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Sara Fortuna

A Cellular Automata model of Polymers growth


The cellular automata model to simulate polymers growth is implemented here as a Java applet.

 

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Press GO tu run a simulation. To run a new simulation press CLEAR, set new parameters, and press GO. The grid can be flagged out. To directly get the output, press GENERATE OUTPUT FILE.



The persistence is the tendency of a polymer to grow straight.

The simulation runs on a hexagonal lattice. On the lattice, a polymer is defined as a connected chain of monomers (grey sites, in Fig.1).

polymer

Fig.1 - A polymer (grey). The polymer can grow by addition of a monomer in any of the sites a, b (b'), c (c') until it reaches the maximum length L.

To grow a chain, a monomer seed is placed on the lattice, and the polymer grows from the seed by addition of monomers. A new monomer can be inserted in any of the lattice sites highlited in Fig.1 (green, yellow, blue sites), if they are not already occupied by another monomer. To each site is assigned a probability of being occupied: P(a) to the site in the direction of the polymer growth, P(b) identify a 60 degree kink, and P(c) a 120 degree kink. Each probability depends on the current configuration of the system:

probability

where P is the persistence, or the tendency of the polymer to grow straight, Na, Nb, Nc are the number of occupied neighbors of the sites a, b, c respectively, and

Ptot

is the sum of the probabilities associated with each site. P(b') and P(c') are calculated analogously as P(b) and P(c), but they can assume different values depending on the system configuration. If a site is already occupied, its associate probability is set equal to zero.

A polymer growth is stopped when its chain reaches the length L, or when there is no empty lattice site to add a further monomer to its end.

A new simulation starts placing a monomer seed in the center of the lattice. Every successive seed is placed at a random site, chosen to be adiacent to an already occupied site.


Output Examples:


As an example, we discuss the two phases expressed by the sistem. Both the simulations were run on a 100x100 grid, with a maximum polymer lenght L equal to 500.

example2.jpg

Random Coils

Setting the parameter P to zero, let the polymers fold on themselves because the driving force of the process is the Van der Waals interaction between each new monomer and the existing configuration.

example1.jpg

Polycrystalline Phase

Setting the parameter P to 1000, let the polymers grow linearly because the driving force of the process is the persistence of the chain. The Van der Waals interaction between each new monomer and the existing configuration is three order of magnitude smaller than P, this contribution however opens the possibility to random kinks of the growing chains.