Chemical Engineering Education222

Oneofthefundamentalchallengesinteachingapoly-mersciencecourseistodevelopthestudent’sintu-itionregardinghowthisclassofmaterialsbehaves.

Professorsoftendescribepolymersasentangledmassesofspaghettiorkitestringtoexplaintheuniquebehaviorofpoly-mers.Thereasonthisiscommonlydoneisthatifstudentscanvisualizehowpolymerchainsinteractandfunctionthroughtangibleexamples, then theyarebetter able tounderstandmany of the basic concepts in polymer science and engi-neering.Neartheendofmygraduatepolymerengineeringcourse, I tell my students that they are prepared for the final exam when they are able to “think like a polymer.” Stated in amoredidacticfashion,studentsmustbeabletovisualizeandunderstandthemodelsusedinpolymerscienceinordertointerpretmicrostructures,predicteffectsonproperties,andderivethecorrespondingequations.

Oneimportanttopicinpolymerscienceisthekineticsofpolymerizationreactions.Modelingpolymerizationreactionsdoesnottypicallyrequireadetailedknowledgeoftheorganicchemistryinvolved,sincemostpolymerizationreactionsfol-lowoneofseveralmotifs.Forinstance,inatypicalstepwisegrowthpolymerization,therearetwomonomertypessuchthat each “type A” monomer will react with two “type B” monomers.EachtypeBmonomerwillreactwithtwotypeAmonomers,andeachmonomerdoesnotreactwithitsown

type.Astoichiometricreactionathighconversionwillresultinlongpolymerchainsofalternatingmonomertypes.Aclas-sicexampleofthisreactionisthesynthesisofpolyesterfromamonomerwithtwoalcoholgroupsandasecondmonomerwithtwocarboxylicacidgroups.Modelingthekineticsofthemolecularweightdevelopmentdoesnotrequireknowingthedetailsofthechemistry,exceptforknowingtheaforemen-tionedbondingrules.

Withthesethoughtsinmind,twopolymerizationsimula-torsweredevelopedfortwodifferentpolymerizationtypes:stepwisegrowthandfree-radicalchainpolymerizations.Inthesesimulators,thedetailsofthechemistryareneglected,and computer models of polymerization are created by

polymEriZaTion simulaTor For Introductory Polymer and

Material Science Courses

William m. cHirdon University of Louisiana at Lafayette • Lafayette, LA 44130

William M. Chirdon is an assistant professor at the University of Louisiana at Lafayette in the Chemical Engineering Department. He received his Ph.D. in macromolecular science and engineering at the University of Michigan. Dr. Chirdon also serves as the faculty advisor for the local chapter of the American Institute of Chemical Engineers. His research interests include the modeling of heat generation and transfer in cementi-tious composites, simultaneous thermal property determination in exothermic solids, thermal analysis of polymers, appearance properties of translucent composite materials, and nanoscratch modeling for polymer surfaces.

© Copyright ChE Division of ASEE 2010

ChE classroom

Vol. 44, No. 3, Summer 2010 223

consideringmonomersassimplespheresofdifferenttypesthat obey defined bonding rules. These simulators allow for studentstoquicklyobtainanunderstandingofhowthesepo-lymerizationreactionsoccurandthedifferencesbetweenthetwo.Forinstance,atmoderateconversions,thestep-growthpolymerizationwill result inavarietyofoligomers,whilethefree-radicalchainpolymerizationwillresultinafewlongpolymersalongwithunreactedmonomers,asseeninFigure1.Aninstructorcandemonstratetheseconceptsmoreeffectivelyandexpeditiouslywithacomputersimulationratherthanwithablackboard.Thesimulatorsfeaturedinthisarticlearealsoconvenientforinstructorsandinstitutionsbecausetheyarefreetouseforacademic,noncommercialpurposes.

TargET auDiEnCE Thissimulatorisanidealtoolforintroducingpolymeriza-

tionreactionsorsimplytheconceptofapolymer.Ithasbeenfoundtobeusefulforatleasttwostudentgroups.First,thismodulehasbeenfoundtobeeffectiveinabasicmaterialsscience/engineeringclasstointroducepolymermaterials.In-stead of simply giving the definition of a polymer, introducing polymerswiththeuseofthissimulatorallowsforthestudentstoquicklydevelopanappreciationforwhatpolymersareandhowtheyaremade.

