UV-induced switching behavior of novel fluoroalkyl end-capped vinyltrimethoxysilane oligomer/titanium oxide nanocomposite between superhydrophobicity and superhydrophilicity with good oleophobicity

Fluoroalkyl end-capped vinyltrimethoxysilane oligomer suffered the sol–gel reaction under alkaline conditions in the presence of titanium oxide nanoparticles in tetrahydrofuran to afford the corresponding fluorinated oligomer/titanium oxide nanocomposites[R_F-(VM-SiO₂)_n-R_F/TiO₂] in excellent to moderate isolated yields. These fluorinated composites thus obtained were nanometer size-controlled fine particles, and exhibited good dispersibility and stability in traditional organic solvents except for water. These fluorinated nanocomposites were applied to the surface modification of glass to exhibit not only a completely superhydrophobic characteristic (a water contact angle: 180°) with a non-wetting property against water droplets but also a good oleophobicity imparted by fluoroalkyl segments in the composites on their surface. Of particular interest, we have found that the wettability for water can be switched between superhydrophobicity and superhydrophilicity by alternation of ultraviolet (UV) irradiation and dark storage with keeping a good oleophobicity on the modified surface treated with the anatase-type titanium oxide composite.     

Dispersion of single-walled carbon nanotubes in water by the use of novel fluorinated dendrimer-type copolymers

New fluorinated dendrimer-type block copolymers were applied to the dispersion of single-walled carbon nanotubes (SW-CNTs) and single-walled carbon nanotubes containing carboxy groups [(SW-CNT)-COOH] in water. Fluorinated block copolymer could disperse SW-CNTs more effectively in water, compared to that of the corresponding ABA triblock-type fluoroalkyl end-capped dimethylacrylamide oligomer [R_F-(DMAA)_n-R_F]. Dynamic light-scattering (DLS) measurements and transmission electron microscopy (TEM) images show that SW-CNTs could be smoothly encapsulated into fluorinated copolymeric aggregates cores. Interestingly, it was demonstrated that SW-CNTs could be in part released from the fluorinated copolymeric aggregates/SW-CNTs composites or encapsulated into these composites with increasing the dispersion times. On the other hand, fluorinated block copolymer and R_F-(DMAA)_n-R_F oligomer were not able to disperse well (SW-CNT)-COOH in water; however, ABA triblock-type fluoroalkyl end-capped acrylic acid oligomer was able to disperse quite effectively (SW-CNT)-COOH in water.     

Synthesis and applications of fluoroalkyl end-capped cooligomers having fullerene and mixed fullerenes in the main chain

Fluoroalkanoyl peroxides reacted with FULLERENES [fullerene (C₆₀) and commercially available fullerenes (Nanom Mix^TR and Nanom Black^TR)] and radical polymerizable comonomers such as acrylic acid, N,N-dimethylacrylamide, N-(1,1-dimethyl-3-oxobutyl)acrylamide, and acryloylmorpholine to afford fluoroalkyl end-capped cooligomers having FULLERENES in the main chain under very mild conditions. Fluoroalkyl end-capped Nanom Mix and Nanom Black cooligomers thus obtained were found to exhibit a similar solubility to that of the corresponding fluoroalkyl end-capped cooligomers having fullerene in the main chain. These fluorinated FULLERENES cooligomers were found to form the nanometer size-controlled self-assembled cooligomeric aggregates in aqueous solutions. These fluoroalkyl end-capped FULLERENES cooligomers were more effective for solubilizing fullerene, Nanom Mix and Nanom Black into water, compared to those of the corresponding fluoroalkyl end-capped homooligomers having no FULLERENES in the main chain. Fluoroalkyl end-capped fullerene- and Nanom Mix-acrylic acid cooligomers were found to exhibit fluorescence spectra related to fullerene and Nanom Mix in cooligomers, respectively, in aqueous solutions. Additionally, these fluorinated fullerene- and Nanom Mix-acrylic acid cooligomers were able to increase chemiluminescence intensity related to luminol, effectively, compared to the corresponding fluorinated acrylic acid homooligomers.     

