Sensors and Actuators B 61 Ž1999. 68–74 www.elsevier.nlrlocatersensorb
Maximum separation-distance for a separated-electrode piezoelectric sensor in non-electrolyte liquids. Application to determination of the adsorption human immunoglobulin G onto quartz surface Qi Kang a , Xia Wu b, Yanhui Xue a , Xueyong Liu b, Dazhong Shen a
b,)
Shandong Institute of Mining and Technology, 271019, Taian, China b Chemistry College, Shandong UniÕersity, 250100, Jinan, China
Received 4 November 1998; received in revised form 23 July 1999; accepted 26 July 1999
Abstract In a separated-electrode piezoelectric sensor ŽSEPS., the two excitation electrodes are separated by solution layers. An oscillation condition expressed as, 2 PN F Ž b q 1 q b 2 ., is given for the SEPS to set up its stable oscillation in a non-electrolyte liquid. Here, P s 1 q CorC1 q CorC2 , N s R q v Co , v s 2p F. Co , R q and F are the static capacitance, motional resistance, oscillation frequency of the quartz crystal, respectively. C1 and C2 are the solution capacitance. b is a parameter related to the phase of oscillator. According to this oscillation condition, there is a maximum separation-distance Ž Dmax . between the two excitation electrodes. It is shown that the Dmax values is proportional to the permittivity of the liquid and decreases with increasing viscosity and density of the liquid phase. The SEPS was applied for the determination of the adsorption density of human immunoglobulin G onto quartz surface. q 1999 Elsevier Science S.A. All rights reserved.
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Keywords: Piezoelectric sensor; Quartz crystal; Adsorption; Protein
1. Introduction In a separated-electrode piezoelectric sensor ŽSEPS., the two excitation electrodes are separated by solution layers w1–3x. The high-frequency alternating electric field,which induces a shear vibration of the quartz crystal with resonant frequencies in the megahertz ŽMHz. region, is applied to the quartz disc through the liquid layer Žsee Fig. 1A.. Consequently, the oscillation ability of the SEPS depends obviously on the conductance of the liquid layer. In a previous paper, the cease-to-oscillate behavior of the SEPS in electrolyte solutions was investigated w4x. It is shown that the SEPS ceases to oscillate if the separationdistance between the two excitation electrodes is larger than a critical value. The critical value is called the maximum separated-distance Ž Dmax ., which is used to describe the oscillating ability of the SEPS. And the dependence of the Dmax values of the SEPS on solution conductivity was reported. In the present paper, the oscilla-
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Corresponding author. Fax: q86-531-8565211; e-mail:
[email protected]
tion ability of the SEPS in non-electrolyte liquids was discussed. The dependencies of the Dmax value on the permittivity, viscosity and density of non-electrolyte liquids were investigated. As discussed in a previous paper w3x, the electric behavior of the SEPS, in the frequency frame of the quartz crystal, can be described by the equivalent circuit model in Fig. 2. Based on the model, the oscillation condition for the SEPS was derived and expressed as following w4x
(
P F b q 1 q b 2 r2 N
ž
Ps1q
Ž 1.
/
v Co Ž v C1 y b G 1 . G12 q v 2 C12
q
v Co Ž v C 2 y b G 2 . G 22 q v 2 C22
Ž 2. where N s R q v Co , v s 2p F. Co , R q and F are the static capacitance, motional resistance and fundamental frequency of the quartz crystal respectively. C1 and C2 are the solution capacitance, G 1Žs 1rR1 . and G 2 Žs 1rR 2 . the solution conductance, respectively. b is a parameter related to the phase of oscillator, which depends on the type of oscillator and its operating conditions. The typical b value for the oscillator used in this paper is 1.18.
0925-4005r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 5 - 4 0 0 5 Ž 9 9 . 0 0 2 8 1 - 6
Q. Kang et al.r Sensors and Actuators B 61 (1999) 68–74
69
Eq. Ž6. reveals that there is a maximum separation-distance Ž Dmax . for the SEPS. If the separation-distance between the two excitation electrodes is greater than Dmax , the SEPS will cease to oscillate. It can be seen that the Dmax value is proportional to the A ´ and decreases with increasing R q value.
