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see also: ChemRheo,
Algorithm
of Analysis using ChemRheo
In general the
cross-linking reaction of powder points is investigated by
DSC and/or by viscometry. Using DSC, the heat generation
connected with an individual reaction step is recorded.
Therefore, the signal is proportional to the reaction rate
of cross-linking.
Using viscometry the dependence of viscosity on the degree
of reaction is recorded.
The relation between degree of reaction and the signal is
nearly linear if a pure cross linking reaction takes place,
i.e. observed at
vulcanization of rubber.
This relation is strongly nonlinear if the two processes
(growth of polymer chain and cross-linking) are take place
simultaneously, i.e. observed during the curing reaction of
epoxy resin.
The recommended procedure
of the Kinetic analysis of a powder paint
consists:
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in the kinetics
analysis of at least three DSC measurements
executed with different heating rates
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in the kinetic
analysis of at least three isothermal rheometric
measurements executed at different temperatures
with the result of kinetic analysis of DSC
measurements as additional supporting information,
especially to calculate the degree of reaction at a
certain state.
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If DSC measurements as source of information are missing,
then the kinetic analysis is possible using NETZSCH
Thermokinetics.
A high fit quality is
achieved with a triple-step model. The chemical meaning of
the individual steps is unsolved.
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Results of
Kinetic Analysis of DSC Measurements
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Model:
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t:i,f
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Type of
Reactions:
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n-th order
n-th order
n-th order
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Parameter
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Value
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Standard
Dev.
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lg
A1/s^-1
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15.57
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1.270
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Act.Energy
1/(kJ/mol)
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143.3
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10.20
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React. order
1
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1.052
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0.148
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lg
A2/s^-1
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11.83
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0.096
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Act.Energy
2/(kJ/mol)
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124.7
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0.820
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React. order
2
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1.03
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0.085
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lg
A2/s^-1
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5.00
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0.269
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Act.Energy
2/(kJ/mol)
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65.7
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2.479
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React. order
2
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1.32
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0.020
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Independ. react
1
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-
0.027
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0.002
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Follow.React.
2
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0.449
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0.011
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Area
1..3
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52 ...
57
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0.15
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Correlation
Coefficient
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0.9987
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On the basis of this result, the degree of reaction is
calculated for all temperature profiles of rheometric
measurements and used in the program ChemRheo as basis for
modeling. Consequently, the kinetics is calculated on the
basis of DSC measurements and the rheometric behavior on
basis of both DSC and rheometric measurements.
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Rheometric
Measurements
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Instrument:
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Bohlin
Instruments CVO 120 HR
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Heating
rates:
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1, 2, 3
K/min
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In the literature many different models are developed in
order to describe the viscosity behavior during curing and
cross-linking reactions. It is clear that the temperature
dependence of a cured/cross-linked product is different from
the starting material. But with one exception [D.
Hesekamp, M. H. Pahl: Rheol. Acta 35 (1996) 321 - 328 ],
this fact is not taken into account.
The relation between
degree of reaction, calculated on the basis of DSC
measurements and the viscosity is realized in the model
'Exponential Gain + E_Change' by (1):
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with
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x
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= degree of
reaction,
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B1..B3
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= adjustable
parameters.
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In this new model the used
temperature dependence is from the Arrhenius type and two
different activation energies are used: E0 for the starting
material and E1 for the final product. The change from one
to another is also realized using (1):
The complete description
of viscosity is (3):
Kinetic Analysis of
Rheometric Measurements, using ChemRheo and the Model
Exponential Gain, E_Change
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#
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Parameter
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Value
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Standard
Dev.
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0
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E0/(kJ/mol)
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131.5
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0.977
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1
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E1/(kJ/mol)
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32.80
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6.644
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2
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B1
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1.654
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0.050
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3
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B2
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-0.128
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0.150
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4
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B3
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0.0
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constant
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5
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lg
H/Pas
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1.157
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0.206
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6
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Tref/¡C
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75.0
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constant
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7
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lg Eta/(Tr,0)
1
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5.381
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0.015
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8
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lg Eta/(Tr,0)
2
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5.381
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equal to
7
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9
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lg Eta/(Tr,0)
3
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5.381
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equal to
7
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Correlation
Coefficient
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0.991
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There are additional assumptions, applied during estimation
of parameters:
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the maximum
increase of viscosity is the same for all
measurements, independent from the heating rate or
temperature profile.
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the reference
temperature is the same for all
measurements.
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the viscosity of
the starting material at temperature = Tref is the
same for all measurements, independent from the
temperature profile.
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There are two boundary conditions for application of powder
paints:
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if the operating
temperature is too low then the spreading of
lacquer is imperfect, resulting in a so-called
'orange skin'.
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if the
temperature is too high then the lacquer drops from
the surface of support.
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From the theoretical point of view, such a temperature
profile for handling of powder paint is an optimum for which
the viscosity over a long time is constant, independent from
the degree of reaction.
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Conditions of
Optimization
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Parameter
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Value
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Start
temperature/¡C
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70
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Maximum
temperature/¡C
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190
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Minimum heating
rate/(K/min)
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- 1.0
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Maximum heating
rate/(K/min)
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40.0
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log
Eta/Pas
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2.2
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For the given boundary
conditions the temperature profile is estimated using
ChemRheo. Now it is the task of technicians to achieve this
temperature profile within the heating container.
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