Polymer stretching in an elongational flow

Using a constant "velocity gradient'' ensemble approach, the average scalar end-to-end separation is calculated as a function of the gradient for an i deal Gaussian polymer chain experiencing longitudinal elongational flow und er steady-state conditions. The resulting equation, based on a dumbbell mod el, exhibits an initial average end-to-end separation equal to the unpertur bed random coil value; the separation increases monotonically with increasi ng velocity gradient, in agreement with recent experimental measurements an d with a classical treatment based on a diffusion equation. This approach i s contrasted with one based on Hooke's law where the end separation remains zero with increasing gradient until a critical value of the gradient is re ached at which point the chain suddenly expands to an appreciable fraction of its fully extended length. (C) 1999 American Institute of Physics. [S002 1-9606(99)50515-1].