Entropic barrier theory

Polymer crystallization theory is a mature area, and there are several review articles available that present and discuss the different theories in great detail (eg, 103,104). Having said that, over the last 5 years or so there has been a flurry of new interest becanse of the increase in computational power, which has the potential to decisively enter the debate in some areas. In the following the underlying themes of the two principle theories of polymer crystallization, secondary nucleation theory and rough-surface or entropic barrier theory, are outlined. The results of more recent simulations are then briefly discussed, in which the constraints of the above theories, introduced to provide analytical solutions, have been relaxed. Finally, some of the more fundamentally different ideas that have recently appeared are discussed. 

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. 

Figure 6.33 Crystallization according to the entropic barrier theory, (a) Representation of a lamellar crystal, showing stems (chain direction vertical) and a step in the growth face. The inset provides a description of the step in terms of units that are shorter than the length of the surface nucleation theory (one molecule making up a whole stem). The dotted lines indicate where the row of stems in (b) is imagined to occur, (b) The basic row of stems model, showing mers along the chains as cubes, chain direction vertical, as in (a).

The entropic barrier theory has spawned a plethora of computer simulation studies (97-102). For example, simulations by Doye and Frenkel (100) led to the finding that it is unfavorable for a stem to be shorter than /min, the minimum thickness for which the crystal is thermodynamically more stable than the melt. They find instead that the lamellar thickness converges to a value just larger than as the crystal grows. This value is at the maximum rate of crystal growth. 

The deposition of each stem of m repeat units can be treated [8,41] as a set of m equilibria. While this generalization appears to account for more local details, the general conclusions are the same as in the LH theory. In realistic situations, we expect nonsequential deposition of repeat units into various stems. These partially formed stems will then sort out through entropic barriers to attain the lamellar thickness. We remrn to this issue in Section VII. 

High-level computational methods are limited, for obvious reasons, to very simple systems. In the previous section we showed the contribution of the theory for a better imderstanding of the entropic and enthalpic factors that influence the reactions of hydrogen atom with the simplest series of silanes Me4 SiH , where n = 1-3. Calculated energy barriers for the forward and reverse hydrogen atom abstraction reactions of Me, Et, i-Pr and t-Bu radicals with Me4- SiH , where n = 0-3, and (H3Si)3SiH have been obtained at... 

Chang, S. Z. D. and Lotz, B. (2005) Enthalpic and entropic origins of nucleation barriers during polymer crystallization the Hoffman-Lauritzen theory and beyond, Polymer, 46, 8662 8681. 

Chen F, Shanks RA, Amarasinghe G (2004) Molecular distribution analysis of melt-crystallized ethylene copolymers. Polym Int 53(11) 1795-1805 Cheng SZD, Lotz B (2005) Enthalpic and entropic origins of nucleation barriers during polyuner crystallization the Hoffman-Lauritzen theory and beyond. Polymer 46(20) 8662-8681 Cheng SZD, Cao MY, Wunderlich B (1986) Glass transition and melting behavior of poly (oxy-l,4-phenyleneoxy-l,4-phenylenecarbonyl-l,4-phenylene) (PEEK). Macromolecules 19 (7) 1868-1876... 

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