高分子化学浙江大学polymer2-2PolymerizationRate

• For neat monomer, often in cases where the polymer formed is a high Tg material, there can come a point at which even the diffusion of monomer is slow. The mixture has become a hard glass, and unreacted radicals become trapped inside. The reaction shuts down at less than 100% conversion.
at higher concentrations, a pronounced rate acceleration after partial conversion of monomer to polymer. The more concentrated the solution, the earlier the acceleration occurs.
different initiation and termination reactions
RkImMn
The specific mechanism can be deduced by the parameters m and n
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5.3 Influence of Temperature
Arrhenius Equation
kt = kt,c + kt,d
7
Total polymerization Rate
R d d M tR i R p R p k p R • M RkpR•M
The polymerization degree is so large, that the monomer consumed in the initiation reaction can be neglected, or Ri<<Rp.
Initiation
I kd2R•
R•M ki R1•
dd R•t2dd It2kdI Ri dd R1•tddR•t
Ri 2fkd[I]
Ri in the range of 10-8 10-10 mol/L.s, where f is initiation efficiency
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Propagation R i• M k p,i R i 1•(i1 ,2 ,3 ,....)
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Reasons and Explanation
• Termination involves the reaction between two chain ends. The high viscosity hinders the diffusion of chains because of entanglements, so the rate of termination slows considerably.
• Temperature
the higher the Tp, the lower the viscosity
• Monomer concentration
the content of polymer
• Solvent
good solvent in favor of the diffusion of polymer chain
• Polymer consists of chains with a variable number of monomer units.
• Of the key parameters influencing the physical properties of polymers, the average molecular weight usually is the dominant factor, often influencing the other parameters.
5. Polymerization Rate
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5.1 Macro kinetics (宏观动力学)
1. Monomer Conversion and Rp
C (% M )M 0 0 M 1% 0 0 1M M 0 1% 00
Rp
dM
dt
C%
Rp
t 2
Measurement of Rp
E
k Ae RT
1
k
kp
fk d kt
2
1
A
Ap
Ad At
2
EEp12Et 12Ed
For normal polymerization initiated by initiator: Ed 125 KJ/mol, Ep29 KJ/mol, Et 17 KJ/mol, so E=83 KJ/mol
• Note that autoacceleration can be dangerous because the exotherm of polymerization can be released suddenly, leading to a runaway reaction.
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Conditions affecting autoacceleration
R p k p , i R i • M k p R i • M k p R • M
Assuming identical activity of radicals with various length, so kp=kp,i .
[R•]=∑[Ri•]
Rp = 10-4-10-6 M·s; kp = 102-104 M-1·s; [M•] = 10-7-10-8 M; [M]=1-10 mol/L
4. Spectroscopy (光谱法) MMA at 1630 cm-1。
5. Calorimetry (量热法) H C
3
Typical Polymerization Rate Curves
Induction： decomposition of initiator
End：drop of rate (C% =70-90 100)
[R•]=?
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Steady State (稳态)
Steady-state The concentration of radicals is constant or initiation rate is equal to termination speed.
[R•] determined by initiation mode
This corresponds to a two or three fold rate increase for a 10 oC temperature increase.
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5.4 Autoacceleration(自动加速效应)
PMMA polymerization in benzene solution at various concentrations.
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Fra Baidu bibliotek
disproportionation
combination
Termination
Rx•Ry• k t,d P xP y Rx•Ry• kt,c Pxy
R t d d R • t2 k t,c R • 2 2 k t,d R • 2 2 k tR • 2
2 represents two radicals were consumed by one reaction (US)
throughout.
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Polymerization rate with different initiations
Initiator
Rdd M tkp fktk d 12I12M kI12M
1
k
kp
fk d kt
2
ln([M]0/[M]) t: low conversion;
[I] and f are constant
• Tg of polymer • The homogeneity of polymerization media
homogeneous or heterogeneous
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Conversion %
5.5 Typical Polymerization Rate Curves
CB A
t A: Slow initiation-acceleration-drop (“S” shape) B: uniform rate C: fast initiation-drop
1. Direct sampling (直接取样) weight the polymer at different intervals.
2. Dilatometer method (膨胀计法) V C
3. Refraction index (折光指数法) e.g. n PVAc-nVAc=0.071
at low concentrations (<40%), the polymerization proceeds smoothly with no unusual effects.
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Rp
t
Autoacceleration
only occurs during polymerizations with high concentrations of monomer (i.e., little or no solvent). The reaction proceeds normally for a while, then suddenly the rate of polymerization goes up dramatically. The molecular weight of chains that grow during the accelerated period is substantially higher than that of chains that grew earlier.
• The initiation and diffusion of small molecular monomers is hardly affected by viscosity, so propagation proceeds as before.
• Once a low, steady state concentration of radicals gives way to increasing concentration, chains grow without termination, so the conversion is rapid and the MW is high.
Rp
①②
Initial ：C% = 0 510，a low steady rate
C%
③
④
t
Middle ：auto-acceleration C%= 5-10 70-90）
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5.2 Micro Kinetics (微观动力学)
Kinetic equation: Rp vs concentration of reactants
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Bulk polymerization of MMA monitored by ESR spectroscopy
Shen J, Tian Y, Wang G. Makromol Chem 1991;192:2669.
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6. Average Molecular Weight
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Average Molecular Weight
Rt 2ktR•2 Ri 2fkd[I]
1
1
R•2Rkit
2＝fkktd
2
I12
• A steady-state is established early in the reaction. • The concentration of radicals is very small (ca. 10-8 M) and nearly constant
lnM M0 kI12t
Ri ki[M]3 Ri ki[M]2
Self-initiation of Styrene
1
Rkp 2 k k it 2I12M 52kI12M 52
1
Rkp 2 kkit 2I12M 2kI12M 2
1
k
k
p
ki 2kt
2
10
Actual Polymerization rate