Research Highlight

May 2013

Ping Du, PhD

Mechanical Engineering

Boston University

Thesis

– Viscoelastic testing and modeling of PDMS micropillars

Side Projects

– Conducting polymer actuators

– PDMS and conducting polymer nanowire composites

– Silicon oxycarbide thin films

– Tribological study of DLC coatings

CAD and FEA Experience

2/30 Outline

3/30

Viscoelastic Testing and

Modeling of PDMS Micropillars

• Measure the viscoelastic properties of PDMS.

• Developed enhanced cantilever beam bending model.

• Application to PDMS micropillar transducer for cellular

force measurement

Ping Du et al., Journal of Microelectromechanical Systems, 22, 44-53, 2013.

Ping Du et al., Applied Physics Letters, 99, 083701, 2011.

Ping Du et al., Journal of Micromechanics and Microengineering, 20, 095016, 2010.

Background

C.S. Chen, J. Cell Sci., 2008.

X. Zheng and X. Zhang, JMM, 2011.

4/30

Cells: complex entities

1. Sense cues:

respond to stimuli: beneficial, harmful

2. Regulate cell functions

division, growth, apoptosis, migration, etc.

3. Biomechano-transductions: mechanical forces

develop micro/nano sensors, medical devices.

4. Detection of interactions

unique index to probe trivial changes in cells

5. Application fields

physiology, medicine, cell biology.

Background

Methods to measure sub-cellular forces

5/30

Wrinkles on thin film (Harris, 1980)

Embedded beads (Dembo, 1999)

Shallow markers (Balaban, 2001)

High pillars (Tan, 2003)

6/30 Motivation

Polydimethylsiloxane (PDMS)

- bio-compatibility, mechanical compliance,

optically transparency.

- fabrication with ease (low cost, high fidelity)

Timoshenko beam

(low aspect ratio)

Linear viscoelastic

Euler beam

(high aspect ratio)

r=L/d > 10

Linear elastic Material property

Geometry

Traditional Enhanced

PDMS micropillars

- behave as simple cantilever beams, bends

upon cell contraction.

- direction and magnitude of force: deflection

on top of pillars.

Research overview 7/30

PDMS

Time domain

Young’s relaxation modulus

Stress relaxation nanoindentation

Viscoelastic Timoshenko beam

Micro-beam bending test

Case study Loading rate effect

Freq domain

Cellular contraction Fourier series

Complex modulus Dynamic

nanoindentation

Cellular force Finite element

analysis

Time domain: Relaxation modulus

Stress relaxation test

8/30

Transducer Microscope

X-Y moving stage

Hysitron TI 900 Triboindenter

0 20 40 60 80 100 120124

126

128

130

132

134

136

Time (sec)

Lo

ad

(n

m)

Lo

ad

(m

N)

0 20 40 60 80 1000

500

1000

1500

2000

2500

Time (sec)

Dis

p (

nm

)

Test 1

Test 2

Test 3

Test 4

Loading

Unloading

Young’s relaxation modulus of PDMS

tj (sec) 10-1.5 0.1 1 10 100

Ej (kPa) 201.8 58.2 53.7 31.2 25.7

N

j

t

jjeEEtE

1

)(

(𝝀𝒊 = 𝟏/𝝉𝒊)

Holding Holding

9/30

a : shear coefficient

G: shear modulus ])1([

)]1(6[

3)(

12

0

N

j

t

j

j jeE

tEIALL

IAvtP

a

Time domain: Viscoelastic Timoshenko beam model

Combine low aspect ratio and viscoelasticity

100 mm

200 mm

0 2 4 6 8 100

2

4

6

8

10

Time, t (sec)

Fo

rce,

P (m

N)

0 2 4 6 8 100

2

4

6

8

10

Time, t (sec)

Fo

rce

, P

(m

N)

Experiment

Elastic Timoshenko

Viscoelastic Timoshenko

250 nm/s 500 nm/s 1000 nm/s

0 500 1000 1500 2000 25000

2

4

6

8

10

12

Deflection, (nm)

Fo

rce,

P (m

N)

0 500 1000 1500 2000 25000

2

4

6

8

10

12

Deflection, (nm)

Fo

rce

, P

(m

N)

Experiment

Elastic Euler

Elastic Timoshenko

Viscoelastic Euler

Viscoelastic Timoshenko

Reaction force predictions

from different formulas

a) At the same loading rate (250 nm/s)

b) At different loading rates

Euler: overestimate

(violate the slender beam)

Viscoelastic: loading rate dependent

10/30 Time domain: Application to cardiac myocytes

Micropillar displacements

Parametric study

-0.2

-0.1

0

0.1

0.2

Dis

pla

cem

en

t ( m

m)

2.5

3

3.5

4

4.5

Str

ess (

KP

a)

31.8 32.2 32.6 33 33.4-3.5

-3

-2.5

Str

ess (

KP

a)

