Dissociative chemisorption and energy transfer for methane on Ir(111)

A 3-parameter local hot spot model of gas-surface reactivity is employed to analyze and predict dissociative sticking coefficients for CH(4) incident on Ir(111) under varied nonequilibrium and equilibrium conditions. One Ir surface oscillator and the molecular vibrations, rotations, and translational energy directed along the surface normal are treated as active degrees of freedom in the 14 dimensional microcanonical kinetics. The threshold energy for CH(4) dissociative chemisorption on Ir(111) derived from modeling molecular beam experiments is E(0) = 39 kJ/mol. Over more than 4 orders of magnitude of variation in sticking, the average relative discrepancy between the beam and theoretically derived sticking coefficients is 88%. The experimentally observed enhancement in dissociative sticking as beam translational energies decrease below approximately 10 kJ/mol is consistent with a parallel dynamical trapping/energy transfer channel that likely fails to completely thermalize the molecules to the surface temperature. This trapping-mediated sticking, indicative of specific energy transfer pathways from the surface under nonequilibrium conditions, should be a minor contributor to the overall dissociative sticking at thermal equilibrium. Surprisingly, the CH(4) dissociative sticking coefficient predicted for Ir(111) surfaces at thermal equilibrium, based on the molecular beam experiments, is roughly 4 orders of magnitude higher than recent measurements on supported nanoscale Ir catalysts at 1 bar pressure, which suggests that substantial improvements in catalyst turnover rates may be possible.     

Using effusive molecular beams and microcanonical unimolecular rate theory to characterize CH4 dissociation on Pt(111)

The dissociative sticking coefficient for CH4 on Pt(111) has been measured as a function of both gas temperature (Tg) and surface temperature (Ts) using effusive molecular beam and angle-integrated ambient gas dosing methods. The experimental results are used to optimize the three parameters of a microcanonical unimolecular rate theory (MURT) model of the reactive system. The MURT calculations allow us to extract transition state properties from the data as well as to compare our data directly to other molecular beam and thermal equilibrium sticking measurements. We find a threshold energy for dissociation of E0 = 52.5 +/- 3.5 kJ mol(-1). Furthermore, the MURT with an optimized parameter set provides for a predictive understanding of the kinetics of this C-H bond activation reaction, that is, it allows us to predict the dissociative sticking coefficient of CH4 on Pt(111) for any combination of Ts and Tg even if the two are not equal to one another, indeed, the distribution of molecular energy need not even be thermal. Comparison of our results to those from recent thermal equilibrium catalysis studies on CH4 reforming over Pt nanoclusters ( approximately 2 nm diam) dispersed on oxide substrates indicates that the reactivity of Pt(111) exceeds that of the Pt nanocatalysts by several orders of magnitude.     

Effusive molecular beam study of C2H6 dissociation on Pt(111)

The dissociative sticking coefficient for C2H6 on Pt(111) has been measured as a function of both gas temperature (Tg) and surface temperature (Ts) using effusive molecular beam and angle-integrated ambient gas dosing methods. A microcanonical unimolecular rate theory (MURT) model of the reactive system is used to extract transition state properties from the data as well as to compare our data directly with supersonic molecular beam and thermal equilibrium sticking measurements. We report for the first time the threshold energy for dissociation, E0 = 26.5 +/- 3 kJ mol(-1). This value is only weakly dependent on the other two parameters of the model. A strong surface temperature dependence in the initial sticking coefficient is observed; however, the relatively weak dependence on gas temperature indicates some combination of the following (i) not all molecular excitations are contributing equally to the enhancement of sticking, (ii) that strong entropic effects in the dissociative transition state are leading to unusually high vibrational frequencies in the transition state, and (iii) energy transfer from gas-phase rovibrational modes to the surface is surprisingly efficient. In other words, it appears that vibrational mode-specific behavior and/or molecular rotations may play stronger roles in the dissociative adsorption of C2H6 than they do for CH4. The MURT with an optimized parameter set provides for a predictive understanding of the kinetics of this C-H bond activation reaction, that is, it allows us to predict the dissociative sticking coefficient of C2H6 on Pt(111) for any combination of Ts and Tg even if the two are not equal to one another.     

