Polymer Physics

additional free energy contributions. The first contribution is from each chain
crossing over the interfaces, as

DHint¼kTw

Adint

v

(9.42)

wherevis the volume of each chain unit,dintis the interface thickness, the interface
area contributed from each coil isA¼rv/d,dis the long period, andrrepresents
the number of chain units on each chain. We know that at the critical phase
separation, symmetric polymer blends contain

wc¼

2

rc

(9.43)

At the interfaces, the critical mixing coil sizes (proportional to the reciprocal of
the mixing interaction parameter) are comparable to the interface thickness.
Accordingly,

dintv^1 =^3 rc^1 =^2 v^1 =^3 w^1 =^2 (9.44)

Therefore,

DHintkTw^1 =^2 v^1 =^3

r

d

(9.45)

Fig. 9.11 Illustration of specific geometric shapes of microdomains formed by diblock
copolymers. Fromlefttorightare spheres, cylinders, gyroids and lamellae

Fig. 9.12 Illustration of microdomain sizes of symmetric diblock copolymers

180 9 Polymer Phase Separation