Solvated Electron

Abstract

Here I discuss the use of visible to IR femtosecond laser pulses for generating solvated electrons in pure water by direct multiphoton ionization (MPI), with the purpose of studying the solvation dynamics, the physical and chemical properties of the solvated electron, as well as its role in the chemical phase following the photoionization events. In the past, direct MPI of pure water using visible to IR laser pulses was considered inappropriate for the study of the solvation process. The main concern was that if optical breakdown occurs, the medium – bulk water in our case – is greatly disturbed, and the solvation dynamics observed in these conditions is not directly applicable to normal bulk water molecular dynamics. In another paper we demonstrated that for certain experimental conditions optical breakdown can be deterministically avoided, by operating in the self-focusing regime. A filamentary ionization pattern is obtained, with an average electron density in the order of 10¹⁷ electrons/cm³. There is no indication that the structure of bulk water is locally affected right after the passage of the fs laser pulse. My conclusion is that sub-picosecond laser pulses in the visible-IR can be safely used to study solvation processes in polar media, charge transfer processes, and a whole spectrum of photolytic and radiolytic effects of chemical and biological interest.

The study of the solvated electron has two important aspects. First, a detailed understanding of the solvation process, and its dynamics, results in a deeper understanding of the solvent itself, and of charge-transfer processes. Second, a description of the intrinsic properties of the solvated electron, of its formation and its recombination, as well as of its role in other relevant chemical chain reactions, is essential for our understanding of radiolytic, and photolytic effects. Some questions in biology related to oxidative stress can as well be elucidated.

The solvation process

In a polar liquid an electron can occupy a localized state as a result of its interaction with surrounding molecules. Thus, the fate of a free electron in this kind of medium is to lose its kinetic energy through collisions with surrounding molecules, and to recombine, or to solvate. Solvation is the process by which the solvent molecules reorient themselves around the charge to minimize the energy of interaction. Water is the most important solvent in biology and biochemistry, and for this motive I will concentrate my attention on this particular material.

Solvated electrons can be created in liquid water by directly ionizing the water molecules, or by ionizing impurities (electron donors). Ionizing radiation (gamma, X-rays, high energy electrons, or ions), or laser light can be used for this purpose. Following the ionization process, the electron looses its kinetic energy (it thermalizes), and binds weakly to shallow potential traps, existing naturally in the structure of the polar medium. A period of non-radiative structural readjustment follows, where the interaction between the electron and its environment becomes increasingly large, until the electron finds itself in a stable fundamental state. In general, the duration of the solvation process depends on the type of solvent, and is controlled by the characteristic times of librations, vibrations, and translation of the molecules composing the medium.

The fine details of the solvation process are not resolved yet, but a broad picture has emerged. Here is the general account in the case of water. The solvation process takes a little more than one picosecond, and proceeds in two stages. For the first 100 fs, the stabilization mechanisms of the charge are libration, and the stretchings/compressions of O-H bonds. Gradually, translations of water molecules become increasingly important after 300 fs, and continue approximately until the first picosecond. One picosecond after ionization, and without any external influence on the system, the electron will reach its fundamental solvated state.

We should mention here that the salvation dynamics also depends on the ionization method. If the quasi-free electron is produced by MPI using high power laser pulses, it is subjected to an optoelectric field form its birth, until the end of the laser pulse. Moreover, for high local intensities the local structure of the medium can also be temporarily modified. However, in the case of ionizing radiation (gamma, X-rays, high energy electrons, or ions) there is no optoelectric field to influence the solvation dynamics. Only for high linear energy transfer (LET) particles, at the location of Bragg’s pick, where the plasma density can reaches very high values, the local properties of the medium can be greatly affected, and the solvation process can deviate from the normal conditions.

Properties of the solvated electron

In its fundamental state, six water molecules surround the electron in the first solvation shell, oriented with the O-H bond towards the interior. The solvated electron is a genuine chemical species, with well-defined thermodynamic properties [1]. It is in fact the most reductive chemical species known to man. The solvated states, which are believed to be a s-like fundamental state, and a p-like degenerate excited state, are strongly coupled to thermal fluctuations of the medium. This results in a very broad and homogeneous absorption spectrum, see Figure 1. For a very complete description of the solvated electron and the solvation dynamics in water, see the work of A. Baltuška [7]. It consists of an in-depth study, based on experiments conducted with 5 fs temporal resolution.

