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

our earlier approximations (when deriving Eq. 1). Supplementary Fig. S11 shows that

although in the intermediate range of CNaCl there is a difference between the different

curvatures, they are all on the order 1/R in the entire range of CNaCl.

Remark 1. The imposed metric is not continuous, as it 'jumps' between the PG and

the BG stripes. This feature, however, is not crucial for the generation of curvature and

the formation of the helical structure. Even a continuous metric of the form

(( ⁄ )

( ⁄ ) ) (where A takes the role of , and takes the

role of the 'stripes' widths) generates helical structures that are qualitatively similar to

those observed in the experiments. It is only for very thin sheets with that the

qualitative differences between the continuous and discontinuous cases are expected.

Remark 2. In the main text, we used the approximation

, thereby assuming

an approximately constant curvature along the y-direction within each BG stripe. This

assumption is valid as long as the sheets are not much thinner than the stripes width. In

the experiments, we have

, which justifies the approximation (see also Fig. 3c,

main text).

3. Structural characteristics of the helix

Helix parameters, such as the pitch, p, and number of turns, N, are determined by the

value of radius R, the angle , and the sheet length, X as

~cos

2

~

~tan2

R

XN

Rp

(S24)

We note however, that in this expression is not the angle in the as-prepared gel sheet,

and is not the length of the as-prepared sheet. Due to the anisotropic shrinkage of the

entire sheet (the largest contraction normal to the stripes and the smallest contraction

along them), for

2BGPG

0

BG

2

BGPG

2

PGBGPG

BG

3

BGPG

3

PG

~tan1

2cos

~

tan2~

tan

ffXX

EfEfff

EfEf

(S25)

where and are the relative changes in dimensions of PG and BG (Fig. 2a) and

is the initial length of as-prepared sheet.

4. The addition of a spontaneous curvature

When one of the surfaces of the patterned gel sheet is exposed to the ambient atmosphere

and polymerization of PAMPS is quenched, the sheet develops a spontaneous curvature

within the BG regions (Supplementary Fig. S14. This sheet is no longer a NEP and the

bending energy of the BG stripes should be measured, compared to their isotropic

reference curvature, . We therefore replace the term for the bending energy of the

binary stripes in Eq. S23 with

S

BG

S

2

S

BG2

S

3

BGBGBG12

1 yxyxtwE

(S26)

The other terms in Eq. S23 remain unchanged.

Supplementary Methods

1. Characterization of helix morphology

Supplementary Fig. S12a illustrates the structural characteristics of the helix: the length L

of the helix, the pitch p (the distance between the two neighboring turns of the helix), the

number of turns N, and the relation between them. In NaCl solutions, the value of L was

influenced by CNaCl. Thus both N and p were required to characterize helix morphology.

Alternatively, the value of N was determined as N=/360, where is the degree of

rotation (Supplementary Fig. S12b and c) and the pitch was determined as p =L/(/360).

This method enabled the determination of the value of N and p in solutions with a low

CNaCl, in which the gel sheet did not form a full turn.

2. Imaging of the cross-section of the walls of the helical structures

The imaging of the cross-section of walls of the helices in a NaCl solution at CNaCl=1M

was carried out in transmission mode using an optical microscope (Olympus BX51) with

a 2x objective. An optical micrograph was analyzed using Image-Pro Plus 5.0 software

(Media Cybernetics, Inc.). The simultaneous observation of the inner and outer surface

topographies of the helix wall (shown in Fig. 3c) was achieved by moving the focal plane

of the microscope to view the cross-section at the edge of the helix.

3. Formation of helices by subjecting the gel sheet to elevated temperature

Helices were generated using heating-induced differential shrinkage of PG and BG. In

the control experiments, we determined the ratios of dimensions of PG and BG at 45 oC

to those at room temperature to be 0.61 and 0.98, respectively. The PG samples exhibited

a strong contraction in the range of 30-32 oC, the Lower Critical Solution Temperature of

PNIPAm21

. The BG samples did not shrink owing to the strong retention of water by the

large content of PAMPS23

.

