Impedance analysis of an electrode-separated piezoelectric sensor as a surface-monitoring technique for gelatin adsorption on quartz surface

Journal of Colloid and Interface Science 281 (2005) 398–409 www.elsevier.com/locate/jcis

Impedance analysis of an electrode-separated piezoelectric sensor as a surface-monitoring technique for gelatin adsorption on quartz surface Dazhong Shen a,c,∗ , Minghui Huang b , Fei Wang a , Mengsu Yang b a School of Chemistry, Chemical Engineering and Material Science, Shandong Normal University, Jinan 250014, People’s Republic of China b Department of Biology and Chemistry, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, People’s Republic of China c State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan University, Changsha 410082, People’s Republic of China

Received 27 January 2004; accepted 11 August 2004 Available online 28 October 2004

Abstract The early events pertaining to gelatin adsorption and desorption onto quartz surfaces were studied, employing an electrode-separated piezoelectric sensor (ESPS). The adsorption of gelatin on a quartz crystal surface corresponds to a mass increase, which can be monitored in real time by the changes in the impedance parameters of the ESPS. It was shown that the adsorption of gelatin on a quartz surface is partly irreversible with respect to the dilution of the bulk phase. The observed adsorption kinetics is compatible with a mechanism that involves adsorption, desorption, and transformation from a reversible adsorption state to irreversible one. A progressive approach method was established to simulate the adsorption process. The adsorption densities and kinetic parameters in the early adsorption process were obtained from the responses of the ESPS in the adsorption process. The influence of pH and ionic strength was tested. A comparison with the Langmuir adsorption model was made.  2004 Elsevier Inc. All rights reserved. Keywords: Adsorption kinetics; Gelatin; Piezoelectric sensor; Electrode-separated

1. Introduction Biomacromolecules such as proteins show a strong tendency to physically adsorb at liquid/solid interfaces due to favorable van der Waals, ionic, and polar interactions [1]. Adsorption of proteins at solid/liquid interfaces is an important and challenging interdisciplinary field of the natural sciences [2–4]. Understanding the mechanism and the processes involved in protein interaction at the solid/liquid interface is essential for a number of medical and biochemical applications, including implantation and function of biomaterials/medical implants in soft and hard tissue and in the bloodstream, fouling of contact lenses, food processing equipment; extracorporeal therapy, drug delivery, bacteria and cells in culture, and a variety of medical sensors and * Corresponding author. Fax: +86-0531-82615258.

E-mail address: [email protected] (D. Shen). 0021-9797/$ – see front matter  2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.08.062

other diagnostic tools. Effective adsorption of proteins is important in protein separation, immobilization of enzymes, biosensors and protein chips, etc. But in other processes, e.g., membrane filtration, biofouling of membranes, and artificial organs, protein adsorption is highly undesirable. A number of techniques have been utilized in the study of protein adsorption, including ellipsometry [5–7], atomic force microscopy [8,9], rediabeling [10], circular dichroism [11], ATR-FTIR spectroscopy [12,13], vibrational sum frequency spectroscopy [14], surface plasmon resonance (SPR) [15–18], total internal reflected fluorescence (TIRF) [19–21], and quartz crystal microbalance (QCM) [22–28]. So far, the techniques of ellipsometry, ATR-FTIR, SPR, TIRF, and QCM have demonstrated real-time kinetic measurements of protein adsorption. The QCM is well known for its very high sensitivity to slight mass loading variation on the electrode surface of the quartz crystal. It is suitable for time-resolved in situ measurements and can be manufactured in large quantities at

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low costs. QCM sensors allow on-line and direct detection of label-free proteins, thus saving time and providing the opportunity to study the kinetics of the adsorption process. Usually, a QCM sensor is constructed with an AT-cut quartz disc sandwiched between two metal electrodes, which induce the quartz crystal to oscillate at a frequency in the MHz region. In this work, a modified QCM device, an electrodeseparated piezoelectric sensor (ESPS), was used. In the design of the ESPS, a naked quartz surface is in directly contact with the liquid phase [29–32]. This configuration offers the advantages of long life of the sensor and convenience of monitoring the mass change on the quartz surface. The quartz surface is an important interface in capillary electrophoresis, biochips, and measurement cells in UV spectrometry or fluorometry. On the other hand, the quartz surface has good similarity to silicon dioxide or silica surfaces extensively used as model surfaces in adsorption investigations. Gelatin is a polydisperse polypeptide derived from the structural protein collagen. It is one of the most commonly used polymers in industry and has become the preeminent polymer of industrial importance because it is an excellent colloidal stabilizer and produces optically transparent, thermoreversible gels at near body temperatures. Gelatin is ubiquitous in the photographic [33], food [34], and pharmaceutical industries [35] and as an adhesion agent for depositing different types of small particles from aqueous dispersions onto substrates [36]. Gelatin is obtained by acid or alkali denaturation of collagen, which consists of three polymer chains in a triple helix and contains both acidic carboxyl and basic amino groups which, in solution, transform into the corresponding negatively and positively charged groups [37]. The adsorption behavior of gelatin is expected to complex. Some recent experimental investigations of gelatin adsorption onto mica [38], phosphatidyl choline-coated silica [39], fumed silicas [40,41], carbon particles [42], and polystyrene latices [43] have been reported. Several experimental methods have been employed for studying gelatin adsorption, including solution depletion [44,45], ellipsometry [46], surface force apparatus [47,48], and small-angle neutron scattering [49]. Despite much work devoted to gelatin adsorption, much still remains to be done to understand the adsorption mechanisms. In this work, the early events pertaining to gelatin adsorption and desorption onto quartz surfaces were studied, employing the ESPS device. To characterize the ESPS more completely, an impedance analysis method has been employed. In the impedance analysis method, the magnitude and phase of the impedance of the piezoelectric sensor were scanned with frequency from the externally applied voltages. Electrical properties of the quartz crystal can be found from the impedance–frequency curves [50–54]. An advantage of the impedance analysis method is its ability to give some insight into the viscoelastic behavior of the adsorbed materials, which is achieved by monitoring the motional resistance. During the adsorption of gelatin on quartz crystal

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surfaces, the resonant frequency of the ESPS decreases with increasing adsorption mass. The frequency change arising from the nonmass effect was distinguished from the correlations of motional resistance and resonant frequency. The influence of surface roughness was calibrated by dye adsorption. A modified adsorption kinetics model was developed to describe the experimentally observed early adsorption behavior of the gelatin on the quartz surface. By using a progressive approach method, adsorption kinetics parameters were estimated from the responses of the ESPS in the adsorption process. The influence of pH and ionic strength was tested. A comparison with the Langmuir adsorption model was made.

