Leakage pressures for gasketless superhydrophobic fluid interconnects for modular lab-on-a-chip systems

Chip-to-chip and world-to-chip fluidic interconnections are paramount to enable the passage of liquids between component chips and to/from microfluidic systems. Unfortunately, most interconnect designs add additional physical constraints to chips with each additional interconnect leading to over-constrained microfluidic systems. The competing constraints provided by multiple interconnects induce strain in the chips, creating indeterminate dead volumes and misalignment between chips that comprise the microfluidic system. A novel, gasketless superhydrophobic fluidic interconnect (GSFI) that uses capillary forces to form a liquid bridge suspended between concentric through-holes and acting as a fluid passage was investigated. The GSFI decouples the alignment between component chips from the interconnect function and the attachment of the meniscus of the liquid bridge to the edges of the holes produces negligible dead volume. This passive seal was created by patterning parallel superhydrophobic surfaces (water contact angle ≥ 150°) around concentric microfluidic ports separated by a gap. The relative position of the two polymer chips was determined by passive kinematic constraints, three spherical ball bearings seated in v-grooves. A leakage pressure model derived from the Young–Laplace equation was used to estimate the leakage pressure at failure for the liquid bridge. Injection-molded, Cyclic Olefin Copolymer (COC) chip assemblies with assembly gaps from 3 to 240 µm were used to experimentally validate the model. The maximum leakage pressure measured for the GSFI was 21.4 kPa (3.1 psig), which corresponded to a measured mean assembly gap of 3 µm, and decreased to 0.5 kPa (0.073 psig) at a mean assembly gap of 240 µm. The effect of radial misalignment on the efficacy of the gasketless seals was tested and no significant effect was observed. This may be a function of how the liquid bridges are formed during the priming of the chip, but additional research is required to test that hypothesis.


Materials and Methods
Radial Misalignment. The superhydrophobic assembly consisted of two identical polymer chips with through-holes that were aligned and assembled using three pairs of kinematic alignment structures (see Figs. 1(b) and 4(b)). The alignment structures both passively set the gap and concentrically aligned the through holes. Offset measurements from edge alignment standards (see Fig. 1(b) and 4(a)) coupled with a mathematical model quantified the performance of the alignment structures and elucidated the effect of radial misalignment on the maximum pressure capability of the superhydrophobic seal. Cartesian base and feature coordinate frames were defined on each chip (see Fig. S1). Homogeneous coordinate transformation matrices mapped information in the feature coordinates on each chip to the base coordinate system. Similar transformations related features between chips that enabled the coupling of offset measurements along the edge of the assembly to the geometry. A least squares approximation was used to solve the linear system and determine the Body-fixed Cartesian Coordinate Systems on Test Chips Figure S1. Location of Cartesian base and feature coordinate frames used in the evaluation of the effect of misalignment on the chips forming the superhydrophobic stack.

S4
variation transformation between each chip's base coordinate frame. The variation transformation matrix helped derive the equation for radial misalignment between the superhydrophobic through holes. Each chip was assumed to be a rigid body. The base coordinate system was located at the geometric center of each chip and four feature coordinate frames were located at the left, top, and right alignment standards and the chip's through-hole. Fig. S1 shows the locations of the coordinate frames on the chips. The homogeneous coordinate transformation matrices consisted of a 3 x 3 rotation matrix, R, which described the orientation of the feature coordinate frame with respect to the base coordinates, and a 3 x 1 translation vector, p, which located the origin of the feature coordinates in the base coordinate frame. Eq. S1 shows the general form of the nominal coordinate transformation matrix.
The offset measurements collected with an optical microscope at the left, right, and top alignment standards were projections on the x-z and y-z planes. The rigid body assumption coupled the transformations between the assembly's alignment standards to each other (Fig. S1).
The coordinate transformation matrices used to couple the bottom chip's base coordinate frame, A, to the feature coordinate frames, 1, 2, 3 and 7, were identical to the transformations used to connect the top chip's base coordinate frame, B, to its feature coordinate frames, 4, 5, 6 and 8.
The top and bottom chip transformations were as shown in Eqs. S2-S5: where the rotation matrix was the identity matrix since the coordinate systems were aligned.
where 3 1111 is the distance between the A and 3 coordinate frames (31.459 mm), 2 1111 is the distance between A and 2 coordinate frames (30.345 mm), and 7 1111 is the distance between the A and 7 coordinate frames (29.223 mm).
The two rigid body chips were assembled with a nominal gap between them equal to the infinity norm of the assembly's gap measurements. The infinity norm is defined by Eq. S11.
The fixed distance assumption constrains the translation along the z axis and rotation about the x and y axes for the transformation between the A and B coordinate frames. The relationship between the base coordinate frames of the assembly (A and B) can be described by the variation transformation matrix that combines translation along the x and y axes and rotation about the z axis. Eq. S12 describes the variation transformation between the A and B coordinate frames. It assumes small angles of rotation about the z-axis.
Homogeneous coordinate transformations were used to map location of the alignment standards on the top and bottom chips into the base coordinates. This framework coupled the measurements to the geometry of the assembly. Eqs. S19-S21 show the variation transformations relating each chips left, right, and top alignment standards.
The average of the measurements at the left alignment standards, #% estimated the y-offset of the S7 edge projected on to the bottom chip's y-z plane. Similarly, the averages of the right and top alignment standards estimate the y-and x-offset of the edge projected on the bottom chip's y-z and x-z planes. Eqs. S22-S24 show the offset measurements sample means.
Eqs. S22-S24 can be equated to the appropriate components of the coordinate transformations in Eqs. S19-S21 to derive Eqs. S25-S27 Eqs. S25-S27 can be written as a linear system = as follows (Eq. S28): where * is the least squares approximation of [ 1 2 0 ], = is the pseudoinverse of A, and b is the averages of the measurements at the alignment standards. Eq. S32 and Eq. S12 give the coordinate transformation that connects the base coordinate frame of the bottom chip, A, with the base coordinate frame of the top chip, B (Fig. S8). Using similar coordinate transformations, this least squares approximation can be translated to the coordinate frames connecting the top and bottom chips through holes.
The x and y translation components from Eq. S35 give the radial misalignment between the through holes.

