Three-dimensional folding of pre-strained polymer sheets ... · Three-dimensional folding of...
Transcript of Three-dimensional folding of pre-strained polymer sheets ... · Three-dimensional folding of...
Three-dimensional folding of pre-strained polymer sheets via absorption of laser lightYing Liu, Matthew Miskiewicz, Michael J. Escuti, Jan Genzer, and Michael D. Dickey
Citation: Journal of Applied Physics 115, 204911 (2014); doi: 10.1063/1.4880160 View online: http://dx.doi.org/10.1063/1.4880160 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/20?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Study on the activation of styrene-based shape memory polymer by medium-infrared laser light Appl. Phys. Lett. 96, 111905 (2010); 10.1063/1.3353970 Polymer/carbon nanotube composite patterns via laser induced forward transfer Appl. Phys. Lett. 96, 041104 (2010); 10.1063/1.3299004 Three-dimensional pulse tube simulations AIP Conf. Proc. 613, 934 (2002); 10.1063/1.1472114 A three-dimensional, performance model of segmented thermoelectric converters AIP Conf. Proc. 608, 998 (2002); 10.1063/1.1449830 Resonant absorption of a short-pulse laser in a doped dielectric Appl. Phys. Lett. 74, 2912 (1999); 10.1063/1.123963
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
125.207.175.111 On: Fri, 30 May 2014 04:30:40
Three-dimensional folding of pre-strained polymer sheets viaabsorption of laser light
Ying Liu,1 Matthew Miskiewicz,2 Michael J. Escuti,2,a) Jan Genzer,1,a)
and Michael D. Dickey1,a)
1Department of Chemical and Biomolecular Engineering, North Carolina State University,911 Partners Way, Raleigh, North Carolina 27695, USA2Department of Electrical and Computer Engineering, North Carolina State University,2410 Campus Shore Drive, Raleigh, North Carolina 27695, USA
(Received 4 April 2014; accepted 15 May 2014; published online 29 May 2014)
Patterned light from a laser can induce rapid self-folding of pre-strained polymer sheets. Black ink
coated on the sheet absorbs the light, which converts the photon energy into thermal energy that
heats the sheet locally; the temperature of the sheet is highest at the surface where the light
impinges on the sheet and decreases through the sheet thickness. The gradient of temperature
induces a gradient of strain relaxation through the depth of the sheet, which causes folding within
seconds of irradiation. The pattern of laser light that irradiates the compositionally homogeneous
two-dimensional (2D) substrate dictates the resulting three-dimensional (3D) shape. Unlike most
approaches to self-folding, the methodology described here requires no patterning of pre-defined
hinges. It opens up the possibility of using a patterning technique that is inherently 2D to form 3D
shapes. The use of lasers also enables systematic control of key process parameters such as power,
intensity, and the pattern of light (i.e., beam width and shape). The rate of folding and folding
angle measured with respect to these parameters provide an indirect quantification of heat loss in
the sample and thereby identify the threshold power and power intensity that must be delivered to
the hinge for folding to occur. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4880160]
INTRODUCTION
This paper describes the use of light from a laser to
induce rapid folding of planar, pre-strained polymer sheets
into three-dimensional (3D) shapes without pre-patterning
hinges. Self-folding is similar to origami, but accomplishes
folding without direct human intervention. It is an attractive
method to convert two-dimensional (2D) substrates into 3D
structures for applications including actuators, sensors, and
reconfigurable devices.1–6
Self-folding is usually accomplished by pre-defining
hinges in a 2D substrate that facilitate the formation of 3D
structures in a deterministic way. In “conventional” self-
folding, a hinge typically differs from the rest of the sheet in
composition, property, or layout; as a result, multiple fabri-
cation steps are typically required to create the hinge. These
hinges respond to some external stimuli (e.g., heat, light, pH)
to induce folding.2,7–11 Light is a particularly attractive stim-
ulus to induce folding because it can be delivered remotely,
efficiently, and with adjustable wavelength, spatial distribu-
tion, and intensity. Uniform irradiation (i.e., non-patterned
light) can induce folding if the “hinged” regions of the sheet
absorb light preferentially relative to the rest of the sheet.
