3055

Sensors and Materials, Vol. 31, No. 10 (2019) 3055–3066
MYU Tokyo
S & M 1992

Distinguishing Mass Loading Effect from
Damping Loading Effect of Piezoelectric Immunosensor
Using Energy Transfer Model
Yan Chen,1* Feng Tan,2 and Wen Cao1
1

Southwest University of Science and Technology, Mianyang 621010, China
University of Electronic Science and Technology of China, Chengdu 611731, China

2(Received June 30, 2019; accepted September 12, 2019)

Keywords: piezoelectric (PZ) immunosensor, energy transfer model (ETM), mass loading effect,
damping loading effect, NuTu-19 IgG

For a piezoelectric (PZ) immunosensor operating under damping loading conditions, themass loading and damping loading effects cannot be distinguished by frequency measurement
alone. In this work, a special relationship between the vibrational amplitude on the surface
of a quartz crystal and the viscosity and density product of the tested liquid is derived using
the energy transfer model (ETM). To detect the NuTu-19 antibody concentration in immune
serum, we simultaneously measure the resonant frequency and rectified load voltage of the PZ
immunosensor. Excellent agreement is obtained between the ETM-calculated value and theactual value obtained by the Bradford method. The experimental results proved the correctnessof the deduced equation and showed that the presented analytical method laid a foundation forfurther development of all types of quartz crystal sensors in the liquid phase.

1.

Introduction

In recent years, the attention of many researchers in the fields of medicine and electronic
information has been concentrated on piezoelectric (PZ) immunosensors. It is an ultrasensitive
mass biosensor that combines the highly sensitive PZ effect of quartz crystals and the highly
specific recognition of immunoreaction. The very small change in mass caused by antigen–antibody binding is identified by a corresponding change in the resonant frequency of the quartz
crystal. Yang et al.(1) and Chen et al.(2) used PZ immunosensors to detect cervical and ovariancancer in women; Montoya et al.(3) used them to detect tuberculosis; Pirinçci et al.(4) used themto detect ochratoxin A. Test results showed that in addition to some influencing factors, such as
test temperature, humidity, and circuit jitter, there are still errors. These errors are sometimes
large, and more severe cases can result in false positive rates. The reason for this is that theapplication is based only on the Sauerbrey theory.(5)There are several points worth noting with respect to the accurate application of the
Sauerbrey equation. First, the coating layer on the quartz surface must be thin and uniform*

Corresponding author: e-mail: ychen@swust.edu.cn
https://doi.org/10.18494/SAM.2019.2495
ISSN 0914-4935 © MYU K.K.
https://myukk.org/

3056

Sensors and Materials, Vol. 31, No. 10 (2019)with high rigidity.(6) However, the coatings, whether adhesive or bioactive substances,are viscoelastic films that give rise to a change in resonant frequency on account of theiranelastic effect.(7,8) Therefore, if we blindly ascribe the total frequency variation of the PZ
immunosensors to the change in mass on the surface of the quartz crystal, we will introduce
analytic error.(9) Second, the mass attached to the quartz electrode surface is limited, usuallyless than 2% of the mass of quartz.(10) When the mass exceeds the tolerance, the quality
factor of the resonator will drop sharply, significantly reducing the accuracy of measurement.
Moreover, the resonator may even stop.(11) This poses a serious challenge to the operationof medical experiments. In addition, the application of gas-phase PZ sensing suffers fromdisadvantages, such as the tedious “dip and dry” process, and the on-line real-time data output
analysis cannot be conducted.
Fortunately, the liquid-phase detection method using a PZ immunosensor can avoid the above
disadvantages, but new problems are introduced. Martin et al.(12) pointed out that when a PZ
sensor is operated in the liquid phase, both the mass loading and liquid damping loading effects
can contribute to the change in resonant frequency. Therefore, it is impossible to distinguishthe two different loading effects by frequency measurement alone. The modified ButterworthVan Dyke model (M-BVD)(12) and quartz crystal microbalance-D (QCM-D)(13) are the two mostcommon methods of analyzing the loading effects. Nevertheless, they are not practical. In the
M-BVD model, both the dynamic resistance and the resonant frequency must be measured.(13,14)
Since many component parts of the circuit have the equivalent impedance, the measurement iscomplicated. On the other hand, a small external interference easily interferes with the QCM-D
method, resulting in inaccurate analysis results.
The goals of the present work are (i) to derive the explicit relationship between the vibration
amplitude on the surface of quartz crystal and the viscosity and density product of the tested
liquid using the energy transfer model (ETM), (ii) to detect NuTu-19 IgG from immune serumin the liquid phase by measuring both the resonant frequency and the vibration amplitude, and (iii)
to distinguish the effect of mass loading from that of damping loading on a PZ immunosensor
using the measured data.

