3 Regulation principle of the film-forming kinetics
The kinetics can influence the morphology and properties. In the solution processing, the nucleation, crystallization and crystal growth occurs with the solvent volatilization, which is coupled with the phase separation process, making the process more complex.
In the solution processing, the initial state is the dissolved state. The process of dissolution is the dispersion of molecules into solution by solvent. And dissolution rate is related to molecular diffusion, reaction activation energy, surface energy and other factors. It can be calculated by Fick’s law, that is, the dissolution rate is proportional to the concentration, which can be described by the following formula:[82]
\(\text{\ \ \ \ \ \ \ \ \ }\frac{\partial C}{\partial t}=D\frac{\partial^{2}C}{\partial x^{t}}\)(1)
Where C is the concentration of the substance in the solution,t is the time, x is the spatial coordinate, and Dis the diffusion coefficient.
As the concentration starts to increase, the solution starts to nucleate. The nucleation rate can be expressed by the following formula:[83, 84]
rate\(\propto D\left(T\right)\bullet exp(-\frac{W^{*}}{\text{kT}})\)(2)
D(T) represents the diffusion coefficient while W* denotes the energy expended in the creation of a nucleus with the minimum required size.Determining a molecule’s ability to participate in nucleation is heavily influenced by the diffusion coefficient. Viscosity is inversely proportional to η , as stated by the Stokes-Einstein relation. An equation of the Vogel-Fulcher-Tammann type effectively describes the exponential increase in the diffusion coefficient when T -T g is less than 100 °C:[85]
\(D(T)\propto exp(\frac{-B}{T-T_{0}})\) (3)
both B and T 0 are constants.
To form the critical size nucleus, energy input is necessary to balance the following two aspects: (1) the volume free energy difference between the liquid and crystalline states, \(G_{1c}=G_{1}-G_{c}\), (2) the interfacial energy \(\gamma_{1c}\) is related to the surface of the nucleus.
As the degree of undercooling increases, the energy barrier for uniform nucleation indeed decreases, making it easier for nucleation to occur in supercooled liquids. On the other hand, in the event of heterogeneous nucleation, the formation of the nucleus occurs on an existing solid surface, there is a notable decrease in the energy barrier for nucleation. This reduction in the energy barrier facilitates and accelerates the nucleation process.
Various factors, including the volatility of the solvent, spinning speed, and the temperature of the solution and substrate, determine the rate of solvent removal from the upper layer.[82] The initially dilute solution becomes enriched in both solutes as the solvent is depleted. This enrichment leads to increased interaction between the solutes and leads to morphology evolutions. When the solvent is extracted, the mixture enters the spinodal range, leading to phase separation. As the solvent is depleted, the solution begins to be rich in these two solutes. The interaction between solutes will increase and the morphology will change. As the solvent is removed, the mixture reaches the spinodal region (immiscible conditions), resulting in the phase separation.[86] Under these conditions, the resolution becomes precarious, and even slight variations lead to rapid separation of phases. In general, the solution is divided into two phases enriched with donor and acceptor, respectively. Following these two initial formation stages, there is a subsequent slow coarsening process. The rate at which the solvent is removed affects the kinetics of phase separation and coarsening.[82]
The crystal growth rate is given in the following format:[84]
rate\(\propto D^{{}^{\prime}}\left(T\right)\bullet[1-exp(-\frac{G_{k}}{\text{kT}})\)] (4)
The crystal growth involves long range diffusion, while nucleation only requires particles to diffuse over a short distance near the interface between the crystal and the melt.[87]
Typically, the maximum rates of nucleation and crystal growth occur nearT g and T m, respectively. To achieve crystallization, it is necessary to have nucleation and the growth of crystals at a decent speed. Hence, the extent of intersection between nucleation and crystal growth regime plays a crucial role in determining if crystallization takes place in the molten state while undergoing cooling. The highest rate of crystallization takes place within the temperature range of T g andT m. Alternatively, the process of crystallization can be initiated by initially subjecting the material to annealing at a temperature in proximity to T g, and subsequently conducting a second annealing phase at a temperature nearer toT m, which promotes accelerated growth of crystals.[85]
Crystal growth is also affected by many factors, such as temperature, additives, molecular interactions, and so on. With the complete evaporation of solvent, the crystal structure tends to be stable, and the film-forming process is basically completed. Finally, through the interaction of these dynamic processes, the final morphology of the organic solar cell film is formed if there is no post annealing process.
In summary, understanding the film-forming process in detail is crucial for investigating the thermodynamics and kinetics of thin film drying and optimizing the morphology of the active layer to achieve high device performance. Schmidt Hansberg et al. utilized in situ GIWAXS to reveal the kinetics and thermodynamics of molecular ordering during the thin film drying process, which deepened the understanding of the film-forming process.[31] In the initial stage, the DCB content was only 3 wt%, and as the solvent gradually evaporated, the DCB content increased to 14 wt%. As DCB gradually evaporated, PCBM reached its maximum solubility first, while P3HT transitioned from the solution state to the gel state. The stacking signal of the P3HT side chains in the out-of-plane direction (100) increased, but the aggregation diffraction peak of PCBM appeared only after the ordering of P3HT, indicating that the interaction between the polymer and the fullerene inhibited the aggregation and clustering of the fullerene molecules, leading to the formation of clusters in the final stage of thin film drying after complete stacking of P3HT molecules. As the solvent further evaporated, P3HT crystallization became more complete, and PCBM entered the amorphous region of P3HT, aggregating to form clusters.
The morphology of thin films significantly influences photoelectric properties like charge transfer and energy transfer. It’s important to recognize that the actual dynamics of film-forming are highly intricate. Therefore, further theoretical models and experimental investigations are required to delve deeper into these processes.