FIG 5 - uploaded by Sahin Buyukdagli
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(a) SC-level pressure (86) renormalized as˜Pas˜ as˜P = βP/(2ππ B σ 2 m ) against the rescaled distance˜ddistance˜ distance˜d = d/μ for flexible solute molecules, and (b) its rigid solute limit (88). The semilog plots in the insets display the pressure curves over a larger distance interval. The solute size (˜ a = a/μ) or flexibility ( ˜ α = α/μ) for each curve and symbol is indicated in the legend of its panel by the same color.
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The structural diversity of the solute molecules involved in biomolecular processes necessitates the characterization of the forces between charged macromolecules beyond the point-ion description. From the field-theoretic partition function of an electrolyte confined between two anionic membranes, we derive a contact-value identity valid for genera...
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Citations
... First of all, this approach allows the treatment of many-body interactions via systematic and controlled perturbation techniques [38][39][40][41] as well as self-consistent computation schemes [42][43][44][45]. Then, the field theory formalism enables the straightforward incorporation of the specific molecular details of electrolytes beyond the primitive model, such as structured solute charges [46,47], explicit solvent molecules [48,49], structured membranes [50], and polyelectrolytes with conformational degrees of freedom [51][52][53][54]. ...
... Additionally, the field theory approach to charged systems has proved to be an efficient way to incorporate various relevant details of electrolytes, such as the intramolecular ion structure [46,47], explicit solvent [48,49], inhomogeneous liquid partition in nanofludic charge transport [56] and polymer translocation through nanopores [58], and conformational polymer fluctuations in salty polymeric solutions [51][52][53][54]. The application of the CCDH theory to the aforementioned systems can extend the quantitative validity of the predictions by purely electrostatic formalisms into the regime of molar salt concentrations. ...
The Debye−Hückel (DH) formalism of bulk electrolytes equivalent to the Gaussian-level closure of the electrostatic Schwinger−Dyson identities without the interionic hard-core (HC) coupling is extended via the cumulant treatment of these equations augmented by HC interactions. By comparing the monovalent ion activity and pressure predictions of our cumulant- corrected DH (CCDH) theory with hypernetted-chain results and Monte Carlo simulations from the literature, we show that this rectification extends the accuracy of the DH formalism from submolar to molar salt concentrations. In the case of internal energies or the general case of divalent electrolytes mainly governed by charge correlations, the improved accuracy of the CCDH theory is limited to submolar ion concentrations. Comparison with experimental data from the literature shows that, via the adjustment of the hydrated ion radii, CCDH formalism can equally reproduce the nonuniform effect of salt increment on the ionic activity coefficients up to molar concentrations. The inequality satisfied by these HC sizes coincides with the cationic branch of the Hofmeister series.
... 3 The mean-field formulation of the Poisson-Boltzmann (PB) theory, with its associated ionic screening, has been investigated on various levels of detail [4][5][6] and is standardly used for describing the nanoscale electrostatics. 7 While the PB paradigm has well-defined limits of applicability, stemming either from the model 8 and/or from the methodology, 9,10 it is still used as a preferred estimation tool, often providing a quantitatively correct form of electrostatic interactions. 11 In many contexts, but most importantly for protein and complex macroion solutions, the usual PB paradigm assumption of constant surface charge density or constant surface potential 12 breaks down, as the dissociable molecular moieties respond to their environment, especially to the presence of each other, in a way that modifies both the charge density as well as the surface potential, adjusting them according to the separation between them and the bathing solution conditions. ...
We present a derivation of the screening length for a solution containing a charge-regulated macroion, e.g. protein, with its counterions. We show that it can be obtained directly from the second derivatives of the total free energy by taking recourse to the “uncertainty relation” of the Legendre transform, which connects the Hessians or the local curvatures of the free energy as a function of density and its Legendre transform, i.e., osmotic pressure, as a function of chemical potentials. Based on the Fowler–Guggenheim–Frumkin model of charge regulation, we then analyze the “screening resonance” and the “overscreening” of the screening properties of the charge-regulated macroion solution.
