J. Phys. Chem. C 2007, 111, 1131-1135
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Adsorption Kinetics and Adsorption Isotherm of Poly(N-isopropylacrylamide) on Gold Surfaces Studied Using QCM-D Bing Wu,† Kun Wu,† Ping Wang,† and Da-Ming Zhu*,†,‡ Department of Modern Physics, UniVersity of Science and Technology of China, Hefei, China 230027, and UniVersity of Missouri-Kansas City, Kansas City, Missouri 64110 ReceiVed: October 4, 2006; In Final Form: October 19, 2006
The adsorption kinetics and the adsorption isotherm of poly(N-isopropylacrylamide) (PNIPAM), in its stretching state, on a gold surface have been studied using a quartz crystal microbalance with dissipation monitoring (QCM-D). The adsorption process exhibits an exponential behavior following a concentration change in the solution; the decay constant (reciprocal time constant) of the adsorption shows a linear relationship with concentration, from which the adsorption and desorption rates of the molecule on the gold surface have been determined. The equilibrium coverage of the adsorbed PNIPAM rises sharply at low concentration and approaches a plateau as the concentration reaches 20 ppm in weight. The plateau is interpreted as monolayer completion of PNIPAM. The dissipation factor increases with concentration at low coverage and shows a slight decrease as the monolayer completion of PNIPAM is approached.
Introduction Adsorption of macromolecules on solid surfaces from solutions is of paramount importance to the fundamental understanding of various interfacial processes, as well as to many technologies and industrial applications.1-10 Among various systems being extensively studied in recent years, adsorption of poly(N-isopropylacrylamide) (PNIPAM), a neutral proteinlike homopolymer, on solid surfaces and on small particles has continuously drawn considerable interest from researchers in different fields.11-35 This is due to the fact that the polymer displays a fully reversible lower critical solution temperature (LCST) in water at around 32 °C, below which the polymer chain swells with a random coil conformation and is water soluble, while above the LCST the polymer collapses into a globular state and the polymer phase separates from solution.14-35 Since its LCST lies between typical room temperature and human body temperature, PNIPAM is considered to have the potential to be used for drug delivery and other biological applications.11,12 Because of the similarity between the configuration changes in the coil-to-globule transition in PNIPAM and that involved in protein folding, the polymer has also been used as a simple model system for investigating the detailed mechanisms that govern the folding process.31,32 However, as PNIPAM is being adsorbed on solid surfaces, certain alternations in the transitions and in the related properties of the polymer have been observed. The differences are attributed to the reduced degree of freedom imposed to the polymer chains by the surfaces and to the binding of the polymer to the surface that may alter the configuration of the polymers from that of free polymer chains in solutions. Recent studies found that surface-grafted PNIPAM displays a number of interesting behaviors, such as a gradual dehydration and a continuous collapse/swelling transition, and a pancake-to-brush transition.27-29 These properties allow a fine-tuning of the thickness and the softness of the adsorbed polymer layer. * To whom correspondence should be addressed. E-mail:
[email protected]. † University of Science and Technology of China. ‡ University of Missouri-Kansas City.
In contrast to chemisorption, which is often realized by attaching polymer chains with special functional groups that interact with the surface strongly, physisorption of polymers occurs spontaneously and puts lesser constraints on the configurations of the molecules. Thus, the process is relatively easier to analyze, and the fundamental mechanisms that govern the adsorption process might be revealed more clearly.33-35 In a recent study of physisorption of PNIPAM, evidence of layer growth via thickness growth mode was found in the adsorption process.30 Such a result is in contrast to the growth via densification of the polymers, observed in the chemical grafting processes.27-29 In this paper, we present the results of a study of the physisorption of PNIPAM on gold surfaces using quartz crystal microbalance with dissipation monitoring (QCM-D). This study focuses on the concentration dependence of the adsorption kinetics and the adsorption isotherm. From the concentration dependence of the adsorption time constant, the adsorption and desorption rates have been unambiguously derived from the experimental data; the adsorption isotherm is constructed from the equilibrium coverage vs the concentration. The QCM-D results suggest that the adsorption is via a densification process of PNIPAM on the surface. Experimental Section QCM-D has been increasingly used in the studies of chemical and biological systems in recent years, primarily due to the sensitivity and simplicity of the technique.36-49 The detailed descriptions of the technique have been well documented.36-41 The technique relies on the measurement of the resonant frequency shift of a quartz crystal oscillating in a thickness shear mode to detect a small amount of mass deposited on its surfaces. For rigid, evenly distributed, and sufficiently thin adsorbed layers, the resonant frequency decreases linearly with the deposited mass following the Sauerbrey equation36
∆m ) -
Fqlq ∆f f0 n
10.1021/jp066529l CCC: $37.00 © 2007 American Chemical Society Published on Web 12/15/2006
(1)
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Wu et al.