2. Materials and methods 2.1. Apparatus and reagents The configuration of the ESPS used was illustrated in Fig. 1. A 5 MHz AT-cut quartz crystal disc of 25.4 mm in diameter was used. A keyhole-shaped gold electrode with a diameter of 12 mm was evaporated on the center of one side of the quartz disc on a chromium adhesion layer. The quartz disc was flexibly fixed and sealed to a glass detection cell by silicon glue with the side of the bare quartz facing the liquid phase and the other side with the gold electrode in the air in a closed chamber. A graphite disk electrode with a diameter of 3 cm was used as the separated electrode. The aver-

Fig. 1. Experimental setup for monitoring the adsorption process on a quartz crystal surface by the ESPS method: (1) impedance analyzer, (2) computer, (3) quartz crystal and gold electrode, (4) graphite separated electrode, (5) stirrer, and (6) outlet valve.

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aged distance between the separated-electrode and the quartz crystal disc was 6 mm. The separated electrode and gold electrode were connected to a network/spectrum/impedance analyzer (Hewlett-Packard 4195A) connected to a PC. The impedance–frequency curves of the ESPS were recorded and two impedance parameters, the series resonant frequency at the phase of impedance of zero, f , and the motional resistance, R m , of the ESPS were measured. The surface roughness of the quartz crystal was observed by scanning electron microscopy (Hitochis 520). It should be noted that the design of the detection cell is an important aspect in the experiment related to QCM in the liquid phase. When the quartz disc is oscillating in the thickness–shear model (TSM) in liquid phase, a weak longitudinal wave is also generated [55–59]. A plausible explanation for generation of longitudinal waves is that the TSM wave on an AT-cut quartz plate fulfills a nonuniform surface displacement. The longitudinal wave may also result from contributions of longitudinal and/or flexure acoustic modes in the quartz crystal that are coupled to the shear mode. In the cell design of the ESPS, the longitudinal wave may become a potential error source for the measurements because the separated electrode acts as the reflection surface for the longitudinal wave [60]. A simple and efficient way to eliminate the longitudinal wave effect is to employ a separated electrode with a rough surface, which can break the incident longitudinal wave into many small waves of different directions and phases. The interaction between the disorderly and unsystematic reflection waves results in a significant decrease in the intensity of the total reflection longitudinal wave. As a result, the interference between the incident and reflected longitudinal waves on the surface of the quartz disc was greatly weakened. In this work a graphite disk electrode was employed to eliminate the longitudinal wave effect. It was shown that the incident longitudinal wave was diffused by the rough surface and adsorbed by the graphite electrode body effectively. The longitudinal wave effect in the ESPS used is negligible. Analytical reagent grade chemicals and Mini-Q water were used. Gelatin, type A (mol. wt. 80–120 kD; isoelectric point 4.6–4.8; ash content 0.3–0.5%) was purchased from Sigma and used as received. Gelatin stock solutions were freshly prepared by the measuring medium used in adsorption experiments. The pH of the medium was controlled at 3.1 and 4.7 by acetate buffer and 6.0 and 7.4 by phosphate buffer, respectively. The conductivity of the gelatin stock solution was adjusted to be the same as the measuring medium in each adsorption experiment. Quartz powder was purchased from No. 2 Shanghai Reagent Manufacture. The specific surface area of the quartz powder was determined to be 1.2 ± 0.1 m2 g−1 by gas adsorptiometry (Omnisorp 100CX, Coulter). All the experiments were preformed at room temperature at 25 ± 1 ◦ C. Each experiment was carried out three times and the averaged values were reported.

2.2. Adsorption on quartz crystal surface in ESPS method Prior to each run, the quartz crystal was cleaned with 0.1 mol dm−3 NaOH, followed by 0.1 mol dm−3 HCl, and then rinsed thoroughly with water and then with measuring medium. A 50-cm3 quantity of measuring medium was added in the detection cell. After 30 min of stabilization, the impedance of the ESPS was measured with a time interval of 15 s (scanning time 12.8 s, data calculation and saving time 2.2 s). The impedance parameters were the averaged values over the scanning time of 12.8 s. A certain amount of gelatin stock solution was added into the cell while stirring. The shifts in the impedance parameters were monitored as a function of adsorption time, and the adsorption rate constants and adsorption mass were calculated accordingly. After a given adsorption time, the gelatin solution in the cell was pumped through the outlet valve. The cell walls, except the wall with the quartz disc, were washed by the measuring medium to remove most of the residual gelatin solution. A 50-cm3 measuring medium was added in the detection cell. The solution replacement process was finished within 1 min. Then the impedance parameters of the ESPS in the washing process were recorded with the washing time. 2.3. Adsorption on quartz powder surface in solution method To correct the influence of the surface roughness of the quartz crystal on the adsorption amount in the ESPS method, a solution depletion method was used as the reference. In the depletion method, 2 g of quartz powder was mixed with 30 cm3 of malachite green (MG) solutions prepared in a medium of pH 6.0 (0.01 mol dm−3 phosphate + 0.09 mol dm−3 NaCl) in a group of capped glass vials. The vials were shaken 12 h for equilibrium, and the vial samples were then subjected to centrifugation at 1 × 104 rpm for 30 min. The residual concentration of MG in the supernatants was analyzed using a UV spectrophotometer (Lambda 35, Perkin–Elmer Instrument) at a wavelength of 620 nm. Adsorption densities were estimated from the decrease in the concentration of MG after agitation with quartz powder.

3. Results and discussion 3.1. Adsorption of gelatin on quartz surface The QCM is a mass sensor with high sensitivity to mass changes on the surface of an oscillating quartz crystal. When the Sauerbrey relation holds, the adsorbed mass (Γ ) is directly proportional to the change in frequency (f ) and is given by Γ = m/A = αf,

(1)

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Fig. 2. Frequency shifts of the ESPS with adsorption time during the adsorption of gelatin on quartz surface. The measuring medium is 0.1 mol dm−3 HAc + 0.1 mol dm−3 NaAc (pH 4.7). Concentration of gelatin: (1) 0.071 g dm−3 ; (2) 0.251 g dm−3 ; (3) 0.667 g dm−3 .

