Polyelectrolyte and rheological studies on the polysaccharide welan

This paper investigates the polyelectrolyte behaviour of welan in aqueous solution. From conductivity and activity measurements it is demonstrated that a double-helical conformation is adopted irrespective of pH and ionic strength. The intrinsic pK of its carboxylic groups is found to be abnormally low (pK₀ = 2.2) and no conformational transition was observed during neutralization. The viscometric behaviour was studied as a function of degree of neutralization, polymer concentration, shear rate and ionic strength. The linear relation [η]=f(C_s^−1/2) allows the determination of B, the stiffness parameter from Smidsrod, whose value characterizes a very stiff molecule.     

Kinetics of ultrasonic degradation and polymerisation degree distribution of sonochemically degraded chitosans

The process of physical degradation by means of the ultrasonic action towards chitosans with mole fraction of 2-acetamido-2-deoxy-β- -glucopyranose units (the degree of N-acetylation, F_A) in the range of 0.10≤F_A≤0.28, and the weight average polymerisation degree in the range of has been investigated. The decrease of as well as changes in the distribution of the degree of polymerisation (P) has been determined as a function of time, F_A, temperature, concentration of chitosan solution and concentration of acetic acid in the solution. The use of low-power ultrasound emitter allowed to establish that in the case of chitosan (binary heteropolysaccharide) the general rate parameter (k) increased with F_A. This can be explained by the relatively stronger aggregation of macromolecules with higher F_A, which results in size increase of macromolecular individuals and hence in their higher susceptibility to ultrasonic action. It was also observed that k decreased with chitosan concentration and temperature. The value of limiting degree of polimerisation (x_e) was found to be influenced by structural parameters of chitosan chains (F_A, aggregation). The increase of acetic acid concentration caused the increase in the k value, what indicated accelerating effect of ultrasound towards acidic hydrolysis of chitosan. The shape of the P curve of sonochemically degraded chitosans are in good correlation with the mid-point breakage concept of degradation accepted in sonochemical degradation of polymers.     

Heteroxylans from maize bran in aqueous solution. Part II: Studies of polyelectrolyte behaviour

Potentiometric and viscosimetric behaviours of four samples of heteroxylans, extracted from corn bran at different temperatures with varying type and concentration of alkali were studied in dilute solutions. All four samples behave as typical polyelectrolytes with a low charge density parameter (λ = 0.15). They could be described by the Lifson and Katchalsky model pK₀≈3.15), indicating a rather homogeneous repartition of the charges along the macromolecules. Their intrinsic viscosities varied linearly with the reciprocal of the square root of the ionic strength. Their flexibility parameters, B (≈0.024), were similar to those of semi-flexible macromolecules, and their intrinsic viscosities extrapolated to infinite ionic strength were between 144 and 177ml/g. Their conformational dimensions depended on the type of counter-ion in solution (dimensions minimal with divalent cations and decreasing with size of monovalent alkali metal ions), of the temperature and the pH of the solution. The radius of gyration for unchanged heteroxylans was estimated from intrinsic viscosities extrapolated to infinite ionic strength (R²_g∞^1/2 = 21−25 nm).     

Comparative studies on solution characteristics of mannuronan epimerized by C-5 epimerases

Both dilute and concentrated solutions of bacterial Mannuronan (MANNA) and its epimerized products by AlgE1 at 5 and 24 h, named MANNAEp1t5h and MANNAEp1t24h, respectively, and AlgE4 (MANNAEp4) have been studied as a function of variables such as polymer concentration and ionic strength (NaCl) in order to investigate the macromolecular solution properties of these innovative polyuronic acids having the same charge density but different composition and sequence of β-d-mannuronic acid (-M-), -l-guluronic acid (-G-) or MG-blocks.

Measurements of intrinsic viscosity [η] as a function of ionic strength, I, by capillary viscometry has led to an estimate of the Smidsrød-Haug parameter B, an index useful to characterize the stiffness of polymeric chains. The results are largely consistent with much of the published data relative to chain extension and conformational freedom around the torsional angles of the glycosidic linkages occurring in alginates.

Steady shear rheometry provided information about the coil-overlapping parameter c*, which marks the transition from dilute to concentrated solution. The slopes of the double logarithmic plots of η_sp vs. c[η] both at low and high degrees of coil overlap suggest that all samples solutions behave like linear polymer entangled network systems. The value of c* is strictly influenced by the stiffness of the chains, and hence by the primary structure.

