Polar Solvent Structure in the Debye-Hückel Theory of Strong Electrolytes

1976 ◽  
Vol 31 (12) ◽  
pp. 1601-1608 ◽  
Author(s):  
K. Holub ◽  
A. A. Kornyshev
Keyword(s):  
Free Energy ◽  
Potential Energy ◽  
Spatial Correlation ◽  
Polar Solvent ◽  
Excess Free Energy ◽  
Solvent Structure ◽  
Ionic Solution ◽  
Ionic Atmosphere ◽  
Hückel Theory ◽  
Strong Electrolytes

Abstract A general formula is derived for the potential energy of an ion in an ionic solution using all assumptions of the Debye-Hückel theory except the assumption of constant permittivity. For the solvent the spatial correlation of polarization fluctuations is taken into account. The potential energy of an ion in it's ionic atmosphere is calculated for different models of the spatial correlation of polarization fluctuations and the corresponding excess free energy and activity coefficient of an ion is evaluated. It is concluded that the Debye-Hückel theory using a constant value of e should only be valid for electrolyte concentrations lower than 10-7 mol · dm-3 . The paper intends to show the consequences of dropping the assumption of constant permittivity and so encourage further efforts towards a more exact treatment of the problem.

Influence of solvent structure and hydrogen bonding on catalysis at solid–liquid interfaces

2021 ◽  
Author(s):  
David S. Potts ◽  
Daniel T. Bregante ◽  
Jason S. Adams ◽  
Chris Torres ◽  
David W. Flaherty
Keyword(s):  
Free Energy ◽  
Hydrogen Bonding ◽  
Excess Free Energy ◽  
Catalytic Reactions ◽  
Liquid Interfaces ◽  
Solvent Structure ◽  
Solid Liquid ◽  
Influence Of Solvent

A pedagogical review that deconvolutes the excess free energy effects of several solvent phenomena and connects findings across a variety of catalytic reactions and materials.

scholarly journals On the foundations of a new approach to statistical mechanics of classical systems

1980 ◽  
Vol 3 (4) ◽  
pp. 607-674
Author(s):  
S. N. Bagghi
Keyword(s):  
Free Energy ◽  
Statistical Mechanics ◽  
Configuration Space ◽  
Excess Free Energy ◽  
Alkali Halides ◽  
Computational Techniques ◽  
New Approach ◽  
Long Time ◽  
Strong Electrolytes ◽  
The Individual

It has been known for a long time that the fundamental approaches to equilibrium and nonequillbrium statistical mechanics available at present lead to physical and mathematical inconsistencies for dense systems. A new approach, whose foundation lies in the more powerful statistical method of counting complexions, had been formulated which not only overcomes all these difficulties but also yields satisfactory physical results for dense 'hard sphere' systems as well as for systerns containing charged particles for which a mathematically consistent theory cannot even be formulated if we follow the available formalisms. The specific computational techniques rely on the following four recipes which also are justified theoretically.(i) The phase space (μ-space) is separated into configuration space and momentum space.(ii) The configuration space is partitioned into cells of sizeb, the exclusion volume of Boltzmann.(iii) The partition function (pf) due to the kinetic energy is obtained directly from Planck's “Zustandssumme” pertaining to the kinetic energies of the individual particles.(iv) Instead of calculating Gibbs' configuration integral, one obtains the average potential of the system from a suitable nonlinear partial differential equatlon (pde) and finally the “excess” free energy of the system due to the potential field alone by utilizing Debye-Hueckel's concept of ion-atmosphere and their technique for calculating the free energy.Even in the linear approximation of the ion-atmosphere potential this method gives reliable results for both equilibrium and transport properties of fused alkali halides.In order to emphasize that this new approach has a secure theoretical foundation and has also considerable advantages over all other existing methods, this review offers a few brief critical remarks about the limitations and inadequacies of the concepts used in the conventional treatments of classical statistical mechanics. Further, in view of the fact that the literature on the subject of Debye-Hueckel (DH) theory of strong electrolytes is replete with many assertions, already disproved in the past, a brief review of the controversial aspects of this theory is also presented. The next paper will show that this new approach as well as the modified DH theory yields physical results for actual dense systems much more satisfactorily than those which could be obtained by any other available method.

