Two‐dimensional chromatography as a tool for studying band broadening in size‐exclusion chromatography

Comprehensive 2‐D size‐exclusion chromatography (SEC×SEC) has been realized. SEC×SEC is not a useful technique for characterizing complex polymers. However, it is potentially an elegant tool to study band‐broadening phenomena. If narrow fractions can be collected from the first dimension, the band broadening in the second dimension is only due to chromatographic dispersion. This would allow a clear distinction to be made between chromatographic band broadening (column and extra‐column) and SEC selectivity (band broadening due to sample polydispersity). In comparison with MALDI‐MS, SEC×SEC allows the study of polymers across a much broader molar‐mass range.     

Evaluation of packed capillary liquid chromatography columns and comparison with conventional-size columns

Apart from extracolumn effects peak dispersion in liquid chromatographic columns is caused by the column inlet, the packed bed, and the column outlet. A strategy applicable for independent evaluation of the individual sources of column band broadening was developed on the basis of the linear extrapolation method (LEM). This method was applied to compare the performance of packed capillary LC columns from various commercial suppliers with conventional-size columns. The columns differed widely in their performance with respect to peak shapes and widths for standard substances. The capillary columns were found well packed, but in some cases overall performance would benefit from improving the design of the area between the packed bed and the connecting capillaries, containing frits as well as dead volumes.     

Effect of steric exclusion on the separation of proteins by hydrophilic size-exclusion chromatography

On the basis of studying the retention and band broadening of proteins on the TSK SW column, diffusion coefficients (Ds) of solute in stationary phase were obtained which elucidate the hydrodynamic process of chromatographic resolution of proteins by hydrophilic size-exclusion chromatography (SEC). After calculating the correlation between Ds and the molecular weight of the solute, the molecular dimensions of proteins in the process of chromatographic separation can be predicted. Deviations in diffusion coefficient of a protein from the calculated value reflect differences of measured molecular dimensions from molecular volumes predicted from the calibration curve of the SEC column. This study illustrates a convenient method for estimating the purity of proteins by SEC. Deviations from 2 lambda dp (where dp is the particle diameter) in the intercept of the theoretical plate height (H) versus flow-rate (U) curve from the band broadening equation H = CsU + 2 lambda dp + f(alpha M)T (where CsU represents mass transfer resistance caused by solute diffusion in the stationary phase and f(alpha M)T an added term for polydisperse solutes as proposed by Knox and McLennan [Chromatographia, 10 (1977) 75]) reflect impurities in the proteins.     

Improved computer algorithm for characterizing skewed chromatographic band broadening : II. Results and comparisons

A newly developed method using an exponentially modified Gaussian peak shape model produces results that are more precise and less subject to baseline noise than previous methods for characterizing chromatographic band broadening. The method requires only precisely measurable experimental peak parameters: peak retention time, peak height, peak area, and peak centroid (first moment). Accuracy and precision of the new method were compared with other digital approaches by using computer-synthesized peaks and experimental chromatographic data from many HPLC columns. The proposed method offers a reasonable compromise between accuracy, precision, and convenience. A rapid visual estimate of peak skew can be made by inspecting peak shape and referring to a calibration plot involving peak parameters. Peak variance and skew data from this method are also useful for finding column dispersion corrections in size-exclusion chromatography calibrations.     

Estimation of the instrumental band broadening contribution to the column elution profiles in open tubular capillary liquid chromatography

In comparison with conventionally packed HPLC columns, from a theoretical point of view, open capillary liquid chromatography (OTLC) systems offer a number of advantages like high plate numbers and short analysis times. On the other hand, drastic changes have to be made to the instrumentation. In particular, the contribution to band broadening by the chromatographic equipment must be considerably reduced. In the present study an OTLC system was developed and evaluated, which yields satisfactory results for 26 μm i. d. columns. The determination of the contribution of the chromatographic equipment to the total band broadening is discussed.     

