Insights from a Thermodynamic Study and Its Implications on the Freeze-Drying of Pharmaceutical Solutions Containing Water and tert-Butyl Alcohol as a Cosolvent.

In the production of several anticancer drugs, tert-butyl alcohol (TBA) is present as a co-solvent in the aqueous drug solution. In order to ascertain if TBA should be removed beforehand or if it could be retained to facilitate the freeze-drying of the drug solution, it is important to acquire both qualitative and quantitative knowledge of the variations occurring with respect to time in heat and mass transfer during the freeze-drying process. In this work, a thermodynamic model employing the UNIFAC (Dortmund) method was developed to determine the values of the currently experimentally unavailable partial vapor pressures of the binary gas mixture of water and TBA in equilibrium with their frozen solid mixtures. The results agree satisfactorily with relevant experimental measurements and indicate that TBA vapor has constantly higher pressures than water vapor and also promotes the vapor pressure of water during sublimation. The responses of the partial pressures of water and TBA vapors are found, through the analysis of their partial and total differentials, to be increasingly more sensitive to temperature change at elevated temperatures and to compositional change when the mole fraction of water in a frozen binary mixture approaches zero. The increased vapor pressures due to TBA lead to higher total pressures at the moving interface separating the dried and frozen layers, resulting in larger total pressure gradients and convective mass transfer rates in the dried layer during primary drying. But the higher total pressures reduce the magnitude of the bulk diffusivity of the gas mixture, and combined with the smaller Knudsen diffusivity of TBA, the pressures could significantly affect the competing mass transfer mechanisms during freeze-drying. The approach presented in this work could provide a general thermodynamic modeling approach for predicting the vapor pressures of multicomponent vapor mixtures in equilibrium with their multicomponent solid frozen mixtures.LAY ABSTRACT: tert-Butyl alcohol (TBA) is present as a cosolvent in a number of anticancer drug solutions. Its presence is known to affect the freeze-drying process of the drug solutions. In order to determine a better operational policy with respect to the freeze-drying process, a thermodynamic approach was developed in this work to provide the needed data of water and TBA vapors that are currently experimentally unavailable. The results agree satisfactorily with experimental measurements. They indicate that TBA vapor has constantly higher pressures than water vapor, promoting faster sublimation and generating higher total pressures at the moving interface to enhance convective mass transfer during primary drying. However, the higher total pressures also reduce the magnitude of the bulk diffusivity of the gas mixture, and combined with the smaller Knudsen diffusivity of TBA, these pressures could significantly affect the competing mass transfer mechanisms during freeze-drying. The thermodynamic method and analysis developed in this work are useful in their own physicochemical importance and also provide a necessary component for a new class of freeze-drying mathematical models. Moreover, they could provide a general modeling approach for predicting the vapor pressures of multicomponent vapor mixtures in equilibrium with their frozen solid mixtures.

Modeling the construction of polymeric adsorbent media: effects of counter-ions on ligand immobilization and pore structure.

Molecular dynamics modeling and simulations are employed to study the effects of counter-ions on the dynamic spatial density distribution and total loading of immobilized ligands as well as on the pore structure of the resultant ion exchange chromatography adsorbent media. The results show that the porous adsorbent media formed by polymeric chain molecules involve transport mechanisms and steric resistances which cause the charged ligands and counter-ions not to follow stoichiometric distributions so that (i) a gradient in the local nonelectroneutrality occurs, (ii) non-uniform spatial density distributions of immobilized ligands and counter-ions are formed, and (iii) clouds of counter-ions outside the porous structure could be formed. The magnitude of these counter-ion effects depends on several characteristics associated with the size, structure, and valence of the counter-ions. Small spherical counter-ions with large valence encounter the least resistance to enter a porous structure and their effects result in the formation of small gradients in the local nonelectroneutrality, higher ligand loadings, and more uniform spatial density distributions of immobilized ligands, while the formation of exterior counter-ion clouds by these types of counter-ions is minimized. Counter-ions with lower valence charges, significantly larger sizes, and elongated shapes, encounter substantially greater steric resistances in entering a porous structure and lead to the formation of larger gradients in the local nonelectroneutrality, lower ligand loadings, and less uniform spatial density distributions of immobilized ligands, as well as substantial in size exterior counter-ion clouds. The effects of lower counter-ion valence on pore structure, local nonelectroneutrality, spatial ligand density distribution, and exterior counter-ion cloud formation are further enhanced by the increased size and structure of the counter-ion. Thus, the design, construction, and functionality of polymeric porous adsorbent media will significantly depend, for a given desirable ligand to be immobilized and represent the adsorption active sites, on the type of counter-ion that is used during the ligand immobilization process. Therefore, the molecular dynamics modeling and simulation approach presented in this work could contribute positively by representing an engineering science methodology to the design and construction of polymeric porous adsorbent media which could provide high intraparticle mass transfer and adsorption rates for the adsorbate biomolecules of interest which are desired to be separated by an adsorption process.