where f0 is the fundamental frequency of the quartz crystal, Fq and lq are the specific density and the thickness of the quartz crystal, respectively, and n ) 1, 3, 5... is the overtone where the frequency is monitored. For an adsorbed film which is not entirely rigid, its viscoelastic property can be characterized by measuring the change of a dissipation factor (D) which is defined by
∆D )
1 Edissipated ) Q 2πEstored
(2)
where Q, Edissipated, and Estored are the quality factor, the dissipated energy, and stored energy during one oscillation, respectively.37-41 The technique has been in recent years applied to the studies of macromolecules and biological entities deposited in solutions.40-49 In solutions, the relationship between the frequency shift and the deposited mass can be rather complicated.39 But, if the solvent can be treated as a Newtonian liquid with a sufficiently small viscosity and the adsorbed film is sufficiently thin, then a linear relationship between the deposited mass and the frequency shift still holds, although the layer thickness obtained using the Sauerbrey relation is often found to be much thicker than that determined using other methods.39,40 The simultaneously measured dissipation factor provides additional information on the interactions in the adsorbed layer and between the layer and the solution.26-35 The QCM-D used in this study employs an AT-cut quartz crystal with a fundamental resonant frequency of 5 MHz and a diameter of 14 mm.50 The results presented in the following are all from the measurements where the quartz was operated at its third harmonics (n ) 3 in eq 1). A quartz crystal with gold-plated electrodes was mounted in a liquid flow cell with one electrode exposed to the solution. The temperature of the QCM-D was controlled in a range from 20 to 40 °C to an accuracy of (0.02 °C. The frequency stability of the QCM was within (1 Hz in an aqueous medium. The root-mean-square roughness of the gold electrode on the quartz crystal was less than 3 nm.27-29 Prior to use, the quartz crystal was cleaned with piranha solution (H2SO4 (96%):H2O2 (30%) ) 3:1) for 15 min, then rinsed with Milli-Q water, followed by being blown with a stream of nitrogen gas. Several wash/dry cycles were performed until concordant frequencies were obtained. PNIPAM was synthesized by reversible addition-fragmentation chain transfer (RAFT) polymerization in THF with cyanoisopropyl dithiobenzoate as the chain transfer agent and AIBN as the free radical initiator. The number-average molar mass (Mn ) 20 149) and polydispersity index (Mw/Mn ) 1.17) were determined by size-exclusion chromatography (Waters 1515) using monodisperse polystyrene as the standard and THF as the fluent with a flow rate of 1.0 mL/min. In the experiment, a freshly cleaned quartz crystal was installed in the QCM-D’s flow cell. The flow cell was initially filled with water; the frequency shift and the dissipation factor of the crystal were measured to check against the calibration standards provided by the manufacturer.50 The flow cell was then emptied and refilled with solution of a given concentration of PNIPAM. The frequency shift and the dissipation factor change due to adsorption of PNIPAM were recorded vs time. Typically, an adsorption vs time measurement lasted several hours until equilibrium in adsorption was clearly reached. Then a solution with a higher concentration of PNIPAM was dosed into the flow cell to start the next run of the adsorption vs time measurement. During the adsorption measurements, the temperature of the flow cell was maintained at 20 °C where
Figure 1. Frequency shift and the dissipation factor change of the quartz resonator immersed in an aqueous PNIPAM solution as a function of time. The PNIPAM concentration of the solution had undergone a series of increases, as indicated by the spikes in the adsorption curves.