Aqueous sec analysis of cationic polymers as gene carriers

Cationic polymers have been receiving much attention as non-viral gene vectors.The aqueous mobile phase was optimized in combination with Shodex OHpak SB columns for size-exclusion chromatography(SEC)analysis of disulfide-containing poly(ethylene imine)(PEI)derivatives used in gene delivery.Addition of acetonitrile in mobile phase was shown to be able to suppress the hydrophobic interactions between polymer analytes and the stationary phase.The absolute molecular weights and distributions of the cationic polymers were determined directly from online SEC-MALS(multi-angle light scattering)/RI(refractive index detector).The results demonstrate that a good SEC separation of disulfide-containing PEI derivatives used in gene delivery with little band broadening was achieved.     

Improved performance of protein separation by continuous annular chromatography in the size-exclusion mode.

In size-exclusion chromatography (SEC), proteins and peptides are separated according to their molecular size in solution. SEC is especially useful as an effective fractionation step to separate a vast amount of impurities from the components of interest and/or as final step for the separation of purified proteins from their aggregates, in a so-called polishing step. However, the throughput in SEC is low compared to other chromatographic processes as good resolution can be achieved only with a limited feed volume (i.e., maximal approximately 5% of the column volume can be loaded). This limitation opposed widespread application of conventional SEC in industry despite its excellent separation potential. Therefore a continuous separation process (namely preparative continuous annular chromatography) was developed and compared to a conventional SEC system both using Superdex 200 prep grade as sorbent. An immunoglobulin G sample with a high content of aggregates was chosen as a model protein solution. The influence of the feed flow-rate, eluent flow-rate and rotation rate on the separation efficiency was investigated. The height equivalent to a theoretical plate was lower for preparative continuous annular chromatography which could be explained by reduced extra column band broadening. The packing quality was proved to be identical for both systems. The productivity of conventional batch SEC was lower compared to continuous SEC, consequently buffer consumption was higher in batch mode.     

Data processing method for the determination of accurate molecular weight distribution of polymers by SEC/MALDI-MS.

A novel data processing method for a hyphenated technique, size exclusion chromatography/matrix-assisted laser desorption/ionization-mass spectrometry (SEC/MALDI-MS), has been proposed to determine accurate molecular weight distributions on the basis of the individual oligomer species of a polymer. This method is based on the concept that the individual peak intensities of MALDI mass spectrum observed for every SEC fraction with narrow molecular weight distribution could be adjusted to the quantified values to reveal the accurate molecular weight distribution using the signal intensity of the corresponding fraction on the SEC chromatogram observed with a refractive index detector. At first, the theory of the proposed date processing is described in detail. Then, experimental verification of the method is described. This was performed through the characterization of mixtures of three kinds of monodispersed polystyrene reference materials (weight average molecular weight = ca. 6000, 10000, and 18000) as model samples. An accurate trimodal molecular weight distribution for the individual oligomer species of the sample was obtained without any influence of the chromatographic band broadening observed in the original SEC chromatogram. Moreover, the method for depicting the elution profiles of individual oligomer species during SEC separation was also obtained as a "mass chromatogram" using the data processing procedure.     

Stochastic theory of size exclusion chromatography by the characteristic function approach

A general stochastic theory of size exclusion chromatography (SEC) able to account for size dependence on both pore ingress and egress processes, moving zone dispersion and pore size distribution, was developed. The relationship between stochastic-chromatographic and batch equilibrium conditions are discussed and the fundamental role of the 'ergodic' hypothesis in establishing a link between them is emphasized. SEC models are solved by means of the characteristic function method and chromatographic parameters like plate height, peak skewness and excess are derived. The peak shapes are obtained by numerical inversion of the characteristic function under the most general conditions of the exploited models. Separate size effects on pore ingress and pore egress processes are investigated and their effects on both retention selectivity and efficiency are clearly shown. The peak splitting phenomenon and peak tailing due to incomplete sample sorption near to the exclusion limit is discussed. An SEC model for columns with two types of pores is discussed and several effects on retention selectivity and efficiency coming from pore size differences and their relative abundance are singled out. The relevance of moving zone dispersion on separation is investigated. The present approach proves to be general and able to account for more complex SEC conditions such as continuous pore size distributions and mixed retention mechanism.     

