Supplementary Figures Supplementary Figure S1. Preparation of composite gel sheets and their transformation in helical structures. a, Schematic of the photolithographic patterning of the hydrogel sheet. A sheet of PNIPAm gel (a primary gel or PG) is swollen with a monomer mixture, sandwiched between the two glass slides, and exposed through a photomask to ultraviolet irradiation. The mask contains black stripes (1 mm wide, 1 mm apart) passing at an angle to the long axis of the mask. b, Photoinitiated polymerization of the monomer and subsequent removal of unreacted monomer and linear polymer yield a PNIPAm/PAMPS binary gel (BG) in the light-exposed regions of PG. c, A helix formed by the patterned gel sheet in a 1M NaCl solution or in water heated to 45 o C, above the dehydration temperature of PNIPAm.The dark and light-blue colors correspond to the stripes of PG and BG, respectively. a b c stimulus Photopolymerization
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a b c - Nature Research€¦ · b, Photoinitiated polymerization of the monomer and subsequent removal of unreacted monomer and linear polymer yield a PNIPAm/PAMPS binary gel (BG)
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Supplementary Figures
Supplementary Figure S1. Preparation of composite gel sheets and their
transformation in helical structures. a, Schematic of the photolithographic patterning
of the hydrogel sheet. A sheet of PNIPAm gel (a primary gel or PG) is swollen with a
monomer mixture, sandwiched between the two glass slides, and exposed through a
photomask to ultraviolet irradiation. The mask contains black stripes (1 mm wide, 1 mm
apart) passing at an angle to the long axis of the mask. b, Photoinitiated polymerization
of the monomer and subsequent removal of unreacted monomer and linear polymer yield
a PNIPAm/PAMPS binary gel (BG) in the light-exposed regions of PG. c, A helix
formed by the patterned gel sheet in a 1M NaCl solution or in water heated to 45 oC,
above the dehydration temperature of PNIPAm.The dark and light-blue colors correspond
to the stripes of PG and BG, respectively.
a b cstimulus
Photopolymerization
Supplementary Figure S2. Heat mediated helix formation. A photograph of the helix
formed after 2 h incubation in deionized water at 45 oC. After photopolymerization of
PAMPS, the patterned gel was exposed for 5 min to the air. The scale bar is 1 cm, t0 =
0.44 mm,
1 mm, = 45o. Experimental details are described in
Supplementary Methods.
Supplementary Figure S3. Reversibility of planar-to-helical transitions. a, A planar
patterned gel sheet floating in deionized water at 23 oC. b, A helix floating at the air-
liquid interface. The helix is formed following transfer of a sheet shown in (a) in a 1M
NaCl solution. c, A planar gel sheet formed by transferring a helix as in (b) in deionized
water at 23 oC. The scale bar is 0.5 cm. d, Variation in the number of turns, N, and pitch,
p, of the helix, following its repetitive 2 h-long incubation in deionized water and in a 1M
solution of NaCl. The error bars represent standard deviation calculated from 3
measurements. Following photopatterning, the top surface of the patterned gel was
exposed for 5 min to the ambient air. t0=0.44 mm,
= 1 mm, = 45o.
Experimental details are described in Supplementary Methods.
0
0.5
1
1.5
2
0
6
12
18
Tu
rns
of
heli
x Pitc
h (c
m)
C (M)NaCl
1 1 10 0
N
p (c
m)
a
b
c
d
Supplementary Figure S4. Deformation of the patterned gel sheet. a, A phototomask
used for gel patterning with stripes parallel to the long axis of the sheet. b, Corresponding
multi-roll hydrogel sheets formed after their 2 h incubation in a 1M NaCl solution. c, A
phototomask used for hydrogel patterning with stripes perpendicular to the long axis of
the sheet. d, A corresponding arc-like hydrogel sheet formed after its 2 h incubation in a
1M NaCl solution. Following polymerization, the gels were exposed for 5 min to the
ambient atmosphere. t0 = 0.44 mm,
1 mm. The scale bar is 1 cm.
b d
a c
= 0
Θ=0o
Θ=30o
Θ=45o
Θ=60o
Θ=90o
b
θ
65 mm
10 mm
1 mm1 mm
a
Θ=0o
Θ=30o
Θ=45o
Θ=60o
Θ=90o
b
θ
65 mm
10 mm
1 mm1 mm
a
b = 90o
Supplementary Figure S5. Helices with different chiralities formed without gradient
in composition across the gel sheet. a, Helix with both right- and left-handedness. b,
Helix with three sections with alternating right- and left-handedness. The scale bar is 0.5
cm. c, A fraction of helices with right-handed (RH), left-handed (LH) and helices with
both types of handedness (RH&LH, as shown in a,b), formed upon transfer without post-
polymerization air exposure of the gel sheet into a 1M NaCl solution. The results were
obtained for 102 helices. The gel sheet was patterned using a mask with the angle =
45o. t0 = 0.44 mm,
1 mm. Experimental details are described in
Supplementary Methods.
