Intramolecular Form Factor in Dense Polymer Systems: Systematic Deviations from the Debye formula

TL;DR

This paper reveals that dense polymer systems deviate from the classical Debye form factor due to incompressibility effects, showing non-monotonic behavior and a correction term dependent solely on concentration.

Contribution

It provides a theoretical and numerical analysis demonstrating systematic deviations from Debye's formula in dense polymer melts, highlighting the role of incompressibility.

Findings

Up to 20% non-monotonic deviations from Debye's formula.

Kratky plot lacks the expected plateau for Gaussian chains.

A correction term proportional to q^3/32ρ depends only on concentration.

Abstract

We discuss theoretically and numerically the intramolecular form factor $F(q)$ in dense polymer systems. Following Flory's ideality hypothesis, chains in the melt adopt Gaussian configurations and their form factor is supposed to be given by Debye's formula. At striking variance to this, we obtain noticeable (up to 20%) non-monotonic deviations which can be traced back to the incompressibility of dense polymer solutions beyond a local scale. The Kratky plot ($q^2F(q)$ {\it vs.} wavevector $q$) does not exhibit the plateau expected for Gaussian chains in the intermediate $q$-range. One rather finds a significant decrease according to the correction $\delta(F^{-1}(q)) = q^3/32\rho$ that only depends on the concentration $\rho$ of the solution, but neither on the persistence length or the interaction strength.