Construction of orthogonal subspaces

An orthogonalization procedure is presented that allows construction of at least (n?m) vectors orthogonal to {X_j}, j equals; 1, m, by linear combinations solely among {η_i}, i equals; 1, n, n>m, and 〈X_j/η_i〉≠0. An important application of the procedure is in effective core potential methods for which valence orbitals can be constructed that are orthogonal to the core orbitals and yet involve no component of the core. Thus, a separate calculation for only the valence electrons can be performed without any explicit reference to the core electrons (orbitals).     

A New Approach to Prepare Efficient Blue AIE Emitters for Undoped OLEDs

Two aggregation‐induced emission active luminogens (TPE–pTPA and TPE–mTPA) were successfully synthesized. For comparison, another six similar compounds were prepared. Because of the introduced hole‐dominated triphenylamine (TPA), fluorene groups with high luminous efficiency, and unconjugated linkages, the π conjugation length of the obtained luminogens is effectively restricted to ensure their blue emission. The undoped organic light‐emitting diodes based on TPE–pTPA and TPE–mTPA exhibited blue or deep‐blue emissions, low turn‐on voltages (3 V), and high electroluminescence efficiencies with L_max, η_C,max, and η_P,max values of up to 26 697 cd m^?2, 3.37 cd A^?1, and 2.40 Lm W^?1.     

Synthesis,spectroscopy, thermodynamics and structure of [ZnCl2 (η3-dpktch)] (η3-dpktch = N,N,O- di-2-pyridyl ketone thiophene-2-carboxylic acid hydrazone)

When dpktch was reacted with ZnCl₂ in refluxing acetonitrile in air [ZnCl₂(η³-dpktch)] was isolated in good yield. Infrared spectra suggest weaker binding of dpktch in [ZnCl₂(η³-dpktch)] than in [CdCl₂(η³-dpktch)]. ¹H-NMR studies in non-aqueous media show that [ZnCl₂(η³-dpktch)] is sensitive to changes in its environment and exchanges its amide proton. Electronic absorption spectral measurements confirmed the sensitivity of [ZnCl₂(η³-dpktch)] to changes in its surroundings and show inter-conversion between two intra-ligand-charge-transfer transitions (ILCT) at 330?±?2 nm and 404?±?2 associated with [ZnCl₂(η³-dpktch)] and its conjugate base. Thermo-optical measurements in non-aqueous dmf and dmso show facile inter-conversion between [ZnCl₂(η³-dpktch)] and its conjugate base, respectively. Also, it is shown that protonation of dmf by [ZnCl₂(η³-dpktch)] is exothermic (standard enthalpy of protonation ΔH^θ ?=??40.7?±?1.8 kJ mol^?1), but endothermic for dmso (ΔH^θ ?=?+8.3?±?1.5 kJ mol^?1). Chemical stimuli in concentrations as low as 5.0?×?10^?7 M can be detected and determined using [ZnCl₂(η³-dpktch)] in non-aqueous media. X-ray crystallographic studies on a monoclinic, P2₁/n single crystal of [ZnCl₂(η³-dpktch)] confirmed the N,N,O-coordination of dpktch and revealed interdigitated units of [ZnCl₂(η³-dpktch)] connected via a web of hydrogen bonds.     

Proposed relationship between the exponents γ and η at liquid–vapour critical point via the dimensionality d

In earlier work, Ma [S.K. MA, Phys. Rev. Lett., 29, 1311 (1972)] has studied the critical exponents γ and η for charged and neutral Bose gases. Here we use the result of Ma, valid for general dimensionality d but only to O(m ^?1), where m is the number of components of the Bose field, to write a relation between γ(d) and η(d) to O(m ^?1). This then motivates, but now for the Ising model, a relationship between the critical exponents γ and η, via the dimensionality d. We finally demonstrate a connection between the two renormalisation group eigenvalues y _t and y _h , via the critical exponent δ with a dimensional dependence.     

Twist versus Linkage Mode: Which One is Better for the Construction of Blue Luminogens with AIE Properties?

Two new blue luminogens, Py‐4MethylTPE and Py‐4mTPE, constructed with a pyrene core and tetraphenylethene peripheries, have been successfully obtained. These two luminogens show AIE and AEE effects, respectively, as a result of minor differences in their structures. An OLED device based on Py‐4mTPE exhibits a good performance (η_C,max=4.02 cd A^?1, λ_EL,max=436 nm) and reveals the powerful effect of a different linkage mode for the construction of blue AIE luminogens.     

