The Instrument Spreading Correction in GPC. II. The General Shape Function Using the Fourier Transform Method with a Nonlinear Calibration Curve

Abstract

The instrument spreading function suggested in Part I of this series is investigated for use with the Fourier transform method for generating corrected elution volume chromatograms. The instrument spreading parameters are obtained using linear theory on narrow molecular weight distribution standards, as indicated in Part I. The corrected chromatogram is then combined with a nonlinear molecular weight calibration curve which was fit with a function suggested by Yau and Malone to generate true values of the number- and weight-average molecular weights.

The instrument spreading function is shown to qualitatively and quantitatively describe the dispersion, skewing, and flattening effects ordinarily found in GPC chromatograms due to imperfect resolution by the GPC columns. The Yau-Malone function is shown to be a very useful function for fitting nonlinear molecular weight vs elution volume calibration data. Although the Fourier transform method is shown to work well with analytically generated data, it is shown that a number of numerical problems must be overcome before it can quantitatively produce corrected elution volume chromatograms. Some of these numerical problems are discussed.     

Correction method for a concentration effect in the calculation of molecular weight averages from GPC chromatograms

In the calculation of molecular weight averages by GPC, the traditional method uses the calibration curve obtained at the same concentration as the samples, which results in a large degree of disagreement between molecular weight averages at several concentrations. Because of the concentration dependence of peak elution position in gel permeation chromatography of polymers, correct molecular weight averages cannot be obtained if calibration concentrations are the same as sample concentrations. A computation approach which uses calibration curves at finite and zero concentrations and can correct concentration effects is shown. The concentration used varied from 0.1% up to 0.4%. The elution chromatogram was divided into several parts, and concentration of species at each elution point was obtained from a concentration–peak height calibration curve. Molecular weight at the point was obtained from a molecular weight–elution volume calibration curve corresponding to a concentration of species at the point, and molecular weight averages were calculated by using the usual method. Nearly identical values for molecular weight averages could be obtained at different concentrations, and additional support for this approach is that these values for molecular weight averages were in fair agreement with NBS data.     

High-temperature coupling of high-speed GPC with continuous viscometry. I. Long-chain branching in polyethylene

The coupling of a high-temperature liquid chromatograph (Waters 150C) with a home-made continuous capillary viscometer is described. This detector is the only one suitable for high-speed GPC when the small volume of the mobile phase prohibits the coupling with a classical viscometer. The pressure drop of the GPC effluent through the capillary is continuously measured along with the refractive index change. This dual detection leads to the determination of the intrinsic viscosity as a function of the elution volume, thus allowing a precise use of Benoit's universal calibration. The accuracy of our system is demonstrated in the case of the characterization of linear and branched polyethylene samples. The results concerning the average molecular weights as well as the branching factors (structure parameter g′ and long-chain branching frequencyλ) are in close agreement with those obtained by the classical way (coupling traditional GPC and discontinuous viscometry). It is well known that an estimate of the λ coefficient is extremely dependent on several hypotheses. However, for a set of commercial low-density polyethylenes, we obtained λ values about 0.5 × 10_?4, with no marked change along the molecular weight range.     

Heating/Drying Using Particulate Medium : A Review Part I. General and Heat transfer parameters

ABSTRACT

This paper presents an Overview of particulate medium drying and heat treating of cereal grains. While the conventional air drying of grains is well documented, studies on the drying of grains using heated granular medium do not appear to exist. The scientific study of the different aspects of drying with a heated granular medium began in the early 1970's. Progress on the utilization of particle-to-particle heat transfer was slow as evidenced by the fact that there is no commercial dryer using the method as of today.

The first section of this paper deals with conduction heating and how it led to the use of granular medium in heating the grain. Starting with the earliest work on conduction heating reported by Kelly ( 1939), the developments in the heating of grain using granular media is discussed. For decades since Kelly's report, work in the subject area dealt mostly with the theoretical aspects of solid-to-solid heat transfer. Thus, in the succeeding section of the paper, heat transfer parameters and mechanisms involved in the process are thoroughly investigated.     

Heating/Drying Using Particulate Medium : A Review Part I. General and Heat transfer parameters

This paper presents an Overview of particulate medium drying and heat treating of cereal grains. While the conventional air drying of grains is well documented, studies on the drying of grains using heated granular medium do not appear to exist. The scientific study of the different aspects of drying with a heated granular medium began in the early 1970's. Progress on the utilization of particle-to-particle heat transfer was slow as evidenced by the fact that there is no commercial dryer using the method as of today.

