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The effects of stationary phase and solute chain length are probed by carrying out Monte Carlo simulations of dimethyl triacontyl (C₃₀), dimethyl octadecyl (C₁₈), dimethyl octyl (C₈), and trimethyl (C₁) silane grafted, and bare silica stationary phases in contact with a water/methanol mobile phase and by examining the retention of solutes from 1 to 14 carbons in length. Fairly small differences in structure are observed when comparing the C₃₀, C₁₈, C₈ systems and the retention mechanism of nonpolar alkane solutes shows contribution from both partitioning and adsorption on all three of these stationary phases. Unlike in the other systems, the mobile phase solvent is highly structured at its interface with the C₁ and bare silica phases, the former being enriched in methanol and the latter in water. Alkane solutes are unretained at the bare silica surface while alcohol solutes are only slightly enriched at the silica surface due to hydrogen bonding with surface silanols and surface bound solvent. With regard to solute size, it appears that the retention mechanism is not affected by the chain length of the solute., (Copyright © 2011 Elsevier B.V. All rights reserved.)

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.

The chromatographic dimensionality was recently proposed as a measure of retention time spacing based on a power law (fractal) distribution. Using this model, a statistical overlap theory (SOT) for chromatographic peaks is developed that estimates the number of peak maxima as a function of the chromatographic dimension, saturation and scale. Power law models exhibit a threshold region whereby below a critical saturation value no loss of peak maxima due to peak fusion occurs as saturation increases. At moderate saturation, behavior is similar to the random (Poisson) peak model. At still higher saturation, the power law model shows loss of peaks nearly independent of the scale and dimension of the model. The physicochemical meaning of the power law scale parameter is discussed and shown to be equal to the Boltzmann-weighted free energy of transfer over the scale limits. The scale is discussed. Small scale range (small β) is shown to generate more uniform chromatograms. Large scale range chromatograms (large β) are shown to give occasional large excursions of retention times; this is a property of power laws where "wild" behavior is noted to occasionally occur. Both cases are shown to be useful depending on the chromatographic saturation. A scale-invariant model of the SOT shows very simple relationships between the fraction of peak maxima and the saturation, peak width and number of theoretical plates. These equations provide much insight into separations which follow power law statistics., (Copyright © 2011 Elsevier B.V. All rights reserved.)

Reversed-phase liquid chromatography (RPLC) is the foremost technique for the separation of analytes that have very similar chemical functionalities, but differ only in their molecular shape. This ability is crucial in the analysis of various mixtures with environmental and biological importance including polycyclic aromatic hydrocarbons (PAHs) and steroids. A large amount of effort has been devoted to studying this phenomenon experimentally, but a detailed molecular-level description remains lacking. To provide some insight on the mechanism of shape selectivity in RPLC, particle-based simulations were carried out for stationary phases and chromatographic parameters that closely mimic those in an experimental study by Sentell and Dorsey [J. Chromatogr. 461 (1989) 193]. The retention of aromatic hydrocarbons ranging in size from benzene to the isomeric PAHs of the formula C(18)H(12) was examined for model RPLC systems consisting of monomeric dimethyl octadecylsilane (ODS) stationary phases with surface coverages ranging from 1.6 to 4.2 μmol/m(2) (i.e., stationary phases yielding low to intermediate shape selectivity) in contact with a 67/33 mol% acetonitrile/water mobile phase. The simulations show that the stationary phase acts as a very heterogeneous environment where analytes with different shapes prefer different spatial regions with specific local bonding environments of the ODS chains. However, these favorable retentive regions cannot be described as pre-existing cavities because the chain conformation in these local stationary phase regions adapts to accommodate the analytes., (Copyright © 2011 Elsevier B.V. All rights reserved.)

The flow behavior of a commercial polymeric monolith was investigated by direct numerical simulations employing the lattice-Boltzmann (LB) methodology. An explicit structural representation of the monolith was obtained by serial sectioning of a portion of the monolith and imaging by scanning electron microscopy. After image processing, the three-dimensional structure of a sample block with dimensions of 17.8 μm × 17.8 μm × 14.1 μm was obtained, with uniform 18.5 nm voxel size. Flow was simulated on this reconstructed block using the LB method to obtain the velocity distribution, and in turn macroscopic flow properties such as the permeability and the average velocity. The computed axial velocity distribution exhibits a sharp peak with an exponentially decaying tail. Analysis of the local components of the flow field suggests that flow is not evenly distributed throughout the sample geometry, as is also seen in geometries that exhibit preferential flow paths, such as sphere pack arrays with defects. A significant fraction of negative axial velocities are observed; the largest of these are due to flow along horizontal pores that are also slightly oriented in the negative axial direction. Possible implications for mass transfer are discussed., (Copyright © 2011 Elsevier B.V. All rights reserved.)

