Particle-size distribution effects in batch adsorption

Particle size distribution measurement based on the angular scattering efficiency factor spectra inversion-simulation and experiment

The quantification of the particle size distribution (PSD) within a particle system is significant to various domains, including atmospheric and environmental sciences, material science, civil engineering, and human health. The scattering spectrum reflects the PSD information of the particle system. Researchers have developed high-precision and high-resolution PSD measurements for monodisperse particle systems through scattering spectroscopy. However, for polydisperse particle systems, current methods based on light scattering spectrum and Fourier transform analysis can only obtain the information of the particle component, but cannot provide the relative content information of each component. In this paper, a PSD inversion method based on the angular scattering efficiency factors (ASEF) spectrum is proposed. By establishing a light energy coefficient distribution matrix, and then measuring the scattering spectrum of the particle system, PSD can be measured in conjunction with inversion algorithms. The simulations and experiments conducted in this paper substantiate the validity of the proposed method. Unlike the forward diffraction approach that measures the spatial distribution of scattered light I(θ) for inversion, our method uses the multi-wavelength distribution information of scattered light β(λ). Moreover, the influences of noise, scattering angle, wavelength, particle size range, and size discretization interval on PSD inversion are studied. The method of condition number analysis is proposed to identify the appropriate scattering angle, particle size measurement range, and size discretization interval, and it can reduce the root mean square error(RMSE) of PSD inversion. Furthermore, the method of wavelength sensitivity analysis is proposed to select the spectral band with higher sensitivity to particle size changes, thereby improving the computational speed and avoiding the problem of diminished accuracy caused by the reduction of the number of wavelengths used.

Direct 3D printing of monolithic ion exchange adsorbers

Monolithic adsorbers with anion exchange (AEX) properties have been 3D printed in an easy one-step process, i.e. not requiring post-functionalization to introduce the AEX ligands. The adsorber, 3D printed using a commercial digital light processing (DLP) printer, was obtained by copolymerisation of a bifunctional monomer bearing a positively charged quaternary amine as well as an acrylate group, with the biocompatible crosslinker polyethylene glycol diacrylate (PEGDA). To increase the surface area, polyethylene glycol was introduced into the material formulation as pore forming agent. The influence of photoinitiator (Omnirad 819) and photoabsorber (Reactive Orange 16, RO16) concentration was investigated in order to optimize printing resolution, allowing to reliably 3D print features as small as 200 μm and of highly complex Schoen Gyroids. Protein binding was measured on AEX adsorbers with a range of ligand densities (0.00, 2.03, 2.60 and 3.18 mmol/mL) using bovine serum albumin (BSA) and c-phycocyanin (CPC) as model proteins. The highest equilibrium binding capacity was found for the material presenting the lowest ligand density analysed (2.03 mmol/mL), adsorbing 73.7 ± 5.9 mg/mL and 38.0 ± 2.2 mg/mL of BSA and CPC, respectively. This novel 3D printed material displayed binding capacities in par or even higher than commercially available chromatographic resins. We expect that the herein presented approach of using bifunctional monomers, bearing commonly used chromatography ligands, will help overcome the material limitations currently refraining 3D printing applications in separation sciences.

Impact of Two-Dimensional Particle Size Distribution on Estimation of Water Vapor Diffusivity in Micrometric Size Cellulose Particles

This work aims at assessing the impact of two-dimensional particle size distribution (2D-PSD) on the identification of water vapor diffusivity in micrometric size cellulose particles displaying a size aspect ratio lower than 2 and a cylindrical shape. First, different methodologies to obtain the two-dimensional (2D) particle size distribution (diameter versus length) were compared, based on image analysis. Then, experimental sorption kinetics were obtained by using a quartz crystal microbalance (QCM) coupled with a water vapor adsorption system. Diffusivity values were estimated when considering either the 2D-PSD or global descriptors, such as the mean or median diameter and length of particles. Results revealed that the use of an analytical approach when considering the 2D mean-PSD or the median-PSD was the most accurate way to get diffusivity values at the scale of particles in a polydisperse sample of cellulose particles. Following this approach, a water vapor apparent diffusivity of 3.1 × 10⁻¹² ± 2.3 × 10⁻¹² m²·s⁻¹ was found for the considered cellulose sample. Neglecting PSD in diffusivity estimation led to an underestimation of a factor of 2. This procedure could be extended for all the polydisperse samples in order to have an accurate estimation of water vapor diffusivity at the scale of single particles.

