Thermodynamics of mixtures containing alkoxyethanols. Part XXV. Densities, excess molar volumes and speeds of sound at 293.15, 298.15 and 303.15 K, and isothermal compressibilities at 298.15 K for 2-alkoxyethanol + 1-butanol systems

Densities, ρ, and speeds of sound, u, of systems formed by 2-methoxyethanol (2ME), 2-ethoxyethanol (2EE), 2-propoxyethanol (2PE), or 2-butoxyethanol (2BE) and 1-butanol have been measured at 293.15, 298.15 and 303.15 K and atmospheric pressure using a vibrating tube densimeter and sound analyser Anton Paar model DSA-5000. The ρ and u values were used to calculate excess molar volumes, V^E, at those temperatures and deviations from the ideal behaviour of the thermal expansion coefficient, Δ_P, or of the isentropic and isothermal compressibilities, Δκ_S and Δκ_T at 298.15 K. From the data, it is apparent that the interactional contribution to V^E is more important for systems with 2ME or 2EE, while structural effects are more relevant in the 2PE or 2BE mixtures, and that dipolar interactions decrease with the size of the 2-alkoxyethanol. Several methods are applied to predict speeds of sound: free length theory (FLT), collision factor theory (CFT), and Nomoto, Junjie and Van Dael equations. CFT and Nomoto's equation provide the better predictions. Finally, 1-butanol + 2-alkoxyethanol, or + 2-(2-alkoxyethoxy)ethanol mixtures have been studied using ERAS. Poorer results were obtained for systems including 2-(2-alkoxyethoxy)ethanols, which may be due to dipolar interactions and structural effects are more important in such solutions.     

Effect of substrate bias on SE, XPS and XAES studies of diamond-like carbon films deposited by saddle field fast atom beam source

This paper reports the effect of positive substrate bias (V_s) varying from 0 to 180 V on the spectroscopic ellipsometry (SE), X-ray photoelectron spectroscopy (XPS) and X-ray Auger electron spectroscopy (XAES) studies of diamond-like carbon (DLC) films deposited using CH₄ gas as a feedstock into a saddle field fast atom beam (FAB) source. The values of optical constants like refractive index (n) and extinction coefficient (k) of the deposited DLC films were determined using a two phase model. The values of ‘n’ were found to fall in the range from 1.505 to 1.720 and ‘k’ from 0.03 to 0.125 by application of different values of V_s. Value of these optical constants were found to decrease with the increase of substrate bias up to 90 V and then increase beyond this value. Position of C 1s peak evaluated from XPS data was found to occur at 286.09±0.18 eV in DLC films deposited by application of different values of V_s. Observation of full width at half maximum (FWHM) (τ) value (1.928 eV at V_s=0 V, 2.0 eV at V_s=90 V and 1.89 eV at V_s=180 V) clearly hinted the existence of a point of inflection in the properties of DLC films deposited using FAB source this way. A parameter ‘D’ defined as the distance between the maximum of positive going excursion and the minimum of negative going excursion was calculated in the derivative XAES spectra. The values of ‘D’ evaluated from XAES data for DLC films were found to be 14.8, 14.5 and 15.2 at V_s=0, 90 and 180 V, respectively. The sp² percentage was calculated for samples deposited this way and was found to be low and lie approximately at 5.6, 2.8, 2.3, 5.7 and 11.5 for different values of V_s=0, 50, 90, 150 and 180 V. The sp³ content percentage and sp³/sp² ratio was found to be 94.4 and 16.7, 97.7 and 42.5 at V_s=0 and 90 V, respectively. Beyond V_s=90 V these values started decreasing. Mainly, a point of inflection in all the properties of DLC films studied over here at around 90 V of applied substrate bias has been observed, which has been explained on the basis of existing theories in the literature.     

Structure of some liquid alcohols, diols and triols: an analysis of dielectric data

This work is a continuation of our studies of the liquid structure of polyhydric alcohols and their solutions. Dielectric parameters (relaxation time, average cluster dipole moment μ¯_c, etc.) have been calculated for 1-hexanol in a wide temperature range in the framework of the cluster model proposed by Dissado and Hill; the values of apparent activation enthalpy ΔH_DHexp^≠ have been evaluated. These data were compared with the parameters previously determined by us for 2,5-hexanediol and 1,2,6-hexanetriol; the ratio μ¯_c/μ¯_v was used for an estimation of the number of molecules in clusters. It was found that at all temperatures in the range 303–393 K, the μ¯_c/μ¯_v values for 1-hexanol are significantly larger than the values of average degree of association p¯ calculated from equilibrium dielectric data; the ΔH_DHexp^≠ values for 1-hexanol are considerably lower than those for 2,5-hexanediol and 1,2,6-hexanetriol.     

