I am working on a model for the generation of thunder on Titan, including (semi-quantitatively) the dissociation/ionization of the N2-CH4 mixture. For methane, I am using the approximate reaction CH4->C+H+H+H+H, for which the dissociation energy is ~1600 kJ/mol ( from ~400 kJ/mol for each of the 4 reactions CH4->CH3+H, CH3->CH2+H, CH2->CH+H, and CH->C+H). Is this a reasonable assumption at T=30,000K?
Boltman distribution says that the probability of your system having energy E is proportional to
EXP ( -E / RT)
in kJ/mol R=8.31E-03
T = 3.E04
Relative probablities are
400kJ 0.20
800kJ 0.04
1200kJ 0.008
1600kJ 0.0016
if this analysis is correct, then even at 30 000K very little of the method is completely dissociated.
George, thanks for the input. Nevertheless, if I solve numerically the equation for the equilibrium degree of dissociation for the mentioned reaction, I obtain that alpha~1 close to 30,000 K, with an inflexion point at 5,000 K. I will attach a plot of alpha vs T shortly.
Andi....I refer you to Blanksby and Ellison, Accounts of Chemical Research, 2003, 36, 255-263 for C-H bond dissociation energies. The thermal energy needed to remove the first H from CH4 is 104.99 x 10^3 cal/mol / 1.985 cal/(K-mol) = 52.89 x 10^3 K. So, coming at this from a different direction, I concur with George in general. However, I see the probablility of removing one H from CH4 as 47%, 2 as about 22%, 3 as about 10% and 4 as about 5%. Another thing to bear in mind though is that, if an electrical discharge such as lightning is involved, non thermal plasma formation is likely, and the species present can include a number of ionic carbon/hydrogen moieties.
Frank and George, thank you both for your inputs. In my simplified model, I admit I make some assumptions that may be too strong, given that I am not a chemical physicist. Among these are the equilibrium approximation (thus not considering dissociation/ionization kinetics) and the assumption that CH4 and N2 are decomposed entirely and the N, C, H atoms singly ionized during the discharge. I calculate the adiabatic indices of the dissociated and ionized N2 and CH4, based on T-dependent degrees of dissociation and ionization, which I obtain using the law of mass action. I am attaching plots of the dissociation degrees for N2 and CH4, along with their respective Gammas (=Cp/Cv). I am concerned by the dip in Gamma for CH4 at ~5,000 K. Another question would be, What would be an acceptable approximation for the behavior of the N2-CH4 mixture during a fast heating to 30,000 K, followed by a slow cooling to the ambient 95 K?
well, with respect to your idea, i think it is accepted for some specified limits. Of course, from a chemical viewpoint, it is totally right assumption BUT as a photonics-worker, we cannot consider such process in the dissociation experiments as we have to know all about the aimed point. Otherwise, this complex may dissociate throughout several paths dependent on the aim. I think lightening with low intensity radiation would take the result to a kind of photomixing by the fluorescence aspects of this experiment.
Oday, indeed, a super-rigorous (and accurate) model would have to include as many reactions as possible (e.g. those leading to the formation of HCN, higher hydrocarbons, radicals etc.) as well as photo-dissociation and -ionization, in non-equilibrium conditions as the gas cools down after the initial discharge. Such a thorough treatment, however, would require an entire project - right now I am looking for a "quick and dirty" ---albeit reasonably accurate--- method to incorporate dissociation and ionization processes in a general way.
Andi, I think you also need to consider the chemical mechanism behind that 30,000 K lightning temperature. I'm sorry I don't have the literature in front of me but I'll do my best to remember. When the electric field experienced by the atmosphere is great enough (the dielectric breakdown of air on Earth occurs at about 30 kV/cm), some of the molecules ionize. For example, you could end up with a CH4+ ion and a free electron. The CH4+ accelerates in one direction, while the electron accelerates in the other; each hits other molecules. At that point, all bets are off: they could ionize those other molecules (e.g. leading to N2- or N2+) or react with them. Each charged species accelerates in the massive electric field to energies great enough to react and ionize the atmosphere further. Could CH4 break up in to C + 4H? Sure! But that's not necessarily a high probability reaction. The 30 kK temperature relates to molecules zipping by each other quickly, and you should consider the likely chemical reactions that will occur when they collide and ionize. So one thing to consider instead of the CH bond dissociation energy is the ionization energies and electron affinities of CH4 and N2. Also consider the energy for the heterolytic cleavage of bonds (e.g. CH4 --> CH3- + H+) in addition to the homolytic cleavage.
Thunder is the supersonic passage of a plasma of ions including disassociated ions away from the hot lightning strike column and into the ambient atmosphere.
Outrush is supersonic no time for more disassociation.
Inrush is subsonic and slowly restores atmospheric pressure.