Tortuosity and mass transfer limitations in industrial hydrotreating catalysts: effect of particle shape and size distribution

Comparison of the tortuosity factor of γ-alumina supports and hydrotreating catalysts evaluated with PFG-NMR, inverse liquid chromatography and catalytic experiments.

A semi-empirical model for transport of inorganic nanoparticles across a lipid bilayer: implications for uptake by living cells

Due to increasing application, release of nanoparticles (NPs) and nanomaterials into the environment becomes likely. Knowledge about NP uptake in organisms is crucial for risk assessment including estimations on the behavior of NPs based on their physicochemical properties. In the present study, the authors have applied current scientific knowledge to construct a mathematical model, which estimates the transport of NPs through a model biological membrane. The semi-empirical model developed showed all parameters studied to substantially affect the agglomeration of the NPs in suspension, thereby also affecting passive transport. The authors quantified the effects of pH, ionic strength, organic matter concentration of medium, and NP size of several inorganic NPs on the permeation through the lipid membrane. Model outcomes and experimental results described in literature were strongly correlated for several metal oxide NPs. With caution, the model may be used to explain some of the existing variance in nano-uptake and toxicity experiments.

Patterns of protein adsorption in chromatographic particles visualized by optical microscopy

A new method is presented to image transient patterns of protein adsorption in individual spherical chromatographic particles under strong binding conditions. The method takes advantage of the difference in refractive index between the protein-free and protein-saturated adsorbent matrix. When the particles are viewed with an ordinary microscope using white light illumination, the adsorption front appears as a bright ring that moves in time from the surface of the particle to its center. Experimental data are obtained for the proteins lysozyme and albumin with a commercial agarose-based cation exchanger. Sharp rings are observed in both cases confirming that protein mass transfer within the particles occurs via a shell-progressive diffusion mechanism. Quantitative analysis based on the shrinking core model provides an accurate and precise way of determining the intraparticle diffusivity for individual particles as a function of protein concentration and mobile phase composition.

Chromatography of proteins on charge-variant ion exchangers and implications for optimizing protein uptake rates

Intraparticle transport of proteins usually represents the principal resistance controlling their uptake in preparative separations. In ion-exchange chromatography two limiting models are commonly used to describe such uptake: pore diffusion, in which only free protein in the pore lumen contributes to transport, and homogeneous diffusion, in which the transport flux is determined by the gradient in the total protein concentration, free or adsorbed. Several studies have noted a transition from pore to homogeneous diffusion with increasing ionic strength in some systems, and here we investigate the mechanistic basis for this transition. The studies were performed on a set of custom-synthesized methacrylate-based strong cation exchangers differing in ligand density into which uptake of two proteins was examined using confocal microscopy and frontal loading experiments. We find that the transition in uptake mechanism occurs in all cases studied, and generally coincides with an optimum in the dynamic binding capacity at moderately high flow rates. The transition appears to occur when protein-surface attraction is weakened sufficiently, and this is correlated with the isocratic retention factor k' for the system of interest: the transition occurs in the vicinity of k' approximately 3000. This result, which may indicate that adsorption is sufficiently weak to allow the protein to diffuse along or near the surface, provides a predictive basis for optimizing preparative separations using only isocratic retention data.

