Fundamentals of Water Radiolysis

Definition

Radiolysis of water and aqueous solutions refers to the decomposition of water and its solutions under exposure to ionizing radiation, such as γ-rays, X-rays, accelerated particles, or fast neutrons. This exposure leads to the formation of highly reactive species, including free radicals like hydroxyl radicals (^●OH), hydrated electrons (e⁻_aq), and hydrogen atoms (H^●), as well as molecular products like molecular hydrogen (H₂) and hydrogen peroxide (H₂O₂). These species may further react with each other or with solutes in the solution. The yield and behavior of these radiolytic products depend on various factors, including pH, radiation type and energy, dose rate, and the presence of dissolved solutes such as oxygen or ferrous ions, as in the case of the ferrous sulfate (Fricke) dosimeter. Aqueous radiation chemistry has been pivotal for over a century, driving advancements in diverse fields, including nuclear science and technology—particularly in water-cooled reactors—radiobiology, bioradical chemistry, radiotherapy, food preservation, wastewater treatment, and the long-term management of nuclear waste. This field is also vital for understanding radiation effects in space.

1. Introduction: Some History

Radiation chemistry research focuses heavily on water and aqueous solutions, emphasizing their critical importance in biological systems and a variety of practical applications. This research spans fundamental scientific aspects and extends into areas such as nuclear science and technology—especially in water-cooled nuclear power reactors, where controlling radiolytic processes is crucial to prevent deleterious (corrosion) effects, radiation effects in space, radiotherapy, diagnostic radiology, and the long-term environmental management of nuclear waste materials (for a selection of articles and books published since 1980, see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]). Additionally, water is the standard reference material in clinical radiation therapy, chosen for its ionizing radiation absorption properties, which closely mimic those of biological tissue [31].

Water radiolysis, the decomposition of water under ionizing radiation, has been an active research area for over a century. In fact, it is known that only a few months after the discovery of X-rays by Wilhelm C. Röntgen at the University of Würzburg, Germany, natural radioactivity was, in turn, discovered in February–May 1896 by Henri Becquerel in Paris. Following this, polonium [32] and radium [33] were identified in 1898 by Pierre and Marie Sklodowska Curie, along with Gustave Bémont. The Curies and Becquerel were awarded the Nobel Prize in Physics in 1903 for these discoveries. Early observations by Curie and Debierne [34], Giesel [35,36], and Ramsay and Soddy [37] revealed that dissolved radium salts continuously decompose aqueous solutions, releasing hydrogen and oxygen gases primarily due to the emission of α-particles from radium, a process Marie Curie [38] compared to “electrolysis without electrodes”. Notably, the pivotal experiment by Rutherford and Royds [39] providing direct evidence that alpha particles are ionized helium atoms dates from 1909.

Various other studies on the gaseous emissions resulting from the action of radon on water were subsequently conducted by Ramsay and Cameron [40,41] and by Usher [42]. These authors demonstrated that α-particles are primarily responsible for the observed chemical effects. Conversely, Kernbaum [43] found that X-rays do not produce any observable gas release under similar conditions, a finding later corroborated by Risse [44] and Fricke and Brownscombe [45]. In fact, it is now well established that α-rays induce the radiolysis of water into measurable stable products, whereas X-ray-induced radiolysis in the absence of air is notably weak due to significant and rapid reverse reactions.

Most importantly, André Debierne [46], in 1914, first suggested that water radiolysis produces hydrogen atoms (H^●) and hydroxyl radicals (^●OH), a hypothesis that predated the general acceptance of such reactive intermediates by about 30 years. Debierne proposed, “On peut supposer que chaque molécule d’eau est décomposée en un atome H et un radical hydroxyl OH, deux atomes d’hydrogène se soudant pour faire une molécule d’hydrogène, et deux radicaux hydroxyls donnant lieu à la production d’une molécule d’eau oxygénée” [One can suppose that each water molecule is decomposed into one hydrogen atom and one hydroxyl radical OH, with two hydrogen atoms bonding to form a hydrogen molecule, and two hydroxyl radicals resulting in the production of a hydrogen peroxide molecule]. Such an interpretation, founded in solid principles, was overlooked for years until Risse [47], the group led by M. Burton and J. Franck (see, e.g., [48,49]), and Weiss [50] independently stated it.

With these brief reminders in mind, we direct readers to comprehensive historical accounts of aqueous radiation chemistry published in the last few decades [51,52,53,54,55,56,57,58,59,60] for further details.

