Generalized Universal Molecular Weight Calibration Parameter in GPC

Abstract

In this report we show by experimental and theoretical investigations that the commonly used GPC universal calibration parameter, the intrinsic viscosity multiplied by the weight average molecular weight ([η] M^w) is incorrect. The error which can arise by using [η] M to calculate the molecular weight across the GPC chromatogram for nonuniformly branched polymers [poly(vinyl acetate) and low density polyethylene] and copolymers with compositional drift, could be very large. We also show conclusively that the number average molecular weight M_n is the correct average to use for the universal calibration parameter. We therefore recommend that our general universal Calibration parameter [η] M_n be used for calculating the molecular weight across the chromatogram for all polymer systems (linear and branched homopolymers, copolymers with or without compositional drift and for polymer blends).     

Universal Calibration and Molecular Weight Averages in Gel Permeation Chromatography Illustrated by Cellulose Nitrate and Poly(oxypropylene)

Abstract

The nature of the averaging process in the analysis of gel permeation chromatograms was examined for cases where the molecules in the detector cell of the apparatus were of different molecular weight and of the same molecular weight. When the molecules have the same molecular weight, the hydrodynamic volume (1), [?]M, averaged across a chromatogram was found to become KM^a+1 for any molecular weight average at the elution volume corresponding to that average. [η] is intrinsic viscosity, M is molecular weight, and K and a are the appropriate Mark-Houwink constants. Thus when size separation is by molecular weight, the universal GPC calibration functions include KM_n ^a+1 where M_n is the number average molecular weight.

Cellulose nitrate and poly(oxypropylene) were analyzed using three sets of columns and two GPC instruments. KM_n ^a+1, KM_w ^a+1, and [η]M_w were found to represent the hydrodynamic volume since these functions fell on the universal calibration plot for nearly nono-disperse polystyrene standards. The function [η]M_n was displaced from the polystyrene universal calibration plot by factor which equaled M_w/M_n. The slopes and intercepts of the universal calibration plots were found to be completely consistent with the slopes and intercepts of the molecular weight calibration plots showing that the Mark-Houwink constants were correct. Intrinsic viscosity - molecular weight relations were presented for 12.0–12.6%N cellulose nitrate and for low molecular weight poly(oxypropylene), the latter relation being a correction of that of Sholtan and Lie (18).     

Remarks on the Calibration of Steric Exclusion Liquid Chromatography by Polymolecular Standards

Abstract

The relation of polymer molecular characteristics versus chromatographic parameters in steric exlusion liquid chromatography (GPC) was considered as a typical black box problem. Practical problems were discussed for cases of the GPC black box calibration with polymolecular polystyrene standards and of using an improper calibration model. It was concluded that checking the reliability of the GPC black box calibration is of utmost importance especially when narrow calibration standards are not available.     

Use of a Programmable Pocket Calculator for Data Reduction in GPC: Calculation of Molecular Weights and Molecular Weight Distribution

Abstract

A short program was written for a pocket programmable calculator (HP-29C), to reduce data from a Gel Permeation Chromatogram. The output of this program consists of weight-and number-average molecular weights, polydispersity, and normalized weight distribution. All were uncorrected for dispersion. Mathematical approximation of the GPC calibration curve was made by exponential fit, also performed on the programmable calculator. The program and its application to NBS 706 and one narrow-molecular weight distribution (NMWD) polystyrene standards are presented. With slight modification, the program can be used on newer, more powerful calculators such as the HP-41C, on which dispersion correction subroutines could be performed.     

Dispersion-Compensated Calibration for Gel Permeation Chromatography: Theory and Utilization for Direct and Universal Calibration

Abstract

This paper describes the error involved in the utilization of nonmonodisperse polymer standards for the calibration of GPC columns. It also demonstrates that the computer technique developed by McCrackin (1) produces a calibration equation from poly-disperse standards that avoids this error. This equation, referred to as dispersion-compensated, can successfully be incorporated into the theory of universal calibration to remove the necessity of assuming infinite instrumental resolution. Furthermore, it is shown that only the calibration equation compensated for number-average molecular weights is a true universal form.     

Analysis of Low Molecular Weight Polymers with Gel Permeation Chromatography

Intrinsic viscosities and gel permeation chromatography (GPC) elution times were determined in toluene on commercially available standards of polystyrene (PSTY) and polymethyl methacrylate (PMMA) having M_n in the range of 10³ to 10⁵ and 10⁴ to 10⁶, respectively. In addition, elution times were determined on the discrete GPC peaks of dimer, trimer, tetramer, etc. as seen in lower molecular weight PSTY and PMMA. Intrinsic viscosities of oligomers were estimated by extrapolation of the Mark-Houwind-Sakurada equations determined from our data, and the results were used to establish a universal calibration curve over a wide range of molecular weights. A similar approach was taken by using literature data for the intrinsic viscosities of PSTY and PMMA in tetra-hydrofuran. It was verified by proton NMR that the universal calibration curve so constructed is useful at M_n, values as low as 300. No correction was necessary for chain length dependence of the detector response.     

