Coarse-Graining of Ionic Microgels: Theory and Experiment

Riest, Jonas; Mohanty, Priti S.; Schurtenberger, Peter; Likos, Christos N.

doi:10.1524/zpch.2012.0258

Cited by 45 publications

(79 citation statements)

References 67 publications

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Section: Model and Theorysupporting

confidence: 88%

“…U dd 100k B T , captures the small microgels 9 behavior. This estimate is consistent with scaling arguments of the Hertzian model as a function of particle size [52,53] with respect to the large microgels.Numerical calculation of the effective potential Microgel configurations are built as disordered, fully-bonded networks generated as in Ref. [8,40] using ≈ 5000 monomers of diameter σ m in a spherical confinement of radius Z = 25 σ m and crosslinker concentration c = 5%.…”

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confidence: 88%

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A new look at effective interactions between microgel particles

et al. 2018

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Thermoresponsive microgels find widespread use as colloidal model systems, because their temperature-dependent size allows facile tuning of their volume fraction in situ. However, an interaction potential unifying their behavior across the entire phase diagram is sorely lacking. Here we investigate microgel suspensions in the fluid regime at different volume fractions and temperatures, and in the presence of another population of small microgels, combining confocal microscopy experiments and numerical simulations. We find that effective interactions between microgels are clearly temperature dependent. In addition, microgel mixtures possess an enhanced stability compared to hard colloid mixtures - a property not predicted by a simple Hertzian model. Based on numerical calculations we propose a multi-Hertzian model, which reproduces the experimental behavior for all studied conditions. Our findings highlight that effective interactions between microgels are much more complex than usually assumed, displaying a crucial dependence on temperature and on the internal core-corona architecture of the particles.

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Section: Model and Theorysupporting

confidence: 88%

supporting

confidence: 88%

A new look at effective interactions between microgel particles

et al. 2018

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“…The resulting effective pair potential, obtained by coarse-graining the electrolyte degrees of freedom, has been used to predict the phase behaviour of uniform ionic microgel suspensions. [14][15][16] Recently, it has been shown that this formalism is in good agreement with experimental data of particle microstructure, when adding the elastic repulsion. 16 Here, we extend the study to the more general case of core-shell microgel structures and analyse the effect of the shell extension on the ion penetration inside the microgel, the effective charge of the particles, and on the electrostatic effective interaction between pairs of particles.…”

Section: Introductionsupporting

confidence: 56%

“…By applying the HNC closure equation given in Eq. (16) to the microgel-ion correlations and assuming that g m+ (r) ≈ g m− (r) ≈ 1, it is a simple task to show that then the HNC closure reduces to e −c mi (r)−βV mi (r) = 1 and, hence, to the Random Phase approximation. 44 The screening of the microgel bare charge can be estimated using the internal net particle charge, Z in , which can be calculated by integration of the ionic density profiles inside the particle …”

Section: Resultsmentioning

confidence: 99%

Effective electrostatic interactions arising in core-shell charged microgel suspensions with added salt

Moncho-Jordá

Anta

Callejas-Fernández

2013

The Journal of Chemical Physics

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The mixture formed by charged (ionic) microgels in the presence of 1:1 added salt, with explicit consideration of a core-shell structure of the microgel particles, is studied. By solving numerically the three-component Ornstein-Zernike integral equations, the counter- and coion penetration inside the microgel network and the resulting effective microgel-microgel electrostatic interaction are calculated. This is done in the limit of very low microgel concentration, so that the resulting pair-wise effective potential is not affected by many-body particle-particle interactions. The ion-ion, microgel-ion, and microgel-microgel correlations are all treated within the Hypernetted-Chain approximation. The results obtained clearly show that the addition of salt to the microgel suspension has a deep impact on the screening of the bare charge of the particles, confirming an already well-known result: the strong reduction of the effective charge of the microgel occurring even for diluted electrolyte concentrations. We show that this effect becomes more important as we increase the shell size of the particle and derive a semi-empirical model for the effective charge as a function of the electrolyte concentration and the shell extension. The resulting microgel-microgel effective pair potential is analysed as a function of the shell extension and salt concentration. In all cases the interaction is a soft potential when particles overlap. For non-overlapping distances, our theoretical results indicate that microgel particles can be regarded as hard spherical colloids bearing an effective charge given by the net charge inside the particle and the microgel-microgel interaction shows a Yukawa-like behaviour as a function of the interparticle distance. It is also observed that increasing the bare-charge of the microgel induces a strong microgel-counterion coupling in the limit of very low electrolyte concentrations, which cannot be justified using linearized theories. This leads to an even more important adsorption of counterions inside the microgel network and to a reduction of the microgel-microgel effective repulsion.

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“…Under from an experimental viewpoint surprisingly general conditions, a h is unequivocally determined from the measurement of a single-particle transport property such as the translational diffusion coefficient D t 0 or the intrinsic viscosity [η]. The definition of the HRM includes also spherical particles with fuzzy hydrodynamic structure and no sharp outer boundary, and with a soft pair potential such as for weakly cross-linked ionic microgels [1, 27,28]. For spherical particles having excluded volume interactions only with a h < a, the HRM reduces to the so-called spherical annulus model.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of suspensions of hydrodynamically structured particles: analytic theory and applications to experiments

et al. 2015

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We present an easy-to-use analytic toolbox for the calculation of short-time transport properties of concentrated suspensions of spherical colloidal particles with internal hydrodynamic structure, and direct interactions described by a hard-core or soft Hertz pair potential. The considered dynamic properties include self-diffusion and sedimentation coefficients, the wavenumber-dependent diffusion function determined in dynamic scattering experiments, and the high-frequency shear viscosity. The toolbox is based on the hydrodynamic radius model (HRM) wherein the internal particle structure is mapped on a hydrodynamic radius parameter for unchanged direct interactions, and on an existing simulation data base for solvent-permeable and spherical annulus particles. Useful scaling relations for the diffusion function and self-diffusion coefficient, known to be valid for hard-core interaction, are shown to apply also for soft pair potentials. We further discuss extensions of the toolbox to long-time transport properties including the low-shear zero-frequency viscosity and the long-time self-diffusion coefficient. The versatility of the toolbox is demonstrated by the analysis of a previous light scattering study of suspensions of non-ionic PNiPAM microgels [Eckert et al., J. Chem. Phys., 2008, 129, 124902] in which a detailed theoretical analysis of the dynamic data was left as an open task. By the comparison with Hertz potential based calculations, we show that the experimental data are consistently and accurately described using the Verlet-Weis corrected Percus-Yevick structure factor as input, and for a solvent penetration length equal to three percent of the excluded volume radius. This small solvent permeability of the microgel particles has a significant dynamic effect at larger concentrations.

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Coarse-Graining of Ionic Microgels: Theory and Experiment

Cited by 45 publications

References 67 publications

A new look at effective interactions between microgel particles

A new look at effective interactions between microgel particles

Effective electrostatic interactions arising in core-shell charged microgel suspensions with added salt

Dynamics of suspensions of hydrodynamically structured particles: analytic theory and applications to experiments

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