Fabrication and thermoelectric properties of heavily rare-earth metal-doped SrO(SrTiO3)n (n = 1, 2) ceramics

To clarify the effect of substitutional electron doping on the thermoelectric figure of merit (ZT = S²σTκ⁻¹) of Ruddlesden–Popper phase SrO(SrTiO₃)_n (or Sr_n+1Ti_nO_3n+1), measurements were conducted for several thermoelectric parameters, e.g. electrical conductivity (σ), Seebeck coefficient (S) and thermal conductivity (κ), of (Sr_1−xRE_x)_n+1Ti_nO_3n+1 (n = 1 or 2, RE (rare earth): La or Nd, x = 0.05 and 0.1) dense ceramics prepared by a conventional solid-state reaction and hot-pressing technique. Crystal structures of the resultant ceramics were represented as (Sr_1−xRE_x)_n+1 Ti_nO_3n+1 evaluated by powder X-ray diffraction followed by the Rietveld analysis. All the ceramics exhibited electrical conductivity and the σ values simply depended on the dopant concentration, indicating that both La³⁺ and Nd³⁺ ions act as electron donors. The |S| values increased with temperature due to decrease in the chemical potential. Significant reduction of the κ values was observed as compared to cubic-perovskite SrTiO₃. The ZT value increased with temperature and reached 0.15 at 1000 K for (Sr_0.95La_0.05)₃Ti₂O₇.     

Effect of macromolecular length on anisotropic scattering of light in an electric field

Light scattering by monodisperse solutions of rigid rod-like anisotropic macromolecules, with linear dimensions l of the order of incident wavelength λ, oriented in an external d.c. electric field, →E has been analysed. The relative variations δV^E_v, δH^E_v, δV^E_h, δH^E_h of the scattered light components are discussed for the three values [l/λ] = 1, 0·5, 2, and various reorientation parameters, p = [μE/kT] of the permanent dipole moment μ and q = [(₃ − ₁)E²/2kT] of the moment induced by the principal polarizabilities ₁ = ₂ ≠ ₃. The saturation orientation field strength has been calculated for certain macromolecules with the aim of determining their optical anisotropy numerically.     

The solubility of ettringite at 25°C

Available solubility constants indicate that ettringite should be the stable form of calcium aluminate sulfate hydrate with respect to monosulfate in cement porewater. However, monosulfate is generally present in mature cement pastes, usually in the absence of ettringite. The objectives of this study were to determine the solubility product of ettringite under equilibrium conditions and to examine the solubility data used in predictive thermodynamic models. Solubility products were calculated for ettringite prepared from both supersaturated and undersaturated solutions with a pH range between 10.4 and 13.7. The mean solubility product for ettringite dissolution: Ca₆Al₂O₆(SO₄)₃ · 32H₂O → 6Ca²⁺ + 2Al(OH)₄⁻ + 3SO₄²⁻ + 4OH⁻ + 26H₂O was 10^−44.91, i.e. Log K_sp = -44.91 ± 1.06 (2 S.D.). Activity coefficients were calculated using the specific ion interaction approach. The mean solubility product was close to other values calculated from concentrations reported elsewhere for the solubility of ettringite. As is the case for all solubility products, this value cannot be inserted directly into the databases of other thermodynamic models because of differences in the methods used to calculate activity coefficients and the manner in which ion-pairing is handled by different models. However, raw solubility data are provided for recalculation of the solubility product for use in other models.     

Correlation between equation of state and temperature and pressure dependence of self-diffusion coefficient of polymers and simple liquids

Correlation between the equation of state and the temperature dependence of the self-diffusion coefficient D for polymers such as polystyrene (PS) and polydimethyl siloxane (PDMS) and simple liquids such as argon, methane and benzene and the pressure dependence of D for oligomers such as dimethyl siloxane (DMS) and simple liquids such as cyclohexane and methanol has been examined based on the equation of state derived previously. The experimental data used were published by Antonietti et al. and McCall et al. for polymers, by McCall for linear dimethylsiloxanes and by Jonas et al. and Woolf et al. for simple liquids. The expression for D in this work is given by

where A₁(M) is a function of molecular weight M_w, C₁(T) and P₁(T) are functions of temperature and B₁, n₁ and m₁ are constants determined experimentally. For simple liquids, the values of n₁ obtained range from 0.3 to 1.2, with an average , and m₁ is in the range 0.5–1.2, with . For polymers, values of n₁ are in the range 2.5–7.0 for PS and 0.5–1.3 for PDMS and m₁ for DMS is in the range 0.8–1.0. The relation Dη/T = f(M) is found to be useful for simple liquids over a wide range of temperature including the critical region and for pressures up to ≈5 kbar