where m is the mass adsorbed onto the active area of the quartz crystal and A is the geometric area of the active region of the quartz crystal disc. For a 5-MHz AT-cut quartz crystal, α = −17.8 ng cm−2 Hz−1 was estimated according to the Sauerbrey equation [61]. In this way, monitoring the frequency shifts of QCM gives real-time information for the apparent adsorbed mass. As shown in Fig. 2, the series resonant frequency of the ESPS decreases after the addition of gelatin. The decrease in the frequency of the ESPS corresponds to an increase in the amount adsorbed due to the adsorption of gelatin on the quartz crystal surface. The resonant frequency decreases rapidly in the initial few minutes and approaches a stable value. The time to reach a stable frequency increases as the concentration of gelatin decreases. When the gelatin solution in the cell was replaced with a gelatin-free medium, poorly bound gelatin was washed out and the frequency rose and reached a new stable value that was lower than the previous baseline level. The part of gelatin desorbed by the buffer is referred to as reversible adsorption and indicated by Γ1 . Hence, the adsorption of gelatin was partly reversible with respect to the dilution of the bulk phase. Part of the gelatin was adsorbed in an irreversible state that was not washed off by the buffer. This part is referred as irreversible adsorption, indicated by Γ2 . When the quartz disc was washed again by a fresh buffer, the further desorption was undetectable as the frequency of the ESPS was unchanged. To renew the quartz surface, the detection cell was rinsed several times with 3% sodium dodecyl sulfate (SDS) solution. SDS solution is used because it is the most common

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Fig. 3. Frequency shifts in adsorption and desorption processes with different adsorption times. Measuring medium is the same as in Fig. 2. Concentration of gelatin: 0.667 g dm−3 .

elution regent for protein remove from solid surface [62]. The gelatin adsorbed irreversibly can be efficiently eluted by SDS solution. The removal efficiency was verified in an independent experiment, where gelatin with FITC fluorescence labeled was adsorbed on a quartz chip. Then the chip was washed with buffer and the fluorescent intensity of the chip was measured in a laser scanning confocal microscope. The adsorption of gelatin on the quartz chip was observed. After being rinsed with 3% SDS, the fluorescent signal decreases to the level of the background of the blank chip. As shown in Fig. 3, most of the adsorption mass is finished within 10 min. As the adsorption time is further prolonged, the increase in the frequency shift during the adsorption process is small, while the frequency shifts in the washing process decrease slightly. This result suggests that part of the gelatin adsorbed in reversible state was transformed into the irreversible state. Hence, the irreversible adsorption extent increases as the adsorption time is prolonged. But the transformation rate declines with the adsorption time. The irreversibility of the adsorption might arise from various causes, although details are not known. The adsorption of gelatin onto the quartz surface is nonspecific; i.e., no special receptor exists. The interaction between the hydrophilic quartz surface and gelatin is mainly via hydrogen bonds, which may involve water molecules simultaneously bonded to both gelatin and quartz surface. As is well known, hydrogen bonds are individually weak and hence readily broken, but as soon as several exist, the probability of breaking them simultaneously becomes very small. According to Kurrat et al. [63], the desorption rate constant decreases from 10−4 to 10−11 s−1 when a protein molecule’s hydrogen bonus to

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the surface increase from 4 to 6, respectively. Hence, a possible explanation for the irreversible adsorption is that the gelatin undergoes structural deformation in the adsorption period, resulting in multipoint attachment with more interacting points. 3.2. Estimation of amount adsorbed An inherent feature of the QCM when used in liquids is that the change in frequency includes the contributions from both the mass and nonmass effects, which can be seen as either an advantage or a disadvantage. In liquid, the Sauerbrey relation is not necessarily valid, even for thin adsorbed layers. One reason is that the coupling between the oscillating crystal and the bulk liquid may change, due to changes in density or viscosity [64–69], when the bulk composition of the test liquid is varied. In the current work, the concentration of gelatin is small, the density of the test solution should be the same as the buffer. The viscosity of the gelatin solution was measured by capillary viscometry. It was shown that the viscosity of gelatin solutions increases slightly with gelatin concentration. The regressed relationship of the viscosity (η, cP) and concentration (C, g dm−3 ) of gelatin solutions is given by (n = 6, r = 0.9984). (2) The increase in viscosity will result in an increase in motional resistance as well as a drop in resonant frequency of the ESPS. As shown in Fig. 4, the motional resistance increases after the addition of gelatin. When gelatin stock solutions was added to the detection cell, it takes a few minutes to reach the viscosity equilibrium. Hence, the initial fast increase in motional resistance is mainly due to η = 1.0034 + 0.0216C + 0.0135C 2

Fig. 4. Changes in motional resistance of the ESPS with adsorption time during the adsorption of gelatin on the quartz surface. The experimental conditions are the same as in Fig. 2.

the increases in viscosity of the bulk liquid phase. As the gelatin adsorption layer is somewhat soft, the adsorbed layer of gelatin on quartz surface also causes an additional energy loss for the oscillating quartz surface. Thus, a slight increase in the motional resistance during the adsorption processes was observed. Because the increase in liquid viscosity and the viscoelasticity of adsorbed film also causes an additional frequency decrease, the nonmass response will result in an error in adsorbed mass from the Sauerbrey equation. To correct for the influence of the viscosity effect, the shifts in the motional resistance and resonant frequency of the ESPS used were measured in 0–12% sucrose solutions containing 0.5 mol dm−3 NaCl. The regressed relationship between f and R was given by f (Hz) = 0.532 − 3.17Rm () (n = 6, r = 0.996). (3) The good linearity between f and R m offers the possibility of correcting the influence of bulk viscosity and viscoelastic behavior of the adsorbed film on adsorption density estimation from the change in R m in the adsorption process. To do this the slope in the plotting of f vs R m of −3.17 Hz/ was used in a modified frequency shift, F = f + 3.17Rm , which was used in the estimation of adsorption mass. This strategy helps us to distinguish the additional frequency shifts arising from the viscoelastic response of the quartz crystal. On the other hand, the modified frequency shift (F ) has better stability than the series resonant frequency shift (f ). The merit is attributed to the fact that the nonmass response in f arising from the variation in viscosity and liquid temperature was counteracted by the correlation with R m in the combined impedance parameters. Hence, the modified frequency shift was used below. An additional complication in adsorption estimation occurs when a rough quartz crystal surface is used for adsorption. As illustrated in Fig. 5, the quartz crystal surface is rough. Because the true adsorption area on the quartz crystal surface is greater than its geometric area, greater apparent adsorption densities were given by Eq. (1) with F used. On the other hand, the surface roughness of quartz crystal decreases a little after adsorption of gelatin. To calibrate the influence of surface roughness, the adsorption isotherms of cationic dye (MG) on the quartz surface were determined by the ESPS method and compared with the classical solution depletion method. The isoelectric point of quartz is about 1.8–2.2. Under the pH condition used, quartz surface is negatively charged and adsorbs MG+ cations. The adsorption isotherms for MG on quartz surface are shown in Fig. 6. The apparent adsorption densities in the ESPS method were calculated using the frequency–mass coefficient in Eq. (1). As excepted, the apparent adsorption densities in the ESPS method are significantly greater than those in the solution depletion method. The adsorption isotherms were well fitted by the Langmuir model in the equation Γ = Γ∞ CK/(1 + CK),

(4)