Light-scattering Characterization of the Molecular Weight Distributions of Some Intractable Polymers

Recent developments of using laser light scattering (LLS) to characterize the molecular weight distribution f(M) of special polymers such as Kevlar, Tefzel, Teflon, branched epoxy clusters, gelatin, dextran, segment copolymers and polymer mixtures, are reviewed. The basic principle of combining static (classic) and dynamic LLS results is outlined. In dynamic LLS, the line-width (or the translational diffusion coefficient) distribution G(Γ) can be obtained from the precisely measured intensity–intensity time correlation function. The key problem is transforming G(Γ) to a corresponding molecular weight distribution f(M) is to establish a calibration between D (the translational diffusion coefficient) and M. Typical examples were used to illustrate different calibration methods, including the methods of using a series of narrowly distributed polymer standards with different molecular weights, using two or more broadly distributed polymer samples, and one broadly distributed polymer samples plus an additional experimental method (e.g. viscometry or size exclusion chromatography). The advantages and disadvantages of the LLS method are discussed by comparison with size exclusion chromatography. © 1997 John Wiley & Sons, Ltd.     

Determination of Molecular Weight of PDPS Modified Copolymers

Molecular weight (MW) determinations of polydiphenylsiloxane‐co‐polydimethylsiloxane (PDPS/PDMS), polydiphenylsiloxane‐co‐polymethylphenylsiloxane (PDPS/PMPS) and polydiphenylsiloxane‐co‐polymethyl(3,3,3‐trifluoropropyl)siloxane (PDPS/PMFPS) statistical copolymers by gel permeation chromatography (GPC), GPC coupled differential viscometer (GPC‐DV) and light scattering (LS) techniques have been compared and discussed. The MW obtained by GPC‐DV in the PDPS/PDMS and the PDPS/PMPS series agreed with that obtained by LS very well. In PDPS/PDMS copolymers, it was found that the MW obtained by GPC was much lower than that obtained by GPC‐DV and LS, as Ph₂SiO) content is higher than 50 mol%. In PDPS/PMFPS copolymers, the MW obtained by GPC was far different from that obtained by GPC‐DV and the deviation decreased with increasing Ph₂SiO) mol%. The α values of the copolymers can be explained by the structure of the polymer in tetrahydrofuran (THF). Based on the relatively soluble copolymers, not only the differential refractive index increments (dn/dc) of PMPS, PDMS and PMFPS homopolymers but also that of the PDPS homopolymer in THF could be calculated by their corresponding copolymers.     

Determination of the Molecular Weight Distribution of Polyethylene Terephthalate by Gel Permeation Chromatography

Abstract

The determination of the molecular weight distribution of polyethylene terephthalate by GPC at room temperature is described. The solvent used is o-chlorophenol-chloroform (1:9) and pure chloroform is used as eluent. K and alpha of the Mark-Houwink equation of polyethylene terephthalate and of polystyrene in this solvent system were obtained. It was shown that the universal calibration can be applied.     

Peculiarities of polyacrylamide analysis by aqueous GPC

Various commercially available stationary phases of gel permeation chromatography (GPC) were tested to determine their effectiveness in aqueous exclusion chromatography. It was found that controlled pore glass (GPG) is the most suitable material for the separation of polyacrylamides and poly(acry1amide-co-sodium acrylate), dextrans, and poly(sodium styrene–sulfonates) in 0.1M aqueous Na₂S0₄ solutions of ionic strength 0.3. A calibration curve was established by using broad molecular weight distribution polyacrylamide standards in a trial and error procedure. To avoid artificial oscillations on the evaluated distribution curves a cubic B-spline representation of the calibration curve was used instead of the conventional polynomials. By applying this system the solution instability of polyacrylamides was observed by GPC and is discussed because of its general importance to the applicability of indirect molecular weight determination methods for polyacrylamides. The effectiveness of aqueous GPC was demonstrated in an evaluation of thermal degradation measurements of polyacrylamides. Finally, the feasibility of universal calibration of aqueous GPC by means of poly(sodium styrene–sulfonates) was investigated. It is apparent that in spite of some problems concerning adsorption of the polymer universal calibration is a successful tool for calibrating aqueous GPC.     

