ARTICLE pubs.acs.org/Langmuir
Influence of Surface Roughness on Cetyltrimethylammonium Bromide Adsorption from Aqueous Solution Shuqing Wu,† Liu Shi,§ Lucas B. Garfield,§ Rico F. Tabor,‡ Alberto Striolo,§ and Brian P. Grady*,§ †
School of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China Particulate, Fluids Processing Centre, University of Melbourne, Parkville, Victoria 3010, Australia § School of Chemical, Biological and Materials Engineering and Institute of Applied Surfactant Research, University of Oklahoma, Norman, Oklahoma 73019, United States ‡
ABSTRACT: The influence of surface roughness on surfactant adsorption was studied using a quartz crystal microbalance with dissipation (QCM-D). The sensors employed had root-mean-square (R) roughness values of 2.3, 3.1, and 5.8 nm, corresponding to fractal-calculated surface area ratios (actual/nominal) of 1.13, 1.73, and 2.53, respectively. Adsorption isotherms measured at 25 °C showed that adsorbed mass of cetyltrimethylammonium bromide per unit of actual surface area below 0.8 cmc, or above 1.2 cmc, decreases as the surface roughness increases. At the cmc, both the measured adsorbed amount and the measured dissipation increased dramatically on the rougher surfaces. These results are consistent with the presence of impurities, suggesting that roughness exacerbates well-known phenomena reported in the literature of peak impurity-related adsorption at the cmc. The magnitude of the increase, especially in dissipation, suggests that changes in adsorbed amount may not be the only reason for the observed results, as aggregates at the cmc on rougher surfaces are more flexible and likely contain larger amounts of solvent. Differences in adsorption kinetics were also found as a function of surface roughness, with data showing a second, slower adsorption rate after rapid initial adsorption. A two-rate Langmuir model was used to further examine this effect. Although adsorption completes faster on the smoother surfaces, initial adsorption at zero surface coverage is faster on the rougher surfaces, suggesting the presence of more high-energy sites on the rougher surfaces.
’ INTRODUCTION Adsorption of surfactant at the solid/liquid interface has been extensively studied experimentally, theoretically, and via simulations to understand interactions between the surfactant and the solid surface. The surfactant adsorption process at the solid/ liquid interface and the morphology of the aggregates on the substrate surfaces are influenced by several factors such as charge, surface chemistry, solution pH, ionic strength, etc. Electrostatic, hydrophobic, and van der Waals interactions between the substrate, the surfactant, and the solvent, as well as intermolecular surfactantsurfactant interactions, largely determine the properties of the adsorbed layer. Various experimental methods such as quartz crystal microbalance (QCM),1,2 atomic force microscopy (AFM),3,4 ellipsometry,5,6 and neutron reflection7,8 have been used to study adsorbed amount, layer structure, and adsorbed aggregate thickness on different substrates. However, only a relatively limited number of studies have been reported which attempt to understand the influence of surface roughness on the adsorbed surfactant amount. On inhomogeneous surfaces, the adsorption energy is a function of the spatial location because of the availability of different adsorption sites.9 Furthermore, intermolecular interactions also depend on the proximity and density of adsorbed species.10,11 A very recent study observed that adsorption of fibrinogen was not only influenced by surface morphology but also by the characteristic shapes and sizes of nanorough surface r 2011 American Chemical Society
features.12,13 The surface aggregate morphology was found to change with roughness, and the adsorbed amount increased at a higher rate than the root-mean-square (R) surface roughness. Schniepp and co-workers9 observed that for sodium dodecyl sulfate (SDS) on Au(111), topographic surface features led to differences in the orientation of micelles on rough and flat surfaces. The structure of cetyltrimethylammonium bromide [CTAB, CH3(CH2)15N(CH3)3Br] layers adsorbed on smooth and rough silicon surfaces has been investigated by neutron reflection.7 On a hydrophilic surface, CTAB forms a bilayer-like structure. Compared to smooth surfaces, the bilayer on rough surfaces was found to be thicker, the surface coverage was lower, and the molecules were less-densely packed. A number of authors have interpreted experimental QCM results invoking the presence of additional mass of solvent trapped within the surface aggregates.1420 Urbakh,21 Daikhin22 and their co-workers described surface roughness as “slight roughness” and “strong roughness” based on the surface density and morphological properties of cavities and bumps, their average height and size, etc. They treated the flow of a liquid through a nonuniform surface layer as the flow of a liquid through a porous medium. Based on Brinkman’s equation for the velocity Received: February 26, 2011 Revised: March 23, 2011 Published: April 13, 2011 6091
