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.     

The History of Interferometry for Measuring Diffusion Coefficients

The history of the development and use of interferometric and other optical techniques for the measurements of diffusion coefficients in liquid mixtures is reviewed. The greatest emphasis is on Gouy and Rayleigh interferometry because they have been extensively developed to yield the most precise results.     

Protein diffusion coefficients determined by macroscopic-gradient Rayleigh interferometry and dynamic light scattering

Dynamic light scattering (DLS) is extensively used for measuring macromolecule diffusion coefficients. Contrary to classical techniques based on macroscopic concentration gradients, DLS probes microscopic fluctuations in concentration. DLS accuracy and its concordance with macroscopic-gradient techniques remains an outstanding important issue. We measured lysozyme diffusion coefficients in aqueous salt using both DLS and Rayleigh interferometry, a highly accurate macroscopic-gradient technique. The precision of our results is unprecedented. We find that our DLS values were systematically 2% higher than interferometry values. We believe that our interferometric measurements have produced the most accurate diffusion data ever reported for a protein, providing a new standard for quality control of DLS measurements. Furthermore, by interferometry, we have determined the whole diffusion coefficient matrix required for rigorously describing lysozyme-salt coupled diffusion. For the first time, we experimentally demonstrate that DLS does not provide the protein diffusion coefficient but one eigenvalue of the diffusion coefficient matrix.     

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.     

Determination of preferential interaction parameters by multicomponent diffusion. applications to poly(ethylene glycol)-salt-water ternary mixtures

Poly(ethylene glycol) (PEG) is a hydrophilic nonionic polymer used in many biochemical and pharmaceutical applications. We report the four diffusion coefficients for the PEG-KCl-water ternary system at 25 degrees C using precision Rayleigh interferometry. Here, the molecular weight of PEG is 20 kg mol(-1), which is comparable to that of proteins. The four diffusion coefficients are examined and used to determine thermodynamic preferential interaction coefficients. We find that the PEG preferential hydration in the presence of KCl is 1 order of magnitude larger than that previously obtained under the same conditions for lysozyme, a protein of similar molecular weight. In correspondence, the coupled diffusion in the PEG case was greater than that observed in the lysozyme case. We attribute this difference to the greater exposure of polymer coils to the surrounding fluid compared to that of globular compact proteins. Moreover, we observe that the PEG preferential hydration significantly decreases as salt concentration increases and attribute this behavior to the polymer collapse. Finally, we have also employed the equilibrium isopiestic method to validate the accuracy of the preferential interaction coefficients extracted from the diffusion coefficients. This experimental comparison represents an important contribution to the relation between diffusion and equilibrium thermodynamics.     

Velocity‐correlation analysis in polymer–solvent mixtures

The subject of this article is the combined interpretation of intradiffusion and mutual‐diffusion data for polymer–solvent mixtures in terms of integrals over velocity self‐correlation functions and velocity cross‐correlation functions. The combination of mutual‐diffusion, intradiffusion, and activity data allows the evaluation of velocity‐correlation coefficients (VCCs) and distinct‐diffusion coefficients in systems containing one monodisperse solute. This study is the first attempt to extend these approaches to polymers that are polydisperse solutes. Because of the polydispersity, this correlation analysis may become critical for polymers. Its application to polydisperse samples requires the reduction of intradiffusion and mutual‐diffusion coefficients to the same average. After such a reduction, the VCCs and distinct‐diffusion coefficients are evaluated for a homologous series of poly(ethylene glycol)s (PEGs). Attractive PEG–PEG interactions depend on the chain length and concentration of PEG. In this analysis, network formation in PEG–water systems appears to be a smooth process. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 43–51, 2002     

Small-angle neutron scattering from typical synthetic and biopolymer solutions

Small-angle neutron scattering (SANS) has been used to investigate the solution properties of four model polymers, two poly-amino acids [poly(lysine) and poly(proline)], and two water-soluble synthetic polymers [poly(acrylic acid) and poly(ethylene oxide)]. In each case, one of the two polymers is charged, while the other is neutral. SANS measurements were made in the semi-dilute concentration regime in two different solvents [d-water and d-ethylene glycol]. The scattering signals were decomposed into low-Q clustering and high-Q solvation contributions. The temperature dependence of the scattering parameters was determined for poly(lysine) and poly(ethylene oxide) solutions over the temperature range of 13 to 82 °C. Analysis of the SANS spectra revealed that with increasing temperature, the solvation intensity increased in both solvents, while the clustering intensity increased in d-water and decreased in d-ethylene glycol. Significant differences were observed between the SANS spectra of charged and neutral polymer solutions. However, biopolymers and synthetic polymers exhibited qualitatively similar behavior.     

