Langmuir Formula Research Articles

Production of sorption functional media (SFM) from clinoptilolite tailings and its performance investigation in a biological aerated filter (BAF) reactor

The few reuse and large stockpile of zeolite tailings led to a series of social and environmental problems. This study investigated the possibility of using the zeolite tailings as one of principal raw materials to prepare sorption functional media (SFM) by a high temperature sintering process. The SFM was used to serve as a biomedium in a biological aerated filter (BAF) reactor for domestic wastewater treatment, and its purification performance was examined. The physical, chemical and sorption properties of SFM were also determined. The microstructure of the SFM was analyzed by scanning electron microscopy (SEM). Results revealed that: (1) zeolite tailings could be used to produce the SFM under the optimal sintering parameters; (2) the sorption and desorption isotherm of ammonia nitrogen on SFM could be well described by the Langmuir formula; (3) in terms of removing organic matter, ammonia nitrogen, turbidity and colourity, the performance of the biofilter with SFM was superior to that with haydite; and (4) SFM BAF has a stronger adaptability to low temperature (6–11°C) for NH3-N removal compared to haydite BAF. Therefore, the SFM produced from the zeolite tailings was suitable to serve as the biomedium in the domestic wastewater treatment.

Absorption of Methyl Orange by Modified Fly Zeolites

In the present study, three kinds of zeolite (NaP1, NaA, and NaX) were synthesized by a hydrothermal method. These zeolites were modified by cetyl trimethyl-ammonium bromide (CTAB), and used to adsorb methyl orange (MO). NaP1 had the highest adsorption capacity, with a 99.7% MO removal percentage. An orthogonal experiment was conducted to determine the influence of adsorbent dosage, solution pH, initial MO concentration, contact time, and solution temperature on NaP1. The results showed that the initial MO concentration had the most significant effect. The adsorption isotherms of the zeolites are in a good agreement with the Langmuir formula, and the adsorption mechanism is also discussed.

Preparation of crosslinked polystyrene-supported ethylenediamine via a S-containing spacer and adsorption properties towards metal ions

Two novel chelating resins were prepared by anchoring ethylenediamine to crosslinked polystyrene via a spacer containing sulfide. Their structures were characterized by Fourier transform-infrared spectra (FTIR) and scanning electron microscopy (SEM). Porous structure parameters of the resins were measured by ASAP 2020 using BET and BJH methods. Their adsorption capacities for several heavy metal ions especially Hg 2+ were investigated. The results showed that for the two resins, the more N contents did not mean the better adsorption capacity and the saturated adsorption capacity of poly(2-ethylenediamidomercaptomethylstyrene) (PSM-EDA) for Hg 2+ could reach to 3.0 mmol/g at room temperature. Isothermal adsorptions of the resins for Hg 2+ could be described by Langmuir formula. The adsorption mechanism of the resins for Hg 2+, Cu 2+ and Ag + was confirmed by X-ray photoelectron spectroscopy (XPS) and FTIR.

Many-particle diffusion in continuum: Influence of a periodic surface potential

We study the diffusion of Brownian particles with a short-range repulsion on a surface with a periodic potential through molecular dynamics simulations and theoretical arguments. We concentrate on the behavior of the tracer and collective diffusion coefficients DT(θ) and DC(θ), respectively, as a function of the surface coverage θ. In the high friction regime we find that both coefficients are well approximated by the Langmuir lattice-gas results for up to θ≈0.7 in the limit of a strongly binding surface potential. In particular, the static compressibility factor within DC(θ) is very accurately given by the Langmuir formula for 0⩽θ⩽1. For higher densities, both DT(θ) and DC(θ)show an intermediate maximum which increases with the strength of the potential amplitude. In the low friction regime we find that long jumps enhance blocking and DT(θ) decreases more rapidly for submonolayer coverages. However, for higher densities DT(θ)/DT(0) is almost independent of friction as long jumps are effectively suppressed by frequent interparticle collisions. We also study the role of memory effects for many-particle diffusion.

