Dissociative recombination of C2H+ and C2H4+: Absolute cross sections and product branching ratios

Dissociative recombination (DR) of the hydrocarbon ions C2H+ and C2H4+ has been examined at the heavy-ion storage ring CRYRING (Manne Siegbahn Laboratory, Stockholm, Sweden).

Absolute DR cross sections were measured for center-of-mass collision energies between 1 meV and 0.1 eV for both ions, giving cross sections at 1 meV of 7.6 × 10−13 cm2 for C2H+ and 1.7 × 10−12 cm2 for C2H4+.

The dissociative recombination branching ratios were determined at minimal collision energy, showing that the carbon bond is broken in 57% of the dissociative recombination events for C2H+, while this happens in only 7% of the events for C2H4+.

In the case of C2H4+, three-particle breakup into C2H2 and 2H is the dominant product channel with a branching ratio of 66%.

The present results are compared with previous DR measurements made at CRYRING for DR of C2H2+ and C2H3+.


Dissociative recombination (DR), the process whereby a molecular ion captures a free electron and then stabilizes the capture by dissociating into neutral fragments, plays an important role in determining the chemical composition of plasmas cold enough to contain a molecular component.

Kinetic modeling of such plasma environments requires knowledge of both the energy dependent DR cross sections and the product branching ratios.

For most triatomic and larger systems, the rate constants for recombination are expected to be large (>10−7 cm3 s−1 at 300 K).1,2

Until recently, however, there has been little known about the product distributions that result from recombination.

Calculating the DR product branchings for polyatomic ions from first principles has proven to be exceedingly challenging, due to the difficulty of treating molecular dissociation of such a highly excited species along multidimensional potential surfaces.

The ability to study DR reactions experimentally has improved considerably with the advent of storage rings3–5 where both energy dependent rate constants and product distributions can be measured.

We have examined the recombination of several small hydrocarbon ions at the CRYRING heavy ion storage ring.

In this paper we present absolute cross sections and product branching ratios for the dissociative recombination of two hydrocarbon ions, C2H+ and C2H4+.

The results are compared to previously reported measurements of C2H2+ and C2H3+.6,7

The significance of these results is discussed with respect to modeling the abundance of various molecular species in interstellar clouds8 and also to the modeling of plasma-enhanced combustion environments9,10.


The experiments were carried out at the heavy-ion storage ring CRYRING at the Manne Siegbahn Laboratory in Stockholm, Sweden.

The experimental apparatus has been described previously.11

Both ions were produced in a hot-cathode discharge ion source, using ethylene as the precursor compound, and extracted with a translational energy of 40 keV.

After mass selection, the ions were injected into the storage ring, which has a circumference of 51.6 m.

Using a radiofrequency accelerator system, the ions were further accelerated in the ring to 3.43 MeV (C2H4+) and 3.84 MeV (C2H+), which is the maximum beam energy as limited by the magnetic rigidity of the ring.

The ring's vacuum system maintained the pressure below 10−11 torr, minimizing beam losses from collisions with residual gas molecules.

The beam lifetime was in both cases measured to be 2.9 s.

After acceleration, the ions were merged with a monoenergetic, magnetically-confined electron beam over a length of 85 cm in one of the 12 straight sections of the ring.

The transversal temperature of the electrons was reduced to about 1–2 meV in this electron cooler section via adiabatic expansion of the electron beam.

Heat is transferred from the ion beam to the electron beam, resulting in a reduction of the momentum spread of the ions.

The 85 cm long interaction region also serves as the electron target during the recombination measurements.

The neutral products resulting from recombination were detected with ion implanted surface barrier detectors at a distance of approximately 3.4 m from the electron cooler.

At that distance, it is possible for the transversal spread of the fragments to be larger than the radius of the 900 mm2 detector; therefore, a larger detector with an area of 3000 mm2 was also used.

Although the larger detector has a higher collection efficiency, it has poorer energy resolution.

The detector's output signal is proportional to the energy of the incoming particle, and this signal was amplified and read by a multichannel analyzer (MCA) to give a pulse height spectrum.

The count rate as a function of storage time was measured by recording the amplified signal by means of a multichannel scaler (MCS) via a single channel analyzer (SCA).


Cross section measurements

Cross section measurements were started 5 s after the ions were produced, which allowed time for the ions to relax into the ground vibrational state.

