Always end in a group Forms branches, not crosslinks

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1 Synthesis of Polymers Prof. Pul Hmmond Lecture 8: Network Formtion, Sttisticl Approch, Pw Bsed, A Word on MWD for Nonliner Polymeriztion Network formtion Consider first cse: + [ 3 ] monomers so fr hve een difunctionl H N R CH difunctionl = groups tht cn rect HC R' CH (prticipte in rxn) H R" H trifunctionl: H R" H H Alwys end in group Forms rnches, not crosslinks Wht is the moleculr weight or MW distriution? (Peeles, Schefgen, Flory) for + f systems f = func of f π = conversion of -groups (=minority) (N B ) o r = 1.0 (N A ) o frπ + 1 rπ p n = 1 rπ p w = ( f 1) (rπ ) + (3 f )rπ + 1 ( frπ + 1 rπ )( 1 rπ ) Cittion: Professor Pul Hmmond, Synthesis of Polymers Fll 006 mterils, MIT pencoursewre ( Msschusetts Institute of Technology, Dte.

2 p w 1 + frπ = z = p n frπ + 1 rπ ) polydispersity Consider limit s r 1.0 ( lim z = p w = r 1.0 r 1.0 p n f π = 1.0 Specific cses: Let f = 1 + x end cpper sme s + end cpper z =.0 sme result discussed for generl difunctionl systems let f = + liner polymer z = 1 + ½ = 1.5 nrrower MWD does this mke sense? Recll: + : Join chins together with Get rid of extremeties of MWD. Longer chins re joined together with short chin. Long chins cn join w/long chins ut much less likely. Consider n exmple with f : 1 mol mol 3 : (0.01) f = 3 1 group to 1.03 groups Note: for r = 0.97 nd typicl polymeriztion: 1 + r p n = 66 = 1 r , Synthesis of Polymers, Fll 006 Lecture 8 Prof. Pul Hmmond Pge of 6 Cittion: Professor Pul Hmmond, Synthesis of Polymers Fll 006 mterils, MIT pencoursewre ( Msschusetts Institute of Technology, Dte.

3 1 r = (0.97) p n = Systems forming networks Solule frction sol Polymer chins, oligomers, monomers not connected to network Gel frction insolule, intrctle constitutes network Gel point: π t which n infinite network is formed π c Aove gel point π c : Determine π c s: gel frction sol frction p n p w Crothers p n Consider simplest cse: Equl # of, functionl groups N i f i Define f AVG = N i f i = functionlity of given monomer f i 1.0 N i = # of molecules with f i 3 HC CH H 1 H CH CH CH H 1.5 HCH CH H + 3 )+ 1.5() 1. 0 = = = f AVG 3() 1( Cn define conversion N o = initil # of monomer molecules N = # of remining molecules Initil # of functionl groups = f AVG N o , Synthesis of Polymers, Fll 006 Lecture 8 Prof. Pul Hmmond Pge 3 of 6 Cittion: Professor Pul Hmmond, Synthesis of Polymers Fll 006 mterils, MIT pencoursewre ( Msschusetts Institute of Technology, Dte.

4 r=1.0 6 HCH 6 H # of functionl groups rected = (N o -N) For ech rection, lose 1, 1 functionl groups For ech rection, decrese # of molecules y 1 # of functionl groups rected (N o N ) π = = totl # of functionl gruops N o f AVG p n = N o (see originl definition) N # vg degree of polymeriztion Rerrnge : N o f AVG π = N o N Rerrnge Crothers: N o (πf AVG ) = N N o = N πf AVG Universl expression Crothers Eqution N o πf AVG Works for ll the cses, ut f AVG must e djusted when r 1.0 N p n = = π = p n f AVG f AVG Consider gel point: p n generl expression π c = π t gel for Crothers f AVG point e.g. f AVG =.18 π c = = Consider less perfect cse: more functionlity gel t lower conversion N i f i f AVG = N i (N) only time for r = o = 1.0 (N) o If r 1.0 only gin in incresed MW + crosslinking when using + (i.e. deficient group quntity determines how mny of these rections tke plce) , Synthesis of Polymers, Fll 006 Lecture 8 Prof. Pul Hmmond Pge 4 of 6 Cittion: Professor Pul Hmmond, Synthesis of Polymers Fll 006 mterils, MIT pencoursewre ( Msschusetts Institute of Technology, Dte.

5 Excess of only decreses p n Count only groups + ( N i f i ) f AVG = N i f A,i = function in - of monomer i N A,i = # of molecules of monomer i y end cpping Exmple: N A HCH CH H f A = f,i = B HC CH 4 f B = f,i = f i C H HCH CH CHCH H 1 f C = f,i = 3 Enter ody copy in Verdn 10. 8, 7 deficient where = H = CH f AVG = N ( N f + N f ) (( )( ) + ( 1 )( 3) ) + N c + N c c = =.0 π c = = nly t full conversion do you form network. π c > 1.0 physiclly impossile to crete network Cse of exct stoichiometry: doesn t mtter which is deficient. ther cse: Let N B = 3.5 π c = = Flory-Stockmyer p w Generlized cses: , Synthesis of Polymers, Fll 006 Lecture 8 Prof. Pul Hmmond Pge 5 of 6 Cittion: Professor Pul Hmmond, Synthesis of Polymers Fll 006 mterils, MIT pencoursewre ( Msschusetts Institute of Technology, Dte.

6 π c = {r( f 1)( w,a 1 f w,b 1/ 1)} f A,i N A,i i f w,a = where f w,i cn e 1.0 f A,i N A,i f B,i N B,i i f w,b = f B,i N B,i f A,i N A,i r = 1.0 f B,i N B,i For our erlier exmple, π c = 0.90 (N B = 3.5) Crothers: π c = 0.93 Lower π c longest chins form more of infinite network , Synthesis of Polymers, Fll 006 Lecture 8 Prof. Pul Hmmond Pge 6 of 6 Cittion: Professor Pul Hmmond, Synthesis of Polymers Fll 006 mterils, MIT pencoursewre ( Msschusetts Institute of Technology, Dte.