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Coalescence of Repelling Colloidal Droplets: A Route to Monodisperse Populations

Roger, Kevin; Botet, Robert and Cabane, Bernard LU (2013) In Langmuir 29(19). p.5689-5700
Abstract
Populations of droplets or particles dispersed in a liquid may evolve through Brownian collisions, aggregation, and coalescence. We have found a Set of conditions under which these populations evolve spontaneously toward a narrow, size distribution. The experimental system of poly(methyl methacrylate) (PMMA) nanodroplets dispersed in a solvent (acetone) + nonsolvent (water) mixture. These droplets carry electrical charges, located on the ionic end groups of the macromolecules. We used time-resolved Small angle X-ray scattering to determine their size distribution. We find that the droplets grow through coalescence events the average radius < R > increases logarithmically with elapsed time While the relative width sigma(R)/< R >... (More)
Populations of droplets or particles dispersed in a liquid may evolve through Brownian collisions, aggregation, and coalescence. We have found a Set of conditions under which these populations evolve spontaneously toward a narrow, size distribution. The experimental system of poly(methyl methacrylate) (PMMA) nanodroplets dispersed in a solvent (acetone) + nonsolvent (water) mixture. These droplets carry electrical charges, located on the ionic end groups of the macromolecules. We used time-resolved Small angle X-ray scattering to determine their size distribution. We find that the droplets grow through coalescence events the average radius < R > increases logarithmically with elapsed time While the relative width sigma(R)/< R > of the distribution decreases as the inverse square root of < R >. We interpret this evolution as resulting from coalescence events that are hindered by ionic repulsions between. droplets. We generalize this evolution through a simulation of the Smoluchowski kinetic equation, with fa kernel that takes into account the interactions. between droplets. In the case of vanishing or attractive interactions, all droplet encounters lead to coalescence. The corresponding,kernel leads to the well-known "self-preserving" particle distribution Of the coalescence process, where sigma(R)/< R > increases to a plateau Value. However, for droplets that interact through long-range ionic repulsions, "large + small" droplet encounters are. more suceessful at. coalescence than, "large + large" encounters. We show that the corresponding kernel leads to a particular scaling of the droplet-size distribution-known as the "second-scaling law" in the theory of critical phenomena, where sigma(R)/< R > decreases as 1/root < R > and becomes independent of the initial distribution. We argue that this Scaling explains the narrow size distributions of colloidal dispersions that have been synthesized through aggregation processes. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Langmuir
volume
29
issue
19
pages
5689 - 5700
publisher
The American Chemical Society
external identifiers
  • wos:000319185100007
  • scopus:84877757325
ISSN
0743-7463
DOI
10.1021/la400498j
language
English
LU publication?
yes
id
9301dd32-7d5e-489a-96ab-55923e5b6eef (old id 3932203)
date added to LUP
2013-07-15 13:58:20
date last changed
2019-09-04 01:23:36
@article{9301dd32-7d5e-489a-96ab-55923e5b6eef,
  abstract     = {Populations of droplets or particles dispersed in a liquid may evolve through Brownian collisions, aggregation, and coalescence. We have found a Set of conditions under which these populations evolve spontaneously toward a narrow, size distribution. The experimental system of poly(methyl methacrylate) (PMMA) nanodroplets dispersed in a solvent (acetone) + nonsolvent (water) mixture. These droplets carry electrical charges, located on the ionic end groups of the macromolecules. We used time-resolved Small angle X-ray scattering to determine their size distribution. We find that the droplets grow through coalescence events the average radius &lt; R &gt; increases logarithmically with elapsed time While the relative width sigma(R)/&lt; R &gt; of the distribution decreases as the inverse square root of &lt; R &gt;. We interpret this evolution as resulting from coalescence events that are hindered by ionic repulsions between. droplets. We generalize this evolution through a simulation of the Smoluchowski kinetic equation, with fa kernel that takes into account the interactions. between droplets. In the case of vanishing or attractive interactions, all droplet encounters lead to coalescence. The corresponding,kernel leads to the well-known "self-preserving" particle distribution Of the coalescence process, where sigma(R)/&lt; R &gt; increases to a plateau Value. However, for droplets that interact through long-range ionic repulsions, "large + small" droplet encounters are. more suceessful at. coalescence than, "large + large" encounters. We show that the corresponding kernel leads to a particular scaling of the droplet-size distribution-known as the "second-scaling law" in the theory of critical phenomena, where sigma(R)/&lt; R &gt; decreases as 1/root &lt; R &gt; and becomes independent of the initial distribution. We argue that this Scaling explains the narrow size distributions of colloidal dispersions that have been synthesized through aggregation processes.},
  author       = {Roger, Kevin and Botet, Robert and Cabane, Bernard},
  issn         = {0743-7463},
  language     = {eng},
  number       = {19},
  pages        = {5689--5700},
  publisher    = {The American Chemical Society},
  series       = {Langmuir},
  title        = {Coalescence of Repelling Colloidal Droplets: A Route to Monodisperse Populations},
  url          = {http://dx.doi.org/10.1021/la400498j},
  volume       = {29},
  year         = {2013},
}