Crystallization conditions effect on molecular weight of solid-state polymerized poly(ethylene terephthalate)

Number-average molecular weight ( $ \overline{M}_{n} $ ) variation of polyethylene terephthalate with respect to crystallization temperature and time, and solid-state polymerization (SSP) time were studied using response surface experimental design method. All experiments were conducted in a fluidized bed reactor. $ \overline{M}_{n} $ values were calculated by Mark?CHouwink equation upon determining intrinsic viscosity (IV) of samples. Two suitable models were proposed for $ \overline{M}_{n} $ and IV, based on the regression coefficient. It was observed that $ \overline{M}_{n} $ increases with decrease in crystallization temperature and increase in crystallization time and SSP time. It was shown that SSP time is the most important parameter based on statistical calculations. Crystallization time, crystallization temperature and SSP time were determined 60?min, 160?°C and 8?h, respectively, in order to achieve maximum $ \overline{M}_{n} $ . Density measurements were applied to study the overall crystallinity of samples. Based on density results it was revealed that percent of crystallinity is not the only factor that affects the $ \overline{M}_{n} $ of polymer. Differential scanning calorimeter was used to analyze thermal properties of the samples. All samples showed two melting peaks. It was observed that the lower melting temperature peak is related to the isothermal crystallization process temperature. Polarized light microscopy was used to study spherulitic structures of polymer films after crystallization process. It was shown that the sample with smallest spherulite size had the maximum $ \overline{M}_{n} $ equal to 26,000?g/mol.     

Hansen solubility parameters of cellulose acetate butyrate–poly(caprolactone) diol blend by inverse gas chromatography

The specific retention volumes, $ V_{\text{g}}^{0} $ , for adsorption of 21 solute probes on the solid surface of cellulose acetate butyrate (CAB)–poly(caprolactone) diol (PCLD) blend determined in the temperature range by inverse gas chromatography were used to evaluate Hansen solubility parameters (HSP). The effect of plasticizer, PCLD, on the HSP of CAB was investigated. The three components of HSP namely dispersive $ \delta_{2}^{\text{d}} $ , polar $ \delta_{2}^{\text{p}} $ , and hydrogen bonding $ \delta_{2}^{\text{h}} $ of the blend surface were compared with the CAB surface. The $ \delta_{2}^{\text{h}} $ of CAB was increased due to the addition of PCLD, while the change in the dispersive and polar components was found to be insignificant. The three HSP were decreasing linearly with increase of temperature for the blend as well as for pure CAB. The variation of HSP with weight fraction of CAB shown that the $ \delta_{2}^{\text{p}} $ was positively deviating from linearity whereas $ \delta_{2}^{\text{d}} $ and $ \delta_{2}^{\text{h}} $ were negatively deviating from linearity.     

Inverse gas chromatography characterization of polyaniline complexes: application to volatile organic compounds sensing

Surface thermodynamic characteristics of two polyaniline complexes with inorganic and organic acids were investigated using inverse gas chromatography technique. Thirteen solutes were injected into two separate chromatographic columns packed with polyaniline (PANI) complexes as stationary phases without any chromatographic support. The retention volumes of these solutes were measured to show their strong retention with both PANI complexes, particularly the xylene isomers: ortho, meta and para. The free energy of adsorption, $\Updelta G_{a}$ Δ G a , consisting of dispersive term $\Updelta G_{a}^{d}$ Δ G a d and the acid–base interaction term, $\Updelta G_{a}^{s}$ Δ G a s was also determined showing that it is mainly based on its dispersive contribution. The dispersive surface energy of hydrochloric acid polyaniline complex is ranging from 70.39 mJ/m² at 130 °C to 65.75 mJ/m² at 150 °C while the surface energy of dodecylbenzenesulfonic acid polyaniline complex has shown slight upper difference ranging from 70.90 to 66.23 mJ/m² in the same temperature’s interval, thus reflecting a behavior comparable to that of high surface energy materials. Furthermore, the obtained PANI complexes powders were characterized using fourier transform infrared spectrometry, Raman spectroscopy, UV–visible, XRF and SEM techniques. The measured retention volumes were combined with linear solvation energy relationship (LSER), called Abraham law, to determine physicochemical parameters describing dispersive, polar and acid–base properties, the surface of both polyaniline was found out exhibiting a basic nature.     