1 kbar = 100 MPa There is a close correlation between ln(D/T) and _p and β_T through ln(D/T)ln D_c−⁻¹_p−β⁻¹_T, where D_c is D at the critical temperature and _p and β_T are the thermal expansion coefficient and compressibility, respectively. The molecular weight dependence of D for polymers and simple liquids is discussed based on the experimental data and recent theory of Doi and Edwards. A new model for the mechanism of self-diffusion in the liquid state is proposed.     

Dilute solution properties of carboxymethylchitins in high ionic-strength solvent

The hydrodynamic characteristics in aqueous solution at ionic strength I=0.2  of carboxymethylchitins of different degrees of chemical substitution have been determined. Experimental values varied over the following ranges: the translational diffusion coefficient (at 25.0°C), 1.1<10⁷×D<2.9 cm² s⁻¹; the sedimentation coefficient, 2.4<s<5.0 S; the Gralen coefficient (sedimentation concentration-dependence parameter), 130<k_s<680 mL g⁻¹; the intrinsic viscosity, 130<[η]<550 mL g⁻¹. Combination of s with D using the Svedberg equation yielded ‘sedimentation–diffusion' molecular weights in the range 40 000<M<240 000 g mol⁻¹. The corresponding Mark–Houwink–Kuhn–Sakurada (MHKS) relationships between the molecular weight and s, D and [η] were: [η]=5.58×10⁻³ M^0.94; D=1.87×10⁻⁴ M^−0.60; s=4.10×10⁻¹⁵ M^0.39. The equilibrium rigidity and hydrodynamic diameter of the carboxymethylchitin polymer chain is also investigated on the basis of wormlike coil theory without excluded volume effects. The significance of the Gralen k_s values for these substances is discussed.     

Electrical resistivity and thermopower of (La1−xSrx)MnO3 and (La1−xSrx)CoO3 at elevated temperatures

Electrical resistivity and Seebeck (S) measurements were performed on (La_1−xSr_x)MnO₃ (0.02x0.50) and (La_1−xSr_x)CoO₃ (0x0.15) in air up to 1073 K. (La_1−xSr_x)MnO₃ (x0.35) showed a metal-to-semiconductor transition; the transition temperature almost linearly increased from 250 to 390 K with increasing Sr content. The semiconductor phase above the transition temperature showed negative values of S. (La_1−xSr_x)CoO₃ (0x0.10) showed a semiconductor-to-metal transition at 500 K. Dominant carriers were holes for the samples of x0.02 above room temperature. LaCoO₃ showed large negative values of S below ca. 400 K, indicative of the electron conduction in the semiconductor phase.     

Kinetics of Fischer–Tropsch synthesis on titania-supported cobalt

Rate data have been obtained for CO hydrogenation on a well-characterized 11.7% Co/TiO₂ catalyst in a differential fixed bed reactor at 20 atm, 180–240°C, and 5% conversion over a range of reactant partial pressures. The resulting kinetic parameters can be used to model precisely and accurately the kinetics of this reaction within this range of conditions. Turnover frequencies and rate constants determined from this study are in very good to excellent agreement with those obtained in previous studies of other cobalt catalysts, when the data are normalized to the same conditions of temperature and partial pressures of the reactants. Based on this comparison CO conversion and the partial pressure of product water apparently have little effect on specific rate per catalytic site. The data of this study are fitted fairly well by a simple power law expression of the form −r_CO=kP_H2^0.74P_CO^−0.24, where k=5.1×10⁻³ s⁻¹ at 200°C, P=10 atm, and H₂/CO=2/1; however, they are best fitted by a simple Langmuir–Hinshelwood (LH) rate form −r_CO=aP_H2^0.74P_CO/(1+bP_CO)² similar to that proposed by Yates and Satterfield.     