The absorption of light converts the photon energy into ther-
mal energy via the photothermal effect. Light absorption
may be localized by printing black ink on a pre-strained
polymer sheet12 or by fabricating distinct hinges that absorb
light.13,14 Light absorption can induce folding by stimulating
local changes to the volume within hydrogels.15,16 Light
absorption can also induce molecular changes to photosensi-
tive polymers that may be harnessed for folding.9,10,17–19
Here, we show that it is possible to use patterned light
as a means to deliver heat to specific locations on a polymer
sheet. These exposed regions act as “hinges” during self-
folding. The absorption of light by a uniform coating of
black ink on a pre-strained sheet converts photon energy
into heat and causes the polymer beneath the ink to warm
and relax in a gradient across the thickness of the sheet,
which induces folding. This approach has many attractive
features. First, it induces folding in an inexpensive homoge-
neous plastic sheet without requiring any pre-processing
steps such as patterning or lithography. Second, the location
of the folds can be programmed arbitrarily by changing the
pattern of light on the 2D sheet, e.g., by either a dynamically
scanned beam or by a static pattern of light. Third, each fold
actuates independently, which enables sequential folding;
that is, folding that occurs in a controlled and prescribed
order. Fourth, the use of plastic sheets and lasers are com-
patible with high throughput manufacturing. Fifth, laser
light can propagate easily through air without significant
attenuation of power and can be tightly focused at locations
distant from the source. Last, the laser light delivers precise
doses of energy to well-defined areas on the polymer sheet,
which provides opportunities to study the fundamental fold-
ing response as a function of laser beam power, intensity,
width, and time.
In addition to providing quantitative information about
folding time and final folding angle, the approach we employ
provides insight into the heat dissipation within and outside the
a)Authors to whom correspondence should be addressed. Electronic addresses:
[email protected]; [email protected]; and [email protected]
0021-8979/2014/115(20)/204911/6/$30.00 VC 2014 AIP Publishing LLC115, 204911-1
JOURNAL OF APPLIED PHYSICS 115, 204911 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
125.207.175.111 On: Fri, 30 May 2014 04:30:40
sheets and hence the threshold energy required to induce
folding.
RESULTS AND DISCUSSIONS
Our experiments use a cylindrical lens to focus a
continuous-wave 1064 nm Nd:YAG laser into the shape of a
line. While other beam shapes are possible, a line results in
a single, straight hinging response in the polymer film that is
easy to observe and characterize, as illustrated in Figure
1(a). The polymer underneath the irradiated region heats and
shrinks locally to create a 90� fold within seconds of irradia-
tion (cf. Figure 1(b)). Video V1 in supplementary material
shows the complete folding process. The pre-strained poly-
mer sheet (GrafixVR
Clear Inkjet Printable Shrink Film, thick-
ness d� 0.3 mm, contracts in-plane biaxially by �55% when
heated above Tg) coated with black ink from a desktop laser
printer absorbs �95% of the incident light at 1064 nm based
on UV-Vis absorption measurements as shown in Figure S1
in the supplementary material.20
Figure 1 demonstrates that laser light can trigger self-
folding of polymer sheets with crisp, well-defined hinges
within seconds. To identify conditions that lead to folding
and characterize the folding response, we varied the beam
power (mW) illuminating the sample (i.e., within the dimen-
sion L in Figure 1(a)), the beam width (i.e., the dimension Win Figure 1(a)), and indirectly, the irradiance (i.e., mW/cm2,
calculated by normalizing the power by the footprint of the
irradiating light, L � W). After aligning the substrate normal
to the laser beam, we adjusted the beam width W by position-
ing the sample relative to the focal plane of the beam. We
assume the beam width W defines the hinge width.