Study on Isothermal Formation Dynamics of Calcium Barium Sulphoaluminate Mineral

The formation dynamics of calcium barium sulphoaluminate mineral with the composition of 2.75CaO·1.25BaO·3Al₂O₃·SO₃ (C_2.75B_1.25A₃ $\overline{\text{S}}$ S ¯ ) was studied. The results suggest that, under the preparative conditions, the formation of C_2.75B_1.25A₃ $\overline{\text{S}}$ S ¯ mineral is controlled by a diffusion mechanism from 1,100 to 1,380 °C; and, the formation dynamics fits nicely with D ₄ = 1 ? 2α/3 ? (1 ? α)^2/3 = Kt. From 1,100 to 1,300 °C, the apparent activation energy is 227.45 kJ mol^?1. From 1,300 to 1,380 °C, the apparent activation energy decreases to 175.94 kJ mol^?1, making the formation of C_2.75B_1.25A₃ $\overline{\text{S}}$ S ¯ mineral faster and easier.     

Polymerization of cyclohexene oxide by methyl-4-[bis(4-bromophenyl)amino]benzoate cation radical salts

Methyl-4-[bis(4-bromophenyl)amino]benzoate cation radical salts having non-nucleophilic anions such as $ {\text{SbF}}^{ - }_{6} $ , $ {\text{PF}}^{ - }_{6} $ and $ {\text{AsF}}^{ - }_{6} $ were newly prepared and found to be very active initiators for the polymerization of cyclohexene oxide at room temperature, in dichloromethane without any external stimulation. The effects of counter ion structure, salt and monomer concentration on the polymerization yield and molecular weight, and the mechanism of initiation are presented.     

Thermodynamic Properties of Sulfobetaine-Type Surfactants

Sulfobetaine-type surfactants containing a hydroxy group were synthesized by the reaction of long chain monoalkyl dimethyl tertiary amine with 3-chloro-2-hydroxypropanesulfonic acid sodium salt. The structures were characterized by ¹H NMR and ESI-MS. Their critical micelle concentrations (CMC) in aqueous solution were determined by the plate method in the temperature rang from 298.15 to 328.15 K. The thermodynamic parameters of micellization ( $\Delta G_{\text{mic}}^{\theta}$ , $\Delta H_{\text{mic}}^{\theta}$ and $\Delta S_{\text{mic}}^{\theta}$ ) and surface adsorption ( $\Delta G_{\text{ad}}^{\theta}$ , $\Delta H_{\text{ad}}^{\theta}$ and $\Delta S_{\text{ad}}^{\theta}$ ) were calculated from CMC data. The results showed that the micellization and surface adsorption of these surfactants in aqueous solution was a spontaneous and entropy-driven process. The micellization and surface adsorption became easier when the alkyl chain length increased from 12 carbon atoms to 14. The enthalpy–entropy compensation of micellization and adsorption was investigated. The compensation temperature were found to be (311 ± 2) K for both micellization and adsorption. The $\Delta H_{\text{mic}}^{*}$ and $\Delta H_{\text{ad}}^{*}$ decreased, but the $\Delta S_{\text{mic}}^{*}$ and $\Delta S_{\text{ad}}^{*}$ increased with increasing the hydrophobic chain length from 12 to 14.     

Thermodynamics of Micellization of Sulfobetaine Surfactants in Aqueous Solution

The thermodynamics of micellization of the sulfobetaine (SB) amphoteric surfactants, that is N-alkyl-N,N-dimethyl-3-ammonio-1-propanesulfonate and N-alkyl-N,N-dimethyl-3-ammonio-1-butanesulfonate (the carbon atom number of the alkyl chain is 12, 14 and 16 respectively) in aqueous solution, have been studied by surface tension measurements with the temperature range from 298.15 to 318.15?K. The critical micelle concentrations (CMC) of SB n-3 and SB n-4 surfactants were determined from the drop-volume methods at different temperatures. The obtained results indicated that the values of critical micelle concentration strongly depended on the surfactants species and temperatures. Thermodynamic parameters ( $ \Updelta G_{\text{mic}}^{ \circ } $ , $ \Updelta H_{\text{mic}}^{ \circ } $ and $ \Updelta S_{\text{mic}}^{ \circ } $ ) of the micelle formation were determined. The micellization was found to be enthalpy-driven at lower temperatures, while this process was entropy-driven at higher temperatures. The enthalpy?Centropy compensation were also investigated. The compensation temperature T _c and $ \Updelta H_{\text{mic}}^{*} $ decreased, while $ \Updelta S_{\text{mic}}^{*} $ increased with the increase in the hydrophobic chain length.     