Molecular simulations of water/acetonitrile and water/methanol mobile phases in contact with a C(18) stationary phase were carried out to examine the molecular-level effects of mobile phase composition on structure and retention in reversed-phase liquid chromatography. The simulations indicate that increases in the fraction of organic modifier increase the amount of solvent penetration into the stationary phase and that this intercalated solvent increases chain alignment. This effect is slightly more apparent for acetonitrile containing solvents. The retention mechanism of alkane solutes showed contributions from both partitioning and adsorption. Despite changes in chain structure and solvation, the molecular mechanism of retention for alkane solutes was not affected by solvent composition. The mechanism of retention for alcohol solutes was primarily adsorption at the interface between the mobile and stationary phase, but there were also contributions from interactions with surface silanols. The interaction between the solute and surface silanols become very important at high concentrations of acetonitrile., (Copyright © 2011 Elsevier B.V. All rights reserved.)

The box-counting or capacity dimension algorithm, known from the fractal mathematics literature, is used to measure the dimensionality D of chromatographic separation techniques for any number of dimensions. It is shown that D has limit properties that match Giddings' sample dimensionality s. D values are shown to be sensitive to the uniformity of peak spacing. A number of examples are given where D is calculated for various limits in one- and two-dimensional separations and for heart-cutting separations. The use of D as a quantitative measure of multidimensional orthogonality is suggested as D, due to the scale-free nature, is not dependent on the effective separation area. The connection to statistical peak overlap theory is discussed., (Copyright © 2010 Elsevier B.V. All rights reserved.)

Particle-based simulations using the configurational-bias and Gibbs ensemble Monte Carlo techniques are carried out to probe the effects of various chromatographic parameters on bonded-phase chain conformation, solvent penetration, and retention in reversed-phase liquid chromatography (RPLC). Specifically, we investigate the effects due to the length of the bonded-phase chains (C(18), C(8), and C(1)), the inclusion of embedded polar groups (amide and ether) near the base of the bonded-phase chains, the column pressure (1, 400, and 1000 atm), and the pore shape (planar slit pore versus cylindrical pore with a 60A diameter). These simulations utilize a bonded-phase coverage of 2.9 micromol/m(2)and a mobile phase containing methanol at a molfraction of 33% (about 50% by volume). The simulations show that chain length, embedded polar groups, and pore shape significantly alter structural and retentive properties of the model RPLC system, whereas the column pressure has a relatively small effect. The simulation results are extensively compared to retention measurements. A molecular view of the RPLC retention mechanism emerges that is more complex than can be inferred from thermodynamic measurements.

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.

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.

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.

A detailed, molecular-level understanding of the retention mechanism in reversed-phase liquid chromatography (RPLC) has eluded analytical chemists for decades. Through validated, particle-based Monte Carlo simulations of a model RPLC system consisting of dimethyloctadecylsilanes at a coverage of 2.9 micro mol/m2 on an explicit silica substrate with unprotected residual silanols in contact with a water/methanol mobile phase, we show that the molecular-level retention processes for nonpolar and polar analytes, such as alkanes and alcohols, are much more complex than what has been previously deduced from thermodynamic and theoretical arguments. In contrast to some previous assumptions, the simulations indicate that both partitioning and adsorption play a key role in the separation process and that the stationary phase in RPLC behaves substantially different from a bulk hydrocarbon phase. The retention of nonpolar methylene segments is dominated by lipophilic interactions with the retentive phase, while solvophilic interactions are more important for the retention of the polar hydroxyl group.

