The differences in the extent of reaction
may indicate differences in the affinity of the HDS for the isomers and differences in the thermodynamic equilibrium constants of the systems.
The algorithm given by Seader and Henley (1998) for conventional distillation columns was modified for reactive distillation columns and incorporated the equations to calculate the extent of reaction
. Figure 1b shows the adapted algorithm, where T is the temperature, [xi] is the extent of reaction
, B is the bottoms; D is the distillated product; V is the vapor flow; L is the liquid flow; x is the mole fraction of the liquid phase, y is the mole fraction of the vapor phase, h is the enthalpy of the liquid phase, H is the enthalpy of the vapor phase, Q is the stage's heat flow to the neighborhood; and indexes i, j and k represent the component, stage and reaction, respectively.
The model allows to evaluate not only the curing temperature within the whole thickness of the system "coating + substrate", but also the resulting evolution of the extent of reaction
as a function of time.
The time of occurrence in a peak in a particular [epsilon]"[omega] line (i.e., at a particular frequency) can be used to monitor the buildup in [T.sub.g] and thereby extent of reaction
. Together the ionic and dipolar mobility can be used to monitor the occurrence of critical cure points such as dry-to-touch, dry-to-hard, and the achievement of end-use durability.
Critical extent of reaction
at the gel point of bifunctional epoxy and tetrafunctional crosslinker is reported to be about 57.73% .
The middle signal in the spectrum is associated with the resultant copolymer whose magnitude, which is indicative of extent of reaction
(X) and RD, depends on processing parameters such as time and temperature.
Based on the Flory theory , the extent of reaction
at gelation is constant, so the above equation can be expressed as:
To predict the extent of reaction
at the gel point, Flory and Stockmayer used a statistical approach by calculating when the weight average molecular weight becomes infinite [9, 23].
Here, we present the experimental reaction kinetics (conversion or extent of reaction
Figure 7 shows the extent of reaction
([alpha]) as a function of time for the cured DGEBA/PVPh/DDS mixtures.
In addition, the characteristic peak due to the oxirane ring is not strong enough to be useful as a basis for monitoring the extent of reaction
. As a result, the FTIR method was discontinued in favor of the chemorheological method described below.
For r = 1/2, the extent of reaction
is further increased to 95% insoluble.