Structural colour enhanced microfluidics

Advances in microfluidic technology towards flexibility, transparency, functionality, wearability, scale reduction or complexity enhancement are currently limited by choices in materials and assembly methods. Organized microfibrillation is a method for optically printing well-defined porosity into thin polymer films with ultrahigh resolution. Here we demonstrate this method to create self-enclosed microfluidic devices with a few simple steps, in a number of flexible and transparent formats. Structural colour, a property of organized microfibrillation, becomes an intrinsic feature of these microfluidic devices, enabling in-situ sensing capability. Since the system fluid dynamics are dependent on the internal pore size, capillary flow is shown to become characterized by structural colour, while independent of channel dimension, irrespective of whether devices are printed at the centimetre or micrometre scale. Moreover, the capability of generating and combining different internal porosities enables the OM microfluidics to be used for pore-size based applications, as demonstrated by separation of biomolecular mixtures.

| Example reflectance spectra for OM microfluidic films. Polymer is a, polystyrene (PS), b, poly(methyl methacrylate) (PMMA), and c, polycarbonate (PC). These OM microfluidic films were printed on silicon wafer using stainless steel stencil as the shadow mask. Photoinitiator is 9,10-phenanthrenequinone (PQ) for (a) and 4,4′-bis-(diethylamino)-benzophenone (BDABP) for (b, c). Photocrosslinking was conducted in a custom oven (λ i , 375 nm). After the development step, a periodic structure is formed at the irradiated region of the films, which is indicated by the Bragg peak on their reflectance spectra (blue curves); in contrast, the non-irradiated region of these films shows a thin film reflectance profile (black curves). Bragg peak location can be tuned by illumination wavelength (λ i ) and other experimental conditions.  Fig. 3d in the main text. Series 1, 2 are flow measurement from 3-mm-width channels; series 3, 4 are flow measurement from 5-mm-width channels. Series 5, 6 are flow measurement from micron-sized channels (features from 5 to 40 microns). The channels, prepared under different photoinitiator and illumination conditions, are specified in Supplementary Table 3. Bragg peak of microchannels was estimated through converting microscope photo hue value to wavelength value (see the calibration in Supplementary Fig.  6). Here, macrochannels were fabricated in straight-line shape using stainless steel stencil as the shadow mask (Series 1-4). Microchannels were fabricated using a micro-LED illumination instrument (Series 5&6). The liquid is n-hexadecane and the substrate is silicon wafer. Error bars are S.D. across 3 measurements. b, Optical microscope photos for the fabricated microchannels (Series 5&6). Scale bar, 200 μm. Fig. 6 | Calibration for converting microscope photo hue value to Bragg peak. a, The calibration plot for converting microscope photo hue value to Bragg peak. b, The example reflectance spectra for OM channels. c, The corresponding microscope photos for OM channels. Scale bar, 500 μm. The Bragg peak of these channels was measured by a spectrometer (MCPD-3700, Otsuka Electronics). Correspondingly, photos were recorded by an optical microscope (Axioscope A1 MAT, Carl Zeiss, white balanced prior to photo-taking). The wavelength value is converted from microscope photo hue value according to the visible light spectrum chart, using ImageJ software (version 1.52p). The dashed line in the calibration plot displays the ideal case where wavelength value equals to the Bragg peak. The red dots denote the experimental results, which shows the error between spectrometer measured Bragg peak and microscope recorded wavelength value is 2.2% on average and less than 4.5% for all the OM channels fabricated. These results justify using the wavelength value of the microscope photo to estimate Bragg peak. This produces a convenient way for studying OM microchannels, especially when the channel print area is tiny and thus the direct measurement of Bragg peak using the spectrometer becomes difficult. Supplementary Fig. 9 | Impact of bending on the structural colour of OM film. a, In situ reflectance spectrum of the OM film during the bending test. The spectrum reference was aluminium (LUXAL UV, 60-μm-thick, Toyo Aluminium K.K.). b, Bragg peak shift versus the curvatures of OM film. c, d, Side-view and top-view photos of an OM film on the aluminium foil before the bending test. e, f, Side-view and top-view photos of the film during the bending test. g, Hue and colour shift versus the curvatures of OM film. h, In the end, bending was released and the OM film was placed back onto silicon wafer for spectral comparison. Scale bar in (c) and (e), 10 mm. The OM films were made using Polycarbonate (PC)/4,4′-bis-(diethylamino)-benzophenone (BDABP) on silicon wafer (LED λ i = 385 nm). The film was peeled off from the substrate carefully in water and transferred onto a piece of aluminium foil. A vice was used for the bending to apply various curvatures to the OM film. As the bending was increased, the in situ reflectance spectrum was recorded. Side-view photos were taken at the same time to obtain the curvature. The curvature was calculated by the software Fiji (version 2.1.0/1.53c) using the built-in plugin Kappa. Reported values are the average curvature of a 2.5-mm-length curve at the apex region of the bent film where its reflectance spectrum was recorded. In situ measurements show little spectral change when the curvature of OM film is ≤ 0.1 mm -1 (radius of curvature: ≥ 10 mm). As the curvature further increases to 0.5 mm -1 (radius of curvature decreases to 2 mm), the Bragg peak shift of OM film remains in the small range of 1-4 nm.