Thefullpotentialofthesimulator,however,canbereal-izedinagraduate-levelintroductorypolymerscourse,wherebasicpolymerconceptsandformulaecanbequantitativelyanalyzedbythestudentsbyexportingtheiracquireddataintospreadsheets.Studentsarelikelytobecomemoreengagedinaclasswhentherearelivedemonstrationsofpolymerizations,such as the “Nylon Rope Trick,”[1]oriftheycanuseprocessingorcharacterizationequipmentthemselves.ThesesimulatorsoffermuchofthevisualstimulusofalivedemonstrationwiththeconvenienceofaPowerPointpresentation,andtheyallowstudentstoconducttheirownsimulatedexperiments.

From the students’ perspective, the simulators representaneasiermechanismforlearningthematerialthatismorecontemporary, visual, and interactive. One major benefit is thatthismethodofinstructionallowsstudentswithdifferentlearningstylesthatarelessreceptivetolecturestograspthekey concepts by executing their own model experiments.Surveys conducted at the end of my graduate polymerengineering courses confirm that the simulations help the studentsvisualizeandunderstandpolymerizationreactionsand develop new insights as shown later in the “Results” section.Mostprofessorshaveknownsomeindividualswhowereratherlacklusterstudents,yettheyexcelinmorehands-onactivitiessuchaslaboratorywork,independentresearch,orfutureemploymentinindustry.Similarly,instructorsmayfind these students that do not respond well to passive learn-inginlecturesmayhaveachancetoexceliftheyaregivenanopportunitytoperformtheirownmodelexperimentsandanalyzethedatathattheycollect.

molECular simulaTion moDEls Thesimulatorsdemonstratedinthispaperweredeveloped

asanEtomicamolecularsimulationmodule.Thesemodulesareavailableonline,codedinJava,andfreeforpurposesofacademicresearchandinstruction.Themodulesarepubliclyavailableat<www.etomica.org>.Fromthehomepage,thepolymerization simulator can be found by navigating to“Modules” and then selecting the “Polymerization” module. Thepolymerizationmodulemayalsobeaccesseddirectlyat<http://rheneas.eng.buffalo.edu/wiki/Polymerization>.Themoduleisdesignedtobeself-explanatorywiththeessentialbackgroundmaterialincludedonthewebsitewithexamplesand problems.The module is even more effective whencoupledwithaformalpolymercourse,however.

17

a)

b)

Figure 1. Molecular simulation of a) a stepwise growth polymerization and b) a free­radical chain polymeriza­

tion. Both simulations are at 80% conversion. Figures are reproduced in black and white, but the monomer types

are color­coded in the simulation.

Chemical Engineering Education224

Inthesemodels,theaveragespeedoftheparticlesisde-terminedbythesystemtemperature.Thetemperaturecanbecontrolled using a “thermostat” which will change particle speedstoobtainthesettemperatureforthesystem.Theuserisabletosetadiabaticorisothermalconditionsandchangethetemperaturewhilethesimulationisrunning.Thisallowsthestudentstoseetheeffectsoftemperatureonpolymeriza-tionreactions.Thebondenergyisalsoprogrammable,whichaffectsboththestrengthof thebondandtheheatreleasedduring reaction. Users can then monitor the number- andweight-averagemolecularweights,chain-lengthhistogram,temperature,andconversionovertime.

sTEpwisE growTh simulaTion Stepwisegrowthpolymersarecreatedbyreactingatleast

twodifferentmonomertypes.Inthesimplestcase,therewillbea typeAanda typeBmonomer,whereeachmonomerwillreactandbondtwicewiththeothertypebutnotitsowntype.Monomersthatformtwobondsareknownasdi-func-tional. Specific chemical mechanisms are neglected in this simulation,but themonomersaregivennames forclarity.ThetypeAmonomersaredi-functionalalcohols,annotatedasdi-ols.ThetypeBmonomersaredi-functionalcarboxylicacids,annotatedasdi-acids.Mono-olsandMono-acidsaremono-functional groups that act as end-capping agents.Atri-functionalacidisalsoavailableasacross-linkingagent.Thedi-ols,di-acids,andcross-linkingagentsarerepresentedasred,blue,andgreendots,respectively.Usingthissimplemodel,avarietyofbasicconceptsinstepwisegrowthpolym-erizationcanbedemonstratedasdiscussedinthe“StudentActivities” section.

