Axial dispersion in coiled tubular reactors

A theoretical and experimental treatment of axial dispersion in coiled tubes is presented. The dispersion, δ, is related to the theoretical plate height divided by four times the radius of the tube (H/4r). This parameter, when plotted against the product of the Reynolds number and the Schmidt number (ReSc), accurately predicts maxima in dispersion curves. Variations in the boundary layer thickness and the velocity profile cause the dispersion to pass through a maximum at a constant value of log (De²Sc^1·14) equal to 6.13 for unretained solutes (De is the Dean number). A new measure of dispersion is proposed; the reduced dispersion, ? = 256/(Re^0.667Sc), is derived from the experimental behavior of dispersion at values of log (De²Sc^1·14) smaller than 6.13. The logarithm of ? is found to be approximately zero for 2.2 < log (De²Sc^1·14) < 6.1 and to decrease linearly with log (De²Sc^1·14) at higher values. Experiments with four solutes that have a wide range of molecular diffusivities are reported. Results agree with theory.     

New compounds in the cesium sulfobromide rhenium octahedral cluster chemistry: syntheses and crystal structures of Cs4Re6S8Br6 and Cs2Re6S8Br4

The exploration of the CsReSBr system, in order to identify new phases based on octahedral cluster anions, has produced single crystals of Cs₄Re₆S₈Br₆ (1) (trigonal, space group P-6c2, a=9.7825 (3) Å, c=18.7843 (5) Å, V=1556.77 (1) ų, Z=2, density=5.09 g cm⁻³, μ=36.07 mm⁻¹) and Cs₂Re₆S₈Br₄ (2) (monoclinic, space group P2₁/n, a=6.3664 (1) Å, b=18.4483 (4) Å, c=9.3094 (2) Å, β=104.2618 (8)°, V=1059.69 (4) ų, Z=2, density=6.14 g cm⁻³, μ=45.83 mm⁻¹). These two compounds have been obtained by high-temperature solid state route. Their structures have been solved and refined from single crystal X-ray diffraction data. The structure of Cs₄Re₆S₈Br₆ presents isolated anionic cluster units inscribed in a (Cs⁺)₁₂ cuboctahedron and the one of Cs₂Re₆S₈Br₄ exhibits ReS^i-a,a-iRe inter-unit bridges. The framework of the latter presents then a strongly 1-D character.     

Metal solid solutions obtained by thermolysis of Pt and Re salts. Crystal structure of [Pt(NH3)4](ReO4)2

A complex salt of tetraammineplatinum(II) perrhenate [Pt(NH₃)₄](ReO₄)₂ has been synthesized. Crystal data: a = 5.1847(6) Å, b = 7.7397(8) Å, c = 7.9540(9) Å, α = 69.531(3)°, β = 79.656(3)°, γ = 77.649(3)°, V = 290,19(6) ų, space group $P\bar 1$ , Z = 1, d _x = 4.370 g/cm³. The products of decomposition of [Pt(NH₃)₄](ReO₄)₂ in a hydrogen atmosphere were investigated using X-ray phase analysis. In definite temperature modes, these are Pt_0.33Re_0.67 solid solutions based on Re with hcp cell parameters a = 2.76 Å, c = 4.42 Å. The products of thermolysis obtained from other precursor complex salts containing both Pt and Re were investigated. Thus Pt_0.75Re_0.25 solid solution with a = 3.905(3) Å was obtained from (NH₄)₂[ReCl₆]_0.25[PtCl₆]_0.75.     

The structure type of Re2Te5, a new [M6X14] cluster compound

Re₂Te₅ crystallizes in a new structure type, having space group Pbca (No. 61) with a = 13.003(5), b = 12.935(7), c = 14.212(5) Å, Z = 12. All atoms are in the general positions 8(c), apart from one Te atom which occupies the special position 4(a) in a center of symmetry. The Re atoms are arranged in octahedral [Re₆] clusters and all the atoms in general positions can be grouped as {[Re₆Te₈]Te₆} complexes. The centers of these units and the Te atom in 4(a) are arranged like a slightly distorted rock salt structure. The Te atoms can be replaced by Se atoms up to at least 40%. Re₂Te₅ and Re₂Se₂Te₃ reveal a semiconductor-like electric behavior which is accounted for by the chemical bonding.     

