An analytical solution to Tung's axial dispersion equation. Applications in gel permeation chromatography

Equations developed for correcting M_n, M_w, and [μ] for imperfect resolution are generally satisfactory. Choosing the appropriate instrumental spreading function is however a very difcult task. There is need for further research on this problem, in particular with polymer standards for which the DMWD or even M_z is known (in addition to M_n and M_w). A criterion for resolution in GPC which is based on a solution of Tung's axial dispersion equation has been proposed. The operation of GPC in recycle mode appears very promising. Equations have been developed to interpret data obtained in this operational mode. It is probable that a great deal of work will be done in this area in the very near future.     

Gel permeation chromatography: Dispersion effects on molecular weight monitor-installed gel permeation chromatograph

Computer simulation was carried out to examine the performance of a molecular weight (MW) monitor-installed gel permeation chromatograph (GPC), by taking account of the effects of limited column resolution according to Tung's phenomenological scheme. Efficiency of GPC fractionation was discussed also in the same light. For simulated GPC fractionation results of model polymers having log-normal distribution, various average MW's and MWD functions were calculated from the data obtained by the MW monitor method as well as the conventional MW calibration methods, and compared with the given true values. The MW monitor method generally tends to predict narrower distributions than the true ones, as opposed to the conventional calibration methods which usually predict broader distributions. For certain simple cases, semiquantitative relation between the extent of column resolution and these deduced average MW's was derived. The efficiency of GPC fractionation (as judged, for example, by the polydispersity of recovered fractions) is limited by such factors as fraction size, column resolution, and polydispersity of the original sample itself.     

Preparative gel permeation chromatography. I. Polypropylene

Preparative gel permeation chromatography was used to produce a number of polypropylene reference samples, within the molecular weight range of 10,000–600,000, from commercial materials. Some of these materials were degraded in a controlled manner to give base materials having suitable molecular weight characteristics. A procedure has been developed using a single preparative column packed with equal quantities of Styragel with nominal exclusion limits of 10², 10³, 10⁴, and 10⁵ nm. The volume of solvent for recovery was minimized by use of higher loading factors than in analytical GPC (some 2–20 times more polymer was thus fractionated in each experiment). Under these conditions the fractions first eluted were sharpest having polydispersities of about 1.5. First fractions, from different base materials, were characterized by analytical GPC, and those of similar molecular weight and polydispersity were combined to give the reference samples. Refractionation was necessary with the highest molecular weight base material because the first stage fractions were not sharp enough. Some of these fractions were recovered at elution volumes where much lower molecular weight material was expected. Comparison with results from the other base materials indicates that the primary cause of the spreading is not overloading. This spreading is explained in terms of slower partitioning of the larger molecules between the interstitial fluid and the gel particles.     

High-speed gel permeation chromatography. A study of operational variables

Systematic studies of operational variables affecting GPC separation using μ-Styragel of nominal porosity 10⁶, 10⁵, 10⁴, and 10³ Å are reported. The dependences of (1) flow rate, (2) injection volume, and (3) concentration on elution volume (V_e), the theoretical plate number (N), and peak width at half-height were examined. The values of V_e changed with changing (1), (2), and (3). The values of N were inversely proportional to the root of flow rate. The relation between sample load and N showed that lower concentration and larger injection volume were desirable for N than the opposite. The concentration dependence for high-speed GPC was significantly higher than classical low-speed GPC. The methods of minimizing the effects produced by the individual variables and the optimum operational conditions are discussed. Recommended operational conditions are as follows: flow rate, 1 to 2 ml/min; injection volume, 0.1 ml; sample concentration, below 0.4% (or if injection volume 0.5 ml, sample concentration below 0.1%).     

