High Power Laser Science and Engineering, (2017), Vol. 5, e27, 7 pages.
© The Author(s) 2017. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/
licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
doi:10.1017/hpl.2017.27
Modeling the mechanical properties of ultra-thin
polymer films
Francisco Espinosa-Loza, Michael Stadermann, Chantel Aracne-Ruddle, Rebecca Casey, Philip Miller, and
Russel Whitesides
Lawrence Livermore National Laboratory, 7000 East Avenue, L-471, Livermore, CA 94550, USA
(Received 3 November 2016; revised 17 August 2017; accepted 30 August 2017)
Abstract
A modeling method to extract the mechanical properties of ultra-thin films (10–100 nm thick) from experimental data
generated by indentation of freestanding circular films using a spherical indenter is presented. The relationship between
the mechanical properties of the film and experimental parameters including load, and deflection are discussed in the
context of a constitutive material model, test variables, and analytical approaches. Elastic and plastic regimes are
identified by comparison of finite element simulation and experimental data.
Keywords: indentation; optimization; ultra-thin films
1. Introduction
Freestanding ultra-thin polymer films are utilized in a variety
of applications, including sensors, catalysis, filtration, and
tissue engineering
[1–4]
. At the National Ignition Facility
(NIF), nanometer scale polyvinyl formal films are routinely
used as load-bearing elements to support fuel capsules in
complex millimeter-scale inertial confinement fusion (ICF)
targets
[5]
. Since even very thin films appear to introduce
significant perturbation to the implosion
[6, 7]
, there is an
impetus to minimize the thickness of such support films.
To make certain that thinner films can withstand the rigors
of target assembly and handling, their mechanical properties
must be well understood.
The mechanical properties of ultra-thin films are known to
change as the film dimensions approach the molecular size
scales
[8–10]
. Measuring these properties has been difficult
even for substrate-supported thin films, and there are only
few measurements that have been attempted on freestanding
films
[11]
.
Here, we utilize indentation
[12, 13]
to characterize mecha-
nical properties of such thin films. Closed-form expre-
ssions
[14, 15]
for interpreting data gathered from this method
have been derived, but such approximations typically per-
form poorly for pre-stressed films or tests that extend beyond
the elastic regime of the polymer. We present a method
that can be used to extract mechanical data from such
tests and construct full stress–strain curves for films of this
Correspondence to: M. Stadermann, 7000 East Ave Livermore,
CA 94550. Email: stadermann2@llnl.gov
thickness regime. Finite element analysis is used to simulate
the indentation test, and an optimization algorithm is used to
derive the constitutive material models.
2. Experimental
2.1. Preparation of the thin films
Freestanding polyvinyl formal films with a thickness of
10–100 nm were made by a spin coating method, as
described in detail elsewhere
[16, 17]
. In brief, a solution of
0.25 wt% Vinylec E (SPI Supplies, West Chester, PA) in
ethyl lactate (98%, Sigma-Aldrich, St. Louis, MO) was spin
coated onto Si wafers pretreated with polydiallyldimethyl-
ammonium chloride PDAC (Sigma-Aldrich St. Louis, MO.
Mw ∼ 1× 10
5
–2× 10
5
g/mol), and baked for 1 min at 50
◦
C
on a hot plate. The resultant films were then lifted from the
wafer, in water, and mounted on ring-shaped holders with
an inner diameter of 11 mm. The films were typically dried
overnight under ambient conditions before being tested using
the indentation method. Prior to testing, the thickness of
each film was measured by ellipsometry (Woollam M-2000).
Since the hydrated polymer swells the films, as mounted on
the holders for testing, typically have significant residual
stress.
2.2. Indentation test
Indentation tests are conducted on the film using a custom-
built system as shown in Figure 1(a); the film is glued
1