denotes partially averaged quantities. In eq 1,4 is the angle between the optic axis n' (mesophase_director) and the direction of the spectrometer magnetic field B and cf,, is the partially averaged component of the deuterium nuclear quadrupole-electric field gradient interaction tensor measured parallel to n'. The latter is given by Qzz

(31) Griffiths, R. B. Phys. Rcu. Lett. 1910,24, 715. (32) McMillan, W. L. Phys. Rev. A 1971, I, 1238; 1912.6.936. (33) Holmes,M. C.; Boden, N.; Radley, K. Mol. Cryst. Li9. Cryst. 1983, 100,93.

= ~ P n x n & % -k qn(% n

- 86))/31

(2)

(34) Boden, N.; Jones, S. A. NATO ASI Ser. C Math. Phys. Sci. 1985, 141,473.

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The Journal of Physical Chemistry, Vol. 91, No. 15, 1987

where the S , 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 = ($qQ/h), is the corresponding quadrupole coupling constant, and 7“ is the asymmetry parameter. The actual values of x,,and vn will vary from site to site in a manner which has yet to be established, but the values for heavy ice, xD = 21 5 kHz and vD = 0.1 1, may be used as a first approximation. The observation of a single doublet spectrum implies that the microscopic motions of the water molecules are fast on the time scale of the experiment (=lo5 SKI). If this were not so, the spectrum would be more complex and consist of a superposition of doublets. These motions, which must have uniaxial symmetry, include the following: (i) anisotropic reorientation of the water molecule in its local site (lo8 s-I), (ii) exchange over the distrim2 s-l so that (p)1/2 = ( 6 D t ) ] i 2= 250 bution of sites (D N nm, which is of the order of 50 times the typical interaggregate separation), (iii) reorientation of individual water molecules about their local mesophase directors (IO8 s-l), and (iv) long-range collective fluctuations in the spatial orientation of the mesophase director itself ( l o 5 s-’). All of these factors contribute to the motional averaging of the quadrupole splitting in both the nematic and lamellar phases of the C S P F O / ~ H ~system. O Since the reorientation of the individual water molecules about the local nematic directors has been shown to be decoupled from the collective director fluctuations,28the effective average nematic order parameter can be written

(ezl)= (PZ(COS@)(Pz(cos P I ) = P2,mP2,a

(3)

where 0 is the angle between the symmetry axis of the micelle and the local director E, while P is the angle between Z and the symmetry axis of the mesophase. The bar and the angular brackets denote averaging over the orientations of the micelle in the local director frame and the director fluctuations, respectively. Equation 1 may, therefore, be conveniently expressed as

Boden et al. (a)

TIK 331.45

(C)

(d)

329.89

1

1

x8

5 0 0 HZ

Figure 4. *H NMR spectra of 2H20observed when the sample CSPFO/~H~O (wA = 0.5495) is cooled from the isotropic micellar solu-

(4)

tion phase (a), across the isotropic-nematic phase coexistence region (b), and into the nematic phase (c). The spectrum in (d) was obtained by spinning the nematic phase at 0.25 Hz about an axis perpendicular to the direction of the magnetic field.

where ~ i j z zis~solely s determined by the detailed structure of the aggregate and the concentration of the solution (see section iv of the Discussion). For an isotropic micellar solution ( Q z z ) will be zero and the deuterium spectrum will be a characteristic singlet. For a nematic phase or a lamellar phase in which the lamellae are considered to consist of two-dimensional arrays of discoid micelles, as in the CsPFO/water system, 0 < (ezz)< 1, while for a classical lamellar phase, in which the bimolecular aggregates are envisaged to be planar and infinite in extent, ( Q Z z ) must, by inference, be unity. Thus, both of these phases will be characterized by a doublet spectrum. They can, however, be distinguished by the nature of the response of the mesophase director to changes in the orientatio_n of the sample with respect to the spectrometer magnetic field B. The nematic phase of the CsPFO/water system has positive diamagnetic anisotropy. The nematic director will, therefore, couple with and undergo spontaneous alignment along the direction of B to give a sample with a homeotropic distribution of directors which is characterized by a single doublet spectrum (+ = 0). This is demonstrated by the sequence of spectra (Figure 4) observed for a wA = 0.55 sample on cooling from the isotropic phase ( a ) , across the isotropic-nematic phase coexistence region (b), and into the nematic phase (c). The spectrum of the nematic phase is a simple doublet characteristic of a homeotropic distribution of directions. When the tube containing the sample is spun about ifs axis which is aligned perpendicular to the direction of the field B at an angular velocity (0.25 Hz) which is much greater than the critical value R, [R, = AxB2/2poAl, where A, is the rotational viscosity coefficient of the nematic phase],20the spectrum shown in Figure 4d was observed. This spectrum corresponds to a two-dimensional (planar) distribution of nematic directors in a plane perpendicular to the axis of rotation. This confirms that the mesophase has positive diamagnetic anisotropy. For a mesophase with negative diamagnetic anisotropy a sample with a

homeotropic distribution of directors parallel to the axis of rotation would have been obtained. This would have given a single doublet spectrum with one-half of the maximum splitting. When the spinning is stopped, the spectrum relaxes quickly to a single doublet. The lamellar phase, in constrast, has an infinite valued rotational viscosity coefficient, and the lamellar director (normal to the planes of the lamellae) is locked into the mesophase. This behavior is nicely illustrated by the spectra for the same sample in Figure 5. The spectrum (Figure 5a), obtained when the sample is slowly cooled in the spectrometer magnet from the nematic into the lamellar phase, is a simple doublet whose splitting is proportional to P2(c0s +), consistent with a homeotropic director distribution. If the experiment is now repeated, but the sample is cooled outside of the magnet, a “Pake” spectrum (Figure 5b) is obtained, consistent with an isotropic distribution of director orientations. Thus, we now have a simple procedure for preparing macroscopically “aligned” or “unaligned” lamellar phases for materials which form nematic phases with positive diamagnetic anisotropy. However, it will be demonstrated later that the same procedure is applicable even when there is no intervening nematic phase. It is thus possible to distinguish between isotropic, nematic, and lamellar phases by their characteristic 2H NMR spectra and thereby to locate the phase boundaries. But to precisely locate the phase boundaries, we make use of the variation with temperature of the magnitude of the quadrupole splitting A’V. (Henceforth 4 is taken to be 0 deg unless stated otherwise.) There are two types of A‘V vs. temperature curves depending upon composition. For samples with w A > 0.535, separate lamellar and nematic doublets are observed at the lamellar to nematic transition, while for samples with lower concentrations only a single doublet is seen. The behavior at high concentrations is illustrated by the results shown in Figure 6 for a wA = 0.5495 sample. On cooling from

The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 4091

Lyotropic Mesomorphism of the CsPFO/Water System T = 3 0 3 0 6K

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