This review investigates the effects of ionizing radiation on water and dilute aqueous solutions, starting with the basics of water radiolysis. Given the breadth of this topic and space limitations, a comprehensive analysis is beyond the scope of a single manuscript. Instead, we provide a concise assessment of key parameters, including pH, radiation type and energy, dissolved solutes (e.g., oxygen), and dose rate. The review concludes with an examination of the radiolysis of the ferrous sulfate (Fricke) dosimeter under various experimental conditions. Much of the content aligns with the curriculum of the author’s graduate-level Introduction to Radiation Chemistry course at the Université de Sherbrooke.

2. Fundamentals of Water Radiolysis

2.1. Radiolysis of Pure, Deaerated Water: Time Scale of Events and Formation of Primary Radical and Molecular Products

In condensed phases like liquid water, the initial products of radiolysis—including water cations (H₂O^●+), excited water molecules (H₂O*, where the asterisk * denotes an excited state), and ejected secondary electrons—are produced during the “physical” stage of radiation action [61,62]. The uncertainty principle (Δt.ΔE~ħ) determines the minimum time required for events involving specific energy transfers. For instance, producing a 100-eV event takes about 10⁻¹⁷ s, while generating a 10-eV event takes around 10⁻¹⁶ s (1 eV ≈ 1.602 × 10⁻¹⁹ J) [7]. Furthermore, ionization of the inner K-shell of an oxygen atom, which requires approximately 532 eV, can lead to the emission of Auger electrons [11,23]. This process, combined with subsequent molecular interactions, can result in the formation of doubly ionized water cations (H₂O⁺⁺). Due to their high energetic and chemical instability, these species undergo a rapid sequence of reactions and rearrangements during the subsequent “physicochemical” stage, which lasts up to ~10⁻¹² s (1 picosecond) after the initial energy deposition.

When ionized into H₂O^●+, water molecules become highly unstable. With a very short lifetime of ~50 × 10⁻¹⁵ s (50 femtoseconds) [63], they can undergo random migration through a series of resonant electron transfers—about 20, on average—spanning a few molecular diameters [64,65]. These transient H₂O^●+ radical cations subsequently decompose through a pseudo-first-order proton transfer reaction with a neighboring H₂O molecule, producing hydronium ions (H₃O⁺ or H⁺_aq) and hydroxyl radicals (^●OH):

H₂O^●+ + H₂O → H₃O⁺ + ^●OH.

(1)

At this stage, secondary (or “dry”) electrons—initially produced in large quantities (~10⁴ electrons per MeV of deposited energy) with kinetic energies predominantly below ~50–100 eV [18,66,67,68]—gradually slow down to subexcitation levels (below ~7.3 eV, the first electronic excitation threshold of water [69]) and eventually reach thermal energies (~0.025 eV at 25 °C). As thermalization nears, the ejected electron may quickly localize and become trapped in a pre-existing potential energy well of suitable depth within the liquid, forming a “wet” or “incompletely relaxed” electron [3,16,70]. The precise physicochemical properties of this wet electron are still being investigated. This precedes its transition to a fully relaxed, hydrated state (e⁻_aq) within about 240 fs to 1.3 ps [71,72,73,74], as nearby molecular dipoles reorient in response to the electron’s negative charge [75,76,77]. In liquid water at 25 °C, thermalization, trapping, and hydration then proceed in quick succession [16]:

e⁻ → e⁻_sub → e⁻_th → e⁻_tr → e⁻_aq.

(2)

As the ejected electron slows down, it may be temporarily captured resonantly by a water molecule to form a transient molecular anion. This anion primarily dissociates into H⁻ and ^●OH according to

e⁻ + H₂O → (H₂O^●−)* → H⁻ + ^●OH,

(3)

followed by a rapid proton transfer reaction, where the hydride ion reacts with another water molecule:

H⁻ + H₂O → H₂ + OH⁻.

(4)

Reaction (4), referred to as the “dissociative electron attachment” (DEA) process [78], was initially observed in condensed amorphous water at ~20 K for electron energies between 5 and 12 eV, with the maximum H⁻ desorption yield occurring around 7.4 eV [79].

