Specificity of Counterion Binding to a Conjugated Polyelectrolyte: A Combined Molecular Dynamics and NOESY Investigation

Poly(thiophen-3-ylacetic acid) (PTAA) is a representative of conjugated polyelectrolytes which are used in many optoelectronics devices. The performance of these devices is affected by the polymer conformation, which, among others, depends on the nature of the counterion. In this study, the binding of tetrabutylammonium counterions (TBA+) on PTAA was determined using a combination of nuclear Overhauser effect spectroscopy (NOESY) and molecular dynamics (MD) simulation. It was found that TBA+ ions specifically bind on the hydrophobic main chain of PTAA, while, according to MD simulations, alkali counterions predominantly bind in the vicinity of negatively charged carboxylic groups located on side chains. The MD trajectories were used to compute the relaxation matrices and the NOESY spectra. With the help of these latter calculations, the changes of intensities in experimental NOESY spectra upon binding of TBA+ ions to PTAA were interpreted.

: Dependence of diagonal peaks signal intensities (I) on the mixing time (t m ), calculated for simulated 0.2 mol L −1 solutions of TBACl. phydrogen atoms nearest to the central TBA + nitrogen atom (H 1 ),u -hydrogen atoms bound to the second most inner TBA + carbon atom (H 2 ), q -hydrogen atoms, bound to the third carbon atom from the central TBA + nitrogen atom (H 3 ), s -hydrogen atoms bound to the outer TBA + carbon atom (H 4 ).
The farther from the central N atom the proton is, the slower is its relaxation. This dependence is also expected from equation (2) in the main paper. In general, faster molecular dynamics of a proton leads to lower J(nω 0 ) and longer relaxation time. Signal intensities at mixing time t m = 0 are zero since no magnetization exchange has taken place yet.
At the beginning of mixing (low values of the mixing time) the signals start to increase (in the absolute sense) with the increase of the mixing time (t m ). This initial increase of signals is followed by a subsequent decrease to zero. In Figure S4, all the signals are negative. This feature is a consequence of the fact that the system dynamics is fast when compared to the Larmor frequency of the instrument. Figure S5: Dependence of intramolecular cross-peaks intensities of simulated PTATBA system on the mixing time In Figure S5, all the signals, except the signal corresponding to the interaction between H 3 and H 4 type hydrogen atoms, are positive as a result of a slow dynamics of PTATBA system.

Radial distribution function
The radial distribution function g i j (r), or more generally the pair distribution function, is a function that measures the probability density of finding a particle j at a radial distance r of another particle i. It can also be seen as a reduced local density of particles j at a radial distance r of another particle i. 1 The number of particles j contained in a spherical shell of thickness dr at a radial distance r of a particle i is then 4πρ 0 g i j (r)r 2 dr. 2 In the present study, the pair distribution functions were calculated between different types of atoms using the following procedure: distances between two atoms of different type (e.g. between oxygen atoms and Li + counterion) were calculated for all the atom pairs and the calculated distances were then sorted into histogram with bin width (∆r) of 10 pm. g(r) was finally computed following the expression for the k-th bin: where N (k) AB is the number of distances that corresponds to the k-th bin, V is the volume of the system, N A and N B is number of atoms A and B in the system, respectively (e.g. number of oxygen atoms and Li + counterions), r (k) is the distance of the k-th bin for which g(r) is calculated.
Beyond depicting how the density of counterions varies with the distance of those conterions from the oxygen or sulfur atoms of PTAA, the g(r) functions can be also used to compute spatial averages of meaningful quantitities. One of such quantities is for example the 1/r 6 average which is related to the average dipolar coupling the different spins, which might be computed as: