Polyacrylamide and its derivatives for oil recovery

Figure 6. 
Proposed swelling mechanism of the crosslinked microgels in DI water at 40 
º
C and 80 º
C.
 
Crosslink density is one of the most important factors that determines the 
properties of crosslinked hydrogels and is typically reported as an average molecular 
weight (
M
c
) between crosslinks. The 
M
c
of polyacrylamide hydrogels was calculated 
using the Flory-Rehner equation:
45,46,47
𝑀
𝑐
=
𝜌
𝑝
∗𝑉
1
(𝑣
2
1
3 
− 
1
2
𝑣
2
)
−[𝑙𝑛(1−𝑣
2
)+𝑣
2
+𝜒
1
𝑣
2
2
]
Equation 2 
where 

1
is the interaction parameter,
V
1
is the molar volume of water (18.062 cm
3
/mol), 
and 

2
is the average volume fraction of polymer in the hydrogel when it reaches the 
equilibrium swelling state. The 

1
parameter of crosslinked pure polyacrylamide 
hydrogel has been reported to be 0.48 at 25 °C.
48,49
The value of 

2
can then be calculated using the following equation:
46,47
𝑣
2
= (
1
𝜌
𝑝
)/[(
𝑆
𝜌
𝑠
) + (
1
𝜌
𝑝
)]
Equation 3 
In Equation 3, 

p
is the polymer density (1.11 g/cm
3
), S is the gel swelling ratio 
and 

s
is the density of water. It is supposed that 

s
=1 g/cm
3
, yet It should be note that 

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154 
the water molecule in hydrogel are ordered which leading to a larger density than free 
water.