2166
J. Phys. Chem. 1994,98, 2166-2173
Transport and Ion-Exchange Dynamics in Langmuir-Blodgett Films of Fatty Acids Tracy L. Marshbankst and Elias 1. Franses' School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907- 1283 Received: October 4, 1993; In Final Form: December 21, 1993' The rate of ion exchange of Ca2+ by H+in ultrathin organic LB films of calcium stearate was probed by in-situ Fourier transform infrared attenuated total reflection (FTIR-ATR). Calcium stearate was contacted with aqueous solutions of hydrochloric, acetic, or sulfuric acid. Data and calculations for various film thicknesses and film structures indicate that the ion-exchange process was limited by the rate of mass transfer through the film. Heating at 136 OC and cooling changed the film microstructure and made the ion exchange process much faster. Mass transfer was a t directions both normal to the film/solntion interface and laterally, reflecting possible film defects, which either were present or were induced by the ion-exchange process. The acid counterion (Cl-, CH$OO-, or S04") had little effect on the exchange dynamics. No accumulation of the counterion in the film was detected. Microstructural I R information showed that calcium stearate films recrystallized and became more ordered upon conversion to steric acid. The results have implications on the possible uses of LB films as ion-exchange materials or sensors.
Introduction
0.80
Calcium stearate and other salts of fatty acids have been extensively studied as materials for Langmuir-Blodgett (LB) films because of their good deposition and film qualities.'-5 Their ionic composition depends on pH and ion concentrationand affects their cohesion, electrical properties, and optical properties.'" For possible uses as barrier materials, membranes, or sensors, LB films need to be characterized with respect to their transport properties. Whereas the gas transport properties of LB films have been s t ~ d i e d , ~transport -l~ of water and ions has received little attention.I3 Using radioactively labeled compounds, Adam and Zull showed that calcium ions readily moved across a bilayer." This paper focuses on using FTIR-ATR to monitor in situ the ion exchange within LB films exposed to various acids. In a previous paper, we have reported the transport of water and the effect that the ion exchange had on the film microstructure and hydration level.I4 Calcium stearate films which were exchanged with HCl producedstearic acid films which were highly crystalline. Adetailed analysis of the water transport rates indicated that the mechanism involved transport through defects or pores, in addition to Fickian-type diffusion. An analogous mechanism emerges from the data in this paper for ion exchange in LB films.
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Materials and Experimental Methods Stearic acid (puriss grade 99%), calcium chloride dihydrate (99+%), and hydrochloric acid were purchased from Fluka Chemical Co. Sulfuric and acetic acids were reagent grade, from Fisher Scientific. Millipore water was used. The germanium internal reflection plates were trapezoids, 50 X 10 X 2 mm3, with face angles of 45'. For the thinnest film (25 reflections, 13 on the top surface), a trapezoid with 1-mm thickness (5 1 reflections, 26 on top) was used. The Langmuir trough was a Joyce-Loebl Trough-4. LB film deposition details are presented elsewhere.14Js The transfer ratio ranged from 0.95 to 1.0. Infrared spectra were obtained with a Nicolet 800 FTIR spectrometer, equipped with a DTGS room temperature detector and a narrow-band MCT-A cryogenic detector. The ATR optics were built by Connecticut Instruments Co. A sample chamber on the top surface of the ATR plate allowed liquid to contact the LB film.14 The LB film on the t Present address: Ammo Oil, Amoco Research Center, P.O. Box 301 1, Naperville, IL 60566-701 1. * To whom correspondence should be addressed. .Abstract published in Advance ACS Absrracrs, February 1, 1994.
0022-365419412098-2166$04.50/0
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Figure 1. FTIR spectra with unpolarized infrared beam of a 29-layer LB film of Cast2 on Ge contacted with an aqueous solution of HCl, pH * 3, on Ge; water bands were not subtracted: r = 0-,initially; r = 0+, immediately (-3 s) after contact, 3 and 58 min after contact.
bottom side of the ATR plate and some film outside the contact area were removed (using a cotton swab or a thin wooden rod). The spectra during exchange were collected at a low resolution (8 cm-1) to allow for fast acquisition (a few seconds) for probing exchange within seconds. The spectra of the dry samples were obtained at high resolution (1 cm-I). Spectra were fit with a nonlinear least-squares algorithm. Certain films were heated in a laboratory oven and then cooled to room temperature.