Pressure–temperature studies on conductivity of TlX(X=Cl,Br,I) compounds:: I: phase diagram. II: ionic mobility

We have measured the conductivity σ of TlX(X=Cl, Br, I) compounds up to 5.3 GPa and between 300–823 K. The σ–T dependence for all compounds can be divided into three distinct regions: (i) low temperature (LT), <400 K, with unusual negative σ–T dependence, (ii) intermediate temperature (IT), 400<650 K, with positive σ–T dependence and (iii) high temperature (HT), T>650 K, with positive σ–T dependence. The σ–T isobars were used to construct the T–P solid phase diagram for each compound. The LT region data indicate a new meta-stable phase in the 1.0–3.5 GPa range. The LT→IT transition is characterized by an inverse σ–T dependence followed by normal Arrhenius behavior up to and including the HT region. The extrapolation to 1 atm of the P-dependent boundary between IT and HT regions above 3 GPa for each compound in the P–T plot yields a value close to its respective normal (1 atm) T_melt suggesting a solid order–disorder transition type paralleling -AgI behavior. The abrupt drop in conductivity in the LT region for P between 2.5–4.1 GPa of all compounds is at variance with the Arrhenius behavior observed for unperturbed ion migration implying the appearance of a second factor overriding the Arrhenius temperature dependence. Normal Arrhenius σ–T dependence prevails in both IT and HT regions with Q_c values of 85–100 kJ mol⁻¹ and 50–75 kJ mol⁻¹, respectively. The higher conductivities at 0.4 GPa for TlBr and TlI relative to their 1 atm data and the increasing σ with P are in strong contrast to the normal σ-P behavior of TlCl. The dependence of activation volume ΔV^‡ on T for TlCl, i.e. ΔV^‡>0, shows abnormally high values with a maximum at 500 K for P<3.0 GPa but reasonable ΔV^‡ values appear above 3.0 GPa. The ΔV^‡–T dependence for both TlBr and TlI with ΔV^‡<0 is incompatible with an ion transport mechanism suggesting an electronic conduction process and implying an ionic–metallic transition at higher pressures. These contrasting conductivity features are discussed and interpreted in terms of electronegativity differences and bonding character rather than structure.     

Direct measurement of the magnetocaloric effect in La0.67Ca0.33MnO3

Polycrystalline perovskite La_0.67Ca_0.33MnO₃ was synthesized by a sol–gel method. Its adiabatic temperature change ΔT_ad induced by a magnetic field change was measured directly. At 268 K, near its Curie temperature T_C, ΔT_ad of La_0.67Ca_0.33MnO₃ induced by a magnetic field change of 2.02 T reaches 2.4 K. The latent heat Q and magnetic entropy change −ΔS_M induced by a magnetic field change were calculated from the temperature dependence of ΔT_ad and zero-field heat capacity C_p. The maximum values of Q and −ΔS_M in La_0.67Ca_0.33MnO₃ induced by a magnetic field change of 2.02 T are 1.85 J g⁻¹ and 6.9 J kg⁻¹ K⁻¹, respectively. The former is larger than the phase transition latent heat of heating or cooling, which is about 1.70 J g⁻¹.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Characterization of heterogeneous interaction in binary mixtures of ethylene glycol oligomer with water, ethyl alcohol and dioxane by dielectric analysis

