Effect of Adsorbed Layer Surface Roughness on the QCM-D

Oct 18, 2007 - Quantitative Analysis of Diffusive Reactions at the Solid–Liquid Interface in Finite Systems. Thomas C. T. Michaels , Alexander K. Bu...
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Langmuir 2007, 23, 12436-12444

Effect of Adsorbed Layer Surface Roughness on the QCM-D Response: Focus on Trapped Water Lubica Macakova,*,† Eva Blomberg,†,‡ and Per M. Claesson†,‡ DiVision of Surface Chemistry, Department of Chemistry, Royal Institute of Technology, SE-10044 Stockholm, Sweden, and Institute for Surface Chemistry, Box 5607, SE-11486 Stockholm, Sweden ReceiVed May 16, 2007. In Final Form: July 18, 2007 The effect of surface roughness on the quartz crystal microbalance with dissipation monitoring (QCM-D) response was investigated with emphasis on determining the amount of trapped water. Surfaces with different nanoroughnesses were prepared on silica by self-assembly of cationic surfactants with different packing parameters. We used surfactants with quaternary ammonium bromide headgroups: the double-chained didodecyltrimethylammonium bromide (C12)2DAB (DDAB), the single-chained hexadecyltrimethylammonium bromide C16TAB (CTAB), and dodecyltrimethylammonium bromide C12TAB (DTAB). The amount of trapped water was obtained from the difference between the mass sensed by QCM-D and the adsorbed amount detected by optical reflectometry. The amount of water, which is sensed by QCM-D, was found to increase with the nanoroughness of the adsorbed layer. The water sensed by QCM-D cannot be assigned primarily to hydration water, because it differs substantially for adsorbed surfactant layers with similar headgroups but with different nanoscale topographies.

Introduction The quartz crystal microbalance with dissipation monitoring (QCM-D) technique is a well-established method for adsorption studies at solid surfaces. Further development of this technique for use in liquid environments1 made it suitable for biotechnology and surface chemistry applications, where the liquid and especially water environments are often of main interest. The QCM-D technique enables us to follow changes in the viscoelastic environment of the quartz crystal during an adsorption process by monitoring both the resonant frequency of the crystal and the dissipation of the energy of oscillations. With other techniques, one can follow different aspects of the adsorption process. For example, optical techniques are sensitive to changes in the refractive index close to the substrate, which occurs due to a difference between the refractive index of the adsorbed film and that of the bulk liquid. While optical techniques are sensitive only to the “dry” mass of the film, QCM-D senses also the part of the solvent that is coupled to the adsorbed film and thus oscillates along with the sensor crystal.2 For this reason, the mass sensed by QCM-D and the adsorbed amount detected by optical techniques are expected to differ. Indeed, large differences between the mass sensed by QCM and the adsorbed mass obtained by optical techniques have been found in many cases, for instance, in studies concerned with the adsorption of surfactants,3 polypeptide multilayers,4 vesicles,5 supported lipid bilayers,6 and proteins and DNA molecules onto supported lipid bilayers.2,7 * To whom correspondence should be addressed. Telephone: +46 8 7909911. Fax: +46 8 7908998. E-mail: [email protected]. † Royal Institute of Technology. ‡ Institute for Surface Chemistry. (1) Rodahl, M.; Hook, F.; Krozer, A.; Brzezinski, P.; Kasemo, B. ReV. Sci. Instrum. 1995, 66, 3924-3930. (2) Reimhult, E.; Larsson, C.; Kasemo, B.; Hook, F. Anal. Chem. 2004, 76, 7211-7220. (3) Stålgren, J. J. R.; Eriksson, J.; Boschkova, K. J. Colloid Interface Sci. 2002, 253, 190-195. (4) Halthur, T. J.; Elofsson, U. M. Langmuir 2004, 20, 1739-1745. (5) Reimhult, E.; Zach, M.; Hook, F.; Kasemo, B. Langmuir 2006, 22, 33133319. (6) Richter, R. P.; Brisson, A. R. Biophys. J. 2005, 88, 3422-3433. (7) Larsson, C.; Rodahl, M.; Hook, F. Anal. Chem. 2003, 75, 5080-5087.

Water sensed by QCM-D can be either “bound” in the adsorbed film, as in hydration layers, or mechanically trapped in cavities on a rough surface. It is difficult to separate these two contributions completely. In this study, we aimed at creating surfaces with controlled nanoscale roughnesses to vary the amount of water trapped in surface cavities, while keeping the surface chemistry as similar as possible to avoid varying the extent of hydration of these surfaces. To this end, surfactants with the same headgroup, but with a different surfactant packing parameter, were used to generate surfaces with different nanoroughnesses. In aqueous solutions, surfactants self-assemble into micelles once their concentration exceeds the critical micellar concentration (cmc). The micelles can differ in size and shape, and their final geometry is determined by the molecular structure of the surfactants and by the properties of the solvent. Different bulk geometries can be characterized, for example, by the surfactant packing parameter.8 Similar structures have been proven to form also on solid substrates, and they were imaged for the first time as hemimicelles on hydrophobic graphite by Manne et al.,9 while full micelles are formed on silica.10 The adsorbed micelles are probably deformed,11 and flattening at the area of interaction with the substrate has been predicted by molecular dynamics simulations.12 By varying the surfactant structure or properties of the solvent, it is possible to achieve different surface topographies, for example, spherical micelles, rodlike micelles, or flat bilayers.10,13,14 We note that there are several advantages with using surfactants for modifying the surface roughness when studying mechanically trapped water. For instance, the structures (8) Evans, F.; Wennerstrom, H. The Colloidal Domain, 2nd ed.; Wiley-VCH: New York, 1999. (9) Manne, S.; Cleveland, J. P.; Gaub, H. E.; Stucky, G. D.; Hansma, P. K. Langmuir 1994, 10, 4409-4413. (10) Liu, J. F.; Ducker, W. A. J. Phys. Chem. B 1999, 103, 8558-8567. (11) Fragneto, G.; Thomas, R. K.; Rennie, A. R.; Penfold, J. Langmuir 1996, 12, 6036-6043. (12) Shah, K.; Chiu, P.; Jain, M.; Fortes, J.; Moudgil, B.; Sinnott, S. Langmuir 2005, 21, 5337-5342. (13) Grant, L. M.; Tiberg, F.; Ducker, W. A. J. Phys. Chem. B 1998, 102, 4288-4294. (14) Velegol, S. B.; Fleming, B. D.; Biggs, S.; Wanless, E. J.; Tilton, R. D. Langmuir 2000, 16, 2548-2556.

