Thermodynamics of nitrogen adsorption on the zeolite H-FER

Adsorption (at a low temperature) of nitrogen on the protonic zeolite H-FER results in hydrogen bonding of the adsorbed N₂ molecules with the zeolite Si(OH)Al Brønsted acid groups. This hydrogen bonding interaction leads to activation, in the IR, of the fundamental NN stretching mode, which appears at 2331 cm⁻¹. From the infrared spectra taken over a temperature range, while simultaneously recording integrated IR absorbance, temperature and nitrogen equilibrium pressure, the thermodynamics of the adsorption process was studied. The standard adsorption enthalpy and entropy resulted to be ΔH° = −20(±1) kJ mol⁻¹ and ΔS° = −131(±10) J mol⁻¹ K⁻¹, respectively.     

Variable temperature FT-IR studies on hydrogen adsorption on the zeolite (Mg,Na)-Y

Variable-temperature infrared spectroscopy was used for the thermodynamic studies on the adsorption of hydrogen on the zeolite (Mg,Na)-Y. Adsorption renders the HH stretching mode infrared active, and simultaneous measurement of IR absorbance and hydrogen equilibrium pressure, over a range of temperature, allowed adsorption enthalpy and entropy to be determined. The standard adsorption enthalpy and entropy resulted to be ΔH° = −18.2(±0.8) kJ mol⁻¹ and ΔS° = −136(±10) J mol⁻¹ K⁻¹, respectively. The adsorption enthalpy is substantially higher than the hydrogen liquefaction heat, which suggests that magnesium-containing porous materials are potential candidates in the search for suitable adsorbents for reversible hydrogen storage.     

Hydrogen adsorption on the faujasite-type zeolite Mg-X: An IR spectroscopic and thermodynamic study

Hydrogen adsorption (physisorption) on the faujasite-type zeolite Mg-X was studied by means of variable-temperature (80-140 K) FT-IR spectroscopy. Perturbation of the adsorbed H₂ molecules by the cationic adsorbing centres of the zeolite renders the H-H stretching mode IR active, at 4065 cm⁻¹. Simultaneous measurement of IR absorbance and hydrogen equilibrium pressure, for a series of spectra recorded at the increasing temperature, allowed standard adsorption enthalpy and entropy to be determined. They resulted to be ΔH⁰ = −13 kJ mol⁻¹ and ΔS⁰ = −114 J mol⁻¹ K⁻¹, respectively. Both, spectroscopic and thermodynamic results are discussed in the broader context of corresponding data for hydrogen adsorption on other alkali and alkaline-earth cation exchanged zeolites, showing that, while an approximate correlation exists between ΔH⁰ and H-H stretching frequency, deviations can be expected for the case of zeolites containing small metal cations.     

Intermittent temperature-programmed desorption study of perovskites used for catalytic purposes

A differential desorption technique, called intermittent temperature-programmed desorption (ITPD), was used to give new insights into the properties of La_1−xSr_xCo_0.8Fe_0.2O₃ perovskites as a contribution to improve their performances with respect to various important application fields such as catalysis, electrocatalysis and solid oxide fuel cells (SOFC). Both ITPD and interrupted TPD (carried out at different heating rates) evidenced two distinct oxygen adsorbed states, desorbing at temperatures lower than 400 °C, corresponding to less than 5% of a compact monolayer of oxide ions. The first one, for low desorption temperatures (lower than 290 °C) exhibits a heat of adsorption (ΔH) distribution from 101 to 121 kJ mol⁻¹. The second one, for higher desorption temperatures (between 290 and 400 °C) corresponds to ΔH = 146 ± 4 kJ mol⁻¹. Additionally, for temperatures higher than 400 °C, we observed a continuous desorption of oxygen species, probably originating from the sub-surface or semi-bulk, with an associated activation energy of desorption ≥175 kJ mol⁻¹.     

