Theoretical calculations of the ionic strength dependence of the ionic product of water based on a mean spherical approximation

A modified version of the restricted primitive model for electrolyte solutions based on the mean spherical approximation (MSA) is applied to estimate the ionic strength dependence of the ionic product of water in aqueous solutions containing different salts, which are commonly used as background electrolytes (NaCl, KCl, KNO₃, and NaC10₄). The modification involves the use of permittivity of the solvent as concentration-dependent parameter and a single average effective diameter. This is a way of including effects originated from the solvent which do not exist in the primitive model. In the case of potassium nitrate and sodium perchlorate, a complete methodology to calculate the effective diameter and density dependence of the dielectric constant has been proposed and developed. Fits between calculated and experimental pK_w values are possible over wide concentration ranges using a single adjustable parameter, namely, the average hard core diameter of water.     

介孔La2O3的制备及性能研究

采用SDS-PEG复合模板剂,用均相沉淀法制备了不同孔径的介孔La2O3,用XRD,BJH,TG-DSC等方法对材料的结构和性能进行了表征,用IR-2型红外发射率测量仪测定了材料在8-14μm波段的红外发射率。结果表明：通过控制复合模板剂中PEG的量,可以有效调节介孔La2O3的孔径大小,PEG的添加可以明显增大介孔La2O3的孔径,且随PEG添加量的增多而逐渐增大。PEG的添加明显提高了介孔La2O3的热稳定性和结构稳定性。PEG与孔壁间存在较强的相互协同作用,介孔La2O3在8-14μm波段具有较低的红外发射率,且其红外发射率随材料的焙烧温度、最可几孔径的减小而逐渐降低。     

制备不同孔径的氧化铝模板

将适量的有机溶剂加入电解液中，在15 ℃左右制备得到孔径大于200 nm的氧化铝模板.该法使电解时间缩短，加快了制备模板的过程， 是氧化铝模板的有效制备方法.将该方法与传统方法相结合，可以制备孔径在20～250 nm间的氧化铝模板. 实验表明：有机溶剂的加入可有效避免电解时热量的迅速产生, 通过改变实验条件可调控氧化铝模板的孔径.     

氧化硅对金红石相纳米TiO2微结构的影响

通过硅酸钠水解生成的无定形氧化硅对金红石相纳米TiO₂进行修饰,利用红外光谱、紫外-可见漫反射光谱、X射线衍射、透射电镜和比表面仪对纳米TiO₂进行了表征。结果表明,氧化硅沉积在纳米TiO₂的表面和颗粒之间形成一个空间网络体系,有效地抑制了TiO₂晶粒尺寸和原始粒径的长大。当热处理温度低于700 ℃时,经氧化硅处理的纳米TiO₂的晶粒尺寸、原始粒径和比表面积几乎不变;当热处理温度高于700 ℃时,经氧化硅处理的纳米TiO₂的晶粒尺寸和原始粒径开始缓慢变大,比表面积快速下降,在900 ℃下煅烧2 h,经氧化硅处理的纳米TiO₂原始粒径仍为20～40 nm。氧化硅的存在使纳米TiO₂吸收紫外线的能力增强并使其平均孔径变小。     

生物大分子液相色谱分离中色谱柱长与柱径比的优化研究

用厚度为 1cm、而直径不同的色谱饼 (或饼形色谱柱 )对 7种蛋白质进行了色谱谱分离 ,得出了柱长与柱径比对生物大分子分离度影响不大的结论。还对柱内腔几何体积相同、而柱长 柱径比不同的色谱柱和色谱饼对分离度的影响以及它们压力降作了比较 ,结果表明色谱饼可在几乎不降低分离度的前提下显著降低色谱系统的压力。通过对 1 0× 5 0mmI.D .色谱饼体积和质量负载量以及质量回收率的测定 ,表明色谱饼对生物大分子的分离已达到制备规模。     

The integer Chebyshev problem

We are concerned with the problem of minimizing the supremum norm on an interval of a nonzero polynomial of degree at most with integer coefficients. This is an old and hard problem that cannot be exactly solved in any nontrivial cases.

We examine the case of the interval in most detail. Here we improve the known bounds a small but interesting amount. This allows us to garner further information about the structure of such minimal polynomials and their factors. This is primarily a (substantial) computational exercise.