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Langmuir field in the nonuniform interfacial region, their model suggests that both the effect of viscous dissipation in the interfacial layer and the effect of the liquid mass rigidly coupled to the surface affect the resonant frequency shift and width in the QCM response.23 They proposed a theoretical approach that accounts for the multiscale nature of roughness to describe the response of a bare QCM sensor in contact with a liquid. Both the apparent adsorbed mass and dissipation increase with surface roughness according to this approach. In our previous experiments,24 we showed that roughness on as-manufactured and cleaned crystals used for QCM-D experiments was considerable. Thus the amount adsorbed must be calculated using the actual, roughness-corrected, surface area rather than the nominal area obtained assuming a smooth, flat surface. At bulk concentrations above the critical micelle concentration (cmc), our results showed that adsorbed CTAB yields a bilayer-like structure on both silica and hydrophilic gold. To reach these conclusions, the roughness of the solid surfaces and the surface area per headgroup at the airwater interface were used. Had we not considered surface roughness, our results would have been consistent with either the formation of multilayered CTAB aggregates or large amounts of trapped water. Although most industrially relevant surfaces are expected to be rough rather than atomically smooth, adsorption studies generally employ one of two types of surfaces: those that are extremely rough and particulate, and those that are atomically smooth (or close to). Besides surface morphology, another significant difference between the experiments performed with the two types of surfaces is that in the former the amount of surfactant adsorbed is a significant fraction of the amount in solution while in the latter the amount adsorbed is many orders of magnitude less than the amount in solution. The experiments reported herein are intermediate to these two extremes in that the surface morphology is rougher than that used in studies on atomically smooth surfaces, but the amount adsorbed is still many orders of magnitude less than the amount in solution. CTAB adsorption isotherms at the solidwater interface were measured using the QCM-D with sensor crystals of quantified different roughness. The sensor surfaces were gold, although they display substantial hydrophilic character, as noted previously.25 AFM was used to determine the morphology of the bare surfaces. The actual surface areas were estimated using the roughness values obtained from analysis of the AFM images. The results presented below are discussed in terms of both adsorption isotherms and kinetics of adsorption and interpreted in the light of the different surface roughness values employed.
’ EXPERIMENTAL DETAILS Materials. CTAB (purity >99%, purchased from Sigma-Aldrich) was recrystallized three times in acetone and dried completely under vacuum. A 15 mM stock solution was prepared with the purified surfactant and ultrapure water (resistivity = 18 MΩ cm, obtained from a Millipore Milli-Q system of ion exchange and activated carbon cartridges). The sensing elements (crystals) were purchased from Q-Sense. These crystals were specially made by Q-Sense to have higher surface roughness than standard sensing elements. Method. Adsorption isotherm measurements at pH ∼7 were performed using a QCM with dissipation (QCM-D, model E4, purchased from Q-Sense). The temperature of the measuring chamber was kept at 25.0 ( 0.05 °C. Data reproducibility was checked by performing independent measurements and the reported results are averages of three to five measurements. The adsorption isotherm measurement
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procedure is described in detail in refs 24 and 25. Adsorption measurements were made at surfactant concentrations ranging from 0 to approximately 1.6 cmc by increasing the concentration in steps of 0.1 or 0.2 cmc. A value of 0.88 mM was measured for the cmc of CTAB as described in an earlier publication.25 At each concentration, the surfactant solution was pumped through the instrument using an Ismatec peristaltic pump at a constant flow rate of 0.1 mL/min for 1 h, after which the flow was stopped for 1 h to allow the system to reach equilibrium. Because CTAB adsorption can be slow to equilibrate near the cmc,26 at concentrations near the cmc the equilibration time was extended to 23 h when necessary. Longer equilibration times were not possible because of instrument drift, although longer times would have been desirable close to the cmc. The approach to equilibrium was close enough so that an accurate determination of the equilibrium adsorbed amount could be made. Kinetic experiments were conducted by suddenly increasing the bulk surfactant concentration from 0 to the concentration of interest (results are discussed for bulk concentration of 0.1 and 1.2 cmc) with no prior adsorbed surfactant. Theory. QCM-D measures the variation in resonance frequency and dissipation of a sensor quartz crystal in real time as molecular layers form on the sensor’s surface.27,28 The attached films are either rigid or viscoelastic. In the former case, the frequency shift is proportional to the added mass. Within this scenario the Sauerbrey equation29 can be used to describe the mass/frequency relationship between the layers adsorbed onto the quartz crystal30,31 Δm ¼
