Effect of Humidity and Temperature on Molecular Mobility in Surfactant

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Effect of Humidity and Temperature on Molecular Mobility in Surfactant Monolayers Confined between Two Solid Surfaces Jong-Choo Lim,† Ronald D. Neuman,‡ and Sangkwon Park*,† Department of Chemical and Biochemical Engineering, Dongguk University, 3-26, Phil-Dong, Choong-Gu, Seoul, 100-715, Korea, and Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849 Received December 13, 2001. In Final Form: May 6, 2002 The lateral diffusion coefficient (Ds) of fluorescent-labeled probe molecules in surfactant monolayers of fatty acids confined between two silica surfaces was directly measured as a function of relative humidity (RH) and temperature by the fluorescence recovery after photobleaching (FRAP) technique. The RH dependence of Ds in myristic acid monolayers showed a general trend that the molecules become more mobile with increasing RH. Two distinct RH regimes of different mobility behavior were observed. The molecular mobility characteristics in each regime are explained in terms of the formation of a hydration layer and the capillary condensation of water vapor from the ambient atmosphere. The RH dependences of Ds in stearic acid monolayers and oleic acid monolayers showed similar trends to those in myristic acid monolayers, except that stearic acid monolayers yielded a much smaller Ds and no immobile fraction, whereas oleic acid monolayers gave a somewhat larger Ds and immobile fraction than those in myristic acid monolayers. As the temperature is raised, Ds increases in an exponential manner under dry (0% RH) conditions. At 45 and 55% RH, Ds initially decreases upon heating, and then increases and appears to remain constant above 65 °C. This trend was proposed to be because of the combined effect of RH reduction and thermal energy increase upon heating. Finally, upon repeated heating and cooling, Ds becomes lower, which implies that the monolayers undergo some irreversible structural change. These findings provide new information on the general mobility behavior of surfactant molecules in confined geometry relevant to boundary lubrication.

1. Introduction Boundary lubrication is referred to as “a condition of lubrication in which friction and wear between two solid surfaces in relative motion is determined by the properties of the solid surfaces and boundary lubricant films other than bulk viscosity”.1 Conventional studies have provided macroscopic pictures of the tribological characteristics of thin organic films by investigating the effects of film material,2-8 film thickness,3,6 nature of substrate surface,3,6 relative humidity (RH),9-12 and temperature3,6-8,13,14 on boundary lubrication performance. Recently, with the development of the surface forces apparatus (SFA)15-17 * To whom correspondence should be addressed. † Dongguk University. ‡ Auburn University. (1) Fein, R. S. Lubr. Eng. 1991, 24, 1005. (2) Hardy, W. B.; Doubleday, I. Proc. R. Soc. London, Ser. A 1922, 102, 550. (3) Bowden, F. P.; Gregory, J. N.; Tabor, D. Nature 1945, 156, 97. (4) Levine, O.; Zisman, A. J. Phys. Chem. 1957, 61, 1068. (5) Levine, O.; Zisman, A. J. Phys. Chem. 1957, 61, 1188. (6) Bowden, F. P.; Tabor, D. The Friction and Lubrication of Solids, Part II; Clarendon: Oxford, 1964. (7) Briscoe, B. J.; Scruton, B.; Willis, F. R. Proc. R. Soc. London, Ser. A 1973, 333, 99. (8) Briscoe, B. J.; Evans, D. C. B. Proc. R. Soc. London, Ser. A 1982, 380, 389. (9) Tingle, E. D. Nature 1947, 160, 710. (10) Li, Y.; Trauner, D.; Talke, F. E. IEEE Trans. Magn. 1990, 26, 2487. (11) Tanimoto, K.; Rabinowicz, E. Tribol. Trans. 1992, 35, 537. (12) Tian, H.; Matsudaira, T. Trans. ASME 1993, 115, 28. (13) Frewing, J. J. Proc. R. Soc. London, Ser. A 1942, 181, 23. (14) Matveevsky, R. M.; Buyanovsky, I. A. ASLE Trans. 1987, 30, 526. (15) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1978, 74, 975. (16) Parker, J. L.; Christenson, H. K.; Ninham, B. W. Rev. Sci. Instrum. 1989, 60, 3135.

and friction force microscopy (FFM),18-20 much effort has been made to understand boundary lubrication at the molecular level.21,22 Israelachvili and co-workers have reported that the structure, thickness, mobility, phase state, and adhesion of surfactant monolayers confined between two mica surfaces strongly depend on the ambient environmental conditions such as RH and temperature.23-26 In particular, they have shown that adhesion hysteresis is directly related to friction force and is significantly influenced by RH and temperature.27,28 They speculated that RH and temperature significantly affect not only the structure of the surfactant monolayers in the contact region between two solid surfaces but also the molecular mobility in the monolayers. (17) Israelachvili, J. N.; McGuiggan, P. M. J. Mater. Res. 1990, 5, 2223. (18) Noy, A.; Frisbie, C. D.; Rozsnyai, L. F.; Wrighton, M. S.; Lieber, C. M. J. Am. Chem. Soc. 1995, 117, 7943. (19) Liu, Y. L.; Evans, D. F.; Song, Q.; Grainger, D. W. Langmuir 1996, 12, 1235. (20) Clear, S. C.; Nealy, P. F. J. Colloid Interface Sci. 1999, 213, 238. (21) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1992. (22) Meyer, E.; Overney, R. M.; Dransfeld, K.; Gyalog, T. NanoscienceFriction and Rheology on the Nanometerscale; World Scientific: New Jersey, 1998. (23) Chen, Y. L. E.; Gee, M. L.; Helm, C. A.; Israelachvili, J. N.; McGuiggan, P. M. J. Phys. Chem. 1989, 93, 7057. (24) Chen, Y. L. E.; Helm, C. A.; Israelachvili, J. N. J. Phys. Chem. 1991, 95, 10736. (25) Chen, Y. L. E.; Helm, C. A.; Israelachivili, J. N. Langmuir 1991, 7, 2694. (26) Chen, Y. L. E.; Israelachvili, J. N. J. Phys. Chem. 1992, 96, 7752. (27) Yoshizawa, H.; Chen, Y. L. E.; Israelachvili, J. N. J. Phys. Chem. 1993, 97, 4128. (28) Yoshizawa, H.; Chen, Y. L. E.; Israelachvili, J. N. Wear 1993, 168, 161.