Preparation and properties of fluorinated aliphatic alcohols/silica nanocomposites – Application to the encapsulation of anatase titanium oxide nanoparticles into these composite cores

A variety of fluorinated aliphatic alcohols [R_F-CH₂CH₂OH; R_F = CF₃(CF₂)₃CH₂(CF₂)₅, CF₃(CF₂)_n; n = 3, 5, 7] were applied to the preparation of the corresponding fluorinated alcohols/silica nanocomposites [R_F-CH₂CH₂OH/SiO₂] through the sol–gel reactions with tetraethoxysilane (TEOS) and silica nanoparticles under alkaline conditions. R_F-CH₂CH₂OH/SiO₂ nanocomposites thus obtained have a good dispersibility and stability in not only water but also traditional organic solvents such as methanol, ethanol, 1,2-dichloroethane and tetrahydrofuran. FE–SEM (field emission scanning electron microscopy) and dynamic light scattering (DLS) measurements show that these composites are nanometer size-controlled fine particles in methanol. These fluorinated nanocomposites were also applied to the surface modification of glass to exhibit a superhydrophilic characteristic with a superoleophobicity on the modified surface. Interestingly, R_F-CH₂CH₂OH/SiO₂ nanocomposites were found to exhibit no weight loss behavior corresponding to the contents of the alcohols in the composites even after calcination at 800 °C. In addition, anatase TiO₂ nanoparticles (an-TiO₂) were effectively encapsulated into R_F-CH₂CH₂OH/SiO₂ nanocomposite cores under the similar sol–gel reactions to give the corresponding fluorinated alcohol/SiO₂/an-TiO₂ nanocomposites. These obtained nanocomposites can give a higher photocatalytic activity even after calcination at 1000 °C for the decolorization of methylene blue under UV light irradiation than that of the an-TiO₂ nanoparticles under the similar conditions, although the parent TiO₂ nanoparticles after calcination were unable to give a photocatalytic activity.     

Preparation and properties of fluoroalkyl end-capped oligomer/fluoresceins nanocomposites

Self-assembled fluorinated oligomeric aggregates formed by fluoroalkyl end-capped N-(1,1-dimethyl-3-oxobutyl)acrylamide oligomers, N,N-dimethylacrylamide oligomers, and acrylic acid oligomers in methanol could recognize selectively fluoresceins as guest molecules to form a new class of fluorinated aggregates/fluoresceins nanocomposites. These fluorinated fluoresceins nanocomposites were found to exhibit an extraordinarily enhanced light absorption (λ_max: ca. 440 nm) compared to that (λ_maxs: 452 and 480 nm) of the parent fluorescein in the absence of fluorinated aggregates. On the other hand, fluoroalkyl end-capped 2-carboxyethyl acrylate oligomers, which possess no aggregate characteristic in methanol solutions, could not afford such an enhanced light absorption peak under similar conditions. Not only fluorescein but also fluorescein derivatives such fluoresceinamine, carboxyfluorescein, and fluorescein isothiocyanate afforded similar enhanced narrow absorption peaks under similar conditions. Naphthofluorescein was also encapsulated into these fluorinated oligomeric aggregate cores to afford fluorinated aggregates/naphthofluorescein composites, and these fluorinated naphthofluorescein composites afforded an extremely enhanced narrow absorption peak around 520 nm.     

Free vibration analysis of a Timoshenko beam carrying multiple spring–mass systems by using the numerical assembly technique

From the equation of motion of the ‘bare’ Timoshenko beam (without any spring–mass systems attached), an eigenfunction in terms of four unknown integration constants is obtained. The substitution of the eigenfunction into the three compatible equations, one force–equilibrium equation and one governing equation for the sprung mass (ν=1,…,n) yields a matrix equation of the form [B_ν] {C_ν}=0. Similarly, when the eigenfunction is substituted into the two boundary‐condition equations at the ‘left’ end and those at the ‘right’ end of the beam, one obtained [B_L] {C_L}=0 and [B_R] {C_R}=0, respectively. Assembly of the coefficient matrices [B_L], [B_ν] and [B_R] will arrive at the eigen equation [B̄] {C̄}=0, where the elements of {C̄} are composed of the integration constants C_νi (ν=1,…,n and i=1,…,4) and the modal displacements of the sprung mass, Z_ν. For a Timoshenko beam carrying n spring–mass systems, the order of the overall coefficient matrix [B̄] is 5n+4. The solutions of ∣B̄∣=0 (where ∣·∣ denotes a determinant) give the natural frequencies of the ‘constrained’ beam (carrying multiple spring–mass systems) and the substitution of each corresponding values of C_νi into the associated eigenfunction at the attaching points will define the corresponding mode shapes. In the existing literature the eigen equation [B̄] {C̄}=0 was denoted in explicit form and then solved analytically or numerically. Because of the lengthy explicit mathematical expressions, the existing approach becomes impractical if the total number of the spring–mass systems is larger than ‘two’. But any number of spring–mass systems will not make trouble for the numerical assembly technique presented in this paper. Copyright © 2001 John Wiley & Sons, Ltd.     