Experimental Results and Discussion Transport and Ion-Exchange D y ~ m i c swith Aqueous HCI. Figure 1 shows spectra collected at various times before and during 0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2167
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Figure 2. Same as Figure 1, except that the bulk water and water vapor bands were subtracted from the spectra.
TABLE 1: Peak Assignments for Cast2 LB Films oeak 1 2 3 4
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
vibration CH, .Y ip
comment methyl asymmetric stretch, in backbone plane methyl asymmetric stretch, out of backb&e plane appears in Casta a-CH2, COO- overtone Fermi resonance methylene asymmetric stretch Fermi resonance methyl symmetric stretch CHI v8, a-methylene methylene symmetric stretch carbonyl stretch carboxylate asymmetric stretch methylene scissor carboxylate symmetric stretch COOH deformation progression band COO- deformation, OH deformation carbon-carbon vibration OH deform op 0-H out-of-plane deformation methylene chain totally in-phase rock CHI r
the exposure of a 29-layer LB film to an aqueous HCl solution. The assignments of the various peaks are given in Table 1.lkl7 Theabsorptionduetowaterat ca. 1620cm-'obscures thecarbonyl and carboxylate bands. Figure 2 shows the same spectra as in Figure 1 but with the water lines subtracted (based on a pure water spectrum). With this subtraction thedetails of thecarbonyl and carboxylate species can be detected better. The water transport data have been analyzed e1~ewhere.l~ The conversion of Cast2 to StH was followed from the carbonyl (1700 cm-l) and the carboxylate (1590 and 1540 cm-l) vibrations. The carbonyl stretch was initially absent but could be seen clearly 3 s ( t r 0+) after exposure to the acid solution. This signal increased with time, as did the COOH deformation band at 1300 cm-'. The COO- vB doublet band decreased in intensity as the salt was converted. Peak 16 (unassigned, but probably due to COW, Table 1) also decreased in intensity during the ion exchange. Additionally, the CH2 (y a)progression band intensified with prolonged exposure to aqueous hydrochloric acid, indicating an increase in ~rystallinity.1~ Experiments were conducted with Y-type films having 19,29, 39, or 119 molecular layers. Each layer is about 25 A, as determined from the bilayer thickness obtained by X-ray diffraction.14 Quantitative analysis was accomplished by integrating the CH spectral region from 3000 to 2800 cm-l, the C = O region from 1740 to 163Ocm-', and theCOO-asymmetricstretch region from 1600 to 1500 cm-I by the use of a linear base line between the integration limits. The integrated absorbances are shown in Figures 3-6. The carbonyl band intensities reached steady values as the film became 100% fatty acid. The carboxylate band intensities
+
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Figure 3. Integrated absorbances: (A) in cm-I; (B) c-0mole fraction vs time; data for a 19-layer Cast2 LB film contacted with aqueous HCl solution at pH = 3. (A) 0,CH, 3000-2800 cm-I; A, C O O v., 1640-1550 cm-I; C 4 v , 1750-1650 cm-I. (B) 0, C = O mole fraction in film.
reached nonzero steady values, because some film on the ATR crystal had not contacted the aqueous solution and had not been fully removed.15 The steady values were subtracted from the carboxylate absorbances. Then, the integrated absorbances were normalized between 0 and 1 to yield quantities proportional to the number of moles of each group, and the mole fractions of carbonyl in the contacted films were calculated (Figures 3B6B). This proceduretakes into account the different absorptivities of the two bands and the slight loss of hydrocarbon intensity observed for all films.l5 The loss of hydrocarbon intensity stopped as soon as ion exchange ceased. Moreover, the films displayed some opalescence after the exchange, and their interference colors changed, reflecting the loss of material. About 14% of the hydrocarbon intensity was lost from the 19-layer film, and 16% and 14% of the intensity were lost from the 29- and 39-layer film, respectively. The thickest film (1 19 layers) showed only about a 5% loss (Figure 6A). These data can be explained if there is a loss of some material from the film, although no direct evidence of material loss is available. Change in hydrocarbon intensity due to molecular reorientation of the chains is unlikely, because both bands of the symmetric and asymmetric CH2 stretch vibrations (and the CHs bands) were integrated. However, the change can be due in part to film reorganization and crystallite formation, which recently was observed for LB films of cadmium salts of fatty acids by atomic force microscopy.'* Such reorganizationcan cause surface roughness, which increases the thickness of the film in some regions and can indeed decrease the film absorbance, as detailed below. Nonetheless, the loss affected little the ion-exchange data and their interpretation.
