Drone Delivery of Dehydro-Sulfurization Utilizing Doubly-Charged Negative Ions of Nanoscale Catalysts Inspired by the Biomimicry of Bee Species’ Bio-Catalysis of Pollen Conversion to Organic Honey

Abstract

The sulfur dioxide (SO₂) compound is a primary environmental pollutant worldwide, whereas elemental sulfur (S) is a global commodity possessing a variety of industrial as well as commercial functions. The chemical relationship between poisonous SO₂ and commercially viable elemental S has motivated this investigation using the Density Functional Theory calculation of the relative transition state barriers for the two-step dehydro-sulfurization oxidation–reduction reaction. Additionally, doubly-charged nanoscale platelet molybdenum disulfide (MoS₂), armchair (6,6) carbon nanotube, 28-atom graphene nanoflake (GR-28), and fullerene C-60 are utilized as catalysts. The optimal heterogeneous and homogeneous catalysis pathways of the two-step oxidation–reduction from SO₂ to elemental S are further inspired by the biomimicry of the honeybee species’ multi-step bio-catalysis of pollen conversion to organic honey. Potential applications include environmental depollution, the mining of elemental sulfur, and the functionalization of novel technologies such as the recently patented aerial and amphibious Lynchpin^TM drones.

1. Introduction

Environmental depollution and mineral synthesis continue to be areas of international interest, given the dynamics of an ever-changing analog-to-digital-to-cloud economy, developing and maintaining sustainable green industrial processes, and future pandemic avoidance [1]. Specifically, elemental S synthesis and SO₂ reduction reactions remain integral to present and future commercial applications and adherence to clean environmental protocols [2,3]. Herein, we use Density Functional Theory to investigate the two-step dehydro-sulfurization reaction. The oxidation–reduction for this two-step reaction entails increased water molecules between steps one and two, with the product of elemental S remaining as the final solute and molecular water remaining as the solvent within the resulting solution. Therefore, the reaction can efficiently serve a two-fold function, namely as an environmental cleaning agent, while simultaneously creating the commercially profitable elemental S as shown by equations 1 and 2 [4,5].

It has previously been predicted and demonstrated that the application of the muon-catalyzed fusion concept is efficient in tuning chemical reaction barriers due to orbital distortion that accelerates reaction bond breakage. Hence, in this work, we extend the muon-catalyzed fusion concept by applying double-charged negative ions to nanoscale molecules that also have been previously shown to be efficacious for tuning chemical reactions [6,7,8]. Transition metals such as gold, palladium, and silver have been shown previously to be highly inert in the bulk scale. In this theoretical work, we overcome the tendency for the typical chemical inert behavior of the transition metals by investigating semi-metallic and metallic systems at the nanoscale versus bulk scale and exciting the nanoscale catalysts by an electrical charge equivalent to two negative charges. The introduction of doubly-charged negative ions results in single and double bond breakage in the transition state (TS) and bond reformation in the final state or product in the desulfurization redox reaction [9,10,11]. Hence, we show the intrinsic value of optimizing the two-step dehydro-sulfurization reaction by the addition of two negative charges to the catalysts molybdenum disulfide, graphene-nanoflake (GR-28), (6,6) armchair carbon nanotube, and fullerene (C-60) [12]. The varying of homogeneous and heterogeneous nanoscale catalysts in each of the two steps of the dehydro-sulfurization reaction is motivated by the novel biomimicry of the fundamental role that the four different enzymes invertase, amylase, glucose oxidase, and catalase play in the bio-catalysis of sucrose conversion to organic honey. We further propose that this study may have future applications in the realm of aero-amphibious drone natural resource mining technologies [13,14,15,16,17].

2. Results

The calculations predict the chemical tunability of two-step transition state paths of the doubly-charged heterogenous and homogenous nanoscale catalysts for the potential application to toxic SO₂ purification systems. As shown in

Table 1. Direct comparison of the calculated relative transition state barrier differential heights from initial states (ΔTS = TS-initial state) for steps 1 and 2 of the oxidation–reduction reaction to atomic sulfur are represented by ΔTS-1 and ΔTS-2 in electron-volts (eV). Armchair (6,6), carbon nanotube (CNT (6.6)), molybdenum disulfide (MoS₂), graphene flake containing 28 atoms (GR-28), and fullerene (C-60) are the doubly-charged catalysts.

