8804
J. Phys. Chem. 1995,99, 8804-8811
Electrochemical Measurements of Anisotropic Diffusion in Thin Lyotropic Liquid Crystal Films Using Interdigitated Array Electrodes Chun-hsien Chen, Timothy A. Postlethwaite, James E. Hutchison,? Edward T. Samulski,” and Royce W. Murray” Kenan and Venable Laboratories of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290 Received: January 12, 1995; In Final Form: March 27, 1995@
A new application of interdigitated array (IDA) electrodes is described for diffusion measurements of electrochemical probes dissolved in thin, lyotropic liquid crystalline films. The liquid crystal is a solution of 32% (w/w) lithium 4-trans-n-pentyl cyclohexanoate (LiSCH) in water, which can be prepared as well-ordered films of thickness less than ca. 12 pm. Apparent diffusion coefficients (DApp) of the electrochemical probes are calculated from steady-state currents of generator/collector voltammograms. The diffusional anisotropy, measured parallel and perpendicular to the liquid crystal director, increases with increasing hydrophobicity of the probes. A simplified model has been developed to explain the diffusional anisotropy of hydrophobic probes in the ordered film. The transition temperature of the liquid crystal is determined from an activation p 1,l’-dimethylferrocene. plot of D ~ p for
Introduction Electrochemical methods have been used to study transport in a wide range of materials including liquids,’ supercritical fluids,2 molten oligomeric material^,^ and rigid polymer elect r o l y t e ~ . ~These . ~ studies have mostly relied on single microelectrodes or planar macroelectrodes; transport studies utilizing interdigitated microelectrode or planar macroelectrodes; transport studies utilizing interdigitated microelectrode array (IDA) electrodes have also been reported.6-’0 Microelectrode arrays offer advantages over single electrodes such as well-defined diffusion distances, smaller uncompensated resistances, and steady-state current measurements that simplify interpretation. Additionally, IDA electrode geometries are easily adapted to measurements in thin film samples by integration of working, reference, and counter electrodes into one coplanar ensemble. This laboratory has used IDA electrodes to study electron transport in electroactive polymer films6 as well as probe diffusion in solid polymer electrolyte filmsS7 Wrighton et al. have employed microband array electrodes to study physical diffusion in fluid electrolytes,8 solid polymer electrolyte^,^ and polymer gels.I0 Microelectrode arrays can be used to measure transport and diffusion constants in several modes. In an electrochemical “time of flight” meas~rement,6c-~.~ the potential of one electrode or set of electrodes is pulsed to generate a species which is subsequently detected at the other electrode or electrodes in the array. The transit time of the species is related through the electrode spacing to its diffusion coefficient. In the related generatorlcollector mode, the potential of one electrode or set of electrodes (the generator) is slowly scanned to oxidize or reduce a chemically reversible redox species; the other adjacent electrode or set of electrodes (the collector) is held at a potential to reverse the redox process. The steady-state currents resulting at both electrodes are related to the diffusion coefficient of the redox probe. Aoki et al. have described the theory for steady-state limiting currents for a chemically reversible reaction in the generator1 + Present address: Deoartment of Chemistrv. Universitv of Oreeon. Eugene, OR 97403-1253.’ Abstract published in Advance ACS Abstracts, May 1, 1995. @
collector mode of an IDA electrode. The steady-state currents are due to the redox-cyclingI2of analyte between generator and collector electrodes with little net analyte loss to or gain from bulk solution. This redox-cycling causes intergap diffusion to contribute significantly to the steady-state currents measured. In this study we exploit this preponderance of intergap diffusion to detect diffusional anisotropies in films of a lyotropic liquid crystal that is aligned relative to the fingers of the IDA. Lyotropic liquid crystals are ordered fluid phases formed by addition of solvent to certain crystalline solutes, e.g. water added to an amphiphilic substance.I3 Specific solvent-solute interactions promote aggregation of the solute into micelles, rodlike aggregates, and lamellae. These aggregates mutually orient in the solutions to display liquid crystalline phases (e.g., nematic, hexagonal, lamellar) over certain concentration and temperature ranges. These ordered phases can often be aligned over macroscopic distances by magnetic field^'^^.'^ or through surface treatment^.'^ NMR methods,I6 ionic conductivity,” optical techniques,I8 and more recently electrochemistryl 9 have been utilized to study transport and transport anisotropy in these ordered systems. In turn, such data can give insights into transport in certain biological structures such as cell membranes, which display liquid crystalline-like b e h a ~ i o r . ’ ~ ~ , * ~ Electrochemical diffusivity measurements in micellar systems have been reported by Rusling2I and others.22 In general, these studies have involved the diffusion of electroactive probe solutes in “conventional” micellar solutions that are oriented microscopically but not macroscopically (Le., isotropic solutions). We recently described the diffusional anisotropy of electroactive probe solutes in the lamellar phase of a macroscopically oriented discotic micellar liquid crystalline system.l 9 That study established the feasibility of electrochemical measurements in lyotropic liquid crystals. Electrochemical measurements are facilitated in these systems by their inherent ionic conductivity and good solvation properties for both hydrophilic and hydrophobic redox probes. An unusual amphiphilic lyotropic system, lithium 4-transn-pentyl cyclohexanoate (LiSCH, I) in water, has been described by Marcus,23who concluded that it forms an optically birefrin-
0022-365419512099-8804$09.00/0 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 21, 1995 8805
Measurements of Anisotropic Diffusion gent, micellar nematic phase in which elongated micelles comprise the ordered phase. The micelles*of the nematic phase could be uniaxially aligned in thin films when sandwiched between two treated glass slides. The optic axis or director of the film is influenced by the direction in which the glass slides are rubbed, a phenomenon commonly used to align thermotropic liquid crystals,24but relatively unexplored in lyotropic systems.
