A protocol for the measurement of all the parameters of the mass transfer kinetics in columns used in liquid chromatography

Band broadening in chromatography results from the combination of the dispersive effects that are associated with the different steps involved in the migration of compound bands along the column. These steps include longitudinal diffusion, trans-particle mass transfer, external film mass transfer, overall eddy diffusion, including trans-column, short-range inter-channel, trans-channel eddy diffusion, and the possible, additional mass transfer contributions arising from heat friction and the thermal heterogeneity of the column. We describe a series of experiments that provide the data needed to determine the coefficients of the contributions to band broadening of each one of these individual mass transfer steps. This specifically designed protocol can provide key information regarding the kinetic performance of columns used in liquid chromatography and explain why different columns behave so differently. The limitations, accuracy and precision of these methods are discussed. Further avenues of research that could improve the characterization of the mass transfer mechanisms in chromatographic columns, possibly contributing to the development of better columns, are suggested.     

Relationship between trans-column eddy diffusion and retention in liquid chromatography: Theory and experimental evidence

Experimental results demonstrate that trans-column eddy diffusion depends on the retention of compounds. The combination of elution profiles recorded in different points of the exit column cross-section and of the height equivalent to a theoretical plate (HETP) of small molecules clearly show a strong link between retention and column performance in liquid chromatography. These results validate a new model of trans-column eddy diffusion in packed columns. The contribution to the column HETP of the trans-column eddy diffusion term decreases with increasing retention factor from k′ = 0 to k′ = 3 above which it becomes negligible. The best column performance in RPLC is observed for the most retained compounds. This is due to the combination of the lack of a residual trans-column eddy diffusion contribution and the vanishing contribution of the instrument to band broadening.     

Retention equilibrium and mass transfer characteristics in reversed-phase liquid chromatography using methanol-water mixtures

Pulse response experiments (i.e., elution chromatography) were made in reversed-phase liquid chromatography (RPLC) using a C18 silica gel column and methanol-water mixtures of different compositions (phi). The moment analysis of the elution peak profiles measured in the RPLC system provided some items of information about four parameters characterizing the retention equilibrium and the mass transfer kinetics in the column, i.e., adsorption equilibrium constant, isosteric heat of adsorption, surface diffusion coefficient and activation energy of surface diffusion. Characteristics of the chromatographic behavior were studied by analyzing the dependence of the four parameters on phi and the correlation between them. It was found that surface diffusion was one of the important processes of molecular migration having a significant contribution to the mass transfer kinetics in the column. Both the adsorption equilibrium constant and the surface diffusion coefficient varied depending on phi. The direction of their changes was approximately opposite, suggesting that the mass transfer in the manner of surface diffusion was restricted owing to the retention of the sample molecules on the stationary phase.     

The mass transfer kinetics in columns packed with Halo-ES shell particles

The average mesopore size of the new Halo-ES-Peptide shell particles is 160 ?, markedly larger than that of the classical Halo shell particles (90 ?). We found that this change causes a considerable decrease of the film mass transfer resistance measured for columns packed with these particles. We analyze data obtained by systematic measurements of the C term of the van Deemter equation for the peptide β-lipotropin (MW = 769 Da), the protein insulin (MW = 5800 Da), and a series of non-retained polystyrene standards (MW = 6400 and 13,200). The improvement in column performance is explained by an increase of the fraction of the external surface area of the shell that allows the entrance of the sample molecules inside the particle. The fraction of the shell surface accessible to a probe controls the rate of its external film mass transfer, i.e. its rate of transfer between the interstitial and the stagnant eluent. Although measurable, the increase in sample diffusivity through the porous shells does not account for the better performance of Halo-ES-peptide columns. Furthermore, the analysis of the HETPs data of small molecules (uracil, acetophenone, toluene, and naphthalene, MW< 150) reveals that the eddy diffusion (A) term of these new columns is 25% lower than that of the classical Halo columns. This result is consistent with the impact of intra-particle diffusivity on the eddy diffusion mechanism in packed columns. As shell diffusivity increases, so does the rate of transfer of sample molecules between the eluent stream-paths flowing through the packed particles and across the column diameter. Dispersion through short-range inter-channel and trans-column eddies is reduced.     

Kinetic study of the mass transfer of S-Tr?ger's base in the system cellulose triacetate and ethanol.