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Fig. 5. Scanning electron microscopy of quartz crystal surface (A) before adsorption, (B) after adsorption in 1.00 g dm−3 gelatin for 24 h and washing with buffer.

tivity coefficient, α = −6.64 (−17.8/2.68) ng cm−2 Hz−1 , was used in Eq. (1) after correction for the influence of surface roughness of quartz crystal. By using the calibrated frequency–mass coefficient, the adsorption densities for MG on the quartz surface obtained in the ESPS method were very close to those estimated in the solution depletion method. So the adsorbed mass of gelatin on the quartz surface in the ESPS method was calculated by Γ = −6.64F . But the obtained adsorbed mass is still a kind of apparent one because total mass, including water and electrolyte molecules bonded to gelatin, was detected by the ESPS device. 3.3. Adsorption isotherms and kinetics for gelatin on quartz surface

Fig. 6. Comparison of the adsorbed amounts for malachite green on quartz surface: (1) on quartz crystal surface measured by the ESPS method; (2) on quartz powder surface measured by the solution depletion method.

where Γ∞ is the saturation adsorption density, C the equilibrium bulk concentration, and K the adsorption equilibrium constant, respectively. Based on the date in Fig. 6, the adsorption equilibrium constants, K = 35.9 ± 4.3 g−1 dm3 and K = 38.5 ± 4.7 g−1 dm3 , were obtained in the ESPS and depletion methods, respectively. It can be seen that the K values are closed, which reveals that the two isotherms are similar in shape. But the saturation adsorption densities, Γ∞ = 0.459 ± 0.032 µg cm−2 and Γ∞ = 0.171 ± 0.014 µg cm−2 , were estimated from the ESPS and depletion methods, respectively. The Γ∞ value in the ESPS method is 2.68 times of that in the depletion method. The higher apparent Γ∞ value in the ESPS method is assumed to be the influence of surface roughness of quartz crystal. Hence, a new sensi-

Fig. 7 depicts the dependence of various adsorbed amounts on gelatin concentration in the bulk phase. It can be seen that the adsorption isotherms are in a Langmuir type shape. By using Eq. (4) as the model, the adsorption isotherms can be well fitted. The regressed parameters are listed in Table 1. The kinetic parameters for gelatin adsorption on the quartz crystal surface can also be estimated from the time-response curves of the ESPS in the adsorption process. When the Langmuir kinetics model was used, the frequency shifts of the ESPS during the adsorption process were fitted using as a model F =

  F∞ ka C
1 − exp −(ka C + kd )t , ka C + kd

(5)

where k a and k d are the rate constants for adsorption and desorption, t is the adsorption time, and F∞ is the frequency shift corresponding to a saturation adsorption monolayer, respectively. When the responses of the ESPS were fitted by the mathematical model F = a[1 − exp(−kobst)], the observed adsorption rate constant kobs = ka C + kd was obtained.

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Table 1 Adsorption kinetics parameters for gelatin on quartz surface Adsorption conditions

pH 3.1 0.1 mol dm−3 Na+

pH 4.7 0.1 mol dm−3 Na+

pH 4.7 0.5 mol dm−3 Na+

ka (×10−2 g−1 dm3 s−1 ) Langmuir fitting

5.14 ± 0.28 5.58 ± 0.37

5.65 ± 0.26 6.04 ± 0.31

9.42 ± 0.34 9.54 ± 0.52

kb (×10−3 s−1 )a Langmuir fitting

4.94 ± 0.97 1.96 ± 0.40

7.08 ± 1.19 2.85 ± 0.58

6.28 ± 0.94 2.63 ± 5.0

K (g−1 dm3 L) Langmuir model kf (×10−3 s−1 ) (µg cm−2 )

Γ∞ Langmuir model

10.4 ± 1.3 28.4 ± 3.9

7.98 ± 0.97 21.2 ± 3.2

15.0 ± 1.7 36.2 ± 4.9

pH 4.7 0.1 mol dm−3 Na+ 13.6 ± 0.53 13.5 ± 0.65 5.65 ± 0.83 2.61 ± 0.44 24.1 ± 2.6 51.8 ± 6.3

pH 6.0 0.1 mol dm−3 Na+

pH 7.4 0.1 mol dm−3 Na+

4.36 ± 0.22 4.89 ± 0.46

2.14 ± 0.18 2.87 ± 0.41

12.5 ± 2.0 5.1 ± 1.1

17.6 ± 3.79 6.5 ± 2.0

3.49 ± 0.38 9.58 ± 1.2

1.22 ± 0.16 4.41 ± 0.72

1.53 ± 0.045

1.32 ± 0.047

1.24 ± 0.049

1.10 ± 0.042

1.12 ± 0.044

1.21 ± 0.036

0.405 ± 0.019 0.385 ± 0.023

0.489 ± 0.017 0.478 ± 0.027

0.556 ± 0.021 0.532 ± 0.032

0.628 ± 0.021 0.608 ± 0.039

0.392 ± 0.018 0.357 ± 0.026

0.352 ± 0.017 0.286 ± 0.027

a k = k /K. a b

Fig. 7. Influence of pH and ionic strength on the adsorption isotherms for gelatin on quartz crystal surface. Measuring medium: (1) acetate buffer (pH 4.7, 1.0 mol dm−3 Na+ ); (2) acetate buffer (pH 4.7, 0.5 mol dm−3 Na+ ); (3) acetate buffer (pH 4.7, 0.1 mol dm−3 Na+ ); (4) acetate buffer (pH 3.1, 0.1 mol dm−3 Na+ ); (5) phosphate buffer (pH 6.0, 0.1 mol dm−3 Na+ ); (6) phosphate buffer (pH 7.4, 0.1 mol dm−3 Na+ ).

When the adsorption time is limited to reach 90% of the final adsorption at 30 min, the response of the ESPS can be well described by the Langmuir model in Eq. (4). But as the adsorption time is prolonged, the fitting deviation increases, especially for adsorption from low-concentration gelatin solutions. The concentration dependence of the observed rate constants is illustrated in Fig. 8. It can be seen that the plots of kobs vs C show good linearity. According to Eq. (5), the slope and intercept of the plot kobs vs C correspond to k a and k d , respectively. The values of k a obtained from Fig. 8 are listed in Table 1. For the reason of large scatter for k d estimation from the intercepts in Fig. 8, the k d values in Table 1 were calculated by kd = ka /K using k a in Fig. 8 and K in Fig. 7.

