Transport properties and size exclusion effects in wide-pore superficially porous particles.

The effects of hydrodynamic radius on the transport of solute molecules in packed beds of wide-pore superficially porous particles (SPP) are studied using pore-scale simulation. The free molecular diffusion rate varies with radius through the Stokes-Einstein relation. Lattice Boltzmann and Langevin methods are used to model fluid motion and the transport of an ensemble of solute molecules in the fluid, providing statistics on solute concentration, flux, molecule age and residence time, as a function of depth in the SPP. Intraparticle effective diffusion and bed dispersion coefficients are calculated and correlated with the hydrodynamic radius and accessible porosity. The relative importance of convection and diffusion are found to depend on the molecule (tracer) size through the diffusion rate, and convection effects are more significant for larger, slower-diffusing molecules. When larger molecules are utilized, the intraparticle concentration is reduced in proportion to the local particle porosity, leading to a natural definition of the accessible porosity used in size exclusion chromatography (SEC). Although the pore shape is complex, the SEC constant K can be calculated directly from simulation. Simulation demonstrates that the effective diffusion coefficient is elevated near the particle hull, which is largely open to interstitial flow, and decreases with depth into the particle. All molecules studied here have transport access to the entire particle depth, although the accessible volume at a given depth depends on their size. The first passage time into the particle is well predicted by the diffusion rate, but residence time is influenced by convection, shortening the average visit duration. These results are of interest in "perfusion" chromatography where convection is thought to increase separation efficiency for large biomolecules.

Comparison of orthogonality estimation methods for the two-dimensional separations of peptides.

In two-dimensional chromatography, the orthogonality of separation is important for achieving high peak capacity. In this paper, a number of different metrics are compared as measures of orthogonality. Six peptide elution data sets acquired on different stationary phases are plotted against reversed phase retention data and examined as two-dimensional chromatographic pairs. The data, including six in silico prepared data pairs, are utilized to challenge and compare selected orthogonality metrics. The metrics include correlation coefficients, mutual information, box-counting dimensionality, and surface fractional coverage with different hulls. Although correlation coefficients were found to be less suited for the intended purpose, other methods can provide a suitable measure of orthogonality. The presented results are discussed in terms of method utility, simplicity, and applicability for statistically small sets of chromatographic data. Two of the methods, box counting dimensionality and fractional coverage, were found to be mathematically related.

Molecular simulations of retention in chromatographic systems: use of biased Monte Carlo techniques to access multiple time and length scales.

The use of configurational-bias Monte Carlo simulations in the Gibbs ensemble allows for the sampling of phenomena that occur on vastly different time and length scales. In this review, applications of this simulation approach to probe retention in gas and reversed-phase liquid chromatographic systems are discussed. These simulations provide an unprecedented view of the retention processes at the molecular-level and show excellent agreement with experimental retention data.

A comparison of 2 micron inner diameter open tubular column liquid chromatography with pressure-driven isocratic, slip-flow, and electrochromatographic modes of operation: a theoretical study.

Modifications to the flow profile used in open tube capillary liquid chromatography (OT-CLC) include using slip-flow walls and using electroosmosis as a fluid pump as practiced in electrochromatography. These modifications are implemented experimentally by changing the capillary surface and solvent conditions which results in the change of boundary conditions at the capillary wall. In this paper we employ a theory-based study and compare the zone broadening of simple solutes using parabolic flow from a liquid pump, slip-flow from a highly hydrophobic inner surface with water eluent, and electroosmosis for the conditions of pure water and dilute salt utilizing 2 µm inner diameter OT capillaries. In general, the two types of flow other than parabolic exhibit thin zones in the early part of the chromatogram, consistent with previous studies of slip-flow and electroosmotic flow used in electrochromatography. Electrochromatography is shown to yield higher efficiency and less zone broadening than parabolic and slip-flow conditions used in this study. Nonetheless, it is found that the zone standard deviations are shown to be similar for these flow profiles as is the number of plates for these different flow profiles under the conditions utilized here. It is revealed that these modifications do not warrant the effort to maintain the special solvent conditions when compared to gradient elution OT-CLC, which gives a nearly constant peak width throughout the chromatogram, is easiest to implement, and is the method of choice for complex analysis.

