Entropic Forces in Colloidal Suspension Self-Assembly
DOI:
https://doi.org/10.5281/zenodo.22698392Ključne besede:
entropic forces, depletion interaction, colloidal self-assembly, Brownian dynamics, excluded-volume effects, phase behavior, hard-sphere suspensions, packing fractionPovzetek
Purely repulsive, hard-sphere colloidal particles can nonetheless self-assemble into ordered structures driven
entirely by entropy maximization of the suspension as a whole, a phenomenon with no direct analogue in
energy-minimizing molecular crystallization. We used Brownian dynamics simulations of binary hard-sphere
colloidal suspensions, with large-particle diameter fixed at 1.0 micrometre and small-particle (depletant) diameter
varied from 0.05 to 0.35 micrometres, to quantify how depletion-driven entropic forces govern self-assembly across
54 combinations of total packing fraction (0.35-0.58) and size ratio (0.05-0.35). Depletion attraction strength,
computed from the Asakura-Oosawa potential, increased with depletant packing fraction and reached a maximum
contact well depth of 6.8 k_BT at the highest depletant concentration tested (packing fraction 0.30, size ratio 0.10),
a value sufficient to drive reproducible aggregation within our simulated timescales. At total packing fractions above
0.52, suspensions crystallized into face-centered-cubic ordered domains within a mean simulated time of 340
Brownian relaxation times, versus no crystallization observed within 2,000 relaxation times at packing fractions
below 0.44, defining a comparatively narrow transition window. The entropy gain per depletant particle released into
the bulk upon large-particle contact, calculated from excluded-volume overlap, averaged 1.9 k_B at size ratio 0.10,
rising to 3.4 k_B at size ratio 0.30, confirming that entropic driving force scales positively with depletant size relative
to the large colloid over the range tested. Mean crystallite domain size at the highest packing fraction tested (0.58)
reached 42 +/- 6 large-particle diameters (mean +/- SD across 12 independent simulation replicates), 2.6-fold larger
than domains formed at packing fraction 0.48 (16 +/- 4 diameters). A control series with no depletant present
showed no ordered assembly within 2,000 relaxation times at any packing fraction tested below the known
hard-sphere freezing transition, confirming that depletion attraction, rather than packing constraints alone, was the
dominant driver of accelerated ordering in the binary mixtures. These results provide a quantitative
depletion-strength and packing-fraction map for engineering colloidal self-assembly kinetics and target crystallite
size through depletant size and concentration alone, without requiring any direct interparticle attraction.
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