The bending angle and onset time provide metrics to
characterize folding. The “bending angle,” aB, is the angular
displacement of the fold (relative to the sheet plane);
consequently, the “folding angle,” aF, (¼180�- aB) represents
the angle between two adjacent facets on the side of the laser
exposure. The “onset of folding” is the time interval between
the initial exposure of the substrate to light and the first fold-
ing motion. As expected, short onset times correspond to
rapid folding as shown in Figure S2 in the supplementary
material.20 Finally, note that any results reported in terms of
power (mW) are unique to the sample geometry employed
consistently throughout this study. However, the power
(mW) values scale directly with respect to the sample width
(L) (i.e., if polymer sheets twice as wide are used, then the
power needed to reproduce these results would be twice as
large, in principle).
We observe the folding response of samples while vary-
ing the incident power (50�150 mW) and the beam widths
(0.5�1.7 mm). Figures 2(a) and 2(b) show three observed
regimes of behavior: no-folding; folding with aB less than
90�; and 90� folding. The reported aB represents the final,
maximum folding angle after exposing the samples for 2 min
or until bending stopped. As expected, increasing the power
decreases the onset time and increases aB. The aB plateaus at
90� because the folded “panels” of the polymer sheet block
the path of the incident beam, preventing further heating of
the hinge. Although the sample can fold to aB> 90� by
changing the incident angle of the laser, we only investigated
the folding performance when the laser was normally inci-
dent to the sample.
As shown in Figure 2(a), folding rarely occurs below a
certain power threshold (�60 mW) regardless of beam width.
In the following sections, we suggest that this value represents
heat dissipation based on both scaling and in depth analysis of
the data. Figures 2(a) and 2(b) also show that narrower beams
require less power for a given onset time of folding (or a
given bending angle) because of their smaller footprint. We
initially hypothesized that all beam widths would fold in the
same manner when exposed to the same irradiance based on
the logic that a finite pixel of the hinge would receive the
same dose of energy, regardless of the width of the hinge.
Instead, Figures 2(c) and 2(d) show that normalizing the
power by the footprint of the illuminating light (i.e., the irradi-
ance) produces a different trend: narrower hinges require
larger irradiances than the wider hinges (for a given onset
time or bending angle). There also appears to be a threshold
irradiance (�1 W/cm2), below which no folding occurs. These
observations suggest a strong dependence of folding on beam
width W, which we believe relates to heat dissipation.
We seek to understand better the source of the threshold
values of power (�60 mW) and irradiance (�1 W/cm2) in
Figure 2 below which folding does not occur. We make
three assumptions: (1) In order to fold, the polymer sheet
must exceed the glass transition temperature of the sheet
(Tg� 103 �C); (2) In the absence of wasted heat, the volume
of polymer beneath the exposed region (cf. Figure 1(a),
L�W � d) needs an areal energy dose of �4 J/cm2 to heat
the polymer sufficiently to induce folding; and (3) Samples
that do not fold within 2 min dissipate the power sufficiently
fast to prevent folding from occurring. This last assumption
is based on the fact an irradiance �1 W/cm2 delivers 4 J/cm2
in only 4 s.
FIG. 1. (a) Schematic of the polymer sheet exposed to laser light. The laser
irradiates the sample over an area defined by L � W; (b) Photographs of the
folding of a pre-strained polymer sheet coated with black ink. The sample is
10 mm � 50 mm and is irradiated with a laser beam that spans the width of
the sample and irradiates from the left side of the images. The beam can be
seen impinging on the sample at times 1 and 2 s. The sample is held in place
at the bottom by a clamp supported by a laser table.
204911-2 Liu et al. J. Appl. Phys. 115, 204911 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
125.207.175.111 On: Fri, 30 May 2014 04:30:40
Based on these assumptions, we estimate the maximum
power and irradiance that each hinge can withstand without
folding. After 2 min of continuous exposure to the laser, heat
dissipation should approach steady state with a surface tem-
perature that does not exceed �100 �C, according to our
assumptions. As illustrated in Figure 3(a), heat dissipation
can occur either (1) into the air, or (2) laterally inside the
polymer (the relative impact of this loss mechanism
increases as the beam width narrows). To a first approxima-
tion, heat dissipation to the air should be constant if normal-
ized by the area of the hinge (mW/cm2), whereas heat lost
laterally into the bulk of the polymer sheet should be inde-
pendent of the beam width (W). Our measurements provide
estimates for both effects.