Characterization of Textured Aluminum Lines and Modelling of Stress Voiding

1994 ◽  
Vol 343 ◽  
Author(s):  
S.C. Wardle ◽  
B.L. Adams ◽  
C.S. Nichols ◽  
D.A. Smith
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
Mean Field ◽  
High Energy ◽  
Polycrystalline Structure ◽  
Field Approach ◽  
Bamboo Structure ◽  
Automated Technique ◽  
Theory And Modeling

ABSTRACTIt is well known from studies of individual interfaces that grain boundaries exhibit a spectrum of properties because their structure is misorientation dependent. Usually this variability is neglected and properties are modeled using a mean field approach. The limitations inherent in this approach can be overcome, in principle, using a combination of experimental techniques, theory and modeling. The bamboo structure of an interconnect is a particularly simple polycrystalline structure that can now be readily characterized experimentally and modeled in the computer. The grain misorientations in a [111] textured aluminum line have been measured using the new automated technique of orientational imaging microscopy. By relating boundary angle to diffusivity the expected stress voiding failure processes can be predicted through the link between misorientation angle, grain boundary excess free energy and diffusivity. Consequently it can be shown that the high energy boundaries are the favored failure sites thermodynamically and kinetically.

Higher Order Conditional Probabilities and Thermodynamics of Binary Molten Alloys

1997 ◽  
Vol 11 (02n03) ◽  
pp. 93-106 ◽  
Author(s):  
O. Akinlade
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Cluster Model ◽  
Excess Free Energy ◽  
Higher Order ◽  
Thermodynamic Quantities ◽  
Equiatomic Composition ◽  
Conditional Probabilities ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

The recently introduced four atom cluster model is used to obtain higher order conditional probabilities that describe the atomic correlations in some molten binary alloys. Although the excess free energy of mixing for all the systems studied are almost symmetrical about the equiatomic composition, most other thermodynamic quantities are not and thus, the study enables us to explain the subtle differences in their physical characteristics required to describe the mechanism of the observed strong heterocoordination in Au–Zn or homocoordination in Cu–Ni within the same framework. More importantly, we obtain all calculated quantities for the whole concentration range thus complimenting experimental evidence.

scholarly journals Simulation of FUS protein condensates with an adapted coarse-grained model

2020 ◽  
Author(s):  
Zakarya Benayad ◽  
Sören von Bülow ◽  
Lukas S. Stelzl ◽  
Gerhard Hummer
Keyword(s):  
Free Energy ◽  
Phase Separation ◽  
Potential Energy ◽  
Energy Function ◽  
Potential Energy Function ◽  
Scaling Factor ◽  
Coarse Grained ◽  
Disordered Proteins ◽  
General Strategy ◽  
Droplet Shape

AbstractDisordered proteins and nucleic acids can condense into droplets that resemble the membraneless organelles observed in living cells. MD simulations offer a unique tool to characterize the molecular interactions governing the formation of these biomolecular condensates, their physico-chemical properties, and the factors controlling their composition and size. However, biopolymer condensation depends sensitively on the balance between different energetic and entropic contributions. Here, we develop a general strategy to fine-tune the potential energy function for molecular dynamics simulations of biopolymer phase separation. We rebalance protein-protein interactions against solvation and entropic contributions to match the excess free energy of transferring proteins between dilute solution and condensate. We illustrate this formalism by simulating liquid droplet formation of the FUS low complexity domain (LCD) with a rebalanced MARTINI model. By scaling the strength of the nonbonded interactions in the coarse-grained MARTINI potential energy function, we map out a phase diagram in the plane of protein concentration and interaction strength. Above a critical scaling factor of αc ≈ 0.6, FUS LCD condensation is observed, where α = 1 and 0 correspond to full and repulsive interactions in the MARTINI model, respectively. For a scaling factor α = 0.65, we recover the experimental densities of the dilute and dense phases, and thus the excess protein transfer free energy into the droplet and the saturation concentration where FUS LCD condenses. In the region of phase separation, we simulate FUS LCD droplets of four different sizes in stable equilibrium with the dilute phase and slabs of condensed FUS LCD for tens of microseconds, and over one millisecond in aggregate. We determine surface tensions in the range of 0.01 to 0.4mN/m from the fluctuations of the droplet shape and from the capillary-wave-like broadening of the interface between the two phases. From the dynamics of the protein end-to-end distance, we estimate shear viscosities from 0.001 to 0.02Pas for the FUS LCD droplets with scaling factors α in the range of 0.625 to 0.75, where we observe liquid droplets. Significant hydration of the interior of the droplets keeps the proteins mobile and the droplets fluid.

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