Studies on organometallic compounds with hetero multiple bridges : V. Crystal and molecular structure of the parent rhenium complex Re2Br2(CO)6(THF)2 and substituted products of tricarbonylrhenium(I) derived from it

Reactions of the tetrahydrofuran adduct Re₂Br₂(CO)₆(THF)₂ with some phosphorous- and nitrogen-containing donors under mild conditions are reported, which led to the formation of substituted products of tricarbonylrhenium(I). Bromide abstraction from the THF adduct by secondary amines and CS₂ produced the dithiocarbamato derivatives Re(S₂CNR₂)(CO)₃(HNR₂) whose behaviour in solution with CO was also investigated. Mass spectral data for some of the substituted products have been measured. The title compound crystallizes in the space group P2₁/n with cell constants a = 8.661(2), b = 11.251(3), c = 11.424(3) Å and β = 110.36(2)°, U = 1043.67 ų and D_calc = 2.686 g cm^?3, Z = 2. The molecule consists of a planar Re₂Br₂ moiety, as demanded by symmetry. The two THF groups are on opposite sides of this plane and the three CO groups around each rhenium atom are arranged in a fac arrangement. The unique ReBr distances are 2.642(5) and 2.644(4)Å, while the ReO distance is 2.129(31) Å. The ReBrRe and BrReBr angles are 97.3(2) and 82.7(1)°, respectively. The Re?Re nonbonding distance is 3.967(3) Å. The THF ligands consist of a nearly planar C₄ fragment (maximum deviation from planarity 0.06 Å), while the oxygen is 0.348 Å out of that plane, the angle defined by the C₄ plane and the COC fragment of the THF ligand being 24.99°. Final values of the discrepancy indices are R(F) = 0.074 and R_w(F) = 0.095.     

Synthesis and Crystal Structure of the [Re2(CH3COO)2Cl4((CH3)2NCOCH3)2] Complex

Compound [Re₂(CH₃COO)₂Cl₄((CH₃)₂NCOCH₃)₂] is synthesized. The influence of parameters of the hydrothermal synthesis under elevated pressure on the yield of a target product and its molecular structure and physicochemical properties is studied. In the neutral complex with cis-arrangement of the bridging acetate and terminal chloride ligands with respect to the multiply bonded Re₂ ⁶⁺ complex-forming center, the Re–Re bond length is 2.2418(3) Å. Dimethylacetamide molecules are in the axial positions, the Re–O bond lengths being 2.304(3) and 2.321(4) Å. The influence of the donor ability of the axial substituents in analogous structures of the rhenium(III) binuclear clusters on the Re–Re and Re–L_ax bond lengths is analyzed.     

ReV‐Phthalocyaninate und ReV‐Tetraphenylporphyrinate mit Oxo‐Liganden: Synthese,Eigenschaften und Kristallstruktur

Re^V‐Phthalocyaninates and Re^V‐Tetraphenylporphyrinates: Synthesis, Properties, and Crystal Structure Hexa‐coordinated Re^V phthalocyaninates (pc) and Re^V tetraphenylporphyrinates (tpp) of the type [Re(O)(X)p] (p: pc, tpp) with X = OCH₃, ReO₄, Cl/pc, F/pc, OH/tpp, [{Re(O)p}₂(μ‐O)] and (cat)^trans[Re(O)₂p] (cat: ⁿBu₄N, Et₄N/tpp) have been isolated and characterised by their UV‐Vis‐NIR, IR and resonance Raman (RR) spectra. In the RR spectra, the intensity of the (Re=O) and (Re–X) stretching vibrations (ν(Re=O/–X)) in [Re(O)(X)p] and [{Re(O)p}₂(μ‐O)] is selectively enhanced with excitation in coincidence with O → Re–CT between ca 19000 and 22000 cm^–1. In accordance to selection rules, data of ν(Re=O/–X) compare well with those of the complementary IR spectra. Because of the trans influence ν(Re=O) depends on the axial ligand X, ranging from 940 to 1010 cm^–1. The crystallographic characterization of [Re(O)(ReO₄)tpp] · CHCl₃ ( 1 ), [{Re(O)tpp}₂(μ‐O)] · py ( 2 ), (ⁿBu₄N)^trans[Re(O)₂tpp] ( 3 ), and (Et₄N)^trans[Re(O)₂tpp] · 2 H₂O ( 4 ) is described. The tpp centered Re atom is in a distorted octahedron of four N atoms of the porphyrinate and two axial O atoms in a mutual trans position. Average Re–N distances are 2.062 Å in 1 , 2.086 Å in 2 , 2.089 Å in 3 , and 2.082/2.086 Å in 4 . The Re–O distance of the terminal rhenyl group varies from 1.64(1) Å ( 1 ), 1.73(1)/1.70(1) Å ( 2 ) to 1.80(1) Å ( 4 ), that of the monodentate rhenate(VII) from 1.70(1) to 1.75(1) Å. The Re–O distances in the bridge of the linear O=Re–O–Re=O skeleton in 2 are 1.95(1)/1.89(1) Å. In 1 , with a bent O=Re–O^ ReO₃ moiety (∢(Re–O^ReO₃) = 143(1)°) and a mostly ionic coordinated rhenate(VII), these distances differ significantly (2.20(1) Å vs 1.75(1) Å). The porphyrinate in 1 is saucer‐shaped with a distal rhenate(VII), and the tpp centered Re atom is displaced by 0.31 Å out of the (N)₄ plane towards the rhenyl‐O atom. The distorted porphyrinates in 2 are rotated by 30.4(4)°, and the Re atoms are 0.1 Å out of their (N)₄ planes towards the terminal O atoms. In 3 and 4 the porphyrinates are almost planar with the Re atom in their centre.     