Supramolecular host–guest systems constructed of pyrrole derivatives and 3D-coordination polymers

Pyrrole derivatives have been shown to be completely or partially oxidized within the expandable channels of the 3D-coordination polymers [(R₃Sn)₃Fe(CN)₆] _n and [(R₃Sn)(R₃^′Sn)₂Fe(CN)₆] _n , R and R′ = Me, n-Bu, or Ph, to give novel class of supramolecular host–guest systems. The structures and physical properties of these host–guest systems depend on the reaction time, nature of the host and guest, the space empty within the network of the 3D-coordination polymers. Pyrrole undergoes oxidative polymerization in the channels of the 3D-coordination polymers to form semiconducting diamagnetic supramolecular host–guest systems. Whereas N-methylpyrrole and 2,5-dimethylpyrrole are not polymerized under these experimental conditions, but give paramagnetic charge transfer (CT) supramolecular host–guest systems.     

Crystal Structure of K[UO2(NO3)3] and Some Features of Compounds M[UO2(NO3)3] (M = K,Rb, and Cs)

Greenish-yellow transparent crystals of K[UO₂(NO₃)₃] were prepared from aqueous solutions as by-product in synthesis of potassium chromatouranylates. The crystal structure was solved by the direct methods and refined to R ₁ = 0.037 (wR ₂ = 0.070) for 1452 reflections with |F _hkl| 4|F _hkl|. Mono- clinic system, space group C2/c, a = 13.4877(10), b = 9.5843(7), c = 7.9564(6) Å, = 116.124(2)°, V = 923.45(12) ų. The structure of K[UO₂(NO₃)₃] contains isolated complex ions [UO₂(NO₃)₃]^- whose uranyl groups are aligned parallel to the [-101] plane. The K⁺ cations, coordinated by twelve oxygen atoms, are located between the complex anions. Comparison of the structure with known data on M[UO₂(NO₃)₃] compounds (M = K, Rb, Cs) suggests the possibility of phase transitions due to relatively small displacements of [UO₂(NO₃)₃]^- anions and K⁺ cations, retaining the general structural motif.     

Core electron level structure in C<Subscript>60</Subscript>F<Subscript>18</Subscript> and C<Subscript>60</Subscript>F<Subscript>36</Subscript> fluorinated fullerenes

The structure of C1s and F1s core electron levels in C₆₀F₁₈ and C₆₀F₃₆ fluorinated fullerenes has been studied by X-ray photoelectron spectroscopy using synchrotron radiation. It is established that C1s levels of carbon atoms not bound to fluorine in these compounds are shifted down by 1.0 and 1.6 eV relative to the C1s level in the usual C₆₀ fullerene, so that the binding energies of the core electron levels in C₆₀F₁₈ and C₆₀F₃₆ amount to E _b (C1s, C-C) = 285.7 and 286.3 eV, respectively. These values are characteristic and can be used for the identification of both homogeneous fluorinated fullerenes and combined materials comprising a mixture of various fluorinated fullerenes with each other and with different carbon-containing based materials.     

Structural Evolution and Magnetic Properties of Underfluorinated C2F

A series of layered inclusion compounds based on fluorinated graphite C₂F _x (x≤1) was obtained by a room temperature synthesis. Inclusion compounds (intercalates) of fluorinated graphite matrix were n-hexane and dichloromethane, i.e., organic guest molecules that differ in size and symmetry. The changes in C₂F _x stoichiometry are shown to have a decisive effect on magnetic properties of produced complexes. The spin concentration decreases with the increase of fluorine content in fluorocarbon matrix. All samples have groups of correlated spins; at the temperatures 1.75–5 K nonlinear magnetization is observed, indicating a high-spin state. Application of the Langevin formula shows that the clusters consist of 10–20 interacting spins.     

