Other related functions

There are now two additional PPFs available in this software that are based on the Flory polymer swelling model, and the McKenzie-Domb model that takes on the more general form of the equation above. The weight on the distribution function ( $4 \pi (r_{ij})^{2 \gamma} \Delta r$) is a partial measure of the self-avoidance of the polymer chain. The effect is to cause the chain to expand. We can estimate the root-mean-square separation distance of the polymer chain from from the following thermodynamic relationship

$$f(r) = \frac{ \partial S(r) }{\partial r} = \delta k_B T \... ...ta \frac{ \vartheta_{ij} }{b^\delta} r^{\delta - 1} \right\}.$$ (6)

where $S(r) = k_B \ln(p)$ is the entropy with $p$ corresponding to Eqn (1). Solving Eq. (6) for $f(r) = 0$ yields

$$r = \left( \frac{ \gamma}{ \vartheta_{ij}} \right)^{1/\delta} b.$$ (7)

Thus, when $\delta > 2$, the rms for $r$ must decrease and likewise, for $\delta < 2$, the rms tends to increase exponentially. On the other hand, $\gamma$ only shows a direct weight on $r$ for any fixed $\delta$. Ultimately, both $\delta$ and $\gamma$ show a complex interdependence on the excluded volume. To make intelligent physical estimates, you will need to consider this behavior in your choice of parameters.

Increasing the size of your excluded volume will tend to encourage your stems to form shorter domains. Likewise, compacting the size of the polymer to a globular structure will encourage longer stems. Understanding the solvent environment is very important in such cases.