Evaporation-driven transport-control of small molecules along nanoslits

Understanding and controlling the transport mechanisms of small molecules at the micro/nanoscales is vital because they provide a working principle for a variety of practical micro/nanofluidic applications. However, most precedent mechanisms still have remaining obstacles such as complicated fabrication processes, limitations of materials, and undesired damage on samples. Herein, we present the evaporation-driven transport-control of small molecules in gas-permeable and low-aspect ratio nanoslits, wherein both the diffusive and advective mass transports of solutes are affected by solvent evaporation through the nanoslit walls. The effect of the evaporation flux on the mass transport of small molecules in various nanoslit-integrated micro/nanofluidic devices is characterized, and dynamic transport along the nanoslit is investigated by conducting numerical simulations using the advection-diffusion equation. We further demonstrate that evaporation-driven, nanoslit-based transport-control can be easily applied to a micro/nanofluidic channel network in an independent and addressable array, offering a unique working principle for micro/nanofluidic applications and components such as molecule-valves, -concentrators, -pumps, and -filters.


Supplementary Notes Supplementary Note 1: Dynamics of solute transport along the nanoslit
In the nanoslit, the mass transport of the solute is governed by the advection-diffusion equation: where ( , ) c c x t  is the solute concentration, D is the diffusion coefficient of the solute, and where J is the evaporation flux of the solvent through the nanoslit walls, ρ is the solvent density, and h is the nanoslit height. Therefore, the governing equation was simplified as follows for a low Péclet number (i.e., In the dimensionless form, this becomes is the dimensionless distance, o c is the solute concentration in the reservoir, o t is the dehydration time, and the nanoslit length is defined as 2L. The large dimensional difference between the nanoslit at nanoscales and the test chamber at microscales makes the simulation of the entire device challenging, in terms of time, cost, and accuracy. In addition, for the parametric study, 1D approximation was conducted by focusing on the nanoslit of interest. In this context, we assumed that the concentration of the solution at the drain-channel-sided end of the nanoslit (x = L) is zero. This assumption represents a conditional set because the molecules concentrated at the nanoslit originate only from the source channel and not from the drain channel. For our micro/nanofluidic system, the test chamber has a significantly larger cross-sectional area orthogonal to the diffusion direction than that of the nanoslit. Because of this substantial difference in the cross-sectional areas, the concentration gradient drops mostly within the nanoslit to satisfy the continuity of the solute transport. Therefore, even if the concentration in the test chamber is not exactly zero, its value is significantly low in comparison with that in the nanoslit. By separating the nanoslit and the test chamber under this assumption, the concentration of the test chamber represents the mass transport rate from the nanoslit to the test chamber rather than the concentration at the end of the nanoslit (x = L). From this point of view, the nanoslits of 50, 100, and 200 μm, wherein the solutes are not concentrated, as depicted in Fig. 3c, show good agreement with those depicted in Fig. 2c. In other words, the same linear concentration gradient was observed for the S-4 dimensionless distance and concentration cases. The shorter nanoslit has a steeper concentration gradient, and the diffusion into the test chamber increases according to Fick's law. Therefore, as depicted in Fig. 2b, as the length of the nanoslit decreases, the fluorescence intensity at the steady state increases, and vice versa.
In summary, the fluorescence intensities of the test chamber are a result of the diffusion from the nanoslit to the test chamber; thus, the shorter the nanoslit, the greater the fluorescence intensities at the test chamber. Therefore, we concluded that the results of Fig. 3c and 2b show good agreement. This is why that the test chamber is integrated with the nanoslit to quantify the mass transport rate along the nanoslit.
In particular, we performed numerical simulations on the diffusion along the nanoslit and the test chamber using COMSOL Multiphysics (ver 5.5). The dimensions of the numerical domain are identical with those of the micro-/nanofluidic system described in the manuscript.
The dimensionless concentration, o c c , at the end of the nanoslit (i.e., the junction between the nanoslit and source channel) was set to 1, and the o c c at the end of the test chamber was set to 0 (i.e., the junction between the inlet of the test chamber and the drain channel). In the steadystate study, as depicted in Supplementary Fig. 12a, b, the concentration level drops mainly in the nanoslit and the concentration of the test chamber is considerably close to zero, and seems negligible enough, as depicted in Supplementary Fig. 12c Fig. 1 Characterization of fluorescence intensity with test chamber. a Fluorescence intensities (FIs) of the test chamber acquired over time. A global, evaporationcontrolled, micro/nanofluidic device (GECMN) with nanoslits of 400 µm is depicted for better presentation of the micro/nanofluidic system, while the experiments were performed using GECMN with nanoslits of 800 µm as depicted in (b), (c) and Fig. 2a. b Time-lapse fluorescence images of a fully hydrated polydimethylsiloxane (PDMS) system, which is exposed to a high humidity (relative humidity; RH ~95%) to maintain hydration. The fluorescein isothiocyanate (FITC) molecules are continuously transported along the nanoslit and then arrive at the test chamber. c Time-lapse fluorescence images of a fully dehydrated PDMS system, which is exposed to a low humidity (RH ~20%) to maintain dehydration. No FI is detected, confirming that evaporation-driven advective transport of the FITC molecules is stronger than diffusive transport. After lifting off the PDMS device, the NAQD is cleaned by 30 min of sonification while soaked in acetone. Then, the NAQD is transferred from the glass substrate to a UV-curable adhesive, which is immediately cured by a UV lamp before the adhesive permeates into the NAQD structure. Apparently, the SEM images show that the quantum dots (QDs) are close-packed.

Supplementary Fig. 8 NAQD sample preparation for transmission electron microscopy (TEM) using dual-beam focused ion beam (FIB).
The NAQD is generated on the Si substrate. After lifting off the PDMS device, the NAQD is cleaned by sonification for 30 min while soaked in acetone. a SEM image of the NAQD deposited with Pt to protect its original structure from FIB milling. The maximal thickness of the NAQD may consist of about 100 QD layers into the depth direction of the Si substrate. b SEM image of the cross-section of the NAQD milled by FIB. The cross-section of the sample is delivered to TEM grids and its two ends are fixed by another Pt deposition. c TEM image of the cross-section of the NAQD sample.
Supplementary Fig. 11 Schematic of experimental setup. Global humidity in the cell incubator is controlled by the Global RH control setup. The RH data measured by the RH sensor are delivered to the computer through a data acquisition system, Arduino. Using the RH data, the computer controls an actuation valve whose inlet is connected to the N2 gas chamber; one of the outlets is directly connected to the cell incubator, and the other outlet is connected to the cell incubator through a humidifier. A syringe pump is used for introducing the solutions into the source, drain, and rehydrating channels at a fixed flow rate. A pressure regulator is connected to the N2 gas chamber and the device to apply a fixed pressure to the dehydrating microchannel.

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Supplementary Fig. 12 3D Supplementary Fig. 12a) to the inlet of the test chamber (x = 310 μm in Supplementary Fig. 12a); all calculations in the measurement are conducted at y = 0 μm and z = 0.1 μm as depicted in Supplementary Fig. 12a, 100 nm above the substrate. The concentration drops significantly inside the nanoslit. c The concentration distribution of the test chamber is rescaled from that in (b) to focus on the test chamber. The level of the concentration is considerably low in comparison with that in the nanoslit.