New Rhenium(V) Nitrofuryl Semicarbazone Complexes.Crystal Structure of [ReOCl2(PPh3)(3‐(5‐Nitrofuryl)acroleine semicarbazone)]

The synthesis and characterization of the first two Re complexes with semicarbazone ligands is presented. Selected ligands are 5‐Nitro‐2‐furaldehyde semicarbazone (Nitrofurazone) ( L1 ) and its derivative 3‐(5‐Nitrofuryl)acroleine semicarbazone ( L2 ). Complexes of general formula [Re^VOCl₂(PPh₃) L ], where L = L1 and L2 , were prepared in good yields and high purity by reaction of [Re^VOCl₃(PPh₃)₂] with L in ethanol or methanol solutions. The complexes formula and molecular structures were supported by elemental analyses and electronic, FTIR, ¹H, ¹³C and ³¹P NMR spectroscopies. In addition, the crystal and molecular structure of [Re^VOCl₂(PPh₃) L2 ] was determined by X‐ray diffraction methods. [ReOCl₂(PPh₃)(3‐(5‐Nitrofuryl)acroleine semicarbazone)] crystallizes in the space group P‐1 with a = 11.2334(2), b = 11.3040(2), c = 12.5040(2) Å, α = 81.861(1), β = 63.555(1), γ = 83.626(1)°, and Z = 2. The Re(V) ion is in a distorted octahedral environment, equatorially coordinated to a deprotonated semicarbazone molecule acting as a bidentate ligand through its carbonylic oxygen and azomethynic nitrogen atoms, to an oxo ligand and a chlorine atom. The six‐fold coordination is completed by another chlorine atom and a triphenylphosphine ligand at the axial positions.     

Framework polymers based on octahedral chalcocyanide cluster [Re6Q8(CN)6]4−/3− anions (Q = Se, Te) and [Nd(Bipy)n]3+ Complexes (n = 1, 2)

Interaction of salts of the cluster anions {Re [Re₆Q₈(CN)₆]^4?/3? (Q = Se, Te) with Nd salts in the presence of 2,2′-bipyridyl (Bipy) ligand brings about new coordination polymers: Pr ₄ ⁿ N[{Nd(Bipy)(H₂O)₄} {Re₆Se₈(CN)₆}] · 2H₂O (I) (space group C2/c, a = 18.2918(16) Å, b = 14.9972(13) Å, c = 37.513(3) Å, β = 102.046(4)°, V = 10064.2(15) ų, Z = 8), [{Nd(Bipy)₂(H₂O)} {Re₆Se₈(CN)₆}] (II) (space group C2/c, a = 15.8668(3) Å, b = 13.5403(3) Å, c = 20.5189(4) Å, β = 110.135(1)°, V = 4138.89(15) Å₃, Z = 4), and [{Nd(Bipy)(EtOH)(H₂O)₄}{Re₆Te₈(CN)₆}] · EtOH (III) (space group $P\bar 1$ , a = 9.4733(6) Å, b = 12.5326(8) Å, c = 17.2374(11) Å, α = 96.561(2)°, β = 90.310(2)°, γ = 94.876(2)°, V = 4138.89(15) Å₃, Z = 4). The compounds synthesized are characterized by single-crystal X-ray diffraction and IR methods. Compounds I and III have layered (2D) structures, compound II is a framework (3D) polymer.     