c-c-
0
Li+
I This paper reports the first use of IDA electrodes to measure diffusion anisotropy of electroactive probes in films of a surfacealigned, micellar nematic liquid crystal, 32% (w/w) Li5CW water. We present voltammetric experiments in which diffusional anisotropies and phase transitions are detected and a diffusional model which predicts a diffusional anisotropy for hydrophobic probes in this and similar systems.
Experimental Section Reagents. Li5CH was prepared by dissolving stoichiometric amounts of 4-trans-n-pentyl cyclohexanoic acid (Aldrich) and LiOH in Nanopure water (18 M k m , Bamstead) and boiling for cu. 30 min. The water was then removed by evaporation in an oven, and the resulting material was washed with n-hexane (to remove any unreacted acid), dissolved in warm absolute ethanol, and filtered (to remove any remaining LiOH). The solution was then dried in an oven, and the product was dissolved in water and lyophilized. The final product was flocculent, and 32% Li5CH solutions (w/w) in water are easily prepared. Ferrocene and 1,l'-dimethylferrocene were purified by sublimation. [Ru(NH3)6]C13 (Strem), &Fe(CN)6-6H20 (Mallincrodt), and tetramethylphenylenediamine (TMPD, ICN Biomedicals) were used as received. (2-Ferrocenylethyl)trimethylammonium perchlorate (FcETMAC104) was prepared as follows. Ferrocenylacetonitrilewas synthesized according to literature procedure^.^^ A solution of ferrocenylacetonitrile(20.79 g, 0.092 mol) in diethyl ether (315 mL) was added dropwise over 4.5 h to a degassed solution of lithium aluminium hydride (7.0 g, 0.185 mol) in 340 mL of diethyl ether. The resulting orange solution was refluxed for 2.5 h and then cooled to room temperature. The excess lithium aluminum hydride was quenched with moist ether and then with water. The mixture was filtered, the ethereal solution dried over anhydrous sodium sulfate, and the ether removed to yield 18.2 g of crude 2-ferrocenylethylamine as a brown oil. Distillation of the oil at reduced pressure (135-140 "C, 0.5 mmHg)25 afforded ferrocenylethylamineas a red-brown oil (12.81 g, 61% yield). 'H NMR (200 MHz, CDC13, ppm): 6 4.09 (s, 5H), 4.06 (m, 4H), 2.79 (t, 2H), 2.46 (t, 2H), 1.22 (s 2H). Methyliodide (68.4 g, 0.482 mol) was added to a degassed solution of 2-ferrocenylethylamine (3.1 g, 0.014 mol) in acetonitrile (30 mL). The flocculent precipitate which formed was redissolved upon addition of 30 mL of acetonitrile. The solution was stirred for 70 min, and then a solution of sodium bicarbonate (2.65 g, 0.032 mol) in water (40 mL) was added. The mixture was stirred for an additional 4.5 h, and the crude (2-ferrocenylethy1)trimethylammoniumiodide was isolated by precipitation upon pouring the mixture into 300 mL of anhydrous diethyl ether. The resulting yellow solid was recrystallized from water and dried to yield 4.12 g (76%) of (2ferrocenylethy1)trimethyla"onium iodide. 'H NMR (200
MHz, D20, ppm): 6 4.08 (s, 5H), 4.07 (m, 4H), 3.32 (m, 2H), 2.98 (s, 9H), 2.73 (m, 2H). (2-Ferrocenylethyl)trimethylammoniumiodide (2.0 g, 0.005 mol) was dissolved in 125 mL of water with gentle heating. Concentrated perchloric acid (69-77%, 2 mL) was added dropwise to the room temperature solution. The crude (2ferrocenylethy1)trimethylammoniumperchlorate was collected as a yellow precipitate. (WARNING: caution should be exercised in handling perchlorate salts as they are potentially explosive!) The crude material was dissolved in 140 mL of dichloromethane and filtered to remove the insoluble impurities. Diethyl ether was carefully layered on top of the dichloromethane solution. After cooling overnight at 0 "C, small orange crystals of (2-ferrocenylethyl)trimethylammonium perchlorate formed and were collected and dried in vacuo to yield 0.45 g (25% yield) of the desired product. 'H NMR (200 MHz, D20, ppm): 6 4.06 (s, 5H), 4.07 (m, 4H), 3.32 (m, 2H), 2.98 (s, 9H), 2.73 (m, 2H). Analysis calculated for C15HzN04ClFe: C, 48.48; H, 5.97; N, 3.77. Found: C, 48.46; H, 5.85; N, 3.69. Apparatus and Electrochemical Measurements. Optical microscopy was performed with a reflective-mode microscope (Carl Zeiss, Universal) and a transmission-mode microscope (Nikon, Microphot-fx) equipped with a thermostated stage. The IDA electrodes, a generous gift from Nippon Telegraph and Telephone Corp. (NTT), consist of 50 pairs of 3 pm wide, 2000 pm long Au bands (fingers) with 5 pm gaps. The reference and auxiliary electrodes were an electrodeposited Ag patch and a thermally evaporated Au patch, respectively. Because of the inherent ionic conductivity of the lyotropic liquid crystalline material afforded by high concentrations of both lithium ions and surfactant, no other supporting electrolyte was added to the Li5CH solutions. Generatodcollector experiments were performed using a Pine RDE4 bipotentiostat (Pine Instruments), a triangle wave-form generator of local design, and an XYY' recorder (Yokogawa). Experimental and fabrication details of the IDA electrodes have been described previously.' During electrochemical measurements, sample temperature was controlled by a thermostated oven via a thermocouple attached to the film substrate. Film Preparation. LiSCWwater (32%) was prepared in a 5 mL, air-tight vial with a magnetic stirring bar. To dissolve