murthy arelekatti 2.821 structural...
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MurthyArelekatti
2.821–StructuralMaterials
30thNovember2017
SiliconeOils-Polydimethylsiloxane(PDMS)
1.Aboutthepaper
Highviscosityfluidscanbeextremelyusefulinachievingveryhighforcetopackaging-volume
ratioindampers.AspartoftheresearchatMIT’sGEARLab[1],therehasbeenafocusonlow-
costandpassivemethodsofachievinghigh-dampingforcesandtorquesforapplicationinthe
designofapassiveprostheticknee.Replicatinghumankneebehaviorinvolvesmimickinghigh
levelsofdampingtorqueexertedbylegmusclesonthekneejoint.
Very useful materials in this context are Silicones, which are polymeric organosilicon
compounds. Specifically, the generic chemical composition is Polydimethylsiloxane (PDMS).
However,themechanicalpropertiesvaryalot,basedonthesynthesisreaction.Applications
for these compoundsare varied, fromcontact lenses to shampoos, lubricants anddamping
Indiamart.com
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fluids. The focus of this paperwill be primarilyon PDMS properties -why these polymers
mechanicallybehavethewaytheydo,andparticularly,howthesecouldbeusedinhighshear-
dampingapplications,suchasthedamperrequiredinapassivekneeprosthesis.
Aparticularphenomenonofinterestisshear-thinningpropertyofsiliconeoils.TheyareNon-
Newtonian in behavior and lose their high viscosity behaviorwhen the velocity gradient is
large.Thishaspracticalconsequencesindampingapplications,asthiscouldleadtoapseudo
stick-slip effect, where high-viscosity fluids effectively behave like solids, exhibiting kinetic
friction-likebehavior.
2.Introduction
To understand the basics of Silicone oils, it is important to first consider their polymeric
molecular structure. Siliconeoil is any typeof polymerized Siloxane liquid,with side chains
thatareorganic. InaSiloxanepolymer,thebackboneiscomposedofalternatingSiliconand
Oxygenatoms(-Si-O-Si-O-Si-O-).Thetwoavailabletetravalentpositionsin–Si-canbeattached
todifferentgroups.Themostcommongroupsaremethylorphenylsubstitutes.Whenthetwo
substitutesaremethylgroups,itresultsinoneofthemostimportantandwidelyusedtypesof
Silicone oils -Polydimethylsiloxane, hereby abbreviated as PDMS. The chemical formula for
PDMSisCH3[Si(CH3)2O]nSi(CH3)3,asshowninFig.1.
Because of their high viscosity and immiscibility with water, they have been colloquially
referredtoasoils.WhilehydrocarbonpolymersrelyonabackboneofC-Cbonds,Siliconeoils
have a backboneof Si-O linkages. These linkagesare very similar to those found in quartz,
glass, and sand. This backbone ismuch stronger that typical C-C chains, resulting inmany
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interestingproperties,suchasresistancetohightemperature,shearstresses,andchemicals.It
ismostlychemicallyinertandnon-toxic.
Themajordifferencesamongdifferentsiliconeoilscomesfromtheirmolecularweight,which
is related to the length of the linear chain, and the chemical structure of the side groups
attached to Si-O chains. At highermolecularweights (i.e. high value of n in Fig. 1), the oil
becomesmore viscous. At very highmolecularweights, the flexible chains become loosely
entangled,contributingtotheviscoelasticbehavior.Oneofthepopulartoysforkids,theSilly
putty,exploitsthisviscoelasticbehaviorofhighmolecularweightsiliconeoil.Sillyputtyflows
like a very sticky liquid when left alone for a period of time. However, under pressure, it
behaves likeanelasticsolid.Acommonplaywithsillyputty isrolling it intoaballandthen
bouncingitoffahardsurface.However,itshouldbenotedthatsillyputtyisnotpuresilicone
oil.Boricacidisaddedtocreatecrosslinksbetweenadjacentpolymerchains,whichareshort-
lived.Duringslowdeformation,thesecrosslinkshaveenoughtimetobreakdownandreform,
allowingviscous flow.Rapidmotions,however,donotallow forenough time for thecross-
linkstobreakdown,leadingtotheelasticbounce-back.
Anothermodern application of the viscoelastic behavior of siliconeoil in toys is in “Kinetic
sand”.Bymixing2%Siliconeoil(withcrosslinkingboricacid)and98%regularsand,onecan
usetheresultingkineticsandinmanydifferentsculptingandmodelingapplications[3].
