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Improved Accuracy in Dynamic Quartz Crystal Microbalance Measurements of Surfactant Enhanced Spreading Zuxuan Lin,† T. Stoebe,† Randal M. Hill,‡ H. Ted Davis,*,† and Michael D. Ward*,† Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, and Dow Corning Corporation, 2200 West Salzburg Road, Midland, Michigan 48686-0994 Received June 26, 1995. In Final Form: September 25, 1995X Our previously reported quartz crystal microbalance (QCM) method for measuring dynamic wetting on solid substrates has been modified slightly to obtain more accurate spreading rates of aqueous dispersions of nonionic surfactants. Spreading rates are determined from analysis of frequency changes that occur as a result of an aqueous film containing dispersed surfactant spreading radially over the resonator surface following introduction of a small droplet to the center of QCM. The modification involves larger QCM electrodes, which increase the area over which the spreading event is measured compared to previously used smaller electrodes, and a frequency counter capable of more rapid data acquisition. The larger electrodes permit spreading to be measured over a larger area relative to the initial drop size and for longer time, while faster data acquisition provides more data immediately following introduction of the droplet to the QCM surface. This obviates overweighting of data acquired in the later stages of spreading when the aqueous film approaches the electrode edges and advances along the electrode tabs. These wetting rates were corroborated by real-time video microscopy of the wetting processes on identical surfaces. Comparison of the wetting rates on gold electrodes modified with various organosulfur monolayers reveals that the dependence of rates on surface energy is identical for the different electrode sizes, the rates being systematically larger for the larger electrodes.
Introduction We recently reported a convenient method, based on the quartz crystal microbalance (QCM), for measuring the spreading rates of aqueous solutions on solid surfaces.1 In particular, we described the “superspreading”2 of aqueous dispersions of nonionic trisiloxane surfactants on the gold electrodes of the QCM. These surfactants enhance the spreading of water on solid substrates, leading to fast spreading even for substantially hydrophobic surfaces. Spreading rates were determined by analyzing the frequency decrease that accompanied the radial spreading of an aqueous film across the gold electrodes following introduction of a small droplet to the center of the QCM. The method relied on radial sensitivity of the QCM to the effective mass of the Newtonian liquid film contained within the decay length of the shear wave induced by the vibrating quartz crystal. The frequency change due to radial spreading of the liquid film from the center to a distance r was described by eq 1, where C1 was a constant determined experimentally from the frequency change measured after the drop had spread across the entire gold surface (r ) re) and β was an experimentally measured constant describing the radial dependent sensitivity of the QCM.3-5 The spreading rate, vr (units of area/time), was then determined directly from the frequency change by eq 2. Linear extrapolation of ln(∆f(t) + C1) vs ∆t afforded the constant C2, which in turn * Authors to whom correspondence should be addressed. † University of Minnesota. ‡ Dow Corning Corp. X Abstract published in Advance ACS Abstracts, December 1, 1995. (1) Lin, Z.; Hill, R. M.; Davis, H. T.; Ward, M. D. Langmuir 1994, 10, 4060. (2) (a) Ananthapadmanabhan, K. P.; Goddard, E. D.; Chadar, P. Colloids Surf. 1990, 44, 281. (b) Hill, R. M.; He, M.; Scriven, L. E.; Davis, H. T. Langmuir 1994, 10, 1724. (c) Zhu, X.; Miller, W. G.; Scriven, L. E.; Davis, H. T. Colloids Surf. 1994, 90, 63. (3) Martin, B. A.; Hager, H. E. J. Appl. Phys. 1989, 65, 2630. (4) Ward, M. D.; Delawski, E. J. Anal. Chem. 1991, 63, 886. (5) Hillier, A. C.; Ward, M. D. Anal. Chem. 1992, 64, 2539.
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was used to determine the area of the aqueous droplet just prior to spreading (t0).
