External Porosity Research Articles

Extending the Total Pore Blocking method to normal phase high performance liquid chromatography

It has been demonstrated that it is possible to extend the Total Pore Blocking (TBP)-method for the determination of the external porosity ( ɛ e) of packed bed columns from reversed-phase (RP) chromatography to normal-phase (NP) chromatography conditions by switching the nature of the blocking agent and the interstitial void flushing liquid, i.e., by using a hydrophilic blocking agent (pure or buffered water at pH 3.0 or pH 7.0) and a hydrophobic flushing liquid (linear alkanes such as decane). Several parameters that might influence the accuracy of the method, such as the applicable range of flow rates and the meso-pore size of the particles have been investigated. The influence of several different parameters on the obtained external porosity value has been investigated. From a wide selection of possible t 0-markers, the class of linear alkanes has been shown to be the single possible one. This brings along the need to use refractive index detection to measure the signal of the linear alkane tracer (e.g., dodecane) in a stream of (another) linear alkane. The results of the newly established NP-TPB method have been compared to the values of the external porosity obtained by ISEC and proved to generate the same results, however with a much smaller read-out error (being only of the order of 0.1%).

High performance liquid chromatography column packings with deliberately broadened particle size distribution: Relation between column performance and packing structure

The effect of the addition of 25%, 50% and 75% (weight percent, wt%) of larger particles (resp. 3 and 5 μm) to a commercial batch of 1.9 μm particles has been investigated as an academic exercise to study the effects of particle size distribution on the kinetic performance of packed bed columns in a magnified way. Comparing the performance of the different mixtures in a kinetic plot, it could be irrefutably shown that the addition of larger particles to a commercial batch of small particles cannot be expected to lead to an improved kinetic performance. Whereas the addition of 25 wt% of larger particles still only has a minor negative effect, a significantly deteriorated performance is obtained when 50 or 75 wt% of larger particles are added. In this case, separation impedance number increases up to 200% were observed. Studying the packing structure through computational packing simulations, together with the experimental determination of the external porosity, helped in understanding the obtained results. This showed that small particles tend to settle in the flow-through pores surrounding the larger particles, leading to very high packing densities (external porosities as low as 32% were observed) and also negatively influencing the column permeability as well as the band broadening (because of the broadened flow-through pore size range).

Structure–transport correlation for the diffusive tortuosity of bulk, monodisperse, random sphere packings

The mass transport properties of bulk random sphere packings depend primarily on the bed (external) porosity ɛ, but also on the packing microstructure. We investigate the influence of the packing microstructure on the diffusive tortuosity τ = D m/ D eff, which relates the bulk diffusion coefficient ( D m) to the effective (asymptotic) diffusion coefficient in a porous medium ( D eff), by numerical simulations of diffusion in a set of computer-generated, monodisperse, hard-sphere packings. Variation of packing generation algorithm and protocol yielded four Jodrey–Tory and two Monte Carlo packing types with systematically varied degrees of microstructural heterogeneity in the range between the random-close and the random-loose packing limit ( ɛ = 0.366–0.46). The distinctive tortuosity–porosity scaling of the packing types is influenced by the extent to which the structural environment of individual pores varies in a packing, and to quantify this influence we propose a measure based on Delaunay tessellation. We demonstrate that the ratio of the minimum to the maximum void face area of a Delaunay tetrahedron around a pore between four adjacent spheres, ( A min/ A max) D, is a measure for the structural heterogeneity in the direct environment of this pore, and that the standard deviation σ of the ( A min/ A max) D-distribution considering all pores in a packing mimics the tortuosity–porosity scaling of the generated packing types. Thus, σ( A min/ A max) D provides a structure–transport correlation for diffusion in bulk, monodisperse, random sphere packings.

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.

Computational study of the relationship between the flow resistance and the microscopic structure of polymer monoliths

The present article reports on a numerical study of the permeability and flow resistance of ordered and random-structured polymer monolith mimics with different structures. Comparing the permeability of the different monolith structures with the same domain size and the same external porosity, it is found that the larger the degree of globule clustering, the lower is the resulting permeability. More or less independently of the external porosity, a 40% decrease in permeability is observed when comparing a purely cylindrical branch-type skeleton with a strongly clustered globular skeleton with the same external porosity. Correlations allowing to estimate the flow resistance as a function of the external porosity are presented for each considered degree of globule clustering.