Reversible heat effects in high temperature batteries: Transported entropy and thomson coefficients in cells with β″-alumina

The transported entropy and the Thomson coefficient for charge conducting ions are needed to predict reversible heat effects in batteries. Transported entropies and Thomson coefficients have been calculated from Seebeck coefficients of the cell Fe(s, T₁)|Me| β″ alumina | Me | Fe(s, T₂) for Na and K (Me). The result is S*_Na⁺ = 56 ± 3 J K⁻¹ mol⁻¹ at 500 K, with a Thomson coefficient τ_Na⁺ = 30 ± 2 J K⁻¹ mol⁻¹ in the temperature interval 333–773 K. The transported entropy of Na⁺ did not change by freezing Na at 370. The results for K⁺ are identical to those of Na⁺ within the accuracy of the experiments. The Thomson coefficient derived from measurements at different values of T₁ was consistent with the observed variation in emf with ΔT for a given T₁. The reversible heat changes at the electrodes have been calculated for sodium sulphur and potassium sulphur batteries. During discharge both batteries produce a net reversible heat, the production always being largest at the alkali metal anode. At the cathode, the heat effect becomes relatively small when the composition of Na and S is within the one phase region. A change in composition from the one phase to the two phase region is expected to lead to changes in local temperature gradients. The systems were described by the electric work method, a method which has practical advantages compared to other electrochemical methods.     

Nanosized perovskite-type oxides La1−xSrxMO3−δ (M = Co, Mn; x = 0, 0.4) for the catalytic removal of ethylacetate

Nanometer perovskite-type oxides La_1−xSr_xMO_3−δ (M = Co, Mn; x = 0, 0.4) have been prepared using the citric acid complexing-hydrothermal-coupled method and characterized by means of techniques, such as X-ray diffraction (XRD), BET, high-resolution scanning electron microscopy (HRSEM), X-ray photoelectron spectroscopy (XPS), temperature-programmed desorption (TPD), and temperature-programmed reduction (TPR). The catalytic performance of these nanoperovskites in the combustion of ethylacetate (EA) has also been evaluated. The XRD results indicate that all the samples possessed single-phase rhombohedral crystal structures. The surface areas of these nanomaterials ranged from 20 to 33 m² g⁻¹, the achievement of such high surface areas are due to the uniform morphology with the typical particle size of 40–80 nm (as can be clearly seen in their HRSEM images) that were derived with the citric acid complexing-hydrothermally coupled strategy. The XPS results demonstrate the presence of Mn⁴⁺ and Mn³⁺ in La_1−xSr_xMnO_3−δ and Co³⁺ and Co²⁺ in La_1−xSr_xCoO_3−δ, Sr substitution induced the rises in Mn⁴⁺ and Co³⁺ concentrations; adsorbed oxygen species (O⁻, O₂⁻, or O₂²⁻) were detected on the catalyst surfaces. The O₂-TPD profiles indicate that Sr doping increased desorption of the adsorbed oxygen and lattice oxygen species at low temperatures. The H₂-TPR results reveal that the nanoperovskite catalysts could be reduced at much lower temperatures (<240 °C) after Sr doping. It is observed that under the conditions of EA concentration = 1000 ppm, EA/oxygen molar ratio = 1/400, and space velocity = 20,000 h⁻¹, the catalytic activity (as reflected by the temperature (T_100%) for EA complete conversion) increased in the order of LaCoO_2.91 (T_100% = 230 °C) ≈ LaMnO_3.12 (T_100% = 235 °C) < La_0.6Sr_0.4MnO_3.02 (T_100% = 190 °C) < La_0.6Sr_0.4CoO_2.78 (T_100% = 175 °C); furthermore, there were no formation of partially oxidized by-products over these catalysts. Based on the above results, we conclude that the excellent catalytic performance is associated with the high surface areas, good redox properties (derived from higher Mn⁴⁺/Mn³⁺ and Co³⁺/Co²⁺ ratios), and rich lattice defects of the nanostructured La_1−xSr_xMO_3−δ materials.     

Polymers in mixed solvents: application of the new representation of viscosity data as a function of molecular weight

The relation proposed between the intrinsic viscosity and the molecular weight of a polymer^1,2 (1/[η]versus 1/M^1/2), has been applied in this paper in cases when the polymer is dissolved in a binary solvent mixture. We have then shown that even in this case we can calculate in a very accurate way the molecular weight of the polymer from its intrinsic viscosity, especially in the molecular weight range where the Mark-Houwink-Sakurada equation is the least applicable (M_w < 150 000).     

