MODULE J: RUBBERS AS ENTROPIC SPRINGS EXAMPLE OF A SILICONE RUBBER
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Group 3: Robert Learsch, Lina Song, Keisuke Matsushita, Chloé Lepert, Herman Li, Sally Lin, Tshiamo Lechina, Roseannie Langomas, Daniel Lizardo
3.014 Materials Laboratory Fall 2012
OBJECTIVES
Prepare poly(dimethylsiloxane) (PDMS) samples to study the
proper9es of rubbers
Study the thermodynamic principles related to the entropic nature of
rubber elas9city
Learn about nanoimprint so> lithography using PDMS
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CROSSLINK POLYMER BEHAVIOR Schema9c of Modulus vs. Temperature for Crosslinked Polymers
and Linear Polymers
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THERMODYNAMICS ASPECTS OF RUBBER DEFORMATION Change in Internal Energy
Helmholtz Free Energy (F)
Change in Helmholtz Free Energy
Force
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STATISTICAL ASPECTS OF RUBBER DEFORMATION
Ideal chain (random walk) sta9s9cs
• Mean square end-‐to-‐end distance
Probability Distribu9on Func9on
• RelaXonship to chain entropy
• Simpler terms:
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TASKS
• Prepare silicone rubber samples
• Perform nanoimprint lithography
• Measure swelling ra9o of PDMS in THF solvent
• Measure stretch vs. stress values
• Verify theore9cal equa9on rela9ng extension and temperature of a
rubber under uniaxial stress
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NANOIMPRINT USING PDMS MASK Replica9ng nanopaWerns with a cheaper process PDMS proper9es that are ideal for so> lithography: § Mould processing, flexibility § S9cky, viscous fluid § Residue-‐free removal due to covalent network
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Master with nanopa\ern Prepared by opXcal or electron beam lithography Expensive
Replica of master with nanopa\ern Prepared with so` lithography ie using PDMS mask and hardening liquid Cheaper
PREPARATION OF PDMS MOULD Materials
Sylgard 184 elastomer and crosslinker (Dow Corning)
Procedure
Mixed 10:1 and 8:1 weight ra9os (elastomer: crosslinker)
Poured into moulds
Degassed under vacuum
Cured in oven at 150 oC for 15 min
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NANOIMPRINTING PROCEDURE
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Master
Pour pre-‐crosslinked PDMS on master Cure at 150 oC, 15 min
Contact PDMS stamp with a hardening liquid/ crosslinkable polymer ie (SU-‐8)
Replica of master
Remove cross-‐linked PDMS from master
Cure at 95oC, 20 min Remove PDMS mask
PDMS mask
LIMITATIONS OF SOFT LITHOGRAPHY • Uneven contact with SU-‐8 bead leads to defects in
replicated paWern
• Deforma9on of PDMS causes slight differences in nanopaWern
• Reflec9on from different surfaces makes it difficult to compare paWerns using an op9cal microscope
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SWELLING EQUILIBRIUM Network crosslink density can be determined from swelling equilibrium
Using the Flory-‐Rehner equa9on:
-‐[ln(1 – v2) + v2 + Xv22 = V1v[v21/3 – (v2/2)]
§ X = polymer-‐solvent interacXon parameter § v1 = molar volume of solvent § v2 = volume fracXon of polymer in the swollen network § v = network crosslink density
§ From v (Crosslink density) we can find Shear Modulus (G)
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PROCEDURE FOR SWELLING EXPERIMENT Cut a small por9on of PDMS (~4 mm3)
Recorded ini9al mass
Placed PDMS in 4 mL THF
Dried PDMS and measured mass at 9me= 15min, 30min, and 40min
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SWELLING EXPERIMENT DATA Star9ng mass = .0324g
Saturated mass ~= .0655g
Corresponds to a Shear modulus (G) of 2.73 MPa
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0
5
10
15
20
25
30
35
40
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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Time (m
in)
Mass (g)
DISCUSSION Possible sources of error:
• Drying step before measurement • EvaporaXon • Insufficient Xme • Value of Chi
Recommenda9on:
• Set up this experiment at the beginning of the lab session
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STRETCH FORCES We can relate the entropic force required to stretch to the stretch ra9o λ
We can then connect engineering stress, σ, to (λ – 1/ λ2)
They’re related by G, the shear modulus, which is nkT/V
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MATERIALS Poly(dimethylsiloxane) PDMS
• In 10:1 and 8:1 raXos of polymer:linking agent
Micrometer
Rubber bands
Masses of 760g and 1525g
Tes9ng apparatus
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PROCEDURE FOR STRESS VS. STRETCH
Measured cross sec9on of band
Marked reference lines
Hanged weights of increasing mass
Measured distance between reference marks using camera
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STRESS VS. STRETCH DATA
Shear modulus: 8:1 => G = 2.154 MPa
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y = 2.154x -‐ 2.1333
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
λ – 1/λ2
Stress, σ
Grey: 10 to 1 sample Yellow: 8 to 1 sample
IDEAL BEHAVIOR
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0 0.5 1 1.5 2 2.5 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
λ
Stress, σ
Stress = G(λ – 1/λ2)
Grey: ideal case Yellow: 8 to 1 sample
DISCUSSION Modulus matches from our different tests
Possible sources of error:
• Bands snapped at 1525g Recommenda9on:
• Smaller increments of stress/mass
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TODO
TEMPERATURE Extension and temperature of a rubber under uniaxial stress
We can relate stress to elonga9on by shear modulus
We can then connect shear modulus to temperature
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MATERIALS Poly(dimethylsiloxane) PDMS
• In 10:1 raXo of polymer:linking agent Micrometer
Rubber bands
760g weight
Apparatus in tube to allow the hea9ng to rest on top
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PROCEDURE FOR TEMPERATURE EXTENSION RELATION Hanged constant weight of 760g
Increased temperature to 30 C up to 60 C
Measured height of weight using camera
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TEMPERATURE EXTENSION DATA
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0
10
20
30
40
50
60
70
0 10 20 30 40 50 60 70 80
Temperature (Degrees C)
Shear M
odulus (M
Pa)
DISCUSSION Confirm rela9on of extension and temperature of a rubber
Possible sources of error:
• Temperature was uneven • Weight was caught by fricXon against tube
Recommenda9on:
• More Xme to heat to temperatures • Hang weight enXrely verXcal
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TODO
CONCLUSIONS § Nanoprin9ng is a valid method for reproduc9on of a nano-‐scale paWern
§ Connec9on between theore9cal first principles and physical tes9ng done in lab
§ Shear Modulus by two methods
§ G = ~2.2 Mpa
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REFERENCES “Module J: Rubbers as Entropic Springs: Example of a Silicone Rubber,” Lab Handouts, Course 3.014 Materials Laboratory, Massachuse\s InsXtute of Technology, (2012). [posted on Stellar]
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