Effect of a resistance-free tank on the resistance to gas transport in high vacuum tube

The expression for the time lag in a cylindrical tube, into which a gas at very low flow rate enters at one end while the other end is connected to a resistance-free accumulation tank, has been derived assuming that the gas transport in the tube is a diffusive process. Assuming a constant diffusion coefficient of the gas in the tube allowed obtaining an analytical expression for the time lag using the concept of linear asymptotes and Laplace transformation of the governing partial differential equation. The obtained expression indicates that if the pressure response is monitored in the tube, the presence of the tank at the end of the tube would lead to a negative time lag in the tube. The time lag becomes more negative as the distance from the tank increases and the volume of the tank increases while the cross-sectional area of the tube decreases.

The comparison of the model with the experimental data obtained in tests with nitrogen in which the pressure response to a step increase in feed pressure of membrane was monitored in the tube at two different distances from the membrane cell, indicates that the error due to resistance to gas transport in the tube on the experimental time lag of tested medium is even greater than that predicted by the model. This is because of the assumption of constant diffusion coefficient in the tube, which does not allow predicting the experimentally observed increase in the slope of the asymptote with the distance from the membrane cell.     

正常拖尾色谱峰的塔板模型表达式

得到了描述正常拖尾色谱峰的塔板模型表达式,根据这一表达式,正常的色谱流出曲线应是非对称的拖尾峰,而对称的高斯型分布函数是对塔板模型进行近似处理的结果。和扩散模型的色谱流出曲线方程相比,二者在形式上完全相同,因此,尽管塔板模型和扩散模型的机理不同,但它们对于色谱流出曲线的数学描述是完全相同的。     

线性非理想条件下液相色谱柱末端峰形规律

色谱流出曲线的二阶中心矩μ２和三阶中心矩μ３以及描述峰形非对称程度的偏态系数∑ｋ＝μ３／μ１．５２是反映色谱峰形的重要参数。从液相色谱过程动力学方程出发，运用电子计算机证明了在线性非理想条件下高效液相色谱体系中不同保留值组分在柱末端峰形的分布基本一致的结论。     

Measurement of adsorption of a single component from the liquid phase: modelling investigation and sensitivity analysis

In this work, we consider an alternative approach for the measurement of adsorption from the liquid phase. Consider a mixture consisting of a non-adsorbed component (B) and an adsorbed component (A) present at some low concentration. Initially, a feed of component B only flows through a column packed with an adsorbent. Then, the feed is switched to the mixture of A and B. As soon as the mixture enters the column, there will be a reduction in the outlet flow rate as component A leaves the liquid phase and passes into the adsorbed phase. There are three stages to this work. The first is to develop overall and component balances to show how the amount adsorbed of component A can be determined from the variation in the column outlet flow rate. The second is to determine the actual variation in the column outlet flow rate for both plug flow and axial-dispersed plug flow. The final stage is to consider the suitability of a gravity-fed system to deliver the feed to the column. An analysis of the results shows that the experimental arrangement should be able to accurately monitor adsorption from the liquid phase where the mass fraction of the solute is of the order of 1%: the limiting experimental factor is how constant the volumetric flow rate of the liquid feed can be maintained.     

线性非理想条件下液相色谱柱末端峰形规律

 色谱流出曲线的二阶中心矩μ２和三阶中心矩μ３以及描述峰形非对称程度的偏态系数∑ｋ＝μ３／μ１．５２是反映色谱峰形的重要参数。从液相色谱过程动力学方程出发，运用电子计算机证明了在线性非理想条件下高效液相色谱体系中不同保留值组分在柱末端峰形的分布基本一致的结论。     

基于随机扩散理论的色谱模拟辅助化学教学研究

为了满足当今教学的信息化发展趋势,本研究基于随机扩散理论建立了气相色谱仿真模型并开发了相关的计算模拟软件Stochastic Diffusion-Chroma。以混合组分分别在气相色谱填充柱和毛细管柱中的扩散分离模拟为例,探究了随机扩散理论模型在色谱理论教学和实验教学方面的应用。基于随机扩散理论的仿真教学改变了传统的教学模式,将学生较难理解的抽象色谱动力学基本理论转变为动态的具体形象,激发了学生的学习兴趣,提高教学质量。     