Prior to the formation of the helix, a gel sheet comprising PG and BG stripes was

exposed for 5 min to the air, and subsequently, immersed into a large volume of

deionized water at 25 oC. After 2 h incubation, the gel sheet exhibited weak bending to

the direction of the air-exposed surface. The temperature of the water was gradually

increased to 45 oC. After 2 h, the gel sheet transformed into a helix with N=1.2 and

p=4.48 cm (Supplementary Fig. S2).

4. Reversibility of planar-to-helical transitions

The reversibility of the formation of the helical structures was examined by the multiple-

time transfer of the patterned gel between a 1M NaCl solution and deionized water. In

each liquid medium, the gel was incubated for ~2 h to achieve a stable configuration.

Supplementary Fig. S3a-c shows planar-to-helical transitions of the free-floating gel

sheet patterned with BG and PG stripes, following its transfer from a 1M NaCl solution

to deionized water and again, in a 1M NaCl solution, respectively.

Supplementary Fig. S3d shows the number of turns, N, and the pitch, p, of the

helix, which were measured in a series of experiments. In a 1M NaCl solution, the planar

gel sheet formed a compact, highly reproducible helical structure with p=2.97±0.18 mm

and N=1.44±0.06. In deionized water the helix relaxed and exhibited weak bending.

5. Evolution of helixes

Supplementary Fig. S13a illustrates the evolution of the helical structure following the

transfer of the patterned hydrogel sheet from water into a 1M NaCl solution. During the

swelling process, the NaCl ions diffused into the gel matrix, leading the differential

shrinkage of PG and BG stripes and the change in their Young’s moduli. The increase in

the number of turns N and the reduction of pitch p of the helix with incubation time is

illustrated in Supplementary Fig. S13b. After 1 h, the helix reached a stable

configuration. Reversible formation of helices is shown in Supplementary Videos S1 and

S2.

6. Effect of the oblique angle θ on the deformation of the patterned hydrogel sheet

We examined the effect of the angle θ between the long axis of the patterned hydrogel

sample and the stripes of PG and BG on the hydrogel structure in the NaCl solution.

After two-step photopolymerization, the upper glass slide of the reaction cell was

removed, the patterned gel was exposed to the ambient air for 5 min, and subsequently,

immersed into a 1M NaCl solution for 2-3 h. For θ=0o and θ=90

o, the patterned gels

formed a multi-layer roll and an arc, respectively (Supplementary Fig. S4b and d). For

30≤ θ≤60o, the hydrogel sheet transformed into a helix (Fig.1b) with the structural

characteristics presented in Supplementary Table S1.

7. Control of helix handedness

When a patterned gel sheet was transferred without air-exposure into the solution of NaCl,

right- and left-handed helices formed with close-to-equal probability, or even on the two

ends of the same gel sheet (Supplementary Fig. S5).

To achieve control of helix chirality, after photopolymerization of PAMPS, one of

the glass slides from the polymerization cell was removed and the corresponding surface

of the patterned gel was exposed to the ambient atmosphere to quench polymerization by

molecular oxygen24

. In this manner, the concentration of PAMPS was selectively reduced

at the air exposed surface. The importance of this step was evaluated in a series of control

experiments conducted with a patterned gel and with non-patterned PG and BG. A left-

handed helix formed in the solution of NaCl when the top surface of the patterned gel

was exposed to the air (Supplementary Fig. S6a). A right-handed helix was generated

when the bottom surface of the gel was exposed to the air (Supplementary Fig. S6b).

Both types of helices were formed from the gel patterned with the same mask at =45o.

We conclude that the exposure of a particular surface of the gel to the ambient

environment determined the handedness of the helix, since the air-exposed surface of the

patterned gel formed the inner surface of the helix.