Fig. 8. Concentration dependence of the observed adsorption rate constants from the Langmuir model in Eq. (12) for gelatin on quartz crystal surface. Measuring medium: (1) acetate buffer (pH 4.7, 1.0 mol dm−3 Na+ ); (2) acetate buffer (pH 4.7, 0.5 mol dm−3 Na+ ); (3) acetate buffer (pH 4.7, 0.1 mol dm−3 Na+ ); (4) acetate buffer (pH 3.1, 0.1 mol dm−3 Na+ ); (5) phosphate buffer (pH 6.0, 0.1 mol dm−3 Na+ ); (6) phosphate buffer (pH 7.4, 0.1 mol dm−3 Na+ ).

Though the adsorption isotherms and kinetics for the early adsorption of gelatin on quartz can be well fitted by the classical Langmuir model, the irreversible adsorption aspect cannot be interpreted by the reversible adsorption model. As shown in Fig. 2, the adsorption of gelatin on quartz is only partly reversible with respect to the dilution of the bulk phase. It can be seen in Fig. 3 that the extent of reversible adsorption declines as the adsorption time is prolonged. Fig. 9 shows that the reversible adsorption ratio (Γ1 /Γ ) increases with increasing adsorption amount from higher bulk concentration of gelatin. To describe the adsorption processes better, a modified Langmuir model is used.

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partly transformed into the irreversible one, which cannot be washed off by the buffer. Similarly to the Langmuir adsorption kinetics model, the adsorption rate is also assumed to be proportional to the concentration of protein in solution and to the free surface area. The desorption rate is proportional to the number of reversibly adsorbed molecules. The transformation rate is related to the number of reversibly adsorbed molecules and to the uncovered surface area, as the irreversibly adsorbed protein molecule usually occupies a larger surface area [78]. Under such assumptions, in the adsorption process, we have

Fig. 9. Influence of pH and ionic strength on the reversible adsorption ratio for gelatin on quartz crystal surface. Adsorption time: 30 min. Measuring medium: (1) acetate buffer (pH 4.7, 1.0 mol dm−3 Na+ ); (2) acetate buffer (pH 4.7, 0.5 mol dm−3 Na+ ); (3) acetate buffer (pH 3.1, 0.1 mol dm−3 Na+ ); (4) acetate buffer (pH 4.7, 0.1 mol dm−3 Na+ ); (5) phosphate buffer (pH 6.0, 0.1 mol dm−3 Na+ ); (6) phosphate buffer (pH 7.4, 0.1 mol dm−3 Na+ ).

3.4. Simplified kinetics model for gelatin adsorption The adsorption of proteins onto a solid interface involves complicated processes. A number of groups have proposed kinetic models for protein adsorption. Wahlgren et al. tested five adsorption models for lysozyme adsorption on hydrophilic silicon oxide [5] and β-lactoglobulin adsorption onto methylated silica [70] surfaces in ellipsometry. Docoslis et al. adapted von Smoluchowski’s flocculation kinetics equation for the early adsorption of human serum albumin adsorption onto silica particles [71]. Talbot reported a scaled particle theory approach to molecular thermodynamics of binary mixture adsorption [72]. Van Tassel et al. presented a sequential random adsorption (SRA) model for irreversible adsorption of proteins onto solid surfaces [73–76]. In the situation of irreversible adsorption, the SRA kinetics model is commonly used to analyze the adsorption parameters. But the mathematical treatment in the SRA model is very complicated [77]. In this work, only the early fast adsorption process is monitored by the ESPS method. A simple adsorption kinetics model was developed to describe the early adsorption behavior of the gelatin on the quartz surface: ka

kf Gelatin(sol) −→ ←− Gelatin(sur)1 −→ Gelatin(sur)2 . kd

θ1

θ2

In the adsorption kinetics model, gelatin is assumed to adsorb on the surfaces initially in a reversible state, which can be desorbed by the buffer. Differently from the Langmuir model, gelatin adsorbed in the reversible state can be

dθ1 /dt = ka C(1 − θ ) − kd θ1 − kf θ1 (1 − θ ),

(6)

dθ2 /dt = kf θ1 (1 − θ ),

(7)

dθ/dt = dθ1 /dt + dθ2/dt = ka C(1 − θ ) − kd θ1 ,

(8)

where θ (= θ1 + θ2 , 0
θ
1) denotes the fraction of the surface area covered with protein. θ1 and θ2 are the fractions of surface area occupied by gelatin in reversible and irreversible adsorption states, respectively. The rate constants for adsorption, desorption, and transformation are k a , k d , and k f , respectively. For all experiments carried out here, the amount of protein in solution is much larger compared to the amount on the surface. Hence, C is considered constant and k a C is treated as a pseudo-first-order rate constant with units of reciprocal seconds. 3.5. Time dependence of adsorption amount After correction for the influence of the viscoelasticity of the adsorbed film and the viscosity of the bulk phase, the calibrated frequency shifts of a piezoelectric sensor are in linear correlation with the adsorption densities. If the adsorption layer is homogeneous, the frequency shift of the sensor is in a linear relationship with the surface coverage ratio; i.e., F = θ Fsat . Here Fsat was the frequency shift corresponding to the adsorbed mass of a saturation adsorption layer of the gelatin. The values of Fsat can be obtained from the adsorption isotherm. Hence, the change in θ can be monitored in real time from the F of the ESPS. Based on the analysis of the response of the ESPS in the adsorption process, the three kinetic parameters can be estimated. To estimate the adsorption kinetics parameters above, the expression of θ as a function of adsorption time should be known. However, we fail to get an algebraic expression for θ because of the difficulty in solving the differential equation group above. In this paper, a progressive approach method was employed to simulate the adsorption process. The data fitting method is described below. With θ1 = βt θ used, Eq. (8) was rewritten as dθ/dt = ka C − [ka C + βt kd ]θ.

(9)

As discussed later, the reversible adsorption ratio, βt , decreases with adsorption time and is also related to the concentration of gelatin. If the values of βt at different adsorption times and concentrations are known, an expression for

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θ is given by θ=

in F is given by


  ka C 1 − exp −(ka C + βt kd )t , k a C + βt k d

(10)

where βt was treated as a parameter with a group of different values at different adsorption times in the progressive approach method. Hence, the determination of suitable βt values was the key to the method. Because βt = 1 − θ2t /θ , the values of θ2t are needed for βt calculation. According to Eq. (7), θ2t can be calculated as follows: t θ2t = kf

βt θ (1 − θ ) dt.

(11)

0

If the value of kf is known, the values of βt can generally be approached by a computer program. With βt values known, the adsorption and desorption rate constants, k a and k d , can be obtained from the curves of θ vs t using Eq. (10) as the fitting model. According to Eq. (10), if the irreversible adsorption amount after a given adsorption time (t0 ), θ20 , is known, the transformation rate constant can be given by  t0 kf = θ20

−1 βt θ (1 − θ ) dt

.

