Modulation of drug transport properties by multicomponent diffusion in surfactant aqueous solutions

Diffusion coefficients of drug compounds are crucial parameters used for modeling transport processes. Interestingly, diffusion of a solute can be generated not only by its own concentration gradient but also by concentration gradients of other solutes. This phenomenon is known as multicomponent diffusion. A multicomponent diffusion study on drug-surfactant-water ternary mixtures is reported here. Specifically, high-precision Rayleigh interferometry was used to determine multicomponent diffusion coefficients for the hydrocortisone-tyloxapol-water system at 25 degrees C. For comparison, diffusion measurements by dynamic light scattering were also performed. In addition, drug solubility was measured as a function of tyloxapol concentration, and drug-surfactant thermodynamic interactions using the two-phase partitioning model were characterized. The diffusion results are in agreement with a proposed coupled multicomponent diffusion model for ternary mixtures relevant to nonionic drug and surfactant molecules. Theoretical examination of diffusion-based drug transport in the presence of concentration gradients of micelles shows that drug fluxes and drug concentration profiles are significantly affected by coupled multicomponent diffusion. This work provides guidance for the development of accurate models of diffusion-based controlled release in multicomponent systems and for the applications of micelle concentration gradients to the modulation of diffusion-based drug transport.     

The effect of salt stoichiometry on protein-salt interactions determined by ternary diffusion in aqueous solutions

We report the four diffusion coefficients for the lysozyme-MgCl2-water ternary system at 25 degrees C and pH 4.5. The comparison with previous results for the lysozyme-NaCl-water ternary system is used to examine the effect of salt stoichiometry on the transport properties of lysozyme-salt aqueous mixtures. We find that the two cross-diffusion coefficients are very sensitive to salt stoichiometry. One of the cross-diffusion coefficients is examined in terms of common-ion, excluded-volume, and protein-preferential hydration effects. We use the four ternary diffusion coefficients to extract chemical-potential cross-derivatives and protein-preferential interaction coefficients. These thermodynamic data characterize the protein-salt thermodynamic interactions. We demonstrate the presence of the common-ion effect (Donnan effect) by analyzing the dependence of the preferential-interaction coefficient not only with respect to salt concentration but also with respect to salt stoichiometry. We conclude that the common-ion effect and the protein-preferential hydration are both important for describing the lysozyme-MgCl2 thermodynamic interaction.     

Form of multicomponent Fickian diffusion coefficients matrix

The form of multicomponent Fickian diffusion coefficients matrix in thermodynamically stable mixtures is established based on the form of phenomenological coefficients and thermodynamic factors. While phenomenological coefficients form a symmetric positive definite matrix, the determinant of thermodynamic factors matrix is positive. As a result, the Fickian diffusion coefficients matrix has a positive determinant, but its elements — including diagonal elements — can be negative. Comprehensive survey of reported diffusion coefficients data for ternary and quaternary mixtures, confirms that invariably the determinant of the Fickian diffusion coefficients matrix is positive.     

Onsager consistency checks for multicomponent diffusion models

The Onsager reciprocity relations are applied to several recently proposed multicomponent diffusion models in an attempt to gauge their validity and ascertain their applicability. Each of these friction‐based diffusion models stems from the more general Bearman formalism through various assumptions regarding the individual friction coefficients. By assessing the compliance of the Bearman model with respect to the Onsager relations, we ascertain the validity of the simplifications introduced to each diffusion model and suggest which postulates lead to results consistent with the Onsager relations. Although some models are not consistent with the Onsager relations, each model predicts the multicomponent drying of polymer films reasonably well. The necessity for consistency with the Onsager development is, therefore, revisited. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1496–1504, 2001     

Mixture diffusion in nanoporous adsorbents: equivalence of Fickian and Maxwell-Stefan approaches

Nanopore diffusion in multicomponent adsorption is described using different macroscopic theories: Onsager irreversible thermodynamics, Maxwell-Stefan, and Fickian approaches. A new equivalence between Fickian and Maxwell-Stefan formulations is described by [D]=[n(s)][B](-1)[Gamma][n(s)](-1). The elements of D and B are explicitly related to the Fickian and Maxwell-Stefan diffusivities, respectively. Only when the saturation loadings ni(s) for different components are the same can the matrix be reduced to the generally accepted equation [D]=[B](-1)[Gamma]. On the basis of the relationship between the irreversible thermodynamics and Maxwell-Stefan approaches, an equation is derived for a binary system with the symmetric form (1/Eth1 + theta2/Eth12)(1/Eth2 + theta1/ Eth21)=(L11L22)/(L12L21)(theta1theta2)/(Eth12Eth21) The Maxwell-Stefan binary exchange coefficients Ethij are shown to depend not only on the Maxwell-Stefan diffusivities, Ethi, but also on the Onsager coefficients. For a strong molecular interaction, that is, Ethi>Ethij , the ratio of Onsager coefficients will approach unity, giving the commonly used relation L12=square root L11L22 . In addition, the Maxwell-Stefan diffusivities, Ethi, are shown to depend on the interaction effects in mixtures, and Ethi in mixtures will not generally be equal to pure component values evaluated at the same total fractional loading.     