Additionally, low-energy “dry” secondary electrons can also be recaptured by their short-lived H₂O^●+ parent cations through Coulomb attraction, resulting in the formation of excited water molecules:

e⁻ + H₂O^●+ → H₂O* (electron–cation “geminate” recombination)

(5)

This recombination occurs only with electrons formed near the parent water cation and happens during the initial steps of their random walk [80]. Reaction (5) must occur prior to the H₂O⁺ cation undergoing reaction (1), specifically within a timescale of ~50 fs [63].

Excited water molecules can be formed either directly through an initial event [23] or via the neutralization reaction (5). Currently, the decay pathways of excited water molecules in the liquid phase and their associated branching ratios remain poorly understood. Nonetheless, the influence of water’s excited states on the primary radical and molecular products during water radiolysis is relatively minor compared to ionization processes. Consequently, the limited understanding of these states has only a minimal impact. As a result, the deexcitation mechanisms of H₂O* are generally assumed to closely resemble those observed in isolated water molecules, as described below (see, e.g., [23,65,81]):

H₂O* → H^● + ^●OH

(6)

H₂O* → H₂ + O(¹D)

(7)

H₂O* → 2H^● + ^●O^●(³P)

(8)

H₂O* → H₂O + release of thermal energy

(9)

Here, O(¹D) and ^●O^●(³P) refer to oxygen atoms in their singlet ¹D first excited state and triplet ³P ground state, respectively. Notably, O(¹D) atoms produced in reaction (7) possess a high-energy state and react efficiently with water, forming H₂O₂ or potentially 2^●OH [82,83]. In contrast, ^●O^●(³P) atoms produced in reaction (8) exhibit low reactivity with water but readily react with a broad range of organic and inorganic additives in aqueous solutions [84].

An excited water molecule with energy exceeding ~6.5 eV can also undergo decomposition through a “photoionization” process [70,71,72,85,86,87], resulting in the production of a hydrated electron and a water cation, as shown in the reaction

H₂O* → e⁻_aq + H₂O^●+ (threshold at ~6.5 eV)

(10)

The produced H₂O^●+ cation may then participate in further reactions, such as reaction (1).

It is worth noting that DEA [reactions (3) and (4)] and the decomposition of excited water resulting from the geminate recombination of the dry electron with H₂O^●+ [reactions (5) and (7)] have been proposed as key mechanisms for molecular hydrogen production during the early stages of liquid water radiolysis [65,78,88,89,90,91,92,93]. Experimental evidence strongly supports these mechanisms, indicating that the traditionally accepted “nonscavengeable” H₂ yield [94]—which cannot be removed by scavenger experiments—originates from precursors of e⁻_aq and can be significantly reduced by high concentrations of appropriate dry-electron scavengers [15]. However, the exact source of H₂ from water radiolysis at early times continues to be a subject of ongoing debate [95,96].

Another interesting aspect is that a thermalized electron, once trapped in the liquid, can engage in chemical reactions due to its localized nature before fully relaxing into the e⁻_aq state (see, e.g., [97,98,99,100,101]). One such reaction is [102]

e⁻_tr + H₂O → H^● + OH⁻.

(11)

This reaction would occur on a timescale comparable to electron hydration, competing with it and providing a novel pathway for generating an “initial” yield of H^● atoms in water. At these early times, the primary source of atomic hydrogen in water radiolysis is typically the dissociation of excited water molecules, as indicated by reactions (6) and (8).

Finally, regarding the doubly charged cation H₂O⁺⁺ left after Auger emission, it is generally believed to dissociate in solution through a two-step process involving sequential deprotonation reactions (see, e.g., [23,68,103] and cited references), namely,

H₂O⁺⁺ + H₂O → H₃O⁺ + OH⁺,

(12)

quickly followed by

OH⁺ + H₂O → H₃O⁺ + O(³P)

(13)

By ~1 ps, the various “initial” radiolysis products formed in pure, deaerated water include e⁻_aq, H₃O⁺, OH⁻, H^●, ^●OH, H₂, H₂O₂, O(¹D), ^●O^●(³P), O^●−, and others, with H₃O⁺, e⁻_aq, and ^●OH being produced in the highest concentrations. This moment marks the onset of the “chemical” stage, during which these reactive species begin diffusing away from their original formation sites. Notably, at this stage, all radiolytic species are spatially distributed within a distinct, highly nonhomogeneous “track structure” that strongly depends on the type and energy of the radiation—often referred to as “radiation quality” (see, e.g., [5,16,17,23,53,104,105,106]). This distribution is quantified by the “linear energy transfer” (LET), also known as “stopping power”, denoted by (–dE/dx). Usually, LET values are expressed in units of keV/μm [16,107].