2168 The Journal of Physical Chemistry, Vol. 98, No. 8, 1994
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Figure 4. Same as Figure 3, but for 29-layer film.
Figure 5. Same as Figure 3, except for 39-layer LB film.
The integrated intensities (per reflection of the I R beam) of the CH band increased with thickness but in a nonlinear fashion: A / N = 0.57,0.75, 1.17, and 1.78 cm-l for the four films. If the films are effectively isotropic and of the same density pf and if they have a uniform thickness I, an absorptivity af,and an attenuation coefficient yf, then the absorbance per reflection should be as f o l l ~ w s : ~ ~ J ~ - ~ ~
the observed loss in hydrocarbon intensity is due to material loss or crystallite reorganization.ls It is interesting to note that no intensity change was observed in the reverse ion-exchange process, when 19- and 23-layer films of stearic acid were contacted with aqueous Ca(OH)*.1s We will now focus on the time dependence of the ion exchange (Figures 3J3-6B). Noneofthecurvesshow any periodicity (which could be expected from an ideal multibilayer structural model; seemodel section later), suggesting that thetransport rate through the film is fast compared to the reaction (ion-exchange) rate. If the mass transport were slow compared to the reaction rate, then for a perfectly lamellar structure the reaction rate would oscillate as consecutive COO- layers would be fully exchanged. For a uniform one-dimensional diffusion process, this means that the ratio of the reaction rate to the diffusion rate is small. However, if there were transport through the film via defects, followed by lateral transport and reaction along the polar group planes, then no periodic reaction rate would be observed either. In both cases, material in all of the polar regions would be reacting simultaneously. In the first scenario, the reaction rate would determine the overall exchange rate. In the second, either the lateral transport along the polar planes or the reaction rate, or both, could determine the overall ion-exchange rate. Ion exchange in the 19-layer film was complete within 15 min. For the 29-layer film the time was about the same. This suggests that for films of -47-72 nm in thickness the rate-limiting process does not depend on the film thickness. Having no dependence on the film thickness indicates that transverse, Le., normal to the film surface, mass transfer is not the rate-limiting process. The 39-layer film (Figure 4) took about 25 min to equilibrate, and the 119-layer film (1 zz 300 nm) took ca. 150 min. We infer that above a thickness of approximately 100 nm the transverse mass transport through the film starts affecting the overall
Here,
where npand nf are the refractive indices of the plate and the film, respectively, 0 is the incident angle (0 = 45'), and X is the wavelength in vacuo; also, np = 4.02, nf = 1S O , 0 = 45, and X = 3.4 pm.I4 Then, yf = 4.40 pm-'. From these equations we obtain for the four films K pmf/2yf = 1.66, 1.59,2.03, and 1.92 cm-l, respectively, from which af can be calculated. The values differ by ca. 10% from the average of 1.80 cm-1. This variation may reflect some differences of the densities or transfer ratios of the films. Overall, these results are useful for evaluating the contributions to the total absorbance of portions of the sample differing distances from the surface. For the carboxylate band, however, Tf = 2.4 pm-l, and for the carbonyl band, yf = 2.6 pm-1. If the films are nonuniform in thickness or become nonuniform after exposure to the acid solution, then eq 1 shows that the absorbance should decrease as the distance I of some molecules from the ATR crystal/film interface will increase. Without detailed roughness data or AFM data, we cannot establish whether
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2169
Langmuir-Blodgett Films of Fatty Acids
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OCOOOOOO 0 0 0 0 0 0 0 0
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Figure 7. ATR-FTIR spectra (unpolarized) of Na~S04and Cas04 deposited from aqueous solution on a Ge crystal.