Adsorption and solid phase extraction of 8-hydroxyquinoline from aqueous solutions by using natural bentonite

The nitrogen-heterocyclic compound 8-hydroxyquinoline (8HQ) is one of the components of coal tar and has a wide variety of uses in industry. Because of its toxicity for aquatic organisms and harmful effects for human health, the removal of 8HQ from aqueous solutions by adsorption onto natural bentonite was investigated in the present work. The experimental results show that the optimum pH value of 2.5 is favourable for the 8HQ adsorption. The experimental data were fitted well with the pseudo-second-order kinetic and Langmuir adsorption isotherm models at all studied temperatures. The maximum adsorption capacity obtained from the Langmuir isotherm model at 20 °C was 120.6 mg g⁻¹. The calculated thermodynamic results such as ΔG° (−24.3 kJ mol⁻¹) and ΔH° (−9.56 kJ mol⁻¹) indicate that the adsorption process is spontaneous and exothermic in nature. Solid phase extraction of 8HQ was also performed. The X-ray diffractometry (XRD), Fourier Transform Infrared (FTIR) and thermogravimetric (TG) analyses were carried out in order to confirm the 8HQ adsorption onto bentonite. According to the obtained results, natural bentonite can be a reusable and effective adsorbent for the removal of 8HQ.     

Heat capacities of the electron acceptor 7,7,8,8-tetracyano- quinodimethane (TCNQ) and its radical-ion salt NH4(TCNQ) showing spin-Peierls transition

Heat capacities of the electron acceptor 7,7,8,8-tetracyanoquinodimethane (TCNQ) and its radical-ion salt NH₄-TCNQ have been measured at temperatures in the 12-350 K range by adiabatic calorimetry. A λ-type heat capacity anomaly arising from a spin-Peierls (SP) transition was found at 301.3 K in NH₄-TCNQ. The enthalpy and entropy of transition are Δ_trsH=(667±7) J mol⁻¹ and Δ_trsS=(2.19±0.02) J K⁻¹ mol⁻¹, respectively. The SP transition is characterized by a cooperative coupling between the spin and the phonon systems. By assuming a uniform one-dimensional antiferromagnetic (AF) Heisenberg chains consisting of quantum spin (S=1/2) in the high-temperature phase and an alternating AF nonuniform chains in the low-temperature phase, we estimated the magnetic contribution to the entropy as Δ_trsS_mag=0.61 J K⁻¹ mol⁻¹ and the lattice contribution as Δ_trsS_lat=1.58 J K⁻¹ mol⁻¹. Although the total magnetic entropy expected for the present compound is R ln 2 (=5.76 J K⁻¹ mol⁻¹), a majority of the magnetic entropy (∼4.6 J K⁻¹ mol⁻¹) persists in the high-temperature phase as a short-range-order effect. The present thermodynamic investigation quantitatively revealed the roles played by the spin and the phonon at the SP transition. Standard thermodynamic functions of both compounds have also been determined.     

Ethylene adsorption on the Pt-Cu bimetallic catalysts. Density functional theory cluster study

The adsorption of ethylene on Cu₁₂Pt₂ clusters has been studied within the density functional theory (DFT) approach to understand the high ethylene selectivity of Cu-rich Pt-Cu catalyst particles in the reaction of hydrogen-assisted 1,2-dichloroethane dechlorination. The structural parameters for Cu₁₂Pt₂ clusters with D_4h, D_2d, and C_3v symmetry have been calculated. The relative stability of the isomeric Cu₁₂Pt₂ clusters follows the order: C_3v > D_2d > D_4h. Each isomer has an active site for ethylene adsorption that consists of a single Pt atom surrounded by Cu atoms. The interaction of ethylene with the active site yields a π-C₂H₄ adsorption complex. The strongest π-C₂H₄ complex forms with the cluster of C_3v symmetry; the bonding energy, ΔE_π(C₂H₄), is −15.6 kcal mol⁻¹. The bonding energies for the π-C₂H₄ complex with Cu₁₄ and Pt₁₄ clusters are −6.5 and −18.8 kcal mol⁻¹, respectively.The addition of Pt to Cu modifies the valence spd-band of the cluster as compared to a Cu₁₄ cluster. The DOS near the Fermi level increases when C₂H₄ adsorbs on the Cu₁₂Pt₂ cluster. As well, the center of the d-band shifts toward lower binding energies. Ethylene adsorption also induces a number of states below the d-band. These states correspond to those of gas-phase C₂H₄.The vibrational frequencies of C₂H₄ adsorbed on the clusters of D_4h and C_3v symmetry have been calculated. The phonon vibrations occur below 250 cm⁻¹. The intense bands around 200 cm⁻¹ are attributed to stretching vibrations of the Pt-Cu bonds normal to the cluster surface. The stretching vibrations of the Pt-C bonds depend on the local structure of the active site: ν_s(Pt-C) = 268 cm⁻¹ and ν_as(Pt-C) = 357 cm⁻¹ for the cluster of the D_4h symmetry; ν_s(Pt-C) = 335 cm⁻¹ and ν_as(Pt-C) = 397 cm⁻¹ for the cluster of the C_3v symmetry. Bands in the range of 800-3100 cm⁻¹ are attributed to vibrations of the adsorbed C₂H₄ molecule. The signature frequencies of the π-C₂H₄ adsorption complex are the δ_s(CH₂) deformation vibration at ∼1200 cm⁻¹ and the ν(C-C) stretching vibration at ∼1500 cm⁻¹. These vibration are absent for di-σ-C₂H₄ adsorption complexes.     