Inferences on dynamic water structure in aqueous solutions from diffusion measurements

The dynamic, hydrogen-bonded structure of water can be profoundly affected by addition of solutes as reflected by the resulting solute—solvent interactions. Measurements of diffusion coefficients for the solute species and for water are a useful probe for studying those interactions and changes in the dynamic water structure.

The analysis of transport properties of electrolyte solutions is presently approached both theoretically and experimentally by the use of generalised transport coefficients such as Onsager phenomenological coefficients, velocity correlation coefficients or the closely related distinct diffusion coefficients of Friedman. However, two of these approaches generally use a solvent-fixed frame of reference and thereby exclude the information available from studying the diffusion of the solvent.

The velocity correlation coefficient approach is used here to examine hydrogen-bonding effects in binary solution containing water as one component. We discuss also examples where intra-diffusion data for water in aqueous solutions give important insights into the dynamic structure of aqueous solutions.     

Composition of Coexisting Liquid Phases Determined by Rayleigh Interferometry

Rayleigh interferometry is a precise macroscopic gradient technique that has been utilized for the determination of multicomponent diffusion coefficients. Because concentration gradients in multicomponent systems drive a diffusion-based partial separation of different solutes, this interferometric technique may be potentially used for the determination of solute concentrations. We have therefore theoretically examined how Rayleigh interferometry can be applied for the determination of composition of ternary aqueous mixtures. The effect of cross-term diffusion coefficients on the accuracy of this method is also discussed. Furthermore, since the poly(vinyl)alcohol+poly(ethylene)glycol+water system undergoes liquid–liquid phase separation (LLPS), we have experimentally characterized its LLPS boundary at 25 °C. The corresponding tie-lines were characterized by determining the composition of the two coexisting liquid phases using Rayleigh interferometry.     

Diffusion NMR spectroscopy in supramolecular and combinatorial chemistry: an old parameter--new insights

Intermolecular interactions in solution play an important role in molecular recognition, which lies at the heart of supramolecular and combinatorial chemistry. Diffusion NMR spectroscopy gives information over such interactions and has become the method of choice for simultaneously measuring diffusion coefficients of multicomponent systems. The diffusion coefficient reflects the effective size and shape of a molecular species. Applications of this technique include the estimation of association constants and mapping the intermolecular interactions in multicomponent systems as well as investigating aggregation, ion pairing, encapsulation, and the size and structure of labile systems. Diffusion NMR spectroscopy can also be used to virtually separate mixtures and screen for specific ligands of different receptors, and may assist in finding lead compounds.     

Interaction effects in multicomponent separation by reverse osmosis

Separation of multicomponent mixtures, in particular ternary systems, was investigated theoretically and experimentally. The interactions in various multicomponent mixtures were determined. Using data from literature as well as the limited data obtained in our laboratory, we identified the situations where the multicomponent effects are strong. A correlation between the coupled permeability coefficients and straight permeability coefficients and concentration of components in ternary systems was obtained. Capabilities of thermodynamic models in describing the electrolyte–nonelectrolyte systems consisting of a weak acid were also investigated. The results of this work show that the multicomponent effects can be used in improving the separation properties of membranes. The findings of this study may be applied to several processes including recovery of small amounts of metals from wastes, separation of ionic compounds from organic, and separation of weak and strong electrolytes.     

Numerical calculation of the Onsager transport coefficients for isothermal binary electrolytes

The Ebeling-Falkenhagen diffusion equations are applied to calculate the Onsager transport coefficients as well as the electrical conductances, transference numbers, and mutual diffusion coefficients for isothermal binary electrolytes. For this purpose the hierarchy of diffusion equations is closed on the level of the binary distribution functions by the superposition approximation. The resulting system of common differential equations is solved by numerical methods. Hydrodynamic interactions are taken into account up to first order. Some results are given for symmetrically charged binary electrolytes with hard-core ions (restricted primitive interaction model). The model parameters (Bjerrum parameter and Debye screening length) are chosen to represent strong electrolytes up to the molar region.     

