Diffusiophoresis is the isothermal migration of a colloidal particle through a liquid caused by a cosolute concentration gradient. Although diffusiophoresis was originally introduced using ...hydrodynamics, it can also be described by employing the framework of multicomponent diffusion. This not only enables the extraction of diffusiophoresis coefficients from measured multicomponent-diffusion coefficients but also their theoretical interpretation using fundamental thermodynamic and transport parameters. This review discusses the connection of diffusiophoresis with the 2 × 2 diffusion-coefficient matrix of ternary liquid mixtures. Specifically, diffusiophoresis is linked to the cross-term diffusion coefficient characterizing diffusion of colloidal particles due to cosolute concentration gradient. The other cross-term, which describes cosolute diffusion due to the concentration gradient of colloidal particles, is denoted as osmotic diffusion. Representative experimental results on diffusiophoresis and osmotic diffusion for polyethylene glycol and lysozyme in the presence of aqueous salts and osmolytes are described. These data were extracted from ternary diffusion coefficients measured using precision Rayleigh interferometry at 25 °C. The preferential-hydration and electrophoretic mechanisms responsible for diffusiophoresis are examined. The connection of diffusiophoresis and osmotic diffusion to preferential-interaction coefficients, Onsager reciprocal relations, Donnan equilibrium and Nernst-Planck equations are also discussed.
•Diffusiophoresis is the migration of a macromolecule caused by a cosolute gradient.•Preferential hydration is the thermodynamic excess of water molecules near protein surface.•A hydrodynamic model ...describing how preferential hydration drives diffusiophoresis of globular particles is developed.•Experimental data on lysozyme diffusiophoresis indicate that mean-force potential describing preferential hydration is weak compared to thermal energy and interaction range is an appreciable fraction of protein size.
Diffusiophoresis is the migration of a colloidal particle through a fluid, caused by a cosolute concentration gradient. Preferential hydration is a thermodynamic phenomenon responsible for particle diffusiophoresis from high to low cosolute concentration in water. Here, steady-state Navier-Stokes equation for incompressible fluids, with particle modeled as an inpenetrable rigid sphere, is employed for deriving a mathematical expression of the diffusiophoresis coefficient. Mean-force potentials with arbitrary interaction range but with interaction energies small or comparable with thermal energy are employed to describe water-mediated particle-cosolute interactions. This choice of potential is movitated by previous work showing that only fluid particles weakly interacting with the colloildal particle can cause diffusiophoresis. Preferential hydration has been extensively investigated for proteins. Thus, the proposed model is applied to available experimental diffusiophoresis coefficients of lysozyme in aqueous NaCl and KCl at pH 4.5 and 25 °C. This analysis also includes data on salt osmotic diffusion, describing salt diffusion caused by protein concentration gradients. The preferential-hydration contribution of experimental lysozyme diffusiophoresis is obtained after removing electrophoretic diffusiophoresis. Examination of these experimental data shows that the mean-force potential describing preferential hydration is indeed weak, with an interaction range that is an appreciable fraction of particle size.
Display omitted
Salt-induced diffusiophoresis is the migration of a colloidal particle in water due to a directional salt concentration gradient. An important example of colloidal particles is represented by ...micelles, generated by surfactant self-assembly in water. For non-ionic surfactants containing polyethylene glycol (PEG) groups, PEG preferential hydration at the micelle–water interface is expected to drive micelle diffusiophoresis from high to low salt concentration. However, micelles are reversible supramolecular assemblies, with salts being able to promote a significant change in micelle size. This phenomenon complicates the description of diffusiophoresis. Specifically, it is not clear to what extent the salt-induced growth of micelles affects micelle diffusiophoresis. In this paper, a multiple-equilibrium model is developed for assessing the contribution of the micelle growth and preferential hydration mechanisms to the diffusiophoresis of non-ionic micelles. The available experimental data characterizing the effect of NaCl on Triton X-100 aggregation number are combined with data on diffusiophoresis and the preferential hydration of PEG chains to show that the contribution of the micelle growth mechanism to overall diffusiophoresis is small compared to that of preferential hydration.