A recent study of the mass transfer kinetics of (-)- or S-Tr?ger's base (TB) between ethanol and microcrystalline cellulose triacetate (CTA) allows an analysis of the concentration dependence of the mass transfer rate coefficient (k(m)). S-TB elutes before R-TB. The retention time of the both compounds decreases with increasing temperature. In this study, experimental data measured between 30 and 50 degrees C were analyzed to provide information on the kinetics of several mass transfer processes which take place in the chromatographic column, i.e., axial and intraparticle dispersion, the fluid-to-particle mass transfer, and the kinetics of adsorption/desorption at the actual adsorption sites. Intraparticle diffusion has the dominant contribution to band broadening at high flow-rates. Both intraparticle diffusivity and the surface diffusion coefficient exhibit a small concentration dependence. The positive dependence of k(m) on the concentration of S-TB seems to result from the properties of the adsorption/desorption kinetics and can be interpreted by considering the phase equilibrium properties. A quantitative analysis of the activation energy of the mass transfer kinetics of S-TB in the CTA column was also attempted.     

毛细管色谱过程动力学研究——径向扩散对流出曲线的影响

考虑到毛细管色谱分析过程中径向浓度梯度对传质过程的影响,建立了相应的色谱质量平衡模型,模仿Ｇｉｄｄｉｎｇｓ的假设,将模型适当化简,并通过数学变换的方法得到了流出曲线的一级矩及二、三级中心矩表达式。结果表明,溶质的径向扩散不仅对柱效、峰展宽、峰形特征等有影响,而且对溶质的保留时间也有一定的影响。     

Theoretical evaluation of methods for extracting retention factors and kinetic rate constants in liquid chromatography

A three-dimensional stochastic simulation is used to provide a detailed understanding of mass transfer processes in liquid chromatography. In this simulation, the migration of individual molecules is established through diffusion and laminar convection within the mobile phase. The molecules interact with the stationary phase by a partition (absorption) mechanism. For these studies, the column length, linear velocity, stationary-phase diffusion coefficient, interfacial mass transfer coefficient, and equilibrium constant are varied in a system with a homogeneous surface. Heterogeneous surfaces are also investigated by having multiple types of interaction sites that are equally or unequally distributed. For each simulation, the molecular distribution is examined and characterized at specified times or column lengths. Five individual methods are then applied to extract the thermodynamic and kinetic information for transport between the mobile and stationary phases. In the first method, all of the molecules are initially distributed in the mobile phase and the fraction remaining is monitored as a function of time. These simulation data are fit to a single exponential decay by nonlinear regression to determine the "true" retention factors and rate constants. The other methods rely on evaluating the shape of the zone profiles along the column. The statistical moments of the profiles are used to calculate the mean and the variance, which are related to the retention factors and the rate constants, respectively. The profiles are also fit to the exponentially modified Gaussian equation, the Giddings equation, and the Thomas equation. The fitting parameters from these equations are then used to calculate the retention factors and rate constants. Comparisons of the accuracy relative to the "true" retention factors and "true" rate constants, as well as the advantages and limitations of each method are discussed.     

Surface diffusion in reversed-phase liquid chromatography

More than 40 years ago, Giddings pointed out in “Dynamics of Chromatography” that surface diffusion should become an important research topic in the kinetics of chromatographic phenomena. However, few studies on surface diffusion in adsorbents used in chromatography were published since then. Most scientists use ordinary rate equations to study mass transfer kinetics in chromatography. They take no account of surface diffusion and overlook the significant contributions of this mass transfer process to chromatographic behavior and to column efficiency at high mobile phase flow rate. Only recently did the significance of surface diffusion in separation processes begin to be recognized in connection with the development of new techniques of fast flow, high efficiency chromatography. In this review, we revisit the reports on experimental data on surface diffusion and introduce a surface-restricted molecular diffusion model, derived as a first approximation for the mechanism of surface diffusion, on the basis of the absolute rate theory. We also explain how this model accounts for many intrinsic characteristics of surface diffusion that cannot properly be explained by the conventional models of surface diffusion.     