Adsorption in columns packed with porous adsorbent particles having partially fractal structures.

A mathematical model is constructed and solved that could describe the dynamic behavior of the adsorption of a solute of interest in single and stratified columns packed with partially fractal porous adsorbent particles. The results show that a stratified column bed whose length is the same as that of a single column bed, provides larger breakthrough times and a higher dynamic utilization of the adsorptive capacity of the particles than those obtained from the single column bed, and the superior performance of the stratified bed becomes especially more important when the superficial velocity of the flowing fluid stream in the column is increased to accommodate increases in the system throughput. This occurs because the stratified column bed provides larger average external and intraparticle mass transfer and adsorption rates per unit length of packed column. It is also shown that increases in the total number of recursions of the fractal and the ratio of the radii between larger and smaller microspheres that make up the partially fractal particles, increase the intraparticle mass transfer and adsorption rates and lead to larger breakthrough times and dynamic utilization of the adsorptive capacity of the particles. The results of this work indicate that highly efficient adsorption separations could be realized through the use of a stratified column comprised from a practically reasonable number of sections packed with partially fractal porous adsorbent particles having reasonably large (i) total number of recursions of the fractal and (ii) ratio of the radii between larger and smaller microspheres from which the partially fractal particles are made from. It is important to mention here that the physical concepts and modeling approaches presented in this work could be, after a few modifications of the model, applied in studying the dynamic behavior of chemical catalysis and biocatalysis in reactor beds packed with partially fractal porous catalyst particles.

The dynamic behavior of a stratified column bed packed with porous adsorbent particles having partially fractal structures and a nonuniform ligand density distribution.

The dynamic behavior of adsorption in a single column and in stratified column beds packed with porous adsorbent particles having partially fractal structures is studied when all columns have the same total length and the spatial ligand density distribution in the porous microspheres from which the porous adsorbent particles are made, is either uniform or nonuniform and such that the concentration of the immobilized ligands (active sites) increases monotonically from the center of the microspheres to their outer surface. The total number of immobilized ligands in the porous adsorbent particles has the same value whether the spatial ligand density distribution is uniform or nonuniform. The results in this study clearly show that for a given value of the superficial velocity of the flowing fluid stream in the column (for a given value of throughput) the breakthrough time is significantly increased when the radius of the microspheres is decreased, the total number of sections of the stratified column bed is increased, and the spatial ligand density distribution employed in the microspheres is nonuniform. Furthermore, when the superficial velocity of the flowing fluid stream in the column is increased (throughput is increased) the effect that (i) the reduction in the radius of the microspheres and (ii) the increase in the number of sections of the stratified column bed have on providing robust and effective dynamic adsorptive capacity and smaller reductions on the breakthrough time is substantially larger than that realized through the use of the nonuniform ligand density distribution. Similar trends are also observed in the dynamic behavior of adsorption in the systems studied here when the value of the concentration of the adsorbate in the flowing fluid stream entering the column (inlet concentration) has such a high magnitude that the value of the equilibrium concentration of the adsorbate in the adsorbed phase determined from the equilibrium Langmuir isotherm that would correspond to the inlet concentration of the adsorbate in the flowing fluid stream is, for all practical purposes, at its saturation limit.

Molecular modeling of polymeric adsorbent media: the effects of counter-ions on ligand immobilization and pore structure.