10.1021/la011802q CCC: $22.00 © 2002 American Chemical Society Published on Web 07/09/2002

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The molecular mobility in boundary lubricant monolayers is a good indication of lateral and vertical interactions between the monolayer molecules, and therefore it indirectly reflects the physicochemical status such as the structure and phase of lubricant monolayers. Historically, a few attempts to measure the mobility of surfactant monolayer molecules on and/or between solid surfaces have been made. In the 1950s, Rideal and Tadayon measured the surface mobility of radioactive-labeled stearic acid molecules and concluded that the molecular transfer from one mica surface to another occurs by overturning and migrating along the contact point between the substrates.29,30 At about the same time, Young observed that stearic acid molecules weakly adsorbed on unreactive surfaces such as quartz or glass are easily desorbed, and he speculated that the desorbed molecules readsorb onto either another part of the same surface or the second surface after diffusing over a considerable distance in the vapor phase.31 Levine and Zisman reported that condensed monolayer molecules of hexadecylamine hydrochloride between sliding surfaces rapidly transfer onto the other surface by desorption and readsorption, and they considered this molecular transfer as one of the causes of lubrication failure.5 Recently, Adamson and Slawson32 confirmed Young’s hypothesis by demonstrating the transfer of radioactive-labeled palmitic acid molecules from one silica gel plate to the surface of another vertically separated plate by an evaporative-hopping mechanism. Although these studies have provided knowledge on the surface mobility of surfactant molecules, in the literature there does not appear to be any detailed information (probably because of difficulties of experimental approach) regarding the effects of RH and temperature on the molecular mobility in confined surfactant monolayers, which is crucial for better understanding of the dynamic behavior of boundary lubricant molecules. In our laboratory, we have employed the fluorescence recovery after photobleaching (FRAP) technique to directly measure the lateral diffusion coefficient (Ds) of fluorescentlabeled probe molecules in myristic acid monolayers confined between two silica surfaces as a function of RH at constant (ambient) temperature.33 Herein, the study of lateral mobility was extended to oleic acid and stearic acid monolayers. In addition, the temperature dependence of Ds in the myristic acid monolayers was examined at two initial RH conditions as well as the effect of heatingcooling cycles on Ds. The effects of RH, temperature, and heating-cooling cycles on the molecular mobility in confined surfactant monolayers are discussed in terms of the monolayer structure and phase behavior. 2. Experimental Section 2.1. Materials. Myristic acid (99.5+%, Aldrich), stearic acid (99.9+%, Applied Science Laboratories Inc.), and oleic acid (99.9+%, J. T. Baker) were employed as model boundary lubricants because fatty acids are known to significantly reduce friction between two solid surfaces.3,6 Fused silica of opticalgrade finish with surface roughness of about 3.0 nm (rms value, which was measured by alpha-stepper, Tencor Instrument), rather than atomically smooth mica, was chosen as the solid substrate, because silica represents a technologically important class of materials. The silica substrates also allow us to study (29) Rideal, E.; Tadayon, J. Proc. R. Soc. London, Ser. A 1954, 225, 357. (30) Rideal, E.; Tadayon, J. Proc. R. Soc. London, Ser. A 1954, 225, 346. (31) Young, J. E. Aust. J. Chem. 1955, 8, 173. (32) Adamson, A. W.; Slawson, V. J. Phys. Chem. 1981, 85, 116. (33) Park, S.; Shah, P.; Neuman, R. D. J. Phys. Chem. 1994, 98, 12474.

