Cross-linked Polymers: Part II - Dynamic Method I

Welcome to part two of cross-linked polymers. I will cover a dynamic cross-linking approach where LAMMPS will put resin and curing agent molecules into motion and molecules will be bonded together external to LAMMPS. This approach is based on LAMMPS as a callable library from a larger cross-linker application. If anyone has invented this wheel why not at least give me some feedback. While reading the literature on molecular dynamics, it is easy to find descriptions of cross-linking. Many authors speak to creating some automation code and seem to never publish it. I suppose in order to be a molecular dynamic scientist one must fashion his or her own cross-linker  - just as a Jedi must fashion his or her own light saber.  Another piece of vaporware I am interested in building will do the following to create an amorphous polymer matrix:

• The cross-linker application will defined an internal geometry data structure for all molecules taking part in the simulation. The data structure will consist of sub-structures defining molecules, atom types, individual atoms, bonds, angles and dihedral angles. All of this information will change over time as bonds are broken and others are created. As the cross-linking occurs over time the number of molecules will decrease! 
• The "start points" previously defined in part one, to attach molecules, will be used in this new software for the same purpose. A DGEBA molecule will have two start points and an IPD molecule will have four start points. The user will define the probability of when an IPD molecule is attached to a DGEBA molecule and the same information for DGEBA molecule for an IPD or another DGEBA molecule. Keep in mind that your molecules my be different - just create a template for each one. 
• A radius of reaction will be defined by the user for every start point. Only start points within the radius of reaction can be considered for cross-linking. Perhaps you flip a fair or unfair coin to determine if the cross-linking occurs or not. The software will be flexible enough to support this.
• A number of LAMMPS simulation steps will be defined by the user so that LAMMPS can be executed for this number of steps. The number of steps and the time duration could be based on your knowledge of the system kinetics.  
• A maximum number of LAMMPS executions will be defined so that the cross-linker software does not execute forever. 
• A desired cross-linking percent will be defined by the user to tell the cross-linker how far to execute.
• A user defined convergence value will be used to test cross-linking percentage so the cross-linker can terminate in the event the desired cross-linking could not be obtained.
• If specified, the cross-linker will tell LAMMPS to run a molecular mechanics energy minimizer, MMEM, to help take some of the stress out of the geometry created by the new bonds. Perhaps, prior to running the MMEM the software could be instructed to run the structure cleaner. I would like to see quantify how useful the structure cleaner could be in reducing times to achieve low potential energy values.
• The cross-linker will call LAMMPS to stir up the soup of resin and curing agent molecules and get the system away from bad dynamics.
• The cross-linker will run LAMMPS for some user defined number of simulation steps and return to the cross-linker so it can test molecule start points against one another for possible cross-linking.
• A new bond will be formed if the radius of reaction criteria is met and the number of molecules in the cross-linker will decrease retyping atoms in the area of the new bond(s) will occur. 
• Some atoms will be deleted due to the cross-linking and will be removed from the simulation.
• Termination criteria will be tested.
• LAMMPS will be executed again from inside the cross-linker program.

The above approach to "chemical reaction" will result in an amorphous cross-linked polymer. I intend to compare it to an approach using the ReaxFF. Additional infrastructure software will have to be modified to accomplish the goal of amorphous cross-linked polymers. One interesting feature of PACKMOL is that it packs the molecules given to it in a serial fashion. The first molecule is packed then the second and so on. This leads to a segregated MD cell. PACKMOL requires an enhancement to distribute all molecules across the entire MD cell volume. This will provide the best mixed environment for cross-linking. One work around is to create a PACKMOL input file that specifies DGEBA and IPD in alternating references for the total number of desired molecule in the MD cell. It you need one hundred of each this works well. 

Another use of PACKMOL would take advantage of creating a fixed molecule structure, such as the cross-linked polymer created above, and then instruct PACMOL to distribute additional molecules into the structure. Fixed molecules are used only to take up space in the MD cell and the new molecules added will be no closer than the tolerance limit provided by the user. This approach will require converting the final cross-linked polymer MD cell into a molecular machine part (MMP) file so PACKMOL can read it. A small molecule could then be packed into a small portion of the MD cell that contains the cross-linked polymer. Water could be placed into a well defined MD cell at desired temperature and density. 

The dynamic cross-linking approach will be prototyped by building software in C++ to do specific tasks. The "knitter" application will read a LAMMPS output file and build the MD cell geometry in MMP file format in order to check for "start points" that meet the reaction radius requirements and "knit" molecules together. Next, a new MMP file containing new geometry, atom types, molecules, etc. will be created. MSI2LMP will be used to create the new LAMMPS Geometry Input File and LAMMPS will be executed again base on the desired number of steps. All the applications involved will be called from a script.

Cross-linked Polymers Part III will examine an idea that could allow PACKMOL to generate cross-linked systems as it packs molecules. PACKMOL uses constraints to put molecules as close together as possible without violating the user defined tolerance - usually 2 angstroms, which stops atoms from different molecules from being too close. 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.