CΔf n
ð1Þ
In eq 1 Δm is the added mass per unit area on the sensor’s surface; the frequency shift Δf = f f0 is the difference between the resonant frequency of the crystal sensor (f) and its nominal value f0; C is the mass sensitivity constant (C = 17.7 ng cm2 Hz1 for the crystals used in our experiment at 5 MHz); and n is the overtone number (n = 1, 3, 5, ...). Equation 1 is considered satisfactory as long as the dissipation is 2 106 or less.31,32 When the dissipation is larger, the adsorbed film is classified as viscoelastic.33 Within this scenario, according to the Voigt model the adsorbed layer is represented by a homogeneous viscoelastic film characterized by an effective layer density, layer thickness, shear elastic (storage) modulus, and shear viscosity (loss modulus).31,34 The energy dissipation in QCM experiments can be determined by measuring the dissipation factor D33,35 D ¼ 1=πf τ
ð2Þ
where f is the resonant frequency and τ is the time constant for the decay of the vibration amplitude. Our raw data were fitted to the Voigt model using the Q-tool software, assuming that the required input parameters for the density of the adsorbed layer, the density of the supernatant, and the viscosity of the supernatant were 1090 kg/cm3, 1000 kg/cm3, and 0.001 kg/(m 3 s), respectively. Adsorbed amounts were determined by multiplying the fitted layer thickness by the assumed layer density. In the Appendix the adsorbed amounts estimated using either the Sauerbrey or the Voigt models are compared, with the former yielding a result significantly lower than the latter when both models are expected to apply. The results discussed in the main part of the manuscript were obtained using the Voigt model, but the conclusions, in a qualitative sense, are not dependent on the model used. Surface Characterization. The crystal surfaces were characterized before the crystals came in contact with the aqueous surfactant solutions. An atomic force microscope (AFM, Nanoscope IIIa; Digital Instruments, Santa Barbara, CA) was used to quantify the surface roughness and the height variations across the crystal surfaces. AFM images were acquired for the dry surfaces in the tapping mode at scan frequencies of 12 Hz under ambient conditions using noncontact silicon 6092
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Figure 1. AFM images and sectional analysis of crystal surfaces with different roughness. The three root-mean-square roughnesses (R) were 2.3, 3.1, and 5.8 nm (top to bottom). cantilevers with a typical resonance frequency of 325 kHz and a spring constant of 40 N/m (NSC15/50, from MikroMasch Ultrasharp). The image resolution was 512 pixels. AFM images and sectional analyses of the gold crystals used in our experiments are reported in Figure 1. The rootmean-square roughness (R) of the crystals, estimated with the Nanoscope IIIa software, were 2.3, 3.1, and 5.8 nm, and these values will be used to refer to the crystals. Both AFM images and sectional analysis consistently show that the surface morphologies were significantly different. Cleaning Procedure. Consistent and thorough cleaning procedures were essential for obtaining reproducible measurements. As in our prior work, plasma cleaning (PDC-32G from Harrick plasma) and an ammonia-peroxide mixture were used for the crystals with R = 2.3 nm.24,25 A different cleaning protocol was implemented for the crystals with R = 5.8 nm. The new R = 5.8 nm crystals received from the manufacturer were heated in a freshly prepared ammonia-peroxide mixture at 75 °C for 10 min, and then rinsed with nanopure water and dried with flowing N2. This procedure was repeated three times, without plasma cleaning, to thoroughly remove any contaminants without changing the surface roughness. The R = 5.8 nm crystals were only used once in the adsorption experiment. When these crystals were cleaned using the plasma cleaner, following the original cleaning procedure, the R = 3.1 nm crystals were obtained. Surface Chemical Composition. X-ray photoelectron spectroscopy (XPS) (Physical Electronics ESCA System PHI 5800) was used to
Table 1. Surface Atomic Composition from XPS Analysis for Gold Surfaces after the Cleaning Procedure atomic concentrationa (%)
a
roughness (nm)
C 1s
O 1s
Mn 2p
Sn 2p
Au 4f
R = 5.8
30.58
12.21
8.71
1.12
47.38
R = 3.1
25.74
11.16
7.49
7.65
47.96
R = 2.3
37.46
11.42
2.22
6.45
42.45
Average values of three analysis areas in one crystal.