Dynamically biased RRKM model of activated gas-surface reactivity: vibrational efficacy and rotation as a spectator in the dissociative chemisorption of CH4 on Pt(111)

The reactivity of CH(4) impinging on a Pt(111) surface was examined using a precursor-mediated microcanonical trapping model of dissociative chemisorption wherein the effects of rotational and vibrational energy could be explored. Dissociative sticking coefficients for a diverse range of non-equilibrium effusive beam, supersonic beam, and eigenstate-resolved experiments were simulated and an average relative discrepancy between theory and experiment of better than 50% was achieved by treating molecular rotations and translation parallel to the surface as spectator degrees of freedom, and introducing a dynamically-biased vibrational efficacy. The model parameters are {E(0) = 57.9 kJ mol(-1), s = 2, η(v) = 0.40} where E(0) is the apparent threshold energy for reaction, s is the number of surface oscillators participating in energy exchange within each gas-surface collision complex formed, and η(v) is the mean vibrational efficacy for reaction relative to normal translational energy which figures in the assembly of the active exchangeable energy which is available to surmount the activation barrier to dissociative chemisorption. GGA-DFT electronic structure calculations provided vibrational frequencies for the transition state for dissociative chemisorption. The asymmetry of the rotational state populations in supersonic and effusive molecular beam experiments allowed kinetic analysis to establish that taking rotation as a spectator degree of freedom is a good approximation. Surface phonons, rather than the incident molecules, are calculated to play the dominant role in supplying the energy required to overcome the activation barrier for dissociative chemisorption under the thermal equilibrium conditions relevant to high pressure catalysis. Over the temperature range 300 K ≤T≤ 1000 K, the thermal dissociative sticking coefficient is predicted to be well described by S(T) = S(0) exp(-E(a)/RT) where S(0) = 0.62 and E(a) = 62.6 kJ mol(-1).     

Microcanonical unimolecular rate theory at surfaces. II. Vibrational state resolved dissociative chemisorption of methane on Ni(100)

A three-parameter microcanonical theory of gas-surface reactivity is used to investigate the dissociative chemisorption of methane impinging on a Ni(100) surface. Assuming an apparent threshold energy for dissociative chemisorption of E(0)=65 kJ/mol, contributions to the dissociative sticking coefficient from individual methane vibrational states are calculated: (i) as a function of molecular translational energy to model nonequilibrium molecular beam experiments and (ii) as a function of temperature to model thermal equilibrium mbar pressure bulb experiments. Under fairly typical molecular beam conditions (e.g., E(t)>/=25 kJ mol(-1), T(s)>/=475 K, T(n)/=100 K the dissociative sticking is dominated by methane in vibrationally excited states, particularly those involving excitation of the nu(4) bending mode. Fractional energy uptakes f(j) defined as the fraction of the mean energy of the reacting gas-surface collision complexes that derives from specific degrees of freedom of the reactants (i.e., molecular translation, rotation, vibration, and surface) are calculated for thermal dissociative chemisorption. At 500 K, the fractional energy uptakes are calculated to be f(t)=14%, f(r)=21%, f(v)=40%, and f(s)=25%. Over the temperature range from 500 K to 1500 K relevant to thermal catalysis, the incident gas-phase molecules supply the preponderance of energy used to surmount the barrier to dissociative chemisorption, f(g)=f(t)+f(r)+f(v) approximately 75%, with the highest energy uptake always coming from the molecular vibrational degrees of freedom. The predictions of the statistical, mode-nonspecific microcanonical theory are compared to those of other dynamical theories and to recent experimental data.     

Microcanonical unimolecular rate theory at surfaces. III. Thermal dissociative chemisorption of methane on Pt(111) and detailed balance