The associating behaviour of the binary mixtures of ethylene glycol oligomer (EGO), i.e. ethylene glycol (EG), diethylene glycol (DEG) and poly(ethylene glycol)s (PEG200, PEG300, PEG400 and PEG600) with water (W), ethyl alcohol (EA) and 1,4-dioxane (DX) over the entire concentration range at 25 °C have been investigated through their accurately measured values of dielectric constant. The static dielectric constant ε_o, high frequency limiting dielectric constant ε_∞, dielectric relaxation strength Δε, excess dielectric parameters ε^E₀ and ε^E_∞, effective Kirkwood correlation factor g^eff and corrective correlation factor g_f of EGO–W, EGO–EA and EGO–DX mixtures were determined to obtain qualitative and quantitative information about the complex formation through H-bond in these systems. Most of the evaluated dielectric parameters of EG and DEG in different ‘cosolvents’ have different characteristics as compared to the PEG–cosolvent mixture. The observed linear and non-linear behaviour of Δε against EGO monomer unit mole fraction X confirms the variation in the homogeneous structures in their binary mixtures with concentration variation. Appearance of the maximum in ε^E₀ against X plots indicates that a complex stable adduct is formed in the EGO–W mixtures at stoichiometric ratio 1:1.7 for lower oligomers but this ratio seems to be 1.7:1 for higher EGO molecules, which confirms that the EGO size and chain flexibility affects the complex formation between EGO and W. In case of EG–EA mixture 1:1 stoichiometric ratio form stable adduct whereas for higher EGO–EA, it is 3:1, at EGO monomer unit level. The complex formation behaviour of DEG–EA has entirely different characteristics when compared to the other studied EGO–EA mixtures. Although, 1,4-dioxane has weak polar behaviour dielectric properties of EG–DX and DEG–DX confirm the formation of stable adducts at the stoichiometric ratio 2:1 of EGO monomer unit mole fraction to the DX. For the higher EGO–DX mixtures, stable adduct forms at the stoichiometric ratio 9:1. Except DEG–EA mixtures, the EGO–W and EGO–EA form the complex with reduction in the effective number of dipoles. In EG–DX mixtures, the heterogeneous species form with a large reduction in the effective number of dipoles, which changes as the effective number of dipoles increases with the increase in monomer repeat units of EGO. Further the net electronic polarization in these binary mixtures increases due to heterogeneous interaction over the entire mixing concentration range.     

Analysis of frequency-dependent series resistance and interface states of In/SiO2/p-Si (MIS) structures

In this work, the investigation of the interface state density and series resistance from capacitance–voltage (C–V) and conductance–voltage (G/ω−V) characteristics in In/SiO₂/p-Si metal–insulator–semiconductor (MIS) structures with thin interfacial insulator layer have been reported. The thickness of SiO₂ film obtained from the measurement of the oxide capacitance corrected for series resistance in the strong accumulation region is 220 Å. The forward and reverse bias C–V and G/ω−V characteristics of MIS structures have been studied at the frequency range 30 kHz–1 MHz at room temperature. The frequency dispersion in capacitance and conductance can be interpreted in terms of the series resistance (R_s) and interface state density (D_it) values. Both the series resistance R_s and density of interface states D_it are strongly frequency-dependent and decrease with increasing frequency. The distribution profile of R_s–V gives a peak at low frequencies in the depletion region and disappears with increasing frequency. Experimental results show that the interfacial polarization contributes to the improvement of the dielectric properties of In/SiO₂/p-Si MIS structures. The interface state density value of In/SiO₂/p-Si MIS diode calculated at strong accumulation region is 1.11×10¹² eV⁻¹ cm⁻² at 1 MHz. It is found that the calculated value of D_it (≈10¹² eV⁻¹ cm⁻²) is not high enough to pin the Fermi level of the Si substrate disrupting the device operation.     

Structural and optical properties of thermally evaporated Bi2Te3 films

Bi₂Te₃ films were prepared by thermal evaporation technique. X-ray diffraction analysis for as-deposited and annealed films in vacuum at 150 °C were polycrystalline with rhombohedral structure. The crystallite size is found to increase as the film thickness increases and has values in the range 67–162 nm. The optical constants (the refractive index, n, and absorption index, k) were determined using transmittance and reflectance data in the spectral range 2.5–10 μm for Bi₂Te₃ films with different thicknesses (25–99.5 nm). Both n and k are independent on the film thickness in the investigated range. It was also found that Bi₂Te₃ is a high refractive index material (n has values of 4.7–8.8 in the wavelength range 2.5–10 μm). The allowed optical transitions were found to be direct optical transitions with energy gap  eV. The optical conductivities σ₁ = ƒ(hν) and σ₂ = f(hν) show distinct peaks at about 0.13 and 0.3 eV, respectively. These two peaks can be attributed to optical interband transitions.     

The electrical characterization of Zn(Phen)q/p-type Si/Al diode with interfacial layer by current–voltage characteristics

The current–voltage characteristics of Zinc (II) [(8-hydroxyquinoline)(1,10-phenanthroline)] complex (Zn(phen)q)/p-type Si/Al diode with interfacial layer have been investigated. The barrier height and ideality factor of the diode were found to be 0.71 eV and 2.05. Zn(phen)q/p-type Si/Al diode shows a metal–insulator–semiconductor structure resulted from presence of series resistance and an interfacial layer. The n and φ_B values obtained the presence of interfacial layer are 1.02 and 0.70 eV, respectively. The effect of series resistance was evaluated using a method developed by Cheung. The R_s and n values were determined from the d ln(I)/dV plot and were found to be 30.43 kΩ and 2.16, respectively. The barrier height and R_s values were calculated from the H(I)–I plot and were found to be 0.70 eV and 30.99 kΩ. The density of the interface states of the Zn(phen)q/p-type Si/Al diode was calculated and was found to be an order of 10¹³ eV⁻¹ cm⁻².     

Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

Thermal-expansion anomalies and spontaneous magnetostriction of Lu2Fe17−xSix intermetallic compounds

The thermal expansion of Lu₂Fe_17−xSi_x solid solutions has been measured by X-ray powder diffraction. The magnetic ordering in all compounds within the homogeneity range (x3.4) is accompanied by a large spontaneous volume magnetostriction, distributed anisotropically over the principal axes of the hexagonal crystal structure. The volume effect ω_s in the ground state reaches 14.7×10⁻³ in Lu₂Fe₁₇ and decreases monotonously to 8.9×10⁻³ for x=3.4, following the reduction of magnetic moment. Despite a still large ω_s, the Invar behavior observed in Lu₂Fe₁₇ changes to a positive thermal expansion for x>1 due to an increasing Curie temperature.     

Desorption of H2 from W(110) and Fe covered W(110) surfaces

The kinetics of H₂ desorption from H/W(110) and H/Fe₁/W(110) were studied by measuring work function changes Δø vs time at a number of temperatures. Combination with previously determined Δø vs coverage data and differentiation at various fixed coverages gave rate vs T data from which activation energies of desorption could be obtained. E vs coverage results agree well with previously determine ΔH_des results. In the case of H/Fe₁/W(110) this includes a rise from 20 to 30 kcal mol⁻¹ of H₂ at H/Fe = H/W > 0.3. Plots of rate −dθ/dt vs θ (θ being coverage in units of H/W) vary much more steeply than θ² at most coverages for both systems. The θ dependence can be explained almost quantitatively in terms of the variations of ΔH_des and surface entropy S_s with coverage, by assuming that rates of desorption are equal to the equilibrium rates of adsorption. The latter can be formulated thermodynamically, except for a sticking coefficient, s. Values for s(θ, T) can also be obtained and show relatively little temperature dependence.     

Structural properties of diamond fine particles and clusters prepared by detonation and decomposition of TNT

The thermal parameter B for three different particle sizes of diamond samples (bulk powder 1–4 μm, fine particle 144–195 Å and cluster 55–61 Å) was determined by the grazing incidence X-ray diffraction method. The values of B were found to be in the range 0.50–0.70 Å² for particles in the size range 195–55 Å and 0.27 Å² for 1–4 μm. All of them are larger than that of diamond bulk. A clear size dependence of B, increasing with decreasing particle size, was found. By analysing X-ray diffraction data at several temperatures the magnitude of B was found to be due to B_S (static part) instead of B_T (dynamic part). The average B_S values obtained were 0.04 Å², 0.19 Å² and 0.27 Å² for bulk powder, fine particle and cluster samples respectively. Ultrahigh resolution transmission electron microscope (TEM) observation confirmed the presence of strain, distortion, roughness and dislocation lines in many particles. TEM images of particles indicate that the clusters were not spherical in shape; they were mostly cubiform and some were truncated prism-like polyhedral. The present study reveals that the B_S component is responsible for the large B value in diamond fine particles and clusters. No clear surface local atomic distortion was found in the particles.     

The dependence of I–V and C–V characteristics on temperature in the H-terminated Pb/p-Si(1 0 0) Schottky barrier diodes

The current–voltage (I–V) and capacitance–voltage (C–V) characteristics of H-terminated Pb/p-Si/Al contacts fabricated by us have been measured in the temperature range of 77–300 K. The experimental values of the barrier height (BH) Φ_bo and the ideality factor n for the device range from 0.674 and 1.072 eV (at 300 K) to 0.352 and 2.452 eV (at 77 K), respectively. The ideality factors become larger with lowering temperature while the barrier height decreases. The Φ_bo(n) plot shows a linear dependence in the temperature range of 77–300 K that can be explained by the barrier inhomogeneity at the metal/semiconductor interface. The extrapolation of the linear Φ_bo(n) plot to n = 1 has given a homogeneous barrier height of approximately 0.713 eV for the Pb/p-Si(1 0 0) contact. A Φ_bo versus 1/T plot was drawn to obtain evidence of a Gaussian distribution of the BHs, and values of and σ_s = 80.5 mV for the mean BH and zero-bias standard deviation have been obtained from this plot, respectively. Then, a modified versus 1/T plot gives and A^* as 0.828 eV and 54.89 A/cm² K², respectively. Furthermore, an average value of −0.687 meV/K for the temperature coefficient has been obtained, the value of −0.687 meV/K for hydrogen terminated p-type Si differs from those given for p-type Si without hydrogen termination in the literature.     