Fast and efficient size-based separations of polymers using ultra-high-pressure liquid chromatography

Ultra-high-pressure liquid chromatography (UHPLC) has great potential for the separations of both small molecules and polymers. However, the implementation of UHPLC for the analysis of macromolecules invokes several problems. First, to provide information on the molecular-weight distribution of a polymer, size-exclusion (SEC) columns with specific pore sizes are needed. Development of packing materials with large pore diameters and pore volumes which are mechanically stable at ultra-high-pressures is a technological challenge. Additionally, narrow-bore columns are typically used in UHPLC to minimize the problem of heat dissipation. Such columns pose stringent requirements on the extra-column dispersion, especially for large (slowly diffusing) molecules. Finally, UHPLC conditions generate high shear rates, which may affect polymer chains. The possibilities and limitations of UHPLC for size-based separations of polymers are addressed in the present study. We demonstrate the feasibility of conducting efficient and very fast size-based separations of polymers using conventional and wide-bore (4.6 mm I.D.) UHPLC columns. The wider columns allow minimization of the extra-column contribution to the observed peak widths down to an insignificant level. Reliable SEC separations of polymers with molecular weights up to ca. 50 kDa are achieved within less than 1 min at pressures of about 66 MPa. Due to the small particles used in UHPLC it is possible to separate high-molecular-weight polymers (50 kDa ≤ M(r) ≤ 1-3 MDa, upper limit depends on the flow rate) in the hydrodynamic-chromatography (HDC) mode. Very fast and efficient HDC separations are presented. For very large polymer molecules (typically larger than several MDa, depending on the flow rate) two chromatographic peaks are observed. This is attributed to the onset of molecular deformation at high shear rates and the simultaneous actions of hydrodynamic and slalom chromatography.     

A theoretical basis for parameter selection and instrument design in comprehensive size-exclusion chromatography x liquid chromatography

A novel approach for the selection of the operational parameters (linear velocity, column length) for a comprehensive 2D-LC system is discussed. Starting point for the calculations is a given second dimension ((2)D) separation and a desired peak capacity for the 2D system. Using the theory developed here the optimum settings for the first dimension ((1)D) column can be derived. Theory clearly indicates that the choice of the (1)D conditions is basically limited to just one set of column lengths and linear velocities. The new method is tested on a comprehensive two-dimensional liquid chromatography system which uses size-exclusion chromatography (SEC) followed by reversed phase liquid chromatography (RPLC). A novel LC/LC interface, using a six-port valve rather than storage loops, joins the two chromatographic dimensions. From a theoretical comparison of continuous low flow and stop-flow operation the latter method was found to be an attractive mode of interfacing. The common idea that stop-flow operation results in additional band broadening is shown to be incorrect. The new interface design operated in the stop-flow mode permits the use of conventional analytical diameter HPLC columns, 7.8mm for SEC and 4.6mm for RPLC. The reversed phase chromatography utilizes a monolithic C-18 modified silica column, which produces fast and efficient analyses. As test samples complex mixtures of peptides were analyzed.     

