Case 6: Molecular Weight Distribution and Low-Density Construction (Polyethylene)

Case 6: Molecular Weight Distribution and Low-Density Construction (Polyethylene)

When constructing polymer systems, especially those with intertwined long chains, performing packing at high density from the start can make relaxation difficult. This case explains a recommended workflow of constructing at low density and performing density relaxation in a subsequent MD process.

Target System

• Polymer: Polyethylene (PE)
• Composition: 10 chains with DP ranging from 30 to 70 (Molecular weight distribution included)
• Total Atoms: 3,020
• Initial Target Density: 0.10 g/cm³ (Low-density start)

Calculation Code (run.py)

import fbtk

# 1. Define the DP distribution
distribution = {30: 1, 40: 2, 50: 4, 60: 2, 70: 1}

# 2. Initialize the Builder (Specify low density of 0.10)
builder = fbtk.Builder(density=0.10)

# 3. Add polymers
for dp, count in distribution.items():
    builder.add_polymer(
        name=f"PE_DP{dp}", smiles="*CC*", count=count, degree=dp
    )

# 4. Build the system and perform relaxation
system = builder.build()
print("Starting relaxation for Polyethylene...")
system.relax()

# 5. Output results
system.to_file("pe_dist_cell.mol2")
print("Done.")

Reviewing the Execution Log

Atoms:     3020       | Bonds:     3010
--------------------------------------------------------------------------------
       | Fmax           | FRMS           | Total E          |
Iter   | (kcal/mol/Å)   | (kcal/mol/Å)   | (kcal/mol)       | Status
--------------------------------------------------------------------------------
     0 |     24405.0680 |      1918.2996 | 50226003837.2583 |
    10 |      1694.8894 |        75.8715 |       42352.9137 |
    20 |       863.2683 |        31.7036 |       32491.4982 |
   ...
   780 |         2.9120 |         0.6215 |       12265.6533 |
   790 |         1.5248 |         0.4868 |       12192.9054 |
   793 |         1.7364 |         0.4949 |       12187.2791 | FRMS-Conv
--------------------------------------------------------------------------------
=== Optimization Finished ===
Reason: FRMS-Conv
Total Time: 7.263s     (Avg: 9.148ms / step)
Final Energy: 12187.2791      kcal/mol
Final FRMS:   0.4949          kcal/mol/Å
Min Distance: 1.0927          Å (Atoms 1240 and 1242)
--------------------------------------------------------------------------------

Result Explanation

Advantages of Low-Density Packing

When constructed at a density of 0.10 g/cm³, the Min Distance is 1.0927 Å, resulting in a very high-quality initial structure. The relaxation process also proceeds very smoothly, converging in fewer steps.

Recommended Workflow

For large-scale polymer systems, the following steps are the most robust:

1. Use fbtk to create a structure with consistent topology at low density (around 0.10 to 0.30).
2. Pass the obtained structure to MD software and slowly compress and equilibrate the system to the target density using an NPT ensemble.