Diffusion models in chromatographic columns packed with fully and superficially porous particles

Most theoretical analyzes of molecular diffusion in chromatographic columns are based on more or less approximate models. Macroscopic sample diffusion along packed columns results from a complex combination of the local sample diffusivity in the external porosity of the bed ( D m ) and in the porous particles ( Ω D m ). A further complication arise from the use of the new superficially porous (or core–shell) particles. The obstruction to axial diffusion caused by the presence of their impermeable core has to be quantified. Two original models of longitudinal diffusion in packed beds are derived for these ternary composite materials. They account for the actual 3D micro-structure of the packed column bed. The micro-structure results from the presence of (1) the impermeable spherical cores; (2) the porous shells surrounding these cores; and (3) the eluent within which the particles are randomly dispersed. The theoretical approach is based on the combination of the effective medium theory of Garnett for core–shell spherical inclusions and of the probabilistic theory of Torquato for randomly dispersed spheres in a continuous matrix. The impacts of the core to the shell diameter, ρ , and of the porous shell to the bulk diffusivity, Ω , on the longitudinal diffusion B coefficient of chromatographic columns packed with core–shell particles are analyzed from a theoretical point of view.

Use of pressure drop profiles to assess the accuracy of Total Pore Blocking measurements of the external porosity of chromatographic columns

By comparing the pressure drop in a column where the meso-pores of the particles have been blocked using the Total Pore Blocking (TPB) method to measure the interstitial volume of the column with that in the same column when the particle meso-pores are fully open, it could be demonstrated in a very sensitive way that the interstitial volume is completely devoid of any significant amount of remaining pore blocking agent in the final phase of a TPB experiment. Monitoring the pressure signal until it returns to its original value can hence be used as a reliable indicator that all blocking agent has been removed from the interstitial void at the end of the flushing period. As a consequence, any small molecular weight dead volume marker that is employed in this phase can explore the full interstitial volume, so that the value of the latter can be measured without being underestimated by the fact that some fractions of the interstitial void would still be occupied by the blocking agent.

Theoretical investigation of diffusion along columns packed with fully and superficially porous particles

Abstract Chromatographic columns packed with shell particles are now nearly twice more efficient than columns packed with conventional, fully porous particles. Shell particles are made of a solid core surrounded by a porous shell of constant thickness. Diffusion through the bed of packed columns is complex due to their heterogeneity. It involves diffusion through the external and the internal fluid, and surface diffusion. Six diffusion models are compared that combine these diffusion mechanisms. They involve the external porosity of the bed ( ϵ e ), the ratio of the core to the particle diameters ( ρ), and the ratio of the shell diffusivity to the bulk diffusion coefficient ( Ω). Four different theoretical approaches were considered. They are based on (1) the additivity of the mass flux densities modulated by the obstruction factors caused by non-porous spherical inclusions; (2) the effective medium theory of Landauer; (3) the effective medium theory of Garnett for spherical inclusions; and (4) the probabilistic theory of Torquato (for binary composite materials only). The two Landauer models fail because they cannot account for the obstruction factor imposed by the presence of non-porous spherical inclusions. The ternary Garnett model (3) provides an excellent approximation of the actual diffusion mechanism but the most physically relevant model seems to be the one derived from a combination of the Garnett model for a binary core–shell particle and of the Torquato model for random dispersion of contacting spheres in a matrix. Accurate measurements of axial dispersion coefficients are needed to validate or reject the semi-empirical parallel diffusion models and to select the most appropriate one. The results of such measurements made with the peak parking method for various compounds are reported in the companion paper.

An overview of the use of monoliths in sample preparation and analysis of milk

Monolithic columns with a unique structure possess some exceptional characteristics, which make them an excellent tool in the hands of analytical chemists, not only for separation but also for sample preparation. Their much higher external porosity compared to conventional particle-packed columns results in higher permeability and low-pressure drop with higher separation efficiency. Till now, monolithic columns have been applied to the analysis of different analytical matrices: pharmaceuticals, biofluids, food matrices, environmental samples, biochemical species, proteomics, etc. Since they offer a great potential for the separation of complex mixtures, it can be expected that the interest in applying these columns will increase. As long as more experience is gained with monolithic column technology, the emergence of applications is expected to continue. The need of reduction in organic solvent consumption also justifies this trend, in the frame of environmentally friendly methods. More and more applications using monolithic columns arise. In the future, monolithic columns are expected to prevail especially in the field of miniaturization and in chip-based nano-LC systems. In this review, we try to summarize any attempt that has been reported in the analysis of a sample of great complexity like milk using the technology of the monoliths.