Protein adsorption and transport in agarose and dextran-grafted agarose media for ion exchange chromatography

This work examines the relationship between the physical properties of agarose and dextran-grafted agarose cation exchangers and protein adsorption equilibrium and rates. Four different sulfopropyl (SP) matrices were synthesized using a neutral agarose base material--two based on a short ligand chemistry and two obtained by grafting 10 and 40kDa dextran polymers. The pore accessibility, determined by inverse size exclusion chromatography (iSEC) with dextran probes, decreases dramatically as a result of the combined effects of crosslinking, dextran grafting, and the introduction of ionic ligands, with pore radii decreasing from 19nm for the base matrix to 6.1nm for the 40kDa dextran-grafted SP-matrix. In spite of this reduction, while the adsorption isotherms were similar, protein uptake rates were greatly increased with the dextran-grafted SP-matrices, compared to SP-matrices based on the short ligand chemistry. The effective pore diffusivities were 4-10 times higher than free solution diffusivity for the dextran-grafted matrices, indicating that the charged dextran grafts result in enhanced protein mass transfer rates.

Fabrication and characterization of superporous cellulose bead for high-speed protein chromatography

Novel superporous cellulose (SC) matrix has been fabricated by water-in-oil emulsification-thermal regeneration using granules of calcium carbonate as porogenic agents. As a control, microporous cellulose (MC) bead was fabricated in the absence of calcium carbonate. Simultaneously, double cross-linking was applied to enhance the mechanical strength of the particles. The photographs by scanning electron microscopy of the SC bead illustrated that there were more "craters" of several microns scattering on the surface of the beads. It led to a higher water content and effective porosity of the SC medium. The two beads were then modified with diethylaminoethyl (DEAE) group to prepare anion exchangers. The dynamic uptake results of bovine serum albumin (BSA) exhibited that the pore diffusivity of BSA in the DEAE-SC bead was two to three times larger than that in the DEAE-MC bead. In addition, the column packed with the DEAE-SC showed lower backpressure, higher column efficiency and dynamic binding capacity than the column packed with the DEAE-MC at a flow rate range of 150-900cm/h. Moreover, the column efficiency of the DEAE-SC column was independent of flow velocity up to a flow rate of 1200cm/h. All the results exhibited the superior characteristics of the SC bead as a potential medium for high-speed protein chromatography.

Modeling and simulation of protein uptake in cation exchanger visualized by confocal laser scanning microscopy

Confocal laser scanning microscopy (CLSM) has been extensively applied in the area of protein chromatography to investigate the uptake mechanism of protein in adsorbents. However, due to the light attenuation in the deeper layers of a specimen, quantitative analysis using CLSM data is still far from reality. In this work, an attenuation equation for describing the darkening of the CLSM image in the deeper scanning layers was developed. Bovine serum albumin (BSA) adsorption to SP Sepharose FF was performed by batch adsorption and micro-column chromatography on which protein concentration in single absorbents were visualized by CLSM. The parameters in the equation were estimated by fitting it to the fluorescence intensity profiles obtained at adsorption equilibrium, and then the equation was used to simulate the effect caused by the light scattering and absorption. CLSM analysis demonstrated that BSA adsorption to SP Sepharose FF followed the shrinking core pattern and was predicted reasonably well by the pore diffusion model in combination with the attenuation equation. By comparison of the CLSM data with the simulations, it shows that the attenuation equation was useful to demonstrate the validity of an intraparticle mass transport model for the estimation of intraparticle protein concentration profiles.

Analysis of mass transport models for protein adsorption to cation exchanger by visualization with confocal laser scanning microscopy

The mass transfer of bovine serum albumin (BSA) to a cation exchanger, SP Sepharose FF, has been studied by finite batch adsorption experiments. The uptake curve was simulated with three mass transport models (i.e., effective pore diffusion model, surface diffusion model and Maxwell-Stefan model) incorporating the particle size distribution of the adsorbent particles. All the three models can simulate the uptake curves reasonably well. However, how well these models could simulate the real concentration profile within the adsorbent particle cannot be verified by the fitness of the models to the uptake curve. Thus, confocal laser scanning microscopy (CLSM) was used to visualize protein uptake to the porous adsorbent particles during the batch experiments. Using a fluorescent dye-labeled bovine serum albumin (BSA) for the dynamic adsorption experiments, the radial concentration profiles of the labeled BSA molecules into individual adsorbent particles at different times were obtained from the CLSM images. The protein distribution profiles within various particle diameters at different time were compared with the radial protein distributions predicted from the models. It reveals that surface diffusion model describes the intraparticle protein concentration profiles better than the other two models.