For radiations with low LET—such as Compton electrons from ⁶⁰Co γ-rays, fast electrons (e.g., MeV), or a few hundred MeV protons with typical LET values around ~0.3 keV/μm—and in the absence of dose-rate effects (i.e., no track interactions), the initial track structure is composed of small, well-separated Magee-type “spurs” (clusters of radiolytic species with a nearly spherical shape) along the radiation path [16,108,109,110]. At this stage, radiolysis is primarily characterized by diffusion processes governed by Fick’s macroscopic diffusion laws and the chemical reactions among reactive species as the tracks evolve over time. At room temperature, track expansion effectively concludes when spurs merge through diffusion, about 0.2 microseconds after the initial ionization event [111]. At this point in time, the radiation track structure has dissipated, and the species escaping spur/track reactions are homogeneously distributed throughout the solution. The main reactive species existing at homogeneity include e⁻_aq, H^●, and ^●OH (the “radical” products) along with H₂ and H₂O₂ (the “molecular” products) [1,2,5,7,13,20,53]. These species are traditionally referred to as “primary” species, although this designation can be somewhat misleading, since they themselves result from a complex sequence of reactions involving species that existed prior to them [112]. Some authors [113], however, have used the term “primary” in the sense that these species are produced directly within the radiation track itself. Their yields, also known as “primary” or “escape” yields, are denoted by the lowercase symbols g(e⁻_aq), g(H^●), g(^●OH), g(H₂), and g(H₂O₂). These yields measure the number of each species formed or consumed per 100 eV of absorbed radiation energy, remaining available after spur/track expansion to react with added solutes in dilute aqueous solutions [114]. Observed or final radiation chemical yields are always denoted by the uppercase form G(X) and reported in these units. Additionally, using “molecules per 100 eV” as a unit for yields is more insightful than SI units (mol/J). In these so-called “old” units, the yield of a given species offers a good measure of the actual average number of that species present within a spur. This is particularly relevant given that the average energy deposited in a spur is about 50 to 100 eV [18,66,67,68]. For this reason, the author prefers these units and advocates for their continued use. However, for those who prefer SI units, the conversion relationship is given by 1 molecule/100 eV ≈ 0.10364 μmol/J [53].

Finally, beyond a few microseconds, reactions in the bulk solution can generally be described using conventional homogeneous chemistry methods (see, e.g., [115]). The time scale for various processes involved in the low-LET radiolysis of deaerated water is illustrated in Figure 1.

The radiolysis of pure deaerated (air-free) liquid water can be described by the following global equation (denoted by the symbol ~~->), written for an absorbed energy of 100 eV [23,53]:

g(–H₂O) H₂O ~~-> g(e⁻_aq) e⁻_aq + g(H^●) H^● + g(H₂) H₂ + g(H₃O⁺) H₃O⁺ + g(OH⁻) OH⁻ +
+ g(^●OH) ^●OH + g(H₂O₂) H₂O₂ + …,

(14)

where the coefficients g(X) represent the “primary” radical and molecular yields. At this stage, g(–H₂O) indicates the yield associated with water decomposition. For ⁶⁰Co γ-rays (photons with energies of 1.17 and 1.33 MeV) or fast electrons of similar energies in neutral water at 25 °C, the reported primary yields, expressed in molecules per 100 eV, are (see, e.g., [1,5,7,17,20,117,118,119,120])

g(e⁻_aq) = 2.65          g(H^●) = 0.60          g(H₂) = 0.45
g(^●OH) = 2.80 g(H₂O₂) = 0.68        g(–H₂O) = 4.15.

(15)

These yields, which remain pH-independent over the range of ~3–11 [2,6,11,119,121,122,123], are governed by the following electroneutrality and material balance relationships:

g(e⁻_aq) + g(OH⁻) = g(H₃O⁺)

(16)

g(–H₂O) = g(e⁻_aq) + g(H^●) + 2g(H₂) = g(^●OH) + 2g(H₂O₂).

(17)

Finally, it is important to note that molecular hydrogen, produced by radiolysis, is a gas that is largely chemically inert and tends to escape readily from the solution [124]. In this instance, oxygen can also be produced by low-LET radiation, though indirectly, as a secondary and minor radiolytic product through the following reactions [20,125]:

^●OH + H₂O₂ → HO₂^● + H₂O          k = 2.9 × 10⁷ M⁻¹ s⁻¹ at 25 °C

(18)

followed by

^●OH + HO₂^● → O₂ + H₂O

(19)

and

HO₂^● + HO₂^● → O₂ + H₂O₂.

