The rehabilitation of irreversible processes and dissipative structures' 50th anniversary

In 2017, Ilya Prigogine would have been 100 years of age. As for any human being, this centenary is a notable event. For him, as a scientist, 2017 was also above all the 50th anniversary of dissipative structures It was indeed in 1967 that for the first time he used this denomination at the occasion of an important scientific event and in publications. The attribution of this qualification for self-organized behaviours of matter only possible far from equilibrium coincided with the outcome of a research effort of more than 25 years. Centred in thermodynamics and statistical physics on the role played by irreversible processes in the physical evolution of matter, the aim of this research is clear from the outset of his scientific career. With visionary personal intuition and iron-willed determination, it was pursued. The road to success had been long and sinuous, but finally it led to what he called the rehabilitation of irreversible processes The progresses that stand out as major landmarks of this endeavour that imposed a U-turn with respect to conceptions of classical physics deeply rooted since the nineteenth century will be described. This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (Part 1)'.

Adsorption of charged and neutral polymer chains on silica surfaces: the role of electrostatics, volume exclusion, and hydrogen bonding

We develop an off-lattice (continuum) model to describe the adsorption of neutral polymer chains and polyelectrolytes to surfaces. Our continuum description allows taking excluded volume interactions between polymer chains and ions directly into account. To implement those interactions, we use a modified hard-sphere equation of state, adapted for mixtures of connected beads. Our model is applicable to neutral, charged, and ionizable surfaces and polymer chains alike and accounts for polarizability effects of the adsorbed layer and chemical interactions between polymer chains and the surface. We compare our model predictions to data of a classical system for polymer adsorption: neutral poly(N-vinylpyrrolidone) (PVP) on silica surfaces. The model shows that PVP adsorption on silica is driven by surface hydrogen bonding with an effective maximum binding energy of about 1.3k(B)T per PVP segment at low pH. As the pH increases, the Si-OH groups become increasingly dissociated, leading to a lower capacity for H bonding and simultaneous counterion accumulation and volume exclusion close to the surface. Together these effects result in a characteristic adsorption isotherm, with the adsorbed amount dropping sharply at a critical pH. Using this model for adsorption data on silica surfaces cleaned by either a piranha solution or an O(2) plasma, we find that the former have a significantly higher density of silanol groups.

Emulsions stability, from dilute to dense emulsions -- role of drops deformation

The present paper starts with a review of fundamental descriptions based on physico-chemical laws derived for emulsions with a special interest for eventual evidences of drops deformation. A critical analysis of theories and experiments is given that leads the authors to propose new static and dynamic models for the approach to flocculation and coalescence of two deformable drops in dense and dilute environments of other neighboring drops. The model developed is based on an old paper by Albers and Overbeek for W/O dense emulsions with non-deformable particles, that has been improved recently first by Sengupta and Papadopoulos and then by Mishchuk et al. to account for all the interaction forces (electrostatic, van der Waals and steric). The basic idea here rests in the assumption that the flat surface area of the two coalescing drops, interacting in the field of other particles, increases when the distance between the particles decreases according to an exponential law with a characteristic length related to the disjoining force in the inter-particle film and to the capillary pressure that opposes flattening. The difficulty lies, indeed, in manifold interpretations on experimental observations so that no clear conclusion can be derived on mechanisms responsible for the deformation of droplets. This is why, from a pure theoretical and physical point of view, according to rather complicated models, we propose a much more simple approach that permits to define a capillary length as part of virtual operations. In a static approach, this length is based on analogy with electricity, namely repulsion leads to flatness while attraction to hump. Therefore this brings us to a definition of a length depending on the maximum value of the disjoining pressure in competition with the capillary pressure. Gravity also promotes flocculation, therefore we compare the maximum values of the surface forces acting between the surfaces of two floculating particles to gravity. Finally, considering that in most publications on emulsions foams and colloidal systems, much attention is paid on the role of the drainage in the stability process, we devote the last section to the drainage between flattened drops. We first describe briefly Taylor's approach and extend Reynolds revisited formulae taking into account the viscous friction, the disjoining pressure, the film elasticity and the wetting angle weighting the capillary pressure through the characteristic length. Our calculated values are compared to some experimental data. In conclusion to make this long paper as useful as possible for research purposes, we have the hope that our understanding of emulsion stability is not only based on knowledge of numerous theoretical and experimental works sometimes controversial given in a critical way but that it gives a new approach based on an interpretation of the drop deformation in terms of a characteristic length linked to a deformation number analogous to a Bond number.