Two-component protein adsorption kinetics in porous ion exchange media

This work provides a theoretical analysis of multicomponent adsorption kinetics for conditions typical of protein adsorption in porous ion exchangers as well as experimental results for the adsorption of lysozyme/cytochrome c mixtures in the cation exchanger SP-Sepharose-FF. The theory predicts the formation of overshoots in the intraparticle concentration profiles and in the total amount adsorbed for the more weakly adsorbed component. An analytical solution valid for the case where the isotherms are rectangular is developed and found to be in good agreement with the limiting behavior of the general numerical solution of the model equations. The experimental results show that the two proteins are competitively adsorbed and that an overshoot of adsorbed cytochrome c occurs during simultaneous adsorption. Model predictions based on the assumption that the adsorption isotherms are rectangular and that lysozyme completely displaces cytochrome c are in qualitative and quantitative agreement with the experimental kinetics suggesting that the overshoot phenomena observed with multicomponent systems in these resins can be explained with a diffusion model without the need to account for flux coupling or electrophoretic contributions to transport.

Influence of particle diameter distribution on protein recovery in the expanded bed adsorption process

The General Rate model has been developed and solved to describe protein adsorption in an expanded bed. The model takes into account axial and local variation of particle size distribution (PSD), external and intra-particle mass transfer resistances, and dispersion in liquid phase. The influence of PSD on breakthrough profiles has been analysed. The simulation results show that for a significantly high expanded bed the lower part of the breakthrough curve profiles, calculated for local particle size distribution (LPSD) and for axial average particle size distribution (APSD) are very similar. However, the upper part of breakthrough profiles calculated for LPSD approaches inlet concentration much more slowly than those calculated for APSD. The retention times of the lower part of uptake curves calculated with average particle diameter are constantly shorter than those obtained from LPSD. For the calculation of the dynamic capacity (DC), the LPSD can be replaced by APSD for large expanded bed heights. Using breakthrough profiles calculated for average particle size, DC values are constantly underestimated.

Intraparticle phosphorus diffusion in a drinking water treatment residual at room temperature

Phosphorus (P) has been recognized as one of the major limiting nutrients that are responsible for eutrophication of surface waters, worldwide. Efforts have been concentrated on reducing P loads reaching water bodies, via surface runoff and/or leaching through a soil profile. Use of drinking water treatment residuals (WTRs) is an emerging cost-effective practice to reduce soluble P in poorly P-sorbing soils or systems high in P. Literature suggests that WTRs have huge P sorption capacities. We hypothesized that P sorption would be limited by diffusional constraints imposed by the WTR particles. Selected chemical and physical (specific surface area, particle size distribution) characteristics of an iron-based WTR were measured. Sorption P isotherms at room temperature were constructed, and sorption kinetics were monitored. An intraparticle diffusion model was utilized to fit the kinetic data. Results showed that the WTR dramatically reduced soluble P, showing nonequilibrium characteristics, even after 80 d of reaction. Specific surface area (SSA) measured with CO2 gas was significantly greater than the traditional BET-N2 value (28 versus 3.5 m2 g(-1)), suggesting that a large amount of internal surfaces might be present in the WTR. The intraparticle P diffusion model was modified to include the wide particle size distribution of the WTR. The intraparticle diffusion model fitted the data well (r2 = 0.83). We calculated a maximum apparent P diffusion coefficient value of 4 x 10(-15) cm2 s(-1), which agrees with published values for intraparticle diffusion in microporous sorbents. This work may be useful for predicting long-term sorption characteristics of WTRs, since WTRs have been suggested as potential long-term immobilizers of sorbed P in P-sensitive ecosystems.