xBehavior of Non-Doped and Carbon Black
Doped PDMS for Micro-Implantable Strain
Gauge
Arrays____________________________________
_
Integrated Micro/Nano
Summer Undergraduate Research Experience
Lillian Shido
California State University, Los Angeles
2007 IM-SURE Fellow
Professor William Tang
Gloria Yang
University of California, Irvine
Department of Biomedical Engineering
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Abstract
There is little quantitative knowledge regarding muscle and tendon injury or prosthetics,
such as artificial heart valves. The behavior of soft tissue must be measured to acquire
this knowledge. Because soft tissues strain up to 30%, an implantable micro-strain gauge
array has been developed, allowing for strain measurement on muscles. Strain gauges
currently in use are too large to make accurate measurements. Furthermore, the new array
would provide real-time monitoring with little effort and low cost. The strain gauge array
was fabricated using soft-lithography on polydimethylsiloxane (PDMS). To quantify the
ability of PDMS to reflect the strain of the tissue, its behavior was observed under cyclic
stresses. PDMS specimens were prepared to ASTM standards for elastic materials and a
cycling test was performed. Non-standard specimens were also fabricated. Once the
tensile properties for a non-doped PDMS specimen were established, a specimen
containing Carbon Black (CB), which may be an alternative design, was tested. The
resistance was measured simultaneously. These tests revealed the behavior of doped and
non-doped PDMS is typical of documented elastomers that have experienced cycling.
However, the resistance of the CB PDMS unexpectedly decreased as it stretched. One
possible explanation for this is the increased distance between CB particles. While the
mechanical data reinforces the PDMS compatibility to this application, the resistance data
implies the CB PDMS may still be used as an alternative design. These findings will
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contribute to the creation of advanced strain gauges and to gaining a better understanding
of soft tissue behavior.
Introduction
Direct surface strain measurements on bone and soft tissue would be invaluable in
helping early detection of osteoporosis, metastatic tumors, sports-related muscle injuries,
and development of prosthetic implants such as artificial heart valves. Currently existing
strain gauges are much too large to make the sensitive measurements needed for this
application. The newly developed flexible, implantable micro-strain gauge array would
be implanted on soft tissue, such as a muscle, and would be able to provide real-time
monitoring with little effort and low cost.
Manufacturing
Because of the tendency for soft tissue to
stretch up to 30%, a flexible material
needed to be selected as the housing for
the
strain
gauge.
The
polymer
Polydimethylsiloxane (PDMS) was chosen
for its bio-compatibility and compatibility
to micro-electronic mechanical systems
(MEMS). This polymer is made from a
base agent and a curing agent. The ratio of
Figure 1. Fabrication process. [1]
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the two agents is 10:1. At room temperature, the mixture will cure in 24 hours; however,
in a convection oven set to ~70 °C it cures in 2 hours. The fabrication process for the
strain gauge is as follows: A layer of PDMS approximately 75 microns thick is spun onto
a silicon wafer and cured in a convection oven. A layer of Kapton film is then attached to
the PDMS, making it easier for the subsequent layers to be peeled off. Another layer of
PDMS approximately 50 microns thick is then spun on and cured. This forms the bottom
layer of the strain gauge. Then, a 220 nm thick Gold/Chromium layer is deposited onto
the PDMS. A photoresist mask is exposed on that layer and the excess is etched away.
Two wires are then attached to the conductive pads. Finally, another layer of PDMS is
spun onto the metal, forming the top layer of the strain gauge. The strain gauge is then
peeled off of the Kapton film. (Yang, et al., 2004)
Theory
To quantify the ability of the PDMS to reflect the actual
strain the muscle is experiencing, it is necessary to
understand the mechanical behavior of PDMS. It is also
important to characterize the Young’s Modulus of
PDMS to confirm that its stiffness is lower than that of
Figure 2. Actual Strain Gauge. [1]
the material the strain gauge is measuring, muscle tissue
in this case. In addition, there is a need to correlate the change in strain with a change in
resistance in order to translate the voltage change across the strain gauge into a change in
length. For this test, a Carbon Black doped PDMS specimen will be tested for conductive
behavior as well as mechanical behavior. To characterize these qualities of the PDMS, a
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standard stress-strain curve and a resistance-strain curve will be produced from cycling
the test specimens on a tensile tester. The quantitative values will then be calculated
using the following equations:
 
P
A
(Eq. 1)
where P is applied force, and A is cross-sectional area, and  is engineering stress,

l
l0
(Eq. 2)
where l is the change in length (displacement) of the specimen, l 0 is the original length,
and  is the engineering strain, and
  E
(Eq. 3)
where E is Young’s Modulus. Young’s Modulus can also be found graphically by
calculating the slope of the linear portion of the stress-strain curve on most materials.
