Quartz crystal microbalance sensor design

Quartz crystal microbalance sensor design

Sensors and Actuators B 123 (2007) 27–34 Quartz crystal microbalance sensor design I. Experimental study of sensor response and performance Henrik An...

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Sensors and Actuators B 123 (2007) 27–34

Quartz crystal microbalance sensor design I. Experimental study of sensor response and performance Henrik Anderson a,b , Mats J¨onsson b,∗ , Lars Vestling b , Ulf Lindberg b , Teodor Aastrup a b

a Attana AB, Bj¨ omn¨asv¨agen 21, SE-113 47 Stockholm, Sweden ˚ The Angstr¨om Laboratory, Solid State Electronics, Uppsala University, P.O. Box 534, SE-751 21 Uppsala, Sweden

Received 31 March 2006; received in revised form 19 July 2006; accepted 24 July 2006 Available online 7 September 2006

Abstract This paper investigates a novel quartz crystal microbalance (QCM) biosensor with a small and rectangular flow cell along with a correspondingly shaped crystal electrode. The sensor was evaluated with impedance analysis and compared to standard circular sensor crystals and sensor crystals with small circular electrodes. Comparative QCM measurements on an antibody–antigen interaction system were carried out on the rectangular and standard circular sensor systems. Impedance analysis and subsequent data extraction of the three different sensor crystals showed that the smaller sensors had significantly higher Q-values in air, but that liquid load on the electrodes lowered the Q-values radically for all crystals. Under liquid load, Q-values for the standard circular and the rectangular sensors were similar whereas the Q-value for the small circular sensor was 50% higher. QCM experiments showed that the QCM system with rectangular crystal electrodes was fully functional in a liquid environment. The rectangular system showed higher and more rapid responses for series of antibody injections, albeit at a higher noise level than the standard system. The study elucidates a significant potential for improvement of sensor performance by optimising the sensor electrode size and shape together with the flow cell geometry. © 2006 Elsevier B.V. All rights reserved. Keywords: QCM; Biosensor; Sensitivity; Mass transport; Protein interactions

1. Introduction Biosensors have the potential of being applied within an array of fields such as medical diagnostics, environmental protection and food analysis [1,2]. At present, biosensors are being increasingly employed within biotechnology and pharmaceutical research to study interactions between proteins and between potential drug molecules and their receptors. A biosensor consists of two principal components: a transducer, that converts a chemical or biochemical signal into an electrical signal, and a functional sensor chemistry that ascertains a selective sensor response [3]. Optical transducers such as the surface plasmon resonance (SPR) and acoustical transducers such as the quartz crystal microbalance are among the most popular and widespread. Both the techniques measure a change in mass on a surface, the SPR transducer by measuring opti-



Corresponding author. Tel.: +46 18 471 7257; fax: +46 18 555095. E-mail address: [email protected] (M. J¨onsson).

0925-4005/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2006.07.027

cal parameters, and QCM by measuring a change in resonator behaviour e.g. resonance frequency. While the QCM was conceived already in 1959 by Sauerbrey [4] and has been widely used to monitor for instance deposition thickness in vapour deposition processes, it is mainly during the last 10 years that it has been used in biosensor applications. Most of the QCM research from this period lies within biosensor applications or as a tool in surface science [5–9], but efforts have been made to improve the transducer and the measurement principle. Hayden et al. have developed a QCM sensor with two different sensors on the same crystal, with the intention to use one of the sensors surfaces as a reference [10]. Tatsuma et al. carried the multi-electrode concept further and developed an array of sensors with four electrodes on the same crystal [11]. Rodahl et al. developed a novel method of measuring the energy loss, the Q-value, of the crystal during sensor operation [12]. The Q-value, or its reciprocal value, the dissipation, is in many cases a mirror of the frequency change, but may in some applications provide additional information on structural and viscous changes on the sensor surface [13]. Uttenthaler investigated the potential