2. Experimental 2.1. Apparatus and reagents
Fig. 1. ŽA. Schematic diagram of the SEPS system in oscillational ability experiment. Ž1. Blank piezoelectric quartz crystal disc. Ž2. Separatedelectrode; Ž3. Detection cells. ŽB. Schematic diagram of the simulated SEPS setup in oscillational ability experiment. Ž1. Normal piezoelectric quartz crystal; Ž2. Separated-electrode; Ž3. Aluminum electrode connected to the excitation electrode on the quartz surface; Ž4. Cell ŽI. for viscosity and density influence; Ž5. Cell ŽII. for permittivity influence.
When the cells in the SEPS were filled with a non-electrolyte liquid, the permittivity of the liquid layer was the dominant way for the conductance of the high-frequency alternating electric field. The liquid layers in the cells act like the capacitors of C1 and C2 . Under the condition of G 1 < v C1 ,G 2 < v C2 , Eq. Ž2. can be simplified as Ps1q
Co
Co
q
C1
Ž 3.
C2
where C1 s ´ A1rD1 , C2 s ´ A 2rD 2 . A1 and A 2 are the areas of the separated-electrodes, D 1 and D 2 are the distances between the separated-electrode and the quartz crystal disc. ´ is the permittivity of the liquids. By combining Eqs. Ž1. and Ž3., we get 1 C1
(
bq 1qb 2
1 q
F
2 Rq v
C2
Co2
1
The configuration of the SEPS used in the oscillational ability experiment was shown in Fig. 1A. A 5 MHz AT-cut polished blank piezoelectric quartz crystal disc Ždiameter of 12.5 mm, Beijing No 707 Manufacturing. was fixed between two glass tubes Žinternal diameter of 10 mm, external diameter of 14 mm. with silicone resin. The solutions in the two detection cells were insulated for a direct current signal. Two platinum disc electrodes with diameter of 8 mm were used as the separated-electrodes. The separated-electrodes were concentric with the quartz disc, and their leading wires were short as possible. The two leading wires were physically fixed with a parallel distance of f 10 cm. A TTL oscillator Ždesigned and built by the last author. was employed to drive the SEPS, its oscillating frequency being recorded by a frequency counter ŽModel 7200, Shijiazhuang No 4 Radio Factory.. An impedance analyzer ŽHP 4192A. was used to measure the equivalent circuit parameters of the solution and the quartz crystal. All the experiments were performed at room temperature of 258C. Each experiment was carried out three times and the averaged value was reported. Human immunoglobulin G ŽIg G. was purchased from Sigma. The water used was passed through an ion exchanger, then distilled twice in a quartz still. All chemicals were of analytical grade or better. Phosphate buffered saline ŽPBS, pH s 7.4, 0.01 mol ly1 phosphate, 0.15 mol ly1 NaCl and 0.1% NaN3 . was employed in the adsorption experiment. Ig G solutions were prepared with the PBS. The stock solution of Ig G was stored at q48C.
Ž 4.
y Co
With the same test solution filled in the two cells in the SEPS, Eq. Ž4. can be expressed as: D1 A1
q
D2 A2
F
ž
(
bq 1qb 2 2 Rq v
Co2
1 y Co
/
´
Ž 5.
Under our experimental conditions, A1 f A 2 s A, Eq. Ž5. is rewritten as
Ž D1 q D 2 . F
ž
(
bq 1qb 2 2 R q v Co2
1 y Co
/
A ´ s Dmax
Ž 6.
Fig. 2. Equivalent circuit for the SEPS. C1 , C2 , solution capacitance; R1 , R 2 , solution resistance; Co , Lq , R q , Cq , static capacitance, motional inductance, motional resistance and motional capacitance of the quartz crystal.