Lim et al. the effect of surface roughness on the molecular mobility behavior of surfactants. For FRAP measurements, 4-(hexadecylamino)7-nitrobenz-2-oxa-1,3 diazole (NBD-hexadecylamine, 98+%, Molecular Probes) was selected as the fluorescent probe because its effect on the surface pressure-area isotherm of myristic acid has been shown to be negligible at 1 mol % concentration.34 The myristic acid and NBD-hexadecylamine were further purified by recrystallization five times from double-distilled chloroform (Optima, Fisher). The stearic acid and the oleic acid, however, were used without any further purification. 2.2. Langmuir-Blodgett Monolayer Deposition. A dilute (typically about 2-3 mM) chloroform solution of a fatty acid/ NBD-hexadecylamine mixture was spread onto the surface of double-distilled water. The spread monolayer was compressed to 12 mN/m and deposited by the Langmuir-Blodgett technique onto the cylindrical surfaces (R ≈ 2 cm) of two silica disks identical to those employed in surface forces studies. All glassware and Teflon components used for monolayer deposition were cleaned with a hot concentrated nitric acid/sulfuric acid (50/50) mixture. Prior to the deposition, the silica disks were washed with doubledistilled petroleum ether (Optima grade, Fisher), soaked overnight in a hot nitric acid/sulfuric acid mixture, and copiously rinsed with double-distilled water. 2.3. Fluorescence Recovery after Photobleaching. The basic principle of the FRAP technique employed in this study is to monitor the fluorescence recovery because of the diffusional exchange of bleached and unbleached probe molecules across an illuminated circular region after quenching the fluorescence inside the illuminated region. The detected fluorescence recovery reflects the lateral diffusion rate of the fluorescent probe molecules assuming that spontaneous recovery does not occur. The characteristic diffusion time (τd) is obtained by fitting the experimental fluorescence recovery to a theoretical recovery curve according to an error-minimization algorithm.35 Ds is then calculated by the relationship of

Ds )

ω2 4τd

(1)

where ω is the radius of the photobleached circular spot.36 If a significant portion of the molecules within the photobleached region are immobile or of much lower lateral mobility than the other molecules, the fluorescence intensity after photobleaching does not recover to the prebleaching fluorescence level, but instead it converges to a constant level which is less than the prebleaching fluorescence. This fraction of immobile or slowly diffusing molecules is called the immobile fraction (φ) and is formulated as

φ)

F(-) - F(∞) F(-) - F(0)

(2)

where F(-), F(0), and F(∞) denote the prebleaching fluorescence intensity, fluorescence intensity immediately after photobleaching, and fluorescence intensity at infinite time, respectively.37 The laser fluorescence apparatus is schematically illustrated in Figure 1a. The argon-ion laser beam (488 nm) is modulated by an acousto-optic modulator to generate monitoring and photobleaching beams. The modulated laser beam is spatially filtered, expanded, collimated, and guided to the intermediate image plane of a fluorescence microscope (Zeiss ACM). A pinhole mounted at the image plane produces a uniformly illuminated (within 2%) circular laser beam by allowing only the central portion of the Gaussian laser beam to pass through. The laser beam of uniform intensity is impinged onto the contact area between the silica surfaces via a microscope objective (Zeiss UD (34) Himes, R. L. Ph.D. Dissertation, Auburn University, Auburn, AL, 1991. (35) Tournier, J. F.; Lopez, A.; Tocanne, J. F. Exp. Cell Res. 1989, 181, 105. (36) Axelrod, D.; Koppel, D. E.; Schlessinger, J.; Elson, E.; Webb, W. W. Biophys. J. 1976, 16, 1055. (37) Peterson, N. O.; Felder, S.; Elson, E. L. In Handbook of Experimental Immunology, Weir, D. M., Ed.; Blackwell Scientific: Oxford, 1984; Chapter 24.

Molecular Mobility in Surfactant Monolayers

Figure 1. Schematic diagram of (a) the FRAP apparatus and (b) the setup for heating silica disks. 40). The resulting fluorescence signal is collected back through the objective and filtered to remove extraneous signals and the signal at the excitation wavelength by a dichroic mirror and a long-pass filter. The filtered signal is sent to a photomultiplier tube for photon counting or an ISIT camera for fluorescence microscopic observation and digital image processing and analysis. As can be seen in eq 1, the accurate measurement of the illuminated spot radius, ω, is critical to obtain dependable Ds values. The digital image processing and analysis system (Universal Imaging Corporation) was capable of accurately determining the spot dimensions (within 5%). The laser fluorescence apparatus was set up in a temperature-controlled room (20-21 ( 0.5 °C). The monolayer-coated silica disks were aligned and brought into contact in crossed-cylinder geometry as shown in Figure 1a and enclosed in a chamber. Freshly deposited monolayers as well as virgin spots on the same pair of myristic acid monolayers were used for each FRAP measurement. The monitoring laser beam was focused onto the monolayer-coated silica surfaces in contact using a minimum power so that unnecessary photobleaching was avoided. For study of the RH dependence of Ds, the RH in the chamber was controlled with saturated salt solutions such as phosphorus pentoxide (P2O5), potassium acetate (CH3COOK), calcium chloride (CaCl2‚6H2O), zinc nitrate (ZnNO3‚ 6H2O), sodium bisulfate (NaHSO4‚H2O), sodium nitrite (NaNO2), ammonium sulfate ((NH4)2SO4), and ammonium chloride (NH4Cl). Several hours were allowed for equilibration with the RH monitored using a calibrated humidity gauge, and the humidity inside the chamber was maintained constant within (2% throughout the duration of the experiment. To measure Ds as a function of temperature, the contacting silica disks were heated to a target temperature using the setup shown in Figure 1b with a clean band of aluminum foil and silicon rubber heating tape wrapped around the contacting silica disks, thereby permitting the uniform transfer of thermal energy to the silica disks. The temperature was monitored by four thermistors (Physitemp Co.) installed at different locations near the silica disks. The readings from the temperature probes were always identical within (0.1 °C, which indicates that no significant temperature gradients existed around the silica disks. The target temperature was attained within a few minutes and maintained constant within (0.2 °C for the experimental duration. For the study of the effect of heating-cooling cycles, 45 and 55% RH were chosen as the initial RH conditions. The monolayer-coated silica disks were heated from 20 °C to a target temperature for an hour, cooled back to 20 °C, and then finally reheated to the target temperature. The FRAP experiments were then conducted on the contacting monolayers heated the second time. For each temperature, a new sample was freshly prepared, and the same procedure as above was repeated.

