Introduction to statistical mechanics of charged systems

Levin, Yan

doi:10.1590/s0103-97332004000600006

Cited by 14 publications

(10 citation statements)

References 87 publications

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“…2b. In addition, the high-T energy scaling of a Coulomb system must reduce to that of the Debye-Hückel theory: U ∼ −T −1/2 [48]. We confirm that condition as well.…”

Section: Appendix: Methodssupporting

confidence: 77%

Describing screening in dense ionic fluids with a charge-frustrated Ising model

Ludwig

Dasbiswas

Talapin

et al. 2018

The Journal of Chemical Physics

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Charge correlations in dense ionic fluids give rise to novel effects such as long-range screening and colloidal stabilization which are not predicted by the classic Debye-Hückel theory. We show that a Coulomb or charge-frustrated Ising model, which accounts for both long-range Coulomb and short-range molecular interactions, simply describes some of these ionic correlations. In particular, we obtain, at mean field level and in simulations, a non-monotonic dependence of the screening length on the temperature. Using a combination of simulations and mean field theories, we study how the correlations in the various regimes are affected by the strength of the short ranged interactions.

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“…2b. In addition, the high-T energy scaling of a Coulomb system must reduce to that of the Debye-Hückel theory: U ∼ −T −1/2 [48]. We confirm that condition as well.…”

Section: Appendix: Methodssupporting

confidence: 77%

Describing screening in dense ionic fluids with a charge-frustrated Ising model

Ludwig

Dasbiswas

Talapin

et al. 2018

The Journal of Chemical Physics

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“…The Debye-Hückel approach can be used in principle only for symmetric electrolytes, i.e. when the valence of positive and negative ions is the same, as it is for the present case 43 Note that the use of a larger value of σ would significantly decrease λ B , thus resulting in a very small effect of the Debye-Hückel repulsion as compared to the neutral case.…”

Section: Monomer Interactionsmentioning

confidence: 97%

“…The Debye-Hückel approach can be used in principle only for symmetric electrolytes, i.e. when the valence of positive and negative ions is the same, as it is for the present case 43 since the multiple dissociation of single polyelectrolyte monomers is highly unlikely. We work with reduced units, with σ, m, being the units of length, mass and energy, respectively.…”

Section: Monomer Interactionsmentioning

confidence: 99%

Numerical insights on ionic microgels: structure and swelling behaviour

et al. 2019

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Recent progress has been made in the numerical modelling of neutral microgel particles with a realistic, disordered structure. In this work we extend this approach to the case of co-polymerised microgels where a thermoresponsive polymer is mixed with acidic groups. We compare the cases where counterions directly interact with microgel charges or are modelled implicitly through a Debye-Hückel description. We do so by performing extensive numerical simulations of single microgels across the volume phase transition varying the temperature and the fraction of charged monomers. We find that the presence of charges considerably alters the microgel structure, quantified by the monomer density profiles and by the form factors of the microgels, particularly close to the volume phase transition (VPT). We observe significant deviations between the implicit and explicit models, with the latter comparing more favourably to available experiments. In particular, we observe a shift of the VPT temperature to larger values as the amount of charged monomers increases. We also find that below the VPT the microgel-counterion complex is almost neutral, while it develops a net charge above the VPT. Interestingly, under these conditions the collapsed microgel still retains a large amount of counterions inside its structure. Since these interesting features cannot be captured by the implicit model, our results show that it is crucial to explicitly include the counterions in order to realistically model ionic thermoresponsive microgels.

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“…As regards the OCP theory developed by Levin, overcharging occurs as the result of highly favorable gain in electrostatic free energy due to strong positional correlations between the condensed counterions. 2,32 In particular, the model considers a OCP made of multivalent counterions condensed on the surface of a spherical macroion with a uniform neutralizing background charge. Therefore, the electrostatic energy of the OCP is expressed as a sum of contributions arising from the counterion-counterion interaction, counterionbackground interaction, and the self-energy of the background.…”

Section: ͑I͒mentioning

confidence: 99%

“…29 The theory allows for analytic calculations of all the thermodynamic functions as well as the structure factor. a͒ Precisely, the OCP is the common starting point in the overcharging studies performed by Shklovskii and co-workers 3,30,31 on one hand, and Levin on his own 2,32 and Pianegonda et al, 33 on the other. According to the former, the overcharging is a direct consequence of ionic correlations due to an arrangement of multivalent counterions in a twodimensional liquid called strong correlated liquid ͑SCL͒.…”

Section: Introductionmentioning

confidence: 99%

Testing one component plasma models on colloidal overcharging phenomena

Maroto-Centeno¹,

Hidalgo‐Álvarez²,

Quesada‐Pérez³

2006

The Journal of Chemical Physics

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In this paper, the mechanisms of overcharging of a colloidal macroion in the presence of multivalent counterions are investigated by means of Monte Carlo simulations. This computational technique appears as a powerful tool for probing the validity of semianalytical models developed for this issue. In particular, the simulations performed are compared with the predictions of two different models based on the one component plasma (OCP) theory. Therein, the multivalent ionic atmosphere confined at the macroion surface is approximated by a two-dimensional Wigner crystal. These kinds of models are largely used in the literature since (in some cases) they present quite simple equations to describe the electric double layer (EDL) of macroions with different geometries in the presence of much smaller (but still multivalent) ions. In this sense, charge inversion phenomena of membranes, polyelectrolytes, DNA molecules, etc., are straightforwardly predicted in terms of these expressions. Unfortunately, comparisons between these predictions and experimental results are scarce, mostly due to the difficulty to reproduce the experimental conditions in the laboratory. Accordingly, the goal of the present paper is to simulate EDLs under real conditions (in which overcharging phenomena are expected to happen) and use the results obtained in this way for comparing with those obtained from OCP models.

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Introduction to statistical mechanics of charged systems

Cited by 14 publications

References 87 publications

Describing screening in dense ionic fluids with a charge-frustrated Ising model

Describing screening in dense ionic fluids with a charge-frustrated Ising model

Numerical insights on ionic microgels: structure and swelling behaviour

Testing one component plasma models on colloidal overcharging phenomena

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