Synthesis and crystal structure of a uranyl bichromate, [CH6N3]2[(UO2)(CrO4)(Cr2O7)](H2O)

Crystals of the first uranyl bichromate, [CH₆N₃]₂[(UO₂)(CrO₄)(Cr₂O₇)](H₂O), were obtained by evaporation from aqueous solutions. The compound crystallizes in the triclinic system, space group $P\bar 1$ , a = 7.1829(17), b = 9.304(3), c = 14.884(4) Å, α = 102.43(2)°, β = 97.98(2)°, γ = 101.07(2)°, V = 936.3(5) ų, Z = 2. The structure was solved by direct methods and refined by the full-matrix least-squares method to R ₁ = 0.064 (wR ₂ = 0.138) for 2225 reflections with |F _hkl | ≥ 4σ(|F _hkl |). The structure is based on infinite [(UO₂)(CrO₄)(Cr₂O₇)]^2? chains where [UO₇]^8? pentagonal bipyramids are linked by tridentate [Cr(1)O₄]^2? groups and [Cr₂O₇]^2? groups; these chains run along x axis and are oriented parallel to $(0\bar 11)$ . Trigonal [CH₆N₃]⁺ cations and water molecules are arranged between the chains.     

A study of mechanical configuration optimisation in micro-systems

This paper shows that there are three main categories of factors that make the optimum mechanical design of micro-systems different from macro-systems: scale effects, a limited range of materials, and a limited range of production processes. The combined effect of these factors can make the optimum configuration of a micro-system potentially very different from that of the same system on a macro-scale. In particular, the use of flexible elements for hinges is much more feasible and desirable on a micro-scale.Notation a acceleration (m/s²) - A cross-sectional area (m²) - B magnetic flux [wb/m²] - b width [m] - C constant - d depth [m] - D drag [N] - E Young's modulus [N/m²] - E*= - f resonant frequency [Hz] - F _D drive force [N] - F _E electrostatic pulling force [N] - F emmisivity function - F _G geometric view factor - g gravitational constant [m/s²] - h _c convention heat transfer coefficient [W/m²K] - h height [m] - i current [A] - I _A second moment of area [m⁴] - I _I moment of inertia [kg m²] - J polar second moment of area [m⁴] - k stiffness [N/m] - K thermal conductivity [W/m K] - l length [m] - m mass [kg] - M moment [N m] - P load [N] - P _H Hertz contact pressure [N/m²] - P _C cylinder pressure [N/m²] - q heat transfer rate [W] - R, r radius [m] - Re Reynolds number - T, t temperature [K] - T _A atomic friction torque [N m] - T _D drive torque [N m] - T _F Coulomb friction torque [N m] - T _I inertial resistive torque [N m] - u velocity [m/s] - mean velocity [m/s] - V volume [m³] - V _e voltage [V] - x distance between electrodes [m] - y maximum distance to neutral axis [m] - angular acceleration [rad/s²] - _d thermal diffusivity [1/K] - rolling friction factor - P pressure difference [N/m²] - ₀ dialectric constant [F/m] - strain - dynamic viscosity [Pa s] - scale factor - _S coefficient of sliding friction - _R coefficient of rolling friction - _{1, 2} Poisson's ratio - density (kg/m³) - temperature rise [°C] - _B bending stress [N/m²] - _y yield strength [N/m²] - shear stress [N/m²] - reliability constant     

FATIGUE CRACK GROWTH IN D16T A1-ALLOY SHEET SUBJECTED TO BIAXIAL OUT-OF-PHASE LOADING

Abstract— Fractographic peculiarities of fatigue crack development are studied in cruciform specimens of D16T aluminium alloy under out-of-phase biaxial tension and tension-compression. In the range of the biaxial load ratios λ from ?0.5 to +0.5 and an R-ratio of 0.3, fatigue striation formation took place beyond a crack growth rate near to 4 × 10^?8 m/cycle. The striation spacing and the crack growth rate increase as the φ-angle of the out-of-phase biaxial loads increases in the range of φ-angles from 0° to 180°. The ratio between the increment of crack growth, da/dN, and the striation spacing, δ, is approximately 1 to 1 when da/dN is greater than 4 × 10^?8 m/cycle. The relationship between the number of cycles from the beginning of a test up to the growth rate of 10^?6 m/cycle (N_d), and the crack growth period, N_P, from when the crack initiates up to the instant when that growth rate is reached, was determined for different λ ratios and φ angles. The value of N_d decreases as the φ angle is increased in the range from 0° to 1807deg;. Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method that involves an equivalent stress intensity factor K_e=K_IF₁(λ, R)F₂(φ). The values of F₂(φ) were determined. The calculated fatigue crack growth period, N_c, applicable up to and including the stage of fatigue striation formation (predicted by using both of the F₁(λ, R) and F₂(φ) functions) is correlated with the experimental data and the error is of the order of 15%.     