We also examine some of the structure of such minimal ``integer Chebyshev' polynomials, showing for example that on small intevals and for small degrees , achieves the minimal norm. There is a natural conjecture, due to the Chudnovskys and others, as to what the ``integer transfinite diameter' of should be. We show that this conjecture is false.

The problem is then related to a trace problem for totally positive algebraic integers due to Schur and Siegel. Several open problems are raised.

     

Dead volume–free flow splitting in capillary electrophoresis

In recent years, several dual detection concepts (DDCs) for CE were developed, which consisted of at least one nondestructive detector. For these DDCs, a linear detector arrangement could be used, which is not possible when both detectors are destructive. To overcome this problem, we developed a concept for the splitting of the CE stream utilizing commercially available flow splitters (FSs) that allow the parallel positioning of two destructive detectors. In this proof-of-concept study, T- and Y-shaped FSs were characterized regarding their suitability for DDCs. To keep it simple, a UV detector (UV) and a C⁴D were used for the characterization. The model system consisted of an acetonitrile-based background electrolyte and the two model substances, (ferrocenylmethyl)trimethylammonium iodide and caffeine. CE hyphenated to a UV detector (CE-UV) measurements revealed that the split ratio was about 50% for both FSs. CE-C⁴D was used to evaluate the peak shape in front of and behind the FSs. These measurements showed that there was no significant peak broadening introduced by the FSs. Additionally, there were no changes in the LODs in front of and behind the FSs. Furthermore, the flexibility of the new FS approach allowed the usage of capillaries with different ids (25–75 µm) for injection and detection.     

Upper bounds for the volume and diameter of -dimensional sections of convex bodies

In this paper some upper bounds for the volume and diameter of central sections of symmetric convex bodies are obtained in terms of the isotropy constant of the polar body. The main consequence is that every symmetric convex body in of volume one has a proportional section , dim ( ), of diameter bounded by

whenever the polar body is in isotropic position ( is some absolute constant).

     

Nanoparticle Tracking Analysis: Enhanced Detection of Transparent Materials

This study proposes a novel and simple in-house design of a nanoparticle tracking analysis (NTA) device for the online characterization of nanoparticles in an aqueous solution. The particle size distribution of two sets of model nanoparticles, for example, transparent (SiO₂) and opaque (TiO₂) materials with respect to water as a dispersion medium could be successfully analyzed. Experiments are conducted using two different laser wavelengths of 632.8 (red) and 510 nm (green) and a range of concentrations. The accuracy of the green laser is larger compared to the red laser for all particle concentrations used. The measured average diameter using the presented in-house NTA setup is in the acceptable range compared to the electron microscopy data. The average diameter of the transparent (SiO₂) and opaque (TiO₂) samples is calculated as 36.29 and 27.26 nm using NTA, 36.44 and 27.8 nm analyzing field emission scanning electron microscopy images, and 23.97 and 19.7 nm analyzing transmission electron microscopy images. In the new viewing sample holder, nanoparticles undergo mere Brownian motion with no bulk drift velocity. The effect of solid concentration and wavelength of the laser light on the performance of the NTA sensor is investigated, and the optimal concentration range for model particles is reported.     

Numerical Investigation of Particle Focusing Patterns in Laminar Pipe Flow With High Reynolds Numbers北大核心CSCD

The inertial focusing characteristics of particles in laminar flow pipes with high Re numbers were studied based on the “relative motion model”. In order to solve the problem of long pipes with high Re number flow, periodic boundary conditions were imposed on the inlet and outlet of the pipe. The research results show that the use of periodic boundary conditions can effectively reduce the computational, and the mechanical properties of particles in high Re flow can be calculated by using L=4D pipe. The difference from the low Re number is that as the Re number continues to increase,the lift force of the particles in the radial direction is no longer distributed as a parabola. The lift curve has a concave area between r+ =0.5 ~ 0.7, and there is a tendency for a new inertial focus point to appear in this section. By means of particles of a+ =1/17 for Re > 1 000, this new focus point position is solvable. In addition, in the analysis of the flow field, a secondary flow occurs around the particle, and its intensity gradually increases with the Re number and the closeness of the particle to the wall. The generation of the secondary flow affects the spatial distribution of the particle lift. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.