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Theory and Monte Carlo simulations for the stretching of flexible and semiflexible single polymer chains under external fields
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10.1063/1.4772656
/content/aip/journal/jcp/137/24/10.1063/1.4772656
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/24/10.1063/1.4772656

Figures

Image of FIG. 1.
FIG. 1.

A polymer chain in an external field. The first monomer is clamped at position while the others are free to fluctuate. Each monomer is subjected to an external force (different in strength and direction for any K): all these forces mimic an external field. Another external force, playing the role of a main pulling load, , is applied to the last monomer at the position .

Image of FIG. 2.
FIG. 2.

Average values of the longitudinal component of the positions induced by the external field for the 2D FJC case. The red solid lines correspond to the analytical results Eqs. (28) and (32), MC results are superimposed in black circles. Top panel: each curve corresponds to different chain lengths N = 10, 20, 30, 40, 50 for a fixed value gl/(k B T) = 1 (e.g., corresponding to l = 1 nm, g = 4 pN at T = 293 K). Bottom panel: each curve corresponds to the different values gl/(k B T) = 0.1, 0.25, 0.5, 1, 2, 10 for a fixed chain length N = 20.

Image of FIG. 3.
FIG. 3.

Average values of the longitudinal component of the positions induced by the external field for the 3D FJC case. The red solid lines correspond to the analytical results Eqs. (29) and (33), MC results are superimposed in black circles. Top panel: each curve corresponds to different chain lengths N = 10, 20, 30, 40, 50 for a fixed value gl/(k B T) = 1. Bottom panel: each curve corresponds to the different values gl/(k B T) = 0.1, 0.25, 0.5, 1, 2, 10 for a fixed chain length N = 20.

Image of FIG. 4.
FIG. 4.

Longitudinal (top panel) and transversal (bottom panel) component of the variance of positions for the 3D FJC case. The red solid lines correspond to the analytical result Eq. (42), MC results are superimposed in black circles. Each curve corresponds to different chain lengths N = 10, 20, 30, 40, 50 for a fixed value of the external field defined by gl/(k B T) = 1.

Image of FIG. 5.
FIG. 5.

Longitudinal (top panel) and transversal (bottom panel) component of the variance of positions for the 3D FJC case. The red solid lines correspond to the analytical result Eq. (42), MC results are superimposed in black circles. Each curve corresponds to different values of the external field amplitude defined by gl/(k B T) = 0.1, 0.25, 0.5, 1, 2, 10 for a fixed chain length N = 20.

Image of FIG. 6.
FIG. 6.

Force-extension curves of a FJC polymer in an external field (or external force) with N = 20. The red line corresponds to the approximated expressions given in Eqs. (32) and (33) while the black circles have been obtained through MC simulations. The 2D (Eq. (30)) and 3D (Eq. (31)) FJC expressions (without an external field) are plotted for comparison with f = g and f = Ng.

Image of FIG. 7.
FIG. 7.

Force-extension curves of a WLC polymer in an external field (or external force) with N = 20. The red line corresponds to the approximated expressions given in Eqs. (46) and (48) while the black circles have been obtained through MC simulations. The 2D (Eq. (44)) and 3D (Eq. (47)) WLC expressions (without an external field) are plotted for comparison with f = g and f = Ng. The value of the bending spring constant is κ = 0.4 × 10−19 Nm ≃ 10k B T at T = 293 K.

Image of FIG. 8.
FIG. 8.

Action of a pulling force f (along the y-axis) perpendicular to the applied field g (along the z-axis). We adopted different values of the bending spring constant: κ = 0.08, 0.6, 2, 8 × 10−19 Nm. The chain length is fixed (N = 20), the external field amplitude is g = 4 pN and the force applied to the last monomer of the chain corresponds to f = 8 pN. The red solid lines correspond to the analytical results for the FJC case (see Eqs. (29) and (42)). Black circles correspond to the MC simulations with the different bending spring constants. In the top panel, we reported the average positions, while in the others the three variances of the x, y, and z components.

Image of FIG. 9.
FIG. 9.

Average positions of the chain for different angles between the external traction force f and the direction of the applied field g. We adopted N = 20, g = 4 pN, and f = 60 pN. The red solid lines correspond to the FJC analytical result, Eq. (29). The symbols represent the MC results for the WLC model with κ = 0.08, 0.6, 2 × 10−19 Nm (circles, triangles, and squares, respectively). For both FJC and WLC models, we used different values of the angle between the applied field and the traction force θ = π/2, 3π/4, 5π/6, 15π/16 from the right left.

Image of FIG. 10.
FIG. 10.

Monomer variances versus the position along the chain (i) and the angle between force and field (0 < θ < π) for the FJC model. As before, we used N = 20, g = 4 pN, and f = 60 pN.

Image of FIG. 11.
FIG. 11.

Monomer variances versus the position along the chain (i) and the angle between force and field (0 < θ < π) for the WLC model. As before we used N = 20, g = 4 pN, and f = 60 pN. We also adopted a bending stiffness κ = 0.6 × 10−19 Nm.

Tables

Generic image for table
Table I.

Asymptotic forms of the force-extension curves for all cases described in the paper: FJC and WLC models in 2D and 3D geometry with force applied f or field applied g.

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/content/aip/journal/jcp/137/24/10.1063/1.4772656
2012-12-28
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Theory and Monte Carlo simulations for the stretching of flexible and semiflexible single polymer chains under external fields
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/24/10.1063/1.4772656
10.1063/1.4772656
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