0.8
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Figure 6. Same as Figure 3, except for 119-layer LB film.
conversion rate. The equilibration time does not scale with 12, suggesting that the process is not controlled by one-dimensional diffusion. Transport and Ion Exchange with Aqueous HzS04 and CH3COOH. These experiments were done to get information as to whether the acid counterions affect the ion-exchange process. One additional question is whether the exchanged calcium remains within the film in the form of a salt of the acid anion (CaC12). Another question is whether the H30+ions “carry” along their counterions into the film for electroneutrality. Although C1- is not directly detectable using IR spectroscopy, it could be detected indirectly through water of hydration in the CaC12 crystal, if such crystals remained within the film. To further probe this issue, we studied two acids with anionsother than C1-. The sulfuric acid was selected for its strong infrared band due to the S042ion. The acetic acid group was chosen because it is an organic acid of bigger molecular size. The experiments were carried out under the same conditions as with HCl acid, i.e., pH = 3 and 29 layers of Cast;! on Ge. High-resolution spectra were collected before and after the ion-exchange process. No S042-ions were detected during ion exchange with aqueous HzS04. The following control experiment was done to check for the sensitivity in detecting the presence of the S O P ion within the film. The spectra of Na2S04 and CaS04 deposited on an ATR crystal were obtained, as shown in Figure 7. The Na2S04 was dissolved in water and the solution was placed on an ATR crystal and dried at 90 OC. The deposited Na2S04contained a molar amount of S042-equivalent to the number of moles of Cast2 in 29 LB layers. Therefore, if all of the calcium in an LB film formed CaS04, the peaks would be similar in intensity to those in Figure 7. A comparable amount of C a s 0 4 was also tested (but due to its low solubility in water its amount was not precisely known). The ion has absorbances at 1125-1080
cm-l, due to the asymmetric stretch vibration, and a weak peak a t 1000 cm-1, due to the symmetric stretch vibration,I7.2*which is forbidden in the infrared because of symmetry arguments” but is occasionally visible, though weak, as in this case. The spectra of Cas04 and Na2S04 clearly showed an intense S042va band at 1100-1 130 cm-I and the vs band a t about 1000 cm-1. Absorbances as small as 0.003 units can easily be distinguished, especially if they are as sharp as the S042-bands shown. Thus, had just 1% of the original calcium formed CaS04and remained in the film, it would have been observable in the spectra. Since no Sod2band was seen, we inferred that there was no measurable S042-in the film after the ion exchange of Cast2 with H2SO4. Furthermore, it is well-known that Cas04 is a strong desiccant and readily absorbs water. In Figure 7,a water peak at 1620 cm-I was visible in the CaS04 spectrum, indicating that Cas04 absorbed some water in the infrared spectrometer which was purged with “dry” air. If Cas04 can absorb water in the purged spectrometer, it would certainly have retained water if it had just been in contact with an aqueous solution. Since the spectra showed that the final S t H films were free of any measurable water (just as was observed for the HC1-exchanged films), we infer that no measurable amount of sulfate salt was present within the LB film. For the acetic acid exchange, no additional bands due to the acetic acid (which has similar groups as StH) could be resolved.*s Nonetheless, since no water was detected, it is unlikely that calcium acetate was present to any significant extent. Exposure to acetic acid caused a 29%drop of the hydrocarbon intensity, compared to only 7% for the sulfuric acid and to 14% for the hydrochloric acid. Again, the drop occurred rapidly during the ion penetration and ceased when the reaction was completed. The rates of the ion exchange with aqueous H2S04 and CH3COOH were similar, with the CH3COOH being slightly slower (Figure 8). Both were somewhat slower than in the aqueous HCl exchange (Figure 4). Thus, it appears that the anion type did not affect significantly the ion-exchange rate. Effect of Prior Film Annealing on Ion-Exchange Rates. Whereas annealing at 120 “C had a minimal effect on the film structure, annealing a t 136 “ C resulted in an amorphous film, as detailed elsewhere.14J5 This latter annealing caused a loss of 37% of the material.15 In order for the effect of the microstructure on the ion-exchange rate to be investigated, films previously treated a t both temperatures were contacted with HCl solutions. In the 120 OC treated film there was a slight slowing of the overall ion-exchange rates. However, for the 136 O C treated film the effect was quite dramatic. Figure 9 gives examples of certain
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The Journal of Physical Chemistry, Vol. 98, No. 8. 1994
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Figure 8. Mole fraction of c=O vs time for 29-layer LB films e x p e d to pH = 3 acetic acid and sulfuric acid solutions: 0, acetic acid: 0 ,
sulfuric acid. 1.70
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Figurelo. Sameas Figure4, but for filmafter 136OCthermaltreatment.
