Parallel Diffusion Research Articles

Understanding the steric effect of graphene in graphene wrapped silicon suboxides anodes for Li-ion batteries

Due to high electrical conductivity and excellent mechanical properties, graphene has attracted extensive attention for Li-ion batteries, but generally as a functional additive with the content ≤1 wt%. Unfortunately, single graphene sheets and orderly stacked graphene films are likely to impede Li-ion transportation as a physical barrier. Herein, we compare pure graphene anodes with different stacking manners and SiO anodes wrapped with variant mass of graphene to unveil the steric hindrance. The rapidly fading capacity indicates a serious steric effect on lithium-ion diffusion once graphene mass loading goes beyond the critical value of ∼0.3 mg cm−2. When graphene stacked to parallel Li-ion diffusion direction, it delivers near-theoretical specific capacity, even for thick electrode up to 5.5 mg cm−2. Furthermore, no remarkably adverse impact from graphene is shown in graphene wrapped SiO anodes even with 19 wt% graphene and at 4C in the half cells. Importantly, polarization associated voltage leap and average voltage demonstrate a significant steric effect when the graphene mass loading exceeds 0.33 mg cm−2 in the commercial level pouch cells. In conclusion, the steric effect on electrochemical performances can be eliminated once the critical value of graphene mass loading in the electrode is below ∼0.3 mg cm−2.

Impact of surface diffusion on transport through porous materials

The peak parking method was applied to evaluate the surface diffusivity Ds of polystyrenes dissolved in a THF/heptane mixture and transported through porous silica materials with various morphologies. With this method, the overall effective diffusivity D is measured experimentally with coarse-grained models like Maxwell equation allowing one to infer the particle diffusivity Dpz. Such particle diffusivity has two main contributions: in-pore diffusivity Dp and surface diffusivity Ds. The diffusion within the pores is determined experimentally using either non-adsorbing conditions or calculated from particle porosity, particle tortuosity, and hydrodynamic hindrance. The surface diffusion coefficient Ds is usually determined using models considering parallel diffusion in the pores and at the surface but this assumption is rather crude. In this paper, to address this problem, another approach is proposed using the Brownian motion of molecules in the pore space. These two approaches lead to similar equations relating the effective diffusion coefficient D, the in-pore diffusion Dp and surface diffusion Ds. The surface diffusion is analyzed as a function of the surface affinity of the probes considered here (polystyrenes of different molecular weights/lengths). Such surface affinity depends both on the probe chain length and surface chemistry of the host solid (the latter being characterized here through the silanol surface density). For short chain lengths, a non-monotonic change in the surface diffusion with affinity (i.e. retention factor) is observed in some cases. Yet, generally, as expected, surface diffusion decreases upon increasing the surface affinity. In contrast to short chain lengths, the longest chain lengths are less sensitive to the silanol surface density.

Impact of Adsorbed Phase Protein Mobility on Chromatographic Separation Performance

Elucidation of protein transport mechanism in ion exchanges is essential to model separation performance. In this work we simulate intraparticle adsorption profiles during batch adsorption assuming typical process conditions for pore, solid and parallel diffusion. Artificial confocal laser scanning microscopy images are created to identify apparent differences between the different transport mechanisms. Typical sharp fronts for pore diffusion are characteristic for binding strengths as low as K = 1. Only at K = 0.1 and lower, the profiles are smooth and practically indistinguishable from a solid diffusion mechanism. During hold and wash steps, at which the interstitial buffer is removed or exchanged, continuation of diffusion of protein molecules is significant for solid diffusion due to the adsorbed phase concentration driving force. For pore diffusion, protein mobility is considerable at low and moderate binding strength. Only when pore diffusion if completely dominant, and the binding strength is very high, protein mobility is low enough to restrict diffusion out of the particles. Simulation of column operation reveals substantial protein loss when operating conditions are not adjusted appropriately.