Characterisation of the equilibrium behaviour of lipase PS (from Pseudomonas) and lipolase 100L (from Humicola) onto Accurel EP100

The present work characterised the equilibrium behaviour of lipases from Pseudomonas and Humicola immobilised on polypropylene-based hydrophobic support Accurel EP100. The support capacity for both lipases was evaluated, and activities of immobilised lipases were assayed. Also, the stability of immobilised Chromatographic was tested. Experimentally, the adsorption isotherm for each lipase was produced and the activity of immobilised lipase was assayed by esterification of oleic acid and octanol. Also, immobilised lipase activities, using different support particle sizes and masses, were assayed. The immobilised lipase stability was tested by a series of successive esterifications done on the same immobilised lipase sample. Analytically, the lipase adsorption isotherm was modelled by the Langmuir and Freundlich formulas. It was found that lipase PS exhibited the Freundlich behaviour, which suggests multilayer adsorption, while lipolase 100L reflected the Langmuir formula, i.e. formed a monolayer. Also, Accurel EP100 capacities for lipase PS and lipolase 100L were 4500 mg (1.35 × 10 5 LU) and 1200 mg (1.20 × 10 5 LU), respectively for each gram of support. It was also found that the activity of lipase PS initially increased with loading and then levelled off, while it continued to increase with loading of lipolase 100L. Moreover, lipase activity decreased with mean particle diameter increase. Stability studies showed that lipase PS guarded its activity to more than 60% for more than 8 runs. Lipolase 100L showed the same behaviour.

C60 photoluminescence spectra related to gas adsorption

The influence of surrounding gas pressure upon PL spectra of C60 is observed. The relationship between intensity of PL spectra and pressure agrees well with the Langmuir formula of a monomolecular adsorption layer. This phenomenon is attributed to the fact that the disturbance of molecules adsorbed on C60 lowers the symmetry of C60 and reduces the inhibition of the electronic transition, hence influencing PL emission.

The distribution of tin in a carbon fibre-reinforced copper-matrix composite

The distribution of tin in a carbon fibre-reinforced Cu-5%Sn composite material has been analysed quantitatively. It was found that the distribution of tin along the radial direction of the fibre section is heterogeneous; the nearer the fibre surface, the higher the concentration of tin appears. The saturation concentration of tin on the carbon fibre/Cu-Sn interface can be determined by the Langmuir formula for isothermal adsorption. The effect of the heterogeneous distribution of tin on the properties of the composite is discussed.

Prediction of multicomponent adsorption equilibrium data using empirical correlations

In this study, extended empirical Langmuir, Freundlich and Redlich-Peterson formulate have been applied for the calculation of multicomponent adsorption equilibrium data for all combinations of three basic dye systems: Basic Blue 69 (B), Basic Red 22 (R) and Basic Yellow 21 (Y) on Activated Carbon (F400). Extended Langmuir application yielded average variances (σ 2) of 3.3%, 589%, 51% and 47% for RY, RB, YB and RYB system components respectively. The Redlich-Peterson relationship gave σ 2 of 8%, 62%, 50% and 44% respectively. Introducing an interaction term (η) lowered σ 2 to 0.5%, 23%, 16% and 11% for RY, RB, YB and RYB system components respectively for the Langmuir formula and to 0.4%, 21.3%, 15% and 11% respectively for the Redlich-Peterson equation. The Freundlich empirical extended formula for bisolute systems produced variances of 0.69%, 9.1% and 8.8% for RY, RB and YB system components respectively. The latter formula is the most accurate for bisolute systems as it is obtained by single and multisolute correlation of all constants in the formula.

Laser-pulse vaporization of uranium dioxide and other refractory materials

The nature of the vapor produced by pulse surface heating of UO2 and several other materials was investigated using normal-mode laser pulses with peak power densities between 104 and 106 W/cm2. Maximum surface temperatures measured by optical pyrometry ranged from 1900 to 4200 K. At temperatures below ∼2400 K for UO2, the vapor pulse followed the Hertz–Langmiur vacuum vaporization theory. More energetic transients produced gasdynamic blowoffs accompanied by significant supersaturation in the expanding plume. Neutron activation analysis of the collected vapor indicated that the total quantity of liquid UO2 evaporated in the pulse followed the Hertz–Langmuir formula. However, mass spectrometric analysis of the emitted vapor showed large deviations in the quantity and waveform shape of the monomer species. These and other features of the blowoff were satisfactorily explained in terms of nucleation and growth of polymeric species. Although UO2 clusters were undetectable by the mass spectrometer, polymers of MgO and ZrO2 were observed.

Elektronenstrom zylindrischer Langmuirsonden bei Nichtmaxwellverteilungen

AbstractOne of the main assumptions of the conventional Langmuir probe theory is the demand for a Maxwellian distribution function.In this paper is tried to calculate probe currents for non‐Maxwellian electron energy distributions.The classical Langmuir formula for the orbital‐motion‐limited current of cylindrical probes is simplified. The new equation permits a very easy detailed examination of the effects of non‐Maxwellian electron energy distributions on the current‐voltage characteristics in the accelarating region for large probe voltages.It is shown that the electron current is independent of the form of the electron energy distribution, if the mean electronenergy Ē is constant.Variations of the mean energy change the probe current slightly.As examples currents are computed for two non‐Maxwellian distribution functions.

