Polymer Physics

r

R^5 =^2

Rf^3 =^2

(4.81)

The total free energy

F¼kT

n

g

¼kTð

Rf

R

Þ^5 =^2 (4.82)

and the stretching force

f¼

@F

@Rf

¼

kT

b

ð

Rf

nb

Þ^3 =^2 (4.83)

with the conditionRf<Nb. Apparently, with the consideration of the volume
exclusion of the polymer, the Hooke’s Law based on the ideal chain model will
not be satisfied. The non-Gaussian distribution of the end-to-end distance is further
obtained with

PðxÞexp½ð

x

R

Þ^5 =^2 Š (4.84)

where x>R (Pincus 1976 ).

4.4.2 Compression

Nano-materials of polymers are the important issue in many high-technology fields,
such as micro-electronics, drug delivery and device technology. If polymer chains are
compressed into various geometries of nanoscale compartments, such as ultra-thin
films, nano-pores and nano-spheres, their deformation causes an entropy loss of chain
conformation. Therefore, deformation of polymer chains often influences their phys-
ical performances. The blob model has been widely applied in the scaling analysis of
single-chain conformation under nano-confinement (Rubinstein and Colby 2003 ).

Fig. 4.14 Illustration of the blob model for a deformed single coil with its two ends imposed with
a stretching force

4.4 Single-Chain Conformation Under External Forces 67