Concentration Dependence of Elution Volumes in size Exclusion Chromatography of Polymer Molecules. II. Poly(Methyl Methacrylate) in Ideal Solvent

Abstract

The concentration effects occurring in size exclusion chromatography of polymer molecules have been investigated for the case of elution of macromolecules in an ideal solvent. It is shown that increases in the elution volumes with polymer concentration are detectable with the high efficiency columns employed. The concentration dependence of elution volumes is much lower than that previously determined with good solvents. The main factor contributing to the shift of elution volumes seems to be the viscosity of the polymer solutions, but another effect appears also to be present. This latter effect possibly suggest that in semi-concentrated solutions of polymer molecules in ideal solvents a continuous contraction of the polymer chains occurs, below their unperturbed dimensions, similar to that happening when the temperature of ideal solutions is decreased. More investigation on this point is needed. the ideal solutions is increased. Further investigations will be carried out to clarify this point.

In conclusion, the concentration dependence of polymer elution volumes in SEC has been found to be detectable also in a thermodynamically ideal solvent, though it is much lower than that observed in good solvents. In such a system, the main cause of the shift of elution volumes appears to be the viscosity of the polymer solutions, but a small additional contribution is also seen to be present. At the moment, it seems not possible to evaluate with certainty the origin of this latter contribution, especially in the absence of data on the macromolecular conformations in semi-concentrated solutions in ideal solvents.     

Quantitative Prediction of Concentration Effects in Steric Exclusion Chromatography

Abstract

A semiempirical model, based on a previous one quantitatively describing the dependence of the elution volume, V(c_A), on the concentration of injected polymer, c_A, in exclusion chromatography (SEC) at dilute solutions, has been developed. In the derived equation, concentration effects are mainly governed by the Huggins' coefficient, k_A, and by the quadratic coefficient in the polynomial expansion of the reduced specific viscosity, k_A. Because of the incertitudes on reliable k_A and k_A' values, these are respectively removed from the model through she Imai's equation and the empirical correlation k_A' + 0.122=k_A, here obtained. Thus, A predicted elution volumes besides polymer concentration only depend on the polymer intrinsic viscosity and on its unperturbed dimensions constant,K_θ. The polymer concentration range of model applicability is up to Jerately diluted polymer solutions, as a comparison between predicted and experimental elution volumes for diverse literature systems shows.     

Concentration Effects in Sec for Polymer/Polymer/Solvent Systems

Abstract

A model quantitatively describing the experimental shifts in elution volumes of polymeric solute A in the presence of another polymer B is developed. The concentration-dependent shrinkage of A coils has been evaluated from the intrinsic viscosity displayed by polymer A in the ternary solution formed by itself at c_A concentration + polymer B at c_B concentration + solvent. Resulting concentration effects depend on both polymer concentrations (c_A and c_B), on the intrinsic viscosities of both polymers in the solvent (|η|A and |η|B), on the Huggins' coefficients k_A and k_B, and on the quadratic concentration coefficients in the polynomial expansion of ηsp/c, namely k^′ _A and k^′ _B. Predicted elution volumes are compared with experimental ones for two different types of literature systems: those studying polymer A elution at diverse c_A concentrations in eluents consisting of mixtures of polymer B + solvent and those in which polymer A + polymer B mixtures are injected at once in the pure solvent used as eluent. In order to eliminate experimental uncertainties about k_i and k^′ _i (i=A, B) values, applied k^′ _i values were those obtained from the empirical correlation k^′ _i + 0.122 = k_i ² whereas k_i ones were obtained from Imai's equation.     

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.     

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.     

Development of gel permeation chromatography for polymer characterization. II. Universal calibration

GPC appearance volumes have been determined for a series of linear polyethylene, polystyrene, and polybutadiene fractions (M_w/M_n < 1.1) in trichlorobenzene at 130°C. and for the latter two series in tetrahydrofuran at 23°C. A polymer-type independent relationship between appearance volumes and the equivalent hydrodynamic radii of the polymer molecules has been demonstrated. The equivalent hydrodynamic radius is calculated from intrinsic viscosity data. It is proposed that this relationship can be used to construct a universal GPC calibration curve for polymers that assume a spherical conformation in solution. Methods for applying the universal curve to the determination of molecular weight averages and molecular weight distribution are described. In addition, a method is outlined by which the universal calibration curve can be empolyed for determining number-average Mark-Houwink constants from polydisperse samples.     

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.     

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).     

Characterization of Macrocycles Formed from Cationic Copolymerization of Tetrahydrofuran with Propylene Oxide by GPC and GC/MS

Abstract

The copolymers obtained from a THF/PO-BF₃O(C₂H₅)₅-glycerin-ethylene chloride cationic copolymerization system were analyzed by GPC. The chromatograms show two groups of peaks, one located in the high molecular weight (MW) region and the other in the low MW region. In order to examine the low MW region in detail, the oligomers were separated from the copolymer by distillation under high vacuum, and further identified by GC/MS, NMR. It was found that these were an expected series of cyclic oligomers, i.e., PO:THF crown ethers: 1:2, 3:1, 2:2, 1:3, 3:2, 2:3, 1:4, 4:2, 3:3, 2:4, 4:3. Through the study of the elution behavior of these crown ethers in toluene with GPC, a linear relationship of the elution time against the logarithm of their MW's was obtained. Under the same GPC conditions, the relationship between the elution time and MW of n-alkanes was also determined. It was found that the hydrodynamic volume of the crown ethers is less than that of the n-alkanes with same MW, and they can be treated as homologous series as in the case of n-alkanes on the study of GPC elution behavior ignoring the influence of PO:THF composition ratios in crown ether rings.     

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.     

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.     