(20)

When H₂ is retained in the solution, as in water-cooled nuclear reactors where extra H₂ is added to the coolant to prevent corrosion of in-core components (see, e.g., [20,29,58,126] and references therein), it reacts with the oxidizing radical ^●OH as follows:

^●OH + H₂ → H₂O + H^●

(21)

with a rate constant of k = 3.9 × 10⁷ M⁻¹ s⁻¹ at 25 °C [20], 8.0 × 10⁸ M⁻¹ s⁻¹ at 300 °C [127], and 1.5 × 10⁸ M⁻¹ s⁻¹ at 400 °C with a pressure of 25 MPa [128].

This reaction, along with reaction (22), initiates a chain reaction—sometimes referred to as the “Allen chain reaction” [129,130]—that results in the destruction of hydrogen peroxide:

H^● + H₂O₂ → ^●OH + H₂O.

(22)

2.2. The Effect of Dissolved Oxygen

Oxygen is soluble in many environments, notably in water. Without taking specific precautions, the irradiated target will contain oxygen. For instance, at 1 atmosphere and 25 °C, air-saturated water contains about 2.5 × 10⁻⁴ M dissolved oxygen. This concentration increases to ~1.3 × 10⁻³ M in oxygen-saturated water at room temperature.

The chemistry of oxygen is fundamentally concerned with electron transfers in oxidation–reduction (redox) reactions. As a diradical, molecular oxygen possesses two unpaired electrons, enabling it to readily react with primary radicals formed during the radiolysis of aerated aqueous solutions, such as e⁻_aq and H^● atoms. These reactions proceed as follows [5,20,53,131]:

O₂ + e⁻_aq → O₂^●−          k = 2.3 × 10¹⁰ M⁻¹ s⁻¹

(23)

O₂ + H^● → HO₂^●          k = 1.3 × 10¹⁰ M⁻¹ s⁻¹,

(24)

where the superoxide anion radical O₂^●− is always in pH-dependent equilibrium with its conjugate radical, the hydroperoxyl radical HO₂^● [125]:

O₂^●− + H⁺ ↔ HO₂^●, pK_a(HO₂^●/O₂^●−) = 4.8 in water at 25 °C

(25)

Based on this pK_a, the Henderson–Hasselbalch equation indicates that O₂^●− is the predominant form of the hydroperoxyl radical in neutral water (pH 7). Using the reciprocal of the “scavenging power”—defined as the product of a solute’s (or scavenger’s) concentration and its rate constant for reaction with a primary radical species (units of s⁻¹) [5,13]—we can estimate the time scale over which O₂ scavenges e⁻_aq or H^● atoms. In aerated water, these reactions occur within about 0.2–0.4 μs. This time scale roughly corresponds to the end of track expansion observed during low-LET irradiation (see supra).

In this context, the two-electron reduction product of oxygen, H₂O₂, can be generated through the dismutation reactions of the HO₂^●/O₂^●− radicals as follows [125]:

HO₂^● + HO₂^● → H₂O₂ + O₂,              k = 8.3 × 10⁵ M⁻¹ s⁻¹

(26)

HO₂^● + O₂^●− + H⁺ → H₂O₂ + O₂,       k = 9.7 × 10⁷ M⁻¹ s⁻¹

(27)

O₂^●− + O₂^●− + 2H⁺ → H₂O₂ + O₂,       k = 0.3 M⁻¹ s⁻¹.

(28)

Given the rate of reaction (28), the reaction between two O₂^●− radicals in neutral aqueous solutions is negligible for all practical purposes. In living cells, superoxide dismutase (SOD) catalyzes this reaction, increasing the rate constant to ~4 × 10⁹ M⁻¹ s⁻¹ at physiological pH [131,132,133]. This makes it one of the fastest enzyme-catalyzed reactions known, if not the fastest.

The presence of oxygen greatly influences the outcome of radiolysis, increasing the yield of oxidative products and creating a more oxidative, less reductive chemical environment. This is not only important for advancing our understanding of fundamental chemical processes but also holds broad practical significance. It is particularly relevant in diverse fields such as biology, radiobiology, radiation therapy, nuclear reactor chemistry, radioactive waste management, food preservation, and environmental chemistry, where radiolysis can affect the behavior and fate of pollutants. In addition, research on the radiolysis of aerated solutions has greatly enhanced our knowledge of both radical and bioradical oxygen chemistry (see, e.g., [11,53,132] and cited references).