Studies on Simultaneous Molecular Weight and Spreading Calibration in Steric Exclusion Liquid Chromatography

Abstract

Two improved methods of molecular weight calibration are described where simultaneously parameters of a symmetrical spreading function are obtained through the use of polymolecular molecular weight standards and of average retention volumes. In the first method a linear molecular weight calibration is assumed and the second method is based on a universal molecular weight calibration curve obtained with narrow MWD polystyrene standards.

The proposed methods have been tested using two polymolecular polystyrene standards confirming good convergence of the applied iteration procedures and giving very promising results.     

Data Treatment in Aqueous GPC with On-Line Viscometer and Light Scattering Detectors

Abstract

Gel Permeation Chromatography (GPC) is becoming a very powerful tool for polymer characterization with the coupling of mass detectors using viscometry and light scattering techniques. The triple coupling seems to be the best way since the light scattering detector gives absolute molecular weights and viscometric detection provides intrinsic viscosity, leading to absolute molecular weights through universal calibration and information on long-chain branching. However, instrumentation becomes more sophisticated, expensive and, simultaneously, very sensitive to several parameters which are not critical in classical GPC. Moreover, an on-line computer is required for data acquisition and appropriate software for reliable interpretation of chromatograms.

Our experiments were performed with a Waters Associates room temperature instrument in which a home-made continuous viscometer, using pressure transducers, and a light scattering detector (LALLS Chromatix-CMX 100) were inserted on-line between the column set and the refractometer. Data were interpreted through personal software written on HP9836 and PC-AT computers.

We describe, here, the behavior of some polymers in aqueous solutions, mainly those that are commonly used as calibration standards (polyethylene oxides, pullulans). Experiments were run using two different sets of columns (‘Ultrahydrogel’ from Waters Associates and ‘Shodex OH-Pak’ from Showa Denko K.K.) in several aqueous solvents, pure water or water with various salts (LiNO₃, NaNO₃, LiCl, NaCl, Na₂SO₄) at different concentrations. Intrinsic viscosities were determined through viscometric detection and weight average molecular weights through the LALLS detector, leading to a plot of universal calibration curves Log([ηl.M) versus elution volumes.     

Molecular weight analysis of pitches and polymeric pitches by gel-permeation chromatography

The technique of gel-permeation chromatography (GPC) has been developed as a method for measuring molecular weight distribution in pitch materials. Molecular weight calibration data were obtained from measurements made on GPC fractions collected from a standard pitch. By solubilization of the polymeric portion of pitch through a reduction with lithium in ethylenediamine, the molecular weight range for analysis was extended to in excess of 3000. Mass spectroscopy has been used to further analyze some of the GPC fractions. The GPC calibration data can be employed, with the aid of computer analysis, to determine quantitatively number-average molecular weights M?_n weight-average molecular weights M?_w, and molecular weight distribution D (= M?_w/M?_n) in pitch materials.     

Molecular Weight Distributions and Monodisperse Intrinsic Viscosity-Molecular Weight Equation of Silicone Elastomer

Abstract

The experimental curves of Gel Permeation Chromatography of methyl vinylsilicone elastomer polymerized by a basic catalyst and containing a small amount vinyl groups are given.

They are in consistent with the theoretical curves calculted from logarithmic-normal distribution function. Thereby, the molecular weight distribution of the samples determined belong to the logarithmic-normal distribution. With GPC, [η] and 〈M〉_n of the polydispersed sample the monodispersed [η]-M relationship of the methyl vinyl silicone elastomer was established.

This relation agrees with the monodispersed [η]-M relation established by Qian Ren-yuan, et al.⁽¹⁾     

Size Exclusion Chromatography Calibration Assessment Utilizing Coupled Molecular Weight Detectors

Abstract

This paper shows that the usual method of representing an SEC calibration curve by a single polynomial curve may often be inadequate with new high resolution columns. Data points wind about the fitted line. The significant magnitude and systematic nature of these deviations clearly appear when a plot of residuals is derived from the conventional calibration curve and expressed in terms of the percent error in molecular weight. The deviation of the calibration data from the fitted line was approximately 10% for the conventional molecular weight and intrinsic viscosity calibration curves. It became 20% for the universal calibration curve. LALLS and DV detectors were used together with the DRI detector to provide evidence that the calibration curve deviations were due to the column packings and not due to some other cause (e.g., vendor values of molecular weight). Use of a polynomial fit to a portion of the curve corresponding to the retention volume range of an unknown was used to show the significant improvement in results which occurred when the calibration variations were taken into account. At present, use of many individual narrow standards is necessary to elucidate the effect.     