Dynamic shear rheometry shows that the frequency dependence of dynamic viscosity is only partially superimposable to the shear rate dependence of viscosity. Such behaviour may be ascribed to the presence of semiflexible polymeric coils in a non-totally destructured entangled state.

By solvent/non-solvent (H₂O/isopropanol) fractionation carried out on mannuronan, a set of samples with different average molecular weights and narrow polydispersities were obtained. Triple detection GPC allowed the evalutation of the Mark–Houwink–Sakurada parameters as well as of the characteristic ratio C_∞ for one of the fractionated MANNA samples. The chain persistence length was estimated by the wormlike chain model.     

Tricarbonyl(1,10-phenanthroline) (imidazole) rhenium(I): a powerful photooxidant for investigations of electron tunneling in proteins

The structure of [Re(CO)₃(phen)(im)]₂SO₄·4H₂O has been determined by X-ray crystallography. The yellow crystals are orthorhombic, space group Pccn (No. 56), with a=17.456(6), B=18.194(5), C=12.646(4) Å, R=0.063 for F_o²>0, R=0.032 for F_o²>3σ. The compound, which also has been characterized by IR, ¹H NMR, and UV---Vis spectroscopies, exhibits room temperature luminescence in aqueous solution (τ=120 ns) as well as reversible oxidation and reduction in acetonitrile solution (1.85 and −1.30 V versus SCE). The redox properties of the excited state of the complex (E⁰(Re^+*/0 = 1.2; E⁰(Re^2+/+*) = −0.7 V) are being exploited in studies of laser-induced electron tunneling in Re(CO)₃(phen)(histidine)-modified proteins.     

The use of the borocaptate anion as a ligand. Synthesis and X-ray crystal structure of pentaammine (1-thiolato-closo-undecahydrododecaborane)ruthenium(III) dihydrate

The complex [Ru(SB₁₂H₁₁)(NH₃)₅]·2H₂O has been prepared by the reaction of Cs₂B₁₂H₁₁SH with [RuCl(NH₃)₅]Cl₂ in aqueous solution. The complex represents the first reported example of the borocaptate anion acting as a ligand. The structure of the complex has been determined by single crystal X-ray diffraction analysis. The crystal parameters are monoclinic, space group P2₁/c, A = 8.056(1), B = 14.240(2), C = 15.172(2) Å, β=98.48° and Z = 4. The ruthenium atom has a distorted octahedral coordination. The distortion is probably due to the high (3⁻) charge and the large bulk of the borocaptate ligand. These features can also be observed in the spectroscopic properties of the complex.     

Dinuclear silver(I) complexes of 24-membered bibracchial tetraimine Schiff base macrocycles derived from 2,5-diformylthiophene

The cyclocondensation of 2,5-diformylthiophene and the amines N,N-bis-(2-aminoethyl)-2-phenylethylamine, N,N-bis-(2aminoethyl)-t-butyl-amine and N,N-bis-(2-aminoethyl)-t-butyl-amine in the presence of silver(I) salts yields homodinuclear bibracchial tetraimine Schiff base macrocyclic complexes. The structures of two such complexes are also reported. The complex Ag₂L⁴(NO₃)(PF₆) (2) crystallises in the triclinic space group , No. 2) and has unit-cell dimensions a = 12.834(6), B = 13.183(6), C = 14.588(7) Å, = 64.86(4), β = 79.77(4), γ = 69.44(3)° with Z = 2; there is a monodentate and singly bridging nitrate anion present and the Ag---Ag separation is 4.161 Å. The complex Ag₂L⁴(CH₃CN)₂(BF₄)₂·CH₃CN (9) crystallises in the triclinic space group , No. 2) and has unit-cell dimensions a = 9.297(4), B = 12.985(3), C = 21.770(5) Å, = 91.570(10), β = 92.33(3), γ = 97.92(3) ° with Z = 2; there is a strongly bonded acetonitrile molecule coordinated to each silver atom and the Ag---Ag separation is 4.920 Å.     

