Saturday, February 23, 2013

Cross-linked Polymers: Part III - Dynamic Method II

Welcome to Cross-linked Polymers Part III which will examine an idea that could allow PACKMOL to generate cross-linked systems as it packs molecules. Adding such a capability to PACKMOL would be a great leap forward in building pseudo-random geometries that are in fact cross-linked!!! But first, I want to expand on an idea  of fixed atoms from last time. Previously, I stated using a cross-linked MD cell in the fixed mode PACKMOL provides thus locking the polymer matrix in place and then adding water or other molecules into the space remaining in the polymer matrix. After having such a thought I only recently asked why couldn't one distribute monomers into the MD cell using a large tolerance between atoms of different molecules using PACKMOL and then run a second time with the monomers fixed and then have it pack cross-linking molecules into the remaining empty space? Being no free lunch, we must use the first output MMP file generated to create a PACKMOL input file specifying the coordinate of each monomer's baricenter (not the center of mass) and it's Euler angles in order to rotate it into the correct attitude to match the MMP file. This is not to horrible to generate. For thousands of monomers there will be the following entry in the PACKMOL input file:

structure monomer.mmp
number 1
fixed x,y,z,a,b,g
end structure

Obviously, either a new piece of vaporware is needed to generate the fixed monomer portions of a second PACKMOL input file or PACKMOL could be extended to make multiple passes in order to build up an MD cell.
In this case a second pass would recreate the monomers in fixed geometry and then the cross-linker molecules would be packed into spaces around them. An important question to ask about dynamic method one is where does the well mixed MD cell consisting of monomers and cross-linking molecules come from? As stated before the current PACKMOL packs the first molecule template followed by the second and so on. This segregates the molecules. If polymerization continues using dynamic method one we  will eventually have a system that will not allow the diffusion of monomers or cross-linking molecules. Building a PACKMOL input file of alternating DGEBA and IPD molecules is doable with a Perl or Python script. An now back to our irregularly schedule blog entry...

 PACKMOL uses constraints to put molecules as close together as possible without violating the user defined tolerance. In a nutshell, what if a dynamic constraint could be added to PACKMOL so that after adding DGEBA an IPD molecule is added but the "start point" on the DGEBA defines the position for a start point on the "to be added" IPD molecule. Remember, the molecular machine part file (MMP) created in NanoEngineer-1 can contain a "starting point", which I refer to as a "hot spot" If you think of a monomer in a polymer it has two hot spots. They are located at the sites where they react with other molecules. For my system of DGEBA and IPD these are at opposite ends of the monomer. DGEBA has two hot spots - male and female. IPD has four. IPD has two amine groups that have two hydrogens each. One IPD bonds with a maximum of four DGEBA. Therefore, if one wants to create a cross-linked epoxy system at 50 percent cross-linking one would specify only two of the IPD hot spots could be bonded and the number of IPD and DGEBA molecules would need to specified so that excess of either molecule does not occur - unless your system wants to study such a situation.

PACKMOL software changes could be moderate to complex. PACKMOL would pack molecules in a different manner than today. PACKMOL would have to understand the hot spots. When it encounters a hot spot it would use the coordinates of the hot spot to place the other molecule. The molecule to place would be based on the information stored in the hot spot when created in NanoEngineer-1.  If there were a 50 percent probability of placing another monomer or a cross-linking molecule at the hot spot PACKMOL would flip a coin. If an atom has multiple hot spots and one has a better chance of reaction then PACKMOL will use this information stored in the hot spot. This new approach to accessing molecules for packing will not affect the packing algorithm. So what does this have to do with building cross-linked MD cells?

PACKMOL currently uses static constraints. One  defines the MD cell dimensions and the tolerance between atoms of different molecules. One can select many 3-D MD cell shapes (e.g. spheres, boxes, etc...). Adding hot spots to PACKMOL will add a dynamic constraint. Every monomers would add two dynamic constraints as to where two IPD molecules have to exist. Specifying the placement of the hot spot of molecule B at tolerance distance from hot spot on molecule A sets up the necessary condition for cross-linking the two molecules. Keep in mind that PACKMOL will pack the molecules and maintain the value of the cost function over many attempts and then select the optimal packing configuration as the solution. Keep in mind that only the position of one hot spot is constrained while the attitude of the molecule to be place will vary in the packing algorithm.
PACKMOL will then write the best solution to an MMP file. 

The final product is special due to the distance between DGEBA and IPD molecules are now close enough to be cross-linked!!! Either another piece of vaporware could be written to cross-link the molecules or the code could be added to PACKMOL. The code will work as described in the "knitter" vaporware referenced in dynamic method one. The code will find the hot spots and the distances between molecules will be near perfect for cross-linking. The advantage of this approach is that LAMMPS does not need to execute to achieve cross-linking. The question is: is this really a dynamic method? Running LAMMPS in method one makes it dynamic. Running PACKMOL packing optimization is dynamic since multiple configurations of molecules are generated and cost functions calculated. Keep in mind that PACKMOL also allows for a pseudo-random seed to be specified allowing the researcher to generate multiple unique geometries for simulations. As mentioned in the "Cleaning House" article posted on 11 January, a structure cleaner would be a great piece of vaporware. I intend to test a structure cleaner against a final MD cell created using dynamic method two. This will be more complex given the number of molecules.  

For those of you who read my blog please feel free to comment on my entries. I would love to hear your comments and please tell me where I am going wrong. I want to produce software that can be used. I welcome collaboration to create open source software for everyone. My next topic will address having to run LAMMPS prior to running LAMMPS. This is rather cryptic, but I have found that I must run LAMMPS on an initial MD cell to generate an initial MD cell at the correct density prior to going forward with simulations for scientific investigation.  

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