Theoretical analysis of the ice crystal size distribution in frozen aqueous specimens

To estimate theoretically how suited different freezing techniques are for freezing of freeze-etch specimens, it is necessary to know the relationship between specimen cooling rate and the resulting average ice crystal size. Using a somewhat simplified theoretical analysis, we have derived the approximate ice crystal size distribution of nonvitrified frozen aqueous specimens frozen at different cooling rates. The derived size distribution was used to calculate the relationship between relative change in average ice crystal size, (delta l/l), and relative change in specimen cooling rate delta (dT/dt)/(dT/dt). We found this relationship to be (delta l/l) = -k X delta (dT/dt)/(dT/dt) where k = 1.0 when specimen solidification takes place at about -6 degrees C, and k congruent to 1.3 when it takes place at about -40 degrees C.