Synthesis and problematic crystal structures of [Al(CH3CN)6][MCl6]3(CH3CN)3 (M=Ta, Nb or Sb)

Compounds of formula [Al(CH₃CN)₆][MCl₆]₃(CH₃CN)₃ (M=Ta (1); Nb (2); Sb (3)) have been synthesized from the reactions of MCl₅ and AlCl₃ in acetonitrile and characterized by X-ray crystallography. Complex 1 crystallizes in the tetragonal space group P4/mbm with a = B = 10.408(2), C = 7.670(3) Å, V = 830.9(4) ų and Z = 2/3. Complex 2 crystallizes in the tetragonal space group P4/mnc with a = B = 330(a), C = 15.320(3) ų V = 1634.8(4) ų and Z = 4/3. Complex 3 also crystallizes in the tetragonal space group P4/mnc with a = B = 10.313(1), C = 15.238(2) Å, V = 1621.0(1) ų and Z = 4/3. The non-integer Z values for complexes 1–3 result unusual problems of disorder and/or twinning in these crystal structures due to their high symmetry. The M---Cl distances range from 2.329(3) Å in the Ta complex to 2.355(1) Å in the Sb complex, while the Al---N distances are similar in all three complexes, ranging from 1.92(1) to 1.97(1) Å, respectively. Complexes 1–3 are the first structurally characterized complexes that contain a (hexaacetonitrile)aluminum(III) cation.     

Hydroxyethyl Methacrylate Combined with Polyethylene Glycol 400 and Water; an Embedding Medium for Routine 1-2 Micron Sectioning

Pieces of tissue, with the largest dimension not exceeding 7 mm, are fixed and dehydrated by the procedures of choice. Two stock solutions: A, for infiltration; and B, the accelerator, are used in embedding. Formulas: A, 80 ml of glycol methacrylate (2-hydroxyethyl methacrylate—Rohm and Haas Co., Philadelphia, Pa.) is mixed well with 12 ml of polyethylene glycol (Carbowax) 400 and 8 ml of water; then 0.27 gm of benzoyl peroxide added, heated to dissolve the peroxide, and allowed to cool to room temperature. B, polyethylene 200 or 400, 15 parts, and N,N-dimethylaniline, 1 part, mixed thoroughly. Tissues are first infiltrated completely with solution A, then cast in a mixture consisting of 42 parts of A mixed with 1 part of B. Polymerization occurs in 45 min to 3 hr, depending on the temperature. In a water bath at 20 C, the time required was found to be about 3 hr; at 25 C, 1.5 hr; and at 30 C, 45 min. The plastic block can be trimmed easily, and sections 1-2 μ thick readily cut. Sections can be attached to slides by water flotation, without adhesive, and should be dried at room temperature. Staining with aqueous solutions of basic and acid dyes, without removing the embedding matrix, is sharp and brilliant. When staining of the matrix by basic dyes occurs, this background stain can be completely removed by differentiating in either 2-butoxyethanol, pure ethanol, or a mixture of the two. A number of histochemical reagents have been found compatible with this embedding procedure.     

Molecular structures of Fe(II) complexes with mono- and di-protonated ethylenediamine-N,N,N′,N′-tetraacetate (Hedta and H2edta), as determined by X-ray crystal analyses

The molecular structure of the title complexes [Fe(H₂O)₄][Fe(Hedta)(H₂O)]₂ · 4H₂O (I) and [Fe(H[₂edta)(H₂O)] · 2H₂O (II) have been determined by single-crystal X-ray analyses. The crystal data are as follows: I: monoclinic, P2₁/n, A = 11.794(2), B = 15.990(2), C = 9.206(2) Å, β = 90.33(1)°, V = 1736.1(5) ų, Z = 2 and R = 0.030; II: monoclinic, C2/c, A = 11.074(2), B = 9.856(2), C = 14.399(2) Å, β = 95.86(1)°, V = 1563.3(4) ų, Z = 4 and R = 0.025. I is found to be isomorphous with the Mn^II analog reported earlier and to contain a seven-coordinate and approximately pentagonal-bipyramidal (PB) [Fe^II(Hedta)(H₂O]⁻ unit in which Hedta acts as a hexadentate ligand. The [Fe^II(H₂edta)(H₂O)] unit in II has also a seven-coordinate PB structure with the two protonated equatorial glycine arms both remaining coordinated, and thus bears a structural resemblance to the seven-coordinate [Co^II(H₂edta)(H₂O)] reported previously.     

