Sadler Gilmer Theory

In the case of the crystallization of low molecular mass materials at temperatures above TV, the growth is proportional to AT, whereas experiments on crystal growth in the case of polymers indicate that the growth rate is proportional to IjTciAT. Sadler suggested that the difference in temperature dependence above 7 was of an entropic origin. In colloid science entropic barriers as a 

The Sadler Gilmer theory leads to a prediction of the growth rate  

The dynamics of this process are encapsulated in the Sadler-Gilman modeP that considers the balance between the forward and backward reactions in terms of the ratio k /k +  

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Fig. 5.19 Addition of chain segments to a growing crystallite according to (a) the Lauritzen-Hoffman theory and (b) the Sadler-Gilmer theory. Note that, in the Sadler-Gilmer theory, there are no perfectly regular fold surfaces, ((a) Adapted by permission of Kluwer Academic Publishers.)...

The Sadler-Gilmer theory not only is consistent with the observations made by electron microscopy (Fig. 8.22), but also predicts a temperature dependence of the linear growth rate and of the crystal thickness... 

Simulations by Mnthukumar and co-workers (133-135) have also thrown considerable doubt on some of the imderlying premises of secondary nncleation theory, and also on some of the constraints that are in place in the Sadler-Gilmer model. Specifically, the assumption is generally made that each layer as formed has a particular thickness that is the final thickness of the crystal, the reorganization of the chain within the crystal is not allowed for. The simulations find that... 

The entropic barrier theory was developed by Sadler and Gilmer (95,96). This latter theory is based upon the interpretation of kinetic Monte Carlo simulations and concomitant rate-theory calculations. The phrase Monte Carlo suggests chance events, or in this case, random motion. While individual motions of the molecules are governed by chance, they move according to rules laid out on the computer such as excluded volume considerations and secondary bonding energies and/or repulsive forces. 

Sadler DM, Gilmer GH (1988) Selection of lamellar thickness in polymer crystal growth a rate-theory model. Phys Rev B 38(8) 5684—5693... 

This chapter presents first some fundamental aspects of nucleation, and second the general Avrami equation, which is frequently used to describe overall crystallization. The growth theories of Lauritzen and Hoffman and Sadler and Gilmer are discussed in sections 8.4.2 and 8.4.3. Molecular fractionation and orientation-induced crystallization are dealt with in sections 8.5 and 8.6. 

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