The first section of this paper deals with conduction heating and how it led to the use of granular medium in heating the grain. Starting with the earliest work on conduction heating reported by Kelly ( 1939), the developments in the heating of grain using granular media is discussed. For decades since Kelly's report, work in the subject area dealt mostly with the theoretical aspects of solid-to-solid heat transfer. Thus, in the succeeding section of the paper, heat transfer parameters and mechanisms involved in the process are thoroughly investigated.     

The dispersion model for hydration of portland cement I. General concepts

This paper introduces an analytical mathematical model for development of the hydration of Portland cement: t₀ + t₁A + t₂A² = t t is time, and t₀, t₁ and t₂ are time-constants depending on temperature, cement type, admixtures etc. A is the hydration ratio, i.e. the ratio of hydrated to unhydrated cement. The dispersion model has been derived on basis of the typical particle size distribution for tube-milled products. Earlier findings by us have proven the particle size distribution to be a dominant factor in the correct modelling of cement hydration. The parameterization of hydration curves, which is easily performed with this dispersion model, gives a sufficient characterization of these for purposes of practical interpretations of the effects of factors decisive for the development of hydration.     

Color Matching in Paints Using a Method of Linear Programming

This note is based on 2-constant Kubelka-Munk theory and the first-order approximat ion ofspectrum, presenting a method of linear programming to compute the recipes and to get the basic database quickly. A lot of experimental results in paints have shown that matching precision may be achieved by following this practice. © 1994 John Wiley & Sons. Inc.     

The instrument spreading correction in GPC. III. The general shape function using singular value decomposition with a nonlinear calibration curve

The Gram-Charlier series was suggested as an empirical instrument spreading function in the first paper (part I) of this series. In the second paper (part II) of this series, the Fourier transform method was used together with the suggested series to solve Tung's integral equation. In this paper, an alternate method for solving Tung's equation is proposed which eliminates some of the limitations of the Fourier transform method. In the approach used in this study, Tung's integral equation is approximated by a set of linear equations. Since no unique least-squares solution can be computed, a closely related problem whose solution closely approximates the original problem is formulated and solved using singular value decomposition. By avoiding the use of the smallest singular values and forcing the equality of the areas of the corrected and the uncorrected chromatograms, an approximate solution to the original problem is obtained in which the oscillations inherently present due to the ill-posed nature of the problem are filtered out. The performance of the method with the experimental data given in Part II is indicated.     

A computer approach toward automation of a chemical services laboratory: I. Instrument support

The use of a medium scale computer for instrument support results in several distinct advantages. Instruments of differing data rates and calculation requirements may be supported on the same system at the same time. There is no interference between any of the instruments since each is assigned its own block of time for scanning and its own set of programs for data support. The use of both the on-line and off-line modes permits the easy development of programs and their subsequent incorporation into the program library. It becomes advantageous to look at data supporting instruments that require only small computer support since the off-line mode can be used for this purpose. Instruments previously considered too low in volume to support can enjoy the benefits of off-line computer support at little additional cost. The use of high level languages such as are supported on the medium scale computers make it possible to train laboratory personnel to write and modify their own programs. Their involvement in the programming effort can result in a greater acceptance of the computer as a useful tool in the laboratory, instead of the attitude that sometimes prevails that the computer is a hindrance rather than a help. The ease with which program changes can be made makes the program modification task easier for the programming staff of the computer installation, if laboratory personnel do not perform this function. The medium scale computer provides computational power far exceeding that available on a series of small dedicated computers. The “pooling” of resources results in having available a larger scale computer for those programs and instruments that require it. The degree of sophistication of software available on the medium scale computers is far above that available on the smaller units. One of seven papers being published from the Symposium, “Computer Systems and Application in the Oil and Fat Industry” presented at the ISF-AOCS World Congress, Chicago, September 1970.     

Gel Permeation Chromatography Calibration. I. Use of Calibration Curves Based on Polystyrene in THF and Integral Distribution Curves of Elution Volume to Generate Calibration Curves for Polymers in 2,2,2-Trifluoroethanol

Abstract

A general method is proposed for obtaining gel permeation chromato-graphic (GPC) molecular weight (MW) and hydrodynamic volume (HDV) calibration curves for polymer-solvent systems where primary polymer standards are unavailable. The method is demonstrated by using a HDV calibration curve based on polystyrene in tetrahydrofuran (THF), in conjunction with integral distribution curves of elution volume for poly(methyl methacrylate) (PMMA) in THF and in 2,2,2-tri-fluoroethanol (TFE) for the generation of a HDV calibration curve in TFE. Transformation methods for generating secondary MW calibration curves from HDV calibration curves are discussed and applied to PMMA in THF and TFE, and to poly(trimethylene oxide), poly(vinyl acetate), and certain polyamides in TFE. The utility and reliability of the secondary calibration curves are demonstrated by comparing MW average and intrinsic viscosites obtained by GPC and by the classical methods. Molecular structural differences among th polyamide samples associated with the distribution of short- and long-chain branches are discussed in relation to their secondary calibration curves.     

