Universal calibration in GPC

The M[η]-elution volume calibration curve for gel-permeation chromatography (GPC) is based on the implicit assumption that the hydrodynamic volume of a solvated polymer species in the GPC columns is that which pertains at infinite dilution. This is not true of highly solvated high molecular weight fractions and results in apparent failure of this calibration in some instances. A model is presented to estimate hydrodynamic volumes of polymers at finite concentrations. The parameters required are polymer concentration, molecular weight, amorphous density, and the Mark-Houwink constants for the particular polymer–solvent combination. The calculated log (hydrodynamic volume)–elution volume relation provides a universal GPC calibration. The model accounts for the occasional shortcomings of the infinite dilution calibration and is essentially equivalent to it in noncritical cases. The use of the proposed calibration method is illustrated.     

Gel permeation chromatography of polyethylene: Effect of long-chain branching

The effect of long-chain branching on the size of low-density polyethylene molecules in solution is demonstrated through solution viscosity and molecular weight measurements on fractionated samples. These well-characterized fractions are analyzed by gel permeation chromatography (GPC), and it is shown that the separation of the polymer molecules by this technique is sensitive to the presence of long-chain branching. By using fractions of branched polyethylene possessing differing degrees of branching, one observes that a single curve is adequate in relating elution volume to molecular weight. This calibration curve is applied in the GPC analysis of a variety of commercial low-density polyethylene resins and it is shown, by comparison with independent osmometric and gradient elution chromatographic data, that realistic values for molecular weight and molecular weight distribution are obtained. The replacement of molecular weight M by the parameter [η]M as a function of elution volume, leads to a single relationship for both linear and branched polyethylenes. This indicates that GPC separation takes place according to the hydrodynamic volumes of the polymer molecules. The comparison of data for polyethylene and polystyrene fractions suggests that this volume dependence of the separation will be observed for other polymer–solvent systems.     

SIMULTANEOUS CALIBRATION OF MOLECULAR WEIGHT SEPARATION AND COLUMN DISPERSION OF SEC WITH CHARACTERIZED POLYMER STANDARDS

With the aid of the theoretical relationship between the calibration relation of a SEC column for the monodisperse polymer species under ideal working condition and the effective relations between the molecular weight and the elution volume for characterized polymer samples, a computational procedure for simultaneous calibration of molecular weight separation and column dispersion is proposed. From the experimental chromatograms of narrow MWD polystyrene standards and broad MWD 1,2-polybutadiene fractions the spreading factors of a SEC column was deduced by the proposed method. The variation of the spreading factor with the elution volume is independent upon the polymer sample used.     

用多分散高聚物标样作凝胶色谱的分子量分离和扩展效应同时校准

根据凝胶色谱柱在理想工作条件下单分散高分子组分的校准关系与多分散试样的实效关系之间的理论联系,建议了一种简单的觅数方法,同时作凝胶色谱柱的分子量分离和扩展因子的校准。用本法从窄分布的聚苯乙烯和宽分布的1,2-聚丁二烯级分的实验谱图得到的所用凝胶色谱柱的扩展因子与淋出体积间的关系相互重合,与试样种类无关。     

Gel-permeation chromatography: Examination of universal calibration procedures for polydimethylsiloxane in a poor solvent

Various procedures for universal calibration in gel-permeation chromatography with polystyrene gels are examined for polystyrene and polydimethylsiloxane fractions. For o-dichlorobenzene at 138°C, experimental intrinsic viscosity–molecular weight data show that the Mark-Houwink exponents are 0.70 and 0.57 for polystyrene and polydimethylsiloxane, respectively. In principle, this difference permits a distinction between the various polymer size parameters proposed for universal calibration. An interpretation of the experimental polydimethylsiloxane calibration for o-dichlorobenzene at 138°C requires a consideration of errors in average molecular weights and errors arising from the use of average molecular weight instead of peak molecular weight. When calibration procedures utilizing hydrodynamic volume and unperturbed dimensions are examined, the difference between them is comparable with experimental error. If the Flory-Fox viscosity expression is employed, the perturbed end-to-end distance (or radius of gyration) and the hydrodynamic volume give equivalent universal calibrations. The experimental data are sufficiently accurate to show that the perturbed dimension determined with the Ptitsyn-Eizner relation does not give an adequate universal calibration.     