To understand the contribution of the PG and BG in the development of gel

curvature, we carried out experiments with the corresponding individual non-patterned

gels. Following the polymerization procedure and a 5 min-long exposure of PG and BG

to the ambient atmosphere, the gel sheets were immersed for 2 h into NaCl solutions with

varying concentrations. The BG sheet bent in the direction of the air-exposed surface,

whereas the PG remained almost planar (Supplementary Fig. S14). The bending of BG

was reversible: the gel acquired a planar shape when incubated in deionized water and

developed an arc-like shape when transferred into a solution of NaCl. The curvature, ,

of the BG sheet was determined as =1/R, where R is the radius of the arch formed by the

gel along the long axis of the sheet.. The value of increased with increasing CNaCl. The

curvature of the BG sheet was significantly smaller than the curvature of the helical

structure formed by the patterned gel sheet in NaCl solutions with similar concentration.

To determine the difference in polymer content at the top (air-exposed) and the

(air-protected) surface of the PAMPS hydrogel film, we conducted Attenuated Total

Reflection Fourier Transform Infrared Spectroscopy (ATR-FTIR) experiments. We

prepared a film from the monomer mixture (the recipe is given in Supplementary Table

S3) and irradiated it for 70 s with ultraviolet light. The top surface of the film was

exposed to the ambient air for 5 min, the gel was transferred into a large volume of

deionized water for 12 h and subsequently, dried for 15 h at room temperature. In the

control experiment, the hydrogel film was transferred in deionized water without air

exposure.

The bottom and the top surfaces of the films were examined using a Fourier

Transform Infrared spectrometer (Veratex 70, Bruker Inc.). A single beam absorption

spectrum was collected using the spectrum of air as background. Supplementary Fig. S15

shows IR spectra in the spectral window from 850 to 1350 cm-1

, in which the two

dominant bands at 1200 and 1040 cm-1

correspond to the sulfonate groups of the

PAMPS32

. The air-exposed surface showed a lower intensity of both bands than the air-

protected surface. In contrast, the top and the bottom surfaces of the gel film transferred

in deionized water without air-exposure exhibited the same intensity of the two dominant

bands.

We also examined the conditions of photopolymerization of PAMPS at the top

and the bottom surface of the film. During photopolymerization of PAMPS, the

thermocouple-measured temperatures were ~1.2 and ~0.7 oC at the top and the bottom

surfaces, respectively. The intensities of ultraviolet irradiation (measured using a

radiometer (AccuMAX XRP-3000)) were ~8.6 and 8.1 mW/cm2 at the top and bottom of

the gel, respectively. Thus we concluded that the insignificant difference in

polymerization conditions across the gel sheet did not produce the gradient in gel

composition across the film, in agreement with IR characterization of the film surfaces.

Based on the control experiments, we ascribe the different content of PAMPS at

the air-exposed and air-protected surfaces to the inhibition of polymerization by

molecular oxygen at the air-exposed surface24

. Following a 70 s-long photoirradiation,

the polymerization and crosslinking of PAMPS were not complete, and exposure of the

gel surface to the ambient atmosphere quenched polymerization. When the film was

transferred into water or into the NaCl solution, the unreacted monomer diffused from the

film, and the bottom glass-protected gel surface had a higher content of PAMPS. The

bending of the gel sheet originated from the stronger swelling of the polymer-rich

surface, with the curvature increasing with CNaCl (Supplementary Fig. S14).

To examine the effect of the variation in the time of exposure of the patterned gel

to the air, following polymerization, we removed the top cover glass, exposed the gel to

the air for various time intervals, and immersed it overnight into a NaCl solution with a

CNaCl of 1M. Supplementary Table S4 shows that the number of turns and pitch of the

helices did not change with the time of air-exposure of the hydrogel sheet in the time

range from 5 to 20 min.

