Elastic Constants and Defects

When the layers of a lamellar block copolymer are distorted, the free energy density is augmented by a distortional term that can, like the smectic-A phase, be described as the sum of layer compression/dilation and layer-bending energies  

In the weak-segregation limit, Amundson and Helfand (1993) estimated 

From Eqs. (13-7) and (13-8), one can estimate that typical values for B and K for weak to moderately segregated diblocks should be B 10 -10 dyn/cm and K 10 -10 dyn. By compressing shear-aligned diblocks, Hudson et al. (1995) have extracted experimental estimates of B that are around a decade or so lower than these values. 

The compressive modulus predicted for a triblock (/ = 0.5) in the strong-segregation limit is theoretically the same as for the diblock formed by cutting the triblock in the middle. The bend modulus for the triblock is predicted to be about twice as large as that of the diblock because of the presence of bridging configurations (Turner 1995). 

The bend and especially the compressive moduli of lamellar block copolymers are therefore typically lower, or at least no higher, than those of small-molecule smectic-A liquid crystals, while the viscosities of the former are usually much larger than the latter. By analogy with nematics, for layered materials one can define characteristic Ericksen numbers as Erj = r]yh /K and Er = where is a characteristic viscosity and 

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