Calibration procedures in gel permeation chromatography

Procedures for the determination of the log molecular weight vs. elution volume calibration relation are reviewed for linear homopolymers. The calibration curve is readily established with narrow molecular weight distribution fractions. For broad molecular weight distribution fractions the peak molecular weight at the peak elution volume of a fraction's gel permeation chromatogram has to be calculated from average molecular weights. When well-characterised fractions of the polymer requiring analysis are unavailable, a calibration curve can be established by procedures which assume that the hydrodynamic volume of a polymer molecule in solution controls fractionation in gel permeation chromatography. These universal calibration procedures require information on Mark-Houwink viscosity constants or polymer unperturbed dimensions. The validity of hydrodynamic volume as the universal calibration parameter is discussed with special reference to the goodness of the solvent for a polymer and polymer polarity. Examples are given of the various calibration procedures which are employed in the determination of molecular weight distribution and average molecular weights for poly(methylmethacrylate), polyethylene and polyisoprene.     

A new instrument for preparative gel permeation chromatography

A preparative liquid-phase chromatograph was built for the purpose of obtaining sufficiently large quantities of very narrow fractions of different polymeric species, such as polystyrene, PVC, polybutadiene, and polyethylene. This apparatus allows the fractionation of approximately 20 g of polymer per day; the fractions so obtained have polydispersities of about 1.1 over a very wide range of molecular weights. Polydispersities of less than 1.01 were obtained after recycling of the sample.     

Applications of gel permeation chromatography. III. Formulation

This paper describes a general theory for the optimization of multicomponent blending to achieve a desired chromatographic distribution. A procedure for compound blending is also discussed, where optimum replication of both the chromatographic spectra and a second independent parameter can be achieved. Lastly, this theory is applied in a hypothetical example.     

Extraparticle diffusional effects in gel permeation chromatography. I. Theory

A systems approach is applied to the analysis of chromatogram resolution dispersion, or zone broadening, in gel permeation chromatography (GPC). Three possible sources of dispersion are considered; these are: the packed columns; the empty tubing between pump and columns, columns and detector, etc.; and the detection system, viz., the differential refractometer cell. It is shown that empty tubing can contribute significantly to the degree of dispersion and to skewness of elution curves and that this dispersion should depend on molecular weight of solute (polymer) and diameter and length of the tubing. The importance of dispersion in the empty tubing is compared with that in the packed columns and refractometer cell.     

A study of urea-formaldehyde resins using gel permeation chromatography

Gel permeation chromatography is a powerful technique for the investigation of molecular weight distributions of UF resins. Combinations of aqueous solvents with hydrophilic gels, or of organic solvents with organophilic gels, can be used to follow urea-formaldehyde reactions and also to analyse the condensates obtained. Useful additional information is obtainable by analysing a given material on several different gels of the same type but having different exclusion limits. Recent work has indicated that g.p.c. gels based on vinyl acetate can give excellent resolution of low molecular weight species in UF resins.     

Comments on data treatment in gel permeation chromatography

The effects of variables on treatment of the gel permeation chromatogram are reported. Variables investigated include (1) the molecular weight distribution of polymers for preparing the calibration curve, i.e., the logarithm molecular weight–elution count relationship, (2) nonlinearity of the calibration curve, and (3) fluctuation of the baseline. The deviation of the calibration curve prepared by the polymer having broad molecular weight distribution was evaluated in detail by assuming log-normal distribution function for the distribution. The polymer having a D value less than 1.3 was recommended for this purpose. Generally, the shape of the chromatogram is fairly different from that of the true molecular weight distribution curve when the calibration curve is not linear over the entire range of interest. By fitting polynomials to the calibration curve, the chromatogram was sufficiently converted to the molecular weight distribution curve. The apparent difference between them was removed. Slight deviation of the baseline from the true one gave rise to obvious error in the calculated molecular weight and its distribution, especially for the sample having a broad distribution.     