Limiting law for distinct diffusion coefficients in ionic solutions

The limiting laws for the distinct diffusion coefficient and the corresponding Onsager phenomenological coefficient are obtained from the cluster theory of electrolyte conductance. Results are given for single electrolytes and common-ion mixtures with unrestricted charges and friction coefficients in both cases.     

Activity of water in aqueous systems; a frequently neglected property

In this critical review, the significance of the term 'activity' is examined in the context of the properties of aqueous solutions. The dependence of the activity of water(l) at ambient pressure and 298.15 K on solute molality is examined for aqueous solutions containing neutral solutes, mixtures of neutral solutes and salts. Addition of a solute to water(l) always lowers its thermodynamic activity. For some solutes the stabilisation of water(l) is less than and for others more than in the case where the thermodynamic properties of the aqueous solution are ideal. In one approach this pattern is accounted for in terms of hydrate formation. Alternatively the pattern is analysed in terms of the dependence of practical osmotic coefficients on the composition of the aqueous solution and then in terms of solute-solute interactions. For salt solutions the dependence of the activity of water on salt molalities is compared with that predicted by the Debye-Hückel limiting law. The analysis is extended to consideration of the activities of water in binary aqueous mixtures. The dependence on mole fraction composition of the activity of water in binary aqueous mixtures is examined. Different experimental methods for determining the activity of water in aqueous solutions are critically reviewed. The role of water activity is noted in a biochemical context, with reference to the quality, stability and safety of food and finally with regard to health science.     

On the mutual diffusion properties of ethanol-water mixtures

The structural organization, the number of hydrogen bonds (H bond), and the self- and mutual diffusion coefficients of ethanol-water mixtures were studied by molecular dynamics simulation. It was found that both the numbers of H bonds per water and per ethanol decrease as the mole fraction of ethanol increases. The composition dependences and the relationships between the self- and the mutual diffusion coefficients were further discussed. The self-diffusion coefficient of water has a large drop as the concentration of ethanol increases from 0 to 0.3 and then it nearly keeps constant, while that of ethanol has a minimum around ethanol mole fraction of 0.5. The mutual diffusion coefficient could be divided into two parts, the kinematic factor and the thermodynamic factor. Both the kinematic and thermodynamic factors for ethanol-water mixtures were calculated. It was found that the change trend of mutual diffusion coefficients with the composition is mainly dependent on the thermodynamic factors.     

Rapid diffusion of CH4/H2 mixtures in single-walled carbon nanotubes

Equilibrium molecular dynamics (EMD) are used to examine the self-diffusion and macroscopic diffusion of CH4/H2 mixtures adsorbed inside a (10,10) single-walled carbon nanotube. EMD can be used to determine the macroscopic diffusion coefficients of adsorbed mixtures by evaluating the matrix of Onsager transport coefficients. Earlier studies have indicated the diffusion of light gases adsorbed as single components in carbon nanotubes is extremely rapid compared to that in other known nanoporous materials. The results presented here indicate that extremely rapid diffusion can also occur for mixtures of adsorbed molecules. The rapid diffusion of adsorbed molecules and the strong coupling between the fluxes of the adsorbed species in a mixture have interesting implications for uses of carbon nanotubes in membrane-based applications.     

A self-diffusion study of poly(ethylene-oxide) alkyl alcohols

The self-diffusion coefficients of HDO and some surfactants in aqueous mixtures at different concentrations, below the critical micelle concentration, have been determined by means of the NMR, spin-echo pulsed field gradient method. The surfactant solutes chosen were ethylene glycol-pentyl alcohol (diethylene glycolpentylalcohol, ethylene glycol-hexyalcohol, diethylene glycol-hexyl alcohol, triethylene glycol-hexyl alcohol, tetraethylene glycol-hexyl alcohol, pentaethylene glycol-hexyl alcohol). The interactions in solution are studied by analyzing the solute self-diffusion coefficients extrapolated to infinite dilution. These values are compared with those of 1-alkanols. The slope of the self diffusion coefficientsvs. the solute concentration are correlated with the microscopic friction coefficients. A model for interpreting the experimental data is suggested.     

