ELECTRICAL PROPERTIES AND
STRUCTURE OF POLYMER COMPOSITES
WITH CONDUCTIVE FILLERS
I. Influence of filler geometry
and spatial distribution
Ye. P. Mamunya
Institute of Macromolecular Chemistry
National Academy of Sciences of Ukraine
Kiev, Ukraine
[email protected]
National Academy of Sciences of Ukraine
Institute of Macromolecular Chemistry
A d m i n i s t r a t i o n of the I n s t i t u t e
Director of the Institute
academician, professor
E. Lebedev
Associate directors
on science
Professor Yu. Kercha
DSc Yu. Savelyev
Academic secretary
PhD V. Myshak
General
departments
Scientific departments
1. Chemistry of heterochain
polymers and interpenetraiting
networks
Synthesis, mechanisms of forming
and methods of creation in water
and organic medium, investigation
of
interpenetrating
polymer
networks and composites on their
base (personnel - 30)
DSc Yu. Savelyev
2. Physical chemistry of
polymers
Physical chemistry of multi-component polymer systems, polymer
blends and melts, structure of
multicomponent
systems
(personnel - 28)
DSc T. Todosiychuk
3. Polymer modification
Structural, chemical and physical
modification
of
heterogeneous
polymers and related systems
(personnel - 22)
DSc, professor Yu. Kercha
4. Polymers for medical
purposes
Elaboration
of
biocompatible
polymer materials for medical
applications and medical-biological
testing
of
polymer
materials
(personnel - 25)
DSc N. Galatenko
Chief engineer
V. Krulitskiy
Accountant-general
M. Kolchenko
6. Chemistry of oligomers and
cross-linked polymers
Synthesis reactive oligomers and
creation
of
polymer
systems
based on synthesized oligomers.
Development of functional polymers
(personnel - 17)
DSc, professor V. Shevchenko
7. Physics of polymers
Physics of polymer systems and
nanocomposites. Characterization
of microheterogeneous state of
polymer systems and composites
(personnel - 10)
DSc V. Klepko
Scientific-technical information,
patent-license and publishing
activities (personnel - 7)
A. Dyakova
Standards and metrology
(personnel - 6)
V. Krulitskiy
Personnel management
(personnel - 2)
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Ancillary technical department
(personnel - 37)
V. Krulitskiy
5. Polymer composites
Structure and properties of polymer
composites based on conventional
polymers and organic-inorganic
systems (personnel - 33)
Academician, professor
E. Lebedev
www.macromol.kiev.ua
General information
General numbers of personnel
Scientific personnel
including:
DSc
PhD
PhD students
-
253
92
17
75
23
3
Scope of the Institute for the application of new
polymer materials and technologies
Produced materials
Adhesives
Pilot plant
(personnel - 23)
N. Gladyreva
Mastics
Lacquers
Paints
Polymer composites
Materials and technologies
Protective dampproofing of concrete constructions
based on elaborated materials:
- water protection in the metro tubes and stations
Technical
laboratory
- breakdown elimination of the concrete pipelines
“MONOLITH”
- protection and insulating of the nuclear station
constructions
(personnel - 9)
PhD V.Kolyada
- moisture protection of the concrete bridges
- soil solidification
- flooding floors in the special factory sections
4
New polymer materials elaborated in the Institute
New lacquer and
paint compositions
New film materials
New
protective
composite materials
and technologies of
their use
5
The topics proposed:
• structure of conductive polymer composites
• influence of shape of conductive particles on electrical properties
• influence of spatial distribution of filler on electrical characteristics
• methods of conductivity measurements
• influence of polymer-filler interaction on structure and electrical
properties
• filled conductive polymer blends: structure and properties
• phase inversion in filled polymer blends
• conductive composites with carbon nanotubes: technology, structure,
conductivity, dielectric properties
6
Electrical characteristics of materials
σ, S/cm
106
Conductors
104
102
Carbon materials
100
Polymers with intrinsic
conductivity
10-2
Semi-conductors
Metals
10-4
10-6
Organic conductors,
ionic conductors
10-8
10-10
Insulators
Antistatic materials
10-12
10-14
10-16
Polymer materials
7
Types of conductive and insulating materials
Conductive
Metals
Carbon materials: carbon black,
carbon fibers and tissue, carbon
nanotubes
Conductive ceramic
Polymers with intrinsic conductivity
(polyaniline, polypyrol, polythiophen
and others)
Nonconductive
Polymer
materials
Advantages
• low density, low weight
• high mechanical characteristics
• procesability by highly
productive industrial methods
• low cost
Advantages
• high conductivity
Disadvantages
• metals – high density, high weight
• carbon – low mechanical characteristics
• rest – impossibility of processing by
highly productive industrial methods
• high cost
Disadvantages
• no conductivity
• impossible to use at high
temperatures
8
Conductive polymer composites
Two-phase system
polymer-insulator
Advantages
• presence of conductivity
• low density, low weight
• high mechanical characteristics
• possible to process by highly
productive industrial methods
• low cost
+
conductive filler
9
Types of conductive fillers
• Conductive composite is two-phase system with insulating
phase (polymer matrix) and conductive phase (filler).
