RELAXATION AND STIFFENING DYNAMICS OF A SINGLE SEMIFLEXIBLE POLYMER CHAIN

Undergraduate

ABSTRACT

Both synthetic and biological polymers are a challenge to study because of the many features and functional roles they carry. A good understanding of the macromolecule’s dynamical properties is essential for biological processes such as the cytoskeleton dynamics of actin or in creating novel materials such as biodegradable nanocomposites. Here we focus on the Brownian dynamics of single semiflexible polymer chains, specifically the relaxation and stiffening behaviors. To date, the transient modeling of dilute solutions has concentrated mainly on flexible chains. Semiflexible polymers, with a persistence length comparable to or larger than their contour length show distinct properties in solution.

Brownian dynamics simulations based on a discretized version of the KratkyPorod chain model were employed. First, the relaxation of a bead-rod polymer chain from an initially straight configuration was followed. Through a scalinglaw analysis, universal relaxation laws were determined covering all time scales. A correlation describing the properties studied by the single parameter of chain length was noticed. Based on this, we were able to confirm and explain the chain’s stress and optical properties, as well as derive a nonlinear stress-optic law valid for semiflexible chains at any time period. Also, we determine the relaxation for long semiflexible chains exhibit two intermediate-time behaviors, as a result of the interplay of Brownian and bending forces on the link tensions.

A second project involved the relaxation dynamics of a worm-like bead-spring chain. Existing relaxation simulations of this bead-spring model are limited to the stress behavior. Here we monitor the short and intermediate-time relaxation behaviors of a nearly extended semiflexible chain. We also look at the effects of the Kuhn length on a chain of constant length.

Finally, the interesting behavior of the coil-helix-rod stiffening transition was studied. When subjected to external forces or a change in solution conditions the macromolecule may stiffen. Being able to control the chain stiffness is of technological importance especially for nanotechnology devices where the constraint of the walls limits the entropy available to the chain. We have successfully simulated the transient conformational behavior and subsequently understand the chain dynamics involved through analysis of the chain’s length, width, and stress.


Polymer Physics

Introduction

Polymers are one of the most commonly used class of material in today’s world. The diversity of this material is seen by its application in the food, plastic, defense, pharmaceutical and various other industries. Polymers can be divided into two groups, synthetic polymers and biopolymers. Synthetic polymers are known as man-made polymers because of the scientist’s ability to control the synthesis and growth of the macromolecule. Teflon, nylon, polycarbonate, and polyethylene are some of the common names that describe such polymers. In contrast, biopolymers occur naturally and are found in living organisms. Examples of biopolymers include the tobacco mosaic virus, cellulose, DNA, actin filaments, and microtubules.

A good understanding of the polymer’s dynamical properties is essential towards the study of biological processes such as the cytoskeletal dynamics of actin or the dynamics of protein deposition on implant materials , or in creating novel materials such as enhanced flat panel displays or biodegradable nanocompos-ites.


Because of the many features and functional roles they carry, both synthetic and biological polymers are a challenge to study. This challenge is proven true by noticing the many different experimental techniques such as fluorescence microscopy, electrophoresis, light scattering, optical microscopy, force spectroscopy, and along with the different simulation methods ranging from Monte Carlo to Brownian dynamics, bead-spring models to bead-rod models, and shear to extensional flow studies, used to gain insight on the different properties of the macromolecule.

Here we are concerned with the physics of single semiflexible polymer chains. In particular, the transient bead-rod and bead-spring chain properties are examined to understand the dynamics of the chain under various dilute solution conditions. A dilute solution is defined such that the chain is surrounded by solvent molecules and there is no chance of contact with another chain. The non-Newtonian properties of the chain are captured through a Brownian dynamics study. Among the properties studied are the chain length, stress, tension, and the birefringence; all these properties can help give the full picture of chain conformation and behavior in solution.

In the past, attention has been mainly focused on flexible polymers. Semiflexible polymers however, with a persistence length comparable to or larger than their contour length, show distinct properties in solution. Examples of biopolymers, in order of increasing stiffness, are DNA, actin, microtubules, and collagen.

Some properties of these biomolecules include: DNA, molecular weight (MW) of 108 with a polymer persistence length of only 50 nm; actin, MW of 42,000 with a persistence length of about 1.5-20 µm; the monomer MW of microtubules is 110,000 and the persistence length is up to 7 mm; finally, the stiff biopolymer collagen is known to have a monomer weight of 300,000 with a persistence length of 14.5 nm. Common examples of semiflexible synthetic polymers include Kevlar, polyvinyl chloride (PVC), polyamide (nylon), and polyesters. The stiffness shown in these polymers results in unique properties of their solutions. For example, the importance of the semiflexibility in F-actin can be seen by recognizing that as the persistence length increases the polymer bundles and adsorbs onto surfaces easily. In the case of synthetic polymers, the aromatic and amide molecular groups in Kevlar result in its common use of providing strength for light-weight materials.

Three simulation projects have been studied in this thesis. First, the relaxation of bead-rod polymer chains with both chain stiffness and the chain length being the adjustable parameters. Polymer behavior of an initially extended chain was monitored and through scaling-law analysis universal relaxation laws were determined for semiflexible chains. Studies of the stiff relaxation behavior show the long chains exhibit two intermediate behaviors due to the presence of bending energy. A correlation was noticed such that the properties studied can be predicted by the single variable of chain length. Because of this correlation, we were able to also define a non-linear stress-optic law valid for stiff chains at all time periods.