Estimation of low-level components lost through chromatographic separations with finite detection limits.

The search for biomarkers allowing the assessment of disease by early diagnosis is facilitated by liquid chromatography. However, it is not clear how many components are lost due to being present in concentrations below the detection limit and/or being obscured by chromatographic peak overlap. First, we extend the study of missing components undertaken by Enke and Nagels, who employed the log-normal probability density function (pdf) for the distribution of signal intensities (and concentrations) of three mixtures. The Weibull and exponential pdfs, which have a higher probability of small-concentration components than the log-normal pdf, are also investigated. Results show that assessments of the loss of low-intensity signals by curve fitting are ambiguous. Next, we simulate synthetic chromatograms to compare the loss of peaks from superposition (overlap) with neighboring peaks to the loss arising from lying below the limit of detection (LOD) imposed by a finite signal-to-noise ratio (SNR). The simulations are made using amplitude pdfs based on the Enke-Nagels data as functions of relative column efficiency, i.e., saturation, and SNR. Results show that at the highest efficiencies, the lowest-amplitude peaks are lost below the LOD. However, at small and medium efficiencies, peak overlap is the dominant loss mechanism, suggesting that low-level components will not be found easily in liquid chromatography with single channel detectors regardless of SNR. A simple treatment shows that a multichannel detector, e.g., a mass spectrometer, is necessary to expose more low-level components.

Simulation and theory of open-tube dispersion in short and long capillaries with slip boundaries and retention.

Using random walk techniques, high resolution simulations of zone shape are conducted in open capillary tubes for short and long tube conditions. Finite size solutes are used as tracers in this treatment. Slip flow boundary conditions and wall retention are utilized as needed. These simulations are able to reproduce previous work in short and long tubes. For the short tube case where dispersion does not asymptotically approach the classic Taylor-Aris and Golay solutions, the effect of slip flow boundaries in the transient region shows zone shapes with abbreviated tails where the larger slip flow values cause zone compression. The use of slip flow to lower dispersion in capillary-based, wall-coated separations is shown to favor long tube behavior. This is because slip flow is relevant for cases where slip lengths are fractions of small capillary tube diameters. Incorporating slip flow into transport in capillaries favors a very small capillary radius where the cross-sectional diffusion length is very small and sampling times are fast. The purely convective zone shape with slip flow boundaries is derived analytically. Applications for this type of separation, guided by both analytical theory and simulation, show the potential for nano-sized capillary tubes less than 1 µm in diameter and favor very fast isocratic separations. Using long tube retention theory with slip boundaries shows that the dispersion-reducing region is most important in the range 0 ≤ k' ≤ 1, a relatively small retention window. Further discussion of the gradient elution technique and dispersion in packed beds suggests that the general usage of slip flow boundaries is restricted in liquid phase separation systems.

Column selection for comprehensive two-dimensional liquid chromatography using the hydrophobic subtraction model.

Two-dimensional (2D) liquid chromatography (2DLC) methods have grown in popularity due to their enhanced peak capacity that allows for resolving complex samples. Given the large number of commercially available column types, one of the major challenges in implementing 2DLC methods is the selection of suitable column pairs. Column selection is typically informed by chemical intuition with subsequent experimental optimization. In this work a computational screening method for 2DLC is proposed whereby virtual 2D chromatograms are calculated utilizing the Snyder-Dolan hydrophobic subtraction model (HSM) for reversed-phase column selectivity. Towards this end, 319 225 column pairs resulting from the combination of 565 columns and 100 sets of 1000 diverse analytes are examined. Compared to other screening approaches, the present method is highly predictive for column pairs that are able to resolve the largest number of analytes. This approach shows a strong sensitivity to the choice of the second dimension column (having a shorter operating time) and a preference for those with embedded polar moieties, whereas a relatively weak preference for C18 and phenyl columns is found for the first dimension.

