10.569 Synthesis of Polymers
Prof. Paula Hammond
Lecture 12: Free Radical Kinetic Chain Length, MWD, Chain Transfer, Energetics
Energetics
General Equation
−E
k = Ae RT
ln k = ln A −
E
RT
For thermal decomposition of initiator
⎛k
R p = k p [M ][M ⋅] = k p ⎜⎜ d
⎝ kt
1
⎞2
⎟⎟ f
⎠
1
2
1
[M ][I ]2
net rate “fudge factor” constant
Arrhenius expression:
⎡
⎢ ⎛k
ln ⎢k p ⎜⎜ d
k
⎢⎣ ⎝ t
⎤
⎡
⎛A
⎟⎟ ⎥⎥ = ln ⎢⎢ A p ⎜⎜ d
A
⎠ ⎥
⎢⎣
⎝ t
⎦
1
⎞2
constant
w.r.t. Temp
E
E ⎤
⎡
⎤ ⎢ E p + d − t
⎥
2
2⎦
⎟⎟ ⎥⎥ − ⎣
RT
⎠ ⎥
⎦
1
⎞2
Ep = activation energy for propag. step
⎡
Ed Et ⎤
⎢ E p + 2 − 2 ⎥ is activation energy for polymerization
⎣
⎦
ER = E p +
Ed Et
−
2
2
Overall:
⎡
⎢ ⎛A
ln R p = ln ⎢ A p ⎜⎜ d
A
⎢⎣ ⎝ t
1 ⎤
1
⎞2 ⎥
⎡
⎤ E
⎟⎟ ⎥ + ln ⎢( f [I
]) 2 [M ]⎥ − R
⎣
⎦ RT
⎠ ⎥
⎦
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
Sample Values of Ep and Et in kJ/mol
Monomers
Ep (kJ/mol)
Et (kJ/mol)
Vinyl chloride
16
17.6
Methyl acrylate
29.7
22.2
Methyl metacrylate
26.4
11.9
Styrene
26.0
8.0
Initiator
Ed (kJ/mol)
AIBN
123.4
Acetyl Peroxide
136
Benzoyl Peroxide
124.3
On Average: Ep ∼ 20 – 30
Et ∼ 10 - 15
Ed ∼ 100 – 150
⇒ ER = Ep + Ed/2 - Et/2
is dominated by Ed
ER ∼ 80 – 90 kJ/mol
Because Rp is a positive number → positive activation energy
If T ↑, k ↑
e.g. if T ↑ ∼ 10oC, Rp ↑ by 2-3x
(rate of polymerization increases by 2 or 3 times) What about p n ?
(assume no chain transfer)
p n = 2aν
let a = 1 (coupling)
p n = 2ν =
k p [M]
( fk d k t [I ])
⎡ A
p
ln p n = ln ⎢
1
⎢
⎢⎣ ( Ad At ) 2
Large value
1
2
⎤
⎡
⎥ + ln ⎢ [M ]
1
⎥
⎢
⎥⎦
⎣ ( f [I ]) 2
E d E t ⎤
⎡
− ⎥
⎤ ⎢E p −
2
2 ⎦
⎥− ⎣
⎥
RT
⎦
⇒ on average, get negative value for [ ] E term
⇒
[E p ] is negative
n
RT
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
Lecture 12
Page 2 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
ln pn
(das
(da
shed
hed
line)
line)
ln Rp (solid line)
1
T
high T
low T
Thermodynamics
ΔG = ΔH - TΔS
should be negative for polymerization to take place
1. ΔH → strongly exothermic rxns
ΔHp (enthalpy of propagation) → ∼ -160 to -60 kJ/mol
2. ΔS → lose entropy with polymerization ΔS → ∼ -90 to -120 J/(mol⋅K) or -0.09 to -0.12 kJ/(mol⋅K)
Usually ΔH is much larger than T ΔS term
⇒ negative ΔG (thermodynamically favorable to polymerize)
At certain Temp range, its possible for ΔG → 0
⇒ get near equilibria conditioning
M + M
kp
MM
kdp
depropagation rate constant
At equilibrium (or near):
d [M ]
= k p [M ] − k dp [M ⋅]
dt
at equilibrium = 0
−
K eq =
[M n +1 ⋅]
[M n ⋅][M ]
=
kp
1
=
[M ] k dp
(
)
[Mn+1⋅] and [Mn⋅] approx. equal
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
Lecture 12
Page 3 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
[M eq ] = kkdp = K1
p
eq
equilibrium monomer
concentration at
a given temp
Will always define with respect to monomer conc or
temperature.
Standard States Defns:
ΔG o = ΔH o − TΔS o = −RT ln K eq
ΔG = ΔG o + RT ln K eq = 0
ΔH o − TΔS o = −RTc ln
1
[M ]eq
= RTc ln[M ]eq
Solve for T:
Tc =
“ceiling
temp”
ΔH o
ΔS o + R ln[M ]eq
[M]eq defined as ratio:
= highest T for
polymerization to occur
⇒ ln
[M ]e
[M ]os
= ln[M
]eq =
[M ]e
[M ]os
Equilibrium monomer conc
Standard state monomer conc
[M]os = 1 M soln
(or bulk conc’n)
ΔH o ΔS o
−
RTc
R
determine [M]e from T
ceiling temperature term when no monomer conc is specified, is usually
assuming that [M]c = [M]bulk
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
Lecture 12
Page 4 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
(at 25oC)
Examples
Vinyl acetate
Methyl methacrylate
α-methyl styrene
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
[M]c (M)
1x10
-4
Tc (assuming bulk monomer)
--
--
220oC
2.2
61oC
Lecture 12
Page 5 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.