Attenuated total reflectance spectroscopy of coumarin organosilane molecules adsorbed on a fused silica surface

Attenuated total reflectance (ATR) spectroscopy was used to investigate the adsorption of coumarin organosilane molecules onto a fused silica surface. The difference between the absorption spectra of the molecules on the surface and in solution was explained by the interaction of the adsorbed coumarin organosilane molecules with the hydroxyl groups on the fused silica surface. This interaction produces a perturbation of the π electron distribution and the electronic transitions of the coumarin chromophore of the organosilane molecules adsorbed on the surface. From the kinetics adsorption curves, the calculated enthalpy values of 74.8 ± 5.2 kJ mol⁻¹ and free energy of −38.22 ± 0.70 kJ mol⁻¹ at 23 °C indicates a chemisorption process. The high sensitivity of ATR spectroscopy allows the detection of a monolayer formed by a 10 nM concentration of coumarin organosilane molecules, which covers more than half of the maximum surface coverage at 60 °C.     

High-resolution FTIR spectroscopy of the 3ν2 band of PH3

High-resolution Fourier transform spectrum of phosphine (PH₃) at room temperature has been recorded in the region of the 3ν₂ band (2730-3100 cm⁻¹) at an apodized resolution of 0.005 cm⁻¹. About 200 vibration-rotation transitions have been least squares fitted with an rms of 0.00039 cm⁻¹ after taking into account the ΔK = ±3 interaction.     

Nuclear hyperfine structure in the XΣ state of ZrC

Electronic band systems of zirconium monocarbide, ZrC, in the 16 000-19 000 cm⁻¹ region have been observed following the reaction of laser-ablated Zr atoms with methane under supersonic free-jet conditions. Rotational analyses of high-resolution spectra have shown that the ground state of ZrC is a ³Σ state, with r₀=1.8066 Å and an unexpectedly small spin-spin parameter, λ=0.5139 cm⁻¹. The spectra are dense because of the five naturally occurring isotopes of Zr. Four of these, with mass numbers 90, 92, 94, and 96, have I=0, but the fifth, ⁹¹Zr, present in 11.22% abundance, has I=5/2. Lines of ⁹¹ZrC can be assigned in some of the strongest bands, and are found to display sizeable hyperfine splittings, with widths of up to 0.2 cm⁻¹. Analysis shows that the largest hyperfine effects are in the ground state, where b=−0.03133±0.00015 cm⁻¹ and c=−0.00123±0.00037 cm⁻¹ (3σ error limits). The large Fermi contact parameter, b, indicates that an unpaired Zr 5sσ electron is present, which, taken together with the small value of λ, means that the ground state must be a ³Σ⁺ state, from the electron configuration (Zr 5sσ)¹ (C 2pσ)¹. Internal hyperfine perturbations occur between the F₁ and F₃ electron spin components of the ground state in the range N=2-4, producing extra lines in some of the branches; the perturbations are of the type ΔN=0, ΔJ=±2, and are a second-order effect arising because the F₁ (J=N+1) and F₃ (J=N−1) spin components both interact with the F₂ (J=N) component through ΔN=0, ΔJ=±1 matrix elements of the Fermi contact operator. Second-order perturbations of this type can only occur in states that are very close to case (b) coupling.     