Molecular dynamics modeling and simulations are employed to study the immobilization of ligands on the surface of the pores of a base porous polymeric matrix. The results show the significant effects that the counter-ions have on the spatial distribution of the density of immobilized ligands as well as on the pore size and pore connectivity distributions of the porous adsorbent medium being constructed. The results for the systems studied in this work indicate that by using doubly charged counter-ions whose numbers during ligand immobilization are half to those of singly charged counter-ions, the ligand immobilization process proceeds faster and the magnitude of local nonelectroneutrality becomes smaller. More importantly, the pore structures of the adsorbent media resulting from the system using doubly charged counter-ions have porous structures that are characterized by more mid-sized pores and higher pore connectivity than the porous adsorbent structures generated by the system employing singly charged counter-ions and, furthermore, the density distribution of the immobilized ligands in the porous structures where doubly charged counter-ions are employed tends to be more uniform laterally and the ligands are surrounded by fewer counter-ions. These characteristics affected by the use of doubly charged counter-ions could provide important advantages with respect to the transport and adsorption of adsorbate biomolecules of interest. Furthermore, the results of this work indicate that the type of counter-ions being used in the ligand immobilization process could represent an additional control variable for affecting the ligand density distribution as well as the pore size and pore connectivity distributions of the porous structure of the adsorbent medium being constructed.

Adsorbents and columns in analytical high-performance liquid chromatography: a perspective with regard to development and understanding.

A brief historical survey is presented on the evaluation of silica adsorbents in analytical HPLC. The theory of analytical HPLC is mostly still being based on the height equivalent to a theoretical plate concept and the van Deemter equation that was derived from gas phase adsorption involving a linear adsorption isotherm and fast mass transfer kinetics. One can obviously wonder whether the use of the van Deemter equation is relevant and valid for the evaluation of the performance of HPLC systems, where most often the liquid solutes involve charged molecules in electrolytes and in very many cases the adsorbates are macromolecules having diffusion coefficients of small magnitude. Instead of the van Deemter equation, a multi-scale modelling approach that involves microscopic and macroscopic dynamic non-linear mass-transfer-rate models should be employed. Furthermore, advanced experimental methods for the characterisation of porous media and the distribution of the density of immobilised active sites (e.g., ligands) on surfaces as well as microscopic pore-network modelling and molecular dynamics modelling and simulation methods could be used for the design of novel adsorbents whose porous structures and immobilised active sites would provide effective mass transport and adsorption rates for realising efficient separations as well as high dynamic capacities when larger throughputs are required.

Adsorption in a stratified column bed packed with porous particles having partially fractal structures and a distribution of particle diameters.

Stratified column bed systems whose sections are formed by packing adsorbent particles with a partially fractal structure are proposed and studied. The simulation results clearly show that the breakthrough times and the shape of the breakthrough curves obtained from stratified column beds are significantly larger and sharper than those obtained from conventional columns. The stratified column beds provide, to the designer and user of chromatographic column systems, more degrees of freedom with respect to the number of parameters and variables that could be controlled in the design, construction, and operation of efficient chromatographic adsorption systems. Furthermore, the results suggest that the stratified column beds could provide a higher dynamic adsorptive capacity than conventional columns when it is required to increase the column throughput.

Effects on the dynamic utilization of the adsorptive capacity of chromatographic columns induced by non-uniform ligand density distributions.

The dynamic behavior of the breakthrough curves of a single adsorbate obtained from columns employing adsorbent media which differ from one another only on the spatial distribution of the immobilized ligands in the porous particles is examined. The spatial distributions of the immobilized ligands considered in this study are uniform and non-uniform, but the total number of immobilized ligands in the particles has the same value whether the spatial distribution is uniform or non-uniform. The results clearly show that the columns employing adsorbent particles in which the spatial distribution of the immobilized ligands is non-uniform and such that the concentration of the immobilized ligands increases monotonically from the center of the particle to the outer particle surface, exhibit (i) larger breakthrough times, (ii) steeper breakthrough curves, and (iii) higher dynamic utilization of the adsorptive capacity of the column as the superficial velocity of the flowing fluid stream in the column increases (throughput increase) than the columns using adsorbent particles in which the spatial distribution of the immobilized ligands is uniform. The importance of employing in the columns adsorbent media whose spatial ligand density distributions satisfy the mathematical property of monotonically increasing ligand concentration with increasing from the particle center radial position, will be significantly enhanced when (i) the size of the particle radius is increased, and (ii) continuous counter-current and periodic counter-current (simulated moving beds) operations are employed.