2.3. Spurs/Tracks Are Highly Acidic

Experimental evidence [5,134,135] and Monte Carlo-based simulations [136,137,138] have demonstrated the occurrence of transient, highly acidic spikes immediately following water radiolysis. The underlying causes of this acidity are outlined below.

As described in Section 2.1, water molecules ionized into H₂O^●+ dissociate within ~50 fs via the pseudo-first-order proton transfer reaction (1), producing H₃O⁺ and ^●OH radicals close to the ionization site. Meanwhile, the secondary “dry” electron generated during ionization is ejected with several tens of electron-volts of kinetic energy, enabling it to travel an average distance of about 10 nm [139] before becoming thermalized and hydrated, a process that occurs within roughly one picosecond. At this stage, the hydrated electron, on the one hand, and H₃O⁺ and the ^●OH radical, on the other hand, are quite far apart [140,141,142]. This spatial separation precludes immediate recombination through the following reactions [20]:

e⁻_aq + H₃O⁺ → H^● + H₂O,        k = 2.1 × 10¹⁰ M⁻¹ s⁻¹

(29)

e⁻_aq + ^●OH → OH⁻,                k = 3.55 × 10¹⁰ M⁻¹ s⁻¹.

(30)

As a result, this initial charge separation generates a highly acidic environment surrounding the “native” radiation tracks. This acidity persists until the slow diffusion of H₃O⁺ and ^●OH allows them to reach the distant location of e⁻_aq, where reactions (29) and (30) eventually produce H^● and OH⁻. This transient acid response, termed an “acid spike” [137], draws an analogy to the “thermal spike” sometimes used in radiation chemistry to describe a transient region of excess temperature formed around high-LET heavy ion tracks in water [54].

Figure 2a illustrates the temporal variations in H₃O⁺ and OH⁻ yields from track chemistry simulations of low-LET radiolysis in pure, deaerated water at ambient temperature [116,137]. It also includes experimental data from ⁶⁰Co γ-ray or fast electron irradiation [143,144,145,146,147], demonstrating close agreement between simulated and measured yields of H₃O⁺ and OH⁻. Figure 2b displays the evolution of the corresponding pH, defined as −log[H₃O⁺], where [H₃O⁺] represents the spur/track concentration of hydronium ions. For times shorter than ~1 ns, the pH remains stable at about 3.3 before gradually increasing to 7 (neutral water) at ~1 μs.

Although experiments and simulations confirm early acidity, acid-spike effects have been largely overlooked in studies of water exposed to ionizing radiation [148]. For example, from a radiation and free-radical biology perspective, this oversight is particularly surprising, given the high sensitivity of many biological structures and cellular processes to pH fluctuations [137,148,149,150].

2.4. LET and Dose-Rate Effects

Numerous experimental and theoretical studies have demonstrated that radiation quality, or equivalently, LET, significantly affects the yields of products in water radiolysis (see, e.g., [16,17,23,54] and references therein). As discussed in Section 2.1, low-LET radiation, often termed “sparsely” ionizing radiation, produces localized energy-loss events within small, nearly spherical volumes known as spurs. These spurs are spaced far enough apart to allow reactive species within them to engage in individual chemical pathways without significant interaction with neighboring spurs. In this scenario, the predominant effect of radiolysis is the formation of free radicals. In contrast, high-LET radiation, such as low-energy protons or heavy ions, neutrons, or α-particles, generates “densely” packed, continuous ionizing tracks of a cylindrical shape. This results in a concentrated and overlapping distribution of reactive species, fostering radical–radical interactions that enhance combination and recombination reactions within the diffusing tracks. Consequently, this reduces the yield of free radicals while promoting the formation of stable molecular entities like H₂, H₂O₂, and reformed water [5,53,54].

Under standard low- or high-LET irradiation conditions without dose-rate effects, radiation tracks do not overlap, which allows the chemical effects of irradiation to be considered as the sum of the effects of individual tracks, each evolving independently. However, increased radiation dose rates significantly alter the physicochemical and spatiotemporal dynamics due to overlapping radiation tracks, leading to enhanced inter-track chemistry (see, e.g., [5,53,116,136,151,152,153]). These intertrack radical–radical reactions increase the proportion of molecular products at the expense of radical products (e⁻_aq, H^●, and ^●OH radicals).