Preparation, Crystal Structure and Magnetic Properties of Two 1,2-Di(4-pyridyl)ethylene-Bridged Manganese(II) Complexes

Two polymeric carboxylato-bridged manganese(II) complexes, $ {}_{\infty }^{1} $ ∞ 1 [Mn(bpe)(NBA)₂] (1) and $ {}_{\infty }^{1} $ ∞ 1 [Mn(bpe)(MBA)₂] (2) (bpe = 1,2-di(4-pyridyl)ethylene; HNBA = m-nitrobenzoic acid; HMBA = m-methyl-benzoic acid), were synthesized and characterized. Compounds 1 and 2 are isostructural. X-ray diffraction studies show that the title compounds possess a double chain structure. The chains in 1 and 2 are assembled into 2-D layers via C–H···O hydrogen bonds interactions. Furthermore, owing to the offset face-to-face π–π stacking interactions, the adjacent 2-D layers embed into each other to form a 3-D supramolecular framework. Variable-temperature (2–300 K) magnetic susceptibility measurements show the presence of weak antiferromagnetic interactions between the high-spin Mn(II) (S = 5/2) ions through a carboxylato bridge with the best fit parameters for 1 being J = ?0.13 cm^?1, zJ′ = ?0.098 cm^?1 and for 2, J = ?0.33 cm^?1, zJ′ = ?0.001 cm^?1.     

Surface characterization of cellulose acetate propionate by inverse gas chromatography

The purpose of this paper is to study the surface energetics of the polymer excipient cellulose acetate propionate (CAP) in the solid form. The net retention volumes, V _N, for n-alkanes and polar solutes have been measured in the temperature range 353.15–403.15 K by inverse gas chromatography. The dispersive surface free energy, $ \gamma_{\text{S}}^{\text{d}} $ , and Lewis acid–base parameters $ K_{\text{a}} $ and $ K_{\text{b}} $ , have been determined using V _N values. The $ \gamma_{\text{S}}^{\text{d}} $ values are decreased linearly with increase of temperature. The $ \gamma_{\text{S}}^{\text{d}} $ value at 353.15 K is 24.50 ± 1.54 mJ/m², and the temperature gradient was found to be ?0.287 mJ/m²/K¹. The $ K_{\text{a}} $ and $ K_{\text{b}} $ values are 0.410 ± 0.021 and 1.708 ± 0.388, respectively, which suggest that the CAP solid surface contain relatively more basic sites. The K _a and K _b values of CAP are compared with the similar values obtained on the cellulose acetate butyrate solid surface.     

Surface and Solution Properties of Amphiphilic Drug-Nonionic Surfactant Systems

A surface tension study was performed on mixed amphiphilic drug-nonionic surfactant systems. The drugs used were adiphenine hydrochloride and nortriptyline hydrochloride whereas surfactants were ethoxylated sorbitan esters and polyethylene oxide?Cpolypropylene oxide?Cpolyethylene oxide triblocks. The critical micelle concentration (CMC) and CMC^id (CMC at ideal mixing condition) values suggest nonideal and attractive interactions among the components. The micellar mole fraction $ (X_{ 1}^{\text{m}} ) $ values calculated using Rubingh??s model indicate predominance of the nonionic surfactant in micelle formation. The mole fraction of surfactant in mixed monolayer $ (X_{1}^{\sigma } ) $ values are greater than $ X_{ 1}^{\text{m}} $ values, indicating a greater contribution of surfactant in monolayer formation. Thermodynamic parameters, viz. Gibbs energy of micellization $ (\Updelta G_{\text{m}}^{\text{o}} ) $ , Gibbs energy of adsorption $ (\Updelta G_{\text{ad}}^{\text{o}} ) $ , and excess free energy of mixed micelles $ (\Updelta G_{\text{ex}}^{\text{m}} ) $ and monolayers $ (\Updelta G_{\text{ex}}^{\sigma } ) $ were also evaluated. All these values suggest stable mixed micelle and mixed monolayer formation.     