Effect of the carrier gas pressure on the dynamic and separation characteristics of divinylbenzene-based monolithic capillary columns for gas chromatography

The efficiency and dynamic characteristics of divinylbenzene-based monolithic capillary columns for gas chromatography were analyzed using a test mixture composed of five light hydrocarbons. The chromatographic properties of these columns were evaluated within the framework of two varieties of the van Deemter equation, the classical one and that proposed by Giddings (with consideration given to the pressure drop across the column). An analysis of the van Deemter curves demonstrated that the main contribution to peak smearing comes from the diffusion processes in the mobile phase. The contribution from the resistance to mass transfer between the mobile and stationary phases is less important. Negative values obtained for A in the van Deemter equation and for C _s in the Giddings model, parameters that characterize the stationary phase structure and mass transfer kinetics in the stationary phase, have no physical meaning, a result calling for further studies of this type of monolithic capillary columns since the classical theory supposed these parameters to be strictly positive. Under optimal conditions, the HETP of the monolithic columns was found to be 3 to 4 times smaller than that typical of open capillary columns of the same diameter.     

Mass transfer mechanism in liquid chromatography columns packed with shell particles: Would there be an optimum shell structure?

The mass transfer mechanisms in columns packed with old (55 μm Zipax and 5 μm Poroshell) and recently commercialized shell particles (2.7 μm Halo-C(18) and Kinetex-C(18)) were investigated from a physico-chemical point of view. Combining a model of diffusion in heterogeneous packed beds (effective medium theory) with values of the heights equivalent to a theoretical plate (HETPs derived from the first and second central moments of the elution profiles) and of the peak variances provided by the peak parking method, we demonstrate that columns packed with current shell particles perform better than those packed with fully porous particles in resolving low molecular weight compounds because the eddy diffusion term of the van Deemter equation of the former is markedly smaller. The calculation of eddy diffusion in column beds suggests that the smaller A terms are due to smaller trans-column velocity bias in columns packed with shell particles. We also show that the mass transfer of large molecules (e.g., proteins) is faster when the internal volume accessible to the analyte increases. Therefore, it is suggested that shell particles made of concentric layers with average pore sizes increasing with increasing diameter would provide columns with higher efficiency.     

Unusual behavior of the height equivalent to a theoretical plate of a new poroshell stationary phase at high temperatures

The reduced HETPs of naphtho[2,3-a]pyrene (a polycyclic aromatic hydrocarbon with six condensed phenyl rings) was measured on three different RP-C18columns packed with 5 and 3 microm totally porous silica-B particles, and with 2.7 microm Halo shell particles. The measurements were made at temperatures between ambient and 323 K, the retention factor being kept constant by modifying the eluent composition (water/acetonitrile mixtures). This compound was chosen because (1) it is strongly retained on RP-C18 stationary phases and is eluted only by acetonitrile-rich mobile phases, which have a low viscosity (approximately 0.35 cP). As a result, the C-term of the HETP plots was measured very precisely; (2) this compound does not interact strongly with the bare silica surface. Its adsorption isotherm remains linear up to high concentrations, its UV-absorbance (at lambda=294 nm) is high, and its HETP can be measured accurately and precisely (relative error of 2%). The experimental data were fitted to a general HETP model derived recently. The B term was measured independently, using the parking method to validate the fit in the low velocity range. The kinetics parameters derived from this model allow a qualitative comparison of the performances of the three columns. The column packed with the C18-Halo particles exhibit an unusual rate of HETP increase at high linear velocities, particularly at elevated temperatures (310 and 323 K). A comparison of the HETP data measured for naphtho[2,3-a]pyrene and for bovine serum albumin (BSA), a large protein that is excluded from the mesopore network of all three columns, demonstrates that this behavior is related not to the mass transfer kinetics in the stationary phase but to some unexpected variation of the eddy dispersion with the linear velocity at high temperatures. The coupling theory of eddy dispersion proposed by Giddings fails to describe the data obtained for the Halo column while they predict well those measured on the totally porous materials. The explanation does not reside in the width of the particle size distribution (5% for Halo and approximately 15% for the silica-B particles) but more likely in the roughness of the external surface of the Halo particles.     

Retention and mass transfer characteristics in reversed-phase liquid chromatography using a tetrahydrofuran-water solution as the mobile phase.

The characteristics of the retention and the mass transfer kinetics in reversed-phase liquid chromatography (RPLC) were measured on a system consisting of a C18-silica gel and a tetrahydrofuran-water (50:50, v/v) solution. These parameters were derived from the first and the second moments of the elution peaks, respectively. Further information on the thermodynamic properties of this system was derived from the temperature dependence of these moments. Some correlations previously established were confirmed for this system, namely, an enthalpy-entropy compensation for both retention and surface diffusion and a linear free-energy relationship. These results are compared with those observed in other similar systems using methanol-water (70:30, v/v) and acetonitnile-water (70:30, v/v) solutions. The contribution of surface diffusion to intraparticle diffusion in C18-silica gel particles was shown to be important. The analysis of the thermodynamic properties of surface diffusion suggests that, in these three RPLC systems, its activation energy is lower than the isosteric heat of adsorption. The nature and the extent of the influence of the mobile phase composition on the parameters describing the retention and the mass transfer kinetics are different but the chromatographic mechanisms involved in RPLC systems appear similar, irrespective of the nature of the organic modifier in the mobile phase.     