PNIPAM is in its stretched random coil state and has a good solubility in aqueous solutions. To characterize the drift in frequency and in dissipation factor during the experiment, the solution was replaced with pure water several times after the adsorption at a particular concentration of PNIPAM was completed. The drift was found to be negligible. In general, the frequency shift and the dissipation factor change depend on the mass of the adsorbed layer and on the changes of the density and viscosity of the solution.39,40 To avoid complexity from the latter, the concentration of the solution was limited to a low range (less than 0.008% in weight of PNIPAM); within this concentration range, the viscosity and the density of the solution are assumed to remain constant. Results and Analysis Figure 1 displays the changes of the resonant frequency and the dissipation factor of the QCM-D under a series of changes of PNIPAM concentration in aqueous solution. The sharp spikes in both the frequency and the dissipation curves immediately following the concentration changes are obviously the responses of the QCM-D to the disturbance to the cell by the inflow of the solutions with higher concentrations. Excluding the initial responses, the time dependences of the frequency shift and the dissipation factor change at a longer time scale reflect the adsorption process of PNIPAM on the surface. Assuming that the surface coverage of PNIPAM is governed by a balance of the adsorption and desorption of the polymer, the change of surface coverage θ of the molecules can be described by a Langmuir equation51,52
dθ ) ka(1 - θ)c - kdθ dt
(3)
where ka and kd are the adsorption and desorption rate constants of the polymer on the surface and c is the concentration of PNIPAM in solution. Assuming that ka and kd are independent of coverage, integrating eq 3 yields the time dependence of the surface coverage approaching a new equilibrium value after the concentration change
θ ) θeq + (θi - θeq) exp(-kot)
(4)
Poly(N-isopropylacrylamide) on Gold Surfaces
Figure 2. Magnitude of resonant frequency shift after the concentration changes as a function of time. For the purpose of clarity, the data at concentrations of 2.5 and 5.0 ppm, in weight, are multiplied by a factor of 2. The solid lines are the least-square root fits to the experimental data.
where ko ) kac + kd is the decay constant, θeq ) c/(c + kd/ka) is the equilibrium coverage at concentration c, and θi is the initial coverage. Equation 4 shows that the surface coverage approaches the equilibrium value exponentially. Assuming that the frequency shift is proportional to the thickness of adsorbed PNIPAM (Sauerbrey equation applies), the frequency shift of the QCM-D follows that described by eq 4, that is, f(t) - feq ∼ ∆θ ) θ - θeq ∼ exp(-k0t). Figure 2 is a semilog plot of the resonant frequency f(t) subtracting off the equilibrium resonant frequency feq at a given concentration, f(t) - feq vs time t, after each change of the PNIPAM concentration in the solution. Clearly, f(t) - feq follows an exponential time dependence with the decay constant ko increasing with concentration (the time constant decreases with concentration). The time constants determined from these curves are comparable with those shown in the chemisorption of PNIPAM on the same types of the surfaces,27 indicating that the slow adsorption process is primarily due to the size and the configuration of the polymer chains. A least-square root fit to each set of the data shown in Figure 2 yields the decay constant, which is the reciprocal of the time constant, at a given concentration. A plot of the decay constant ko vs the concentration of PNIPAM, shown in Figure 3, demonstrates that the decay constant follows a linear dependence with concentration. A linear fit to the decay constant vs concentration yields the adsorption and desorption coefficients ka ) 152.2 (M-1 s-1) [755.1 × 10-4 (mass%-1 s-1)] and kd )1.746 × 10-4 (s-1) for PNIPAM on gold surfaces. While the mass uptake by the QCM would decrease its resonant frequency, the mass uptake may not necessarily result in an increase in its dissipation factor. A simple example to illustrate the difference is the adsorption of a perfectly rigid layer which decreases the resonant frequency but has no effect on the dissipation factor of the QCM.26,39,40 A closer look at the variation of the dissipation factor vs concentration in Figure 1 reveals that the dissipation factor becomes flat as the concentration reaches about 40 ppm, and decreases slightly as the concentration rise to above that, indicating that the adsorbed PNIPAM layer becomes more rigid at that coverage as additional molecules are added to the adsorbed layer. Figure 4 shows the change of the dissipation factor relative to the equilibrium value, D - Deq, vs time. Below 20 ppm, the rise of the dissipation factor follows roughly exponential time dependence, similar to
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Figure 3. Decay constant k0 obtained from the fits in Figure 2 as a function of PNIPAM concentration. The solid line is a linear fit to the data, which gives the adsorption and desorption rates of PNIPAM on gold surfaces.
