Block copolymer nanostructures are one of the leading candidates to create long-range ordered microstructures. Solvent evaporation and annealing is one of the most common methods to create the block copolymer structure in thin films and improve its alignment. In this study I use the real space method to investigate the microstructure evolution of the diblock copolymer thin films in solvent.
I also use the pseudospectral method to obtain the morphology of the block copolymers formed in the confined system with two controlled interfaces.
Significance of the study
Introduction
To be applied to real industry, the domain of the nanometer size needs a structure that repeats to macro size without defects, but it is not easy to make a nanostructure such a defect-free macro size in a system of thermodynamic self-assembly. So, for a study of the theory of large-area BCPs, recently developed new algorithms should be actively introduced, and it is necessary to develop an efficient algorithm through parallel computations such as OpenMP (Open Multi-Processing) or MPI (Massage Passing Interface) to use. to increase computational efficiency.
Introduction of self-consistent field method and its application
Self-Consistent Field Theory
Third, the size of BCPs in periodic domain that can be obtained from the laboratory is currently about hundreds of nm, from an academic point of view, it is enough for the purpose of the study, but for practical application, an area of micro square meters or larger is necessary. Among them, our focus is on the adaptation of a wide range of nanostructures with new electrical, optical or magnetic properties on the scale of approx. 10 nm or less16-19, which could initiate the innovation of energy and information technology. The partial partition function q†( , )rs of the polymer segments of length (1-s N) starting from the B end is calculated by solving equation (2) subject to the initial condition q†( , ) 1r s.
Calculating the distribution function by solving equation (1) requires the field w( )r, but this field can be calculated using equations (6-7) only after the distribution function is calculated. It is impossible to find a solution in one go if we avoid this loop structure, so it is necessary to find a self-consistent field with agreed input and output using iteration. In other words, if a test input field is entered at the beginning, a partition function is calculated and an output field is obtained from the calculated polymer density, and a new input field is made from this information, which changes .
This algorithm process is explained in Figure 3 below (in this figure, the unit length is set to a2N = 1). The most essential part in the SCFT calculation is the solution of the modified diffusion equations (1) and (2) itself. Commonly used methods for their solution can be classified into the real space method, the spectral method 20-2425-27 and the pseudospectral method, 28-31 and this study uses the real space method to calculate the behavior of the polymer model in the films of thin, and using the pseudospectral method, the morphology of the block copolymer formed in the blocked system was calculated.
Real Space Method
The advantage of this method is that the above three equations can be transformed into the following three equations which have the right form to apply the alternative-direction implicit (ADI) technique. Assuming that M space lattices and N polymer backbone lattices are used, the number of operations required for one full partition function calculation is O(MN).
Pseudospectral Method
Theoretical study on the nanostructure evolution of the diblock copolymer thin films in
Introduction
In this chapter I study theoretical nanostructure evolution on the diblock copolymer thin films in solvent annealing by using modified SCFT method for solvent system.
Simulation Method
④ The newly obtained field energies calculated from the previous step are compared with the randomly chosen input field in the first step. And then the ratio is redetermined by convergence test in such a way that the ratio of old field increases by 1% for positive convergence or decreases by 30% for negative convergence. Using this newly obtained input field energy, we can continue another iterative simulation cycle by going back to step 1.
In the case of a solvent-free system, BCP alignment is mainly dependent on heat and time, so it is difficult to make a sample free of errors due to entropic fluctuation. By the way, in the case of the solvent annealing system, it is observed that the density of the solvent is higher at the site of the domain defects. As annealing proceeds, the solvent fluidizes into the defects, and the defects are locally in the disordered regime.
Because such solvent evaporation is a continuous process, it is impossible to perform digitized SCFT calculations with analog data. As the film thickness h and the solvent volume fraction ψ decrease during the solvent evaporation process, I model the quasi-static morphology evolution by using the morphology of the thicker film as an input to the thinner film. In this study, I set cABN=25, cACN=12, cBCN=10 to represent a well-separated microdomain for both lamellar and cylindrical domain cases.
Results and Discussion
- Lamellar Domain ( f = 0.5)
- Cylindrical Domain ( f = 0.3)
For example, the comparability between the bulk lamellar domain spacing L0 and the diameter D of the nanotube container is one of the most important parameters to control the lamellar morphology in isolation. Furthermore, depending on the eccentricity of the ellipsoid, the curvature of the spherical geometry affects the lamellar morphology for ellipsoidal constraints. The degree of comparability did not greatly affect the lamellar arrangement compared to the surface selectivity on the cavity wall.
Selectivity of the top surface of the cavity can also be controlled by coating three different types of films such as PMMA homopolymers, PS homopolymers and PS-run-PMMA copolymers. To describe the preference of the upper surface layer for each block component, I introduced two new parameters, and hB. As mentioned above, the preference of the upper surface was assigned to each type of material by setting either hA or hB parameter as 0.4.