Preparation and characterization of NASICON type Li+ ionic conductors

The new scandium/aluminium co-doped NASICON phases Li_1?+?x Al _y Sc _x???y Ti_2???x (PO₄)₃ (x?=?0.3, y?=?0,0.1,0.2,0.3) were prepared by mechanical milling followed by annealing of the mixtures at 950 °C. X-ray diffraction of all samples showed the formation of NASICON structure with space group R-3c along with a minor impurity. Rietveld refinement of the X-ray data was performed to identify the structural variation. Doping with Sc³⁺ caused elongation of a- and c- axes for all the compounds when compared with undoped LiTi₂(PO₄)₃. The compound Li_1.3Sc_0.3Ti_1.7(PO₄)₃ showed a maximum of a?=?8.5504(7), c?=?20.986(3) Å at room temperature and exhibited highest coefficient of thermal expansion. The highest ionic conductivity (σ), 7.28×10^?4 S cm^?1 was observed for Li_1.3Sc_0.3Ti_1.7(PO₄)₃, two orders of magnitude higher than for the undoped phase.     

Mononuclear rhenium(III) and rhenium(II) complexes of 1,2-bis(diphenylphosphino)ethylene: The structure of trans-ReCl2(dppee)2

The mononuclear rhenium(III) complexes trans-[ReX₂(dppee)₂]X · nH₂O (X = Cl or Br, dppee = Ph₂PCHCHPPh₂) have been prepared by the reaction of (n-BU₄N)₂Re₂X₈ with dppee in methanol-conc. HX; in the case of X = Cl, ethanol may also be used as the reaction solvent. These salts undergo anion exchange reactions with ClO₄⁻ and/or PF₆⁻. The rhenium(II) complex trans-ReCl₂(dppee)₂ can be prepared by the cobaltocene reduction of trans-[ReCl₂(dppee)₂]Cl · 4H₂O and the reaction of Re₂Cl₆(PBu₃)ⁿ₂ with dppee in refluxing ethanol. The spectroscopic and electrochemical properties of [ReX₂(dppee)₂]⁺ have been investigated. Cyclic voltammetry (in 0.1 M tetra-n-butyl-ammonium hexafluorophosphate-CH₂Cl₂ with a Pt-bead electrode) shows reversible redox processes at E_1/2(ox) ca +1.5 V, E_1/2(red) ca −0.2 V, and E_1/2(red) ca −1.4 V vs Ag-AGCl that correspond to the Re(IV)-Re(III), Re(III)-Re(II) and Re(I)-Re(l) couples, respectively. The single-crystal X-ray crystal structure of trans-ReCl₂(dppee)₂ has confirmed its octahedral geometry. This complex crystallizes in the monoclinic space group P2₁/c with the following unit-cell dimensions: a = 11.321(2)Å, b = 13.011(2)Å, c = 17.242(3)Å, β = 95.79(2)°, V = 2527(1)ų, and Z = 2. The structure was refined to R = 0.041 (R_w = 0.070) for 2430 data with F² > 3.0σ(F²). The ReCl and ReP distances are 2.422(2) and 2.405(2)Å, respectively.     

μ‐Oxo‐bis{{2,2′‐[2,2‐di­methyl­propane‐1,3‐diyl­bis­(nitrilomethyl­idyne)]­diphenolato}­oxo­rhenium(V)}

The title compound, [Re₂O₃(C₁₉H₂₀N₂O₂)₂], is a hexacoordinate complex containing an [Re₂O₃]⁴⁺ core with a linear O=Re—O—Re=O bridge. The distorted octahedral coordination of the Re^V atom is achieved by an N₂O₂ donor set from the tetradentate imine–phenol ligand. The overall charge of the compound is neutral due to deprotonation of the phenol groups, and the terminating and bridging O atoms. The Re=O and Re—O bond distances of the [Re₂O₃]⁴⁺ core are 1.699 (4) and 1.911 (1) Å, respectively. The Re—O and Re—N bond distances of the equatorial plane are in the ranges 2.024 (4)–2.013 (4) and 2.128 (5)–2.120 (5) Å, respectively.     

Rhenium(I), (III) and (V) complexes of tridentate ONX (X = O,N, S)-donor Schiff bases

The reactions of the potentially tridentate Schiff bases 2-[(2-hydroxyphenyl)iminomethyl]phenol (H₂ono) and 2-(2-aminobenzylideneimino)phenol (H₃onn) with trans-[ReOBr₃(PPh₃)₂] were studied, and the complexes [Re^IIIBr(PPh₃)₂(ono)] (1) and [Re^VBr(PPh₃)₂(onn)]Br (2) were isolated. In 1ono acts as a dianionic tridentate ligand, and in 2onn is coordinated as a tridentate trianionic imido-imino-phenolate. The complex [Re^I(CO)₃(ons)(Hno)] was isolated from the reaction of [Re(CO)₅Br] with 2-[(2-methylthio)benzylideneimino]phenol (Hons; Hno = 2-aminophenol), with ons coordinated as a bidentate chelate with a free SCH₃ group. These complexes were characterized by X-ray crystallography, NMR and IR spectroscopy.     