(12)

0

As can be seen in Fig. 2, θ20 may be estimated from the frequency changes of the ESPS in the washing process, where the protein in the reversible adsorption state was removed. However, part of the protein in the reversible adsorption state was transformed to irreversible states during the washing process. Consequently, the influence of the transformation process on the measurements of θ20 should be considered. When quartz surface with adsorbed protein was washed by protein-free buffer, the kinetics for θ1 and θ2 is given as dθ1 /dt = −kd θ1 − kf θ1 (1 − θ ), t θ2 = θ20 + kf θ1 (1 − θ ) dt,

(13) (14)

0

t θ = θ20 + kf


 θ1 (1 − θ ) dt + θ10 exp −kd t + kf (1 − θ )t ,

0

(15) where θ10 is the initial value for reversible adsorption before washing. 3.6. Estimation of kinetics from the response of the ESPS Based on the derivation above, the estimation of kinetic parameters should start from the calculation of θ20 . According to Eq. (10), the adsorption isotherm of gelatin expressed

F ≈

Fsat KC Fsat ka C = . k a C + β0 k d KC + β0

(16)

In the progressive approach method, the initial values of Fsat and K were obtained from fitting the adsorption isotherm by Eq. (16) using the Γ1 /Γ values in Fig. 9. Then the frequency shifts of the ESPS were transformed to surface coverage by θ = F /Fsat . By using kf = 0 as the initial value, the retained adsorbed amount after washing is used as the first approximation of θ20 . Then the first approximation for kf was obtained from Eq. (12) with βt = 1. The approximated θ2 values in the adsorption step were calculated with the obtained kf value and βt = 1. And βt = 1 − θ2 /θ was used in Eq. (10) to fit ka and kd . In the next progressive loop, the values of θ20 are calculated from the responses in washing process by t θ20 = θ − kf 0


 θ10 exp −kd t + kf (1 − θ )t (1 − θ ) dt
 −θ10 exp −kd t + kf (1 − θ )t . (17)

The renewed θ20 and βt values were submitted in Eq. (12) to calculate the newer kf value. After then renewed θ2 and βt were given and used to regress ka and kd . The process was repeated until constant ka , kd , and kf were obtained. When a group of β0 values in the isotherm were obtained, the values of Fsat and K were fitted again. The θ values were recalculated by the new Fsat value. The progressive approach method was repeated until constant ka , kd , kf , Fsat and K were obtained. The results are listed in Table 1. 3.7. Comparison of the two adsorption kinetics models Under the experimental conditions, the early adsorption behavior of gelatin on quartz surfaces can be described by the simplified kinetics model. On the other hand, the classical Langmuir model can also be used to fit the adsorption kinetics process and isotherm. As shown in Table 1, the regressed parameters in two models are somewhat different. The values of k a regressed by two models are similar. The Γ∞ values in Langmuir isotherm are slightly less than those in the simplified model. But the values of K in Langmuir isotherm are about two times of those in the simplified model. Consequently, the values of kd fitted the Langmuir model were less than those by the simplified model. To explain why the partly irreversible adsorption process can be fitted by the Langmuir model, the theoretical simulations for the adsorption isotherm, adsorption process, and washing process are shown in Figs. 10–12. As can be seen in Fig. 10, with increasing gelatin concentration, θ , β0 , and θ1 increase, and θ2 increases to a maximum and then declines. The results are similar to the simulation curves obtained by the SRA method [73]. The decline in the irreversible adsorption amount at higher concentrations is due to the decrease in

D. Shen et al. / Journal of Colloid and Interface Science 281 (2005) 398–409

Fig. 10. Simulation of the adsorption isotherms for gelatin on quartz surface. Parameters used: ka = 0.0565 dm3 g−1 s−1 , kd = 7.08 × 10−3 s−1 , kf = 1.32 × 10−3 s−1 , ta = 30 min. θ , θ1 , and θ2 are the surface coverage ratio for the total adsorbed amount, the reversible adsorbed amount, and irreversible adsorbed amount, respectively. β0 is the reversible adsorption ratio. Line 1 is plotted according to the Langmuir isotherm in Eq. (4). Line 2 presents the regressed adsorption isotherms using Eq. (4) as the fitting model.

Fig. 12. Simulation of the time dependence of the surface coverage ratio in the washing processes. The parameter used are θ10 = 0.533, θ20 = 0.302, ka = 0.0565 dm3 g−1 s−1 , kd = 7.08 × 10−3 s−1 , kf = 1.32 × 10−3 s−1 . θ , θ1 , and θ2 are the surface coverage ratio for the total adsorption amount, reversible adsorption amount, and irreversible adsorption amount, respectively.

concentration region, β0 ≈ a0 + b0 C, Eq. (16) can be written in the Langmuir isotherm format: [Fsat /(1 + b0 kd /ka )]ka (1 + b0 kd /ka )C (18) . (1 + b0 kd /ka )ka C + a0 kd Because a0 < 1, the adsorption equilibrium constant in the Langmuir isotherm is greater than ka /kd . The saturation adsorption amount in the Langmuir isotherm is slightly less than Fsat . In the high-concentration region, the influence of β0 on the adsorbed amount decreases as KC  β0 in Eq. (16). Hence, the adsorption isotherm can also be fitted by the Langmuir model (curve 2) within experimental error. In the estimation of the kinetic parameters of kf , k a , and k d , the parameters of θ , θ1 , and θ2 in the adsorption and washing processes are used. But θ1 and θ2 cannot be measured by the ESPS method directly. To understand the adsorption process, the dependence of the parameters on time is shown in Fig. 11. In the adsorption process, the θ1 values first reach a peak and then decrease with adsorption time. The θ2 increases but βt decreases nearly linearly with the time. According to Eq. (10), the increase in amount adsorbed with time is attributed to two terms. The term [1 − exp(−(ka C + βt kd )t)] corresponds to the rapid increase in amount adsorbed in the early adsorption process. The term of (ka C + βt kd )−1 causes a slow increase in amount adsorbed. Because part of the protein molecule adsorption in the reversible state is transformed to the irreversible state, the reversible adsorption equilibrium is shifted. New protein is adsorbed from solution, which corresponds to the slight increase in total amount adsorbed. Hence, the adsorption amount curve is slightly greater than the Langmuir model F ≈

Fig. 11. Simulation of the time dependence of the surface coverage ratio in the adsorption processes. The parameters used are ka = 0.0565 dm3 g−1 s−1 , kd = 7.08 × 10−3 s−1 , kf = 1.32 × 10−3 s−1 , and C = 0.4 g dm3 . θ , θ1 , and θ2 are surface coverage for the total, reversible, and irreversible adsorption amounts, respectively. βt is the reversible adsorption ratio. Line 1 is plotted according to Langmuir model in Eq. (5). Line 2 presents the regressed adsorption amount using Eq. (5) as the fitting model.