Measuring porosities of chromatographic columns utilizing a mass-based total pore-blocking method: Superficially porous particles and pore-blocking critical pressure mechanism.

Experimentally determined total, interstitial and intraparticle porosity values are necessary to equate theory, simulation and experimental column performance. This paper reports a study of a mass-based technique for determining total, interstitial and intraparticle porosity measurements based on the total pore-blocking (TPB) method. Commercially available superficially porous particle (SPP) columns, in a variety of small-pore and wide-pore materials, with both hydrophobic and hydrophilic surfaces, are utilized as samples. The results are compared with previously determined literature values for a number of columns and contrasted with HPLC-based elution methods. This method uses only a high-precision balance and an HPLC pump. A simple theoretical analysis of the TPB method using the Young-Laplace equation shows the pressure bounds and flow rate constraints of the method which ensure pore blocking stability. The results suggest that particles with small-pore diameters can be analyzed over a range of solvent clearing pressures and flow rates. However, wide-pore materials, typically with pore diameters in excess of 400 Å, have very low critical pressures and are difficult to determine without losing the pore blocking component. Small mass differences between clearing solvents are shown to present a challenge for measuring the interstitial volume.

Molecular-level comparison of alkylsilane and polar-embedded reversed-phase liquid chromatography systems.

Stationary phases with embedded polar groups possess several advantages over conventional alkylsilane phases, such as reduced peak tailing, enhanced selectivity for specific functional groups, and the ability to use a highly aqueous mobile phase. To gain a deeper understanding of the retentive properties of these reversed-phase packings, molecular simulations were carried out for three different stationary phases in contact with mobile phases of various water/methanol ratios. Two polar-embedded phases were modeled, namely, amide and ether containing, and compared to a conventional octadecylsilane phase. The simulations show that, due to specific hydrogen bond interactions, the polar-embedded phases take up significantly more solvent and are more ordered than their alkyl counterparts. Alkane and alcohol probe solutes indicate that the polar-embedded phases are less retentive than alkyl phases for nonpolar species, whereas polar species are more retained by them due to hydrogen bonding with the embedded groups and the increased amount of solvent within the stationary phase. This leads to a significant reduction of the free-energy barrier for the transfer of polar species from the mobile phase to residual silanols, and this reduced barrier provides a possible explanation for reduced peak tailing.

Influence of bonded-phase coverage in reversed-phase liquid chromatography via molecular simulation II. Effects on solute retention.

Particle-based Monte Carlo simulations were employed to examine the molecular-level effects of bonding density on the retention of alkane and alcohol solutes in reversed-phase liquid chromatography. The simulations utilized octadecylsilane stationary phases with various bonding densities (1.6, 2.3, 2.9, 3.5, and 4.2 micromol/m(2)) in contact with a water/methanol mobile phase. In agreement with experiment, the distribution coefficient for solute transfer from mobile to stationary phase initially increases then reaches a maximum with increasing bonding density. A molecular-level analysis of the solute positional and orientational distributions shows that the stationary phase contains heterogeneous regions and the heterogeneity increases with increasing bonding density.

Influence of bonded-phase coverage in reversed-phase liquid chromatography via molecular simulation I. Effects on chain conformation and interfacial properties.

Particle-based Monte Carlo simulations were employed to examine the effects of bonding density on molecular structure in reversed-phase liquid chromatography. Octadecylsilane stationary phases with five different bonding densities (1.6, 2.3, 2.9, 3.5, and 4.2 micromol/m(2)) in contact with a water/methanol (50/50 mol%) mobile phase were simulated at a temperature of 323 K. The simulations indicate that the alkyl chains become more aligned and form a more uniform alkyl layer as coverage is increased. However, this does not imply that the chains are highly ordered (e.g., all-trans conformation or uniform tilt angle), but rather exhibit a broad distribution of conformations and tilt angles at all bonding densities. At lower densities, significant amounts of the silica surface are exposed leading to an enhanced wetting of the stationary phase. At high densities, the solvent is nearly excluded from the bonded phase and persists only near the residual silanols. An enrichment in the methanol concentration and a disruption in the mobile phase's hydrogen bond network are observed at the interface as bonding density is increased.