It was found that the number of layers in the cavities can be controlled by varying the depth of the nanocups. In simulating block copolymer thin films in a solvent annealing process, I used the morphology of the thicker film as input to the thinner film to model the quasi-static evolution of the morphology. As the solvents evaporate, it was found that the film thickness h decreased and the number of defects decreased, resulting in a well-aligned domain structure.
Arrangement of Microdomains of Diblock Copolymers Confined in Half-Ellipsoid-Shape
Introduction
Confinement of the diblock copolymers under certain geometries may offer new methods to develop unique morphologies never before known in bulk or thin film.46-49 For example, symmetric diblock copolymers usually exhibit lamellar arrangement in the bulk state. On the other hand, recent experimental results report that new interesting bulbous lamellar morphologies were observed in a hemispherical confinement. In this Chapter IV, I theoretically study different block copolymer morphologies in hemispherical and ellipsoidal nanobowl inclusions and compare the results with experiments.
The key parameters for the morphology determination in ellipsoidal inclusion are the size and shape of the container and the surface tension between surface of confining geometry and each block components of polymers. Above all, affinity between surface of confining geometry and block copolymer are the most important parameters to control the morphologies. Predictions based on the SCFT calculation were compared with the morphologies obtained in experiment and found to be quite consistent.
In this study, I model polystyrene-block-poly(methyl methacrylate) copolymer (PS-b-PMMA) as AB block copolymers (A and B correspond to PMMA and PS, respectively) using the SCFT method. In this chapter, I investigate the arrangement of not only the lamellar domain (symmetric diblock copolymer domain), but also the cylindrical domain and the spherical domain (asymmetric diblock copolymer domain) by varying the parameter f (A fraction of AB diblock copolymer). The effect of the curvature of the ellipsoidal geometry is also investigated to determine how the eccentricity of the ellipsoid affects the morphology of the block copolymers in the confined spaces of the ellipsoidal-shaped nanocups.
Theory and Numerical Implementation
PMMA-OH and PS-OH brushes act as selective surfaces, and PS-ran-PMMA copolymer brushes act as a neutral brush. When these two interfaces are controlled independently, the alignment of BCP microdomains can be significantly changed and thus new types of morphology are observed. The simulation box consisted of a three-dimensional 64x64x64 grid and the modified diffusion equations for the partition functions of block copolymers and homopolymers were solved using the SCFT with pseudospectral method adapted for this study.51-52 For both block copolymers and a homopolymer, 50 mesh- points used in the polymer longitudinal direction.
For all boundaries, the Neumann boundary condition was used to correctly represent the polymer-film interface while minimizing the unit cell size.
Results and Discussion
- Symmetric Diblock Copolymers (Lamellar Domain f = 0.5)
- Asymmetric Diblock Copolymers (Cylindrical Domain f = 0.25)
- Asymmetric Diblock Copolymers (Spherical Domain f = 0.2)
- Effect of the Curvature of the Ellipsoidal Geometry on Morphology of Symmetric
Also, the top surface preference is given as a delta function-like potential with hA and hB, representing the strength of the delta function. In this case, the arrangement of the lamellae is highly dependent on the interaction of the upper surface (Figures 6a-6c). If the upper surface prefers a segment type (Figures 6a and 6b), a parallel lamellar structure is observed on the upper surface due to preferential surface interaction and concentric lamellae are observed at the bottom of the cavity due to the inner wall brush. which prefers a segment type.
On the other hand, when the top layer becomes neutral, concentric lamellae with the outer PMMA shell are observed until they meet the top layer, as shown in Figure 6c. When the top surface is favored for one type of segment, expanded lamellae are observed (Figs. 6g and 6h), while bi-continuous structures with interconnected lateral and vertical lamellae are observed for a neutral top layer (Fig. 6i). The cavity has a bowl shape and it is clear that the lamellae at the bottom of the cavity must be deformed even if they are perpendicular to the top surface.
Our simulation results show that only morphologies whose AB boundary is perpendicular to the top surface can survive if the top surface is not favored. a) Three-dimensional visualization of the bi-continuous morphology corresponding to Figure 6i after cutting the sample at two different angles (bottom view (left) and lateral (right) view). Alignments of microdomains of asymmetric AB block copolymer (PS-b-PMMA) confined in a hemispherical cavity calculated by the SCFT pseudospectral method for cylindrical domain. When the wall of the nanobowl container is coated with a PMMA-OH brush (χCAN = 25), the outer ring structure of the A-block domain is formed along the wall of the container with the help of attractive wall interaction by an A-selective brush .
Conclusion