Investigations by electrochemical quartz crystal impedance system-electrodeposition of silver and polyaniline

An electrochemical quartz crystal impedance system (EQCIS) which allows rapid and simultaneous measurements of admittance spectra of piezoelectric quartz crystal resonance during electrochemical processes was developed by combining an HP 4395A Network/Spectrum/Impedance analyzer with an EG & G M283 potentiostat. Non-linear least square regression analyses of simultaneously acquired conductance and susceptance data were discussed in detail, giving that R_m, C_s, 1/C_m (or L_m) and of as estimation parameters is the best choice among various fitting routines. Equivalent electrical circuit parameters of quartz crystal resonance during electrodeposition of silver and polyaniline and electrochemical processes of the deposits were obtained and discussed according to changes in electrode mass, electrode surface roughness and film conductivity etc. The significant changes of motional resistance R_m and static capacitance C, observed in the silver case was believed to result mainly from changes in electrode surface roughness and the linear relationship between them was well explained by the following equation, C_s = C_q+ C_e = ε_qA_q/ h_q + ε_ek²R_m/[h_e(ωρ_Lη_L]1/2.     

Simple Bipolar Hosts with High Glass Transition Temperatures Based on 1,8‐Disubstituted Carbazole for Efficient Blue and Green Electrophosphorescent Devices with “Ideal” Turn‐on Voltage

Two hybrids based on 1,8‐disubstituted carbazole, 1,8‐OXDCz and 1,8‐mBICz , have been designed and synthesized through a facile process. The incorporation of oxadiazole or N‐phenylbenzimidazole moieties at the 1,8‐positions of carbazole greatly improves its morphological stability, giving glass transition temperatures (T_g) as high as 138 and 154 °C, respectively. Blue phosphorescent organic light‐emitting devices (PhOLEDs) with 1,8‐mBICz exhibit almost the same performance as a similarly structured device based on the mCP host, and green PhOLEDs employing the new host material 1,8‐OXDCz exhibit an ideal turn‐on voltage (2.5 V at 1.58 cd m^?2), a maximum current efficiency (η_c,max) of 73.9 cd A^?1, and a power efficiency (η_p,max) of 89.7 lm W^?1. These results are among the best performances of [Ir(ppy)₃]‐based devices with simple device configurations.     

Studies in negative ion mass spectrometry: XIV—Electron attachment reactions of a series of η6-arenetricarbonylchromium(O) complexes

Electron attachment reactions of a series of (η⁶-arene)tricarbonylchromium(O) complexes have been examined in the gas phase. The electron capture process has been shown to be influenced by the structure of the η⁶-arene ligand and its substituents. Whereas (η⁶-benzene)- and (η⁶-mesitylene)tricarbonylchromium(O) undergo dissocative electron capture, or reductive decarbonylation, yielding [M? CO]^?˙ ions of highest abundance in their negative ion mass spectra, [η⁶-(2,2-dimethylindan-1,3-dione)]tricarbonylchromium(O) forms a molecular negative ion which undergoes sequential CO eliminations and finally a demetallation to give the arene radical ion. A localization of charge on the coordinated arene ligand is proposed for the formation of [M]^?˙ in this case. (η⁶-Methylbenzoate)tricarbonylchromium(O) also forms a molecular negative ion by secondary electron attachment which decomposes by simultaneous and consecutive eliminations of up to four CO molecules. The elucidation of a mechanism and sequence for these CO eliminations has been achieved by synthesizing and examining the negative ion mass spectrum of [η⁶-(C₆H₅·¹³CO₂Me)]Cr(CO)₃. The first CO loss in the principal fragmentation pathway occurs solely from the –Cr(CO)₃ group of [M]^?˙. The effect of para substituent groups on the stabilities of molecular negative ions and their fragmentations has been ascertained using a series of para-substituted (η⁶-methylbenzoate)tricarbonylchromium(O) compounds containing the groups NH₂, OH, OCH₃, CL and COOMe. The stabilities of the [M]^?˙ ions have been rationalized in terms of the Hammett and Taft parameters σ_P, σ_I, σ_R^P, σ_P^O and σ_R^O. The overall electronic substituent effect transmitted to the carbonyl groups of the –Cr(CO)₃ unit involves both resonance and inductive components. In this series of compounds the stability of [M]^?˙ decreases as the electron withdrawing capacities of the para substituents increase.     