The glass temperature of polymer blends

The entropy theory of glasses is used to derive the glass temperature, T_g, of a binary polymer blend in terms of the glass temperatures of the two substituents. The formula is T_g = B₁T_g1 + B₂T_g2, where B_i is the fraction of flexible bonds of substituent i. A bond is flexible if rotation about it changes the shape of the molecule. Bonds in side groups as well as in the backbone are to be counted. This formula assumes that the free volume, taken here to be the volume fraction of empty lattice sites, is the same for each of the three materials. It has no parameters. The above equation expressed in weight fractions, W_i, is (T_g − T_g1)W₁(γ₁/ω₁) + (T_g − T_g2)W₂(γ₂/ω₂) = 0, where ω_i is the weight of a monomer unit and gg_i is the number of flexible bonds per monomer unit. A more general treatment is given. One variation of the more general treatment which expresses the properties of the blend in purely additive terms gives T_g = B₁T_g1 + B₂T_g2 + KB₁B₂(T_g1 − T_g2)(V₀₁ − V₀₂), where V_0i are the free volume fractions of the homopolymers at their glass temperatures and K is a constant. The added term is usually small. The most general form of the equation requires the energy of interaction between the two unlike molecules, which can be estimated by volume measurements on the blend.     

Electrosorption and inhibition properties of p-norborn2-yl phenolate ions at the mercury/solution interface

The electrosorption properties of p-norborn-2-yl phenolate ions in alkaline solutions were investigated by ac polarographic and electrocapillary measurements.

Two adsorption regions were found. At low bulk surfactant concentrations the adsorption at the positively charged electrode (−0.2 E −0.6 V) is predominant while at higher surfactant concentrations the adsorption at the negatively charged electrode (−0.6 E −1.0 V) is more pronounced. At E = −0.40 V the adsorption parameters were determined (a ≈ 2; ΔG°_A = −32.5 ± 1 kJ mol⁻¹. Between −0.6 E −1.0 V one potential of maximum adsorption for all concentrations does not exist and therefore the adsorption parameters could not be calculated.

At E = −0.40 V progressive two-dimensional nucleation with a nucleation order of 3 was observed which corresponds well with the high attraction constant.

The electrode reaction S₂O²⁻₈ + 2e⁻ → 2 SO²⁻₄ is inhibited by norborn-2-yl phenolate ions in the potential range −0.2 E −0.6 V. In the second potential range of capacity decrease the electrode process is much less retarded. At E = −0.40 V, in a similar manner as described for neutral molecules, a linear dependence of the log k_s (k_s apparent rate constant) on ln c_A and π (π = surface film pressure), respectively, has been found.     

AFeO3 (A=La, Nd, Sm) and LaFe1−xMgxO3 perovskites as methane combustion and CO oxidation catalysts: structural, redox and catalytic properties

Catalytic methane combustion and CO oxidation were investigated over AFeO₃ (A=La, Nd, Sm) and LaFe_1−xMg_xO₃ (x=0.1, 0.2, 0.3, 0.4, 0.5) perovskites prepared by citrate method and calcined at 1073 K. The catalysts were characterized by X-ray diffraction (XRD). Redox properties and the content of Fe⁴⁺ were derived from temperature programmed reduction (TPR). Specific surface areas (SA) of perovskites were in 2.3–9.7 m² g⁻¹ range. XRD analysis showed that LaFeO₃, NdFeO₃, SmFeO₃ and LaFe_1−xMg_xO₃ (x·0.3) are single phase perovskite-type oxides. Traces of La₂O₃, in addition to the perovskite phase, were detected in the LaFe_1−xMg_xO₃ catalysts with x=0.4 and 0.5. TPR gave evidence of the presence in AFeO₃ of a very small fraction of Fe⁴⁺ which reduces to Fe³⁺. The fraction of Fe⁴⁺ in the LaFe_1−xMg_xO₃ samples increased with increasing magnesium content up to x=0.2, then it remained nearly constant. Catalytic activity tests showed that all samples gave methane and CO complete conversion with 100% selectivity to CO₂ below 973 and 773 K, respectively. For the AFeO₃ materials the order of activity towards methane combustion is La>Nd>Sm, whereas the activity, per unit SA, of the LaFe_1−xMg_xO₃ catalysts decreases with the amount of Mg at least for the catalysts showing a single perovskite phase (x=0.3). Concerning the CO oxidation, the order of activity for the AFeO₃ materials is Nd>La>Sm, while the activity (per unit SA) of the LaFe_1−xMg_xO₃ catalysts decreases at high magnesium content.     