frEE-raDiCal Chain aDDiTion simulaTionFree-radicalchainadditionisanentirelydifferentmecha-

nismofpolymerizationthathascompletelydifferentreactionkineticsandresultsinadifferentdistributionofmolecularweights. The first step in a free-radical chain addition simula-tionisknownastheinitiationstep,whereaninitiatormoleculeformsfreeradicals.Inthissimulation,theinitiatorisconsid-eredtobehaveasatypicalperoxideinitiator,whichsplitstoformtwofreeradicalswhenheated.Thissimulationmodelseachinitiatorastwoparticlesthatarenotreactivewhentheyare together. The initiators are held together by a finite bond energy,however,sothatasthetemperatureisincreased,morebondsarespontaneouslybrokenbythethermalenergy.Whenaninitiatorsplits,itformstwofreeradicalspecies,eachofwhichcanreactwithamonomer.Oncethefreeradicalreactswithamonomer,theformerlyreactiveparticlepermanentlybondstothemonomer,whichthenbecomesreactivetowardsothermonomers,andtheinitiationstepiscomplete.

Theinitiationstepresultsinthenucleationofagrowingpolymerchainandleadstothesecondstageinthispolymer-ization:propagation.Inthepropagationstage,monomersare

addedonebyonetothegrowingchain.Eachtimeamonomerisadded,theradical(reactive)natureofthechainispassedtothenewlyaddedmonomersothattheunitontheendistheonlychemicallyactiveunitinthechain.Thelaststageofthispolymerizationistermination,wherethepropagationisterminatedinoneoftwowayswhentheactiveendsoftwopropagatingchainscollide.Interminationbycombination,theactiveendswillbondwitheachother,effectivelydoublingtheaveragemolecularweightinthisstep.Alternatively,thechainscanterminatebydisproportionation,wheretheradicalistransferredfromonechaintotheother,killingthereactiv-ityofbothchainsandresultingintwopolymerchainswiththesameaveragemolecularweightasbeforetheterminationstep.Theprobabilityofcombinationvs.disproportionationisaninputparameter.

sTuDEnT aCTiviTiEs These computer simulations can serve to teach students

overarangeoflevelsfromasophomorematerialssciencecourse through a graduate-level introduction to polymers.Sincethedetailedreactionmechanismshavebeenreplacedbysimplebondingrules,thelevelofchemistryincludedinthe corresponding lecture can be tailored to fit the learning objectivesofthecourse.

For a materials science course where the students haveneverbeenformallyexposedtopolymerscienceororganicchemistry,thedetailsofthechemistrycanbeneglectedandonlythebondingrulesofthemonomersneedtobediscussed.Thismaybeparticularlyadvisableifthecourseincludesasignificant number of students from disciplines other than chemistryorchemicalengineering.Thesesimulationswillstill serve to give the students a firm, intuitive grasp of what isapolymerandhowtheyareformed.Afterademonstrationinfrontoftheclass,whichmaytakelessthan30minutes,thestudentsshouldbeabletodescribehowinitiatorconcen-tration affects the conversion rate and the final molecular weightofapolymer,thethreebasicstepsofafree-radicalchainpolymerization,effectsofterminationmechanismonmolecularweight,effectsoftemperature,theimportanceofstoichiometryinstepwisegrowthpolymerizations,theeffectofmono-functionalgroups,andtheconceptofgelation.Thesecriticalconceptscanbecoveredquicklyandeffectivelybyusingthissimulationasavisualaid.Afterthisbrieftutorial,studentswillbebetterpreparedforpolymerworkinunder-graduateresearchprojects,industrialinternships,orgraduate-levelpolymercourses.Thestudentscanthenbereferredtothewebsiteiftheywishtolearnmoreaboutpolymerizationreactions.