Ellipsoidal particles for liquid chromatography: Fluid mechanics, efficiency and wall effects.

Ellipsoidal particles are investigated as packing media for liquid chromatography using high resolution fluid mechanics and Brownian dynamics simulations. The simulations are conducted with packed capillary columns, as well as beds with periodic boundary conditions (PBCs) to study transport in the absence of wall effects. The performance of ellipsoidal particles is evaluated over a range of aspect ratios. The definition of effective diameter used to compare sphere and ellipsoidal particle performance metrics is presented and discussed along with scaling relationships which are necessary to compare sphere and ellipsoidal particle packs. Ellipsoidal particle packs are found to be inferior to sphere packs using PBCs to study chromatographic dispersion. The separation impedance was calculated with PBCs and shown to be approximately the same with ellipsoidal particles as those of spheres. Efficiency of ellipsoidal packs, as measured by plate height, is lower than spherical particle packs and the pressure drop is higher than sphere packs when using PBCs. However, a smaller wall effect is shown for ellipsoidal particles when packing cylindrical capillaries. Radial variations in packing porosity and in flow within the wall region are smaller for ellipsoidal packings. The minimum reduced plate height and the separation impedance for the packed capillaries clearly demonstrate the advantages of ellipsoidal particles compared to spherical particles. This predicted performance advantage remains to be demonstrated in actual practice.

Using molecular simulations to probe pore structures and polymer partitioning in size exclusion chromatography.

Molecular simulations have been extensively utilized to understand and predict the polymer partitioning in size-exclusion chromatography (SEC). However, idealized pore models (e.g., cylindrical, spherical, and slit pores) were often used to represent the porous media in an SEC column, which leads to significant deviations in describing the geometry and the size of the pores. In this work, several complex pore models were derived from body-centered cubic, random, and gel packing of monodisperse spherical sol particles using simulation methodology. The mechanical stabilities of these structures were determined based on particle coordination numbers. Pore size distributions of these porous structures were compared to a commercially available, wide-pore superficially porous particle. Then, Gibbs ensemble Monte Carlo simulations were performed to compute the pore-to-bulk partitioning coefficient KSEC of a polymer chain with complex pore models. The effects of particle size, packing structure, and porosity on KSEC were explored. In addition, structural analysis provides insight into the conformation of polymers in the pores and its effect on the partitioning behavior. This study promotes the understanding of pore structures in SEC columns and enables more accurate predictions of KSEC with less ambiguity in pore geometry.

Size exclusion chromatography with superficially porous particles.

A comparison is made using size-exclusion chromatography (SEC) of synthetic polymers between fully porous particles (FPPs) and superficially porous particles (SPPs) with similar particle diameters, pore sizes and equal flow rates. Polystyrene molecular weight standards with a mobile phase of tetrahydrofuran are utilized for all measurements conducted with standard HPLC equipment. Although it is traditionally thought that larger pore volume is thermodynamically advantageous in SEC for better separations, SPPs have kinetic advantages and these will be shown to compensate for the loss in pore volume compared to FPPs. The comparison metrics include the elution range (smaller with SPPs), the plate count (larger for SPPs), the rate production of theoretical plates (larger for SPPs) and the specific resolution (larger with FPPs). Advantages to using SPPs for SEC are discussed such that similar separations can be conducted faster using SPPs. SEC using SPPs offers similar peak capacities to that using FPPs but with faster operation. This also suggests that SEC conducted in the second dimension of a two-dimensional liquid chromatograph may benefit with reduced run time and with equivalently reduced peak width making SPPs advantageous for sampling the first dimension by the second dimension separator. Additional advantages are discussed for biomolecules along with a discussion of optimization criteria for size-based separations.

Orthogonality measurements for multidimensional chromatography in three and higher dimensional separations.