High dose rates and high LET values similarly affect radiolysis yields, despite their differing underlying mechanisms of action. Both conditions lead to increased radical densities, which favor radical–radical reactions either in the bulk of the solution (inter-track reactions) under high-dose-rate conditions or within individual radiation tracks (intra-track reactions) during high-LET irradiations.

3. The Ferrous Sulfate (Fricke) Dosimeter: The Most Thoroughly Studied System in Radiation Chemistry

3.1. The Primary Radical and Molecular Yields in Irradiated 0.4 M H₂SO₄ Aqueous Solutions

The vast majority of radiolysis experiments on acidic aqueous solutions were conducted starting in the 1950s, preceding those on neutral solutions (see, e.g., [121,129]). Sulfuric acid in 0.4 M aqueous solutions, with a pH of ~0.46, was the acid most commonly used [5,53]. This choice was primarily based on the understanding that the dominant anion, HSO₄⁻, did not intervene in radiolysis processes under these conditions. Additionally, it is important to acknowledge the historical contributions of Hugo Fricke [154,155,156,157], who developed the ferrous sulfate dosimeter between 1927 and 1929. This dosimeter, a dilute solution of Fe²⁺ ions in 0.4 M H₂SO₄, was used in X-ray therapy. Fricke established that a 0.4 M sulfuric acid medium was necessary to match the response of the ferrous sulfate solution to that of air under X-ray exposure. Although using the 0.4 M sulfuric acid dosimeter offers no specific benefits in purely chemical studies, its continued use has largely been a matter of tradition [114].

The radical and molecular yields, derived from studies on a variety of mineral and organic systems in sulfuric acid environments, exhibit remarkable agreement [119], validating Allen’s initial 1948 hypothesis of heterogeneous zones (“spurs”) [158]. For all selected solutes within specific concentration limits, the generally accepted primary yields of radical and molecular products resulting from ⁶⁰Co γ-irradiation of 0.4 M H₂SO₄ aqueous solutions at 25 °C are [1,119,159]

g(e⁻_aq) = 0          g(H^●) = 3.70          g(H₂) = 0.40
g(^●OH) = 2.90      g(H₂O₂) = 0.80      g(HO₂^●) = 0.02      g(–H₂O) = 4.50,

(31)

where the HO₂^● radical is produced in only very small yields and can generally be disregarded. These values also apply to hard X-rays and fast electrons of similar energies. Additionally, other acids, such as HCl, HClO₄ (perchloric acid), and (COOH)₂ (oxalic acid), have been utilized in determining radical and molecular yields at low pH (see [119] and references therein). A systematic review of the data indicates that the primary yield values in Equation (31) are generally consistent across solutions with the same pH, regardless of the anion type.

3.2. The Ferrous Sulfate, or Fricke, Dosimeter

In chemical dosimetry, the radiation dose is determined by the chemical changes occurring in a specific medium. Any well-characterized quantitative chemical reaction can serve as the basis for a dosimeter. The most thoroughly studied system in radiation chemistry is the air-saturated solution (~2.5 × 10⁻⁴ M O₂) of 1 mM ferrous sulfate in 0.4 M aqueous H₂SO₄, commonly known as the “Fricke dosimeter”, named after Fricke [157]. Among all aqueous systems studied, this dosimeter stands out as the most widely used and best-understood chemical dosimeter. Its popularity stems from its accuracy, its reproducibility, and the linearity of its response to varying doses, making it essential in radiation-chemical research [5,160,161,162].

The chemistry of this system is based on the oxidation of ferrous ions to ferric ions by the oxidizing species ^●OH, HO₂^●, and H₂O₂, which are generated during the radiolytic decomposition of water. The reaction scheme is as follows [5,129,157,163,164]:

e⁻_aq + H₃O⁺ → H^● + H₂O            k = 2.1 × 10¹⁰ M⁻¹ s⁻¹

(29)

H^● + O₂ → HO₂^●                       k = 1.3 × 10¹⁰ M⁻¹ s⁻¹

(24)

^●OH + Fe²⁺ → Fe³⁺ + OH⁻            k = 3.4 × 10⁸ M⁻¹ s⁻¹

(32)

HO₂^● + Fe²⁺ → Fe³⁺ + HO₂⁻               k = 7.9 × 10⁵ M⁻¹ s⁻¹

(33)