Diffusiophoresis is the migration of a colloidal particle in water driven by concentration gradients of cosolutes such as salts. We have experimentally characterized the diffusiophoresis of tyloxapol ...micelles in the presence of MgSO
, a strong salting-out agent. Specifically, we determined the multicomponent-diffusion coefficients using Rayleigh interferometry, cloud points, and dynamic-light-scattering diffusion coefficients on the ternary tyloxapol-MgSO
-water system at 25 °C. Our experimental results show that micelle diffusiophoresis occurs from a high to a low salt concentration (positive diffusiophoresis). Moreover, our data were used to characterize the effect of salt concentration on micelle size and salt osmotic diffusion, which occurs from a high to a low surfactant concentration. Although micelle diffusiophoresis can be attributed to the preferential hydration of the polyethylene glycol surface groups, salting-out salts also promote an increase in the size of micellar aggregates, ultimately leading to phase separation at high salt concentration. This complicates diffusiophoresis description, as it is not clear how salt-induced surfactant aggregation contributes to micelle diffusiophoresis. We, therefore, developed a two-state aggregation model that successfully describes the observed effect of salt concentration on the size of tyloxapol micelles, in the case of MgSO
and the previously reported case of Na
SO
. Our model was then used to theoretically evaluate the contribution of salt-induced aggregation to diffusiophoresis. Our analysis indicates that salt-induced aggregation promotes micelle diffusiophoresis from a low to a high salt concentration (negative diffusiophoresis). However, we also determined that this mechanism marginally contributes to overall diffusiophoresis, implying that preferential hydration is the main mechanism causing micelle diffusiophoresis. Our results suggest that sulfate salts may be exploited to induce the diffusiophoresis of PEG-functionalized particles such as micelles, with potential applications to microfluidics, enhanced oil recovery, and controlled-release technologies.
The role of salting-out strength on (1) polymer diffusiophoresis from high to low salt concentration, and (2) salt osmotic diffusion from high to low polymer concentration was investigated. These two ...cross-diffusion phenomena were experimentally characterized by Rayleigh interferometry at 25 °C. Specifically, we report ternary diffusion coefficients for polyethylene glycol (molecular weight, 20 kg·mol–1) in aqueous solutions of several salts (NaCl, KCl, NH4Cl, CaCl2, and Na2SO4) as a function of salt concentration at low polymer concentration (0.5% w/w). We also measured polymer diffusion coefficients by dynamic light scattering in order to discuss the interpretation of these transport coefficients in the presence of cross-diffusion effects. Our cross-diffusion results, primarily those on salt osmotic diffusion, were utilized to extract N w, the number of water molecules in thermodynamic excess around a macromolecule. This preferential-hydration parameter characterizes the salting-out strength of the employed salt. For chloride salts, changing cation has a small effect on N w. However, replacing NaCl with Na2SO4 (i.e., changing anion) leads to a 3-fold increase in N w, in agreement with cation and anion Hofmeister series. Theoretical arguments show that polymer diffusiophoresis is directly proportional to the difference N w – n w, where n w is the number of water molecules transported by the migrating macromolecule. Interestingly, the experimental ratio, n w/N w, was found to be approximately the same for all investigated salts. Thus, the magnitude of polymer diffusiophoresis is also proportional to salting-out strength as described by N w. A basic hydrodynamic model was examined in order to gain physical insight on the role of n w in particle diffusiophoresis and explain the observed invariance of n w/N w. Finally, we consider a steady-state diffusion problem to show that concentration gradients of strong salting-out agents such as Na2SO4 can produce large amplifications and depletions of macromolecule concentration. These effects may be exploited in self-assembly and adsorption processes.
