Polymer Physics

We can regard the motion of polymer coils in a dilute solution as in thenon-
draining modeof spherical particles, which means that a polymer coil moves
together with the holding solvent molecules, as shown in Fig.5.1a. There is no
relative velocity for those holding solvent molecules to the polymer, and all the
frictional interactions for polymer motions only occur at the surface of the spherical
particle. We then have

c¼

Vp

V

¼

c

cint



cR^3

n

(5.10)

whereVpis the volume of polymer coil,Vis the total volume,cis the average
volume concentration of monomers,Cintis the volume concentration of monomers
inside each coil,Cint~n/R^3 , andnis the number of monomers in each chain. We
define the specific viscosity

sp

s

s

(5.11)

and further define theintrinsic viscosity

½Š

sp

c

jc! 0 (5.12)

According to (5.9), we obtain theFox-Flory equation(Fox and Flory 1948 )

½Š

R^3

n

(5.13)

According to the Fox-Flory equation, in a theta solvent, we can have

Rn^1 =^2 (5.14)

from which we can further obtain theEinstein-Kuhn viscosity equation(Kuhn
1934 )

½Šn^1 =^2 (5.15)

Fig. 5.1Illustration of the flow profiles for the solvent to pass through the polymer coil with
(a) the non-draining mode and (b) the free-draining mode

5.1 Simple Fluids 79