10.1021/la7014308 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/18/2007

Effect of Surface Roughness on the QCM-D Response

are self-assembled and regular, and the interior of the surfactant aggregates is essentially water free. For the modification of the surface nanoscale roughness of silica coated QCM-D crystals, cationic surfactants with quaternary ammonium headgroups and hydrophobic tails with different structures were used. The surfactants employed were the doublechained didodecyldimethylammonium bromide (DDAB), the single-chained hexadecyltrimethylammonium bromide (CTAB), and dodecyltrimethylammonium bromide (DTAB). The adsorbed mass of the adsorbed surfactant films was determined by optical reflectometry. To our knowledge, this is the first systematic QCM study concerned with water trapped in topographical irregularities of adsorbed layers. However, we note that the paper by Patel and Frank discusses similar issues for adsorbed vesicle systems.15 Experimental Section Chemicals. All surfactants used were purchased from Fluka: didodecyltrimethylammonium bromide (DDAB, art. number 36 785, purum g 98%), hexadecyltrimethylammonium bromide (CTAB, art. number 52 369, Ultra g 99%), and dodecyltrimethylammonium bromide (DTAB, art. number 44 239, purriss. p.a. g 99%). They were all used as received. For all experiments, deionized MilliQ water (>18.2 MΩ cm-1) was used, which was deaerated under vacuum for at least 0.5 h. The water purification process was carried out by a combined Milli-RO 10 Plus and MilliQ plus 185 system (Millipore, Billerica, MA), including multiple filtration, reverse osmosis, passing of the water through ion exchange and activated carbon cartridges, and UV photo-oxidation. The critical micellar concentrations measured in MilliQ water were as follows: 0.08 mM for DDAB, 1 mM for CTAB, and 15 mM for DTAB. All surfactants were adsorbing from a concentration of 1.2 × cmc except for DTAB, for which we used concentrations between 1.2 and 3.0 × cmc. Substrate. Silica was used as a substrate in all the reflectometry, QCM-D, and AFM experiments. The plates used in the reflectometry experiments contained a 1000 Å thick silica layer that was thermally grown on the silicon substrate (WaferNet GmbH, Eching, Germany), while the silica layer on the QCM crystals (Q-sense, Va¨stra Fro¨lunda, Sweden) was e-beam evaporated on top of the gold electrode.2 Both substrates were cleaned in the same way. First, the reflectometry plate and QCM crystal were immersed in a 2% water solution of Deconex 11 (Borer Chemie AG, Zuchwil, Switzerland), which is an alkaline cleaning agent with an oxidizing effect. They were next thoroughly rinsed with MilliQ water and left to stand at least overnight in MilliQ water. Before use, the substrates were rinsed with 99% ethanol, dried with a nitrogen stream, and exposed to air plasma for 5 min at a radio frequency (RF) power of 9 W (Harrick Scientific Corp., model PDC-3XG, Ossining, NY). After the plasma cleaning process, the substrates were stored in 99% ethanol until use but not for longer than 0.5 h. Special care was dedicated to cleaning the equipment. Before each experiment, all tubing and the measuring chambers were filled with a 10 mM (>cmc) solution of SDS and left to stand for at least 15 min. In the next step, the tubing and chambers were rinsed with at least 500 mL of water. The substrates were introduced into the equipment after additional rinsing with ethanol and drying with filtered nitrogen gas. Reflectometry. The reflectometry equipment was assembled according to the design of Dijt et al.16 During the experiments, we maintained the gravity flow of the solution through the measuring chamber at a flow rate between 1.2 and 1.5 mL/min. Experiments were done at room temperature, which was 25 ( 1 °C. The measured signal is the ratio between the intensities of the light polarized parallel (p) and perpendicular (s) after reflection at the sample surface: (15) Patel, A. R.; Frank, C. W. Langmuir 2006, 22, 7587-7599. (16) Dijt, J. C.; Cohen Stuart, M. A.; Fleer, G. J. AdV. Colloid Interface Sci. 1994, 50, 79-101.

Langmuir, Vol. 23, No. 24, 2007 12437 S)

Ip |Rp| ∝ Is |Rs|

(1)

where Rp and Rs are the complex reflectancies for reflection at the substrate. This ratio changes during adsorption onto the silica surface, which is due to changes in the optical properties at the solid/liquid interface. The adsorbed amount is determined as follows: (S - S0) S0

Γ)Q

(2)

where S0 is the reference signal before the onset of adsorption and Q is a sensitivity coefficient. The light source was a He-Ne laser with a wavelength of 633 nm. The incidence angle was 70°, which is close to the Brewster angle for the silicon/water interface (71°). The sensitivity factor Q was calculated as follows: |Rp|/|Rs| Q ) δΓ δ(|Rp|/|Rs|)

(3)

where Rp and Rs were obtained by optically modeling our system using Fresnel’s equations. The optical model consists of four layers with corresponding refractive indices and thicknesses: silicon (3.882, semi-infinite); amorphous silicon dioxide (1.457, 100 nm); an adsorbed layer of surfactant; and water (1.333, semi-infinite). The layer of surfactant was modeled as a flat layer, with a refractive index changing linearly with the average concentration in the layer, cj, with the proportionality constant equal to the refractive index increment, dn/dc: Nlayer ) Nwater + (dn/dc) × cj

