When solutions of molecularly nonuniform polymers in single solvents are rapidly (1 K/s) cooled into the two-phase region, up to 20% of the polymer mass and 1.5% of the solvent molecules that would be found in the more dilute phase (sol) under equilibrium conditions are instead found in the more concentrated phase (gel). The higher molecular weight material of the equilibrium sol is preferentially incorporated into the nonequilibrium gel, with a capture probability increasing linearly with log M. Qualitatively the observations can be explained by the following consideration: For high cooling rates the polymer coils shrink so rapidly that the mobility of some chains no longer suffices for their withdrawal from the overlap region with others in order to become part of the sol phase. Quantitative calculations performed on the basis of this concept demonstrate that all experimentally observed features can be well reproduced if two (measurable, but presently unknown) parameters are adjusted.
The transient diffusion behavior of boron during rapid thermal annealing is simulated by adapting a recently developed pair diffusion model. Boron is assumed to reside on interstitial sites after ion implantation, forming boron-interstitial pairs (BI). Decay into substitutional boron (B) and interstitials (I) starts, as the temperature rises, due to the reaction BI⇄B+I. Implantation damage has been taken into account. The model accounts for the temperature dependence of the transient diffusion effect. To reduce the problems in determining the parameters of the diffusion model and to account for equilibrium diffusion an equation is derived. This equation can be used to reduce the number of unknown parameters and to assure diffusion under equilibrium conditions to be consistent with literature values at the same time. The effectiveness is demonstrated for the simulation of the transient diffusion of boron during rapid thermal annealing.
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