Sulphur Atom Popping Model Mechanisms
- The sulphur atom popping model describes discrete sulfur-centered events—such as mantle desorption, defect relocation, or state-selective branching—that trigger broader chemical and electronic responses.
- It spans diverse systems including astrochemical freeze-out and sublimation in Orion KL, field-induced sulfur displacement in MoS₂ memristors, and state-resolved production in SH⁺ recombination.
- The model highlights how local sulfur transformations, through tailored reaction dynamics, can govern observable shifts like nonvolatile switching and phase transitions.
Searching arXiv for the cited papers and related usage of the term. arXiv search query: (Shumovskyi et al., 2021) OR (Esplugues et al., 2014) OR (Mitra et al., 24 Sep 2025) OR (Boffelli et al., 2022) “Sulphur atom popping model” denotes several sulfur-centered mechanisms in which sulfur or sulfur-bearing species undergo a discrete release, relocation, or state-selection event that then controls a larger chemical or electronic response. In the Orion KL astrochemical literature, the term refers to a two-phase UCL_CHEM scenario in which sulfur is depleted onto grains during collapse, converted predominantly into HS on ice mantles, and then returned to the gas during protostellar heating or C-type shocks (Esplugues et al., 2014). In monolayer MoS memristors, it refers to an intrinsic electric-field-driven process in which a sulfur atom adjacent to a vacancy is displaced from the chalcogen plane into the Mo plane, generating a metastable, charge-trapping defect associated with nonvolatile resistive switching (Mitra et al., 24 Sep 2025). In dissociative recombination of SH, an analogous “popping” picture describes the state-selective appearance of atomic sulfur in either the ground or the lowest excited state, with the branching controlled by dissociative pathways and Landau–Zener flux redistribution (Boffelli et al., 2022). A separate sulfur literature models liquid polyamorphism through maximum valence and polymerization-driven phase separation rather than through a popping mechanism (Shumovskyi et al., 2021).
1. Terminological scope and domains of use
In the cited literature, the expression is not attached to a single universal formalism. Instead, it labels distinct sulfur-centered events at different scales, from grain-surface desorption chemistry to defect-mediated electronic switching and state-resolved atomic production.
| Context | What “pops” | Governing picture |
|---|---|---|
| Orion KL astrochemistry | Sulfur-bearing mantle species return to gas | Phase I freeze-out, Phase II sublimation during warm-up or shock |
| MoS memristor | A sulfur atom moves into the Mo plane at a vacancy | Field-driven reactive dynamics plus charge trapping |
| SH dissociative recombination | Atomic sulfur emerges in a specific electronic state | MQDT branching and Landau–Zener redistribution |
| Liquid sulfur polyamorphism | No popping event is invoked | Maximum-valence polymerization and LLPT |
This multiplicity matters because superficially similar language can conceal very different ontologies. In Orion KL, the relevant event is thermal or shock-induced release of mantle material. In MoS, it is a local lattice rearrangement under electric field. In SH recombination, it is a state-selective dissociation product channel. The sulfur polyamorphism model, by contrast, concerns reversible covalent bonding and an additional attraction among fully bonded atoms, not a sulfur-pop process (Shumovskyi et al., 2021).
2. Orion KL: freeze-out, mantle storage, and thermal or shock release
The Orion KL formulation is a two-stage gas-grain model implemented with UCL_CHEM. Phase I is a modified collapse with freeze-out of gas-phase material onto grain mantles; Phase II begins either when a central protostar forms in the hot core or when a non-dissociative C-type shock passes through the plateau (Esplugues et al., 2014). The model adopts initial abundances relative to H nuclei of H , He 0, O 1, C 2, N 3, and S 4, and also explores sulfur reduced to 5 and 6.
A central control parameter in Phase I is the accretion efficiency,
7
where 8 is mantle CO at the end of Phase I. The explored ranges are 9 to 0 for the hot core and 1 for the plateau. Non-thermal desorption is switched off.
