P. M.
Fordyce
*ab,
C. A.
Diaz-Botia
c,
J. L.
DeRisi
ab and
R.
Gomez-Sjoberg
*ac
aDepartment of Biochemistry and Biophysics, University of California San Francisco, 1700 4th Street Byers Hall Room 403, San Francisco, CA 94158, USA. E-mail: polly@derisilab.ucsf.edu
bHoward Hughes Medical Institute, 4000 Jones Bridge Road, Chevy Chase, MD 20815-6789, USA
cEngineering Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road Mail Stop 70A3362, Berkeley, CA 94720-8178, USA. E-mail: RGomez@lbl.gov
First published on 11th July 2012
Multilayer soft lithography (MSL) provides a convenient and low-cost method for fabricating poly(dimethyl siloxane) (PDMS) microfluidic devices with on-chip valves for automated and precise control of fluid flow. MSL casting molds for flow channels typically incorporate small patches of rounded positive photoresist at valve locations to achieve the rounded cross-sectional profile required for these valves to function properly. Despite the importance of these rounded features for device performance, a comprehensive characterization of how the rounding process affects feature dimensions and closing pressures has been lacking. Here, we measure valve dimensions both before and after rounding and closing pressures for 120 different valve widths and lengths at post-rounding heights between 15 and 84 μm, for a total of 1200 different geometries spanning a wide range of useful sizes. We find that valve height and width after rounding depend strongly on valve aspect ratios, with these effects becoming more pronounced for taller and narrower features. Based on the measured data, we provide a simple fitted model and an online tool for estimating the pre-rounding dimensions needed to achieve desired post-rounding dimensions. We also find that valve closing pressures are well explained by modelling valve membranes in a manner analogous to a suspension bridge, shedding new light on device physics and providing a practical model for estimating closing pressures during device design.
Fig. 1 Experimental geometries. (A) Top view of an MSL valve. (B) Side view of two-layer “push-down” and “push-up” devices. Pressurization of control channel deflects membrane separating the layers, closing valve (compare top and bottom). Valves with square flow channel profiles leave pockets of fluid flow (blue), creating a sieve (“push-up” configuration, left column). Valves with rounded flow channel profiles seal completely (“push-up” configuration, right column). (C) Slow heating of square channels made of positive photoresist allows reflow. (D) Rounded photoresist feature widths should match flow channel width (Fw); lengths are defined by control channel width (orange, Cw), spacing between rounded (dark green) and square (light green) photoresists (S), and overlap between photoresists (O). (E) Device design including 240 different valves of 6 different widths and varying lengths. (F) Photograph of device with detail showing individual channels. |
Devices can be configured in two geometries: “push-down”, in which flow channels are located below control channels, and “push-up”, in which flow channels are located above control channels (Fig. 1B). “Push-down” configurations allow flow channels to be in direct contact with a substrate, facilitating applications in which the substrate surface is modified and/or patterned before mounting the microfluidic device.6,7 Closing pressures depend on valve dimensions and the thickness of the membrane separating the channels for both configurations;13,14 however, higher pressures are required to close “push-down” valves, limiting the maximum flow channel height of these devices.2,13,14 The lower pressures required to close “push-up” valves allow construction of devices with much taller channels, providing lower fluidic resistances and facilitating manipulation of cells,8 beads, droplets, and other large objects.
In both configurations, the performance of these valves is highly dependent on the cross-sectional profile of the flow channel. If the flow channel has a cross section with sharp corners at a valve location, the membrane is not able to completely seal the corners, creating a “sieve” that can be opened and closed on command (Fig. 1B). Although such sieve valves can be very useful for trapping beads (to create chromatography columns,15 for example) or changing the fluidic resistance of a channel, they cannot control fluid flow within the device. To produce fully sealing valves, flow channels must have a rounded cross-sectional profile at the point where the valve is formed (Fig. 1B).9 Rounded profiles are typically generated using a positive photoresist (e.g. AZ50 XT or SPR 220) that is melted and reflowed by heating after photolithographic patterning, causing the initial rectangular cross-section to become parabolic (Fig. 1C).