(4)

where cj ) Γ/h, Γ is the adsorbed amount, and h is the thickness of the adsorbed layer. The calculation of the sensitivity factor is an iterative procedure, and it was repeated until self-consistent results were achieved in terms of input and output adsorbed amounts. The refractive index increments were measured at a wavelength of 589 nm with an Abbe´ refractometer and at a wavelength of 450 nm with a Wyatt differential refractometer. By assuming a linear dependence of the refractive index increment on 1/λ2 (ref 17) the results were extrapolated to 633 nm, which is the wavelength of the laser used for reflectometry measurements. The parameters used in the evaluation of the reflectometric data are summarized in Table 1: refractive index increments, thicknesses of the adsorbed layers, resulting sensitivity factors, and relative changes of the signal. The sensitivity factor Q is relatively insensitive to the thickness of the adsorbed layer (see Figure 1). We note that the layer thickness is not determined in our experiments, but we have to rely on literature values. In the calculations, we used thicknesses determined by neutron reflectivity measurements for the surfactant layers adsorbed from solutions with concentrations above cmc onto hydrophilic silica. These thicknesses, with the exception of that for DDAB, are significantly smaller than the diameter of the free micelles in bulk solution, presumably due to flattening of the micelles upon adsorption.11 In bulk solution, DTAB and CTAB form elliptical micelles with dimensions of 4.4 nm × 4.4 nm × 5.2 nm and 5.4 nm × 5.4 nm × 8.6 nm, respectively, as determined by small angle neutron scattering measurements.18 Using these parameters, we would obtain lower sensitivity factors than those reported in Table 1 with the lower limit being equal to 39.8 for DTAB and 39.7 for CTAB. If these values were used instead of those listed in Table 1, the adsorbed mass would be 6% lower than the reported value. Quartz Crystal Microbalance. The QCM-D D300 equipment, from Q-Sense (Va¨stra Fro¨lunda, Sweden), was employed in this investigation. The equipment is described in detail elsewhere.1 During the experiments, we maintained the gravity flow of the solution (17) Carlfors, J.; Rymden, R. Eur. Polym. J. 1982, 18, 933-937. (18) Berr, S. S. J. Phys. Chem. 1987, 91, 4760-4765.

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Table 1. Parameters Used for Evaluation of the Reflectometric Dataa

DDAB CTAB DTAB

dn/dc450nm (cm3/g)

dn/dc589nm (cm3/g)

dn/dc633nm (cm3/g)

thickness (nm)

Q-factor (mg/m2)

∆S/S0

0.149 ( 0.002 0.152 ( 0.001 0.151 ( 0.001

0.146 ( 0.004 0.143 ( 0.004 0.142 ( 0.004

0.146 ( 0.005 0.142 ( 0.005 0.140 ( 0.005

2.4 ( 0.3b 3.2 ( 0.1c 2.2 ( 0.2d

43.4 ( 2.8 42.4 ( 2.0 42.3 ( 2.0

0.0560 ( 0.0022 0.0447 ( 0.0011 0.0217 ( 0.0013

a The refractive index increments for different wavelengths, the thickness of the adsorbed layers, and the resulting sensitivity Q-factors. The last column contains the values of the relative change in the reflectometric signal ∆S/S0 after 0.5 h of surfactant adsorption from solutions with concentrations of 1.2 × cmc. b Neutron reflectivity,22 mean value for the data obtained in D20 (2.1 nm) and contrast matched D20/H2O (2.6 nm). c Neutron reflectivity11 on a smooth silicon block covered with a 10 Å thick SiO2 layer. d Neutron reflectivity35 in phosphate buffer with ionic strength 0.02 M at pH ) 7.0 (D2O).

between 10 and 13 Hz and with integral and proportional gains between 1 and 2. Surfactants were left to adsorb for 30 min before imaging.

Results and Discussion The Average Surfactant Packing Parameter and Its Implications for Surface Topography. The surfactant packing parameter (SPP) was calculated from the formula

SPP ) Figure 1. Effect of the thickness of the adsorbed CTAB layer on the calculated Q-factor. through the measuring chamber at a flow rate between 1.2 and 1.5 mL/min. The flow rate during each experiment was kept constant by continuous manual adjustment of the vertical position of the sample container, to keep the height difference between the sample liquid level and the measuring chamber constant. All experiments were done at 25.00°C ( 0.02 °C. The QCM-D equipment has the capability to simultaneously monitor changes in the resonant frequency and in the dissipation of the energy of oscillations, both at the nominal frequency of the crystal as well as at three overtones (third, fifth, and seventh). For viscoelastic adsorbed films, the relation between mass and frequency change is rather complicated.19 However, we used the Sauerbrey equation20 relating the change in the resonance frequency to the sensed mass. This approximation is valid provided the surfactant aggregates can, from a QCM perspective, be viewed as rigid objects. The validity of this assumption will be discussed later in this paper. In the Sauerbrey equation, the mass is related to the change in frequency as ∆m(ΓQCM) ) -C∆f/n

(5)

where ∆f is the change in the frequency measured at the nth overtone and C is a proportionality constant, which is characteristic for a certain type of QCM-D crystal. In our case, we used AT-cut crystals with a nominal frequency of 5 MHz, and the proportionality constant is equal to 0.177 mg/m2. Atomic Force Microscopy. Images were obtained with a Nanoscope III atomic force microscope (AFM, Digital Instruments). The QCM-D crystals and reflectometry substrates were imaged on the scale of 1 µm × 1 µm in air, in tapping mode. Surfactants were imaged on the scale of 200 nm × 200 nm in liquid, in “soft contact” mode.9 During imaging in “soft contact” mode, the tip is kept at a finite distance from the substrate due to long-range repulsion between the tip and the adsorbed surfactant layer on the substrate. We used silicon nitride cantilevers with a nominal spring constant of 0.12 N/m, which were cleaned by air plasma treatment for 5 min. Reflectometry plates were used as substrates. All surfactant images shown are deflection images. They were obtained with scan rates (19) Voinova, M. V.; Rodahl, M.; Jonson, M.; Kasemo, B. Phys. Scr. 1999, 59, 391-396. (20) Sauerbrey, G. Z. Phys. 1959, 155, 206-222.

