A PDMS melt has plateau modulus

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Polymer dynamics and viscoelasticity

Problem

G_N^0 = 0.20\,\mathrm{MPa}

, density

\rho = 970\,\mathrm{kg\,m^{-3}}

, at

T = 300\,\mathrm{K}

. Separately, a dilute solution of polystyrene of molar mass

M = 2.0\times10^{5}\,\mathrm{g\,mol^{-1}}

in toluene has Kuhn length

b = 1.8\,\mathrm{nm}

, Kuhn monomer molar mass

M_0 = 720\,\mathrm{g\,mol^{-1}}

, and toluene viscosity

\eta_s = 0.59\,\mathrm{mPa\,s}

. ((a)) Using

G_N^0 \approx \tfrac45\rho RT/M_e

(the rubber-elasticity modulus relation,

G=n_sk_BT

, applied to the entanglement network, with the quoted correction

4/5

), find

M_e

for the PDMS melt. ((b)) Using the ideal-chain result

R_g^2=Nb^2/6

with

N=M/M_0

(Chapter 3), find

R_g

for the polystyrene coil, then estimate

\tau_{\rm Z}\approx\eta_sR_g^3/k_BT

and

D=k_BT/(6\pi\eta_sR_g)