Figure1:PolymericstructureofPDMSSiliconeoil[2]
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3.PropertiesandApplications
Asdiscussedintheintroduction,whenthepolymericchainsareverylong,withacrosslinking
element,viscoelasticbehaviorcanbeobserved.Therearemanyotherinterestingproperties
thatshouldbeconsideredtotrulyappreciatetheversatilityofPDMSindifferentapplications.
Siliconeoils,comparedtomostotherhydraulicfluids,exhibitverysmallchanges inviscosity
duetotemperaturechanges.TheSiloxanechainshaveahighbondenergyof~445kJ/molwith
its chemically inert methyl (CH3) functional groups, which makes PDMS a very chemically
stable material. The oxidation stability of PDMS is also excellent, especially in applications
where reaction with atmospheric oxygen is not desirable. It has an extremely low glass
transitiontemperature(pourpointof-55°C),highflashpoint(315°C),and lesstemperature-
dependent viscosity,which enables it to perform across a broader temperature range than
most hydrocarbon fluids. PDMSalsohas the lowest glass transition temperature among all
polymers.With a low surface tension of 20.4mN/m, PDMS easily wetsmost surfaces; for
comparison, surface tension for water-air is around 72 mN/m. Its methyl groups align
themselveswhich results inwater-repellent films. The critical surface tension ofwetting of
PDMSisaround24mN/m,whichisslightlyhigherthanitsownsurfacetension(20.4mN/m).
ThisleadstoPDMSflowingoveritself.Thisenablesittogreatlyoutperformhydrocarbonsin
formingextremelythinself-levelingfilms,sothinthattheymaybeonlyafewmoleculelevels
thick.Thelowsurfacetension,coupledwithgoodwettingproperties,makesitveryusefulin
cosmeticapplications,suchasshampoos,moisturizers,andconditioners.
ThoughSiliconeoilsarehighlyinert,theyhaveahighfreevolume,comparedtohydrocarbon
polymers.ThisleadstohighpermeabilitytoOxygen,Nitrogen,andwatervapor-evenifwater
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is not capable of “wetting” a silicone surface. This is particularly valuable in healthcare
industry,wherediffusionofvariousdrugsandgasesmaybeneeded.
Figure2:Siliconechemistryenablesdevelopmentofvastarrayofproducts.EachSiliconeisauniquecombination
ofmolecularweight,structure,functionalityanddeliverysystem.Figurefrom[4].
4.ViscosityofSiliconeoils
The viscosity ofdifferent types of silicone oil, expressed in centistokes (1 cSt = 10−6m2/s),
resultsfromthemolecularweightandthepolymerlength; increasingsiliconeoil’smolecular
weight results in an increased polymer chain length and consequently an increase in its
viscosity (Fig.3).PurePDMS fluidscan range inviscosity from0.65cSt (thinner thanwater,
whichis1cSt)to20millioncSt(moreviscousthanchewinggum).Atlowmolecularweight,
PDMSpolymersbehavelikeidealNewtonianfluids,whereinfluid’sviscositydoesnotchange
with rate of shear stress. However, as themolecular weight goes up (> 10,000 Da), PDMS
polymers become entangled and exhibit a viscoelastic response, along with a decrease in
viscosityathighshearrates(alsoknownasshearthinning)(Fig.4).
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Figure3:Viscosityvs.MolecularweightofPDMS.DatafromClearcoproducts[5]
Figure4:Shearthinningbehavior.DatafromClearcoproducts[5]
5.Specificapplicationtodamping
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Theneedfordampinginprosthetickneejointshasbeenwellunderstoodforoverfivedecades
[6].Dampinghas twoprimary roles in thehumangait: firstly limitmaximum flexionof the
kneetolessthan70degrees.Flexioniswhenthekneeflexesbackwards,asthefootleavesthe
ground.Secondly,asthelegswingsforwardinairrightbeforeheelstrike,furtherdampingis
needed to slow the knee down as the knee extends back to zero degrees. Conventional
dampingtechniquesinprosthetickneeshaveimplementedlinearhydraulicdampers(Fig.5).
The piston pushes relatively low viscosity hydraulic oil through a small orifice from one
chamber to another, which provides the requisite damping. This braking force is inversely
proportional to the orifice diameter and directly proportional to the square of the piston
velocity.
Figure5:Hydraulicdamperarchitecture
As part of the research being done atGEAR lab, the focus has been onunderstanding the
fundamental principles of humanwalking in order to design a low-cost prosthetic knee for
developingcountries(<$100,specificallyforIndia)[7].Usingalineardamperwithapistonis
anexpensiveproposition,withmanyprecisionmanufacturedpartsandcomplicatedassembly.
Thisiswhatledtothedesignofalow-costviscousdamperthatusesathinfilmofSiliconeoil.
