Advanced Powder Technol., Vol. 18, No. 6, pp. 615– 629 (2007) © VSP and Society of Powder Technology, Japan 2007. Also available online - www.brill.nl/apt
Invited paper Examining soft particulates using an atomic force microscope and a quartz crystal microbalance CHRIS HODGES ∗ and SIMON BIGGS Institute of Particle Science and Engineering, University of Leeds, Leeds LS2 9JT, UK Received 20 March 2007; accepted 14 June 2007 Abstract—The adsorption of a simple surfactant [cetyltrimethylammonium chloride (CTAC)], in relatively high concentration salt solutions has been studied using atomic force microscopy (AFM) and a quartz crystal microbalance (QCM). Two oppositely charged surfaces were investigated: silica and alumina. The AFM images demonstrated clear adsorption of spherical CTAC micelles on silica but not on alumina, as expected. However, AFM images indicated the presence of rod and wormlike micelles of CTAC on both surfaces in agreement with what was expected from the solutions being used. This was explained in terms of the much greater stability of these larger structures in the vicinity of the AFM tip compared to the much smaller spherical micelles, even though no bonding will take place at the alumina surface. The QCM data on these solutions also shows a significant difference in the behavior for the spherical micelle system when compared with the rod or worm-like systems. From the QCM data we infer that a slip plane is present for the worm-like solutions and that the effect of slip on the data increases as the salt concentration increases. Keywords: Atomic force microscope; quartz crystal microbalance; micelles; worm-like micelles; adsorption; slip; cetyltrimethylammonium chloride; structured fluids.
1. INTRODUCTION
Soft particulates include surfactant micellar aggregates in various forms, and these are being more widely used in technology areas such as foods [1] and personal care products [2] where control over the deposition behavior at the solid–liquid interface is required. Many of these products are highly viscous and readily adsorb to most surfaces of interest. However, knowledge of the interfacial behavior generally remains poorly understood. This is frequently due to the difficulty of accurately decoupling adsorption from bulk solution properties in highly structured fluids. One technique that may offer insight into this problem is the quartz crystal microbalance with dissipation (QCM-D). In this technique a laterally vibrating ∗ To
whom correspondence should be addressed. E-mail:
[email protected]
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circular plate is forced to oscillate at its resonant frequency and changes in this frequency are monitored as the crystal is immersed into different fluids. Should any adsorption take place at the crystal surface, this can be observed in real time and so this technique is potentially very interesting as far as a whole host of industrial applications are concerned, where product quality needs to be maintained over a wide range of complex materials that are often introduced at high concentrations. QCM as a technique to measure mass changes has been around for more than 50 years, but the early measurements involved mounting the QCM crystal in a gaseous environment. This was because it was widely believed that if the QCM crystal was immersed in liquid, the crystal would cease to oscillate due to the large extra mass it needed to support. The QCM was shown to be very sensitive to different gases [3 –5] as well as the deposition of solid layers onto the QCM crystal where the thickness of the deposited layer could be determined to within a few nanometres by assuming a common layer density [6]. It was shown that when the QCM is operating in a gaseous environment, provided the adsorbed mass was relatively small, there was a linear relation between mass adsorbed and the measured change in frequency. The first person to sequentially investigate this relation was Sauerbrey in the late 1950s [7] and this relationship is named after him. However, in the early 1980s it was demonstrated that a QCM crystal could successfully continue to oscillate under liquid [8]. This opened up a new world for QCM experiments, and many liquids with different densities and viscosities were soon investigated. Kanazawa and Gordon [9] showed by a simple wave model that the frequency shift √ expected from the presence of a liquid above a QCM crystal was related to ρL ηL , where ρL and ηL are the liquid density and viscosity, respectively. Theoretical work, particularly by Johannsmann [18], went on to show that adsorbed layers of elastic or viscoelastic nature may be modeled. However, to date there has been very little work on adsorbing systems where the effect of the bulk fluid cannot be ignored. The present work will examine experimentally just such a system. Many groups present arguments based on adsorption QCM experiments, but they often need to support the QCM evidence with data from atomic force microscopy (AFM), since this invokes the localized behavior at the interface, whereas the QCM is a surface average technique. Much has been published on AFM of surfactants at interfaces and the interested reader should refer to some of the excellent reviews available (e.g. Ref. [10]). In summary, it has been shown that AFM is able to distinguish between several different conformations of surfactants (unimers, spherical micelles, rod and worm-like micelles) at idealized surfaces (usually mica or silica) and to monitor the adsorption process with time. In some cases the adsorption process is complex and multi-staged, and force–distance curves from these experiments often present the best evidence for a possible mechanism of adsorption. In this paper we will attempt to demonstrate that over a range of surfactant concentrations the QCM cannot only detect differences in the adsorption process, but that the QCM is sensitive to the interface–bulk transition region, something
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that AFM cannot easily detect. We will also demonstrate that the well-established equations for frequency shift versus mass adsorbed are not always obeyed for the case of high-concentration surfactants and we will discuss possible ways forward to try to interpret the QCM data.
