Polymer crystallization folding theories

The particular models used to demonstrate the theory obviously have many drawbacks as true representations of polymer crystals. These could include the lack of a fold energy, no distinction between new molecules and those already attached, neglect of chain ends, a somewhat arbitrary choice of pinning rules etc. However, they all serve their purpose in that they show that an energetic free energy barrier is not necessary to obtain the experimental curves. A truly representative growth picture can probably only be achieved via molecular dynamics. 

Lauritzen, J. I., jr., and J. D. Hoffman Theory of formation of polymer crystals with folded chains in dilute solutions. J. Research Natl. Bur. Standards 64 A, 73-102 (1960). 

Polymer crystal growth is predominantly in the lateral direction, because folds and surface entanglements inhibit crystalliza- 4 don in the thickness direction. Neverthe-1 less, there is a considerable increase in the fold period behind the lamellar front during crystallization from the melt and, as we have j seen, polymers annealed above their crys-tallization temperature but below Tm also irreversibly thicken. Nevertheless, in most theories of secondary nucleation, the most i widely used being the theory of Lauritzen and Hoffman,28 it is assumed that once a part of a chain is added to the growing crystal, its. fold period remains unchanged. 

The theory of Lauritzen and Hoffman, perhaps still the most commonly used model for the analysis of polymer crystallization data, then seeks to evaluate c5Z (usually of the order of 40 angstroms) by considering the rates at which stems and folds are successively laid down. We will not go into the details of this derivation, but the expressions that have been derived for the growth rate have the following form at low undercoolings (Equation 10-41) ... 

Hoffman, J. D. and Lauritzen, J. I. (1961) Crystallization of bulk polymers with chain folding theory of growth of lamellar spherulites, J. Res. Natl. Bur. Standards, 65A, 297-336. 

Hoffman JD, Lauritzen JI (1961) Crystallization of bulk polymers with chain folding theory of growth of lamellar spherulites. J Res Natl Bur Stand 65A 297-336 Hoffman JD, Guttman CM, DiMarzio EA (1979) On the problem of crystallization of polymers from the melt with chain folding. Faraday Discuss Chem Soc 68 177-197 Hoffman JD (1983) Regime in crystallization in melt-crystallized polymers The variable cluster model of chain folding. Polymer 24 3-26... 

Lauritzen JI, Hoffman JD (1960) Theory of formation of polymer crystals with folded chains in dilute solution. J Res Natl Bur Stand 64A 73-102 Liu JP, Mo ZS (1991) Crystallization kinetics of polymers. Polym Bull 4 199-207 Maier W, Saupe A (1958) Eine einfache molekulare theorie des nematischen kristallinflussigen zustandes. Z Naturforsch A 13 564-566... 

Recently, Crystal (1970) has studied in detail the crystallization of selenium. By application of the Hoffman-Lauritzen (1961) theory of polymer crystallization. Crystal obtains values for the liquid-crystal interfacial tension of selenium of 9.5 ergs/cm for the lateral face and 337 ergs cm for the chain folded face. He also finds e 0.1 to be a valid approximation for this inorganic polymer. 

The major theory [3 7] of polymer crystallization, due primarily to Lauritzen and Hoffman (LH), is a generalization of small-molecule crystallization theory of surface nucleation and growth to incorporate chain folding. In the model of LH theory (Fig. 1.3a), polymer molecules are assumed to attach at the growth front in terms of stems, each of length comparable to the lamellar thickness L. For each polymer molecule, the first step is to place its first stem at the growth surface, whose lateral dimension is taken as Lp. This step is assumed to be associated with a nucleation. The barrier for this step was assumed... 

I.C. Sanchez and E.A. DiMarzio, Dilute solution theory of polymer crystal growth a kinetic theory of chain folding, J. Ghem. Phys. 55, 893-908 (1971). 

The above insight, gained soon after the discovery of polymer single crystals, and the subsequent discovery of chain folding (1-3), has mapped out the route taken by much of the research into polymer crystallization over the subsequent decades. It soon became clear that the thickness of polymer lamellae was controlled by the supercooling at which they were crystallized and defined by the kinetics of crystallization. The crystal thickness, or alternatively the thickness of each new crystalline layer in a growing crystal, is the one that grows the fastest (4,5) rather than the one that is at equilibrium (6). There is now a wealth of information available on the crystallization of many polymers, as well as several theories that aim to predict the crystallization rates, crystal shapes, and lamellar thickness. 

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