Microwave-enhanced catalytic degradation of phenol over nickel oxide

A mix-valenced nickel oxide, NiO_x, was prepared from nickel nitrate aqueous solution through a precipitation with sodium hydroxide and an oxidation by sodium hypochlorite. Further, pure nickel oxide was obtained from the NiO_x by calcination at 300, 400 and 500 °C (labeled as C300, C400 and C500, respectively). They were characterized by thermogravimetry (TG), X-ray diffraction (XRD), nitrogen adsorption at −196 °C and temperature-programmed reduction (TPR). Their catalytic activities towards the degradation of phenol were further studied under continuous bubbling of air through the liquid phase. Also, the effects of pH, temperature and kinds of nickel oxide on the efficiency of the microwave-enhance catalytic degradation (MECD) of phenol have been investigated. The results indicated that the relative activity affected significantly with the oxidation state of nickel, surface area and surface acidity of nickel oxide, i.e., NiO_x (>+2 and S_BET = 201 m² g⁻¹)  C300 (+2 and S_BET = 104 m² g⁻¹) > C400 (+2 and S_BET = 52 m² g⁻¹) > C500 (+2 and S_BET = 27 m² g⁻¹). The introduction of microwave irradiation could greatly shorten the time of phenol degradation.     

Effect of structural and electrochemical properties of different Cr-doped contents of Li[Ni1/3Mn1/3Co1/3]O2

Layered Li[Ni_(1−x)/3Mn_(1−x)/3Co_(1−x)/3Cr_x]O₂ materials with x = 0, 0.01, 0.02, 0.03, 0.05 are prepared by a solid-state pyrolysis method. The oxide compounds were calcined with various Cr-doped contents, which result in greater difference in morphological (shape, particle size and specific surface area) and the electrochemical (first charge profile, reversible capacity and rate capability) differences. The Li[Ni_(1−x)/3Mn_(1−x)/3Co_(1−x)/3Cr_x]O₂ powders were characterized by means of X-ray diffraction (XRD), charge/discharge cycling, cyclic voltammetry, and SEM. XRD experiment revealed that the Li[Ni_(1−x)/3Mn_(1−x)/3Co_(1−x)/3Cr_x]O₂ (x = 0, 0.01, 0.02, 0.03, 0.05) were crystallized to well layered -NaFeO₂ structure. The first specific discharge capacity and coulombic efficiency of the electrode of Cr-doped materials were higher than that of pristine material. When x = 0.02, the sample showed the highest first discharge capacity of 241.9 mAh g⁻¹ at a current density of 30 mA g⁻¹ in the voltage range 2.3–4.6 V, and the Cr-doped samples exhibited higher discharge capacity and better cycleability under medium and high current densities at room temperature.     

The electrochemistry of tellurium in methylene chloride

It was found that TeCl₄ in methylene chloride (containing tetrabutylammonium perchlorate as a supporting electrolyte) is reduced to TeCl₂, Te⁰ and Te⁻² in potential applied. Two reduction waves are observed during the reduction of TeCl₄ at a platinum rde (Ep₁ = 0.08 ± 0.02 V, Ep₂ = −1.10 ± 0.02 V) due to the reduction of TeCl₄ to Te and Te⁻² respectively. A cathodic deposition of tellurium from TeCl₄ is followed by anodic stripping wave (Ep₁ = 0.42 ± 0.02 V), corresponding to the oxidation of Te to TeCl₂. It has been shown that reduction of TeCl₄, or TeCl⁻²₆ to Te causes coating of the electrode with metallic tellurium, on whose surface chloride ions are strongly bonded. It was found that when the electrolysis solution contains excess of chloride ion with respect to Te^IV the peak potentials of the cathodic waves shift to more cathodic values (Ep₁ = 0.30 ± 0.02 V, Ep₂ = −1.25 ± 0.02 V). After cathodic deposition of at least a monolayer of tellurium from such a solution two anodic waves appear (Ep₁ = 0.12 ± 0.03 V, Ep₂ = 0.24 ± 0.03 V) which are both due to the oxidation of Te to Te^II.     

Mass spectra of negative ions in air-like gas mixtures at atmospheric pressure

We have obtained mass spectra of negative ions produced by rays in artificial air at atmospheric pressure (N₂: 80%, O₂: 20%, H₂O: 20–1500 ppm, CO₂: 0.2–300 ppm, NO, NO₂ 0.02 ppm). We observed two main categories: hydrates built on simple ions (O₂⁻, O₃⁻, OH⁻, CO₃⁻, CO₄⁻, HCO₃⁻, NO₂⁻, NO₃⁻), hydrates built on complex ions (NO_x⁻, HNO_γ, HCO₃⁻HNO_x, x = 2,3; Y = 2, 3). For high values of hygrometry, CO₂ content and ageing time (5 msec) we observe the disappearance of O₂⁻, O₃⁻, OH⁻ hydrates whereas the major part of the spectrum consists of complex ions.     