To estimate these values, we fit aB with a hyperbolic
tangent function (Figure 2(a)) as described by
aB ¼U2
tanhP� Pinf
b
� �þ 1
� �: (1)
In Eq. (1), U is the maximum bending angle (�90� in our
experiments), P is the incident power, and Pinf and b are fit-
ting parameters.18 Table SI in the supplementary material
lists all fitting parameters.20 The best fits, which are plotted in
Figure 2, identify the inflection point (Pinf). The tangent line
of this hyperbolic function at the point of Pinf intercepts the
x-axis, which we utilize as an estimate of the characteristic
largest power P0 that the polymer can dissipate without fold-
ing, as listed in Table SI of the supplementary material.20
Figure 3(b) plots the dependence of P0 on W. As
expected from Figure 2(a), wider hinges dissipate more
power; likewise, larger hinges require more power to induce
folding. A linear fit results in a y-intercept of 57.5 mW. We
interpret this value as the amount of heat dissipated from the
edges of the hinge since a hinge that approaches a width of
zero would only consist of edges. The slope of this line
(140 mW/cm) can be normalized by the sample width
(L¼ 4 mm) to get the power loss from the hinge itself via
conduction into the air (350 mW/cm2).
FIG. 2. Bending angle (a, c) and onset
time of folding (b, d) of pre-strained
polymer sheets as a function of illumi-
nating laser power (a, b) and irradiance
(c, d).
FIG. 3. (a) Cross-sectional schematics
of heat transfer across the film thick-
ness (dashed red line), away from the
edge of the hinged region (dotted yel-
low line) and to the air (curved line in
orange). W1 and W2 are the beam
widths (W2>W1), and d is both the
sheet thickness and the characteristic
dimension of the heat loss at the edge
of the hinge (outlined by the dashed
line and noted by yellow arrows); and
(b) Power required to initiate folding
as a function of beam width. The inter-
cept of the linear fit is 57.5 mW and
the slope is 140.2 mW/cm.
204911-3 Liu et al. J. Appl. Phys. 115, 204911 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
125.207.175.111 On: Fri, 30 May 2014 04:30:40
From the power loss (350 mW/cm2), we estimate the
thermal conductivity of air. Based on our assumptions, the
maximum difference between the surface of the polymer
(�103 �C) and the air (�23 �C) would be �80 �C. For this
temperature, the heat transfer coefficient is 22 W/m2/K
assuming the heat dissipates from the top and bottom of the
hinge. This value is in good agreement with literature values
(hc, �1� 50 W/m2/K),21 which helps justify the assumption.
In terms of power, the widest hinge (2 mm) only loses an
additional �28 mW of power due to this mechanism and
thus, convective heat loss contributes to less than 50% of the
heat loss in our experiments.
A simple scaling argument can also estimate the heat
loss from the edges of the hinges in the polymer sheet and
thereby support our interpretation of the intercept in Figure
3(b). The heat dissipates laterally away from both sides of
the hinge (outlined by dotted lines, Figure 3(a)). For scaling
purposes, we estimate this region as radial heat flux even
though the actual heat loss through the edge is complex. We
justify this assumption by first estimating the characteristic
length scales involved with heat transport. If we assume (1)
the temperature of polymer is close to Tg at its hottest and at
room temperature at its coldest, (2) a measured thermal con-
ductivity (k) of the polymer (0.14 W/m/K), (3) a heat flux of
60 mW, and (4) the heat transfers through a cross-sectional
area equal to a cross-section of the sheet, then the tempera-
ture drop necessary to support this heat flux should occur
over a length scale 0.2�0.3 mm, which is nearly the thick-
ness of the sheet. The heat loss through a cylindrical cross-
section, depicted in Figure 3(a), can be described using
Eq. (2) as
_Q ffi pkLDT
lnr2
r1
� � : (2)
In Eq. (2), k is thermal conductivity of the polymer
(0.14 W/m/K); L is the width of the polymer sample (4 mm);
r2 is r1 plus the film thickness (d¼ 0.3 mm); and DT is the
temperature gradient across the polymer sheet (�80 �C).