Synthesis of carbon foam covered with carbon nanofibers as catalyst support for gas phase catalytic reactions

Mesophase pitch based carbon foam (MPCF) covered with a layer of carbon nanofibers (CNFs) was prepared as catalyst support for gas phase catalytic reactions. Owing to the CNF layer, the specific surface area of MPCF increases from 40 to 198m2/g. This kind of catalyst support plays an important role in the enhancement of mass/heat transfer due to the large external surface area, high porosity and high thermal conductivity. When selective catalytic NO reduction was taken as a model reaction, more than 90% NO conversion could be achieved in a wide temperature range of 180–220°C over MnOx–CeO2/MPCF–CNF catalyst.

3D geometry and topology of pore pathways in Opalinus clay: Implications for mass transport

Clay-rich sedimentary rocks are considered as seal lithologies for hosting radioactive waste or as caprocks for geological carbon sequestration sites. Evaluation of the rock's sealing capacity requires a comprehensive understanding of mass transport processes, which, in turn, demands knowledge of the 3D structure of pore space. Here, the use of focused ion beam nanotomography (FIB-nt) in building realistic pore space models is demonstrated along with a novel approach employed to analyze the topology of the pore space. The method was applied to three samples of the Opalinus clay of in northern Switzerland which is considered as a candidate host rock formation for the disposal of radioactive waste. Due to resolution limitations the lower limit of analyzed pore radii was about 10 nm. Pore radii > 10 nm were related to a physical porosity of about 2 vol.%. Comparing the pore size distribution determined by FIB-nt with the one obtained by N 2 adsorption analysis, FIB-nt revealed the structure of about 20% of the total pore space. The total external porosity determined by N 2 adsorption analysis was in the range of 10 to 12 vol.%. Our approach to analyze the complex 3D structure of the pore space was based on converting the voxel based 3D structure into a 3D graph of the pore skeleton. A 3D graph representation permitted determination of the spatial distribution of pore space geometrical properties such as pore path orientation, pore path tortuosity and pore path length. Pore-paths in Opalinus clay show a preferred orientation within the bedding plane in combination with a comparatively low pore path tortuosity. Pore path tortuosity perpendicular to the bedding plane is higher by a factor of as much as five. Anisotropy in pore space is caused by spatial density variations of pore path orientation (i.e. preferred orientations of pore paths) in combination with an elongated pore shape (i.e. low tortuosity).

Comparison between the Efficiencies of sub-2 μm C18 Particles Packed in Narrow Bore Columns

The chromatographic performance of two types of core-shell particles and two fully porous particles packed in 2.1 ID × 50 mm columns was investigated. Comparisons of the performances of the EiS-150-C(18) to that of the Kinetex-1.7 μm-C(18), Acquity-BEH-1.7 μm-C(18), and Zorbax-XDB-1.8 μm-C(18) are made and discussed. The physical factors that govern the performance of these columns, such as particle size distribution and column external, total, and particle porosity of the C(18) packing materials were among the prime foci of investigation. The differences in the mass transfer behavior measured using naphtho[2,3-a]pyrene between these columns provides an indication of improved performance of the new EiS-150-C(18) column. The minimum reduced height equivalent to a theoretical plate (HETP) value for the EiS-150-C(18), h(min) = 1.95, was achieved and was comparable to that obtained from the C(18) phases of the Kinetex (h(min) = 2.53), the Acquity (h(min) = 2.26), and the Zorbax (h(min) = 2.57) columns. This study reveals the importance of the dimension of the shell thickness in controlling the performance of columns packed with shell particles in narrow bore columns.

