Homogeneous nucleation under acoustic levitation

The goal is to control specifically the progress of crystallization and, therefore, one of the most important part is to identify the influencing parameters and manipulate them. One main interest is the study of nucleation processes over a wide range of low and high super-saturation. To access these levels of supersaturation, homogeneous nucleation has to be warranted and any surfaces which might act as heterogeneous nucleation sites have to be circumvented. The implementation of a genuine homogeneous nucleation under ambient condition is demanding due to the present of impurities, vessel walls, and gravity. Previ-ous ways to limit the role of surfaces on crystallization process from solution included the division of the sample into tiny portions that most of them do not contain heterogeneous nucleation sites. Another possibility is to generate conditions where the nucleation rate is high and the crystal growth rate is low. However, these methods are complicated and the application is not suitable for each system.

The use of strong acoustic fields for particle manipulation is a widely used technique for many applications. The ever increasing technical finesse in generating and shaping ul-trasonic fields has introduced tools, such as ulul-trasonic motors^[57], and contactless sample holders for sensitive materials^[58] that go into large scale product processing. While there are various methods, as the magnetic, electrostatic or aerodynamic levitation, acoustic levitators generating an ultrasonic standing wave for the containerless levitation of objects have gained considerable interest in the past few years. The straightforward technical im-plementation and the minimal sample requirements are the reasons for the wide range of application in analytical chemistry and material processing.^[59–61] The crystallization experiments in this research are performed in a custom-made acoustic levitator consisting of three main components: the sonotrode, the reflector, and an atmosphere control unit (see Figure 2.4, p. 14).^[62] This device works in the most commonly used single axis geom-etry, where a transducer and reflector are arranged in a coaxial fashion, sharing the same axis of cylindrical symmetry. The sonotrode is an ultrasound transducer transforming the alternating voltage into mechanical waves with a piezo-electric crystal. This crystal works with an oscillating frequency of 58 kHz. A concentric reflector reverberating the longitudinally expanding ultrasonic waves locates on the opposite side of the sonotrode.

Thus, a standing wave with several sound pressure nodes emerges by adjusting the dis-tance between the sonotrode and the reflector resulting in a multiple of half the used wavelength. The Bernoulli effect, which describes the correlation between the velocity in-crease and the pressure dein-crease during the flow of gases, induces radial and axial forces.

These forces hold liquids and solid samples in a fixed, levitated, and contactless position.

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Figure 2.4: The acoustic levitator serves as a contactless sample holder. The device has three main components: the sonotrode, concentric reflector, and the control unit. The sonotrode emits the ultrasonic field which is deliberated by the reflector resulting in a standing wave with pressure nodes.

Droplets of liquids are transferred in the levitator by using a pipette. The size of the droplet is a function of the wavelength and can reach a maximal diameter of half the used wavelength. The maximal volume is dependent on the surface tension and the spe-cific density of the liquid.^[63] The acoustic levitator is used as a method to hold liquids and solid samples.^[59] This technique uses the ultrasonic frequencies to position materials containerless in a fixed gaseous environment.^[29,64–71] The special control unit allows the influence of the humidity and temperature of the sample surrounded by introducing a heatable/coolable nitrogen gas flow, which is tempered with the control device and can keep dust and impurities away from the sample. In view of recent studies, this is impor-tant for the crystallization control. Molecular dynamics simulations of titanium dioxide demonstrated the influence of humidity on the mediating particle interactions and the particle attachment event.^[72] In vacuum, nanocrystalline titanium dioxide merges along its direction of approach forming a polycrystalline structure. However, the presence of water molecules with a high moisture content causes a reorientation of the

nanocrys-14

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tals resulting in an aggregation process via the oriented attachment to develop a single crystal. Another example presents the strong impact of the temperature on the polymor-phic structures. The synthesis of 7,14-bis((trimethylsily)ethynyl)dibenzo[b,def]-chrysene (TMS-DBC) and the following purification by growth of single crystals from solution and vapor deposition indicated the dramatic influence of the substrate temperature on the resultant polymorphs of TMS-DBC: fine red needles with 1D slipped-stack motifs at low temperature and large yellow platelets with 2D brickwork structures at high tempera-ture.^[73] By means of electronic-structure calculations, a distinct mobility property of the polymorphs was proven which affects the charge transport and is a strong interest in elec-tronic applications. Besides the temperature and humidity, the nature of the used solvent is also crucial for crystallization pathways. Nifedipine which has the polymorphs α,^[74]

β^[75], and γ^[76] interacted strongly with solvents leading to different progresses. By using acetone or ethanol, hydrogen bonds between the solvent and solute were formed and the thermodynamically stableα polymorph arose including theβ form as an intermediate.^[67]

The solvents dichlormethane and acetonitrile were not able to satisfy such interactions, so that the glassy modification is formed intermediately prior to the crystallization of the α form. These observations are consistent with the Ostwald’s rule of stages.

The examples demonstrate the importance of crystallization control by the consideration of formation conditions and surfaces. The different crystallization theories imply surfaces as a controlling parameter of crystallization pathways for the simple reason that they lower the barriers to nucleation by reducing the interfacial free energy.^[77] Holding sam-ples in terms of levitated droplets is a good approach to avoid the interference with solid surfaces from vessels and, therefore, eliminates this parameter from the crystallization process. Additionally, the higher interfacial free energy of the droplets ensures achieving highly supersaturated systems where processes are comparable with genuine homogeneous nucleation processes. Thus, the acoustic levitator is an ideal analytical tool to control the reaction pathways by the selective setting of the crystallization environment, and it pro-vides the possibility to perform homogeneous crystallization.

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