Interaction of indigo carmine dye with silica modified with humic acids at solid/liquid interface

Two distinct humic acids, one extracted from Brazilian peat soil, HA_PS, and another one obtained from commercial source, HA_FL, were attachment onto silica gel modified with aminopropyltrimethoxysilane, producing two material named SiHA_PS and SiHA_FL, respectively. The ability of these materials in removing indigo carmine dye from aqueous solution was followed through series of adsorption isotherms adjusted to modified Langmuir equation. The maximum number of moles adsorbed gave 6.82 ± 0.12 × 10⁻⁴ and 2.15 ± 0.17 × 10⁻⁴ mol g⁻¹ for SiHA_PS and SiHA_FL, respectively. Same interactions were calorimetrically followed and the thermodynamic data showed endothermic enthalpic values: 12.31 ± 0.55 and 24.69 ± 1.05 kJ mol⁻¹ for SiHA_PS and SiHA_FL surfaces, respectively. Gibbs free energies for two adsorption processes of indigo carmine dye presented negative values, reflecting dye/surface interactions must be accompanied by an increased in entropy values, which are 65 ± 3 and 98 ± 5 J mol⁻¹ K⁻¹ for SiHA_PS and SiHA_FL materials, respectively. The adsorption processes for both materials were spontaneous in nature although they presented an endothermic enthalpy for the interaction, resulting in an entropically favored process.     

Single crystal EPR and optical absorption study of Cr doped l-histidine hydrochloride monohydrate

EPR study of the Cr³⁺ ion doped l-histidine hydrochloride monohydrate single crystal is done at room temperature. Two magnetically inequivalent interstitial sites are observed. The hyperfine structure for Cr⁵³ isotope is also obtained. The zero field and spin Hamiltonian parameters are evaluated from the resonance lines obtained at different angular rotations and the parameters are: D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.9108±0.0002, g_y=1.9791±0.0002, g_z=2.0389±0.0002, A_x=(252±2)×10⁻⁴ cm⁻¹, A_y=(254±2)×10⁻⁴ cm⁻¹, A_z=(304±2)×10⁻⁴ cm⁻¹ for site I and D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.8543±0.0002, g_y=1.9897±0.0002, g_z=2.0793±0.0002, A_x=(251±2)×10⁻⁴ cm⁻¹, A_y=(257±2)×10⁻⁴ cm⁻¹, A_z=(309±2)×10⁻⁴ cm⁻¹ for site II, respectively. The optical absorption studies of single crystals are also carried out at room temperature in the wavelength range 195-925 nm. Using EPR and optical data, different bonding parameters are calculated and the nature of bonding in the crystal is discussed. The values of Racah parameters (B and C), crystal field parameter (Dq) and nephelauxetic parameters (h and k) are: B=636, C=3123, Dq=2039 cm⁻¹, h=1.46 and k=0.21, respectively.     

Preparation of activated carbon from a renewable bio-plant of Euphorbia rigida by H2SO4 activation and its adsorption behavior in aqueous solutions

The use of activated carbon obtained from Euphorbia rigida for the removal of a basic textile dye, which is methylene blue, from aqueous solutions at various contact times, pHs and temperatures was investigated. The plant material was chemically modified with H₂SO₄. The surface area of chemically modified activated carbon was 741.2 m² g⁻¹. The surface characterization of both plant- and activated carbon was undertaken using FTIR spectroscopic technique. The adsorption process attains equilibrium within 60 min. The experimental data indicated that the adsorption isotherms are well described by the Langmuir equilibrium isotherm equation and the calculated adsorption capacity of activated carbon was 114.45 mg g⁻¹ at 40° C. The adsorption kinetics of methylene blue obeys the pseudo-second-order kinetic model and also followed by the intraparticle diffusion model up to 60 min. The thermodynamic parameters such as ΔG°, ΔH° and ΔS° were calculated to estimate the nature of adsorption. The activation energy of the system was calculated as 55.51 kJ mol⁻¹. According to these results, prepared activated carbon could be used as a low-cost adsorbent to compare with the commercial activated carbon for the removal textile dyes from textile wastewater processes.     