3. Results and Discussion 3.1. Effect of RH. Although we have already published a part of the results of the effect of RH on the Ds of fluorescent-labeled probe molecules in myristic acid

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monolayers elsewhere,33 herein we present more complete results and discuss the effect in greater detail to draw similar but more explicit conclusions. In general, when two cylindrical surfaces of the same radius are brought into contact in crossed geometry, the apparent contact area is approximately of circular shape. In the case of our submicroscopically rough silica disks, such as used in this study, the real contact area actually consists of numerous contacting micro- and nanoasperities. The study of the lateral mobility of surfactant molecules confined between two contacting surfaces requires that the illuminated spot associated with the FRAP technique is smaller than the apparent contact area. Therefore, the size of the apparent contact area was determined before the main FRAP measurements were performed. Because the fluorescence intensity profiles inside and outside the apparent contact area should be somewhat different, the fluorescence intensity distribution within illuminated spots of different diameters was observed with the ISIT camera and analyzed with the digital image processing/analysis system. Figure 2 shows representative fluorescence micrographs of a 28-µm diameter spot of illumination on myristic acid monolayers containing 1 mol % NBD-hexadecylamine confined between two silica surfaces at different RH values. At RH e 45%, the spot appears to be essentially uniform with yellow and/or green color. However, a few tiny domains of high intensity with red color are sporadically observed at about 50% RH. At higher RH, the domains increase in both number and size mainly at the center region of the spot. It should be noted that the shapes of some domains seemingly change from circular spots to dumbbell-like or interconnected circles. The average diameter of the approximately circular region of nonuniform fluorescence was measured to be about 21 ((1) µm, which presumably corresponds to the apparent contact area of the two monolayer-coated silica surfaces. Therefore, two different spot sizes, one smaller (18 µm) and one larger (28 µm) than the diameter of the apparent contact area, were used to investigate the effect of confinement, that is, whether the monolayer molecules are within or outside the apparent contact area. Figure 3 shows the data obtained for a representative FRAP experiment and the excellent agreement between the experimental fluorescence recovery and the theoretical recovery. Figures 4 and 5 present the RH dependence of the lateral diffusion coefficient (Ds) and the immobile fraction (φ), respectively, for the two spot sizes. As shown in Figure 4, with increasing RH values from 0 to 45% RH, Ds increases by more than 1 order of magnitude from 2.6 × 10-11 to 8.1 × 10-10 cm2/s. In this RH range, Ds is independent of the size of the illuminated spot, which indicates that the average lateral mobility in the myristic acid monolayer is the same regardless of whether the surfactant molecules are within or outside the apparent contact area. As RH increases from 45 to 65% RH, Ds appears to increase slightly and remains independent of spot size within experimental error. At higher RH values, however, Ds prominently depends on the illuminated spot size. With increasing RH, the lateral diffusion coefficient for the 18-µm spot, which is within the apparent contact area, remains constant within experimental error ((0.5 × 10-9 cm2/s), whereas the lateral diffusion coefficient for the 28-µm spot continues to increase. Figure 4 also shows the values of Ds measured when there was a very small gap (∼1 µm) present between the two silica surfaces coated with myristic acid monolayers, so that the evaporative net loss of monolayer molecules31,32 was minimized during the FRAP measurements. These

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Figure 2. Flourescence micrographs of 28-µm spots of illumination on the myristic acid monolayers containing 1 mol % NBDhexadecylamine confined between two silica surfaces at (a) 50, (b) 70, and (c) 87%.

Figure 3. Representative experimental fluorescence recovery (-) for the myristic acid monolayers confined between two silica surfaces at 70% RH and theoretical fluorescence recovery (- - -).

Figure 4. Lateral diffusion coefficient in the myristic acid monolayers confined between two silica surfaces as a function of RH for 18-µm (b) and 28-µm (O) spots of illumination and in an unconfined single monolayer (]).

results are taken to be representative of Ds outside the apparent contact area. Furthermore, it should be noted that no immobile fraction was observed; that is, the fluorescence recovered completely to the prebleaching fluorescence level. As can be seen in Figure 4 for RH > 65%, the Ds values for the 28-µm spot are larger than those inside and smaller than those outside the apparent contact area. This is because the measured Ds for the 28µm spot is an average value of the lateral diffusion coefficients of the fluorescence probe molecules inside and outside the apparent contact area. As shown in Figure 5, at RH e 45%, the immobile fraction within the illuminated spot is negligible within experimental error ((3%) for both spot sizes. For RH >

Figure 5. Immobile fraction in the myristic acid monolayers confined between two silica surfaces as a function of RH for 18-µm (b) and 28-µm (O) spots of illumination.

