Polymer crystallization Lauritzen-Hoffman

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. 

In the classical Lauritzen-Hoffman theory for the mechanism of polymer crystal growth [106], it is assumed that the observed lamellar thickness corresponds to those crystallites that happen to have the largest growth velocity. However, this picture is hard to reconcile with the experimental observation that the thickness of polyethylene single crystals can be modulated by varying the temperature at which they are grown [117,118]. In fact, simulations by Doye et al. [119,120] suggest that the observed lamellar thickness does... 

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) ... 

Figure 50. Free energy of a new layer of stems on the lateral growth face of a polymer crystal as a function of stem length 1 and the number of stems in the layer, j. Calculated according to the Lauritzen-Hoffman theory, with p = 1. (a) AT= 11 °C, (b) AT = 80 °C. Standard data for polyethylene were used. Case a predicts 1 = lmin + 61 with a small 61, while (b) predicts 7— ...

Lauritzen, J. I. and Hoffman, J. D. (1959) Formation of polymer crystals with folded chains from dilute solution, J. Appl. Phys., 31, 1680-1681. 

Hu WB (2005) Molecular segregation in polymer melt crystallization simulation evidence and unified-scheme interpretation. Macromolecules 38 8712-8718 Hu WB, Cai T (2008) Regime transitions of polymer crystal growth rates molecular simulations and interpretation beyond Lauritzen-Hoffman model. Macromolecules 41 2049-2061 Jeziomy A (1971) Parameters characterizing the kinetics of the non-isothermal crystallization of poly(ethylene terephthalate) determined by DSC. Polymer 12 150-158 Johnson WA, Mehl RT (1939) Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Pet Eng 135 416-441... 

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... 

The regime-transition phenomena of polymer crystal growth have been well explained on the basis of the Lauritzen-Hoffman model [14,15]. Nevertheless, the assumptions about the details of secondary crystal nucleation can be replaced by the intramolecular crystal nucleation, without a substantial loss of semi-quantitative predictions about regime transitions. 

From the classical Lauritzen-Hoffman model to the molecular-nucleation concept, and then the intramolecular-nucleation model, polymer crystal nude-... 

The impression of many in the community that the mechanism of polymer crystallization is principally understood and the issue essentially settled was, however, wrong. With the Nineties a renewed thinking set in, triggered by new experimental observations. In fact, the experimental basis of the Hoffman-Lauritzen theory had always been rather narrow. Putting the focus on growth rates only, the basis of validation were growth rate measurements exclusively. The Hoffman-Lauritzen treatment includes several implications. In particular, it assumes that... 

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... 

Lauritzen JI, Hoffman JD (1973) Extension of theory of growth of chain-folded polymer crystals to large undercoolings. J Appl Phys 44 4340-4352 Lee J-H, Koh CY, Singer JP, Jeon S-J, Maldovan M, Stein O, Thomas EL (2014) 25th anniversary article ordered polymer structures for the engineering of photons and phonons. Adv Mater 26 (4) 532-568... 

The Hoffman-Weeks Method. Lauritzen and Hoffman (Lauritzen and Hoffman 1960 Hoffman and Weeks 1962) observed a linear relationship between the melting points and the crystallization temperatures of a polymer crystallized isothermally at various temperatures. Hoffman and Weeks (1962) then realized that the lamellar thickness and the crystal perfection increases with increasing crystallization temperature, and they proved that the T =f(T ) curves must intercept the curve at the... 

The rough lateral surfaces shown in Fig. 7.15 constitute a serious problem in the light of some of the current theories of polymer crystallization. Regime I crystallization (a term first introduced by Lauritzen and Hoffman (1960) see Chapter 8) prevailing at 130°C occurs by sequential addition of mono-... 

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