Structure analysis and general characterization of the fluorogallophosphate Mu-2: A new microporous material built from double-four-ring units hosting F− anions

A new three-dimensional microporous fluorogallophosphate, named Mu-2,was synthesized from a fluoride-containing aqueous medium in thepresence of 4-amino-2,2,6,6-tetramethylpiperidine as organictemplate. The new material was characterized by microprobe analysis,thermal analysis, X-ray diffraction and solid state NMR spectroscopy.Its structure was determined from X-ray powder as well as singlecrystal data. The structure of Mu-2[Ga₃₂P₃₂O₁₂₀(OH)₁₆F₈(C₉H₂₀N₂H)₄(C₉H₂₀N₂H₂)₂ · 12H₂O,M _r = 6687.0, cubic, space group I23 (no. 197), a = 16.3782(2) Å, V = 4393.38(1) ų, Z = 1, R _F = 7.7% R _wp = 10.7%] consists of acubic arrangement of double-four-ring units (D4R) hosting F^– anionswhich are interconnected to form a three dimensional but interruptedframework. This arrangement generates a three-dimensional pore systemof eight-membered ring channels. Besides the D4R units, two othertypes of cages are present in the structure occluding the protonatedamine and a (OH)₈-(H₂O)₆-cluster respectively.     

Rewriting Techniques and Degree Bounds for Higher Order Symmetric Polynomials

Any symmetric polynomial f∈R[X ₁, …, X _n] has a unique representation f = p(σ₁, …, σ_n) with p∈R[X ₁, …, X _n] in the elementary symmetric polynomials σ₁, …, σ_n. This paper investigates higher order symmetric polynomials; these are symmetric polynomials with a representation p, which is also symmetric. We present rewriting techniques for higher order symmetric polynomials and exact degree bounds for the generators of the corresponding invariant rings. Moreover, we point out how algorithms and degree bounds for these polynomials are related to Pascals triangle, Fibonacci numbers, Chebyshev polynomials, and cardinalities of finite distributive lattices of semi-ideals. Received: December 16, 1997     

Monodisperse micron-sized polymethylmethacrylate particles having a crosslinked network structure. V

Highly monodisperse micron-sized polymethylmethacrylate (PMMA) particles crosslinked with carboxylic group-containing urethane acrylates (CUA) were produced by simple dispersion polymerization in methanol. In proper condition, CUA employed as a crosslinker had an excellent ability to achieve the monodisperse PMMA particles to the concentration of about 10 wt%. This arose from the fact that CUA formed monomer-swellable primary particles due to its structurally long tetramethylene oxide groups in the molecule. The influence of the concentrations of the initiator and CUA on the particle diameter (D _n), particle number density (N _p), and polymerization rate (R _p) was found to obey the following approximate relationship, D _n [initiator]^0.41[CUA]^–0.06, N _p [initiator]^–1.22 [CUA]^0.21, and R _p [initiator]^0.34±0.03, respectively. The power law dependence of D _n and N _p on the initiator concentration coincided well with that of linear polymers in the literature. Especially, in this study, it was found that CUA did not have a serious influence on the nucleation. However, the dependence of R _p on the initiator concentration was observed to be higher than that of linear polymers, suggesting that uniquely, the solution polymerization process competed with the heterogeneous polymerization during polymerization, because of the crosslinked network structure of the primary particles.     

Crystal structure of the potassium tantalum oxyfluoride K6Ta6.5O14.5F9.5

The crystal structure of K₆Ta_6.5O_14.5F_9.5 has been determined from 714 automatic diffractometer data, and refined in the space group P6 to an R-factor of 0.061. Its structure can be described as a three-dimensional framework lattice formed by the interpenetration of two distinct sublattices with the formulations [Ta₆X₂₁]_n and [Ta_0.5X₃]_n respectively, in which are inserted the K atoms. The three-dimensional skeleton [Ta₆X₂₁]_n is formed entirely of octahedra TaX₆, while the sublattice [Ta_0.5X₃]_n is an infinite chain of trigonal prisms.     