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for increase the sensitivity of the QCM by using thinner crystals with higher resonance frequencies, since the sensitivity scales inversely to the square of the frequency [14]. The crystals chosen are for biosensing applications have large circular electrodes since the operation of the crystal in liquid sets high demands on the crystal performance. The flow cells in which the crystal operates are designed with respect to the electrode since the walls of the flow cell should not interfere with the oscillations of the crystal. In more demanding applications e.g. when measuring the kinetics of biochemical interaction, the dispersion of the sample caused by large flow cells can limit the sensor performance. A different approach would be to have a flow cell with better hydrodynamic properties and then design the crystal electrode with respect to the flow cell. This paper investigates a novel QCM biosensor with a small and rectangular flow cell with a correspondingly small and rectangular crystal electrode. The study relies on crystal impedance analysis and characterization as well as QCM measurements on an antibody–antigen interaction system. Sample plug behaviour and dispersion phenomena are investigated in a separate paper [15]. 2. Background The linear relationship between the mass adsorbed to a QCM device and the resonance frequency discovered by Sauerbrey can be described with the equation: f = −

2f 2 m , ρv A

(1)

where f is the resonance frequency, ρ the density of quartz, v the shear wave velocity in quartz, A the electrode area, and m is the sample mass. The equation is valid if the added mass is small in relation to the mass of the crystal and that the added mass forms an evenly distributed rigid layer on the active sensor area. For studies of biological systems in liquid environments this will not be the case, since biomolecules bound to a sensor surface cannot be considered completely rigid and since the biomolecules will coordinate water which will enhance the sensor signal. However, Muratsugu and coworkers have shown with radio-isotope labelling methods that the linearity between adsorbed mass and frequency response will persist under these conditions, but with a different coefficient for the frequency–mass relationship [16]. From the Sauerbrey equation it is also evident that the frequency shift from the adsorption of a certain mass will also depend inversely on the area of the QCM device. For instance, the same adsorbed mass will elicit twice the frequency response if the electrode area is halved. This means that if the same mass can be adsorbed onto the surface of the smaller electrode and the noise level of the QCM device can be kept intact, the detection limit will be lowered by a factor corresponding to the ratio of the electrode areas. Given a continuous flow biosensor system with a liquid sample flowing over the sensor surface, we should be able to harvest an effect of the relationship above if from the liquid sample the same fraction of sample molecules are transported down to the

Fig. 1. Sensor surfaces with different areas A1 and A2 in a flow cell with the height h. The thickness of the stagnant layer above the sensor surface is denoted b.

sensor surface for the two sensors. In turn, this will be valid in two cases: (i) if the entire sample is consumed by its binding to the sensor surfaces, and no sample is wasted and (ii) if a higher efficiency of the transport of the sample molecules to the sensor surface can be achieved for the smaller sensor. To understand the aspects of mass transport to the sensor surface in a surface based biosensor a few basic concepts should be described. The transport of sample to the sensor surface is facilitated by a combination of convective and diffusive flow, both of which are important in different domains of the sensor. The convective flow takes the sample from the injection valve to just above the sensor surface. The flow profile under laminar flow conditions can be described as parabolic, which means that the flow in the centre of the flow channel is the highest and that the flow at the channel walls is zero. The diffusive flow during this process has a limited effect on delivery of the sample to the sensor surface, although diffusion combined with the laminar parabolic flow in small fluid channels will cause dispersion of a sample plug. Due to the parabolic flow profile, the convective flow has little influence in the vicinity of the channel walls and in the vicinity of a sensor surface situated in the fluid channel. With respect to mass transport to the sensor surface situated in a flow channel, this behaviour is described as there being a stagnant layer at a distance b from the sensor surface under which the convective flow has little importance [2,17,18]. The distance b, as illustrated in Fig. 1, can be described as the distance where the concentration is 99% of the bulk concentration [18]. Within the stagnant layer, then, diffusion is the predominant mechanism for mass transport. Diffusion can be described by Fick’s law, here in one dimension, J = −D

∂[L] , ∂z

(2)

where J is the flux of ligands, [L] the ligand concentration and D is the diffusion constant. With the concentration of ligands in the bulk, [L]B and the distance to the surface b, the rate of ligands hitting the surface A is given by: dn [L]B A = −D . (3) dt b The biosensor response of an injected sample will behave differently depending on the role of mass transport limitations to the system. To provide a comprehensive description of the role of mass transport limitations to biosensor system different cases should be discussed; sample depletion, mass transport limitation and reaction rate limitation. For sample depletion to be the relevant mechanism of the sensor response the sample concentration