45%, however, the immobile fraction is significant on the time scale of the experiment. Furthermore, the immobile fractions for the 18-µm and 28-µm spots are different. For the 18-µm spot, the immobile fraction increases for 45% < RH < 65% and then appears to remain constant at a value of about 0.17 within experimental error ((0.05) or decreases somewhat at RH g 65%. The RH dependence of the immobile fraction for the 28-µm spot shows a similar trend, except that for RH > 45% the immobile fraction values are smaller by about 0.41, a factor corresponding to the ratio of the area of the 18-µm spot to that of the 28-µm spot. These results indicate that the immobile molecules exist only within the apparent contact area. When one combines the results of the fluorescence micrographs and the measurements of Ds and φ, it is possible to identify and characterize two distinct RH regimes of different molecular mobility behavior: (i) at RH e 45%, the molecular mobility increases with increasing RH regardless of whether the molecules are inside or outside the apparent contact area, and all of the molecules are mobile. (ii) At RH > 45%, the molecular mobility inside the apparent contact area is hindered, whereas that outside the apparent contact area continues to increase, and a significant portion of the molecules inside the apparent contact area are immobilized (or diffuse much slower than the other molecules). The Ds trend observed in the first regime of RH e 45%, that is, the continuous increase in Ds with increasing RH, is explained by the formation of a hydration layer because of the adsorption of water molecules from the surrounding atmosphere at the monolayer headgroup/silica interface. This explanation is supported by recent surface force studies of surfactant monolayer-coated mica surfaces,


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wherein it was reported that ambient water vapor adsorbs at the monolayer headgroup/mica interface and forms a hydration layer with increasing monolayer thickness.23-26 The hydration layer reduces not only the lateral interactions between the headgroups of the monolayer molecules within a monolayer, but also the adhesion between the monolayer molecules and the silica substrate. As a result, the monolayer molecules become more mobile as the RH increases, that is, as the hydration layer builds up. In addition, the formation of the hydration layer is inferred to be uniform both inside and outside the apparent contact area on the basis of the uniform fluorescence intensity profile and the independence of the Ds values on spot size. From the Ds and immobile fraction results at RH e 45%, the myristic acid monolayers appear to behave as if they are solidlike. In this regime, the following empirical equation is derived from the linear relationship between log Ds and RH (see the inset of Figure 4).

Ds (RH) ) exp(0.007734RH - 24.28)

(3)

In the second regime of RH > 45%, the nonuniformity of fluorescence intensity within the apparent contact area can be explained in terms of the bridging of hydration layers and the capillary condensation of water molecules from the surrounding atmosphere. Somewhere in the vicinity of 45-65% RH - the actual RH depends on the local radii of curvature - water vapor starts to condense around the contacting microasperities and forms capillary bridges within the apparent contact area of the silica surfaces. Simultaneously, any annular liquid bridges of juxtaposed hydration layers or capillary-condensed regions begin to draw surfactant molecules into them because of capillary pressure, which results in domains of high fluorescence intensity. This interpretation agrees well with Israelachivili and co-workers’ observations of the capillary condensation of water molecules from the surrounding atmosphere at the periphery of two contacting surfactant monolayer-coated mica surfaces at high RH.23,24 It is generally considered that capillary condensation is not significant below about 65% RH. As the RH is raised above 65% RH, the number and the size (or area) of the capillarycondensed regions become larger because of the accumulation of water molecules, whereas the area outside those regions becomes relatively reduced. The molecular mobility in the capillary-condensed regions presumably becomes less because of confinement, whereas the molecular mobility of the monolayer molecules outside the capillary-condensed regions continues to increase because of thicker hydration layers and reduced molecular packing. Therefore, the average Ds measured in the 18-µm spot remains approximately constant and even drops somewhat for RH g 65%. The increase in the immobile fraction with increasing RH for 45% < RH < 65% is explained by the interdigitation of the hydrocarbon tails of the two monolayer-coated silica surfaces. At RH > 45%, the monolayer molecules become sufficiently mobile such that the hydrocarbon chains of the two contacting monolayers between the local microasperities of the silica surfaces start to interpenetrate and interdigitate, thereby giving rise to an immobile fraction of the monolayer molecules. As the RH increases further, the molecular mobility, that is, the monolayer fluidity and the molecular packing density, in the capillary condensed regions increases, and thus more interdigitation occurs. At RH g 65%, the immobile fraction approximately remains constant although the area fraction of the domains continuously increases. These results support the view

that the immobile fraction appears to be related to the contacting microasperities, that is, the real contact area. As such, at RH > 45%, the apparent contact area between the monolayer-coated silica surfaces is actually heterogeneous. It consists of domains of higher fluorescence intensity with high molecular packing density and relatively low mobility, and the remainder of the monolayer-coated silica surfaces is of lower fluorescence intensity with low molecular packing density and relatively high mobility, which is hereafter denoted as the “fluid” phase because the monolayer molecules are more fluidlike in these regions. For this heterogeneous system, the conventional FRAP theory which is based on a homogeneous and uniform continuum is not valid. However, a further analysis of the lateral diffusion results can be achieved by application of the effective medium model,38,39 in which low mobility regions, that is, the capillary-condensed regions, are considered as semipermeable obstacles. The lateral diffusion coefficient in the domains, Dd, is obtained from the equation:

r)K

Dd Df

(4)

where r, K, and Df are the relative permeability, the ratio of the concentration of diffusing molecules in the domains to that in the fluid phase, that is, K ) Adomain/Afluid, and the lateral diffusion coefficient of the molecules in the fluid phase, respectively. In the effective medium model, the measured Ds is expressed in terms of Df, r, and x by the Bruggeman-Landauer equation:40