Syntheses,crystal structures,and photoluminescence of two new coordination polymers derived from dicarboxylate and N-donor ligands

Two metal-organic coordination polymers, [Co(tda)(ip)(H₂O)₂] _n (1) and [Mn(tda)(ip)(H₂O)] _n (2) [H₂tda?=?thiophene-2,5-dicarboxylic acid, ip?=?1H-imidazo[4,5-f][1,10]-phenanthroline], have been synthesized and characterized by elemental analyses, IR, PXRD, and X-ray diffraction. Single-crystal X-ray analyses reveal that 2,5-tda is a bridging ligand, exhibiting two coordination modes to link metal ions: μ₁-η¹?:?η⁰/μ₁-η¹?:?η⁰ and μ₂-η¹?:?η¹/μ₁-η¹?:?η⁰. Compound 1 demonstrates a 1-D structure in which Co²⁺ centers are connected via tda anions into 1-D chains; the chains are further connected via hydrogen-bonding and π?···?π interactions. Compound 2 displays a 2-D structure in which tda connects two Mn ions forming a dinuclear molecule. In 2 the 3-D supramolecular structure arrays through hydrogen-bonding and π?···?π interactions. In addition, photoluminescence for 1 and 2 is also investigated in the solid state at room temperature.     

Synthesis and structural characterization of 2D Zn(II), Cd(II), and Co(II) coordination polymers containing 3-chloro-1,2-benzenedicarboxylate and positional isomers of triazole-bipyridine

Three compounds, [Zn₂L₂(4,4′-bpt)₂] _n (1), [Cd₂L₂(3,4′-bpt)(H₂O)₂] _n (2) and {[CoL(3,3′-bpt)(H₂O)]?H₂O} _n (3) (L?=?3-Cl-1,2-benzenedicarboxylate dianion, 4,4′-bpt?=?1H-3,5-bs(4-pyridyl)-1,2,4-itriazole, 3,4′-bpt?=?1H-3-(3-pyridyl)-5-(4-pyridyl)-1,2,4-triazole and 3,3′-bpt?=?1H-3,5-bis(3-pyridyl)-1,2,4-triazole), based on three positionally isomeric triazole-bipyridine ligands, were synthesized. Structural analyses of 1–3 reveal diverse 2-D network structures, which are based on different [ML] _n (M?=?Zn, Cd, Co) chains. In the [ZnL] _n chains of 1, the carboxylic groups of L connect the adjacent Zn(II) centers with a monodentate bridging coordination mode (μ₂-η^{1 ?}/^? η¹ ). In 2, [CdL] _n is a double chain connected by the carboxylic groups of L with μ₃-η^{1 ?}/^? η²/η² and μ₃-η^{1 ?}/^? η^{1 ?}/^? η² bridges. The [CoL] _n chains of 3 are formed by the carboxylic groups of L with the μ₂-η^{1 ?}/^? η² coordination mode. The powder X-ray diffraction and the thermal stability of 1–3, the luminescent properties of 1 and 2, and the magnetic behavior of 3 have been briefly investigated.     

Determination of composition of ethylene–propylene copolymers by intrinsic viscosity

Intrinsic viscosities have been measured at 25° on five ethylene–propylene copolymer samples ranging in composition from 33 to 75 mole-% ethylene. The solvents used were n-C₈ and n-C₁₆ linear alkanes and two branched alkanes, 2,2,4-trimethylpentane and 2,2,4,4,6,8,8-heptamethylnonane (br-C₁₆). This choice was based on the supposition that the branched solvent would prefer the propylene segments and the linear solvent the ethylene segments, due to similarity in shape and possibly in orientational order. It was found that [η]_n ? [η]_br ≡ Δ[η] is indeed negative for propylene-rich copolymers, zero for a 56% ethylene copolymer, and positive for ethylene-rich copolymers. The Stockmayer–Fixman relation was used to obtain from Δ[η] a molecular-weight independent function of composition. The quantities (Δ[η]/[η])(1 + aM^?1/2) and Δ[η]/M are linear with the mole percent ethylene in the range investigated with 200 ≤ a ≤ 2000. The possibility of using these results for composition determination in ethylene–propylene copolymers is discussed. Intrinsic viscosities in the same solvents are reported for two samples of a terpolymer with ethylidene norbornene.     

