Semiflexible polymers characterized by the contour length L and persistent length \ell_p confined in a spatial region D have been described as a series of ``{\em spherical blobs}'' and ``{\em deflecting lines}'' by de Gennes and Odjik for \ell_p < D and \ell_p \gg D respectively. Recently new intermediate regimes ({\em extended de Gennes} and {\em Gauss-de Gennes}) have been investigated by Tree {\em et al.} [Phys. Rev. Lett. {\bf 110}, 208103 (2013)]. In this letter we derive scaling relations to characterize these transitions in terms of universal scaled fluctuations in d-dimension as a function of L,\ell_p, and D, and show that the Gauss-de Gennes regime is absent and extended de Gennes regime is vanishingly small for polymers confined in a 2D strip. We validate our claim by extensive Brownian dynamics (BD) simulation which also reveals that the prefactor A used to describe the chain extension in the Odjik limit is independent of physical dimension d and is the same as previously found by Burkhardt {\em et al.}[  T. W. Burkhardt, Y. Yang, G. Gompper, Phys. Rev. E {\bf 82 }, 041801 (2010 )]. Our studies are relevant for optical maps of DNA stretched inside a nano-strip.
Semiflexible polymers characterized by the contour length L and persistent length \ell_p confined in a spatial region D have been described as a series of ``{\em spherical blobs}'' and ``{\em deflecting lines}'' by de Gennes and Odjik for \ell_p < D and \ell_p \gg D respectively. Recently new intermediate regimes ({\em extended de Gennes} and {\em Gauss-de Gennes}) have been investigated by Tree {\em et al.} [Phys. Rev. Lett. {\bf 110}, 208103 (2013)]. In this letter we derive scaling relations to characterize these transitions in terms of universal scaled fluctuations in d-dimension as a function of L,\ell_p, and D, and show that the Gauss-de Gennes regime is absent and extended de Gennes regime is vanishingly small for polymers confined in a 2D strip. We validate our claim by extensive Brownian dynamics (BD) simulation which also reveals that the prefactor A used to describe the chain extension in the Odjik limit is independent of physical dimension d and is the same as previously found by Yang {\em et al.}[ Y. Yang, T. W. Burkhardt, G. Gompper, Phys. Rev. E {\bf 76 }, 011804 (2007 )]. Our studies are relevant for optical maps of DNA stretched inside a nano-strip.
R
Burkhardt
Yang
A
Y. Yang,
D
Y. Yang,
R
82
76
R
041801 (2010
011804 (2007