An Unfound Associated Resonant Model and its Impact on Response

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An Unfound Associated Resonant Model and its Impact on Response of A Quartz Crystal Microbalance in Liquid Phase Qi Kang, Qirui Shen, Ping Zhang, Honghai Wang, Yan Sun, and Dazhong Shen Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b04906 • Publication Date (Web): 29 Jan 2018 Downloaded from http://pubs.acs.org on February 5, 2018

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Analytical Chemistry

An Unfound Associated Resonant Model and its Impact on Response of A Quartz Crystal Microbalance in Liquid Phase Qi Kang†, Qirui Shen‡, Ping Zhang†,*, Honghai Wang†, Yan Sun†, and Dazhong Shen†,* †

College of Chemistry, Chemical Engineering and Materials Science, Collaborative Innovation Center of Functionalized Probes for Chemical Imaging in Universities of Shandong, Key Laboratory of Molecular and Nano Probes, Ministry of Education, Shandong Provincial Key Laboratory of Clean Production of Fine Chemicals, Shandong Normal University, Jinan 250014, P. R. China ‡ College of Chemistry, Chemical Engineering and Material Science, Zaozhuang University, Zaozhuang 277160, P.R. China ABSTRACT: Quartz crystal microbalance (QCM) is an important tool to detect in real time the mass change in nanogram level. But for a QCM operated in liquid phase, the Sauerbrey equation is usually disturbed by the changes in liquid properties and longitudinal wave effect. Herein, we report another unfound associated high frequency resonance (HFR) model for the QCM, with the intensity two orders of magnitude higher than that of the fundamental peak in liquid phase. The HFR model exhibits obvious impact on the response of QCM in thickness-shear model (TSM), especially for overtones. The frequency of HFR peak is decreased dramatically with increasing conductivity or permittivity of the liquid phase, resulting in considerable additional frequency shifts in the TSM as baseline drift. Compared to that with a faraway HFR peak, the overlapping of HFR peak to a TSM overtone results in the frequency shifts of ±50~70 kHz with its intensity enhancement by three orders of magnitude in the later. The HFR behavior is explained by an equivalent circuit model including leading wire inductance, liquid inductance and static capacitance of QCM. Taking into account of the HFR model, the positive frequency shifts of the QCM at high overtones during the cell adhesion process is understandable. Combining the TSM and HFR is an effective way to improve the stability of QCM and provides more reliable information from the responses of QCM. The HFR may have potential application in chemical and biological sensors.

Quartz crystal microbalance (QCM) has become an important tool to detect in real time the mass change in nanogram level since the pioneering work of Sauerbrey.1 For a QCM applied in gaseous circumstances, the mass change (∆m) on the surface of the electrode (area of A) can be calculated by the Sauerbrey equation. 

∆f = 2.26×10-6 nf02∆m/A

(1)

where ∆f and f0 are the frequency shift and fundamental frequency of the QCM, n is the overtone order in the thicknessshear model (TSM), respectively. The success oscillating for a QCM in liquid phase expands greatly its application area in analytical chemistry.2-10 For a QCM operated in a liquid phase, the viscoelasticity of the liquid film damps markedly the intensity of the resonance. The resonant frequency is also related to the changes in liquid properties, including viscosity, density, conductivity and permittivity.11-14 The frequency response of a QCM in Newtonian fluid is expressed by 15 1/2

 ηρ  (2) ∆f = − f    πµq ρ q  where η and ρ are the viscosity and density of the liquid, respectively, and µq and ρq are the elastic modulus and the density of the quartz, respectively. When a QCM is oscillating in TSM in liquid phase, a weak longitudinal wave (LW) is usually generated, 16–18 resulting in periodic frequency shift due to the change in reflection dis3/2 0

tance or velocity of LW.19 Obviously, the frequency shifts resulted from such the non-mass effects invalidate the Sauerbrey equation, especially in an oscillator method, because only the oscillating frequency is recorded. An impedance analysis (IA) method is advantageous to correct the influence from the non-mass effect, as the resonant frequency and equivalent circuit parameters of QCM are measured simultaneously.20 According to Muramatsu et al., 21 the motional resistance, Rm, of QCM in contact with a liquid can be expressed by

A( 2πf 0ηρ )1/2 (3) K2 where K is the electromechanical coupling factor. Hence, the motional resistance of the QCM is a useful indicator to viscoelasticity of the loading film. In a research QCM (RQCM) 22 or quartz crystal analyzer (QCA), 23 the changes in resonant frequency and motional resistance are measured simultaneously. Similarly, the changes in resonant frequency and oscillating energy dissipation (D) are measured by QCM-D technique.23-26 To obtain more information, the responses in the overtones are measured in QCM-D or IA method. According the changes in the frequency and motional resistance in fundamental and harmonic peaks, the rigidity and viscoelasticity of polymer films were judged. 27-29 Generally, the fundamental frequency of QCM is in the range of 5~10 MHz based on the compromise between the sensitivity and mechanical strength of the quartz resonator. According to eq.1, a higher frequency-mass coefficient is obtained in a QCM with higher fundamental frequency, which is Rm =