free surface area for transformation. The β0 vs C curve can be fitted by the mathematical model β0 = a − b exp(−C). Because β0 < 1, the adsorbed amounts are greater than the Langmuir isotherm with K = ka /kd (curve 1). In the low-

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(Eq. (4) and curve 1). But the regressed line (curve 2) is close to the adsorption amount curve. When the regression analysis is limited in the early rapid increase step, the adsorption amount curve can be well fitted by Eq. (5). In a short adsorption time, the βt values may be considered constant. Hence, the observed adsorption constant kobs = ka C + βt kd has a good linear relation to the concentration C. As shown in Fig. 12, the values of θ1 and θ decrease in exponential decay in the washing process. The increase in θ2 is small. Hence, the delay in replacement of gelatin solution to buffer in the adsorption experiment has only slight influence on kinetics parameter estimation. And the experimental values of Γ1 /Γ were good approximations for β0 . It is worthy of note that the adsorption of protein on solid surface involves very complicated processes, especially the conformational changes of the adsorbed protein on the surface. The modified Langmuir model used here may be still too simple to describe the complicated conformational changes. The main flaw of this model is that it is suitable only for the initial adsorption process. Because the transform from the reversible state to the irreversible state is assumed to be irreversible, the adsorption equilibrium will not reach. If the adsorption time is long enough, the surface coverage will reach 100% in all concentration. And all the protein was adsorbed in an irreversible adsorption state. Obviously, this is not the true picture of the protein adsorption process. For example, in an independent experiment, the detection cell was in contact with a 1 mg/mL gelatin solution for 24 h. After then the cell was rinsed with gelatin-free buffer. However, a frequency increase of 21.7 Hz was still observed in the washing process. This result indicates that irreversible adsorption ratio cannot reach 100% even after a long adsorption time. Hence, limit conditions should be added for the transform processes in this model if long adsorption time is concerned. As several limits were used in the SRA model, the irreversible adsorption amount approaches a plateau value in the conformational adjusting process [1,73].

4. Conclusions We concluded that the ESPS is a useful device to monitor the initial kinetics of adsorption of proteins on quartz surface. Combined with mathematical models, valuable information about the interaction processes can be obtained. It was shown that the early adsorption process of gelatin on quartz surfaces can be described by a model that involves reversible adsorption and transformation from the reversible state to the irreversible one. Using a progressive approach computing method, the rate constants were estimated. It should be noted that these kinetics parameters were the averaged values for proteins of various adsorption conformations because total mass change was reflected by the frequency shift of the ESPS. The difference in kinetic parameters of different adsorption conformations was not discussed here because the adsorption density data cannot give informa-

tion about the microstructure of the adsorption layer. Within the experimental error, the adsorption isotherm as well as the early adsorption process can also be analyzed by the Langmuir model. When the Langmuir adsorption isotherm model is used, the adsorption equilibrium constant is greater than the one of the reversible adsorption state in our model. The saturation adsorption amount in the Langmuir model is slightly lower than that estimated by our model. The values of k a regressed by the two models are close. The values of kd fitted by the Langmuir model a less, than those by the proposed model. The proposed kinetic model can explain the irreversible adsorption phenomenon for protein adsorption. But as the contact time increases, protein will unfold, denature, and spread on the surface. The mass change during the conformational adjustment of adsorbed protein is usually slight. So the ESPS as a kind of mass sensor were used to monitor the initial adsorption of gelatin, where the mass changes are relatively obvious in both the adsorption and desorption processes.

Acknowledgments This work is supported by the National Science Foundation of China (No. 20275021) and open foundation of the State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan University.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

P.R.V. Tassel, P. Viot, G. Tarjus, J. Chem. Phys. 106 (1997) 761. W. Norde, Cells Mater. 5 (1995) 97. E. Dickinson, Colloids Surf. B Biointerfaces 15 (1999) 161. S. Sun, Y. Yue, X. Huang, D. Meng, J. Membrane Sci. 222 (2003) 3. M. Wahlgren, T. Arnebrant, I. Lundström, J. Colloid Interface Sci. 175 (1995) 506. M. Malmstrn, Veide, J. Colloid Interface Sci. 178 (1996) 160. S.W. Lee, P.E. Laibinis, Biomaterials 19 (1998) 1669. G. Sagvolden, I. Giaever, J. Feder, Langmuir 14 (1998) 5984–5987. C.C. Dupont-Gillain, P.G. Rouxhet, Langmuir 17 (2001) 7261. S. Jo, K. Park, Biomaterials 21 (2000) 605. M. Tanaka, T. Motomura, M. Kawada, T. Anzai, Y. Kasori, T. Shiroya, K. Shimura, M. Onishi, A. Mochizuki, Biomaterials 21 (2000) 1471. R.J. Green, I. Hopkinson, R.A.L. Jones, Langmuir 15 (1999) 5102. P. Schwinté, J.C. Voegel, C. Picart, Y. Haikel, P. Schaaf, B. Szalontai, J. Phys. Chem. B 105 (2001) 11,906. J. Kim, G.A. Somorjai, J. Am. Chem. Soc. 125 (2003) 3150. R.J. Green, J. Davies, M.C. Davies, C.J. Roberts, S.J.B. Tendler, Biomaterials 18 (1997) 405. Y.Y. Luk, M. Kato, M. Mrksich, Langmuir 16 (2000) 9604. E. Ostuni, R.G. Chapman, R.E. Holmlin, S. Takayama, G.M. Whitesides, Langmuir 17 (2001) 5605. R.G. Chapman, E. Ostuni, M.N. Liang, G. Meluleni, E. Kim, L. Yan, H.S. Warren, G.M. Whitesides, Langmuir 17 (2001) 1225. C.F. Wertz, M.M. Santore, Langmuir 18 (2002) 706. A. Akkoyun, U. Bilitewski, Biosens. Bioelectron. 17 (2002) 655. S. Petrash, T. Cregger, B. Zhao, E. Pokidysheva, M.D. Foster, W.J. Brittain, V. Sevastianov, C.F. Majkrzak, Langmuir 17 (2001) 7645. F. Caruso, E. Rodda, D.N. Furlong, J. Colloid Interface Sci. 178 (1996) 104.