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spectra of annealed (I36 "C) Cast2 film (29layer) exposed to hydrochloric acid solution at various times. Water and water vapor bands were subtracted. Figure 9. ATR-FTIR
transient spectra collected during the ion exchange. The entire exchange process was completed in less than 25 s (Figure IO). Clearly, the disruption of the structure of the LB film, by melting a t 136 OC and refreezing, dramatically altered the ratecontrolling mechanism in the ion-exchange process. From the fast exchange compared to the previous data, it is inferred that for the nonmelted films there were significant mass-transfer limitationson the overall exchange rate. This experiment provided a lower bound for the intrinsic rate of ion exchange. We conclude that the ion-exchange rate in previous LB films is significantly controlled by mass transfer. Structure defects may also be important in determining the mass-transfer rate. Annealingat 120°C, with nomelting, slowedtheexchange process slightly compared to that of untreated films. The 120 "C treatment may have healed some defects within the film and increasedtheeffectivemass-transfer resistance. The film probably melted at 136 OC. When it was cooled and recrystallized, a large number ofdefects (orgrain boundaries) probably formed, resulting in increased mass-transfer rates. The increase could be due to either increasing theeffective diffusivityor reducing the effective diffusion length, or both.
One-Dimensional Diffusion and Reaction Model In order to gain further insight into the mechanisms affecting the ion-exchange process, a simpleone-dimensional diffusion and reaction model was developed. Two limiting cases, diffusion controlled or kinetic limited, were used to p i n t which process
0
Figure 11. Geometry of LB film used in modelcalculations. Illustration of actual distribution of polar groups in multibilayer structure and of
continuous distribution used in model calculations. was ratedeterminiug. The model uses one-dimensional, Fickiantype diffusion with diffusivity DA(or simply D) of the aqueous ions (species A) into a film of carboxylate groups (species B). Thecarboxylategroupsofthefilmarefixedinspace(Figure11). The reaction between A and B was assumed to have irreversible bimolecular kinetics with rate constant k.
(RCOO-),Ca2+ + 2H,O+
+ 2CT-
2RCOOH + CaCI,
+ H,O
The mass conservation equation describing the accumulation of A within the film is
ac, -=
at
a2cA
D - -at2
kCACB
(3)
The ATR crystal is of course impenetrable, resulting in no flux ofAatx=/(Figurell). Furthermore,CAoatx=Owasassumed
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2171
Langmuir-Blodgett Films of Fatty Acids to be constant to account for the solubility of A (H30+) in the film. Initially, there was no A within the film. In mathematical terms these considerations lead to the following boundary conditions and initial condition for A:
CA=CAo
acA/ax= o CA(X) 0
atx=O
W B / ~ T= -aP$A$B
=
(16)
Solving eq 16 with the initial condition (15) yields15
(4)
+B(T) = e*gr
at x = I
(5)
at t = 0
(17)
or
(6)
Species B is described by a similar differential equation, with its diffusivity set equal to zero. The consumption of B is equal to the rate of reaction.