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favorable to improve the sensitivity. Hence, QCM with the fundamental frequency of 27 MHz was frequently employed by Okahata group.30-32 A wireless QCM with fundamental frequency of 170~180 MHz was applied in the immunoassay. 33, 34 However, for a QCM operated at high frequency, some abnormal frequency responses were observed. For example, during the initial cell adhesion of pre-osteoblastic MC3T3-E1 cells to a Ta-coated QCM, 35 the fundamental frequency (n=1) was decreased by -41 Hz, but the frequency shifts in the 3rd ,5th and 7th overtones were only -6 Hz, -3 Hz and -2 Hz, respectively, which is contradictory to the prediction in eqs. 1 or 2. In the adsorption process of negatively charged poly(sodium 4-styrenesulfonate) terminated mesoporous TiO2 particles on positively charged aminothiol self-assembled monolayer, the observed frequency shifts were negative at the fundamental resonant, close to zero at 3rd overtone, and positive at high overtones,36 which cannot be explained by eqs. 1 or 2. On the other hand, how to improve the stability of a QCM in liquid is concerned in the applications of QCM. In this work, we report an unfound associated resonance model for QCM, which exists in high frequency region, defined as the high frequency resonance (HFR) for the convenience in discussions. The intensity of the HFR peak is more than two orders of magnitude higher than the fundamental peak of a QCM in liquid phase. Importantly, the HFR model has obvious impact on the frequency responses and intensity of TSM, especially for the overtones nearby. The behavior of the HFR model was investigated by an IA method. The influence of the permittivity and conductivity of the liquid phase, as well as the leading wire length, on the resonant frequency of the HFR peak was tested. The interaction between the TSM and HFR peaks was discussed. The HFR phenomenon was explained by an equivalent circuit model including leading wire inductance, liquid inductance and static capacitance of QCM. To correct the influence of HFR on the frequency responses of the TSM overtones, the additional frequency shifts from the HFR peak movement were estimated by an interpolation algorithm. By using the cell adherence process as the model, the responses in HFR and TSM overtone peaks were measured. Taking into account of the HFR model, some abnormal responses of QCM, such as the positive frequency shifts of the QCM at high order overtones during the cell adherence process, is understandable. In addition, the stability of a QCM in liquid is improved by after correcting the additional frequency shifts resulting from the shift in HFR peak. Combining TSM and HFR is helpful to obtain more reliable information from the responses of QCM. The HFR model itself may have potential applications in chemical and biological sensors.

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Electronics Co., Ltd. (Beijing, China) and used for immersion experiments. Another QCM resonator of 5 MHz with a diameter of 25.4 mm was obtained from Maxtek Inc., USA. An asymmetric pattern of gold electrodes on chromium underlayers were deposited on both sides of the quartz wafer (Figure 1). In conductivity experiments, the side having the larger gold electrode (with diameter of 11.5 mm) was faced the solution and opposite side having the smaller gold electrode (with diameter of 6.5 mm) was exposed to air. Experimental setup to monitor cell adherence process. The schematic depiction of the QCM measurement setup for monitoring cell adhesion process is shown in Figure 1. A QCM resonator of 5 MHz was mounted by a silica-gel O-ring at the bottom of a purpose-designed Teflon measurement chamber, which was placed in a CO2 incubator with temperature control (37°C) and 5% (v/v) CO2 provision. A rough glass ball was put in the liquid to eliminate the interference from LW.19 The top of the LW eliminator was covered by a polyethylene frit to prevent evaporation of the medium. The excitation electrodes on the QCM were electrically contacted to the patterned Au films on a printed circuit board (PCB) and were connected to a precision impedance analyzer (Agilent 4294A) by two leading wires (diameter of 1.2 mm, length of 70 cm). A user-program written in Visual Basic 6.0 was designed to control the instrument, to acquire and process the impedance data. The conductance (G)–frequency (F) spectra of the TSM overtones (n=1,3,5,7,9) and the HFR peak were measured by six independent impedance scans in one measurement cycle. In the measurement of a G–F spectrum, the center was set close to the resonant frequency and the span was 5 times of the half peak width of the target resonant peak. Prior to cell culture experiment, the QCM surface was treated by 50 µL of 1:3 H2O2 : H2SO4 heated to 80°C then washed with Milli-Q water, and dried with N2 stream. Subsequently, 2.0 mL of culture medium were added to the measurement chamber. The resonant frequencies of the TSM overtone and HFR peaks were recorded with the incubating time. After the stability of the baselines,1.0 mL of the medium were replaced by the same volume of media containing 2.0×105 H9C2 cells, and data were continually collected for an additional 18 h.