On the use of corresponding orbitals for the construction of mutually orthogonal orbital sets

Consider two orbital sets χ_k, k = 1…m and η₁, 1 = 1…n, which are mutually nonorthogonal. Provided that n > m, at least n ? m orbitals of the set {η} can be orthogonalized to the set {χ} by a transformation within the set {η}. The orthogonalization of the remaining orbitals of {η} to the set {χ} requires a transformation in which the χk appear explicitly. The orthogonalization of one orbital set to another is relevant for SCF optimizations in a truncated basis set, in the presence of frozen occupied orbitals. Examples are frozen core calculations, ECP calculations, and embedded cluster calculations, where the cluster is embedded in a frozen environment. A simple orthogonalization scheme, which makes use of a corresponding orbital transformation, is presented. It is suggested that with a small, well-defined extension of the set {η} the complete orthogonalization can be done with a transformation in which the {χ} do not appear explicitly. © 1993 John Wiley & Sons, Inc.     

Survismeter Unit for Surface Tension,Viscosity, and Dipole Moment Determination for Polystyrene Interactions in Benzene

Novel instrumental set up is developed for surface tension (γ, N m^?1), viscosity (η, N s m^?2)) and dipole moment (μ/Debye) measurements. A new instrument is economic, viable and pollution free in use, the γ, η and μ from viscosities (η, N s m^?2) and surface tension (γ, N m^?1) for 0.005 to 0.125 g% polystyrene at an interval of 0.0005 g% in benzene are measured at 288.15, 293.15, and 298.15 Kelvin temperatures. The γ, η, and μ are reported stronger frictional and cohesive forces due to stronger interactions of polystyrene with benzene. The survismeter is highly accurate and mechanically operated for pulling up liquid from reservoir bulb B1 to operational bulbs B2, B3, and B4. Densities are higher than those of benzene and also infer stronger polystyrene–benzene interactions, and hydrodynamic volume (HV) calculated with intrinsic viscosity [η] is noted in 293.15 (HV) >298.15 (HV) >288.15 (HV) order with higher values at 293.15 K. Surface tension (γ) values are slightly higher than of benzene and fall in a range of 33.47 to 33.35 N m^?1.     

Cellular Mechanistic Considerations on Cytotoxic Mode of Action of Phosphino Ru(II) and Ir(III) Complexes

Two piano-stool ruthenium(II) complexes Ru(η⁶-p-cymene)Cl₂PPh₂CH₂OH ( RuPOH ) and Ru(η⁶-p-cymene)Cl₂P(p-OCH₃Ph)₂CH₂OH ( RuMPOH ) and two half-sandwich iridium(III) complexes Ir(η ⁵-Cp*)Cl₂PPh₂CH₂OH ( IrPOH ) and Ir(η ⁵-Cp*)Cl₂P(p-OCH₃Ph)₂CH₂OH ( IrMPOH ) have been studied in terms of potential anticancer activity on previously selected cell line (human lung adenocarcinoma). Based on experimental results obtained in monoculture in vitro model mechanistic considerations on the possible cellular modes of action have been carried out. ICP-MS analysis revealed the higher cellular uptake for less hydrophobic Ir(III) complexes in comparison to the corresponding Ru(II) compounds. Cytometric analysis showed a predominance of apoptosis over the other types of cell death for all complexes. The apoptotic pathway was confirmed by a decrease in mitochondrial membrane potential and the activation of caspases-3/9 for both Ru(II) and Ir(III) complexes. It was concluded that in the case of Ru(II) complexes the intense ROS generation is mainly responsible for the resulting cytotoxicity. The corresponding Ir(III) complexes trigger simultaneously at least three different cytotoxic pathways i. e., depletion of mitochondrial potential, activation of caspases-dependent apoptosis, and ROS-associated oxidation. Thus, it can be assumed that the final accumulation of toxic effects over time via parallel activation of different pathways results in the highest cytotoxicity in vitro exhibited by Ir(III) complexes when compared with Ru(II) complexes.     

