PDMS is a popular material for fabricating microfluidic devices due to its advantages such as highly biocompatible, chemical inert, impermeable to water, inexpensive, flexible, and easy to be fabricated and bonded to other surfaces. PDMS M-chips were fabricated via injection molding (Sia and Whitesides, 2003) (Notes S1 and S2 of the Supplementary Material). Figure 1A is a three-dimensional (3D) schematic view of a fabricated M-chip, including an inlet, an outlet, a cavity with an elliptic cylinder shape, and two channels tangential to the wall of the cavity. The M-chip has upper wall and side wall, but no bottom (Figure 1B). This design ensures an aqueous sample in the cavity to contact with the ATR prism base without any barriers, enabling the sample to be directly probed with the evanescent filed generated by the total internal reflection occurring at the sample-prism interface (Figure 1C). Before a THz TD-ATR measurement, the M-chip was aligned carefully to make the cavity to fully cover the elliptical THz beam spot, and securely attached and sealed on the prism base by applying an even loading. A syringe or pump was employed to infuse a sample solution through a soft tube into the inlet by a pressure-driven mechanism, and the solution passed through the channel connected with the inlet to fill the cavity. The excess sample solution and air bubbles were drained out through the outlet.

For proper application of the THz TD-ATR spectroscopy integrated with a PDMS M-chip, namely, the THz TD-ATR microfluidics system, we have to carefully consider the possible influence of the configuration of the M-chip on THz spectra. It is a non-trivial work to extract the true THz spectra of an aqueous sample filled in the cavity if the side wall of the M-chip interacts with the evanescent field. Fortunately, for a certain THz TD system, the cross section of the evanescent filed at the sample-prism interface can be estimated. In our case, the diameter of the THz beam is about 12 mm, yielding an elliptical beam spot on the prism base with major axis length of ∼31 mm (12/sin² 38.4°) and minor axis length of ∼12 mm. Thus, we designed a M-chip with a cavity cross section larger than that of the evanescent field. With proper alignment of the M-chip, we ensured only the cavity region overlaid on the evanescent field, by which the influence of the side wall was avoided (Figure 2A). Although the effects of the side wall can be eliminated with this design, the influence of the upper wall of the M-chip has to be taken into account, i.e., the THz reflection occurred at the interface formed by the sample and PDMS upper wall needs to be considered, in order to extract reliable THz spectral data of the sample measured by the THz TD-ATR microfluidics system.

The sample complex dielectric constant is key for analyzing the sample properties. For our THz TD-ATR microfluidic system, the Fresnel’s formulae for two-interface model are used to extract the complex dielectric constant of the sample for general cases (Møller et al., 2007), r ∼ 12 = ε S i 1 − ε S i / ε ∼ sin 2 ⁡ θ − ε ∼ cos ⁡ θ ε S i 1 − ε S i / ε ∼ sin 2 ⁡ θ + ε ∼ cos ⁡ θ (1) r ∼ 23 = ε ∼ 1 − ε S i / ε ∼ w sin 2 ⁡ θ − ε ∼ w 1 − ε S i / ε ∼ sin 2 ⁡ θ ε ∼ 1 − ε S i / ε ∼ w sin 2 ⁡ θ + ε ∼ w 1 − ε S i / ε ∼ sin 2 ⁡ θ (2) where r ∼ 12 and r ∼ 23 are the Fresnel’s reflection coefficients of prism-substance interface and the substance-PDMS upper-wall interface, respectively; ε ∼ w , ε ∼ , and ε S i are the complex dielectric constants of the PDMS, substance filled in the cavity and silicon prism, respectively; and θ is the incident angle of the THz beam in the prism.

For a cavity with a depth of d and an incident wave with a wavelength of λ , the ultimate Fresnel’s reflection coefficient ( r ∼ ) that contains the information of the substance in the cavity and PDMS upper-wall due to their interactions with the evanescent wave is calculated by (McIntyre and Aspnes, 1971) r ∼ = r ∼ 12 + r ∼ 23 ⁡ exp i 4 π d λ ε ∼ − ε S i sin 2 ⁡ θ 1 + r ∼ 12 r ∼ 23 ⁡ exp i 4 π d λ ε ∼ − ε S i sin 2 ⁡ θ (3)

It needs to point out that if the evanescent field cannot penetrate the cavity to reach the upper wall of the M-chip, r ∼ 23 is zero, thus r ∼ 12 is equal to r ∼ . In this case, the two-interface model is degenerated to the one-interface model.