Inject cells LW eliminator screw

EXPERIMENTAL SECTION Chemicals and materials. All reagents were of analytical grade or better. Ultra-pure water (specific resistance of 18 MΩ·cm) was used throughout this study. H9C2 cardiomyoblasts purchased from Shanghai Bogoo Biotechnology Co. Ltd. The cells were grown in Dulbecco's Modified Eagle's Medium (DMEM, Gibco, Co., USA) containing 10% fetal bovine serum (FBS, Gibco). Two type of electrode configuration AT-cut QCM resonators were used in this work. The QCM with a fundamental frequency of 9 MHz (quartz disc diameter 14 mm, gold electrode diameter 6.5 mm) were obtained from Beijing Chengjin

Computer

CO2 Incubator leading wire

O-ring

4294A Impedance analyzer

QCM

Au film

PCB

water bath PCB QCM

leading wire

Figure 1. Schematic drawing of the QCM measurement setup for monitoring cell adhesion process (not to scale). The measurement chamber and QCM resonator were placed inside the thermostated CO2 incubator.


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RESULTS AND DISCUSSION An unfound associated resonant model for QCM in high frequency region. In this work, we report the performance of an unfound associated high-frequency resonant model in the QCM. Figure 2A shows representative the TSM and HFR resonant peaks of a 9 MHz QCM immersed in pure water. Noted that the resonant peaks were measured independently in seven impedance scans with the center frequency close to the resonant frequency and the span 5 times of the half peak width of each target peak. In the large abscissa scaling of 110 MHz, the TSM overtone peaks are squeezed to line shape as their peak width is much less than the abscissa scaling. Under the experimental conditions used, the HFR peak occurred at 51.1 MHz with the peak intensity 170 times of that of the TSM fundamental peak (n=1). Usually, the intensity of the TSM harmonics is reduced obviously with increasing overtone order,37 but which is only true for in the ranges of n=1 to 3, and n=5 to11 in Fig.2A. Due to the impact from the HFR peak, the intensity of the 5th and 7th overtones is even 15.3 and 5.8 times of the fundamental peak, respectively. Put the same QCM in gaseous phase, the HFR peak occurred at 90.8 MHz (Figure 2B). Although the intensity of the TSM overtones in air is much enhanced as compared to that in water, the height of HFR peak is still 1.52 times of the height of the fundamental peak. Similarly, the 9th and 11th overtone peaks are much

HFR

A

450

G (mS)

n=1 300

n=3 150

×102

n=5 ×5

×102

n=9 n=7

×103

×10

n=11 ×103

0

G (mS)

360

HFR

B n=1

240

120

n=9

n=3 n=5

n=11

n=7

0

C

240

G (mS)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


160

1.6

80

HFR

n=1

3.2

in water

0.0 8.97

8.99

n=1

250

in air

125

0 8.9994

9.01

8.9997

9.0000

0 0

20

40

60

80

100

F (MHz)

Figure 2. TSM overtone and HFR resonant peaks of a 9 MHz QCM immersed in water (A) and in air (B) in seven impedance scans with the span of 5 times of the half peak width of corresponding target resonant peak. The conductance-frequency spectrum of a 9 MHz QCM immersed in water measured at a large span of 80 MHz (C). Inserts: expanding conductance-frequency spectra of the fundamental peak a 9 MHz QCM in water and air.

enhanced by the HFR peak nearby.

As shown in Figure 2, the HFR peak can be observed easily due to its high intensity. It seems to be confusing that the HFR phenomenon has not been reported yet. The overdue HFR report may be due to the following reasons. (i) Only the fundamental frequency of QCM is measured in an oscillator method. The oscillator method cannot observe the HFR peak as it occurs in the frequency region which is much higher than the fundamental frequency of a normal QCM (5~10 MHz). (ii) In an IA method, the impedance analyzer is usually controlled by a user-program for the need of continuous monitoring. In order to improve the measurement accuracy, the impedance scan is performed with the center frequency close to the resonant frequency of the target TSM peak and span as narrow as possible. Due to the limitation in scan rate, the G-F spectrum of the fundamental peak is most commonly measured. To measure the harmonics responses, each target peak is measured in an independent impedance scan in a narrow frequency region using the parameters set by the user-program. As a result, the measuring frequency range does not cover the HFR peak, which is usually separated by several MHz from the TSM peaks. (iii) Due to the inertial thinking, it may be difficult to consider the fact that there is even an unfound associated resonant model in QCM after its extensive applications for more than 50 years. Consequently, it is very possible to ignore the HFR phenomenon once it occurs by chance. (iv) The HFR peak in QCM resonator in air without additional leading wire occurs at much higher frequency region, which is beyond the maximum measuring frequency of 110 MHz in 4294A impedance analyzer. As shown in Figure S-1 in Supporting Information (SI), the resonant frequency of HFR peak in 9 MHz QCM in air without additional leading wire is at 125.9 MHz. As the HFR peak is faraway, the intensity of the TSM harmonics is reduced with increasing overtone order in the range from n=1 to n=11. If 4294A impedance analyzer is employed, the abnormity in the 13 th and 15 th overtones cannot be observed. In fact, we observed the HFR peak by chance from a mistake in a manual measurement mode, due to the abrupt stoppage of the communication interface between the impedance analyzer and computer. In an impedance scan for 5th overtone peak (9 MHz QCM in a liquid phase) at the center frequency of 45 MHz, the initial span of 80 kHz was set to 80 MHz in a mistake key-press operation. Surprisingly, a very strong resonant peak (HFR) was observed in the high frequency region (see Figure 2C). Under the experimental conditions used, the half peak width of the TSM overtone peaks is in the ranges of 4~55 kHz, which is much less than the scan step of 200 kHz. With such large scan step, the real information and accuracy of quartz response is lost, as no point or at most only one point is measured in the QCM resonant peaks. This result also reveals the importance in the span set in IA method. Afterwards, more than 300 QCM resonators with different dimension were tested in a 4395A network/spectrum/impedance analyzer with measuring frequency up to 500 MHz, indicating the existence of an HFR peak in each QCM. The resonant frequency of the HFR peak in the same type QCM is similar but independent of the fundament frequency. As compared to that in gaseous phase, the intensity of the HFR is even higher for the QCM immersed in a non-electrolyte liquid regardless of viscosity, revealing that the HFR peak is hardly damped by the viscous effect of the liquid phase. Hence, it is sure that HFR is an unfound associated resonant model for QCM.