Neutrally buoyant particle in the boundary layer at a plate. II. Inertial effects

This study deals with the asymptotic modeling of the disturbance flow field created by a neutrally buoyant solid particle suspended in a by drodynamic boundary layer past a plate. The range of dimensions studied isL/Re _i ^5/4 <R _p<L/Re _i ^1/2 (Re_i being the total Reynolds number of the back-ground flow stream,L is the lenghth of the plate). The concept of local particle's Reynolds number Re_p is introduced. The obtained asymptotic equations for the disturbance field are classified in three basic groups: viscous perturbation (Re_p<1/Re _i ^1/2 ); intermediate case (Re_p1/Re _i ^1/2 ) and inertial perturbation (Re_p>1/Re _i ^1/2 ).     

[Re(η2-CS3)4]3−, a new trithiocarbonate-containing rhenium(V) dodecahedral anion

The mononuclear complex (NMe₄)₃[Re(²-CS₃)₄] has been prepared by adding CS₂ to ReS^– ₄ in a mixture of MeOH and NH₃. During the reaction, Re^VII is reduced to Re^V, the measured diamagnetism (X = –3.04 × 10^–4cm³mol^–1) of the complex showing that the two added electrons are coupled. (NMe₄)₃[Re(²-CS₃)₄] crystallizes in the space group Fddd, a = 11.985(4) Å, b = 23.001(11) Å, c = 47.463(19) Å, V = 13085(9) ų. The reaction of CS₂ results in the formation of trithiocarbonates bonded to the rhenium in a dodecahedral geometry.     

Facile Synthetic Access to Rhenium(II) Complexes: Activation of Carbon–Bromine Bonds by Single‐Electron Transfer

The five‐coordinated Re^I hydride complexes [Re(Br)(H)(NO)(PR₃)₂] (R=Cy 1 a , iPr 1 b ) were reacted with benzylbromide, thereby affording the 17‐electron mononuclear Re^II hydride complexes [Re(Br)₂(H)(NO)(PR₃)₂] (R=Cy 3 a , iPr 3 b ), which were characterized by EPR, cyclic voltammetry, and magnetic susceptibility measurements. In the case of dibromomethane or bromoform, the reaction of 1 afforded Re^II hydrides 3 in addition to Re^I carbene hydrides [Re(?CHR¹)(Br)(H)(NO)(PR₃)₂] (R¹=H 4 , Br 5 ; R=Cy a , iPr b ) in which the hydride ligand is positioned cis to the carbene ligand. For comparison, the dihydrogen Re^I dibromide complexes [Re(Br)₂(NO)(PR₃)₂(η²‐H₂)] (R=Cy 2 a , iPr 2 b ) were reacted with allyl‐ or benzylbromide, thereby affording the monophosphine Re^II complex salts [R₃PCH₂R′][Re(Br)₄(NO)(PR₃)] (R′=? CH?CH₂ 6 , Ph 7 ). The reduction of Re^II complexes has also been examined. Complex 3 a or 3 b can be reduced by zinc to afford 1 a or 1 b in high yield. Under catalytic conditions, this reaction enables homocoupling of benzylbromide (turnover frequency (TOF): 3 a 150, 3 b 134 h^?1) or allylbromide (TOF: 3 a 575, 3 b 562 h^?1). The reaction of 6 a and 6 b with zinc in acetonitrile affords in good yields the monophosphine Re^I complexes [Re(Br)₂(NO)(MeCN)₂(PR₃)] (R=Cy 8 a , iPr 8 b ), which showed high catalytic activity toward highly selective dehydrogenative silylation of styrenes (maximum TOF of 61 h^?1). Single‐electron transfer (SET) mechanisms were proposed for all these transformations. The molecular structures of 3 a , 6 a , 6 b , 7 a , 7 b , and 8 a were established by single‐crystal X‐ray diffraction studies.     