the LiSCH, the solution was heated to the boiling point and the water allowed to reflux off the top and sides of the vial until complete dissolution appeared attained; the solution was then stirred at room temperature at least 24 h before use. Before use, it was confirmed that the solution was homogeneous and birefringent using polarized light microscopy. A film of the solution was sandwiched between an IDA electrode (or a plain glass substrate) and a glass coverslide (Coming Micro Slides, no. 2947) with a metal clip. The film thickness was defined by a 12.5 pm Teflon (DuPont) spacer. Prior to use, the glass coverslide, trimmed to a suitable size, was polished along one direction with an aqueous slurry of 0.3 pm A1203 (Buehler), sonicated, and rinsed with copious Nanopure water to ensure complete removal of the polishing powder. While polishing, the coverslide was butted against a straight-edge to keep the polishing direction constant and linear. Ordered films in the sandwich were obtained after an annealing treatment in which the film was held in the isotropic state (vide infra) at 72 "C for 5 min and then slowly cooled to 45 "C over about 15 min in a thermostated oven. Isz6
Results and Discussion Characterization of Liquid Crystalline Films Using Optical Microscopy. Polarized light microscopy was used to
8806 J. Phys. Chem., Vol. 99, No. 21, 1995
Chen et al.
examine the homogeneity and alignment of the liquid crystalline films. This technique exploits the birefringence of liquid crystalline materials. The transmission of plane-polarized light is viewed through an orthogonal polarizer (analyzer). For a homogeneously ordered liquid crystalline sample (that is, orientational director is in a plane normal to the viewing direction), the transmitted light is a function of the angle between the director and the crossed polarizers. No light transmittance is observed when the director is parallel to a polarizer (maximum extinction); maximum transmittance occurs at an angle of 45". It is typical when surface treatments are used to orient thinlayer, liquid crystal cells that both confining substrate surfaces are treated. In previous studies of the LiSCWwater system,23 both glass slides were coated with a nylon film or surfactant layer and unidirectionally rubbed. In the present study, with the liquid crystal sandwiched between a glass slide and the IDA electrode, surface treatment is possible only on the glass slide. However, in control experiments with a cell with two glass slides, satisfactory orientation of nematic LiSCWwater was achieved when only one slide was rubbed (see the Experimental Section) and the other was untreated. The qualitative degree of alignment as determined with polarized light microscopy appeared as good as that obtained with two treated slides. When the untreated slide was replaced with an IDA electrode, good orientation was also achieved. A typical photomicrograph of an unannealed, 12.5 p m film on an IDA electrode is shown in Figure 1A. This image shows light and dark areas representing relatively large domains of aligned material that most likely occur by shear orientation of the sample upon film formation (Le., the mechanical act of sandwiching the film). This alignment generally relaxes within 1 h, and the domain sizes become smaller. Annealing a sample like that shown in Figure 1A results in films shown in Figure IB,C. In Figure lB, the director of the film is at 45" with respect to the polarizer axes. The film appears transparent, and the IDA electrode fingers can be clearly observed. This confirmed that the film is a monodomain liquid crystal containing only small defects which appear as small dark streaks. (These streaks generally lie in the direction in which the glass slide had been rubbed.) When the director (rubbing direction) of the film is parallel to one of the polarizer axes, the image is completely dark (Figure 1C). These results show that monodomain Li5CH films can be prepared by surface treatment and annealing. We believe that the annealing step relaxes shear-induced order resulting from cell fabrication, and the process of slowly cooling into the nematic phase allows the treated (rubbed) glass slide to effectively align the nematic director along the rubbing direction throughout the entire sample. Microscopy shows no distinguishable difference between films with and without electroactive solutes (1-3 mM); therefore, we conclude that the probes do not disturb the liquid crystallinity of the film. We should note, however, that the same procedure does not yield homogeneously aligned films when the sandwiched film is 25 pm thick or thicker. Electrochemical Measurement of the Apparent Diffusion Coefficient. The apparent diffusion coefficient ( D ~ p p ) is calculated from the steady-state currents of generatorkollector voltammograms using the Aoki et al.'I equation:
ZLIM = mbnFC* D[0.637 1n{2.55( 1
+ wdw,)} 0.19/(1
+ w&v,)*]
(1)
where ZLIM is the steady-state limiting current (generator or collector), m is the number of generator or collector electrodes