acB/at = -kCACB
(7)
For a Y-type LB film, the reactive polar groups are located two hydrocarbon chain lengths away from each other (-50 A for StH). In this model, it is taken that the carboxylate groups are distributed uniformly throughout the film. This assumption creates an effective concentration of B which is lower than the actual maximum concentration of B within the film (Figure 11). Since no periodicity in the reaction rate was observed (Figure 3 4 , the assumption of a uniform and continuous initial distribution appears to be appropriate and implies the following initial condition for B:
CB(x) = CBo
1 throughout the film. This uncouples eqs 9 and 10, resulting in
at t = 0
Thus, +B is constant throughout the film. The total amount of component B, ZB,is given as I)B or Z B / Z ~= e-cA&t. The parameters in the exponent show that the amount of B depends on the reaction rate constant and the solubility CAOof the mobile species A, but not on the thickness of the film. Therefore, the reaction rates for thin films which have a low CY should not be a function of the film thickness in this limiting case. The second limiting case is that of fast reaction compared to diffusion. In this case, any amount of A which reaches some B reacts immediately. There is no coexistence of the two species, and the concentration profiles would appear as fronts (Figure 12). In this limit, the flux of A ( N A )Can be written in terms of the distance e that the front has traveled a t time c. The concentration of A at x = e is zero, and CAis described by the steady-state, linear solution for diffusion across a slabof thickness e, which depends on time. Then,
(8)
where Ce0 is about 3 mol/L (based on a film density of -1 g/cm3). The differential equations are cast in dimensionless form as follows:
The total amount of remaining B is J!B
(9)
= zBO(1 - 6 )
(20)
Conservation of species dictates that the rate of disappearance of B per unit area is equal to the flux of A. Therefore,
which yields
Moreover, c=O
att=O
The solution to eqs 22 and 23 is
where
‘A0
(15)
Consequently, the total amount of B is
LBO
Two dimensionless groups emerge and were used as adjustable parameters, since no independent measurements of CAO,k,and Dare available. The parameter,a is the ratio of the reaction rate to the diffusion rate, and j3 is the ratio of the solubility of A within the film to the initial concentration of B. This problem has been solved numerically, as detailed elsewhere.15 This model does not account for the intensity attenuation implied by eq 1.14 Before we discuss the solution of the full problem, it is useful to describe the model behavior in two limiting cases. If the diffusion rate of A is much faster than the reaction rate, or CY 1 the total amount of B is zero; Le., all the B has reacted. When this case is valid, one should observe a length dependence of 1/ P in the equilibration times for films of differing thicknesses, as is common for diffusional processes. In the next section, it is shown that these simple one-dimensional models cannot adequately represent the data. They do provide,
2172
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994
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Figure 14. Comparisonofdiffusion/reactionmcdelwith (L = 0.01 (curves 1 and 2) and a = 10.0 (curves 3 and 4) and 0 = 0.0005 to mole fraction ofC4vstimefor 19-layerLBfiImofCaStzexposed topH = 3 aquwus HCI solution. The following values of diffusivitv (in cm2/s) were used forcurves 1,2,3,and4,resp;ctively: 7.5X IIF.3.i X 1+,3.3 X IV'O,
and 8.3 X IV".
0.6 0.4
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diffusivities which are lower than those of ions in liquid water. The diffusivity for HCI in water at 25 OC at 0.1 M is 3 X 16-s cmZ/s.21 The value of the dimensionless reaction rate a was first chosen to be relatively low, a = 0.01, to better describe the data. For this value, data for the 19-layer film are compared to the model for two values of diffusivity (Figure 14). No single value of diffusivity could fit the entire curve. Figure 14 also shows a similar comparison, but f o r a = 10.0. The general agreement is worse than for o( = 0.01. We infer that there may be other processes involved in addition to one-dimensional diffusion and reaction. Similar results were obtained for other films.'s The diffusivity value which can fit the initial data cannot fit the latter portion of the curve. This suggests that the "effective diffusivity" (the value that fits the data at each point) is not constant. One possible reason is the change in the structure and crystallinity of the film as the exchange progresses. The diffusivities of ions in the wetted film, estimated with large values of f3 (0.0005) and a (0.01), are around 1V cm2/s. Bycontrast, thediffusivityofwaterin the barefilm wasestimated to range between 10-10 and 16-13 cm2/s.l' If f3 were taken as lower than 0.0005, the disparity would be increased. If 01 were raised, the difference in diffusivity would be smaller, hut the fit would be worse. Despite its low diffusivity, the water saturates the film faster, because its concentration is higher and because it is not consumed. Then, the ions may propagate with a higher diffusivity, but with low overall rate (larger timescale), through the ahsorbed water. Our diffusivity estimates are 1000 times smaller than those of HCl in liquid water, which may not be unreasonable for ions through the polar regions of a solid. To quantitatively interpret the absorbance data, one needs to account for the different intensity of the evanescent wave at different distances from the crystal-film interface. This problem wasdiscussed in the first Resultssubsection (eq 1) andelsewhere.14 For the thinnest film (I = 0.047 pm) 2yll = 0.25, and Beer's law is a fair approximation. For the thicker films, some correction in the model would be appropriate. On the hasis of the thickness dependence of the equilibration times, the time dependence of equilibration, and the model calculations, we have developed the hypothesis that transport occurs substantially through film defects. This idea is consistent with the hydrocarbon regions being little permeable to water (and ions). Then, there would be three stages of transport in the fihqassketchedin Figure 15. Thecrystallitesofaveragedomain thickness I could, of course, be more polydisperse in size or more
, 0
10
5
15
TIME, min.
