?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F274%2F&rft.title=Modelling+Li%2B+Ion+Battery+Electrode+Properties&rft.creator=Anderson%2C+D.+M.&rft.creator=Bohun%2C+C.+S.&rft.creator=Breward%2C+C.&rft.creator=Fehribach%2C+J.+D.&rft.creator=Melara%2C+L.&rft.creator=Please%2C+C.P.&rft.creator=Richardson%2C+G.&rft.creator=Vernescu%2C+B.&rft.creator=Arroyo%2C+A.&rft.creator=Bellsky%2C+T.&rft.creator=Bui+Boi%2C+A.+M.&rft.creator=Chi%2C+H.&rft.creator=Cipcigan%2C+I.&rft.creator=Franklin%2C+M.&rft.creator=Nguyen%2C+L.&rft.creator=Siddique%2C+J.&rft.creator=Swaminathan%2C+S.&rft.creator=Trichtchenko%2C+O.&rft.creator=Wang%2C+Y.&rft.creator=Zhang%2C+C.&rft.subject=Energy+and+utilities&rft.subject=Materials&rft.description=We+formulated+two+detailed+models+for+an+electrolytic+cell+with+particulate+electrodes+based+on+a+lithium+atom+concentration+dependent+Butler-Volmer+condition+at+the+interface+between+electrode+particles+and+the+electrolyte.+The+first+was+based+on+a+dilute-ion+assumption+for+the+electrolyte%2C+while+the+second+assumed+that+Li+ions+are+present+in+excess.%0D%0A%0D%0AFor+the+first%2C+we+used+the+method+of+multiple+scales+to+homogenize+this+model+over+the+microstructure%2C+formed+by+the+small+lithium+particles+in+the+electrodes.%0D%0AFor+the+second%2C+we+gave+rigorous+bounds+for+the+effective+electrochemical+conductivity+for+a+linearized+case.%0D%0AWe+expect+similar+results+and+bounds+for+the+%22full+nonlinear+problem%22+because+variational+results+are+generally+not+adversely+affected+by+a+sinh+term.%0D%0A%0D%0AFinally+we+used+the+asymptotic+methods%2C+based+on+parameters+estimated+from+the+literature%2C+to+attain+a+greatly+simplified+one-dimensional+version+of+the+original+homogenized+model.+This+simplified+model+accounts+for+the+fact+that+diffusion+of+lithium+atoms+within+individual+electrode+particles+is+relatively+much+faster+than+that+of+lithium+ions+across+the+whole+cell+so+that+lithium+ion+diffusion+is+what+limits+the+performance+of+the+battery.+However%2C+since+most+of+the+potential+drop+occurs+across+the+Debye+layers+surrounding+each+electrode+particle%2C+lithium+ion+diffusion+only+significantly+affects+cell+performance+if+there+is+more+or+less+complete+depletion+of+lithium+ions+in+some+region+of+the+electrolyte+which+causes+a+break+in+the+current+flowing+across+the+cell.+This+causes+catastrophic+failure.+Providing+such+failure+does+not+occur+the+potential+drop+across+the+cell+is+determined+by+the+concentration+of+lithium+atoms+in+the+electrode+particles.+Within+each+electrode+lithium+atom+concentration+is%2C+to+leading+order%2C+a+function+of+time+only+and+not+of+position+within+the+electrode.+The+depletion+of+electrode+lithium+atom+concentration+is+directly+proportional+to+the+current+being+drawn+off+the+cell.+This+leads+one+to+expect+that+the+potential+of+the+cell+gradually+drops+as+current+is+drawn+of+it.%0D%0A%0D%0AWe+would+like+to+emphasize+that+all+the+homogenization+methods+employed+in+this+work+give+a+systematic+approach+for+investigating+the+effect+that+changes+in+the+microstructure+have+on+the+behaviour+of+the+battery.+However%2C+due+to+lack+of+time%2C+we+have+not+used+this+method+to+investigate+particular+particle+geometries.&rft.date=2008&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F274%2F1%2FTIAXFinal.pdf&rft.identifier=++Anderson%2C+D.+M.+and+Bohun%2C+C.+S.+and+Breward%2C+C.+and+Fehribach%2C+J.+D.+and+Melara%2C+L.+and+Please%2C+C.P.+and+Richardson%2C+G.+and+Vernescu%2C+B.+and+Arroyo%2C+A.+and+Bellsky%2C+T.+and+Bui+Boi%2C+A.+M.+and+Chi%2C+H.+and+Cipcigan%2C+I.+and+Franklin%2C+M.+and+Nguyen%2C+L.+and+Siddique%2C+J.+and+Swaminathan%2C+S.+and+Trichtchenko%2C+O.+and+Wang%2C+Y.+and+Zhang%2C+C.++(2008)+Modelling+Li%2B+Ion+Battery+Electrode+Properties.++%5BStudy+Group+Report%5D+++++