Fast Chaotic Image Encryption Algorithm Using a Novel Divide and Conquer Diffusion Strategy

To protect image privacy in real-time transmission, a fast chaotic image encryption algorithm using a novel divide and conquer diffusion strategy is proposed in this paper. Firstly, a fast pseudo-random sequence generator is constructed using 2D hyperchaotic systems. And by performing bitwise XOR operation between two integer sequences obtained from different systems, the final key stream used for diffusion will have better randomness and unpredictability. Secondly, to achieve divide and conquer diffusion, the plain image is divided into three parts, then a parallel CBC-based diffusion method can simultaneously act on upper and bottom parts (or left and right parts), which achieves a time complexity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {O}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$W+H$ </tex-math></inline-formula> ). Moreover, within the diffusion process, the mechanism of information interaction on the central row or column further enhances avalanche effect to resist differential attack. Thirdly, the session key of the proposed algorithm is a mixture of the plain image’s hash value and a true random sequence, which not only improve plaintext sensitivity but also realize one-time pad. Finally, experimental results indicate the superiority of our algorithm to resist statistical, chosen-plaintext, entropy, and other common attacks. Furthermore, by comparison with previous works, our algorithm preforms much faster execution speed with only average of 0.08s to encrypt images of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$512\times 512$ </tex-math></inline-formula> , while it provide the same or even higher level of security. Therefore, the proposed algorithm can meet security and efficiency requirements of real-time communications of image data.

Dynamics of a colloid-in-tube host-guest system.

Originated from supramolecular chemistry, the host-guest concept is generalized and appreciated across the fields of enzyme catalysis, biological channel conduction, and carbon nanotube transport, to name a few. Despite the extensive study of host-guest thermodynamics, it is still a fundamental challenge to directly measure its dynamics in real-space and real-time. Herein we approach such dynamics by direct imaging and tracking in a colloid-in-tube system, where self-assembled tubes are the hosts and sphere particles are the guests. The key difference from a previously reported static 1D confinement is that the present tubes are thermally actuated and capable of translations and rotations. It is the host tube thermal motions that impose a number of anomalies to guest particle dynamics including broadened distribution perpendicular to the tube, enhanced diffusion parallel to the tube phenomenologically resembling the rapid flow in ion channels or carbon nanotubes, and induced long-range particle-particle attraction analogous to capillary condensation. This work in the colloidal system is of wide implications for host-guest systems that are naturally embedded in thermal fluctuations such as transmembrane ion channels and carbon nanotube arrays in a soft matrix.

Persistent myelin abnormalities in a third trimester-equivalent mouse model of fetal alcohol spectrum disorder.

Abnormal diffusion within white matter (WM) tracts has been linked to cognitive impairment in children with fetal alcohol spectrum disorder. Whether changes to myelin organization and structure underlie the observed abnormal diffusion patterns remains unknown. Using a third trimester-equivalent mouse model of alcohol exposure, we previously demonstrated acute loss of oligodendrocyte lineage cells with persistent loss of myelin basic protein and lower fractional anisotropy (FA) in the corpus callosum (CC). Here, we tested whether these WM deficits are accompanied by changes in: (i) axial diffusion (AD) and radial diffusion (RD), (ii) myelin ultrastructure, or (iii) structural components of the node of Ranvier. Mouse pups were exposed to alcohol or air vapor for 4h daily from postnatal day (P)3 to P15 (BEC: 160.4±12.0mg/dl; range=128.2 to 185.6mg/dl). Diffusion tensor imaging (DTI) and histological analyses were performed on brain tissue isolated at P50. Diffusion parameters were measured with Paravision™ 5.1 software (Bruker) following ex vivo scanning in a 7.0T MRI. Nodes of Ranvier were identified using high-resolution confocal imaging of immunofluorescence for Nav 1.6 (nodes) and Caspr (paranodes) and measured using Imaris™ imaging software (Bitplane). Myelin ultrastructure was evaluated by calculating the G-ratio (axonal diameter/myelinated fiber diameter) on images acquired using transmission electron microscopy. Consistent with our previous study, high resolution DTI at P50 showed lower FA in the CC of alcohol-exposed mice (p=0.0014). Here, we show that while AD (diffusion parallel to CC axons) was similar between treatment groups (p=0.30), RD (diffusion perpendicular to CC axons) in alcohol-exposed subjects was significantly higher than in controls (p=0.0087). In the posterior CC, where we identified the highest degree of abnormal diffusion, node of Ranvier length did not differ between treatment groups (p=0.41); however, the G-ratio of myelinated axons was significantly higher in alcohol-exposed animals than controls (p=0.023). High resolution DTI revealed higher RD at P50 in the CC of alcohol-exposed animals, suggesting less myelination of axons, particularly in the posterior regions. In agreement with these findings, ultrastructural analysis of myelinated axons in the posterior CC showed reduced myelin thickness in alcohol-exposed animals, evidenced by a higher G-ratio.

