Biomedical Engineering Reference
In-Depth Information
By applying equilibrium condition
A
B
=
(5.82)
p
p
Therefore
A
a
a
p
π
=
RT
ln
/
v
(5.83)
p
B
p
Thus, partition coefficient is
A
v
RT
γ
γ
π
p
p
ln
K
=
ln
−
(5.84)
p
B
p
This equation suggests that the higher the osmotic pressure in the membrane, the lower
the partition coefficient from aqueous phase to the membrane.
In most experiment setups, ions are present in the buffer solution; therefore, an electro-
, ions are present in the buffer solution; therefore, an electro-
static potential exists at the interface, at equilibrium, and the protein partition coefficient
is given by
s, ions are present in the buffer solution; therefore, an electro-
A
Z
Z
A
x
x
γ
γ
a
a
p
p
B
γ
ln
K
=
ln
=
ln
−
ln
−
π
v
p
(5.85)
p
B
B
A
p
γ
γ
To alter the partition of protein drug in membrane, the ion concentration is set to be
constant (factor that is not controlled); therefore, by increasing solute activity coefficient
and/or increase osmotic pressure in the membrane, drug partition is reduced, and vice
versa.
To figure out what are the factors that affect activity coefficient and how they affect it, we
need the mathematical models to express activity coefficient in solution.
Excess Function and Activity Coefficient (for Nonelectrolytes)
In the previous section, it can be seen that if the activity coefficient of a component in a
system can be calculated, its partition coefficient will be known. Moreover, to calculate the
activity coefficient, excess Gibbs free energy (excess function) is needed. In this section,
different models of excess function and activity coefficient will be reviewed; therefore, fac-
tors that affect activity coefficient, thus partition coefficient, can be understood.
Gibbs free energy of a solution is determined by an entropy term and an enthalpy term;
if we assume heat of mixing is zero, molecules are of the same size, and the intermo-
intermo-
lecular force of different molecules is identical, the Gibbs free energy is solely contrib-
uted by entropy change (athermal solution). An idealized description of solution is the
liquid lattice theory, in which a solution is considered as a regular array in space, and
solvent and solute molecules are located in the lattice sites. (First introduced by Flory and
Huggins [36]).
the intermo-
