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Experiments were conducted to evaluate the influence of ambient photoconversion on rheology for a range of photopolymerizable urethane dimethacrylate (UDMA) resins containing varying amounts of three comonomers including 1,6 hexane diol-dimethacrylate (HDDMA), an alkoxylated cyclohexane dimethanol diacrylate monomer (CD-582), and hydroxyethyl methacrylate (HEMA). Experiments were performed both as a function of composition and time-dependent dose varying the intensity using a photorheometer. A semilog-based sigmoidal model allowed the determination of four physical model parameters to define the relationship between reaction kinetics and its dynamic influence on viscosity. We have observed induction times and viscosity changes associated with the model that shows a trend in reaction kinetics in the following order from most to least reactive: UDMA [ CD582 [ HDDMA [ HEMA. With increasing amounts of reactive diluent included in the formulation, the kinetics of reaction was more sluggish. The value of this sigmoidal model is that it could help define formulation and process conditions most likely to control crosslinking to maximize dimensional stability or other thermophysical properties.

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The relative stability of chip‐underfill composite materials was modeled as a function of glass filler concentration between 10 and 70 wt.‐%, filler particle size (between 5 and 25 microns), and the curing temperature of the resin (150 vs. 180 °C), yielding different dynamic viscosity profiles. The stability was gauged using a modified sigmoidal chemorheology model for the dynamic viscosity, and incorporating the time‐dependent viscosity into a model for Stokes' law of sedimentation. We also incorporated a hindered sedimentation term, due to filler concentration due to the higher loadings. Several important findings were observed. First, it appears to be the high concentration of filler that is maintaining the stability of these dispersions during cure. Smaller concentrations of the same particles were predicted to have a larger sedimentation velocity leading to stratification in the resin with time. Second, higher cure temperatures led to a shorter period of sedimentation in a pre‐cured state and resulted in less sedimentation, even though there was probably a slightly smaller viscosity in the pre‐cured condition. While these process models adequately describe the physics of the competitive processes of cure and sedimentation, a full picture may be incomplete without a larger determination of how this also affects polymerization shrinkage and residual shear stress upon cure.

Prior rheology results on chip‐underfill epoxy resins have been re‐analyzed by a sigmoidal model that contains three variable physical parameters, including the terminal cured viscosity of the gel, an induction or dwell time and a time factor associated with the speed of conversion as viscosity undergoes large dynamic changes during rapid crosslinking. The analyses were conducted with resins that were originally cured between 150 and 180 °C and show obvious non‐linearity, even on a semi‐log plot of dynamic viscosity. The sigmoidal models more accurately represent a wider range of dynamic viscosity than power‐law‐based rheological models, which are both more common and more generally accepted for practical application. If total flow is the critical design parameter in terms of chip underfill, perhaps these alternative sigmoidal models need to be more thoroughly evaluated to gauge their practical use and validity.

Published curing profiles of epoxy resins mixed with an anhydride curing agent and subsequently crosslinked were reanalyzed with a modified sigmoidal model to describe the dynamic viscosity accompanying resin curing. The sigmoidal analysis yielded two kinetic parameters, one relating to the induction time required to observe meaningful viscosity changes and one relating to the rate of viscosity rise in the rapidly polymerizing zone. Both of these kinetic factors decreased with increasing polymerization temperature. The analysis also led to the interpretation of the upper limit in viscosity in the model that correlated with a higher network density at higher temperatures. The initial viscosity was fixed in our model. The sigmoidal analysis led to a closer representation of the dynamic viscosity data than the Williams-Landel-Ferry (WLF)-based analysis presented with the original data sets and, although from a more semiempirical basis, might be both easier and more adaptable for incorporating into other flow models. As a final observation, the induction time identified by the log-sigmoidal model correlated closely with the gelation time identified with a modified-WLF-based model by Ivankovic et al. (J Appl Polym Sci 2003, 90, 3012); this suggested a similar activation energy threshold for curing advancement.

Earlier published rheological data of methyl methacrylate (MMA) heated and isothermally polymerized at temperatures between 50 and 80 C have been reanalyzed using three semiempirical models of viscosity advancement including a modified Boltzmann sigmoidal model, a microgel model for cure, and a first-order isothermal kinetic model. These alternative models possessed few fitting parameters and could be used without requiring more experiments to be run. For each dataset as a function of temperature, the analysis resolved time constants associated with both the induction time for polymerization and the rate of viscosity rise, which were inversely related to the polymerization temperature. We found the sigmoidal model the most robust to accommodate nonlinearities in viscosity advancement with radical polymerization of MMA.

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