Pyrazolonato complexes of lead. Crystal structures of bis(1-phenyl-3-methyl-4-acetyl pyrazolonato)lead(II) and bis(1-phenyl-3-methyl-4-butanoylpyrazolonato)lead(II)

The structures of the complexes [PbL₂], L = 1-phenyl-3-methyl-4-acylpyrazolonato, RCOC₁₀H₈N₂O, R = Me (2) or Pr (3), have been determined by X-ray diffraction studies. Compound 2 is monoclinic, space group P2₁, A = 11.285(4), B = 14.727(4), C = 20.749(5) Å, β = 95.83(3)°, R = 0.039 for 4486 reflections, and 3 is monoclinic, space group C2/c, A = 27.528(11), B = 7.245(11), C = 14.264(7) Å, β = 113.6(3)°, R = 0.021 for 2118 reflections. There are three different lead environments in 2 but only one in 3. In each case the lead atom makes four strong bonds to oxygen and two weaker bonds to either oxygen or nitrogen in adjacent molecules.     

Thermodynamics of the disproportionation of adenosine 5'-diphosphate to adenosine 5'-triphosphate and adenosine 5'-monophosphate, II. Experimental data

High-pressure liquid-chromatography and microcalorimetry have been used to determine equilibrium constants and enthalpies of reaction for the disproportionation reaction of adenosine 5′-diphosphate (ADP) to adenosine 5′-triphosphate (ATP) andadenosine 5′-monophosphate (AMP). Adenylate kinase was used to catalyze this reaction. The measurements were carried out over the temperature range 286 to 311 K, at ionic strengths varying from 0.06 to 0.33 mol kg⁻¹, over the pH range 6.04 to 8.87, and over the pMg range 2.22 to 7.16, where pMg = -log a(Mg²⁺). The equilibrium model developed by Goldberg and Tewari (see the previous paper in this issue) was used for the analysis of the measurements. Thus, for the reference reaction: 2 ADp³⁻ (ao) AMp²⁻ (ao)+ ATp⁻ (ao), K° = 0.225 ± 0.010, ΔG° = 3.70 +- 0.11 kJ mol ⁻¹, ΔH° = −1.5 ± 1. 5 kJ mol ⁻¹, °S ° = −17 ± 5 J mol⁻¹ K⁻¹, and ACP_p°≈ = −46 J mo1l⁻¹ K⁻¹ at 298.15 K and 0.1 MPa. These results and the thermodynamic parameters for the auxiliary equilibria in solution have been used to model the thermodynamics of the disproportionation reaction over a wide range of temperature, pH, ionic strength, and magnesium ion morality. Under approximately physiological conditions (311.15 K, pH 6.94, [Mg²⁺] = 1.35 × 10⁻³ mol kg⁻¹, and I = 0.23 mol kg⁻¹) the apparent equilibrium constant (K_A′ = m(ΣAMP)m(ΣATP)/[ m(ΣADP)]²) for the overall disproportionation reaction is equal to 0.93 ± 0.02. Thermodynamic data on the disproportionation reaction and literature values for this apparent equilibrium constant in human red blood cells are used to calculate a morality of 1.94 × 10⁻⁴ mol kg⁻¹ for free magnesium ion in human red blood cells. The results are also discussed in relation to thermochemical cycles and compared with data on the hydrolysis of the guanosine phosphates.     

The synthesis and structural characterization of carborane oligomers connected by carbon-carbon and carbon-boron bonds between icosahedra

The reaction of dilithiated o-carborane (closo-1,2-Li₂-1,2-C₂B₁₀H₁₀) with CuCl₂ gives 1,1′-bis(o-carborane) (1), 1,3′-bis(o-carborane) (2) and 1,4′-bis(o-carborane) (3). Compound 2 (C₄B₂₀H₂₂) crystallizes in the monoclinic space group P2₁/n with A = 6.9275(6), B = 9.7655(8), C = 12.356(1) Å, β = 90.028(2)° and Z = 2. The structure was solved by direct methods and refined to R = 0.048 and R_w = 0.074. Compound 3 (C₄B₂₀H₂₂) crystallizes in the orthorhombic space group P2₁2₁2₁ with A = 6.8854(5), B = 12.523(1), C = 19.847(1) Å and Z = 4. The structure was solved by direct methods and refined to R = 0.078 and R_w = 0.091. The coupling reaction of dilithiated m-carborane (closo-1,7-Li₂-1,7-C₂B₁₀H₁₀) with CuCl₂ results in the formation of 1,1′-bis(m-carborane) (4) and tetra(m-carborane) (5).     