∆f ) -C1 [1 -exp(-βr2/re2)] ln(∆f(t) + C1) ) ln C2 -
(
C2 ) C1 exp -β
β νr ∆t πre2
)
πr2(t0) πre2
(1) (2)
(3)
The ability to modify the gold electrodes with various organosulfur monolayers enabled measurement of spreading rates on substrates whose surface energies could be systematically adjusted. Interestingly, measurement of the spreading rates of aqueous solutions of the nonionic surface M(D′E8)M revealed that the spreading rate (at [M(D′E)8M] ) 0.16 wt %) depended upon the surface energy of the substrate. The maximum rates were observed on moderately hydrophobic surfaces, that is, those which exhibited contact angles for pure water of ≈70°.
We discovered recently, by comparison with data obtained using real-time video microscopy,6 that the spreading rates measured with the apparatus described in ref 1 are systematically five times smaller on all substrates than the actual spreading rates. However, by simply increasing the diameter of the QCM electrodes by a factor of 2 and acquiring data at faster rates, the measured rates were identical to those measured by video (6) Stoebe, T.; Lin, Z.; Hill, R. M.; Davis, H. T.; Ward, M. D. Langmuir 1996, 12, 337.
© 1996 American Chemical Society
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Lin et al. The water-surfactant mixtures were hand-shaken prior to use in order to disperse the surfactant. The surface energies of the gold electrode substrates were systematically adjusted by modification with organosulfur monolayers. These monolayers were prepared by immersing the resonators in a 1 mM ethanol solution of either HS(CH2)16OH, HS(CH2)15CH3, or solutions containing mixtures of varying amounts of them. The crystals were rinsed with ethanol three times and dried with nitrogen gas prior to use. The surface energies, in terms of cos θ, were determined from the contact angle, θ, with 2 µL 18 MΩ water droplets before and after spreading measurements.
Results and Discussion
Figure 1. Schematic representation of the smaller electrode format used in ref 1 (left) and the larger electrode format used in the present work (right). The smaller lower electrodes are depicted by the light gray lines. Only the dimensions of the upper electrodes, on which spreading occurs, are given.
microscopy reported in a companion paper.6 The discrepancy is attributed to the larger temporal window available for measuring the spreading rate when larger electrodes are used, as the initial droplet occupies 50% of the smaller electrode area compared to 9% of the larger electrode. Faster data acquisition also improves the accuracy of determining the time at which spreading begins immediately following the introduction of the droplet to the surface. Consequently, the contribution of the electrode edges and the conducting tabs are reduced. Although the spreading rates are systematically lower for all concentrations and surface energies, the unique dependence of spreading on these parameters is identical to that described in ref 1. With these modifications, the QCM provides convenient, accurate measurement of dynamic wetting of solid surfaces. Experimental Section Apparatus. The experimental apparatus was identical to that described in ref 1. Gold electrodes (=2000 Å thick) were deposited on titanium underlayers (=200 Å thick) on both sides of the crystals by electron beam evaporation (Figure 1). The electrode patterns were arranged so that the gold leads on opposite sides running from the outer edges of the crystal to the center circular pad did not overlap. The previously reported smaller electrode format consisted of an electrode on the upper side of the crystal with a radius of re,upper ) 0.32 cm and area Ae,upper ) 0.32 cm2. The electrode on the opposite side of the crystal was smaller, with re,lower ) 0.18 cm and Ae,lower ) 0.24 cm2. The larger electrode format consisted of an upper electrode with re,upper ) 0.6 cm and Ae,upper ) 1.13 cm2 and a lower electrode with re,lower ) 0.45 cm and Ae,lower ) 0.64 cm2. The quartz crystals were mounted horizontally in the experimental cell with two electrodes connected to the oscillator. The quartz crystal was driven at its resonant frequency with a homemade oscillator circuit and a Hewlett-Packard 6234A dual-output power supply (Hewlett-Packard Corp., San Diego, CA). Frequency measurements were performed using a Model SR 620 universal time interval counter (Stanford Research Systems, Inc., Sunnyvale, CA), at a gate time of 10 ms, interfaced to a personal computer with an IEEE bus. This configuration enabled data collection rates of approximately 70 data points per second. The spreading measurements were performed by introduction of a 2 µL aqueous droplet to the center of the upper QCM electrode using a procedure described in ref 1. However, the 2 µL volume of droplet used here was larger than that used in ref 1 (1 µL) to ensure that the thickness of the aqueous film at the end of the spreading event exceeded the decay length over the entire QCM electrode surface. No dependence of spreading rates on droplet volume was observed. All data were collected at 85% relative humidity. Materials. The trisiloxane surfactant M(D′E8)M was obtained from Dow Corning Corp. The ethylene oxide tail is polydisperse, that is, the “8” in E8 represents an average composition. The density of pure M(D′E8)M at room temperature is F ) 1.007 g cm-3, the viscosity is η ) 21 cP, and the solubility limit is 0.007 wt %.2 Milli-Q reagent water (18 MΩ) (Millipore Corp., Bedford, WA) was used for the preparation of all aqueous dispersions.
