POLYMERIZATION KINETICSTHERMODYNAMICSTells us where the systemwould like to go eventually !!ie.defines relationshipsbetween macroscopicvariables at equilibriumKINETICSTells us how fast the system takes variousreaction pathsEXAMPLESSUGAR + OXYGEN PRODUCTS + ENERGYCRYSTALLIZATION IS ALSO A PROCESS CONTROLLEDBY KINETICS, AS WE WILL SEE LATERPOLYMERIZATION KINETICSSTEP GROWTH - SLOWCan use statistical methodsas well as kinetics to describemol. wt. distributions - more on this laterCHAIN Polymerization - FASTCan apply statistical methodsto an analysis of themicrostructure of the products,but not the polymerizationprocess and things like mol .wt.KINETICS OF STEP GROWTH POLYMERIZATIONWHY BOTHER ?•How long does it take to make polymer ?•Can we speed up the reaction ?•What is the relationship between kinetics and the Mol. Wt. Of the product ?REVISIONRATE OF REACTION= CONSTANT x CONCENTRATION TERMS[ ]nRATE OF DISAPPEARANCE OF MONOMER= - dMdt__ k x CONCENTRATION TERMS [ ]n=KINETICS OF POLYCONDENSATIONKEY ASSUMPTION - FLORYThe reactivity of a functional groupis independent of the length of thechain to which it is attachedEXAMPLE:DIBASIC ACID + GLYCOL POLYESTERHO~~~~~~~~~~~~~~~OHHO~~~~~~OHHO - C ~~~~~~~~~~~~~~~~~~~~~~ C - OHO OHO - C ~~~~~~ C - OHOOThis groupreacts asreadily asThis groupWAS FLORY RIGHT?201510500510152025Chain Length: NkA x 104 (g equiv / l)-1 sec-1Redrawn from the data of Flory,P.J.,Principles of Polymer Chemistry,CornellUniversity Press, 1953, p71KINETICS OF POLYCONDENSATIONKinetic equation for this type ofreaction is usually of the form:Reaction Rate = - d[A]dt = k2[A][B]N.B. [A] AND [B] ARE THE CONCENTRATIONSOF FUNCTIONAL GROUPSHowever, esterifications are acid catalyzedand in the absence of added strong acid - d[A]dt = k3[A]2[B]A - A + B - B A- AB - BMORE KINETICSc = [A] = [B]IfHence33ckdtdc=−[A] = [B]∫∫==ttccdtkcdco033223112occtk −= - d[A]dt = k3[A]2[B]EXTENT OF REACTIONDefinep = EXTENT OF REACTIONIn this exampleLET p = # OF COOH GROUPS REACTED# OF COOH GROUPS ORIGINALLY PRESENT____________________________________20001000001002003004001000020Time (mins)1(1 - p)2ThenAnd2 c k t =1(1-p)- 1_____2302c = c (1-p)0Redrawn from the data of Flory,P.J.,J.A.C.S.,61, 3334 (1939)ACID CATALYZED REACTIONd [COOH ]dtdc1(1-p)+ constant2 0 k' [COOH ] [OH ]-_______=-__dt=k'cc k't = ___8006004002000020406080100Time (mins)1(1 - p)Note; the concentration of the acidcatalyst (a constant) is included in k'Redrawn from the data of Flory,P.J.,J.A.C.S.,61,3334(1939)NUMBER AVERAGE DEGREE OF POLYMERIZATIONMc1(1-p)x = = n0__Nn_x =n_0c0_____ie= Mx =n_0M__(1-p)__1.00.80.60.40.20.00100200Conversion, p 1(1 - p)=c0__(1-p)c0NKINETICS OF FREE RADICAL POLYMERIZATIONWe need to consider the following steps •INITIATION•PROPAGATION•(CHAIN TRANSFER)•TERMINATIONINITIATIONBenzoyl peroxideC OO2O COC OO CH2CHXR CH2CHXR +I 2Rk2d.R. + MkiM1.DecompositionAdditionINITIATIONI 2Rkd.R. + MkiM.ASSUME DECOMPOSITION IS THE RATE LIMITING STEPi.e.kdki>>THEN WE SHOULD ONLY HAVE TO CONSIDERBUT; ONLY A FRACTION f OF RADICALS INITIATE CHAIN GROWTHriM dt = 2 f k [ I ]1.