A two-state stochastic model for nanoparticle self-assembly: theory, computer simulations and applications

Schwen, Eric; Mazilu, Irina; Mazilu, Dan

doi:10.1088/0143-0807/36/2/025003

Cited by 4 publications

(7 citation statements)

References 32 publications

(36 reference statements)

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“…We will be interested in computing the effective force between the plates after averaging over the microscopic configurations of the microions 7 . This can be obtained by several means.…”

Section: The Modelmentioning

confidence: 99%

“…Note that the difficulty with the contact theorem is that, in general, the contact densities 0 r ( ) and L r ( ) are not known. Yet, equation (7) amounts to a remarkable connection between them that should always hold.…”

Section: Contact Theoremmentioning

confidence: 99%

“…. Invoking one last time the contact theorem, in its asymmetric formulation embodied in equation (7), we get the force as…”

Section: An Odd Number Of Counterions N ¼ 2n +mentioning

confidence: 99%

“…It is at the root of key phenomena, outlined below. Soft matter is in itself a relatively new field, but it is starting to enter the classroom [2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

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Like-charge attraction in a one-dimensional setting: the importance of being odd

Trizac

Téllez

2018

Eur. J. Phys.

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From cement cohesion to DNA condensation, a proper statistical physics treatment of systems with long range forces is important for a number of applications in physics, chemistry, and biology. We compute here the effective force between fixed charged macromolecules, screened by oppositely charged mobile ions (counterions). We treat the problem in a one dimensional configuration, that allows for interesting discussion and derivation of exact results, remaining at a level of mathematical difficulty compatible with an undergraduate course. Emphasis is put on the counter-intuitive but fundamental phenomenon of like-charge attraction, that our treatment brings for the first time to the level of undergraduate teaching. The parity of the number of counterions is shown to play a prominent role, which sheds light on the binding mechanism at work when like-charge macromolecules do attract. I. INTRODUCTIONSoft matter refers to a wealth of systems that may seem disparate at first sight: foams, glues, paints, liquid crystals, colloids, polymers etc. [1]. What they have in common is threefold: a) they are sensitive to 'gentle' mechanical of thermal fluctuations; b) they feature at least two distinct lengthscales (one being microscopic, the other being intermediate between microscopic and macroscopic; c) they often exhibit strong collective effects, such as the property to self assemble into complex entities. As a consequence, their properties are often difficult to rationalize and the sole knowledge of the basic interaction forces between the individual components is not enough to understand the resulting properties. Here, our interest goes to one such collective effect, that challenges intuition and takes place when charges are considered. It is at the root of key phenomena, outlined below. Soft Matter is in itself a relatively new field, but it is starting to enter the classroom [2][3][4][5][6][7][8].In vacuum, two like-charges interact via Coulomb law, which yields a repulsive force. In a solvent like water, containing mobile cations and anions, the situation becomes more complex. It is highly relevant in soft matter physics [1], and more precisely for colloidal suspensions, where large charged macromolecules, typically of micronsize, are surrounded by much smaller ions, called microions. As microions move on a much shorter time scale than the macromolecules, the relevant concept to discuss interactions is that of effective potential: the direct interactions between the charged macromolecules are modified as a result of the fluctuations of the medium. This yields an effective interaction which is mediated by the microions, and it is obtained by performing a thermal equilibrium average over the fluctuations of the positions of the microions [9]. A first effect of the microions is to screen the bare Coulomb repulsion, resulting in a short range effective interaction between the macromolecules [10]. In a small coupling regime (when the typical electrostatic energy is smaller than the thermal one), the effective interaction rem...

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“…We will be interested in computing the effective force between the plates after averaging over the microscopic configurations of the microions 7 . This can be obtained by several means.…”

Section: The Modelmentioning

confidence: 99%

Section: Contact Theoremmentioning

confidence: 99%

“…. Invoking one last time the contact theorem, in its asymmetric formulation embodied in equation (7), we get the force as…”

Section: An Odd Number Of Counterions N ¼ 2n +mentioning

confidence: 99%

“…It is at the root of key phenomena, outlined below. Soft matter is in itself a relatively new field, but it is starting to enter the classroom [2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Like-charge attraction in a one-dimensional setting: the importance of being odd

Trizac

Téllez

2018

Eur. J. Phys.

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“…In this thesis, we present a few example stochastic models and use them to introduce the basic techniques employed to study complex systems and the methods used to solve them. This thesis provides a broad overview of the recent work completed by our research group [19,20,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

An introduction to stochastic self-assembly: theory, simulation and experimental applications

Schwen

2015

Preprint

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We introduce three stochastic cooperative models for particle deposition and evaporation relevant to ionic self-assembly of nanoparticles with applications in surface fabrication and nanomedicine. We present a method for mapping a stochastic model onto the Ising model, which allows us to use the established results for the Ising model to describe the properties of the system. After completing the mapping process, we investigate the time dependence of particle density using the mean field approximation. We complement this theoretical analysis with Monte Carlo simulations that support our models. These techniques, which can be used separately or in combination, are useful as pedagogical tools because they are tractable mathematically and they apply equally well to many other physical systems with nearest-neighbor interactions including voter and epidemic models.

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On the origin of cooperativity effects in the formation of self-assembled molecular networks at the liquid/solid interface

Rinkovec,

Kalebic,

Dehaen

et al. 2024

Chem. Sci.

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A two-state stochastic model for nanoparticle self-assembly: theory, computer simulations and applications

Cited by 4 publications

References 32 publications

Like-charge attraction in a one-dimensional setting: the importance of being odd

Like-charge attraction in a one-dimensional setting: the importance of being odd

An introduction to stochastic self-assembly: theory, simulation and experimental applications

On the origin of cooperativity effects in the formation of self-assembled molecular networks at the liquid/solid interface

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