Unimodal and bimodal networks of physically crosslinked polyborodimethylsiloxane: viscoelastic and equibiaxial extension behaviors

Unimodal and bimodal networks of physically crosslinked polyborodimethylsiloxane (PBDMS) were prepared by end-linking hydroxy-terminated polydimethylsiloxane (PDMS) with boric acid. Their viscoelastic and equibiaxial extension behaviors were investigated. Three PDMS precursors with different number-average molecular weight ( M ¯ n $ {\overline{M}}_n $ ) were employed, of which the shortest chain had M ¯ n $ {\overline{M}}_n $ lower than the entanglement molecular weight. Bimodal networks were prepared from the mixture of the shortest and the longer PDMS chains. Linear viscoelastic behavior of unimodal network of the shortest chain gave the best fit to the Maxwell model with single relaxation time of 1.59 s, and equilibrium elastic modulus (G _e ) of the network was well-explained by phantom network model. The unimodal networks from the other two long chain precursors, however, showed multi-relaxation behavior with the longest relaxation times of 1.00–1.26 s. Moreover, their G _e was close to affine model and deviated from the phantom model with trapped entanglement factors of ~ 0.13. The bimodal networks with high mole percentage of short chains gave G _e values approximate to the predicted values of phantom model. Such bimodal networks showed an extremely large increase in modulus at high biaxial extension, attributed by the limited extensibilities of short chains and un-relaxed crosslinked junctions.     

CLA Supplementation and Aerobic Exercise Lower Blood Triacylglycerol,but Have No Effect on Peak Oxygen Uptake or Cardiorespiratory Fatigue Thresholds

This study examined the effects of 6 weeks of conjugated linoleic acid (CLA) supplementation and moderate aerobic exercise on peak oxygen uptake ( \(\dot{V}{\text{O}}_{ 2}\) peak), the gas exchange threshold (GET), the respiratory compensation point (RCP), and serum concentrations of cholesterol, triacylglycerol, and glucose in humans. Thirty-four untrained to moderately trained men (mean ± SD; age = 21.5 ± 2.8 years; mass = 77.2 ± 9.5 kg) completed this double-blind, placebo controlled study and were randomly assigned to either a CLA (Clarinol A-80; n = 18) or placebo (PLA; sunflower oil; n = 16) group. Prior to and following 6 weeks of aerobic training (50 % \(\dot{V}{\text{O}}_{ 2}\) peak for 30 min, twice per week) and supplementation (5.63 g of total CLA isomers [of which 2.67 g was c9, t11 and 2.67 g was t10, c12] or 7.35 g high oleic sunflower oil per day), each participant completed an incremental cycle ergometer test to exhaustion to determine their \(\dot{V}{\text{O}}_{ 2}\) peak, GET, and RCP and fasted blood draws were performed to measure serum concentrations of cholesterol, triacylglycerol, and glucose. Serum triacylglycerol concentrations were lower (p < 0.05) in the CLA than the PLA group. For \(\dot{V}{\text{O}}_{ 2}\) peak and glucose, there were group × time interactions (p < 0.05), however, post hoc statistical tests did not reveal any differences (p > 0.05) between the CLA and PLA groups. GET and RCP increased (p < 0.05) from pre- to post-training for both the CLA and PLA groups. Overall, these data suggested that CLA and aerobic exercise may have synergistic, blood triacylglycerol lowering effects, although CLA may be ineffective for enhancing aerobic exercise performance in conjunction with a 6-week aerobic exercise training program in college-age men.     

Structure and Biological Behaviors of Some Metallo Cationic Surfactants

In this study, different cationic surfactants were prepared by esterification with bromoacetic acid of different fatty alcohols, i.e., dodecyl, tetradecyl and hexadecyl species. The products were then reacted with diphenyl amine, and the resulting tertiary amines were quaternized with benzyl chloride to produce a series of quaternary ammonium salts. The metallocationic surfactants were prepared by complexing the cationic surfactants with nickel and copper chlorides. Surface tension of these surfactants were investigated at different temperatures. The surface parameters including critical micelle concentration (CMC), maximum surface excess (Γ _max), minimum surface area (A _min), efficiency (PC₂₀) and effectiveness (π _CMC) were studied. The thermodynamic parameters such as the free energy of micellization ( $\Updelta G_{\text{mic}}^{^\circ }$ ) and adsorption ( $\Updelta G_{\text{ads}}^{^\circ }$ ), enthalpy ( $\Updelta H_{\text{m}}^{^\circ }$ ), ( $\Updelta H_{\text{ads}}^{^\circ }$ ) and entropy ( $\Updelta S_{\text{m}}^{^\circ }$ ), ( $\Updelta S_{\text{ads}}^{^\circ }$ ) were calculated. FTIR spectra and ¹H-NMR spectra were obtained to confirm the compound structures and purity. In addition, the antimicrobial activities were determined via the inhibition zone diameter of the prepared compounds, which were measured against six strains of a representative group of microorganisms. The results indicate that these metallocationic surfactants exhibit good surface properties and good biological activity on a broad spectrum of microorganisms.     