During this time, the electron energy was held at the cooling voltage, which implies zero center-of-mass collision energy.

The center-of-mass energy, Ecm, can be deduced from the electron energy, i.e. cathode voltage, Ee through where Eecool is the laboratory electron energy at cooling, which is at minimal collision energy due to the energy spread.

In order to measure the dissociative recombination cross section, the cathode voltage was systematically detuned to give an energy relative to the ions of 1 meV to 1 eV in the center-of-mass frame.

As shown in Fig. 1a, the cathode voltage was first increased rapidly from the cooling energy to a voltage corresponding to 1 eV center-of-mass collision energy.

It was then decreased linearly to a voltage below the cooling energy.

The output from the MCS, shown in Fig. 1b, represents a measure of the DR signal from the detector.

Since the cathode voltage was detuned linearly, the time scale corresponds to the cathode voltage.

At collision energies near 1 eV (times corresponding to 5 s and 6.5 s in Fig. 1), the DR cross section is very low.

Signals at those energies are considered to originate solely from background processes12 and were used to determine the exponential decay of the background, which was subtracted from the signal.

During the cross section measurement, the ion current was intentionally kept low in order to prevent saturation of the surface barrier detectors.

Consequently, the ion current intensity could not be monitored directly during the measurement; instead, neutral fragments arising from collisions between the stored ion beam and the residual gas molecules were monitored with a scintillation detector, consisting of a BaF2-window and a photomultiplier tube, in another straight section of the storage ring.

After the measurement with the surface barrier detectors, the ion current was increased and could then be measured directly with a current transformer, which essentially measures the weak magnetic field created by the stored ion beam, while the background was measured with the scintillation detector in the same way as during the previous measurement.

These two background measurements could then be related to each other to give an absolute value for the cross section.

The experimental DR rate coefficient in the interaction region at a given center-of-mass energy, 〈〉, is determined by where C is the circumference of the storage ring, l the length of the electron cooler, and ne the electron density.

NDR and Nb are the signals resulting from DR processes and background processes, respectively.

The destruction rate per ion per unit time, Rb, is given bywhere vi is the velocity of the ions, and Ii is the ion current.

The absolute DR cross sections are obtained by dividing the measured rate coefficient by the electron velocity.

The center-of-mass collision energy was corrected for the effect of electron space charge.13

In the two toroidal sections of the electron cooler, where the electrons are steered in and out of the beam path, the collision energy is different than in the straight section.

Thus, some of the events measured at a specific center-of-mass energy actually result from processes occurring at other energies.

Corrections have been made to account for this effect.14

The measured cross sections for C2H+ and C2H4+ are both shown in Fig. 2.

Both ions exhibit large DR cross sections at low collision energy, with no resonances observed over the energy range from 1 to 100 meV.

At a collision energy of 1 meV, the cross sections are 7.6 × 10−13 cm2 and 1.7 × 10−12 cm2 for C2H+ and C2H4+, respectively.

The error bars indicate the statistical uncertainties.

There are also systematic errors arising from the uncertainty in the length of the electron cooler, the circumference of the storage ring, the ion beam current, and the electron density.

These combined errors are estimated to be 12%.

Integrating the energy dependent cross section, σ(Ecm), over an isotropic Maxwellian electron velocity distribution, gives the thermal rate coefficient α (in cm3 s−1) as a function of the electron temperature Te: The extracted thermal rate coefficients are shown in Fig. 3 for temperatures between 20 K and 1000 K. The 300 K rate coefficients for DR were found to be 2.7 × 10−7 cm3s−1 for C2H+ and 5.6 × 10−7 cm3s−1 for C2H4+, with both ions exhibiting a DR rate dependence on Te of −0.76.

The error bars given in Fig. 3 originate from the statistical error of the cross section.

Branching ratio measurements

In the dissociative recombination of C2H+ the following channels are energetically accessible: where the indicated kinetic energy release is the maximum, which assumes all products are formed in their ground state.

For the C2H4+ ion, the following channels are energetically accessible:

In order to measure the branching ratios of the molecular ions as they dissociatively recombine with electrons into the various product channels shown above, a stainless steel grid with a transmission15 of 0.297 ± 0.015 was placed in front of the surface barrier detector.

The signal from the detector was recorded with an MCA to give the energy spectra shown in Figs. 4a and 5a for C2H+ and C2H4+, respectively.