Analytical Chemistry Influence of the permittivity of the liquid phase on HFR performance. As shown in Figure 2, the frequency of HFR was decreased by about 40 MHz when the QCM was immersed in water, indicating that HFR is also sensitive to the change in the impedance of the medium. The influence of medium permittivity on HFR performance was tested in the mixture of dioxane-water, as its permittivity is increased with increasing water content. As shown in Figure 3A, with increasing relative permittivity (εr) from 2.2 to 80, the resonant frequency of HFR peak was reduced by 38.1 MHz, indicating the sensitive frequency response of the HFR model to the permittivity of the medium. The half peak width (Γ), as an indictor of the dissipation of the resonance curve, is in the range of 0.54 ~0.78 MHz, varies slightly with the composition of the mixture. As shown in Figures 3B and 3C, the resonant frequencies of the TSM resonant peaks were also changed. One reason is that the viscosity and density of the dioxane-water mixture are varied with the mixing ratio.38 Another reason is ascribed to the impact from the shift of the HFR peak, because the variation tendency of the TSM harmonics is different, especially for the 5th overtone in the mixture of higher permittivity. The

∆ FHFR (MHz)

0.6

-15

A -30

0.3

-45

0.0

n=1

0

∆ Fn (kHz)

Γ HFR (MHz)

0.9

0

n=3 -3

B

-6

n=5

-9

0

20

40

60

80

Relative permittivity 63.08 0.45

0.30 62.98

Gmax7 (S)

C

F7 (MHz)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.15

62.88 57

60

63

66

0.00 69

FHFR (MHz)

Figure 3. Influence of the relative permittivity on the resonant frequency and half peak width of the HFR peak (A) and resonant frequency of overtone (n=1,3,5) (B). The changes in the frequency and intensity in 7th overtone in the case of overlap with HFR peak (C). A 9 MHz QCM was immersed in waterdioxane mixture.