Fourier transform emission spectroscopy of the EΠ-XΣ transition of CaH and CaD

The emission spectra of CaH and CaD have been recorded at high resolution using a Fourier transform spectrometer and bands belonging to the E²Π-X²Σ⁺ transition have been measured in the 20 100-20 700 cm⁻¹ region. A rotational analysis of 0-0 and 1-1 bands of both the isotopologues has been carried out. The present measurements have been combined with the previously available pure rotation and vibration-rotation data to provide improved spectroscopic constants for the E²Π state. The constants ΔG(½) = 1199.8867(34) cm⁻¹, B_e = 4.345032(49) cm⁻¹, α_e = 0.122115(92) cm⁻¹, r_e = 1.986633(11) Å for CaH, and ΔG(½)=868.7438(46) cm⁻¹, B_e = 2.212496(51) cm⁻¹, α_e = 0.036509(97) cm⁻¹, r_e = 1.993396(23) Å for CaD have been determined.     

Binding of rare earth metal complexes with an ofloxacin derivative to bovine serum albumin and its effect on the conformation of protein

The water-soluble Pr (Ⅲ) and Nd (Ⅲ) complexes with an ofloxacin derivative have been prepared and characterized. The single-crystal X-ray diffraction showed that the Pr (III) and Nd (III) complexes have the similar molecular structure. Under physiological pH condition, the effects of [PrL(NO₃)₂(CH₃OH)](NO₃) and [NdL(NO₃)₂(CH₃OH)](NO₃) on bovine serum albumin (BSA) were examined using fluorescence spectroscopy in combination with UV-vis absorbance and circular dichroism (CD) spectra. The result reveals that the quenching mechanism of fluorescence of BSA by two complexes is a static quenching process and the number of binding sites is about 1 for both. The thermodynamic parameters (ΔH=−14.52 kJ mol⁻¹, ΔS=56.54 J mol⁻¹ K⁻¹ for [PrL(NO₃)₂(CH₃OH)](NO₃) and ΔH=−24.63 kJ mol⁻¹, ΔS=22.07 J mol⁻¹ K⁻¹ for [NdL(NO₃)₂(CH₃OH)](NO₃)) indicate that hydrophobic and electrostatic interactions are the main binding force in the complexes-BSA system. The binding average distance between complexes and BSA was obtained on the basis of Förster's theory. In addition, it was proved by the CD spectra that the BSA secondary structure was changed in the presence of complexes in an aqueous solution.     

Interatomic potentials for the ground state X 0 and the two excited states 1, 0 of the intercombination cadmium line 326.1 nm broadened by Kr pressure

The temperature dependence of the Cd line absorption profile at 326.1 nm perturbed by Kr has been carefully studied over a spectral range extending from 800 cm⁻¹ in the blue wing to 1200 cm⁻¹ in the red wing using a high-resolution double-beam spectrometer. The atomic densities of krypton (N_Kr) and cadmium (N_Cd) were (2.015±0.07)×10¹⁹ and (3.62±0.05)×10¹⁸ cm⁻³, respectively. The temperature dependence of the studied line profile was analyzed in the framework of the quasi-static theory. The van der Waals coefficient differences between the ground ¹0⁺ state and the two excited states ³0⁺ and ³1 (ΔC₆⁰ and ΔC₆¹) were obtained from the near red wing profile using Kuhn's law. The values of ΔC₆⁰ and ΔC₆¹ are found to be equal to 37.8±2 and 58.5±3 eV Å⁶, respectively. The ground (X ¹0⁺), and the excited (³1, ³0⁺) state potentials at the internuclear separations from 3.2 to 6.3 Å were determined. The well depths with their positions for these states are respectively equal to 134±7 cm⁻¹, 3.95±0.2 Å; 72.3±4 cm⁻¹, 4.95±0.3 Å; and 471±12 cm⁻¹, 3.6 Å. The obtained well depths with their allowable errors are in good agreement with the values obtained before for the Cd-Kr system from some theoretical results and molecular beams experiments.     