Using the threshold power (�60 mW) and the given parame-
ters, we estimate r1 to be 0.3� 0.4 mm, which is approxi-
mately half the width of the hinges used in this study. This
estimate of heat loss dissipated at the edges of the sample
helps explain why folding does not occur at powers below
�60 mW and helps support the interpretation of the intercept
of Figure 3.
The characteristic power loss (�60 mW) also arrives
from a separate analysis of the data. It is challenging to
deconvolve the roles of all the interrelated parameters on
folding, i.e., the beam width, exposure time, energy dose,
power, and power intensity. Although we explored many
combinations of these parameters via graphical analysis,
there was one in particular that produced a surprisingly linear
relationship. Figure 4 depicts a plot of onset energy for fold-
ing (i.e., power multiplied by onset time of folding) with
respect to onset time of folding. Data points for the entire
range of beam widths (symbols) and power intensities (color
scheme) fall onto a single “master” plot with a slope of
57.8 mW, which gives a measure of energy lost per time and
agrees surprisingly well with the threshold power (�60 mW)
shown in Figure 2, the intercept (57.5 mW) of Figure 3(b),
and the scaling argument posed here by Eq. (2).
The remarkable and unexpected result of Figure 4 sug-
gests, counter-intuitively, that increased amounts of energy
delivered by the laser results in increased onset times. A
more intuitive interpretation of the data is that long onset
times associate with increased amounts of “wasted energy,”
which implies more heat dissipation and supports our inter-
pretation of the slope as a measure of heat loss. It is diffi-
cult to directly compare the slope of Figure 4, which plots
data from experiments in which folding occurs, with the
analysis resulting from Figure 3, which plots data from
experiments in which folding does not occur (and are
assumed to have steady state heat loss). Nevertheless, the
agreement in the rate of heat loss (�60 mW) in both cases
is remarkable. We interpret this recurring number as a char-
acteristic heat loss associated with the characteristic length
scales (0.1�1 mm), material properties (polystyrene), tem-
peratures (Tg¼ 103 �C), and time scales (tens to hundreds
of seconds) associated with the experiments here.
In addition to analyzing the power, we also analyze the
irradiance associated with folding. Figures 2(c) and 2(d)
shows that narrower hinges require larger irradiances than
wider hinges to achieve the same folding behavior, which is
ultimately due to heat loss. Figure 5 plots dissipated irradi-
ance (I0), (i.e., the largest irradiance that the polymer can
dissipate without folding, P0 divided by the area of the
beam) against beam width W. As expected, narrower hinges
dissipate greater irradiance than wider hinges. The line in
Figure 5 is the linear fit of power versus W (Figure 3(b))
normalized by the area of the beam (W x L). The dissipated
irradiance starts to level off near �1 W/cm2, which is
consistent with the threshold irradiance identified in
Figure 2(c).
A simple scaling analysis is also consistent with the
observed minimum power intensity of �1 W/cm2 associated
with folding. Folding necessitates the rapid delivery of heat
FIG. 4. Onset energy as a function of onset time of folding for various beam
widths (legend) and beam irradiance.
204911-4 Liu et al. J. Appl. Phys. 115, 204911 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
125.207.175.111 On: Fri, 30 May 2014 04:30:40
to the hinge so that there is a gradient of temperature, and
thus, a gradient of strain relaxation (i.e., shrinkage) from the
irradiated side to the opposing side of the sheet. Our previous
thermal simulations suggest that for these polymer sheets
there is �20 �C difference in temperature between the top
and the bottom of the sheet assuming that the bottom side of
polymer film is near Tg (�103 �C) while the hinge tempera-
ture exceeds 120 �C when the folding occurs.12 Based on the
thermal conductivity, k, of the polymer (0.14 W/m/K) and
the thickness of the sheets (300 lm), there should be
�0.93 W/cm2 of heat flux through the sheet due to this ther-
mal gradient.