Thefullpotentialofthesimulationcanbeusedinagraduate-levelpolymerscourse.Thesimulationsarenotidealforad-vancedgraduateworkorforresearchpurposessincetheyaretwo-dimensional,containasmallnumberofmolecules(withrespecttothestatisticsoflargenumbersofpolymers),andthe

Vol. 44, No. 3, Summer 2010 225

specific chemical mechanisms are neglected. This simplicity, however,makesthesimulationsidealforillustrativepurposesforanintroductorypolymerscienceorengineeringcourse,becausemostofthefundamentalpolymerformulaestillap-ply.Thestudentscanthenusethesimulationstocollecttheirowndata,copythedatatoaspreadsheet,analyzethedata,interprettheresults,anddiscusshowtheirresultsagreeordisagreewiththeoreticalpredictions.

Students in a polymer science course should be able toquantitativelypredicttheresultsofthegivenpolymerizationfromtheconcentrationsofthereactants.Forinstance,inanunbalanced step-wisegrowthpolymerizationconsistingoftwodi-olsforeachdi-acidmonomer,astudentshouldpredictthatthemaximumnumber-averagedegreeofpolymerizationwould be three, which is verifiable by the simulation. Fur-thermore,thesimulationwouldalsohelpthestudentvisual-izethatwhilethenumber-averagedegreeofpolymerizationapproaches three, there is significant polydispersity. Students should also be able to quantitatively predict the effect ofmono-functionalgroups.Thenumber-andweight-averagemolecularweightscanbepastedintoaspreadsheet,plotted

asinFigure2,andcomparedtotheoreticalpredictionsfromthefollowingequations.[2]

Xnp

Xwpp

PDI p=−

=+−

= +1

111

1 1, , ( )

where Xn, Xw,PDI,andprepresentnumber-averagedegreeofpolymerization,weight-averagedegreeofpolymerization,polydispersityindex,andconversion,respectively.

Inafree-radicalchainpolymerization,thestudentsshouldbe able to predict the final number-average molecular weight forapolymerizationreactioniftheinitiator-to-monomerratioandterminationmodearegiven.

Gelationcanbemodeledbyusing the step-wisegrowthsimulator.Gelationoccurswhenthepolymernetworkreachesan infinite average molecular weight, which can be easily visualizedwiththeperiodicboundaryconditionbypressing“1” as seen in Figure 3 (next page). If the average monomer functionality, f, is greater than two for a stoichiometricmixtureofreagents, thengelationwill typicallyoccuratahighconversion.Thecriticalconversionatwhichgelationwill occur (where a polymer of infinite size appears) can be predictedasp f

c= −( )−1

12foralargenumberofmonomers

inastoichiometric,3-Dsystem.[3]Sincethesimulatorfeaturesarelativelysmallnumberofmonomersina2-Dsystemforvisualizationpurposes,however,thisequationonlyworksasanapproximation.

Theeffectsoftemperatureonthepolymerizationcanalsobeobserved.Thesimulationscanberununderisothermaloradiabatic conditions, and students can plot the conversionover time forbothconditions.Underadiabaticconditions,the heat of reaction will raise the temperature during thepolymerization reaction, resulting in faster reaction rates.Inthestepwisegrowthsimulator,however,thereactionsarereversible,sothelargertemperaturesgeneratedinthereactionwill cause depolymerization, which will result in a lower final molecularweight.Thisauto-accelerationisarealeffectasisthethermaldegradationwhichcanresultathightemperatures.Oneunrealisticaspect,however,isthatthethermallybrokenpolymerchainsareabletoreformbonds.Inreality,thermallydegradedpolymerstypicallyresultinchainendsthatarenotreactivewithmonomersorotherpolymerends.

Astudentcancopytheconversiondataovertimebyright-clickingontheplotandthenpastingthedataintoaspreadsheetwherethereactionratekineticscanbeanalyzed.Areactionrateequationfortheconsumptionofmonomercanbepro-

posedsuchasd M

dtk M

n =−

,whereM,t,k,andnarethe

monomer concentration, time, rate constant, and order ofreaction,respectively.Thestudentcanperformhis/herownanalysis to thendetermine thevalues for the rateconstantandtheorderofreaction.Thestudentcanalso investigatetheeffectoftemperatureontherateconstant.18

0

0.5

1

1.5

2

2.5

3

3.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Conversion

Deg

ree

of P

olym

eriz

atio

n XwXw(theory)XnXn(theory)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Conversion

Poly

disp

ersi

ty In

dex

PDI

PDI(theory)

Figure 2. a) Simulation results for number­ and weight­average degrees of polymerization plotted vs. conversion and compared to theory. b) Polydispersity

index of simulation plotted vs. conversion and compared to theory.