8. Synthesis of the ternary bistable gel

A hydrogel with dimensions of 75 mm × 50 mm × 0.25 mm was synthesized in an

aqueous medium by copolymerizing N-hydroxyethylacrylamide (HEAm) and NIPAm in

a molar ratio 3:7 (the total monomer concentration was 16 wt%). A photoinitator V-50

and a crosslinking agent MBAA were each used at the concentration of 1 wt%. The

reaction mixture was introduced into the reaction cell comprising two 1 mm-thick glass

slides separated with a 0.25 mm-thick silicone rubber spacer. The cell was exposed for 0 s

to ultraviolet light irradiation (365 nm, Hönle, UV Print at intensity 9 mW/cm2). The

resulting P(HEAm-co-NIPAm) hydrogel (denoted as H1) was washed in deionized water.

A sheet of H1 was swollen for 18 h in an aqueous solution of NIPAm (14 wt%),

MBAA (1 wt%) and V-50 (1wt %), and exposed to ultraviolet light irradiation for 60 s

through a photomask containing black stripes (2 mm wide, 1 mm apart) passing at an

angle =45o with respect to the long axis of the mask. Following photopolymerization of

NIPAm in the light-exposed regions, the sheet contained 2 mm-wide stripes of H1 and 1

mm-wide stripes of the P(HEAm-co-NIPAm)/PNIPAm hydrogel (denoted as H2). The

composite gel sheet was washed with deionized water and swollen for 18 h in a solution

of 2-acrylamido-2-methylpropane sulfonic acid (AMPS) (20 wt%), MBA (0.25 wt%) and

V-50 (0.5 wt %). After swelling, the widths of stripes of H1 and H2 became 2.1 and 1.05

mm, respectively. The swollen sheet was exposed to ultraviolet light irradiation for 60 s

through a photomask containing black stripes (2.1 mm wide, 1.05 mm apart) passing at

=45o with respect to the long axis of the mask. The mask was laterally shifted to

polymerize 1.05 mm-wide stripes of the P(HEAm-co-NIPAm)/PAMPS hydrogel

(denoted as H3) in the light-exposed regions of H1. After washing in deionized water, the

resulting gel sheet was composed of the stripes of H1, H2 and H3.

9. Temperature-mediated deswelling of the components of ternary gels

The PNIPAm gel was prepared using photoirradiation of a solution of NIPAm (14 wt%),

MBAA (1 wt%) and V-50 (1 wt%) for 25 s. The P(HEAm-co-NIPAm) gel (H1) was

synthesized by photoirradiating a solution containing 16 wt% of a HEAm:NIPAm

mixture (3:7 molar ratio, respectively), 1 wt % of MBAA and 1 wt% of V-50 for 25 s.

The P(HEAm-co-NIPAm)/PNIPAm gel (H2) was prepared by swelling H1 in an aqueous

solution of NIPAm (14 wt%), MBA (1wt%) and V-50 (1wt%), followed by a 70 s

photoirradiation. All the gels were thoroughly washed in deionized water to remove an

unreacted monomer prior to measurements. A hydrogel composed of P(HEAm-co-

NIPAm)/PAMPS (indicated as H3 in Fig. 5a) did not show any change in the temperature

range from 25 to 80 oC.

Disks of H1, H2 and PNIPAm gel with a diameter of 21 mm and a thickness of 2

mm were cut from the corresponding gel sheets and incubated for 1 h in deionized water

at a particular temperature. The weight of the gel disk was rapidly measured.

Supplementary Fig. S9 shows the variation in the weight of the gel disk at a particular

temperature normalized by the gel weight at 25 oC. The corresponding dehydration

temperatures were 34 oC (PNIPAm), 34 and 53

oC (H1) and 53

oC (H2).

