arXiv subjects

Pramod Kumar Mishra

Publications and source records attributed to Pramod Kumar Mishra.

18 recordsLinked to original sources

arXiv2020

A nano polymer aggregate on a substrate: A Theoretical study

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.

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arXiv2020

Aggregation of a macromolecule in a nano cube

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.

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arXiv2020

Defects induced polymer aggregates: A theoretical study

. 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.

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arXiv2020

A theoretical estimate on the probability of the formation of a self-avoiding copolymer macromolecule

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.

cond-mat.stat-mech↗

arXiv2020

Theoretical estimate of the probability for macromolecule formation

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.

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arXiv2020

The response of a macromolecule near a tiled substrate

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.

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arXiv2020

The Role of annealed defects on conformational statistics of a selfavoiding semi-flexible polymer chain: Exact Results (I)

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.

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arXiv2020

Statistics of Quenched Defects Containing Semi-Flexible Polymer Chain: Exact Results (II)

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.

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arXiv2019

The bending energy of a semi-flexible polymer chain and the polygons of the polymer chain

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.

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arXiv2016

The effect of confinement and stiffness on the conformational change of a semiflexible homopolymer chain

We analyse the nature of the confinement of an infinitely long (and finite) linear semiflexible homo-polymer chain confined in between two geometrical constraints (A&B) under good solvent condition in two dimensions. The constraints are stair shaped impenetrable lines. A lattice model of fully directed self avoiding walk is used to list information of walks of the confined chain and the exact enumeration technique is used for the canonical ensemble of conformations of the confined chain to discuss equilibrium statistics of the chain. We obtain the probability of polymerization of the confined flexible chain segments with either one end (polymer trains) or both the ends of the confined chain lying on the stair shaped constraints (polymer bridge and arc). We have also calculated the force of confinement exerted by the constraints on to the chain or the force exerted by the chain on the geometrical constraints using grand canonical ensemble theory and discuss nature of variation of the force.

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arXiv2014

Equilibrium statistics of an infinitely long chain in the severe confined geometry: Rigorous results

We analyze the equlibrium statistics of a long linear homo-polymer chain confined in between two flat geometrical constraints under good solvent condition. The chain is ocupying two dimensional space and geometrical constraints are two impenetrable lines for the two dimensional space. A fully directed self avoiding walk lattice model is used to derive analytical expression of the partition function for the given value of separation in between the impenetrable lines. The exact values of the critical exponents ($ν_{||}, ν_{\perp}, ν$ and $ γ_1$) were obtained for different value of separations in between the impenetrable lines. An exact expression of the grand canonical partition function of the confined semiflexible chain is also calculated for the given value of the constraints separation using generating function technique.

cond-mat.stat-mech↗

arXiv2014

A semiflexible polymer chain under geometrical restrictions: Only bulk behaviour and no surface adsorption

We analyse the conformational behaviour of a linear semiflexible homo-polymer chain confined by two geometrical constraints under a good solvent condition in two dimensions. The constraints are stair shaped impenetrable surfaces. The impenetrable surfaces are lines in a two dimensional space. The infinitely long polymer chain is confined in between such two (A and B) surfaces. A lattice model of a fully directed self-avoiding walk is used to calculate the exact expression of the partition function, when the chain has attractive interaction with one or both the constraints. It has been found that under the proposed model, the chain shows only a bulk behaviour. In other words, there is no possibility of adsorption of the chain due to restrictions imposed on the walks of the chain.

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arXiv2010

Divergence Of Persistent Length Of A Semiflexible Homopolymer Chain In The Stiff Chain Limit

In this brief report, we revisit analytical calculation [Mishra, {\it et al.}, Physica A {\bf 323} (2003) 453 and Mishra, NewYork Sci. J. {\bf{3(1)}} (2010) 32.] of the persistent length of a semiflexible homopolymer chain in %the extremely stiff chain limit, {\bf $k\to0$ (where, $k$ is stiffness of the chain)} for directed walk lattice model the extremely stiff chain limit, $k\to0$ (where, $k$ is stiffness of the chain) for directed walk lattice model in two and three dimensions. Our study for two dimensional (square and rectangular) and three dimensional (cubic) lattice case clearly indicates that the persistent length diverges according to expression $(1-g_c)^{-1}$, where $g_c$ is the critical value of step fugacity required for polymerization of an infinitely long linear semiflexible homopolymer chain and nature of the divergence is independent of the space dimension. This is obviously true because in the case of extremely stiff chain limit the polymer chain is a one dimensional object and its shape is like a rigid rod.