V lA0

(6)

where V is the volume of the hydrocarbon tail of surfactants, l is the length of the alkyl chain of the surfactants in all-trans conformation, and A0 is the area per headgroup in a certain (micellar) arrangement. Generally, the higher the SPP, the less curved are the aggregates,8,21 as long as SPP < 1. In the context of this work, we find it useful to extend this concept to adsorbed surfactant aggregates, and below we define a surface surfactant packing parameter, sSPP. The parameters used for calculation of the sSPP at the silica/water interface for the surfactants employed in this study are summarized in Table 2. The length and volume of the hydrophobic tail are linearly dependent on the number of carbons in the tail. Calculated values are based on empirical formulas, and they are the same as those used for calculating the SPP.8 The average area per headgroup was calculated from the reflectometric adsorbed amount assuming a bilayer type structure of the adsorbed layers. The sSPP obtained in this way should be seen as an “average” surfactant packing parameter of aggregates with a certain polydispersity in size and shape that coexists at the surface. Further, the area of voids between the aggregates and eventually some defects in the adsorbed layer influence this value. Thus, the relation to the critical packing parameters for bulk aggregates is not straightforward, and one can obtain an average sSPP even lower than 1/3, which corresponds to the most curved, spherical geometry in bulk. However, we found that the average sSPP is useful for comparison of different adsorbed films. This is due to the fact that, with decreasing sSPP, the curvature of the adsorbed micellar structures and thus the nanoscale surface roughness increase. The Structure of Adsorbed DDAB Layers. The reflectometric adsorbed amount obtained for DDAB at 1.2 × cmc (2.43 ( 0.18 mg/m2) is in good agreement with reported values. Schulz at al. studied the adsorption of DDAB from solutions above the critical micellar concentration onto silica by the neutron reflection technique. They determined the adsorbed amount of DDAB on silica to be 1.94 ( 0.09 mg/m2 in D2O and 2.22 ( 0.09 mg/m2 in contrast matched D2O/H2O.22 For DDAB, the average surfactant packing parameter at the silica surface is equal to (21) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press Inc.: San Diego, CA, 1992. (22) Schulz, J. C.; Warr, G. G.; Butler, P. D.; Hamilton, W. A. Phys. ReV. E 2001, 63, 041604.

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Table 2. Reflectometric Adsorbed Amount ΓREFL, Average Area Per Molecule A0, Length l and Volume W of the Hydrocarbon Part, and Average Surface Surfactant Packing Parameter sSPP for Surfactants Considered in This Work DDAB CTAB DTAB

ΓREF (mg/m2)

ΓREF (µM/m2)

A0 (Å2)

l (nm)

V (nm3)

sSPP

expected shape

2.43 ( 0.18 1.90 ( 0.10 0.92 ( 0.07

5.25 ( 0.38 5.21 ( 0.27 2.98 ( 0.23

64 ( 6 65 ( 4 111 ( 10

1.674 2.182 1.674

0.702 0.459 0.351

0.65 ( 0.05 0.32 ( 0.02 0.19 ( 0.02

flat bilayer spheres/rods spheres

Figure 2. AFM images of bare SiO2 showing no features (A), an adsorbed layer of DDAB showing large scale undulations (B), an adsorbed layer of CTAB showing prolonged rodlike micelles, with an average spacing of ∼9 nm (C), and an adsorbed layer of DTAB showing small micellar aggregates with an average spacing of ∼5-6 nm (D). The surfactants were adsorbed from aqueous solutions with concentration of 1.2 × cmc. Image A was obtained in contact mode, and images B-D were obtained in “soft contact” mode.

0.65. The number is higher than the critical packing parameter for infinite cylinders, which is 0.50. Therefore, we can expect adsorption in the form of a flat bilayer. AFM images of the layer (Figure 2B) do not reveal any distinctive features except for large undulations. These undulations were not observed on bare silica (Figure 2A). Our images of DDAB layer on silica are in good agreement with images obtained under similar conditions as reported by Schulz et al.22 The sSPP and AFM images are both consistent with a planar bilayer structure of DDAB on silica. The Structure of Adsorbed CTAB Layers. For CTAB, the reflectometric adsorbed amount is 1.90 ( 0.10 mg/m2 at 1.2 × cmc. It corresponds well with the neutron reflection value of 2.04 ( 0.15 mg/m2 (at cmc) for adsorption on smooth silica surfaces obtained by Fragneto et al.11 and with the reflectometric value of 1.7 ( 0.2 mg/m2 (for concentrations between 1 and 10 cmc) obtained by Velegol et al.;14 both values were obtained in high purity water without any added salt, that is, under similar conditions as in our experiments. The average sSPP for CTAB is 0.32. This number is very close to the critical packing parameter for spheres, which is 0.33. Taking into account that the sSPP is an average packing parameter, we can conclude that it is consistent with a combination of longer and shorter rodlike micelles with an average separation of ∼9 nm, the structure that was identified in the AFM images (Figure 2C). The average separation was obtained from 2D Fourier transforms of several images, where deflection variations, which were regularly repeated in the x-y plane, can be distinguished as bright spots (Figure 3A). Similar AFM images have previously been obtained on silica surfaces by Velegol et al.;14 however, some authors report spherical

Figure 3. Fourier transform of the AFM deflection images of CTAB (A) and DTAB (B).

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Figure 5. Reflectometric adsorbed amount (black filled squares) and QCM sensed mass (orange filled tilted squares) and change in dissipation (yellow filled circles) for DTAB as a function of the bulk DTAB concentration. The arrows represent extrapolations to zero bulk concentration.