in the IDA, b is the length of a finger electrode, n is the number of electrons transferred per redox probe in the electrochemical reaction, F is the Faraday constant, C*is the bulk concentration of redox probe, D is the diffusion coefficient, and w f and w g are the widths of the fingers and the gaps, respectively. In the theoretical derivation, no assumption regarding physical boundaries was made, while in the current study the electrochemical medium is only 12.5 pm thick. Under semi-infinite diffusion conditions, there is a higher possibility for species to escape from the redox-cycling process between generatorkollector fingers to yield a lower collection current than in a diffusionconfined thin-layer cell. Therefore, it was necessary to determine whether the Aoki equation is applicable to thin-layer cells. To test Aoki's formulation in a thin-layer cell configuration, we employed voltammetry of a 1 mM [Ru(NH&l3+ solution in 0.1 M KCl(aq). This situation represents an extreme case because the diffusion coefficient and diffusion layer thickness of [Ru(NH3)6I3+will be much larger than those of probes in the Li5CH medium (vide infra). Figure 2A,B depicts cyclic voltammograms obtained in a thin-layer (12.5 pm) and a largevolume cell. The differences in wave shapes and peak currents result from the differing cell geometries, and the differences in potentials are due to drift of the silver quasi-reference electrode. However, the difference in cell geometries does not significantly affect the steady-state generatorkollector currents, as shown in Figure 2C. We conclude that D ~ p pof probe solutes in thinlayer cells can be calculated by applying Aoki's equation." The similarity of the voltammograms in Figure 2C indicates that the effective recycling layer thickness of redox species over the IDA electrodes is less than 12.5 pm. This suggests that the IDA electrode can be a powerful tool for studying material properties near interfaces and in thin films. The diffusional anisotropy of a probe in the ordered Li5CH film is described by DI'APPID~APP, where D l l ~ p pand D l ~ p are p the apparent diffusion coefficient of the probes parallel and perpendicular to the liquid crystalline director, respectively. When the IDA is operated in the generator/collector mode, the dominant diffusion pathway is perpendicular to the IDA electrode finger sets. Therefore, D'APP is obtained when the rubbing direction (Le. the director) of the glass slide of the cell is perpendicular to the IDA fingers, and @APP is measured when the rubbing direction of the glass slide is parallel to the IDA fingers. This is illustrated in Figure 3, which shows a cutaway view of redox-cycling of the oxidized (0)and reduced (R) probe in a film sandwiched between a treated glass slide and two adjacent IDA fingers. Figure 3 defines the two different diffusion coefficients measured (along dotted arrows) with respect to the director of the elongated micelles (shown as rods). Figure 4 shows the generatorkollector voltammograms of 2.25 mM 1,l'-dimethylferrocene in 32% LiSCWwater at room temperature (ca. 23 "C). The disparity in the steady-state currents in the two film orientations indicates a substantial diffusional anisotropy. The value of D ~ p was p dependent upon the film quality and varied somewhat from sample to sample; the average anisotropy measured from six pairs of samples is 8.3 (h1.4) for this probe at room temperature. The concentration of electroactive probe was varied from 1.O to 3.0 mM with no significant variation in the diffusional anisotropy. We did not study the effect of concentration upon diffusional anisotropy outside of this range because at lower concentrations D l ~ p is p difficult to measure and at higher concentrations the electrochemical probes may disrupt the micelle structure. The results of analogous generatorkollector experiments for five different electrochemical probes are summarized in Table 1. The reported values are averages of at least three samples,
A
C
B
500 pm Figure 1. Optical photomicrographs (crossed polarizers) of a 12.5 pm film of 32% Li5CWwater containing 2.8 mM 1,l’-dimethylferrocene on an IDA electrode with a treated glass coverslide (A)
prior to thermal annealing, (B) after annealing, with the rubbing direction at an angle of 45’ with respect to the polarizers, and (C) with the rubbing direction parallel to one of the polarizers.
8808 J. Phys. Chem., Vol. 99, No. 21, 1995 10.0
C
Chen et al.
TABLE 1: Apparent Diffusion Coefficients and Anisotropies of Electrochemical Probes in 32 % LiSCWWater
80.0
generator
5.0
60.0 0.0
40.0
-5.0
20.0
5
0.0
v
.-
30.0
-.
E v
-20.0
20.0
probe
DIApp
[Fe(CN)6]4-a FcETMA+ TMPDC ferrocene 1,l'-dimethylferrocene
(1.1 f O . l ) (4.4 i 0.9) (2.2 f 0.3) (8.4 f 0.9) (2.0 f 0.3)
(cm*/s)
DlApp
(cm2/s)
x low6 ( l . O f O . l ) x x (1.9 i 0.4) x x (6.1 i 0.1) x x (1.5 f 0.2) x x (2.4 f 0.2) x
D"APP/D'APP 1.1 f 0 . 1 2.3 0.7 3.6 0.1 5.6 f 1.0 8.3 f 1.4
**
a Added as K.@e(CN)6. Added as FcETMAC104. TMPD may decompose during the annealing process; see text.
-40.0
10.0
-60.0
0.0
- thin cell
-- large-volume cel -80.0 1
0.0
-0.2
0.2
,
1
1
1
0.0 -0.2 -0.4 -0.6
E (volt vs. AgQRE)
Figure 2. Cyclic voltammograms of 1.0 mM [Ru(NH&J3+ in 0.1 M KCl at an IDA electrode in (A) a 12.5 p m thin-layer cell, (B) a largevolume electrochemical cell, and (C) the generator/collector mode in both cells (Y = 10 mV/s). In parts A and B both sets of IDA fingers were shorted and scanned together.