2.
2.1

Materials and Methods
Methods

2.1.1 Analysis of loading effect on PZ immunosensor using ETM
In the gas phase, the relationship between the changed mass and the corresponding changed
frequency was shown by Sauerbrey(5) in 1959 as
2nf q2 ∆m,∆f m =−µq ρ q S(1)

Sensors and Materials, Vol. 31, No. 10 (2019)3057

where Δm is the weight change on the surface quartz crystal, S is the area of the electrodesurface, n is the overtone number, fq is the fundamental frequency of the quartz crystal, μq is
the shear modulus of quartz, ρq is the density of quartz, and Δfm is the observed frequency shift
caused by the mass loading effect.
In the liquid phase, the frequency change was described in terms of the viscosity and density
product as(15)∆f L =−

3f q2

πµq ρ q(2)

ρ Lη L ,where ρL and ηL are the density and absolute viscosity of the attached liquid, respectively, andΔf L is the observed frequency shift caused by the liquid loading effect.
In fact, owing to the effect of the microstructure on the quartz electrode surface, the massloading effect will also be caused by the deposited liquid film under certain conditions,(12) asshown by3
 2nf q2 ∆m
f q2∆ftotal = ∆f m + ∆f L = − +
πµq ρ q
 µq ρ q Aρ Lη L  ,




(3)

where Δftotal is the measured total frequency shift. Therefore, the two different loading effects
cannot be distinguished by the frequency testing theory alone in a liquid environment.
The main idea of the ETM is that the PZ resonator and deposited film form a compound
resonator. When a foreign film is deposited on the surface of the quartz crystal, a portion of theenergy stored in the unloaded resonator vibration system will be transferred to the film. The
transferred energy will be shared between the stored and dissipated energies in accordance withthe elastic and anelastic properties of the deposited film, respectively. It is assumed that thefilm deposited on the quartz surface does not have its own vibrational frequency, but vibrates
synchronously with the quartz crystal surface with a frequency fc(16) corresponding to that of
the compound resonator.
Sauerbrey’s experimental data led to the conclusion that the mass sensitivity depends on thevibrational amplitude distribution on the surface of the quartz crystal resonator. It has beenstated that the mass sensitivity of a PZ immunosensor with a configuration of two identicalcircular and concentric electrodes follows a Gaussian-like distribution. Therefore, we assume
that the vibrational amplitude distribution on the unloaded quartz resonator surface obeys
 πr 
A(r ) = A0 cos 2 , 2 Re 

(4)

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Sensors and Materials, Vol. 31, No. 10 (2019)

where A0 is the maximum amplitude of vibration at the quartz resonator surface, Re is theradius of the electrode, which is smaller than or equal to that of the quartz crystal, and r is the
distance of a certain point on the quartz surface from the center of the plate. Furthermore, thevibrational amplitude of every point within the quartz resonator can be defined as(16,17)
π y  2  πr A(r , y ) = A0 sin  cos ,
 hq 
 2 Re (5)where A0 = A(0, hq/2), −hq/2 ≤ y ≤ +hq/2, and hq is the thickness of quartz. Then, theinfinitesimal energy unit stored in an unloaded quartz crystal resonator is(18)=dEqs

π y  4  πr 
1 2 2
1
=
ωq A (r , y )dmρ qωq2 A02 sin 2  cos  rdr dφ dy, hq 
22
 2 Re (6)where 0 ≤ ϕ ≤ 2π, 0 ≤ r ≤ Re. The stored vibrational energy of the unloaded quartz crystal
resonator can be obtained as
=
Eqs

1
1 
 3
ρ q hqωq2 A02π Re 2  − 2  .
2 16 π (7)

When a foreign film is deposited on the quartz resonator surface, in accordance with themain idea of the ETM, it vibrates synchronously with the quartz resonator surface at a newresonant frequency fc. When the film is completely elastic, the amplitude of the resonator will
not be affected by shear wave propagation. The vibrational amplitude within the adhesive film
will be identical to that of the unloaded resonator, A0. The energy transferred from the unloaded
quartz resonator will be stored in the film, thus there is no energy loss. However, when thedeposited film is anelastic, there is frictional force between adjacent cell layers. A portion of
the transferred energy will be lost, resulting in the attenuation of the resonant amplitude, andthe rest of the transferred energy will be stored in the film, maintaining its own vibration. In
this case, the vibrational amplitude of the quartz surface is Alq, and the vibrational amplitude ofthe deposited film can be expressed as
1 
1



2
2












ω
ω
r
r
π
π
c
c
A f (r , y ) =A1q cos 2  y  = A1q cos 2  vf t, exp  −  exp  − 
 2 Re  2 Re   2γ f    2γ f 






(8)

where γf = ηf / ρf is the kinematic viscosity of the attached film and vf is the velocity for a shear
wave traveling in the anelastic film. The vibration amplitude of the compound resonator isshown in Fig. 1.

