How to Define Variation of Physical Properties Normal to an Undulating One-Dimensional Object

TL;DR

This paper introduces a method to define the variation of physical properties normal to undulating one-dimensional objects, using an intrinsic length scale related to their stiffness, exemplified through simulations of bottle-brush polymers.

Contribution

It proposes a novel intrinsic length scale based on stiffness to characterize property variation normal to undulating lines, applicable to flexible polymers and similar structures.

Findings

Defined a natural measure of property variation normal to undulating lines.

Demonstrated the method through computer simulations of bottle-brush polymers.

Provided a framework for analyzing environmental influence of one-dimensional objects.

Abstract

One-dimensional flexible objects are abundant in physics, from polymers to vortex lines to defect lines and many more. These objects structure their environment and it is natural to assume that the influence these objects exert on their environment depends on the distance from the line-object. But how should this be defined? We argue here that there is an intrinsic length scale along the undulating line that is a measure of its "stiffness" (i.e., orientational persistence), which yields a natural way of defining the variation of physical properties normal to the undulating line. We exemplify how this normal variation can be determined from a computer simulation for the case of a so-called bottle-brush polymer, where side chains are grafted onto a flexible backbone.