\\\\
treated glass slide \
, ,
\
,
A\\
oriented LiSCH/H,O
director
-+
0
Figure 3. Illustration of the measurement scheme used to study diffusion in oriented films of Li5CWwater. A cutaway view of the rubbed glass/liquid crystalADA electrode sandwich is shown. The redox-cycling of the oxidized (0)and reduced (R) probe, including the intergap diffusion (dashed arrows), is indicated. The two different diffusion coefficients measured with respect to the director of the elongated micelles (represented as rods) are also shown. In the D l l ~ p p case, the director is in the plane of the page, and in the D l ~ p case p the director is normal to the page.
60
/A
0.2
T = 23OC
0.0 -0.2 0.2 0.0 E (volts vs. AgQRE)
-0.2
Figure 4. Generatodcollector voltammograms of 2.25 mM 1,l'dimethylferrocene in oriented films of 32% Li5CWwater measuring diffusion (A) parallel and (B) perpendicular to the liquid crystal director (Y = 2 mV/s and ECOlleCtOr = -0.1 V versus AgQRE).
at room temperature. The data clearly indicate that the probe hydrophobicity affects both the absolute diffusion coefficient values and the diffusional anisotropies. Hydrophobic probes exhibit lower difSusion coeflcients and higher difisional anisotropies. [Fe(CN)sI4- represents a hydrophilic probe; its diffusion coefficient is large and independent of film orientation. (Fer-
rocenylethy1)trimethyla"onium (FcETMA+) is charged and consequently more soluble than its parent, ferrocene, in the water phase of the liquid crystal, and exhibits a smaller anisotropy than ferrocene. 1,l'-Dimethylferrocene is more hydrophobic than ferrocene and gives the largest observed anisotropy. Tetramethylphenylenediamine(TMPD) is light-sensitive and may have partially decomposed during the film preparation. This decomposition would result in artificially low apparent diffusion coefficients when calculated from steady-state currents (see eq 1). Nevertheless, the diffusional anisotropy is based on the ratio of the apparent diffusion coefficients and should be unaffected. Thus, TMPD gives an anisotropy qualitatively agreeing with the trend of hydrophobicity. The observed dependence of D ~ p on p hydrophobicity can be rationalized considering the differences between the two regions of the micellar medium: the continuous aqueous phase versus the isolated, discontinuous hydrophobic regions. A hydrophobic probe will preferentially reside in the hydrophobic micelles, and its diffusion over macroscopic distances will require either (i) physical diffusion of the entire micelle, which we consider to be slow in the concentrated liquid crystalline solution, or (ii) a series of steps involving diffusion of the probe within the micelle,*' followed by (unfavorable) partitioning of the probe from the micelle into the water, and probe diffusion in the water. The banier of partitioning hydrophobic probes into the aqueous region will slow their diffusion compared to hydrophilic probes. Hydrophilic probes can diffuse over macroscopic distances without such a partitioning step, resulting in relatively larger diffusion coefficients. Therefore, the diffusion coefficient of a probe that resides exclusively in the aqueous region will be only modestly, as a result of an obstruction effect28caused by the rodlike micelles, diminished from values in pure water. Other factors, such as effective hydrodynamic radius and ion-pairing interactions, may also affect the apparent diffusion coefficient. The effect that probe hydrophobicity has on the magnitude of the diffusional anisotropy will be discussed after presentation of a theoretical model. Theoretical Model for Diffusion of Hydrophobic Probes. One objective of this study was to develop a model to describe anisotropic diffusion for hydrophobic probes in the oriented, elongated micellar medium at steady state. Several conditions and hypotheses are set up to simplify the mathematical treatment: (i) At temperatures below the nematic-isotropic transition temperature, TN.I,the rodlike, and hexagonally packed micelles23 in the LiSCWwater film are of uniform size and are stationary (on the time scale of probe diffusion). (ii) The partition coefficient of the redox probe solute to the water phase, p = is small so that most probe molecules reside in the hydrophobic micellar phase. (iii) The generator and collector electrodes approximate a parallel plate geometry, so that the D " ~ p pand D l ~ p are p clearly definable. The net flux of the redox probe is always in a
J. Phys. Chem., Vol. 99, No. 21, 1995 8809
Measurements of Anisotropic Diffusion *IDA electrode gap (wJ+
From Fick’s first law, the flux (j) of the probe in the water and micellar phases are equal and defined as
where subscripts W and M denote water phase and micellar phase, respectively. D ~ p is p defined by the apparent concentration difference, A c ~ p p , across the distance of the parallel electrodes, wg,
-d
t‘
t+d
(i-Iy+d it
2t‘
X
+
A general equation for C(il d) is required to derive ACAPP and to determine the diffusional anisotropy, D”APP/@APP. In the first unit cell? by applying eq 2 and the partition relationship at watedmicelle interfaces, the concentration of the reactant form of the probe at the x = 0, d, and l positions in the micellar and water phases, at steady state, can be written explicitly as the following:
Cw(0) = 0 water
d Cw(d)= -j DW
--
+ d” +
(4)
p”
Figure 5. (A) Schematic representation of the laminar model of diffusion of hydrophobic probes in the oriented micellar medium. The inset shows the probe concentration gradients (AC~pplw,) which form in the gaps of the IDA electrode at steady state. The lower left corner of the inset is expanded to reveal the individual laminae (separated by dashed lines) and the probe concentration profiles in the hydrophobic laminae. Concentration gradients do exist in the aqueous laminae; however, they are assumed to be small compared to those in the hydrophobic laminae due to differences in the diffusion coefficients in the two regions.27 (B) Definitions of I and d , the dimensions for the micellar unit cell. The shaded regions represent the micelles separated by water. A unit cell is contained within the dashed line. The superscripts correspond to the diffusional directions measured.
