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We consider the lattice model for an ideal-linear polymer chain to mimic the conformations of the semi-flexible homo-polymer chain. The polymer chain is assumed to confine in the fairly small area, such that the flexible chain conformations are easily polymerized in the nano-area. It has been described using analytical calculations that such a situation may lead to interesting and distinct theoretical findings of the thermodynamics of semi-flexible homo-polymeric macromolecules where the macromolecules are confined in the nano-length scale. We also discuss the characteristics of the persistent length and the elastic force due to the nano scale confinement of an infinitely long ideal polymer chain., Comment: 06 Pages

We model a macromolecule as an infinitely long Gaussian semi-flexible polymer chain and the conformations of the chain were realized in the nano cube using a cubic lattice. A modified version of the recursion relations is used to calculate the grand canonical partition function of the chain to investigate distinct thermo-dynamical properties of the nano polymer aggregate than corresponding bulk behaviour of the macromolecule. Our analytical estimates on the thermodynamical properties of the macromolecule clearly show that the nano aggregate of the polymer chain has interesting and distinct conformational statistics than its corresponding bulk state, and the method described in the present report can be easily extend to investigate the thermodynamics of the selfavoiding polymer chain in the nano dimensions., Comment: 08 Pages

We consider three dimensional model of the Gaussian polymer chain in the presence of defects to understand the formation of a polymer aggregate where the aggregate is induced by the defects. The defects are acting as an attractive centres of the monomers and it induces aggregation of the monomers of the chain around the defects. It has been shown using the analytical calculations that the formation of a polymer aggregates are favoured when the defects have extensions in all the possible three dimensions. We have also calculated relevant other thermo-dynamical parameters (i. e. the average number of the monomers and the average size of the chain about the defect line) of the polymer aggregates to justify our findings., Comment: 06 Pages

A lattice model of the directed self-avoiding walk is used to estimate the possibility on the formation of an infinitely long linear semi-flexible copolymer chain. The copolymer chain is assumed to composed of four different types of the monomers. A method of the recursion relations is used to solve the proposed model analytically to show that the probability of the formation of a self-avoiding semi-flexible copolymer chain is independent of the stiffness of the chain. It is a distinct result from our earlier study on the formation of a Gaussian semi-flexible copolymer chain and the Gaussian chain is made up of these four monomers, [P. K. Mishra, J. of Adv. Appl. Sci. Res. 2(4) 1-8 (2020)]. We have also calculated the average number of different types of the bonding in the copolymer chain to show the distinctions in the behaviour of the self-avoiding copolymer chain from the Gaussian polymer chain., Comment: 8 Pages

We estimate the probability regarding polymerization of a macromolecule which is made of distinct monomers. The lattice model of the random walk has been used to mimic the conformations of an ideal chain in two and three dimensions. It has been shown through analytical estimates that the flexible macromolecules may be easily formed than the stiff macromolecules in two and three dimensions., Comment: 08 Pages, 04 Figures and a Table

We study equilibrium statistics of single semi-flexible polymer chain in the presence of defects. The defects are lying along a line in the two and three dimensions and the monomers are interacting with the onsite potential of the defects. A fully directed self-avoiding walk model is used in two and three dimensions to describe thermo-dynamical behaviour of the chain in the presence of m defects. We have found that the number of conformations of the semiflexible polymer chain may be controlled by means of introduction of such defects so that a particular fraction of the chain conformations may be either suppressed or populated as per our requirements for synthesizing the polymer-nanoaggregates. We discuss the role of annealed defects for its Q realizations and m defects analytically, i. e. when the defects are in the thermal equilibrium with the monomers of the semi-flexible chain., Comment: 08 Pages, 01 Table and 01 Figure

We analyze response of a macromolecule near to a substrate; the substrate is tiled in the sequential and specific manner so that repeat units of the macromolecule may have different response on its adsorption in different directions onto the substrate. The lattice model of random walk has been used to analyze the adsorption-desorption behavior of an infinitely long homo-polymer molecule on a sequentially tiled substrate in three dimensions. The lattice model for the Gaussian chain and directed self-avoiding chain has been solved analytically. It has been emphasized on the basis of analytical estimates that a suitable coating may modify affinity of the macromolecule on the living surfaces and on the non living substrates in the complex manner which may be suitable means to control growth and also a route to restrict the spread of the deadly microbes., Comment: 07 Pages and 03 Fiures

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., Comment: 05 Pages and 01 Figure

We consider random walk model of a semi-flexible polymer chain on a square and a cubic lattice to enumerate conformations of the polymer chain in two and three dimensions, respectively. The bending energy of the chain is assumed as the key factor which controls the minimum average length of the chain in between two successive bends in the chain; and the average length of the chains per unit bend is defined as the persistence length of the polymer chain. It has been found that the minimum energy required to bend the chain is expressed in the form of simple relation which includes space dimensionality, step fugacity and persistence length., Comment: Four pages including two figures