Science - USA (2022-02-25)

by the Young’s modulus and the membrane
thickness following the relationship

p^2

4

P^20

1 v^21

E 1

þ

1 v^22

E 2

"# 2 1 = 3

þ

p^2

8

P 0

1 v^21

E 1



rcurve^3

t^3

¼ 1 ð 2 Þ

whereP 0 is the maximum contact pressure;E 1
andv 1 are the Young’s modulus and Poisson’s
ratio of the membrane, respectively;tis the
membrane thickness; andE 2 andv 2 are the
Young’s modulus and Poisson’s ratio of
the sphere, respectively ( 34 , 35 ). TheE/(1−v^2 )
is regarded as the plane-strain modulus, which
is 130 kPa for human skin ( 36 ), 4 MPa for

PDMS ( 37 ), and 2.8 GPa for polyimide ( 22 ).

The difference in plane-strain modulus illus-

trates the large mechanical mismatch between

human skin and the soft polymeric elastomer

or typical plastics.

UsingEqs.1and2,wecancalculatethe

maximumfilmthicknessallowedtoachievea

conformal interface with a topography of a giv-

enrcurveunder a certain contact pressure for

materials with a different plane-strain modulus

(Fig. 1E). For example, to achieve a conformal

interface with a skin topography ofrcurve~5mm

under a maximum contact pressureP 0 of 1 kPa

(the gentlest touch that a human can feel is

1kPa)( 38 ), the maximum allowed thickness

is 0.3mm for PDMS and 39 nm for polyimide.

Similarly, we can also calculate the maximum

contact pressure needed to form a conformal

interface with a givenrcurveof 5mm for mate-

rials with a different plane-strain modulus

and thickness (Fig. 1F).

These analyses highlight that the contact

pressure needed to achieve a conformal inter-

face is proportional to the Young’s modulus

and thickness of the membrane and inversely

proportional to the curvature of the radius of

the surface topography. Although, in principle,

the contact pressure on biological tissue can

be minimized by reducing membrane thick-

ness, the thickness cannot be reduced indefi-

nitely for most polymeric materials owing

to the limitation of the characteristic size of

individual polymer chains and a precipitous

decrease in mechanical properties below a

critical thickness (e.g., 25 nm) ( 23 ). Conduct-

ing polymers that are suitable for electronic

SCIENCEscience.org 25 FEBRUARY 2022•VOL 375 ISSUE 6583 853

A BC

D F

G H

E

Fig. 1. Conceptual comparison of unstretchable and stretchable membranes.
(AandB) Illustrations showing the wrapping of a piece of (A) unstretchable and
(B) stretchable membrane around a pen. (C) Illustrations showing stretchable
membranes with grid lines gradually conforming to a curved surface topography.
(D) Diagram of a spherical indentation model and relevant parameters. (Eand

F) Contour maps showing the relationship between plane-strain modulus, film

thickness, and (E) contact radius at a contact pressure of 1 kPa or (F) maximum

contact pressure for a contact radius of 5mm, highlighting that reducing thickness and

plane-strain modulus favors a conformal interface. (GandH) Schematic diagram

of (G) VDWTFs and (H) CVDTFs before and after stretching.

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