Total concentration of main components in solutions for metal electroplating as a criterion for classifying and choosing resource-saving compositions of solutions

A comparative analysis is performed of the variations in the total concentration of the main components $\left( {\sum\limits_i {c_i } } \right)$ , in the solutions proposed and used in different years for electroplating individual metals (Cr, Cu, Ni, Zn, Sn, Cd, Pb, and Fe). A quantitative concentration criterion is determined for classifying solutions into resource-saving ( $\left( {\sum\limits_i {c_i \leqslant 2.32} } \right)$ mol-equiv/L) and resourceintensive ( $\left( {\sum\limits_i {c_i \geqslant 2.78} } \right)$ mol-equiv/L) compositions. In addition to scientific interest, this material can be useful for developing studies aimed at reducing the negative environmental impact of electroplating shops or sections.     

Cu nanoparticles for improving the mechanical performances of oil palm empty fruit bunch fibers as analyzed by Weibull model

Cu nanoparticles (CuNPs) were impregnated in oil palm empty fruit bunch (EFB) fibers via the cationization process. The fiber surface modification by CuNPs has been verified by Fourier-transformed infrared spectroscopy, field emission scanning electron microscopy and energy dispersive X-ray study. Mechanical properties were measured by the tensile test and analyzed by the Griffith and the Weibull models. The 10 mm length EFB fiber modified by CuNPs shows an increment in characteristic strength ( $ \sigma_{ 0} $ σ 0 ) and modulus (Y ₀) by about 20 and 10 % compared to the unmodified fiber, as assessed by the Weibull model. This improvement in mechanical properties is associated with the incorporation of CuNPs in the fibers. Weak-link scaling model has been applied to predict the mechanical properties of unknown fiber.     

Salt Effect on Mixed Micelle and Interfacial Properties of Conventional Cationic Surfactants and the Ionic Liquid Surfactant 1-Tetradecyl-3-methylimidazolium Bromide ([C14mim]Br)

The surface properties and mixed micellization behavior of binary combinations of an ionic liquid surfactant, namely, 1-tetradecyl-3-methylimidazolium bromide ([C₁₄mim]Br) with common cationic surfactants viz. tetradecyltrimethylammonium bromide and tetradecylpyridinium bromide in the presence of sodium bromide (NaBr) were investigated by surface tension and conductivity measurements. The critical micelle concentration (CMC) and interfacial parameters, such as the maximum surface excess (Γ_max), minimum area per molecule (A_min) and surface pressure at the CMC (π_CMC) were determined from the surface tension data. The CMC and Γ_max values were found to decrease with increasing salt concentrations. The $ \Updelta G_{\text{ad}}^{ \circ } $ and $ \Updelta G_{\text{m}}^{ \circ } $ values are negative indicating the spontaneity of micelle formation.     

Formation and characterization of nanoporous structures on surface of LPD-derived GeO2 ceramic film

This work represents an idea of forming nanoporous structures on surface of a LPD (liquid phase deposition)-derived GeO₂ ceramic film by thermal reduction of GeO₂ under hydrogen atmosphere. SEM, XRD and Raman analyses show that well-defined nanopores with size in range of 10–100 nm have been formed on surface of GeO₂ film by annealing at 600 °C for 5–10 min. The pore formation process is furthered by structural defects which serve as active sites for the thermal reduction reaction. Fast phase transformation from hexagonal GeO₂ to tetragonal GeO₂ has occurred within the first 5 min of annealing. Green-yellow (2.32 eV) and violet (2.9 eV) photoluminescences originating from $ {\text{O}} {-} \mathop {\text{Ge}}\limits^{ \bullet \bullet } {-} {\text{O}} $ and ≡Ge–Ge≡ defects are observed in the film samples. The photoluminescence peak intensity decreases with increase of annealing time due to diminution of O/Ge ratio. The film annealed for 5 min exhibits a maximum green-yellow to violet PL peak ratio, which is related to generation of some new $ {\text{O}} {-} \mathop {\text{Ge}}\limits^{ \bullet \bullet } {-} {\text{O}} $ defects at the phase interface.     

