Cure versus Flow in Dispersed Chip‐Underfill Materials

Abstract

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.

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

“…(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).…”

In situ Dynamic Rheological Study of Polyacrylamide during Gelation Coupled with Mathematical Models of Viscosity Advancement

“…Separately, we have developed other nonlinear mathematical models as predictors of structure and controlled flow in reactive resins including epoxies [21][22][23][24][25] and acrylates. [26,27] Fundamentally, acrylamide polymerization and its use as a regulating structure in protein separation and electrophoresis requires a sensitivity analysis to determine what temperature and compositional parameters have the most effect on controlling the rate of polymerization and viscosity advancement.…”

“…[25,26,[30][31][32][33][34] The gel time has been interpreted several different ways including the crossover point between the storage modulus, G 0 , and the loss modulus, G 00 , [35,36] the inflection point of G 00 [37] or the point where the loss tangent is frequency invariant [38][39][40][41] using dynamic mechanical spectroscopy or rheology. Other non-linear rheological models are based on resin reactivity, [42,43] thermodynamics, [44] and other semi-empirical models to describe time dependent viscosity including our work on the Boltzmann sigmoidal model, [21,23,26,27,44] according to…”

Modeling the effect of the curing conversion on the dynamic viscosity of epoxy resins cured by an anhydride curing agent

“…There are other interpretations of the gel point, including the crossover point between the storage modulus and loss modulus,25, 26 the inflection point of the storage modulus,27 and the point at which the loss tangent is frequency‐invariant28–30 according to dynamic mechanical spectroscopy. There are other nonlinear models based on other reactivity parameters,31, 32 thermodynamic influences similar to the Williams–Landel–Ferry (WLF) model,17 and semiempirical models to describe the time‐dependent viscosity 17, 24, 33–35. The WLF‐based chemorheological model used by Ivankovic et al1 defined the conversion‐dependent viscosity with temperature as: where C 1 and C 2 are WLF constants, η g is the viscosity at T g , T is the polymerization temperature, T g 0 is the glass‐transition temperature of the uncured resin, and α and α g are the instantaneous conversion and the conversion at the gel point, respectively.…”

“…The initial success of the use of the sigmoidal chemorheological model for acrylate24, 33 and epoxy conversion35 led to interest in the further evaluation of its scope. The dynamic viscosity is related to time by the Boltzmann log–sigmoidal model: where η 0 is the initial viscosity of the formulated resin; η ∞ is tied to the viscosity approaching the torque limit in the rheometer as network formation evolves; t 0 is the induction time, corresponding to the time necessary for a change in the viscosity from log η 0 to (log η 0 + log η ∞ )/2 and probably most closely associated with the gel time; t is the time; and Δ t corresponds to the period associated with the sigmoidal transition region as the viscosity deviates from η 0 in the semilog linear regime.…”