Figure 4. Reflectometric adsorbed amount ΓREFL (black) and QCM sensed mass ΓQCM (dark color) and change in dissipation DQCM (light color) for DDAB (A), CTAB (B), and DTAB (C). For clarity, the lines are also distinguished by text and/or arrows. The baseline, which was recorded in pure water from -15 to 0 min, is followed by injection of a 1.2 × cmc surfactant solution from 0 to 30 min and then by rinsing with pure water from 30 to 60 min.

aggregates.10 The reflectometric adsorbed amount and the AFM images are consistent with the CTAB layer adsorbing in the form of micelles that look like rods in their projected shape along the silica surface. The Structure of Adsorbed DTAB Layers. The reflectometric adsorbed amount of DTAB is 0.92 ( 0.07 mg/m2 at a concentration of 1.2 × cmc, which is lower than the value of 1.3 mg/m2 in 10 mM NaBr at pH ∼ 6 reported by Cardenas et al.23 This difference can be expected, since surfactants are less tightly packed when adsorbed from water, as in our case, compared to the case when they are adsorbed from 10 mM NaBr where the electrostatic repulsion between surfactant headgroups is reduced due to the added salt. The average packing parameter for DTAB is 0.19, and the AFM image (Figure 2D) reveals spherical micelles with an average separation of 5.7 nm. An example of a Fourier transform (FT) of an image of a DTAB layer is shown in Figure 3B. Spherical micelles have been observed by AFM also for the surfactant C14TAB (TTAB),22 which has a chain length in between that of CTAB and DTAB. Since surfactants with shorter tails are (23) Cardenas, M.; Campos-Teran, J.; Nylander, T.; Lindman, B. Langmuir 2004, 20, 8597-8603.

expected to form more curved structures, it is expected that if TTAB forms spherical micelles, then DTAB should also form spherical micelles. The reflectometry and AFM results are consistent with the layer of DTAB consisting of an array of micelles that are nearly circular in their projected shape on silica. Relative Water Content in the Adsorbed Layers. The results of the reflectometric and QCM-D experiments are shown together in Figure 4. For the flat bilayer structure formed by DDAB, the adsorbed mass obtained by reflectometry is virtually identical to the mass sensed by the QCM-D. However, for CTAB forming cylindrical structures, the QCM-D senses a larger mass than that detected by reflectometry. The difference is even larger for the DTAB layer consisting of spherical structures. Thus, the difference between the reflectometric adsorbed amount and the mass sensed by QCM-D is increased with increasing surface roughness (decreasing average sSPP). For the DDAB and the CTAB layers, the dissipation change is close to zero. This indicates that they form rigid, elastic adsorbed layers. On the other hand, we can see a relatively large increase in dissipation (1.5 × 10-6) upon injection of DTAB. For all surfactants, the concentration during injection is 1.2 times the critical micellar concentration. The critical micellar concentration (cmc) of DTAB, which is 15 mM, is 1 order of magnitude higher than the cmc of CTAB, which is 1 mM, and 2 orders of magnitude higher than the cmc of DDAB, which is ∼0.08 mM. Thus, for DTAB, the changes in bulk density and viscosity during injection cannot be neglected. To account for that, the concentration of DTAB was increased stepwise from 1.2 to 3.0 times the cmc (from 18 to 45 mM), and for each concentration the reflectometric adsorbed amount and the mass sensed by QCM-D were determined. These results are shown in Figure 5 together with the measured change in dissipation. Above the cmc, the adsorbed amount obtained by reflectometry does not change with the bulk concentration, while the QCM sensed mass and dissipation are increasing. A constant reflectometric adsorbed amount demonstrates that the structure of the adsorbed film does not change within the range of the bulk concentrations studied, which is as expected since the surfactant activity is essentially constant. Because the structure of the adsorbed film is not changing, the increase of the QCM sensed mass and dissipation with concentration is a consequence of the change of the viscoelastic properties of the bulk liquid. In the purely viscous limit of the

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Figure 6. Simple geometrical model of surfactant structures at the interface. An ideal bilayer (A), rodlike micelles (B), and spherical micelles (C). The envelope represents the total volume of the film sensed by QCM-D. Cross sections of a hemimicelle (i), deformed micelle (ii), and regular micelle (iii). Table 3. Theoretical Ratios φv of the Volume of Mechanically Trapped Water to the Volume of Adsorbed Surfactants for Surfactant Layers Adopting Specific Regular Topographies, and Corresponding Relative Water Content w in the Layer (in Volume %) φv

flat monolayer flat bilayer halve rods rods spheres-hcpa spheres-rcpb

w

deformed micelles

regular micelles

0.12 0.32 1.18

0.00 0.00 0.27 0.27 0.65 1.73

deformed micelles

regular micelles

11% 24% 54%

0% 0% 21% 21% 39% 63%

a hcp: hexagonally closed packed arrangement. b rcp: randomly closed packed arrangement.

Voight model,19,24 the changes in sensed mass and dissipation due to changes in bulk viscosity and density are related as follows:

∆ΓQCM ∝ ∆xηbFb ∆D ∝ ∆xηbFb

(7)

Since the adsorbed mass, and thus the structure of the adsorbed micellar aggregates, does not change for concentrations between 1.2 and 3.0 cmc, the data in Figure 5 combined with eq 7 demonstrate that the density and viscosity of the solutions increase linearly with concentration in the studied range and the increments of sensed mass and dissipation are proportional to the concentration. Thus, by extrapolation of a linear fit through the experimental data (Figure 5) to zero bulk concentration for both the sensed mass and dissipation change, the data corresponding only to the changes due to the adsorbed film are obtained. It is interesting to notice that the corrected change in dissipation is negligible. The same results were observed for all the overtones. This supports our assumption that we can treat the film of the adsorbed surfactant aggregates as rigid (nonelastic), and it also justifies our use of the Sauerbrey relation for the data analysis. (The issue of the validity of the Sauerbrey equation is discussed in more detail in the Supporting Information.) The relative increase of the mass of the adsorbed surfactant layers due to water was calculated from the difference between the QCM-D sensed mass and the reflectometric adsorbed amount as follows:

φM )

ΓQCM - ΓREFL ΓREFL

(8)

(24) Kanazawa, K. K.; Gordon, J. G. Anal. Chim. Acta 1985, 175, 99-105.