Isurf = JA =

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would have to be very low and the sample residence time over the sensor surface to be very long since the mean diffusion path would be half of the flow cell height. Sj¨olander and Urbaniczky reported that they could achieve adsorption efficiency from a sample of up to 3% in a SPR based sensor system with a flow cell height of 50 ␮m [19]. Consequently, it is unlikely that sample depletion is a relevant mechanism of the sensor response. 2.1. Mass transport limited system Given instead a biosensor system where the sample concentration is such that the consumption of sample at the surface causes no significant reduction of sample concentration, then the concentration at the distance b from the surface will be almost the same as in the bulk concentration. Given also that the reaction at the surface takes place much faster than new material can be transported down to the surface, then the concentration of ligands at the surface will be zero and the biosensor can be said to operate under mass transport limited conditions. The observed binding rate, the sensor signal, will then correlate directly with the bulk concentration of the sample. To compare the sensor systems with different electrode areas and geometry it is useful to derive an equation for the response. Combining the derivative of the Sauerbrey equation with Fick’s equation the derivative of the sensor response reads: df 1 dm M dn MD [L]B =− =− = , dt CA dt CA dt C b

(4)

where M is the molar weight of the analyte, and the diffusion coefficient are properties of the analyte and will consequently be the same for both systems. The ligand concentration at the distance b from the surface is per definition the same. The distance b is the only property that changes between the systems. The thickness of the stagnant layer is dependent on the flow velocity in the system; an increase in the flow velocity will lead to a thinner stagnant layer, and consequently a higher rate of diffusion to the surface and a faster sensor response. According to Coulson and Richardson the thickness of the stagnant layer correlates inversely with the square root of the Reynolds number under certain circumstances. Reynolds numbers obtained from simulations carried out for the rectangular and circular sensor systems of 4 and 0.25, respectively, provides the ratio of 2.6 between the sensor systems [15]. Although significant uncertainties exist in the estimate, the derived ratio suggests that the increase in response rate should be in this order of magnitude for a mass transport limited sensor system.

equilibrium reaction, the equilibrium dissociation constant is defined according to the law of mass action as Kd =

1 kd [L][RS ] = . = Ka ka [LRS ]

d[LR]S df ∝ = ka [RS ][L] − kd [LR]. dt dt

(7)

Given a high affinity system where the association rate constant is high, the dissociation rate constant is low and the concentration of the surface bound complex is low, then the second term of the expression will be insignificant for the initial response of the sensor. The initial response will then depend on the association rate constant, the free receptor concentration on the surface and the ligand concentration. If the association rate is low relative to the rate of diffusion, then the sensor system will be reaction rate limited and the concentration of ligand at the surface can be assumed to be the same as the bulk concentration of ligand. 2.3. Resonator characteristics A quartz crystal resonator near resonance frequency can be described by an equivalent circuit model, e.g. the modified Butterworth–Van Dyke (MBVD) model [20], consisting of the left static arm and the right motional arm as seen in Fig. 2. When the crystal is freely oscillating in a gas or in vacuum, Z0 (C0 in series with R0 ) can be replaced by a capacitance, C0 . When an oscillating crystal is short circuited, the electrical energy that is stored in the motional arm will be dissipated in R1 . Since no current will flow through Z0 , the equivalent circuit which determines the resonant condition, i.e. the resonant frequency for the crystal in short-circuit condition (series mode) is Zs , i.e. R1 , C1 , and L1 in series. Under open-circuit condition, the current will go through Z0 , and hence the equivalent circuit will be equal to Zp , i.e. R1 , C1 , L1 , and Z0 in series. A more detailed investigation of how a liquid load affects the performance of a QCM could be found in literature [21–23]. The

The chemical reaction by a ligand to a receptor on a sensor surface can in the simplest case be described by a 1:1 interaction model, or Langmuir binding model which assumes that the ligand binds the receptor in a 1:1 relationship according to (5)

where L denote the free ligand, RS the surface bound receptor and LRS the surface bound receptor–ligand complex. For this

(6)

In an equilibrium reaction, the association rate, ka , will compete with the dissociation rate, kd , and their ratio will also equal the equilibrium constant according to the equation above. The derivative of the sensor response will be proportional to the rate of formation of the surface bound LR complex:

2.2. Reaction rate limited system

L + RS ↔ LRS ,

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Fig. 2. Equivalent circuit of a quartz crystal resonator near resonance.

