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

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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:

mjescuti@ncsu.edu; mddickey@ncsu.edu; and jan_genzer@ncsu.edu

0021-8979/2014/115(20)/204911/6/$30.00 VC 2014 AIP Publishing LLC115, 204911-1

JOURNAL OF APPLIED PHYSICS 115, 204911 (2014)

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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)

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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)

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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)

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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

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