Sensors and Materials, Vol. 31, No. 10 (2019)

Fig. 1.

3059

Vibration amplitude of quartz-anelastic film.

The total vibrational energy dissipated by the anelastic film can be expressed as
1



2




 
ω
1
3
1

 
ρ f ωc v f A12qπ Re 2  − 2  × 1 − exp  −2  c  l f   ,
=
E df


2
 16 π    2γ f 


 


(9)

where lf is the thickness of the anelastic film. Then, the rest of the energy of the quartz
resonator is
=
E sfq

1
1 
 3
ρ q hqωc2 A12qπ Re 2  − 2  .
2 16 π (10)

At a constant frequency, we assume that the vibrational energy dissipated within the
anelastic film will decrease the compound resonator vibrational amplitude; thus, from Eqs. (7), (9),and (10), we obtain
1
1 
 3
ρ q hqωq2π Re 2  − 2  ( A02 − A12q )2
 16 π 
1



2




 
ω
1
3
1



ρ f ωc v f A12qπ Re 2  − 2  × 1 − exp  −2  c  l f   .
=2 16 π    2γ f 


 


(11)

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Sensors and Materials, Vol. 31, No. 10 (2019)

Furthermore, the shear wave velocity vf can be determined from the acoustic impedance.(19,20)
1

 ωc ρ f η f  2=
Z  (1 + j ).
2



(12)

Z = ρ f vf .

(13)

Solving both Eqs. (12) and Eq. (13), we have11
 η f 2v f = (π f c ) 2  .
 ρf 
(14)Then, substituting fq = 1/2hq (µq/ρq)1/2, γf = ηf / ρf , and Eq. (14) into Eq. (11), we obtain1=(ρ f η f ) 2

=

1
)2

 A2

f q  20 − 11   A1q
3
 ωc  2   2f c 1 − exp  −2 
 l f 
  2γ f 



 
(πρ q µq

1
)2

(15)

 A2

f q  20 − 1 .
1   A1q
3




π
f c ρ f 2   
2f c 1 − exp  −2 
 l f 
  2η f 



 
(πρ q µq

The exponent in Eq. (15) contains the reciprocal of the characteristic decay length δ, definedas1

 η f 2δ = .
 π fc ρ f 



(16)

Since the thickness of the anelastic film is far greater than the characteristic decay length,
Eq. (15) can be simplified as1=(ρ f η f ) 2

12(πρq µq ) f  A02 − 1 .
3
2
fc

q

 A12q





(17)

Sensors and Materials, Vol. 31, No. 10 (2019)3061

The equation explains the correlation between the product of viscosity and density of theanelastic film and the vibrational amplitude of the resonator surface. Therefore, the amplitude
testing theory can be applied to measuring the damping loading effect on a PZ sensor in adamping environment.
2.1.2 Amplitude testing theory of quartz resonator
Because of the PZ effect, the relationship between the voltage across the quartz-resonator
electrodes and the mechanical strain is shown as(17,21)=V π f e
1 − cos  c   A1q ,ε 
 f q  

(18)

where e is the PZ constant and ε is the quartz permittivity. During testing, the rectified voltage
can be used to represent the amplitude information. Thus, by applying both the amplitudeand frequency testing theories, the two different loading effects can then be successfully
differentiated by solving Eqs. (18), (17), (2), and (3) in turn.
2.2. Materials
To verify the correctness of the theoretical derivation, the concentration of NuTu-19 IgG in
immune serum was tested and verified.
2.2.1 PZ immunosensor selection and preparation
Four 3rd-overtone AT-cut PZ sensors (10 MHz) were obtained from Tangshan Jing Yuan
YuFeng Electronics Co., Ltd. (Hebei, China). Before use, all the sensors must be pretreated bya three-step process. First, the quartz crystals were mechanically cleaned with a cleaning agent
and then with distilled water. Second, the quartz crystals were immersed in 1 mol/L sodiumhydroxide solution for 10 min and then rinsed with distilled water. Lastly, the quartz crystals
were immersed in 1 mol/L hydrogen chloride solution for 10 min, rinsed with deionized water(DW), and then dried in air.
2.2.2 NuTu-19 antigen and antibody preparation
NuTu-19, a rat ovarian cancer cell line, was purchased from American Type Culture
Collection (Manassas, VA, USA) and cultured in accordance with the supplier’s protocols. To
obtain NuTu-19 IgG, inoculated rabbit heart blood was collected under light anesthesia one week
after the last NuTu-19 cell injection. Then, serum IgG was separated using a protein separation
column, and nonimmune rabbit serum was used as a negative control.