Kinetic investigation of narrow-bore columns packed with prototype sub-2 μm superficially porous particles with various shell thickness

The recent successful breakthrough of sub-3 μm shell particles in HPLC has triggered considerable research efforts toward the design of new brands of core-shell particles. We investigated the mass transfer mechanism of a few analytes in narrow-bore columns packed with prototype 1.7 μm shell particles, made of 1.0, 1.2, and 1.4 μm solid nonporous cores surrounded by porous shells 350, 250, and 150 nm thick, respectively. Three probe solutes, uracil, naphthalene, and insulin, were chosen to assess the kinetic performance of these columns. Inverse size exclusion chromatography, peak parking experiments, and the numerical integration of the experimental peak profiles were carried out in order to measure the external, internal, and total column porosities, the true bulk diffusion coefficients of these analytes, the height equivalent to a theoretical plate, the longitudinal diffusion term, and the trans-particle mass transfer resistance term. The residual eddy diffusion term was measured by difference. The results show the existence of important trans-column velocity biases (7%) possibly due to the presence of particle multiplets in the slurry mixture used during the packing process. Our results illustrates some of the difficulties encountered by scientists preparing and packing shell particles into narrow-bore columns.     

Kinetic study of the mass transfer of bovine serum albumin in anion-exchange chromatography

A kinetic study was made on the mass transfer phenomena of bovine serum albumin (BSA) in two different anion-exchange columns (Resource-Q and TSK-GEL-DEAE-5PW). The analysis of the concentration dependence of the lumped mass transfer rate coefficient (km,L) provided the information about the kinetics of the several mass transfer processes in the columns and the anion exchangers, i.e., the axial dispersion, the fluid-to-particle mass transfer, the intraparticle diffusion, and the adsorption/desorption. In the Resource-Q column, the intraparticle diffusion had a dominant contribution to the band broadening compared with those of the other processes. The surface diffusion coefficient (Ds) of BSA showed a positive concentration dependence, by which the linear dependence of km,L on the BSA concentration seemed to be interpreted. On the other hand, in the TSK-GEL-DEAE-5PW column, the contribution of the adsorption/desorption was also important and almost same as that due to the intraparticle diffusion. There are some differences between the intrinsic properties of the mass transfer kinetics inside the two anion exchangers. It was likely that the positive concentration dependence of Ds was explained by the heterogeneous surface model.     

小鼠血清IgG的蛋白G灌注亲和色谱行为的研究

通过实验考察了小鼠血清ＩｇＧ的蛋白Ｇ灌注亲和色谱行为,虽然未发现非特异性吸附,但在通常情况下对ＩｇＧ存在不可逆性吸附。洗脱液组成及ｐＨ的不同决定ＩｇＧ在灌注亲和色谱柱上具有不同的解离常数ＫＤ,产生不同的色谱行为。流动相的流速对ＩｇＧ与蛋白Ｇ的结合／解离动力学过程产生一定的影响。结果表明,对于小鼠血清中的ＩｇＧ灌注亲和色谱的分离,由于解离速率影响到传质过程,使之在高流速下的分离受到一定的限制。     

Effect of the ionic strength of salts on retention and overloading behavior of ionizable compounds in reversed-phase liquid chromatography I. XTerra-C18

The influence of the salt concentration (potassium chloride) on the retention and overloading behavior of the propranolol cation (R'-NH2+ -R) on an XTerra-C18 column, in a methanol:water solution, was investigated. The adsorption isotherm data were first determined by frontal analysis (FA) for a mobile phase without salt (25% methanol, v/v). It was shown that the adsorption energy distribution calculated from these raw adsorption data is bimodal and that the isotherm model that best accounts for these data is the bi-Moreau model. Assuming that the addition of a salt into the mobile phase changes the numerical values of the parameters of the isotherm model, not its mathematical form, we used the inverse method (IM) of chromatography to determine the isotherm with seven salt concentrations in the mobile phase (40% methanol, v/v; 0, 0.002, 0.005, 0.01, 0.05, 0.1 and 0.2 M). The saturation capacities of the model increase, q(s,1) by a factor two and q(s,2) by a factor four, with increasing salt concentration in the range studied while the adsorption constant b1 increases four times and b2 decreases four times. Adsorbate-adsorbate interactions vanish in the presence of salt, consistent with results obtained previously on a C18-Kromasil column. Finally, besides the ionic strength of the solution, the size, valence, and nature of the salt ions affect the thermodynamic as well as the mass transfer kinetics of the adsorption mechanism of propranolol on the XTerra column.     