Polystyrene nanoparticles based on poly(butyl methacrylate-g-methoxypoly(ethylene glycol)) and poly(methyl methacrylate-g-methoxypoly(ethylene glycol)) graft copolymers

The solubilization of styrene by poly(butyl methacrylate-g-methoxypoly(ethylene glycol)) and poly(methyl methacrylate-g-methoxypoly(ethylene glycol)) graft copolymers has been examined. From turbidity measurements the solubility limit of the monomer in the micelles was obtained and the distribution coefficients were evaluated. Dynamic light scattering revealed that below the solubility limit, solubilization leads to a slight increase in micelle size, while above the solubility limit, there is a dramatic increase in particle size and turbidity as oil-in-water emulsions are formed through coalescence of monomer-swollen micelles. Polymerizations carried out below the solubility limit using the graft copolymer micelles as templates resembled microemulsion polymerizations in nature and led to very fine sterically stabilized polystyrene latex particles. Through careful control of the monomer concentration and the polymerization temperature it was possible to obtain spherical nanosize latex particles with similar size to those of the micelle precursors (10 nm) up to 11% monomer by weight. Polymerizations above the solubility limit, on the other hand, showed similarities with emulsion polymerizations and resulted in larger particles with higher polydispersity.     

Series expansion methods for extracting ternary diffusion coefficients from Rayleigh interferometric data

Three series expansions are examined for use in extracting ternary diffusion coefficients from Rayleigh interferometric data for free diffusion experiments. Convergence comparisons show that, providing enough terms are used, two of the three are suitable, including one used earlier by Albright and Sherrill. A new simpler analysis, using only linear least squares, has been applied to simulated and real data with good results. Advantages and disadvantages of series methods are compared to a direct non-linear least squares analysis.     

On the interpretation of ternary diffusion measurements in low-molecular weight fluids by dynamic light scattering

Dynamic light scattering (DLS) allows for efficient measurement of physical transport properties in fluids. It is now a well established technique for determination of mutual mass diffusion coefficients in binary mixtures and multicomponent macromolecular solutions. More recently, ternary systems of low-molecular weight compounds have been analyzed by DLS where it was found that only one of the two mass diffusion modes can be observed. In this work, a theoretical interpretation of these findings is provided. For this purpose, a simple theory is developed that describes the observed signals. Thereby, it can be shown that both diffusion modes contribute to the signal but one mode is strongly enhanced for situations typically encountered in DLS experiments. The developed theory thus clarifies the relationship between ternary DLS measurements and other diffusion experiments. It provides the practical basis for quantitative analysis of DLS experiments in ternary low-molecular weight fluids.     

Poly(ethylene glycol)-b-poly(epsilon-caprolactone) and PEG-phospholipid form stable mixed micelles in aqueous media

Novel mixed polymeric micelles formed from biocompatible polymers, poly(ethylene glycol)-b-poly(epsilon-caprolactone) (PEG(5000)-b-PCL(x)) and 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-methoxy poly(ethylene glycol) (PEG-DSPE), possess small size and high thermodynamic stability, raising their potential as long circulating carriers in the context of delivery of antineoplastic and antibiotic drugs. Formation of mixed polymeric micelles was confirmed using size exclusion chromatography and 1H NMR NOESY. Steady-state fluorescence measurements revealed depressed critical micellar concentrations indicative of a cooperative interaction between component hydrophobic blocks, which was quantified using the pseudophase model for micellization. Steady-state fluorescence measurements indicated that the mixed polymeric micelle cores possess intermediate micropolarity and high microviscosity. Pulsed field gradient spin-echo measurements were used to characterize micellar diffusion coefficients, which agree well with those obtained using dynamic light scattering. NOE spectra suggested that the hydrophobic polymer segments from individual components are in close proximity, giving evidence for the formation of a relatively homogeneous core. Contrary to one-component PEG(5000)-b-PCL(x) micelles, the mixed polymeric micelles could incorporate clinically relevant levels of the poorly water soluble antibiotic, amphotericin B (AmB). AmB encapsulation and release studies revealed an interesting composition-dependent interaction of the drug with the mixed polymeric micelle core.     