Solvation and Adsorption Effects in Gel Permeation Chromatography

Abstract

Saturated hydrocarbons are generally eluted according to molecular volumes in gel permeation chromatography (GPC). Other compounds, containing polar groups such as hydroxyl and carbonyl groups, deviate from the molecular volume/elution count relationship which is prepared using saturated hydrocarbons. The deviation is more or less observed regardless of the kinds of eluents. In this paper, this problem is investigated in detail with respect to infrared(IR) and proton magnetic resonance(NMR) spectra, and concentration dependences of peak heights and elution volumes in GPC. IR and NMR spectra reveal that alcohols, ketones and esters are strongly solvated by eluent molecules such as chloroform and tetrahydrofuran(THF). The solvation effect leads to faster elution for these compounds than expected for aliphatic hydrocarbons. On the other hand, the concentration dependences of elution counts and peak heights prove the adsorption of amines on polystyrene gel in chloroform. In fact, the elution rates of amines and polychlorides are retarded. In the case of aliphatic carboxylic acids, the elution mechanism is more complicated: association and adsorption effects would be overlapped.     

Excess Molar Volumes and Partial Molar Volumes for Binary Mixtures of Water With 1,2-Ethanediol, 1,2-Propanediol,and 1,2-Butanediol at 293.15, 303.15 and 313.15 K

Abstract

From dilatometric method at 293.15,303,15, and 313.15K for binary mixtures of water and 1,2-alkane diols, the excess molar volumes, V^E and the partial molar volumes, V _i of both components at 293.15 K have been obtained as a function of mixtures composition. Excess molar volumes were calculated and correlated by a Redlich-Kister type function in terms of mole fraction. The partial molar volumes have been extrapolated to zero concentration to obtain the limiting values at infinite dilution, V ⁰ _i . All mixtures showed negative values and decreases with the chain length of diols. The values become less negative with increasing temperature. The results are explained in terms of dissociation of the self-associated diol molecules and the formation of aggregates between unlike molecules.     

On-line viscometry combined with gel permeation chromatography. I. Instrumental calibration and testing with linear polymers

Gel permeation chromatography (GPC) was combined with flow time measurements on the eluent to provide both the distribution of hydrodynamic volumes and the distribution of intrinsic viscosities in linear polymers. Standard polystyrene samples were used to establish a universal hydrodynamic volume calibration as well as the zone spreading and viscometer transfer line tailing parameters. Viscometry data are particularly helpful in establishing the zone spreading parameters and the calibration curve at very high molecular weights. The results were applied to measurements on samples of linear polybutadiene and polyvinyl acetate. Agreement between values of M _w from GPC with those obtained by light scattering confirmed the universal calibration principle.     

Concentration effects in gel-permeation chromatography

Peak elution volume in gel-permeation analysis of polymers depends on sample concentration as well as molecular weight. Elution volume is related to the logarithm of the hydrodynamic volume of the solvated polymer species. The hydrodynamic volume of a given species is, in turn, inversely related to the concentration. Since molecular weight and concentration are interacting variables, the elution volume–molecular weight relation is not uniquely determined. A model is presented which accounts quantitatively for concentration effects, using parameters which are available a priori. The data required are polymer molecular weight, concentration, and density and the Mark-Houwink relation for the particular polymer-solvent combination.     

Streaming birefringence. VII. Influence of the intermolecular hydrodynamic interaction on the viscosity and streaming birefringence of polymer solutions

The cavity model used in the theory of dielectrics was applied to hydrodynamics to calculate the force exerted by a system of soft dumbbells on a reference dumbbell in a hydrodynamic field. The influence of this force on the viscosity and flow birefringence and its dependence on both the concentration and velocity gradient were calculated. The system of equations has a real solution only for values of β = M[η]η₀γ/RT which are smaller than a critical value rapidly decreasing with increasing concentration. At zero concentration the results obtained agree with the theory of a single isolated dumbbell model. The calculated Huggins constant is k′ = 0.4. The extinction angle is connected with the relative viscosity very nearly as derived from experiments. However, the theory fails at higher concentrations and gradients yielding an increase in viscosity with the gradient and infinite zero-shear viscosity for the concentration c = 2.5/[η].     

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.     

Proposed GPC and intrinsic viscosity analyses of randomly crosslinked polymers having primary distributions of the schulz-zimm form

A mathematical treatment is presented for the gel-permeation chromatographic and intrinsic viscosity behavior of randomly crosslinked polymers having primary molecular weight distributions of the Schulz-Zimm form. Kimura's serial solution of the integro-differential equation derived by Saito for randomly crosslinked polymers is employed for the distribution function. The intrinsic viscosity of a molecule containing i crosslinks is assumed related to that of a linear molecule of the same number of units through [η]_br/ = g_i^½[η]_l where g_i = (R_br²)_i/R_l² = {[1 + (i/6)]^½ + (4i/3π)}^?½. R_brand R_l denoting the root-mean-square radii of gyration of branched and linear chains of the same mass. It is also assumed that GPC elution is controlled by the hydrodynamic volumes of the molecules. Representative calculation results are displayed for polymers with a narrow primary distribution and the “most probable” primary distribution. Results for the latter polymers are compared with those previously obtained by a somewhat different mathematical approach.     

Atypic Gel Permeation Chromatography of Alcohols

Abstract

The elution behaviour of alcohols in the systems Bio Beads SX-8/dichloromethane and Sephadex LH-20/dichloromethane is investigated. On Bio Beads SX-8 the elution volumes are lower than expected for normal GPC behaviour, which is perhaps due to hydrogen bonding in solution. On Sephadex LH-20 adsorption takes place by means of hydrogen bonding, which can be used for very selective separations.