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The speed of a chemical
reaction, contributed by more than one reactant is
controlled by two steps:
1. the speed of diffusion of the reactants together
(characterized by Kdiff),
2. the speed of chemical reaction (characterized by
Kchem).
The effective reaction
speed is the geometric mean value of both speed
constants:
1/Keff = 1/Kdiff + 1/Kchem (Rabinowitch
equation).
It is obviously that Keff equals Kchem, if Kdiff >>
Kchem is true. Therefore, for the most part, the effect of
diffusion control is not taken into account. If the reaction
temperature is close to or smaller than the glass transition
temperature, then a strong increase of the viscosity is
observed: the material under investigation vitrifies.
Through the restricted mobility of reactants, the curing
process is diffusion-controlled and Kchem >> Kdiff is
true.

Dependence of glass
transition temperature on degree of reaction for the system
2,2¥,6,6¥-tetrabrom-bisphenol-A-diglycidylether
(RUETAPOX VE 3579) + 5% Zn(OCN)2 [Flammersheim,
Opfermann: Thermochim. Acta 337(1999)141]
The temperature dependence
of Kchem is computed by the Arrhenius equation.
Because Kdiff is inversely proportional to viscosity, its
dependence on temperature is used.
If (a) the basis of analysis are DSC measurements, then the
glass transition temperature and its dependence on degree of
reaction is used as the controlling value of viscosity.
According to a special proposal, given by Wise
[C.W.Wise, W.D.Cook, A.A.Goodwin: Polymer 38 (1997)
3251], the speed of diffusion is calculated by means of
a modified Williams-Landel-Ferry (WLF)
equation

For temperatures T lower
than Tg the WLF equation is transformed to a Arrhenius
equation under the both conditions that the transfer and the
1st derivation are continuous. The current activation energy
for T<Tg is:

Otherwise, if (b) the
basis of analysis are viscosity measurements, then the
calculated viscosity is used as the controlling value. Now
the viscosity is calculated by means of an Arrhenius
equation with different activation energies for the uncured
and cured material.

Comparison between
measured (symbols) and calculated (solid lines) DSC
curves.
Taking into account the diffusion control in the kinetic
analysis, a nearly perfect fit is achieved. This high fit
quality is the basic condition for predictions with a high
level of confidence.

Isothermal predictions for
temperatures below glass transition temperature Tg = 165¡C.
The increase of the degree of reaction kinks where the glass
transition temperature reaches the reaction temperature (see
following picture). Without the use of diffusion control
above 120¡C full conversion would already be achieved after
60 min.
This information becomes
understandable by means of the following picture, a
simulation for the heating rate 0.2 K/min: the glass
transition temperature reaches the reaction temperature
after 380 min. From here up to a reaction time of 650 min,
so much reacts that the increase of the glass transition
temperature equals the increase of the reaction temperature.
In this range the reaction is
diffusion-controlled.

Dynamic prediction for a
heating rate of 0.2 K/min. The glass transition temperature
reaches the reaction temperature after 380 min. The DSC
signal breaks down except a constant value. Above 650 min
the glass transition temperature Tg increases less than the
reaction temperature. The system stops the "vitrifying"
condition.
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