direction normal to the electrode surfaces. We treat the micellar array in the gap between the electrodes as alternating laminae of water and micellar phase that lie parallel to the electrode surfaces. (iv) At steady state, the flux through every laminar segment (including water and micellar phases) is the same. (v) The partition coefficient is constant at all micelle/water interfaces, at a fixed temperature. A schematic model of the IDA interfinger laminae and concentration profiles based on the above assumptions is illustrated in Figure 5A. The x-axis and the vertical axis represent the distance normal to the electrode and the concentration of the probe at corresponding positions, respectively. Concentration is described by C(x)instead of C(x,y,z) because the laminar model has no concentration gradients in the y and z directions. Because of the periodicity of the model, i.e., the alternating layers of water and micellar phase, the position of each lamina and thus the concentration of probe can be generally defined in terms of one-dimensional unit cells where d is the length of the water phase, l is the dimension of the unit cell, and l - d is the length of the micellar phase (see Figure 5B).
By repetitively applying the same method, the general form of C(il d) is
+
The number of moles in each lamina can be calculated from multiplying the averaged concentration by volume, and the summation of the number of molecules of probe over all the laminar segments gives the total number of moles, mTOT, i.e.,
1 A
-[CM(iZ 2
+ d) + CM(iZ + Z)]A(Z- d)
where n is the total number of laminar segments (n = wg/Z), and Ad and A(l - d)are the volume of the water phase and the micellar phase, respectively. The apparent concentration is the total number of moles divided by total volume, VTOT.Because the total number of moles (eq 6) is derived for the reactant form of the probe at steady state (where the total amount of product is assumed equal to that of reactant), the apparent
8810 J. Phys. Chem., Vol. 99, No. 21, 1995
Chen et al.
concentration difference, A c ~ p p is , twice the apparent concentration of the reactant. Therefore, A c ~ p pis described by
Temperature ( O C ) 97.2 71.8 60.2 49.4 39.4 29.9 21.0 6.0
lA
:
1,l' dimethylferrocene
4
6.0
By substituting eqs 4 and 7 into eq 3, we obtain equations for DAPPand D'APP/@APP:
6
2.0
ec
-
7.7 7.3 -
For a very hydrophobic probe, p approaches 0, and the anisotropy can be simplified:
D",,, -D'App
t2/hl(l"- d') ll'/d(l'- 8)
(10)
Therefore, the diffusion anisotropy is determined by the dimension of the unit cell. To explore this model, we back calculate the length of a micelle rod by applying the following conditions: (i) The diffusion anisotropy of 8.3 for 1,l'-dimethylferrocene (Table 1) represents a case of p approaching 0. (ii) The volume fraction of LiSCH in the liquid crystalline solution is 0.275 (experimentallymeasured). This value is taken as the volume fraction of a micelle in a hexagonally packed unit cell. (iii) The diameter of the rod-shaped micelle is assumed to be 40 A, a value estimated from twice the length of a LiSCH molecule. This assumption is supported by studies of other rodshaped micelles which showed that the diameter of the micelle is close to twice the amphiphile length.29 (iv) The end-to-end distance of two neighboring micelles is assumed equal to their side-to-side distance (Le. d' = d'). The results are 998 and 31.5 8, for the micelle length (I" dl) and the water layer thickness, d, respectively. No information is available concerning the actual length of LiSCH micelles; however, the calculated micelle length is on the order of that measured for other rod-shaped micelles: 597 A using light scattering on a dilute system based on sodium dodecyl sulfate,30 800 8, measured using deuterium NMR on a lyotropic system based on potassium l a ~ r a t e , ~and ' between 290 and 980 8, (depending on surfactant concentration) using small-angle The qualitaneutron scattering on cetylpyridini~msalicylate.~~ tive agreement in micelle dimension supports the validity of the simple model in describing the diffusion anisotropy of hydrophobic probes. The model presented predicts a substantial diffusional anisotropy for hydrophobic probes with a low partition coefficient, p . This anisotropy is due to the anisotropic shape of the micelles and thus differences in the thickness in the laminae assumed in the model. In the case of probes which appreciably partition into the water phase, the laminar diffusion model is expected to break down. As the partition coefficient increases, the contribution to the net flux of the probe in the continuous water phase increases, leading to a decrease in the diffusional anisotropy. At the limit of large p, any anisotropy measured is due to an anisotropic obstruction effect caused by the elongated
....... I
B
6.9
I
I
I
[Fe(CN),I4.- 8.2
.a.