Oxygen diffusion at the {111} and {110} surfaces of yttrium doped ceria.

Monte Carlo and molecular dynamics simulations have been combined to study the distribution of Y3+ and O2− ions and the diffusion of O2− ions within CeO2 materials. The calculations indicate that at lower temperatures clustering of Y3+ ions in the bulk material inhibits the diffusion of oxygen ions. Y3+ ions and oxygen vacancies have also been shown to be prevalent within the {111} and {110} surface layers although the degree of Y3+ segregation is much greater at the {110} surface. By combining Monte Carlo and molecular dynamics simulations, both the space charge layer and surface structure have been demonstrated to influence oxide ion diffusion. Oxygen ions are able diffuse parallel to the surface within the {111} surface layers and calculated diffusion coefficients are observed to be greater for the {111} surface but reduced for the {110} surface when compared to that of the bulk material. The distribution of ions at the surface is presented and employed to calculate the charge density. Segregation of dopant ions and vacancies to the surface creates a space charge layer that modifies surface diffusion to a depth of approximately 20 Å. These calculations explain, in part, the wide variation in conductivities observed in grain boundaries of polycrystalline materials and the difficulties in interpreting experimental results.

Regimes of cosmic-ray diffusion in Galactic turbulence

Cosmic-ray transport in astrophysical environments is often dominated by the diffusion of particles in a magnetic field composed of both a turbulent and a mean component. This process, which is two-fold turbulent mixing in that the particle motion is stochastic with respect to the field lines, needs to be understood in order to properly model cosmic-ray signatures. One of the most important aspects in the modeling of cosmic-ray diffusion is that fully resonant scattering, the most effective such process, is only possible if the wave spectrum covers the entire range of propagation angles. By taking the wave spectrum boundaries into account, we quantify cosmic-ray diffusion parallel and perpendicular to the guide field direction at turbulence levels above 5% of the total magnetic field. We apply our results of the parallel and perpendicular diffusion coefficient to the Milky Way. We show that simple purely diffusive transport is in conflict with observations of the inner Galaxy, but that just by taking a Galactic wind into account, data can be matched in the central 5 kpc zone. Further comparison shows that the outer Galaxy at >5 kpc, on the other hand, should be dominated by perpendicular diffusion, likely changing to parallel diffusion at the outermost radii of the Milky Way.

Diffusion anisotropy of Ti in zircon and implications for Ti-in-zircon thermometry

Ti-in-zircon thermometry has become a widely used tool to determine zircon crystallization temperatures, in part due to reports of extremely sluggish Ti diffusion perpendicular to the crystallographic c-axis in this mineral. We have conducted Ti-in-zircon diffusion experiments, focusing on diffusion parallel to the c-axis, at 1 atm pressure between 1100 and 1540°C, with oxygen fugacities equivalent to air and the Ni-NiO buffer. There is no resolvable dependence of Ti diffusion in zircon upon silica or zirconia activity, or upon oxygen fugacity. The diffusion coefficient of Ti in zircon is found to be a weak function of its own concentration, spanning less than 0.5 log units across any profile induced below 1300°C. Ti diffusion in zircon, parallel to the c-axis at 1 atm pressure, is well described using:log10⁡DTi=[1.34(±1.44)−555425(±44820)Jmol−12.303RT(K)]m2s−1 where R is the gas constant in J/(mol⋅K). In conjunction with diffusion coefficients for Ti in zircon perpendicular to the c-axis reported by Cherniak and Watson (2007), strong diffusion anisotropy for Ti in zircon is observed. Diffusion parallel to the c-axis is ∼4-5 orders of magnitude faster than diffusion perpendicular to the c-axis within the experimentally constrained temperature range shared between these two studies (1540-1350°C). This difference increases if the data are extrapolated to lower temperatures and reaches ∼7.5-11 orders of magnitude between 950-600 °C, a typical range for zircon crystallization. Diffusion of Ti in natural zircons will predominantly occur parallel to the c-axis, and the Ti-in-zircon thermometer appears susceptible to diffusive modification under some crustal conditions. Temperatures calculated using this system should therefore be evaluated on a case-by-case basis, particularly when considering high-T, slowly cooled, reheated and/or small zircons.

