【求助】请教介电材料的极化机理

可以看看“凝聚态物理学丛书---电介质物理学”
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http://www.wljx.sdu.edu.cn/jpkc/html/yadiantiedianwuli/jiaoxuekejian/20070125/54.html
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Dielectric dispersion in heterogeneous conducting materials is traditionally described by the Maxwell-Wagner theory. (Maxwell 1892, Wagner 1914). Electrical field application makes the possibly
free charges of the material to move to the interfacial zones creating long dipoles in the bulk of the material (i.e. Maxwell – Wagner polarization).

Generally, the Maxwell–Wagner polarization ~also
known as ‘‘interfacial polarization’’ or ‘‘space charge polarization’’!was most widely adopted to explain the high permittivity observed in the materials, including single-phase
ceramics, single crystals, and composites. When applying
this model, a series of barrier phenomena or even a complete
series-parallel array of barrier-volume effects are assumed.
This often arises in a material consisting of grains separated
by more insulating intergrain barriers.This model is applied
to a heterogeneous medium.
On the other hand, Jonscher pointed out that although
the Maxwell–Wagner polarization gives rise to satisfactory
fitting in many cases, no real physical meaning can be
derived.

Korea-Australia Rheology Journal
Vol. 11, No. 3, September 1999 pp.169-195

2.1.2. Behaviour under ac fields:Maxwell-Wagner polarisation
Consider the same isolated particle as before, but now
under a step electric field of magnitude E0 applied from t=0 :
E(t)=0 for t0
=E 0 for t0 (7)
Immediately after the application of the field, the mobile
charge carriers would have only just begun to move and not
travelled any significant distance, and the electrical response
of the system will be governed by the dielectric constants of
the particle material and carrier fluid (ep, ec) (Davis, 1992a). ep,
ec are determined for example by molecular orientations
under the electric field, and this response can be assumed to
be almost instantaneous (over time scales 10-6s at the longest).
This initial response is independent of the conductivities
of the particle or carrier fluid (sp, sc), and a similar calculation
to the above gives for the initial dipole magnitude:
pdielec=4peoeca3bdielecE0 (8)
where
(9)
As time progresses, there is a migration of free charge
which builds up at the carrier fluid/particle interface, and
has the effect of electrically screening the field in the
particle interior (Davis, 1992a). Eventually the electric field
reaches a distribution determined by the conductivities of
the carrier fluid and particle material, and the dipole is given
by eq (5). The characteristic time tMW for charge transport,
describing the transition from the dielectric-dominated to
the conductivity-dominated behaviours, is given by
(10)
This is also sometimes called the “polarisation relaxation
time”. It is easy to show that the dipole will change with
time as follows (Ginder and co-workers, 1995):
p(t)=4peoeca3E0 [bcond+(bdielec-bcond)e-t/tMW] (11)
The model presented here is generally known as the
Maxwell-Wagner model of interfacial polarisation (hence
the subscript MW). This is the simplest physical model
which takes into account the effects of conductive and
bdielec
ep ec –
ep 2ec +
---------------- =
tMW
eo ep 2ec + ( )
sp 2sc +
-------------------------- =

dielectric properties on the polarisation of a particle, and
assumes ep, ec, sp, sc are constants. A typical electrorheological
fluid designed for use under dc field conditions
(as are many proposed devices), such as the carbonaceous
particles in silicone oil suspension (Sakurai and coworkers,
1999), would have ep » 5, ec » 3, sp » 10-7mho/m
with sc<eq (10) tMW » 10-3s.

Materials Science and Engineering: R: Reports
Volume 17, Issue 2, 15 October 1996, Pages 57-103

http://www.sciencedirect.com/science?_ob=ArtICleURL&_udi=B6TXH-3VXHM8W-2&_user=1021782&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050479&_version=1&_urlVersion=0&_userid=1021782&md5=4304350649c7c2a2b702cb338bc87fa4


4.1.2. Maxwell-Wag,qer polarization
All ER suspensions possess some level of conductivity. Anderson [ 551 and Davis [45,56] have
pointed out that for d.c. and low-frequency a.c. electrIC fields, partICle polarization and partICle
interactions will be ccntrolled not by the partICle and fluid permittivities as described above, but rather
by the partICle and fluid conductivities. Conductivity in the bulk of both phases will result in free The field external to the sphere is again equivalent to that of a dipole with moment
peff = $o~ca3 Re{ p *‘ei”e’}EOe,. (1%
The time-averaged force on a sphere at the origin due to a second sphere at (R, 19) may be determined
easily in the point-dipole limit as before,
FyD(Rij,eij) =&@T2f&f( o,)E&
0
4
; { [3 cos2 8,- l]e,+ [sin 20,]e,}, (16)
II
where ErmS - E,l fi, and the “effective relative polarizability” is now
where
Pd=
t =E
EP$2EC
,?NJ Oup + 2a;
(17)
(18)
The force is essentially equivalent to the ideal case except that the effective polarizability is now a
function of field frequency, as well as the permittivities and conductivities of both phases.
The value of Peff, and thus the pair force, depends on the frequency relative to the polarization
time constant t,,. In the limit of large frequencies, permittivities dominate the response,
lim P2ff(wJ = Pi (20) oer,rnv * m
while in the dc. limit,
and thus conductivities control partICle polarization forces, regardless of the permittivities. The nor-
malized polarization force magnitude, pzff, is plotted as a function of frequency in Fig. 4 for different
values of Pd and PC, As we will see below, this likely explains, qualitatively, why high dielectrIC
constant materials such as barium titanate ( eP =@( 103) ) do not show a very large ER effect in d.c.
fields, and why many systems exhibit a decrease in apparent viscosity with increasing electrIC field
frequency [ 3,4,8,62].
For partICles with a surface conductivity, h,, polarization and interactions in the point-dipole limit
are described by the Maxwell-Wagner model as described above, provided the partICle conductivity
is replaced by the apparent conductivity CT~ + 2&/a [ 9,571.

charge accumulation at the partICle/fluid interface-migration of free charges to the interface prompts
the alternative names, “migration” and “interfacial” polarization. In a d.c. field, mobile charges
accumulating at the interface screen the field within a partICle, and partICle polarization is completely
determined by conductivities. In a high-frequency a-c. field, mobile charges have insuffICient time to
respond, leading to polarization dominated solely by permittivities, unaffected by conductivities. At
intermediate frequencies, both permittivity and conductivity play a role.
The Maxwell-Wagner model (see, for instance, Refs. [57-611) is the simplest description of
partICle polarization accounting for both the partICle and fluid bulk conductivities, as well as their
permittivities. In this theory, the permittivities and conductivities of the individual phases are assumed
to be constants, independent of frequency. The complex dielectrIC constants of the disperse and
continuous phases are written Q* ( w,) = ek -j( Us/ ~,,a,), where IC =p,c, j = J-1, and the asterisks
represent complex quantities.
Consider again an isolated sphere in a uniform a.c. electrIC field, E0 = Re{&&‘e,} . The complex
potential will still satisfy Laplace’s equation in the bulk phases [ 571, o”$* = 0, subject to the boundary
conditions at the interface,
$*i = v” (11)
The solution for the complex potential resembles that for the ideal case,
(12)
(13)
(14)

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