Thermodynamics of benzene + alkane and cyclohexane + alkane systems. An estimation of the free volume

A thermodynamic model for multicomponent mixtures is derived introducing the Carnahan and Starling expression for the free volume in the van der Waals partition function. The derivation of the model is equivalent to the one for the Prigogine-Flory-Patterson (PFP) model, and our results are compared with those of the PFP model.Expressions for the equation of state, excess properties, thermal expansion and thermal pressure coefficients are given. The values of the characteristic parameters for some molecules are calculated, and the results of predicted excess properties are compared with those already known for the PFP model. The discussion of binary mixtures is centred on the families of systems formed by benzene or cyclohexane and an alkane.     

Development of a Unifying Framework for the Restrictions in Multi-component Diffusion Close to Equilibrium

In this work a unifying framework is developed for multi-component diffusion close to equilibrium by proposing additional restrictions for the Fickian diffusion coefficients such as the Onsager reciprocal relations. Moreover, it is shown that these additional restrictions can explain the discrepancy, reported in the literature, of calculating negative concentrations in Fickian ternary free diffusion observed even if the second thermodynamic law constraints and the phase stability criteria are satisfied. It is believed that this work could be used to further investigate multi-component diffusion.     

Testing the accuracy of correlations for multicomponent mass transport of adsorbed gases in metal-organic frameworks: diffusion of H2/CH4 mixtures in CuBTC

Mass transport of chemical mixtures in nanoporous materials is important in applications such as membrane separations, but measuring diffusion of mixtures experimentally is challenging. Methods that can predict multicomponent diffusion coefficients from single-component data can be extremely useful if these methods are known to be accurate. We present the first test of a method of this kind for molecules adsorbed in a metal-organic framework (MOF). Specifically, we examine the method proposed by Skoulidas, Sholl, and Krishna (SSK) ( Langmuir, 2003, 19, 7977) by comparing predictions made with this method to molecular simulations of mixture transport of H 2/CH 4 mixtures in CuBTC. These calculations provide the first direct information on mixture transport of any species in a MOF. The predictions of the SSK approach are in good agreement with our direct simulations of binary diffusion, suggesting that this approach may be a powerful one for examining multicomponent diffusion in MOFs. We also use our molecular simulation data to test the ideal adsorbed solution theory method for predicting binary adsorption isotherms and a method for predicting mixture self-diffusion coefficients.     

Local and average diffusion of nanosolutes in agarose gel: the effect of the gel/solution interface structure

Fluorescence correlation spectroscopy (FCS) has been used to study the diffusion of nanometric solutes in agarose gel, at microscopic and macroscopic scales. Agarose gel was prepared and put in contact with aqueous solution. Several factors were studied: (i) the role of gel relaxation after its preparation, (ii) the specific structure of the interfacial zone and its role on the local diffusion coefficient of solutes, and (iii) the comparison between the local diffusion coefficient and the average diffusion coefficient in the gel. Fluorescent dyes and labeled biomolecules were used to cover a size range of solutes of 1.5 to 15 nm. Their transport through the interface from the solution toward the gel was modeled by the first Fick's law based on either average diffusion coefficients or the knowledge of local diffusion coefficients in the system. Experimental results have shown that, at the liquid/gel interface, a gel layer with a thickness of 120 microm is formed with characteristics significantly different from the bulk gel. In particular, in this layer, the porosity of agarose fiber network is significantly lower than in the bulk gel. The diffusion coefficient of solutes in this layer is consequently decreased for steric reasons. Modeling of solute transport shows that, in the bulk gel, macroscopic diffusion satisfactorily follows the classical Fick's diffusion laws. For the tested solutes, the local diffusion coefficients in the bulk gel, measured at microscopic scale by FCS, were equal, within experimental errors, to the average diffusion coefficients applicable at macroscopic scales (>or=mm). This confirms that anomalous diffusion applies only to solutes with sizes close to the gel pore size and at short time (相似文献   

Dynamics of ionic and hydrophobic solutes in water-methanol mixtures of varying composition

We have carried out a series of molecular-dynamics simulations of water-methanol mixtures containing either an ionic or a neutral atomic solute to investigate the effects of composition of the mixture on the diffusion of these solutes. Altogether, we have considered 17 different systems of varying composition ranging from pure water to pure methanol. The diffusion coefficients of ionic solutes are found to show nonideal behavior with variation of composition of the solvent mixture. The extent of nonideality of the solute diffusion is found to be similar to the nonideality that is observed for the diffusion and orientational relaxation of water and methanol molecules in these mixtures and is attributed to the enhanced stability of the hydrogen bonds and formation of interspecies complexes in the mixtures. The neutral solute shows characteristics of hydrophobic solvation and its diffusion decreases monotonically with increase of methanol concentration. The present simulation results are compared with those of experiments wherever available.