Numerical modeling of field-activated combustion synthesis process of the B4C system

Abstract A field-activation combustion synthesis process of the 4B + C reactive system was numerically simulated to investigate the effect of external field and porosity on the combustion reaction by an implicit difference method and a Gauss–Seidel iteration procedure. The new features of the model include a consideration of the melting of each constituent of the reactants and product and the inclusion of considerations involving porosity and dilution. The results show that the self-sustaining reactions are not possible until field-activated temperature is more than 1100 K, which agree with the theoretic calculation. As the reactant porosity values are decreased from 60% to 20%, the combustion velocity first increases because of an increase in the thermal conductivity. The combustion velocity, after reaching a maximum, decreases with a further decrease in the porosity because of the high value of the thermal conductivity of the reactants.

Theoretical optimisation of the side-wall of micropillar array columns using computational fluid dynamics

The present study provides an overview of the ideal side-wall position in micro-pillar array columns for the case of semi-embedded side-walls. The position has been determined using computational fluid dynamics simulations of the flow field in flow domains with different side-wall shifts. Optimal side-wall shift values are presented for a wide range of shapes (cylinders, and diamonds and hexagons with different aspect ratios) and packing densities. Simple linear correlations that allow calculating the optimised side-wall geometries for the different considered variety of shapes and packing densities could be established. Interestingly, only two correlations are needed to represent all investigated cases: one correlation for all diamonds, and one correlation for the cylinders and all hexagons. Compared to the case of a flat side-wall, the minimal feature size on the mask can be increased by a factor of 2.5 in the case of cylindrical pillar bed with external porosity ɛ = 0.4, implying that that much smaller pillar diameters can be used in the bulk of the bed before the minimal feature size on the mask falls below the lithography resolution.

Physical characterization and evaluation of HPLC columns packed with superficially porous particles

Two HPLC columns packed with superficially porous packing material (Kinetex™ 1.7 and 2.6 μm C18 particles) were evaluated in terms of their physical properties and performance characteristics. These columns were compared to a column packed with a sub-2 μm totally porous material and to a Halo(TM) column packed with 2.7 μm C18 superficially porous packing. The columns packed with superficially porous particles displayed a comparably narrower size distribution, which is narrower than the distribution of the totally porous sub-2 μm particles. Physical characteristics of the Kinetex™ particles were evaluated in terms of surface area, pore diameter, and specific pore volume. Total, external, internal, and shell porosities among the four different columns were evaluated and compared. The specific permeability for the Kinetex™ columns showed values close to those predicted by the Kozeny-Carman equation. All four columns were evaluated in terms of their chromatographic performance and compared using the Knox equation. The columns packed with the 2.6 and 2.7 μm superficially porous materials showed reduced plate heights below 2, whereas the sub-2 μm particles showed values of 2.2 and above.

Fabrication and Chromatographic Performance of Porous-Shell Pillar-Array Columns

We report on a new approach to obtain highly homogeneous silica-monolithic columns, applying a sol-gel fabrication process inside a rectangular pillar-array column (1 mm in width, 29 microm in height and 33.75 mm in length) having a cross-sectional area comparable to that of a 200 microm diameter circular capillary. Starting from a silicon-based pillar array and working under high phase-separation-tendency conditions (low poly(ethylene glycol) (PEG)-concentration), highly regular silica-based chromatographic systems with an external porosity in the order of 66-68% were obtained. The pillars, 2.4 microm in diameter, were typically clad with a 0.5 microm shell layer of silica, thus creating a 3.4 microm total outer pillar diameter and leaving a minimal through-pore size of 2.2 microm. After mesopore creation by hydrothermal treatment and column derivatization with octyldimethylchlorosilane, the monolithic column was used for chip-based liquid-chromatographic separations of coumarin dyes. Minimal plate heights ranging between 3.9 microm (nonretaining conditions) and 6 mum (for a retention factor of 6.5) were obtained, corresponding to domain-size-reduced plate heights ranging between 0.7 and 1.2. The column permeability was in the order of 1.3 x 10(13) m(2), lower than theoretically expected, but this is probably due to obstructions induced by the sol-gel process in the supply channels.

Characterization of Convection for Molecularly Imprinted Monolith

Convection of molecularly imprinted polymers monolith in LC mode was discussed in this paper. On the MIPs monolith reported here, a flat van Deemter plot of height equivalent to a theoretical plate (HETP) versus superficial velocity was observed. This typical behavior, similar to perfusion packings, suggests that the unique pore structure of the MIPs monolith allowed convection-enhanced mass transfer. Column parameters, e.g., external porosities, internal porosity, column permeability and equivalent sphere dimension, were obtained. Intraparticle Peclet number (λ) was used to characterize the convection in the monolith. In addition, a ratio of the numbers of transfer units, T, for diffusion in the micropores and through-pores has been introduced to quantify the relative importance of the contribution from convection and diffusion to mass transfer. The results show that the flow in a MIP monolith is extremely sensitive to pore size distribution and can be tuned by polymerization parameters.