0
20
40
60
80
100
RH LH RH&LH
a
b
c
Supplementary Figure S6. Control of the chirality of the helix. a,b A left-handed and
a right-handed helices generated after post-polymerization exposure of the top and the
bottom surfaces of the patterned gel, respectively, to the ambient atmosphere for 5 min
and subsequent transfer of the gel sheet into a 1M solution of NaCl. The scale bar is 1
cm. The insets show the corresponding hand symbols. The gel sheet was patterned using
a mask with the angle = 45o. t0 = 0.44 mm,
1 mm. Experimental details
are described in Supplementary Methods.
a
b
Supplementary Figure S7. Variation in helix morphology in NaCl solutions with
varying ionic strength. Photographs of the left-handed helix formed in solutions at
CNaCl of 0.8M (top), 1.7M (middle), and 2.5M (bottom). The scale bar is 1 cm, t0=0.44
mm, w0
PG=1 mm, w0BG=1 mm, = 45
o. Experimental details are described in
Supplementary Methods.
Supplementary Figure S8. Effect of the ratio of widths of the stripes of PG-to-BG
on helix morphology. Photographs of the gel sheets patterned with PB and BG stripes
with different widths, after 24 h equilibration in a 1.2M solution of NaCl. White stripes
correspond to the PG regions. The insets indicate the ratio of the original widths of PG-
to-BG stripes (determined by the photomask). =45o, t0=0.44 mm. The scale bar is 1 cm.
Experimental details are described in Supplementary Methods.
Supplementary Figure S9. Temperature-dependent deswelling of the structural
components of binary and ternary gels. Variation of the normalized weight of an
hydrogel sheet with increase in temperature for PNIPAm (), P(HEAm-co-NIPAm)
(H1) (), P(HEAm-co-NIPAm)/ PNIPAm (H2) (). Experimental details are described
in Supplementary Methods.
Supplementary Figure S10. Schematic of as-prepared gel sheet. The dark- and light-
blue colors correspond to the stripes of PG and BG, respectively.
Supplementary Figure S11. Variation in curvatures of PG and BG calculated from
energy minimization of Eq. S1 and S2. In the entire range of CNaCl the values of
() and () are of the order of ().
0
10
20
30
40
50
0 0.5 1 1.5 2 2.5
Cu
rva
ture
C (M)NaCl
Supplementary Figure S12. Determination of the number of turns of the helix. a,
The structural characteristics of the helix. b, The side view (left) and the front, cross-
section view (right) of the helix in a NaCl solution at high CNaCl. c, The side view (left)
and the front, cross-section view (right) of the helix in NaCl solution at low CNaCl.
N =φ
360
b
c
x
y
zA
B
x
y
zA
B
y
z
A
Bφ
A
y
z
B
φ
Side view Front view
L
p
N =L
p
a
Supplementary Figure S13. Evolution of helical structures. a, Photographs of the
patterned hydrogel taken at different time intervals after transferring it from deionized
water into a 1M NaCl solution. The scale bar is 1 cm. b, Variation in pitch p and the
number of turns N of the left-handed helix, plotted as a function of time. After
polymerization of PAMPS, the top sheet surface was exposed for 5 min to the ambient air.
t0 = 0.44 mm,
1 mm, = 45o.
p
a b
5 min
30 min
10 min
60 min
Supplementary Figure S14. Variation in the curvature of the PG and BG sheets. The
top surface of the sheets of PG () and BG () with dimensions of 65 mm × 5 mm × 0.4
mm were exposed for 5 min to the ambient atmosphere and immersed for 2 h into a NaCl
solution with a particular concentration.
0
0.1
0.2
0.3
0.4
0.5
0 0.5 1 1.5 2 2.5
k (
cm
-1)
C (M)NaCl
a
0
0.1
0.2
0.3
0.4
0.5
0 0.5 1 1.5 2 2.5
k (
cm
-1)
C (M)NaCl
a
Supplementary Figure S15. Characterization of the top and the bottom surfaces of
PAMPS hydrogel. a, ATR-FTIR spectra were collected for the top, air-exposed surface
(--) and the bottom, air-protected surface () of the film. The sheet was exposed to the
ambient air for 5 min. b, ATR-FTIR spectra collected for the top surface (--) and the
bottom surface () of the hydrogel film transferred in deionized water without air
exposure. The thickness of the gel film was 0.44 mm gel. The concentration of PAMPS
in the gel is 30 wt%. Each spectrum was generated from 70 scans at a scan rate of 10 kHz
and spectral resolution 4 cm-1
.