Orthogonality metrics (OMs) for three and higher dimensional separations are proposed as extensions of previously developed OMs, which were used to evaluate the zone utilization of two-dimensional (2D) separations. These OMs include correlation coefficients, dimensionality, information theory metrics and convex-hull metrics. In a number of these cases, lower dimensional subspace metrics exist and can be readily calculated. The metrics are used to interpret previously generated experimental data. The experimental datasets are derived from Gilar's peptide data, now modified to be three dimensional (3D), and a comprehensive 3D chromatogram from Moore and Jorgenson. The Moore and Jorgenson chromatogram, which has 25 identifiable 3D volume elements or peaks, displayed good orthogonality values over all dimensions. However, OMs based on discretization of the 3D space changed substantially with changes in binning parameters. This example highlights the importance in higher dimensions of having an abundant number of retention times as data points, especially for methods that use discretization. The Gilar data, which in a previous study produced 21 2D datasets by the pairing of 7 one-dimensional separations, was reinterpreted to produce 35 3D datasets. These datasets show a number of interesting properties, one of which is that geometric and harmonic means of lower dimensional subspace (i.e., 2D) OMs correlate well with the higher dimensional (i.e., 3D) OMs. The space utilization of the Gilar 3D datasets was ranked using OMs, with the retention times of the datasets having the largest and smallest OMs presented as graphs. A discussion concerning the orthogonality of higher dimensional techniques is given with emphasis on molecular diversity in chromatographic separations. In the information theory work, an inconsistency is found in previous studies of orthogonality using the 2D metric often identified as %O. A new choice of metric is proposed, extended to higher dimensions, characterized by mixes of ordered and random retention times, and applied to the experimental datasets. In 2D, the new metric always equals or exceeds the original one. However, results from both the original and new methods are given.

Superficially porous particles with 1000Å pores for large biomolecule high performance liquid chromatography and polymer size exclusion chromatography.

To facilitate mass transport and column efficiency, solutes must have free access to particle pores to facilitate interactions with the stationary phase. To ensure this feature, particles should be used for HPLC separations which have pores sufficiently large to accommodate the solute without restricted diffusion. This paper describes the design and properties of superficially porous (also called Fused-Core®, core shell or porous shell) particles with very large (1000Å) pores specifically developed for separating very large biomolecules and polymers. Separations of DNA fragments, monoclonal antibodies, large proteins and large polystyrene standards are used to illustrate the utility of these particles for efficient, high-resolution applications.

Conformation and solvation structure for an isolated n-octadecane chain in water, methanol, and their mixtures.

Configurational-bias Monte Carlo simulations in the isobaric-isothermal ensemble (T = 323 K and p = 10 atm) were carried out to probe structural properties of an isolated n-octadecane chain solvated in water, methanol, water-rich, or methanol-rich mixtures and, for comparison, of an isolated chain in the gas phase and for neat liquid n-octadecane. The united-atom version of the TraPPE (transferable potentials for phase equilibria) force field was used to represent n-octadecane and methanol and the TIP-4P model was used for water. In all six environments, broad conformational distributions are observed and the n-octadecane chains are found to predominantly adopt extended, but not all-trans conformations. In addition, a small fraction of more collapsed conformations in which the chain ends approach each other is observed for aqueous hydration, the water-rich solvent mixture and the gas phase, but the simulation data do not support a simple two-state picture with folded and unfolded basins of attraction. For chains in these three "poor" solvent environments, the dihedral angles near the center of the chain show an enhancement of the gauche population. The ensemble of water-solvated chains with end-to-end contacts is preferentially found in a U-shaped conformation rather than a more globular state. An analysis of the local solvation structures in the water-methanol mixtures shows, as expected, an enrichment of the methyl group of methanol near the methylene and methyl segments of the n-octadecane chain. Interestingly, these local bead fractions are enhanced by factors of 2.5 and 1.5 for methyl and methylene segments reflecting the more hydrophobic nature of the former segments.

How does column packing microstructure affect column efficiency in liquid chromatography?