Figure 4. Changes in dissipation (D) in reference to the initial equilibrium values after the concentration change as a function of time.
the behavior observed in the frequency shift. However, above that concentration, the dissipation factor becomes flat and eventually decreases as the concentration increases further. The equilibrium coverage of the adsorbed molecules is determined by the chemical potential of the adsorbate which in turn is determined by the concentration in the solution. As mentioned above, in the low concentration (up to 0.008% in weight) range covered by this study, the density and the viscosity of the solution can be considered constants, thus a linear relationship holds between the frequency shift and the adsorbed mass on the QCM-D. So, the equilibrium resonant frequency shift vs concentration at a constant temperature forms an adsorption isotherm, which is plotted in Figure 5. Also plotted is the dissipation factor change as a function of solution concentration. An obvious feature shown in the isotherm is a rapid increase in the frequency shift at low concentration, followed by a gradual approach to the saturation (plateau) as the concentration goes above 40 ppm. The increase in the dissipation factor follows the decrease in the resonant frequency until the concentration reaches about 40 ppm, above which the variation of the dissipation factor changes its direction. The steplike feature in the resonant frequency curve is due to the monolayer completion of PNIPAM on the surface. Such an explanation is consistent with the behaviors found in the dissipation factor. At low coverage, the adsorbed molecules are
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Figure 5. Equilibrium resonant frequency shift and the dissipation change as a function of the concentration of the solution. The solid and dashed lines are guides to the eyes.
attached at a few sites and remain a random coil configuration with little disturbance of the structures by the surface. The adsorbed PNIPAM molecules are mostly isolated and surrounded by solvent molecules. As the adsorption continues, each added PNIPAM molecule to the layer increases the adsorbed mass, as well as the coupling between the adsorbed layer and the solvent, resulting in an increase in the dissipation factor. However, as the layer is approaching its completion, the surface is almost entirely covered by the polymers; adding additional PNIPAM to it would expel solvent molecules from the surroundings of the adsorbed PNIPAM in order for the added PNIPAM molecules to intrude into the adsorbed layer. The intrusion increases the coupling between neighboring polymers, making the adsorbed layer as a whole more rigid, and decreases the coupling between the adsorbed molecules and the solvent, thus reducing the energy dissipation in the layer. The adsorption isotherm and the dissipation factor data suggest that the growth mode of PNIPAM physisorbed on gold up to monolayer completion is via a densification process in which more and more surface sites are covered as more and more polymers are adsorbed. In contrast, the growth of the adsorbed polymer layer can also occur via a thickness growth mode, in which the polymer chains adsorbed earlier adopt a flat conformation and subsequent chains then deposit on top of these chains, and the thickness of the layer would display a continuous growth, rather than steplike characteristics.30 The dissipation factor should display a continuous rise, as the thickness growth should not change the coupling among adsorbed polymers nor the coupling between the adsorbed layer and the solvent. Discussion In a previous study of physisorption of PNIPAM on a gold surface, the resonant frequency shift was monitored at the seventh harmonic overtone of a QCM.30 The adsorption curve measured at 31 °C, a temperature slightly below its LCST, shows a time constant comparable with what we obtained in this study.30 The equilibrium frequency shift at a 20 ppm concentration of PNIPAM was found to be -340 Hz, corresponding to a Sauerbrey film thickness of 10 nm.30 The resonant frequency shift at the same concentration obtained in our study
Wu et al. is -140 Hz. If scaled with the Sauerbrey relation, the frequency shifts obtained in these two studies agree with each other quite well (within 5%). The frequency shift at the monolayer completion obtained in this study is also consistent with the frequency shift that corresponds to the formation of a monolayer pancake-like thiolterminated PNIPAM on gold surfaces (∆f ∼ -150 Hz, for Mw ) 18 332).29 However, a pancake-to-brush transformation of the molecular configuration observed in the adsorption of thiolPNIPAM is absent in this study.29 The transition is interpreted as a result of the competition between the local polymer segment-segment interaction and the segment-surface interaction and can occur only when the former dominates