Wavenumber (cm-1)1300 1400 1500 1600
0.03
0.04
0.05
0.06
0.07A
bso
rpti
on
(ab
s. u
nit
s)
Wavenumber (cm-1)1300 1200 1100 1000
0.03
0.04
0.05
0.06
0.07
Ab
sorp
tio
n (a
bs.
un
its)
ba
Supplementary Figure S16. Shape transformations of poly(acrylamide-co-butyl
methacrylate) primary gel sheet patterned with stripes of pH-responsive polymers.
a, Schematic (left) and a roll shape of the gel (right) patterned with stripes of poly(N-
vinyl imidazole) at pH =2.3. b, Schematic (left) and planar shape of the gel (right)
patterned with stripes of poly(N-vinyl imidazole) at pH=9.5. c, Schematic (left) and a
planar shape of the gel (right) patterned with poly(methacrylic acid) at pH =2.3. d,
Schematic (left) and a helical shape of the gel (right) patterned with poly(methacrylic
acid) at pH =9.5. In (a-d) the stripes of poly(acrylamide-co-butyl methacrylate) (PG) are
shown with a dark-blue color. In (a,b) the light-blue color in the schematics corresponds
to poly(N-vinyl imidazole). = 0o. In (c,d) the light-purple color in the schematics
corresponds to poly(methacrylic acid). = 45o. The gel sheets were equilibrated for 18 h
in corresponding solutions. t0=0.44 mm,
1 mm. The scale bars are 0.5 cm.
pH = 2.3
pH = 9.5
a
b
c
d
Supplementary Tables
Supplementary Table S1. Effect of angle θ on the number of turns, N, the pitch, p,
and the radius, R, of the helix.*
*The standard deviations of N, p, and R were calculated from 3 measurements.
θ N p (cm)
30o
45o
60o0.9±0.1
1.6±0.2
1.4±0.1
5.5±0.4
2.9±0.3
2.1±0.3
R (cm)
0.53±0.03
0.5±0.05
0.52±0.02
Supplementary Table S2. Variation in volume ratio of BG-to-PG in solutions with
varying concentration of NaCl.*
*The ratio of volumes of BG-to-PG was determined as VBG/ VPG = (fBG/fPG)3, where fBG
and fPG are the relative changes in linear dimensions of BG and PG (defined in the main
text).
0.00 3.6
0.10 3.6
0.30 3.8
0.50 4.2
0.75 9.4
1.00 11.5
1.25 11.4
1.50 10
2.00 8.5
2.50 7.2
CNaCl (M) VBG/VPG
Supplementary Table S3. Recipes used for the synthesis of PG and BG.
ComponentsFirst step (PG) Second step (BG)
NIPAm
AMPS
MBAA 1.0
14
-
0.25
20
-
V-50
Concentration (wt%)
1.0 0.50
Supplementary Table S4. Effect of the time of air-exposure of the patterned gel on
the number of turns and pitch of the helix.*
*The standard deviations of N and p were calculated from 3 measurements.
Exposure time (min) N p (cm)
5
10
15
20
1.5±0.1
1.5±0.1
1.4±0.1
1.5±0.1
2.9±0.1
2.9±0.1
2.8±0.1
2.9±0.1
Supplementary Notes
Supplementary Note 1. Theoretical modeling
1. Hydrogel sheet parameters
Due to the shrinkage of the PG and BG stripes in the solution of NaCl, their widths and
thickness change as
where t0 is the thickness of the as-prepared gel film, tPG and wPG are the thickness and the
width of PG stripes, respectively, and tBG and wBG are the thickness and the width of BG
stripes, respectively.
2. Generation and selection of curvature
General considerations
The composite hydrogel sheets are a special type of Non-Euclidean-Plates (NEPs)30,31
,
which are thin elastic sheets that are uniform across their thickness with in plane local
reference (or “rest”) lengths that are described by a non-Euclidean reference metric tensor
. Unlike previously studied cases, in the present work, in the patterned hydrogel sheets
is periodic on a short length scale along the y-direction and invariant along the x-
direction (Supplementary Fig. S10). In order to find the energy-minimizing
configuration, one should express the elastic energy in terms of the reference, and actual
metric and curvature tensors and subsequently, minimize it. This procedure will be
presented elsewhere. Here we simplify the expressions for the energy by using several
approximations that allow the derivation of an analytical expression (Eq. 1 in the main
text). This equation qualitatively predicts the variation in helix properties with properties
of small-scale structural components of the gel sheet. In addition, we relax some of the
approximations and provide a simplified form of the energy (Eq. S22 and S23) that can
be numerically minimized, in order to perform quantitative calculations.