Chemical Engineering Education226

Acidcatalysiscausesthereactionorderformanystepwisepolymerizations to be third order (n = 3).[4]Sinceacidcataly-sisisnotincludedinthesimulationmechanism,however,asecond-orderreactionisexpected,whichhasasolutionoftheform:

1 1

0M M

kt= +,

whereM0istheinitialmonomerconcentration.[5]Fromthisequation,kcanbereadilycalculatedbytakingtheslopeof1/Mplottedover timeas shown inFigure4a.Amodelof

the second order reaction using the fitted k value is shown in Figure 4b. Students can alternatively fit k and n without assumingareactionorder.

For a multidisciplinary polymer engineering course, aminimumamountoforganicchemistrymaybeincludedinthecourse. In my CHEE 417(G): “Polymer Engineering” course, Iremindthestudentsthatalcoholsreactwithcarboxylicacidstoformesters,whichleadstoshowinghowadi-olandadi-acidcanreacttoformalongchainofpolyester.Atminimum,thisamountofchemistryisrequiredtounderstandpolymernomenclature, because a student may have some difficulty in understandingwhatapolyesterisandhowitismadewithoutthe basic understanding of an esterification reaction. Students shouldsimilarlybeabletoidentifycommonpolymersandthetypesofmonomersusedtosynthesizethem.Thiswillhelpthestudentsbecomeconversantinpolymerterminologysothattheymaybettercomprehendresearchpapersandpresentationsrelevanttopolymerslaterintheircareers.

In a graduate-level polymer chemistry course with anorganic chemistry prerequisite, the chemistry mechanismswouldbeanessentialelementofthecorrespondinglectures.Insuchacourse,thestudentsmightbeaskedtocritiquethis

19

a)

b)

20

y = 0.0021x + 0.0103

0

0.005

0.01

0.015

0.02

0.025

1 2 3 4 5Time (picoseconds)

1 / (

Num

ber o

f unr

eact

ed b

onds

)

0102030405060708090

100

1 2 3 4 5Time (picoseconds)

Num

ber o

f unr

eact

ed b

onds

Simulation

2nd order fit

Figure 3. a) Simulation of gelation caused by tri­function­al monomers. b) View of the simulation with the periodic boundary condition showing 3 3 3 unit cells. Note that the chain continues from one unit cell to the next and is

of infinite size after gelation.

Figure 4. a) The inverse of the number of unreacted monomer bonds is plotted vs. time to find k. b) The fitted reaction constant can be used to compare the 2nd order

kinetics equation to the simulation data.

Vol. 44, No. 3, Summer 2010 227

polymerizationmodelbydiscussingsomeoftheunrealisticramifications of removing the chemical mechanisms. For instance,thestudentsmaypredicthowtheremovaloftheacid-catalysis mechanism in the polyesterification reaction affectstheorderofthereaction.Aninstructormightalsoexplainhowpolymerchainsmaythermallydegradethrougha beta-scission mechanism or discuss other unfavorablesidereactions.

rEsulTs Theuseofthesesimulationshadapositiveimpactonthe

effectiveness of instruction.As an instructor, I found thiswasanenjoyablevariationfromtheusualPowerPointandchalkboardlectures.Thestudentswelcomedthischangeinthemediumofinstructionevenmoreso.Thisalternationinmediumalonecanhelpaninstructoravoid“DeathbyPow-erPoint” as described by Felder and Brent.[6]Furthermore,thestudents garner other benefits through doing their own simu-latedexperiments,analyzingtheirowndatawithspreadsheets,andperformingthecriticalthinkingrequiredtointerprettheresultsandcomparethemtotheoreticalpredictions.Incorpo-ratingthesetasksisalsovaluableforachievingaccreditationoutcomesandimprovingcourseevaluations.

