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Wertheim's association theory applied to one site patchy colloids: Beyond the single bonding condition
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Image of FIG. 1.
FIG. 1.

Diagram of interacting colloids.

Image of FIG. 2.
FIG. 2.

Diagram of three interacting colloids where colloids 1 and 3 are both in contact with colloid 2.

Image of FIG. 3.
FIG. 3.

Comparison of theoretical (current theory – solid lines, theory of Kalyuzhnyi 13 – dashed lines), and simulation (symbols) predictions for the monomer fractions (blue), fraction of colloids bonded once (red) and fraction bonded twice (green) at packing fractions of = 0.2 top and = 0.4 bottom; each with α = 35°.

Image of FIG. 4.
FIG. 4.

Fractions bonded twice in a ring (solid lines – theory, filled symbols – simulation) and twice in a chain (dashed line – theory, open symbols – simulation) at packing fractions of = 0.2 (red) and = 0.4 (black); for each case α = 35°.

Image of FIG. 5.
FIG. 5.

Energy per colloid * = / at a critical angle α = 35° and packing fractions = 0.2 (top) and = 0.4 (bottom). Symbols are simulation results, solid line is from the current theory Eq. (38) , long dashed line is predictions from the theory of Kalyuzhnyi , 13 and short dashed line is TPT1 predictions.

Image of FIG. 6.
FIG. 6.

Energy per colloid * = / as a function of critical angle α. The packing fraction is fixed at = 0.3, symbols give simulation results, solid curves give current theory predictions Eq. (38) , and dashed curves are TPT1 predictions. Color code: red represents ɛ* = 5 and black represents ɛ* = 3. Inset gives the simulated fraction of colloids bonded 3 times .

Image of FIG. 7.
FIG. 7.

Change in pressure due to association Δ* for α = 35° (left) and α = 45° (right). Symbols give simulation results, solid curves give theoretical predictions from the current work and dashed curves give theoretical predictions using the theory of Ref. 13 .


Generic image for table
Table I.

Numerical results for geometric integrals Γ and Ψ and angles and .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Wertheim's association theory applied to one site patchy colloids: Beyond the single bonding condition