Step polymerization

Step polymerization ~100 kg/mol

Chain polymerization ~10,000 kg/mol

R1A + R2B -> R1R2

Ester condensation

RA₂ + RB₂ reaction

PET/polyester

ARB reaction

Polycondensation

-After the reaction, small molecules (H2O, HCl,,,) are eliminated.

δ-

δ+

Polyester

δ+

δ-

δ-

δ+

δ_B- is more negatively charged than δ_A-

δ-

δ+

δ_B-

RA₂+RB₂

Polyamide

RA₂+RB₂

ARB

Polyether

Dialkoxide (Di+alkoxide)

ARB

RA₂+RB₂

δ-

δ+

Conductive polymer synthesis

Wittig coupling

Methylenetriphenylphosphorane

δ+

δ-

Mechanism

polyurethane

δ-

δ+

Diels-Alder reaction

4+2 cycloaddition

Carothers Theory

N₀ : monomer amount

N : # of molecules after polymerization at a time of t

Degree of polymerization

# of monomer in one polymer

Reaction probability

p=(2N₀-2N)/2N₀=(N₀-N)/N₀

RA₂+RB₂, ARB

All the molecule has two reaction sites, A or B.

If N_A<N_B, N_A =rN_B, r<1

Probability of reaction

# of A site

# of B site

# of polymer

_{Number of polymer is derived from counting unreacted edge sites.}

N₀=N_B(1+r)/2

N₀=N_B(1+r)/2

RA₂+RB₂+RB or ARB+RB

RB : termination monomer

Statistical Theory

The probability of x degree of polymerization

Probability of reaction

Expected # of polymers with x degree polymerization

p=(2N₀-2N)/2N₀=(N₀-N)/N₀

Molar mass of x degree polymeriztion

Expected #

Number average molar mass

Probability of polymer with x degree polymerization

M_x=xM₀

Weight average molar mass

Weight average degree of polymerization

PDI(polydispersity)

< 2

Theoretical distribution

Number average

Weight average

Kinetics of step polymerization

Normal reaction of step polymerization

Kinetics

Since the concentration of catalyst is fixed,

If [A]=[B]=c

Co: initial concetration, t is the time, c is the final concentration

Co/C=No/N

p=(2N₀-2N)/2N₀=(N₀-N)/N₀

If A itself has a function of catalyst,

Co/C=No/N

p=(2N₀-2N)/2N₀=(N₀-N)/N₀

Non-linear step polymerization

-Polymer network reaction (+crosslinker)

-example, epoxy resins

Cross-linkers

Carothers gelation theory (Rough estimation to understand gel point)

-Gelation(high degree of polymer network) is importatn to expain Physics of polymer.

-Gel point indicates the cross-linking degree when viscosity of polymer suddenly increases.

fi=# of functionalities (normal monomer has 2)

Xn=∞

Statistical theory of gelation by Flory

Crossliner: RAf (f>2)

Crosslinker-RR…-Crosslinker structure

RAf + RB2 + [RA2 + RB2]_i + RAf

4 reactions are involved

RAf + RB2 :PA

RB2 + RA2 :PB(1-r)

RA2 + RB2 :PA

RB2 + RAf :PBr

r=fNRAf/(fNRAf+2NRA2)

RAf + RB2 + [RA2 + RB2]_i + Raf =

RAf + RB2 :PA

RB2 + RA2 :PB(1-r)

RA2 + RB2 :PA

RB2 + RAf :PBr

Crosslinking coefficient

Counting all the probabilities of all the kinds of crosslinking length

Σ

Critical branching(crosslinking) coefficient

PB=rPA

Application - dendrimer

1+2 structure ARB2