Acoustic vibration effects in classical nucleation theory

•Theory requires no assumptions not already implicit in classical nucleation theory.•Acoustic pressure increases nucleation rate by reducing critical nucleus size and work required to form it.•We assume that nucleus structure is similar to that of a loosely bound colloidal particle.•With this assumption, the effects of acoustic vibration become potentially observable. Acoustic vibration is often used to improve the yield of crystals and nanoparticles growing from solutions and melts. As there is still a debate on how acoustic vibration actually works, we have examined the possibility that acoustic pressure can affect the rate of nucleation. Our method is based on an expansion of the free energy of the nucleus in powers of the acoustic pressure. With the assumption that the period of the sound wave is short as compared to the time scale for nucleation, we replace the powers of the acoustic pressure by their time averages, retaining the average of the square of the acoustic pressure as the leading term. By assuming a nucleus having spherical shape, we use the Young-Laplace equation to relate the pressure inside the nucleus to the ambient pressure. Without making further approximations not already standard in classical nucleation theory, we find that the proximate effect of acoustic pressure is to reduce both the size of the critical nucleus as well as the work required to form it from monomers. As the work serves as the activation energy, the ultimate effect of acoustic pressure is to increase the rate of nucleation. If we assume that the atomic structure of the nucleus is the same as that of an ordinary solid, however, we find the compressibility is too small for acoustic vibration effects to be noticeable. If on the other hand, we assume that the structure is similar to that of a loosely bound colloidal particle, then the effects of acoustic vibration become potentially observable.