For DTAB, the value obtained by extrapolation of the line in Figure 5 to zero bulk concentration was used for calculations. For the specific topographies adopted by the adsorbate, we can determine the theoretical ratio of the volume of mechanically trapped water to the volume of adsorbed surfactants, φv (Figure 6 and Table 3). The theoretical ratio of the masses of water and surfactant in the layer, φM, can then be determined as follows:

φM )

Fw φ Fads V

(9)

where Fw is density of water and Fads is the density of adsorbed surfactants. In the present case, the density of the employed hydrocarbon surfactants is similar to the density of water (usually within 5% according to the product specification sheets of the producers), and therefore, φM is very close to φv. Based on simple space filling models, we expect that no mechanically trapped water would be sensed for bilayers. For long rodlike micelles on the surface, we expect φ-values between 0.12 and 0.27, and at the most 21% of the sensed mass would be due to mechanically trapped water in the layer. For spheres in a hexagonal close packing arrangement, φ is expected to be between 0.32 and 0.65 (up to 39% of water in the layer), and for randomly close packed spheres φ is expected to be between 1.18 and 1.73 (up to 63% of water in the layer). Our results are in good agreement with these models. For DDAB, the calculated φM is -0.02 ( 0.10, which agrees with values expected for bilayers (Table 4). For CTAB, we obtained 0.42 ( 0.15, which is consistent with short rods or a combination of rods and spherical micelles. For DTAB, φ is 1.34 ( 0.26, which is in good agreement with the value expected for spherical micelles in a randomly closed packed arrangement. Structural Changes During Desorption. Rinsing with water results in the desorption of CTAB and DTAB. Within 30 min, both the reflectometric adsorbed amount and the QCM sensed mass approach zero. However, the DDAB layers behave differently. While the reflectometric adsorbed amount decreases significantly within 30 min of rinsing (on average, it decreases from 2.4 mg/m2 to 0.18 ( 0.11 mg/m2), the QCM sensed mass after rinsing was significantly higher. On average, it decreased to 0.85 ( 0.18 mg/m2 from 2.4 mg/m2. The content of trapped water clearly increases upon rinsing, suggesting that a patchy bilayer of DDAB is formed, where the water is trapped within the voids between the patches (Figure 7). This desorption pathway is in line with the observation that electrostatically anchored hydrophobic monolayers are unstable after transfer into aqueous solutions, where they rearrange to form bilayer patches.25 With (25) Perkin, S.; Kampf, N.; Klein, J. J. Phys. Chem. B 2005, 109, 3832-3837.

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Figure 7. Illustration of our hypothesis that after rinsing a patchy DDAB bilayer is left on the silica substrate with the water trapped in between the patches.

MacakoVa et al.

a larger sensed mass per unit (projected) area can be expected than on a flat substrate. On the other hand, the opposite trend, a lower QCM-D sensed mass in comparison with the mass detected on the flat surface, can be expected if we consider that water initially trapped in the surface wells can be displaced by surfactants without any large change in the mass being detected. Clearly, this issue deserves further analysis, as provided below. The baseline in our QCM-D measurements corresponds to the resonance frequency of the crystal immersed into water, with some water trapped in the surface “wells” (Figure 9A). When a film adsorbs, the volume of this trapped water diminishes by the volume occupied by the surfactants in the wells. Thus, the expected difference between the mass of the film with uniform thickness (e.g., flat bilayer) sensed by QCM-D and the reflectometric adsorbed amount can be expressed as follows:

ΓQCM - ΓREFL ) (Γrough + ∆Γtr) - Γflat ) ∆Γrough-flat + ∆Γtr

(10)

where ΓQCM is the mass sensed by QCM-D, ΓREFL is the reflectometric adsorbed amount, Γrough is the adsorbed amount of surfactants on the rough (QCM-D) substrate, Γflat is the adsorbed amount of surfactants on the flat (reflectometric) substrate, ∆Γtr is the change of the mass of the trapped water per unit area upon adsorption of a uniform film, and ∆Γrough-flat is the difference between the adsorbed amount of surfactants on the rough and flat substrates. The two terms on the right-hand side of eq 10 are of opposite sign:

Figure 8. Topography of a reflectometric plate (A) and a QCM-D crystal (B). Tapping mode AFM images in air.

exception of the very first part of the desorption process, the increase in water content in the film is not accompanied by any significant increase in dissipation. It seems that mechanically trapped water does not dissipate energy in any different way from the bulk water. This is supported by the fact that, after the correction for the bulk effects was done, for CTAB and DTAB, no significant changes in dissipation due to the adsorption of surfactants and the formation of a nanorough surface were observed.

Discussion Roughness of the Underlying Silica Substrate. Some uncertainty is introduced due to the fact that the surface topography of the underlying silica substrates on the QCM-D crystals and the reflectometric plates were not identical. AFM height images of these substrates are shown in Figure 8. The RMS (root-meansquare) roughness of the QCM-D crystal is ∼1 nm/1 µm scan length, with a peak to valley distance of ∼3.5 nm and a distance between peaks of typically 50-75 nm. The reflectometric plates, on the other hand, were essentially flat, with a RMS roughness of 0.2 nm/1 µm scan length. The height oscillations, which can be seen on the picture, are in the order of the noise of the AFM signal and therefore cannot be directly attributed to the real roughness of the substrate. The larger surface roughness of the QCM-D crystal gives rise to a larger surface area and therefore

∆Γrough-flat ) Γflat∆Arough-flat > 0

(11)

∆Γtr ) FH2O∆Vtr/A < 0

(12)

where ∆Arough-flat is the difference in the real surface area between the rough and flat surfaces (per unit flat area), FH2O is the density of water, and ∆Vtr is the change of the volume of the “wells” upon adsorption of a uniform surfactant layer (per unit flat area). Hence, the outcome of eq 10 can be negative or positive depending on the shape of the “wells”. We modeled the roughness of the QCM substrate in two ways. For both models, the difference ΓQCM - ΓREFL was calculated from relation 10 for the adsorption of a uniform layer with a thickness of 2.4 nm (the thickness of the DDAB layer). The first model corresponds to a regular array of orthogonal “wells” with dimensions of d × d × h nm3 alternated by flat areas with dimensions of d × d nm2 (Figure 9A). The depth of the “well” was kept constant at a value of 3.5 nm, which corresponds to the peak to valley difference in our AFM images of the QCM-D crystal, while the lateral dimension, d, of the “well” was varied between 20 and 500 nm. The character of the surface roughness can be different from that of the model used above, with the limiting case being that the volume of the trapped water nearly does not change upon adsorption of the surfactant film. This case corresponds to the second model, which is schematically shown in Figure 9B. The horizontal peak to valley distance, d, was varied between 20 and 500 nm, keeping the vertical peak to valley distance constant at 3.5 nm. The calculated results are plotted as a function of the horizontal dimension of the roughness in Figure 10. For a uniform film, the difference between the mass sensed at the rough QCM substrate and the adsorbed amount detected at the flat reflectometric substrate is decreasing with an increasing value of d. This observation is independent of the exact shape of the roughness. In our case, AFM images (Figure 8) indicate that the

