Understanding Solution State Conformation and Aggregate Structure of Conjugated Polymers via Small Angle X-ray Scattering

Donor-acceptor (D-A) conjugated polymers are high-performance organic electronic materials that exhibit complex aggregation behavior. Understanding the solution state conformation and aggregation of conjugated polymers is crucial for controlling morphology during thin-film deposition and the subsequent electronic performance. However, a precise multiscale structure of solution state aggregates is lacking. Here, we present an in-depth small angle X-ray scattering (SAXS) analysis of the solution state structure of an isoindigo-bithiophene based D-A polymer (PII-2T) as our primary system. Modeling the system as a combination of hierarchical fibrillar aggregates mixed with dispersed polymers, we extract information about conformation and multiscale aggregation and also clarify the physical origin of features often observed but unaddressed or misinterpreted in small-angle scattering patterns of conjugated polymers. The persistence length of the D-A polymer extracted from SAXS agrees well with a theoretical model based on the dihedral potentials. Additionally, we show that the broad high q structure factor peak seen in scattering profiles can be attributed to lamellar stacking occurring within the fibril aggregates and that the low q aggregate scattering is strongly influenced by the polymer molecular weight. Overall, the SAXS profiles of D-A polymers in general exhibit a sensitive dependence on the co-existence of fibrillar aggregate and dispersed polymer chain populations. We corroborate our findings from SAXS with electron microscopy of freeze-dried samples for direct imaging of fibrillar aggregates. Finally, we demonstrate the generality of our approach by fitting the scattering profiles of a variety of D-A polymers. The results presented here establish a picture of the D-A polymer solution state structure and provide a general method of interpreting and analyzing their scattering profiles.

. Weight-averaged molecular weight distribution of low and high MW PII-2T Figure S2. Schematic of segment lengths and angles of the PII-2T repeat unit used for persistence length calculation. The three unique dihedral potentials are indicated in red, green, and blue. Table S1. Values of segments lengths and angles of the PII-2T repeat unit from DFT used for persistence length calculation. Angles correspond to the angle between the i-th and i-th + 1 segment.  Figure S3. Transmission SAXS of solid as-synthesized PII-2T showing a lamellar peak at = 0.25 Å -1 .

Section S1. Discussion of SAXS profiles for varying molecular weight and solvent
As discussed in the main text, we are able to infer the solution state structure by comparing the low/high molecular weight and CB/Dec solvent solutions and show that it is consistent with the picture of two elongated, semiflexible populations corresponding to the fibrillar aggregate and the dispersed polymer chains. The first feature discussed is the drastically different scattering at low where low MW solutions exhibit a semiflexible power law slope of ~-1.6 and high MW solutions have a steeper slope of -3.3. Looking at the low region of the high MW PII-2T solutions, we see that not only is the slope steeper at −3.3 but the Guinier knee at ~ 0.025 Å -1 is no longer visible. On an initial analysis, one may conclude that the aggregates for high MW PII-2T have become 3-dimensional in shape or that a Guinier knee may be hidden at ~ 0.02 Å -1 at the concave crossover in slope from −3.3 to −1.3 (similar to a Guinier knee for persistence length occurring at a crossover from −2 to −1). However, we conclude that this is not the case on the basis that a slope of −3 to −4 is indicative of interfacial Porod scattering which in this case indicates that the size of the aggregate is large enough to be outside the experimentalrange. Additionally, while the slope of −3.3 is somewhat close to −3 we note that this is the apparent slope and that since it becomes shallower with increasing the underlying slope contribution must in fact be steeper than −3.3, and is in fact closer to −4 as shown by the model fitting. Because the low scattering is due to Porod scattering, the crossover in slope from −3.3 to −1.3 at ~ 0.02 Å -1 is not due to a hierarchical structural change within a single particle but instead must be a result of the summation of two separate, independent contributions (the fibril aggregate and the dispersed polymer). This is in agreement with our previous conclusion that the high and low scattering features correspond to separate aggregate and polymer contributions.
Additionally, the presence of Porod scattering and the disappearance of the Guinier knee at ~ 0.025 Å -1 both point towards the notion that this Guinier does in fact correspond to the fibril aggregate and that it has likely shifted to the left outside the -range indicating the aggregates are simply larger for high MW PII-2T. This explanation is more plausible and also highly consistent with our imaging results. Finally, as a consequence of the aggregate Guinier knee shifting out of the -range, scattering from the polymer contribution at intermediate (0.03 to 0.1 Å -1 ) is no longer hidden and exhibits a power law slope of −1.3 which further confirms the idea that the high Guinier knee corresponds to the cross-section of a semiflexible polymer. In fact, the scattering profiles for high MW PII-2T are nearly identical in CB and Dec now that aggregate scattering is out of the -range and the polymer scattering is more visible, with the only difference being the lamellar peak in CB. Figure S4. Simulated scattering intensity of fibrils formed by 2D cylinder bundling with increasing diameter. The scattering profile ranges from a single cylinder (red) to a large fibril aggregate consisting of 50 cylinders (purple). The number of cylinders is indicated by the legend. As the fibril diameter increases the cross-sectional Guinier knee shifts to lower q until it is out of range and only contributes its trailing Porod region at low q. A structure factor peak emerges (indicated by arrow) as the cylinders aggregate as well. The length of the cylinders is larger than the fibril radius and its corresponding Guinier knee is out of range in all cases. *Note that due to the 2D nature of the simulation the power law slope of the Porod scattering is -3. For a real 3D system the power law slope would instead be ideally -4. Figure S5. AFM imaging of freeze dried (A) low and (B) high MW PII-2T from Dec. AFM linecuts (right) show that despite these features having widths of several 10's of nm, the heights are consistently ~2.5 nm corresponding to a single lamella. These features are therefore ribbonlike but are believe to be formed during the freeze-drying solution preparation as discussed below.