Instructors should find, as with any model or simulation, thatsometheoreticalequationswillworkexactly,someap-proximately,andothersnotatallduetotheassumptionsandapproximationsofthemodelandhowitfailsorsucceedsinrepresentingreality.Oneunrealisticaspectofthesimulationisthatallofthemonomersinthesimulationweregivenamolecularweightof1g/mole.Therefore,thedegreeofpo-lymerizationisequaltothemolecularweight.Thiswasdoneforthesakeofsimplicity;however,itwasfoundthatitcouldbeconfusingtothestudentswhentheterms“degreeofpo-lymerization” and “molecular weight” are used interchange-

ably.Emphasizingthiscaveatearlyintheintroductionofthesimulation briefly, but clearly, should alleviate this issue.

Equations derived specifically for 3-D systems may only workasapproximationsinthissimulation.Equationsderivedbased strictly on stoichiometry and extent of conversionshouldworkexactly,however.Allowingstudentstopredictwhichequationswillworkorfailwiththismodelexercisestheircritical-thinkingskillsandwillgivethemadeeperun-derstandingoftheequationsandtheirimpliedassumptions.

Beyondmyanecdotalobservations,ananonymoussurveyconsistingof49questions(38multiplechoiceand11openresponse)wastakenbyanindependentpartytoevaluatetheeffectivenessofthismodelfortheCHEE417(G):“PolymerEngineering” course in the Fall of 2008. A sub-selection of thequestionsisshowninTable1forbrevity.Theclassonlyhad seven students, which is excellent for instruction anddiscussion,butpoorforsurveystatisticsevenwithallsevenstudents responding. Regardless, the feedback was verypositiveforallofthestudents.Thesurveydatafortheques-tionsinTableIwascollectedagainintheFallof2009with12outoftheclassof18studentsrespondingwithsimilarlypositiveresults.

In addition to the quantitative survey data, the studentswereaskedopen-endedquestionsregardingthesimulationanditsimplementation.Theseresultsweresimilarlyfavor-able.Manyofthestudentsfoundthesimulationsaidedtheirability tovisualizethepolymerizationreactionsandfoundthesimulatoreasytouse.Somestudentsalsoappreciatedtheopportunitytopracticespreadsheetsskillsintheanalysisofthekinetics.Whilemoststudentsfoundtheinterfaceeasytounderstandanduse,especiallywiththesupportingdocumen-tationandexamplesonthewebsite,itwasrecommendedthattheinstructortaketimeatthestarttoexplainthefeaturestobecontrolledusingtheinterface.Somestudentshavesuggested

TABLE 1 Survey Results of the Simulation Module for CHEE 417(G): “Polymer Engineering”

# Statements Fall 2008 Average

Fall 2009 Average

1 Thecomputersimulationwasaneffectiveuseofmytime. 4.14 4.25

2 I find this computer simulation helped me visualize molecular motion better than I could before. 4.43 4.50

3 Thissimulationwasavaluableexperience. 4.43 4.25

4 Thiscomputersimulationallowedmetostudyaprobleminawaynotpossiblewithaconventionalexperiment.

4.14 4.13

5 Theuseofthismoduleaidedinmyunderstandingofthematerial. 4.43 4.08

6 Ibelievethismoduleshouldbeusednextyear. 4.71 4.25

7 Theuseofthissimulationmodulewasavaluableuseofclasstime. 4.43 4.00

8 Thecontentcoveredinthesimulationwasappropriatetothecourse. 4.71 4.17

9 ThecomputersimulationprovidedmeinsightsIhadnothadbefore. 4.29 4.25

10 Ifeelthecomputersimulationwaseffectiveinincreasingmyunderstandingofmolecularmotion. 4.29 4.25

The individual responses were scored as: 5–Strongly Agree, 4–Agree, 3–Neutral, 2–Disagree, 1–Strongly Disagree. The averages of the responses areshown.

Chemical Engineering Education228

themodelshouldbemorecomplex,featuringmorerealisticchemicalmechanisms,largernumbersofmonomers,andmak-ingthesimulationthree-dimensional.Thiswouldnecessarilymake thesimulatormorecomplicated tosetupandslowertorun,however.Therewasafairbalanceofcommentsthatthesimulatorwastoosimplisticvs.beingtoocomplicatedtosetup,whichseemstoindicatethatagoodbalancehasbeenachievedforstudentsatthislevel.Atrialversionofa3-Dsimulatorwaspartiallydeveloped,butitwasnotused,becausethemoleculesandinteractionswerehardertosee,eventhoughitwasmoreaestheticallyimpressive.

Somestudentswouldprefertheassignmentsbeassignedtosmallgroups;however,anequalnumberofstudentspre-ferredworkingindividually.Runningmultiplesimulationstohighconversionscantakeaconsiderableamountoftime,soallowingdatasharingamonggroupsmightbeareasonableoptioniflargetake-homeprojectsareassigned.Instructors,asinanyexperimentorassignment,areadvisedtoconductthesimulationsthemselvesbeforeassigningthemtomakesurethatthetimedemandsarereasonableandthattheexpectedresultsareproduced.Thissimulatorwasprimarilyusedinindividualtake-homeassignmentstoensurethateachstudenthadanequalopportunitytousethesimulatorandreceivedanindividualassessmentoftheirwork.Theabilitytoworkinteamsisanimportantcareerskillandaccreditationoutcome,however,and thiscouldbeanopportunity to implementateam-basedprojectinapolymercourse.

ConClusions Courses generally benefit from tangible visual aids, demon-

strations,andlaboratoryexperiments.Unfortunately,manyofthesecoursesupplementsarenotimplementedduetothemate-rialcost,preparationtime,safetyconsiderations,orlaboratoryspacerequired.Thesimulationspresentedhereallowstudentsto accrue most of the benefits of running their own experiment astheysetexperimentalparameters,collectandanalyzedata,exercisespreadsheetskills,andtheninterprettheirownresults.Theonlyinvestmentrequiredisasmallamounttimebytheinstructortobecomefamiliarwiththesimulatorandtomakesurethatthestudentshaveaccesstoacomputer.

Overall,thesimulationswerefoundeffectiveinexplainingthefundamentalsofpolymerizationina30-minutedemon-strationforamaterialsscienceandengineeringcourse.Thesimulations were also successful for teaching a polymerengineeringgraduate courseover the courseof themonthin which lecture topics, demonstrations, and assignmentswere conducted and reviewed using the simulations andspreadsheets.Aninstructorcanusethesesimulatorsasabriefqualitativeintroductiontopolymerscienceorasanopportu-nityforrigorousderivation,analysis,andtestingofpolymerequations,oranyintermediatebetweentheseextremesthatfits the learning objectives of the course.

aCknowlEDgmEnTs The development of this and other molecular-simula-

tion-based education modules[7] was supported by grantDUE-0618521fromtheNationalScienceFoundationtotheCAChE (ComputerAids for Chemical Engineering) Cor-poration.[8]Theauthorproposedthepolymerizationmoduleincludingthebasicalgorithmanddevelopedthesupportingdocumentation.Prof.DavidKofkeoftheUniversityatBuf-falomanagesthemoduledevelopmentprojectwithalgorithmimplementationandcodingprovidedbyDr.AndrewSchultz.Additional software support has been provided by RobertRassler. Phil McLaury conducted the assessment of thesimulationunderthesupervisionofProf.GeorgeBodnerofPurdueUniversity.

rEfErEnCEs 1.Painter,P.C.,andM.M.Coleman,Fundamentals of Polymer Science,

2ndEd.,TechnomicPublishing,Pennsylvania(1997) 2.Sperling, L.H., Introduction to Physical Polymer Science, 4th Ed.,

Wiley-Interscience,NewJersey(2006) 3.Odian,G.,Principles of Polymerization,3rdEd.,Wiley-Interscience,

NewYork(1991) 4.Sun,S.F.,Physical Chemistry of Macromolecules,Wiley-Interscience,

NewYork(1994) 5.Noggle, J.H., Physical Chemistry, HarperCollins Publishers, USA

(1989) 6. Felder, R.M, and R. Brent, “Death By PowerPoint” Chem. Eng. Ed.,

39(1),28(2005) 7.Etomica:MolecularSimulationAPI,<http://www.etomica.org> 8. CACHE,<http://www.cache.org>p