Protein adsorption in porous adsorbent particles: a multiscale modeling study on inner radial humps in the concentration profiles of adsorbed protein induced by nonuniform ligand density distributions.

Recently published results determined from molecular dynamics (MD) modeling and simulation studies have shown that the spatial distribution of the density of immobilized charged ligands in ion-exchange porous adsorbent particles is most likely nonuniform and the adsorbent particles also exhibit local nonelectroneutrality. In this work, the functional forms of the nonuniform spatial distributions of the density of the immobilized ligands in four different porous adsorbent media that were determined by MD studies were employed in a macroscopic continuum model describing the transport and adsorption of a single protein in the porous particles of the four different adsorbent media. The results clearly show that inner radial humps in the concentration profiles of the adsorbed protein can occur when the spatial distribution of the density of the immobilized ligands in the porous adsorbent particles is nonuniform and also has local maxima or minima along the radial direction in the particle. The results also indicate that the rate at which the equilibrium condition is approached depends significantly on the functional form of the spatial distribution of the density of the immobilized ligands. When adsorption equilibrium has been reached, the concentration profile of the adsorbed protein exhibits the shape of the spatial distribution of the density of the immobilized ligands. The results suggest that the technique of confocal scanning laser microscopy could be used to measure the concentration profile of an adsorbed protein at equilibrium and this measurement could provide the spatial distribution of the density of the immobilized ligands, and such measurements could also be used for quality control of the adsorbent medium. The results in this work have also implications in the modeling, design, analysis, and quality control of systems involving biocatalysis. Furthermore, the results clearly indicate that it is very important to study the dynamic behavior of an adsorption system having a nonuniform spatial distribution in the density of the immobilized charged ligands and where (i) both monovalent and multivalent interactions between the single charged adsorbate and the immobilized charged ligands occur and (ii) the values of the pH and ionic strength are such that the electrophoretic effects are active.

The effect of the pore structure and zeta potential of porous polymer monoliths on separation performance in ion-exchange mode.

Most often, in bioseparations involving charged macromolecules, the chromatographic systems have low Reynolds and high Peclet numbers. For such systems, an expression is developed and presented in this work for evaluating the throughput in polymeric monoliths where ion-exchange adsorption occurs, as a function of (i) the pressure drop along the length of the monolith, (ii) the functional form and width of the throughpore-size distribution of the monolith, and (iii) the magnitude of the zeta potential on the surface of the throughpores of the monolith. Gaussian and log-normal throughpore-size distributions whose mean throughpore-size and standard deviation values are based on experimentally measured throughpore-size distribution data by mercury porosimetry employed on polymeric monoliths are used in this work, and their effect on the throughput relative to that obtained from a polymeric monolith having a uniform throughpore-size distribution is studied for different values of the ratio of the standard deviation to the mean throughpore-size. The results indicate that relatively modest increases in the throughput, when compared with the throughput that could be achieved in a polymeric monolith having a uniform throughpore-size distribution, could be obtained in polymeric monoliths having disperse throughpore-size distributions, and the magnitude of the increase becomes larger when the disperse distribution is skewed to larger throughpore sizes. Furthermore, the results of this work indicate that, under certain conditions, relatively modest increases in the throughput of a charged analyte could also be achieved by altering the value of the zeta potential on the surface of the throughpores of the monolith. Due to the difficulties inherent in controlling the functional form and width of the throughpore-size distribution during the synthesis of polymeric monoliths, it would appear to be more practical to increase the value of the throughput of a charged analyte by altering the value of the zeta potential through prudent selection of the ion-exchange surface functional groups and fine-tuned with the pH of the mobile phase. Thus, for ion-exchange chromatography systems, the zeta potential could be considered an important parameter for column designers and operators to manipulate, since its alteration could increase the through-put of a charged analyte in polymeric monoliths or in columns packed with charged particles.