Frequency dependence of intrinsic viscosity of macromolecules with finite internal viscosity

In order to explain the observed nonvanishing limiting value of dynamic intrinsic viscosity of polymer solutions at ω = ∞ one has considered the necklace model with finite resistance to the rate of coil deformation introduced long ago by Cerf for the study of gradient dependence of intrinsic viscosity and streaming birefringence. The calculation need not take into account change of hydrodynamic interaction as a consequence of coil deformation because the experimental data are always either obtained at very low gradient or extrapolated to zero gradient so that in the experiment the macromolecule has the same conformation as in the solution at rest. The model indeed yields a finite [η]′_{ω = ∞} in good agreement with experiments on polystyrene in Aroclor. According to the theory [η]′_{ω = ∞}/[η]₀ decreases with increasing molecular weight as M^?1 and M^?1/2 for the free-draining and impermeable coil, respectively. The absolute limiting value [η]_∞′, therefore turns out to be nearly independent of M, at least for small values of internal viscosity. From the observed value [η]_∞′/[η₀] one can obtain the coefficient of internal viscosity of the macromolecule. The value for polystyrene in Aroclor calculated from dynamic experiments on rather concentrated solutions is close to that derived by Cerf from streaming birefringence observations of polystyrene in a series of solvents of widely differing viscosity.     

Viscometric Analysis of Miscibility and Interactions for Binary,Ternary Polycarbonate/Brominated Polystyrene + Chloroform Systems at Different Temperatures

Viscosities of ternary systems consist of polycarbonate (PC)/brominated polystyrene (PBrS) in chloroform and their corresponding binary systems were measured at different temperatures (20, 25, and 30°C). All the measurements were carried out at the concentration ranges of 0.1–0.6 g·dL^?1. The mass ratio of PC to PBrS was selected as 75:25, 50:50, and 25:75 in the ternary solutions. Two empirical expressions of Huggins and Kraemer equations with three-parameters were used for reproducing of the experimental viscosity data. The fitting parameters were obtained for the corresponding temperatures. The miscibility criteria on the basis of the sign of Δ[η]_m based on the difference between experimental and ideal values of [η]_m, was calculated by applying the Garcia et al., theoretical equation. The effect of temperature on the viscosity data was also studied. The results from this method were correlated with the miscibility data obtained for the same system by differential scanning calorimeter (DSC) findings.     

Synthesis and characterization of a cadmium-dichloro compound of N,N , O -di-2-pyridyl ketone thiophene-2-carboxylic acid hydrazone (η 3-dpktch). The structure of [CdCl2(η 3-dpktch)]

The reaction between dpktch and CdCl₂ in refluxing acetonitrile gave [CdCl₂(η³-dpktch)] in good yield. Spectroscopic measurements divulge the coordination of dpktch and the elemental analysis confirmed its formulation. Optical measurements in N,N-dimethylformamide (dmf) and dimethylsulfoxide (DMSO) in the absence and presence of a proton donor/acceptor disclosed two highly sensitivity interlocked intra-ligand-charge-transfer transitions (ILCT) that are sensitive to their surroundings. Under basic conditions, a low-energy electronic transition with an extinction coefficient of 17,400?±?2000?M^?1cm^?1 appeared at ～403?nm and a peak minimum appeared at 326?nm. Under acidic conditions, a high energy electronic transition with extinction coefficient of 13,500?±?2000?M^?1cm^?1 appeared at ～330?nm and a shoulder appeared at ～400?nm. The addition of an acid to a dmf solution of [CdCl₂(η³-dpktch)] caused the disappearance of the low energy absorption band at 403?nm and a peak maximum appeared at 330?nm. The reverse was observed when a base was added to a DMSO solution of [CdCl₂(η³-dpktch)]. Electrochemical measurements reveal reduction of coordinated CdCl₂ and oxidation of electrodeposited cadmium metal along with ligand-based redox processes. X-ray crystallographic analysis on a monoclinic, P2₁/n single crystal of [CdCl₂(η³-dpktch)], confirmed the N,N,O-coordination of dpktch and revealed digitated units of [CdCl₂(η³-dpktch)] interlocked via a web of hydrogen bonds.     