In a previous report we described a method, based on the QCM, for measurement of the spreading rate of aqueous dispersions of the trisiloxane nonionic surfactant M(D′E8)M. The QCM method is convenient as the frequency change associated with the spreading process can be readily measured and analyzed. Furthermore, the gold electrodes of the QCM can be modified readily with organosulfur reagents, which enables measurement of spreading rates on substrates whose surface energies can be systematically adjusted. We have repeated the measurements described in ref 1 using the same analytical approach, but with some minor modifications to the QCM electrode geometry and data acquisition rates that improve the accuracy of these measurements. The spreading rate measurement is performed by introducing an aqueous droplet containing the surfactant to the center of the upper facing QCM electrode, while simultaneously measuring the QCM frequency. The frequency change consists of an instantaneous frequency decrease due to the introduction of the droplet to the QCM, followed by a slower decrease associated with the spreading process. The times of the spreading process range from 1 to 60 s, depending upon the surfactant concentration and substrate surface energy. The modifications to the QCM method consist of two principal changes. The electrode area over which spreading occurs has been increased from 0.32 to 1.13 cm2, and acquisition of frequency data has been increased from 2 data points per second to roughly 70 per second. The frequency changes observed with these modifications for [M(D′E8)M] ) 0.2 wt % on various substrates (Figure 2) were qualitatively similar to those in ref 1. However, the data reflected much higher spreading rates than those measured on smaller electrodes with slower data acquisition. The spreading rates on various monolayers with different surface energies in the range -0.4 e cos θ < 0.9 are larger with these modifications for all surface energies (Figure 3). This indicates that the spreading rates are systematically larger than those in ref 1 by roughly a factor of 5. The rates are also significantly faster on surfaces prepared on rough, unpolished quartz crystals (root mean square roughness ) 0.3 µm) than on polished quartz crystals (root mean square roughness ) 25 nm), consistent with the effects of roughness deduced in a previous study on Parafilm.2c Furthermore, these rates are identical to those measured by real-time video microscopy, reported in a companion paper.6 The discrepancy between the rates reported in ref 1 and those reported here can be attributed to several factors. The larger electrodes increase the temporal window for measuring the frequency changes associated with the spreading process. Our previous measurements on smaller electrodes indicated that the initial drop radius and area were r(t0) ) 0.20 cm and πr2(t0) ) 0.12 cm2, compared to re,upper ) 0.32 cm and Ae,upper ) 0.32 cm2. The measurements performed here with larger electrodes indicated that r(t0) ) 0.18 cm and πr2(t0) ) 0.10 cm2, compared to re,upper ) 0.60 cm and Ae,upper ) 1.13 cm2. Therefore, πr2(t0) was 51% and 9% of Ae,upper for the smaller and larger electrodes, respectively. It is important to note that πr2(t0) deduced from data acquired on the larger electrodes was smaller than that obtained with the smaller
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Figure 3. Spreading rate dependence on substrate surface energy for aqueous dispersions containing 0.2 wt % M(D′E8)M. Surface energy is characterized in terms of cos θ, where θ is the contact angle of 18 MΩ water with the substrate: (9) overtone polished quartz crystals (root mean square roughness ) 25 nm) with large electrodes (re ) 0.60 cm); (0) rough quartz crystals (root mean square roughness ) 0.3 nm) with large electrodes (re ) 0.60 cm); (4) overtone polished quartz crystals (root mean square roughness ) 25 nm) with small electrodes (re ) 0.32 cm). Data were collected at room temperature and 85% relative humidity.