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Fig. 3. Photograph of the examined quartz crystals.

two resonant frequencies under short-circuit and open-circuit conditions are named the series resonant frequency, fs , and the parallel resonant frequency fp , respectively. The series and parallel resonance occur when Zs and Zp are real (purely resistive). The series and parallel angular resonance frequencies are ωp and ωs , respectively, derived from ωi = 2πfi : 1 1 √ , 2π L1 C1  C0 + C 1 1 fp = , 2π L1 C0 C1 fs =

ethanolic solution onto the gold coated electrodes to for a dense and stable monolayer. In a subsequent reaction, the amino terminated biotin derivative was coupled to the carboxyl groups yielding a biotin functionalised surface with the capacity to bind streptavidin. The tetrameric streptavidin could then be used for coupling of biotinylated proteins. All sensor crystals were from Attana AB (Stockholm, Sweden).

(8) 3.1. QCM system (9)

The quality factor Q for a resonant circuit is defined as the ratio between stored and lost energy and is for an RLC circuit calculated for series resonance as √ L1 /C1 ωs L1 1 QS = = = , (10) R1 ωs R 1 C1 R1  ω p L1 C0 + C 1 1 Qp = = L1 × . (11) R0 + R 1 C0 C1 R0 + R 1 The relation between Q-values and measurement resolution have been investigated, e.g. by Rodriguez-Pardo et al. [23], addressing necessary noise reduction, by means of optimisation of oscillator circuit design, when working at Q-values below theoretically. 3. Materials and methods Three different AT-cut 10 MHz shear mode sensor crystals were examined in this study, all with the same crystal diameter, 8 mm, but with different electrode geometries. The electrode geometries for the sensing electrode were 4.5 and 2 mm in diameter for two circular electrodes and 1.4 mm2 for a rectangular electrode (see Fig. 3). Q-value measurements were carried out for all crystals in air and in phosphate buffered saline (PBS), whereas the QCM measurements were done on the circular crystal with a large surface and the rectangular surface. The crystals used for Q-value measurement were plain gold coated surfaces whereas the surfaces used for the QCM measurements were prepared according to Sch¨aferling et al. [24]. Briefly, a carboxyl-terminated n-alkylthiol was adsorbed from

Two Attana 80 QCM biosensor (Attana AB) was used for the experiments. The QCM system consists of a peristaltic pump, an 8-way injection valve and the sensor unit with a flow cell and oscillation electronics. A frequency counter collects frequency data which is transferred to a computer where the data can be monitored and logged. A schematic of the system is shown in Fig. 4. The QCM system operates in a continuous flow mode, where the running buffer is continuously flowed through the flow cell over the sensor surface. Sample is injected by first filling the injection valve with the sample and then switching the valve. The sample is then switched into the flow line and is transported to the sensor surface with the continuous flow. The response from an injection to the resonance frequency is monitored in real-time with the computer and a mass adsorption to the surface will give a negative frequency shift. Desorption from the surface will result in an increase in frequency. One of the systems was used in its standard configuration with a circular crystal and circular flow cell and the other system was modified with a rectangular crystal and a correspondingly rectangular flow cell. The flow cells were 0.2 mm in height and had slightly larger dimensions than the corresponding crystals in order to reduce the dampening of the crystal from the flow cell. The approximate volumes of the circular and rectangular cells were 5 and 1.5 ␮l, respectively. 3.2. Chemicals The chemicals used in this study were obtained from commercial sources as follows: biotinylated bovine serum albumin from Pierce (#29130), anti-bovine albumin antibody from Sigma Aldrich (#B7276), streptavidin from Prozyme. The running buffer for the QCM experiments was phosphate buffer saline

H. Anderson et al. / Sensors and Actuators B 123 (2007) 27–34

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Fig. 4. Schematic over the Attana 80 sensor systems.

(PBS), pH 7.4 from Sigma (#P4417) with an additive of 0.005% of Tween 20, also from Sigma (#P7949). Running buffer was made from MilliQ water from Millipore which was sterile filtered before use. 3.3. Impedance analysis Impedance analyses of the sensors with different electrode geometry have been performed in air and in liquid environment. The resonators were connected via a test fixture (HP 16058A) to an impedance analyser (HP 4291). The set-up was calibrated and compensated for port extension in the frequency range of 9–11 MHz. The oscillation level was 1 V. The liquid load, PBS, was dispensed by a pipette onto the crystal. To cover the circular electrode area of the crystal, 8 ␮l PBS solution was dispensed, whereas 3 ␮l PBS was sufficient to cover the rectangular and small circular electrodes. The crystals were not clamped to a flow cell as in the case for the QCM measurements. To extract the model parameters from the measured data a direct extraction method for the MBVD-model was used [25].