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2.2. Maximum separation-distance for the SEPS in nonelectrolyte liquid The test liquid with known properties was introduced into the detection cells in the SEPS. The distance between the two separated-electrodes was increased gradually until the SEPS ceases to oscillate suddenly. This critical separation-distance is recorded as the maximum separation-distance Ž Dmax .. For the need of the theoretical analysis, the SEPS was connected to the impedance analyzer for the measurements of P value and equivalent circuit parameters of the quartz crystal. First, the total series capacitance of between the two separated-electrodes at the maximum separation-distance, CS , was measured at the measuring frequency of 4.5 MHz and 5.5 MHz. The averaged CS value at the two frequencies was used for the calculation of P value. Because the measuring frequencies used were far beyond the resonant frequency frame of the quartz crystal, the motional branch of the quartz crystal is cut off in the measurements. Thus the quartz crystal is simply equivalent to capacitor of Co . According to the equivalent circuit model in Fig. 2, we have 1
1 s
CS
1 q
C1
1 q
Co
C2
Ž 7.
Hence, the value of P can be estimated by P s CorCS . To estimate the equivalent circuit parameters of the blank piezoelectric quartz crystal, the equivalent circuit parameters of the SEPS were measured by an admittance analysis method w5x. According to equivalent circuit model in Fig. 2, the behavior of the SEPS will be close to that of the quartz crystal if the separated distance approaches to zero. Hence, we measure the equivalent circuit parameters of the SEPS with different distances. Extended the separated distance to zero, the equivalent circuit parameters of the quartz crystal can be obtained.
Fig. 3. Experimental setup of the SEPS for in situ measurement of protein adsorption. Ž1. Oscillator amplifier; Ž2. Frequency counter. Ž3. Blank piezoelectric quartz crystal disc; Ž4. Graphite electrode, Ž5. Platinum grid electrode; Ž6. Stirrer; Ž7. Cell filled with by 1 mol ly1 KCl solution; Ž8. Cell for protein adsorption.
Under the condition of mild stirring, the stable oscillating frequency, F0 , was recorded as the reference. An accurate amount of Ig G was added in the cell. The oscillation frequency, F1 , was recorded with a time window of 10 s. After an adsorption time of 20 min, the decrease in oscillation frequency, D F1 s F10 y F0 , was used for the estimation the total adsorption mass Ž G 1 .. Then the Ig G solution was replaced by the PBS, the stable oscillation frequency, F2 , was recorded again. The increase in frequency, D F2 s F2 y F10 , was used for the estimation of desorption mass of Ig G rising by the PBS Ž G 3 .. After that the quartz crystal and the cell was rinsed repeatedly with 10% sodium dodecyl sulfate and water to remove the protein adsorbed. The SEPS renewed can be used for an another adsorption experiment.
2.3. Adsorption of Ig G on quartz surface 3. Results and discussion The experimental setup of the SEPS for the in situ protein adsorption was illustrated in Fig. 3. The detection cells of the SEPS were made of Teflon with volume of f 1.2 ml. The left cell was filled with 1 mol ly1 KCl solution for electric conduction. The right cell was used for the protein adsorption measurement. The distance between the separated-electrode and the quartz disc was f 2 mm. Before the determination of adsorption, the quartz crystal disc surface in the right cell was cleaned carefully with NH 4 OH:H 2 O 2 :H 2 O Ž 1:1:5, v:v:v . following by HCl:H 2 O 2 :H 2 O Ž1:1:5, v:v:v., then rinsed repeatedly with water and PBS. Then 1 ml of the PBS was addition into the right cell of the SEPS. Then the platinum grid electrode was put into the cells.