Rounding complex continuous channel geometries made with thick (>∼20 μm) positive resist often leads to large variations in channel heights because of capillarity-driven movements of molten photoresist from one area of the design to another. Therefore, MSL flow molds with tall channels are typically composed of “rounding” positive photoresist patches only where valves are required, and SU-8 negative photoresists everywhere else (Fig. 1D). To avoid sharp changes in channel height that could result in dead volumes and edges that could trap particles or cells, the reflowed valve dimensions should match the dimensions of the surrounding SU-8 channel heights as closely as possible. Matching channel profiles can be particularly difficult for applications requiring relatively tall channels, where reflow can drastically change channel dimensions.
To establish a practical guide for the design of these devices, we systematically characterized the reflow process for a variety of microfluidic valve dimensions. Importantly, the range of feature geometries tested here encompasses all feature dimensions likely to be used within microfluidic devices requiring tall channels (20 to 85 μm). We demonstrate that for tall valves, final feature heights and widths after reflow are strongly dependent on design geometry. In addition, we determine that the closing valve pressures for these same valve geometries can be well described by a single physical “thick spring” model.14 The data and software design tool presented here should prove a valuable resource for microfluidics laboratories seeking to optimize photoresist processing protocols and device design.
P = E[4Hh3(W−4 + L−4)] | (1) |
Here and in the other pressure models, E represents the experimentally measured Young's modulus for the PDMS that forms the valve membrane.
P = Eε | (2) |
The strain can be expressed as the difference between the path length of the membrane when pressurized and the path length of the membrane at rest:
ε = (l−W)/l | (3) |
The profilometry measurements suggest that the path traveled by the membrane is approximately parabolic:
(4) |
Integrating along this path to determine a pressurized path length yields:
(5) |
Combining all of these relationships and extending the model to consider strain in both dimensions yields the final relationship:
(6) |
The variable lW represents the path length of the membrane across the width of the valve, and the variable lL represents the path length of the membrane across the length of the valve. Here, we use the post-reflow valve widths determined by profilometry as the valve width (W), and the design width of the control channel as the valve length (L).
F1 = PWL | (7) |
At equilibrium, this force is balanced out by the vertical projections of the force F2 along the cables. Considering only one dimension yields
(8) |
The cross-sectional area of the spring is given by hW, so we can rewrite eqn (2) here as:
F2 = EhLε | (9) |
Substituting this into eqn (8) and adding in the explicit expression for F1 from eqn (7):
(10) |
Finally, extending this to consider both dimensions yields a final expression of (eqn 11):
(11) |
As before, we use the post-reflow valve widths determined by profilometry as the valve width (W), and the design width of the control channel as the valve length (L).
For each model, we generated an initial value for the Young's modulus by fitting the data with the appropriate equation while treating this value as a free parameter. We then performed a linear regression between predicted and measured values and adjusted the value for the Young's modulus by the linear regression slope to maximize agreement between predicted and measured values.
To comprehensively characterize valves encompassing a wide range of practically useful dimensions, we designed and fabricated a device with rounded valves of various common flow channel widths (50 μm, 75 μm, 100 μm, 150 μm, 200 μm, and 250 μm) crossed by control channels either 1 x or 1.5 x the valve width (Fig. 1E, Fig. 1F). For each flow and control channel width combination, we then calculated valve lengths assuming a desired spacing of either 25 μm, 50 μm, or 100 μm between the crossover control channel and the rounded photoresist feature, and desired overlaps of either 25 μm, 50 μm, 100 μm, 200 μm, or 300 μm between the two flow channel photoresists (Table S1†). To facilitate ease of fabrication and device labeling, we then chose a representative series of valve lengths encompassing both the minimum and maximum calculated lengths, with multiple values in between (Table S2†).