The model’s key sulfur assumption is that most sulfur is ionised during Phase I. This is tied to an inhomogeneous, clumpy cloud in which UV photons penetrate and ionise sulfur; the paper emphasizes sulfur’s ionisation potential of 2 eV and states that the collision timescale of S3 with negatively charged grains is about an order of magnitude smaller than for neutral carbon-, oxygen-, or nitrogen-bearing species. The consequence is efficient freeze-out of S4, followed by grain-surface conversion mainly into H5S and secondarily into OCS.
The preferred mantle composition at the end of Phase I is reported as 6, 7, and 8, giving 9 and 0. The paper states that this corresponds to “1” of frozen-out sulfur ending up as H2S when S3 is the accreting ion. A recurrent clarification follows from this: the model is not a literal release of atomic S from grains, but a release of sulfur primarily as H4S, with OCS as a secondary reservoir.
Phase II assumes 5 sublimation efficiency from the grains as the region warms. In the hot core, a central protostar forms, the temperature rises to 6 K, and evaporation is time dependent rather than instantaneous; the warm-up timescale depends on stellar mass, with 7, 8, and 9 cases modeled. In the plateau, the driver is a non-dissociative C-type shock with velocities of 0 km s1 for 2 K and 3 km s4 for 5 K; the density is held fixed during Phase II at either 6 cm7 or 8 cm9. The shock cools on the order of hundreds of years, and the dynamical timescale is 0 years.
3. Orion KL after release: gas-phase sulfur chemistry and observational constraints
Once mantle species desorb, the post-release sulfur chemistry diverges between hot core and plateau conditions. In the hot core, the dominant routes reported are
1
and
2
with a later-time recycling channel
3
The stated consequence is that SO forms mainly from SH, SO is converted into SO4 by OH, and the SO5/SO ratio increases with time (Esplugues et al., 2014).
In the plateau, the chemistry is explicitly time-stratified. Early after the shock, while the gas remains hot (6 yr), the dominant channels are
7
and
8
After the gas cools (9 yr), the chemistry shifts to
0
and
1
The paper identifies this as a chemical transition from O2-dominated to OH-dominated SO/SO3 formation and states that this transition is currently taking place in Orion KL’s plateau.
The best-fitting hot-core conditions are initial sulfur abundance 4, density 5 cm6, and stellar mass 7–8. The preferred hot-core realization is Model 5, with 9, 0, initial sulfur 1, and 2 cm3. Under these conditions the model reproduces all six species well at about 4 yr. The paper also notes that 5 can work only if the density is increased to 6 cm7, whereas solar sulfur produces H8S column densities that are too high.
For the plateau, the best fit is Model 4: initial sulfur abundance 9, final density 0 cm1, and maximum shock temperature closer to 2 K than 3 K. Lowering the density to 4 cm5 worsens SO and often OCS, and 6 underproduces SO and OCS by up to an order of magnitude. The observed source-averaged column densities used for comparison are, for the plateau, SO 7, SO8 9, CS 0, OCS 1, H2CS 3, and no H4S measurement; for the hot core, SO 5, SO6 7, CS 8, OCS 9, H00CS 01, and H02S 03, all in units of 04.
A common misunderstanding is therefore excluded by the model itself: the “sulphur atom popping” picture in Orion KL does not mean direct popping of neutral sulfur atoms from grains. It means efficient freeze-out of ionised sulfur, conversion mainly to H05S on mantles, and thermal desorption followed by rapid gas-phase reprocessing.
4. MoS06 memristors: field-driven sulfur displacement and nonvolatile switching
In monolayer MoS07 memristors, the sulphur atom popping model is an intrinsic switching mechanism in the active layer rather than an electrode-filament model. The proposed event is that a sulfur atom adjacent to a vacancy is pulled by a sufficiently strong electric field out of its original chalcogen plane into the molybdenum plane, producing a metastable popped configuration (Mitra et al., 24 Sep 2025). The physical consequences listed in the paper are the appearance of additional defect states near the Fermi level, stronger local bonding that can resemble a “virtual filament,” and charge trapping under bias. The nonvolatile state is therefore a coupled structure-plus-charge configuration.
