Interactions between polymer particles

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Particle coalescence and breakage in hetero-phase polymer blends determine the resulting morphology and hence the properties of the material. A reliable model of particle interaction in non-Newtonian fluids has not been proposed yet. We introduce a model of particle interaction based upon the discrete element method (DEM). Many hetero-phase polymeric blends present a colloid system of dispersed polymer droplets in a continuous phase. The control of the particle size distribution of the dispersed polymer droplets is the crucial point of the morphology control. The breakage and coalescence of the particles compete and give the resulting particle size distribution. The breakage and coalescence in non-Newtonian fluid is being investigated experimentally, however the systematic approach resulting in the formulation of a realistic mathematical model is still a challenging task.
Figure 1 presents schematics of particle interaction. Figure 1a shows interaction of two particles colliding with certain momenta, which are not sufficient to break through their double layer. Figure 1b depicts particles with sufficient energy of collision to create a single particle. Consequently surface tension drives the new particle into a more favourable shape.
We present a model based upon the discrete element method (DEM), which approximates particles and droplets as discrete elements or agglomerates of discrete elements and considers force interactions between these discrete elements. DEM simulations have a considerable demand on the computational power, so that in spite of the quick development of the computer power, the number of discrete elements and the length of the simulation are still limited.

The model simulates the trajectories of individual discrete elements and force interactions between the elements, which are described by appropriate physical laws. There can be various forces acting on the elements that were formulated to represent the actual forces in the modeled system, for example: van der Waals attraction, hard-core and electrostatic repulsions, Brownian motion, osmotic forces, Stokes drag force, etc. The formulated mathematical model is a system of stiff ordinary differential equations (ODEs). The Gear’s method was used for integration and it is feasible to compute a dynamic evolution of a system composed of thousands or more particles. In our modeling the polymer particle can be represented as a single discrete element or as a cluster of discrete elements.

Surface tension of polymer particles was implemented by several ways using the clusters of discrete elements. In the cluster an artificial force is acting on each element and drags it towards the center of the particle. Figure 3 shows the initial state, the collision of the particles and the reorganization of the particle into the shape with lower interface energies. The magnitude of the force used as the surface tension was validated by the experimental data from rheometer, light scattering and AFM.

Published Results:

Kroupa M., Vonka M., Kosek J.: Modeling the Mechanism of Coagulum Formation in Dispersions, Langmuir, 2014, 30 (10): 2693–2702.

Ledvinková B., Kosek J.: The effects of adhesive forces on the collision behavior of polyolefin particles. Powder Technology, 2013, 243, 27–39.


Juraj Kosek
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+420 220 443 296

University of Chemistry and Technology Prague
Department of Chemical Engineering
Technicka 5
166 28 Prague 6
Czech Republic

University of West Bohemia
New Technologies Research Centre (NTC)
Univerzitní 8
306 14 Pilsen
Czech Republic