# Low viscosity value for polymer system using Green-Kubo (GK) formula

I am currently utilizing the GK method to compute the viscosity of a polymer system comprising primarily benzene rings and hydrocarbon chains. The input script used is as follows:

``````units       real
variable    T equal 408.15       # run temperature
variable    Tinit equal 408.15  # equilibration temperature
variable    V equal vol
variable    dt equal 1
variable    p equal 400     # correlation length
variable    s equal 5       # sample interval
variable    d equal \$p*\$s   # dump interval

# convert from LAMMPS real units to SI

variable    kB equal 1.3806504e-23    # [J/K] Boltzmann
variable    atm2Pa equal 101325.0
variable    A2m equal 1.0e-10
variable    fs2s equal 1.0e-15
variable    convert equal \${atm2Pa}*\${atm2Pa}*\${fs2s}*\${A2m}*\${A2m}*\${A2m}

# setup problem
dimension    3
boundary     p p p
atom_style	full
neighbor	2.0 bin
neigh_modify	delay 5 check yes

bond_style      harmonic
angle_style     harmonic
dihedral_style	harmonic
improper_style cvff
pair_style	lj/cut/coul/long 10
kspace_style pppm 1.0e-4

timestep     \${dt}
thermo       \$d

# equilibration and thermalization

velocity     all create \${Tinit} 102486 mom yes rot yes dist gaussian
fix          NVT all nvt temp \${Tinit} \${Tinit} 10 drag 0.2
run          8000

# viscosity calculation, switch to NVE if desired

velocity     all create \$T 102486 mom yes rot yes dist gaussian
fix          NVT all nvt temp \$T \$T 10 drag 0.2
unfix       NVT
fix         NVE all nve

reset_timestep 0
variable     pxy equal pxy
variable     pxz equal pxz
variable     pyz equal pyz
fix          SS all ave/correlate \$s \$p \$d &
v_pxy v_pxz v_pyz type auto file S0St.dat ave running
variable     scale equal \${convert}/(\${kB}*\$T)*\$V*\$s*\${dt}
variable     v11 equal trap(f_SS[3])*\${scale}
variable     v22 equal trap(f_SS[4])*\${scale}
variable     v33 equal trap(f_SS[5])*\${scale}
variable     v equal (v_v11+v_v22+v_v33)/3.0
thermo_style custom step temp press v_pxy v_pxz v_pyz v_v11 v_v22 v_v33 v_v
run          1000000
variable     ndens equal count(all)/vol
print        "average viscosity: \$v [Pa.s] @ \$T K, \${ndens} atoms/A^3"
``````

However, the outcome I received is:
average viscosity: 0.00180735846760119 [Pa.s] @ 408.15 K, 0.104814548328098 atoms/A^3

approximately 1000 times lower than the actual value ranging from 1-3 pa.s at the same temperature. I am uncertain whether the reason behind this discrepancy is due to the size of the system or simulation settings or whether the GK method is unsuitable for such a polymer system. For reference, my model size is 4040 40 Angstrom. NVT and NVE ensembles give similar results.

Neither of these are questions about LAMMPS and thus they are off-topic for this forum.

You need to discuss your results with somebody that has done similar simulations of similar systems and can guide you to the choices of boundary conditions that are necessary. You didnâ€™t discuss how you equilibrate your system and what your estimates for statistical convergence are. Polymer systems are notoriously difficult to equilibrate and converge. I suggest you contact your adviser or supervisor to find somebody with sufficient expertise to guide you through the science of your problem.

Thanks for the suggestions. I will contact my supervisor for further solutions.