Abstract
AbstractA worm‐like chain model for a single, freely suspended semiflexible macromolecule with an aligning field of arbitrary coupling order is presented. Using a small‐angle approximation and Ginzburg–Landau theory, exact closed‐form solutions of the model are derived in the regime of a strong aligning field in arbitrary dimensions. Expressions for the mean cosine of the chain alignment angle, orientational order parameters, and the two‐point correlation function are found. As a corollary, the persistence length is confirmed as a valid threshold for rigid behavior of the chain. The theoretical results are validated with Monte Carlo simulations in two and three dimensions. It is shown that the solutions for the small‐angle approximation are within of the simulated values for the exact model for chain‐field alignment angles θ ≲ 20°. As a practical application, the findings are applied to carbon nanotubes in an aligning electric field.
Highlights
Introduction mulated in FourierLaplace space and is expressed in terms of complicated continued fractions
carbon nanotubes (CNTs) produced using the floating catalyst chemical vapor deposition (FCCVD) method[42] are suitable for alignment by an electric field as they are freely suspended in hydrogen gas during synthesis
Using Ginzburg–Landau theory and the WLC model, we studied the statistics of a freely suspended macromolecule in an aligning field of arbitrary order
Summary
We characterize the contour of the chain using the d-dimensional normalized tangent vectort(s) as a function of the contour length s. Ν denotes the coupling order of the alignment with respect to the external field. The first term in Equation (1) corresponds to the classical WLC free energy[7] for curvature of the chain. In the second field coupling term, we have assumed that the system obeys Z2 symmetry under the transformationt(s) → −ˆt(s). This is the case for aligning flows, gravitational gradients, and electric fields that polarize the chain in the direction of the field. For example, a non-zero spin density, and we are considering the coupling with an external magnetic field, Z2 symmetry is no longer present.
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