Time (sec)

Relaxation

1 1.5 21

1.5

2

EE

VT

Contraction

(a)

(b)

(c)

-30

-30-30-30

-20

-20

-20 -20-20

-10

-10

-10 -10-10

-8

-8

-8 -8-8

-5

-5

-5

-5 -5

0

0 0 0

5

5 5 5

15

Loading rate, v0 (mm/s)

Asp

ect

rati

o,

r=L

/d

10-3

10-2

10-1

100

101

102

1

2

3

4

5

6

7

8

9

10

Zone 1

Zone 2

Inverted microscope

CCD camera

Computer system For imaging analysis

Buffer solution

Liquid pump

Heating rod

Waste solution

Vacuum pump

Perfusion chamber

Feedback controller

Inlet Outlet

Thermometer

PDMS chip

%100DiffVT

VTEE

P

PP

In-situ force probing system for living cells

D K

Test

sample

Freq. domain: Complex modulus (1)

Dynamic nanoindentation

Agilent G200 Nanoindenter

11/30

Coil/magnet

assembly

Leaf spring

Capacitance

gauge

Dis

p (m

m)

240 242 244 246 248 250

3.29

3.3

3.31

3.32

3.33

3.34

3.35

Time (s)

Fo

rce (

mN

)

12.06

12.08

12.1

12.12

12.14

12.16

12.18

Dis

p (m

m)

Material model for dynamic indentation

- Black box: no constitutive law involved

- General formula: applicable to all linear

viscoelastic solids.

𝐸′ 𝜔 =1 − 𝜈2

2𝑅

∆𝑃0∆ℎ0

cos𝜙

𝐸" 𝜔 =1 − 𝜈2

2𝑅

∆𝑃0∆ℎ0

sin𝜙

Instrument dynamics

𝑃0𝑒𝑖𝜔𝑡 = 𝑚ℎ + 𝐷ℎ + 𝐾ℎ

ℎ 𝑡 = ℎ0𝑒𝑖(𝜔𝑡−𝜙)

Herbert, J. Phys. D, 2008

Freq. domain: Complex modulus (2) 12/30

2. Mathematical expression

Generalized Maxwell model

i 1 2 3 4 5

i (1/sec) 0.1 1 10 100 1000

Ei (kPa) 2.2×10-11 18.4 94.1 119.1 742.3

Angular freq. (rad/s)

Lo

ss

fa

cto

r

101

102

0.7

0.8

0.9

1

1.1

Angular freq (rad/s)

E' (M

Pa)

0

0.05

0.1

0.15

0.2

0.25

0.3

Lo

ss t

an

gen

t

0

0.1

0.2

0.3

𝐸 𝜔 = 𝐸∞ + 𝐸𝑗𝜔

2

𝜆𝑗2 +𝜔2

𝑁

𝑗=1

+ 𝑖 𝐸𝑗𝜆𝑗𝜔

𝜆𝑗2 +𝜔2

𝑁

𝑗=1

2. N. Conte, V. Jardret, MRS Proc. 2001.

1. C.C. White et al., J. Poly. Sci. B, 2005

Du (flat, time) Du (flat, freq)

Conte (flat)

Conte (berk)

E'-Du (flat,time)

E''-Du (flat,time)

E'-Du (flat,freq)

E''-Du (flat,freq)

E'-Conte (berk)

E''-Conte (berk)

E'-Conte (flat)

E''-Conte (flat)

1. Compare to previous results

Freq. domain: Application to cellular force

Contraction force

from FEA simulation

13/30

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.1

0.2

0.3

Dis

p (m

m)

Time (sec)

0

5

10

15

20

Fo

rce

(n

N)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

0.1

0.2

0.3

Dis

p (m

m)

Time (sec)

0

5

10

15

Fo

rce

(n

N)

3 min

Fo

rce (

nN

) F

orc

e (

nN

)

(a)

(b) 7 min

Time (sec)

𝐹 𝑡 =1

𝑁 𝑓𝑘𝑒

𝑖2𝜋𝑘𝑡𝑇

𝑁−1

𝑘=0

- Decompose to Fourier series: sum of

trigonometric functions with different

amplitudes and frequencies.

1

0

21 N

k

N

nki

kn ecN

y

1

0

2

]FFT[N

j

N

jki

nnk effc

Cellular contraction data

Two representative states 3 min: stimulated state, much regulated contraction.

7 min: desensitized state.

0 10 20 30 40 50 600

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Freq. (Hz)

Po

wer

3 min

7 min 3.62 Hz

1.84 Hz Nyquist freq

Power spectra of FFT coefficients ck

14/30 Conclusion

A comprehensive characterization was conducted on the viscoelastic properties

of PDMS in both time domain (relaxation modulus) and frequency domain

(complex modulus) using advanced nanoindentation techniques.

