An Analysis of Imperfect Resolution in the Chromatography of Particle Suspensions

Abstract

Here-in is reported a general method of correction for imperfect resolution in the chromatography of particle suspensions. It overcomes most of the limitations of previously reported methods. A non-linear particle diameter - retention volume calibration curve and a generalised spreading function are considered. Moment equations are developed for two types of general detectors; the first type includes a refractive index detector and a turbidity detector with Rayleigh scattering while the second type includes a tubidity detector with Mie scattering. The moment equations were applied to the analysis of chromatograms of narrow Dow polystyrene latices measured by size exclusion chromatography.     

Inverse Optimal Filtering Method for the Instrumental Spreading Correction in Size Exclusion Chromatography

Abstract

The Kalman filter based techniques are adapted to solve the most general form of Tung's integral formula, i. e. when a non-uniform, non-symmetric calibration model is employed to correct chromatograms obtained in size exclusion chromatography from instrumental broadening errors. Through this method, the inverse smoothing of a chromatogram contaminated with measurement noise of known statistics is optimally performed by minimizing the estimation error variance. The method is numerically very “robust”, improves the signal to noise ratio, provides good validation checks, and does not involve any previous parameter estimation procedure.     

Chromatography of Suspensions - Analytical Corrections for Axial Dispersion

Abstract

An analytical method is proposed to correct the signal from a turbidity detector for axial dispersion in the chromatography of particle suspensions. An earlier analytical method due to Hamielec and Singh [1] is limited to light scattering in the Rayleigh regime. The solution reported herein is derived using the more general Mie light scattering theory and enables the correction of various moments of the particle diameter frequency distribution function. The axial dispersion phenomenon is described by the well known integral equation where the instrumental spreading function is assumed Gaussian. The solution is applicable for both linear and nonlinear particle diameter-retention volume calibration curves.     

Size Exclusion Chromatography (SEC) of Complex Polymers - Generalized Analytical Corrections for Imperfect Resolution

Abstract

Herein is reported generalized analytical solutions which permit correction for imperfect resolution when the molecular weight calibration curve is nonlinear and the variance of single-species chromatograms changes significantly with molecular size of the polymer solute. Two kinds of generalized analytical solutions have been obtained. One is a solution of Tung's integral equation for the corrected chromatogram or the molecular weight distribution and the other is a solution for the corrected molecular weight averages of the whole polymer. Also discussed is the use of local corrections for imperfect resolution across the chromatogram with detectors such as the low angle laser light scattering spectrophotometer (LALLS) when used with micro and macropackings.     

Chromatography of Suspensions,An Absolute Particle Size Detector Based on Turbidity-spectra Analysis - a Simulation Study

Abstract

In the chromatography of particle suspensions the use of a variable wavelength spectrophotometer can provide turbidity spectra continuously with retention volume. As suggested by Hamielec [1] this device could form the basis for an absolute particle size detector provided the size distribution in the detector cell could be represented by a known distribution function. In this work it is shown that the two parameter log-normal distribution function is an adequate representation of the detector cell contents. Further a computational scheme is outlined whereby the distribution parameters and the number of particles in the detector cell are calculated as a function of retention volume. It is then possible to obtain size distribution information of the original suspension.     

A Method of Correcting for Flow-Rate Fluctuations in Size Exclusion Chromatography Calculations: Applications to Methylene Chloride/Hexafluoroisopropanol Solvent System

Abstract

The mixture of methylene chloride/hexafluoroisopropanol (70/30, v/v) is an excellent polyester solvent, but its low boiling point causes unstable flow when it is used for size exclusion chromatography (SEC). In high-performance SEC experiments, retention time is normally used to measure elution volume; however, unstable flow makes it difficult to calibrate an SEC column set or calculate molecular weight parameters from a chromatogram. We have devised a simple and inexpensive method to compensate for the effect of unstable flow in SEC calculations. A calibration marker injected along with each sample is used to indicate flow-rate variations. The ratio of the sample retention time to the marker retention time is invariant to flow-rate changes and is used in place of retention time as a measure of elution volume in the universal calibration technique. Calibrating a column set and analyzing chromatograms by this method result in a large improvement in the accuracy and precision of calculated molecular weight parameters.     

Determination of Morphological Properties of Swellable Solids by Size Exclusion Chromatography

Many technically interesting porous solids, e.g. ion exchangers or adsorbents for catalysis, are swellable polymers, i.e. the pore structure depends on the solvent medium. A method based on exclusion chromatography, permits determination of the pore size and pore size distribution in the swollen state.—Size exclusion chromatography, also referred to as gel permeation, gel filtration, or molecular sieve chromatography, is a widely employed method for the separation of dissolved substances—mostly polymer mixtures—according to their molecular size. Porous solids are used as stationary phase. Conversely, pore sizes and other structural data can be determined by exclusion chromatography. This application requires a series of standards (polymer samples) of known molecular weight. As a simple and rapid method, it has already proven valuable for such determinations in the case of rigid solids; in the case of swellable solids, this constitutes the sole method by which the pore structure can be characterized: classical methods require dry samples.     