Derivation of Eq. 1
We start with the energy density, W, of a plate, based on the theory of non-Euclidean
plates
( )
( )
(S1)
where
(
) is the isotropic homogenous elastic tensor,
and are the curvature and metric tensors of a given configuration, respectively, and
and are the reference metric and curvature tensors respectively, and
( ) is the
strain tensor.
In the experiments, the Poisson ratio is
and the spontaneous curvature is
. Using the in-plane strains, and curvatures, of a configuration, the energy
density is given by:
(
)
(
) (S2)
Assumption of (negligible strains in the y-direction) leads to
(
(
)) (S3)
Approximations
This section uses the notations introduced in the main text. In the main text, we solved
the problem for the case of a very large contrast in Young’s moduli of PG and BG,
similar to the natural fibrous tissue. Since the short PG stripes are significantly stiffer
than the long BG stripes, they were considered to be inextensible. In this case, all the
stretching energy is contained within the soft BG stripes. In addition, the bending energy
density is significantly higher for the rigid PG stripes, as it scales as , and the
curvatures in the x-direction of both soft and stiff stripes are of the same order (
).
Thus the energies per unit length are
(S4)
(
) (S5)
In addition, for bending energy minimization, the curvatures in the x- and y-
directions should be comparable, leading to
(S6)
The composite gel sheets are sufficiently thin to buckle, but not very thin, that is,
they are beyond, but close to the buckling threshold. As a result, the curvature across a
stripe is roughly constant and the stripe has an arc shape in the y-direction (Fig. 3c).
Under such conditions, , the deviation of the centerline of the BG stripes from R (Fig.
3d) is
(S7)
The ratio between the lengths of BG and PG stripes is therefore
(S8)
While the ratio of lengths of the free stripes of (the “rest lengths”) is
(S9)
The strain in the BG stripes, , is the difference between the rest length ratio, , and
the actual length ratio, , per unit length of the BG stripe,
(S10)
and the stretching energy (Eq. S4) is then given by
(
)
(S11)
The total elastic energy in our approximation is
(
)
(S12)
Eq. S8 leads to
(
)
(S13)
The first term is the geometric stretching term, while the second one reflects the bending
term. The simplest estimation of the selected radius of the gel sheet is obtained by
equalizing the bending and stretching energies
(
)
(S14)
Neglecting 4-th orders in
we obtain
( ) (
)
(S15)
and by solving for R
( )
(S16)
Substituting the relations
( ) (S17)
we obtain
( )
(S18)
which is similar to Eq. 1 up to a numerical factor.
If instead of equating the energies, we minimize the energy E (Eq. S13), the result is
(
( ) ) (S19)
Rearranging it using the relation (Eq. S17) yields
( (
)
( ) )
(S20)
Since the second term in the denominator is small (in our experiments it varies in the
range from 0.01 to 0.1), we can expand Eq. S20) to second order in it and obtain
( )
(S21),
which is Eq. 1 in the main text.
This simple analytical expression captures the qualitative dependence of R on
the properties of small-scale structural components of the gel sheet. However, for
quantitative calculations it is preferred to avoid some of the used approximations and to
numerically minimize the energy. The assumptions of inextensibility of the PG stripes
and of the equality of curvatures in the x- and y- directions can be removed. In this case,
the energy includes the different curvatures of PG and BG regions in the y-direction,
and , respectively, as in Eq. S3. In addition, the stretching energy of the PG stripes
and the bending energy of the BG stripes are included in the expression for the elastic
energy and the bending and the stretching energies (ESt and EBend, respectively) are
22
BG
BG
BG
PGBGBGBG
22
PG
PG
BG
PGPGPGPGSt
811
2
1
811
2
1
w
f
ftwE
w
f
ftwEE
yxyx
(S22)
BG2BG23
BGBGBG
PG2PG23
PGPGPGBend12
1
12
1yxyxyxyx twEtwEE
(S23)
where
.
The total energy, can be minimized numerically, thereby
leading to the adjustment of , and
and yielding helix parameters that are close
to the experimental ones. Such energy minimization can be used to check the validity of