2. MATERIALS AND METHODS
The surfactant solutions used were made up from cetyltrimethylammonium chloride (CTAC) surfactant obtained from Sigma-Aldrich (St Louis, Mo) used as-received and with MilliQ grade water (resistivity > 18 Mcm) that had been triply filtered. The surfactant solutions presented in this paper were made either with or without the addition of electrolyte, in this case sodium chloride (Sigma–Aldrich), to the concentrations listed in Table 1. For comparison, sodium chloride solutions at 100 mM, 3 M and 4 M were also made. As can be seen from Table 1, the shapes of the surfactant micelles in the bulk are different in each case and therefore it may be expected that the mechanism for adsorption will not be the same. The density of each solution was measured using a 25-ml glass pycnometer at 25◦ C, the same temperature as the QCM and AFM experiments, which is well above the Krafft point for each of these solutions. Two different QCM crystals were used: silica and alumina. Each was prepared by sputter coating of a crystal with the relevant material by the manufacturer (QSense, Göteberg, Sweden). The roughness of each surface was determined by AFM from a 1-μm2 area of the crystals to be ra = 0.65 and 0.63 nm for silica and alumina, respectively. The QSense D300 QCM houses a single sample cell that will contain approximately 80 μl of liquid. The crystal vibrates at a fundamental frequency of 5 MHz, but the instrument can also detect the third, fifth and seventh harmonics (i.e. up to 35 MHz). Since the fundamental frequency is often slightly noisy (usually due to interactions with the O-ring that supports the crystal), it is common to present third harmonic data. Liquid is introduced into the cell via a simple two-way valve under a gravity feed. Typically 3 ml of liquid is introduced at a time into the sample cell. This ensures that the fluid inside the cell has been exchanged. Table 1. Surfactant solutions used in this paper. Solution
Micelle shape
Contour length (nm)
Reference
Density (kg/m3 )
0.1 mM CTAC + 100 mM NaCl 6.4 mM CTAC + 3 M NaCl 6.2 mM CTAC + 4 M NaCl
spherical rod-like worm-like
N/A 170 630
[17] [16] [16]
1001 1130 1172
All solutions were above the CTAC critical micellar concentration (0.07 mM in 100 mM NaCl [16]). The densities were measured by pycnometry after the solutions were equilibrated. The contour lengths were taken from the indicated reference.
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Rheology of the above solutions was carried out using a Malvern–Bohlin C-VOR 150 (Malvern Instruments, Malvern, UK), with a 2-ml Mooney cell that had a 70-μm gap. Steady shear experiments were carried out between 63 rad/s (10 Hz) and 6283 rad/s (1 kHz). Oscillatory (dynamic) shear experiments were carried out between 3.8 rad/s (0.6 Hz) and 880 rad/s (140 Hz) over a strain range between 0.1 and 1000%. AFM experiments were carried out with a Nanoscope IV (Veeco Instruments, Cambridge, UK) equipped with a liquid cell. The polymeric skirt, used to seal the cell, was cleaned by placing it into a 2% Decon 90 solution and then into an ultrasonic bath for 10 min before washing with MilliQ water. The skirt was then dried using a nitrogen stream. The AFM images shown in this paper were obtained using soft contact mode. This mode relies on the force curve containing a repulsive component before hard wall contact. The advantage of soft contact mode imaging is that the forces used for imaging can be smaller than conventional imaging and hence this compresses the adsorbent less. The silica sample used was cleaned by exposure to UV light and then sonicated in a Decon 90 solution. The alumina sample used for AFM was a QCM crystal that was gently cleaned with a weak Decon 90 solution and water. The roughness of these samples was measured and is described below. A standard NPS tip with a spring constant of 0.12 N/m was used for the AFM imaging.