The fate of the solvated electron

Once the solvation process is completed, the solvated electron can migrate through the medium and recombine with the geminate ion. The recombination time is strongly dependent on the ionization means. It can vary from a few microseconds for electron bream radiolysis, to a few nanoseconds in the case of photoionization. The dependence of recombination time on the ionization method is explained in terms of the average distance between the solvated electron and the geminate ion. This in turn depends on the initial kinetic energy of the photoelectron, and on the ionization density. The properties of the solvent also play an important role.

If produced by single-photon ionization of various cations, the ferrocyanide Fe(CN)₆^4- being the most used, the lifespan also depends on the concentration of ions in solution (Figure 2).

If produced by direct photoionization of the medium, which is water in our case, the time of recombination depends on the wavelength, for photon energies greater then 9.5 eV, and on the input intensity. The dependence of the recombination time on the intensity was studied by Pommeret and al [2], for 2-photon absorption at 266 nm, using 100 fs laser pulses, with intensities up to 1.5x10¹² W/cm² [2]. The works of D.M. Bartels et al. [3], and C.L. Thomson et al. [4], show the effects of the wavelength in the UV domain. Toma Goulet et al. [9] estimated the recombination time by ionizing pure water using 620 nm fs laser pulses, achieving an estimated local intensity in the order of 10¹³ W/cm².

In the UV, for 2-photon ionization of pure water at 266 nm (9.32 eV) the average distance between the solvated electron and the OH^· radical was estimated at approximatively 1 nm [4]. The authors observed that the decay rate of the solvate electron population dose not vary with the intensity of the ionizing pulse, on an energy domain from 7.8 eV to 9.0 eV. They inferred that the average distance between the solvated electron and the OH^· radical is not affected by the wavelength in these experimental conditions. This further suggests that the ionization process is not a direct one, but occurs after the excitation of a water molecule to an excited state 2¹A₁, followed by a spontaneous charge transfer. Other authors proposed different ionization mechanisms [2, 3, 5, 6]: following the absorption of two photons, the electron is transferred directly to a shallow potential from Urbach tail. In this scenario the photoelectron is never truly free, and the average distance between the solvated electron and the OH^· radical is dictated by the spatial distribution of these irregularities in the electronic structure of the bulk. As the photon energy is increased above 9.5 eV, the recombination time begins to manifest a dependence on the wavelength, and we can infer that the photoelectrons are, in this case, mobile at birth. Moreover, from 7.8 eV to 9.0 eV, but for higher intensities (0.7-1.5 TW/cm²), the recombination time exhibits a dependence on the input intensity.

Graphics

This behaviour can be explained in terms of ponderomotive forces, the influence of the optoelectric field on the quasi-free photoelectron. It is also possible that the relative yield of other photolytic species, which act as scavengers for solvated electrons, can be influenced by the input intensity, thus affecting the recombination dynamics.

Toma Goulet et al. [9] used 620 nm fs laser pulses to ionize pure water. The authors estimated the local intensity at 10¹³ W/cm². They also estimated a recombination time of ***, deducing an average separation between the solvated electron and the radical of approximatively 1 nm.

The recombination time is intimately related to the resultant photolytic effects, which ultimately confers the importance of this specie in medicine, radiobiology, and radiochemistry. The concept of escape-rate becomes crucial here: solvated electrons that escape recombination can participate in other chemical reactions, some of which are of great interest in biology.

Production means of solvated electrons vs the study context

Before lasers even existed, the solvated electron was generated by radiolysis, and studied by indirect chemical means. Pulsed radiolysis was later used to gain more insight into the recombination dynamics of the solvated electron, and into its role in the chemistry that follows the ionization events. Different models were proposed to account for the chemical processes involving this ephemeral species. Part of the initial conditions, which must be plugged into these models, is the initial local concentration of the solvated electron population, and its chemical properties. In order to extract valuable information, the generation of the solvated electron population must be faster then the chemistry that follows. This is the reason why sub-ns pulsed electron beams became important. The models predict the final state of the system, which is in fact described by the concentration of stable radiolysis products. These products are easily measurable, so they act as observables, and are used retrospectively to test the model itself. Different types of impurities were also selectively introduced into the system, in order to manipulate the outcomes of the chemistry, and their measured effects were used to calibrate/invalidate the proposed models. These impurities act as scavengers, controlling the population of either solvated electrons, or other important primary photolytic species like OH^·, and OH^-. Time resolved spectroscopy with sub-ns temporal resolution was also used to follow in time the concentration of various radiolytic transient species. This is a more direct method to probe what happens during the physical, physico-chemical, and chemical stages of radiolysis.