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resonant frequency of the fundamental peak was decreased by 1.02 kHz to a minimum with εr increasing from 2.2 to 48, then increased to previous level at εr =80. But the 5th overtone was decreased with increasing permittivity in the range used. Specially, the decrease in frequency of 5th overtone was speeded up with εr increased from 60 to 80. Moreover, with εr increased from 2.2 to 80, the HFR peak was shifted from 89.3 to 51.2 MHz, passing through the 9th and 7th overtones in turn. As shown in Figure 3C, with the HFR shifted from 68 to 58 MHz, the frequency of 7th overtone was decreased slightly when the HFR and TSM peaks were separated enough. In the cases of the peak overlap, the frequency decrease was speeded up then with a jump of 170 kHz from 62.90 to 63.07 MHz. Importantly, the intensity of the 7th overtone was much enhanced. The maximum peak intensity at the FHFR= 63.25 MHz is as high as 397 mS, which is more than three orders of magnitude larger than that in water and 191 times of that of the fundamental peak in this mixture. These results reveal that the frequency response of HFR to permittivity results in additional frequency shifts in the TSM peaks, especially in the overlapped one. Influence of the conductivity of the liquid phase on HFR performance. As shown in Figure S-2 in SI, the salt concentration (or conductivity) also has obvious influence on the resonant frequency, intensity and shape of the HFR peak of the QCM immersed in electrolyte solutions. With increasing NaCl concentration from 0 to 40 mM, the frequency of the HFR peak was shifted from 51.18 to 31.56 MHz. The HFR peak was broadened and its intensity was reduced obviously. For example, the height and half-peak width of the HFR peak are 447 mS and 0.519 MHz in pure water, 40.6 mS and 3.72 MHz in 8 mM NaCl, respectively. Immersed in 80 mM NaCl solution, only half of the HFR peak was observed due to the serious by-pass effect in high conductive solutions. To avoid the by-pass effect in electrolyte solution, the QCM configuration with one side in contact with liquid phase is most commonly employed. Hence, a typical 5 MHz QCM with diameter of 25.4 mm was chosen to test the HFR behavior in electrolyte solutions. As can be seen in Figure 4A, the resonant frequency of the HFR peak is reduced with increasing NaCl concentration. And the absolute values of the frequency shift in HFR, ∆FHFR, are decreased with increasing leading wire length. According to Figure 4B, the value of ΓHFR is also related to the salt concentration and leading wire length. In the case of L1=12 cm, the value of ΓHFR is increased from 1.28 to 4.61 MHz with increasing NaCl concentration from 0 to 50 mM. After then, ΓHFR is decreased with further increase in NaCl concentration. As the leading wire length increases, the value of ΓHFR is reduced and the maximum is occurred at higher NaCl concentration. The dependence of the fundamental resonant frequency of QCM on conductivity has been investigated in detail by several groups but with different results. 39-42 Part of the difference may be due to the influence of the LW effect as the density of the solution is increased with increasing salt concentration. As shown in Figure 5A, the frequency of the fundamental peak of QCM is decreased slightly with increasing salt concentration. The absolute value of ∆F1 is increased with longer wire, implying that there are additional frequency shifts resulting from the movement of HFR peak. Noted that the frequency


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∆F3 (kHz)

∆F1 (kHz) 0.00

∆FHFR (MHz)

0

A

-4

-0.06

L3

B

0.00

A

-0.12

-8

L1 -0.12

L2

-0.24

L1

L2

L2 L3

-12

L3

-0.18

L1

-16

-0.36 0.0

0.4

0.8

1.2

0.0

CNaCl (M)

4.5

Γ HFR (MHz)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


B

0.4

0.8

∆F5 (kHz)

∆F7 (kHz)

0.0

C

0.00

D

3.0 -0.2

-0.15

L1

L1

1.5

L2 -0.4

L2 L3 0.3

0.6

0.9

-0.30

-0.6

0.0 0.0

1.2

CNaCl (M)

1.2

-0.45

L3 0.0

0.4

0.8

L1

1.2

L2 0.0

0.4

CNaCl (M)

CNaCl (M)

Figure 4. Influence of NaCl concentration on the resonant frequency (A) and half peak width (B) of HFR peak a 5 MHz QCM with one side facing aqueous solution. The length of leading wire: L1= 12 cm , L2= 30 cm, L3= 65 cm.

shift of -600 Hz was measured in 1M NaCl for the QCM with the similar dimension by using a plating monitor (PM-710 from Maxtek Inc.) ,41 which equips a long leading wire. As shown in Figures 5B to 5F, the length of the leading wire also has more obvious influence on the frequency response of the TSM overtones to conductivity. For example, the frequency shifts of 5th overtone (∆F5) using a long leading wire (L3=65 cm) is 2.4 times of that using a short wire (L1=12 cm). For 9th overtone, the frequency shifts of (∆F9) with L2=30 cm is 4.3 times of that with L1=12 cm. In the case of L2=30 cm, with increasing NaCl concentration, the HFR peak was shifted to lower frequency region and passed through 11th overtone during the migration of HFR peak. So did for 7th overtone in the case of L3=65 cm. As a result, the resonant frequencies of 7th and 11th overtones were decreased initially with speeding step until to the minima, jumped abruptly to maxima, then decreased again with decaying step (Figure 5F). In the cases of well overlapping, the frequency shifts were increased abruptly from -58.9 kHz in 38.5 mM NaCl to 62.8 kHz in 41.5 mM NaCl for 11th overtone, and from -55.3 kHz in 141 mM NaCl to 57.2 kHz in 168 mM NaCl for 7th overtone, respectively. Moreover, the overlap between the HFR and TSM overtone results in the deformation of the resonant peaks. Figure S-3 exhibits a group of representative G-F spectra during peak overlapping. Under the experimental conditions used, the HFR peak occurred at 59.7 MHz in water. The 11th overtone peak is much weaker in comparison with the HFR peak (Figure S3A), although its intensity is already 35.2 times of that with

0.8

∆Fn (kHz)

∆F9 (kHz)

F

80

E

0.0

1.2

CNaCl (M)

L1

n=11

n=7

40

L3

-0.6 0 -1.2

L2

L3 -40

L2

-1.8 0.0

0.4

0.8

CNaCl (M)

1.2

-80 0.001

0.01

0.1

1

CNaCl (M)

Figure 5. Influence of NaCl concentration on the resonant frequency of TSM overtones of a 5 MHz QCM with one side facing aqueous solution. (A) n=1, (B) n=3, (C) n=5, (D) n=7, (E) n=9, (F) n=7 and n=11. The length of leading wire: L1= 12 cm, L2= 30 cm, L3= 65 cm.

