Simple formulas for dichroism analysis. Orientation of solutes in stretched polymer matrices

The multiplicative property of linear dichroism relative to axes of ’’statistical’’ rotation has allowed a simple, general formulation of the reduced dichroism of solutes oriented in uniaxially stretched polymer matrices: LD_r=3 S_p Σ_iS_iiO_i, i=x, y, z; where S_p=1/2ℱ₀^π/2 (3 cos²ϑ−1) df (ϑ) is a factor characterizing the orientation of the polymer. S_p was derived as a function of stretch for the case when f(ϑ) is the distribution of independent directions p (not necessarily attached to polymer chains) obtained in an isotropic‐substrate sphere when this is deformed into a spheroid at constant volume. S_ii define two independent local orientation parameters which depend on the solute–polymer interaction; O_i are optical factors given by the moment directions of the absorbing transitions. The model was tested for a few solutes, with known moment directions, in stretched films of polyvinyl alcohol (PVA) and polyethylene (PE). The agreement between predicted and observed LD_r, using the model distribution, was excellent for two elongated dyes in PVA but only qualitative in PE. A significant variation of S_ii with the degree of stretch indicates that the solute orientation is not due only to interaction with a single neighbor chain, a behavior which is consistent with a repulsive interaction.