Thermal diffusion behavior of nonionic surfactants in water

We studied the thermal diffusion behavior of hexaethylene glycol monododecyl ether (C12E6) in water by means of thermal diffusion forced Rayleigh scattering (TDFRS) and determined Soret coefficients, thermal diffusion coefficients, and diffusion constants at different temperatures and concentrations. At low surfactant concentrations, the measured Soret coefficient is positive, which implies that surfactant micelles move toward the cold region in a temperature gradient. For C12E6/water at a high surfactant concentration of w1 = 90 wt % and a temperature of T = 25 degrees C, however, a negative Soret coefficient S(T) was observed. Because the concentration part of the TDFRS diffraction signal for binary systems is expected to consist of a single mode, we were surprised to find a second, slow mode for C12E6/water system in a certain temperature and concentration range. To clarify the origin of this second mode, we investigated also, tetraethylene glycol monohexyl ether (C6E4), tetraethylene glycol monooctyl ether (C8E4), pentaethylene glycol monododecyl ether (C12E5), and octaethylene glycol monohexadecyl ether (C16E8) and compared the results with the previous results for octaethylene glycol monodecyl ether (C10E8). Except for C6E4 and C10E8, a second slow mode was observed in all systems usually for state points close to the phase boundary. The diffusion coefficient and Soret coefficient derived from the fast mode can be identified as the typical mutual diffusion and Soret coefficients of the micellar solutions and compare well with the independently determined diffusion coefficients in a dynamic light scattering experiment. Experiments with added salt show that the slow mode is suppressed by the addition of w(NaCl) = 0.02 mol/L sodium chloride. This suggests that the slow mode is related to the small amount of absorbing ionic dye, less than 10(-5) by weight, which is added in TDFRS experiments to create a temperature grating. The origin of the slow mode of the TDFRS signal will be tentatively interpreted in terms of a ternary mixture of neutral micelles, dye-charged micelles, and water.     

(Liquid + liquid) equilibria for ternary mixtures of (ethylene glycol + toluene + n-octane)

Tie-line data for ternary systems of (ethylene glycol + toluene + n-octane) at three temperatures (295.15, 301.15, and 307.15) K are reported. The compositions of liquid phases at equilibrium were determined and the results were correlated with the UNIQUAC and NRTL activity coefficient models. The partition coefficients and the selectivity factor of ethylene glycol are calculated and compared to suggest which ethylene glycol is more suitable for extracting of toluene from n-octane. The phase diagrams for the studied ternary mixtures including both the experimental and correlated tie lines are presented. From the phase diagrams and the selectivity factors, it is concluded that ethylene glycol may be used as a suitable solvent in extraction of toluene from n-octane mixtures.     

Sign change of the Soret coefficient of poly(ethylene oxide) in water/ethanol mixtures observed by thermal diffusion forced Rayleigh scattering

Soret coefficients of the ternary system of poly(ethylene oxide) in mixed water/ethanol solvent were measured over a wide solvent composition range by means of thermal diffusion forced Rayleigh scattering. The Soret coefficient S(T) of the polymer was found to change sign as the water content of the solvent increases with the sign change taking place at a water mass fraction of 0.83 at a temperature of 22 degrees C. For high water concentrations, the value of S(T) of poly(ethylene oxide) is positive, i.e., the polymer migrates to the cooler regions of the fluid, as is typical for polymers in good solvents. For low water content, on the other hand, the Soret coefficient of the polymer is negative, i.e., the polymer migrates to the warmer regions of the fluid. Measurements for two different polymer concentrations showed a larger magnitude of the Soret coefficient for the smaller polymer concentration. The temperature dependence of the Soret coefficient was investigated for water-rich polymer solutions and revealed a sign change from negative to positive as the temperature is increased. Thermodiffusion experiments were also performed on the binary mixture water/ethanol. For the binary mixtures, the Soret coefficient of water was observed to change sign at a water mass fraction of 0.71. This is in agreement with experimental results from the literature. Our results show that specific interactions (hydrogen bonds) between solvent molecules and between polymer and solvent molecules play an important role in thermodiffusion for this system.     

Thermodynamic Study of Poly(ethylene glycol) in Water/1-Propanol Solutions by Viscometry

In this work, the intrinsic viscosities of poly(ethylene glycol) with a molar mass of 20 kg⋅mol⁻¹ were measured in water/1-propanol solutions from 283.1 to 313.1 K. The expansion factors of the polymer chains were calculated from the intrinsic viscosity data. The thermodynamic parameters entropy of dilution parameter, the heat of dilution parameter, theta temperature, polymer–solvent interaction parameter and second osmotic virial coefficient were derived from the temperature dependence of the polymer chain expansion factor. The thermodynamic parameters indicate that mixtures of water/1-propanol become weaker solvents for poly(ethylene glycol) with increasing temperature. Also, the thermodynamic parameters indicate that the solvent ability of mixed water/1-propanol for poly(ethylene glycol) is less than that of pure water.     