CONCLUSIONS
We demonstrate self-folding of pre-strained polymer
sheets induced by the absorbance of patterned light from a
laser. Sharp folds occur within seconds under a wide range
of hinge widths and laser power. The ability to induce fold-
ing of planar films using light without any pre-patterning
represents an advance for self-folding due to the simplicity
of the method, its compatibility with rapid throughput proc-
essing, and its ability to be delivered remotely from long dis-
tances. While here we use a simple pattern of light from the
laser to study the fundamentals of folding, the approach is
broadly appealing because there are several ways to pattern
light in 2D, such as photolithography, digital micromirrors,
and scanned lasers. We use black ink to absorb the light, but
it should also be possible to achieve the same behavior using
infrared wavelengths within the inherent absorption bands of
the polymer or by adding light absorbing molecules or par-
ticles to the polymer.
We utilize the control afforded by the lasers to vary the
power and hinge width to study the effect on folding angle
and time. Changing these variables alters the irradiance and
dose (i.e., the delivered energy, which depends on folding
time), creating a complex multivariable experimental space.
The data show that wider hinges need more power, but less
irradiance, to induce the same folding behavior as narrower
hinges. An analysis of heat loss explains these tendencies
and agrees with a scaling analysis. Folding occurs when the
irradiance exceeds �1 W/cm2 due to systematic heat dissipa-
tion. Likewise, folding occurs only above a certain power
threshold (�60 mW, or more generally �60 mW/4 mm,
where 4 mm is the width of our polymer sheets) required to
compensate for the heat loss. The estimation of energy
required for folding offers insight into thermal dissipation,
and may provide a useful guide for folding process in other
systems using different polymers or different geometries.
EXPERIMENTAL
A Nd:YAG laser generated a 1064 nm beam of light
focused onto the sample using a combination of spherical
and cylindrical lenses. The resulting focused beam was an el-
liptical Gaussian that closely resembled a 1D line. The diam-
eter of the beam (twice the beam waist) in the L dimension
was much larger than the width of the sample; thus, the
focused beam was very uniform in the L dimension. While
our simulation assumes that the beam profile was uniform
over the length of W, in reality the beam had a Gaussian pro-
file. This assumption was made to simplify calculations, and
we do not expect it to significantly affect the results. The
width of the beam, W, was found as twice the beam waist
(i.e., the distance from the center of the beam to 13.5% max
power) in the W dimension, measured using a beam profile
(Thorlabs, BP 104-UV). To achieve different beam widths,
the beam was defocused by moving sample relative to the
beam focus. The beam irradiance was calculated as the ratio
of incident power to the rectangular area of the sample
exposed by the beam (i.e., sample width by beam width).
The onset time was measured using a stopwatch. In this
work, the sample was oriented such that the ink coating
faced the laser; however, folding can also be induced if the
ink coating is facing away from laser.
ACKNOWLEDGMENTS
The authors thank Mr. Neil Demarse and Dr. Ghazal M
Alipour from TA Instruments for the measurement of thermal
conductivity of the polymer sheet used. The authors thank the
National Science Foundation for supporting this work under
the NSF EFRI program (Grant No. 1240438), NSF Grant
ECCS-0955127, and DOE (Grant No. 08NT0001925).
Supplementary material is available online.20
1J. H. Cho, S. Hu, and D. H. Gracias, “Self-assembly of orthogonal three-
axis sensors,” Appl. Phys. Lett. 93, 043505 (2008).2E. Hawkes et al., “Programmable matter by folding,” Proc. Natl. Acad.
Sci.USA 107(28), 12441–12445 (2010).3M. Jamal, A. M. Zarafshar, and D. H. Gracias, “Differentially photo-
crosslinked polymers enable self-assembling microfluidics,” Nat.