Methods and Materials
The tensile testing machine used for these experiments was a Mark-10 TSF Force
Measurement Test Stand on which a Mark-10 Series BG Force Gauge and a Mitutoyo
Extensometer were mounted. The force gauge and extensometer data is transmitted and
saved to the computer through a Microsoft Excel interface. The testing machine is
operated by turning a manual hand crank. As shown in Figure 3, the specimen is loaded
into a specially designed aluminum fixture, which is mounted onto the hooks.
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Force Gauge
Al Fixtures
Crank
Extensometer
Figure 3. Tensile Test Assembly.
The optimal configuration of the specimen also needed to be determined. Four designs
were created, as listed in Figure 4. The ASTM tensile testing standard calls for a “dog
bone” shaped specimen. However, according to Eq. 1, it would be extremely difficult to
calculate a single cross-sectional area from a configuration that has a non-uniform crosssection. The tubular configuration has a uniform circular cross-sectional area; however, it
was extremely robust and very susceptible to slipping out of the aluminum fixture. After
running a few preliminary tensile tests, it slipped out soon after the test started and was
determined to be useless. The square and rectangular cross-sections were both tested on
the tensile tester and produced some valuable results.
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Cross-sectional
Shape
Configuration
Dog Bone Shape
Tubular
(kept slipping)
Square
Rectangular
Figure 4. Different Specimen Configurations.
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The production of each of these specimen
designs varied. The “dog bone” shaped
specimen was manufactured by pouring noncured PDMS into a mold and peeling it out
after it was cured. The tubular configuration
was originally created by pouring the PDMS
into a glass pipet; because of its precise Figure 5. 24-well plate used to make specimens.
dimensions, however, it was very difficult to remove because the glass tended to adhere
to the PDMS. In subsequent tests, a plastic straw was determined to be the most efficient
mold. The square cross-sectional design was made by cutting the already cured PDMS
along a precisely machined steel edge. The rectangular cross-section was the easiest to
produce. A well was cut into an aluminum plate and the liquid PDMS was poured into
the wells and peeled out once it was cured. As seen in Figure 5, once these configurations
were produced, one end was glued to a 24 welled plate and the well was filled with
PDMS. Once the PDMS cured, it was taken out and turned over to do the same to the
other side. Then, the PDMS was trimmed down to make a flat surface to fit into the
aluminum clamps. This modification was not necessary for the dog-bone and rectangular
cross-sectional specimens, but was useful for the tubular as well as the square crosssectional specimens in making them easier to clamp.
A PDMS specimen that was doped with 24% Carbon Black, a conductive powder, was
also tested for mechanical and conductive behavior. This specimen was manufactured to
the rectangular cross-sectional configuration. As shown in Figure 6, the test setup is
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identical to the test for the non-doped PDMS, except that there are two wires connected
to either end of the conductive polymer. The other ends of the two wires are connected to
a Hewlett-Packard 34401A Digital Multimeter which measures the resistance during the
tensile test and transmits the data to a computer.
Computer
Multimeter
Figure 6. Resistance Test with Carbon Black PDMS.
Results
A stress-strain curve obtained for the dog-bone shaped specimen is shown in Figure 7.
This curve was first strained to 65% then to 100%, and then until it finally ruptured.
Figures 8 through 10 show the stress-strain curve obtained for a square cross-section for
strains of 38%, 57%, and 76%. For this set of data, the force gauge was zeroed each time
a cycle to a certain strain was complete, unlike the data in Figure 7.
65-100% Strain
Figure 7.
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38% Strain
Figure 8.
57% Strain
Figure 9.
10
76% Strain
Figure 10.
Resistance-Strain
Two Carbon Black doped polymers, Conductive Polymer 1 (CP 1) and Conductive
Polymer 2 (CP 2), were tested for the stress and resistance measurements. Figures 11 and
12 show the stress-strain curves of both CP 1 and CP 2 when strained to 26-27%. Figures
13 and 14 show the resistance-strain curves of the two polymers at that same strain. The
next set of figures are in the same order, but the polymers were strained to 39-40% strain.
The next set shows an even higher strain—52-54%.
11
Conductive Polymer 1
26-27% Strain
Figure 11.
Conductive Polymer 2
26-27% Strain
Figure 12.
12
Conductive Polymer 1
26-27% Strain
Figure 13.
Conductive Polymer 2
26-27% Strain
Figure 14.
13
Conductive Polymer 1
39-40% Strain
Figure 15.
Conductive Polymer 2
39-40% Strain
Figure 16.
14
Conductive Polymer 1
39-40% Strain
Figure 17.
Conductive Polymer 2
39-40% Strain
Figure 18.
15
Conductive Polymer 1
52-54% Strain
Figure 19.
Conductive Polymer 2
52-54% Strain
Figure 20.
16
Conductive Polymer 1
52-54% Strain
Figure 21.