Fundamental chromatographic equations designed for columns packed with very fine particles and operated at very high pressures. Applications to the prediction of elution times and the column efficiencies

The wall temperatures of three Acquity-BEH-C18columns (2.1 mm x 50, 100, and 150 mm) and the temperature of the incoming eluent were maintained constant at 289 K, using a circulating water heat exchanger. The retention times and the band broadening of naphtho[2,3-a]pyrene were measured for each column as a function of the flow rate applied. Pure acetonitrile was used as the eluent. The flow rate dependence of neither elution volumes nor bandwidths can be accounted for by classical models of retention and HETP, respectively, since these models assume columns to be isothermal. Because the heat generated by friction of the eluent against the column bed increases with increasing flow rate, the column bed cannot remain isothermal at high flow rates. This heat is evacuated radially and/or longitudinally by convection, conduction, and radiation. Radial and axial temperature gradients are formed, which are maximum and minimum, respectively, when the temperature of the column wall is kept uniform and constant. The retention times that we measured match well with the values predicted based on the temperature distribution along and across the column, which we calculated and on the temperature dependence of the retention for the same column operated isothermally (i.e., at very low flow rate). The rate of band spreading varies along non-isothermal columns, so the HETP can only be defined locally. It is a function of the axial coordinate. A new contribution is needed to account for the radial thermal heterogeneity of the column, hence the radial distribution of the flow velocities, which warps the elution band. A new model, based on the general dispersion theory of Aris, allows a successful prediction of the unusually large bandwidths observed with columns packed with fine particles, operated at high flow rates, hence high inlet pressures.     

A study of the elution of macromolecules from columns of thermally-treated controlled-porosity glasses

Summary Controlled-porosity glasses (CPG) are sieves for macromoleculars, very widely applied in chromatographic columns for the separation of polymers and biopolymers by means of size-exclusion chromatography (SEC) and affinity chromatography. This paper deals with the influence of the thermal treatment of CPG on the elution of polymers in SEC columns. The problem is examined for a few mobile phases and for glasses having different porosities. Additionally, the SEC results obtained are compared with the adsorption properties of the glases investigated.     

Characterization of some physical and chromatographic properties of monolithic poly(styrene-co-divinylbenzene) columns

Monolithic capillary columns were prepared by copolymerization of styrene and divinylbenzene inside a 200 microm i.d. fused silica capillary using a mixture of tetrahydrofuran and decanol as porogen. Important chromatographic features of the synthesized columns were characterized and critically compared to the properties of columns packed with micropellicular, octadecylated poly(styrene-co-divinylbenzene) (PS-DVB-C18) particles. The permeability of a 60 mm long monolithic column was slightly higher than that of an equally dimensioned column packed with PS-DVB-C18 beads and was invariant up to at least 250 bar column inlet pressure, indicating the high-pressure stability of the monolithic columns. Interestingly, monolithic columns showed a 3.6 times better separation efficiency for oligonucleotides than granular columns. To study differences of the molecular diffusion processes between granular and monolithic columns, Van Deemter plots were measured. Due to the favorable pore structure of monolithic columns all kind of diffusional band broadening was reduced two to five times. Using inverse size-exclusion chromatography a total porosity of 70% was determined, which consisted of internodule porosity (20%) and internal porosity (50%). The observed fast mass transfer and the resulting high separation efficiency suggested that the surface of the monolithic stationary phase is rather rough and does not feature real pores accessible to macromolecular analytes such as polypeptides or oligonucleotides. The maximum analytical loading capacity of monolithic columns for oligonucleotides was found to be in the region of 500 fmol, which compared well to the loading capacity of the granular columns. Batch-to-batch reproducibility proved to be better with granular stationary phases compared to monolithic stationary phase, in which each column bed is the result of a unique column preparation process.     

Investigation of copolymers of styrene and ethyl methacrylate by size exclusion chromatography and gradient HPLC

Summary Copolymers of styrene and ethyl methacrylate have been separated according to composition by gradient HPLC on silica columns or CN bonded phase columns. This mode of separation according to composition was applied to fractions obtained by size exclusion chromatography (SEC). From viscosity and molecular mass data of copolymers with a styrene content ranging from 7.5 to 95.3 mass-% it can be concluded that SEC separates mainly by molecular mass even in this copolymer system. Thus, chromatographic cross-fractionation is possible by prefractionation by SEC and subsequent separation according to composition by gradient HPLC.