Catalyst (Doubly-Charged)	ΔTS-1 (eV)	Barrier (%) Change (TS-1)	ΔTS-2 (eV)	Barrier (%) Change (TS-2)
CNT (6,6)	4.44	92.6	4.36	73.2
MoS2	1.12	70.5	1.06	−10.4
GR-28	0.49	32.7	4.59	74.5
C-60	0.44	25	4.30	72.8
Doubly-charged only	0.33	0	1.17	0

and

Table 2. Calculated relative initial, transition, and final states in electron-volts (eV) of step 1 and step 2 of the desulfurization redox reaction. The relative states have been calibrated to zero for the lowest calculated potentials that were found in step 1 “or” step 2 for armchair (6,6) carbon nanotube, molybdenum disulfide (MoS₂), graphene flake containing 28 atoms (GR-28), and fullerene (C-60) doubly-charged catalysts. The calculations performed without the assistance of a catalyst for ΔTS-1 and ΔTS-2 are presented as (doubly-charged only) for the introduction of 2e⁻.

Catalyst (Doubly-Charged)	Initial 1 (eV)	TS-1 (eV)	Final 1 (eV)	Initial 2 (eV)	TS-2 (eV)	Final 2 (eV)
CNT (6,6)	0	4.44	15.34	8.89	4.36	5.68
MoS2	10.09	11.21	10.16	0	1.06	0.95
GR-28	10.62	11.10	7.05	0	4.59	10.29
C-60	0	0.44	2.31	11.92	4.30	9.53
Doubly-charged only	0	0.33	0.31	0.19	1.17	1.09

, we report step 1 transition state (TS-1) values of 4.44 eV, 1.12 eV, 0.49 eV, and 0.44 eV for CNT (6,6), MoS₂, GR-28, and C-60, respectively. The step 2 transition state (TS-2) values were 4.36 eV, 1.06 eV, 4.59 eV, and 4.30 eV for CNT (6,6), MoS₂, GR-28, and C-60, respectively. The introduction of doubly-charged negative ions to the dehydro-sulfurization reaction tunes the transition state reaction barriers of metallic and semi-metallic catalysts yielding calculation results that are consistent with previous international academic and commercial findings [18,19]. Figure 1 predicts that each step of the two-step ORR is optimizable via the sequential heterogenous or homogenous utilization of the doubly-charged negative planar catalysts GR-28 for TS-1 and MoS₂ for TS-2 with the calculated respective relative optimal values of 0.49 eV and 1.06 eV. However, a similar TS-1 barrier minimization was realized when spherical C-60 and planar MoS₂ were applied sequentially and step-wise with TS-1 and TS-2 predicted to be 0.44 eV and 1.06 eV. Alternatively, catalysis via the homogenous usage of CNT (6,6) was predicted to slow down significantly the reaction speed with values of 4.44 eV and 4.36 eV for TS-1 and TS-2, respectively. The sole use of the heterogeneous catalyst MoS₂ was to minimize the transition states to 1.12 eV for TS-1 and 1.06 eV for TS-2. Some preliminary neutral transition states were identified according to

Table 3. Calculated neutral relative initial, transition, and final states in electron-volts (eV) of step 1 and step 2 of the desulfurization for armchair (6,6) carbon nanotube, molybdenum disulfide (MoS₂), graphene flake containing 28 atoms (GR-28), and fullerene (C-60) neutral molecular catalysts.

Catalyst (Neutral)	TS-1 (eV)	TS-2 (eV)
CNT (6,6)	10.21	-
MoS2	0.05	-
GR-28	0.35	-
C-60	0.03	2.37

, which suggests the optimal barrier reductions for step 1 of CNT (6,6) and step 2 of C-60 due to the addition of a negative charge. These calculations support the application of the short-lived ion creation fundamental mechanism to multi-step chemical reactions. The transition state barriers presented here suggest efficacy for reaction barrier optimization or “chemical tuning” for future depollution and elemental S acquisition applications [20,21,22,23,24,25].

The desulfurization reaction mechanism may serve as the fundamental process that mimics honeybee bio-catalysis. Moreover, the focus of this work is desulfurization which entails toxic SO₂ elimination with the simultaneous generation of the elemental sulfur commodity rather than organic honey production. It is interesting to note that the mechanism for the biochemical production of honey is documented as an approximated 4-step biocatalytic process involving the four primary enzymes invertase, amylase, glucose oxidase, and catalase [15]. The studied catalysts here are analogously tailored to the two-step desulfurization reaction in lieu of SO₂ elimination, with simultaneous generation of elemental sulfur thereby mimicking the varying of enzymes per each step of the bio-catalysis of organic honey.

