Effects of degradation of methane molecules on self-oscillatory processes in solid methane irradiated with electrons

The work will focus on processes in methane caused by exposure to the nuclear radiation at temperatures below 100 K, when methane is in a crystalline state. Methane is a simple organic system, widespread on the Earth and in space. Solid methane in the form of ice is one of the best neutron moderators of spallation neutron sources.¹ There are hypotheses that explain the presence of molecular methane in the cold clouds of complex organic molecules in interstellar space. The location of molecules outside the grain may be associated with explosive processes of formation and desorption of molecules from the methane grain when it is irradiated by a particle flow.² There are also hypotheses^1,3,4 that the flashes observed on comets are associated with instabilities and explosive processes in methane during nuclear irradiation.

In order to clarify the processes of transformation of molecules during irradiation, many experiments on the interaction of high-energy particles with methane at low temperatures have been conducted. When irradiated with particles of high energy, methane evaporates. Thus, in work Ref. 5, when irradiating solid methane with 9.0 MeV α-particles and 7.3 MeV protons, a sharp increase in pressure in the chamber was observed, and at a dose of 145 eV/mol, up to 90% of the methane sample evaporated. In the work Ref. 6 when bombarding solid deuterated methane with helium and hydrogen ions with energy of 1.5 MeV, it was found that the yield of D₂ from the sample increases significantly upon reaching a certain threshold fluence value. In the paper Ref. 7, the authors proposed that large molecules are formed as a result of three-particle kinetic reactions in the high-density gas phase, arising from processes associated with the recombination of trapped hydrogen atoms and other radicals. Models of the formation of complex organic molecules based on the recombination of radicals are analyzed in the paper Ref. 8, it is emphasized that the role of molecular degradation is insufficiently analyzed. It was observed in Ref. 9 under irradiating pure methane with several sources, simulating the spectra of interstellar media (fast electrons and photons with different energies), that important complex hydrocarbons can arise in interstellar conditions. In our work, we consider irradiation that does not cause a radical change in the shape of the sample.

In the work Ref. 1, the experiments on moderating neutrons with solid methane discovered a temperature flash. The flash was explained by the occurrence of self-oscillations in the concentration of CH₃ radicals created by irradiation. When two CH₃ molecules recombine, an ethane molecule C₂H₆ is formed and the 368 kJ/mol of energy is released. With the accumulation of CH₃ molecules due to irradiation, the system becomes unstable with respect to temperature and molecule concentration variations. A small fluctuation increase in temperature leads to acceleration of the recombination of the molecules, during which the temperature rises further. As a result, a thermal flash occurs.

The authors of the work Ref. 10 revealed a sharp pressure peak in the chamber caused by the desorption of particles from solid methane irradiated with electrons with an 1 keV energy at a beam current density of 2.5 mA⋅cm^–2 at thermostat temperature of 4.2 K. Pressure flashes in the chamber with the irradiated sample were observed in Ref. 10 in the interval from 3000 to 5000 s from the start of irradiation of the samples with electrons. The pressure peak may be explained in the same way as in work Ref. 1, as a result of the appearance and recombination of methane decay products, leading to self-oscillations of the defect density and temperature. For this to happen, CH₃ molecules must be produced in methane during electron irradiation. Sometimes the authors observed also less intense pressure surges with a period of about 10 s.¹¹ These additional peaks were explained in Ref. 12 by the appearance of self-oscillations associated with the processes of formation of hydrogen molecules. In work Ref. 10, the influence of oscillation processes on the yield of the resulting organic molecules from the sample is also considered.

It should be noted that the energy transferred during the collision of an electron with a methane molecule in Ref. 10 is not sufficient to break the CH bond and remove a proton from the methane molecule. Therefore, the creation of methyl (CH₃) in this case is subthreshold. For example, it may occur when sufficient energy is transferred to a proton from electronic excitation of the molecule. Long-lived triplet excitations may be such electronic excitations. The triplet excited states can be formed when a positively charged methane ion captures an electron if the methane ion and the captured electron have the same spin orientation.

