Abstract
We describe method to discuss thermodynamics of a defected semi-flexible homo-polymer chain in the two and three dimensions using fully directed self-avoiding walk lattice model. The defects are located along a line and these defects are not in the thermal equilibrium with the monomers of the semi-flexible polymer chain; i. e. we consider the case of defected semi-flexible polymer chain in the present manuscript for the case of quenched defects. There are m defects on the conformations of the N monomers long semi-flexible polymer chain and we exactly count the number of Q realizations of the defected conformations of N-monomers long self-avoiding semi-flexible polymer chain; and thus we derive the exact expression of the free energy of the defected semi-flexible polymer chain for the finite length (i. e. using the fixed particle ensemble method); and we also derive exact expression of the partition function for the defected self-avoiding semi-flexible polymer chain in the thermodynamic limit using the grand canonical ensemble theory. The method described in this manuscript may be easily extended to another case of the defected polymer chain for isotropic/directed walk lattice models.
Highlights
There are wide range of applications of the polymer materials [1],[2]
The well known applications of the polymer materials may be the steric stabilization of the dispersions of their solutions, use of the Biosensors, and coating on the degradable surfaces using polymer materials, etc. [1],[2],[3]
The advances in the experimental techniques on the single macromolecules made it feasible to manipulate the polymer molecules; and which are due to inventions of the devices like optical tweezers, the atomic force microscope (AFM)
Summary
There are wide range of applications of the polymer materials [1],[2]. These applications involve the technology based intricacies and understanding of the fundamental aspects of these polymer-macro-molecules may be useful to improve technological applications of the polymer materials. The AFM is widely used to measure elastic constants of single macromolecule (DNA, Proteins) and to manipulate the synthetic macro-molecules for its desired applications. We consider a defected single polymer chain to analyze conformational statistics of the polymer molecule for the case when the defects are not in the thermo-dynamical equilibrium with the monomers of the polymer chain; i. E. present manuscript deals with the conformational statistics of a defected semi-flexible polymer chain for the quenched defects case. Vol. (6), Dec 2019, E-ISSN: 2348-3423 to mimic the conformations of the defected semi-flexible homo-polymer chain to study behavior of the self-avoiding polymer chain in the presence of quenched defects. We describe the methods of calculations of the thermo-dynamical parameters of the self-avoiding semi-flexible polymer chain in the section 3. We summarize method of calculating thermo-dynamical properties of the defected chain in the section 4 and conclude the manuscript in the section 5
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