Study of activation parameters and NMR spin-lattice relaxation time in some substituted amines

The present communication reports the experimental values of NMR spin-lattice relaxation time (T₁) and dielectric relaxation time (τ) of piperidine, pyrrole, pyridine, diethylamine, triethylamine and pyrrolidine. The values of activation energy (ΔE_A) obtained using dielectric relaxation time, have been correlated with calculated values of ΔE_A obtained using Arrhenius equation of NMR relaxation time (T₁) for pyridine, diethylamine and pyrrole. Authors have also established a correlation between the experimental values of NMR spin-relaxation time (T₁) with its calculated values obtained using different equations of dielectric relaxation time (τ).     

The use of polarization modulation and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement

A novel common-path polarization modulation and amplitude-sensitive optical heterodyne polarimeter is setup in order to characterize a phase retardation plate (PRP) in real time. The phase retardation ΔΦ and fast-axis angle β of the linear birefringence parameters (LBP) of a PRP are measured simultaneously. Meanwhile, the dynamic ranges of 0° < ΔΦ < 180° and 0° < β < 180° are demonstrated experimentally. In order to measure LBP in real time, a polarization modulation is introduced by continuously rotating the tested PRP such that ΔΦ and β are able to be obtained in terms of the ratio of the amplitudes of S polarization and the ratio of P polarization of the heterodyne signals, respectively. Consequently, this novel method, which combines optical heterodyne interferometry with a polarization modulation technique, not only improves the detection sensitivity, but also provides a real time capability to measure LBP. In addition, the error in the LBP measurement is derived and analyzed.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

Electrical and magnetic properties of polyaniline/Fe3O4 nanostructures

We report on electrical and magnetic properties of polyaniline (PANI) nanotubes (150 nm in diameter) and PANI/Fe₃O₄ nanowires (140 nm in diameter) containing Fe₃O₄ nanoparticles with a typical size of 12 nm. These systems were prepared by a template-free method. The conductivity of the nanostructures is 10⁻¹–10⁻² S/cm; and the temperature dependent resistivity follows a ln ρT^−1/2 law. The composites (6 and 20 wt% of Fe₃O₄) show a large negative magnetoresistance compared with that of pure PANI nanotubes and a considerably lower saturated magnetization (M_s=3.45 emu/g at 300 K and 4.21 emu/g at 4 K) compared with the values measured from bulk magnetite (M_s=84 emu/g) and pure Fe₃O₄ nanoparticles (M_s=65 emu/g). AC magnetic susceptibility was also measured. It is found that the peak position of the AC susceptibility of the nanocomposites shifts to a higher temperature (>245 K) compared with that of pure Fe₃O₄ nanoparticles (190–200 K). These results suggest that interactions between the polymer matrix and nanoparticles take place in these nanocomposites.     

Oxygen diffusion and surface exchange in La1−xSrxFe0.8Cr0.2O3−δ (x=0.2, 0.4 and 0.6)

Oxygen tracer diffusion (D*) and surface exchange rate constant (k*) have been measured, using isotopic exchange and depth profiling by secondary ion mass spectrometry (SIMS), in La_1−xSr_xFe_0.8Cr_0.2O_3−δ (x=0.2, 0.4 and 0.6). Measurements were made as a function of temperature (700–1000 °C) and oxygen partial pressure (0.21–10⁻²¹ atm) in dry oxygen, water vapour and water vapour/hydrogen/nitrogen mixtures. At high oxygen activity, D* was found to increase with increasing temperature and Sr content. The activation energies for D* in air are 2.13 eV (x=0.2), 1.53 eV (x=0.4) and 1.21 eV (x=0.6). As the oxygen activity decreases, D* increases as expected qualitatively from the increase in oxygen vacancy concentration. Under strongly reducing conditions, the measured values of D* at 1000 °C range from 10⁻⁸ cm² s⁻¹ for x=0.2 to 10⁻⁷ cm² s⁻¹ for x=0.4 and 0.6. The activation energies determined at constant H₂O/H₂ ratio are 1.21 eV (x=0.2), 1.59 eV (x=0.4) and 0.82 eV (x=0.6).

The surface exchange rate constant of oxygen for the H₂O molecule is similar in magnitude to that for the O₂ molecule and both increase with increasing Sr concentration.