3. RESULTS
The steady-state shear rheology for the solutions used is presented in Fig. 1. From Fig. 1 it can be seen that the 100 mM NaCl solution has a viscosity very close to that of water, whereas the 3 and 4 M NaCl solutions have significantly higher viscosities. These results agree closely with those tabulated in the literature [11]. Figure 1 (right) shows that the addition of CTAC to the salt results in a solution
Figure 1. Shear rheology data of (left) NaCl solutions and (right) CTAC in NaCl solutions. All experiments were carried out using a 200-s integration period to allow a steady-state condition to be reached.
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with a similar viscosity to water for the 100 mM case. For the 3 M salt plus CTAC solution, the viscosity has risen substantially, as expected for a worm-like micelle structured fluid, but still appears to behave as a Newtonian fluid. In the 4 M salt plus CTAC solution, the worm-like micelles are sufficiently long to interact with each other and form a ‘polymer mesh’. This mesh can deform and break as the fluid shear is increased, as is witnessed by the shear thinning profile seen in Fig. 1 (right). The viscosity in the 4 M salt plus CTAC solution is always much higher than either of the other two CTAC solutions at all shear rates examined. The scatter in the data at low shear rates (particularly for water) is due to surface tension effects. Measurements on the density of the solutions used never deviated from that of water by more than 17% (see Table 1). This means that by far the largest contribution to √ the term ηL ρL is from ηL since the viscosity is seen to alter by a factor of up to 12 from Fig. 1 (right). 3.1. AFM data The AFM experiments carried out using soft contact imaging in the CTAC solutions produced the results shown in Fig. 2. In general the AFM images show that it was marginally easier to image on the silica than the alumina largely due to the larger roughness of the alumina surface that could mask some of the smaller features, (top right image in Fig. 2). At relatively low salt concentration (0.1 M) images of micelles could be obtained on silica but not on alumina. This supports the hypothesis that adsorption occurs on silica but not on alumina when finite charge effects are present, as expected. The spherical micelles observed on silica distributed themselves evenly over the surface, with a mean micelle spacing of 8.3 ± 1.4 nm. At higher salt concentrations (3 and 4 M) images of worm-like micelles could be obtained on both surfaces, although it was less clear for the CTAC in 4 M NaCl on alumina case (last image in Fig. 2). At this point it may be useful to compare the AFM images with the force–separation curves presented in Fig. 3. Since the systems under study are in high salt solutions, the Debye length is always less than 1 nm. The force curves show that under all the conditions used in these experiments a small amount of repulsion always exists. This permitted the use of the soft contact mode of imaging (Fig. 2). Overall the maximum of repulsion before push-through to the hardwall region occurred at shorter separations as the salt concentration increased, as demonstrated in Fig. 4. Figure 4 makes clear that in contrast to the smaller push-through separations at higher salt concentrations there was no such trend in the push-through force. For the case of the spherical micelles (in 100 mM NaCl) the push-through forces were smaller than any of the other solutions. One possibility is that the spherical micelles of CTAC are not close-packed at the silica surface and so the micelles are easily pushed to one side by the AFM tip. This is consistent with the measured peak-topeak separation of the micelles in this case, which is larger than the typical size of a micelle in solution. It has also previously been shown [10] that increases in
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Figure 2. Soft contact mode AFM images on (top row) CTAC in 0.1 M NaCl, (middle row) CTAC in 3 M NaCl and (bottom row) CTAC in 4 M NaCl. The left-hand images were obtained on silica, whereas the right-hand images were obtained on alumina. This figure is published in color on http://www.ingenta.com
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Figure 3. Force–distance curves for CTAC in NaCl on silica (left-hand images) and alumina (righthand images): (top row) 0.1 mM CTAC in 0.1 M NaCl, (middle row) 6 mM CTAC in 3 M NaCl and (bottom row) 6 mM CTAC in 4 M NaCl.
the double-layer repulsion at lower salt levels will produce an increased micelle– micelle spacing. No push-through events were observed for the case of the spherical micelles on alumina, suggesting no adsorption to the surface in this case. This is
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Figure 4. Push-through forces versus the separation at which the push-through occurred for CTAC in NaCl at the salt concentrations and surfaces shown.