A local hot spot model of gas-surface reactivity is used to investigate the state-resolved dynamics of methane dissociative chemisorption on Pt(111) under thermal equilibrium conditions. Three Pt surface oscillators, and the molecular vibrations, rotations, and the translational energy directed along the surface normal are treated as active degrees of freedom in the 16-dimensional microcanonical kinetics. Several energy transfer models for coupling a local hot spot to the surrounding substrate are developed and evaluated within the context of a master equation kinetics approach. Bounds on the thermal dissociative sticking coefficient based on limiting energy transfer models are derived. The three-parameter physisorbed complex microcanonical unimolecular rate theory (PC-MURT) is shown to closely approximate the thermal sticking under any realistic energy transfer model. Assuming an apparent threshold energy for CH(4) dissociative chemisorption of E(0)=0.61 eV on clean Pt(111), the PC-MURT is used to predict angle-resolved yield, translational, vibrational, and rotational distributions for the reactive methane flux at thermal equilibrium at 500 K. By detailed balance, these same distributions should be observed for the methane product from methyl radical hydrogenation at 500 K in the zero coverage limit if the methyl radicals are not subject to side reactions. Given that methyl radical hydrogenation can only be experimentally observed when the CH(3) radicals are kinetically stabilized against decomposition by coadsorbed H, the PC-MURT was used to evaluate E(0) in the high coverage limit. A high coverage value of E(0)=2.3 eV adequately reproduced the experimentally observed methane angular and translational energy distributions from thermal hydrogenation of methyl radicals. Although rigorous application of detailed balance arguments to this reactive system cannot be made because thermal decomposition of the methyl radicals competes with hydrogenation, approximate applicability of detailed balance would argue for a strong coverage dependence of E(0) with H coverage--a dependence not seen for methyl radical hydrogenation on Ru(0001), but not yet experimentally explored on Pt(111).     

甲烷在O/Ni(100)表面上的反应动力学研究

甲烷在Ｏ／Ｎｉ（１００）表面上的反应动力学研究俞华根，程极源（中国科学院成都有机化学研究所，成都６１００１５）关键词甲烷，活化解离，预吸附氧，Ｎｉ（１００）表面，分子动力学，势能面甲烷在金属催化剂表面活化解离是重要的催化反应，受到了高度重视．近年来，...     

Microcanonical transition state theory for activated gas-surface reaction dynamics: application to H2/CU(111) with rotation as a spectator

A microcanonical unimolecular rate theory (MURT) model incorporating quantized surface vibrations and Rice-Ramsperger-Kassel-Marcus rate constants is applied to a benchmark system for gas-surface reaction dynamics, the activated dissociative chemisorption and associative desorption of hydrogen on Cu(111). Both molecular translation parallel to the surface and rotation are treated as spectator degrees of freedom. MURT analysis of diverse experiments indicates that one surface oscillator participates in the dissociative transition state and that the threshold energy for H2 dissociation on Cu(111) is E0 = 62 kJ/mol. The spectator approximation for rotation holds well at thermally accessible rotational energies (i.e., for Er less than approximately 40 kJ/mol). Over the temperature range from 300 to 1000 K, the calculated thermal dissociative sticking coefficient is ST = S0 exp(-Ea/kBT) where S0 = 1.57 and Ea = 62.9 kJ/mol. The sigmoid shape of rovibrational eigenstate-resolved dissociative sticking coefficients as a function of normal translational energy is shown to derive from an averaging of the microcanonical sticking coefficient, with threshold energy E0, over the thermal surface oscillator distribution of the gas-surface collision complexes. Given that H2/Cu(111) is one of the most dynamically biased of gas-surface reactive systems, the simple statistical MURT model simulates and broadly rationalizes the H2/Cu(111) reactive behavior with remarkable fidelity.     

Adsorption dynamics of water on Pt{110}-(1 x 2)

The dynamics of H(2)O adsorption on Pt{110}-(1 x 2) is studied using supersonic molecular beam and temperature programed desorption techniques. The sticking probabilities are measured using the King and Wells method at a surface temperature of 165 K. The absolute initial sticking probability s(0) of H(2)O is 0.54+/-0.03 for an incident kinetic energy of 27 kJmol. However, an unusual molecular beam flux dependence on s(0) is also found. At low water coverage (theta<1), the sticking probability is independent of coverage due either to diffusion in an extrinsic precursor state formed above bilayer islands or to incorporation into the islands. We define theta=1 as the water coverage when the dissociative sticking probability of D(2) on a surface predosed with water has dropped to zero. The slow falling H(2)O sticking probability at theta>1 results from compression of the bilayer and the formation of multilayers. Temperature programed desorption of water shows fractional order kinetics consistent with hydrogen-bonded islands on the surface. A remarkable dependence of the initial sticking probability on the translational (1-27 kJ/mol) and internal energies of water is observed: s(0) is found to be essentially a step function of translational energy, increasing fivefold at a threshold energy of 5 kJ/mol. The threshold migrates to higher energies with increasing nozzle temperature (300-700 K). We conclude that both rotational state and rotational alignment of the water molecules in the seeded supersonic expansion are implicated in dictating the adsorption process.     

