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<br>1-Introduction<br>Polymers are blended with their compounding ingredients in extruders. The blending of basic components such as antioxidants and light stabilisers is done either during the last stages of the polymerisation process or soon after in an extrusion step which is followed by granulation. In fact most if not all plastic granules sold in bags, have been subjected to the effects of heat as well as shear, once after their production and another time at the compounders who produce special grades and colours. Compounding extruders are classified in single screw and twin screw extruders. The mixing effect of single screw extruders relies on the shear generated between the walls of the barrel and the screw. The shear mixing of twin screw extruders is more efficient and as a result the polymer is subjected to less thermal history.

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  1. 10.569 Synthesis of Polymers Prof. Paula Hammond Lecture 2: Molecular W eight Control, Molecular W eight Determination in Equilibrium Step Condensation Polymerizations, I nterchange Reactions: Effects on Processing and Product, Application Example: Common Polyesters Step Grow th Polymerization 2 functional groups: a,b → form new link c, may be a side product d a—a + b—b → a—c—b + d For example, if a—a is a diacid and b—b is a diol: from diacid from diol O O R O R’ C C O n Polyester (one repeat unit consists of 2 structural units) Degree of polymerization M p M = where Mu= molecular weight (MW) of individual repeat units ≡ number of monomer units or structural units incorporated in polymer chain = n p ⋅ n u n 2 Can also have a—b monomers: e.g. O O O O C C HO HO C OH C OH OR” OR” CH2 CH2 n n In this case: • R” = CH2 • The repeat unit is the structural unit n n u M = ⋅ M p Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.

  2. Determining MW as a Function of Conversion How do you determine MW as a function of conversion? total initial # of monomer units total # of molecules remaining Simple thought experiment: 25 a—a 50 monomer units 25 b—b N = = o p n N total react for time t time t react for If have 50% conversion 1) ⇒ 25 a+ b reactions ⇒ lose molecule w/each reaction (2 molecules become 50 − = = 2 p n 50 25 So π (conversion) can be related to (Na)o = initial # of a reactive group = 2 (# of a-a monomers) (Nb)o = initial # of b reactive group = 2 (# of b-b monomers) Na Na ( Nb ( ) ( ) o Nb Stoichiometric ratio Total # of functional groups initially present ( ) ( ) ( ) o o o N Na Nb Na p . n Nb π = − π = − 1 1 ( ) ) a b o o Na ≡ ≤ Define Define: a is minority functional group o 1 r ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ 1 r = + = + 1 o At a given time t, have conversion πa = # of functional groups at time t = t N ( ) ( o ) ( ) ( ) − π + − π Na 1 Nb Na a a o o Na Nb 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date. Lecture 2 Page 2 of 6

  3. ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 1 r ( ) = − π + N Na 1 2 t a o N 1 r + 1 o + N N 1 2 r 2 N = = = = o p ∴ n 1 r − π + 1 r r − π + 1 2 t t a 2 Simple case: r = 1.0 (perfect stoichiometry) At π = 0.995* → π = 0.99 → π = 0.98 → π = 0.90 → *Can take a long time. First 95% takes same time as last 2-3% . πa = π (assume referring to minority) p = 200 n p = 100 n p drops fast n p = 50 n oligomer p = 10 n 1 − π Must ↑π to get high MW As π↑, p = p explodes. n n 1 But, there is a problem: Control of MW How to control MW? a) Control π (conversion) Issue: O O O O HO HO HO HO C OH C OH C OH C OH MW changes when you ship it or store it. T↑ HO HO HO HO OH O O O O OH OH OH HO HO HO HO C OH C OH C OH C OH b) Control stoichiometry: Assume: e.g. π = 1.0 1 + 1 + 1 r r 1 ⇒ = = pn − 1 r − 1 r Add excess of b—b End up “capping” chains w/b groups 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date. Lecture 2 Page 3 of 6

  4. b b b b b b b b b b b b b groups cannot react w/each other Can intentionally cap w/alcohol or ester for certain applications. Can use π, r to predict MW outcome of rxn. e.g. 1% excess of b-b p = ⇒ max 199 n 1000 1000 decreasing π decreasing π 100 100 π = 1.0 π = 1.0 pn pn 10 10 1.0 0.99 0.98 0.97 1.0 0.99 0.98 0.97 r r Can also use monofunctional unit as an end capping agent: \ a—a b—b b—x where x is a desired final group that can’t react w/a or b e.g. phenol x x x x x x x x Here we redefine the ratio r: Assume a—a b—b are in equal quantity Same expression if you’re using a—b monomers. • polyurethanes: longer chain molecules • surface groups x x x x ( ) Na Caveat: (Na)o = (Nb)o a—a b—b for this to work. = o r ( ) + Nb 2 N x o where Nx = # of b-x molecules MW Distribution as a Function of Conversion: Assumptions: 1. Equal reactivities for all a,b functional groups. Reactivities are the same for short a—a and long polymer (length independence) in viscous fluid. 2. Perfect stoichiometry: r = 1 3. For ease of explanation, use a-b monomer (π = π At a given time t, have conversion π Probability that an a group has reacted: p = π b). a 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date. Lecture 2 Page 4 of 6

  5. (will use p, π interchangeably) Probability that a molecule has x structural units = ℘x x structural units ⇒ (x-1) = 1 # of a groups reacted Prob of this combination So, ℘x = px-1(1-p) ℘ = number fraction of chains with degree of polymerization x x # of x-length chains total # of chains total N a group unreacted Prob of x-1 a groups reacted: px-1 Prob of unreacted a: (1-π) or (1-p) N N N − ℘x = = = = p x x x N ( ) − N 1 p N o o o N Every time a molecule reacts lose N p. o =℘ N o(1-p) x x Nx Nx π↑ π↑ ℘x= ℘x= Ntotal Ntotal x x x x increase conversion → narrower and broader Flory-Shulz Distribution: Some Monomer Alw ays Present xN p x xp N ∑ ∑ x ( ) ∑ ∑ − = = ℘ = − x 11 x p n x x x 1 − ∑ − = x 1 p 1 p 1 − ∑ − = x 1 xp ( ) 2 1 p 1 − ⇒ p ( ) n 1 p 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date. Lecture 2 Page 5 of 6

  6. xN N ( ) 2 − = = − x 1 x Weight fraction: w x 1 p p x o + − + − π π 1 1 p p 1 1 = p or w Result of using expression and summations p p As p w = + = + π w PDI = z = 1 p 1 n π → z → 1.0 2.0 increasing π increasing π wx wx x x 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date. Lecture 2 Page 6 of 6

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