supported up by the lack of evidence for micelles on the AFM image of the alumina surface. For the case of the rod-like micelles, two distinct behavioral types may be seen from Fig. 4. The force curves on silica show a significant push-through force, whereas the force curves on alumina show almost no push-through force. This matches the expected behavior of adsorption of the CTA+ ions on silica. The images and push-through data also indicate that the rod-like micelles are somewhat squashed and closely packed on the silica surface; the push-through force is much higher than for spherical micelles on silica and the push-through separation is less than that expected for the micelle diameter [10]. Note that on the alumina surface the push-through separation is similar to that expected for an undeformed rod-like micelle. This supports the notion that these micelles have not directly adsorbed onto the alumina surface. Instead, it seems that the bulk structure persists up to the surface and the micelles are pushed aside by the AFM tip as it approaches the surface. However, the stability of these micelles is such that at a small force these structures are capable of being imaged even though they are not firmly attached to the surface, as demonstrated in Fig. 2. For the worm-like micelles at the highest salt concentration, significant push-through forces existed on both surfaces. The adsorption on silica produced a marginally higher push-through force than on alumina, most likely due to direct adsorption. Again the push-through separation is much smaller than expected for an undeformed CTAC worm diameter [10], suggesting significant flattening of the worms themselves when adsorbed onto the silica substrate. We also expect that there will be very little lateral repulsion between the micelles since the double-layer forces are minimized at such a high salt concentration (4 M). The fact that a similar push-through force at a similar push-through separation on alumina is seen for the CTAC worms is indicative of significant localized structuring near to the solid interface. It was found from
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the rheology data (Fig. 1) that the worm-like micellar solutions behaved quite differently to both the spherical and the rod-like micellar solutions. This is most probably due to the presence of a three-dimensional (3-D) mesh structure within the bulk fluid. This structure persist up to the interface, regardless of any adsorption. Once again, the 3-D structure may provide sufficient repulsion to allow the layer next to the interface to be imaged by an AFM tip even though no direct adsorption has occurred. If this postulate is correct, i.e. there is adsorption onto silica but not alumina, then we might expect some difference in the degree of slip that occurs when the AFM tip scans across the three dimensional mesh at the interface. If the image obtained is clear then it is likely that the micelles are firmly attached to the substrate, in which case no slip occurs at the solid–micelle interface. However, if the AFM images are blurred then either the micelles are weakly attached to the substrate and/or the micelles are themselves structurally weak. Since the last two images shown in Fig. 2 are slightly blurred, it is possible that some slip is taking place, perhaps indicating that little or no bonding occurs even on silica under these high salt conditions. 3.2. QCM data QCM experiments were carried out to investigate further the adsorption for the differently structured solutions onto the different surfaces. The data shown in Fig. 5 illustrate that the sensitivity of the QCM to each solution is very different. This is probably due to two main reasons: (i) each CTAC solution has different bulk properties as was demonstrated earlier by the oscillation rheology data (Fig. 1) and (ii) the manner of adsorption is likely to be different for each solution. Since the model of Kanazawa and Gordon dictates that the relationship √ between the change in frequency is proportional to ρL ηL , it would be expected that any residual frequency change after the bulk property changes have been subtracted
Figure 5. QCM third harmonic data of different CTAC in NaCl solutions on a silica substrate (see Table 1). Frequency data (left) and dissipation data (right) are shown for all the solutions used. Concentrations listed are those of NaCl in each solution. Each figure begins in water with the injection of the CTAC-containing solution at 60 min. Water was then injected to rinse out the CTAC at about 70 min.
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Figure 6. Measured data compared with theoretically expected results for the CTAC in NaCl solutions listed in Table 1. The theoretical lines were drawn using equations for the frequency and dissipation shifts in Ref. [9, 12].