HFR peak at 104.1 MHz using a shorter leading wire (L1=12 cm). Due to the impact from the HFR peak, the right side of 11th overtone is a little cliffy than the left one. In 30 mM NaCl solution, the HFR peak was shifted to 56.7 MHz, resulting in part of overlap between the HFR and 11th overtone peaks. As a result, the intensity of the 11th overtone was enhanced further and the peak was deformed more obviously (Figure S-3B). In 38.5 mM NaCl solution, the HFR peak at 55.19 MHz is very close to the 11th overtone, causing serious deformation in both of the HFR and 11th overtone peaks. The intensity of 11th overtone is only less slightly than that of the HFR peak (Figure S-3C). Afterwards, the HFR peak was moved to the left of 11th overtone. The left side of 11th overtone and the right side of HFR peak were deformed (Figure S-4D). With further increasing salt concentration, the distance between HFR peak and 11th overtone was enlarged, and the intensity



of 11th overtone was reduced and shape of peak returned to regularity gradually (Figures S-3E and S-3F). Equivalent circuit model for QCM including TSM and associated HFR model. The aforementioned experimental results indicate that the HFR model has sensitive frequency response to the change in the permittivity or conductivity of the liquid phase. And the HFR model has obvious impact on the resonance of the TSM overtones nearby. To analyze the HFR behavior, an equivalent circuit model including both of the TSM and HFR resonance was proposed and depicted in Figure 6A. In this model, the motional inductance (Lm), motional capacitance (Cm) and motional resistance (Rm) in the motional branch and the static capacitance (C0) comprise the classical Butterworth-van Dyke equivalent circuit for QCM resonator. Different from the model reported by Rodahl 39, the inductances from the leading wire (L0) and electrolyte solution (Ls) are considered in our model. For a QCM immersed in liquid, the capacitance across quartz disc (Cq) is shorted by the liquid phase. To validate this equivalent circuit model, the sensitive area of the HFR model was checked by a liquid height experiment. As shown in Figure 6B, when the liquid height was below the edge of the outside electrode (point a), the frequency of HFR was decreased slightly with rising liquid height. The decrease in frequency was speeded up gradually with increasing liquid

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height until to the edge of the inside electrode (point b). With the liquid covered the projection of the two electrodes, the additional by-pass path from the outside electrode to inside electrode via the branch of Cq in series combination with solution impedance took effect, indicating by the abrupt drop in frequency. When the liquid height was exceeded the edge of the outside semi-ring of the inside electrode (point c), the frequency of HFR was decreased slightly again with rising liquid height. The results reveal that the sensitive area of the HFR is located between the gap of the inside and outside electrodes for the QCM used (Figure 6A), which is different from the mass sensitive area of the TSM. According to the model in Figure 6A, the HFR peak is the total resonance from the network including the wire inductance, solution inductance, quartz disc and solution capacitance.In a non-electrolyte liquid, the sub-branch of Rs and Ls can be ingored. Beyond the resonant region of TSM peak, the motional branch containing Lm, Cm and Rm is cut off. Accordingly, the resonant frequency of the HFR is expressed by 1

FHFR =

2 2π L0 (C0 +

(4)

As the parasitic inductance of L0 is proportional to the leading wire length, the influence of the wire length on the behavior of HFR was tested. As shown in Figure S-4 in SI, with increasing wire length from 9 to 73.5 cm, the frequency of the HFR was decreased from 106.7 to 30.6 MHz, indicating the significant influence from the leading wire length. Moreover, the frequency of HFR has a linear correlation with the reciprocal of the square root of the wire length, supporting the prediction from eq.4. In addition, as shown in Figure S-5 in SI, the frequency of HFR is increased with parallel leading wire number. The reason is that the value of L0 is reduced with increasing cross-sectional area of the leading wire. When a QCM is immersed in a non-electrolyte liquid, eq. 4 can be simplified as

FHFR =

Figure 6. (A) Equivalent circuit model of QCM including TSM and HFR models. Where L0 is the inductance form leading wire, C0, Cm, Lm and Rm the static capacitance, motional capacitance, motional inductance and motional resistance, Cs, LS and RS the solution capacitance, solution inductance and solution resistance, Cq capacitance across quartz disc, respectively. (B) Influence of the liquid height on the resonant frequency of HFR in a 5 MHz QCM with one side facing 0.1 M NaCl solution. The length of leading wire is 20 cm.