Study of the self‐diffusion of poly(ethylene glycol)s in poly(vinyl alcohol) aqueous systems

We have measured the self‐diffusion coefficients of a series of oligo‐ and poly(ethylene glycol)s with molecular weights ranging from 150 to 10,000, in aqueous solutions and gels of poly(vinyl alcohol) (PVA), using the pulsed‐gradient spin‐echo NMR techniques. The PVA concentrations varied from 0 to 0.38 g/mL which ranged from dilute solutions to polymer gels. Effects of the diffusant size and polymer concentration on the self‐diffusion coefficients have been investigated. The temperature dependence of the self‐diffusion coefficients has also been studied for poly(ethylene glycol)s with molecular weights of 600 and 2,000. Several theoretical models based on different physical concepts are used to fit the experimental data. The suitability of these models in the interpretation of the self‐diffusion data is discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2396–2403, 1999     

Activity Coefficients of NaCl in Ethylene Glycol‐Water Mixtures Using Potentiometric Measurements at 288.15, 298.15 and 308.15 K

The mean activity coefficients of NaCl in ethylene glycol‐water mixtures were determined in the range of w=0.10 to 0.40 ethylene glycol at 288.15, 298.15 and 308.15 K using potentiometric measurements. The Pitzer and extended Debye‐Hückel equations were used to describe the nonideal behavior of the electrolyte. Osmotic coefficients and the standard Gibbs energy of NaCl‐ethylene glycol‐water were calculated.     

Temperature dependence of viscosity and density of viscous liquids determined from thermal noise spectra of uncalibrated atomic force microscope cantilevers

We demonstrate that the thermal response of uncalibrated atomic force microscope cantilevers can be used to extract the density and the viscosity of viscous liquids with good accuracy. Temperature dependent thermal noise spectra were measured in water/poly(ethylene glycol) mixtures. Empirical parameters characteristic of the resonance behavior of the system were extracted from data recorded for one of the solutions at room temperature. These parameters were then employed to determine both viscosity and density values of the solutions simultaneously at different temperatures. In addition, activation energies for viscous flow were determined from the viscosity values obtained. The method presented is both fast and reliable and has the potential to be applied in connection with microfluidic systems, making macroscopic amounts of liquid and separate measurements with a viscometer and a densimeter redundant.     

Measurements of molecular and thermal diffusion coefficients in ternary mixtures

Thermal diffusion coefficients in three ternary mixtures are measured in a thermogravitational column. One of the mixtures consists of one normal alkane and two aromatics (dodecane-isobutylbenzene-tetrahydronaphthalene), and the other two consist of two normal alkanes and one aromatic (octane-decane-1-methylnaphthalene). This is the first report of measured thermal diffusion coefficients (for all species) of a ternary nonelectrolyte mixture in literature. The results in ternary mixtures of octane-decane-1-methylnaphthalene show a sign change of the thermal diffusion coefficient for decane as the composition changes, despite the fact that the two normal alkanes are similar. In addition to thermal diffusion coefficients, molecular diffusion coefficients are also measured for three binaries and one of the ternary mixtures. The open-end capillary-tube method was used in the measurement of molecular diffusion coefficients. The molecular and thermal diffusion coefficients allow the estimation of thermal diffusion factors in binary and ternary mixtures. However, in the ternaries one also has to calculate phenomenological coefficients from the molecular diffusion coefficients. A comparison of the binary and ternary thermal diffusion factors for the mixtures comprised of octane-decane-1-methylnaphthalene reveals a remarkable difference in the thermal diffusion behavior in binary and ternary mixtures.     

Interaction between poly(ethylene glycol) and two surfactants investigated by diffusion coefficient measurements

Dynamic light scattering (DLS) and fluorescence recovery after pattern photobleaching (FRAPP) were used to study the interaction of low molecular weight poly(ethylene glycol) (PEG) with micelles of two different surfactants: tetradecyldimethyl aminoxide (C(14)DMAO, zwitterionic) and pentaethylene glycol n-dodecyl monoether (C(12)E(5), non-ionic). By using an amphiphilic fluorescent probe or a fluorescent-labeled PEG molecule, FRAPP experiments allowed to follow the diffusion of the surfactant-polymer complex either by looking at the micelle diffusion or at the polymer diffusion. Experiments performed with both fluorescent probes gave the same diffusion coefficient showing that the micelles and the polymer form a complex in dilute solutions. Similar experiments showed that PEG interacts as well with pentaethylene glycol n-dodecyl monoether (C(12)E(5)).