Microbiological Antibiotic Assay Validation of Gentamicin Sulfate Using Two-Dose Parallel Line Model (PLM)

Till nowadays microbiological assay is still widely used with several antibiotics that are composed of a mixture of related active compounds. However, obtaining a reasonably valid determination of the potency is dependent on the validity and the suitability of the assay design. The present work aimed to validate an assay design of an aminoglycoside antibiotic (Gentamicin Sulfate) using a two-dose Parallel Line Model agar diffusion assay in a large 8×8 rectangular plate. All preparatory procedures were done following United States Pharmacopeia and the Inhibition Zones were measured using a digital caliper to the nearest 0.01 mm. Analysis of variance of compendial requirements of regression and parallelism were found to be satisfactorily meeting the acceptance criteria. Specificity was achieved for the product under investigation with no detectable IZ that could be found for all components except the antibiotic. The validation method showed acceptable linearity of r2≥0.98. Accuracy and precision parameters showed RSD (%)&lt;2. All relative error value estimates were below 4%. The proposed validation design for 32×32 cm antibiotic plates yielded valid results and can be projected for the routine Quality Control analysis of the antibiotic material, especially which is incorporated into a finished medicinal dosage form. Doi: 10.28991/HIJ-2021-02-04-04 Full Text: PDF

Diffusion of Cosmic Rays in MHD Turbulence with Magnetic Mirrors

Abstract As the fundamental physical process with many astrophysical implications, the diffusion of cosmic rays (CRs) is determined by their interaction with magnetohydrodynamic (MHD) turbulence. We consider the magnetic mirroring effect arising from MHD turbulence on the diffusion of CRs. Due to the intrinsic superdiffusion of turbulent magnetic fields, CRs with large pitch angles that undergo mirror reflection, i.e., bouncing CRs, are not trapped between magnetic mirrors, but move diffusively along the turbulent magnetic field, leading to a new type of parallel diffusion, i.e., mirror diffusion. This mirror diffusion is in general slower than the diffusion of nonbouncing CRs with small pitch angles that undergo gyroresonant scattering. The critical pitch angle at the balance between magnetic mirroring and pitch-angle scattering is important for determining the diffusion coefficients of both bouncing and nonbouncing CRs and their scalings with the CR energy. We find nonuniversal energy scalings of diffusion coefficients, depending on the properties of MHD turbulence.

In vivo detection of damage in multiple sclerosis cortex and cortical lesions using NODDI

ObjectiveTo characterise in vivo the microstructural abnormalities of multiple sclerosis (MS) normal-appearing (NA) cortex and cortical lesions (CLs) and their relations with clinical phenotypes and disability using neurite orientation dispersion...

Does powder averaging remove dispersion bias in diffusion MRI diameter estimates within real 3D axonal architectures?

Noninvasive estimation of axon diameter with diffusion MRI holds the potential to investigate the dynamic properties of the brain network and pathology of neurodegenerative diseases. Recent studies use powder averaging to account for complex white matter architectures, but these have not been validated for real axonal geometries from regions that contain fibre crossings. Here, we present 120−304μm long segmented axons from X-ray nano-holotomography volumes of a splenium and crossing fibre region of a vervet monkey brain. We show that the axons in the complex crossing fibre region, which contains callosal, association, and corticospinal connections, exhibit a wider diameter distribution than those of the splenium region. To accurately estimate the axon diameter in these regions, therefore, sensitivity to a wide range of diameters is required. We demonstrate how the q-value, b-value, signal-to-noise ratio and the assumed intra-axonal parallel diffusivity influence the range of measurable diameters with powder average approaches. Furthermore, we show how Gaussian distributed noise results in a wider range of measurable diameter at high b-values than Rician distributed noise, even at high signal-to-noise ratios of 100. The number of gradient directions is also shown to impose a lower bound on measurable diameter. Our results indicate that axon diameter estimation can be performed with only few b-shells, and that additional shells do not improve the accuracy of the estimate. For strong gradients available on human Connectom and preclinical scanners, Monte Carlo simulations of diffusion confirm that powder averaging techniques succeed in providing accurate estimates of axon diameter across a range of diameters, sequence parameters and diffusion times, even in complex white matter architectures. At relatively low b-values, the diameter estimate becomes sensitive to axonal microdispersion and the intra-axonal parallel diffusivity shows time dependency at both in vivo and ex vivo intrinsic diffusivities.