Isothermal mutual diffusion coefficients (interdiffusion coefficients) were measured for K
2
SO
4
(aq) at 298.15 ± 0.00
5
K, at numerous concentrations ranging from dilute solutions to near ...saturation (0.59648 mol·dm
–3
; 0.61349 mol·kg
–1
) under free diffusion boundary conditions, using high precision Rayleigh interferometry. Under the experimental conditions these diffusion coefficients are on the volume-fixed reference frame
D
v
. Two series of experiments were performed, the first using the traditional experimental approach with a mercury lamp source and with the interference patterns being recorded on glass photographic plates, and the second with a He–Ne laser light source and computerized data acquisition using a photodiode array. The results from both series of experiments are in excellent agreement, and generally yield diffusion coefficients precise to at least 0.002 × 10
–9
m
2
·s
–1
(0.15% to 0.19%) and in most cases to 0.001 × 10
–9
m
2
·s
–1
(0.07% to 0.1%). These experiments also yield accurate values of the refractive index differences for the solution pairs used in the diffusion experiments. The new diffusion coefficients are compared to two sets of published values of diffusion coefficients for K
2
SO
4
(aq) which are somewhat discrepant from each other. This study extends and complements our earlier work on the diffusion coefficients of the most common brine salts: NaCl(aq), KCl(aq), MgCl
2
(aq), CaCl
2
(aq), Na
2
SO
4
(aq),
MgSO
4
(aq), NaHCO
3
(aq), and KHCO
3
(aq) at 298.15 K.
Phase transitions of protein aqueous solutions are important for protein crystallization and biomaterials science in general. One source of thermodynamic complexity in protein solutions and their ...phase transitions is the required presence of additives such as polyethylene glycol (PEG). To investigate the effects of PEG on the thermodynamic behavior of protein solutions, we report measurements on the liquid−liquid phase separation (LLPS) of aqueous bovine serum albumin (BSA) in the presence of relatively small amounts of PEG with an average molecular weight of 1450 g/mol (PEG1450) as a model system. We experimentally characterize two thermodynamically independent properties of the phase boundary: (1) the effect of PEG1450 concentration on the LLPS temperature, (2) BSA/PEG1450 partitioning in the two liquid coexisting phases. We then use a thermodynamic perturbation theory to relate the first property to the effect of PEG concentration on protein−protein interactions and the second property to protein−PEG interactions. As criteria to determine the accuracy of a microscopic model, we examine the model's ability to describe both experimental thermodynamic properties. We believe that the parallel examination of these two properties is a valuable tool for verifying the validity of existing models and for developing more accurate ones. For our system, we have found that a depletion−interaction model satisfactorily explains both protein−PEG interactions and the effect of PEG concentration on protein−protein interactions. Finally, due to the general importance of LLPS, we will experimentally show that protein−PEG−buffer mixtures can exhibit two distinct types of liquid−liquid phase transitions.
The synthesis, characterization, and host–guest chemistry of high-generation triazine dendrimers are described. With pyrene and camptothecin as guests, experiments revealed that the guest capacity of ...odd-generation triazine dendrimers increased until generation 7 but decreased at generation 9. Molecular dynamics simulations conducted in explicit solvent showed a useful fingerprint for this behavior in radial distribution functions of water molecules penetrating the interior of the dendrimers. A linear relationship between the guest capacity of dendrimers measured experimentally and the number of water molecules within the interior determined computationally was observed.
Salt-induced diffusiophoresis is the migration of a macromolecule or a colloidal particle induced by a concentration gradient of salt in water. Here, the effect of salt type on salt-induced ...diffusiophoresis of the protein lysozyme at pH 4.5 and 25 °C was examined as a function of salt concentration for three chloride salts: NaCl, KCl, and MgCl2. Diffusiophoresis coefficients were calculated from experimental ternary diffusion coefficients on lysozyme–salt–water mixtures. In all cases, diffusiophoresis of this positively charged protein occurs from high to low salt concentration. An appropriate mass transfer process was theoretically examined to show that concentration gradients of MgCl2 produce significant lysozyme diffusiophoresis. This is attributed to the relatively low mobility of Mg2+ ions compared to that of Cl– ions at low salt concentration and a strong thermodynamic nonideality of this salt at high salt concentration. These findings indicate that MgCl2 concentration gradients could be exploited for protein manipulation in solution (e.g., using microfluidic technologies) with applications to protein adsorption and purification. The dependence of lysozyme diffusiophoresis on salt type was theoretically examined and linked to protein charge. The effect of salts on hydrogen-ion titration curves was experimentally characterized to understand the role of salt type on protein charge. Our results indicate that binding of Mg2+ ions to lysozyme further enhances protein diffusiophoresis.
PDF
