Pathway and Length Control of Supramolecular Polymers in Aqueous Media via a Hydrogen Bonding Lock

Abstract Programming the organization of π‐conjugated systems into nanostructures of defined dimensions is a requirement for the preparation of functional materials. Herein, we have achieved high‐precision control over the self‐assembly pathways and fiber length of an amphiphilic BODIPY dye in aqueous media by exploiting a programmable hydrogen bonding lock. The presence of a (2‐hydroxyethyl)amide group in the target BODIPY enables different types of intra‐ vs. intermolecular hydrogen bonding, leading to a competition between kinetically controlled discoidal H‐type aggregates and thermodynamically controlled 1D J‐type fibers in water. The high stability of the kinetic state, which is dominated by the hydrophobic effect, is reflected in the slow transformation to the thermodynamic product (several weeks at room temperature). However, this lag time can be suppressed by the addition of seeds from the thermodynamic species, enabling us to obtain supramolecular polymers of tuneable length in water for multiple cycles.


Isodesmic Model 4
The self-assembly of A is described using the isodesmic model. This model assumes that the aggregates are noncyclic and one dimensional. The reversible non-covalent binding doesn't occur any change for each growing step therefore the reactivity of the end groups is equivalent during this process. According to that the equilibrium constants and Gibbs free energy changes are identical for each step, too.

Temperature-dependent Isodesmic Model.
The temperature-dependent data was fitted to the isodesmic model by using the Boltzmann equation. The number-averaged degree of polymerization DP N (T) is obtained from α agg (T) via: The degree of polymerization is related to the equilibrium constant by equation 8.
and 8 combined, depict the Relationship of DP N to the equilibrium constant K and the total concentration of molecules c T via:

Nucleation-Elongation model for Cooperative Supramolecular Polymerizations
The equilibrium between the monomeric and supramolecular species can be described in a cooperative process with the Nucleation-Elongation model developed by Ten Eikelder, Markvoort and Meijer 5,6 . This model is used to describe the aggregation of B which exhibits a non-sigmoidal cooling curve, as shown in the fluorescence and UV-Vis temperature-dependent experiments. The model extends nucleation-elongation based equilibrium models for growth of supramolecular homopolymers to the case of two monomer and aggregate types and can be applied to symmetric supramolecular copolymerizations, as well as to the more general case of nonsymmetric supramolecular copolymerizations.
In a cooperative process, the polymerization occurs by a nucleation step, with a nucleus size assumed of 2, and a following elongation step. The values T e , ΔH°n ucl , ΔH° and ΔS° can be found by a non-linear least-square analysis of the experimental melting curves. The equilibrium constants associated to the nucleation and elongation phases can be calculated using equations 11 and 12:

Denaturation model 7
The denaturation model is based on the concentration-dependent supramolecular polymerization equilibrium model by Goldstein,8 whereas the polymerization is described as a sequence of monomer addition equilibria.
Both sums are evaluated by using standard expressions for converging series: and c tot: the total monomer concentration The sum solved by standard numerical methods (Matlabfzerosolver) results in the dimensionless monomer concentration .
Considering that every species with > 1 is defined as aggregate, the degree of aggregation results in: ) the denaturation curves can be obtained with f defined as volume fraction of good solvent: ∆ 0, = ∆ 0 + It is assumed that the cooperativity factor is independent of the volume fraction and the m value involved in the elongation equals the m value involved in the nucleation. The denaturation data need to be transformed into the normalized degree of aggregation, if fitted to the supramolecular polymerization equilibrium model: The optimization of the four needed parameters (∆G 0 , m, σ and p) to fit the equilibrium model to the experimental data (normalized degree vs f) is done by the non-linear least-squares analysis using Matlab (lsqnonlinsolver). The data is then fitted with the non-linear least squared regression (Levenberg-Marquardt algorithm).

Thermodynamic Parameters
The thermodynamic Parameters for A and B (Table S1-3) were obtained by fitting the respective experimental data to the denaturation [a] , isodesmic [b] and nucleation-elongation [c] model.

Fluorescence Quantum Yields
The fluorescence quantum yields for 1, A and B were calculated using Rhodamine 101 (MeOH) as standard (Φ ref = 1.0) and using the following equation:

Φ = Φ
A: Absorption (set under 0.1) for reference and sample I: Integral of emission-peak for reference and sample     We performed VT absorption and emission studies of A and B ( Figure S5). Due to the high stability of aggregate A and B in aqueous solutions, even at high temperature and very dilute conditions (2.5 M), the addition of 12 vol% THF is required to reach the monomer state.

Semiempirical calculations at the dispersion-corrected PM6 level in vacuum
Cooling a water/THF (88/12) solution at 2.5 M from 340 K to 273 K induces the formation of the characteristic absorption spectrum of aggregate A (Figure S5a-b). This process follows the isodesmic mechanism, in the same manner as also observed in denaturation studies (Figure 3 and S4). VT emission studies using the same conditions exhibit the quenching of the monomer emission band upon cooling with the simultaneous rise of new aggregate bands at around 593 nm and 630 nm ( Figure S5e). The thermodynamic analysis of these parameters calculated from these experiments yields a higher free Gibbs energy (-32.4 kJmol -1 ) than the values obtained from denaturation studies (Figure 3, Table S2). This is justified considering the use of 12 vol% THF in VT studies, which is lowering the aggregation tendency.
On the other hand, for the mechanistic investigations of B, heating experiments were employed, as cooling of the monomer solution preferentially forms aggregate A, even at very low cooling rates of 0.1 Kmin -1 (Figure S5a-b). Because of this retarded formation of B in comparison to A, heating ramps of already transformed B had to be used to monitor the full disassembly process. For VT UV-Vis, the same spectral transition as in denaturation studies is observed ( Figure S5). The VT emission of B exhibits the disappearance of the two aggregate bands at 580 nm and 630 nm and the emergence of the monomer band upon heating ( Figure S5g). Analysis of both experiments and fitting to the nucleation elongation model yielded thermodynamic parameters that are indeed also lower than denaturation studies (-43.5 kJmol -1 ). However, comparison to the VT studies of A, which were performed with the same THF content, supports the higher stability of aggregate B ( Figure S5h, Table S3).
The high nucleation penalty of B, which needs to be overcome during heating, is also reflected in the different values of elongation temperatures (T e = 4K) obtained using different spectral methods. Emission studies exhibit increased T e values in comparison to absorption studies, as the former method is far more sensitive and is able to monitor this nucleation process ( Figure S5h).  After finding the appropriate experimental conditions (10 vol% THF, 25 °C or 40 °C), the kinetics of this transformation were monitored at different concentrations using UV-Vis and emission spectroscopy ( Figure S7). For these studies, we ensured that the selected temperatures always lie below the elongation temperature using 10 vol% of THF in water ( Figure S7e). Aggregate B is prone to form larger structures, which can be broken by roughly shaking, sonicating or stirring the solution, leading to more active polymer ends (faster transformation times, Figure S6-7). Another reasonable explanation is the sedimentation of these large structures. This is also apparent in Figure S8b, where at around 3000 minutes a sudden increase of the molar extinction coefficient () is induced by roughly shaking the cuvettes.      , obtained by SLS studies and corresponding fit to the Guinier Plot) to unravel the differences in morphology. Note that 1 vol% THF has been used for DLS studies and soft phase of THF may also lead to an increased scattering signal, which can influence the results. However, for the kinetic species (A), the differences in comparison to this ideal system (D g = 1.61 D H ) support the discoidal morphology, as found by AFM studies. For the thermodynamic species B, even larger differences between both values are achieved (D g = 3.53 D H ), which points to the transformation to more anisotropic 1D structures, which is also in agreement with the AFM studies.    J-type seeds were prepared by continuous sonication for 10 minutes. In contrast to the fibrous network of Agg B, the seeds of B exhibit a discoidal shape (Fig S21a-b). After 52 minutes, no changes in absorption for the J-seeds is detected ( Figure S20a), and the living supramolecular polymerization was initiated by injection of the kinetically controlled aggregate A in a ratio of 1/1 (v/v). By plotting the maximum of aggregate A (530 nm) vs. time, the completion of the consumption of the monomer reservoir was observed ( Figure 6). The elongation of Agg B at the expense of Agg A is finished after 31 minutes leading to small rods with an average size of 111  24 nm. For the next cycles, the repeated addition of Agg A was performed at the same 1/1 (v/v) ratio. In this manner, the active ends (Seeds B) are diluted every cycle (cycle 0: 1:0, cycle I: 1:1, cycle II: 1:3, cycle III: 1:7, cycle IV: 1:15 (B-seeds/used kinetic Agg A), which in turn leads to a deceleration of the polymerization rate (Figure 6, S10) and further controlled continued elongation of Agg B (Figure 6, S20-22). The length of 25 fibers was extracted from Figure S21-22 to calculate the average size obtained each cycle:    Note that 1 vol% THF has been used for DLS studies and soft phase of THF may also lead to an increased scattering signal, which can influence the results.