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.