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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.