Leakage Pressure Measurement
The leakage pressure experimental apparatus consisted of two branches, the pressurized liquid column, and the microfluidic system. The pressurized liquid column was upstream of the microfluidic system. A simplified schematic of the pressure measurement system is shown in Fig. S2. Ultra high purity nitrogen (1) was regulated to 172 kPa to the computer through a USB port. The GUI displayed the system inputs, pressure measurements, and the system output, the pressure controller set point. There were two input signals, from the rupture pressure (P2 in Fig. S2) sensor and the fluid column pressure controller transducer (P1 in The leakage pressure measurement had a start-up procedure, a priming procedure, and a rupture pressure testing procedure. To prime the system, upstream (7 in Fig. S2) and downstream ball valves (10 in Fig. S2) were opened, connecting the gasketless seal assembly through the microfluidic tee to the deionized water column (6 in Fig. S2), pressurized to 0.345 kPa (0.05 psi), until the liquid bridge was formed, establishing the seal. With the system ready, the upstream and downstream ball valves were closed and the liquid column pressure was set to 0 kPa (0 psi). For the leakage pressure tests, the upstream ball valve was opened and the pressure increased across the seal incrementally until rupture was detected. Once leakage was observed, the upstream microfluidic ball valve (7 in Fig. S2) was closed, and the LabVIEW program halted.

S11
Gap and Misalignment Measurements. The gap and misalignment were measured using the Nikon Measurescope MM-11 (Melville, NY) with a Diagnostic Instruments, Inc microscope camera (Sterling Heights, MI) with SPOT advanced imaging software, and a QUADRA-CHEK 2000 (Metronics, Schaumburg, IL). The gap, the left alignment standard, and the right alignment standard were each measured ten times for every interconnect assembly. The top alignment standard was measured ten times for forty-six of the sample assemblies. The radial misalignment was calculated using the method outlined in the first section (pp. S3-S8). The location of the gap measurements and the left, right, and top misalignment measurements are shown in Fig. S3. Locations of Alignment Standards S12 displays the convention adopted for the misalignment measurements. Both the gap and misalignment measurements had a start-up procedure and a data collection procedure. Convention for Offset Measurement S13 tweezers and the thickness of the Hydrobead-P® was measured using the optical microscope by focusing on the reference surface, zeroing the height gage, and then focusing on the peaks of the adjacent Hydrobead-P®. The resulting number on the height gage was recorded as the thickness of the coating. For each sample, the two long tape edges were each measured four times and the tape edge closest to the chip's flat was measured two times. The average measured thickness was 5.58

Results and Discussion
µm with a standard deviation of 3.41 µm. Fig. S5 shows a histogram of the resulting ninety-six thickness measurements across twelve spin coated samples.
Hydrobead-P® Water Contact Angle Measurements. The water contact angle indicated the wettability of the Hydrobead-P® surface and was used as a parameter in the maximum rupture pressure model. To measure the contact angle, thirteen injection molded COC samples were spin coated with Hydrobead-P® (Hydrobead-P® "old formula", Hydrobead, San Diego, CA) and cured for 1 hour in the VWR 1602 (Radnor, PA) oven preheated to 100⁰C. The contact angle of each sample was measured sixteen times across the surface using the sessile drop technique with a VCA Optima (Billerica, MA). The average contact angle was 149.8ᴼ and the standard deviation was 8.74ᴼ. Fig. S6 is a histogram of the 208 contact angle measurements.
Assembled Chips An example of an unclamped assembly is shown in Fig. S7. Fully Assembled Chips with World-to-Chip Connectors