APPLIED PHYSICS LETTERS
VOLUME 77, NUMBER 14
2 OCTOBER 2000
Simultaneous determination of optical and acoustic thicknesses of protein layers using surface plasmon resonance spectroscopy and quartz crystal microweighing Alexander Laschitsch, Bernhard Menges, and Diethelm Johannsmanna) Max-Planck-Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
共Received 3 May 2000; accepted for publication 8 August 2000兲 The optical and the acoustic thicknesses of protein layers during adsorption were simultaneously determined by a combination of surface plasmon resonance spectroscopy and quartz crystal microweighing. Coupling of the surface plasmon was achieved by etching a diffraction grating into the quartz surface prior to the deposition of the metal electrode. The evolution of the acoustic and the optical thickness was markedly different, which is attributed to surface roughness and partial coverage. © 2000 American Institute of Physics. 关S0003-6951共00兲04440-5兴
Both the quartz crystal microbalance 共QCM兲1–3 and surface plasmon resonance 共SPR兲 spectroscopy4 are well known techniques for the determination of film thickness in the monomolecular range. Being based on the reflection of an acoustic or an optical wave at the substrate–film interface these two methods share some common principles. The existence of standing waves in the layer system defines a resonance condition 共frequency or coupling angle兲, the shift of which is used to determine the film thickness. Provided that the film is much thinner than the wavelength of light5 the shift in the plasmon coupling angle c , 共the angle of minimum reflectivity兲 is to first order in film thickness given by6 n c
⌬ 共 sin c 兲 ⫽⌬k x ⬇
2 c ⫻
冉
m a m ⫹ a
冊冑 2
d opt⬇⌬ 共 sin c 兲
⫺ m a 共 a ⫺ m 兲
␦f*
共1兲
df ,
f0
with n the refractive index of the medium through which the beam reaches the sample, the dielectric permittivity, k x the in-plane component of the wave vector, c the speed of light, the frequency, and d f the film thickness. The indices ‘‘a,’’ ‘‘f ,’’ and ‘‘m’’ denote the ambient medium, the film, and the metal substrate, respectively. Equation 共1兲 can be generalized to account for continuous refractive index profiles, for example created by a dilute adsorbate, as ⌬ 共 sin c 兲 ⬇
2
冉
m a
n m ⫹ a ⫻
冕
⬁
0
冊冑 2
⫺ m a 共 a ⫺ m 兲
f共z兲
dz,
␦f f0
共2兲
册冋 冉 2
m a
n m ⫹ a
冊冑 册 2
1
⫺ m a
⫺1
, 共3兲
⬇⫺
冕
Zq
⬁
0
G f 共 z 兲 ⫺G a dz, G f共z兲
f共z兲
共4兲
⬇⫺
Zq
冕
⬁
0
G ⬘f 共 z 兲 ⫺G ⬘a G ⬘f 共 z 兲
dz.
共5兲
The integral could be called the ‘‘acoustic moment.’’ We define the acoustic thickness d ac as the thickness of a hypothetical compact layer on an ideally flat substrate inducing the same frequency shift as the layer of interest:
7
where the integral is termed the ‘‘ellipsometric moment.’’ This is the quantity determined in any technique based on optical reflectometry, including ellipsometry and SPR spec-
冋
␦ f G ⬘f ⫺G a⬘ d ac ⫽⫺ f0 G ⬘f
a兲
Author to whom correspondence should be addressed; electronic mail:
[email protected]
0003-6951/2000/77(14)/2252/3/$17.00
dry
⫺1
with f 0 the frequency of the fundamental, Z q ⫽8.8 ⫻106 kg m⫺2 s⫺1 the acoustic impedance of AT-cut quartz, the density, and G⫽G ⬘ ⫹iG ⬙ the shear modulus. In the derivation of Eq. 共4兲 it was assumed that the medium is much softer than the quartz. The quantity ␦ f * is the complex frequency shift ␦ f ⫹i ␦ ⌫, where f is the frequency and ⌫ is the half band–half width. Here, we confine ourselves to frequency shifts. In soft matter experiments one may safely assume that the shear modulus varies much more than the density and write
1
共 f 共 z 兲 ⫺ a 兲共 f 共 z 兲 ⫺ m 兲
冋
dry⫺ a
where dry is the permittivity of the adsorbate in its dry state. The term in square brackets is a weight function describing how strongly a film of a certain dielectric permittivity affects the coupling angle. Naturally, similar equations hold for quartz crystal resonators. In the long wavelength limit one has3
1
共 f ⫺ a 兲共 f ⫺ m 兲
f
troscopy. When working with metal surfaces, one can further assume that f (z)⫺ m ⬇ a ⫺ m and pull this quantity out of the integral. We define the ‘‘optical thickness’’ d opt as the thickness of an equivalent compact layer generating the same shift of the surface plasmon as the film under study. One has
2252
册
⫺1
Zq ,
共6兲
© 2000 American Institute of Physics
Appl. Phys. Lett., Vol. 77, No. 14, 2 October 2000
Laschitsch, Menges, and Johannsmann
2253
FIG. 1. Quartz crystal with surface corrugation grating used for simultaneous determination of acoustic and optical thickness.
