Double Helical Conformation and Extreme Rigidity in a Rodlike Polyelectrolyte

The ubiquitous biomacromolecule DNA has an axial rigidity persistence length of ~50 nm, driven by its elegant double helical structure. While double and multiple helix structures appear widely in nature, only rarely are these found in synthetic non-chiral macromolecules. Here we describe a double helical conformation in the densely charged aromatic polyamide poly(2,2'-disulfonyl-4,4'-benzidine terephthalamide) or PBDT. This double helix macromolecule represents one of the most rigid simple molecular structures known, exhibiting an extremely high axial persistence length (~1 micrometer). We present X-ray diffraction, NMR spectroscopy, and molecular dynamics (MD) simulations that reveal and confirm the double helical conformation. The discovery of this extreme rigidity in combination with high charge density gives insight into the self-assembly of molecular ionic composites with high mechanical modulus (~1 GPa) yet with liquid-like ion motions inside, and provides fodder for formation of new 1D-reinforced composites.


Supplementary Note 1: Persistence length (axial rigidity) of PBDT double helix rods
Based on theories developed by Onsager 1 and Flory 2 that describe the formation of nematic liquid crystalline phases by rodlike particles (which were concisely summarized by Samulski 3 ), we can extract the aspect ratio D/L of the rodlike particles and thus the axial rigidity persistence length Lp from the critical volume fraction of rods ϕnematic at which a nematic phase forms.
Onsager used an athermal model of rods to derive Supplementary Equation 1. 1 ∅ nematic ≅ 4.5 (1) in which D is the diameter and L is the length of the rods.
In our earlier study of PBDT in solution, 4 on PBDT with a measured Mw = 17,300, we found that the weight fraction at which the nematic phase forms was 0.015 (1.5 wt%).
Since the bulk polymer has a density of 1.3 g cm -3 , we derive that the volume fraction of polymer will be even lower than the mass fraction. The aspect ratio D/L would be 300. If we assume that the effective diameter of our double helix rods is 0.8 nm, as given by our XRD studies (the present paper and our previous paper 5 ), then the length of the rods will be > 240 nm. This then represents the most conservative value of the axial rigidity persistence length (L = Lp) of PBDT. Here we note that molecular weight determination for rigid and charged polymers such as PBDT is rarely reliable (using any available method), and so we are vigorously searching for new ways to improve such measurements. As a point of additional information and comparison with our original Mw determination for PBDT stated above, 4 we recently determined the "absolute" molecular weight using a Wyatt MiniDawn LS detector to be 78 kg mol -1 (with Rz = 34 nm) for our original polymers, and we observed an apparent 180 kg mol -1 (Rz = 60 nm) for the higher molecular weight polymers that show a isotropic-nematic transition at 0.3 wt% in water, where Rz is the length of the polymer chain. At this point, we cannot be certain of any absolute numbers based on the difficulties in determining molecular weights for highly rigid and charged polymers, as mentioned above.

Supplementary Note 3: Rod-rod distance
According to our previous study 4 , we introduced a hexagonal lattice model for PBDT aqueous solutions. 4 We employed a two-parameter least square regression to find the relationship between the rigid rod-rod distance (r) and the weight percentage (C) of PBDT polymer solutions.
The fitted result is shown as follows with

Supplementary Note 5: MD simulation equilibrations and double helix self-assembly in water.
We performed two analyses to confirm that the double helical structure is stable and equilibrium was reached in our simulations. Finally, we mention that two simulations were performed in water with the OPLS-AA force field (NVT ensemble) and with the AMBER force field (NPT ensemble). In both of these other cases, double helices also formed for PBDT as described in the main paper.