Effect of Light Irradiation on the Diffusion Rate of the Charge Carrier Hopping Mechanism in P3HT–ZnO Nanoparticles Studied by μ+SR

Blended regio-regular P3HT–ZnO nanoparticles are a hybrid material developed as an active layer for hybrid solar cells. The study of the hopping mechanisms and diffusion rates of regio-regular P3HT–ZnO nanoparticles is significant for obtaining intrinsic charge transport properties that provide helpful information for preparing high-performance solar cells. The temperature dependences of the parallel and perpendicular diffusion rates in regio-regular P3HT–ZnO nanoparticles determined from muon spin relaxation measurements were investigated by applying various longitudinal fields. We investigated the effect of light irradiation on the diffusion rates in regio-regular P3HT–ZnO nanoparticles. We found that with increasing temperature, the parallel diffusion rate decreased, while the perpendicular diffusion rate increased. The ratio of the parallel to perpendicular diffusion rate (D‖/D⊥) can be used to indicate the dominant charge carrier hopping mechanism. Without light irradiation, perpendicular diffusion dominates the charge carrier hopping, starting at 25 K, with a ratio of 1.70×104, whereas with light irradiation, the perpendicular diffusion of the charge carrier starts to dominate at the temperature of 10 K, with a ratio of 2.40×104. It is indicated that the additional energy from light irradiation affects the diffusion, especially the charge diffusion in the perpendicular direction.

Filtered Diffusion-Weighted MRI of the Human Cervical Spinal Cord: Feasibility and Application to Traumatic Spinal Cord Injury

In traumatic spinal cord injury, DTI is sensitive to injury but is unable to differentiate multiple pathologies. Axonal damage is a central feature of the underlying cord injury, but prominent edema confounds its detection. The purpose of this study was to examine a filtered DWI technique in patients with acute spinal cord injury. The MR imaging protocol was first evaluated in a cohort of healthy subjects at 3T (n = 3). Subsequently, patients with acute cervical spinal cord injury (n = 8) underwent filtered DWI concurrent with their acute clinical MR imaging examination <24 hours postinjury at 1.5T. DTI was obtained with 25 directions at a b-value of 800 s/mm2. Filtered DWI used spinal cord-optimized diffusion-weighting along 26 directions with a "filter" b-value of 2000 s/mm2 and a "probe" maximum b-value of 1000 s/mm2. Parallel diffusivity metrics obtained from DTI and filtered DWI were compared. The high-strength diffusion-weighting perpendicular to the cord suppressed signals from tissues outside of the spinal cord, including muscle and CSF. The parallel ADC acquired from filtered DWI at the level of injury relative to the most cranial region showed a greater decrease (38.71%) compared with the decrease in axial diffusivity acquired by DTI (17.68%). The results demonstrated that filtered DWI is feasible in the acute setting of spinal cord injury and reveals spinal cord diffusion characteristics not evident with conventional DTI.

Effect of swirl flow on the performance of parallel hub axial annular diffuser

In the present work, the parallel hub axial flow annular diffuser's performance characteristics with divergent casing varying between equivalent cone angle (10°, 15°, and 20°) with area ratio 3 have been evaluated computationally as well as experimentally. The performance of three diffusers were tested at different inlet swirl angles (from 0° to 25°) for swirling and non-swirling flow. Simulations have been carried out on a fully developed flow at Reynolds number 2.5×105. The results were analyzed based on the velocity profiles, static pressure recovery coefficient, and the total pressure loss coefficient. The result analysis shows that the inlet swirl flow improves the recovery of pressure and also delays the flow separation on the casing. Moreover,the findings also show that the best performance was achieved in equivalent cone angle 10° at the inlet swirl angle of 7.5° compared to other diffusers.