Synthesis and Properties of X-Type Alkyl Sulfonate Gemini Surfactants Derived from Cyanuric Chloride

A series of X-type alkyl sulfonate Gemini surfactants (XC_n, n?=?6, 8, 10) was synthesized by a simple method. The chemical structures of the prepared compounds were confirmed by ¹H NMR, ¹³C NMR, ESI?CMS and Elementary analysis. The surface activity and thermodynamic properties of micellization of the X-type alkyl sulfonate Gemini surfactants were compared with sodium dodecylsulfate by means of surface tension. The properties of XC_n are superior to those of SDS such as the ??_CMC and CMC of XC₁₀ are 26.3?mN/m and 0.2?mmol/L respectively. The adsorption isotherms for XC_n were established by fitting the pre-CMC surface tension data with a quadratic function. The thermodynamic parameters of micellization ( $ \Updelta G_{m}^{ \circ } $ , $ \Updelta H_{m}^{ \circ } $ , $ \Updelta S_{m}^{ \circ } $ ) derived from electrical conductivity indicate that the micellization of XC_n is entropy-driven.     

A Micro-manipulation Technique for the Purification of Diatoms for Isotope and Geochemical Analysis

A method is described for the purification and extraction of diatom samples for isotope and geochemical analysis. The technique involves a micro-manipulator attached to an inverted microscope with a cellular micro-injector system used to remove contaminants or separate assemblages into single-species samples. Whilst time consuming, the advances associated with this technique, eliminating issues related to contamination and the impact of species-dependent fractionation factor/isotopic effect, allows ultra-clean as well as species and/or size specific diatom samples to be analysed in palaeoenvironmental research down to seasonal timescale resolution. By further altering the inner dimensions of the commercially available capillary tubes, (3.5–150  $\upmu $ m) this technique can be extended for use with other microfossils including radiolaria (30  $\upmu $ m to 1 mm), pollen (6–100  $\upmu $ m) and phytolith samples (1–200  $\upmu $ m).     

Methane Steam Reforming Kinetics on a Ni/Mg/K/Al2O3 Catalyst

The kinetics of methane steam reforming were studied on a Ni/Mg/K/Al₂O₃ catalyst that was developed for conditioning of biomass-derived syngas. Reactions were conducted in a packed-bed reactor while the concentrations of reactants (methane and steam) and products (hydrogen, carbon monoxide, and carbon dioxide) were varied at atmospheric pressure, with the effects of temperature (525–700 °C) and residence time also being investigated. A power law rate model was developed using nonlinear regression to provide a predictive capability for the rate of methane conversion over this catalyst, to be used for reactor design and technoeconomic analysis of process designs. In order to provide some mechanistic insight, and to compare this catalyst to other non-promoted Ni/Al₂O₃ catalysts reported in the literature, a reaction mechanism consisting of five elementary steps, using a Langmuir–Hinshelwood type approach, was also considered. These five steps included: (i) CH₄ adsorption, (ii) H₂O adsorption, (iii) surface reaction of adsorbed CH₄ and H₂O to form CO and H₂, (iv) CO desorption, and (v) H₂ desorption. Nonlinear regression was then used to fit each of the rate laws to the experimental data. From these results, the model that assumed CH₄ adsorption to be the rate determining step provided the best fit of the experimental data. This finding is consistent with literature studies on non-promoted Ni/Al₂O₃ catalysts, in which methane adsorption has been proposed to be the rate determining step during catalytic methane steam reforming. Both the power rate laws and the rate law assuming CH₄ adsorption to be the rate determining step can be used as predictive tools for determining methane conversion for a given set of process conditions. Additionally, a rate expression that assumed the rate was only a function of methane partial pressure was considered, namely, $rate = k*P_{{CH_{4} }}$ rate = k ? P CH 4 , where $k = k_{0} *e^{{^{{ - {\text{Ea}}/{\text{RT}}}} }}$ k = k 0 ? e ? Ea / RT , with P_CH4 in units of Torr. This first-order-methane rate expression fit the data well, yielding an apparent activation energy over this catalyst of E_a = 93 kJ/mol and the pre-exponential rate constant of k₀ = 7.67 × 10⁵ mol/(g-cat s Torr CH₄).