4. Results and discussion 4.1. Q-value results The results of the resonator analysis are presented in Table 1. Extracted values are stringent and accurate relations between the parameters results in parameter values of use for the evaluation in mind. Values of the quality factor, resonance frequency and the coupling factor are reproducible for the tested resonators. Evaluation of the static capacitance C0 is done by subtracting parasitic capacitance from open circuit measurements. The values are adequately comparable to theoretical values of 3.9, 1.0 and 0.8 pF for circular, rectangular and small circular electrodes, respectively, and follow the relation between the electrode areas A. The low coupling factors kt2 are in the range of theoretical values (0.0077) [26]. Values of the ratio between the Q-values for air and liquid are presented in Table 2. The change ratios are larger for smaller sensors and largest for the rectangular sensor. The higher value of Q for air measurements, see Table 1, for smaller sensors indicates that the quality factor is related to the static capacitance

Table 1 Measured and extracted resonator parameters for different electrode geometries Parameter

Circular air

Rectangular air

Small circular air

Circular PBS

Rectangular PBS

Small circular PBS

C0 (pF) C0 (pF) C1 (fF) L1 (mH) R1 () fs (Hz) Qs fp (Hz) Qp kt2 fp − fs (Hz) A (mm2 ) Q = (Qp − Qs )/Qs

80.1 1.6 7.6 33 71.1 10004109 29360 10004576 29460 0.0115 467 16.0 0.003

78.9 0.6 2.7 90 119 9996695 50070 9996845 56100 0.0037 150 4.0 0.121

79.1 0.6 3.2 80 87.5 10004040 56100 10004230 62250 0.0047 190 3.1 0.110

81.4 3.0 7.8 30 1015 10000258 2020 10000735 2020 0.0118 477 16.0 0.000

80.0 1.6 2.9 90 2659 9991449 2040 9991632 2030 0.0045 183 4.0 −0.004

80.4 2.0 3.2 80 1654 9996567.9 2990 9996767 2990 0.0049 200 3.1 −0.001

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Table 2 Q-value ratios for the different electrode geometries Ratio/sensor

Circular

Rectangular

Small circular

Qs air/Qs PBS Qp air/Qp PBS

15 15

25 28

19 21

C0 which is proportionally dependent to the electrode area. For the liquid case Q is close to zero for all geometries as a consequence of that the motional resistance R1 have increased and thus, the Q-values decrease. The resistance R1 is increasing due to increased energy loss in the resonator at load. Tuning of the sensor activation by adding a tuning inductance can compensate for the increase of R1 [27]. The smaller electrode geometries have higher Q-values due to the area dependent static capacitance C0 [26]. The Q-ratios decrease less for the small circular electrode indicating that the circular geometry is preferable. To achieve higher Q-values with liquid load tuning of the activation circuit is addressed. 4.2. QCM results The two different QCM systems were compared using the biological interaction between an antigen and an antibody. The sensor surfaces were first equilibrated to yield a stable baseline with running buffer. Streptavidin was injected to constitute a linker between the biotinylated surface and the biotinylated receptor, biotinylated BSA, which was subsequently injected. The BSA immobilisation levels corresponded to 37 and 62 Hz, respectively for the rectangular and circular systems. Sequential injections of polyclonal BSA antibodies over BSA coated surface were carried out on both sensor systems. Three injections were carried out at each concentration: 0.67, 3.3, 6.7, 33 and 67 nM (Fig. 5). The injected sample volume was 50 ␮l for all samples and the flow rate was set at 25 ␮l/min, which was the lowest pump setting, in order to ensure that the binding events took place under mass transport limited conditions. The lowest concentration gave responses around 1 Hz for both systems whereas the higher concentrations consistently gave higher responses for the rectangular system. In order to assess the

Fig. 5. Sequential injections of polyclonal BSA antibodies over a BSA coated surface in a circular sensor system. Triplicate injections of antibody at concentrations 0.67, 3.3, 6.7, 33 and 67 nM give increasing responses by the sensor system until the surface start to reach saturation.