An experimental study of wind-driven cross ventilation in partitioned buildings

This study uses wind tunnel experiments to investigate wind-driven cross ventilation in partitioned buildings. The discharge coefficients of internal opening under various flow conditions were determined by a fan technique. It was found that the internal discharge coefficient is dependent on the internal porosity, but independent of external porosity, and opening location. Based on the experimental results, a predictive model for internal pressure and ventilation rate of multi-room buildings was developed and verified. This model also revealed that the ventilation rate increases as the internal porosity increases, and that the maximum ventilation rate occurs when the windward and leeward opening areas are equal. Because internal partitions reduce the difference between external and internal pressure, the ventilation rate of partitioned buildings is always smaller than that of buildings without partition. Furthermore, this study provides a quantitative scheme to regulate the ventilation rate of partitioned buildings by controlling the opening areas of windward, leeward and internal openings.

Drug release from PLGA-based microparticles: Effects of the “microparticle:bulk fluid” ratio

The aim of this study was to better understand the importance of the “microparticle mass:bulk fluid volume” ratio during in vitro drug release measurements from PLGA microparticles. Initially porous/non-porous, ibuprofen/lidocaine/propranolol HCl-loaded systems were exposed to phosphate buffer pH 7.4 in agitated test tubes, varying the microparticle concentration from 5:1 to 20:1 mg:mL. Interestingly, drug release was virtually unaffected by the “microparticle mass:bulk fluid volume” ratio in the case of initially porous, ibuprofen-loaded microparticles, exhibiting complete drug release within about 1 week. Optical microscopy, SEM, DSC and pH measurements of the bulk fluid revealed no major impact of the microparticle concentration on the systems’ properties within the first couple of days. However, a more rapid and pronounced decrease in the pH of the release medium occurred after 10–14 d at elevated “microparticle mass:bulk fluid volume” ratios. This resulted in an accelerated: (i) decrease in the glass transition temperature, (ii) microparticle agglomeration, and (iii) increase in the internal and external microparticle porosity. Importantly, this phenomenon did not significantly affect drug release from initially porous, lidocaine-loaded microparticles, exhibiting complete release within about 18 d. In contrast, drug release became significantly faster at higher “microparticle mass:bulk fluid volume” ratios in the case of initially non-porous, lidocaine-loaded microparticles and initially porous, propranolol HCl-loaded systems, exhibiting complete release after 1 and 2 months, respectively. Thus, depending on the type of system, the “microparticle mass:bulk fluid volume” ratio may or may not affect the observed release kinetics in vitro. This should be carefully taken into account when defining the experimental conditions for drug release measurements from this type of advanced drug delivery systems.

Modeling the effect of species retention on the band broadening in perfectly ordered silica monolithic column mimics with variable external porosity and intra‐skeleton diffusivity

Computational fluid dynamics simulations of the band broadening in an idealized, and highly ordered 3-D model of silica monoliths are reported. As this high degree of order induces only a minimal eddy-dispersion, the band broadening is very sensitive to the intra-skeleton diffusivity and retention factor of the analytes. The simulations hence provide a maximal view on how the C(m)- and C(s)-contributions to the band broadening depend on the intra-skeleton diffusivity and retention factor. By comparing two model-structures with different external porosities, some interesting qualitative insights on the effect of the through-pore diameter are obtained as well. Because of the precisely known intra-skeleton diffusivity, the obtained plate height data also provide an ideal test case for the general plate height expression of chromatography. Writing out this model, identifying the geometrical parameters, and determining their value using a parameter fitting algorithm, a set of parameter values can be found which allows to accurately predict the retention factor dependency of the band broadening over a very broad range of mobile phase velocities. Remaining modeling problems are the apparent intra-skeleton diffusion dependency of the shape factor describing the intra-skeleton mass transfer, and the absence of mathematical expressions to predict the model shape factor values.