Crystal and molecular structure of polymeric [MnCl2(bpy)]n

A crystal and molecular structure determination of MnCl₂(bpy) showed that it exists as polymeric octahedral [MnCl₂(bpy)]_n. [MnCl₂(bpy)_n crystallizes in the monoclinic space group I2/a with A = 7.007(1), B = 9.200(1), C = 16.495(1) Å, β = 91.313(5)° and Z = 4. On the basis of 979 unique observed reflections with I 2.5σ(I) the structure was refined to R = 0.032.     

Carbon–carbon-linked (pyrazolylphenyl)oxazolidinones with antibacterial activity against multiple drug resistant gram-positive and fastidious gram-negative bacteria

In an effort to expand the spectrum of activity of the oxazolidinone class of antibacterial agents to include Gram-negative bacteria, a series of new carbon–carbon linked pyrazolylphenyl analogues has been prepared. The -N-substituted methyl pyrazole (10) in the C3-linked series exhibited very good Gram-positive activity with MICs ≤0.5–1 μg/mL and moderate Gram-negative activity with MICs=2–8 μg/mL against Haemophilus influenzae and Moraxella catarrhalis. This analogue was also found to have potent in vivo activity with an ED₅₀=1.9 mg/kg. β-Substitution at the C3-linked pyrazole generally results in a loss of activity. The C4-linked pyrazoles are slightly more potent than their counterparts in the C3-linked series. Most of the analogues in the C4-linked series exhibited similar levels of activity in vitro, but lower levels of activity in vivo than 10. In addition, incorporation of a thioamide moiety in selected C4-linked pyrazole analogues results in an enhancement of in vitro activity leading to compounds several times more potent than eperezolid, linezolid and vancomycin. The thioamide of the N-cyanomethyl pyrazole analogue (34) exhibited an exceptional in vitro activity with MICs of ≤ 0.06–0.25 μg/mL against Gram-positive pathogens and with MICs of 1 μg/mL against fastidious Gram-negative pathogens.     

Stress relaxation function of bone and bone collagen

Relaxation Young's and shear moduli of bovine bone and bone collagen were investigated. It was found that each relaxation process observed had two stages, which were referred to as process I and process II in order of time. Process II was described by a simple exponential decay while process I was not. The Kohlrausch-Williams-Watts (KWW) function, ψ(t) = exp[t/τ₁)^B] (0 < B < 1), was found to be suitable to describe process I. The normalized relaxation modulus, M_r(t), was expressed by the combination of the simple exponential type relaxation function and the KWW function

M_r=A₁exp[−(t/τ₁)^B]+A₂exp[(t/τ₁)](0<B1)

On the basis of this equation, the relaxation mechanism in bone and bone collagen was identified. According to the model proposed for the KWW relaxation function, the stress relaxation process in bone was considered to be governed by viscoelastic properties of matrix collagen fiber. The model for the KWW relaxation function requires the disordered glassy structure of collagen fiber, which is consistent with the results of the structural investigations.     

Changes in the Mark–Houwink hydrodynamic volume of chitosan molecules in solutions of different organic acids, at different temperatures and ionic strengths

The objective of this study is to explore the cause(s) of changes in the hydrodynamic volume of chitosan molecules in solutions of different organic acids, at different temperatures and ionic strengths. Change in intrinsic viscosity is used as the parameter to elucidate the causes of changes in the hydrodynamic volume of chitosan molecules in these solutions. Results show that the intrinsic viscosity of chitosan decreases in acetic acid or in malic acid over storage time. These decreases are more pronounced in acetic acid solution than in malic acid solution, more significant in higher temperature than in lower temperature solutions, and greater in solutions without NaCl than in solutions containing higher NaCl. The decrease in intrinsic viscosity can perhaps be attributed to the compounded effects of compaction of the chitosan molecules and/or acidic degradation during storage.     