The background signal, originating from collisions with the rest gas, is recorded with the electrons turned off.

These spectra are shown in Figs. 4b and 5b.

Simultaneously with the two measurements for each ion, a background signal is recorded with the scintillation detector, making it possible to normalize the measurements and subtract the background.

The background-subtracted DR signals for C2H+ and C2H4+ are shown in Figs. 4c and 5c, respectively.

From these spectra, it is possible to determine the amount of each neutral fragment detected by fitting the spectra to Gaussian curves and determining the area.

The energy scale is linear, and since the energy is proportional to the mass, each peak can be assigned to a particular fragment or sum of fragments.

A set of linear equations is then used in order to assign the detected fragments to the different dissociation channels.

Consider the relatively straightforward example of C2H+ shown in eqn. (5).

The fragments resulting from dissociation events in channel α pass through the grid with probability T (transmission) and are detected as 2C + H, 2C, or H with probabilities T2, T(1 − T), and T(1 − T), respectively.

The remaining channels are analyzed the same way, yielding the following probability matrix where N(2C + H) is the signal corresponding to detection of 2C + H fragments, and N(α) is the number of events occurring through channel α, etc. With the larger detector, the single hydrogen peak cannot be resolved, so that fragment is excluded from the analysis of the spectra.

As discussed above, not all the high-energy neutral fragments are collected with the smaller detector.

In order to estimate the particle loss, a spectrum was recorded without the grid in front of the detector.

All neutral fragments originating from the same DR event should then appear at an energy corresponding to the full ion beam energy (3.43 MeV and 3.84 MeV respectively).

However, in the case of lost hydrogen atoms the fragments are detected at a slightly lower energy corresponding to the ion beam energy minus the energy of a hydrogen atom.

This is shown in Fig. 6 for the DR of C2H+.

A loss coefficient, c(H), representing the probability that a hydrogen atom is not detected, can then be determined.

For C2H+ the loss coefficient is given by where N(2C + H) is the number of counts in the 2C + H peak etc. This coefficient was determined to be 0.15 ± 0.02 for C2H+ and 0.26 ± 0.02 for C2H4+.

For C2H4+ it is also possible that H2-molecules from channel β miss the detector.

This was found to be the case in 4% of the DR events.

For C2H+, only hydrogen from channel α can have the kinetic energy required to miss the detector; the probability for a hydrogen atom from that channel to be lost is given by where n(α) is the branching ratio for channel α.

This loss factor could be implemented in the analysis through an iterative procedure by modifying the equation system in the following way

For C2H4+, H can be lost from both channel α and γ, while only the total number of lost fragments can be determined from the data.

However, in the analysis it could be determined that there are undetected hydrogen atoms coming from both channels, since fragments coming only from channel α could not contribute in a sufficient amount to the number of lost fragments.

The DR branching fraction for each channel is obtained after normalization, i.e.The product distributions resulting from the dissociative recombination of C2H+ and C2H4+ at minimum collision energy are both shown in Table 1, together with previously reported results for C2H2+6 and C2H3+.7

The present measurements demonstrate that the carbon–carbon bond is broken in 57% of the DR events for C2H+, while the carbon–carbon bond breaking channels account for only 7% of all products for C2H4+.

In the case of C2H4+, three-particle fragmentation, into C2H2 and two hydrogen atoms, dominates the DR process with a branching ratio of 66%.

In order to determine if the undetected fragments were correctly accounted for, the larger detector was used to complement these measurements.

The branching fractions obtained with the small detector agreed with the data taken with the large detector.


Comparing the present cross section measurements for C2H+ and C2H4+ with that previously reported for C2H3+,7 demonstrates that at collision energies between 1 meV and 0.l eV the cross sections for C2H4+ and C2H3+ are approximately the same while that for C2H+ is lower.

All three ions show similar energy dependences, −1.1, −1.4, and −1.2 for C2H+, C2H3+, and C2H4+, respectively.

In the so-called direct mechanism of DR, which was first proposed by Bates,16 the electron is captured directly into a repulsive potential curve, which crosses the ionic potential curve near its minimum.