---

Untersuchung von Copolymeren von Styrol und Ethylmethacrylat durch Ausschluß-Chromatographie und Gradienten-HPLC

     

Moment analysis of chromatographic behavior of superficially porous particles

Peak parking experiments were conducted to study the chromatographic behavior in a RPLC system consisting of a column packed with superficially porous C(18)-particles and a mixture of methanol and water (70/30, v/v). The values of the surface diffusion coefficient and the retention equilibrium constant of a column packed with superficially porous C(18)-particles were comparable to those of columns packed with a C(18)-silica monolith and full-porous C(18)-silica gel particles. The flow-rate dependence of HETP was hypothetically calculated by using moment equations to clarify the influence of the structural characteristics on the chromatographic behavior. The column efficiency of a column packed with the superficially porous particles is higher in the high flow-rate range than that with full-porous spherical particles. This is attributed to the smaller contribution of the intraparticulate mass transfer in the superficially porous particles to band broadening. The moment equations are effective for the quantitative analysis of chromatographic behavior of superficially porous particles.     

Determination of extracolumn effects in recycle gas chromatography with capillary columns

Extracolumn band broadening in multidimensional systems utilizing flow switching is clearly undesirable. In certain cases, i.e. capillary recycle gas chromatography, the success of an experiment is contingent on the minimization of pre- and post-column dispersion of the peaks. Knowledge of these sources of peak distortion is necessary to optimize the experimental design. A system that extracts statistical parameters from real chromatographic peaks is discussed and used to evaluate band broadening in a capillary recycle experiment.     

Longitudinal diffusion in size-exclusion chromatography: a stop-flow size-exclusion chromatography study.

Band broadening in size-exclusion chromatography (SEC) has an adverse effect upon calculated molecular mass averages, distributions, and dilute solution data generated using single- and multi-detector systems. In the past, the longitudinal diffusion contribution to band broadening in SEC has been considered negligible. This assumption has been investigated by using a stop-flow methodology (SF-SEC) that maximizes the potential for longitudinal diffusion while minimizing that for mass transfer. Under the given experimental conditions, the effects of B-term band broadening were manifest only below 30 KDa, irrespective of chemical functionality or molecular mass polydispersity. This type of broadening was found to be flow rate-independent for a representative high molecular mass polymer.     

Flow-rate dependence of post-column reaction chromatographic detectors and optimization of reactor length for slow chemical reactions

In high-performance liquid chromatography, use of any post-column reactor invariably involves a compromise between the conditions needed to obtain complete reaction and avoidance of excessive dispersion by band broadening in the reactor. Flow rate and the reactor geometry interact to establish the final chromatographic performance. Based on the flow-rate dependence of the peak area and peak height, post-column detectors constitute a distinct class of detectors which differ from mass-flow and concentrations-sensitive detectors such as the flame ionization and absorbance detector, respectively. The concept of reactor length optimization is developed for first-order chemical reactions in a post-column detector. The findings are applicable to both chromatographic and flow-injection systems.     

Estimation of the band broadening contribution of HPLC equipment to column elution profiles

Summary Methods to determine the contribution of the chromatographic equipment to the total band broadening which involve replacing the column by a union or a capillary tube are not suitable as they involve a fundamental change in the chromatographic system. The linear extrapolation method, based on the estimation of the relative influence of the instrument variance on solutes with different capacity factors, is a more attractive alternative method since the column remains in the chromatographic system. This method is only valid when a number of conditions are satisfied. By meeting these conditions the error in the instrument variance by using the linear extrapolation method was determined. At the same time, ways to minimise these errors were studied. Use of the linear extrapolation method in combination with conventional columns of 4.6 mm i.d. appears to yield inaccurate results. In combination with microbore columns the method can be used, provided the columns have a maximum length of 5cm and contain a packing material with a particle size of 2 or 3μm. The error in the determined instrument variance is then of the order of 2μl².