the latter.29 For thiol-terminated PNIPAM, the thiol group binds to the gold surface, anchoring the polymer at its tail on the surface. The tail alignment of the polymers should increase their segmentsegment interaction. The lack of a special functional group on PNIPAM used in this work should result in a complete random coil configuration of the polymers as they were physisorbed on the surface, which may be the cause of the absence of the pancake-to-brush transformation found in this study. The results presented here suggest that QCM-D can be used for quantitative study of adsorption kinetics of polymers and biological systems on solid surfaces. The adsorption kinetics in general is strongly influenced by the configurations of adsorbates. Thus, this technique should have important applications in investigating adsorption of homopolymer random coil and globular core states on different substrates. More importantly, due to its simplicity and high sensitivity, the technique has the potential for being used in characterization of protein unfolded and folded states, both in vitro and in vivo. Summary Through the use of QCM-D, the kinetics of PNIPAM in its stretching state physisorbed on gold surfaces at a constant temperature (20 °C) has been studied in detail. The results can be described very well using the Langmuir equation of adsorption isotherm. The reciprocal of the adsorption time constant varies linearly with concentration, indicating that the adsorption and desorption rates of the polymer on the gold surface are independent of the surface coverage and the concentration in the range covered by this study. An adsorption isotherm shows that the monolayer completes at a concentration of about 20 ppm. These results suggest that, using currently developed techniques including QCM-D, many details in the adsorption of macromolecules at a solid-liquid interface can be investigated quantitatively, which may reveal similar interesting characteristics as those discovered in the adsorption of molecules from their vapor phases.52,53 Acknowledgment. We are grateful to Professor Guangzhao Zhang for letting us use his QCM-D instrument and for providing very helpful advice and guidance during the course of the work. We also thank Mr. Yi Hou for assistance in using the QCM-D instrument. B.W. and K.W. contributed equally to this work. This work is supported, in part, by a grant from National Science Foundation of China and by a grant from Academy Science of China. References and Notes (1) Fleer, G.; Stuart, M. A. C.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces, 1st ed.; Cambridge University Press: Cambridge, U.K., 1993; and reference therein. (2) Alexander, S. J. Phys. Fr. 1977, 38, 983. (3) de Gennes, P. G. Macromolecules 1980, 13, 1069.
Poly(N-isopropylacrylamide) on Gold Surfaces (4) Milner, S. T. Science 1991, 251, 905. (5) Walldal, C.; Wall, S. Colloid Polym. Sci. 2000, 278, 936. (6) Caruso, F.; Mohwald, H. J. Am. Chem. Soc. 1999, 121, 6039. (7) Oya, T.; Enoki, T.; Grosberg, A. Yu.; Masamune, S.; Sakiyama, T.; Takeoka, Y.; Tananka, K.; Wang, G.; Yilmaz, Y.; Field, M. S.; Dasari, R.; Tanaka, T. Science 1999, 286, 1543. (8) Hu, T.; Jun Gao, J.; Wu, C. J. Phys. Chem. B 2002, 106, 9815. (9) Daoulas K.; Terzis, A. F.; Mavrantzas, V. G. J. Chem. Phys. 2002, 116, 11028. (10) MacDowell, L. G.; Muller, M. J. Chem. Phys. 2006, 124, 84907. (11) Schild, H. G.; Prog. Polym. Sci. 1992, 17, 163. (12) Graziano, G. Int. J. Biol. Macromol. 2000, 27, 89. (13) Zajac, R.; Chakrabarti, A. Phys. ReV. E 1994, 49, 3069. (14) Jian Xu, J.; Zhu, Z.; Luo, S; Wu, C.; Liu, S. Phys. ReV. Lett. 2006, 96, 027802. (15) Hu, T.; You, Y.; Pan, C.; Wu, C. J. Phys. Chem. B 2002, 106, 6659. (16) Hu, T.; Jun Gao, J.; Wu, C. J. Phys. Chem. B 2002, 106, 9815. (17) Wu, C.; Wang, X. Phys. ReV. Lett. 1998, 80, 4092. (18) Schild, H. G. Prog. Polym. Sci. 1992, 17, 163. (19) Amiya, T.; Hirokawa, Y.; Hirose, Y.; Li, Y.; Tanaka, T. J. Chem. Phys. 1987, 86, 2375. (20) Katayama, S.; Hirokawa, Y.; Tanaka, T. Macromolecules 1984, 17, 2641. (21) Hirotsu, S. J. Phys. Soc. Jpn. 1987, 56, 233. J. Chem. Phys. 1988, 88, 427. (22) Asano, M.; Winnik, F. M.; Yamashita, T.; Horie, K. Macromolecules 1995, 28, 5861. (23) Mukae, K.; Sakurai, S.; Sawamura, S.; Makino, K.; Kim, S. W.; Ueda, I.; Shirahama, K. J. Phys. Chem. 1993, 97, 737. (24) Otake, K.; Inomata, H.; Konno, M.; Saito, S. Macromolecules 1990, 23, 283. (25) Zhu, P. W.; Napper, D. H. J. Colloid Interface Sci. 1996, 177, 343. Phys. ReV. E 2000, 61, 6866. (26) Heskins, M; Guillet, J. E.; James, E. J. Macromol. Sci. (27) Zhang, G. Macromolecules 2004, 37, 6553. Liu, G.; Zhang, G. J. Phys. Chem. B 2005, 109, 743. (28) Ding, Y.; Ye, X. G.; Zhang, G. Macromolecules 2005, 38, 904. (29) Liu, G.; Cheng, H.; Yan, L.; Zhang, G. J. Phys. Chem. B 2005, 109, 22603. (30) Plunkett, M; Wang, Zhehui; Rutland, M. W.; Johannsmann, D. Langmuir 2003, 19, 6837.