Figure 13. Best fit of reaction-rate-limited and diffusian-rate-limited cases to mole fraction of C 4 vs time for 19-layer LB film of Cast2 exposed to pH = 3 aquwus HCI solution.
however, a framework for gaining a clearer understanding of what type of mechanism may control the physical process and may providea starting p i n t for further theoreticaldevelopments. Comparison of Data with Model
Data for a 19-layer film of CaStz are compared in Figure 13 to simulations for the two limited cases. The curves are the best fit of the acid ( C 4 ) mole fraction data to eqs 18 and 25, using A'-= (l-XB)=(l-ZB/ZBO), Althoughneitherfitisadequate, the reaction-limited model does provide a curve shape which tracks the experimental data better. The diffusion-limited case does not describe the data qualitatively. Nonetheless, the adequacy of the fit of the model to the data cannot be used to establish the mechanism, as will be detailed later. In the simulations presented, a value of f3 CH,o+/Ccoo= 0.0005 was used. This value is probably an upper limit for reasonable values of the ion solubility in the LB film. No informationis availableabout the actual value of CH@ A smaller estimate is actually reached if one assumes that two molecules of water are taken up in the film per CaSg unit and H1O+ partitions as the water phase (pH = 3); then i3 = 0.000 02. If we usetheupper limit of 16wt % forwatercontent inthefiIm,l4then the molar concentration of water is 9 M and f3 = 0.000 06. The value of 0 has a strong impact on the time scale 1' of the overall ion-exchange time, as it controls the maximum concentration of the mobile ion in the film. Using lower values of f3 would cause one to raise the dimensionless completion time for the reaction ( T ) and would require using larger values of diffusivity to match the data (as 1* = d 2 / D ) . If values of f3 less than le5are used, thediffusivity would becomeunreasonably high for ions in a solid phase. The large value of f3 (0.0005) was chosen for yielding
Langmuir-Blodgett Films of Fatty Acids
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The Journal OfPhysical Chemistry, Vol. 98, No. 8. 1994 2173
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2.. or 7.3
T I
Figure 15. Schematic of possible mechanism of ion exchange showing the various time scales.
