Step Growth Polymerization

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10.569 Synthesis of Polymers Prof. Paula Hammond Lecture 2: Molecular Weight Control, Molecular Weight Determination in Equilibrium Step Condensation Polymerizations, Interchange Reactions: Effects on Processing and Product, Application Example: Common Polyesters

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

C R C O R’ O n

Polyester (one repeat unit consists of 2 structural units)

Degree of polymerization ≡ number of monomer units or structural units incorporated in polymer chain

= pn

⋅ Mp un M = where Mu = molecular weight (MW) of individual repeat units n 2

Can also have a—b monomers: e.g. O O

HO CH2 C OH OR” C n

In this case:

• R” = CH2 • The repeat unit is the structural unit

Mpnn=⋅Mu

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. Determining MW as a Function of Conversion How do you determine MW as a function of conversion?

total initial # of monomer units No pn == total # of molecules remaining Ntotal

Simple thought experiment: 25 a—a 50 monomer units 25 b—b

react for time t

If have 50% conversion ⇒ 25 a+b reactions ⇒ lose molecule w/each reaction (2 molecules become 1) 50 p = = 2 n − 2550

So π (conversion) can be related to pn .

(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 Nb π=1 − π=1 − a Na b Nb ()o ()o

()Na Define r ≡≤o 1 Define: a is minority functional group Nb ()o

Stoichiometric ratio

Total # of functional groups initially present ⎡ 1⎤ NNaNbNa=+=1 + o ()oo () () o⎢ ⎥ ⎣ r ⎦

At a given time t, have conversion πa N = # of functional groups at time t = Na 1− π+Nb − Na π t ( )oo( aa) ( )()o

Na Nb 10.569, Synthesis of Polymers, Fall 2006 Lecture 2 Prof. Paula Hammond Page 2 of 6

N 1 o 1 + N 1 + r ∴ p ===2 o r = n N Nr1 12− π+r t t 12−π+ 2 a r

πa = π (assume referring to minority)

Simple case: r = 1.0 (perfect stoichiometry)

At * π = 0.995 → pn = 200 π = 0.99 → p = 100 n p drops fast n π = 0.98 → pn = 50 oligomer π = 0.90 → pn = 10

*Can take a long time. First 95% takes same time as last 2-3%.

1 Must ↑ π to get high MW p = As π ↑, p explodes. n 1 − π n But, there is a problem:

Control of MW How to control MW? a) Control π (conversion) Issue: O

HO C OH MW changes when you T↑ HO OH ship it or store it. O

HO C OH

b) Control stoichiometry: Assume: e.g. π = 1.0 1 1 + 1 + r ⇒ p = r = n 1 1 r 1 − − r Add excess of b—b End up “capping” chains w/b groups

10.569, Synthesis of Polymers, Fall 2006 Lecture 2 Prof. Paula Hammond Page 3 of 6

e.g. 1% excess of b-b

⇒ max pn = 199 Can intentionally cap w/alcohol or ester for certain applications. Can use π, r to predict MW outcome of rxn.

1000

decreasing π 100 π = 1.0 pn 10

1.0 0.99 0.98 0.97 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 xx• polyurethanes: longer chain x x molecules x x • surface groups

Here we redefine the ratio r:

Assume Na ( )o Caveat: (Na) = (Nb) a—a r = o o ()Nb+ 2 N a—a b—b b—b o x for this to work. are in equal where N = # of b-x molecules x quantity

Same expression if you’re using a—b monomers.

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 (πa = πb).

At a given time t, have conversion π Probability that an a group has reacted: p = π

10.569, Synthesis of Polymers, Fall 2006 Lecture 2 Prof. Paula Hammond Page 4 of 6

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. (will use p, π interchangeably) Probability that a molecule has x structural units = ℘x x structural units ⇒ (x-1) # of a groups reacted = Prob of this combination 1 a group unreacted

Prob of x-1 a groups reacted: px-1 Prob of unreacted a: (1-π) or (1-p)

x-1 So, ℘x = p (1-p)

℘x = number fraction of chains with degree of polymerization x

# of x-length chains NNxx N x ℘x = == = total # of chains NNpNNtotal o ()1 −−o o p

Every time a molecule reacts lose Nop.

Nx = ℘xNo(1-p)

N x π↑ ℘x = Ntotal

increase conversion → narrower and broader

Flory-Shulz Distribution: Some Monomer Always Present

∑ xNx x x −1 pnx==℘=−∑∑xxp()1 p ∑ Nx x 1 px−1 = ∑ 1 − p

1 xpx −1 = ∑ 2 ()1 − p

1 p ⇒ n ()1 − p

10.569, Synthesis of Polymers, Fall 2006 Lecture 2 Prof. Paula Hammond Page 5 of 6

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.

xNx 2 x −1 Weight fraction: wxpx ==−()1 p No

11++p π p = or w 11−−p π

Result of using pw expression and summations

p PDI = z = w =+11p =+π pn

As π→1.0 z → 2.0

increasing π

10.569, Synthesis of Polymers, Fall 2006 Lecture 2 Prof. Paula Hammond Page 6 of 6

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.