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Sensors and Materials, Vol. 31, No. 10 (2019)

2.2.3 NuTu-19 antigen immobilization
NuTu-19 cells were cultured onto the surfaces of preprocessed quartz crystals in Dulbecco’s
modified Eagle medium (DMEM) (Gibco BRL, Grand Island, N.Y.) supplemented with 10%
fetal bovine serum (Gibco BRL, Grand Island, N.Y.) and 100 μg/mL Amikacin. The cells weremaintained in a humidified chamber at 37 °C in 5% CO2 atmosphere. 36–48 h later, the numberof cells reached maximum. Then, the quartz crystals were removed from the humidified
chamber and dipped into 2% paraformaldehyde phosphate-buffered solution for 5 min toenhance cell immobilization.
2.2.4 Measurement procedure
To prevent the frequency stability from being affected by ambient temperature fluctuation,
all tests were carried out in a thermostatic chamber at 25 °C. The resonance frequency f0 of
all preprocessed quartz crystals and the voltage U0 of the unloaded QCM were first recorded.
The quartz crystals on which NuTu-19 cells were immobilized were washed with PBS (pH 7.4)
and DW, and then put in bovine serum albumin (BSA) (0.1 mg cm−3) to reduce the interference
from nonspecific adsorption. After thorough rinsing with PBS and DW, the crystals weredried at 25 °C, and the frequency f1 and voltage U1 were measured in the gas phase. Then, theserum-free NuTu-19 IgG was made to flow over the crystal surface through flow injection.
When the frequency was stable, the frequency f2 and voltage U2 were detected under the liquid
phase condition. Finally, the quartz crystals were covered with NuTu-19 IgG serum. Whenthe reaction between the immobilized antigen and NuTu-19 IgG was complete, the steady-state
resonant frequency f3 was measured, and the steady-state voltage U3 was also recorded under
the liquid phase condition. Figure 2 shows that the target antibody is recognized by the NuTu19 antigen on the electrode surface.

Fig. 2.

(Color online) Reaction process of NuTu-19 antigen and NuTu-19 IgG.

Sensors and Materials, Vol. 31, No. 10 (2019)3.

Results and Discussion

3.1

Loading effect of antigen immobilization

3063

Theoretically, the gas-phase testing was considered to reveal only the mass loading effect,
but the ETM calculation results showed that although the analysis and quantification are carriedout under the gas phase condition, NuTu-19 cell immobilization causes a relatively small
damping loading effect, as shown in Table 1. The main reason for this is that the NuTu-19 cell
membrane does not have strict rigidity with anelastic characteristics.
Figure 3 shows the frequency changes caused by NuTu-19 cell immobilization. Although thefrequencies based on the Sauerbrey theory and those of the ETM were not the same, the error
between the two methods can be ignored upon antigen immobilization. The main reason forthis is that the two curves almost coincide, as shown in Fig. 3, indicating that the damping effectis relatively small. Therefore, the change in frequency can be considered a consequence of thechanged mass of the NuTu-19 cell immobilization; in other words, the damping loading effect of
the NuTu-19 cell film can be ignored in gas phase measurements.
3.2

Interaction

When the serum without NuTu-19 IgG was made to flow over the PZ sensor electrodesurface, the resonator was markedly affected by liquid damping and its output amplitude

Table 1Mass loading effect and damping loading effect on the surface of crystals caused by NuTu-19 cell immobilization.
Crystal1﹟2﹟
3﹟
4﹟
ΔU1 (mV)
10
15
23
28
276
310
402
479
Δftotal1 (Hz)
272
303
393
468
Δfm1 (Hz)47911Δf L1 (Hz)ΔU1 is the changed voltage in the gas phase after NuTu-19 cell immobilization, ΔU1 = U1 − U0, Δftotal1 is the measured totalfrequency shift in the gas phase after NuTu-19 cell immobilization, Δftotal1 = f1 − f0, Δf m1 is the mass loading effect in the gas
phase after NuTu-19 cell immobilization, and Δf L1 is the liquid loading effect in the gas phase after NuTu-19 cell immobilization.