Cs Cq ) Cs + Cq

1

(5)

2 2π L0(C 0 + C s )

With increasing permittivity, the value of CS is increased and results in the decrease in FHFR, which agrees the experimental results in Figure 3A. When the QCM with one side facing an electrolyte solution with increasing conductivity, the solution resistance of Rs is reduced and the solution inductance of Ls is increased, leading to the decrease in the frequency of the FHR peak, which agrees the experimental results in Figure 4A. When the QCM is immersed in an electrolyte solution with increasing conductivity, the increase in solution inductance leads to the decrease in the frequency of the FHR peak. But the energy loss due to solution resistance causes the damping of the HFR peak. In a high conductive solution, the by-pass effect of solution resistance has a short-circuit effect for the static capacitance of QCM and solution capacitance, dying away HFR peak. Influence of HFR model on the TSM response. In the experiments related to the response to permittivity and conductivity, the HFR model exhibits obvious impact on the frequency and intensity of the TSM peaks. But the variation in liquid composition itself also results in the frequency shift of the TSM peaks. In order to distinguish between the frequency


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shifts purely due to the influence of HFR effect, as an alternative strategy, the frequency of HFR was adjusted by leading wire length. The constant solution conditions were obtained by using the QCM with one side facing 0.15 M NaCl solution. Thus, the changes in resonant frequency and intensity of the TSM peak are ascribed only to the influence from HFR peak. For the overtones in the left side of HFR peak (n=1, 3, 5), as shown in Figure S-6 in SI, the resonant frequencies are increased while the intensity is reduced with HFR peak moved to higher frequency region. As the distance between the TSM and HFR peaks is enlarged, the influence of HFR peak on TSM peaks is weakened gradually. For example, when the HFR peak was moved from 30.6 to 50.6 MHz, the resonant frequency of the fundamental peak was increased by 198 Hz, which is a rather large frequency shift in QCM measurements. However, the shift of HFR peak from 79.6 to 106.7 MHz also resulted in a frequency shift of 41Hz, indicating that influence of HFR peak on TSM peaks does exist even at a much large distance. For the overtones with the initial HFR peak in the left side (n=7, 9, 11), as shown in Figure S-7 in SI, the HFR peak has significant impact on resonant frequencies and the intensity of overtone peaks in the case of overlapping. With increasing frequency of HFR peak, the frequency of the overlapped TSM overtone was increased but had a sudden drop about 135 kHz while the peak intensity was approached its maximum, which is about three orders of magnitude larger that far away the HFR peak. The aforementioned experimental results reveal that the frequency shift in the HFR peak can cause considerable additional frequency shifts in QCM in TSM, especially for the high order overtones. The HFR model may be another potential error source for the frequency shift measurements in the applications of QCM, such as baseline drift. Hence, it is necessary to reduce the influence of HFR by shifting the HFR peak to higher frequency region using leading wire with parasitic inductance as little as possible. On the other hand, the additional frequency shifts in QCM in TSM, ∆F(HFR)n, may be corrected in the IA method. According to the correlations between ∆Fn and FHFR in Figure S-6A, the corresponding additional frequency shifts in QCM in TSM due to the shift of HFR peak (∆F(HFR)n, n=1,3,5) in Figures 5 were estimated by using an interpolation algorithm. Under the experimental conditions used, as shown in Figure 7A, the absolute value of ∆F(HFR)n is increased with increasing salt concentration, wire length and overtone order. After subtracting the ∆F(HFR)n from the total frequency shifts, the corrected frequency shifts, ∆Fn−∆F(HFR)n, are independent of the wire length (Figure 7B). The decrease in the corrected frequency shifts is due mainly to the increase in the viscosity and density of the liquid accompanied with increasing NaCl concentration. Similarly, as shown in Figure S-8 in SI, the variation tendency of the corrected frequency shifts to permittivity is the same in the overtones (n=1,3,5), which is due mainly to the changes in the viscosity and density of the water-dioxane mixture with the mixing ratio. Hence, we consider that the frequency response of QCM to conductivity or permittivity themselves is neglectful. The observed frequency response is from the additional frequency shifts due to the shift of HFR peak caused by the changes in conductivity or permittivity as well as to the changes in viscosity and density of the liquid phase. On the other hand, the stability of a QCM in liquid is improved by

A

B

Figure 7. (A) Frequency shifts of TSM overtones (n=1, 3, 5) arising from the HFR peak shift in NaCl solution with different concentration. (B) Dependence of the corrected frequency shifts of TSM overtones (n=1, 3, 5) on NaCl concentration. The experimental conditions are the same as Figure 5.