A New Packing for Aqueous Size Exclusion Chromatography Polyvinylpyrrolidone-Coated Silica

Abstract

Adsorption of polyvinylpyrrolidone on silica in aqueous medium is studied. Adsorption isotherms, thermogravimetry and elementary analysis show that a complete surface coverage is reached with large pore microbeads. The coating stability and its ability to prevent non-steric effects when used as packing in exclusion chromatography are demonstrated. Four different pore size packings were prepared for chromatographic evaluations. It is shown that water soluble polymers like polyethylene oxide, polyvinylalcohol, polyacrylamide and hydroxyethylcellulose can be chromatographied in pure water according to the steric exclusion mechanism.     

Instrumental Broadening Correction in Size Exclusion Chromatography. Comparison of Several Deconvolution Techniques

Abstract

Several deconvolution techniques (1–7) and a novel method herein presented, are compared in relation to their ability for correcting size exclusion chromatograms for the undesirable effect of instrumental broadening. Such methods are evaluated on the same computer, and through a “synthetic” example of known solution. Methods based on the frequency domain are only applicable to uniform deconvolution problems with stationary statistics. However, in the herein presented heuristic method (based on the Wiener filter in the frequency domain), it is possible to relax this last restriction, and generate solutions that are equivalent to considering signals with time-varying statistics. The evaluated techniques are compared on the basis of quality of results, computational considerations and adjustment facility. Stochastic techniques provide the best (and nearly identical) numerical solutions. This is mainly due to their increased facility to introduce “a priori” information about the expected solution. As a counterpart, stochastic techniques are conceptually more complex, more difficult to implement, and normally inolve more elaborate adjustment procedures.     

High Performance Size Exclusion Chromatography on Microparticulate Silicas and its Application to Forensic Analysis

Abstract

Size exclusion chromatography (SEC) on irregular silicas of 5–10 um particle size and 60–130 Å average pore size is shown to provide a rapid method for the comparison of a variety of forensically significant samples. Use of dual detectors (UV/fluorescence of UV/Refractive Index) was found to enhance the value of the technique for forensic screening.     

Characterization of Nonionic Polyacrylamides by Aqueous Size Exclusion Chromatography Using a DRI/LALLSP Detector System

Abstract

Herein is reported an experimental investigation of the molecular weight characterization of nonionic polyacrylamides by aqueous SEC with a DRI/LALLSP detector system. Methodology for the use of the DRI/LALLSP detector responses to determine the molecular weight calibration curve and the peak broadening parameter, [sgrave]² (variance of a Gaussian instrumental spreading function) over a wide molecular weight range has been developed. The method is based on the use of a broad MWD standard made by blending Polysciences broad MWD standards and a generalized analytical solution of Tung's integral equation for the detector response corrected for peak broadening. Molecular weight averages measured by SEC/DRI/LALLSP are in excellent agreement with those measured offline by LALLSP.     

Instrumental Broadening Correction in Size Exclusion Chromatography through Fast Fourier Transform Techniques

Abstract

This paper shows the practicability of the use of the fast Fourier transform (FFT), with appropriate filtering in the frequency domain, as a means of deconvoluting Tung's integral formula (1). The method is limited to uniform instrumental spreading functions, but presents several important advantages: it is numerically efficient, no assumptions about the shape of the spreading function are made, it eliminates the highfrequency measurement noise components from the corrected chromatogram without modifying the original data, and provides a means of physically interpreting the results.     

用已知数均分子量的多个多分散标样校准尺寸排除色谱柱

Hamielec双因子觅数法曾广泛应用于多分散标样校准尺寸排除色谱(SEC)柱.其后,有人将它改进为单因子觅数法,他们一般只使用了一个已知两种标定量(_n和_w或_η)的样品.在已知某一种标定量的多个多分散试样的校准工作中,有的为前述方法在非线性校准上的扩展,仍采用试凑法逼近目标函数;Szewczyk则利用与标定量对应的平均保留体积的概念,提出了一种较为有效的方法.     

Calculation of hydrodynamic parameters of random coil polymers from size exclusion chromatography and comparison with parameters by conventional methods

A new method of treating data from size exclusion chromatography, originally evaluated for native proteins, has been extended to random coil polymers using data from dextran and polyethylene glycol as specific examples. Columns are calibrated with globular proteins of known molecular weight. Multiplication by a constant transforms the abscissa to molecular radii. The constants in the equation r = gM^Z are then evaluated directly from the size exclusion chromatographic data and compared with the corresponding constants obtained from viscometry, sedimentation velocity and light scattering, relating Stokes radius, root mean square end-to-end distance and radius of gyration to molecular weight.     

