Transient Acid pH Effect in Tracks in The Radiolysis of Water: Does This Effect Contribute to Biological Damage Caused by Ionizing Radiation?

    

    

    Figure 2:  Time evolution of the yield (in molecule/100 eV) of hydrogen ions
for the radiolysis of pure, deaerated liquid water by 300- and 0.15-MeV
incident protons (LET ~ 0.3 and 70 keV/μm, respectively) at 25 °C from ~1
ps to 1 ms. The solid and dashed lines show the corresponding values of
G(H3O+) obtained from our Monte Carlo simulations (see text). Experimental
data for 60Co γ/fast electron (~0.3 keV/μm) irradiation: (□) [30], (▼) [31], (?)
[32], (●) [33], and (○) [34]. There are no experimental data available for 0.15-
MeV irradiating protons with which to compare our results.
    
    

H₃O⁺ + OH- → 2H₂O k₆ = 1.18 × 10¹¹ M^-1 s^-1 (6)

H₃O⁺ + e^- _aq → H• + H₂O k₇ = 2.13 × 10¹⁰ M^-1 s^-1 (7)

where k₆ and k₇ are the rate constants for the two individual reactions [13,28]. The time dependence of the cumulative yield variations ΔG (H₃O⁺) for the different reactions that contribute to G (H₃O⁺) (data not shown here) confirms that the decrease of G (H₃O⁺) at long times is predominantly due to reaction (6) in the stage of homogeneous chemistry. To our knowledge, there are no experimental data of G (H₃O⁺) available for 0.15-MeV irradiating protons with which to compare our results. In this case, our simulations show that the decay of H₃O⁺ with time still largely results from reactions (6) and (7), although there is also a relatively small contribution due to the following reactions [13,28].

H₃O⁺ + O•- → •OH + H₂O k8 = 5 × 1010 M-1 s-1 (8)

H₃O⁺ + HO2 - → H₂O2 + H₂O k9 = 5 × 1010 M-1 s-1 (9)

however, as shown in Figure. 2, the decrease in G (H₃O⁺) occurs as early as ~102 picoseconds up to microseconds, which is clearly different from what is observed for irradiation with 300-MeV incident protons (which mimic ⁶⁰Co γ/fast electron irradiation). As expected, this is consistent with differences in the initial spatial distribution of primary transient species (i.e., in the track structure). As mentioned earlier, in the track (columnar) geometry of the higher-LET 0.15- MeV irradiating protons, the reactive intermediates are formed locally in much closer initial proximity than in the spur (spherical) geometry, which favours the incidence, at shorter time scales, of an increased amount of intervening intra-track reactions.

With the objective of calculating the pH values prevailing in the spur/track regions, we now need to estimate the concentrations of H₃O⁺ generated in situ in these regions as a function of time. Two models are considered depending on the quality (LET) of the radiation.

For 300-MeV incident protons (LET ~ 0.3 keV/μm), we assume that the hydronium ions are produced evenly in an isolated spherical spur whose initial radius r_o (prior to spur expansion) is equal to the average electron thermalization distance obtained from our simulations (r_o = 11.7 nm) [23]. The low-LET spur concentrations of H₃O⁺ are derived from

$\left[{\text{H}}_3{\text{O}}^{+}\right]\left(t\right)=\text{G}\left({\text{H}}_3{\text{O}}^{+}\right)\left(t\right)\times \left(\frac{\text{Mean energy loss/event}}{\frac{4}{3}\pi r{\left(t\right)}^3}\right)\text{ (10)}$

where the mean energy loss in a single event (i.e., the mean energy deposited in a spur) is taken to be ~47 eV [21,28,35] and

r(t)² = r_o ² + 6 D t (11)

represents the change with time of r_o due to the (three dimensional) diffusive expansion of the spur. Here, t is time and D is the diffusion coefficient of H₃O⁺ in water (D = 9.46 × 10^-9 m² s^-1 at 25 °C) [17,22].

For 0.15-MeV irradiating protons (LET ~ 70 keV/μm), we consider the track as being a cylinder, homogeneous along its axis, of length L = 1 μm and initial radius rc equal to the radius of the physical track “core” (which corresponds to the tiny radial region within the first few nanometers around the impacting ion path, at ~10^-13 s) [8,36]. In this case, the high-LET track concentrations of H₃O⁺ can be obtained from [9].

$\left[{\text{H}}_3{\text{O}}^{+}\right]\left(t\right)=\text{G}\left({\text{H}}_3{\text{O}}^{+}\right)\left(t\right)\times \left(\frac{\text{LET}}{\pi r{\left(t\right)}^2}\right),\text{ (12)}$

Where

r(t)² = r_o ² + 4 D t (13)

represents the change with time of r_c due to the (two dimensional) diffusive expansion of the track. Here, r_c was obtained from our simulations [29] and is taken to be ~25 nm.

Using Eqs. (10) and (12) readily gives the concentrations of H₃O⁺ as a function of time for both isolated “spherical” spurs and axially homogeneous “cylindrical” tracks. The pH in the corresponding spur/track regions is then simply given by the negative logarithm of [H₃O⁺]:

$\text{pH}\left(t\right)=-\log \left\{\left[{\text{H}}_3{\text{O}}^{+}\right]\left(t\right)\right\}.\text{ (14)}$

The time evolution of the pH values calculated as indicated above for 300- and 0.15-MeV incident protons in pure, deaerated liquid water (LET ~ 0.3 and 70 keV/μm, respectively) using the spherical spur and cylindrical track models at 25 °C is shown in Figure. 3. As can be seen, for both radiations considered, there is an abrupt transient acid pH effect at times immediately after the initial energy release. This effect, which we call an “acid spike” in analogy with the “thermal spike” used in radiation chemistry to describe the formation of a transient excess temperature region around the tracks of high-LET accelerated heavy ions [14,37], is found to be greatest for times shorter than ~1 ns. In this time range, the pH remains nearly constant, equal to ~3.3 in spherical spurs and ~2.5 in cylindrical tracks. Beyond ~1 ns, the pH increases gradually for the two cases studied, ultimately reaching a value of 7 (neutral pH) at ~1 μs for the spherical spur geometry (corresponding to the end of spur expansion and the beginning of homogeneous chemistry [9-12]) and at a somewhat longer time (~0.1 ms) for the cylindrical track geometry.

    

    

    Figure 3:  Variation of pH with time calculated for 300-MeV incident protons
(LET ~ 0.3 keV/μm) using the isolated “spherical” spur model (solid line),
characteristic of low-LET radiation, and for 0.15-MeV incident protons (LET ~
70 keV/μm) using the axially homogeneous “cylindrical” track model (dashed
line), characteristic of high-LET radiation, at 25 °C from ~1 ps to 1 ms (see
text).