Lattice knots in a slab

Gasumova, D.; Rensburg, E J Janse van; Rechnitzer, Andrew

doi:10.1088/1742-5468/2012/09/p09004

Cited by 6 publications

(10 citation statements)

References 31 publications

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“…It was found [37] that in the case of a narrow slit more complex knot types in a ring polymer exert higher forces on the confining walls of the slit in comparison to unknotted polymer chains of the same length, and for the relatively wide slits the opposite situation takes place. As it was shown in [49], confining ring polymer to a slab results in the loss of configurational entropy and leads to the arising of a repulsive force which depends on the entanglements between the two walls of the confining slab. It should be mentioned, that in [49] the profiles of critical forces which are necessary to apply in order to overcome this entropically induced repulsion were obtained in the framework of a new numerical approach which was the implementation of the generalized atmospheric sampling (GAS) algorithm for lattice knots proposed by Rensburg and Rechnitzer in [50].…”

Section: The European Physical Journal Special Topicsmentioning

confidence: 89%

“…As it was shown in [49], confining ring polymer to a slab results in the loss of configurational entropy and leads to the arising of a repulsive force which depends on the entanglements between the two walls of the confining slab. It should be mentioned, that in [49] the profiles of critical forces which are necessary to apply in order to overcome this entropically induced repulsion were obtained in the framework of a new numerical approach which was the implementation of the generalized atmospheric sampling (GAS) algorithm for lattice knots proposed by Rensburg and Rechnitzer in [50]. Recently advanced MC simulation techniques [51] have been used in order to study the effect of nanoslit confinement on topological properties of circular model DNA, which was modeled as a semiflexible polymer chain.…”

Section: The European Physical Journal Special Topicsmentioning

confidence: 89%

“…In [46] it was established, that ring polymers with more complex knots are more compact and have a smaller radius of gyration and this decreases their ability to spread out under confinement. A series of papers have been devoted to the investigation of ring polymers compressed or squeezed by a force in a slab [47][48][49]. For example, the results of MC simulations performed in [47] suggest that the knotted ring polymers will exert higher entropic forces on the walls of the confining slit than unknotted or linear polymers.…”

Section: The European Physical Journal Special Topicsmentioning

confidence: 99%

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Linear and ring polymers in confined geometries

Usatenko

Kuterba

Chamati

et al. 2017

Eur. Phys. J. Spec. Top.

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Abstract. A short overview of the theoretical and experimental works on the polymer-colloid mixtures is given. The behaviour of a dilute solution of linear and ring polymers in confined geometries like slit of two parallel walls or in the solution of mesoscopic colloidal particles of big size with different adsorbing or repelling properties in respect to polymers is discussed. Besides, we consider the massive field theory approach in fixed space dimensions d = 3 for the investigation of the interaction between long flexible polymers and mesoscopic colloidal particles of big size and for the calculation of the correspondent depletion interaction potentials and the depletion forces between confining walls. The presented results indicate the interesting and nontrivial behavior of linear and ring polymers in confined geometries and give possibility better to understand the complexity of physical effects arising from confinement and chain topology which plays a significant role in the shaping of individual chromosomes and in the process of their segregation, especially in the case of elongated bacterial cells. The possibility of using linear and ring polymers for production of new types of nano-and micro-electromechanical devices is analyzed.

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Section: The European Physical Journal Special Topicsmentioning

confidence: 89%

Section: The European Physical Journal Special Topicsmentioning

confidence: 89%

Section: The European Physical Journal Special Topicsmentioning

confidence: 99%

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Linear and ring polymers in confined geometries

Usatenko

Kuterba

Chamati

et al. 2017

Eur. Phys. J. Spec. Top.