Thermodynamic characterization of the adsorption of selected chiral compounds on immobilized amyloglucosidase in liquid chromatography

Immobilized amyloglucosidase was used as a chiral stationary phase (CSP). First, the retention and enantioselectivity of several model chiral amines and acids were investigated. We found that this CSP was unable to separate the enantiomers of acids, though all selected amines could be resolved. The adsorption of (R)- and (S)-propranolol and its influence on column temperature and 2-propanol content in the eluent were then studied in detail, using a three-step methodology. The adsorption was first evaluated using Scatchard plots; thereafter, the adsorption was characterized in detail by calculating the adsorption energy distribution. With this model-independent information, a better judgment could be made of the possible adsorption models selected in the last step, the model fitting to the data. In the case examined, the bi-Langmuir model (containing nonselective and enantioselective sites) describes the system well. The retention of (R)- and (S)-propranolol at low temperatures increases with the content of 2-propanol in the eluent, due to the increased saturation capacity of the enantioselective sites. The retention is an enthalpy-driven process at both types of sites, whereas the enantioseparation is due to differences between the entropy changes of the two enantiomers at the enantioselective sites. The enthalpy of adsorption at the nonselective sites is almost identical at the two concentrations of 2-propanol in the eluent. Enantioselective adsorption, on the other hand, is more exothermic at higher modifier content (20%). Thus, at high temperatures the retention decreases with increasing modifier content, whereas the opposite (unusual) trend is the case at low temperatures.     

Hypercross-linked polystyrene and its potentials for liquid chromatography: a mini-review

A recently introduced method [Biotechnol. Prog. 13 (1997) 429] for determining intraparticle mass transfer parameters in high speed liquid chromatography is considered in the present study for the case where the eluite adsorbs onto the stationary phase. The validity of the method was verified theoretically using simulated elution profiles and then applied to experimental data obtained using columns packed with either a macroporous or a gel-filled gigaporous stationary phase. For this purpose, experimental measurements were made using alpha-lactalbumin and bovine serum albumin as eluites at several retention factors. Apparent intraparticle diffusivities measured for the gel-filled gigaporous stationary phase were seen to increase with the retention factor, which indicates that for this material surface diffusion is a significant mechanism of mass transfer under retained conditions. Data obtained on the macroporous stationary phase revealed that the intraparticle diffusivity was independent of the retention factor, which suggests that pore diffusion remains the principal mass transfer mechanism even under conditions where proteins are adsorbed on the column packing.     

Analysis of diffusion models for protein adsorption to porous anion-exchange adsorbent

The ion-exchange adsorption kinetics of bovine serum albumin (BSA) and gamma-globulin to an anion exchanger, DEAE Spherodex M, has been studied by batch adsorption experiments. Various diffusion models, that is, pore diffusion, surface diffusion, homogeneous diffusion and parallel diffusion models, are analyzed for their suitabilities to depict the adsorption kinetics. Protein diffusivities are estimated by matching the models with the experimental data. The dependence of the diffusivities on initial protein concentration is observed and discussed. The adsorption isotherm of BSA is nearly rectangular, so there is little surface diffusion. As a result, the surface and homogeneous diffusion models do not fit to the kinetic data of BSA adsorption. The adsorption isotherm of gamma-globulin is less favorable, and the surface diffusion contributes greatly to the mass transport. Consequently, both the surface and homogeneous diffusion models fit to the kinetic data of gamma-globulin well. The adsorption kinetics of BSA and gamma-globulin can be very well fitted by parallel diffusion model, because the model reflects correctly the intraparticle mass transfer mechanism. In addition, for both the favorably bound proteins, the pore diffusion model fits the adsorption kinetics reasonably well. The results here indicate that the pore diffusion model can be used as a good approximate to depict protein adsorption kinetics for protein adsorption systems from rectangular to linear isotherms.