characterize the chemical nature of the surfaces. The collective data for sample surfaces after cleaning is reported in Table 1. The relative amounts of gold, oxygen, and manganese remain approximately constant for all of the crystals tested. The increase in concentration of tin on R = 3.1 and 2.3 nm crystals after the cleaning cycle suggests that the plasma cleaner might contaminate the surfaces. A higher concentration of carbon on R = 5.8 and 2.3 nm crystals may be due to incomplete removal of organic impurities. Note the high concentration of oxygen, consistent with our prior work, which renders these surfaces hydrophilic. Effective Surface Area. A 2D data array (512 512), whose elements express the height information of each point in a 2D-scanned image grid, was extracted by AFM to estimate the fractal nature of the 6093
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Table 2. Parameters from Model Fits to Kinetic Adsorption Data for the 0.1 cmc Casea fitted value parameter
units
R = 2.3
R = 5.8
error
M
105 cm s1
7
7
0.6
cb
108 mol cm3
9
9
0.5
kads a kdes a
105 cm s1 1013 mol cm2 s1
2.5 5.5
2.5 5.5
0.1 0.1
kads b
107 cm s1
4.0
4.0
0.1
kdes b Γmax a Γmax b Γmax tot
1014 mol cm2 s1
2.1
2.1
0.1
1010 mol cm2
2.99
1.20
0.04
1010 mol cm2
1.11
0.72
0.04
1010 mol cm2
4.10
1.92
0.04
a
Note: units are reported in cm to remain consistent with previous reports. Errors represent statistical fitting errors between the model and the experimental data. surface. The evaluation of the fractal dimension surface used a program, written in C, that used a variation method.36 Using this estimate of the fractal dimension of the surface, the effective areas were 4.52 μm2, 6.90 μm2 and 10.12 μm2 for R = 2.3, 3.1, and 5.8 nm crystals, respectively. These surface areas correspond to 1.13, 1.53, and 2.56 times the nominal crystal surface area (4 μm2). This surface area calculation is affected by several significant issues. Because the AFM tip is of finite size, the roughness is underestimated. Given the size of a surfactant headgroup, this underestimation is important. The use of a fractal approach to calculate the surface area attempts to circumvent this problem, but there is no reason to believe that the roughness follows a fractal-type relationship. Using a line integral method,24 the surface area ratio for the R = 2.3 nm surface is estimated as 1.25. Following the fractal approach, a 1.13 ratio is found for the same surface. A variance of 10% in the surface area is much smaller than the effects described in this paper, preserving the generality of our conclusions. Kinetic modeling. The two-rate model used to fit the adsorption data as a function of time has been described previously,37 as an extension of a previous single-rate adsorption model developed by Koopal and Avena.38 Briefly, this model applies two uncoupled Langmuir-type adsorption steps, a and b, which may have different adsorption ads des des rate constants, kads a and kb , desorption rate constants, ka and kb and max and Γ . In other words, different maximum adsorbed amounts, Γmax a b the surface is modeled as consisting of two categories of adsorption sites a and b with different binding characteristics. The model accounts for mass transfer to the region of solution adjacent to the crystal (the subsurface) using a mass transfer coefficient, M, which depends on the flow conditions and diffusion within the system. The model is appropriate for analyzing adsorption data that are transport-limited, attachment-limited or intermediate between these two cases. The parameters from data fitting with their units and associated uncertainties are shown in Table 2. The mass transfer coefficient, M was determined by fitting the constant slope region of the adsorption data at low concentrations,39 where surface coverage is low. Maximum adsorption values were taken directly from QCM-D data, and the bulk concentration is equivalent to the bulk surfactant concentration used. The rate constants for adsorption and desorption in each mode are constrained because the overall adsorption isotherm is known.39
’ RESULTS AND DISCUSSION Adsorption Isotherms. Adsorption isotherms calculated using the Voigt equation are shown in Figure 2 as a function of bulk surfactant concentrations at 25 ( 0.05 °C. The uptake mass
Figure 2. Experimental adsorption isotherms for CTAB on gold surfaces with different roughness at 25 ( 0.05 °C, based on actual surface area.