Effect of Surface Roughness on the QCM-D Response

Langmuir, Vol. 23, No. 24, 2007 12443

Figure 9. Topological models of a rough QCM crystal. (A) Schematic drawing of the system of “wells” with the dimensions d × d × 3.5 nm3. (B) Schematic drawing of the “pyramidal” roughness, where the amount of trapped water does not change upon adsorption.

and ∆Γh is the change in the amount of hydration water due to adsorption. ∆Γh can be expressed as

∆Γh ) Γh(substrate + ads) - Γh(substrate) ) Γh(substrate + ) + Γh(ads) - Γh(substrate-) ) ∆Γh(substrate) + Γh(ads)

Figure 10. Expected difference between the mass sensed by QCM-D and the reflectometric adsorbed amount due to the roughness of the underlying substrate. The calculations were done using two different models of surface roughness. Filled tilted squares ([) show the values calculated from the model illustrated in Figure 9A, and empty tilted squares (]) show the values calculated from the model illustrated in Figure 9B. Table 4. Mass Sensed by QCM-D ΓQCM-D, Reflectometric Adsorbed Amount ΓREFL, and Experimental Ratio φM of the Extra Mass Sensed by QCM-D and the Mass of the Adsorbed Surfactants (Per Unit Area)

DDAB CTAB DTAB

ΓQCM-D (mg/m2)

ΓREF (mg/m2)

φM ) (ΓQCM-D - ΓREFL)/ΓREFL

2.37 ( 0.04 2.70 ( 0.12 2.15 ( 0.06

2.43 ( 0.18 1.90 ( 0.10 0.92 ( 0.07

-0.02 ( 0.10 0.42 ( 0.15 1.34 ( 0.26

roughness of the QCM-D crystal would correspond to d > 20 nm, and therefore, using the square-well model, it can be shown that the mass sensed by QCM is not underestimated by more than 0.26 mg/m2. The other model of the topographical features for d > 20 nm shows that the possible overestimation of the sensed mass due to the roughness of the QCM-substrate can be neglected. Hence, we conclude that the observed difference in the mass sensed by the QCM-D and the adsorbed mass obtained by reflectometry is not due to differences in the roughness of the two substrates. Water in Hydration Layers. Water sensed by QCM-D can be of another origin than mechanically trapped water. A change in hydration water upon adsorption is also expected to contribute to the sensed mass. Generally,

ΓQCM ) Γdry + ∆Γtr + ∆Γh

(13)

where Γdry is the dry mass of the adsorbent, ∆Γtr is the change in the amount of mechanically trapped water due to adsorption,

(14)

where Γh(substrate+)is the hydration of the substrate in complex with the adsorbate, Γh(substrate-) is the hydration of the bare substrate, Γh(ads) is the hydration of the adsorbate, and ∆Γh(substrate) is the change in hydration of the substrate due to the formation of complexes with the adsorbate. We do not set Γh(substrate+) automatically equal to zero because there are indications that there might be an up to ∼0.46 nm thick layer of water present between a charged substrate and the headgroups of adsorbed surfactants in a humid environment and in aqueous solution.26,27 In the case of the flat DDAB layer, there is presumably no mechanically trapped water. From experiments, we know that ΓQCM(DDAB) is equal to ΓREFL(DDAB) within experimental error. Thus, from eqs 13 and 14, we can conclude that

∆Γh(silica) ≈ -Γh(DDAB)

(15)

Clearly, the change in the amount of hydration water coupled to the crystal due to the adsorption of DDAB, ∆Γh(DDAB), is

∆Γh(DDAB) ) ∆Γh(silica) + Γh(DDAB) ≈ 0

(16)

In terms of the number of adsorbed molecules, ΓREFL(DDAB) is equal to ΓREFL(CTAB) within experimental error. Therefore, the total amount of hydration water coupled to the DDAB and CTAB molecules is expected to be very similar and

∆Γh(CTAB) ) ∆Γh(silica) + Γh(CTAB) ≈ -Γh(DDAB) + Γh(DDAB) )0

(17)

Thus, for CTAB, we conclude that the difference observed between the sensed mass obtained by QCM-D and the adsorbed (26) Briscoe, W. H.; Titmuss, S.; Tiberg, F.; Thomas, R. K.; McGillivray, D. J.; Klein, J. Nature 2006, 444, 191-194. (27) Chen, Y. L.; Israelachvili, J. N. J. Phys. Chem. 1992, 96, 7752-7760.

