Effect of geometrical constraint on conformational properties and adsorption transition of a semiflexible polymer chain (original) (raw)
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Effect of geometrical constraint on conformational properties of a polymer chain
Phase Transitions, 2011
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.
Condensed Matter Physics
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.
2009
Essential physics associated with the conformational behavior of a linear semiflexible homopolymer chain have been derived from a model of directed self avoiding walk (DSAW) on a two dimensional rectangular lattice. The DSAW model has been solved analytically to study phase transitions occurring in the polymer chain and exact values of conformational properties and transition points have been reported. We have analyzed the variation of critical value of step fugacity and persistent length with bending energy of the semiflexible polymer chain for a case when the chain is in the bulk. In presence of an attractive impenetrable surface, variation of critical value of monomer-surface attraction with bending energy of the polymer chain shows that adsorption of a stiff polymer chain takes place at a smaller value of monomer surface attraction than a flexible polymer chain. We have compared the results obtained for a two dimensional rectangular lattice case to the corresponding results obtained using square lattice and found that qualitative nature of phase diagrams are similar in the case of both the lattices. [
Collapsed and Adsorbed States of a Directed Polymer Chain in Two Dimensions
Phase Transitions, 2002
A phase diagram for a surface interacting long flexible partially directed polymer chain in a two-dimensional poor solvent where the possibility of collapse in the bulk exists is determined using exact enumeration method. We used a model of self attracting self-avoiding walk and evaluated 30 steps in series. An intermediate phase in between the desorbed collapsed and adsorbed expanded phases having the conformation of a surface attached globule is found. The four phases, viz. (i) desorbed expanded, (ii) desorbed collapsed, (iii) adsorbed expanded, (iv) surface attached globule are found to meet at a multicritical point. These features are in agreement with those of an isotropic (or non directed) polymer chain.
The Bending Energy of a Semi-Flexible Polymer Chain and the Polygons of the Polymer Chain
International Journal of Engineering Research and
We consider random walk model for a semiflexible polymer chain using a square and the cubic lattices 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 chain in between its two successive bends is defined as the persistence length (lp) of the polymer chain. Our analytical estimate suggests that the minimum energy required to bend the chain is Eb=kB*T*Log [2*(d-1)*g*lp], (where d, g and lp represents the dimensionality of the space, the step fugacity of the chain and the persistence length of the polymer chain, respectively), which is required to bend the chain so that a polymer loop of the perimeter 4*lp may be formed. Our estimate of the bending energy is independent of the fact that whether chain is ideal or the self-avoiding polymer; where in the case of ideal chain the vortex of the chain is treated as a monomer (the vertex version) while in the case of the selfavoiding polymer model each bond of the walk is treated as a monomer of the polymer chain (the bond version). The method of calculations of thermodynamics of the chain may be easily extended to the case of isotropic walk polymer model, the partially and the fully directed walk models of the polymer chain.
Semi-flexible compact polymers in two dimensional nonhomogeneous confinement
Journal of Physics A: Mathematical and Theoretical, 2019
We have studied the compact phase conformations of semi-flexible polymer chains confined in two dimensional nonhomogeneous media, modelled by fractals that belong to the family of modified rectangular (MR) lattices. Members of the MR family are enumerated by an integer p (2 ≤ p < ∞) and fractal dimension of each member of the family is equal to 2. The polymer flexibility is described by the stiffness parameter s, while the polymer conformations are modelled by weighted Hamiltonian walks (HWs). Applying an exact method of recurrence equations we have found that partition function Z N for closed HWs consisting of N steps scales as ω N µ √ N , where constants ω and µ depend on both p and s. We have calculated numerically the stiffness dependence of the polymer persistence length, as well as various thermodynamic quantities (such as free and internal energy, specific heat and entropy) for a large set of members of MR family. Analysis of these quantities has shown that semi-flexible compact polymers on MR lattices can exist only in the liquidlike (disordered) phase, whereas the crystal (ordered) phase has not appeared. Finally, behavior of the examined system at zero temperature has been discussed.
Adsorption and collapse transitions in a linear polymer chain near an attractive wall
Physical Review E, 2002
We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated numerically from series expansion up to 19 sites of a self-attracting self-avoiding walk in three dimensions. In two dimensions, we calculate phase boundaries analytically in some cases for a partially directed model. Both the numerical and analytical results corroborate the proposed qualitative phase diagram.
Divergence Of Persistent Length Of A Semiflexible Homopolymer Chain In The Stiff Chain Limit
Arxiv preprint arXiv:1010.2837, 2010
In this brief report, we revisit analytical calculation [Mishra, et al., Physica A 323 (2003) 453 and Mishra, NewYork Sci. J. 3(1) (2010) 32.] of the persistent length of a semiflexible homopolymer chain in the extremely stiff chain limit, k → 0 (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.
Exact results for the adsorption of a semiflexible copolymer chain in three dimensions
Arxiv preprint arXiv:0909.4653, 2009
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.