Figure 3. Measured energy dissipation for CTAB on gold surfaces of different roughness corresponding to the adsorption isotherms shown in Figure 2.
of CTAB per unit of actual (roughness-corrected) surface area is shown. Results for the R = 2.3 nm crystal show reasonable agreement with those reported in refs 19 and 24. The amount of CTAB adsorbed per unit of actual surface area increases continuously on all surfaces up to the bulk concentration of 0.8 cmc in a manner consistent with typical adsorption isotherms. However, the amount adsorbed per unit area at a given concentration is less with higher roughness. Above 1.2 cmc the experimental data show that adsorption has reached a plateau, different on the three surfaces. Consistent with the behavior below 0.8 cmc, the amount adsorbed per unit area decreases as R increases. Further, for each sample the amount adsorbed at and above 1.2 cmc appears to be consistent with the amount adsorbed at and below 0.8 cmc, i.e the adsorbed amounts at these two values are similar which is characteristic of typical adsorption isotherms. The observation that as roughness increases, adsorption per unit area decreases is consistent with expectations because a higher fraction of the surface should become unfavorable for 6094
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Langmuir adsorption due to roughness. Increasing roughness could cause a significantly lower fraction of the surface to be covered with surfactant (e.g., patchy adsorption), or the morphology of the adsorbed aggregates could change as a function of the surface roughness leading to spreading. Both neutron reflectivity data7 as well as recent simulation results40 suggest that surface roughness could affect not only the morphology of the adsorbed surfactant aggregates, but also the amount of surfactant adsorbed. These effects will depend on the length scale that characterizes surface roughness. Patchy adsorption (i.e., some areas of the surface are covered by surfactants at high density, other areas by a low density of surfactants) has generally been accepted to be the dominant mechanism in the case of atomically smooth surfaces for cationic surfactants.41 Further, above 1.2 and below 0.8 cmc, dissipation data (see Figure 3) are approximately the same when R = 2.3 nm and when R = 3.1 nm, but are markedly larger for R = 5.8 nm. This suggests that the aggregates formed on the roughest surface are less compact, and therefore more flexible, than those formed on the less rough surfaces. Our experimental data do not provide sufficient information to totally elucidate the surfactant aggregate morphology. When the bulk surfactant concentration is between 0.8 and 1.2 cmc, our data show the most differences as a function of the surface roughness. In particular, the amount adsorbed at the cmc shows a maximum on all three surfaces. A maximum is typically not observed in adsorption isotherms on atomically smooth or rough particulate surfaces.19,25,4143 We can only speculate on the reasons for this striking, yet reproducible, observation. The increase in adsorption at the cmc can be explained by making an analogy to the well-known impurity behavior for adsorption at the airliquid interface. For some ionic surfactants, e.g., SDS, impurities in the surfactant will cause a dip in the surface tension at the cmc because of an increased packing density, i.e., higher adsorption density.44 Above the cmc, these same impurities solubilize in micelles causing a reduction in adsorption density at the airliquid interface, and consequently an increase in surface tension. The peak observed in our QCM adsorption data could be due to similar phenomena: impurities adsorbed at the solidliquid interface at the cmc become part of micelles above the cmc causing a reduction in the amount adsorbed. Note that the term “impurity” could be misleading; a distribution of surfactant isomers could also lead to this effect. The interpretation just proposed is supported by literature data. Tilton and co-workers observed anomalous adsorption data for CTAB on silica due to impurities introduced by poly(vinyl chloride) tubing.4547 Although these references measure adsorption isotherms using ellipsometry, the isotherms obtained in the presence of impurities are remarkably similar to those reported in Figure 2. Once the impurity disappeared, plateau adsorption without peaks at the cmc was restored.45 A similar peak in the adsorption isotherm at the cmc was observed for SDS isotherms on chromium monitored via ellipsometry; this particular sample also showed a dip in surface tension. Upon purification, the peak in the adsorption isotherm decreased but did not disappear.48 Three arguments can be raised against the proposed interpretation. First, three recrystallizations were performed on the CTAB to remove impurities; however, the very small amount of surfactant that adsorbs relative to the amount of surfactant in the system would require the removal of impurities to roughly the nanomolar level. Second, our aqueous CTAB solutions do not show a dip in surface tension at or above the cmc. The data reported by
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Figure 4. Typical response of an R = 2.3 nm surface when exposed to a CTAB solution with step-by-step adsorption. For each step, the concentration is 0.1, 0.2, 0.3, 0.4, 0.6, 0.8, 1.0, 1.2, and 1.4 cmc, respectively. Inset shows the QCM response of crystals with R = 2.3, 3.1, and 5.8 nm when the bulk concentration changes from 0.8 to 1 cmc (the circled part of the adsorption isotherm).
