Equations of Langmuir turbulence and Zakharov equations:smoothness and approximation

A family of systems parameterized by H 〉 0, which describes the Langmuir turbulence, is considered. The asymptotic behavior of the solutions （E^H, nH） when H goes to zero is studied. The results of convergence of （EH, nH） to the couple （E, n） which is the solution to the Zakharov equations are stated.

Innovative Methods of Synthesis and Characterization for Molecularly Imprinted Polymers

The characterization of these molecularly imprinted polymers is essential to understanding their binding dynamics and structural properties. Through the analysis of the current research, it is found that there are overlaps in the methods used by scholars. The Langmuir equation is frequently applied to model the adsorption isotherms of MIPs, providing critical insight into the capacity and affinity of the binding sites. Infrared Spectroscopy (IR) plays a crucial role in identifying the functional groups involved in the imprinting process and confirming the successful formation of specific binding sites. UV-visible spectrophotometry is employed to monitor the absorption characteristics of the polymers, offering data on the interactions between the template molecules and the polymer matrix. Transmission Electron Microscopy (TEM) provides detailed visualization of the internal structure of MIPs at the nanoscale, revealing the morphology and size of the imprinted cavities. Thermogravimetric Analysis (TGA) assesses the thermal stability and composition of the polymers, identifying decomposition patterns that are indicative of the material’s robustness under different conditions. Finally, the Laser Particle Size Analyzer is used to measure the size distribution of the polymer particles, which is critical for determining the uniformity and efficiency of the imprinting process. The six characterization methods discussed in this paper provide a comprehensive understanding of MIP, and it is hoped that in the future, more optimized design solutions will emerge and their applications in various fields will be enhanced.

Equilibrium of Organic Matter in Heavy Fraction for Three Long-term Experimental Field Soils in China

Considerable evidence that the soil organic matter （OM） level in agricultural soils will gradually over time reach an equilibrium state under certain bioclimatic conditions and for certain cropping systems has been accumulating. Although models or long-term experiments have been used, this research used physical fractionation procedure to attain an soil OM equilibrium value. To obtain soil OM equilibrium values in the heavy fraction, typical soils from three long-term field experiments at Fengqiu and Yingtan State Key Agro-Ecological Experimental Stations in China were studied using a simple density fractionation procedure and employing the Langmuir equation. Results for the fluvo-aquic soil with organic fertilizer treatments indicated that the soil OM equilibrium value in the heavy fraction was twofold more than that in the inorganic treatments; however, for the paddy soil developed on red soil the OM equilibrium value in the heavy fraction for both treatments was almost identical. It suggested that for fiuvo-aquic soils the increased potential of OM for the heavy fraction in the long run was larger for the organic than the inorganic fertilizer applications, whereas for paddy soils developed on red soils under the same conditions the present OM content in the heavy fraction was at or close to this equilibrium level for all treatments, and increased potential was very limited.

Effect of Anions on Adsorbability and Extractability of Lead Added in Soil

The effect of accompanying anions on the adsorbability and extractability of Pb added in soils was studied by using bach equilibria and incubation-extraction mothods.Pb concentration ranged between 0.48-2.41 mM in the adsorption experiment,and Pb added to soil from 2.14 to 19.31mM Pb/kg with an incubation time of 2-16 weeks in the incubation-extraction test in which 1M NH4OAc(pH 7) was taken as an extraction agent,and the Pb compounds used are PbCl2,Pb(NO3)2 and Pb(OAc)2.The values of pH50 for Pb retention and the parameters,b and k values,of Langmuir equation were used to distinguish the difference of adsorbability and extractability of Pb affected by anions,respectively.Judging from the results of either pH50 value or b value,the influences of Cl^- and NO3^- on the adsorbability and extractability of Pb in soils were similar but quite different from those of OAc^-.The relative loading capacities of soils to Pb calculated according to the extraction rate showed that the values of Pb(OAc)2 were higher than those of PbCl2 and Pb(NO3)2.

Exchange Reaction Between Selenite and Hydroxyl Ion of Variable Charge Soil Surfaces: Ⅱ. Kinetics of Hydroxyl Release

A self-made constant pH automated titration instrument was used to study thekinetics of hydroxyl release during selenite reacting with variable charge soils. The rate ofhydroxyl release was very rapid at the first several minutes, then gradually slowed down, and atlast did not change any more. The experimental data was well fitted by the Langmuir kineticequation, arid with increasing selenite concentration or decreasing solution pH, the reaction lastedlonger, the maximum of hydroxyl release (x_m) increased, and the binding constant (k) decreased.The time of hydroxyl release with Xuwen latosol was much longer than that with Jinxian red soil.