In the work Ref. 2, organic molecules of a mixture of methane and carbon monoxide (CO) were studied under irradiation with electrons with energy of 5 keV. One of the chains of reactions in such system is the formation of CH₃ radicals followed by their fusion to create ethane molecules. At some point in time, a sharp peak in pressure increase was observed in the chamber with the irradiated sample. Using infrared spectroscopy, the authors determined the time dependence of the components of various molecules in the chamber. It turned out that the density of the reaction product C₂H₆ increases with time, but at some point, in time the density of methyl CH₃ molecules decreases. Qualitatively, the phenomenon can be considered as a manifestation of instability in a methane sample at low temperature when irradiated with neutrons in work Ref. 1 and electrons in work Ref. 10. The decrease in the density of CH₃ radicals can be explained by the emergence of instability in the reaction of radical CH₃ fusion associated with the accumulation of radicals. As a result of the fusion, the density of the C₂H₆ reaction products increases, and the density of CH₃ radicals decreases due to their effective fusion under instability conditions. Accordingly, their desorption from the sample decreases, and their density in the chamber drops. The results explain the nucleation of organic molecules in the condensed phase and their presence in cold molecular clouds outside interstellar grains in the gas phase.

Let us pay attention to one more circumstance. In methane irradiated with electrons, self-oscillations may appear for another reason, different from the one considered. If there are traps for electrons in the crystal, the electrons of the incident flow and those knocked out of methane molecules by the incident electrons will be captured by the traps, accumulate on the traps, and instability may arise with respect to the release of electrons from the traps, because when a positively charged methane ion and an electron recombine, energy is released. As a result, energy accumulation can lead to the emergence of self-oscillations. Such type of self-oscillations in a presence of traps was calculated and observed in a system of excitons generated by ultraviolet radiation in a crystal of deuterobenzophenone with traps created by an admixture of benzophenone.¹³ However, the application of such a mechanism to methane irradiated by electrons raises an objection. So, in the work Ref. 2, a separate study was carried out, namely, the system was irradiated with ultraviolet radiation with a quantum of energy being greater than the ionization energy of the methane molecule. With this irradiation, there was no flow of electrons, but free electrons were created in the crystal by ultraviolet radiation. However, the occurrence of the above-considered instabilities was not obtained. At the same time, the influence of the electronic subsystem on self-oscillatory processes requires additional investigation.

In our work, we have taken into account that the concentration of methane molecules decreases due to the formation of methyl molecule from methane molecule under the influence of electron flow and other processes. This should influence the process of self-oscillations. We have studied the effect of the destruction of methane molecules by the flow of electrons on self-oscillations, both with the formation of methyl molecules and other molecules. We have taken into account the changes in the number of CH₄ and CH₃ molecules and the temperature over time. Also, we have considered the process of accumulation of ethane molecules C₂H₆ over time. Thus, using a simple model, we trace the patterns of formation of the reaction product—an organic molecule.

In this work, we will consider the manifestations of self-oscillations and the role of degradation processes of methane molecules during irradiation in the formation of the final product. We will use kinetic equations for the concentrations of molecules similar to those studied when considering self-oscillations in methane,^1,3,12 adding terms describing the degradation of molecules and the appearance of ethane molecules.

Here, G is the probability of the formation of the molecule n₂ (CH₃) from the molecule n₁ (CH₄) by irradiation per unit time, K₀ is the kinetic coefficient of recombination of radicals CH₃, c(T) is the heat capacity of a methane volume unit, P is the part of the energy spent by the electron flux to heating of a sample per unit time, E_a is the activation energy of two CH₃ radicals fission, b is the coefficient of energy transfer from the sample to the thermostat. In this work, we have taken into account not only the process of the transformation of CH₄ into CH₃, but also other processes leading to the disappearance of methane and methyl molecules during irradiation, describing the disappearance of the molecules by the terms with r₁, r₂, and r₃ for the CH₄, CH₃, and C₂H₆ molecules, respectively. The value Gr_i determines the probability of the transformation of the ith molecule into other molecules per unit of time by irradiation, r_i is a dimensionless coefficient of degradation.

Equations (1)–(4) were solved numerically. The parameters of the equations were determined from the irradiation parameters and the data from the analysis of self-oscillations of considered system obtained in Ref. 12. In our calculations, we assumed that $G= 10 − 5 s − 1$⁠, $E a=180 K$ (an energy in temperature units), $T b=4 K.$ The dependence of the heat capacity on the temperature was taken into account. The role of the magnitude of the degradation coefficients r_i on the qualitative and quantitative behavior of the solution was analyzed.