Fig. 2 Effects of heat-induced reflow on rounded feature heights. (A) Feature heights as a function of spin speeds for features before (left) and after (right) reflow. Light grey circles show individual valve height measurements, dark grey circles show average feature heights for each spin speed. (B) Change in average feature height after reflow as a function of spin speed. Change is expressed as the ratio of average heights. (C) Average feature heights as a function of design feature width for each spin speed before (left) and after reflow (right). (D) Change in average feature height after reflow as a function of both design feature width and spin speed. (E) Feature heights as a function of both design feature widths and lengths for each spin speed after reflow. All error bars correspond to the standard deviation of the measurements. |
To understand the cause of this increased variance, we examined the dependence of feature height on the designed feature width (Fig. 2C). Before hard baking and reflow, feature heights showed no dependence on design width and depended only on the photoresist spin speed (Fig. 2C, left). After hard baking and reflow, feature heights showed a strong dependence on feature width (Fig. 2C, right). For all spin speeds, narrow features appeared to become shorter after reflow, while wider features appeared to become slightly taller (Fig. 2D). This effect plateaued at larger valve widths, with the inflection point determined by the cross-sectional aspect ratio of the valves (Fig. 2C, 2D).
Next, for each photoresist spin speed and feature width, we examined whether the final post-bake feature height showed any dependence on feature length (Fig. 2E). For all features at all spin speeds, shorter features tended to be a bit taller; this effect was more pronounced for lower spin speeds and narrower features (Fig. 2E).
Fig. 3 Rounded feature widths before and after reflow. (A) Stereoscope images of two representative features before and after reflow. Right hand columns show feature edges (green) as defined by a custom edge-finding algorithm. (B) Profilometer data showing feature height as a function of cross-sectional position for a single valve both before (left) and after (right) reflow. Before hard baking, valve profiles are trapezoidal with both a minimum (orange) and maximum (blue) width. After baking, valve profiles are parabolic, with a single width defining the extents of the feature base (blue). (C) Widths measured using both image analysis and profilometry as a function of design width both before (top row) and after (bottom row) hard baking and reflow. |
Nearly all of the designed device valve lengths were greater than 200 μm. Consequently, we expected measured valve lengths to be similar to design dimensions. Consistent with this, we find that measured lengths largely reflect design parameters, although the shortest valves (<300 μm) are about 10% longer than expected after reflow (Fig. S1†).
z = 0.630 + 0.175x + 0.052y +0.742x2 − 0.048xy | (12) |
Fig. 4 Model of post-bake feature heights as a function of pre-bake aspect ratios. (A) Height ratio (pre-bake height/post-bake height) as a function of the pre-bake cross-sectional aspect ratio (measured height/width). The black line corresponds to the fit to the data shown on the figure. (B) Height ratio (pre-bake height/post-bake height) as a function of the pre-bake planar aspect ratio (measured length/width). The color of each point reflects the spin speed of the wafer. |
The last polynomial can be re-written as an easily-solvable quadratic equation with the pre-bake height (h) given as a function of the desired rounded height (H), pre-bake width (w), and pre-bake length (l):
(13) |
Where A = 0.630, B = 0.175, C = 0.052, D = 0.742, and E = −0.048. Solving this equation will provide a good approximation to the required pre-bake height needed to achieve a desired post-bake height, given a certain pre-bake width and length. However, it should be kept in mind that this is a purely empirical model based on the measurements made here. Consequently, it remains to be seen if this model can predict post-bake changes in height for features with drastically different dimensions. Additionally, baking changes the width and length of features in a way that cannot be predicted by this simple equation. To make the design of AZ50 XT features easier, we have developed an online tool that allows users to specify desired post-bake channel dimensions (available at http://derisilab.ucsf.edu under the “Software” tab). The tool calculates the appropriate pre-bake height determined by this model and looks up empirical measurements of valves that most closely match the desired dimensions. In addition, the accompanying data files are available for download (Table S3†).