3. Discussion

The dehydro-sulfurization reaction is an oxidation–reduction mechanism (ORM), also referred to as a redox reaction. The reactant includes the introduction of diatomic oxygen into sulfur dihydride. Our research approach further introduces two electrons into the chemical reaction in order to increase the catalytic reactivities of heterogeneous (moly-disulfide) MoS₂ as well as the homogeneous molecules armchair (6,6) carbon nanotube, fullerene (C-60), and graphene (Gr-28) as modelled in

Table 4. Respective rows of geometrical optimized nanoscale molecules catalyzing the two-step desulfurization reactions. The relative initial, transition, and final state energies are reported in electro-Volts (eV) for the armchair carbon nanotube CNT (6,6), molydisulfide MoS₂, 28-atom graphene Gr-28, and fullerene C-60 nanoscale catalysts. The sulfur, carbon, oxygen, and hydrogen atoms are represented by the yellow, gray, red, and white spheres, respectively.

Nanoscale	STEP 1			STEP 2
Molecules	Initial-1	TS-1	Final-1	Initial-2	TS-2	Final-2
Armchair Carbon Nanotube CNT (6,6)
Energy Levels	0 eV	4.44 eV	15.34 eV	8.89 eV	4.36 eV	5.68 eV
MoS2 Molydisulfide
Energy Levels	10.09 eV	11.21 eV	10.36 eV	0 eV	1.06 eV	0.95 eV
Gr-28 28-atom Graphene
Energy Levels	10.62 eV	11.10 eV	7.05 eV	0 eV	4.59 eV	10.29 eV
C-60 Fullerene 60
Energy Levels	0 eV	0.44 eV	2.31 eV	11.92 eV	4.30 eV	9.53 eV

.

The resulting product is sulfur dioxide precipitated in 2 molar waters due to bond breakage and reformation as indicated by Equation (1). Additionally, two more electrons are added to the catalysts in order to further break the bond arrangements of the reactant in step 2 containing Sulfur dihydride and 2 molar Sulfur dioxide. Hence, the oxygen is removed from the sulfur dioxide due to bond breakage to form 3 molar diatomic sulfurs and 4 molar water in the final product of step 2. The addition of doubly-charged negative ions to the spherical, cylindrical, and planar nanoscale catalysts functions as a “chemical tuning” agent for each step of the dehydro-sulfurization reaction [18,19,20,21,22]. Moreover, the varying of the catalysts with each step of the redox reaction mimics the biocatalytic mechanism of sucrose conversion to organic honey through the flow of 2e- electrons that similarly cause bond breakage and bond reformation occurring in the reaction barriers. The relative barriers generated by the 2e⁻ electrons addition are compared with reference to the initial states according to Equation (3). The two-step chemical reaction can therefore be tailored with various levels of control at each step of the reaction by the sequential application of homogeneous and/or heterogeneous catalysts, as indicated by Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7. The percentage barrier changes are calculated with Equation (5) and are presented in Table 1, showing that the reaction barriers are increased in Figure 3 by 92.6% and 73.2% for CNT (6,6) calculations of TS-1 and TS-2, respectively. Hence, CNT (6,6) catalysts are predicted to slow the rate of reaction as a substrate for desulfurization. However, MoS₂ is calculated to have a barrier increase of 70.5% for TS-1 and a barrier decrease of −10.2%, as shown in Figure 4, which indicates that MoS₂ is predicted to be an excellent accelerator of reaction for step 2 of desulfurization. Figure 5 illuminates that Gr-28 tends to slow the desulfurization reaction by 32.7% and 74.5% for TS-1 and TS-2, respectively. C-60 is calculated to have the lowest reaction impedance of 25% for step 1, as presented in Figure 6. However, for step 2, the reaction barrier is reported to be 72.8%. Figure 8 shows the respective calculated transition state energies and geometrically optimized view of the catalysis steps when C-60 and MoS2 catalysts are applied to step 1 and step 2, respectively. The two materials are predicted to effectively maintain or lower transition state barriers when applied sequentially; C-60 changes the barrier by 25%, whereas MoS2 reduces the transition state energy by −10.4%, according to Table 1. Figure 8, Figure 9, Figure 10 and Figure 11 are geometrical optimizations of the pollen conversion to the organic honey mechanism that honey bees use, wherefore the enzymes invertase, amylase, glucose oxidase, and catalase are applied in nature for honey production. Similarly, the enzymes are initiated by the flow of 2e-; therefore, we have applied two varying inorganic molecules to each step of the reaction rather than applying the catalysts uniformly to all steps. This approach may find efficacy in the optimization to a plethora of other multi-step reactions.