Measurement of the infinite dilution diffusion coefficients of small molecule solvents in silicone rubber by inverse gas chromatography

The infinite dilution diffusion coefficients of n-hexane, n-heptane and n-decane in crosslinked silicone rubber with different crosslinking agent concentrations were measured in the temperature range of 348.15 K-368.15 K by inverse gas chromatography. The crosslinked silicone rubber was obtained by dissolving PDMS prepolymer, crosslinking agent and catalyst in n-heptane solvent and characterized by FTIR spectra. The Van Deemter equation was used to determine diffusion coefficients from the variation in chromatographic peak width with carrier gas flow rate. The good linear relation indicated the Van Deemter equation used in this work was reliable. The influences of small molecule solvent, crosslinking agent concentration and temperature on the infinite dilution diffusion coefficient were investigated. The results showed that the infinite dilution diffusion coefficient decreased with an increasing number of CH₂ group in the alkane series. The increase in crosslinking agent concentration resulted in decrease of the infinite dilution diffusion coefficient. The infinite dilution diffusion coefficient increased with the rising of temperature. The interdependence on the infinite dilution diffusion coefficient and temperature accorded with Arrhenius equation well. Diffusion constant and activation energy obtained from the Arrhenius equation provided straight lines with the specific critical volume and crosslinking agent concentration.     

Effect of the pressure of the carrier gas on the parameters of the Van Deemter equation for monolithic silica gel gas chromatography columns

The chromatographic properties of monolithic capillary silica gel columns for gas chromatography were examined with the use of four different variants of the Van Deemter model. The corresponding experimental curves were measured for the elution of light hydrocarbons with the helium carrier gas in the isothermal mode at 60°C. Despite the models tested are based on different mechanisms of the smearing of chromatographic peaks, the values of the Van Deemter equation parameters proved to be very close to each other for three of the four models. All models yielded negative values of the parameter A. Physically reasonable values of the parameters of the Van Deemter equation were obtained only for the Giddings model, which takes into account the pressure drop across the column. At the same time, this model overestimated the contribution from diffusional smearing (parameter B). It was concluded that none of the models tested adequately described the chromatographic properties of monolithic capillary columns for gas chromatography.     

Hold-up time in gas chromatography. V. Dependence of the retention of n-alkanes on the chromatographic variables in isothermal gas chromatography

The chromatographic behaviour of n-alkanes and other homologous series in isothermal gas chromatography has been shown to depart from the "linear" representation of the logarithms of the adjusted retention times vs. carbon number. One of the expressions proposed to describe this behaviour is tR(z)=A+exp(B+CzD). In this paper, a regression analysis shows that three of the parameters of the equation depend on different chromatographic variables such as hold-up time, average linear gas velocity, volume and polarity of the stationary phase and temperature of the column. The fourth parameter (D), responsible for the departure from the "linearity", does not depend on any chromatographic variable, and represents a gradual decrease of the contribution of the methylene groups to the general properties of n-alkanes, with no relation to the chromatographic phenomenon.     

Factors determining flow rate in chromatographic columns

Summary It is shown that the flow in chromatography is nearly always laminar in nature. Starting from the Darcy equation, expressions are given for the flow rate in both gas and liquid chromatography columns. The concepts of specific permeability, chromatographic permeability and column resistance factor are discussed for packed as well as open tubular columns. The experimental determination of all these factoers is demonstrated. The influence of the shape and pore volume of porous and non-porous supports on the column resistance factor and the chromatographic permeability is discussed.     

Interpreting the difference between conventional and bi-directional plate-height measurements in liquid chromatography

An experimental and theoretical study was conducted of the column characterization technique in which plate heights determined using the conventional pulse-response method are compared with those determined using a bi-directional method where an eluite sample is introduced into one end of a chromatographic column and elution occurs at the same end after the flow direction is reversed inside the column. Experiments are presented for a micropellicular HPLC column before and after its performance has been degraded by repeated sample injections, for a low-pressure column containing nonporous glass particles, and for an HPLC column containing particles with 300 Å pores. The results obtained are interpreted in terms of several different theories which apply in various Fourier number ranges. It was shown that the transcolumn contribution to convective dispersion in a chromatographic column is largely responsible for the difference observed between conventional and bi-directional plate-height measurements and that a collocation method can be employed to develop a useful analytical expression for this contribution.     