Electrostatics of B-DNA in NaCl and CaCl2 solutions: ion size, interionic correlation, and solvent dielectric saturation effects

The epsilon-modified Poisson-Boltzmann (-MPB) equations ( J. Phys. Chem. B, 2007, 111, 5264) have been solved on a three-dimensional grid for an all-atom geometry model of B-DNA. The approach is based on the implicit solvent model including finite sizes of hydrated ions and a dielectric approximation of the ion hydration shell. Results were obtained for the detailed geometry model of B-DNA in dilute and moderately concentrated solutions of NaCl and CaCl(2). All -MPB parameters of ions and dielectric medium were extracted from published results of all-atom molecular dynamics simulations. The study allows evaluations of the ion size, interionic correlation, and the solvent dielectric saturation effects on the ion distributions around DNA. It unambiguously suggests that the difference between the -MPB and Poisson-Boltzmann distributions of ions is low for Na(+) counterions. Such a difference in the case of divalent counterions Ca(2+) is dramatic: the dielectric saturation of the ion hydration shell leads to point-like adsorption of Ca(2+) on the phosphate groups of DNA. The -MPB equations were also applied to calculate the energy of interaction between two B-DNA molecules. Results agree with previously published simulations and experimental data. Some aspects of ion specificity of polyelectrolyte properties are discussed.

Effective interaction potentials for alkali and alkaline earth metal ions in SPC/E water and prediction of mean ion activity coefficients

The potential of mean force (PMF) acting between two simple ions surrounded by SPC/E water have been determined by molecular dynamics (MD) simulations using a spherical cavity approach. Such effective ion-ion potentials were obtained for Me-Me, Me-Cl-, and Cl(-)-Cl- pairs, where Me is a Li+, Na+, K+, Mg2+, Ca2+, Sr2+, and Ba2+ cation. The ionic sizes estimated from the effective potentials are not pairwise additive, a feature in the frequently used primitive model for electrolytes. The effective potentials were used in Monte Carlo (MC) simulations with implicit water to calculate mean ion activity coefficients of LiCl, NaCl, KCl, MgCl2, CaCl2, SrCl2, and BaCl2. Predicted activities were compared with experimental ones in the electrolyte concentration range 0.1-1 M. A qualitative agreement for LiCl and a satisfactory agreement for NaCl were found, whereas the predictions for KCl by two K+ models were less coherent. In the case of alkaline earth metal ions, all experimental activities were successfully reproduced at c = 0.1 M. However, at higher concentrations, similar deviations occurred for all divalent cations, suggesting that the dependence of the permittivity on the salt concentration and the polarization deficiency arising from the ordering of water molecules in the ion hydration shells are important in such systems.

Dielectric saturation of the ion hydration shell and interaction between two double helices of DNA in mono- and multivalent electrolyte solutions: foundations of the epsilon-modified Poisson-Boltzmann theory

Potentials of mean force between single Na+, Ca2+, and Mg2+ cations and a highly charged spherical macroion in SPC/E water have been determined using molecular dynamics simulations. Results are compared to the electrostatic energy calculations for the primitive polarization model (PPM) of hydrated cations describing the ion hydration shell as a dielectric sphere of low permittivity (Gavryushov, S.; Linse, P. J. Phys. Chem. B 2003, 107, 7135). Parameters of the ion dielectric sphere and radius of the macroion/water dielectric boundary were extracted by means of this comparison to approximate the short-range repulsion of ions near the interface. To explore the counterion distributions around a simplified model of DNA, the obtained PPM parameters for Na+ and Ca2+ have been substituted into the modified Poisson-Boltzmann (MPB) equations derived for the PPM and named the epsilon-MPB (epsilon-MPB) theory. epsilon-MPB results for DNA suggest that such polarization effects are important in the case of 2:1 electrolyte and highly charged macromolecules. The three-dimensional implementation of the epsilon-MPB theory was also applied to calculation of the energies of interaction between two parallel macromolecules of DNA in solutions of NaCl and CaCl2. Being compared to results of MPB calculations without the ion polarization effects, it suggests that the ion hydration shell polarization and inhomogeneous solvent permittivity might be essential factors in the experimentally known hydration forces acting between charged macromolecules and bilayers at separations of less than 20 A between their surfaces.