Ds 1 12 ) x - (1 - r) + x x (1 - r)2 + r Df 2 2

(

)

[(

)

]

(5)

where x is the fraction of the fluid phase. Thus, Dd can be evaluated upon determination of the parameters of x, Df, and K. The values of x at different RHs were determined by measuring the area fraction of the low fluorescence intensity regions within the apparent contact area of the fluorescence micrographs (with subtraction of the immobile fraction). Because the fluorescence intensity of the fluid phase is essentially identical to that outside the apparent contact area, these two regions can be assumed to be in the same physical state. Therefore, Df was taken to be the lateral diffusion coefficient (see Figure 4) measured for a myristic acid monolayer-coated silica surface separated from another myristic acid monolayercoated surface by ∼1 µm. The values of K were determined by measuring the fluorescence intensities of the domain and fluid phases, which were assumed to be proportional to Adomain and Afluid, respectively. A plot of Ds/Df versus x is shown in Figure 6. The bestfit value of r, 0.31, was determined by applying eq 5 over the entire data range, and then Dd was calculated from eq 4. Table 1 summarizes the measured x, K, Ds, Df values and the calculated Dd values at different RHs. It should be noted that up to about 67.5% RH (x ) 0.42), the measured relationship between Ds/Df and x agrees well with the theoretical curve for r ) 0.37. At RH g 70%, however, the data deviate from it. This implies that between 67.5 and 70% RH, some type of change, for example, interconnection among the domains, happens in the apparent contact area. Further analysis on this point is in progress. (38) Saxton, M. J. Biophys. J. 1982, 39, 165. (39) Tamada, K.; Kim, S.; Yu, H. Langmuir 1993, 9, 1545. (40) Landauer, R. J. Appl. Phys. 1952, 23, 779.

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Figure 6. An experimental plot (O) of Ds/Df versus x and a theoretical plot (-) by eq 5. Table 1. Measured Parameters and Calculated Dd for the Effective Medium Model for r ) 0.31 as a Function of RH RH

Ds

Df

X

K

Dd

50 55 60 65 70 80 87

1.42 1.39 1.68 2.33 2.64 2.80 2.84

1.45 1.50 1.98 3.33 6.56 8.18 10.4

0.99 0.94 0.85 0.62 0.26 0.16 0.12

1.26 1.30 1.33 1.31 1.39 1.37 1.46

0.33 0.34 0.43 0.74 1.37 1.73 2.07

Figure 7. Lateral diffusion coefficient in the myristic acid monolayers (b), stearic acid monolayers (9), and oleic acid monolayers (0) confined between two silica surfaces as a function of RH for 18-µm spots of illumination.

3.2. Effect of Surfactant Structure. The lateral diffusion coefficient (Ds) and the immobile fraction were also measured as a function of RH for oleic acid and stearic acid monolayers to investigate the effect of surfactant structure on the lateral mobility of confined monolayers between silica surfaces. The Ds and immobile fraction results are shown in Figures 7 and 8. As shown in the inset of Figure 7, the Ds for stearic acid greatly increases by about 5 times with increasing RH from 45 to 60% and gradually increases at higher RH. Over the whole range of RH of investigation, the Ds values for stearic acid are much smaller than those for myristic acid by about 2 orders of magnitude. As shown in Figure 8, no immobile fraction is observed for stearic acid, which implies that all of the probe molecules in stearic acid monolayers have low mobility of about the same level. The Ds values for oleic acid are approximately 2 times larger than those for myristic acid for RH > 45%. As presented in Figure 8, the immobile fraction values for oleic acid are somewhat larger

Figure 8. Immobile fraction in the myristic acid monolayers (b), stearic acid monolayers (9), and oleic acid monolayers (0) confined between two silica surfaces as a function of RH for 18-µm spots of illumination.

than those for the myristic acid, but the RH dependency of immobile fraction is similar to that for myristic acid. The small Ds values and zero immobile fractions for the stearic acid at all RH conditions are explained by the condensed phase of the stearic acid monolayers. Stearic acid monolayers are more condensed than myristic acid monolayers because of longer hydrocarbon chains of stearic acid, thus causing stronger attractive lateral interactions between the monolayer molecules. Even at very high RH, the stearic acid molecules have such a low mobility that their hydrocarbon chains between local asperities are not or are much less interdigitated, thereby resulting in zero immobile fraction. On the other hand, the immobile fraction for the oleic acid starts to appear at lower RH than for the myristic acid. It appears that the stearic acid monolayers maintained their condensed structure despite increasing RH but oleic acid monolayers are much more susceptible to the change in RH. The Ds values for the stearic acid level off at RH > 60% presumably because of the capillary force by the capillary-condensed water. The RH dependency of Ds for the oleic acid monolayers is also similar to those for the myristic and the stearic acid monolayers. 3.3. Effect of Temperature. To investigate the effect of temperature alone on the lateral mobility without any complications of RH, FRAP measurements were conducted on myristic acid monolayer-coated silica surfaces in contact as a function of temperature when the water content of the ambient environment is zero (dry). Figures 9 and 10 show the effect of temperature on the lateral diffusion coefficient and the immobile fraction when an 18-µm spot of illumination is used for the FRAP experiments. As shown in Figure 9, Ds increases with increasing temperature when the RH was maintained constant at 0% RH using phosphorus pentoxide. The Arrhenius equation explains the relationship between Ds and temperature:

( )

Ds(T) ) Ds0 exp -

Ea RT

(6)

where Ds0 is the preexponential factor for lateral diffusion, and Ea is the activation energy for lateral diffusion. By fitting the experimental data to eq 6, we obtained Ea ) 20.0 ((1.1) kcal/mol and Ds0 ) 28 850 ((4000) cm2/s. Rideal and Tadayon30 have reported that the activation energy for the surface diffusion of radioactive carbon-labeled stearic acid molecules on a mica substrate was 42 kcal/


Figure 9. Lateral diffusion coefficient in the myristic acid monolayers confined between two silica surfaces as a function of temperature at 0 (9), 45 (O), and 55% (b) RH for 18-µm spots of illumination.

Figure 10. Immobile fraction in the myristic acid monolayers confined between two silica surfaces as a function of temperature at 0 (9), 45 (O), and 55% (b) RH for 18-µm spots of illumination.

mol when the temperature was below the bulk melting point. The measured Ea for myristic acid monolayers on a silica substrate is smaller than the reported value for stearic acid, which is seemingly reasonable because the lateral interactions between myristic acid molecules are smaller than those between stearic acid molecules. Not only is the molecular packing less for the myristic acid monolayer, but the myristic acid molecules are in the liquid-expanded state, whereas the stearic acid molecules are in the liquid-condensed (or solid-condensed) state. Figure 10 shows that the immobile fraction increases from 0 to about 0.36 when the temperature is raised from 20 to 50 °C. The immobile fraction (φ) of the myristic acid monolayer even at 30 °C is 0.2 which is already higher than the maximum φ value measured at 20 °C and RH g 65%. With increasing temperature, the molecular mobility increases, which leads to an increase in monolayer fluidity. As results, we speculate that the interpenetration of the hydrocarbon tails of the two contacting fatty acid monolayers between the local microasperities becomes more effective, and thus the immobile fraction increases more than that arising from an increase in RH. 3.4. Combined Effect of Temperature and RH. In a practical situation, when a lubrication system heats because of its operation, neither only temperature nor only RH changes, but there is typically a simultaneous change in both conditions. Therefore, to simulate this

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practical lubrication situation, Ds was measured using an 18-µm spot of illumination as a function of temperature at specified initial relative humidity conditions of 45 and 55% RH. These RH conditions were selected on the basis that capillary condensation likely occurs at some small scale at 55% RH, whereas it does not at 45% RH, to examine the combined influence of temperature and relative humidity. The Ds and immobile fraction results obtained as a function of temperature at the two initial RH conditions are also shown in Figures 9 and 10. At 45% RH, Figure 9 shows that Ds remains constant from 20 to about 45 °C, gradually increases up to 60 °C, suddenly jumps to 2.4 × 10-9 cm2/s at 65 °C, and then levels off above 65 °C. The abrupt jump of Ds between 60 and 65 °C is attributed to a phase transition or melting of the myristic acid monolayers. The monolayer melting temperature is a little higher than that of bulk myristic acid, that is, 58 °C, which is presumably because of a confinement effect similar to the higher viscosity found for surfactant monolayers when confined between two solid surfaces.41,42 At 55% RH, Ds decreases slightly as the temperature rises from 20 to 45 °C, and then it increases as the temperature increases to 65 °C. The Ds values at 55% RH are somewhat larger than those at 45% RH over the whole temperature range except at 65 °C because of the RH effect as previously discussed. At 65 °C, however, the lateral mobility of the molten monolayers is not significantly affected by the initial RH. As shown in Figure 10, at both initial RH conditions, the immobile fraction appears to increase linearly within experimental error ((0.05) over the whole temperature range of investigation, although the trend of the immobile fraction above the monolayer melting temperature is not conclusively known. The overall trend in immobile fraction, increasing with increasing temperature and decreasing with increasing initial RH at constant temperature, is because of the combined effect of temperature and relative humidity on the interpenetration of the hydrocarbon tails of the contacting myristic acid monolyaers between the local microasperities of the silica surfaces. When the temperature is raised, there is an increase in the thermal energy of the system, which results in an increase in the lateral mobility of the monolayer molecules. Simultaneously, however, the RH in the surrounding atmosphere decreases, which reduces the lateral mobility. These two opposing effects combine to produce the apparent trend of Ds, remaining constant or gradually decreasing up to 45 °C and increasing later on up to 65 °C. 3.5. Effect of Heating-Cooling Cycles. At 45% RH, a series of FRAP measurements were conducted to examine the effect of heating-cooling cycles on the molecular mobility of myristic acid monolayers confined between two silica surfaces. The monolayer-coated silica surfaces in contact were heated to a target temperature equal to or higher than 45 °C, cooled to the ambient temperature, and then reheated to the target temperature. As shown in Figure 11, upon the second heating to a target temperature higher than 45 °C, the measured Ds is significantly smaller than the value of Ds determined at the first heating. In fact, the Ds value obtained upon the second heating is about the same as that measured at 20 °C without any reheating, that is, a Ds value corresponding to a condensed monolayer. This finding indicates that upon repeated heating and cooling, the myristic acid monolayers go through a structural change to a condensed phase, and the process is irreversible. The difference in the Ds values (41) Chan, D. Y. C.; Horn, R. G. J. Chem. Phys. 1985, 83, 5311. (42) Israelachvili, J. N. J. Colloid Interface Sci. 1986, 110, 263.