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mass obtained by reflectometry is not due to changes in the amount of hydration water. For DTAB, the adsorbed amount in terms of adsorbed molecules per unit area is only 57% of that of DDAB. For a hexagonally closed packed arrangement of DTAB micelles, where ∼91% of the substrate area is covered, we can estimate

∆Γh(DTAB - hcp) ) 0.91∆Γh(silica) + Γh(DTAB) ≈ -0.91Γh(DDAB) + 0.57Γh(DDAB) ) -0.34Γh(DDAB)

(18)

For a randomly closed packed arrangement of DTAB micelles, when only ∼55% of the substrate area is covered, we can estimate

∆Γh(DTAB - rcp) ) 0.55∆Γh(silica) + Γh(DTAB) ≈ -0.55Γh(DDAB) + 0.57Γh(DDAB) ) -0.02Γh(DDAB)

(19)

It is difficult to exactly determine the extent of the “QCM active” hydration layer, since different techniques report vastly different amounts of hydration water. For instance, force measurements demonstrate the presence of hydration forces extending up to 3 nm from two interacting surfaces.8 However, viscosity measurements indicate that, down to surface separations of 1 nm, the viscosity is essentially equal to that of bulk water.28 Specifically, for charged quaternary ammonium groups (the headgroup of our surfactants), the hydration number has been estimated by NMR to range from 5 to 629 down to zero30 as estimated from viscosity measurements. The results reported in this article do not allow us to provide yet another “hydration number” that would be QCM specific. The data do, however, allow us to conclude that, for the cationic surfactants employed in this study, the QCM sensed mass due to mechanically trapped water is the most important reason for the larger mass sensed by QCM compared to the adsorbed mass detected by reflectometry. Comparison with Other Studies. Stålgren et al.3 studied the adsorption of hexa(ethylene glycol) mono-n-tetradecyl ether (C14EO6) by ellipsometry and QCM-D on both hydrophilic silica and silica that was hydrophobized by dimethyldichlorosilane. The effect of hydration is most evident when we concentrate on the adsorption of C14EO6 on the hydrophobized silica. The ellipsometric adsorbed amount was found to be 1.58 ( 0.10 mg/m2. Assuming monolayer adsorption on the hydrophobic substrate,31 the sSPP would be 0.42 ( 0.03. This value indicates that the surfactant aggregates on the substrate are present in the form of long rodlike hemimicelles. The calculated value is also consistent with a flat layer if also the hydrocarbon part of the silane contributes to the volume of the hydrophobic aggregate core and thus increases the effective sSPP. If the layer consisted of rodlike hemimicelles, then it would contain 0.45 mg/m2 of mechanically trapped water. The mass sensed by QCM-D was 2.73 ( 0.06 mg/m2. By subtracting the mechanically trapped water, the change in the hydration between the hydrophobic substrate and the adsorbed layer exposing hydrophilic oligomeric ethylene oxide headgroups is at least +0.54 mg/m2. This is reasonable considering that the water density is reduced in the vicinity of nonpolar surfaces32and considering the extensive hydration of ethylene oxide headgroups reported by vibrational sum frequency spectroscopy33and by dielectric relaxation measurements where (28) Raviv, U.; Klein, J. Science 2002, 297, 1540-1543. (29) Hsieh, C. H.; Wu, W. G. Biophys. J. 1996, 71, 3278-3287. (30) Nightingale, E. R. J. Phys. Chem. 1959, 63, 1381-1387. (31) Tiberg, F. J. Chem. Soc., Faraday Trans. 1996, 92, 531-538. (32) Chandler, D. Nature 2005, 437, 640-647.

3-4 bound water molecules per ethylene oxide unit has been found.34 Thus, in general, one needs to consider not only mechanically trapped water but also changes in hydration water. Reimhult et al.2 detected an increase in coupled water corresponding to +0.6 mg/m2 upon adsorption of a lipid bilayer on silica by means of spreading 1-palmitoyl-2-oleoyl-sn-glycero3-phosphocholine (POPC) lipid vesicles. In terms of moles per square meter, the adsorbed amount of POPC is the same as the adsorbed amount of DDAB. However, for DDAB, we detected that the change in the amount of sensed water was -0.05 ( 0.24 mg/m2, that is, within experimental error equal to zero. DDAB and presumably also POPC are forming flat bilayers with no mechanically trapped water due to surface roughness effects. Therefore, the difference between DDAB and POPC is suggested to reflect the different hydration of the DDAB and POPC headgroups. This explanation is qualitatively consistent with the fact that while both headgroups contain a trimethylammonium cation, the POPC headgroup also contains a phosphate group, providing extra hydration by two H2O molecules per headgroup in the primary hydration shell.29

Conclusions The change in the amount of water sensed by QCM-D increases with the nanoscale roughness for adsorbed layers of cationic surfactants with quaternary ammonium headgroups. This water should be viewed as primarily being mechanically trapped. It cannot be assigned to hydration water, because it substantially differs for adsorbed layers with similar hydrations but different topographies. The topography of the adsorbed surfactant layers can be predicted by using a surface surfactant packing parameter calculated from the effective area per headgroup in the layer. The observed amount of mechanically trapped water is consistent with expectations for the observed surface topographies. We thus conclude that QCM-D effectively senses water located in cavities with sizes in the nanometer range. In this context, it is important to mention the results of Patel and Frank15 showing that a significant amount of water was trapped in between molecules of adsorbed streptavidin and in between tethered vesicles only if their coverage exceeded a certain critical value. This suggests that the sensitivity of QCM-D can be lower for water located in cavities with larger sizes than those present in our study. Changes in the amount of mechanically trapped water should be taken into account whenever one interprets changes in the QCM-D sensed mass due to adsorption processes that might involve changes in surface topography. We must emphasize that, though we have proved that QCM-D effectively senses the water trapped in nanocavities created by adsorption in the form of rough molecular layers, the quantitative contribution of this water to the sensed mass will be very dependent on the viscoelastic properties of the “matrix” inside which it is trapped. Our results can be directly applied only if the “matrix” is rigid and thus a change in the dissipation upon adsorption is negligible. Acknowledgment. This work has been financially supported by the Swedish Research Council (VR) and the Swedish Foundation for Strategic Research, SSF. Supporting Information Available: Remarks concerning the validity of the Sauerbrey equation in a liquid medium. This material is available free of charge via the Internet at http://pubs.acs.org. LA7014308 (33) Tyrode, E.; Johnson, C. M.; Kumpulainen, A.; Rutland, M. W.; Claesson, P. M. J. Am. Chem. Soc. 2005, 127, 16848-16859. (34) Shikata, T.; Takahashi, R.; Sakamoto, A. J. Phys. Chem. B 2006, 110, 8941-8945. (35) Green, R. J.; Su, T. J.; Lu, J. R.; Webster, J. R. P. J. Phys. Chem. B 2001, 105, 9331-9338.