In the experiments, the M-chip without and with an aqueous sample was measured in tandem to obtain the information of the reference (i.e., air) and the sample, respectively. The above three equations are applicable to both the reference and the sample. By substituting Eqs 1, 2 into Eq. 3, the ultimate Fresnel’s reflection coefficients of the reference ( r ∼ r e f ) and the sample ( r ∼ s a m ) were obtained, respectively. Furthermore, the relationship between the ultimate reflected electromagnetic field amplitudes of the sample ( E ∼ s a m ) and reference ( E ∼ r e f ) from the prism-substance interface and their corresponding reflection coefficients can be described by Eq. 4, E ∼ s a m E ∼ r e f = r ∼ s a m r ∼ r e f (4)

In the above equations, ε S i (3.42), d ; λ , θ (51.6°) and the dielectric constant of air (1) are all known, and ε ∼ w was measured using the THz TD spectroscopy in transmission mode (Supplementary Figure S3). With the above information, the complex dielectric constant of the measured sample can be calculated.

THz absorption coefficient ( α ) is also often used to describe the properties of samples, which is calculated according to the following equations (Jepsen et al., 2011; Zhang et al., 2022a), ε ∼ ν = ε ′ ν − i ε ″ ν (5) ε ′ ν = n 2 ν − k 2 ν (6) ε ″ ν = 2 n ν k ν (7) α ν = 4 π ν k ν c (8) where ε ′ and ε ″ are the real and imaginary part of ε ∼ , respectively; ν is the frequency; n and k are the refractive index and extinction coefficient, respectively; and c is the speed of light in vacuum.

Pure water is commonly used as the solvent for many biological samples. Therefore, we measured the THz spectra of pure water (Milli-Q water, 18.2 MΩ cm) using our fabricated M-chips with various cavity depths. By applying the two-interface model, we can see that the complex dielectric constants of pure water measured in the M-chips of various depths are highly consistent with each other (Figures 3A,B). They are also highly consistent with those measured without using the M-chips, for pure bulk water through which the THz evanescent field cannot penetrate. The results tell us that the two-interface model is accurately enough to be used to extract the THz properties of pure water in the cavity of M-Chips.

In contrast, the complex dielectric constants are not necessarily consistent with each other when the one-interface model was applied to analyze the data. Although the complex dielectric constant of pure water measured in the cavity with a depth of 210 μm is consistent with that of pure bulk water, the parameters extracted for the pure water in the cavities with depths of 90, 130, and 170 μm deviate from those of pure bulk water at the lower THz frequency range (Figures 3C,D). These observations indicate that the evanescent field penetrated the pure water with a thickness less than 210 μm, and reached the upper wall of the PDMS M-chip. Obviously, it is inappropriate to apply the one-interface model when the cavity depth is less than 210 μm because the one interface model is only suitable for the situation where the evanescent field does not penetrate the pure water. The influence of the cavity depth on the detected THz wave was further explored by analyzing the depth-related term contained in Eq. 3 for the two-interface model, as shown below, Φ ∼ = r ∼ 23 ⁡ exp i 4 π d λ ε ∼ − ε S i sin 2 ⁡ θ (9)

This term is associated with the cavity depth when the evanescent wave reaches the upper wall of the PDMS M-chip. However, this term is zero, so the two-interface is degenerated to the one-interface model when the evanescent wave cannot penetrate through the aqueous sample in the cavity to reach the upper wall of the PDMS M-chip.

Experimentally, indeed, we observed that both the real and imaginary parts of Φ ∼ show a cavity-depth and frequency dependent character, particularly for the lower frequency range (Figures 4A,B). Interestingly, it is found that both the real and imaginary parts of Φ ∼ for the pure water with a thickness of 210 μm are nearly the same as those of the pure bulk water for the frequency is higher than 0.3 THz. The result verifies that the two-interface model can be degenerated to the one-interface model when the pure water thickness is no less than 210 μm, and that the two-interface model should be applied for pure water with the thickness less than 210 μm. These observations well explain the phenomena observed for the dielectric complex constants in Figure 3. For a commonly used THz TD-ATR spectroscopy system, the THz signal below 0.3 THz is very noisy and often not included in the data analysis. Thus, we recommend to use a M-chip with a cavity depth no less than 210 μm in THz TD-ATR microfluidic system, by which one can employ the simple one-interface model to analyze the data with enough reliability while avoid the complexity of the two-interface model. Specifically, the one-interface model is also applicable for M-chips with cavity depths of 90 μm and above when only the frequency beyond ∼1.0 THz is considered in data analysis (Figure 4).