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and Evans8 reported abnormally high and variable readings in the shear strength on cooling the myristic acid monolayers and explained this behavior by an irreversible degradation of the monolayer structure. Further study on the details regarding the structural change is expected to provide information on the rupture mechanism of boundary lubricant films upon repeated heating-cooling cycles.

Figure 11. Lateral diffusion coefficient in the myristic acid monolayers confined between two silica surfaces as a function of temperature at 45% RH (O) and upon the second heating (0) for 18-µm spots of illumination.

Figure 12. Immobile fraction in the myristic acid monolayers confined between two silica surfaces as a function of temperature at 45% RH (O) and upon the second heating (0) for 18-µm spots of illumination.

upon the first and second heatings at or above 65 °C becomes very large, which implies that the structure of even the molten monolayers irreversibly turns to that of the condensed state upon the second heating. As shown in Figure 12, the immobile fraction in the reheated monolayers is almost the same as that in the first-heated monolayers. The Ds and immobile fraction results suggest that only the structure of the monolayer molecules outside the contacting microasperities is transformed to some kind of disordered structure, whereas the monolayer molecules pinned between the contacting microasperities remain interdigitated and thus immobile. This interpretation is supported by several reports on the irreversible phase transition of Langmuir-Blodgett monolayer and multilayers from ordered to disordered structures above the bulk melting point in the literature.43-49 Furthermore, Briscoe and Evans8 reported that myristic acid monolayers between sliding mica surfaces yielded a normal and reversible shear strength behavior up to 42 °C, whereas there is a significant decrease in the shear strength and the original thickness of the myristic acid monolayers as the temperature was raised to 46 °C. In addition, Briscoe (43) Ball, P. C.; Evans, R. Langmuir 1989, 5, 714. (44) Naumovets, A. G.; Vedula, Y. S. Surf. Sci. Rep. 1985, 4, 365.

4. Conclusions Direct measurements of the lateral diffusion coefficient of fluorescent-probe molecules in surfactant monolayers confined between two silica surfaces revealed that the molecular mobility is significantly influenced by the RH and temperature. For myristic acid monolayers at ambient temperature, we identified two RH regimes of different dynamic behavior: At RH e 45%, the monolayers are solidlike, and all of the molecules are mobile with low Ds, whereas at RH > 45%, they turn fluidlike because of hydration layers formed at the interface of the headgroup/ silica substrate, and their dynamic behavior becomes very complicated by capillary condensed water at the peripheries of the contacting microasperities inside the apparent contact area. The increase in RH brings about the interdigitation between hydrocarbon tails of myristic acid monolayer molecules at contacting asperities of rough silica surface, thus giving rise to immobile fraction. Importantly, the magnitude of the immobile fraction appears to be directly related to the real contact area between the rough silica surfaces. The RH dependencies of Ds for the stearic acid and the oleic acid showed trends similar to that for myristic acid; however, the stearic acid yielded much lower mobility and no immobile fraction presumably because of the condensed phase of the stearic acid monolayers, whereas the oleic acid monolayers gave a somewhat larger Ds and immobile fraction than those for the myristic acid. At zero RH, the lateral mobility behavior in the myristic acid monolayers confined between two rough silica surfaces was well analyzed by application of the Arrhenius equation. When the myristic acid monolayers were heated to 65 °C at initial RH conditions of 45 and 55%, a Ds trend of initially decreasing and increasing was observed, which was deduced by a combined effect of RH reduction and thermal energy increase. Upon heating to a target temperature above a bulk melting temperature, cooling at the ambient temperature, and reheating at the target temperature, we found that the Ds for myristic acid monolayers was much lower than that for the first heating, which implies that an irreversible structural change occurs during the heating-coolingreheating process. These findings provide important information on understanding the complex molecular dynamic behavior of surfactant monolayer molecules confined between two “rough” surfaces and more importantly intuitive clues on comprehending the mechanism of lubrication failure of boundary lubricant films. Acknowledgment. The authors greatly appreciate the financial support of Dongguk University and the critical comments of the reviewers. LA011802Q (45) Naselli, C.; Rabe, J. P.; Rabolt, J. F.; Swalen, J. D. Thin Solid Films 1985, 134, 173. (46) Naselli, C.; Rabolt, J. F.; Swalen, J. D. J. Chem. Phys. 1985, 82, 2136. (47) Almirante, C.; Minoni, G.; Zerbi, G. J. Phys. Chem. 1986, 90, 852. (48) Rabe, J. P.; Novotny, V.; Swalen, J. D.; Rabolt, J. F. Thin Solid Films 1988, 159, 359. (49) Bohm, C.; Steitz, R.; Riegler, H. Thin Solid Films 1989, 178, 511.

Effect of Humidity and Temperature on Molecular Mobility in Surfactant

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