Fig. 6. Sensor response of the rectangular and circular sensor systems upon injection of 3.3 nM or 500 ng/ml of polyclonal anti-BSA. The sensor responses were 8.5 and 1.7 Hz, respectively for the rectangular and circular system.

detection limits of the two systems it is necessary to determine the signal-to-noise ratio of the two systems. The noise level was evaluated by examining the peak-to-peak noise over a period of 120 s. The noise level of the rectangular system was 0.66 Hz of the period whereas the noise level in the circular system was significantly lower at 0.29 Hz. Given a criterion for detection limit of 3 times the noise level the rectangular system would be considered to have a detection limit of 2 Hz and the circular system a detection limit of 0.9 Hz. Consequently, by this definition the rectangular system would disqualify for detection at the lowest concentration tested, 0.67 nM, whereas the signal would be on the detection limit of the circular system. In this context, however, it should be noted that the noise levels compared here are noise due to physical effects such pressure fluctuations from the peristaltic pump and electrical effects such as noise from the oscillation and measurements electronics. Under more applied circumstances the contribution from these sources of noise may be insignificant compared to sensor signal due to non-specific binding from sample matrix. Furthermore, the higher and periodic, noise level of the rectangular system is likely to be due to pressure fluctuations in the sensor flow cell for the rectangular system. The rectangular system has a significantly smaller cross sectional area perpendicular to the flow direction which elevates the pressure drop over the sensor and likely also its sensitivity to pressure fluctuations. Provided the periodicity of these fluctuations it is not unlikely that this contribution can be minimised by data filtering or other data treatment. Given that the signal from the lowest concentration was below or just at the detection limits of the systems, presenting data from the higher concentration may be more interesting. Fig. 6 shows the response from 3.3 nM injections of the polyclonal anti-BSA to BSA coated surfaces in the rectangular and circular sensor system. The rectangular system displays a significantly higher sensor response as a result of the injection, although the noise level is also substantially higher. The ratio of the responses is 5 in favour of the rectangular system shows that the improvement from changes in crystal geometry and flow cell can be significant. Graphically obtained maximum derivatives of the sensor responses were 0.06 and 0.015 Hz/s, respectively for the rectangular and circular systems. This corresponds to a maxi-

H. Anderson et al. / Sensors and Actuators B 123 (2007) 27–34

Fig. 7. Averaged responses of the sequential and triplicate injections at respective antibody concentrations for the rectangular and circular systems. The data shows that the rectangular system gives consistently higher responses and that the rectangular system saturates more quickly than the circular system.

mum response rate ratio between the two sensor systems of 4. As discussed above, the maximum response rate should depend on the thickness of the stagnant layer over the sensor surface and the estimated theoretical ratio between the circular and rectangular system was found to be 2.6. Due to the uncertainty of the theoretical estimate, the experimentally derived value can be considered to have reasonable agreement with the theoretical value. This indicates that the sensor systems operated under mainly mass transport limited conditions and that the effect of a smaller flow cell can be major. To get a more comprehensive view of the performance of the two sensor systems the average response at each concentration is displayed in Fig. 7. In addition to displaying the higher response of the rectangular system for the whole set of concentrations, the data also shows that the rectangular system appears to saturate more quickly than the circular system. This is demonstrated by the decrease in response for the 33 nM concentration to the 67 nM concentration for the rectangular system. In the circular system the 67 nM injections still give the higher responses than the prior injections at 33 nM. This, in turn, indicates that the sample transport to the surface is more efficient in the rectangular system, and consequently support the analysis above, that mass transport limitation has a significant influence on the sensor responses. 5. Summary and conclusions Impedance analysis and subsequent data extraction of the three different sensor crystals showed that the smaller sensors had significantly higher Q-values in air, but that the application of liquid load onto the electrodes lowered the Q-values radically for all crystals. Under liquid load Q-values for the standard circular and the rectangular sensors were similar whereas the Q-value for the small circular sensor was 50% higher, which makes it an interesting subject for further investigations. Since the dampening from the flow cell was not accounted for in the Q-value measurements, the actual Q-value during QCM operation may differ from those derived here. The higher noise level and a high sensitivity to the flow cell attachment to the crystal indicate that