Infrared detection of polymers in gel permeation chromatography

A gel permeation chromatograph equipped with an on-line Grubb-Parsons infrared spectrometer is described. The versatility, specificity, sensitivity, and limitations of such an infrared detector are discussed with particular reference to spectrometer specification, eluent absorbance, and solute absorbance. A stable baseline is produced when this detector is operated at high temperatures, e.g., for the separation of polyethylene in o-dichlorobenzene at 135°C. Individual functional groups in a chemically inhomogeneous solute, such as a copolymer, may be monitored by repeated injections of the solute, changing the wavelength setting between separations. This procedure is illustrated with AB poly(styrene-b-t-butyl methacrylate) block copolymer in trichloroethylene at 35°C.     

Extraparticle diffusional effects in gel permeation chromatography. II. Experimental results

Experiments coupled with a systems analysis were conducted on chromatogram dispersion, or zone broadening, in gel permeation chromatography (GPC). Three components of a Waters Associates Model 200 chromatograph, each of which is a potential cause of dispersion, were considered; these are: the packed column, with extraparticle dispersion only; the empty tubing, between pump and columns, columns and detector, etc.; and the detection system, viz., the differential refractometer cell. Toluene solvent was used and the solutes whose dispersion was studied included orthodichlorobenzene (ODCB) and narrow-molecular-weight polystyrene standards having molecular weights of 900, 20,400, 51,000, 97,200, and 160,000. Nonporous glass beads, 50 μ in diameter, were used as column packing. Two diameters, 1 mm and 0.5 mm, of stainless steel tubing were studied. In addition to the usual rectangular pulse sample injection, a step input mode for solute introduction was also used. The empty tubing was found to contribute significantly to the degree of dispersion and to skewness of elution curves. Anomalous bimodal characteristics of the elution curves were also observed which could only be ascribed to the empty tubing. These phenomena depended markedly on parameters such as tube diameter and length, and solute concentration and molecular weight. Dispersion in the packed column, although important, was found to be symmetrical (Gaussian) and less sensitive to these parameters than in the empty tubing, especially with respect to molecular weight. Dispersion in the cell was believed to be insignificant relative to the packed column and empty tubing.     

Universal calibration assessment in aqueous gel permeation chromatography

It was the objective of this paper to assess the applicability of the universal calibration method to aqueous GPC/SEC with nonionic and anionic polymers using the Viscotek differential viscosity detector. Three water-soluble polymers—polyacrylic acid, dextran, and polyethylene oxide—were chromatographed using four Ultrahydrogel^TM columns with 0.3 M NaCl and 0.1M KH₂PO₄ as the mobile phase adjusted to pH 7. Three distinct calibration curves were obtained. Upon addition of 10% methanol, a reasonably good universal calibration curve was obtained. However, quantitative analysis of the data exhibited about 5% deviation in average M_w and M_n for sodium polyacrylate as calculated from the single curve as opposed to about 40% when calculated from the composite curve. The applicability of three theoretical models for the universal calibration method was assessed, and a recommendation was made for future work. © 1993 John Wiley & Sons, Inc.     

A generalized method for correcting instrument spreading in gel permeation chromatography

A general method of chromatogram correction for skewed instrument spreading in gel permeation chromatography is presented. The correction method is so general that there is no restriction on the shape of the spreading function. It admits nonsymmetric, non-Gaussian as well as nonconvolution type. Aspects of solution techniques are discussed and an illustrative example is given to elucidate the method.     

Fractionation of linear polyethylene with gel permeation chromatography. IV

Reproducibility was examined on the GPC fractionation of linear polyethylenes. The experiences over the period of two and a half years were used. Calibration was done with the same batches of narrow distribution polystyrene standards. A control sample of broad-distribution polyethylene was run at each calibration. The reproducibility over ten calibrations with this control was in terms of standard deviation of ca. ±10% for the number-average and ca. ±15% for the weight-average chain length. The fractionation data of 36 commercial resins were corrected by using the control samples as an additional standard. The correction was very effective in decreasing the scattering of the data in the intrinsic viscosity–molecular weight plot, especially when the viscosity average was used for the molecular weight expression.