Biology Reference
In-Depth Information
determined by considering the solution to be divided into laminae
paralleltotheelectrode.Thelaminaeareinthermalequilibrium,but
at differing energies due to the potential ϕ , so the concentration n i
of species i with valence z i is related to its bulk concentration n i by
the Boltzmann factor
n i = n i exp( z i e ϕ/ kT )
(6.3)
The net charge density ρ ( x ) is related to the potential by the
Poissonequation
ρ ( x ) = εε 0 d 2
ϕ
d x 2
(6.4)
where ε istherelativedielectricpermittivity, ε 0 isthepermittivityof
freespace,and x isthedistancefromtheelectrode.Useofboundary
conditions leads to the non-linear Poisson-Boltzmann equation.
For ϕ k T / e , the linearized Poisson-Boltzmann equation results.
Alternatively, the non-linear Poisson-Boltzmann equation may be
solved for a symmetrical electrolyte that contains only one cationic
and one anionic species, both with charge magnitude z ,givingthe
Grahame equation for the charge per unit area on the electrode
σ 1 :
OHP =
8k T εε 0 n 0 sinh | z | e ϕ OHP
2k T
σ 1 =− εε 0 d d x
(6.5)
6.3.1.2 DNA charge fraction
dsDNA is a semi-flexible chain with persistence length 100 nm,
where the persistence length is the distance in which tangent
vectors decorrelate, a measure of the rigidity of a polymer. Short
duplexes can be considered as cylinders of 2 . 0nmdiameterand
axiallengthperbasepairof0.34nm.Thecorrespondingparameters
for ssDNA have not been established. Stacking interactions between
hydrophobic bases tend to produce a stiff single-stranded helix and
ssDNAhasbeenmodeledasacylinderofdiameter 1.4nmandaxial
length per monomer of 0.34 nm [19]. However, if ssDNA is assumed
to be a freely jointed chain with a length per base of 0.43 nm [20],
itspersistencelengthvariesfrom5nmat1mMionicstrengthto0.8
nm at 100 mM ionic strength [21]. This is consistent with a much
stronger rigidity of dsDNA compared to ssDNA.
 
Search WWH ::




Custom Search