Theoretical prediction of devitrification tendency: determination of critical warming rates without using finite expansions.
Previously, critical warming rates vcr above which ice did not have enough time to crystallize had been roughly evaluated for many wholly amorphous aqueous solutions. These evaluations were obtained by extrapolation of the linear variation of the devitrification temperature Td with log v, where v is the warming rate, observed experimentally between 2.5 and 80 degrees C/min. Theory also gives such a linear variation, but only using the first term of a finite expansion. The other terms can be neglected only for small variations of Td. These evaluations were sufficient for classification of the solutions, but large errors were made in vcr. A new and more accurate method of determination of the variation of Td with v is presented here. The general equation giving in our models the derivative of the quantity of ice formed versus temperature T is differentiated, instead of integrated using a finite expansion. This gives an explicit expression of v versus Td assuming that the ratio xd of the quantity of ice formed at Td to the total quantity of ice formed on warming is constant. Experimentally, xd is constant within a good approximation. Theoretical curves representing the variation of Td with v have been drawn for solutions of 35 or 45% (w/w) 1,2-propanediol in water. Td never reaches the temperature of the end of melting Tm, but as v tends toward infinity, Td tends toward an asymptotic value of 0.96Tm for 35% solute. For that solution, above about 10(3) degrees C/min, Td deviates appreciably from linearity with log v, but 1/Td remains almost linear with log v up to Td congruent to 0.95Tm. Therefore, systematic comparison of the theoretical variation of Td with v with a linear variation of 1/Td with log v has been done, varying the parameters of the equations within the entire experimental range. Similar conclusions can be given for all the solutions. Experimentally for Td = 0.95Tm, the quantity of ice crystallized is generally less than 0.1% of the solution, reaching 1% only once. Therefore, a new definition of the critical warming rate vcr has been used, corresponding to extrapolation of the linear variation of 1/T with log v up to Td = 0.95Tm. New values of vcr have been calculated for all the binary systems previously studied. The order of the solutions is almost the same, but the new values of vcr are significantly smaller than the former.