Imaging and Manipulation of Biomolecules - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 118

The dielectric particle model applies in certain limits to bacteria, cells, and
viruses because all of them contain mobile ions in their biological structures and are
living in a conducting electrolyte ( Pethig 2010 ). However, the dielectric permittivity
of biological entities in an ac field is complex and given by

" p D " 0 " p i p =!;

(3.25a)

the corresponding expression for conductivity being

p D p C i!" 0 " p :

(3.25b)

The CM factor becomes also complex:

" p " m
" p C 2" m

! ;

CM D (3.26a)

or equivalently,

p m
p C 2 m

! :

CM D (3.26b)

At low frequencies, the current is due to the conduction of free carriers, while at high
frequencies, the dielectric displacement current becomes predominant, and there is a
=2 phase difference between the current and the applied electric field. Considering
that the field is given by

E.r;t/ D ReŒE.r/ exp.i!t/; (3.27)

the effective dipole moment can be written as

p.r;t/ D ReŒ4" m R 3 CM E.r/exp.i!t/;

(3.28)

so that the DEP force is

F DEP .t/ D ReŒp exp.i!t/ r ReŒE exp.i!t/: (3.29)

As a result, the time-average DEP force becomes

2 :

h F DEP iD 2" 0 " m R 3 ReŒCM rj E j (3.30)

Below 50 kHz, we can use the approximation
ReŒCM Š " m p m
p C 2 m

;

(3.31)