Conductive Polymer 2
52-54% Strain
Discussion
Figure 22.
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The stress-strain curves for both the doped and non-doped specimens were very
repeatable and predictable. The PDMS was observed to have behavior typical of other
rubbers that have been documented (Axel Products, Inc., 2001). For instance, in Figure 7,
there is a single cycle that clearly has behavior different from the other cycles. This can
be explained by one of the factors of what is known as the Mullin’s effect. The Mullin’s
effect is the tendency for an elastomer to undergo a significant change in its structure the
first several times it is put under a strain. The PDMS is undergoing a significant change
the first time that it is strained to 100% percent, but from the second cycle to that strain
level, the behavior is stable and repeatable. You can also see this effect in the data from
the square cross-sectional specimen. However, it is less apparent, possibly because the
cross-section is so small that it is less sensitive to changes. From this we can conclude
that the square cross-section is not preferable for such a quantity-based study.
The Carbon Black doped specimen with the rectangular cross-section, on the other hand,
was more sensitive to the significant changes the specimen underwent at different strain
levels. By studying the stress-strain curves for both CP 1 and CP 2 it can be seen that the
data is once again repeatable, but more importantly, the differences in the cycles are
amplified compared to the square cross-sectional specimen and can be observed in a
quantitative manner.
According to these observations, one of the questions that was answered relatively
quickly in the tests was that the rectangular cross-sectional configuration was the one best
suited to the needs of these experiments. The rectangular configuration has a uniform
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cross-section and therefore a single cross-sectional area that can be used in the stress
equation (Eq. 1). Furthermore, the specimen is large enough to reflect some important
behaviors in the PDMS. Also, as mentioned in the Materials and Methods section, the
rectangular cross-sectional specimen was the simplest and, therefore, the fastest to
manufacture.
In general, however, the mechanical behavior of doped and non-doped PDMS specimens
was quite stable and predictable after the first few cycles at a higher strain. This data will
aid in making more sound assumptions about the mechanical behavior of PDMS for
future tests.
Another important component of the results, is the resistance-strain curves. Once again,
these curves show some Mullin’s effects; however, after one cycle, they are completely
stable and repeatable. One of the unpredicted behaviors of the resistance curves, however,
was that the resistance decreased as the strain increased. Normally, when resistors
increase in length, they tend to increase in resistance. Here, though, it was the opposite. It
is theorized that the stretching motion rearranged the Carbon Black particles to break and
create new conductive pathways. It is clear that more new conductive pathways were
consistently created relative to the number of destroyed conductive pathways by the
rearrangement of the particles. Another unpredicted occurrence was the failure of CP 2 at
54% strain. It is believed that this failure was due to a pre-existing defect in CP 2. Until
the failure, however, the stress-strain curve and the resistance-strain curve follow the
same path as CP 1, which, once again, shows a repeatable behavior.
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This experiment showed exactly what needed to be demonstrated for the further
development of the micro-strain gauge array: It showed that the mechanical and
conductive behavior of PDMS is very repeatable and predictable after the first cycle to a
higher strain level. It also showed that the Carbon Black PDMS may potentially be used
as an alternative design to the strain gauge, rather than the metal being sandwiched
between two PDMS layers. In addition, the predictability of the behavior shows the
compatibility of PDMS to the strain-gauge application. Once the micro-strain gauge array
is implanted into a body, it will be impossible to conduct this type of extensive testing on
it, and it is extremely beneficial to know its behavior without having to perform further
experiments.
Future Study
There will be improvements made to the manufacturing process of the specimen based on
the information that was learned during this set of experiments. In addition, the Carbon
Black specimens will be more carefully produced to avoid having large defects. There
will also be more calculations done on the stress-strain curve of each of these specimens
to graphically calculate the Young’s modulus and compare it to that of the soft tissue.
This will contribute to ultimately building a large database with stress-strain and
resistance-strain data of PDMS to gain a more complete knowledge of its behavior.
Acknowledgements
Dr. Adel Sharif (California State University, Los Angeles)
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National Science Foundation (NSF)
Undergraduate Research Opportunities Program (UROP) and IM-SURE
Dr. William Tang
Gloria Yang
IM-SURE Fellows (Special Thanks to Anais Sahabian)
University of California, Irvine Faculty
Said Shokair
References
[1]
G. Y. Yang, V. J. Bailey, Y.-H. Wen, G. Lin, W. C. Tang, and J. H. Keyak,
“Fabrication and characterization of microscale sensors for bone surface strain
measurement,” Proc., 3rd IEEE Int. Conf. Sensors, Vienna, Austria, Oct. 24 – 27,
2004, pp. 1355 – 1358.
[2]
Axel Products, Inc. “Using Slow Cyclic Loadings to Create Stress Strain Curves
for Input into Hyperelastic Curve Fitting Routines.” Cyclic Loadings RevC, April
2001.
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