3.1. Dependence of Dm a x on permittiÕity in non-electrolyte liquids In a given liquid, the separation-distance between the two separated-electrodes of the SEPS should be less than a critical value. If the separated-distance is larger than the critical value, the SEPS will cease to oscillate suddenly. In this case, the oscillating frequency of the oscillator is far beyond the fundamental frequency of the quartz crystal, and the frequency stability is rather poor Ž D F ) "5 kHz.. In fact, a parasitic oscillation of the oscillator was monitored by the frequency counter under such situation. According to Eq. Ž6., the Dmax value of the SEPS is propor-
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tional to the permittivity of the liquid layer. The oscillating ability of the SEPS increase with increasing permittivity. To test this expectation, the Dmax values in mixture of ethanol–water were measured. The permittivity of the mixture increases with increasing water content. As shown in Fig. 4, however, the Dmax value is not in a linear correlation with the permittivity. The reason is that the R q values of the quartz crystal vary with the composition of the mixture Žsee curve 3.. It was shown that the R q value is proportional to Žhr .1r2 w6x, where h and r are the viscosity and density of the liquid, respectively. In the mixture of ethanol–water, the viscosity and density of the liquid are related to the composition of the mixture w7x. As the water content increases from 0% to 50%, the R q values also increase. According to Eq. Ž6., the increase in R q results in the decrease in Dmax . Because part of the increase in Dmax arising from the increase in permittivity is offset by the influence of R q , the Dmax value increases slightly. However, the R q values decrease with the water content in the range of 50 to 100%, which results in an extra increase in Dmax . As a result, the increase in Dmax is more obvious than that in the mixture with water content from 0 to 50%. 3.2. Dependence of Dm a x on Õiscosity and density in non-electrolyte liquids As discussed above, the Dmax value increases with increasing R q value, which is proportional to Žhr .1r2 . The dependence of Dmax on viscosity and density was investigated in the mixture of water–glycerin. With increasing concentration of glycerin, the viscosity and density of the mixture increase w7x. As can be seen in Fig. 5, with increasing Žhr .1r2 , the Dmax value or the oscillating abil-
Fig. 4. Dependence of the maximum separated-distance on the permittivity in ethanol–water mixture. Ž1. Dma x in the SEPS; Ž2. Dmax in the simulated SEPS; Ž3. R q .
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Fig. 5. Dependence of the maximum separated-distance on the viscosity and density in glycerin–water mixture. Ž1. Dma x in the SEPS; Ž2. Dmax in the simulated SEPS; Ž3. R q .
ity of the SEPS decreases. The decrease in Dmax supports the theoretical analysis of Eq. Ž6.. It should be noted that the viscosity is the main influence factor in the mixture as the increase in viscosity is much greater than that in density. The decrease in Dmax value is mainly due to the increase in R q value Žcure 3.. But the permittivity of the mixture decreases slightly as the concentration of glycerin increases, which also causes a small extra decrease in Dmax value. 3.3. InÕestigate the influence of liquid properties on Dm a x by a simulated setup As discussed above, the Dmax value depends mainly on two factors. One is the conductance property of the liquid, which is related to the permittivity in non-electrolyte liquids. Another is the energy loss by oscillating quartz crystal surface to liquid, which is related to the viscosity and density of the contacted liquid. Because the correlation among the liquid properties, it is difficult to difference the influence of the factors on the Dmax value in the SEPS in Fig. 1A. For the convenience of the discussion in the influence factors, a simulated setup was constructed based on the equivalent circuit model of the SEPS. As shown in Fig. 1B, a 5-MHz normal piezoelectric quartz crystal was used in the simulated setup. The excitation electrodes on the surfaces of the quartz crystal were connected to aluminum discs with diameter of 10 mm. The high-frequency alternating electric field was applied to the quartz crystal by the conductance of the liquids in cell ŽII.. The energy loss of the quartz crystal is related only to the liquids in cell ŽI.. In the experiment for permittivity influence, ethanolmixture is filled in cell ŽII. and water in cell ŽI.. Thus, the
