Water and Solute Permeability of Plant Cuticles: Measurement and ...

4.2 Isoelectric Points of Polymer Matrix Membranes 65
4.2 Isoelectric Points of Polymer Matrix Membranes
The polymer matrix (MX) carries immobile (fixed) electrical charges which are
contributed by pectins, polypeptides and cutin. Where are the various polar groups
located, what are their properties and what are the consequences for water permeability
of cuticles? Hydroxyl groups donated by cutin, hydroxyfatty acids, pectins,
cellulosic compounds and polypeptides are permanent dipoles, and are not affected
by pH and cations. Polarity and hydration of carboxyl, amino and phenolic hydroxyl
groups depend on pH and type of counter ions. In this section, we take a look at
location and properties of ionisable groups in the polymer matrix.
Ionised fixed charges electrostatically attract ions of opposite sign, and for this
reason carboxyl groups are surrounded by cations such as K + or Ca 2+ . Amino
groups are electrically neutralised by anions. Fixed charges in a membrane result
in unequal distribution of ions in the membrane and adjacent solutions, and this
concentration difference results in an electrical potential between membrane and
solution. This potential is called Donnan potential, and the phase containing immobilised
charges is the Donnan phase. The sign of the electrical potential in the
Donnan phase relative to the surrounding electrolyte solution is the same as the
charge of the immobile ion. If fixed charges are homogeneously distributed and
identical electrolyte solutions are used on either side of the membrane, the Donnan
potentials are in opposite directions and cancel.
The driving force of ion fluxes is the electrochemical potential, which is the sum
of the chemical potential (2.13) and the electrical potential (zF E), where z is the
charge of the ions (i.e., +1 for K + and −2 for SO2−), F is the Faraday constant
4
and E is the electrical potential (V). A concentration difference of ions across a
membrane results in a difference in electrochemical potential (diffusion potential),
and ions diffuse across the membrane. The mobility of ions in solution differs as they
have different sizes. K + and Cl− are an exception as they have identical mobility,
and this is the reason they are used as electrolyte solutions in electrodes. In a charged
membrane, mobility of cations and anions are also affected by their interactions with
fixed charges.
The membrane potential (Emembrane) can be measured by placing two electrodes
(i.e., calomel or Ag/AgCl) into salt solutions facing the two sides of the membrane.
Emembrane is the sum of the Donnan potentials (EDonnan) and the diffusion potential
(Ediffusion). The Donnan potentials enter with opposite signs (Helfferich 1962):
Emembrane = E outside
Donoan
= −
×
+ Einside Donoan + Ediffusion
RT
�
ln aoutside
counterion
F zcounterion ainside −(zco-ion − zcounterion)
counterion
� �
outside
¯tco-ion dlnasalt .
inside
(4.1)
Here R and T have the usual meaning, a is the activity of ions or salt, z is the valence
of the ions and ¯t is the transference number of the co-ion. The transference number