Control of Drug Release from Coatings: Theories and Methodologies - Biological and Biomedical Coatings - page 232

therefore

x γ

1

p,membrane p,bulk

K = =

p-elec

x

1 3 /

γ

p,bulk p,membrane

φ

p

exp − C v

cross p

φ

p,synthesis

The protein net charge can be calculated by [61]

pK − pH pH p − K

∑

10
10

i +

∑

10

i −

PNC = n × + n × (5.133)

i + i −

pK pH − pH pK −

+ +

1 10 1

i i −

i + i −

i + are the basic groups in the protein and i - are the acid groups in the protein.
In this case, the polymer is taken to be a cylinder of the uniform surface charge density.
This description is often refereed as cell model polyeletrolyte solutions.

( ) +

0 7 . X / z 1

cn

=

γ

counterion

X + 1

(5.134)

0 7 . X z / ( ) + 1

co

= γ

coion

0 53 . X z co / ( ) + 1

X is the ratio of the concentration of charged monomers to the concentration of salt in
the hydrogel, ς = l B / b , where l B is the Bjerrum length, which is equal to 7.14 Å in water at
room temperature, and b is the axial length per unit charge (2.52 Å for poly- N -isoprolacryl-
amide). Z is the valences of ions. Counterion means the charge opposite to the hydrogel,
co-ion means the ion that has a charge identical to that of the hydrogel. For the case of BSA,
the valence of charged BSA at different pH can be found in the work of Lin et al. [69], and
those values are used in the calculation in Appendices A and B.
Since the only intermolecular interaction in consideration of this model is electrostatic
interaction between charged species, and the activity coefficient of charged ion in the mem-
brane was derived by ignoring the interaction between mobile ions (consider only ion-
polymer interaction), the activity coefficient of charged ions in the bulk solution should
therefore also ignore mobile ion interactions, which implies that the bulk solution shall be
treated as an ideal solution ( 1 ). Hence, the partition caused by protein-polymer γ p,bulk =

interaction is

/

1 3

x

φ

p,membrane p

ln K = ln = − ln + C v

cross p

(5.135)

γ

p-elec p,membrane

x

φ

p,bulk p,synthesis

The fraction of ionized monomer (HA type) is obtained by using

α
α

pH p − K − log 10 = 0 (5.136)

a

1 +