Catalyst (−2)

2H₂S + 3O₂ → 2SO₂ + 2H₂O STEP 1

(1)

Catalyst (−2)

4H₂S + 2SO₂ → 3S₂ + 4H₂O STEP 2

(2)

6H₂S + 3O₂ → 3S₂ + 6H₂O (“Net” Chemical Results for the Reaction)

(3)

ΔTS = Transition State − Initial State (Relative T.S. Reaction Barriers)

(4)

$$\frac{TS-std}{TS}\times 100\%=(\mathrm{Barrier} \mathrm{percentage} \mathrm{change} \mathrm{given} \mathrm{reaction} \mathrm{standard})$$

(5)

4. Materials and Methods

[2+1] cyclo-addition is a typical phenomenon that occurs in organo–metallic catalytic systems, oxidation–reduction reactions, and nitrene chemistry. In this work, [2+1] cyclo-addition is specifically used in the geometrical optimization of fullerene C-60, as shown in the inset of Figure 5 [26,27,28]. However, 28-atomed graphene (GR-28), armchair nanotube (6,6), and MoS₂ catalysts are geometrically optimized by covalent and noncovalent bonding as indicated in the insets of Figure 2, Figure 3, Figure 4 and Figure 5 and the entirety of Figure 4, Figure 5 and Figure 6. The doubly-charged MoS₂, GR-28, CNT (6,6), and C-60 catalysis substrates function as reaction barrier tuning mechanisms for the desulfurization oxidation–reduction reaction (ORR), as indicated in Equations (1) and (2) [29,30]. The oxidation–reduction speed is, therefore, predicted to be regulated by the size, type, and charge of any given sample of catalysts used to produce the elemental sulfur and water products for both steps of the reaction. Hence, the quality, quantity, and overall efficiencies of the reactions can be tailored to the reactivity of each step of the ORR reaction, as well as the type of nanoscale catalyst that is used. Transition state theory is executed by performing Density Functional Theory approximations shown to be excellent for predicting chemical, physical, and electromagnetic properties of nanoscopic systems. The initial, transition, and final states are optimized, and are dependent on the application of two negative charges that activate the metallic and semi-metallic planar, cylindrical, and spherical catalysts that cause single and double bond breakage in the transition state consistent with the research findings. The GR-28 nanoflake configuration investigated is due to its similar geometrical structure and chemical function as the “Sulflower” discussed in the 2017 “MOLECULES OF THE YEAR” edition of the C&EN journal [30,31,32,33,34,35]. We use Equation (3) in order to specifically compare the relative transition State (ΔTS) values in Table 1 in order to highlight the most likely efficient heterogenous or homogenous catalyst configuration as indicated in Figure 1 [32,33,34,35,36,37]. Figure 2, Figure 3, Figure 4 and Figure 5 show that the calculated relative reaction barriers for the initial, transition, and final states are zeroed to the minimum potential for initial state calculated values occurring in step 1 or step 2 for each set of nanoscale catalysts. A 3-D triclinic lattice type with lattice lengths a:12.7548, b:12.7548, and c:17.2744 Angstroms with subsequent respective angles consisting of α:90, β:90, µ: 120 degrees being used for the AA stacked MoS₂ catalyst. The values of the MoS₂ are represented by a 1 × 1 × 1 Monkhorst–Pack grid, as shown in the inset of Figure 3, as well as the entirety of Figure 6. Noncovalent bonding is used to predict TS-1 and TS-2 for MoS₂ versus the cyclo-addition and covalent approaches utilized for CNT (6,6), GR-28, and C-60. Geometrical optimizations are performed via density functional theory utilizing local density approximation (LDA) with Vosko–Wilk–Nusair (VWN) functional for calculation efficiency. The transition states are calculated by utilizing linear synchronous transit (LST) and quadratic synchronous transit (QST) methods minimum barrier confirmations, as indicated by the data in Table 2, with minimum basis sets and self-consistent field (SCF) tolerances of 0.01 Ha, and smearing values of 0.05 Ha were applied for calculation efficiency consistent with theoretical studies conducted on nanoscale systems and chemical reactions [38,39].

5. Conclusions

The transition states for spherical C-60, planar MoS₂ and graphene (Gr-28), and CNT (6,6) tubal shaped have been calculated. The results indicate efficacy for the chemical tuning of the dehydro-sulfurization reaction as inspired by nature’s biocatalytic solution to the biocatalytic conversion of pollen or nectar to organic honey. We further propose that our findings may assist in the understanding and development of future innovative technologies by utilizing tangential flight-enabled amphibious Lynchpin^TM drones as patented and developed by T. Dashawn Howard et al. Some unique capabilities of the patented drone technology include aerial bird-like flocks, bee swarms, and “schools” of fish biomimicry that is tailorable to future multidisciplinary engineering solutions. For example, we postulate that the implementation of our doubly-charged negative-ion catalytic desulfurization predictions combined with the Lynchpin^TM drone design may offer promising SO₂ depollution remedies as well as the profitable commercial mining of elemental sulfur [40]. Moreover, the calculations provide some insight into the effects of negative charge on nanoscale systems, as evidenced by recent experimental desulfurization reaction optimizations [41,42].