Effect of Adsorption by Cellulose Acetate Membrane on Reverse Osmosis of Some Monoamino Monocarboxylic and Monoamino Dicarboxylic Acids in Aqueous Solutions

Abstract Taft’s polar and steric parameters, Σσ*, ΣEs, and nonpolar parameter, ΣS* governing the reverse osmosis of nonionized polar aliphatic and alicyclic organic compounds using a cellulose acetate membrane were also applicable to aliphatic monoamino monocarboxylic acids having zwitter ion structure. These three parameters were further extended so as to include the cases of sulfur-containing amino acids, hydroxy-substituted, and aromatic type amino acids. Reverse osmosis of monoamino monocarboxylic acids in binary aqueous solution systems containing l-alanine was carried out. As a result, added amino acids were adsorbed by the membrane when added in low concentration (<0.001 mol dm−3), and the permeation of l-alanine was governed by the difference of Taft’s polar parameter between l-alanine and the added amino acid. Reverse osmosis of monoamino dicarboxylic acids indicated that hydrogen ions were adsorbed by the membrane, and the adsorption isotherms of hydrogen ions were approximately represented by the Langmuir formula for each amino acid. The electrostatic repulsion between R− ionic species in monoamino dicarboxylic acid and the negatively dissociated groups of the membrane was weakened by neutralization of the membrane by hydrogen ion adsorption, resulting in decreased amino acid rejection. It was noted that the ultraviolet spectrum and the titration curve of permeate of amino acids were different from those of the feed solution; relationship between this phenomenon and adsorption of hydrogen ions was investigated.

Electron-Impact Ionization Cross Section in Cesium

The total ionization due to the passage of an electron beam in cesium vapor has been measured with a Tate and Smith-type apparatus. The retarding potential difference method was used in the electron gun to obtain energy resolution better than 0.1 eV. The density of Cs atoms was determined from the Taylor and Langmuir formula and also measured with a surface-ionization detector. The two methods gave the same density to within ±3% when the apparatus was in thermodynamic equilibrium with the Cs reservoir. The cross section for production of Cs+ has been determined from threshold to 100 eV. For energies above 28 eV, the results agree closely with those of McFarland and Kinney. At threshold the slope of the cross-section-vs-energy curve was measured to be 2.7 Å2/eV.

On the measurement of speed of a vacuum pump

After pointing out the drawbacks of the conventional procedures of pumping speed measurement, an improved procedure is described in which the admitted gas is uniformly distributed over a cross section of a tube of the same size as the pump casing. The pressure is measured above this section, where the gas is in a static state. The actual as well as the intrinsic speed of the pump can accurately be determined. As the speed factor for indicating the pumping efficiency the ratio of these speeds is suggested. The intrinsic speed is a function of the intake pressure. The highest value of this speed was found to be 65 per cent of the conductance of a well designed pump. These results do not agree with the conclusions of the diffusion theory. Correction of the Langmuir formula suggested previously by the writer is confirmed.

有機チオール化合物による砒素解毒に関する実験的研究

1. In observing the polarographic catalytic wave of protein by making arsenic acid at various concentrations act on fresh human milk, fresh cow's milk, regulated powdered milk, and milk on the market, no decrease in the degree of the SH activity of milk protein due to the addition of arsenic can be detected. In this instance when the concentration of arsenic acid is gradually increased to a certain point, the reductive wave of arsenic appears on the heel of the proteinic wave. The arsenic acid concentration required to have the appearance of such an arsenic wave is 6 γ/cc in the case of fresh human milk; 5 γ/cc in fresh cow's milk; 4 γ/cc in regulated powdered milk; and 3 γ/cc in milk sold on the market.2. In drawing the polarographic curve of the reductive wave of arsenic by addition of milk at various concentrations to a hydrochloric arsenic acid solution, the arsenic wave falls in proportion to the addition of milk protein. The percentage of the fall in the amplitude of arsenic wave is greatest in fresh cow's milk followed by milk on the market regulated powdered milk and fresh human milk in the order mentioned.3. The rate of decrease in the amplitude of the arsenic wave in fresh human milk and the gelatin-protein of an equal concentration is greater in the latter. Therefore, it is obvious that the reaction between milk protein and arsenic is in no way associated with the SH-group.4. By applying the Langmuir's formula to these results, it has been confirmed that the reactions are induced by the action of surface activity of the milk proteins.

On the Space Charge affected by the Magnetic Field

The characteristic phenomena of the dense space charge of electrons bound by the strong magnetic field are described. The electrons in the outermost sheath of electron cloud are considered to be scattered by mutual interaction and to have excess energies. Calculation based on this view is in good agreement with experiment. It is especially noteworthy that when the anode voltage is raised to the proper value, this sheath is captured by the anode and certain unique oscillations are observed to occur. The frequencies of these oscillations very nearly coincide with those obtained from Langmuir's formula of plasma oscillation.