The solvation dynamics itself became accessible only after the advent of sub-ps pulsed lasers. Here the attention is focussed on the formation of the solvated electron, and not on its effects after being formed. Time resolved spectroscopy was employed to describe the solvation dynamics. There are two crucial parameters that must be kept as small as possible, in order to be able to extract valuable information on the solvation process. The first is the period of time during which the ionization occurs. The second is the temporal resolution of the probing spectroscopic technique. Here is the justification of these requirements: Spectroscopic techniques are used to follow in time the formation of the solvated electron. Essentially, a shift in the spectral characteristics of this species must occur as it forms. This shift must be measured with a temporal resolution smaller then the formation time, hence the importance of the second requirement. But there are no available methods to observe only one solvated electron. The characterisation is statistical, in the sense that a very large population is probed at once. In order to be able to extract valuable information from the measurement, the population must be roughly synchronized: the majority of measured entities must move through different stages almost at the same time. The ideal situation is when all the ionization events happen simultaneously, then the thermalization and the solvation processes become closely packed in time. In this case, the spectroscopic measurement of the entire population can reveal information about the transformations undergone by one individual system, if the time resolution of the spectroscopic technique is smaller then the solvation process itself. But there are no means to realize this ideal situation. Usually pulsed sub-ps electron beams or pulsed sub-ps UV laser beams are used for ionization. The resulting error on the ionization time is the duration of the ionizing pulse. The shorter the ionizing pulse the closer we get to the ideal situation.

There is a third requirement for the experimental study of the solvation process. Suppose we possess a technique to produce free electrons in sufficient quantities, within a period of time much smaller then the solvation-time – the first requirement being met. If one’s goal is to understand the solvation process in normal bulk water, the local properties of the medium should not be greatly modified by this production method. For example, if fs laser pulses are used, one should avoid optical breakdown, which induces important local structural changes that relax within a time much longer than the solvation-time.

We have seen that the method of production of solvated electrons must be carefully chosen in order to meet certain requirements that are specific to the study context: for the study of the solvation process, or for the study of the role that this species plays in the chemical phase of radiolysis or photolysis. In the following sections I will discuss the use of fs pulsed lasers.

Pulsed fs lasers in the study of electron solvation process

Fs lasers play an undeniable role in the study of the solvated electron, as they can be employed to probe fast occurring processes with great temporal resolution, using different time resolved spectroscopic and imaging techniques. Moreover, the use of fs laser pulses for the production of solvated electrons offers an important advantage over the use of an independent ionizing radiation source. The reason is that the synchronization between the ionizing event and the probing event is much better when only one laser source is used to generate, form a unique pulse, both the ionizing pulse and the probing pulse; the accuracy is in the fs range. In the case where two independent sources are used, a laser source (probe) and an ionizing radiation source (pump), such as a pulsed electron cannon, the synchronization must rely on an electronic circuit, and the accuracy drops to the ns range. This latter configuration cannot be used for the study of the solvation process, which occurs in the ps range. Thus, only the first configuration is used for this purpose.

Different experimental schemes are employed to study the solvation process, some of them are simpler, and involve only two laser beams: the pump, or the ionizing beam, and the probe. Others involve three laser beams: the ionizing beam, the excitation beam, and the probe. Later I will describe a very simple pump-probe technique that involves only two beams, and I will demonstrate that some of the more complex techniques used in the past are unnecessary, and that the concerns that justified their use, as a precautionary measure, are unsubstantiated.

But first let’s describe the most popular methods used, and talk about their justification. In the two beams scheme [12, 13] the output of the laser source is split into two beams, one of which is tuned to near-IR to probe the solvation process, it is called the probe, and the other one, called the pump, is tuned to UV and used for ionization. The electrons are produced either by directly ionizing the water by 2-photons absorption, or by ionizing some added impurity by one-photon or two-photon absorption. The main argument for the use of UV light to ionize is to keep the ionization intensity threshold low, to avoid severe local changes of the medium, and also not to interfere in other direct ways with the solvation process itself.