randomly positioned than sketched. In this mechanism, in the first stage the defects or holes would be filled with water by a transverse (normal to the crystal surface) transport mechanism with a time scale rtl. This stage would involve both water and ions and should be related to the water uptake rate measured.15 In the second stage, there would be diffusion into the crystallites, laterally with a time scale rl. At the same time, ions would he transported through the water-filled channels, with another transverse time scale r12. to replenish those lost to reaction (with time scale 7,). The ion exchange would happen in the third stage. The evidence supporting this picture is that all films possess masstransfer limitations, yet for the two thinnest films the thickness had little effect. For the thicker films (39 and 119 layers) the total reaction time increased with thickness. Thus, one gets an essentially mass-transfer-limited process which does not scale with thickness at small thicknesses hut does so better at larger thicknesses. Hence, two other mass-transfer stepsare suggested, with their relative time scales being a function of thickness. For diffusion-typeprocesses with effectivediffusivitiesDt,cwand if t,s I?/LJ~,~w and TI = l?/D~.~ff, then the relative magnitude of the time scales would vary with the film thickness I,. For thin films, rl would be the controlling time scale. As the thickness of the film is increased, T , would increase and eventually become comparable to rI. The dimension I. would probably depend on theLBfilmdeposition processand subsequent treatments. Ifthe two time scales are comparable in magnitude, then the overall ion-exchange rate would show a film thickncss dependence. If lateral transport controlled the rate, then breaking up the film, or melting, could lower thevalue of 11, thus increasing the overall conversion rate. For the thicker films, if transverse transport controlled, then the breakup of the film into smaller particles would have a minor effect as the film thickness would he the controlling length scale. ItispossiblethatD,,~could beincreased hy the breakup into smaller crystallites, as more defects are introduced, increasing the reaction rate even for melted thick films. Future work should help also clarify further the relative importanceoftransverse and lateral transport and clarify further the microstructural basis of the proposed mechanism. The model considers transport of thereactant through the film and is silent about whether the reactant is the reacting ion alone (H,O+)or the ion with its counterion. The evidence that the counterion is not detected and has no effect suggests that the
former possibility is more likely. This would imply some net local charging and would require a more detailed analysis of electrochemical transport. Such an analysis is beyond the scope oftheavailahledata, hut it would beuseful inevaluating possible uses of LB films as ion sensors or materials for ion-exchange or membrane applications.
Conclusions Ion exchangeofCa2+by H+in calcium stearate LB films takes from minutes to hours, depending on film thickness and prior thermal history of samples. The rate does not depend on the counterion type (chloride, sulfate, acetic). No counterion was detected in the film during the ion exchange, and the calcium ions do not remain in the film after the exchange and the removal oftheaqueoussolution. Themain controlling mechanism appears to he mass transfer in the directions both normal and transverse tothe filmsurface. A modelofonedimensional Fickian diffusion and reaction cannot describe well the data, implying a more complex mechanism. The diffusion coefficientof HIO+ ions can only be roughly estimated if the partition coefficient in the film is known.
Acknowledgment. This work was supported in part by NSF (CBT864904andCTS9004147) andhya DavidRossfellowship. We thank Prof. W. N. Delgass and MI. G.J. Howsmon for the use of their curve-fitting routines and Dr. D. J. Ahn for helpful discussions. References and Notes ( I ) Blcdgett, K. B. J. Am. Chem. Sof. 1935.57, 1007. (2) Blcdgett. K. B. Phys. Reo. 1937.41,975. ( 3 ) Gaincs. G. L. Insoluble Monolayerr ot rhe Liquid-Gos Inlcrfocc; Interscience: New York, 1966. (4) Takenaka,T.; Nogami, K.;Gotoh, H.;Gotoh. R.J . Colloidlntcrfaee Sci. 1971, 35, 395. ( 5 ) Kimura, F.: Umcmura, J.; Taekenaka, T.Longmuir 1986, 2. 96. ( 6 ) Ahn, D. J.: Franses, E. 1. J . Chem. Phyr. 1991, 95.8486. (1) Petty, M. C. InLoangmuir-BlodgertF i l ~Roberts, ; G .G.,Ed.; Plenum Press: Ncw York. 1990. (8) Rose, G. D.; Quinn, I. A. 3. Colloid InterJke Sa'. 1968, 27, 193. ( 9 ) Albrwht, 0.; Laschewsky, A,; Ringdorf, H. J. Membr. Sa'. 1985, 22, 187. (IO) Vandewan. R. I.; Bams. G. T.Thin Solid Films 1985.134.221. (11) Bruinrma. P J.; Spmncr. G. J. R.; Colrman, 1. B.. Korcn. R.; Slurason. C ; S l r w c , P Thin Solrd F h r 1992. 2/0/211, 440. (121 Oriandcr. R ;Korpium. P.; Durehl. C.;Knoll. W . Thin SolidFilmr ,a** ,A"
