Is the entropy scaling method for viscosity calculation suitable for polymers?

[Paiding]

I tried the group contribution method for viscosities on polyethylene with the data of Loetgering-lin. Calculated values of viscosity are reasonable for molecular weights less than 3000, while some unreasonably low viscosities are returned if the molecular weight continues to increase. Is this method not suitable for polymers?

[g-bauer]

Hello Paiding,

I personally have no experience with entropy scaling for polymers. I vaguely remember reading papers in which the applicability of entropy scaling as a function of the chain length of polymers was investigated (with success), but I don't know if polymers as large as the ones you are interested in were considered.

Could you provide an example of what you are trying to do? Does viscosity smoothly decrease with increasing size or does it drop abruptly at a certain size?

[Paiding]

Hello g-bauer,

Thank you. Here is my script to calculate the viscosity of polyethylene:

from feos.si import *
from feos.pcsaft import *
from feos.eos import *

import matplotlib.pyplot as plt
import numpy as np

polyethylene = ChemicalRecord(
    identifier=Identifier(
        cas='9002-88-4',
        name='polyethylene',
        formula='[C2H4]n'
    ),
    segments=['CH2']*350
    #segments=['CH2']*int(100000 // 14.02658)
)

ch2r = SegmentRecord(
    'CH2',
    molarweight=14.02658,
    model_record=PcSaftRecord(
        m=0.45606, sigma=3.8900, epsilon_k=239.01,
        viscosity=[-0.9194e-3, -1.3316e-1, -4.2657e-2, -0.01245]
    )
)

segment_records = {r.identifier: r for r in [ch2r]}

def from_segments(chemical_record, segment_records):
    m = 0
    s3 = 0
    eps = 0
    mw = 0
    viscosity = np.zeros(4)
    for s in chemical_record.segments:
        segment = segment_records[s]
        mw += segment.molarweight
        m += segment.model_record.m
        s3 += segment.model_record.m * segment.model_record.sigma**3
        eps += segment.model_record.m * segment.model_record.epsilon_k
        v = segment.model_record.viscosity
        viscosity += np.array([
            v[0] * segment.model_record.m * segment.model_record.sigma**3, 
            v[1] * segment.model_record.m * segment.model_record.sigma**3, 
            v[2], 
            v[3]
        ])
    viscosity[1] /= s3**0.45
    
    # We have to shift the "A" parameter because the implemented reference
    # is eta_CE according to eq. 3 of Loetgerin-Lin (2018)
    # A = A(GC) + log(sqrt(1/m)) = -log(m)/2
    viscosity[0] += np.log(np.sqrt(1/m))
    saft_record = PcSaftRecord(m, np.cbrt(s3 / m), eps / m, viscosity=viscosity)
    return PureRecord(chemical_record.identifier, mw, saft_record)

pr_pe = from_segments(polyethylene,segment_records)

parameters = PcSaftParameters.new_pure(pr_pe)

saft = EquationOfState.pcsaft(parameters)
state_npt = State(
    saft,
    temperature=403.17*KELVIN,
    pressure=1*BAR,
    density_initialization='liquid'
)
print('density : ', state_npt.density)
print('viscosity: ', state_npt.viscosity())

And this is the results when I tried number of segments from 80 to 400