应用配分函数研究极性物质的P-V-T关系

本文把引力项对配分函数的贡献分成极性项和非极性项,由分子位能函数推导出极性项配分函数表达式.由此得出了VdW方程引力参数“a”的极性项关联式.并提出用临界压缩因子和对比偶极矩共同关联极性物质.所推导出的“a”的表达式改进了SRK方程的计算精度.对45种极性物质的饱和蒸汽压和汽化热进行了计算,获得良好的结果.     

Effective Ozone Generation in Oxygen Using a Mesh Electrode in an Ozonizer with Variable Linear Velocity

Results of studies on ozone synthesis under discharges proceeding in a metal mesh-ceramic dielectric system have been presented. The experiments were carried out in the reactor with unique reaction space geometry, in which the reacting gas flew with consequently increasing linear velocity. The high voltage electrode was made of a metal mesh, which caused intensification of the gas mixing in the reaction space. Using a simple reactor with one-side cooling of the reaction space, high ozone maximum concentrations (100 g/Nm³) and energy efficiencies (180–200 g/kWh) were obtained at 25 °C.     

The Aerodynamic Behavior of Fibers in a Linear Shear Flow

Lung deposition behavior for straight versus curved aerosol fibers is known to be different based on existing experimental data. However, our understanding of actual fiber dynamics in the respiratory system remains far from being complete. In particular, it is not clear how fiber shape influences particle motion in the lungs. This article presents the results of direct numerical simulations in a linear shear flow of the rotational dynamics of high aspect ratio fibers with complex shapes such as elliptic rods, torus segments, and helices. Our findings show that as expected the rotational behavior of complex fibers is different from that observed for straight symmetrical particles. In particular, we observe secondary rotation for our particles, which is perpendicular to the shear plane (a plane with the unit normal parallel to the local vorticity) as well as more frequent flipping (for helical particles) than observed for straight fibers with the same lengths and diameters. In view of our results, it can be suggested that respiratory tract deposition for particles with complex shapes will exhibit enhanced interception compared with the deposition of particles with simpler shapes.     

Characterization of polyvinyl chloride part II. The unperturbed end to end distance values obtained from a new GPC method and viscometry

A new gel permeation chromatography (GPC) method is proposed for determining the unperturbed end-to-end distance, \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2 }}{M}} \right)^{0.5} $\end{document}, of polymers of known molecular weights, Mn and Mw. This method requires the value of \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2 }}{M}} \right)^{0.5} _{{\rm ps}} $\end{document} of polystyrene which was determined through viscometry to be 0.735 \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{{\rm {\AA}}^2-{\rm mole}}}{{gm}}} \right)^{0.5} $\end{document} Polyvinyl chloride (PVC) was chosen to illustrate the method and \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2}}{M}} \right)^{0.5} _{pvc} $\end{document} was found to be 0.99 from GPC data which is in agreement with the result obtained from viscometry, \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2}}{M}} \right)^{0.5} _{pvc} $\end{document} = 1.01. All \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2 }}{M}} \right)^{0.5} $\end{document} values were determined at 30°C. The advantage to this method lies in its speed and economy of materials.     

The reaction between ethylene and chlorine-water in a wetted-wall column. I. The mechanism of reaction

A wetted-wall column was used to measure rates of sorption of ethylene into the following liquids: pure water, aqueous hypochlorous acid, and chlorine-water acidulated with hydrochloric acid. Experimentally determined diffusivities of ethylene in water, at 20° and 30°, are consistent with previously reported values. The experimental evidence supports Shilov's mechanism viz., that the reaction between ethylene and chlorine-water takes place via a liquid-phase complex of ethylene and free chlorine.     

珠串反应器中流出曲线对传递系数和吸附系数的敏感性

在珠串反应器上,使用Fourier分析的方法,考察了正戊烷-Pt-Sn/Al_2O_3体系的传递系数和吸附系数对流出峰影响的敏感性.在所有这些参数中,只有吸附平衡常数和粒内有效扩散系数能从单一次脉冲应答试验中准确地获得.研究结果说明,珠串反应器的行为类似于通常的填料床反应器.在计算中也考察了不同的目标函数、周期和步长对参数计算值的影响.