Tetrakis(μ‐benzothiazole‐2‐thiolato)‐1:2κ4N:S2;1:2κ4S2:N‐dichloro‐1κCl,2κCl‐dirhenium(III)(Re—Re) dichloromethane solvate: a bridged complex with a long Re—Re quadruple bond

The title compound, [Re₂(C₇H₄NS₂)₄Cl₂]·CH₂Cl₂, consists of dirhenium mol­ecules with bridging N,S‐benzo­thia­zole‐2‐thiol­ate ligands, axial Cl^? ligands and intramolecular hydrogen bonding. These mol­ecules adopt somewhat staggered conformations, with a long Re—Re quadruple bond distance of 2.2716 (3) Å.     

Synthese und Struktur von Re4(μ3-Te)4(TeBr2)4Br8

Synthesis and Structure of Re₄(μ₃-Te)₄(TeBr₂)₄Br₈ Re₄(μ₃-Te)₄(TeBr₂)₄Br₈ is obtained from the elements at 550°C in an evacuated glass ampoule. The diamagnetic compound forms air-stable, metallic lustre black crystals crystallizing in the tetragonal space group I4 with a = 1120.2(2), c = 1393.5(3) pm, and Z = 2. The crystal structure is built up by isolated cluster molecules Re₄(μ₃-Te)₄(TeBr₂)₄Br₈ occupying the centres 4 at 1/2, 1/2, 0 and 0, 0, 1/2. The inner sceleton is formed by a Re₄Te₄ heterocubane unit with short Re? Re distances of 277 and 283 pm, which can be discussed as single bonds. Each Re atom coordinates in addition two Br^? ligands and one TeBr₂ molecule. For Re therefore results the oxidation state +IV. Reaction of Re₄(μ₃-Te)₄(TeBr₂)₄Br₈ with I₂ yields (TeI₄)₄.     

Zur Nucleophilie des sterisch anspruchsvollen Basenanions von Lithiumdiisopropylamid beim Protonenersatz gegen das isolobale AuPPh3-Kation in [(μ-H)(μ-PPh2) (CO)8Re2]

Nucleophilic Property of the Bulk Anion of the Base Lithium diisopropylamide at the Proton Exchange vs. the Isolobal AuPPh₃ Cation in [(μ-H) (μ-PPh₂) (CO)₈Re₂] The proton exchange in the starting material [(μ-H)(μ-PPh₂)(CO)₈Re₂] vs. the isolobal [AuPPh₃]⁺ cation when reacted with the steric expansive base LDA depending on reaction temperature leads to the three-membered metal ring substance [(μ-PPh₂)(CO)₈Re₂(AuPPh₃)] or the metallatetrahedron complex [(μ-C-(N i-Prop₂)O)(μ-PPh₂)(CO)₆Re₂(AuPPh₃)₂]. The tetrahedral cluster compound obtained through the nucleophilic property of LDA shows by means of cyclic voltammetry a reversible and a irreversible one-electron transfer redox step. The single crystal X-ray analysis of the compound with a tetrahedral Au₂Re₂ core gives following values of metal-metal bond lengths: Re? Re 312.2(2) pm, Au? Au 270.9(2) pm, and Au? Re 297.7(2) pm. The acyl diisopropylamido groups bridging the Re? Re bond is planar.     

Kinetic study on external mass transfer in high performance liquid chromatography system

External mass transfer coefficients (k_f) were measured for a column packed with fully porous C₁₈-silica spherical particles (50.6 μm in diameter), eluted with a methanol/water mixture (70/30, v/v). The pulse response and the peak-parking methods were used. Profiles of elution peaks of alkylbenzene homologues were recorded at flow rates between 0.2 and 2.0 mL min⁻¹. Peak-parking experiments were conducted under the same conditions, to measure intraparticle and pore diffusivity, and surface diffusion coefficients. Finally, the values of k_f for these compounds at 298 K were derived from the first and second moments of the elution peaks by subtracting the contribution of intraparticle diffusion to band broadening. As a result, the Sherwood number (Sh) was measured under such conditions that the Reynolds (Re) and the Schmidt numbers (Sc) varied from 0.004 to 0.05 and from 1.8 × 10³ to 2.7 × 10³, respectively. We found that Sh is proportional to Re^α and Sc^β and that the correlation between these three nondimensional parameters is almost the same as those given by conventional literature equations. The values of α and β were close to those in the literature correlations, between 0.26 and 0.41 and between 0.31 and 0.36, respectively. The use of the Wilson–Geankoplis equation to estimate k_f values entails a relative error of ca. 15%. So, conventional literature correlations provide correct estimates of k_f in HPLC systems, even for particle sizes of the order of a micrometer.