Theory of crumb firming

The observations that have been made, some of which have just been described, are mostly consistent with an explanation of crumb firming 

The kinetics of crumb firming have been described by an equation derived from the Avrami theory (Avrami 1939). This theory describes the rate of change of a supercooled amorphous material to an ordered crystalline structure when the process is governed by random production of stable nuclei  

9 = fraction of uncrystallized material El = limiting value of the crumb modulus Et = modulus after time t Eq = initial modulus k = rate constant 

The second process is crystal growth, which essentially depends on the diffusion of segments from the melt to the crystal-melt interface. At temperatures well below the melting point, the growth rate of the nuclei, rather than their rate of formation, determines the kinetics of crystallization. This growth rate is normal in that it diminishes with falling temperature. As a result, the rate of crystallization does not increase indefinitely as the temperature is lowered but rather passes through a maximum. 

As the temperature is lowered further, a point is reached where many physical properties of the polymer, such as elastic moduli, viscosity, and specific volume, fall dramatically over a narrow temperature range. This is the glass transition temperature, Tg, which was discussed in Chapter 6. At this temperature, segmental motions of polymer molecules practically cease. It appears that the temperature of around -20°C, at which crumb firming rate becomes negligible, may correspond closely to the Tg of amy-lopectin at the water content of bread. 

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