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“…Tight lattice knots [24] are minimal length lattice knots [28][29][30]. The compressibility of tight lattice knots is known to be a function of knot type [31,32]. In Fig.…”

Section: Compressed Lattice Knotsmentioning

confidence: 99%

Osmotic pressure of compressed lattice knots

Rensburg

2019

Phys. Rev. E

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A numerical simulation shows that the osmotic pressure of compressed lattice knots is a function of knot type, and so of entanglements. The osmotic pressure for the unknot goes through a negative minimum at low concentrations, but in the case of non-trivial knot types 31 and 41 it is negative for low concentrations. At high concentrations the osmotic pressure is divergent, as predicted by Flory-Huggins theory. The numerical results show that each knot type has an equilibrium length where the osmotic pressure for monomers to migrate into and out of the lattice knot is zero. Moreover, the lattice unknot is found to have two equilibria, one unstable, and one stable, whereas the lattice knots of type 31 and 41 have one stable equilibrium each.

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“…It was found [5] that in the case of a narrow slit, more complex knot types in a ring polymer exert higher forces on the confining walls of the slit in comparison to unknotted polymers of the same length, and for the relatively wide slits, the opposite situation takes place. Confining ring polymer to a slab results in a loss of configurational entropy and leads to the appearance of a repulsive force which depends on the entanglements between two walls of the confining slab, as it was shown in the framework of a new numerical approach based on the generalized atmospheric sampling (GAS) algorithm for lattice knots in [17]. Thus, at the moment most of the papers devoted to the investigation of the behaviour of ring polymers compressed in confined geometries like slit or squeezed by a force in a slab of two parallel walls deal with numerical methods and present analytical results are incomplete.…”

mentioning

confidence: 96%

Ring polymers in confined geometries

Usatenko¹,

Halun²,

Kuterba³

2016

Condens. Matter Phys.

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The investigation of a dilute solution of phantom ideal ring polymers and ring polymers with excluded volume interactions (EVI) in a good solvent confined in a slit geometry of two parallel repulsive walls and in a solution of colloidal particles of big size was performed. Taking into account the correspondence between the field theoretical φ 4 O(n)-vector model in the limit n → 0 and the behaviour of long-flexible polymers in a good solvent, the correspondent depletion forces and the forces which exert phantom ideal ring polymers and ring polymers with EVI on the walls were obtained in the framework of the massive field theory approach at fixed space dimensions d=3 up to one-loop order. Besides, taking into account the Derjaguin approximation, the depletion forces between big colloidal particle and a wall and in the case of two big colloidal particles were calculated. The obtained results indicate that phantom ideal ring polymers and ring polymers with EVI due to the complexity of chain topology and for entropical reasons demonstrate a completely different behaviour in confined geometries compared with linear polymers.Key words: colloidal systems,critical phenomena, polymers, phase transitions PACS: 64.70.pv, 61.25.he, 67.30.ej, 68.35.Rh, 64.70.qd As it was shown in a series of the atomic force spectroscopy (AFM) experiments [1, 2], biopolymers such as DNA very often present a ring topology. Such a situation takes place, for example, in the case of Escherichia coli (E.coli) bacteria with a chromosome which is not a linear polymer, but has a ring topology [3]. The biopolymers of DNA of some viruses such as bacteriophages λ that infect bacteria oscillate between linear and ring topology [4,5]. The physical effects arising from confinement and chain topology play a significant role in the shaping of individual chromosomes and in the process of their segregation, especially in the case of elongated bacterial cells [6]. The behaviour of linear ideal and real polymers with excluded volume interaction (EVI) in a good solvent confined in a slit of two parallel repulsive [7,8], inert or mixed walls is well understood [8]. Unfortunately, the physics of confined ideal ring polymers and ring polymers with EVI effects is still unclear. Ring polymers with specified knot type were chemically synthesized a long time ago [9]. Ring topology of polymers influences the statistical mechanical properties of these polymers, for example the scaling properties [10,11] and shape [2,12,13] because it restrains the accessible phase space. An interesting point which was confirmed by numerical studies in [14] is that longer ring polymers are usually knotted with higher frequency and complexity. In [15], it was established that ring polymers with more complex knots are more compact and have a smaller radius of gyration and this decreases their ability to spread out under confinement. The results of Monte Carlo simulations performed in [16] suggest that the knotted ring polymers will exert higher entropic forces on the walls of the confini...

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Lattice knots in a slab

Cited by 6 publications

References 31 publications

Linear and ring polymers in confined geometries

Linear and ring polymers in confined geometries

Osmotic pressure of compressed lattice knots

Ring polymers in confined geometries

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