Supplementary
As an alternative approach to check the impact of bending, top-view photos were taken for colour comparison under different bending conditions. To keep consistency, an 18% neutral grey card was used as the colour reference. Colour comparison focused on the apex region of the bent OM film that held a fixed angle to the camera lens. The wavelength value of the colour is derived from the hue value according to the visible light spectrum chart, using ImageJ software (version 1.52p). Photo comparison indicates that the colour shift of OM film keeps < 3 nm as its curvature increases to 0.5 mm -1 . This is consistent with the results from the spectral measurements.
The results show negligible change of structural colour in this range of bending conditions. In addition, after releasing the bending and placing the OM film back onto silicon wafer, the reflectance spectrum remains almost unchanged in comparison to its pristine status. This indicates bending to such an extent does not permanently deform the OM structure.

Supplementary Fig. 10 | Energy dosage design for the separation microchannel.
The energy dosage is 600 J/cm 2 for the main channel (as indicated by the white colour) while 300 J/cm 2 for the selected side branches (as indicated by the brown colour). In addition, an energy transition region of 32 μm length is applied at the boundary region of the high and low dosage regions. In each transition region, the energy dosage increases gradually by 60 J/cm 2 per 8 μm length from the 300 J/cm 2 side branch to the 600 J/cm 2 main channel. Scale bar, 200 μm. Experiments found that the regions receiving high energy dosage develop faster than the regions receiving low energy dosage during the development step. This is due to the positive relationship between crosslinking energy and the driving force for the development step 2 . Completing the development step based on the high energy regions, the resulting OM structure is found to be fully developed in the high energy regions while not fully developed in the low energy regions. This can generate the final OM microchannel that combines differing internal porosities in a single miniature device. This OM microchannel was made on glass substrate using a micro-LED instrument (λ i = 405 nm). It adopted the energy dosage design in Supplementary Fig. 10 for the illumination step. Supplementary Fig. 12| The SEM image for separation channel. It is the original SEM image for Fig. 5f. Scale bar, 50 μm. Supplementary Fig. 13| Insulin-BSA separation by the OM microchannel. Imaging was conducted by an inverted confocal laser scanning microscope. The green and red colours represent the BSA protein (66 kDa, pre-stained with the dye SYPRO Orange) and fluorescent insulin (Alexa Fluor 680 labeled, 6 kDa), respectively. The OM microchannel was made using polystyrene (PS)/9,10-phenanthrenequinone (PQ) on cover glass using a micro-LED instrument (λ i = 405 nm). The microchannel was printed according to the design in Supplementary Fig. 10 with different energy dosages in the main channel and the side branch. The microscope photo of OM channel is shown in Fig. 5e. Scale bar, 100 μm. Note: The micro-LED machine does not require a separate photomask.

Supplementary
✝The Bragg peak of the tested microchannels is estimated to be 540 ± 10 nm, according to the calibration plot shown in Supplementary Fig. 6. ‡The Bragg peaks of the tested macrochannels are 670 ± 20 nm, measured by spectrometer. §Light source for custom crosslinking ovens is Thorlabs LED, except Fig. 4c where a Thorlabs Laser is used.  Supplementary Fig. 5b: "vessel" refers to a capillary vessel like pattern, and "complex" refers to a collection of miniaturized microfluidic features including a hexagonal lattice, width variation, spiral, and zig-zag channels. DSLR stands for a digital single-lens reflex camera.

Supplementary
✝In Fig. 3e, the flow of pure alkanes was measured by a DSLR camera (EOS Kiss X5) with a macro lens (EFS 60 mm, Canon), while the flow of alkane mixture, pure alcohol, and alcohol mixture was measured by an optical microscope (Axioscope A1 MAT, Carl Zeiss).

