Understanding structure-activity relationships in linear polymer photocatalysts for hydrogen evolution

Conjugated polymers have sparked much interest as photocatalysts for hydrogen production. However, beyond basic considerations such as spectral absorption, the factors that dictate their photocatalytic activity are poorly understood. Here we investigate a series of linear conjugated polymers with external quantum efficiencies for hydrogen production between 0.4 and 11.6%. We monitor the generation of the photoactive species from femtoseconds to seconds after light absorption using transient spectroscopy and correlate their yield with the measured photocatalytic activity. Experiments coupled with modeling suggest that the localization of water around the polymer chain due to the incorporation of sulfone groups into an otherwise hydrophobic backbone is crucial for charge generation. Calculations of solution redox potentials and charge transfer free energies demonstrate that electron transfer from the sacrificial donor becomes thermodynamically favored as a result of the more polar local environment, leading to the production of long-lived electrons in these amphiphilic polymers.

Supplementary Figure 19. Images of contact angle measurement of P1, P7, and P10. The polymers were pressed into pellets with a press at 7 bar pressure between two 1.3 cm dies. Ultrapure water and 1:1 mixtures of water and methanol were used for the measurements. For all materials the contact angles against water/methanol/triethylamine were too low to be measured. We note that the contact angles with water cannot be directly compared to those with water/methanol due to differences in surface tension between the two solvents.    Table S12 other than a subtle inversion of the solvation energies of TEA/TEAR in water and TEA, probably related to an improved description of nonelectrostatic contributions to the solvation energies for these neutral species with small dipoles, which has a very minor effect on the reaction energies and potentials since those are dominated by the solvation energies of the charged species.  Figure 29). ϕ is the dihedral angle between C3, C4 on one monomer and C4, C3 on the next monomer with ϕ defined as 0 when dipole moments align. All constants are in units of kJ mol -1 .  Table 10. Partial charges on monomers of the three polymers used in the molecular dynamics simulations. They were found by calculating partial charges using the CHELPG population for oligomers in different conformations. The partials charges found were then averaged across conformation and monomer (to average edge effects). Minor alterations were then made to ensure a) symmetry was upheld and the b) each monomer was charge neutral, in line with other methods used in the literature 5 (as opposed to the alternative of distinguishing between edge monomers and central monomers 6

Dynamic light scattering methodology
The Brownian motion of each sample was characterized using an intensity correlation function , which compares the intensity at the detector at initial time t to the intensity at later times : Here is the electric field correlation function, the intensity at time t and the angular brackets represent the temporal average 7 . The field function can be expressed as the linear combination of a series of exponential terms: where and are respectively the amplitudes and decay rates for each exponential term in the series.
Each term in the summation correlates to scattering from particles of a different size. 8 All data were fit with single, double and triple exponentials (i=1-3) using OriginPro 2017. In all cases, single exponentials produced poor fits whilst triple exponentials overfitted the data. The data were also fit to sums of stretched exponentials, but this was found to have no significant effect on the extracted particle size. As the inclusion of stretch factors increases the number of fit parameters, a two-term normal exponential model was used to prevent overfitting of the data. 8 The mean hydrodynamic diameter of the dispersed particles (d) was then calculated from each correlation function decay rate using: 8 Here kB is Boltzmann's constant, T is temperature, η is the dynamic viscosity of the liquid medium, n is the solvent refractive index, λ is the incident laser wavelength and θ is the measured scattering angle. This equation was derived from the Stokes-Einstein relation for spherical particles along with the definition of the scattering vector magnitude q in our setup: and the relation between decay rate and translational diffusion coefficient . Extracted particle diameters from repeat measurements were then averaged to produce the values in Supplementary Table   2. The standard deviation of the spread of particle sizes was used to calculate the associated errors.

Atomistic molecular dynamics
Atomistic molecular dynamics (MD) simulations were carried out in the GROMACS package. 9-12 Forcefields, resulting torsional potentials and partial charge distributions are given below. The simulation workflow is illustrated below.
In fully atomistic MD simulations, state-of-the-art simulations deal with hundred of thousands of atoms with production run reaching 100 ns. Interchain interactions with itself (in other word with its periodic images) must be avoided. Therefore, a buffer of solvent of the order of the cut-off used in the force fields for non-bonded interactions must be used. One can easily see how the size of the simulation is scaling with the length of the oligomer. Larger boxes can be studied at the expenses of the length of the simulation; however as a result, the statistics will be poor and the ergodic theorem won't hold. Polymers are therefore especially challenging because of their size and the breadth of their relaxation times. As a consequence, it is common practice to simulate oligomers instead of polymers in fully atomistic MD simulations. Here, we use oligomers containing twelve aromatic rings (hexamers of FSM and P10, tetramers of P7) in mixtures of water and TEA, or of water, methanol and TEA.
All molecular dynamics were run in the following workflow, all at 300 K and 1 bar. When the simulation

Forcefields
The basis forcefield chosen for molecular dynamics was OPLS-AA. 13, 14 We then chose atom types within the OPLS set that most closely matches the local chemistry of the atoms in the oligomers of study. Carbon atoms in the phenyl groups were chosen to be equivalent to benzene ring carbons. The bridging carbon was chosen to be equivalent to the core carbon of neopentane. Sulfur and oxygen in P7 and P10 were chosen from the sulfone group in OPLS. All bond and angle utilized OPLS forces for those atom types with the average bond distance and angle taken from the DFT calculations performed. Dihedral interactions were fitted to DFT calculations. The water forcefield used was TIP4P, 15 methanol was the standard OPLS model for methanol. 4

Computational details of the potential calculations
We calculate the adiabatic IP, EA, IP*, and EA* potentials of the oligomer model P containing twelve phenylene equivalent units of a polymer using a ΔDFT approach from the Gibbs free energy difference (ΔGr) of the following four redox half-reactions, written, in line with convention, as reductions: P + + e --> P (1) P + e --> P - P + + e --> P * P * + e --> P - (4) where P -, P + , and P* are the polymer with an excess electron, hole and (singlet) exciton, respectively. The calculated ΔGr values are converted to reduction potentials E via: Here, F is the Faraday constant and n the number of electrons taking part in the half-reaction. In our calculations on oligomers, we furthermore equate ΔGr to the total energy difference, neglecting as discussed in the text the vibrational, translational and rotational contribution to the free energy. In previous work 16 on oligomers of P1, this was found to be a generally good approximation because of the relative similarity of the structures of P + , P − , P*, and P.
The calculated potential values are finally converted from the vacuum scale to that of the standard hydrogen electrode (SHE) by shifting them by the experimentally obtained value of the SHE absolute potential (SHEAP). A range of experimental SHEAP values have been proposed in the literature, something that is partly related to different possible choices for thermodynamic standard states and partly due to extra-thermodynamic assumptions. Here we use, in line with our previous work, the original IUPAC proposed value of 4.44 V. 17 Effects of the environment the polymer particles exist in during proton reduction are described using the The relevant solution half-reactions were predicted using a similar computational approach and setup as the polymer potentials, other than that in this case the vibrational, translational and rotational contribution to the free energy are not neglected. In contrast to previous work, protons are not modelled as isolated species but rather as adducts with TEA (TEAH + ), allowing us to predict potentials in other media than water.
All free energy of solution species finally include a standard state correction: Where R is the gas constant, T the temperature (293.15 K) and relevant C the standard state concentration;