Probing the interaction of flower-like CdSe nanostructure particles targeted to bovine serum albumin using spectroscopic techniques

The interaction between flower-like CdSe nanostructure particles (CdSe NP) and bovine serum albumin (BSA) was investigated from a spectroscopic angle under simulative physiological conditions. Under pH 7.4, CdSe NP could effectively quench the intrinsic fluorescence of BSA via static quenching. The binding constant (K_A) was 6.38, 3.27, and 1.90×10⁴ M⁻¹ at 298, 304, and 310 K, respectively and the number of binding sites was 1.20. According to the Van't Hoff equation, the thermodynamic parameters (ΔH°=−77.48 kJ mol⁻¹, ΔS°=−168.17 J mol⁻¹ K⁻¹) indicated that hydrogen bonds and van der Waals forces played a major role in stabilizing the BSA−CdSe complex. Besides, UV-vis and circular dichroism (CD) results showed that the addition of CdSe NP changed the secondary structure of BSA and led to a decrease in α-helix. These results suggested that BSA underwent substantial conformational changes induced by flower-like CdSe nanostructure particles.     

Adsorption of iso-butane on ZnO(0 0 0 1)-Zn

Presented are thermal desorption spectroscopy (TDS) and adsorption probability measurements of iso-butane on the Zn-terminated surface of ZnO. The initial adsorption probability, S₀, decreases linearly from 0.57 to 0.22 (±0.02) with impact energy, E_i = 0.74-1.92 eV, and is independent of adsorption temperature, T_s = 91-114 K (±5 K), indicating non-activated molecular adsorption. The coverage, Θ, dependent adsorption probabilities, S(Θ), show a cross-over from adsorbate-assisted adsorption (S increases with Θ) to Kisliuk-like dynamics at about the desorption temperature of iso-butane bi-layers (∼110 K). Thus, the adsorption dynamics are precursor-mediated. The enhanced (gas-surface) mass-match, caused by forming a second layer of the alkane, leads to adsorbate-assisted adsorption. A direct fitting procedure of the TDS data yields a pre-exponential factor of 2.5 × 10¹³/s and a coverage dependent heat of adsorption of E_d(Θ) = 39 − 6 ∗ Θ + 2.5 ∗ exp(−Θ/0.07) kJ/mol.     

EPR and optical absorption study of Cr-doped ammonium oxalate monohydrate single crystals

The electron paramagnetic resonance (EPR) study of the Cr³⁺-doped ammonium oxalate monohydrate (AOM) single crystal is done at room temperature. Two magnetically inequivalent sites for chromium are observed. The hyperfine structure for Cr⁵³ isotope is also obtained. The spin Hamiltonian parameters are evaluated as: D=(309±2)×10⁻⁴ cm⁻¹, E=(103±2)×10⁻⁴ cm⁻¹, g=1.9820±0.0002, A=(161±2)×10⁻⁴ cm⁻¹ for site I and D=(309±2)×10⁻⁴ cm⁻¹, E=(103±2)×10⁻⁴ cm⁻¹, g=1.9791±0.0002, A=(160±2)×10⁻⁴ cm⁻¹ for site II, respectively. On the basis of EPR data the site symmetry of Cr³⁺ doped single crystal is discussed. The optical absorption spectra are recorded in 195-925 nm wavelength range at room temperature. The energy values of different orbital levels are determined. On the basis of EPR and optical data, the nature of bonding in the crystal is discussed. The values of different parameters are B=803, C=3531, D_q=2208 cm⁻¹, h=0.59 and k=0.21, where B and C are Racah parameters, D_q is crystal field parameter and h and k are nephelauxetic parameters, respectively.     

Theoretical study of local crystal structure in KZnF3:Fe system

An analysis of the relationship between the EPR trigonal-field parameters and the local crystal structure of KZnF₃:Fe³⁺system is presented by diagonalizing the complete energy matrices for a d⁵ configuration ion in a trigonal crystal field. We propose a two-layer-ligand model, in which the ligands consist of six nearest-neighbor F⁻ ions in the first layer and eight next nearest-neighbor K⁺ ions in the second layer. The calculation indicates that the local structure distortion of KZnF₃:Fe³⁺system is due to the displacement of a K⁺ ion along C₃ axis towards the Fe³⁺ ion, which leads to the shift of the F⁻ ions away from C₃ axis. By simulating the EPR low-symmetry parameters D and (a−F), the distorted angles between the Fe³⁺-F⁻ bonds and C₃ axis are determined, Δθ₁=2.58°, Δθ₂=−1.4° at room temperature (300 K) and Δθ₁=2.84°, Δθ₂=−1.4° at low temperature (77 K). Those results are in good agreement with the experimental findings Δθ₁=2.8±0.3°and Δθ₂=−1.1±0.3°.