Inhibition effect of a synthesized N,N′-bis(2-hydroxybenzaldehyde)-1,3-propandiimine on corrosion of mild steel in HCl

The corrosion inhibition of mild steel in 1 mol/L HC1 by N, N＇-bis （2-hydroxybenzaldehyde）- 1, 3-propandiimine （2-HBP） has been investigated by using potentiodynamic polarization, electrochemical impedance spectroscopy （EIS） and chronoamperometry measurements. The experimental results suggest that this compound is an excellent corrosion inhibitor for mild steel and the inhibition efficiency increases with the increase in inhibitor concentration. Polarization curves reveal that this organic compound is a mixed type inhibitor. The effect of temperature on the corrosion behavior of mild steel with the addition of the Schiff base was studied in the temperature range from 25 ℃ to 65℃. The experimentally obtained adsorption isotherms follow the Langmuir equation. Activation and thermodynamic adsorption parameters such as Ea, △H, △S,Kads and AG,ds were calculated by the corrosion currents at different temperatures and using the adsorption isotherm. The morphology of mild steel surface in the absence and presence of 2-HBP was examined by atomic force microscope （AFM） images.

Chemical Fractionation and Sorption of Phosphorus in Greek Inceptisols

Phosphorus fractionation and sorption, both separately and jointly, were studied in two cultivated Inceptisols in Northern Greece. Hedley＇s extraction was used to separate soil phosphorus （P） into inorganic Pi （geochemical） and organic Po （biological） fractions. Direct extractable P by Olsen （Olsen-P）, by Mehlich llI （M3-P） and by ammonium oxalate （Pox） was also determined. Phosphorus sorption was carried out with 1：10 soil/solution ratio and sorption parameters were derived from the Langmuir model to the experimental data. Most of the total P occurred in inorganic P forms （74% of Pt）, while organic P comprised only 26% of the Pt. Among the various inorganic P forms relatively large amount of residual P （111 mg kg^-1） was observed, while occluded P in calcium phosphate minerals （d.HCI-Pi） and in Fe, Al-oxides （c.HCI-Pi） existed in equal amounts （83.1 and 83.7 mg kg^-1 respectively）. The phosphorus sorption parameters showed positive relationships with clay content, cation exchange capacity and the sum of exchangeable calcium plus magnesium. Overall, this study indicated that Ca and Mg compounds strongly influence the P chemistry in moderately weathered soils, with relatively high concentration of primary P minerals.

Analogy between adsorption and sorption： An elementary mechanistic approach. I. Monolayer adsorption and sorption without solvent cluster formation

The elementary mechanistic model of adsorption and sorption is based on a simple hypothesis： the adsorption sites are uniformly distnbuted on the surface of the pore walls in the adsorbent, the sorption sites are uniformly distributed in the volume of the polymer. In this first paper we will analyze the simple case where one solute molecule is only allowed to occupy a single adsorption or sorption site. A common elementary occupation law of the free sites is assumed： the differential increase of the number of the adsorbed/sorbed molecules is proportional to the differential increase of the activity of the solute and the concentration of the free （non-occupied） sites in the solid. The proportionality coefficient is called affinity coefficient depending on the solid/solute couple and on the temperature and independent of the concentration of the solute. In adsorption the concentration of the free sites is a surface concentration on the pore walls and in sorption it is expressed by the molarity. The simple monolayer adsorption law of Jovanovic is obtained： n = no（1 - e KP） where n is the number of moles adsorbed when the pressure is P. no is the total number of adsorption sites and K the affinity coefficient for adsorption. The sorption law writes： a = 1/k [Ф/1-Ф] ＋ 1-r/k In [1 ＋ 1/r Ф/1-Ф] where Ф, r and k hold respectively for the volume fraction of the solvent in the polymer, for the ratio of the molar volumes of the solvent to the elementary polymer chain containing one single adsorption site and for the sorption affinity coefficient. The confrontation of these equations to experimental isotherms is satisfactory in comparison with the classical Langmuir and Flory-Huggins equations： the best results are obtained for adsorption of vapors on a 5A zeolite and for all analyzed sorption results.