Block copolymer melts an introduction

The dominant contribution to the free energy of lengthy (rubbery) polymer chains is entropy. This is known to accoimt for rubber elasticity, which can be satisfactorily modelled by the entropy of the cross-linked pol3rmer chains alone. A simple illustrative model of copolymer self-assembly can be developed by extending rubber elasticity theory to include bending as well as stretching deformations, to calculate chain entropy as a function of interfacial curvatures in diblock aggregates. 

The model leads to a variation of structure as the relative fractions of each block within the copolymer molecules changes. This can be seen heuristically as follows. If the in vidual blocks have different relaxed radii of gyration (set by the maximrim entropy constraint imposed on each block species on its own), the existence of a bond that fuses the moieties in the copolymer imposes the condition that assemblies of the copolymers cannot form without perturbation of the original configmations (Fig. 4.23(a),(b)). 

Although this intuitive picture is not exact (for instance, we have not allowed for interdigitation between the chains), it captures the essential physics behind the self-assembly process. Many sophisticated theories have been presented for self-assembly in polymer melts. Most suffer from the usual limitation associated with the usual geometrical problem they caimot 

These local calculations predict the formation of planar, hyperbolic, parabolic (cylindrical) and elliptic (globular) interfaces as the volume fraction of the iMger block increases from 50%. The compositional range of existence of the various interfacial geometries depends to a limited extent on the effective surface tension acting at the interface. 

Some typical results are plotted in Fig. 4.24, which relates the interfacial geometry to the degree of stretching of the larger block [47]. 

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