out would be due to the adsorption process only. However, it seems that the predicted frequency changes based only on the bulk properties are much larger than the total frequency changes measured from the data shown in Fig. 5, as is illustrated in Fig. 6. The exception to this are the frequency data obtained for the 0.1 M NaCl + CTAC √ solution (shown in Fig. 6 as the data point at ηρ ≈ 1) where the measured frequency shifts are larger than the model values. The measured frequency shift is 31 Hz, whereas the Kanazawa predicted frequency shift is only 4 Hz. One should remember that the frequency shift predicted by Kanazawa accounts for changes in bulk fluid properties only. If significant adsorption occurs at the interface then this will contribute strongly to the measured frequency shift provided the bulk properties are not too much larger than those of water. This condition is met for the 0.1 M NaCl + CTAC solution, where the spherical micelles strongly adsorb to the silica surface, and the bulk viscosity and density are both relatively low compared to water. For the CTAC solutions composed of rod or worm-like micelles the situation is somewhat different. Good evidence already exits in the literature that rod and wormlike CTAC micelles can form on mica surfaces [13], and that the cylindrical crosssection is complete (i.e. the micelle is not a semi-cylinder). However, the surface charge density on mica is significantly higher than on silica and in the present case the large NaCl concentration will have reduced the long-range forces. If the coupling between the adsorbed layer and the bulk is weak enough slip can occur [14, 15]. Even on a surface where adsorption occurs, slip is possible between the top of the adsorbed layer and the bulk. For the case where the coupling is zero there effectively exists a thin film of gas between the bulk fluid and the QCM crystal. This thin gaseous film would be detected as a low-density loading, although the shear wave generated by the QCM crystal will still penetrate well into the bulk liquid above this gaseous layer, and so the net effect is a significant reduction to the size of
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the expected frequency shift. Zero coupling in any real system is unlikely, but we suggest that in both cases (adsorbing or non-adsorbing) slip is a possible mechanism for the smaller than expected frequency changes. Theoretical formalism for slip under such conditions has been carried out [19], but to the best of our knowledge no experimental work has been reported in the literature. For the CTAC micelles observed in the present experiments the coupling must still be finite, since the AFM was able to image the micelle structure on silica. The dissipation data shown in Fig. 6 also behave in a similar manner to the frequency, although for the spherical micelles the difference between the measured and theoretically expected dissipation values was very small. However, one can envisage the relaxation of a well-coupled spherical micelle layer to be much closer to the ideal case of intimate contact with a simple liquid since the micelles in this case are relatively small and rigid. For the longer micelles obtained at higher salt concentrations, the relaxation being measured is between a weak coupling and a more flexible structure contained within the bulk liquid. This situation is very different to the ideal case of a simple liquid of a higher viscosity and density resting above the QCM crystal, and the weak coupling will not allow much more energy to be dissipated. Instead the coupling will tend to behave as a weak spring, undergoing simple stretching and compression as the QCM crystal vibrates laterally. Incidentally, it is worth pointing out that a typical lateral vibration amplitude for a 5-MHz oscillator is about 1 nm. This value is less than half that of a CTAC molecule (2.5 nm) and is much less than for the micelle structures formed by the CTAC. Thus when we refer to slip within a QCM we mean that the CTAC micelles are not following the movement of the QCM crystal, even though the CTAC molecule mean position may remain unchanged over time. QCM experiments were also carried out on alumina and the results are presented in Fig. 7. Data for CTAC in water at natural pH (5.5–6) have been included in Fig. 7 for comparison. It is clear that in the absence of salt there is a large difference in the behavior of spherical micelles of CTAC for each surface. The silica surface shows a much larger frequency shift than for the same solution on alumina where virtually no frequency shift is seen, corresponding to the cases of adsorption on silica but no adsorption on alumina. This is based on the idea that the CTA+ ions should be attracted to the negatively charged silica surface, but not the positively charged alumina surface. Indeed, when imaging on alumina was attempted for 10 mM CTAC in water, no structures were observed, whereas the same solution on silica produces well-defined spherical micelles that are slightly deformed due to their attachment points onto the silica [10]. For the spherical CTAC micelles in 0.1 M NaCl there still exists a small but significant difference between the frequency shift on silica to that seen on alumina. The difference between the two surface types is reduced due to the presence of the salt, which reduces the electrostatic repulsion drastically allowing the micelles on alumina to sit much nearer to the solid–liquid interface without being chemically
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Figure 7. QCM third harmonic frequency data for CTAC on either silica or alumina surfaces. Top row: (left) 10 mM CTAC in water and (right) 0.1 mM CTAC in 0.1 M NaCl; bottom row: (left) 6 mM CTAC in 3 M NaCl and (right) 6 mM CTAC in 4 M NaCl. Each figure begins in water before the injection of the solution for approximately 10 min. After this period water was then passed through the system to observe the rinse-off behavior. Usually two injections of the solution of interest were passed into the sample cell to ensure good mixing within the cell.