Aluminum diffusion in zircon

Al diffusion under anhydrous 1-atm conditions has been measured in natural zircon. Experiments used a source consisting of AlPO4-ZrSiO4 powder mixtures. Experiments were run in air in crimped Pt capsules. Al profiles were measured with Nuclear Reaction Analysis (NRA) using the reaction 27Al(p, γ)28Si. For diffusion parallel to c, the following Arrhenius relation is determined:D = 6.24 × 103 exp.(−774 ± 34 kJ mol−1 /RT) m2s−1Diffusivities normal and parallel to c are similar, indicating little anisotropy of diffusion of Al.Al diffuses more rapidly than tetravalent cations that substitute on the Si site in zircon, but more slowly than trivalent cations substituting on the Zr site. These slow diffusivities indicate that Al chemical signatures will be quite resistant to diffusional alteration. For example, Al compositions at the center of 50 μm radius zircon grains would be preserved over times greater than the age of the earth at temperatures in excess of 1000 °C.

Stimulated excitation of thermal diffusion waves in a magnetized plasma pressure filament

Results are presented from basic heat transport experiments using a magnetized electron temperature filament that behaves as a thermal resonator. Using a small cathode source, low energy electrons are injected along the magnetic field into the afterglow of a pre-existing plasma forming a hot electron filament embedded in a colder plasma. A series of low amplitude, sinusoidal perturbations are added to the cathode discharge bias that creates an oscillating heat source capable of driving large amplitude electron temperature oscillations. Langmuir probes are used to measure the amplitude and phase of the thermal wave field over a wide range of driver frequencies. The results are used to verify the excitation of thermal waves, confirm the presence of thermal resonances, and demonstrate the diagnostic potential of thermal waves through measurement of the parallel thermal diffusivity.

Numerical Modeling of Latitudinal Gradients for Galactic Cosmic-Ray Protons during Solar Minima: Comparing with Ulysses Observations

Abstract The latitudinal gradients of galactic cosmic-ray (GCR) protons measured by Ulysses during two successive minima provide a unique opportunity to study the modulation effects in polar regions of the heliosphere. In this work, a GCR modulation model based on numerically solving the Parker transport equation is used to study the latitudinal distribution of GCR protons in the inner heliosphere. Modifications of the standard Parker heliospheric magnetic field, the reduction of particle drifts, the latitudinal-dependent magnetic turbulence characteristics, and the anisotropic perpendicular diffusion coefficient are incorporated in the numerical model to investigate the corresponding modulation effects. It is found that the latitudinal-dependent magnetic turbulence magnitude, which makes the parallel diffusion coefficient decrease with the increasing of latitude, is crucial to obtain the negative latitude gradient in the inner heliosphere during the negative-polarity solar cycle. For the A &gt; 0 period, on the other hand, the latitudinal diffusion coefficient in the inner heliosphere and the reduced drift velocity in the polar region are more important, while the anisotropic perpendicular diffusion coefficient at high latitude might be not essential. Finally, the proton latitudinal gradient and the corresponding differential intensity along the trajectory of Ulysses during its first and third fast latitude scans are computed, and the results show good agreement with the spacecraft observations.

Patterns of protein adsorption in ion-exchange particles and columns: Evolution of protein concentration profiles during load, hold, and wash steps predicted for pore and solid diffusion mechanisms

Elucidation of protein transport mechanism in ion exchanges is essential to model separation performance. In this work we simulate intraparticle adsorption profiles during batch adsorption assuming typical process conditions for pore, solid and parallel diffusion. Artificial confocal laser scanning microscopy images are created to identify apparent differences between the different transport mechanisms. Typical sharp fronts for pore diffusion are characteristic for Langmuir equilibrium constants of KL ≥1. Only at KL = 0.1 and lower, the profiles are smooth and practically indistinguishable from a solid diffusion mechanism. During hold and wash steps, at which the interstitial buffer is removed or exchanged, continuation of diffusion of protein molecules is significant for solid diffusion due to the adsorbed phase concentration driving force. For pore diffusion, protein mobility is considerable at low and moderate binding strength. Only when pore diffusion if completely dominant, and the binding strength is very high, protein mobility is low enough to restrict diffusion out of the particles. Simulation of column operation reveals substantial protein loss when operating conditions are not adjusted appropriately.