Mathematic models for capillary flow dynamics in OM channel
For an incompressible and Newtonian fluid, Hagen-Poiseuille law gives the pressure drop (ΔP) of laminar flow through a long pipe of constant cross-section 6,7 , as shown in Supplementary Equation (1): where μ is the dynamic viscosity of the liquid, l is the actual flow distance, Q is the volumetric flow rate, D h is the hydraulic dynamic diameter of the pipe cross-section.
For a cylindrical tube, the cross-section is a perfect circle so that D h equals to 2r. Therefore, Supplementary Equation (1) can be rewritten as: where r is the radius of cylinder cross-section.
In reality, the cross-section of porous nanomaterials is often not a perfect circle. Hence, the effect of cross-section geometry should be included. Moreover, the effective viscosity of liquid (μ e ) should be considered, since the value when liquid is in nanoscale confinement can be significantly higher than the bulk viscosity 8 . The effective liquid viscosity is influenced by liquid-wall interactions at nano scale [9][10][11] . Hence, Supplementary Equation (2) is modified as follows for an actual porous material: where μ e is the effective viscosity of the liquid in the porous material, α is a dimensionless geometrical correction factor, and r e is the equivalent radius. According to the previous studies, α = 1 when cross-section is a perfect circle; α = 1.094 when cross-section is a square, and α = 1.186 when cross-section is an equilateral triangle 12 .
The above equation only considers a single channel. An actual porous material can be considered as a collection of many sub-channels with geometrically varying cross-sections. Hence, a further modification of the equation is shown as follows: where r a is the average radius of all sub-channels, and α is the corresponding average value for the geometrical factor.
Capillary flow through such kind of porous material is subject to the combined effects of capillary pressure (P c ), hydrostatic pressure (P h ), and atmospheric pressure (P a ) 13,14 , as shown in Supplementary Equation (5).
When pore sizes are in the micro/nano small scales, capillary pressure (P c ) usually plays the dominant role compared to hydrostatic pressure (P h ). Meanwhile, P a equals to 0 when both channel ends are open to the atmosphere. Therefore, Supplementary Equation (5) can be reasonably simplified as follows: According to Young-Laplace law, the capillary pressure (P c ) of the channel can be expressed in Supplementary Equation (7) 15,16 : where γ is the surface tension of the liquid, θ is the contact angle of the liquid on the surface of the channel. (4) and (7) into Supplementary Equation (6) obtains Supplementary Equation (8):

Substituting Supplementary Equation
Volumetric flow rate (Q) equals to A × v τ , where A is channel cross-section area and v τ is the actual flow velocity considering the tortuosity (τ). When channel cross-section is a constant of π × r a 2 , Supplementary Equation (8) can be rearranged as follows: The flow path in a real porous media is often not a straight line at small scales; thus, tortuosity (τ, τ=l/L) should be included for the consideration 17 . In our study, L is the observed flow distance recorded by a microscope or DSLR camera, while τ is the tortuosity of the actual flow pathway at nanometer scale. Substituting actual flow distance (l) and velocity (v τ ) with the observed flow distance (L) and velocity (v, v= v τ /τ), Supplementary Equation (9) can be rewritten as follows: The observed flow velocity (v) can be written as a differential function of dL/dt. The integration of the Supplementary Equation (10) obtains Supplementary Equation (11), which is the same equation shown in the main text: Supplementary Equation (11) is a specific form of Lucas-Washburn model for capillary flow through a media with fluidically relevant pore size at nanometer scale. Hence, this equation is suitable for capillary flow in OM channels. It indicates that the observed flow distance square (L 2 ) is proportional to time (t). The slope of L 2 versus t (dL 2 /dt) is the fluidic parameter describing how fast the liquid is spreading in the porous media. In the case of the OM channel, dL 2 /dt is proportional to r a , the internal porosity size of the OM structure. Since the internal pore size is also related to interlayer spacing, the fluidic property of OM channels is determined by their structural colour (Bragg peak), not the extrinsic channel geometries as printed.

Mathematic models for capillary flow dynamics in conventional hollow channels
In hollow channels fabricated by conventional lithographic techniques, flow dynamics is determined by the extrinsic channel geometries (i.e. printed channel width). In an ideal case of the cylindrical tube (τ = 1, α = 1) with negligible liquid-wall interaction (μ e = μ), the equation describing flow dynamics in such hollow channels can be expressed as follows.