10. Differential swelling of ternary gels triggered at varying pH

A planar sheet of poly(acrylamide-co-butyl methacrylate) gel (PG) was prepared from the

15 wt% mixture of comonomers containing 60 mol% of acrylamide and 40 mol% of

butyl methacrylate, 5 wt% of MBAA and 1 wt% of V-50 in a 1:1 vol. mixture of water

and dimethylformamilde. The solution was placed between the two glass plates separated

by a 0.4 mm-thick silicon spacer and exposed to ultraviolet irradiation for 45 s. The gel

sheet was thoroughly washed with a water/dimethylformamilde mixture and with

deionized water, and subsequently, immersed for 18 h in an aqueous solution containing

22.5 wt% of N-vinyl imidazole, 0.5 wt% of MBAA and 1 wt% of V-50. After 90 s

photopolymerization of N-vinyl imidazole through a photomask ( = 0o), the gel was

washed with deionized water for 24 h, and immersed for 18 h in an aqueous solution

containing 15 wt% methacrylic acid, 0.5 wt% of MBAA and 1 wt% of V-50. Following

incubation, the gel was irradiated for 45 s through a photomask (=45o) to initiate

selective photopolymerization of methacrylic acid. The gel sheet was washed with

deionized water for 24 h. The patterned gel was subsequently cut into 5 cm 1 cm

pieces and immersed in acidic (pH=2.3), close-to-neutral (pH=6.0) and basic (pH=9.5)

solutions. Shape transformations of the gel sheet under these conditions are illustrated in

Fig. 6.

Control experiments were conducted for poly(acrylamide-co-butyl methacrylate)

gel sheets (PG) patterned either with stripes of poly(N-vinyl imidazole), or with stripes

polymethacrylic acid. In the composite gel, these stripes formed the regions of BG. The

compositions of the corresponding reaction mixtures were identical to those described

above.

In the first series of experiments, the primary gel poly(acrylamide-co-butyl

methacrylate) was patterned with N-vinyl imidazole at =0o. Supplementary Fig S16a

and b (left) shows the schematics of the stripes of PG and BG at pH of 2.3 and 9.5,

respectively. At pH=2.3, the regions of BG swelled, leading to the transformation of the

gel sheet into a roll (Supplementary Fig S16a, right). At pH=9.5, the dimensions of the

stripes of PG and BG were similar, and the patterned gel remained flat (Supplementary

Fig S16b, right).

In the second series of experiments, the poly(acrylamide-co-butyl methacrylate)

gels was patterned with stripes of poly(methacrylic acid) at =45o. Supplementary Fig.

S16c shows that the regions of PG and BG had similar dimensions at pH=2.3, resulting in

a planar shape of the gel sheet. Equilibration of the patterned sheet at pH=9.5, caused

expansion of the stripes of BG and the corresponding planar-to-helical transition of the

patterned gel (Supplementary Fig. S16d).

11. Preparation of Supplementary Movies

Hydrogels were immersed in an aqueous environment in a glass Petri dish, which was

placed below a tripod-mounted digital camera (CASIO EX-F1). Lighting was provided

by a LED, with its beam aimed parallel to the bottom of the Petri dish. Time lapse movies

were acquired from a series of images using controller software (EX-F1 Controller) that

was connected to the digital camera through a USB connection. The controller software

was set to record images of the hydrogel sheets at particular time intervals, along with

other parameters including shutter speed, aperture settings, zoom and focusing options.

Generally, time intervals were 10-20 s for the first 5 min after hydorgel transfer to a

particular medium, to capture rapid shape evolution. As the changes in the hydrogel

morphology slowed down, the time interval between image acquisition progressively

increased. Images were arranged into videos using video editing software (Pinnacle

Studio 14).

Supplementary References

30. Efrati, E., Sharon, E. & Kupferman, R. J. Mech. Phys. Solids 57, 762-775 (2009).

31. Sharon E. & Efrati, E. Soft Matter 6, 5693-5704 (2010).

32. Durmaz, S. & Okay, O. Acrylamide/2-acrylamido-2-methylpropane sulfonic acid

sodium salt-based hydrogels: synthesis and characterization. Polymer 41, 3693-

3704 (2000).