Section S2. Discussion of ribbon-like features in freeze-dried imaging of PII-2T in Dec
From our initial analysis of the scattering data we surmised that there exists two populations of scatterers, corresponding to an aggregate and dispersed polymer population, both of which appear to be elongated, semiflexible objects. Considering the imaging data, we can clearly see the presence of fibril aggregates in both CB and Dec as well as further agglomeration in Dec. These objects account for the low scattering features. What is interesting however is that we also observe elongated objects with AFM heights of ~2.5 nm and widths of approximately 50 nm. One notes that that this height of 2.5 nm is the same as both the lamellar stacking distance and the polymer diameter. Thus it appears these objects are ribbon-like consisting of pi-pi stacking to form a single lamella for its cross-section. From our initial analysis and discussion in the main text we were able to infer the existence of the dispersed polymer population based on the fact that a cross-sectional Guinier knee existed at high-q corresponding to ~2.5 nm with a power law slope of -1.3 preceding it in high MW data. Therefore, the existence of these ribbon-like objects gives rise to the questions: Does this cross-sectional Guinier knee that we previously ascribed to the dispersed polymer with a diameter 2.5 nm instead correspond to ribbon-like object with a single lamella thickness of 2.5 nm? And if not, why are they not reflected in the scattering profile? And do they really exist in solution?
First, we address the initial question. Asking whether the high Guinier knee corresponds to the dispersed polymer or the ribbon-like objects is similar to asking whether the knee corresponds to a small isotropic cross-section (2.5 nm) or the minor axis of a highly anisotropic cross-section (2.5 nm by 50 nm). Considering that the length is larger than the crosssectional dimensions in both cases, one can see that the power law slope preceding the crosssectional Guinier knee can be as shallow as -1 for the isotropic cross-section (as it can appear rod-like at length-scales just above the 2.5 nm diameter), but the power slope can only be as shallow as -2 for the highly anisotropic cross-section (as the ribbon object appears plate-like at length-scales just above the 2.5 nm minor diameter but below the 50 nm major diameter). This can also be seen quantitatively based on the calculated form factor of an elongated elliptical cylinder or an elongated parallelepiped having a cross-sectional axis ratio of 1 in the first case and a high ratio of 50/2.5 in the second case. Given that the experimental data shows that the power law just preceding the 2.5 nm knee has a slope of -1.3 it is impossible for this knee to correspond to the minor axis of a highly anisotropic cross-section and therefore the slope of -1.3 is much more reasonably ascribed to the semiflexbility of an elongated object with a cross-sectional aspect ratio closer to 1 (i.e. the dispersed polymer chains). This therefore affirms the picture we developed consisting of fibril aggregates and dispersed polymer chains which is accurate for CB and still applicable for Dec cases.
The next questions are then why do these ribbons not contribute to scattering in Dec cases and if they really exist in solution. Naturally, if these ribbon features do not exist in solution and are instead an artifact of the freeze-dried imaging process then they would not contribute to the solution scattering. We do not yet have a firm answer to these questions and this subject is of interest in our follow up works focusing on the solvent effect of D-A polymer scattering. Despite this, we do note several observations about the ribbon-like objects that brings their existence in the solution state into question. First, consider that during the freeze drying process one would expect that these ribbons exist in the 3D solution volume at random orientations (both the orientation of the long axis and the orientation rotating around the long axis) and then fall onto the substrate surface as the frozen decane is sublimated. One would then expect that when imaging the surface we would see 1) that the ribbons were frozen are different orientations around its long axis such that when fallen upon the substrate the measured heights of various ribbons ranges from the minor diameter to the major diameter (2.5 nm laying flat to 50 nm on its side) and 2) that we would observe overlapping of the ribbons producing nodes where the local thickness is 2 or more ribbons tall which should yield localized heights of 5+ nm in the case of overlapping ribbons both laying flat to ~100+ nm in the case of overlapping ribbons both on their sides. From our imaging of both low and high MW PII-2T in Dec we observe that both of these assertions are false as the peak heights are consistently around 2.5 nm at most, never approaching the major diameter of ~50 nm, and that even in regions where it appears that ribbons are overlapping the measured height is still around 2.5 nm. These observations are inconsistent with the idea that these ribbons exist in the solution state but are instead highly suggestive of surface-induced growth or adsorption of the polymers to the surface during solution preparation. Furthermore, we have observed these ribbon-like features in conjugated polymers solutions with other chlorinated solvents as well indicating it is not specific to Dec and appears to be present due to the sample preparation. Figure S6. Normalized UV-Vis spectroscopy of low and high MW PII-2T solutions in CB and Dec.

Section S3. SAXS theory
As a basis for our models we describe here the general theory for scattering of particle assemblies. The absolute scattering intensity for a dilute solution is where is the number of aggregates and is the volume of the solution. We refer to the scattering intensity as ( ) as absolute intensity calibration is not carried out in this work.
Ideally, a solution of dispersed particles has a scattering intensity of where is the number of primary particles within an aggregate, ( ) is the primary particle form factor and ( ) is the structure factor. In this work we define the form factor as ( ) = Δ 2 2 Σ( ) where Δ 2 is the contrast and Σ( ) is the shape function of the scattering particle such that Σ( = 0) = 1 (in other works this is sometimes referred to as the form factor instead).
The scattering amplitude of the particle is Therefore, in this work the form factor is ( ) = | ( )| 2 and the shape function is Σ( ) = Typically, a solution of homogeneously dispersed primary particles has an excess SLD of where the first term resembles the non-aggregated result but only pertains to the primary particles within the aggregate such that is the number of primary particles within the aggregate, ∞ ( ) is the structure factor of the primary particles within an infinite domain, and * represents the convolution operation. The second term corresponds to the aggregate where ′ ( ) denotes the form factor corresponds to the external shape without regard for internal structure. In the scattering amplitude approach this term derives from convolution of the form factor with the null scattering term that is typically neglected. The scattering intensity can be reduced and rewritten as We then apply this to describe the aggregated cross-section of the fibril consisting of polymer chain cross-sections. In this case, ( ) corresponds to the elliptical cross-section of the aggregated polymer and Σ ′ corresponds to the circular cross-section of the fibril. The elliptical cross-section has the shape function Σ , ( ; ) = ∫ [ 2 1 ( ) ] 2 2 0 where 1 ( ) is the first-order Bessel function and = ( 2 2 sin 2 + 2 cos 2 ) 1/2 with as the major radius and = / as the ratio of the minor radius to the major radius.
For a circular cross-section, the radius is constant and so the shape function simply becomes The aggregated cross-section is then multiplied by the semiflexible axial shape function. Strictly speaking the shape function of elongated objects comes from orientational integration of cross-sectional and axial terms coupled together. However, in the case where the length of the object is much larger than its diameter the function can be decoupled into a product of its cross-sectional and axial terms 35 . The result is then the first term of equation (5) in the main text. One can also use a rectangular cross-section for a semiflexible parallelepiped which should yield similar results to the semiflexible elliptical cylinder. Figure S7. Comparison between structure factors for cross-sectional aggregation within fibrils. Structure factor calculated using the particle assembly theory used in this work for a crosssection consisting of (A) 19 monodisperse cylinders of = 14 Å with = 0.5 and (B) 19 polydisperse cylinders of ̅ = 14 Å and = 0.3 with = 0.6 . The external fibril crosssection and internal structure factor contributions are shown in blue and red, respectively, and are shifted down by 1 decade. The overall structure factor is shown in black. (C) Structure factor for an explicitly positioned bundle of 19 hexagonally close-packed monodisperse cylinders of = 14 Å (solid line) compared to the monodisperse (dash) and polydisperse (dash-dot) structure factors from A and B. Each curve is shifted by a decade. Figure S8. SFC fits using a power law contribution for low and a pseudo-Voigt peak for high applied to High MW PII-2T in (A) CB and (B) Dec.