Tailoring the Acidity of Liquid Media with Ionizing Radiation: Rethinking the Acid–Base Correlation beyond pH

Advanced in situ techniques based on electrons and X-rays are increasingly used to gain insights into fundamental processes in liquids. However, probing liquid samples with ionizing radiation changes the solution chemistry under observation. In this work, we show that a radiation-induced decrease in pH does not necessarily correlate to an increase in acidity of aqueous solutions. Thus, pH does not capture the acidity under irradiation. Using kinetic modeling of radiation chemistry, we introduce alternative measures of acidity (radiolytic acidity π* and radiolytic ion product KW*), that account for radiation-induced alterations of both H+ and OH– concentration. Moreover, we demonstrate that adding pH-neutral solutes such as LiCl, LiBr, or LiNO3 can trigger a significant change in π*. This provides a huge parameter space to tailor the acidity for in situ experiments involving ionizing radiation, as present in synchrotron facilities or during liquid-phase electron microscopy.

S2 S1.1 RELATION OF π * TO pH IN NON-IRRADIATED SOLUTIONS For non-irradiated solutions, the concentrations of H + and OHare coupled and their ratio depends on pH. The following equation is designed to be applied in non-irradiated solutions only, therefore it is avoided to call it the decadic logarithm of this ratio π * here.
This linear relationship is depicted in Figure S1. S1.2 RADIOLYTIC ACIDITY π * AT pH 7. The simulation for neat, aerated water under standard conditions (no radiation, 25 °C, pH 7) is shown in Figure S2. In this case, π * remains at positive values between 0.25 and 2 for all dose rates considered. This can be compared to non-irradiated solutions with pH of 6 -6.875. A π * of 1 can be considered neutral condition (i.e. the ratio of c(H + ) and c(OH -) of almost unity). A peak appears 1 kGy·s -1 with π * of about 2, yielding an acidic environment that can be compared to pH 6 in a non-irradiated environment.
The temporal evolution of these steady state concentrations is depicted in Figure S3.

S1.3 INELASTIC RADIATION-MATTER INTERACTIONS
Inelastic interactions between ionizing radiation and water trigger a relaxation cascade that is summarized in Figure S4 which is based on literature. 1,2 . First, the primary energy transfer and rapid electronic relaxation processes occur, causing excitation of high-energy molecular orbitals or molecule ionization in the temporal order of femtoseconds. This so-called 'physical stage' is highly irradiation dependent. The excited products now undergo further relaxation processes including dissociation and first ion-molecule interactions ('physico-chemical stage'). Figure S4: Illustration of inelastic radiation-matter interactions in water that is modeled using equations (5) and (6) in the main manuscript. According to literature. 1,2 . Afterwards, intermolecular interactions dominate the relaxation cascade, as excited energy states are mostly decayed. Hence, this is referred to as 'chemical stage'. A homogeneous distribution of primary species is achieved usually in the µs-range, which are now interacting with the surrounding liquid-phase environment based on the laws of solution kinetics. The ratio of these primary species is described by a set of G-values which are determined by the character of the ionizing radiation (Table S1).  S6 S1.6 DIFFERENT ADDITIVES In Figure S7 the concentrations of H + and OHfor initial concentrations of the anions Cl -, Brand NO3of 1 mM as well as 10 mM are compared against pure water (blue). Figure S8 displays the evolution of the radiolytic ion product relative to the respective value of pure water.

S1.7 IMPACT OF ALKALI METALS ON THE ACIDITY UNDER IRRADIATION
Albeit the standard potentials of Li + is slightly higher than the reductive potential of solvated electrons (see main manuscript), the difference is close to thermal energy. To demonstrate that its impact is negligible for the discussion within this work, we simulated an extreme case scenario, in which we assume the reactivity of Li + to be similar to the one of Na + . For the latter, Tesler and Schindewolf 5 measured a reduction by solvated electrons. They reported the reaction: Na + + eh -→ Na with a rate constant of 2·10 4 (Ms) -1 As decay, the reaction with H2O was given within the same manuscript as: 2 Na + 2 H2O → H2 + 2 Na + + 2 OHwith a rate constant of 1.5·10 9 (Ms) -1 Particularly the latter reaction has the potential to alter the acidity under irradiation. However, to simulate elementary steps only, the latter reaction was considered in the form of Na + H2O → H + Na + + OHwith a rate constant of 1.5·10 9 (Ms) -1 because the recombination of 2 H → H2 (Reaction 34 in Table S2) is more than five times faster than the value given here, so that the oxidation of Na was assumed to be rate-determining. By incorporating these proposed reactions (Table S6) we simulate the evolution of H + and OHsteady state concentrations of 10 mM solutions of pure Na + , NaBr, NaCl, and NaNO3 under 300 keV electron irradiation ( Figure S9). It is evident that Na + does not alter the obtained concentrations when considered as a hypothetical stand-alone reactant to pure water. This does not S9 change notably when more realistic scenarios (NaBr, NaCl, NaNO3) are regarded. Consequently, a change of Li + is likely to be negligible throughout all simulations within this manuscript.

S1.8 KINETIC MODELS
The following section comprises the reaction sets utilized for simulations shown in this work in tabular and graph network 6,7 format. The latter emphasizes the fundamental difference between irradiated and non-irradiated solutions.
The equilibrium chemistry of pure water is fully described by Equation (1) and shown in Figure 1, the reaction interplay is fully described in (a), while the generation of reactive species by irradiation (Eq. (5)) triggers a reaction cascade comprising 83 reactions and 17 species (b). A tabular representation is shown in Table S2. In addition, the chlorine set comprises 89 reactions and 19 new species (Table S3, Figure S10). Both are a subset of the reaction set used for aqueous HAuCl4 solutions introduced earlier 6 .