Hydrodynamic invariant of polymer molecules

The theories of hydrodynamic properties of macromolecules in solution leading to an invariant relationship between the values of the intrinsic viscosity, [η], the molecular weight, M, and the translational friction coefficient of the molecule, f, have been considered. The review of experimental data comprising as much as about 2000 fractions of various polymers suggests that for all flexible-chain and moderately rigid-chain molecules the hydrodynamic parameter A₀ = kη₀(M[η]/100)^1/3f^?1 is actually an invariant independent of the chain length and the thermodynamic strength of the solvent and for moderately polydisperse samples also independent of the degree of their polydispersity. For polymers with very rigid chains the parameter A₀ has a high value over the experimentally investigated range of M. These conclusions make it possible to recommend the use of the following average experimental values of the invariant A₀ for the determination of M of polymers from the values of [η] and f: for flexible-chain and synthetic polymers with moderately high chain rigidity (3.2 ± 0.2) · 10^?10, for polymers with high chain rigidity (3.7 ± 0.4) · 10^?10, and for cellulose derivatives and other polysaccharides with molecular dispersity of nonelectrolyte solutions (3.30 ± 0.30) · 10^?10 erg deg^?1 mol^?1/3. The fact that the experimental value of A₀ = 3.2 · 10^?10 does not coincide with the value of A_∞ = 3.8 · 10^?10 erg deg^?1 mol^?1/3 predicted by the theories of translational friction and viscosity of macromolecules implies that the theoretical values of P_∞ = 5.11 and Φ_∞ = 2.8 · 10²³ mol^?1 are mutually incompatible and these theories require further development.     

Comparative study of ionic interactions of 1 : 1 and 1 : 2 electrolytes of nitrates salts solutions with water analysed with physicochemical data

Densities (ρ), viscosities (η) and surface tension (γ) as function of the molarity of 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 for LiNO₃, NaNO₃, KNO₃, Sr(NO₃)₂, Ba(NO₃)₂ and Pb(NO₃)₂ electrolytes are reported at 32°C. Data were regressed for limiting values for solute–solvent interactions and effects of shell numbers and electronic configurations. A confidence variance of 95.5% at Gaussian distribution was noted. Densities explained ionic forces and sizes, and viscosities defined frictional forces while the surface tension focused surface energies of hydrated ions. Slopes of densities, viscosities and surface tensions explained the concentration effects on ionic interactions. Limiting densities from Li⁺ to Ba²⁺ increased with increase in sizes. Pb²⁺ smaller in size than the Ba²⁺ had lower limiting densities. The ρ ⁰ are Ba^2+?>?Sr^2+?>?Pb^2+?>?K^+?>?Na^+?>?Li⁺ with 3.24, 2.98, 4.53, 2.109, 2.257 and 2.38?×?10^3?kg?m^?3 densities of nitrate salts, respectively, in the solid state.     

Mitochondrial Responses of Normal and Injured Human Skin Fibroblasts Following Low Level Laser Irradiation—An In Vitro Study

Laser irradiation has proved to be very efficient in speeding and improving the quality of healing in pathological conditions of diverse etiologies. However, the mechanisms by which the beneficial effects are attained are not clear. Mitochondria are the primary phototargets during irradiation. The study aimed to establish if laser irradiation had an effect on hypoxic and acidotic cells. The study also aimed to use existing information regarding the possible mechanism of action (established in wounded cells) and apply these principles to acidic and hypoxic irradiated cells to determine whether laser has a stimulatory or inhibitory effect. Cell cultures were modified to simulate conditions of hypoxia (hypoxic gas mixture 95% N₂ and 5% O₂) and acidosis (pH 6.7) whereas the central scratch model was used to simulate a wound. Cells were irradiated with a helium–neon (632.8 nm, 3 mW cm^?2) laser using 5 or 16 J cm^?2 on days 1 and 4. Mitochondrial responses were measured 1 or 24 h after laser irradiation by assessing changes in mitochondrial membrane potential (MMP), cyclic AMP, intracellular Ca²⁺ and adenosine triphosphate (ATP) cell viability. Hypoxia and acidosis significantly reduced MMP when compared with normal nonirradiated control cells. Wounded, hypoxic and acidotic cells irradiated with 5 J cm^?2 showed an increase in mitochondrial responses when compared with nonirradiated cells while 16 J cm^?2 showed a significant decrease. The study confirmed that laser irradiation with 5 J cm^?2 stimulated an increase in intracellular Ca²⁺ which resulted in an increase in MMP, ATP and cAMP, which ultimately results in photobiomodulation to restore homeostasis of injured cells.