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Thin films, surfaces and nanomaterials

In heterogeneous nucleation, with θ the contact angle between nucleus and substrate, the energy needed to form a critical nucleus is f(θ) = (2 + cosθ)(1 − cosθ)²/4 times that for homogeneous nucleation. Which value is closest to f(θ) for θ = 60°?

  1. AAbout 0.16
  2. BAbout 0.63
  3. C1.0 (the same as homogeneous nucleation)
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Answer: A. About 0.16

cos60° = 0.5, so f = (2 + 0.5)(1 − 0.5)²/4 = 2.5 × 0.25/4 ≈ 0.16. The nucleation barrier thus falls to about 16% of that for homogeneous nucleation, and nuclei form far more readily on substrates, container walls and inclusions. About 0.63 forgets the final division by 4. For θ = 90° (a hemispherical nucleus), f = 0.50 and the barrier is exactly half that of homogeneous nucleation. The closer θ is to 0 (good wetting), the closer f is to 0, while at θ = 180° (no wetting at all) f = 1, the same as homogeneous nucleation. Inoculation to refine grains in casting exploits this heterogeneous nucleation.

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