Bead-Spring Model Calculations of the Viscoelastic and Oscillatory Flow Birefringence Properties of Block Copolymer Solutions

Bead-spring model (BSM) calculations of the polymer contributions to viscoelastic (VE) and oscillatory flow birefringence (OFB) properties of very dilute block copolymer solutions are reported. The original BSM of Rouse and Zimm has been extended to the case of diblock and triblock copolymers, following the model of Wang. The VE properties have been determined via exact calculations of the eigenvalues of the modified matrix, and the OFB properties from the exact eigenvalues and eigenvectors of this matrix; the eigenvectors are required in order to calculate optical weighting factors for each of the normal modes, which depend strongly on the relative values of the optical constants for the various blocks. Different optical constants for different blocks lead to a different effective stress-optic coefficient for each normal mode. Illustrative calculations for four different situations are presented. In all cases, the VE properties are not substantially altered from the homopolymer case. The OFB properties, however, can vary strikingly with modest changes in model parameters due to the mode-dependent optical weighting factors. For chains in which the optical factors for the blocks differ in sign, the OFB properties have frequency dependences that are much more featured than for their homopolymer equivalents, which offers the possibility that OFB measurements of block copolymer solutions may provide extremely powerful and unique characterization information including block lengths and locations. Both mechanically uniform and nonuniform block copolymers have been considered; it is found that small variations between subchain friction coefficients can lead to substantially more striking frequency dependences for OFB properties than are predicted for mechanically uniform chains.