Nonequilibrium activated dissociative chemisorption: SiH4 on Si(100)

A three-parameter local hot spot model of gas-surface reactivity is employed to analyze and predict dissociative sticking coefficients for SiH4 incident on Si(100) under varied nonequilibrium conditions. Two Si surface oscillators and the molecular vibrations, rotations, and translational energy directed along the local surface normal are active degrees of freedom in the 15 dimensional microcanonical kinetics. The threshold energy for SiH4 dissociative chemisorption is found to be 19 kJ/mol, in quantitative agreement with recent GGA-DFT calculations. A simple scheme for increasing the rate of chemical vapor deposition of silicon from SiH4 at low surface temperatures is modeled.     

On the dynamics of H2 adsorption on the Pt(111) surface

The dynamics and kinetics of the dissociation of hydrogen over the hexagonal close packed platinum (Pt(111)) surface are investigated using Car–Parrinello molecular dynamics and static density functional theory calculations of the potential energy surfaces. The calculations model the reference energy‐resolved molecular beam experiments, considering the degrees of freedom of the catalytic surface. Two‐dimensional potential energy surfaces above the main sites on Pt(111) are determined. Combined with Car–Parrinello trajectories, they confirm the dissociative adsorption of H₂ as the only adsorption pathway on this surface at H₂ incindence energies above 5 kJ/mol. A direct determination of energy‐resolved sticking coefficients from molecular dynamics is also performed, showing an excellent agreement with the experimental data at incidence energies in the 5–30 kJ/mol range. Application of dispersion corrections does not lead to an improvement in the prediction of the H₂ sticking coefficient. The adsorption reaction rate obtained from the calculated sticking coefficients is consistent with experimentally derived literature values.     

Dynamics of analyte binding onto a metallophthalocyanine: NO/FePc

The gas-surface reaction dynamics of NO impinging on an iron(II) phthalocyanine (FePc) monolayer were investigated using King and Wells sticking measurements. The initial sticking probability was measured as a function of both incident molecular beam energy (0.09-0.4 eV) and surface temperature (100-300 K). NO adsorption onto FePc saturates at 3% of a monolayer for all incident beam energies and surface temperatures, suggesting that the final chemisorption site is confined to the Fe metal centers. At low surface temperature and low incident beam energy, the initial sticking probability is 40% and decreases linearly with increasing beam energy and surface temperature. The results are consistent with the NO molecule sticking onto the FePc molecules via physisorption to the aromatics followed by diffusion to the Fe metal center, or precursor-mediated chemisorption. The adsorption mechanism of NO onto FePc was confirmed by control studies of NO sticking onto metal-free H2Pc, inert Au111, and reactive Al111.     

甲烷在Ni表面及La薄膜上激活解离化学吸附

利用分子束技术改变甲烷的平动能E_k来研究E_k及其法向分量E_n对甲烷在Ni表面及La薄膜上激活解离吸附的影响。对CH_4/Ni及CH_4/La系统, 当甲烷的平动能E_k分别低于58.5 kJ·mol~(-1)及52.3 kJ·mol~(-1)时, 没观察到甲烷的解离吸附。当甲烷的平动能超过此阈值时, 即对CH_4/Ni系统, 当Ek=58.5增至63.8 kJ·mol~(-1)时, 初始沾着几率s_0由0至0.54线性增加; 对CH_4/La系统, 当E_k=52.3增至63.8 kJ·mol~(-1)时, S_0由0至0.49线性增加。这些结果表明, 两个系统的化学吸附是不经过前趋态的直接化学吸附。最后求出CH_4/Ni, CH_4/La系统的表观活化能分别为46.8 kJ·mol~(-1)和38.1 kJ·mol~(-1)。     

Kinetics and dynamics in physisorption of CH3Cl on HOPG: surface temperature and molecular orientation dependence

We report a study of kinetics and dynamics in physisorption of CH(3)Cl on a highly-oriented pyrolytic graphite (HOPG). Thermal energy atom scattering (TEAS) was used to probe the kinetics of thermal CH(3)Cl adsorption on HOPG during the coverage evolution. The desorption energy of CH(3)Cl on HOPG changes from 0.25 to 0.30 eV with increasing surface coverage, suggesting the attractive interaction between CH(3)Cl molecules on the surface. On the other hand, the oriented molecular beam scattering was used to monitor the dynamical interaction of CH(3)Cl with HOPG at zero coverage, demonstrating that the CH(3)Cl scattering intensity depends on the molecular orientation of the incident CH(3)Cl. The observed steric preference is not sensitive to the surface temperature. These results suggest that the moderate anisotropy in the interaction potential induces the molecular-orientation dependence of energy dissipation during the transient trapping into the physisorption well.     