Figure 1 shows the typical time dependences of the concentrations of CH₄, CH₃, C₂H₆ molecules and temperature in irradiated methane for different values of degradation coefficients r_i. In the calculations, it was assumed that the degradation coefficients under the influence of irradiation are the same, i.e., r = r₁ = r₂ = r₃. In the figures, the degradation coefficient takes the values r_i = 0.1 for the left column, r_i = 1 in the middle and r_i = 4.555 for the right column.

When moving from left to right, the figures on the top row of Fig. 1 describe the decrease in time of the concentration n₁ (methane) with an increase in the degradation coefficient. In the second row, the figures describe the time behavior of the methane decay product n₂ (methyl). At small values of the degradation coefficient, self-oscillatory processes occur in the system, existing for a certain period of time. They consist of quasi-periodic repetitions of the concentration n₂ in time. In each cycle, at the beginning there is a slow increase in the concentration of methyl, caused by the effect of the electron irradiation of methane. Then at a certain value n₂ instability occurs, in which the recombination of two methyl molecules with the formation of an ethane molecule and the release of energy stimulates the recombination of other methyl molecules. As a result, a cascade process of combining methyl molecules develops, during which the methyl concentration decreases. Subsequently, the next cycle of self-oscillations is formed. But with each cycle, the concentration of methane molecules decreases. The occurrence of instability and the emergence of self-oscillations are possible only when the concentration of methane molecules exceeds a certain value. Therefore, after a certain number of oscillations, the concentration of methane molecules is no longer sufficient for the appearance of a new oscillation. At that moment the self-oscillatory process stops. Thus, in the presence of degradation processes, the number of self-oscillations is limited and with an increase in the degradation coefficient this number decreases, as it can be seen in Fig. 1.

Let us analyze the time dependence of ethane concentration (n₃) during one cycle of self-oscillations. At the beginning the ethane concentration slowly increases due to combine of methyl radicals al low temperature. At a certain moment, when an acceleration of the recombination processes of methyl radicals causes a rise in temperature, a jump in the rate of ethane production is observed and, as a result, its concentration quickly increases. This rate drops sharply after the methyl radicals finished recombining and their density became small. Then there is some slow temporary decrease in the concentration of ethane molecules due to their degradation, which is described by the term with the coefficient r₃. Then the density rises due to continued irradiation and the appearance of the next cycle of self-oscillations. Subsequently, this picture is repeated for other cycles of self-oscillations. The dependence of the density of the reaction product on time has the form of a ladder, in which the number of steps is equal to the number of cycles of self-oscillations. After several cycles of oscillations, the next cycle does not occur due to the degradation of methane molecules. A decrease in methane concentration no longer allows the formation of a peak of self-oscillations and a wide band of ethane concentration is formed, the value of the concentration decreases over time due to degradation processes. From a comparison of n_s dependences on time for different values of r, it is obvious that the number of molecules of the reaction products increases with the number of self-oscillations. In the presence of self-oscillations, almost the entire value of ethane density is created during the quick recombination stage of the self-oscillations.

During the intense reaction of methyl fusion, a lot of energy is released and a temperature flash is observed (see the fourth row in Fig. 1). The number of flashes coincides with the number of self-oscillation cycles. Flashes occur in a very short time interval. In the Fig. 1 inset, the temperature dependence of the flash on time is given in an extended time scale.

Self-oscillations do not occur when the degradation coefficient is greater than a certain critical value r > r_c. With the used values of the system parameters, we found r_c = 5.4. However, even when the degradation coefficient r is greater than the critical value r_c, there is a maximum in the time dependence of the concentrations of CH₃ and C₂H₆ molecules. In this case, the nonlinear processes of recombination of CH₃ molecules still stimulate the processes of recombination of other CH₃ molecules due to energy released during the recombination of two CH₃ molecules, but the intensity of this process is insufficient for occurrence of instability and self-oscillations because of small number of CH₃ molecules created by irradiation. That is why the self-oscillations do not occur. Some number of C₂H₆ molecules is created, and then they degrade due to irradiation. The appearance of maxima in the time dependences of the concentrations of CH₃ and C₂H₆ is illustrated in Fig. 2 for the case of two values of the degradation coefficient greater than the critical value.