bonded to it. This effectively improves the coupling of the liquid to the alumina surface causing the larger frequency shift observed in this case. One should note that despite the more intimate contact of the spherical CTAC micelles on alumina in salt, no structures were observed by AFM under these conditions, suggesting that the micelles are not chemically attached to the alumina. For both the CTAC in 3 and 4 M NaCl cases, no significant difference between the frequency shifts observed on silica or alumina could be detected. The larger overall frequency shifts seen for these rod and worm-like micelles compared to the spherical micelle case above is purely due to the increase in the bulk fluid property changes, as was seen earlier from the viscometry data. It was also seen earlier from the AFM data that imaging of the CTAC micelles was possible on both alumina and silica. From the corresponding QCM data we may understand this in terms of the long rod or worm-like micelles experiencing difficulty in moving past each other due to physical constraints, the difference between each surface now being almost
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completely neutralized by the very high salt concentration. The corresponding dissipation data (not shown) for these systems show the same behavior.
4. CONCLUSIONS
It has been demonstrated within this paper that AFM and the QCM can compliment each other with adsorption data for a simple surfactant. Spherical micelles of CTAC in NaCl were able to be observed by AFM on silica but not on alumina. This was explained as being due to the greater affinity of the CTA+ ions for negatively charged silica rather than positively charged alumina even under the relatively high salt concentration (0.1 M) used. However, the QCM data with the same solution showed only a small but significant difference between each surface type, possibly because the coupling between the QCM crystal and the bulk liquid is more efficient under the conditions of relatively high salt. As the salt concentration increases, the mean separation between the CTAC micelles and the alumina surface is expected to decrease, such that the coupling at high salt concentrations is stronger than at lower salt concentrations. QCM data showing CTAC in water without salt on both surface types demonstrated no significant shift in frequency on alumina, but a substantial frequency shift on silica. Therefore, the QCM crystal cannot distinguish between water and water plus CTAC on an alumina surface at low CTAC concentrations. In the absence of salt the long-range repulsive DLVO forces can act, so the effect of surface charge is amplified. With the addition of salt the CTA+ ions can come closer to the alumina surface, leading to micelles being formed in solution at a smaller separation from the substrate than without salt. The QCM detects this as an increase in the density of the liquid that is being sensed, typically out to a separation of about 240 nm into the bulk, at 5 MHz for a liquid with a density similar to water. Since the AFM only images at one plane, it is not as sensitive as the QCM to the localization of the micelles to the substrate, and hence does not show much difference between the salt and no salt solutions on alumina at low CTAC concentrations. As the salt concentration was increased the difference between the measured frequency shifts in the QCM data on silica and alumina decreases, as just described. The AFM images show that the larger structures formed at the high salt concentrations (rod and worm-like micelles) are sufficiently stable to be imaged, even on alumina. Thus it would appear that the AFM operating in soft contact mode can image structures that are not bonded to the substrate, but merely rest above it. The force curves obtained in each solution had a similar general appearance with a small repulsion before a push-through event occurred. The magnitude of the push-through force was larger at higher salt concentrations, which is slightly counterintuitive. One hypothesis is that it is more difficult to move a rod or worm-like micelle to one side compared with moving a spherical micelle on the same surface due to the increased number of attachment points per micelle. This mechanism also fits the observed trend that the push-through forces were observed to be smaller on alumina than on silica, which may be interpreted as the micelle not
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being physically attached to the alumina, but merely easier to push to one side by the AFM tip. When the QCM frequency and dissipation data were compared with the expected shifts from an ideal viscous fluid, the CTAC data fell significantly below the model predictions. The only exceptions to this were the data obtained from spherical micelles where the frequency shift on alumina and silica were larger than the model values. For silica this was explained as being due to adsorption creating an additional frequency shift on top of the shift generated by the fluid bulk properties alone, but the data are more difficult to explain for alumina where the frequency shift is smaller than that observed on silica but still well above the model values. At the higher salt concentrations the coupling between the bulk fluid and the crystal surface decreases, and it is likely that a slip layer forms at the interface. Once the slip layer is formed, the QCM becomes less sensitive to the bulk properties and also less sensitive to any adsorption that may occur. Modeling this slip layer has been attempted by previous researchers [15], but the success of the modeling tends to depend on the system being studied. By comparing relatively simple systems, such as the one studied in the present paper, with more complex systems, it is hoped that predicting frequency changes from an adsorbing fluid can be made more accurate and that a greater understanding of adsorption in these viscous systems can be obtained.
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