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arXiv2010

Effect of Geometrical Constraint on Conformational Properties of a Polymer Chain

In this paper, we analyze the effect of geometrical constraint on the conformational properties of an infinitely long linear semiflexible polymer chain confined in-between two constraints under good solvent condition in two dimensions. The constraints are two impenetrable stair shaped surface and for two dimensional space, the surface is a one dimensional line. The semiflexibility of the chain is accounted by introducing a Boltzmann weight of bending energy required to produce each turn in the chain and good solvent condition was accounted by using self avoiding walk model of the chain. We have calculated exact critical value of step fugacity required for polymerization of an infinitely long polymer chain confined in between the constraints for different values of separation between the constraints for directed version of the model. We have also calculated possible maximum, minimum values of the persistent length for such chains and the maximum value of bending energy required for each turn in the chain for few values of separation between the constraints.

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arXiv2010

Effect of geometrical constraint on conformational properties and adsorption transition of a semiflexible polymer chain

We analyze equilibrium properties and adsorption desorption phase transition behaviour of a linear semiflexible copolymer chain under constrained geometrical situation on square lattice in a good solvent. One dimensional stair shaped line imposes geometrical constrain on the chain. Lattice model of fully directed self avoiding walk is used to model the chain, semiflexibility of the chain is accounted by introducing energy barrier for each bend of the chain. Exact expression of the partition function of the chain is obtained using generating function technique for the cases, viz. (i) constrained copolymer chain is in the bulk, (ii) constrained copolymer chain interacting with an impenetrable flat surface, (iii) constrained copolymer chain interacting with constraint itself and (iv) general expression of the partition function of the copolymer chain, interacting with a flat surface and geometrical constraint (stair shaped line). We have compared bulk properties and adsorption desorption transition behaviour of a linear semiflexible homopolymer chain without constraint to the case when the chain is constrained.

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arXiv2010

Polymer adsorption on curved surface

Lattice model of directed self avoiding walk is used to investigate adsorption properties of a semiflexible sequential copolymer chain on an impenetrable curved surface on a hexagonal lattice in two dimensions. Walks of the copolymer chains are directed in a direction away from the surface at a suitable value of monomer surface attraction, the copolymer chain gets adsorbed on the surface. To calculate exact value of monomer surface attraction, the directed walk model have been solved analytically using generating function method to discuss results when one type monomer of the copolymer chain has attractive, repulsive or no interaction with the surface. Results obtained show that adsorption transition point is independent of bending energy of the copolymer chain.

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arXiv2009

Exact results for the adsorption of a semiflexible copolymer chain in three dimensions

Lattice model of directed self avoiding walk has been solved analytically to investigate adsorption desorption phase transition behaviour of a semiflexible sequential copolymer chain on a two dimensional impenetrable surface perpendicular to the preferred direction of the walk of the copolymer chain in three dimensions. The stiffness of the chain has been accounted by introducing an energy barrier for each bend in the walk of the copolymer chain. Exact value of adsorption desorption transition points have been determined using generating function method for the cases in which one type of monomer is having interaction with the surface viz., (i) no interaction (ii) attractive interaction and (iii) repulsive interaction. Results obtained in each of the case show that for stiffer copolymer chain adsorption transition occurs at a smaller value of monomer surface attraction than a flexible copolymer chain. These features are similar to that of a semi-flexible homopolymer chain adsorption.

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arXiv2002

Does a surface attached globule phase exist ?

A long flexible neutral polymer chain immersed in a poor solvent and interacting with an impenetrable attractive surface exhibits a phase known as surface attached globule ({\bf SAG}) in addition to other adsorbed and desorbed phases. In the thermodynamic limit, the {\bf SAG} phase has the same free energy per monomer as the globular phase, and the transition between them is a surface transition. We have investigated the phase diagrams of such a chain in both two- and three- dimensions and calculated the distribution of monomers in different domains of the phase diagram.

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