Difference between revisions of "Team:CCU Taiwan/Polymer"

Oligomerization Estimate

  Our project is to polymerize new materials, Liggreen. We use Flory-Stockmayer theory for our modeling simulation. Flory-Stockmayer theory can calculate the gelation and condensation in polymerization. Because we hope Liggreen to be better decomposed, we do the oligomerization. Through the calculation we can adjust our polymerization according to modeling.

Flory-Stockmayer assumptions

1. All functional groups on a branch unit are equally reactive
2. All reactions occur between two molecules.
3. There are no intramolecular reactions

Flory-Stockmayer theory of gel point

  The Flory-Stockmayer theory is an ideal prediction for polymers. This theory is mainly to integrate gelation and contraction reactions. Through this theory we can understand the polymerization reaction and adjust the polymerization conditions.

  Our monomer is Coniferyl alcohol. According to the reaction of the enzyme, our monomer will exhibit three resonance states. We want to make the material more biodegradable and chain-like, so we use oligomer polymerization. Because coniferyl alcohol has three resonance states, our functional group is three (f=3).

Polymerization of Liggreen

  In the Flory-Stockmayer theory, our reaction belongs to ABg polymerization. In the Liggreen of ABg type polycondensation, there is an unreacted A and i(g -1)+1 B group on the species with degree of polymerization i, and the species can be derived under the assumption of the inner cyclization reaction and the isocratic assumption.
We assume that our reaction only occur in oligomer and monomer. Because we want to make the material appear chain, we tend to oligomerize. Through ABg reaction, we can achieve oligmorization by adjusting the conditions.

According to the above, our modeling is mainly based on three resonance states and ABg.

The initial conditions for the above equation are:

Because there is only one monomer group on each species.

Then for the following two types of simultaneous. Can get

After getting the above formula, we bring in our parameters.

With this distribution function, the various molecular parameters of Liggreen may be quantitatively known. Figure 1 shows the relationship between the polydispersity index of Liggreen under several g parameters and the conversion of the monomer group. g = 1 is the type AB monomer. Linear polycondensation, after the end of the reaction (x = 1), the polydispersity index of the Liggreen is only 2, if g > 1, the formation of hyperbranched polymer, the polydispersity index of Liggreen becomes very large near the completion of the reaction.

References:

1. Stockmayer, W. H. (1943). Theory of molecular size distribution and gel formation in branched‐chain polymers. The Journal of chemical physics, 11(2), 45-55.
2. Flory, P. J. (1941). Molecular size distribution in three dimensional polymers. I. Gelation1. Journal of the American Chemical Society, 63(11), 3083-3090.
3. Carothers, W. H. (1936). Polymers and polyfunctionality. Transactions of the Faraday Society, 32, 39-49.

Degradation Estimate

We assumed our product consists of three bonds of β-5, β-O-4, β-β, and the enzyme can break these bonds, simulating the degradation curve under ideal conditions, predicting the state of degradation and the treatment reference for the product.

Assumed:

1. The volume of the solution is constant and the concentration is uniform
2. With unlimited nutrition, yeast will not die but exist reproduction upper limit.
3. Lignin degradation is a one-step reaction
4. Both enzymes and Liggreen are first-order reactions
5. Ignore environmental factors (temperature, humidity,etc.)
6. Value of enzyme activity is a constant.

Following were some simulation constants. These used to fit initial condition to approach reference [3] result (fig1 & 2).

1. Only a cup (about 0.72g Liggreen) was degraded in the system (1 liter solution).
2. Initial number of bacteria is 10⁹.
3. Number of bacteria upper limit is 10¹³.
4. Bacterial reproductive cycle is 1800 seconds.
5. Enzyme production cycle is 600 seconds.
6. Enzyme degradation cycle is 4 hours (90% enzyme function time).
7. Reaction rate is proportional to the concentration of enzyme and weight of Liggreen.

Figure 1
From simulation, a cup would be degraded 99% about between 4 days and 5 days in ideal environment.

Figure2
Simulation discovered that initial number not had large influence (only delay about one day), because bacteria had rapidly reproduction ability. We estimated that if a species bacteria would get energy by degrade our material, and ignored some factors. Our cup would be degraded in nature, although number of this species not have high ratio in environment.

In order to degrade our product, environmental adaptability of degradation bacteria was important factor. We used bacteria reproductive cycle to discussion this factor, and the number of each line was mean reproductive magnification.
(For example in Figure 3a, magnification of blue line was 2, it was mean that total quantity of bacteria would become twice in each reproductive cycle.)

Figure 3a. 500000 seconds about 6 days

Figure 3b. 500000 seconds about 6 days

Figure 3c. 2000000 seconds about 23 days

Figure 3d. 6000000 seconds about 69 days

Figure 4

Table 1

From Figure 3a to 3d, Figure 4, and Table 1,
Simulation discovered that magnification vary from 2 to 1.1 not had large influence, and only 1.1 needed more than 5 days. (Figure 3a). Magnification vary from 1.1 to 1 had large different (Figure 3b & 3c), 1.05 needed about 6 days, and inefficient degradation would occur if magnification was smaller 1.05 (Figure 3d & 4).
Form the result, we thought that environmental adaptability would largely influence our product, especially while the species of bacteria is hard to reproduce and exist in degraded environment. Thus we must pay attention to control the environment if we want to use bacteria to recycle product, and try to adjust our product to make bacteria easier degrade.

In the future, more information and data would be collected and revised to modify assumption and make the simulation model more similar to the nature.

Figure 4

Figure 4

References:

1. Barceló, A. R., Ros, L. G., Gabaldón, C., López-Serrano, M., Pomar, F., Carrión, J. S., & Pedreño, M. A. (2004). Basic peroxidases: the gateway for lignin evolution?
   Phytochemistry Reviews, 3(1-2), 61-78.
2. Vanholme, R., Demedts, B., Morreel, K., Ralph, J., & Boerjan, W. (2010).
   Lignin biosynthesis and structure. Plant physiology, 153(3), 895-905.
3. Chang, Y. C., Choi, D., Takamizawa, K., & Kikuchi, S. (2014). Isolation of Bacillus sp. strains capable of decomposing alkali lignin and their application in combination with lactic acid bacteria for enhancing cellulase performance. Bioresource technology, 152, 429-436.
4. Bugg, T. D., Ahmad, M., Hardiman, E. M., & Singh, R. (2011). The emerging role for bacteria in lignin degradation and bio-product formation. Current opinion in biotechnology, 22(3), 394-400.
5. Daina, S., Orlandi, M., Bestetti, G., Wiik, C., & Elegir, G. (2002). Degradation of β-5 lignin model dimers by Ceriporiopsis subvermispora. Enzyme and Microbial Technology, 30(4), 499-505.
6. http://umdberg.pbworks.com/w/page/49681668/Boltzmann%20distribution%20and%20Gibbs%20free%20energy
7. https://en.wikipedia.org/wiki/Boltzmann_distribution