correcting the additional frequency shifts resulting from the shift in HFR peak. Combination of TSM and HFR resonances to monitor the cell adherence process. The applications of QCM in monitoring the cell adherence process have been demonstrated in refs. 43-48 In most of the works, long leading wires are needed to connect the QCM resonator and its measurement unit, especially in the case of using bulky measurement equipment outside the incubator. Hence, the influence of HFR resonant model on TSM is unavoidable and may be another potential error resource for QCM measurements. By using the adhesion process of H9C2 as the model, the responses of the TSM and HFR peaks were measured by an IA method. The low rate of cells adhered to the surface of QCM reduces the requirement in measurement rate, offering the convenience to scan a group of resonant peaks independently. As shown in Figure 8A, under the experimental conditions used, the H9C2 cells were adhered to the surface of the QCM. Hence, the cell adhesion process was monitored by QCM in the TSM and HFR models. After injecting of H9C2 into the detection cell, there were slight drop in frequency of the TSM overtones but rise in the frequency of the HFR model. Such frequency perturbations are due to the temperature drop by cell injection operation, which resulted in the decrease in conductivity but increases in the viscosity and density of the medium in the charmer. After then, the frequency of the TSM overtones were decreased with increasing incubation time, indicating that more and more cell were adhering on the surface of QCM. On the other hand, the frequency of the HFR peak was risen slightly, which may be due to the adhesion of the cells in the sensitive area of the HFR, because the cell layer has higher electrical impedance than the culture medium. It



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TSM overtones is similar. As compared to the observed ∆Fn/n in Figure 8C, the corrected frequency shifts in the fundamental, 3rd and 5th overtones were decreased more obviously in the late stage of the cell adherence process (8-18 h). These results reveal that the influence of the HFR peak on the responses of the TSM overtones can be corrected in the IA method. On the other hand, the initial baseline drift due to the temperature drop was also suppressed by using the corrected frequency shifts.

Figure 8. Morphologies of H9C2 cardiomyoblasts observed on a QCM in the same batch incubation conditions without measurement (A). Frequency shifts of HFR peak (B), TSM overtones (n=1, 3, 5, 7, 9) (C) and corrected frequency shifts of TSM overtones (D) during the adhesion of H9C2 cardiomyoblasts.

can be seen that the response curves among the TSM overtones are somewhat different, especially in the late stage of the cell adherence process. For example, the absolute values of ∆Fn/n are reduced with increasing overtone order in the range of n=1, 3, 5, indicating that the frequency responses includes non-mass effect, as the cell layer is not a rigid film. The increase in motional resistance or energy dissipation factor of QCM was reported during the cell adherence processes.43-48 Under the experimental conditions used, the frequencies of 7th and 9th overtones were risen after an incubation time of 1.7 and 4.3 h, respectively. The positive observed frequency shifts in 7th and 9th overtones is ascribed to the influence from move up of HFR peak which occurred between the two peaks (Figure 8B). According to the correlation of ∆Fn and FHFR, the additional frequency shifts of ∆F(HFR)n during the cell adherence process were estimated to calculate the corrected frequency shifts for the TSM overtones, which are related to the mass and viscoelasticity of the cell layer. As shown in Figure 8D, the variation tendency of corrected frequency shifts in the

CONCLUSIONS In summary, we reported an unfound associated resonant model of the QCM in high frequency region with extraordinary high intensity. The intensity of the HFR peak does not damp in non-electrolyte liquid regardless of the viscosity. The HFR phenomenon is the total resonance from the network including leading wire inductance, static capacitance of QCM, solution capacitance and solution inductance. The frequency of HFR peak is decreased dramatically with increasing conductivity or permittivity of the liquid phase as well as the length of leading wire. The movement of the HFR peak results in considerable additional frequency shifts in the TSM peaks, which causes the baseline drift in the later, especially for higher overtone peaks in the case of peak overlapping. The strong interaction between TSM and HFR peaks can lead to the frequency shifts of ± 50~70 kHz in the overlapped TSM overtone, with intensity enhancement by three orders of magnitude as compared to that with a faraway HFR peak. The influence of HFR on the responses of the TSM overtones can be reduced by shifting HFR peak to higher frequency region using leading wire with parasitic inductance as little as possible. But even the HFR and TSM peaks are separated by 70 MHz, which can be corrected in an IA method. Excluding the additional frequency shifts resulting from the shift of HFR peak and the changes in viscosity and density of the liquid phase, the frequency response of QCM to conductivity or permittivity themselves is neglectful. Taking into account of the HFR resonant model, some abnormal frequency response of the QCM in high order overtone is understandable. After correcting the influence from the HFR, the stability of QCM in TSM is improved. The discovery of HFR model is helpful to obtain more reliable information from the responses of QCM and the HFR may have some potential applications in chemical and biological sensors. ASSOCIATED CONTENT

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. TSM overtones and HFR peak a QCM in air without additional wire, performance of HFR of QCM immersed in NaCl solutions, influence of leading wire length and salt concentration on TSM overtones and HFR, and corrected frequency shifts of QCM in TSM to permittivity.

AUTHOR INFORMATION Corresponding Authors * E-mail: [email protected]. Tel: +86-531-86180740. Fax: +86-531-82615258. * E-mail: [email protected]. Tel: +86-531-86180740. Fax: +86531-82615258.


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Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This project was supported by the National Natural Science Foundation of China (Grant Nos. 21575080 and 21275091).

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An Unfound Associated Resonant Model and its Impact on Response

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