Concentration effects and thermodynamic nonideality in gel chromatography

The dependence of the elution volume V_e on the concentration of injected polymer c in gel chromatography is presented for several systems including poly(styrene) and poly(methyl methacrylate) in a number of pure solvents with SiO₂-based gels. The linear dependence of V_e on c and K_av on c (where K_av is the distribution coefficient) is confirmed in the region of very low concentration. The slopes k of the straight lines increase with increasing relative molecular masses M of the polymer injected and with increasing thermodynamic nonideality of the system (as expressed by the second virial coefficient A₂). The significance of the slope of the GPC calibration curve for meaningful comparison of the concentration effects in various chromatographic systems is pointed out. A recently found correlation between k and (A₂M)γ is confirmed with a γ value of about 0.8. A possible theoretical explanation for the deviation of γ from unity is discussed. Finally, the influence of both the polymer concentration and the thermodynamic quality of the eluent on the resolution index of the chromatographic system is evaluated with the conclusion that thermodynamically poor solvents should be preferred for preparative GPC separations with very high loads.     

Characterization of Copolymers and Polymer Mixtures by Gel Permeation Chromatography

Abstract

Estimation of molecular weights from GPC data is complicated when the polymer sample consists of a mixture of homopolymers or of statistical copolymers with nonuniform compositions. This is because sizes of solvated polymer coils depend on solvent interaction with both the homo-and hetero-units of the copolymers and because the extent of solvation of different homopolymers can differ. The overall degree of solvation may change effectively with composition and use of a single “average” set of Mark-Houwink constants in calibration procedures will then produce false molecular weight data from the GPC data. A new molecular weight average, M _x, is defined to overcome this problem. This average can be determined from the GPC chromatogram and intrinsic viscosity of the sample in the GPC solvent. Mark-Houwink coefficients are not needed. M _x lies between M _w and M _z.     

The initiation of polymerization by organometallic compounds—IV. Initiator efficiency in polymerization of acrylonitrile by tetrakis(dimethylamido)titanium(JV)

A titrimetric method has been developed for following the removal of titanium-dimethylamine bonds during the polymerization of acrylonitrile by tetrakis(dimethylamido)titanium(IV) (T₄). The kinetics of the reaction of T₄ with monomer can be interpreted in terms of a sequence of insertion reactions in which dimethylamino ligands are successively removed from titanium. The calibration of a GPC instrument for measurement of the molecular weights of polyacrylonitrile is discussed. The results of initiator consumption and polymer molecular weight measurements are combined to allow the efficiency of initiation by T₄ to be assessed. Over the whole conversion range, titanium-dimethylamine bonds are broken in about 50 per cent excess over those used for polymerization. However, at high conversions more than one polymer chain is produced per titanium atom reacted.     

Comparison of number–average molecular weights calculated by GPC and membrane osmometry

Data are presented which show that when a polymer contains an appreciable amount of low molecular weight species below the diffusion limit of the osmometer membrane, the osmotic molecular weight, M?_n, is generally higher than the M?_n calculated from gel-permeation chromatography (GPC). Experiments were performed on samples of poly(vinyl chloride) (PVC) and high-cis polybutadiene polymers. Osmotic data were obtained in the usual manner, while GPC data were obtained using the universal calibration approach. It was found that when all polymer species below approximately 10,000 molecular weight were excluded from the calculation of M?_n by GPC, agreement in M?_n was obtained between membrane osmometry and GPC. The data obtained suggest that the choice of M?_n as measured by membrane osmometry in the calibration of the GPC should not be done casually, as the measured M?_n may not reflect the “true” value of that sample, especially when the polymer sample contains an appreciable amount of low molecular weight material.     

Viscosity Molecular Weight Determination of Polyadenylic Acid

Abstract

In this study viscosity measurements of polyadenylic acid (PolyA) in aqueous solution were carried out under different conditions. In the absence of any additives, the polymer degraded during flow through the capillary of a viscometer or when standing still. Degradation during the former was more severe. The degradation of polyadenylic acid can be prevented by addition of an electrolyte such as KCl to increase the ionic strength. However, in this case the deviation from linearity was still considerable at most ionic strength values. The best fit to the Huggins and Kraemer equations was obtained using a Tris–EDTA buffer solution with a final pH of 7.65. Estimation from intrinsic viscosity and weight-average molecular weight values gave k and α as 2.04 × 10^?5 and 0.89 from the equation η = kM ^α. The difference between Huggins (k ₁) and Kraemer (k ₁′) constants was close to 0.50 for all measurements.