Foam Countercurrent Chromatography Based on Dual Counter-Current System

Abstract

A novel method of performing foam separation is described. The method utilizes a gas-liquid dual countercurrent flow through a helical column subjected to a particular type of synchronous planetary motion. Samples introduced at the middle portion of the column, in either batch or continuous mode, are separated according to the foam affinity. Any material having an affinity to the foam is quickly carried with the foaming stream and eluted through one end of the column whereas other materials are carried with the liquid stream in the opposite direction and eluted out through the other end of the column. Capability of this foam countercurrent chromatographic method is demonstrated on separations of rhodamine B and Evans blue with an anionic surfactant, SDS, as a collector of rhodamine B. Successful preliminary separation of protein samples, BSA and sheep hemoglobin, indicates that the present method may be effectively applied to separation and purification of various biological samples such as enzymes, membrane receptors, etc.     

Sorption thermosiphon apparatus (STA): A novel and accurate system for gas mixtures sorption measurements

One of the main challenges in membrane gas separation is the plasticizing effect that reduces selectivity. For a better understanding of this phenomenon, the knowledge of the sorption behavior of each component of the mixture is necessary. For this purpose, the sorption thermosyphon apparatus (STA), was successfully designed and tested with gas sorption measurements. One of the main advantages of the STA compared to actual other methods is to ensure concentration uniformity at the headspace using a thermosiphon, as pressure decay is recorded. The equilibrium condition is not disturbed during the sampling and allow the obtention of accurate data at the end of the sorption experiment. To validate the novel system, the sorption, diffusion and permeation coefficients of pure CO2 and CH₄, as well as for a CO₂/CH₄ (50/50) mixture, in polydimethylsiloxane (PDMS) were obtained through STA and other experimental techniques showing good agreement with literature data.     

基于随机扩散理论的气相色谱分离模拟

色谱分离过程中的粒子扩散问题是色谱动力学研究的基础,深入理解粒子的扩散行为对优化分离操作条件、提升色谱性能和开发新型色谱柱尤为关键.现有的模拟方法多集中于局部过程的热力学研究,而整体的扩散分离过程报道并不多见.为此,该文基于微尺度受限空间内随机扩散的方法,通过动态追踪粒子的运动轨迹,实现粒子在气相色谱开管柱内的扩散全过...     

Prediction of retention times and efficiency in linear gradient programmed pressure analysis on capillary columns

A method for the prediction of the retention time and the resolution of chromatographic peaks in different experimental conditions by starting from few experimental data measured in isothermal and isobaric analyses was published previously. In this paper, the same mathematical model was implemented for calculating the retention times and the column efficiency in programmed pressure runs. Some models originated from the Golay equation and reported in the literature are compared, and a new modified equation for the calculation of the peak width at half height is proposed. The procedure for the prediction of the retention time and the peak width at half height at programmed pressure of the carrier gas and different column temperature and linear gradient by using retention data of different compounds obtained in few isobaric runs is described. The prediction of the retention time and the separation efficiency of compounds with different polarity gave good results for the programmed pressure runs with linear gradient. The effect of the variation of the initial parameters of the experimental analyses and of the mathematical model on the accuracy of the prediction has been evaluated.     