一组线型聚苯乙烯和星形支化聚苯乙烯的凝胶色谱与热场流分级方法的比较

本文应用热场流分级方法,在两种不同的场强下(△T=30℃、△T=50℃),测试了一系列窄分布聚苯乙烯标样和星形支化聚苯乙烯的淋出体积V_r和分子量M的依赖关系。星形支化物的臂数不同,但臂的分子量相同,上述样品进行了GPC测试,实验表明,由TFFF得到的支化的与线型聚苯乙烯在V_r～M关系上的差别大于GPC的结果,表明链结构对扩散系数的影响大于对分子体积的影响。     

Solution properties of ion-containing polymers in polar solvents

The placement of ionic groups within the molecular structure of a polymer produces marked modification in physical properties. A large number of studies have been performed on these ion-containing polymers, but few have focused on the effects of anion–cation interactions (i.e., counterion binding or ionization) on hydrodynamic volume, especially as the molecular structure of the solvent and nature of counterion are varied. In this study changes in hydrodynamic volume are followed through reduced viscosity measurements as a function of the abovementioned molecular parameters. The dilute solution properties of various polyelectrolytes that contain sulfonate and carboxylate groups were investigated as a function of the counterion structure, charge density, molecular weight, and solvent structure. The polymeric materials were selected because of their specific chemical structure and physical properties. In the first instance a (2-acrylamide-2 methylpropanesulfonic acid)-acrylamide-sodium vinyl sulfonate terpolymer was synthesized and subsequently neutralized with a series of bases. Viscometric measurements on these materials indicate that the nature of the cation affects the ability of the polyelectrolyte to expand its hydrodynamic volume at low polymer levels. The magnitude of the molecular expansion is shown to be due in part to the ability of the counterion to dissociate from the backbone chain, which, in turn, is directly related to the solvent structure. The changes in solution behaviour of these inomers lend support for the existence of ion pairs (i.e., site binding) and ionized moieties on the polymer chains. Measurements performed in a variety of solvent systems further confirm this interpretation. In addition, and acrylamide-sodium vinyl sulfonate copolymer was partially hydrolyzed with sodium hydroxide to study the effect of varying the charge density at a constant degree of polymerization and counterion structure. The results show that the charge density has a significant effect on the magnitude of the reduced viscosity and dilute solution behaviour. These observations, made in aqueous and nonaqueous solvents, are related to the interrelation of hydrodynamic volume, counterion concentration, and site binding. Again the controlling factor is the degree of site binding of the counterion onto the polymer backbone. Finally, we observe that the increased hydrodynamic volume affects viscosity behavior beyond the polyelectrolyte effect regime. If the average charge density on the macromolecule is relative high and/or the molecular weight is large (≥ 10⁶) sufficient intermolecular interactions will occur to produce rapid changes in reduced viscosity.     

COMPARISON OF GPC AND THERMAL FIELDFLOW FRACTIONATION METHODS FOR LINEAR AND STAR BRANCHED POLYSTYRENE SAMPLES

The Thermal Field-Flow Fractionation (TFFF) method was used to determine the elution volumeof a series of star branched polystyrene having different number of arms but the same arm molecularweigh and polystyrene standards with narrow distribution whose molecular weight ranged from5.0×10~4 to 8.6×10~5. Results were obtained by measuring at two temperature difference (△T=30℃and △T=50℃in THF. The same star branched samples were measured by means of GPC method.Comparison of Vr-Mrelationships obtained from TFFF and GPC showed that the displacement of V_r-M curves for star and linear polystyrene is larger than that in GPC. This difference is caused by theentirely different mechanism of separation for these two methods. As the controlling factor is hy-drodynamic volume of the polymer chain in solution for GPC, it is the diffusion coefficient of polymermolecules for TFFF. The experimental results indicate that the influence of variance of chain struc-ture on diffusion coefficient is stronger than that on the hydrodynamic volume and that TFFF tech-nique may be used as a method for characterizing branching of polymer molecules. For this pur-pose a proper theoretical model and more accurate experiments are needed.     

Concentration effects in gel permeation chromatography : IV. Contribution of viscosity phenomena and macromolecular expansion

The changes in elution volumes with the changes in the concentration of an injected polymer solution are caused by several contributing effects. Under model conditions, it is possible to assume only the effect of a viscosity gradient in a zone moving along the column and the effect of the concentration dependence of the hydrodynamic volume of a macromolecular coil. The non-Gaussian shape of the zone and the dependence of the width of the elution curve on concentration are factors that complicate the theoretical treatment of concentration effects. The described physico-chemical model allows to evaluate the ratio of mentioned two contributions in the concentration dependence of elution volumes. According to this model, the contribution of the concentration dependence of the hydrodynamic volume does not exceed about 20% of the total change in elution volume with the varying concentration under real experimental conditions. The efficiency of the columns used and the total injected volume of the polymer solution affect this ratio only negligibly. It is obvious from a comparison with earlier results that these conclusions are not fundamentally changed even by the revised model of the concentration dependence of the swelling factor.     

Comments on exclusion of polymer chains from small pores and its relation to gel permeation chromatography.

