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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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