Team:USTC/Model/2
Introduction
In this part, we want to know the precise structure of the crystal to get the actual reaction area. In our photocatalyst system, we need to get precipitation of CdS. S2-are generated from cysteine catalyzed by an aminotransferase CysDes, then it will precipitate with the additional Cd2+ in the media. Subsequently, these precipitation would aggregate as a crystal.
What were we modeling:
In order to simulate the crystal process, we employ a method called DLA(Diffusion-Limited Aggregation) which means particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. Feasibility and rigorous of DLA model are widely studied in previous paper[1],[2],[3],[4].
Firstly, we assume that there was a core of a crystal. Every molecule would aggregate to the nuclei. If a molecule is combined with the core, it would become a part of the nuclei. The molecule and the nuclei would become a new core for the next molecule.
As a molecule, it would walk randomly in the solution. In our system, we ignore the interaction force between molecules. Because of this approximation, we could use a DLA model to describe the structure of a CdS crystal.
We regard every molecule of CdS as a particle in our model and considered the size of the particle equal to 1. With time went by, every particle could move randomly in a 2D/3D spatial area. Every step of these particles is considered as 1 as well.
At the beginning, we consider a simple question--what would happen if the particles just moved in a 2D flat plane? As you can see, in Fig.1, there are 200,000 particles in the flat plane. Most of the experiments show the same picture just like Fig. 1 In reference [5], we can see the simulation is very useful. In some aspects, we consider that this model could be used to fit 3D-reality.
Fig. 1 | 2D DLA result with 0.2 million particles
Fig. 2 | 3D DLA result with 0.5 million particles
In the 3D condition, we also regard a particle as the nuclei of the cluster. Using the same method, we get a 3D figure (Fig. 2) with 500,000 particles. We consider a long time scale to get this figure. This 3D simulation can be used in the solution.
As you can see, all of the particles are not symmetrical. However, the structure is very same as its sub-structure. This phenomenon called self – similar which is natural in our world. In this way, we can say that this simulation is very useful for the true CdS cluster.
In our experiment, the useful CdS precipitates are those that were binding on the membrane of bacteria. So we consider a cluster which grown on a plane in 3D. Fig. 3 shows the dynamic process of this simulation.
Fig. 3 | 3D DLA simulation result on membrane with 0.3 million particles
Finally, we get a valid simulation of CdS cluster in our experiment. In this model, we can get the area which will react with bacteria, the cathode, and the environments.
Results:
Our simulation is very identical with the reality and demonstrate the crystallization process of the semi-conductor on the membrane of E.coli successfully.
a) 3D simulation figure of CdS nanocrystals
b) TEM images of CdS/ZnS nanocrystals[6]
Fig. 4 | Simulation and experiment result of CdS cyrstal on E.coli membrane
Reference
- Ball, R., Nauenberg, M., & Witten Jr, T. A. (1984). Diffusion-controlled aggregation in the continuum approximation. Physical Review A, 29(4), 2017.
- Witten Jr, T. A., & Sander, L. M. (1981). Diffusion-limited aggregation, a kinetic critical phenomenon. Physical review letters, 47(19), 1400.
- Miller, A., & Möhwald, H. (1987). Diffusion limited growth of crystalline domains in phospholipid monolayers. The Journal of chemical physics, 86(7), 4258-4265.
- Kane, R. S., Cohen, R. E., & Silbey, R. (1999). Semiconductor nanocluster growth within polymer films. Langmuir, 15(1), 39-43.
- Batty, M., Longley, P., & Fotheringham, S. (1989). Urban growth and form: scaling, fractal geometry, and diffusion-limited aggregation. Environment and Planning A, 21(11), 1447-1472.
- Chen, D., & Gao, L. (2005). Microemulsion-mediated synthesis of cadmium zinc sulfide nanocrystals with composition-modulated optical properties. Solid state communications, 133(3), 145-150.