Some criticisms of our theoretical treatment of the partial exclusion of flexible-chain polymers in solution from cavities of macromolecular size and its application to gel permeation chromatography are examined. In other discussion, it is confirmed by simple reasoning that the identification, explicit or implicit in various studies, of the mean projection of a polymer molecule onto a line as a characteristic dimension governing the extent of permeation of simple pores does not depend on specific molecular models. Our previous calculation of permeation by certain random-flight branched-chain species is shown to lead, incidentally, to the mean projection for these structures. From relations between the mean projection and the hydrodynamic volume of a molecule, it appears that the product of intrinsic viscosity and molecular weight is not a common calibration factor for elution of all molecular species from a gel chromatographic column, but theory and experience do support the validity of this correlation among solutes with similar molecular architecture.     

Molecular characterization of poly(diisopropyl fumarate) by the absolute calibration method in molecular exclusion chromatography (GPC)

The present work demonstrates that it is possible to obtain the parameters K and a of the Staudinger-Mark-Houwink relationship between the intrinsic viscosity [η] and the molecular weight M of a polymer by applying the absolute method of exclusion chromatography to samples of poly (diisopropyl fumarate). The procedure is based on deducing the relationship between molecular weight and elution volume V from chromatographic runs of a stoichiometrically labeled polymer sample with a broad molecular weight distribution. By using double detection it is possible to obtain the relationship f(V)/h(V) = M(V)/M_n = exp (A-BV)/M_n where M_n is the osmotically determined number average of the molecular weight of the eluted polymer while f(V) and h(V) are the normalized elution curves obtained by the use of the polymer mass detector and the label detector respectively. A and B are the parameters of the calibration curve, i.e., the relationship between M and V which together with the intrinsic viscosity and the elution curves of several samples of the polymer allows us to obtain the relationship between [η] and M. The results have been verified with chromatographic data through the use of the universal calibration concept.     

Simulation of GPC‐Distribution Coefficients of Linear and Star‐Shaped Molecules in Spherical Pores

Simulations of the distribution coefficients of linear and star‐shaped polymers in spherical pores were performed in order to predict the GPC‐elution behavior of star‐shaped polymers relative to that of linear polymers. Self avoiding walks were generated on a tetrahedral lattice to simulate good solvent conditions. It was found that neither the molecular weight nor the mean squared radius of gyration of the polymer serves as a universal factor to determine the distribution coefficient. However, the calculated distribution coefficients correlate well with the calculated hydrodynamic radii even for different topologies. For molecules at same elution volume the ratios of molecular weights of star and linear polymer agree well with exact calculations for Gaussian chains. These ratios are nearly independent of pore geometry (spherical or cylindrical).     

Influence of reptation on localized diffusion in crystallizing polymers

Crystalline texture in polymer spherulites appears to be determined in part by interplay during solidification between interface morphology and the diffusion of species segregated at crystal growth fronts; these species are molecules of lower molecular weight (fractionation) or molecules of stereoirregular structure. Early discussions of this behavior were based upon assumption of a single diffusion coefficient in each case. However, it is now known that, because of reptation, each molecule in a polymer melt diffuses with a diffusion coefficient dependent on its individual molecular weight. In this paper, the influence of reptation upon concentration profiles and diffusion ranges is examined. It is shown that such influence is slight when segregated species have relatively narrow distributions of molecular weight, such as are typical when segregation involves fractionation or is mostly confined to fractionated stereoirregular species blended with crystallizable host polymer. With broad distributions, however, concentration profiles are significantly altered and long segregated molecules dominate morphologically important behavior. Meaningful average diffusion ranges can often be derived and related to appropriately averaged molecular weights of participating molecules. Morphological implications of the various results are outlined.     

Size exclusion chromatography of branched polymers: Star and comb polymers

Monte Carlo simulations were conducted to estimate the elution curve of size exclusion chromatography (SEC). The present simulation can be applied to various types of branched polymers, as long as the kinetic mechanism of nonlinear polymer formation is given. We considered two types of detector systems, (1) a detector that measures the polymer concentration in the elution volume to determine the calibrated molecular weights, such as by using the differential refractive index detector (RI), and (2) a detector that determines the weight‐average molecular weight of polymers within the elution volume directly, such as a light scattering photometer (LS). For polydisperse star polymers, both detector systems tend to give a reasonable estimate of the true molecular weight distribution (MWD). On the other hand, for comb‐branched polymers, the RI detector underestimates the molecular weight of branched polymers significantly. The LS detector system improves the measured MWD, but still is not exact. The present simulation technique promises to establish various types of complicated reaction mechanisms for nonlinear polymer formation by using the SEC data quantitatively. In addition, the present technique could be used to reinvestigate a large amount of SEC data obtained up to the present to estimate the true MWD.     