Amphiphilic derivatives of sodium alginate and hyaluronate: synthesis and physico-chemical properties of aqueous dilute solutions

This paper reports on the synthesis and the physico-chemical characterisation of various amphiphilic derivatives of two natural polysaccharides, sodium alginate and sodium hyaluronate, in which a rather small proportion of the carboxylic groups (≤10% mol) was esterified by long alkyl chains (C₁₂H₂₅ or C₁₈H₃₇).

The derivatives thus prepared were characterised by gas chromatography, ¹H and ¹³C n.m.r. spectroscopy and size exclusion chromatography coupled to a multi-angle laser light scattering detection. The tendency of these water-soluble compounds to hydrophobic association in aqueous solutions was evidenced firstly in dilute regime using capillary viscometry as well as fluorescence spectroscopy in the presence of a molecular probe, 1,1-dicyano-(4′-N,N-dimethylaminophenyl)-1,3-butadiene.     

Molecular structures and some properties of tris(2-aminoethyl) amine cobalt(III) complexes with thiocarboxylato-O,S such as 3-mercaptopropionato, 2-mercaptoacetato and their derivatives

Cobalt(III) complexes with a thiolate or thioether ligand, t-[Co(mp)(tren)]⁺ (2), t-[Co(mtp)(tren)]²⁺ (1Me) and t-[Co(mta)(tren)]²⁺ (2Me), (mp = 3-mercaptopropionate, MA = 3-(methylthio)propionate and MTA = 2-(methylthio)acetate) have been prepared in aqueous solutions. The crystal structures of 1, 2, 1Me and 2Me were determined by X-ray diffraction methods. The crystal data are as follows, t-[Co(mp)(tren)]ClO₄ (1CIO₄): monoclinic, P2₁/n, A = 10.877(8), B = 11.570(4), c = 12.173(7) Å, β = 92.20(5)°, V = 1531(1) ų, Z = 4 and R = 0.060; t-[Co(ma)(tren)]Cl·3H₂O (2Cl·3H₂O): monoclinic, P2₁/n, a = 7.7688(8), B = 27.128(2), C = 7.858(1) Å, β = 100.63(1)°, V = 1627.7(3) ų, Z = 4 and R = 0.066; (+)₄₆₅^CD-t-[Co(mtp)(tren)](ClO₄)₂ ((+)₄₆₅^CD-1Me(ClO₄)₂): orthorhombic, P2₁2₁2₁, A = 10.6610(7), B = 11.746(1), C = 15.555(1) Å, V = 1947.9(3) ų, Z = 4 and R = 0.068; (+)₄₆₅^CD-t-[Co(mta)(tren)](ClO₄)₂ ((+)₄₆₅^CD-2Me(ClO₄)₂): orthorhombic, P2₁2₁2₁, a = 10.564(1), B = 11.375(1), C = 15.434(2) Å, V = 1854.7(4) ų, Z = 4 and R = 0.047. All central Co(III) atoms have approximately octahedral geometry, coordinated by four N, one O, and one S atoms. All of the complexes are only isomer, of which the sulfur atom in the didentate-O,S ligands are located at the trans position to the tertiary amine nitrogen atom of tren. 1 and 1Me contain six-membered chelate ring, and 2 and 2Me do five-membered chelate ring in the didentate ligand. The chirality of the asymmetric sulfur donor atom in (+)₄₆₅^CD-1Me is the S configuration and that in (+)₄₆₅^CD-2Me is the R one. The ¹H NMR, ¹³C NMR and electronic absorption spectral behaviors and electrochemical properties of the present complexes are discussed in relation to their stereochemistries.     

Effect of organic solvents on oxygen mass transfer in multiphase systems: Application to bioreactors in environmental protection

The absorption of oxygen in aqueous–organic solvent emulsions was studied in a laboratory-scale bubble reactor at a constant gas flow rate. The organic and the gas phases were dispersed in the continuous aqueous phase. Volumetric mass transfer coefficients (k_La) of oxygen between air and water were measured experimentally using a dynamic method. It was assumed that the gas phase contacts preferentially the water phase. It was found that addition of silicone oils hinders oxygen mass transfer compared to air–water systems whereas the addition of decane, hexadecane and perfluorocarbon PFC40 has no significant influence. By and large, the results show that, for experimental conditions (organic liquid hold-up ≤10% and solubility ratio ≤10), the k_La values of oxygen determined in binary air–water systems can be used for multiphase (gas–liquid–liquid) reactor design with applications in environmental protection (water and air treatment processes).