Manuscript number: 2005-12-14787
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Supplementary Information for
Smart Microlenses Using Pinned Liquid-Liquid Interfaces
Liang Dong, Abhishek K Agarwal, David J Beebe, and Hongrui Jiang
Microlens properties
The water is stored inside the hydrogel ring. The oil prevents evaporation of the water. The
reflective index (n) of the mineral oil (noil = 1.48) is greater than that of water (nwater = 1.33), so
the convex menisci (bulging upward) form divergent microlenses, while the concave (bowing
downward) menisci form convergent microlenses.
Pressure difference across water-oil interface
We calculated the pressure difference across water-oil interfaces Im at θ = θα and IIm at
θ = -(90 o-θβ) (Fig. 1a) by using Young-Laplace equation P = γ(1/R1+1/R2), where P, γ, R1,2 are
the pressure difference across the meniscus interface, the liquid surface free energy, and the radii
of the meniscus curvature, respectively. For a circular aperture, R1 = R2 = R = r/sinθ, where r is
the radius of the aperture. The water contact angles on the surfaces ‘ts’ and ‘ca’ (Fig. 1a)
obtained by the surface chemistry treatment (see Methods) are θα = 117.5 o and θβ = 28.7 o,
respectively. For an aperture diameter of 1.0 mm, the pressure differences across the interface Im
and IIm are 208 and -265 N/m2, respectively. The negative pressure difference represents that the
pressure at the water side is less than the oil side.
Temperature-sensitive liquid microlens in Fig. 2
Polymer jacket
The polymer jacket made of poly(IBA) in Fig. 2a prevents leakage between the NIPAAm
hydrogel and glass substrate. Potentially, this jacket can be eliminated by improving the adhesion
of the hydrogel to the substrate.
Transition of focal length from a negative to a positive value in Fig. 2d
The microlens starts as divergent at a low temperature (23 C) by intentionally making the liquid
meniscus protrude upward. The increase of temperature causes the liquid meniscus to bow
downward until the temperature reaches 47 C (convergent microlens). The focal length changes
from a negative (divergent microlens) to a positive (convergent microlens) value at 33 C. Here,
a 670 nm-wavelength 2 mm-diameter round laser beam strikes the microlens. The output is
shown on a screen. The equation 1/u + 1/v = 1/f is used to calculate the focal length, where u and
v represent the object and image distance, respectively.
Manuscript number: 2005-12-14787
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pH-sensitive liquid microlens in Fig. 3
Delivery of buffer solution to device
To simulate a change in local environmental pH, a syringe pump is used to deliver buffer
solution to the device through the input channels. The pumping rate is kept at 0.4 mL/min to
avoid the effect of pumping pressure on the shape of meniscus.
Focal length of microlens
In Fig. 3d, the focal length is calculated by treating the microlens as a spherical lens1. To observe
and measure the geometry of the meniscus through a goniometer, the meniscus is kept protruding
above the aperture slip (Fig. 1). Therefore, the microlens is divergent (focal length tuning range,
-2.6 mm ~ -6.6 mm) throughout the range of the pH during the experiment. Initially the liquid
microlens has a low protruding height at low pH (pH = 2.0) and higher pH buffer solutions make
it bulge upward. The initial amount of water-based lens liquid can be properly set to achieve a
microlens that initially starts as a convergent lens (meniscus lower than the aperture slip) and
transits to a divergent one when the meniscus bulges above the aperture slip.
Liquid microlens array in Fig. 4
Both liquid microlenses have the same structure, except utilizing opposite pH-responsive
hydrogels (AA and DMAEMA hydrogels). They are situated in one microchannel and exposed to
the same pH buffer solution at all times during the experiments.
Reference
1. Meyer-Arendt J. R. Introduction to classical and modern optics (Prentice-Hall, Englewood
Cliffs, NJ. 1984).
Manuscript number: 2005-12-14787
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Supplementary Figure S1: The volume of the liquid meniscus of the temperature-sensitive
liquid microlens (Fig. 2a) as a function of temperature. To visualize the water-oil interface
through a goniometer, the liquid meniscus initially has a starting volume of 0.8 μL with a low
protruding height at a high temperature (47 C). As the temperature decreases to 23 C, the
meniscus keeps bulging upward. The reverse temperature cycle from 23 C to 47 C causes the
meniscus to retreat to the starting point. The observed maximum percentage of volume change of
the NIPAAm hydrogel-water system is approximately 18.6 % (the absolute volume change
determined from the liquid meniscus volume, and total volume of the hydrogel-water system are
1.75 μL and 9.42 μL, respectively) over a temperature range of 23 – 47 C. The thermal
expansion of water and other materials (i.e., oil, glass, and non-responsive polymer) of the
device has little impact on the volume change in the liquid meniscus and can be ignored due to
their low volume thermal coefficients on the order of 10-6 – 10-4/ C. Error bars are s.d.
Supplementary Figure S2: The volume of the liquid meniscus of the pH-sensitive liquid
microlens (Fig. 3a) as a function of pH. The liquid meniscus initially has a starting volume of
0.07 μL with a low protruding height at a low pH environment (pH = 2.0). High pH buffer
solutions cause the liquid meniscus to bulge upward. The volume of the liquid meniscus at
varying pH is determined by the net volume change between the hydrogel in the inside periphery
and the water-based lens liquid enclosed by the ring, though the volumetric change also occurs in
the outside periphery of the hydrogel ring. Error bars are s.d.
Manuscript number: 2005-12-14787
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Supplementary Figure S3: Smart cylindrical liquid microlens using NIPAAm hydrogel. A
rectangular window is photopatterned to form the aperture.
Supplementary Figure S4: 3-dimensional 2×4 microlens array distributed on a flexible
substrate. Two polycarbonate cartridges are adhered together to form a 375 μm-thick cavity.
One cartridge acts as the substrate (170 μm-thick), the other as the aperture where 2×4 holes are
punched. An oxygen plasma treatment before adhering the two cartridges renders one side of the
aperture hydrophilic; polycarbonate possesses excellent hydrophobicity without any surface
chemistry treatment. The hydrogel rings are patterned using the fabrication process described in
the Methods section.