Optical Anisotropy of Tethered Chains

The static intrinsic birefringence and dichroism of dense assemblies of tethered chains, or “brushes”, are computed. The classical trajectory analogy is used to calculate the average segmental anisotropy for strongly-stretched chains, as a function of distance from the grafting surface. This result is used to estimate the birefringence and dichroism of planar polymer brushes and strongly-segregated block copolymer lamellae and cylinders. The birefringence, Δn, varies as the ratio L²/M(h²)₀, where L is the layer thickness, M the chain length, and (h²)₀ the mean-square unperturbed end-to-end distance. Consequently, Δn is predicted to be independent of M for tethered chains where L ~ M; however, for block copolymers in the strong-segregation limit, Δn ~ M^−0.67 For lamellar block copolymers, the calculations indicate that the intrinsic birefringence is surprisingly large and, for the most commonly-examined chemical systems, is often comparable to, or even greater than, the estimated form birefringence. This result reflects the orientation of the chains, i.e., the tendency of the block end-to-end vectors to be aligned, more than stretching. Calculations are also performed for labeled sections of a tethered chain, which indicate that it should be possible to assess the validity of the classical trajectory assumption via infrared dichroism measurements on appropriately deuterated samples.