Development of a two‐stage, dual‐Arrhenius rheology model for a high‐performance phenylethynyl‐terminated poly(etherimide)

Abstract

A two‐stage, dual‐Arrhenius rheology model was successfully utilized to model the isothermal complex viscosity of a phenylethynyl‐terminated poly(etherimide) as a function of time and temperature over the experimental temperature range of 325°C to 350°C. Union of the dual‐Arrhenius model with a previously developed combination reaction kinetics model provided a chemoviscosity model giving viscosity as a function of degree of cure. A two‐stage, versus a single, dual‐Arrhenius model was used to accommodate a transition in the reaction process from chain growth to branching and network forming that was found to onset around a degree of cure of 0.37. The reduction in chain mobility brought on by branching and networking was quantified by the almost order of magnitude increase in the apparent activation energy for initial viscosity from the chain growth stage to the networking stage. The calculated apparent activation energies for gelation for the first and second stages, 2.14 × 105 J/mol and 2.05 × 105 J/mol, respectively, agree well with results presented elsewhere from differential scanning calorimetry measurements. The experimental procedures followed to obtain the rheological data and the construction of the model from these data are described; the predictions of the model are compared with experimental results.

Sigmoidal Chemorheological Models of Chip‐Underfill Materials Offer Alternative Predictions of Combined Cure and Flow

“…[10] Recent publications have gauged both reactive stability and defined flow and processing characteristics for reactive injection molding resins and other flowing resins. [11][12][13] Wong et al have targeted research tied to a range of microelectronics problems, including flip-chip assemblies and underfill, by studying different isothermal temperature gelation processes and the resulting network structure of epoxy resins, which are closely related to the reliability of those assemblies. [14,15] This was expanded on in a review published by Li and Wong.…”

Simultaneous study of cure kinetics and rheology of montmorillonite/vinyl ester resin nanocomposites

“…In this case, a phenomenological model as a relatively simple rate of equation represents the main features of the cure kinetics ignoring how the reactive species take part in the reaction 35. Although, a variety of phenomenological models have been proposed so far by different authors,35–37 all theories could be generally expressed as: where θ is the degree of curing used to indicate the extent of resin cross‐linking and can be obtained from the time‐dependent storage modulus ( G ') using the following equation: where G '( t ) is the value of the storage modulus at time t .…”

“…There are two primary mechanisms describing the cure kinetics of the most thermoset resins including n th‐order and auto‐catalytic theories 36. The n th‐order model assumes that the reaction rate is proportional to the concentration of unreacted material (1 − θ ), as shown in Eqn (4), where n is the order of reaction37: …”

“…In the latter case, the final products of the curing process can subsequently catalyze the reaction between resin and hardener. On the other hand, in an auto‐catalytic model, the rate of conversion is proportional to both the concentration of unreacted and reacted material37: where m is also the reaction order. In both auto‐catalytic and n th‐order models, K represents the temperature‐dependent constant rate of reaction obeying the well‐known Arrhenius equation35 as: where A is a frequency factor corresponding to the frequency of the molecular collisions and E , R and T are the activation energy, the gas constant and the absolute temperature, respectively.…”

“…Commonly, isothermal curing of thermoset material may be the result of more than one type of chemical reaction. In this situation, one reaction may be n th‐order or the other auto‐catalytic reactions 37. This combination of reactions can be represented by a generalized expression given by Kamal and Sourour: …”