Simulation of the shape of a chromatographic peak by the method of theoretical plates

The shape of a chromatographic peak and its distortions are investigated in relation to the efficiency of the chromatography column, the nonlinearity of the sorption isotherm of a substance, and “extracolumn” peak spreading. Using simulation by the method of theoretical plates, the efficiency calculated from chromatograms by various equations is related to parameters known in advance (specified beforehand). An empirical equation giving results consistent with the specified parameters is suggested.     

Concentration Effects in Size Exclusion Chromatography Under Equilibrium Stationary Conditions

Abstract

In size exclusion chromatography the elution volume increases with increasing concentration of injected polymer solutions. Several particular processes contribute to this concentration effect. Under model equilibrium stationary conditions, where the phases remain immobile, it is possible to eliminate dynamic phenomena connected with the higher viscosity of polymer solution in the chromatographic zone. The only factors operative here are the effect of changes in the effective size of macromolecules in solution with a change in concentration and the effect of the varying accessible pore volume with varying concentration. The ratio of these two contributions has been investigated both theoretically and experimentally. Theoretical calculations indicated that with both phenomena operating simultaneously, the elution volumes may increase or decrease with increasing concentration according to the given experimental conditions, as a result of the coupled influence of molecular parameters of the samples under study, of the thermodynamic quality of the solvent and of the distribution coefficient on the given porous material. Experimental results showed, however, that at least under stationary conditions secondary exclusion is probably operative to a less important degree.     

Comparing Dichromate Oxidation and Size Exclusion Chromatography of Dissolved Carbohydrates

Standardised methods are used to characterise the pulp or cellulosic material for its alkali resistance and alkali solubility. Today, pulp is usually characterised by its solubility in sodium hydroxide. The characterisation test was based on the treatment of pulp with sodium hydroxide solution of a defined concentration, according to a specified procedure. The dissolved organic matter was then determined by dichromate oxidation. The results obtained by size exclusion chromatography showed that both the amount and the molecular weight of the dissolved carbohydrates vary when investigating solubility and α-cellulose content of pulps. The results show further that S₁₈ values obtained by dichromate oxidation are overestimated when characterising pulps containing higher amounts of hemicellulose and/ or short chain cellulose, compared with results obtained by the SEC method. On the contrary, S₁₀ values are overestimated when determined by dichromate oxidation in higher alpha pulps.     

Modern methods for determining the molar mass distribution of polymers. General considerations and application to sedimentation equilibrium

A new procedure for the determination of the molar mass means M_n, M_w and M_z and of the molar mass distribution W(M) = f(M) of polymers is proposed and applied on measurements of the sedimentation equilibrium. The procedure includes the extrapolation of the experimentally determined polydisperse measurable quantity at different concentrations to zero concentration. From these values the molar mass distribution is calculated by nonlinear least squares routines of the integral equation. This method of calculation is, contrary to the inverse transformation of the integral equation, which has been used up to now, well conditioned and stable. The proposed method has been applied to sedimentation equilibrium. In this case the reduced concentration profiles (interference optic, absorption optic) or reduced concentration gradient profiles (schlieren optic) measured at different concentrations must be extrapolated to zero concentration and followed by nonlinear regression of the integral equation U_w(X) = ∫ W(M) U(X,M) dM. Measurements on polystyrenes with different polydispersities and modalities (e.g. bimodal molar mass distributions), and on the polyelectrolytes sodium polystyrene sulfonate and polyethylene imine exhibit resonable results. The result of the investigation is, that the proposed procedure is a suitable and reasonable possibility for the determination of molar mass distribution of polymers by sedimentation equilibrium. For polyelectrolytes in particular this method is better than gel permeation or size exclusion chromatography.     

Structure of Liquid Metals

Abstract

The structure factors and radial distribution functions of liquid sodium and aluminium were calculated using the Hypernetted chain equation and the Machin-Woodhead-Chihara (MWC) integral equation. Various oscillatory potentials suggested for these metals were considered in an attempt to determine the applicability of these integral equations for these potentials. The calculated results are compared with molecular dynamic simulation results. These results indicate that the HNC equation underestimates the main peak in S(k). When the Friedel oscillations are absent then MWC theory gives good results for S(k). But when Friedel oscillations are present then MWC equation reproduces simulation results beyond the main diffraction peak.     

Size Exclusion Chromatography with Low Angle Laser Light Scattering Detection

Abstract

A review is given of the use of low angle laser light scattering (LALLS) detection in conjunction with size exclusion chromatography (SEC) to measure polymer molecular weight distributions without conventional SEC column calibration methods. A summary of light scattering theory is presented, and instrument configurations and principles of operation are described for two LALLS photometers. Also discussed are the overall performance of the SEC/LALLS technique and data from selected applications.