Tilton and co-workers also did not show a dip in surface tension consistent with the fact that adsorption at the waterair interface can differ from that at the solid-water interface. Common interfacially active impurities at the airwater interface are those that have opposite charge of the surfactant head groups, as well as nonionic compounds that have aliphatic chains that pack well with the hydrophobic tail of the surfactant. In the solidliquid case, driving forces are more varied and include, for example, chargecharge interactions between the impurity and the surface. Because rougher surfaces are expected to have a much wider distribution of charges (both in sign and magnitude) than a smooth surface, the sensitivity of a rough solidliquid interface to impurities could be much greater than that of an airliquid or liquidliquid interface, which is in qualitative agreement with our observations. Third, our prior results for the adsorption of CTAB on relatively smooth gold surfaces in the presence of known amounts of low-molecular weight compounds (toluene, phenol, and 1-hexanol) did not show pronounced enhancement of the adsorbed amount at the cmc, except in the case of phenol.25 However, to yield a maximum in the measured adsorption at the cmc requires not only impurities to be present, but the impurities must partition from the surface to the micelles above the cmc. High levels of impurities may not exhibit such partitioning. The peak in adsorption at the cmc shown in Figure 2 is likely not only due to adsorbed surfactant and impurity; trapped water also likely contributes to the response. First, if only impurities were responsible for the results, the large magnitude of the peak for R = 3.1 and 5.8 nm samples would mostly be due to adsorption of impurities, requiring large amounts of impurities to be present at the surface. Further, at the cmc, the dissipation shows a pronounced maximum, except for the R = 2.3 nm surface (see Figure 3). The value of the measured dissipation increases as R increases (∼0.7 106 for R = 2.3 nm, ∼2.4 106 for R = 3.1 nm, and ∼3.3 106 for R = 5.8 nm). These results are indicative of a significant increase in aggregate flexibility at the cmc, which could be due to the presence of entrapped water. Another possibility for the peak is surface rearrangement of aggregates. According to this interpretation, the rearrangement of the adsorbed surfactant aggregates near the cmc causes both 6095
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Figure 5. Fractional adsorption as a function of time for surfaces of different roughness in solutions with concentrations above and below the cmc. The solution was initially pure water. The surfactant solution of desired concentration was then pumped into the instrument.
the increased dissipation and the increased adsorbed amount near the cmc on rough surfaces, possibly because of the formation of complex interconnected surfactant structures likely containing large amounts of solvent. These interconnected structures then disappear as the bulk surfactant concentration increases. Although this possibility is in part supported by the analysis of raw QCM data [as the concentration changes from 0.8 to 1 cmc there seems to be overshoot in the adsorbed amount (see Figure 4)], the appearance of complex structures made only of surfactant with no impurities stable only in a small concentration range near the cmc seems rather improbable. The possibility that such interconnected structures form with impurities present, and later disappear because the impurities partition to micelles, is much more likely. Typical QCM data obtained when an R = 2.3 nm surface is exposed to a solution with step-by-step increase in bulk CTAB concentration is shown in Figure 4. At every step until the bulk concentration reached 1 cmc, the frequency decreased (i.e., the amount adsorbed increased) as the bulk CTAB concentration increased. At larger concentrations, the amount adsorbed actually decreased when the bulk CTAB concentration was increased (e.g the peak in Figure 2). The change in trend is highlighted by the dotted circle. In the inset of Figure 4 we report the changes in frequency when the CTAB concentration was increased from 0.8 to 1.0 cmc on the three surfaces of interest. On rougher surfaces, the frequency decreased very quickly initially then increased slowly. Note that this is the only concentration change where there was a qualitative difference in adsorption mechanism between the R = 2.3 nm surface and the rougher surfaces. The simplest explanation is an increase followed by a decrease in adsorption; however the dissipation results (Figure 3) imply that the change in frequency cannot be viewed in such a simple manner. Because of the long time required to reach equilibrium, the process likely involves some surface rearrangement of the adsorbed molecules as well as adsorption/desorption phenomena. Dynamics of Adsorption. The dynamics of adsorption for systems with surfactant concentrations below (0.1 cmc) or above the cmc (1.2 cmc) were studied to assess the effect of roughness on adsorption kinetics (Figure 5). The dynamic curve did not show an increase within the first 150200 s after the injection of solution containing surfactant because of an induction time as the solution passed through the volume of the tube connecting the feed vessel to the cell. Neglecting this initial phase, adsorption showed a two-step process: the adsorption percentage increased very quickly in the first step, then increased slowly in the second step until a plateau was reached.