Figure 2. (a) Response of the QCM resonant frequency during the radial spreading of a 2 µL drop containing 0.2 wt % M(D′E8)M on gold electrodes modified with mixed monolayers of differing surface energies prepared from solutions containing HS(CH2)15CH3 and HSCH2(CH2)15OH. (b) Linearized data from part a. Data shown here were collected on rough surfaces with re ) 0.60 cm electrodes, at room temperature and 85% relative humidity. The substrate surface energies were characterized in terms of cos θ, where θ is the contact angle of 18 MΩ water on the substrate. The cos θ values are indicated on the data.
electrodes, even though the droplet volume is twice as large for the former (πr2(t0) ∝ V2/3). The relatively smaller value of πr2(t0) enables more data to be collected before the spreading event is influenced by the electrode edges, which tend to pin the film. Furthermore, the error in the actual spreading rate increases near the electrode edges as the sensitivity profile becomes flat when compared to the center of the resonator. We also note that spreading continues along the electrode tabs after the drop has reached r ) re. Previous reports have demonstrated that these regions are sensitive to mass changes due to field fringing, which would lead to further frequency decreases as the liquid film spreads along the tabs. However, the frequency changes measured when the liquid film spreads along the tabs would lead to smaller apparent spreading rates than the actual spreading rates due to the smaller sensitivity of the tab region compared to that in the region where the opposing electrodes overlap and the smaller area onto which the liquid expands for a given linear velocity. Consequently, if these data are included in the analysis, the calculated spreading rate will be less than the actual one. The use of a frequency counter capable of faster data acquisition not only provides more data during the spreading process, which leads to better statistics when calculating the spreading rates, but it also enables the acquisition of more data immediately following introduction of the droplet to the QCM surface. Acquisition rates
of 70 data points per second enable more accurate determination of the instantaneously formed initial area, πr2(t0), as the frequency corresponding to this area, f(t0), can be determined more precisely. Accurate determination of f(t0) is important when selecting the data window used for calculation of the spreading rates using eq 2. Indeed, the values of πr2(t0) measured in this study were substantially smaller than those determined in ref 1, particularly when the larger drop volume used here is taken into account. This suggests that πr2(t0) is being determined more precisely as more data are collected nearer to t0. In the studies described in ref 1, meaningful data could not be acquired for t < 2 s. Consequently, the data were collected later in the spreading process when the electrode edges and spreading along the electrode tabs influenced the observed frequency changes. In contrast, the linearized data in Figure 2b represent data acquired at t g 70 ms. These results demonstrate that QCM apparatus for measuring of dynamic wetting should have large electrodes and rapid acquisition rates equal to or exceeding the specifications reported here. While video microscopy can also be used to obtain spreading rates, these measurements are difficult in the absence of sufficient contrast between the substrate and the spreading film, which is characteristic of spreading on smooth substrate surfaces. The QCM measurement does not require direct visual observation of contrast between substrate and the leading edge of the spreading film. However, when sufficient contrast is present, as is typical of spreading on rough surfaces, video microscopy can provide visualization of the spreading front and instabilities at this front that may be important to the understanding of the wetting process. Under these conditions the video microscopy method can be automated using standard image analysis routines, although currently data can be collected more rapidly with the QCM. Accordingly, we recommend using both methods when investigating dynamic wetting processes. Acknowledgment. The authors acknowledge the NSF Center for Interfacial Engineering and the Dow-Corning Corporation for financial support. LA950514P