=d[ ]___dkdMd t1.d[ ]___d[ I ]dt___1__2k [ I ]d- = =i.e.1C OO+ CO2C OO+COO2PROPAGATIONrM dt = k[ M ][ M ]= -d[ ]__M1 23.+ M M.kp2M.+ MkpxM.M.+ Mx+1kpM.In general;p p.Assumption; reactivity is independent of chain lengthTERMINATIONCOMBINATIONxM.+x+yMyM.ktcDISPROPORTIONATIONxM.+xMyM.ktd+yMCH2CHXCH2CHX+CH2CHX XHC CH2ktcCH2CHXCH2CHX+CH CHX XHC CH2H+ktdRATE OF TERMINATIONrM dt = 2 k [ M ][ M ]= -d[ ]___tt...Where k = k + ktc tdOBTAINED FROM :Rate of removal of chain radicals= sum of the rates of the two termination reactions..Both reactions are second ordertSUMMARYriMdt = 2 f k [ I ]1.=d[ ]___dPROBLEM : We don't know [ M ].SOLUTION :Assume a steady state concentration of transient speciesrM dt = 2 k[ M ][ M ]= -d[ ]___tt..rM dt = k[ M ][ M ]= -d[ ]___pp..STEADY STATE ASSUMPTION[ M ]. = CONSTANTThis means that radicalsare consumed at the same rate as they are generatedri= rt 2f k [ I ]d= 2 [ M ]t. k2 [ M ]. [ ] fk [ I ]d______tk=1/2RATE OF PROPAGATIONRATE OF PROPAGATION = RATE OF POLYMERIZATION .BUT [ I ] IS NOT CONSTANTRrpp=rp=[ M ]pk[ ] fk [ I ]d______1/2substituting;tktkd[ I ]dt = k [ I ]d__from - obtain [ I ] = [ I ] e-k td0HENCERp= [ M ]pk [ [ ] ] f kd____1/2[ I ] e-k t/2d0[ ]1/2WHAT DOES THIS TELL US ?[ M ] [ I ] pR1. IF WE WANT TO INCREASE INCREASE OR But; changing [ I] also changes mol. wt. - more on this later !3. TROMSDORFF EFFECTk ktp2. pR ~ /1/2k ktp/1/2For ethylene at 130 C and 1 bar pressure~ 0.05For ethylene at 200 C and 2500 bar pressurek ktp/1/2~ 3.00010005000020406080100Time (mins)2000150010%20%40%60%80%100%CONVERSION___________[ M ]pk[ ] fk[ I ]d______tk1/2[ M ] - [ M ]0[ M ]0Amount of monomer used upAmount of monomer at start_______________=DEFINITION ; in initial stages of reaction we can assume [ I ] = [ I ] = constant0d[ M ]dt= -___Integrating[ M ]___Ln1/2= -tpk fk[ I ]d______tk0[ M ]0[ ]1.0tConversionMAXIMUM CONVERSIONd[ I ]dt = - k [ I ]d__i.e.andUSUALLY THERE IS A FIRST ORDER DECAY IN INITIATOR CONCENTRATION[ I ] = [ I ] e-k t0d[ M ]___Ln1/2= -p2 k fk[ I ]d______tk0[ M ]0[ ]kd___d-k t[ ]1 - ehenceCONVERSION = 1 - exp -{ } d1/2p2 k f [ I ]______tk0[ ]-k t/2[ ]1 - e kdMAX CONVERSION ( t ) =1 - exp -1/2p2 k f[ I ]______tk0[ ]kd{ } Conversiont1.0∞∞AVERAGE CHAIN LENGTH DEFINE KINETIC CHAIN LENGTHννRATE OF MONOMER ADDITION TO GROWING CHAINSRATE AT WHICH CHAINS ARE STARTED_____________________________=This is the average number ofmonomers polymerized perchain radical at a particularinstant of time during thepolymerizationKINETIC CHAIN LENGTH CONSIDER A TIME PERIOD tlet us say that1. 100 chains are started2. 1,000,000 monomers are reacted in this time periodThen the average degree of polymerization of these chainsis1,000,00010010,000_________=KINETIC CHAIN LENGTH THERE WILL BE SOME OBVIOUS ERRORS (e.g. What aboutchains that were initiated, but did not terminate just beforethe start of the chosen period ?), BUT THESE DECREASE AS t SMALL IN THE LIMIT OF A TIME PERIOD dtννrpri= __=k [ M