Structural approach to nanoscience: a case study of complex and cluster formation in ZnBr2–ZnCl2 melts

Although the melt structure of glass-forming ZnCl₂ has so far been well studied, there exists quite little information on the structural change due to anion-substitution. In the present work, the short-range structure of ZnCl₂–ZnBr₂ mixture melts was analyzed systematically by time-of-flight pulsed neutron diffraction techniques, Raman spectroscopy, molecular orbital calculations, and molecular dynamics simulations. According to radial distribution analysis, it was found that there were tetrahedral structural units of ligand-substituted [ZnCl_nBr_4−n]²⁻ (n=0–4) in these melts, not implying the simple mixing of [ZnCl₄]²⁻ and [ZnBr₄]²⁻ units. Further detailed estimation indicated that the ligand-substituted complex anions were linked with each other by sharing a common anion.     

New coordination networks constructed from N-(4-pyridyl)isonicotinamide

Crystal structures of new coordination polymers of N-(4-pyridyl)isonicotinamide (pia) were prepared and crystallographically characterized. Compound 1, [Cd(pia)(NCS)₂]_n, provides a rectangular, two-dimensional network, which is constructed by a single bridging of the pia ligand and double bridging of the NCS ligands. Compound 2, [Cu(pzdc)(pia)₂]_n (pzdc = pyrazine-2,3-dicarboxylate), forms a fishbone-type, one-dimensional network, which is comprised of –(Cu-pzdc)– chains with pia ligands. The imino-pyridine donor of the pia binds to the chains, in which the other remains free. The π–π and hydrogen bonding interactions between the pia ligands in the adjacent chains provide a three-dimensional structure.     

Designing and upgrading model of pre-denitrification systems

This paper reports a three-substrate steady-state integrated model, whose unknowns are expressed in explicit terms once concentrations of nitrogen compounds in the effluent flow are fixed. The model can be applied both to design and to upgrade wastewater treatment plants. The model is also able to evaluate the flexibility of existing wastewater treatment plants, which represents the capacity of the system to operate under different working conditions caused by increases in influent load or reductions in effluent quality standards. In this case the admissible variation of influent load or effluent concentration can be measured using suitable dimensionless flexibility indexes.List of symbols Q influent flow [L³ T^–1] - R₁ sludge recycle flow ratio - R₂ aerated mixed liquor recycle flow ratio - V_D denitrification reactor volume [L³] - V_N nitrification reactor volume [L³] - S biodegradable organic substrate concentration [M L^–3] - N-NH₄ ammonia nitrogen concentration [M L^–3] - N-NO₃ nitrate nitrogen concentration [M L^–3] - N_tot total nitrogen concentration [M L^–3] - O₂ oxygen concentration in the nitrification reactor [M L^–3] - X_H heterotrophic biomass concentration [M L^–3] - X_AUT autotrophic biomass concentration [M L^–3] - maximum removal rate of biodegradable organic substrate for an assigned value of temperature [T^–1] - maximum removal rate of nitrate for an assigned value of temperature [T^–1] - maximum removal rate of ammonia nitrogen for assigned values of pH and temperature [T^–1] - _S removal rate of biodegradable organic substrate [T^–1] - _D removal rate of nitrate [T^–1] - _N removal rate of ammonia nitrogen [T^–1] - K_S saturation coefficient for biodegradable organic substrate [M L^–3] - K_D saturation coefficient for nitrate [M L^–3] - K_SD saturation coefficient for organic substrate in the denitrification kinetic [M L^–3] - K_N saturation coefficient for ammonia nitrogen [M L^–3] - saturation coefficient for oxygen [M L^–3] - Y_H yield coefficient for heterotrophic microorganisms in the biodegradable organic substrate removal process - Y_D yield coefficient for heterotrophic microorganisms in the nitrate nitrogen removal process - Y_AUT yield coefficient for autotrophic microorganisms in the ammonia nitrogen removal process - (X_H)_r heterotrophic biomass concentration in the recycle sludge [M L^–3] - (X_AUT)_r autotrophic biomass concentration in the recycle sludge [M L^–3] - biodegradable organic mass consumption for unitary nitrate nitrogen mass reduction in the denitrification reactor - nitrogen consumption in the biodegradable organic oxidation process by mean of heterotrophic biomass