Table 1.

Examples of the use of low‐frequency bulk acoustic waves for the synthesis and manipulation of various materials

Vibration mode	Wave description	Typical frequency range	Examples
Longitudinal	1D pressure wave (particle vibration displacement parallel to the direction of wave propagation) that is the dominant mode in horn transducers such as that employed in probe sonicators	20–100 kHz	Bulk crystals: Crystallization,[ 41 , 42 , 43 , 44 ] including that of metal–organic frameworks[ 45 , 46 ]; crystal fragmentation[ 47 ]
			Nanomaterials: Liquid phase exfoliation of graphene,[ 48 ] transition metal dichalcogenides,[ 49 , 50 ] and IV–VI binary semiconductors[ 51 ] (including quantum dots and nanosheets); dispersion of carbon nanotubes[ 52 ]
			Polymeric and biological materials: Emulsion‐based polymerization[ 53 ]; polymer nanoparticle synthesis[ 54 ]
Plate (thickness expansion mode)	Vibration occurs in the direction of the plate thickness, which determines the resonant frequency; dominant mode associated with the transducers used in bath sonicators and ultrasonic nebulizers (e.g., for spray pyrolysis)	1 kHz–1 MHz, although higher‐frequency operation (up to GHz) can be achieved with ultrathin plate resonators	Ultrasonic bath (typically 1–50 kHz)
			Bulk crystals: Crystallization,[ 55 ] including that of metal–organic frameworks[ 56 , 57 ]
			Nanomaterials: Liquid phase exfoliation of graphene[ 58 ] and transition metal dichalcogenides[ 59 , 60 ]; synthesis of carbon nanotubes,[ 61 ] nanofibers,[ 62 ] and liquid metal droplets[ 63 ]
			Polymeric and biological materials: Polymer synthesis[ 64 , 65 ]; transdermal drug delivery[ 66 ]; intracellular delivery[ 67 , 68 , 69 ]
			Ultrasonic nebulizers (typically 1 kHz–2 MHz)
			Bulk crystals: Spray pyrolysis for nanoparticle and nanowire synthesis[ 70 , 71 , 72 , 73 , 74 ]
			Nanomaterials: Spray pyrolysis for nanocrystallization of molten salts,[ 75 ] synthesis of porous transitional metal dichalcogenides and their composites,[ 76 , 77 ] and, thin film deposition[ 78 ]
			Polymeric and biological materials: pulmonary drug delivery of aerosols and nanoparticles[ 79 , 80 ]