Thedamperusesveryhigh-viscositysiliconeoiltoprovidedampingtorquesashighas20N-m
inasmallcylindricalpackage(4”dia.x1”ht.).Incomparison,standardrotarydampershave
traditionally used low-viscosity fluids to produce damping torques, which makes their
applicationimpracticalinacompact,low-costdevice.
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Aprototypeoftherotarydamperwasconstructedinthreeparts(Fig.6)[8].First,acylindrical
chamberwasmilledfromDelrin.Next,aplungerwasturnedandmilledfromTeflon-infused
Delrin (for lowfriction)and inserted intothechamber.Finally,anacrylic lidwas laser-cutto
size and screwed on top of the device. A rubber O-ring was used between the cylindrical
chamber and the acrylic lid to prevent leaking, and a small spring was used to hold this
rotating plunger tight against the lid. The plunger rotates inside the stationary cylindrical
chamber, exertinga forceon the viscous fluid inside the chamber that causes thedamping
torque.
Figure6:A.Rotarydamperprototypeshowingtheplunger(tan)andthecylindricalchamber(gray);therelevant
parameters are related in the equation below. B. Photograph of the disassembled damper showing chamber
(white)withO-ringandplunger(black).Figureadaptedfrom[8].
Therotarydamperprototypeisgovernedbythefollowinganalyticalrelationship:
𝐵!"#$%&# =!!
= !!!
2𝑙𝑅!! + !!!
!− !!!
!(1)
l R2
t
ωA
B
R1
l R2
t
ωA
B
R1
l R2
t
ωA
B
R1
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where BVISCOUS is the rotary damping coefficient, T is the damping torque,ω is rotational
velocity,μ isliquidviscosity.ParametersR2,R3, l,andtarelabeledinFig.6.Thisrelationship
wasarrivedatbysumminguptheviscoustorqueexertedbytherelativerotationofconcentric
cylindersinaviscousmediumandthetorqueduetotheaannularplaterotatingontopafixed
flatplatewithaviscousmediuminbetween.Thedamperwasassembledandtestedwithpure
Siliconeoil (kinematicviscosity100,000cSt),because it isoneof thehighestviscosity fluids
available. Using a flexural torque wrench, the torque required to rotate the damper 180
degrees in a given time was measured. Thus, the outputs of this experimental test were
torqueandangular velocity,whichwere in approximateagreement to theexpected torque
value. The viscousmaterial has a crucial impact on the amount of damping this prototype
couldachieve.However,movingforward,thenon-Newtonianbehaviorneedstobeaccounted
for,byhavingavariablefilmthicknessalongthecircumferenceofthecylindricaldamper.
References
[1]"GEARLAB-GlobalEngineeringandResearchLab",Gear.mit.edu,2017.[Online].Available:http://gear.mit.edu/projects/knee.html[Accessed:28-Nov-2017].
[2]"File:PmdsStructure.png-WikimediaCommons",Commons.wikimedia.org,2017.[Online].Available:https://commons.wikimedia.org/wiki/File:PmdsStructure.png.[Accessed:28-Nov-2017].
[3]"KineticSand",YouTube,2017.[Online].Available:https://www.youtube.com/watch?v=50_-zqsgDA4.[Accessed:28-Nov-2017].
[4]"FascinatingSilicone™Chemistry–PropertyandPerformanceModification-DowCorning",Dowcorning.com,2017.[Online].Available:http://www.dowcorning.com/content/discover/discoverchem/tailor-performance.aspx.[Accessed:28-Nov-2017].
[5]"SiliconeOilsandLubricantsfromClearco",Clearcoproducts.com,2017.[Online].Available:http://www.clearcoproducts.com/.[Accessed:28-Nov-2017].
[6]J.Michael,"ModernProstheticKneeMechanisms",ClinicalOrthopaedicsandRelatedResearch,vol.361,pp.39-47,1999.
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[7]Y.Narang,V.MurthyArelekattiandA.Winter,"TheEffectsoftheInertialPropertiesofAbove-KneeProsthesesonOptimalStiffness,Damping,andEngagementParametersofPassiveProstheticKnees",JournalofBiomechanicalEngineering,vol.138,no.12,p.121002,2016.
[8]M.Berringer,P.Boehmcke,J.Fischman,A.Huang,Y.Joh,J.Warner,V.Arelekatti,M.MajorandA.Winter,"ModularDesignofaPassive,Low-CostProstheticKneeMechanismtoEnableAble-BodiedKinematicsforUsersWithTransfemoralAmputation",Volume5B:41stMechanismsandRoboticsConference,2017.