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

Abstract

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.

MMA bulk polymerization and its influence on in situ resin viscosity comparing several chemorheological models

“…Both the induction period and the rate of slope rise in viscosity could be accommodated by adjusting the time constants. The model does not predict a viscosity reduction due to the initial cure exotherm but it successfully has tracked viscosity changes of several advancing resins including epoxies, 24,27 polyurethanes, 28 and acrylamides. 29 We compared all of these other models re-evaluating prior published results from Sangwai et al, 30 which could be extracted for reanalysis.…”

“…(4)] that captures not only the nonlinear trend in polymerization but also can be adjusted using form fitting parameters to include an initial viscosity and an end-point asymptotic viscosity limit [24][25][26] as shown in Eq. (4).…”

Cure versus Flow in Dispersed Chip‐Underfill Materials

“…The model incorporates as variables the initial and final viscosities, which are functions of the resin formulation, the corresponding network densities in the cured state, and two kinetic parameters, which are functions of the initiation and propagation steps associated with polymerization. We fixed the initial viscosity for the resin in our analysis [logh (Pa Á s) ¼ À2.2], based on prior results; given that the only formulation difference was the filler content, our modified four-parameter model had only three variable parameters [31] . Chip-underfill materials are often made from latent cure resins that require sufficient thermal heating to trigger network formation.…”

“…Among recent contributions to the literature are efforts to link sedimentation and solidification using a linearly increasing viscosity model, [28] which might apply at early stages of conversion, and a power law model which might be more widely applicable. [3][4][5] The alternative Boltzmann sigmoidal model, shown in Equation (2) for neat resins undergoing viscosity advancement, might be more representative of experimental results than the power law model: [29][30][31] log…”

“…Here, we integrate results from chip-underfill resin conversion using a Boltzmann sigmoidal model for viscosity [31] to Stokes' law using typical filler concentrations and process parameters to describe the relative dispersion stability.…”