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R q value maintains constant and the change in Dmax is due only to the influence of permittivity. As can be seen in Fig. 4 Žcurve 2., a good linearity between the Dmax and permittivity was obtained under in the simulated setup, which supported the expectation of Eq. Ž6.. In addition, according to Eq. Ž1., the critical P value should be the same in the mixture. By using the values of b s 1.18, F s 5 = 10 6 Hz, R q s 420 V, Co s 12.2 = 10y1 2 F, the critical P value in Eq. Ž1. is equal to 8.47. The mean of the 11 critical P values experimentally measured in curve 2 is 7.95 with the relative standard deviation of 8.6%. It can be seen that the critical value expected from Eq. Ž1. agrees well with that experimentally measured. In the experiment for the influence of viscosity and density, water–glycerine mixture is filled in cell ŽII. and water in cell ŽI.. As shown in Fig. 5, the Dmax values in the simulated setup Žcurve 2. is a little greater than that in the SEPS Žcuver1.. The difference between the two curves is due to the fact that the permittivity of the mixture does not influence the Dmax value in this simulated setup. Eq. Ž1. reveals a linear relationship between the critical P value and Ny1 . The regression relationship between the critical P values and Ny1 in Figs. 4 and 5 is given by:
ployed to investigate the adsorption of proteins onto different surfaces. In this paper, the adsorption process of Ig G onto quartz surface was monitored by the SEPS method. When Ig G is adsorbed onto the quartz surface, the mass load of the quartz crystal increases, which will cause a decrease in the frequency of the SEPS. According to the Saurbery equation w8x, the relationship between the adsorption density Ž G in g cmy2 . and the frequency shift Ž D F in Hz. is expressed as:
P s 1.27Ny1 q 0.31 Ž n s 44, r s 0.991 .
D F1 t s 61.24exp Ž ytr4.31 . q 13.57
Ž 8.
The slope of P vs. Ny1 is in good agreement to the theoretically expected value of 1.36 in Eq. Ž1.. 3.4. In situ determination of protein absorbed onto quartz surface by the SEPS method The extensively use of the piezoelectric quartz crystal as microgravimetric sensors was originated from the pioneering work of Sauerbrey w8x, who demonstrated that a shift in the resonant frequency of an oscillating AT-cut quartz crystal is related to the change in mass at the surface of the device. Piezoelectric sensors are suitable for time-resolved in situ measurements and can be manufactured in large quantity at low cost. As the blank quartz surface is in a direct contact with the liquid phase, the SEPS is a useful tool for in situ monitor the mass change onto the quartz crystal surface. In this paper, the SEPS was applied to monitor the adsorption of protein onto the quartz surface. Proteins have an amphiphilic nature and they therefore have a strong tendency to adsorb at different interfaces. The adsorption of protein at solid surfaces constitutes a research area which receives increasing attention w9,10x. Often, this interest originates from the importance of the interfacial behavior of proteins in a variety of applications in medicine, biotechnology, diagnostics and food technology. Various techniques such as ellipsometry w11–13x, radiolabeling w14x, surface plasmon resonance w15x, total internal reflection fluorescence w16x, surface forces technique w17x and quartz crystal microbalance w18x were em-
G s D mrA s yD Fr2.26 = 10y6 F 2
Ž 8.
where D m is the adsorption mass and A the geometric area of the quartz crystal. For a quartz crystal with fundamental frequency of 5 = 10 6 Hz, according to Eq. Ž8., the frequency decrease of 1 Hz corresponds to the adsorption density of 0.0177 mg cmy2 .I As shown in Fig. 6, the frequency of the SEPS decreases upon injection of Ig G. It can be seen that the adsorption rate decreases with adsorption time. After an adsorption time of 20 min, the increase in adsorption density was small. The regression relation between the frequency shift Ž D F1t , Hz. and adsorption time Ž t, min. is given by:
=exp Ž ytr23.89 . y 75.13
Ž 9.
This adsorption kinetics curve is coherent with the two-steps adsorption model w19x. In this model, the initial adsorption process is rapid, the adsorbed protein will undergo conformation rearrangement.
Fig. 6. Frequency changes as a function of time for the adsorption of Ig G onto quartz surface. wIg Gx s 0.50 mg mly1 .