Test of langmuir's three halves power law, deviations due to β2-factor and secondary emission

According to theory a small correction (the so called β2-factor) should be applied to Langmuir's law for the electron current in a cylindrical high vacuum diode. To test this, a method was developed for eliminating the potential drop along the hot cathode filament. The accuracy thus obtained disclosed an unexpectedly large deviation of the coefficient in Langmuir's formula from its theoretical value. This discrepancy is most probably due to the influence of secondary emission of the anode. It is possible to correct for this influence in a simple way by introducing an “effective reflection coefficient” of the anode. For anode voltages in the range of 1–30 V, values of this coefficient of 14% for tantalum and of 5.5% for aquadag give a good description of the experimental results. In a similar way the well known (ζ, η)-tables of Langmuir should be corrected if they are to represent the real situation.

The interaction of atoms and molecules with solid surfaces III—The condensation and evaporation of atoms and molecules

In the first two papers of this series (to be referred to as papers I and II) calculations were made of the probability that an atom adsorbed on a solid surface would be excited to states of higher vibrational energy and to states in the continuum, equivalent to evaporation. In this paper we carry the theory of evaporation a stage further and also develop a theory of condensation and show the relation of the theory to the method of statistical mechanics. Langmuir showed by a simple dynamical argument that under certain assumptions a solid surface in contact with a gas would be partially covered with adsorbed atoms and that the fraction of the surface covered could be expressed in terms of the pressure of the gas by the simple relation θ = ap /(1 + ap ). The parameter a is proportional to the product of a quantity τ, which is the average time spent by an atom in the adsorbed phase, and a quantity c , which is the probability that an atom striking the surface shall be adsorbed. Recently bowlers has shown that Langmuir's formula is essentially a thermodynamic one and can be obtained without involving a precise mechanism either of adsorption or evaporation. By adjusting the parameter a , the formula can be made to fit many of the experimental results and so the value of the product c τ can be inferred. This is probably as far as the statistical method can go. It cannot determine either c or τ uniquely, and if estimates are to be made of then information about c must be obtained from other sources. It is often assumed that c is of the order of unity, but this cannot be true in all cases, or even in the most interesting ones, for, as Roberts has shown, the accommodation coefficient (which is a measure of the probability that an atom will gain or lose energy on striking a solid surface) is sometimes very small. It is as low as 0·05 for helium striking tungsten and only 0·07 for neon striking tungsten at room temperature.

Structures of the metallic carbonyl and nitrosyl compounds

Our knowledge of the compounds containing carbonyl and nitrosyl (NO) group attached to metallic atoms has been greatly extended in recent years, gely through the work of Hieber and Manchot and their collaborators; but structures which have been suggested, especially for the nitrosyl derivaties, are not in every way satisfactory. In this paper an attempt is made to ablish the structures of these compounds on a firmer basis. The nature of the linkage formed between carbon monoxide and a metallic is now well established. In its complexes the CO groups occupies one Co-ordination place as donor-it provides two electrons to form a single link- is shown, for example, by the ferrous pentacyano-compounds of the general formula M 3 [ Fe(CN) 5 X] where X may be CO, H 2 O, NH 3 , pyridine, etc. This formation of a single link is in agreement with the Langmuir formula for carbon onoxide, I. :C ::: O : C - ≡ O + II. M : C ::: O : M - - C ≡ O +

Low Voltage Discharges in Helium

Discharge through helium,.01 to 2.9 mm pressure.\char22{}A hot filament cathode and disk anode were mounted in a glass frame 10 to 12 cm apart, the frame being so arranged that it could be moved magnetically inside a glass tube of diameter about 4 cm, with reference to a fixed exploring electrode. Measurements of potential distribution and of mean energy and concentration of electrons were made at three pressures,.095, 0.5 and 2.9 mm. Although precautions were taken to secure pure He, striations were obtained because of a trace of neon. The results are similar to those obtained by Bramley for ${\mathrm{hydrogen}.}^{1}$ The mean electron energy decreases to a minimum beyond the negative glow, then rises to a maximum beyond the face of the first striation. The electron concentration falls from a maximum in the negative glow to a minimum near the cathode side of the first striation; within the limits of accuracy of the work, it increases in a given region of the discharge with an increase of pressure and is proportional to the current density of the discharge at a given pressure. Calculations of the positive ion concentrations by Langmuir's formula and also by one developed by McCurdy, give results which seem to be equal to the electron concentrations, but as both methods are merely approximations, this result is not very reliable.