. -I
- 7.8
0
1
2.8
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I
I
I
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10001T (K-') Figure 6. Activation plot for collector currents and diffusion coefficients of (A) 1,l'-dimethylferrocene and (B) ferrocyanide in oriented thin films of 32% LiSCWwater.
micelles, which would be unrelated to the laminar model developed for low-p probes. Electrochemical Detection of the Nematic to Isotropic Transition Temperature. The conclusion that the IDA measurement is sensitive in the near-surface region leads to a novel methodology of measuring the transition temperature (TN-I) of nematic materials in a thin-film form. Figure 6 shows activation plots of D ~ p p for 1,l'-dimethylferrocene and [Fe(CN)6I4-. In the case of the hydrophobic dimethylferrocene probe, the anisotropy decreases at higher temperatures, which could be ascribed to several factors such as a change in the micelle dimensions (see eq 10) or a decrease in the liquid crystalline order parameter. An increase in the partition coefficient concomitant with higher temperatures would increase the contribution of diffusion in the water phase to the measured apparent diffusion coefficients, thereby decreasing the anisotropy. The diffusion coefficients converge at about 60 "C, the temperature we assign as the TN.Iof 32% LiSCWwater. This transition temperature was confirmed in thin-layer cells using both deuterium NMR (monitoring the quadrupolar splitting of added D20 as a function of t e m p e r a t ~ r e ~and ~ ) optical microscopy. The slopes of the various regions of the activation plots in Figure 6 represent activation energies of diffusion processes at the corresponding film orientation and phase. The activation energies for dimethylferrocenein the isotropic phase and parallel and perpendicular in the ordered phase are 42.7, 34.6, and 80.1 H/mol, respectively. It should be noted that these values include activation energies resulting from diffusion as well as partitioning processes. The results reveal that the overall diffusion process is easier for the direction parallel to the film director than for the perpendicular direction, and the isotropic state yields an intermediate value. In the hydrophillic case of [Fe(CN)6I4-, the activation plot is not dependent on direction in the oriented film and does not provide a direct measure of &I. Also, the lower activation energy, 12.0H/mol, shows [Fe(CN)6I4- diffuses easier than 1,l'dimethylferrocene, which would be expected on the basis of the continuity of the water phase.
Measurements of Anisotropic Diffusion
Conclusion This study demonstrates that the generatorkollector mode of IDA electrodes is a very useful method to probe the properties andor structures of materials localized within the micron distance range from the electrode. A 12.5 pm film of liquid crystalline 32% LiSCWwater can be homogeneously aligned by surface-induced orientation through the use of a treated glass substrate. IDA electrodes were utilized to measure diffusion coefficients and diffusional anisotropies in the aligned, orientationally ordered, thin films. It was determined that the anisotropy increases with the hydrophobicity of the probe, and a simple diffusional model has been proposed. The model predicts that the anisotropy is dependent upon the dimensions of the elongated micellar aggregates comprising the liquid crystalline films. Finally, we have shown that the transition temperature of the film from the anisotropic (nematic) phase to the isotropic phase can be obtained by monitoring the diffusional anisotropy of hydrophobic probes.
Acknowledgment. This research is supported by grants from the Department of Energy and the National Science Foundation. The authors thank Dr. Chi-Duen Poon (LJNC) for help with the NMR measurements. References and Notes (1) See, for example: Koval, C. A,: Ketterer, M. E.: Reidsema, C. M. J . Phys. Chem. 1986, 90, 4201-4205. (2) Niehaus, D.; Philips, M.: Michael, A.; Wightman, R. M. J. Phys. Chem. 1989, 93, 6232-6236. (3) (a) Velazquez, C. S.; Hutchison, J. E.; Murray, R. W. J. Am. Chem. SOC. 1993,115,7896-7897. (b) Poupart, M. W.; Velazquez, C. S.: Hassett, K.; Porat, Z.: Haas, 0.: Tenill, R. H.; Murray, R. W. J. Am. Chem. SOC. 1994, 116, 1165-1166. (4) For reviews of ion transport measurements in polymer electrolytes see, for example: (a) Polymer Electrolyte Reviews; MacCallum, J. R., Vincent, C. A,, Eds.; Elsevier: London, 1987; Vol. 1. (b) Ratner, M. A,: Shriver, D. F. Chem. Rev. 1988, 88, 109-124. ( 5 ) For probe and self-diffusion measurements in polymer electrolytes see, for example: (a) Geng, L.; Reed, R. A,; Longmire, M.; Murray, R. W. J . Phys. Chem. 1987, 91, 2908-2914. (b) Pinkerton, M. J.; LeMest, Y.: Zhang, H.: Watanabe, M.: Murray, R. W. J. Am. Chem. SOC.1990, 112, 3730-3736. (c) Watanabe, M.: Longmire, M. L.; Murray, R. W. J . Phys. Chem. 1990,94,2614-2619. (d) Longmire, M. L.; Watanabe, M.: Zhang, H.: Wooster, T. T.: Murray, R. W. Anal. Chem. 1990, 62, 747-752. (6) (a) Chidsey, C. E.; Feldman, B. J.; Lundgren, C.; Murray, R. W. Anal. Chem. 1986,58,601-607. (b) Feldman, B. J.; Murray, R. W. Anal. Chem. 1986, 58, 2844-2847. (c) Feldman, B. J.; Feldberg, S. W.; Murray, R. W. J . Phys. Chem. 1987, 91, 6558-6560. (7) Nishihara, H.; Dalton, F.; Murray, R. W. Anal. Chem. 1991, 63, 2955-2960. (8) Licht, S.: Cammarata, V.: Wrighton, M. S. J . Phys. Chem. 1990, 94, 6133-6140. (9) Cammarata, V.; Talham, D. R.; Crooks, R. M.; Wrighton, M. S. J . Phvs. Chem. 1990, 94. 2680-2684. (10) Tatistcheff, H. B.; Fritsch-Faules, I.; Wrighton, M. S. J. Phys. Chem. 1993, 97, 2732-2739.