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tion, the true surface area of the quartz crystal is greater than its geometric area. As a result, the true adsorption densities should be less than the apparent data in Fig. 7.
4. Conclusions Theoretical analysis and experimental measurements show that the oscillating ability of the SEPS, described by the maximum separation-distance, increases with increasing permittivity or decreasing viscosity and density of the liquid layer. 2 PN F Ž b q 1 q b 2 . is the necessary condition for the SEPS to oscillate. The SEPS is a useful tool for in situ measurement the mass change onto the quartz crystal surface. The SEPS method was applied to monitor the adsorption process of Ig G on quartz surface.
(
Fig. 7. Adsorption isotherms of Ig G onto quartz crystal surface. G 1 s total adsorption density for 20 min adsorption; G 2 sadsorption density after rinsing with PBS; G 3 sdesorption density by the rinsing with PBS.
Acknowledgements Upon rinsing with the PBS, part of Ig G adsorbed on quartz crystal surface is desorbed, thus the frequency of the SEPS increases. According to the increase in the frequency, the amount desorbed by the rinsing, G 3 , can be estimated, which may be considered as the part of reversible adsorption. Then the amount of Ig G adsorbed irreversibly on quartz surface, G 2 , was calculated by G 2 s G1 y G 3.
This work is financially supported by the National Science Foundation of China and the National Climb Research Plan of China.
References
3.5. Adsorption isotherm of Ig G on quartz crystal surface Fig. 7 shows the adsorption isotherms of Ig G onto quartz crystal surface. It can be seen that the values of G 1 , G 2 and G 3 increase with increasing concentration of Ig G. After a concentration of 0.1 mgrml, there is a slight increase in G 3 , the slopes of adsorption isotherms for the total adsorption and irreversibly adsorption decrease at higher concentration of Ig G. The result may be explained below. With increasing Ig G concentration, the adsorption rate increases, the possibility for the Ig G adsorbed to undergo conformation rearrangement decreases. The protein layer adsorbed appears to have lower affinity to quartz surface. As a result, the fraction of Ig G desorbed by rinsing with the PBS increases with increasing bulk concentration. It should be noted that the data in Fig. 7 were the apparent adsorption densities. It is difficult to estimate the true adsorption densities according only to the frequency shifts of the SEPS. One reason is that the Sauerbrey equation is frequently not valid in solution because the protein layer adsorbed is not rigid. Another one is that hydrated rather than dry protein was detected. Consequently, the adsorption densities measured include also water and electrolyte bound to the protein layer. In addi-
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Qi Kang received a BSc in Analytical Chemistry from Shandong University in 1984. Since July 1984, she works in Shandong Institute of Mining and Technology, she earned an MSc in Organic Chemical Engineering from China University of Mining and Technology in 1996. She is an associate professor in December 1996. Her research interests include organic chemistry and analytical chemistry. Xia Wu received a BSc in Analytical Chemistry from Shandong University in 1987. Since July 1987, she has been working at Chemistry College, Shandong University. She has been a lecturer since 1992. Her research interests include analytical chemistry and inorganic chemistry. Yanhui Xue received a BSc in Analytical Chemistry from Chengdu Institute of Geology in 1983. After spending 12 years as Assistant Engineer and Engineer in Team for Svlvite of Chemistry Industry Ministry. He is a lecturer in Shandong Institute of Mining and Technology in 1994. His research interest is environmental chemistry. Xueyong Liu received a BSc in Chemistry from Shandong Normal University 1985. He earned his MSc in Inorganic Chemistry from Shandong University in 1994. He is an Engineer at Chemistry College, Shandong University since 1995. His research interests are inorganic chemistry and crystal material. Dazhong Shen received a BSc in Analytical Chemistry from Chengdu Institute of Geology in 1983. After spending 5 years as a teaching assistant in Shandong Institute of Mining and Technology, he earned a PhD in Analytical Chemistry from Hunan University in 1994. Since October 1998, he is a professor in Chemistry College, Shandong University. His research interests include electroanalytical chemistry and chemical sensors.