We aren't told the actual model for Thunder being put in place for Titan. The temperature of 30k (K) is exactly the common spectroscopic peak temperature used on earth for strikes having a duration of 50 microseconds in which 30k is the peak, 20k the average and 10k terminal temperature. All lightning produces thunder by the supersonic flow of plasma generated by the lightning moving outward from the lightning center. However the loudest thunder is the restrike thunder produced by a current flow back up the hot lower pressure atmospheric column left by the original strike, generating new plasma at a much higher speed then the original strike and making the characteristic cracking sound of such restrikes after the first thunderclap.
We do not fully understand the physics of thunder or the true temperature and duration of lightning strikes and restrikes. Having said that I have not seen any author for whom the disassociation of methane, water, O2, N2, or CO2 almost certainly occurring in the earthly plasmas generated by lightning had any significant role in predicting the extant of thunder. The key to determining the exposure at any given location on the surface near the lightning strike is atmospheric pressure, rise time of the lightning strike and the thermal characteristics of the region.
What is the mechanism for further disassociation of methane contributing to the thunder from a lightning strike? The author gives no hint and there is no mechanism to believe that a CH4 ionized to CH3 will not leave the lightning heated region in the supersonic flow of plasma.
CH4 freely extant in Titan's atmosphere may dissociate to CH3 but there is no mechanism to sustain the high temperature environment beyond the lightning strike which will rapidly dissipate to ambient temperature.
Indeed the first step from CH4 to CH3 puts the molecule in a high temperature state and insures that it will rapidly mix with cooler ambient gases as it rushes away from the strike zone. Thus in this normal case even multiple lightning strikes, or continuous lightning could not confine and continue to interact with the subject molecule.
Perhaps Titan has lightning in a bottle which is where the questions about the sequence of lightning induced dissociation belong not in the open atmosphere. One could also imagine a continuous array of lightning strikes in a closely confined area where such dissociation might occur.
Please have a look at http://kinetics.nist.gov/kinetics/ReactionSearch?r0=74828&r1=0&r2=0&r3=0&r4=0&p0=2229074&p1=12385136&p2=0&p3=0&p4=0&expandResults=true&
Even reaction CH4->CH3+H is of rather low probability. It seems to me more complicated kinetic model is needed for proper description.
1. Titan has a atmosphere with twice the pressure of the earth's.
2. It's atmosphere is composed of 98.4% Nitrogen, 1.4% CH4.
The first fact as earthly experiment has long ago established means that the breakdown or lightning propagation voltage must be substantially higher then one on earth.
The second fact means that the role of CH4 dissociation sub- elements is of little or no importance in the overall basic response of Thunder on Titan. So Andi why do you believe this at best 1% effect is significant to the characteristics of Thunder on Titan?
In any event Andi run your model for zero to all hydrogen stripping of CH4 and for the various weights suggested and examine the variation in the Thunder characteristics . Hopefully your sensors have the sensitivity to detect these small perturbations. The matching results will give us an insight to Titan's lightning heart if there is any.
Andi did not inform us that lightning has never been detected on Titan. Andi's quest was announced to world at
http://news.discovery.com/space/thunder-on-titan-110619.html
Hi all, thanks for the very informative posts. I am learning chemical physics more or less as I am typing this post. It seems that my cavalier assumption that CH4 would be decomposed in C+4H is not going to work, not even as a qualitative argument. Indeed, lightning has not been confirmed directly on Titan. Nevertheless, as far as I know, there are cloud electrification models (Tokano, Lammer et al) and some Cassini-Huygens measurements pointing to conditions that may be favorable to electric discharges. Also, convective clouds and significant rainfall have been detected recently. For my project, as Yurii points out, dissociation/ionization processes may not be directly relevant to long-range thunder. So, as a starter, I could use Gamma=1.4 and propagate the initial strong shock through a neutral Titan atmosphere (T~90 K, P~1.4 atm). Later I can consider dissociations, ionizations, chemical reactions in the wake of the shock wave. The way I am looking at the problem now, the only species-altering reactions that could influence the shock characteristics may be precursor ionization from discharge photons overtaking the shock wave.
Sorry, it was Vic who pointed out the small effects of dissociation/ionization...
Andi you may want to look at the link below which suggests that neither the liquid CH4 lakes or the N2 dominated atmosphere is going to be very conductive compared to an even modest water component in other atmospheres.
There is some hope for UV conversion in the upper Titan atmosphere of some CH4 1.4% and the other smaller components (ethane etc.) of the remaining .2% of the atmosphere into some conductive carbon seeds for lightning.
Perhaps Andi, you can suggest the path intracloud, intercloud and/or cloud to an particular conductive ground region?
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19870013966_1987013966.pdf
Many thanks for the very informative answers! In a nutshell, in the context that the initial stages of lightning are not fully understood, can one surmise that the dissociation/ionization/chemistry initiated during the return stroke are produced *by* the strong shock itself? In other words, as was suggested here, one shouldn't worry about propagating the initial shock against a gamma different than 1.4, given that all reactions (that might lower gamma) take place *behind* the shock wave. Am i correct, at least semiquantitatively?
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