When the direct process of DR dominates, the cross section is proportional to E−1cm at low collision energies due to the Coulomb attraction between the molecular ion and the electron.17

Bardsley introduced the indirect mechanism of DR in order to account for experimental rate coefficients that depart from the temperature dependence suggested by the direct mechanism.18

The indirect mechanism involves a sequence of two radiationless transitions, where the electron is first captured into a vibrationally excited Rydberg state, which is then subsequently predissociated by the same state that is reached in the direct process.

The present measurements are in good agreement with the single pass merged beams experiment for C2H+,19,20 which yielded a cross section of 7 × 10−14 cm2 at 10 meV collision energy with an energy dependence of E−1cm.

(Note that the results in ref. 19 have been corrected in ref. 20, and thereby reduced by a factor of two.) The corresponding thermal rate measured in the single pass merged beams experiment was 2.7 × 10−7(Te/300)−0.5 cm3 s−1.

Although the 300 K rate coefficients are in very good agreement, the two experiments exhibit slightly different temperature dependences, the present measurements showing the somewhat steeper temperature dependence.

No previous measurements have been made to determine the products that result from DR of C2H+ and C2H4+.

As noted previously, the complexity of the DR process makes it difficult to develop a general theory capable of predicting branching ratios for DR of polyatomic molecular ions, and there have been relatively few theoretical attempts at understanding the fragmentation mechanism.

One often cited model developed by Bates21 argues that the most favored dissociative channels would be those necessitating the fewest rearrangements of valence bonds, implying the most likely product channel in the recombination of C2Hn+ ions would be loss of a single hydrogen atom.

Previously reported branching measurements for C2H2+ and C2H3+ have generally shown a higher degree of fragmentation than predicted by the Bates model,6,7 and this appears to be the case for both C2H+ and C2H4+ as well.

For C2H4+, a single channel does dominate the DR process, but it is the loss of two hydrogen atoms to form the very stable C2H2 product.

It is not known whether the mechanism involves a concerted loss of two hydrogen atoms or whether this is a two-step process in which sufficient energy remains in the initially formed DR products such that secondary decomposition occurs.

Similarly, it is not known whether the complete dissociation of the C2H+ ion into 2C + H products results from a concerted or a sequential mechanism.

One use of the DR results presented here is inclusion into the chemical models used to predict abundances of complex molecular species in the dense interstellar clouds.

The abundances derived from various models are shown to depend on a number of variables including the choice of product channels and branching ratios for DR of complex ions.

For ions of the form XHn+, two leading chemical models both assume dissociation product distributions in which loss of H and loss of 2H (or H2) occur in equal probability for n > 2.

For species n≤2, the model of Millar and Nejad22 considers only loss of H while the model of Herbst and Leung23 also allows for strong bond breaking channels, a difference that has implications for the growth of carbon chain species in molecular clouds, for example.24

Experiments on XH2+, i.e.n = 2 species, in storage rings have shown that complete fragmentation is the dominant pathway,25 suggesting that the model of Herbst and Leung is more appropriate.

We have examined a series of small hydrocarbon molecular ions of the form C2Hn+ from n = 1–4 and find that the smaller species (n = 1–2) do in fact undergo significant C–C bond breaking during recombination, while 90–95% of the DR process for the n = 3–4 species is attributed to loss of H or 2H (or H2).

The results presented here are of importance not only to the modeling of reactions in interstellar molecular clouds,8,24 but also to the modeling of plasma-enhanced combustion reactions.

This modeling shows that by introducing plasma into a hydrocarbon fuel reactor, the combustion is enhanced due to a reduction in ignition delay.9,10

Because the primary factor in the enhancement is the increased formation of free radicals following dissociative recombination of hydrocarbon ions, accurate modeling of the hydrocarbon combustion depends on knowledge of the neutral product distributions in dissociative recombination.

In earlier models, the two-body fragmentation of molecular ions in dissociative recombination was assumed to be the dominant dissociation channel.26

However, this has been found to disagree with experiments for a majority of polyatomic systems,25 which indicated three-body fragmentation channels are more dominant than first expected.

When the molecule dissociates into three fragments, the total number of radicals produced is larger than in the two-body fragmentation.

Thus the combustion efficiency is enhanced when these experimental results are included in combustion models.

The average number of radicals produced for C2H+ and C2H4+ is 2.2 and 1.9 respectively.

For C2H+, the result is well in line with the results for C2H2+ (2.3),6 and C2H3+ (2.2),7 while the result for C2H4+ is somewhat lower compared to the earlier measurements.