Distribution Function of the End-to-End Distances of Linear Polymers With Excluded Volume Effects

Area of Science:

• Polymer Physics
• Statistical Mechanics
• Computational Chemistry

Background:

• The distribution of polymer chain lengths, particularly those exhibiting excluded volume effects, deviates from a simple Gaussian form.
• Theoretical models based on the Central Limit Theorem and Markov chain theory predict non-Gaussian behavior for polymer chain-end distributions.

Purpose of the Study:

• To determine the precise shape of the polymer chain-end distribution function for chains with excluded volume effects.
• To investigate the dependence of polymer chain moments on the number of segments using computational methods.

Main Methods:

• Utilized a Monte Carlo technique to generate polymer chains on a lattice, simulating excluded volume effects.
• Calculated various moments of the chain-end distribution function and their dependence on the number of polymer segments.
• Extrapolated results from moment combinations to approximate the general form of the distribution function.

Main Results:

• The study confirms that the distribution function for polymer chain lengths with excluded volume effects is not Gaussian.
• A specific mathematical form was found to approximate the chain-end distribution function:
• The parameter 't' was determined to be 3.2, with 'α' being a parameter derived from average mean square chain-end distances.

Conclusions:

• The non-Gaussian nature of polymer chain-end distribution is experimentally and theoretically supported.
• The derived approximate form provides a more accurate representation of polymer chain behavior under excluded volume conditions.
• This research offers a refined model for understanding polymer conformation and chain statistics.