Developed an enhanced viscoelastic Timoshenko beam formula to investigate

the effects of loading rate and pillar aspect ratio on the cellular contraction force

calculation.

Converted the cyclic cardiac myocytes contraction into Fourier series, and

simulated the contraction force in the frequency domain by finite element

analysis.

Publications during PhD study.

6 peer-reviewed journal papers published, 1 paper under review.

24 conference proceeding papers and posters

(Transducers, MicroTAS, MRS, etc.).

15/40

Advisor: Dr. Xin Zhang.

Committee members.

NSF grants CMMI-0826191, CMMI-0700688

Photonics Center at Boston University (BU)

Dr. Catherine Klapperich from BU

Dr. Zhiyong Gu from University of Massachusetts at Lowell

All previous and current LMST members

Mr. Chen Cheng (UT Dallas), Mr. Ronnie Cooper (Hysitron), Mr. Jim Mason

(Solartron Analytical)

All other people who have kindly helped me over the years

All my families

Acknowledgments

16/30

Conducting Polymer

Actuators

• Conducting polymer is a novel actuator material: low activation

voltage, large strain, operating in liquid, bio-compatibility.

• Developed a multilayer model for the trilayer bending actuator.

• Studied the effect of modulus and thickness of each layer.

* Ping Du et al., Sensors and Actuators A: Physical, 163, 240-246, 2010.

17/30 Conducting Polymer (1)

Experiment setup

Actuation animation

Work density

Voltage and Current

18/30

PDMS and Conducting

Polymer Nanowire Composites

• Enhance the electrical responses of PDMS through

incorporation of conducting polymer nanowires, while

maintaining the desirable mechanical flexibility.

• Studied the effect of nanowire concentration on the

dielectric constant and elastic modulus of composites.

* Ping Du et al., Journal of Physics D: Applied Physics, 46, 195303, 2013.

Conducting Polymer (2) 19/30

Nanowire synthesis

SEM of nanowires

Dielectric constant

of composites

Relaxation modulus

of composites

Percolation model Mixture model

20/30

Silicon Oxycarbide Films

• Add silicon carbide into silicon oxides to improve the

mechanical properties, thermal stability, and chemical

resistance.

• Study the effect of carbon content and post-thermal

annealing temperature on the residual stress, modulus

and hardness of SiOC films.

* Ping Du et al., Sensors and Actuators A: Physical, 176, 90-98, 2012.

21/30 SiOC (1)

EDX spectra of SiOC films

FTIR spectra of SiOC films

Residual stress

Scale bar: 100nm

SEM

Thickness reduction

SiOC (2) 22/30

Hardness

Modulus FTIR peak shift

23/30 Tribological study on DLC coatings (Entegris)

Scratch test (linear mode)

– Critical load: normal load at which a particular failure mode between the

coating and substrate initiates.

– Evaluation methods: microscope, friction force, acoustic emission.

Wear test (rotary mode)

– Coefficient of friction: ratio of friction force to normal force

– Wear rate: the ratio of the volume of removed debris to the work done

by friction force.

24/30 CAD (1)

Design Project: Automated Loading Machine for Microtiter Plates

Precision Machine Design and Instrumentation (MN560)

Chien-Hsin Chen (chchen@bu.edu)

Ping Du (pdu@bu.edu)

Nan Shao (nshao@bu.edu)

25/30 CAD (2)

Bottom electrode

Guard ring

Base

Teflon (insulator)

Top electrode (micrometer)

Custom-made test fixture in accordance to the ASTM Standard D150

BNC Connector

26/30 CAD (3)

Certified SolidWorks Associate (CSWA)

R=1.57 mm

=2.5 mm

Original position

Deformed position

Indenter

PDMS

27/30 FEA (1)

Cross section distortion in

circular beam Penetration effect of wedge indenter

Dynamic micropillar bending

1) Element: C3D10 (10-node quadratic tetrahedron)

2) Boundary condition: cellular contraction data

3) PDMS modulus: complex modulus E(w)

4) Direct-solution steady-state dynamic analysis

28/30 FEA (2)

Projects at Medtronic

Numerical modeling support (ABAQUS, ANSYS) for various devices and

manufacturing process development.

• Characterize the elastic/hyperelastic and viscoelastic properties of

common rubbers/plastics used in medical devices; evaluated their effects

on the critical component performance during the device life time.

- Impact of plastic housing complex modulus in the fatigue life of

feed-through wires under cyclic loadings.

- Relaxation of seal contact pressure and creep in surrounding plastic

components during 10 years.

- Weld strength of coils and failure prediction of lead/catheter during

aggressive tensile and bending tests.

• Superelastic behavior of shape memory alloy (Nitinol) components.

• Progressive sheet metal forming process under large plastic deformation.

• Molten solder flow and heat transfer (ANSYS CFX) for laser soldering of

circuit board.

29/30 Questions and Comments