Volume exclusion effects in the ground-state dominance approximation for polyelectrolyte adsorption on charged interfaces

We consider the problem of polyelectrolyte molecules adsorbing on oppositely charged interfaces. For sufficiently long chains, the ground-state dominance approximation can be used which results in a (semi-)analytical solution of the self-consistent field equations (aSCF). Whereas existing aSCF theory assumes a low polyelectrolyte density, here the required electrostatic corrections for a high polymer density are implemented. Adsorbed polymer excludes volume for the solvent and small ions, a volume effect that also leads to a reduced dielectric permittivity and a resulting polarization term in the exchange potential. Calculations show the influence of volume exclusion on the polymer density profile.

A Modified Poisson−Boltzmann Model Including Charge Regulation for the Adsorption of Ionizable Polyelectrolytes to Charged Interfaces, Applied to Lysozyme Adsorption on Silica

The equilibrium adsorption of polyelectrolytes with multiple types of ionizable groups is described using a modified Poisson-Boltzmann equation including charge regulation of both the polymer and the interface. A one-dimensional mean-field model is used in which the electrostatic potential is assumed constant in the lateral direction parallel to the surface. The electrostatic potential and ionization degrees of the different ionizable groups are calculated as function of the distance from the surface after which the electric and chemical contributions to the free energy are obtained. The various interactions between small ions, surface and polyelectrolyte are self-consistently considered in the model, such as the increase in charge of polyelectrolyte and surface upon adsorption as well as the displacement of small ions and the decrease of permittivity. These interactions may lead to complex dependencies of the adsorbed amount of polyelectrolyte on pH, ionic strength, and properties of the polymer (volume, permittivity, number, and type of ionizable groups) and of the surface (number of ionizable groups, pK, Stern capacity). For the adsorption of lysozyme on silica, the model qualitatively describes the gradual increase of adsorbed amount with pH up to a maximum value at pHc, which is below the iso-electric point, as well as the sharp decrease of adsorbed amount beyond pHc. With increasing ionic strength the adsorbed amount decreases (for pH > pHc), and pHc shifts to lower values.

Does capillarity influence chemical reaction in drops and bubbles? A thermodynamic approach

After a brief introduction on the variables which describe the physico-chemical properties of a fluid surface, this paper compares, in a very simple way, the equilibrium constant of homogeneous and heterogeneous reactions taking place in spherical micro-objects (uncharged and charged droplets and bubbles) and in media bordered by a flat interface. This quantity is by definition the exponential of the dimensionless standard chemical affinity whose values (< or = 0, > or = 0) may indicate the direction and the importance of the reaction (strictly true when the mixing term of the affinity is zero). The classical thermodynamic approach combined with the Laplace equation shows that: (i) high surface tension and high curvature influence the equilibrium constant, this effect being, however, much more important for bubbles than for droplets; (ii) charges on droplets reduce this effect; (iii) the constant of reaction taking place in the vapour in contact with a charged droplet depends significantly on the electric field pressure; (iv) reactions in droplets dispersed in the liquid phase are discussed and, in particular, capillarity seems to play a negligible role on reactions in micro-emulsions; (v) the surface amount of a gas bubble component transferred in the continuous liquid can be related to capillary quantities; (vi) expanding (or shrinking) bubble induced by a chemical reaction is analysed by using an extended Laplace law which includes the volumetric flow rate; (vii) the Laplace law is discussed in the frame of the choice of the dividing surface. Numerous actual examples from the atmosphere, sonochemistry and metallurgy illustrate the theory proposed. One of the interest, among other points, is that small objects (specially bubbles) give the potentiality to obtain, for steady or (near) equilibrium states, large amount of components which would not be possible when dealing with large reservoirs.

Electrochemical Diffusion

The methods of irreversible thermodynamics, applied to the problem of steady-state linear diffusion, lead to the conclusion that the flux across any system of parallel membranes or phase boundaries can be expressed as a linear function of the differences in electrochemical potential across the system. The presence of fixed charges, polarizable molecules, or electric fields does not alter the flux-force relation.