Multi-Band Sensing for Dielectric Property of Chemicals Using Metamaterial Integrated Microfluidic Sensor

The growth of the chemical industry has brought tremendous challenges to chemical sensing technology. Chemical sensors based on metamaterials have great potential because of their label-free and non-destructive characteristics. However, metamaterials applied in chemical sensing have mainly been investigated from the measurement of sample concentration or the determination of the dielectric properties at a fixed frequency. Here we present a metamaterial integrated microfluidic (MIM) sensor for the multi-band sensing for dielectric property of chemicals, which is promising for the identification of chemicals. The MIM sensor mainly consists of multiple pair of high sensitive symmetrical double split-ring resonators (DSRRs) and meandering microfluidic channels with a capacity of only 4 μL. A dielectric model has been innovatively established and experimentally verified to accurately estimate the complex permittivity and thus realize the multi-band sensing of dielectric property of chemicals. With the increase in the number of resonators in the sensor, a dielectric spectrum like curve could be obtained for more detailed dielectric information. This work delivers a miniaturized, reusable, label-free and non-destructive metamaterial-microfluidic solution and paves a way of the multi-band sensing for dielectric property of chemicals.


Various designs for microfluidic channels
In order to investigate the effect of the microfluidic channel on the efficiency and sensitivity of the sensor, three shapes of microfluidic channels are proposed and simulated by finite element simulation software, as shown in Figure S1a~c. It is worth noting that the resonators of the sensors in Figure S1a~c are identical, and the S21 spectrums are obtained by simulation software when the channels are empty or filled with ethanol (ε r = 25), as shown in Figure S1d~f. Obvious, the sensor with a large cubic channel is more sensitive than others, which is due to the fact that more samples in the cubic channel result in larger changes in dielectric constant. However, considering that the minimum pressure required to induce flow is inversely proportional to the cross-sectional dimensions of the microfluidic channel according to the Young-Laplace equation [1] , the microfluidic channel of this design suffers from a problem of uneven filling, which makes filling and cleaning of samples in the channel difficult. Meantime, although the sensor with a straight channel is more efficient and requires less volume of samples, it has a relative low sensitivity. Therefore, a sensor with meandering channel is used as the final design to ensure the smooth flow of liquids and achieve higher sensitivity of the sensor. S-3

Analysis of DSRR's resistance, inductance and capacitance
As shown in Figure S2, two pairs of resonators are symmetrically located on both sides of the microstrip line, exciting two different resonances in the entire frequency regime due to their different sizes, which creates favorable conditions for the implementation of dual-channel detection. According to the electrical characteristics of the series circuit, the impedance of the resonator can be expressed as: , R x and R y are parameters related to the radiation and Joule's losses in both loops, the DSRR element can be assumed to be perfectly conducting at this stage. L s is determined by the inductance of the inner ring (L y ), the inductance of the outer ring (L x ) and the mutual inductance between the two rings (M). When the round loop (radius r) is made of a conductive strip (width c) and c ≪ r, the inductance of the round loop is approximately the same as that of a round loop made of the wire (radius r 0 = c/4): where eff  represents the effective permittivity determined by the substrate and chemical sample.
By substituting the corresponding parameter values into Eq. (S8), the capacitance of resonator A and resonator B can be obtained as C SA = 2.510 pF, C SB = 3.232pF. The final values of resistance, inductance and capacitance are listed in Table S1. S-6

Analysis of the relationship between dielectric properties and resonant frequency shifts.
According to Equation (1) in the manuscript, the resonance frequency shift is dependent on the capacitance and inductance of the device. The permeability of non-ferromagnetic materials such as alcohols and water is approximately equal to the vacuum permeability μ 0 . Therefore, the resonance frequency shift depends only on the capacitance of the device. From Equation (S8), it is clear that since it is difficult to change the geometrical dimensions after fabrication, the capacitance is dependent on the effective permittivity around the resonator, which can be expressed as where C   and  S-9

Sensitivity analysis of the MIM sensor
In the manuscript, the sensitivity S of the MIM sensor is defined as the slope of the concentration-frequency curve, which can be expressed as ) were used as substrates and then simulated by finite S-10 element simulation software. It is assumed that the channel is filled with ethanol (ε r = 25), and the reference frequency was set to the frequency when the microfluidic channel is empty. Figure S4 shows that the smaller the permittivity of the substrate, the larger the resonance frequency shift.
This is because the effective permittivity of substrate composed of low dielectric material is relatively easily to change as the sample enters the microfluidic channel. Therefore, it is feasible to use the material with a lower permittivity as a substrate to enhance the sensitivity of the sensor. S-11

Sensing test of alcohol-alcohol solution
The resonance occurring in the DSRR is dominated by the complex permittivity of the sample in the channel. When the permittivity of the binary mixture shows a good linear relation with the volume fraction of one of the components, the sensor can achieve a linear measurement, which indicates that it is also feasible to use alcohol-alcohol mixture like ethanol-methanol as the analyte. To verify this, the S21 spectrum of the sensor is simulated by finite element simulation software when the analyte is ethanol-methanol solution. As shown in Figure S5, the resonant frequency shifts linearly (R 2 =0.995) as the volume fraction of methanol changes from 0% to 100% of 20% increment per step, indicating that alcohol-alcohol solution can also be measured by the sensor. It is worth noting that the permittivity of ethanol-methanol solution used in the simulation is from reference 3, as listed in Table S2.   S-13

Fabrication process of the MIM sensor
The detailed fabrication process is shown in the Figure Figure S7. Dual-band sensing flow diagram for dielectric properties of chemicals. S-16

The interference between resonators
Since the electromagnetic energy of the resonator is almost distributed at the split of the resonator, the interference induced by the adjacencies between the resonators can be considered to be small. To verify this hypothesis, the occurrence of resonance on the resonators is simulated by finite element simulation software, when the minimum spacing between resonators changes. Figure S8 shows the electric field distribution and the corresponding frequency response of resonators, when the minimum spacing between them changes from 0·λ to λ/4. The value of the wavelength is set to the larger resonant wavelength in the two resonators. The results show that only when the resonators are in electrical contact, there will be electrical distribution on both resonators at the same time, indicating that the interference between the two resonators was small before they were electrically contacted. Moreover, although the minimum spacing between resonators is different, their resonant frequency response is almost the same.   Figure S2a.