Here, we examined the ability of these models to accurately predict closing pressures for significantly taller push-up microfluidic valves. To determine valve closing pressures, we connected the control channels to a pressure source, incrementally increased the pressure by either 1.72 kPa (0.25 psi) steps (for pressures below 89.6 kPa = 13 psi) or 6.9 kPa (1 psi) steps (for all other pressures), and recorded the pressure at which each valve closed. Valves were considered closed when a central portion of the valve membrane completely sealed off the flow channel (Fig. 5A). As expected, closing pressures were found to depend strongly on both flow and control channel widths, and flow channel height, with taller features requiring higher pressures to close (Fig. 5B). We observed two experimental failure modes. For very tall and narrow valves, valves remained open at pressures up to 413 kPa (60 psi), and higher pressures led to device delamination before valve closure could be observed. Conversely, for very short and wide valves, the valve membrane would sag and become stuck to the opposite side of the channel, rendering valves permanently open.
Fig. 5 Microfluidic “push-up” valves are best modelled as suspension bridges using a “thick spring” model. (A) Photograph showing six valves of different lengths with a single pressure applied across all of them. The 700 μm long valves are closed completely, but the 600 μm valves are not. (B) Microscope image of a single push-up valve in cross-section showing the flow channel, control channel, and membrane separating them. (C) Measured closing pressure as a function of flow channel width for control valves that are either the same width as the flow channel (left panel), or 1.5 times as wide as the flow channel (right panel). The color of each data point corresponds to the measured flow channel/valve height. (D) Predicted closing pressures plotted versus actual measured closing pressures for 3 different physical valve models: thick beam model (left), thin spring model (middle), and thick spring model (right). The color of each data point corresponds to the measured flow channel width. |
Two of the three models require measurement of the valve membrane thickness as an input; in addition, all three models require measured valve dimensions and the Young's modulus for PDMS. To determine membrane thickness, we imaged cross-sectional slices of 10 valves from 4 devices, yielding an average value of 15.3 ± 2.5 μm (mean ± standard deviation) (Fig. 5B). The Young's modulus of PDMS is dependent on the ratio of the two PDMS components, and ranges from 359.9 kPa (52.2 psi) for a 1:20 (cross-linker:elastomer base) mixture to 868.8 kPa (125.9 psi) for a 1:5 mixture.16 In our fabrication process, the thick flow layer (1:5) and the thin control layer (1:20) are partially cured and then bonded by putting them in contact with each other and baking at 80 °C for at least 1 h. During this bake, excess curing agent from the flow layer diffuses into the control layer and cross-links the interface to form a single slab of PDMS (thereby changing the composition of the thin control layer). Since the Young's modulus for the PDMS membrane forming the valves is unknown, we treat this value as a free parameter in this analysis.
To evaluate each model, we calculated predicted closing pressures for each valve on the device using eqn (1), (6), and (11) and then compared these predicted values with measured closing pressures. Models were evaluated using two criteria: (1) whether predicted and measured pressures appeared to be linearly related, and (2) whether the returned value for the Young's modulus agreed with known experimental values.16 The thick spring model tended to both underestimate the closing pressures at low pressures and overestimate closing pressures at high pressures. In addition, this model returned a vastly inflated value for the Young's modulus (39 MPa = 5598 psi). The thin spring model performed slightly better, returning a low but more reasonable value for the Young's modulus (214 kPa = 31 psi). However, the model overestimated closing pressures at low pressures and underestimated closing pressures at higher pressures. Surprisingly, a version of the thick spring model optimized here for taller valve heights completely recapitulated all measured pressures and returned a value for the Young's modulus (1 MPa = 145 psi) that is very close to the experimentally measured value for a 1:5 mixing ratio of PDMS. Given that we expect the excess cross-linker within the 4 mm thick layer of 1:5 PDMS in the flow layer to diffuse into the very thin (∼30 μm) 1:20 PDMS in the control layer, making this thin layer effectively a 1:5 mixture, this value is in remarkable agreement with theoretical predictions. These results suggest that push-up valves behave fundamentally differently than push-down valves, and can be explained by a simple thick spring model with no need for linear superposition.14 Importantly, this simple relationship only becomes apparent after taking into account the profound effects of the reflow process on all of the valve dimensions.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c2lc40414a |
This journal is © The Royal Society of Chemistry 2012 |