To investigate conformational properties of an isolated n-octadecane chain solvated in water-acetonitrile mixtures, configurational-bias Monte Carlo simulations in the isobaric-isothermal ensemble were performed at T = 323 K and p = 10 atm. The united-atom version of the transferable potentials for phase equilibria force field was used to represent n-octadecane and acetonitrile, and the TIP-4P model was used for water. In all four environments (neat water, 33 and 67 mole percent acetonitrile, and neat acetonitrile), similar conformational distributions are observed as in a previous study for water-methanol solvent mixtures; that is, the n-octadecane chain is found to predominantly adopt extended but not all-trans conformations, and only a small fraction of more collapsed conformations is observed for aqueous hydration, water-rich solvent environments. Analysis of the local solvation structures in the water-acetonitrile mixtures shows an enrichment of the acetonitrile molecules near the methylene and methyl segments of the n-octadecane chain. However, upon increasing the concentration of acetonitrile, the enhancement of acetonitrile and the depletion of water is more pronounced than for water-methanol mixtures because of the weaker interactions between acetonitrile and water.

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.

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.

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.

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.

Configurational-bias Monte Carlo simulations in the Gibbs Ensemble were carried out to investigate the analyte partitioning of n-pentane, n-hexane, n-heptane, 1-propanol, and 2-propanol into a dioctyl ether retentive (stationary) phase used in gas-liquid chromatography. The united-atom version of the TraPPE (transferable potentials for phase equilibria) force field was used to model all analytes and the solvent. The analyte partition coefficients, Gibbs free energies of transfer, and Kovats retention indexes were calculated at four different temperatures ranging from 303.15 to 348.15 K. Although hydrogen bonding is a major contributor to the retention of the alcohol analytes over the entire temperature range, its importance for the separation factor between the primary and secondary alcohol decreases substantially with increasing temperature. The enthalpies and entropies for hydrogen bond formation were also estimated from the temperature dependence of the corresponding equilibrium constants. In agreement with experimental measurements, it is observed that the hydrogen bond involving 1-propanol is enthalpically favored, but entropically disfavored compared to 2-propanol.

The dramatic loss of retention in reversed-phase liquid chromatography when switching to 100% aqueous solvent and stopping flow (depressurizing) has long intrigued separation scientists. Recent experimental evidence suggests that the observed loss of retention is due to the loss of pore wetting with subsequent loss of solvent penetration in the porous matrix. One of the prevalent explanations of this phenomenon has been that the bonded phase chains, typically octadecyl silane bound to porous silica, would undergo significant conformational changes, viz. collapse, under pure aqueous conditions. As a definitive means toward elucidating the conformation of bonded-phase chains under pure aqueous conditions, configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out for a system of dimethyl octadecyl silane of intermediate coverage bound to the (111) face of beta-cristobalite and immersed in pure water. The results of two sets of simulations, which were started from two entirely different starting configurations as a validity check toward reaching the same equilibrium distribution of states, show that chains are neither clustering together nor laying on the surface but rather have a broad distribution of orientations and of conformational states. The interface between the bonded and solvent phases is rough on a molecular level, and clusters of water molecules are sometimes found to adsorb at the silica surface. This computational study lends further evidence that the driving force for the loss of retention when switching to pure aqueous conditions and depressurizing is not the collapse of bonded-phase chains.

Various driving forces have been suggested to explain retention and selectivity in reversed-phase liquid chromatography (RPLC). To provide molecular-level information on the retention mechanism in RPLC, configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out for model systems consisting of three phases: an n-hexadecane retentive phase, a mobile phase with varying water-methanol composition, and a helium vapor phase as reference state. Liquid n-hexadecane functions as a model of a hydrophobic stationary phase, and a wealth of experimental data exists for this system. Gibbs free energies for solute transfers from gas to retentive phase, from gas to mobile phase, and from mobile to retentive phase were determined for a series of short linear alkanes and primary alcohols. Although the magnitude of the incremental Gibbs free energy of transfer for a methylene segment is always larger for the gas- to retentive-phase transfer than the gas- to mobile-phase transfer, it is found that the partitioning of alkanes and alkyl tail groups is mostly affected by the changes in the aqueous mobile phase that occur when methanol modifiers are added. In contrast, the partitioning of the alcohol headgroup is sensitive to changes in both the n-hexadecane and the mobile phases. In particular, it is found that hydrogen-bonded aggregates of methanol are present in the n-hexadecane phase for higher methanol concentrations in the mobile phase. These aggregates strongly increase alcohol partitioning into the retentive phase. The simulation data clearly demonstrate that due to modification of the retentive-phase hydrocarbons by solvent components, neither the solvophobic theory of RPLC, advocated by Horvath and co-workers, nor the lipophilic theory of RPLC, advocated by Carr and co-workers, can adequately describe the separation mechanism of the hexadecane model system of a retentive phase studied here nor the more complex situation present in actual RPLC systems.