Let’s make some estimation for the numerical value of the degradation coefficient r₁. The main channels for the decomposition of the CH₄ molecules under electron irradiation are their transformations into structures CH₃ + H, CH₂ + H₂, CH₂ + 2H and so on. For our estimates, we used the experimental data from work Ref. 14, according to which the relative values for various CH₄ dissociation channels have following values: 0.18 for the CH₃ + H channel, 0.06 for CH₂ + H₂ channel, 0.51 for CH₂ + 2H channel, 0.23 for CH + H₂ + H channel. Hence, for the value of CH₄ decay we obtained r₁ = 4.555 as the ratio of the intensity of the processes without CH₃ creation to the intensity of the processes with CH₃ creation. This process is already taken into account in Eq. (1). The system dynamics for the given value of the degradation coefficient are presented in the right column of Fig. 1. Thus, if we use the experimental data from Ref. 14, one cycle of self-oscillations should be expected in methane with one thermal flash.

As can be seen from Fig. 1, the formation of C₂H₆ mainly occurs during a burst of self-oscillation. It can also be seen that the ethane production decreases as the intensity of degradation processes increases. Figure 3 shows the dependence of the maximum value of ethane density (n_3max) on the degradation coefficient r with other parameters being the same. The interval of change of the parameter r covers the region where self-oscillations are present and the region where they do not occur. The maximum value of ethane density, which would be observed in the absence of degradation, corresponds to the case when many self-oscillations occur in the system and after each one a portion of molecules is born (Fig. 1). However, we have found no features on this graph when the number of self-oscillations changes or when self-oscillations disappear at all.

Self-oscillations exist in a certain range of system parameter values (examples for some systems are given in Ref. 15), in particular in a certain range of thermostat temperature T_b. At the parameter values considered in the work, at T_b > 7 K and higher, self-oscillations are not observed. This temperature limitation agrees with the results of the work Ref. 2, in which, in solid methane irradiated with electrons, the effects of rapid radical–radical reactions are observed at 5 and 10 K and does not longer appear at 15 K.

In several works by Savchenko et al.,^16,17 secondary pressure bursts were detected during electron irradiation of a mixture of argon and methane. It is difficult to attribute them to repeated outbreaks of self-oscillations. Firstly, their distance in time from the first outbreak is much less than the time of appearance of the first outbreak. At the same time, the period of self-oscillations for subsequent oscillations with the mechanism under consideration should increase, and not decrease, with time, since during the self-oscillations under consideration, the number of CH₄ molecules that are sources of oscillations, decreases. Therefore, you should wait longer for the appearance of a new oscillation in order to accumulate the required number of CH₃ molecules. The increase in the period for self-oscillations with increasing oscillation number is also visible in Fig. 1. Secondly, the observed in Refs. 16 and 17 intensities of the pressure jump in the secondary flares are much lower than the intensities in the first flare. The appearance of additional flash may have a different nature than self-oscillation. It may arise due to the heterogeneity of the distribution of methane impurities in argon. Then, in some places of the sample, conditions for self-oscillations with other parameters may appear. Since only one flash is observed, it is difficult to attribute it to typical self-oscillations and the phenomenon may be considered as an effect of thermal concentration instability.

In the considered self-oscillations, the energy released during the recombination of two radicals stimulates the recombination processes of other pairs of radicals, which also occur with the release of energy. This leads to a sharp increase in the number of recombination processes and the release of energy in the system. The resulting self-oscillations are a collective process in a system of many particles. As a result of their occurrence, the kinetic energy of the molecules increases, the temperature and the probability of the release of molecules, in particular, reaction products, from the sample rises. In experiments Refs. 2, and 11 during irradiation of solid methane with electrons, this can cause the appearance of a pressure surge in the chamber with the irradiated sample at a certain moment of time. Thus, the appearance of complex organic molecules in cold molecular clouds outside interstellar grains can be explained by the presence of external irradiation. The pressure surge in the chamber appears in a certain temperature range of the thermostat.

The processes of degradation and transformation of molecules caused by the electron beam lead to a decrease in the density of methane molecules and a decrease in the rate of production of decay products. In the presence of degradation, the number of periodical cycles of self-oscillations is limited, and the period of oscillations increases with the growth of the cycle number. If the degradation processes are intense, then self-oscillations do not occur at all. In this case, the processes of transformation of molecules are possible, but a sharp concentrated release of energy with a jump in temperature does not occur. This should lead to a slowdown in the processes of desorption of molecules from the sample.

The authors thank Prof. E. Savchenko for providing experimental data on electron-irradiated methane and useful discussion of the results of the work.