J. Phys. Chem. C, Vol. 111, No. 3, 2007 1135 (31) Zhang, G.; Wu, C. Phys. ReV. Lett. 2001, 86, 822. (32) Ding, Y.; Ye, X.; Zhang, G. Macromolecules 2005, 38, 904. (33) Weng, Y.; Ding, Y.; Zhang, G. J. Phys. Chem. B 2006, 110, 11813. (34) O’Shaughnessy, B.; Vavylonis, D. Eur. Phys. J. E 2003, 11, 213. (35) O’Shaughnessy, B.; Vavylonis, D. Phys. ReV. Lett. 2003, 90, 0561031. (36) Sauerbrey, G. Z. Phys. 1959, 155, 206. (37) Bottom, V. E. Introduction to Quartz Crystal Unit Design; Van Nostrand Reinhold Co.: New York, 1982. (38) Rodahl, M.; Hook, F.; Krozer, A.; Kasemo, B.; Breszinsky, P. ReV. Sci. Instrum. 1995, 66, 3924. (39) Voinova, M. V.; Rodahl, M.; Jonson, M.; Kasemo, B. Phys. Scr. 1999, 59, 391. (40) Hook, F.; Kasemo, B.; Nylander, T.; Fant, C.; Sptt, K.; Elwing, H. Anal. Chem. 2001, 73, 5796. (41) Hook, F.; Rodahl, M.; Brezinski, P.; Kasemo, B. Langmuir 1998, 14, 729. (42) Keller, C. A.; Glasmaster, K.; Zhdanov, V. P.; Kasemo, B. Phys. ReV. Lett. 2000, 84, 5443. (43) Schneider, T. W.; Buttry, D. A. J. Am. Chem. Soc. 1993, 115, 12391. (44) Ward, M. D.; Buttry, D. A. Science 1990, 249, 1000. (45) Lucklum, R.; Behling, C.; Hauptman, P. Anal. Chem. 1999, 71, 2488. (46) Rodahl, M.; Hook, F.; Fredriksson, C.; Keller, C. A.; Krozer, A.; Brzezinski, P; Voinova, M.; Kase, B. Faraday Discuss. 1977, 107, 229. (47) Bandey, H. L.; Hillman, A. R.; Brown, M. J.; Martin, S. J. Faraday Discuss. 1997, 107, 105. (48) Johannsmann, D. Macromol. Chem. Phys. 1999, 200, 501. (49) Domack, A.; Prucker, Q.; Ruhe, J.; Johannsmann, D. Phys. ReV. E 1997, 56, 680. (50) Q-Sense AB, Redegatan 13, SE-426 77 Va¨stra Fro¨lunda, Sweden. (51) Adamson, A. W. Physical Chemistry of Surfaces, 6th ed.; Wiley: New York, 1997. (52) Karpovich, D. S.; Blanchard, G. J. Langmuir 1994, 10, 3315. (53) Dash, J. G. Films on Solid Surfaces, Academic Press: New York, 1975. (54) Taub, H.; Torzo, G.; Lauter, H. J.; Fain, S. F., Jr. Phase Transitions in Surface Films II; NATO Advanced Study Institute, Series B: Physics; Plenum: New York, 1991.