A computer simulation of chromatographic dispersion in an ordered packed bed of spheres is conducted utilizing a detailed fluid flow profile provided by the Lattice Boltzmann technique. The ordered configurations of simple cubic, body-centered cubic, and face-centered cubic are employed in these simulations. It is found that zone broadening is less for the fcc structure than the sc and bcc structures and less than a random packed bed analyzed in a previous study in the low flow velocity region used for experimental chromatography. The factors which contribute to the performance of the ordered pack beds are analyzed in detail and found to be dependent both on the nearest surface to surface distance and on the distribution of velocities found in the various packing geometries. The pressure drops of the four configurations are compared and contrasted with the pressure drop from monolithic columns.

A computer simulation of a section of the interior region of a liquid chromatographic column is performed. The detailed fluid flow profile is provided from a microscopic calculation of low Reynolds number flow through a random packed bed of nonporous spherical particles. The fluid mechanical calculations are performed on a parallel processor computer utilizing the lattice Boltzmann technique. Convection, diffusion, and retention in this flow field are calculated using a stochastic-based algorithm. This computational scheme provides for the ability to reproduce the essential dynamics of the chromatographic process from the fundamental considerations of particle geometry, particle size, flow velocity, solute diffusion coefficient, and solute retention parameters when retention is utilized. The simulation data are fit to semiempirical models. The best agreement is found for the "coupling" model of Giddings and the four-parameter Knox model. These models are verified over a wide range of particle sizes and flow velocities at both low and high velocity. The simulations appear to capture the essential dynamics of the chromatographic flow process for non-dimensional flow velocities (Péclet number) less than 500. Since the same packing geometry is utilized for different particle size studies, the interpretation of the parameter estimates from these models can be extended to the physical column model. The simulations reported here agree very well with a number of experiments reported previously.

The importance of adsorption at the gas-liquid interface on retention in gas-liquid chromatography has been controversial since the pioneering work of Martin in the 1960s. In particular, experimental studies using chromatographic and static techniques to quantify partitioning and adsorption of polar analytes on nonpolar liquid phases yielded conflicting results. In this work, Monte Carlo simulations were carried out for a free-standing liquid slab of squalane surrounded by a helium vapor to investigate interfacial adsorption effects for n-pentane, n-hexane, n-heptane, 1-butanol, and benzene solutes at infinite dilution. The simulations indicate preferential adsorption for the flexible alkane and alcohol solutes in a narrow region just inside the Gibbs dividing surface, but no such effect was observed for the rigid benzene solute. Nevertheless, the extent of the interfacial enrichment is small, as measured by the partition coefficient between the bulk liquid and the interfacial region (K(bulk-interface) approximately 1.5). In addition, a region that is slightly depleted for all solute molecules is found to separate the interfacial and bulk regions of the squalane slab. Thus, adsorption at the gas-liquid interface should not contribute significantly to the retentive behavior observed in gas-liquid chromatography on nonpolar capillary columns but might play a role in packed-bed columns with low bonded-phase loadings. The origin for the small enrichments and more favorable free energies for solutes at the interface is that the enthalpies of solvation decrease to a smaller relative extent than the entropies of solvation compared to the bulk liquid.

The coupling of field-flow fractionation (FFF) and multiangle light scattering (MAIS) detectors is complementary in that the MALS system allows particle characterization when a narrow dispersity particle population is present in the detector. The fractionation process provides this narrow dispersity. Utilizing discrete particle simulations of FFF and optical calculations based on both the Mie theory of particle scattering and Rayleigh-Gans-Debye (RGD) scattering theory, the extent of polydispersity that can be tolerated for accurate particle quantitation is explored. It is found that flow, electrical, and sedimentation FFF provide adequate separation for accurate particle quantitation by MALS. The Mie theory is more accurate than the RGD theory, which is known to deviate at higher particle size. Low error in the measurement of mean diameters is found when only the particle diameter is of interest. It is shown that the reconstruction of the particle size distribution from time slice data is distorted due to errors in concentration, which result from finite polydispersity and other effects. A number of procedures are evaluated in restoring the size distribution to higher accuracy. None of these procedures is deemed of general purpose and none of these is reliable. The best results are obtained when fractionation is conducted under the minimal possible outlet polydispersity and when steric effects are minimized. In addition, best results are had for inherently narrow dispersity colloidal materials.