... First of all, this approach allows the treatment of many-body interactions via systematic and controlled perturbation techniques [36][37][38][39] as well as self-consistent computation schemes [40][41][42]. Then, the field theory formalism enables the straightforward incorporation of the specific molecular details of electrolytes beyond the primitive model, such as structured solute charges [43,44], explicit solvent molecules [45,46], structured membranes [47], and polyelectrolytes with conformational degrees of freedom [48,49]. ...
... Eq. (44) indicates that the excess energy of the liquid set by the charge correlation function is mainly governed by the electrostatic coupling of opposite charges. Then, according to Eq. (45), the departure of the pressure from the ideal gas behavior is driven by the competition between these attractive charge correlations (the second term on the r.h.s.), and the repulsive HC correlations embodied by the contact densities (the curly bracket term). ...
... Fig. 2(d) shows that upon the further decrease of the HC size down to d = 2.38Å, the CCDH pressure now overestimates the MC result. The overestimation of the MC pressure for small ions stems from the fact that at short interionic distances, the significant strength of the opposite charge attraction enhances the contribution of the attractive electrostatic energy (44) to the pressure (45). Moreover, in Fig. 1(a), it was shown that our cumulant approach overestimating the size-induced attenuation of these attractions underestimates the electrostatic energy. ...
The Debye-Hückel (DH) formalism of bulk electrolytes equivalent to the gaussian-level closure of the electrostatic Schwinger-Dyson (SD) identities without the interionic hard-core (HC) coupling is extended via the cumulant treatment of these equations augmented by HC interactions. By confronting the monovalent ion activity and pressure predictions of our cumulant-corrected DH (CCDH) theory with hypernetted-chain (HNC) results and Monte-Carlo (MC) simulations from the literature, we show that this rectification extends the accuracy of the DH formalism from submolar into molar salt concentrations. In the case of internal energies or the general case of divalent electrolytes mainly governed by charge correlations, the improved accuracy of the CCDH theory is limited to submolar ion concentrations. Comparison with experimental data from the literature shows that via the adjustment of the hydrated ion radii, the CCDH formalism can equally reproduce the non-uniform effect of salt increment on the ionic activity coefficients up to molar concentrations. The inequality satisfied by these HC sizes coincides with the cationic branch of the Hofmeister series.
... It is important to mention several earlier studies in which the authors explored the derivation and explicit evaluation of electrostatic normal stress in Coulomb fluids confined in slit-like pores at both weak-coupling and strong-coupling limits [22][23][24][25]. Moreira and Netz utilized Monte Carlo simulations and statistical field theory, specifically on the level of one-loop approximation and strong coupling theory, to investigate the behavior of highly charged plates in the presence of multivalent counterions. ...
... Furthermore, Jho et al examined the strong-coupling electrostatic interaction between two like-charged nanoparticles using the strong coupling theory and Monte Carlo simulations. In a recent study by Buyukdagli [25], a contact-value identity was derived by considering the fieldtheoretic partition function of an electrolyte confined between two anionic membranes. This identity holds true for a wide range of intramolecular solute structures and electrostatic coupling strengths. ...
... Then, using the expansion (16) and holding first-order terms on 1/β, as mentioned earlier, we can write equation (25) with account of equation (22) as follows: ...
In this paper, we introduce a statistical field theory that describes the macroscopic mechanical forces in inhomogeneous Coulomb fluids. Our approach employs the generalization of Noether’s first theorem for the case of a fluctuating order parameter to calculate the stress tensor for Coulomb fluids. This tensor encompasses the mean-field stress tensor and fluctuation corrections derived through the one-loop approximation. The correction for fluctuations includes a term that accounts for the thermal fluctuations of the local electrostatic potential and field in the vicinity of the mean-field configuration. This correlation stress tensor determines how electrostatic correlation affects local stresses in a nonuniform Coulomb fluid. We also use a previously formulated general covariant methodology (Brandyshev and Budkov 2023 J. Chem. Phys. 158 174114) in conjunction with a functional Legendre transformation method and derive within it the same total stress tensor. We would like to emphasize that our general approaches are applicable not only to Coulomb fluids but also to nonionic simple or complex fluids, for which the field-theoretic Hamiltonian is known as a function of the relevant scalar order parameters.