Full three-dimensional computer simulations of the fluid flow and dispersion characteristics of model nonporous chromatographic packings are reported. Interstitial porosity and packing defects are varied in an attempt to understand the chromatographic consequences of the packing microstructure. The tracer zone dispersion is calculated in the form of plate height as a function of fluid velocity for seven model particle packs where particles are selectively removed from the packs in clusters of varying size and topology. In an attempt to examine the consequences of loose but random packs, the velocities and zone dispersion of seven defect-free packs are simulated over the range 0.36< or =epsilon< or =0.50, where epsilon is the interstitial porosity. The results indicate that defect-free loose packings can give good chromatographic efficiency but the efficiency can vary depending on subtle details of the pack. When the defect population increases, the zone dispersion increases accordingly. For a particle pack where 6% of the particles are removed from an epsilon=0.36 pack, approximately 33% of the column efficiency is lost. These results show that it is far more important in column packing to prevent defect sites leading to inhomogeneous packing rather than obtaining the highest density pack with the smallest interstitial void volume.

Retention in gas-liquid chromatography with a polyethylene oxide stationary phase: molecular simulation and experiment.

Configurational-bias Monte Carlo simulations in the isobaric-isothermal Gibbs ensemble were carried out to investigate the partitioning of normal alkanes, primary and secondary alcohols, symmetric alkyl ethers and arenes between a helium vapor phase and a polyethylene oxide stationary phase (M(W)=382 g mol(-1)). The united-atom version of the transferable potentials for phase equilibria force field was used to model all solutes, polyethylene oxide and helium. The Gibbs free energies of transfer and Kovats retention indices of the solutes were calculated directly from the partition constants at two different temperatures, 353 and 393 K. Chromatographic experiments on a Carbowax 20M retentive phase were performed for the same set of solutes and temperatures ranging from 333 to 413 K. The predicted retention indices for alcohols, ethers and arenes are overestimated by about 120, 70 and 20 retention index units, respectively, pointing to an overestimation of the first-order electrostatic interactions in the model system. Molecular-level analysis shows that hydrogen-bonding and dipole-dipole interactions lead to orientational ordering for the alcohol and ether analytes, whereas the weaker dipole-quadrupole interactions for the arene solutes are not sufficient to induce orientational ordering. The retention indices of alcohols and ethers decrease with increasing temperature because of the large entropic cost of hydrogen-bonding and orientational ordering. In contrast, the retention indices for arenes increase with increasing temperature because the entropic cost of cavity formation is smaller for arenes than for comparable alkanes.

Chain conformation and solvent partitioning in reversed-phase liquid chromatography: Monte Carlo simulations for various water/methanol concentrations.

Many structural models for the stationary phase in reversed-phase liquid chromatography (RPLC) systems have been suggested from thermodynamic and spectroscopic measurements and theoretical considerations. To provide a molecular picture of chain conformation and solvent partitioning in a typical RPLC system, a particle-based Monte Carlo simulation study is undertaken for a dimethyl octadecyl (C(18)) bonded stationary phase on a model siliceous substrate in contact with mobile phases having different methanol/water concentrations. Following upon previous simulations for gas-liquid chromatography and liquid-liquid phase equilibria, the simulations are conducted using the configurational-bias Monte Carlo method in the Gibbs ensemble and the transferable potentials for phase equilibria force field. The simulations are performed for a chain surface density of 2.9 micromol/m(2), which is a typical bonded-phase coverage for mono-functional alkyl silanes. The solvent concentrations used here are pure water, approximately 33 and 67% mole fraction of methanol and pure methanol. The simulations show that the chain conformation depends only weakly on the solvent composition. Most chains are conformationally disordered and tilt away from the substrate normal. The interfacial width increases with increasing methanol content and, for mixtures, the solvent shows an enhancement of the methanol concentration in a 10 Angstrom region outside the Gibbs dividing surface. Residual surface silanol groups are found to provide hydrogen bonding sites that lead to the formation of substrate bound water and methanol clusters, including bridging clusters that penetrate from the solvent/chain interfacial region all the way to the silica surface.