HO₂⁻ + H⁺ → H₂O₂                        k = 5.0 × 10¹⁰ M⁻¹ s⁻¹

(34)

H₂O₂ + Fe²⁺ → Fe³⁺ + ^●OH + OH⁻            k = 52 M⁻¹ s⁻¹

(35)

H^● + Fe²⁺ + H⁺ → Fe³⁺ + H₂            k = 1.3 × 10⁷ M⁻¹ s⁻¹,

(36)

where the rate constants (k) provided here for the reactions between ions are at infinite dilution, corresponding to zero ionic strength. The yield of ferric ions is related to the primary radical and molecular yields given in Equation (31). In the presence of oxygen, the Fricke G-value, G(Fe³⁺), is described by the following expression:

G(Fe³⁺)_aerated = g(^●OH) + 3 g(H^●) + 2 g(H₂O₂) + 3 g(HO₂^•).

(37)

Applying the yield values from Equation (31) results in a calculated G(Fe³⁺)_aerated that falls well within 1–2% of the experimentally observed Fe³⁺ ion yield of 15.5 ± 0.2 ions/100 eV for ⁶⁰Co γ-rays or fast electrons [5,157,160,161,162,165].

In the absence of oxygen, reaction (24) is replaced by reaction (36), where H^• assumes the atypical role of an oxidizing agent, oxidizing one Fe²⁺ ion—compared to three in an aerated solution. Under these conditions, the Fricke G-value becomes

G(Fe³⁺)_deaerated = g(^●OH) + g(H^●) + 2 g(H₂O₂) + 3 g(HO₂^●),

(38)

where the experimentally observed G(Fe³⁺)_deaerated value is 8.2 ± 0.3 ions/100 eV for ⁶⁰Co γ-radiation [5,129,157,165].

In normally air-saturated solutions, oxygen is consumed during irradiation, causing the G(Fe³⁺) value to fall from 15.5 to 8.2 ions/100 eV once the oxygen is depleted. This oxygen consumption imposes an upper usage limit of about 400 Gy for the “standard” Fricke dosimeter. However, the system can be adjusted to extend the dosimeter’s capacity to measure higher radiation doses (up to 2000 Gy) by using an oxygen-saturated solution (~1.3 × 10⁻³ M O₂) and increasing the Fe²⁺ concentration to 10 mM, thereby forming what is known as the “super” Fricke dosimeter. Under these conditions, the accepted value of the Fricke yield is 16.1 ions/100 eV for low-LET radiation within the limit of low dose rates [166].

The kinetics of Fe³⁺ formation in the Fricke dosimeter have been extensively detailed (see, e.g., [163,164,167,168,169] and references therein). G(Fe³⁺) is time-dependent, reflecting differences in the time scales of the reactions of Fe²⁺ with the species produced by the radiolysis of acidic water under aerated or deaerated conditions, as described by reactions (32), (33), (35), and (36). For instance, the fastest Fe³⁺ formation occurs through Fe²⁺ oxidation by ^●OH radicals, while the slowest arises from its reaction with H₂O₂. To illustrate, Figure 3a,b present the time evolution of G(Fe³⁺) obtained from Monte Carlo simulations of the low-LET radiolysis of the Fricke dosimeter under aerated and deaerated conditions, respectively, at 25 °C, over the interval of ~1 ps–200 s, without dose-rate effects [168,169].

Finally, Equations (37) and (38) demonstrate that Fe³⁺ ion formation is highly sensitive to factors affecting the primary free-radical yields (H^●, ^●OH, and HO₂^●), such as LET and dose rate. As previously mentioned, raising the LET or dose rate promotes intra- or inter-track radical–radical reactions that compete with the radicals’ reactions with Fe²⁺, ultimately reducing G(Fe³⁺) [139,151]. This effect is illustrated in Figure 4a,b.

4. Conclusions

This short review of the fundamentals of water radiolysis underscores the importance of a thorough understanding of its mechanisms and outcomes for managing chemical processes in radiation-exposed aqueous environments. This, in turn, emphasizes the ongoing need for both experimental and theoretical studies to further advance knowledge in this critical field.

In an upcoming article, we aim to present a comprehensive review of water radiolysis, focusing on its temperature dependence and behavior in the sub- and supercritical regimes. Special attention will be given to its implications for water chemistry in nuclear reactors, highlighting key mechanisms, experimental findings, and their relevance to reactor operation and safety.