Melting theory, copolymer

Sanchez has also derived a melting theory of random copolymers from the statistics of sequence placements, such that for crystalline content Xc and monomer mole fraction x. 

The first step in the analysis of copolymer crystallization is the development of quantitative concepts that are based on equilibrium considerations. Subsequently, deviations from equilibrium and a discussion of real systems will be undertaken. Problems involving the crystallization and melting of copolymers cannot in general be uniquely formulated since two phases and at least two species are involved. The disposition of the species among the phases needs to be specified. It cannot be established a priori by theory. This restraint is not unique to polymeric systems. It is a common experience in analyzing similar problems that involve monomeric components.(2) Thus, in the development of any equilibrium theory a decision has to be made prior to undertaking any analysis of the disposition of the co-units between the phases. Theoretical expectations can then be developed based on the assumptions made. 

Fraai]e J G E M 1993 Dynamic density functional theory for micro-phase separation kinetics of block copolymer melts J. Chem. Phys. 99 9202... 

The effect of different types of comonomers on varies. VDC—MA copolymers mote closely obey Flory s melting-point depression theory than do copolymers with VC or AN. Studies have shown that, for the copolymers of VDC with MA, Flory s theory needs modification to include both lamella thickness and surface free energy (69). The VDC—VC and VDC—AN copolymers typically have severe composition drift, therefore most of the comonomer units do not belong to crystallizing chains. Hence, they neither enter the crystal as defects nor cause lamellar thickness to decrease, so the depression of the melting temperature is less than expected. 

According to Hoffman s crystallization theory, a drop in the heat of fusion corresponds to an exponential decrease in nucleation and crystal growth rates [63]. Implicitly, the rate of crystallization is severely retarded by the presence of 3HV comonomer [64, 69, 72]. These low crystallization rates can hamper the melt processing of these copolymers since they necessitate longer processing cycle times. 

Table 6.2 Experimental Rouse rates (Wi ) for the pure homopolymers and for the hlock-copolymer melts obtained from the high Q behaviour of JXQ) compared to the predictions of the RPA theory. Values of are given in 10s ...

Water-soluble random copolymers containing u-phenylalanine and A -O-hydroxypropylR-glutamine are prepared. The thermally induced helix-coil transition in these copolymers in water is studied. The incorporation of (.-phenylalanine is found to increase the helix-content of the host polymer. The Zimm-Bragg parameters cr and s for the helix-coil transition in poly(L-phenylaianine) in water are deduced from an analysis of the melting curves of the copolymers. The values of s, computed from both the Lifson and Allegra theories are (Ufson/Allegra a 0.0018) s 1.056/1.061 (273 K), 1.078/1,086 (293 K), 1.041/1.047 (313 K), 1.000/1.003 (333 K). 

There is no comprehensive theory for crystallization in block copolymers that can account for the configuration of the polymer chain, i.e. extent of chain folding, whether tilted or oriented parallel or perpendicular to the lamellar interface. The self-consistent field theory that has been applied in a restricted model seems to be the most promising approach, if it is as successful for crystallizable block copolymers as it has been for block copolymer melts. The structure of crystallizable block copolymers and the kinetics of crystallization are the subject of Chapter 5. 

The dynamic structure factor of block copolymer liquids (melts and solutions) has been accounted for using dynamical mean-field theory by Benmouna et al. (1987a,6). For a block copolymer melt, the dynamic structure factor can be written (Stepanek and Lodge 1996)... 

Theory for block copolymer rheology is still in its infancy. There are no models that can predict the rheological behaviour of a block copolymer from microscopic parameters. Fredrickson and Helfand (1988) considered fluctuation effects on the low frequency linear viscoelastic properties of block copolymers in the disordered melt near the ODT. They found that long-wavelength transverse momentum fluctuations couple only to compositional order parameter fluctua-... 

To date, there has been a very limited effort devoted to developing theory for ionic block copolymers. Gonziilez-Mozuelos and Olvera da la Cruz (1994) studied diblock copolymers with oppositely charged chains in the melt state and in concentrated solutions using the random phase approximation (RPA) (de Gennes 1970). However, this work has not been extended to dilute solutions. 

This chapter is concerned with these phases, where a substantial amount of the experimental work has been on poly(oxyethylene)-containing block copolymers in aqueous solution. From another viewpoint, the phase behaviour in concentrated block copolymer solutions has been interpreted using the dilution approximation, which considers concentrated solution phases to be simply uniformly swollen melt phases. Work on styrenic block copolymers in concentrated solution has been interpreted in this framework. There is as yet no unifying theory that treats ordered micellar phases and diluted melt phases coherently. 

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