J. Phys. Chem., Vol. 99, No. 21, 1995 8811 (1 1) Aok, K.: Morita, M.; Niwa, 0.;Tabei, H. J . Electroanal. Chem. 1988, 256, 269-282. (12) Niwa, 0.;Morita, M.; Tabei, H. Anal. Chem. 1990,62,447-452. (13) (a) Wojtowicz, P. J. In Introduction to Liquid Crystals; Priestley, E. B., Wojtowicz, P. J., Sheng, P., Eds.: Plenum: New York, 1974; Chapter 18. (b) Forrest, B. J.: Reeves, L. W. Chem Rev. 1981, 81, 1-14. (14) Boden, N.; McMullen, K. J.; Holmes, M. C.; Tiddy, G. J. T. Springer Ser. Chem. Phys. 1980, 11, 299-303. (15) Kaeder, U.; Hiltrop, K. Prog. Colloid Polym. Sci. 1991, 84, 2.50.252. (16) (a) Tiddy, G. J. T. J. Chem. SOC.,Faraday Trans. I 1977, 73, 17311737. (b) Chidichimo, G.: Coppola, L.; LaMesa, C.: Ranien, G. A,; Saupe, A. Chem. Phys. Letr. 1988, 145, 85-89. (c) Ukleja, P.: Chidichimo, G.: Photinos, P. Liq. Cryst. 1991, 9, 359-367. (d) Holmes, M. C.; Sotta, P.; Hendriks, Y.; Deloche, B. J . Phys. I1 1993, 3, 1735-1746. (17) (a) Boden, N.; Come, S. A,: Jolley, K. W. Chem. Phys. Lert. 1984, 105, 99-103. (b) Boden, N.: Parker, D.; Jolley, K. W. Mol. Cryst. Liq. Crvst. 1987. 152, 121-127. (c) Photinos. P. J.: Sauoe. A. J . Chem. Phvs. 1986, 84, 517-521. (d) Photinos, P. J.; Saupe, A. >. Chem. Phys. 1986. 85, 7467-7471. (18) Gault, J. D.; Kavanagh, E.; Rodngues, L. A,: Gallardo, H. J . Phys. Chem. 1986, 90, 1860-1863. (19) Postlethwaite, T. A,: Samulski, E. T.: Murray, R. W. Lungmuir 1994, 10, 2064-2067. (20) Brown, G. H.: Wolken, J. J. Liquid Crysrals and Biological Structures: Academic: New York, 1979. (21) Ruling, J. F. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1994; Vol. 18, pp 28-41, and references therein. (22) (a) Mandal, A. B. Langmuir 1993, 9, 1932-1933. (b) Dayalan, E.; Qutubuddin, S.: Texter, J. In Electrochemisty in Colloids and Dispersions: Mackay, R. A., Texter, J., Eds.: VCH: New York, 1992: Chapter 10. (c) Verrall, R. E.; Milioto, S.: Giraudeau, A,: Zana, R. Lungmuir 1989, 5, 1242-1249. (23) Marcus, M. A. Liq. Cryst. 1986, I , 73-80. (24) Cognard, J. Mol. Cryst. Liq. Cryst. 1982, Supplement 1. (25) Lednicer, D.: Lindsay, J. K.; Hauser, C. R. J . Org. Chem. 1958, 23, 653-655. (26) Hutchison, J. E.; Postlethwaite, T. A,: Murray, R. W. Lungmuir 1993, 9, 3277-3283. (27) (a) Probe diffusion within the hydrophobic regions of the micelles (DM)is expected to be much slower than that in the aqueous region (Dw). Diffusion coefficients of small molecules in water are generally in the cm2/s range, whereas values in confined, hydrophobic media (e.g., lateral diffusion in bilayers) lie generally in the cm2/s range. (b) Shin, Y.K.; Freed, J. H. Biophys. J . 1989, 55, 537-550. (c) Goss, C. A,: Majda, M. J . Electroanal. Chem. 1991, 300, 377-405. (d) Kolchens, S.: Lamparski, H.: O’Brien, D. F. Macromolecules 1993, 26, 398-400. (e) Lindblom, G.: Oradd, G. Prog. NMR Spectrosc. 1994, 26, 483-515. (28) Jonsson, B.; Wennerstrom, H.: Nilsson, P. G.; Linse, P. Colloid Polym. Sci. 1986, 264, 77-88. (29) Kalus, J.: Hoffman, H.; Reizlein. K.; Ulbricht, W.; Ibel, K. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 37. (30) Hayashi, S.; Ikeda, S . J . Phys. Chem. 1980, 84, 744-751. (31) Forrest, B. J.: Reeves, L. W. J.Am. Chem. SOC.1981,103, 16411647. (32) See, for example: (a) Boden, N.: Corne, S. A,: Jolley, K. W. J . Phys. Chem. 1987, 91, 4092. (b) Boden. N.; Ukleja, P.: Jolley, K. W. Condens. Matter News 1991, I , 10-16. JP950152U
