Crystallization Flory model

In this modified Flory model, the liquid crystal-isotropic transition of rods in a solution occurs at... 

The Flory model also leads to a prediction of the effect of crystallization on the retractive force (oq) exerted by a stretched rubber... 

The Flory model for AS of mixing a polymer chain with solvents has been influential in polymer chemistry for several decades. The model assumes the validity of the lattice theory to describe the change in the molecular configuration of the polymer in the presence of a solvent, just as it describes the patterns of the crystal stracture of molecules. The central point is the filling of lattice sites in a three-dimensional space by polymer segments and solvent molecules that is, how many ways can we fill up the lattice sites ... 

FigurelO.3 Entropyforthedisordered (a) and ordered (b) states for the Flory model of semiflexible linear chain. Flor/s approximate form for the disordered state gives a negative entropy below g (, indicating the presence of an energy gap in the energy for the disordered configurations with respect to the crystal energy at absolute zero. We are considering a chain that...

Although the copolymers shown in Figure 11.1 were crystallized very slowly to allow most favorable conditions for equilibrium crystallization at each temperature, and the reported melting temperatures, measured by dilatometry, were determined by locating the temperatures where the melting curves merged with the liquidus line [11], these conditions were still far removed from the thermodynamic equilibrium upon which the Flory model was built. Furthermore, the formation of thick crystallites that correspond to the equilibrium melting temperature in Flory s model is an extremely rare occurrence. Even if they were present, their minute quantity would make detection difficult. Thus, the... 

A very recent application of the two-dimensional model has been to the crystallization of a random copolymer [171]. The units trying to attach to the growth face are either crystallizable A s or non-crystallizable B s with a Poisson probability based on the comonomer concentration in the melt. This means that the on rate becomes thickness dependent with the effect of a depletion of crystallizable material with increasing thickness. This leads to a maximum lamellar thickness and further to a melting point depression much larger than that obtained by the Flory [172] equilibrium treatment. 

As the temperature is decreased, the chains become increasingly rigid zc then approaches 1 if we assume that there is only one fully ordered crystalline structure and Zconf for the liquid becomes smaller than 1. This means that, at this level of approximation, the disordered state becomes less favorable than the crystalline ground state. A first-order disorder-order phase transition is expected to occur under these conditions. Flory interpreted this phase transition as the spontaneous crystallization of bulk semiflexible polymers [12], However, since the intermolecular anisotropic repulsion essential in the Onsager model is not considered in the calculation, only the short-range intramolecular interaction is responsible for this phase transition. 

Lateral growth occurs in real systems but is not accounted for in the model of Flory. What allows its incorporation into these new calculations is the assignation of the chains to their most probable positions the chains continuously seek positions of equilibrium as crystallization proceeds. This means that all amorphous links have the same propensity for crystallization, which therefore tends to eliminate a distinction between lateral and longitudinal crystal growth (keep in mind that different levels of crystallinity favor one growth pattern over the other -low crystallinity favors fibrils, high crystallinity favors lamellae). 

The distinct properties of liquid-crystalline polymer solutions arise mainly from extended conformations of the polymers. Thus it is reasonable to start theoretical considerations of liquid-crystalline polymers from those of straight rods. Long ago, Onsager [2] and Flory [3] worked out statistical thermodynamic theories for rodlike polymer solutions, which aimed at explaining the isotropic-liquid crystal phase behavior of liquid-crystalline polymer solutions. Dynamical properties of these systems have often been discussed by using the tube model theory for rodlike polymer solutions due originally to Doi and Edwards [4], This theory, the counterpart of Doi and Edward s tube model theory for flexible polymers, can intuitively explain the dynamic difference between rodlike and flexible polymers in concentrated systems [4]. 

The isothermal crystallization of PEO in a PEO-PMMA diblock was monitored by observation of the increase in radius of spherulites or the enthalpy of fusion as a function of time by Richardson etal. (1995). Comparative experiments were also made on blends of the two homopolymers. The block copolymer was observed to have a lower melting point and lower spherulitic growth rate compared to the blend with the same composition. The growth rates extracted from optical microscopy were interpreted in terms of the kinetic nucleation theory of Hoffman and co-workers (Hoffman and Miller 1989 Lauritzen and Hoffman 1960) (Section 5.3.3). The fold surface free energy obtained using this model (ere 2.5-3 kJ mol"1) was close to that obtained for PEO/PPO copolymers by Booth and co-workers (Ashman and Booth 1975 Ashman et al. 1975) using the Flory-Vrij theory. 

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