The mechanism was first established in reactive-force-field molecular dynamics using ReaxFF. The follow-up paper stresses that ReaxFF is essential because it allows bond breaking and bond formation together with dynamic charge redistribution through charge equilibration. Partial charges are updated every timestep by a QEq scheme, so the force on an atom under bias follows the conceptual relation
08
Under field, the simulations show sulfur atoms moving from the opposite sulfur plane into the Mo plane at vacancy sites, while neighboring atoms also rearrange in-plane during prolonged field exposure. This dynamic evolution is central to the authors’ interpretation: the popped state is not treated as a geometry imposed a priori, but as a field-induced non-equilibrium product of time-dependent atomic motion and charge response.
The density-functional-theory analysis is used to reinterpret the energetics. In a relaxed 09 monolayer MoS10 supercell with a sulfur vacancy and a manually placed sulfur atom in the Mo plane, the survival of the popped atom after relaxation depends strongly on how the structure is prepared. If the vacancy structure is first relaxed and the sulfur atom is inserted afterward, the atom can revert; if the atom is moved directly into the Mo plane in the vacancy-containing structure and then relaxed, it can remain there. The paper argues from this that earlier claims against the model were inconclusive because the local neighborhood and force environment depend on the relaxation history.
At zero field or without extra charge, the popped configuration is reported to be higher in energy than the vacancy state by about 11 eV. Under increasing electric field, the popped-state energy drops while the vacancy-state energy changes little, and the CINEB calculations display an energy valley only when the field is present. Charge-density-difference plots show charge accumulation around the popped atom, supporting the interpretation that the defect becomes a favorable electron trap. Because sulfur vacancies in MoS12 already generate mid-gap states, the popped state is described as creating or enhancing a second vacancy-like trapping environment.
To mimic field-induced electron accumulation after the field is removed, the DFT calculations add electrons manually. With two extra electrons, the popped sulfur atom remains in the Mo plane after relaxation and the added charge localizes around the popped site rather than spreading uniformly. With one extra electron the popped state is unstable, whereas with two or more electrons it becomes stable. The AIMD results further report that at 13 K with two extra electrons the popped state survives for about 14 ps, with three extra electrons it remains stable for about 15 ps, and at 16 K with three extra electrons it persists for about 17 ps. The stated interpretation is that trapped charge stabilizes the popped defect and accounts for persistence after the applied field is removed.
The paper also delineates methodological limits. It argues that ground-state DFT is not well suited to validate a non-equilibrium field-induced state unless the charge state is treated appropriately, that NEB is conceptually questionable when used between a stable vacancy state and an allegedly unstable popped state, and that universal machine-learning interatomic potentials such as M3GNet are unreliable for this problem because they are not charge-aware and are trained mainly on bulk materials rather than on surfaces, interfaces, vacancies, and electric-field-driven reactive processes. These caveats do not eliminate the proposed mechanism; they specify the conditions under which the model is claimed to be meaningful.
5. SH18 dissociative recombination: state-selective sulfur production
A different sulphur-popping usage appears in the dissociative recombination of SH19 in the diffuse interstellar medium. The reaction considered is
20
with competing vibrational excitation
21
The focus is on vibrationally relaxed SH22, 23, and the core issue is that the product sulfur atom is not produced in a single undifferentiated state: the branching into S(24) and S(25) is channel dependent (Boffelli et al., 2022).