Figure 6. Kinetic adsorption data for crystals of different roughness at a surfactant concentration of 0.1 cmc (black and gray symbols), with model fits to the data (solid, red lines). Data for R = 5.8 nm have been shifted horizontally. The dotted lines show for each fit the contribution to the total adsorbed amount from the rapidly adsorbed mode (a) and the slowly adsorbed mode (b).
Equilibrium was established in a couple of hours for all cases except for surfaces with R = 2.3 nm at surfactant concentration above the cmc, in which case the time required to reach equilibrium was much shorter than in any other condition considered. Adsorption is somewhat faster at 1.2 cmc than at 0.1 cmc for all surfaces, although the difference is much smaller for the R = 5.8 nm surface. At bulk CTAB concentrations of 0.1 cmc the second adsorption step takes longer to complete on the R = 5.8 nm surface than on the R = 2.3 nm surface, presumably because the irregular surface morphology, with a likely wider distribution of energy sites, causes more surface rearrangement even at low surface coverage. In order to further understand the apparent two-rate adsorption process seen in the low concentration data, adsorption data as a function of time were modeled using a two-rate model which has been described in detail elsewhere.37 Predicted curves were only generated for two different roughness surfaces at a bulk surfactant concentration of 0.1 cmc, as the transport condition used within the model has only been shown to be accurate at sub-cmc concentrations. Both data sets were fit using identical values of the systemads des des specific parameters (M, kads a , kb , ka , and kb ) but with different relative adsorbed amounts on the a and b adsorption sites. This suggests that roughness is a key parameter in determining the maximum adsorbed amount, but that the mechanism of adsorption does not differ because of roughness. It appears that the slowly adsorbed mode has a greater contribution to total adsorption for the rougher crystal, although both modes represent lower total adsorbed amounts than for the smooth crystal. The adsorption rates at low concentrations are consistent with primarily transport-limited adsorption. Initially, when surface coverage is very close to zero, there is no barrier to adsorption from previously adsorbed surfactant, and hence the initial rate (defined using an area calculated from the total adsorbed amount and the area/headgroup, not the measured surface area via AFM as was done in Figure 2) should depend only on the distribution of energy sites. A faster rate at near-zero adsorption (see inset of Figure 5), is expected to be proportional to the strength of the attraction between an individual surfactant molecule and the surface. A rough surface 6096
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Langmuir will have a wider distribution of site energies, likely exposing high-energy sites that strongly attract surfactants, thus qualitatively explaining the faster adsorption observed during the first adsorption step on the rougher surfaces. At higher concentrations, but still in a low concentration regime, a linear adsorption rate which depends purely on transport to the surface is seen. At later stages, the adsorption rate slows due to the limited number of surface sites available and/or lower energy sites available for adsorption. This behavior is representative of classical Langmuirtype adsorption. However, the reasons for the separate slower step which follows the initial adsorption and results in the long equilibration times for the data shown here are less clear. Possible explanations could be a population of lower energy or less favorable surface sites, a slow rearrangement of preadsorbed surfactant, or surface aggregation which occurs at a slower rate. Recent work by Howard et al,20 suggests that for cationic surfactants, a slow rearrangement of adsorbed surfactant could make further surface sites available, leading to the slow additional adsorption and long equilibration times seen in these systems. In this case, any of the mechanisms cited could be exacerbated by roughness, explaining the increase adsorption in the slow mode for the rougher crystal. It may be expected that a rough surface would have a greater number of unfavorable adsorption sites when compared to a smoother surface, explaining the greater proportion of adsorption in the slowly adsorbed mode. In addition, if the roughness is on the order of the cross-sectional area of a surfactant molecule, surfactant packing might be irregular leading to less favorable tailtail interactions. Hence, above the cmc, adsorption on a rough surface is expected to be slower near completion because of the reduction in driving force. In summary, the fact that the adsorbed amount is less on rough surfaces is one characteristic introduced by roughness; another is that the time required to reach full adsorption is significantly lengthened in the concentration regime where cooperative adsorption is important.
