Semiflexible polymer solutions. I. Phase behavior and single-chain statistics

Abstract

We study the thermodynamics and single-chain statistics of wormlike polymer solutions with Maier-Saupe-type interactions using self-consistent-field ͑SCF͒ theory. The SCF equations are derived using a systematic field-theoretical approach which yields the SCF equations as the lowest order approximation, but permits fluctuation corrections to be incorporated. We solve the SCF equations using the spheroidal functions, which provides a nonperturbative description of the thermodynamics and single-chain statistics in the nematic state for arbitrary degrees of nematic order. Several types of phase diagrams are predicted, with an emphasis on the limit of metastability ͑spinodal͒ associated with each phase. The shape and location of these spinodals suggest interesting scenarios for the phase transition kinetics. A large but finite persistence length is shown to significantly decrease the isotropic-nematic transition temperature relative to that for rigid rods. In the nematic state, the mean-square end-to-end distance in the parallel and perpendicular directions are governed by two separate correlation lengths. An exact relationship between these correlation lengths and the eigenvalues of the spheroidal functions is provided, which reproduces the analytical expressions predicted from earlier studies in the limit of large nematic strength. The dominant contribution to the single-chain thermodynamics is shown to arise from small amplitude undulations in the directions perpendicular to the nematic direction; the presence of hairpins, though crucial for determining the dimensions of the polymer, has insignificant consequences on the single-chain thermodynamics.

DNA confined in nanochannels: Hairpin tightening by entropic depletion

“…Complete analyses of the global persistence length including fluctuations have been given for chains in the nematic state. 27,33 It would be important to have similar rigorous treatments in the case of nanochannels.…”

“…A form similar to Eq. ͑1͒ arises in the theory of nematically confined stiff chains [23][24][25][26][27][28][29][30][31][32][33] and will be rederived below. Note that the B-helix is assumed to remain intact.…”

Orientational order and glassy states in networks of semiflexible polymers

“…In a future extension of our model, one may envisage adding a Maier-Saupe aligning pseudopotential as in Refs. [6,7] and studying its interplay with the cross-link induced interaction. The wormlike chain propagator G(ϕ, s 1 ; ϕ ′ , s 2 ) quantifies the probability that the tangential vector of monomer s 1 points into the direction ϕ provided that the tangential vector of monomer s 2 points into the direction ϕ ′ :…”

“…The isotropic-nematic transition in solutions of partially flexible macromolecules has been studied theoretically using the Onsager approach [5] or the Maier-Saupe approach [6,7]. In Ref.…”

“…In Ref. [7], the role of the solvent is taken into account and a very rich phase transition kinetics is predicted. Aggregation and orientational ordering of Lennard-Jones macromolecules with bending and torsional rigidity, with or without solvent, has recently been investigated in Ref.…”