From the above results we know that the THz TD-ATR spectroscopy integrated with a M-chip with a cavity depth no less than 210 μm can be reliably applied to measure pure water by simply using the one-interface model in the data analysis. To test the wide applicability of the THz TD-ATR system of the above configuration, we measured the THz spectra of phosphate buffered saline (PBS) solution, which is a physiological solution widely used to dissolve biological samples. It is evident that the extracted complex dielectric constants obtained by the one-interface model are well superimposed on those retrieved by the two-interface model (Figure 5).

One of our major purposes is to integrate a suitable M-chip into THz TD-ATR spectroscopy to study biological samples. Thus, we further measured lactic dehydrogenase (LDH) solutions with different concentrations using the PDMS M-chip with a cavity depth of 210 μm, and extracted their THz absorption coefficients which are widely used to assess the character of biological solutions. The THz coefficients were obtained by both the two-interface model and the one-interface model. For example, the THz coefficient of LDH solution with a concentration of 60 mg/mL plotted against a wide-band frequency was shown in Figure 6A. It is clear that for this M-chip configuration, the one-interface model is as accurate as the two-interface model for the measurement of LDH solutions. In addition, we also checked the THz absorption coefficients against the LDH concentrations at certain frequencies (e.g., 0.3, 0.4, and 0.5 THz; Figure 6B). Again, it confirms that there are no observable differences when applying the two models to analyze protein solutions measured by our THz TD-ATR microfluidic system. The THz absorption coefficient decreases with the increase of LDH concentration observed here is consistent with previous studies (Bye et al., 2014), which is very likely due to the solute (LDH) induced dilution and static depolarization effects (Penkov et al., 2017).

Lactic dehydrogenase powder was purchased from Beijing Solarbio Science & Technology Co., Ltd. (Beijing, China), and dissolved in phosphate buffer saline (PBS, pH 7.4, Shanghai Branch of Thermo Fisher Scientific Inc. Shanghai, China) and diluted to desired concentrations with PBS. The prepolymer and the crosslinker of PDMS were ordered from the Shanghai Branch of Dow Corning Corp. (Shanghai, China).

The THz-TD ATR spectroscopy system was established by incorporating an ATR apparatus (BATOP GmbH, Jena, Germany) into the optical path of a commercial THz-TDS system (Tera K15, Menlo Systems GmbH, Münich, Germany). A femtosecond laser with a center wavelength of 1,560 nm, a repetition rate of 100 MHz, and a pulse width less than 90 fs was split into the pump beam and the probe beam. The THz radiation was emitted from a biased photoconductive antenna irradiated by the pump beam, and detected by another photoconductive antenna with the aid of the probe beam. Before experiments, the microfluidic chip fabricated by us was integrated into the system for the measurement of aqueous samples. The whole system was located in a clean room maintained at a temperature of 22°C ± 1.0°C. In experiments, the apparatus including the THz emitter, ATR prism integrated with microfluidic chip and THz detector were enclosed in a sealed container filled with pure nitrogen and kept the humidity to less than 4% to minimize the vapor absorption of THz wave. A p-polarized pulsed THz beam was horizontally incident on the left slanted side of the prism, and the refracted beam was detected from the right side of the prism. The ATR prism and PDMS chip can be re-used after cleaning by ethanol and distilled water in order. Either a milliliter medical syringe (Minkang Medical Materials Co., Ltd. Changsha, China) or a pressure-based flow controller (MFCS-EZ, Fluigent, Paris, France) was used to infuse sample solution into an M-chip.

Time-domain spectra were measured and converted to frequency-domain data by the fast Fourier transform algorithm, from which the electric field amplitude at different frequencies can be obtained. Then the complex dielectric constant and absorption coefficient can be calculated according to Eqs 1–8. The data for each sample represents the average value obtained from three independent measurements.

Microfluidic chips with different cavity depths were fabricated by using a standard protocol, and the details were described in the Supplementary Material.