Theoretical calculations of CH4 and H2 associative desorption from Ni(111): could subsurface hydrogen play an important role?

The results of theoretical calculations of associative desorption of CH(4) and H(2) from the Ni(111) surface are presented. Both minimum-energy paths and classical dynamics trajectories were generated using density-functional theory to estimate the energy and atomic forces. In particular, the recombination of a subsurface H atom with adsorbed CH(3) (methyl) or H at the surface was studied. The calculations do not show any evidence for enhanced CH(4) formation as the H atom emerges from the subsurface site. In fact, there is no minimum-energy path for such a concerted process on the energy surface. Dynamical trajectories started at the transition state for the H-atom hop from subsurface to surface site also did not lead to direct formation of a methane molecule but rather led to the formation of a thermally excited H atom and CH(3) group bound to the surface. The formation (as well as rupture) of the H-H and C-H bonds only occurs on the exposed side of a surface Ni atom. The transition states are quite similar for the two molecules, except that in the case of the C-H bond, the underlying Ni atom rises out of the surface plane by 0.25 A. Classical dynamics trajectories started at the transition state for desorption of CH(4) show that 15% of the barrier energy, 0.8 eV, is taken up by Ni atom vibrations, while about 60% goes into translation and 20% into vibration of a desorbing CH(4) molecule. The most important vibrational modes, accounting for 90% of the vibrational energy, are the four high-frequency CH(4) stretches. By time reversibility of the classical trajectories, this means that translational energy is most effective for dissociative adsorption at low-energy characteristic of thermal excitations but energy in stretching modes is also important. Quantum-mechanical tunneling in CH(4) dissociative adsorption and associative desorption is estimated to be important below 200 K and is, therefore, not expected to play an important role under typical conditions. An unexpected mechanism for the rotation of the adsorbed methyl group was discovered and illustrated a strong three-center C-H-Ni contribution to the methyl-surface bonding.     

Competing channels in the thermal decomposition of azidoacetone studied by pyrolysis in combination with molecular beam mass spectrometric techniques

The thermal decomposition of azidoacetone (CH3COCH2N3) was studied using a combined experimental and computational approach. Flash pyrolysis at a range of temperatures (296-1250 K) was used to induce thermal decomposition, and the resulting products were expanded into a molecular beam and subsequently analyzed using electron bombardment ionization coupled to a quadrupole mass spectrometer. The advantages of this technique are that the parent molecules spend a very short time in the pyrolysis zone (20-30 mus) and that the subsequent expansion permits the stabilization of thermal products that are not observable using conventional pyrolysis methods. A detailed analysis of the mass spectra as a function of pyrolysis temperature revealed the participation of five thermal decomposition channels. Ab initio calculations on the stable structures and transition states of the azidoacetone system in combination with an analysis of the dissociative ionization pattern of each channel allowed the identity and mechanism of each channel to be elucidated. At low temperatures (296-800 K) the azide decomposes principally by the loss of N2 to yield the imine (CH3COCHNH), which can further decompose to CH3CO and CHNH. At low and intermediate temperatures a process involving the loss of N2 to yield CH3CHO and HCN is also open. Finally, at high temperatures (800-1250 K) a channel in which the azide decomposes to a stable cyclic amine (CO(CH2)2NH) (after loss of N2) is active. The last channel involves subsequent thermal decomposition of this cyclic amine to ketene (H2CCO) and methanimine (H2CNH).     