Ein verfahren zur eichung der gelchromatographie (GPC) mit präparaten beliebiger,bekannter molekulargewichtsverteilung

If, in GPC calibration, the mean elution volume (or centre of gravity volume) of the elution curves obtained with monomolecular samples is used, the mean elution volume of a polymolecular mixture is a weight-average. According to the calibration curve, a molecular weight average can be attributed to the mean elution volume. For the special case of a logarithmic-linear calibration curve, this is the geometric (weight) mean of the molecular weight. Thus one can perform broad-standard calibration of GPC without interference by column dispersion. The potential application for non-linear calibration curves is discussed. It is considered how calibration functions for the higher moments of the monomolecular elution curves could be determined and how universal calibration should be performed if the standards are polydisperse relative to hydrodynamic volume. Absolute determination of polydispersity becomes possible with an additional z-detector.     

Analysis of the influence of interdetector volume on local calibration in size exclusion chromatography with dual multiangle-light-scattering/concentration detection

A comparison of the s- and w-detections of molecular weight, a necessary condition for precise determination of interdetector volume in size exclusion chromatography of polymers with the dual light scattering--concentration detection, is examined. From the theoretical analysis for a polymer with the log-normal molecular weight distribution it follows that the error in determination of the local calibration, i.e., of a logarithmic dependence of molecular weight on elution volume obtained by the s-detection, from the known dependence of radius of gyration on elution volume and of molecular weight on the radius of gyration, remains linear and is slightly shifted with respect to that obtained by the w-detection (dual detection giving the weight-average molecular weight) towards higher molecular weights, the difference being below the experimental error. It also follows that the error in the slope of local calibration found by the w-detection is given by the ratio of the error in interdetector volume and the variance of the elution curve. This is demonstrated on several polymer samples with symmetric elution curves of polymer samples differing in polydispersity indices. The range of this rule depends on the broadness and symmetry of elution curves. The precision of the interdetector volume determination depends therefore strongly on the Mw/Mn ratio of the sample.     

Hydrodynamic Fractionation of Macromolecules. I. A Simple Theory

A new mechanism for separation in gel permeation chromatography (CPC) or gel filtration has been developed based upon the postulate that flow occurs through the gel phase. On the basis of the hydrodynamic nature of the separation mechanism, the new name Hydrodynamic Fractionation is proposed. A theory has been formulated for the case of equal pore size in the gel phase and equal sized spaces between the beads. This theory predicts the elution volume vs molecular weight curve. The flow-rate dependence of the separation peaks is investigated.

The theoretically predicted relationship between molecular weight and elution volume compares very well with the gel permeation experiments using glass beads as packing probably because these packings correspond most closely to the assumptions in the theory. In the cross-linked polymer packing where a large distribution of pore sizes exists the theory does not fit well; however, it does predict the general shape of the curve. The flow-rate dependence of the separation peaks is experimentally the same as qualitatively predicted. Also the experimental findings of equilibrium experiments were correlated with the corresponding GPC data using the present theory.     

Cationic polymerization of styrene by acetyl perchlorate: Molecular weight distribution of polystyrene and nature of the propagating species

To clarify the nature of the propagating species in cationic polymerization of styrene catalyzed by acetyl perchlorate, the molecular weight distribution of the polymer was investigated under various conditions. The molecular weight distribution curve for the polymer obtained in methylene chloride at 0°C showed a double peak phenomenon. This suggests that two or more kinds of propagating species participate simultaneously in the propagation reaction. The weight fraction W(H) of the polymer corresponding to the higher molecular weight peak increased with increasing polarity of the solvent. W(H) decreased when the concentration of the ionic species was increased either by an increase of the catalyst concentration or by the addition of the common salt such as tetra-n-butylammonium perchlorate. On the other hand, the position of the peak in the molecular weight distribution curve was independent of polymerization conditions. It was concluded that the higher molecular weight part of the polymer was produced under conditions for conductive to dissociation of the propagating species and the less dissociated propagating species was responsible for the lower molecular weight part of the polymer.     

Method of calibrating gel permeation chromatography with whole polymers

Column systems for gel permeation chromatography are usually calibrated by eluting a series of sharp polymer fractions of known molecular weights and by correlating their elution volumes with molecular size or weight. A different method for calibration is proposed in which only one polymer sample, with a broad, well-characterized molecular weight distribution, is used. The cumulative distribution and the integrated, normalized GPC chromatogram are successively superimposed, and molecular weights and corresponding elution volumes are correlated. It is found that calibration curves obtained in this manner show a definite curvature. A possible explanation and correction for this behavior is given, based on the concentration dependence of elution volumes.