Commun. 2, 527 (2011).4G. Stoychev, S. Turcaud, J. W. C. Dunlop, and L. Ionov, “Hierarchical
multi-step folding of polymer bilayers,” Adv. Funct. Mater. 23,
2295–2300 (2013).5N. Bassik, G. M. Stern, and D. H. Gracias, “Microassembly based on
hands free origami with bidirectional curvature,” Appl. Phys. Lett. 95,
091901 (2009).6W. Small IV, P. Singhal, T. S. Wilson, and D. J. Maitland, “Biomedical
applications of thermally activated shape memory polymers,” J. Mater.
Chem. 20, 3356 (2010).7T. G. Leong, A. M. Zarafshar, and D. H. Gracias, “Three-dimensional fab-
rication at small size scales,” Small 6, 792–806 (2010).
FIG. 5. Dissipated irradiance, I0, as a function of beam width.
204911-5 Liu et al. J. Appl. Phys. 115, 204911 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
125.207.175.111 On: Fri, 30 May 2014 04:30:40
8X. Guo et al., “From the Cover: Two- and three-dimensional folding of
thin film single-crystalline silicon for photovoltaic power applications,”
Proc. Natl. Acad. Sci. 106, 20149–20154 (2009).9H. Y. Jiang, S. Kelch, and A. Lendlein, “Polymers move in response to
light,” Adv. Mater. 18, 1471–1475 (2006).10A. Lendlein, H. Jiang, O. Juenger, and R. Langer, “Light-induced shape-
memory polymers,” Nature (London) 434, 879–882 (2005).11K. Suzuki, H. Yamada, H. Miura, and H. Takanobu, “Self-assembly of
three dimensional micro mechanisms using thermal shrinkage of poly-
imide,” Microsyst. Technol. 13, 1047–1053 (2007).12Y. Liu, J. K. Boyles, J. Genzer, and M. D. Dickey, “Self-folding of poly-
mer sheets using local light absorption,” Soft Matter 8, 1764 (2012).13K. E. Laflin, C. J. Morris, T. Muqeem, and D. H. Gracias, “Laser triggered
sequential folding of microstructures,” Appl. Phys. Lett. 101, 131901
(2012).14A. Piqu�e, S. A. Mathews, N. A. Charipar, and A. J. Birnbaum, “Laser ori-
gami: a new technique for assembling 3D microstructures” in Proceedingsof SPIE (2012), p. 82440B–7.
15E. Wang, M. S. Desai, and S.-W. Lee, “Light-controlled graphene-elastin
composite hydrogel actuators,” Nano Lett. 13, 2826–2830 (2013).16S. Fusco, et al., “An integrated microrobotic platform for on-demand, tar-
geted therapeutic interventions,” Adv. Mater. 26, 952–957 (2014).17K. M. Lee, H. Koerner, R. A. Vaia, T. J. Bunning, and T. J. White, “Light-
activated shape memory of glassy, azobenzene liquid crystalline polymer
networks,” Soft Matter 7, 4318–4324 (2011).18K. N. Long, T. F. Scott, H. Jerry Qi, C. N. Bowman, and M. L. Dunn,
“Photomechanics of light-activated polymers,” J. Mech. Phys. Solids 57,
1103–1121 (2009).19J. Ryu et al., “Photo-origami—Bending and folding polymers with light,”
Appl. Phys. Lett. 100, 161908 (2012).20See supplementary material at http://dx.doi.org/10.1063/1.4880160 for a
video of the folding process, the UV-Vis transmission spectra of the black
ink, a list of the fitting parameters for Eq. (1), and a plot of total time of
folding versus onset time.21W. L. McCabe, J. C. Smith, and P. Harriott, Unit Operations of Chemical
Engineering (McGraw-Hill, 2005).
204911-6 Liu et al. J. Appl. Phys. 115, 204911 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
125.207.175.111 On: Fri, 30 May 2014 04:30:40