’ CONCLUSIONS Roughness has a significant effect on adsorption, both in terms of the total amount adsorbed as well as of the kinetics of adsorption. Both below 0.8 cmc and above 1.2 cmc our results show that the amount adsorbed decreases as the surface roughness increases. Near the cmc the adsorption data show pronounced maxima, especially on the rougher surfaces, presumably due to the effect of impurities. The peak observed both in adsorbed amount and in dissipation near the cmc was probably due to enhanced impurity adsorption, trapped water, and possibly other phenomena. Roughness appears to reduce the hydrophobic driving force (e.g., tailtail interaction) for adsorption, which in turn causes a decrease in adsorbed amount at all concentrations. Roughness also increases the initial rate of adsorption both below and above the cmc, which is attributed to the fact that the concentration of high-energy sites should be larger on a rough surface. Roughness also seems to increase the proportion of slowly adsorbed surfactant at concentrations below the cmc, possibly due to a greater concentration of less favorable adsorption sites. In other words, the distribution of surface energy sites seems to be broader for a rough surface. Above the cmc, our kinetic data show a slow second adsorption step on the rougher surfaces, interpreted as a significant surface rearrangement of the aggregates coupled to a weakened driving force for adsorption.
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Table 3. Adsorbed Amount per Unit of Actual Surface Area Calculated with Sauerbrey and Voigt Model on Gold Surface with Different Roughness at 1 cmc adsorbed amount (ng/cm2) model
R = 2.3 nm
R = 3.1 nm
Sauerbrey
233.9 ( 1.2
146.5 ( 0.8
Voigt
378.1 ( 30.7
536.2 ( 175.1
R = 5.8 nm 68.6 ( 10.4 460.9 ( 68.7
’ APPENDIX 1: SAUERBREY VS VOIGT MODELS The use of the Voigt model requires estimate of the adsorption density, which is difficult to estimate accurately. Because the Sauerbrey equation requires no such value, it is useful to compare results at low dissipation to assess the accuracy of the estimates. The absorbed amount as calculated with Sauerbrey and Voigt models on surfaces with different roughness at the cmc are shown in Table 3. When the dissipation is low (R = 2.3 nm) the Sauerbrey model estimates ∼35% less adsorption than the Voigt model. Under these conditions the layer thickness is 3.9 ( 0.3 nm, as calculated by Voigt model, higher than that found via neutron reflection for CTAB absorbed on a silicon surface, 3.2 ( 0.1 nm.7 The Sauerbrey model yields a thickness comparable to that obtained from neutron scattering when the experimental error of both measurements is considered. We conclude that the adsorbed amounts obtained from the Sauerbrey model are likely more accurate when the associated dissipation is low. As the dissipation increases (R = 3.1 and 5.8 nm), the discrepancy between estimates obtained from the Sauerbrey model vs those obtained with the Voigt one become even more siginificant. However, because the Sauerbrey equation is known not to be applicable when the dissipation is large, the Voigt model is likely more accurate at high dissipations. For consistency, all data presented herein were obtained using the Voigt model. Despite the discrepancy between the two models predictions highlighted in Table 3, the conclusions of present study will not be affected by the model employed to extract the adsorbed amount from the raw data. ’ ACKNOWLEDGMENT This research was supported by the Institute of Applied Surfactant Research which has the following corporate sponsors: Akzo Nobel, Church & Dwight, Clorox, Conoco/Phillips, Dow Chemical, Ecolab, GlaxoSmithKline, Halliburton Services, Huntsman, Oxiteno, Procter & Gamble, Sasol, S.C. Johnson, and Shell Chemical. Financial support was also provided by the Chinese National Science Foundation (Grant No. 21073066). The authors thank Mark Poggi of Biolin Scientific for his help in procuring the rough crystals, Dr. Shili Wang for help in programming the actual surface area calculations, Professor Guangzhao Zhang and Miss Xiaojun Tian (South China University of Technology) for very helpful discussions concerning QCM, and Professor Fredericke Jentoft for initial adsorption rates. ’ REFERENCES (1) Johannsmann, D.; Reviakine, I.; Rojas, E.; Gallego, M. Anal. Chem. 2008, 80, 8891. (2) Karlsson, P. M.; Palmqvist, A. E. C.; Holmberg, K. Langmuir 2008, 24, 13414. 6097
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