Photoinduced-reaction dynamics of halogenated alkanes on iron oxide surfaces: CH3I on Fe3O4(111)-(2x2)

The adsorption, thermal chemistry, and photoreaction dynamics of methyl iodide on the (2x2) magnetite termination of natural single-crystal hematite have been investigated by time-of-flight quadrupole mass spectrometry (TOF-QMS), temperature-programmed desorption (TPD) and Auger electron spectroscopy (AES). The methyl iodide thermal desorption spectra, taken after dosing the (2x2) surface at 100 K with CH(3)I, show a multiple-peak coverage-dependent behavior, consistent with the presence of several distinct adsorbed phases, along with defect-mediated dissociative chemisorption in the first monolayer. At >1 ML, methyl iodide forms a metastable physisorbed second layer, which desorbs at 148 K, but at higher coverage converts to a layer, which desorbs at 170 K. In the presence of low-fluence-pulse irradiation at 248 nm, angle-resolved TOF-QMS measurements show that 1.6 and 0.3 eV CH(3) fragments are ejected from the adsorbate surface; these fragments originate from direct photodissociation and dissociative photoinduced electron transfer, respectively. These energetic photoejected fragments have characteristic angular distributions peaked at approximately 0 degree with respect to the surface normal. These results and the coverage-dependent relative intensities suggest that the predominant orientation in the first monolayer of the adsorbed CH(3)I is normal to the crystal plane.     

Oxygen adsorption on Pt/Ru(0001) layers

Chemical properties of epitaxially grown bimetallic layers may deviate substantially from the behavior of their constituents. Strain in conjunction with electronic effects due to the nearby interface represent the dominant contribution to this modification. One of the simplest surface processes to characterize reactivity of these substrates is the dissociative adsorption of an incoming homo-nuclear diatomic molecule. In this study, the adsorption of O(2) on various epitaxially grown Pt films on Ru(0001) has been investigated using infrared absorption spectroscopy and thermal desorption spectroscopy. Pt/Ru(0001) has been chosen as a model system to analyze the individual influences of lateral strain and of the residual substrate interaction on the energetics of a dissociative adsorption system. It is found that adsorption and dissociative sticking depends dramatically on Pt film thickness. Even though oxygen adsorption proceeds in a straightforward manner on Pt(111) and Ru(0001), molecular chemisorption of oxygen on Pt/Ru(0001) is entirely suppressed for the Pt/Ru(0001) monolayer. For two Pt layers chemisorbed molecular oxygen on Pt terraces is produced, albeit at a very slow rate; however, no (thermally induced) dissociation occurs. Only for Pt layer thicknesses N(Pt) ≥ 3 sticking gradually speeds up and annealing leads to dissociation of O(2), thereby approaching the behavior for oxygen adsorption on genuine Pt(111). For Pt monolayer films a novel state of chemisorbed O(2), most likely located at step edges of Pt monolayer islands is identified. This state is readily populated which precludes an activation barrier towards adsorption, in contrast to adsorption on terrace sites of the Pt/Ru(0001) monolayer.     

Applied reaction dynamics: efficient synthesis gas production via single collision partial oxidation of methane to CO on Rh111

Supersonic molecular beams have been used to determine the yield of CO from the partial oxidation of CH4 on a Rh111 catalytic substrate, CH4+12O2-->CO+2H2, as a function of beam kinetic energy. These experiments were done under ultrahigh vacuum conditions with concurrent molecular beams of O2 and CH4, ensuring that there was only a single collision for the CH4 to react with the surface. The fraction of CH4 converted is strongly dependent on the normal component of the incident beam's translational energy, and approaches unity for energies greater than approximately 1.3 eV. Comparison with a simplified model of the methane-Rh111 reactive potential gives insight into the barrier for methane dissociation. These results demonstrate the efficient conversion of methane to synthesis gas, CO+2H2, are of interest in hydrogen generation, and have the optimal stoichiometry for subsequent utilization in synthetic fuel production (Fischer-Tropsch or methanol synthesis). Moreover, under the reaction conditions explored, no CO2 was detected, i.e., the reaction proceeded with the production of very little, if any, unwanted greenhouse gas by-products. These findings demonstrate the efficacy of overcoming the limitations of purely thermal reaction mechanisms by coupling nonthermal mechanistic steps, leading to efficient C-H bond activation with subsequent thermal heterogeneous reactions.     

Reactions of Laser Ablation-magnesium Plasma with Methanol Clusters

IntroductionReactions of metal ions with neutral molecules orclusters produce a variety of metal complex ions andother new series of cluster ions including cations andanions.The laser ablation-molecular beam(LA-MB)method has marked its relevance in the st…