D. Shen et al. / Journal of Colloid and Interface Science 281 (2005) 398–409

[23] F. Caruso, D.N. Furlong, P. Kingshott, J. Colloid Interface Sci. 186 (1997) 129. [24] B.S. Murray, C. Deshaires, J. Colloid Interface Sci. 227 (2000) 32. [25] B.A. Cavic, M. Thompson, Anal. Chem. 72 (2000) 1523. [26] D.B. Hibbert, J.J. Googing, P. Erokhin, Langmuir 18 (2002) 1770. [27] M. Tanaka, A. Mochizuki, T. Motomura, K. Shimura, M. Onishi, Y. Okahata, Colloids Surf. A Physicochem. Eng. Aspects 193 (2001) 145. [28] C.G. Marxer, M.C. Coen, L. Schlapbach, J. Colloid Interface Sci. 261 (2003) 291. [29] Z.H. Mo, L.H. Nie, S.Z. Yao, J. Electroanal. Chem. 316 (1991) 79. [30] T. Nomura, F. Tanaka, T. Yamada, H. Itoh, Anal. Chim. Acta 243 (1991) 273. [31] D.Z. Shen, Q. Kang, X.L. Zhang, L.Z. Wang, C.S. Ma, Anal. Commun. 34 (1997) 97. [32] F. Yin, Y.Y. Zhang, Y.H. Wu, Y. Cai, Q.J. Xie, S.Z. Yao, J. Colloid Interface Sci. 241 (2001) 386. [33] C.E.K. Mees, The Theory of Photographic Process, Macmillan, New York, 1966. [34] A.G. Ward, A. Courts, The Science and Technology of Gelatin, Academic Press, London, 1977. [35] H. Auweter, V. Andere, D. Horm, E. Luddecke, J. Dispers. Sci. Technol. 19 (1998) 163. [36] M. Bele, K. Kocevar, I. Musevic, J.O. Besenhard, S. Pejovnik, Colloids Surf. A 168 (2000) 231. [37] A.G. Ward, A. Courts, The Science and Technology of Gelatin, Academic Press, London, 1977. [38] Y. Kamiyama, J. Israelachvili, Macromolecules 25 (1992) 5081. [39] A. Kamyshny, O. Toledano, S. Magdassi, Colloids Surf. B Biointerfaces 13 (1999) 187. [40] I.F. Mironyuk, V.M. Gun’ko, V.V. Turov, V.I. Zarko, R. Leboda, J. Skubiszewska-Zieba, Colloids Surf. A Physicochem. Eng. Aspects 180 (2001) 87. [41] V.M. Gun’ko, I.V. Mikhailova, V.I. Zarko, I.I. Gerashchenko, N.V. Guzenko, W. Janusz, R. Leboda, S. Chibowski, J. Colloid Interface Sci. 260 (2003) 56. [42] M. Bele, M. Gaberscek, R. Dominko, J. Drofenik, K. Zupan, P. Komac, K. Kocevar, I. Musevic, S. Pejovnik, Carbon 40 (2002) 1117. [43] J.H.E. Hone, A.M. Howe, T.H. Whitesides, Colloids Surf. A Physicochem. Eng. Aspects 161 (2000) 283. [44] A.K. Bajpai, Polym. Int. 33 (1994) 315. [45] K.A. Vaynberg, N.J. Wagner, R. Sharma, Biomacromolecules 1 (2000) 466. [46] T.J. Maternaghan, O.B. Banghan, R.H. Ottewill, J. Photogr. Sci. 28 (1980) 1.

409

[47] N. Kawanishi, H.K. Christenson, B.W. Ninham, J. Phys. Chem. 94 (1990) 4611. [48] Y. Kamiyama, J. Israelachvili, Macromolecules 25 (1992) 5081. [49] T. Cosgrove, J.H.E. Hone, A.M. Howe, R.K. Heenan, Langmuir 14 (1998) 5376. [50] S. Martin, J. Granstaff, G.L. Frye, Anal. Chem. 63 (1991) 2272. [51] A.L. Kipling, M. Thompson, Anal. Chem. 62 (1990) 1514. [52] M. Yang, M. Thompson, Anal. Chem. 65 (1993) 1158. [53] M. Yang, M. Thompson, Langmuir 9 (1993) 1990. [54] M.H. Huang, D.Z. Shen, M. Yang, Analyst 259 (2002) 1990. [55] B.A. Martin, H.E. Hager, J. Appl. Phys. 65 (1989) 2627. [56] L. Tessier, F. Patat, N. Schmitt, G. Feuillard, M. Thompson, Anal. Chem. 66 (1994) 3569. [57] Z. Lin, M.D. Ward, Anal. Chem. 67 (1995) 685. [58] T.W. Schneider, S.J. Martin, Anal. Chem. 67 (1995) 3324. [59] A. Bund, G. Schwitzgebel, Anal. Chim. Acta 364 (1998) 189. [60] M. Huang, D. Shen, M. Yang, Anal. Chim. Acta 440 (2001) 109. [61] G. Sauerbrey, Z. Phys. 155 (1959) 206. [62] P. Vinaraphong, V. Krisdhasima, J. McGuire, J. Colloid Interface Sci. 174 (1995) 251. [63] R. Kurrat, J.E. Prenosil, J.J. Ramsden, J. Colloid Interface Sci. 185 (1997) 1. [64] K.K. Kanazawa, J.G. Gordon, Anal. Chim. Acta 117 (1985) 99. [65] S. Bruckenstein, M. Shay, Electrochim. Acta 30 (1985) 1295. [66] S.Z. Yao, T.A. Zhou, Anal. Chim. Acta 212 (1988) 61. [67] H. Muramatsu, E. Tamiya, I. Karube, Anal. Chem. 60 (1988) 2142. [68] M. Thompson, A.L. Kipling, W.C. Duncan-Hewitt, L. Rajakovi´c, B.A. ˇ c-Vlasak, Analyst 116 (1991) 881. Cavi´ [69] T.A. Zhou, L.H. Nie, S.Z. Yao, J. Electroanal. Chem. 318 (1991) 91. [70] M. Wahlgren, U. Elofsson, J. Colloid Interface Sci. 188 (1997) 121. [71] A. Docoslis, W. Wu, R.F. Giese, C.J. Oss, Colloids Surf. B Biointerfaces 13 (1999) 83. [72] J. Talbot, J. Chem. Phys. 106 (1997) 4696. [73] P.R. Van Tassel, P. Viot, G. Tarjus, J. Talbot, J. Chem. Phys. 101 (1994) 7064. [74] P.R. Van Tassel, P. Viot, G. Tarjus, J. Chem. Phys. 106 (1997) 761. [75] P.R. Van Tassel, L. Guemouri, J.J. Ramsden, G. Tarjus, P. Viot, J. Talbot, J. Colloid Interface Sci. 207 (1998) 317. [76] M.A. Brusatori, P.R. Van Tassel, J. Colloid Interface Sci. 219 (1999) 333. [77] Z. Adamczyk, P. Weronski, E. Musia, J. Chem. Phys. 116 (2002) 4665. [78] R. Dahint, R.R. Seigel, P. Harder, M. Grunze, F. Josse, Sens. Actuators B 35 (1996) 497.