In the three beams scheme [10,11] Figure *** the source laser pulse is split into three beams. The first one, called the synthesis beam, is tuned to UV, and is used to directly ionize the water by 2-photons absorption, or some added impurity by one-photon or two-photon absorption. The photoelectrons solvate, and a second beam, called the pump, is used to excite the solvated electron from its fundamental state. Finally, a third beam, called the probe, is used to probe the subsequent relaxation. The undeniable advantage of this scheme is that it offers the possibility to probe the internal energy structure of the solvated electron, by following in time the relaxation from the p-like state to the s-like state.

Claude Papin et al. were first to study the solvation process by ionizing directly pure water through MPI processes at 620 nm, using a two beams scheme (Figure ***) [8, 14]. The longer the wavelength of the ionizing pulses, the higher the MPI threshold. It is believed that at 620 nm, the local intensity reaches levels in the order of 10¹⁴ W/cm². The concern was that in this case optical breakdown occurs, and that the experimental results don’t reflect the solvation process in normal bulk water. Although the authors ruled out this possibility, they could not substantiate their claims. The fact is that their results were comparable to those obtained using other widely accepted methods. Moreover, their approach presents three important advantages: First, no additional impurities must be introduced into the system. Second, the experimental setup is much more simple, as there is no need to generate second or forth harmonics for lower order UV ionization. Third, the yield of solvated electrons appeared to be much higher in this case.

The answer to this controversy came with this study, where we demonstrated that high concentrations of solvated electrons can be generated by MPI of pure water, using fs laser pulses at 790nm, in the self-focusing regime. Optical breakdown can be deterministically avoided, and the material returns to its normal state practically instantaneously after the passage of the ionizing laser pulse. The two beams scheme used in this case, Figure ***, is similar to the one used by Claude Papin et al. depicted in the figure above.

Visible-IR MPI of pure water in the study of solvated electrons

In the visible-IR domain, and in the sub-ps time regime, the intensity threshold of self-focusing is lower than optical breakdown. This means that there is a certain range of input intensity for every value of pulse duration, where self-focusing occurs and optical breakdown can be deterministically avoided. This is what defines the filamentary ionization mode. The optical Kerr effect, responsible for self-focusing, is counterbalanced by plasma generated through MPI and avalanche ionization (AI), and the intensity is clamped. As the laser pulse propagates, the energy contained within it is gradually channelled towards centers with intensity above the self-focusing threshold, and is gradually depleted in the filament core through photoionization processes. I refer the reader to the Self-Focusing section for a more detailed description. This orderly radial energy flow (towards the filament core), controlled by the equilibrium conditions between the optical Kerr effect and the plasma generation, is what kips optical breakdown from occurring on the intensity range of the F mode. Section Filamentary Mode (F) gives a complete description of this photoionization regime, and the control of the plasma density is explained in terms of laser parameters. Other non-linear optical effects, and thermal effects are discussed. See this article for an objective description of a particular case of filamentary ionization at 790 nm, and 100 fs.

Other than the F mode, variable plasma densities ranging from zero to the threshold of optical breakdown can be generated in a deterministic manner, in the visible-IR wavelength domain, in the Below OB Threshold Ionization Mode (B/OB). This requires the use of very short laser pulses, in the fs regime, and very tight focusing (high NA).

In the F mode, as in the B/OB mode, the duration of the laser pulses used for generating solvated electrons is shorter then the duration of the solvation process itself. This makes possible the extraction of valuable information about the transformations of one individual entity from spectroscopic measurements on a large population. Furthermore, both modes of ionization insure that the local properties of the material do not suffer transformations that could interfere with the solvation process, thermal effects can be minimized. But if these ionization conditions (the F and B/OB ionization modes) enable the study of the electron solvation process, they are also favorable for the study of radiolytic and photolytic effects, which occur at longer time delays.

Conclusion

The solvation process of electrons in polar liquids can be studied in the F and B/OB ionization modes, using a very simple two beam -scheme. Due to its simplicity, the solvated electron system constitutes a perfect model on which molecular dynamic theories can be calibrated. Charge transfer processes can also be better understood, as they are mediated by the solvent, and depend on its properties at the molecular level.

Moreover, the F and B/OB ionization modes possess interesting characteristics that are suitable for the modelisation of the chemical phase of photolysis: the geometry is simple, the ionization density is controllable, and the relative yield of other primary photolytic species are also controllable to a certain extent. Furthermore, these results also suggest that some experiments in radiobiology and radiochemistry involving ionizing radiation can be conducted using laser sources. The replacement of ionizing radiation sources with laser sources brings along important advantages.

Reference

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For comments/ideas/criticism please e-mail me at tiberius.brastaviceanu@gmail.com

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