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the impact of flow cell dampening may be significant for certain sensors. The QCM experiments showed that it was possible to design a QCM system with a rectangular crystal electrode that is fully functional in a liquid environment. Compared to a standard QCM system with circular electrodes the rectangular system had a higher noise level, possibly due to higher pressure drop throughout the flow cell combined with a higher sensitivity towards the attachment of the flow cell to the crystal surface. The rectangular system, however, showed higher and more rapid responses for series of sample injections of antibodies at various concentrations, which indicate that the mass transport of sample down to the surface was more efficient in the rectangular system. This is further supported by the fact that the rectangular system saturated more quickly with a series of consecutive sample injections. The higher rate of mass transport to the surface is consistent with a higher linear flow velocity over the surface, which is a consequence of the uniform and lower cross sectional area of the rectangular flow cell. In summary, this initial study of crystals with smaller and rectangular electrodes for QCM usage has shown that there exist a significant potential for improvement of sensor performance by optimising the sensor electrode size and shape together with the flow cell geometry. Acknowledgements The authors gratefully acknowledge the helpful comments of Bertil H¨ok, fruitful discussions with Ventsislav Yanchev and the experimental assistance of Thomas Weissbach. The authors further acknowledge the financial support from the Swedish Research Council and Attana AB. References [1] A. Katerkamp, Chemical and Biochemical Sensors, Ullman’s Encyclopedia of Industrial Chemistry, Wiley/VCH Verlag GmbH, 2001. [2] C. Duschl, in: E. Gizeli, C. Lowe (Eds.), Biomolecular Sensors, Taylor and Francis, London, 2002, pp. 87–120. [3] W. Gopel, P. Heiduschka, Interface analysis in biosensor design, Biosens. Bioelectron. 10 (1995) 853–883. [4] G. Sauerbrey, Z. Phys. 155 (1959) 206. [5] C. Fredriksson, S. Kihlman, M. Rodahl, B. Kasemo, The piezoelectric quartz crystal mass and dissipation sensor: a means of studying cell adhesion, Langmuir 14 (1998) 248–251. [6] J.A. Forrest, K. Dalnoki-Veress, J.R. Dutcher, Brillouin light scattering studies of the mechanical properties of thin freely standing polystyrene films, Phys. Rev. E 58 (1998) 6109–6114. [7] Y.-C. Liu, C.-M. Wang, K.-P. Hsiung, C. Huang, Evaluation and application of conducting polymer entrapment on quartz crystal microbalance in flow injection immunoassay, Biosens. Bioelectron. 18 (2003) 937–942. [8] Y.S. Fung, Y.Y. Wong, Self-assembled monolayers as the coating in a quartz piezoelectric crystal immunosensor to detect salmonella in aqueous solution, Anal. Chem. 73 (2001) 5302–5309. [9] I. Mannelli, M. Minunni, S. Tombelli, M. Mascini, Quartz crystal microbalance (QCM) affinity biosensor for genetically modified organisms (GMOs) detection, Biosens. Bioelectron. 18 (2003) 129–140. [10] O. Hayden, R. Bindeus, C. Haderspock, K.-J. Mann, B. Wirl, F.L. Dickert, Mass-sensitive detection of cells, viruses and enzymes with artificial receptors, Sens. Actuators B: Chem. 91 (2003) 316–319.

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Biographies Henrik Anderson received his MSc degree in chemical engineering from the Royal Institute of Technology, Sweden, in 2000 and currently holds a position as PhD student at the Department of Solid State Electronics, Uppsala University, Sweden. His research interest is in development of biosensors with regards to transducer and surface chemistry development as well as the development of new applications of QCM biosensors. Mr. Anderson is co-founder of Attana AB. Mats J¨onsson received his MSc degree in material engineering in 2000 and his PhD in Engineering Science with specialization in Microsystems Technology ˚ in 2006 at the Angstr¨ om Laboratory, Uppsala University, Sweden. His research interest is in development of micro systems for biotechnology applications, especially in electric manipulation of bio-particles and QCM-technology. Lars Vestling received his MSc degree in engineering physics and his PhD degree in electronics from Uppsala University, Sweden, in 1996 and 2002, ˚ respectively. He is currently working at the Angstr¨ om Laboratory, Uppsala University, Sweden, as a researcher. His research interests are primarily in the fields of high-frequency and high-voltage MOS-based devices, modelling, and characterization. Ulf Lindberg received his MSc degree in engineering science in 1985 and his PhD degree in solid state electronics in 1993, both at Uppsala University, Sweden. After working at Biacore AB with microfluidics, he rejoined the Department of Solid State Electronics at Uppsala University in 2000. He is currently head of the microstructure technology group with a special interest in Bio-MEMS. Teodor Aastrup received his MSc degree in materials physics at Uppsala University in 1994 and his PhD at the Royal Institute of Technology, Sweden, in 1999. Dr. Aastrup is co-founder and CEO of Attana AB.