The calculation is performed in multichannel quantum defect theory. The model includes both the previously studied 26 manifold and the newly added 27 manifold, uses 33 ionization channels in total—18 vibrational levels on the SH28 29 core and 15 on the excited 30 core—retains only the incident 31-wave electron, and treats the reaction matrix to second order. The DR cross section contains both direct capture into dissociative resonant states and indirect capture into Rydberg states followed by predissociation. Rate coefficients are obtained from the Maxwellian average
32
The 33 contribution is reported to be much smaller than the 34 one: at low collision energies it is about 35–36 orders of magnitude below the 37 contribution, and around 38 K the 39 rate is near 40 whereas the 41 rate is only a few 42. The paper attributes this to a less favorable crossing with the ion and relatively weak valence–Rydberg couplings in the Franck–Condon region.
The state-selective sulfur yield follows from the dissociative branches. In the initial “no-flux-redistribution” picture, S(43) comes from capture into 44 and 45, while S(46) comes from the 47 path. Averaged over 48–49 K, the raw yields are about 50 into S(51) and 52 into S(53). The thermal rate coefficient for S(54) production is about 55 on average between 56 and 57 K, with a maximum of 58 near 59 K. For S(60) production, the rate decreases monotonically from about 61 at 62 K to 63 at 64 K.
The decisive correction arises from the crossing of the two dissociative 65 curves around
66
The crossing is treated with a Landau–Zener model,
67
with 68 Hartree. The redistributed cross sections are
69
70
The quoted probabilities are 71 at 72 eV, 73 at 74 eV, 75 at 76 eV, and 77 at 78 eV. Because 79, the branching ratios invert: for example, at 80 eV the yields change from 81, 82 without Landau–Zener redistribution to 83, 84 with it. After this treatment, the paper states that more than two-thirds of recombination events produce ground-state sulfur at very low collision energy, in good agreement with TSR storage-ring measurements.
For astrochemical use, the DR rate of 85 is fitted as
86
with 87, 88, 89, and RMS 90, where 91 is in 92. In this usage, “popping” thus refers neither to desorption nor to lattice displacement, but to the state-resolved emergence of sulfur atoms from a recombination event.
6. Relation to sulfur polyamorphism models and broader conceptual distinctions
A separate sulfur modeling framework addresses liquid polyamorphism through a maximum-valence approach rather than through any popping event. In this model, each particle has a limited number of covalent bonds, and the sulfur-like case is 93, with states 94, 95, and 96 corresponding to zero, one, and two bonds (Shumovskyi et al., 2021). The interactions are: a van der Waals core-core attraction that generates the liquid–gas transition, a narrow shell-shell attractive well that represents reversible covalent bonding, and an additional attraction between maximally bonded 97 atoms when they are not chemically bonded to one another. The baseline parameters are 98, 99, 00, and for the extra sulfur-like term 01, 02.
For 03, the reversible transitions are
04
with explicit reactions 05, 06, and 07, plus the reverse bond-breaking processes. The model yields both a low-pressure liquid–gas phase transition and a high-pressure liquid–liquid phase transition. The reported critical values are
08
and
09
The LL coexistence line has a positive slope in the 10–11 plane, and the LLPT separates a monomer-rich LDL from a polymer-rich HDL. The paper states explicitly that without the 12-13 attraction no LLPT appears.
Its order-parameter analysis uses 14, 15, and 16, with 17, and identifies 18 as an appropriate order parameter for the LLPT coupled to polymerization because 19 is symmetric across the coexistence curve and centered near 20. This liquid-sulfur framework is mechanistically different from all three popping usages above. It concerns polymerization-driven phase separation, not grain desorption, defect relocation, or state-selective atomic branching.
A plausible implication is that sulfur-focused models often derive their explanatory power from a discrete local transformation that is tightly coupled to a macroscopic observable: mantle conversion and desorption in Orion KL, a defect-plus-charge configuration in MoS21, state-selective dissociation in SH22 recombination, and bond-counting-driven polymerization in liquid sulfur. That common structural motif does not make the mechanisms interchangeable. The phrase “sulphur atom popping model” therefore requires domain-specific interpretation, with the operative physics supplied by the surrounding literature rather than by the phrase itself.