where the quantity in square brackets again is a weight function and G f is the shear modulus of the dry film. For G ⬘f ⰇG ⬘a Eq. 共6兲 is equivalent to the well-known Sauerbrey equation.8 Comparing Eqs. 共3兲 and 共6兲 one might assume that the information contained in surface plasmon resonances and quartz crystal resonances should be rather equivalent. However, this is often not the case. First, the contrast in acoustics is usually much larger than in optics. While refractive indices generally vary by some percent, the shear moduli may easily change by orders of magnitude even for rather dilute adsorbates. In optics the weight function is smaller than unity and roughly proportional to the concentration. Therefore, the plasmon shift is approximately proportional to the adsorbed amount. In acoustics, on the contrary, the weight function easily saturates to unity even for dilute adsorbates.9 The acoustic thickness reaches the geometric thickness at rather low coverage and does not increase further upon densification of the film by prolonged adsorption. In other words, if the adsorbate drags some solvent along in its shear movement, the trapped amount of solvent appears as a part of the film. Densification therefore increases the optical thickness while it leaves acoustic thickness unchanged. A second source of discrepancy between optical and acoustic thickness are rough substrates, where the solvent contained in the troughs and crevices takes part in the shear motion.10 The fraction of the film placed inside such troughs does not contribute to the frequency shift. Because of these two effects the Sauerbrey relation connecting the frequency shift to the adsorbed mass may not be naively trusted in liquids.11 We argue that this shortcoming of the quartz resonator technique may be turned into an advantage if quartz resonance spectroscopy and surface plasmon spectroscopy are simultaneously performed on the same sample. This can be accomplished by ion milling shallow corrugation gratings into the quartz surface prior to evaporation of the electrodes12 and using these gratings for coupling of the surface plasmon 共Fig. 1兲. Details of the fabrication process of the gratings will be given in a later publication. By comparing the acoustic and the optical thickness one can infer the
FIG. 2. Adsorption of streptavidin onto biotinylated self-assembled monolayers 共SAMs兲 simultaneously probed with a quartz resonator and surface plasmon resonance spectroscopy. The optical and the acoustic thickness are markedly different.
layer density. The ‘‘layer density’’ in this context is phenomenologically defined as the ratio of the optical and the acoustic thickness. Its precise interpretation in terms of, for instance, the zeroth and the first moment of the concentration profile (z) obviously requires assumptions about the form of the profile. Density may be of interest for structural investigations as well as screening applications, where the density of the adsorbate on differently functionalized substrates would be part of the ‘‘fingerprint’’ of a certain substance. We illustrate the combination of both techniques on a well studied model system, namely the adsorption of streptavidin on self-assembled monolayers 共SAMs兲 of biotinylated alkyl thiols.13,14 Figures 2共a兲 and 2共b兲 show the frequency shifts and the variation of the SPR coupling angle after the buffer solution had been replaced by a 10⫺6 M solution of streptavidin. At such a low concentration the bulk effects 共increased refractive index and viscosity兲 are negligible. As usual, the adsorption kinetics is a superposition of diffusion and adsorption. Figure 2共c兲 shows the optical and the acoustic thickness as derived with Eqs. 共3兲 and 共6兲. First, the acoustic thickness is smaller than the optical thickness. Presumably, this is caused by surface roughness. Naturally, the corrugation grating adds to the effective roughness, but the natural roughness 共2–4 nm rms according to AFM measurements兲 is the larger contribution. Interestingly, the acoustic and the optical thickness also display a different kinetics. While the acoustic thickness levels off after about 30 min, the optical thickness increases until the end of the measurement 共80 min兲, indicating a densification process. At later stages the coverage increases while the geometric thickness remains constant at about 4 nm, which is the diameter of the streptavidin molecule. The combination of acoustic and optical thickness deter-
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Appl. Phys. Lett., Vol. 77, No. 14, 2 October 2000
mination provides a powerful tool for the elucidation of the structure and structural changes of thin adsorbates in liquid environments. This approach should be particularly valuable in the context of biological interfaces, where such conformational aspects are important. The authors thank Dev Kambhampati and Thomas Neumann for help with the sample preparation. 1
Applications of Piezoelectric Quartz Crystal Microbalances, C. Lu and A. W. Czanderna 共Elsevier, Amsterdam, 1984兲. 2 R. Schumacher, Angew. Chem. Int. Ed. Engl. 29, 329 共1990兲. 3 D. Johannsmann, Macromol. Chem. Phys. 200, 501 共1999兲.
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