宽口径填充毛细管液相色谱柱柱尾结构的改进

 设计并评价了尾锥形填充毛细管液相色谱柱,与粘结型柱尾比较,前者柱效高且van Deemter曲线高流速部分的流速-柱效关系明显改善。在折合流速为10～15时,前者的柱效比后者高出30%～50%。谱带的抛物线状的流形在尾锥形柱内得到改善,使色谱峰的对称性有明显提高。比较了两种结构的色谱柱在芳烃快速分析中的分离效果,结果是尾锥形柱的分离性能优于粘结型柱。     

An absorbance-based micro-fluidic sensor for diffusion coefficient and molar mass determinations

The H-Sensor reported herein is a micro-fluidic device compatible with flow injection analysis (FIA) and high performance liquid chromatography (HPLC). The device detects analytes at two separate off-chip absorbance flow cells, providing two simultaneous absorbance measurements. The ratio of these two absorbance signals contains analyte diffusion coefficient information. A theoretical model for the sensing mechanism is presented. The model relates the signal Ratio to analyte diffusion coefficient. The model is qualitatively evaluated by comparing theoretical and experimental signal Ratio values. Experimental signal Ratios were collected via FIA for a variety of analytes, including sodium azide, benzoic acid, amino acids, peptides, and proteins. Measuring absorbance at multiple wavelengths provides higher order data allowing the analyte signals from mixtures to be deconvolved via classical least squares (CLS). As a result of the H-Sensor providing two simultaneous signals as a function of time for each sample injection, two simulated second-order HPLC chromatograms were generated using experimental H-Sensor data. The chemometric deconvolution method referred to as the generalized rank annihilation method (GRAM) was used to demonstrate chromatographic and spectroscopic deconvolution. GRAM also provides the signal Ratio value, therefore simultaneously obtaining the analyte diffusion coefficient information during deconvolution. The two chromatograms successfully serve as the standard and unknown for the GRAM deconvolution. GRAM was evaluated on chromatograms at various chromatographic resolutions. GRAM was found to function to a chromatographic resolution at and above 0.25 with a percent quantitative error of less then 10%.     

A chromatographic analysis of hindered diffusion of saccharides in silica gels

Summary The chromatographic technique as a means for experimental studies of diffusion in porous solids has been demonstrated. In this paper we report the effective diffusion coefficients which we have chromatographically obtained for two dextran samples and three low molecular weight solutes. The chromatographic method of measuring diffusional resistances in porous solids has the advantages of rapidity and simplicity. This method also provides information on the axial dispersion and distribution of a solute between the moving phase and the solvent held stationary in the pore. The elution curves of a packed column in pulse response experiments were analyzed by the method of moments to give the parameters of interest. The results indicate that pore diffusion of the solutes was appreciably restricted in comparison with diffusion in bulk solution. The degree of hindrance depended on the size of the diffusing substances.     

Effect of the relative pressure on the efficiency and separation properties of open capillary columns

Wide use of a combination of gas chromatographic (GC) separations with mass spectroscopic detection causes the necessity to study the effect of the relative pressure in a capillary column on its efficiency and separation properties. Using n-decane as a sorbate, a decrease in the relative pressure was shown to induce a slight increase in the efficiency of polar capillary columns but results in a considerable decrease in the optimal flow rate of the mobile phase and strongly constricts the Van-Deemter curve profile. In the presence of the restrictor, even minor deviations from the optimal flow rate can result in a considerable decrease in the column efficiency. Since the capillary restrictor is often a component of the interface between the column and mass spectrometer, it is necessary to exactly maintain the optimal operation conditions of the GC column to achieve an optimal efficiency of separation.     

Pressure Effects in Adsorption Systems

A study of the occurrence of large pressure and flow transients when a strongly adsorbed gas is fed to a column which is initially loaded with a lightly adsorbed gas is presented here. Under certain conditions, these transients can cause premature breakthrough and change the shape of the breakthrough curve. This will result in improper estimation of adsorption parameters by the dynamic column loading method and lower apparent adsorption capacity in a full scale unit. A data acquisition system was used to record the pressure and flow transients. An isothermal PDE model developed to study these transients agreed reasonably well with the nonisothermal experimental results. The PDE model predicts that pressure and flow transients will occur during step and pulse~tests conducted to obtain adsorption and mass transfer parameters by the chromatographic method. For instance, lower adsorption capacity will be realized during step tests due to lowering in column pressure. Oscillations were observed when columns are connected in series. The PDE model also predicts these oscillations. Simulations indicate that the extent of oscillations is dependent on the dead volume between columns.