Fig. 3.

(Color online) Changes in frequency caused by NuTu-19 cell immobilization.

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Sensors and Materials, Vol. 31, No. 10 (2019)

dropped sharply. The change in voltage was around 960 mV, as shown in Table 2. The resultsof ETM calculation showed that there were slight frequency shifts caused by the mass loading
effect. Fortunately, they were all no more than 2 Hz and within the error tolerance. Therefore,
it can be considered that no immunoreaction occurred in the negative control group, and all
the frequency changes resulted from the damping effect of the serum solution. In contrast,
when the serum solution with NuTu-19 IgG was made to flow over the sensor electrodesurface, the NuTu-19 antigen specifically combined with its target antibody. The depositedimmunoreactants as the mass loading effect, resulted in a corresponding frequency shift. The
dissipative properties of the immunoreactants also brought about a certain amount of frequency
shift. The two different loading effects were differentiated by the ETM, as shown in Table 3.
3.3

NuTu-19 antibody concentration

The NuTu-19 IgG concentration was obtained on the basis of the Sauerbrey theory, ETM,
and Bradford method. The error between the ETM-calculated value and the actual value
was only 1% [(370 − 366)/370] × 100%, as shown in Fig. 4. However, the error between the
Table 2
Results for negative control.
Crystal1﹟
ΔU2 (mV)
960
997
Δftotal2 (Hz)1.6
Δfm2 (Hz)995.4
Δf L2 (Hz)

2﹟
961
1000
1.2
998.8

3﹟
955
999
1
998

4﹟
954
1001
2
999

ΔU2 is the changed voltage in nonimmune rabbit serum, ΔU2 = U2 − U1, Δftotal2 is the measured total frequency shift in
nonimmune rabbit serum, Δftotal2 = f 2 − f1, Δf m2 is the mass loading effect in nonimmune rabbit serum, and Δf L2 is the liquidloading effect in nonimmune rabbit serum.

Table 3Results of NuTu-19 antibody test.
Crystal1﹟
2﹟
ΔU3 (mV)
200
289
351
423
Δftotal3 (Hz)264290
Δfm3 (Hz)87
133
Δf L3 (Hz)

3﹟
275
511
384
127

4﹟
315
608
457
151

ΔU3 is the changed voltage in immune rabbit serum, ΔU3 = U3 − U2, Δftotal3 is the measured total frequency shift in immune
rabbit serum, Δftotal3 = f 3 − f 2, Δf m3 is the mass loading effect in immune rabbit serum, and Δf L3 is the liquid loading effect inimmune rabbit serum.

(a)

(b)

(c)

Fig. 4. (Color online) NuTu-19 IgG concentration: (a) value calculated on the basis of Sauerbrey theory, (b) ETMcalculated value, and (c) actual value (obtained by Bradford method).

Sensors and Materials, Vol. 31, No. 10 (2019)3065

value calculated on the basis of Sauerbrey theory and the actual value was beyond 30%.
The comparison showed that the mass loading effect was distinguished from the damping
loading effect on the PZ immunosensor using ETM, and that the detection accuracy wassignificantly improved.

4.

Conclusions

A novel method of distinguishing the mass loading effect from the damping loading
effect on a PZ immunosensor using the ETM is introduced in this paper. When the analysis
and quantification are performed under the gas phase condition, a bioactivator is not strictly
applicable to the rigid-layer behavior of a film fabricated by gas-phase mass deposition; thus,
its dissipative effect must be considered. When the reaction and measurement are in theliquid phase, both effects must be considered. Using the ETM and frequency and amplitude
testing theories, we succeeded in distinguishing the frequency shifts caused by the depositedimmunoreactants from the total frequency variation of the PZ immunosensor, improving thedetection accuracy significantly. Moreover, this new analytical method laid a foundation forfurther development of all types of quartz crystal sensors under the liquid phase.

Acknowledgments
We are grateful to Dr. H. S. Shi for his assistance in the experimental test and also to theState Key Laboratory of Biotherapy of Sichuan University for providing the biochemical
experimental materials. This work was supported by the Dr. Foundation of Southwest
University of Science and Technology (14zx7121).

Conflicts of Interest
The authors declare no conflicts of interest.

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