Hydrodynamic radius and dynamic scattering from randomly crosslinked chains

The path-weighting generating function (pwgf) method is applied to calculate the hydrodynamic radii of the randomly crosslinked system as well as its monodisperse faction. Exactly the same relation is found for the z-average reciprocal effective hydrodynamic radius of the linear and the randomly crosslinked system as a function of the weight-average degree of polymerization DP_w′, where bR_h⁻¹_z = C(DP_w)^−1/2 with a constant C depending on the primary chain distribution. The weight-average reciprocal effective hydrodynamic radius, however, depends on the number average degree of polymerization and only moderately changes with crosslinking. The effective hydrodynamic radius of the monodisperse fraction is proportional to the quadratic root of the number of crosslinks. The technique is also applied to the dynamic scattering where formulae for the preaveraged and the non-preaveraged first cumulants are given.     

Adsorption of methane/ethane mixtures on dry coal at elevated pressure

The binary adsorption characteristics of methane and ethane on dry coal to 40 atm pressure have been calculated from pure-component isotherms. In some coal seams, pressures exceeding 40 atm have been recorded and the methane sampled from the virgin coal often shows a few percent of ethane. The binary adsorption characteristics were calculated by employing the ideal adsorbed solution theory of Myers and Prausnitz, and experimentally-determined (Type I) pure gas isotherms at 0, 30 and 50 °C. The coal used in this investigation was high-volatile ‘A’ bituminous (hvab) from the Pennsylvania Pittsburgh seam. Gas nonideality was accounted for by replacing pressure with fugacity. Adsorption of methane on dry coal is purely physical; the isosteric heat of adsorption does not exceed 2.4 kcal/mol^* at 30 °C on the above coal. Isobars on the resulting binary equilibrium diagram exhibited an unexpected phenomenon of intersecting each other which might be attributable to the above nonideality considerations. The region of a few percent of ethane, which is of practical importance from the viewpoint of coal seams, was expanded and reduced to an equation: V(CH₄) = −21.52 + 7.18(VF) + 16.88(VF)² −0.395(P) − 0.00661(P)² + 0.824(T) − 0.00030(T)² + 0.928(VF)(P) − 0.858(VF)(T). V(Total) = 25.9 − 23.6(VF) + 0.655(P) − 0.00875(P)² − 0.795(T) + 0.743(VF)(T) where V(CH₄) and V(Total) = cm³(STP)CH₄ and total gas respectively adsorbed per g dry coal; VF = vol. fraction of methane as analysed at 1 atm (0.94 VF 1.0); P = seam pressure, atm (0 P 40); T=seam temperature, °C(−10 T 50).     

Dry grinding kinetics of binary mixtures of ceramic raw materials by Bond milling

The kinetics of batch dry grinding of binary mixtures of ceramic raw materials, namely quartz–kaolin, quartz–potassium feldspar and kaolin–potassium feldspar, from the feed sizes of −3.350 + 2.360, −2.000 + 1.400, −0.850 + 0.600, −0.500 + 0.355 and −0.300 + 0.212 mm have been determined using a Bond mill with a mixture of ball sizes of 38.10, 31.75, 25.40, 19.05 and 12.70 mm diameter and total mass of 22.648 kg. The Bond mill used was a size of 30.5 cm diameter, 30.5 cm length, with a total volume of 22,272 cm³. The fractional ball filling was 22% of mill volume and the mill speed was 70 rpm. The breakage parameters were obtained for those mineral mixtures to predict the product size distributions. As the feed sized given above, which were ground in the mill, increase, the specific rate of breakage (S_i) values also increase, which means faster breakage with higher S_i value occurs in the order of quartz–kaolin, quartz–potassium feldspar and kaolin–potassium feldspar mixtures when comparing the characteristic values (slope of S_i versus size relationship with higher value). The cumulative breakage distribution function (B_i,j) values obtained for these mineral mixtures were slightly different in terms of the fineness factor, γ. This means that quartz–potassium feldspar mixture produced less fines with higher γ value, while kaolin–potassium feldspar gave more fines with lower γ value. The simulations of the product size distribution for these mixing were very close to the experimental data. Finally, slowing down effect, treated with false time concept, started earlier than the expected for these binary mixtures. There were some correlations found between the simulated time (θ) and experimental time (t).