• Several kinds of materials can be used as conductive
fillers:
•
•
•
•
•
•
•
dispersed metals;
carbon black;
metallized mineral particles;
carbon and metallic fibers;
carbon nanotubes;
conductive ceramic;
polymers with instrinsic conductivity
10
Why such materials are attractive for research
and application ?
They combine the properties of polymer and metals or carbon.
Electrical properties can be close to metals while the processing is
typical for the polymers.
It is relatively easy to adjust the electrical and dielectric properties in
the wide range.
Conductive polymer composites can be extended for application in
various fields :
• heaters with distributed heat-emission and self-regulated heaters;
•
•
•
•
•
shieldings for electromagnetic protection;
contact buttons in computers and media technics;
current-limiting devices;
conductive adhesives;
and many others.
11
Correlation of structure with conductive
properties of composite
nonconductive
Conductivity of composite is a
function of the filler content and
reflects
the
structure
of
composite.
conductive
10 4
Conductivity, log σ
Region 3
10 1
Region 2
Region 1
percolation
threshold
10-16
ϕc
Filler volume fraction, ϕ
Region 1 – the composite is nonconductive, the matrix includes
the
separate
particles
of
conductive filler.
Region 2 – the region of percolation, the conductive cluster is
created, the conductivity sharply
increases at ϕ > ϕc.
Region 3 – the conductivity slowly
increases because of growth of
conductive cluster.
12
Methods of definition of the percolation threshold
5 methods of definition of the percolation
Conductivity, log σ
2
threshold
1. Start of creation of the conductive
cluster
and
sharp
growth of
conductivity of the composite.
4
1
2. When conductive cluster is
completed and the composite is
conductive.
3
ϕc
Filler volume fraction, ϕ
3. At maximum of the derivative
function d(log σ)/dϕ,
it is close to
method 1.
4. At value of conductivity
log σ
5
σ c = σ p ⋅σ f
5. By fitting of equation
log (ϕ-ϕc)
σ ∝ (ϕ − ϕ c )t
13
Main factors that define the conductive properties
of polymer composites with conductive fillers
• value of conductivity of the filler;
• content of filler in the polymer matrix;
• shape of the filler particles;
• spatial distribution of filler in the polymer matrix;
• polymer-filler interaction;
14
Influence of shape of conductive particles and their
distribution on the percolation threshold
log σ
Statistical distribution of the
sperical particles, theoretical
value of percolation threshold,
ϕc = 0.16
ϕ
log σ
ϕc = 0.16
ϕ
log σ
ϕc << 0.16
ϕc < 0.16
ϕ
Statistical distribution of the
anisotropic particles with
l/d > 1, low value of
percolation threshold, ϕc < 0.16
or ϕc << 0.16
Ordered distribution of the
particles, creation of the
regular skeleton structure, low
value of percolation threshold,
ϕc < 0.16
The shape
and spatial
distribution
of the filler
particles are
very important
for the value
of percolation
threshold.
15
What parameter can take into accout the
shape and spatial distribution of the filler
particles?
It is the packing-factor F.
16
What is the packing-factor of filler?
The packing-factor of filler F is one of the most important
characteristics of the fillers and filled polymer composites.
The F parameter means a limit of system filling and is equal to the
highest possible filler volume content:
F=
Vf – volume occupied by the filler particles;
Vf
Vp – volume occupied by the polymer
(space among filler particles).
V f + Vp
For statistically packed monodispersed spherical particles of any size, Fs = 0.64
The value of F depends on:
monodispersed
particles
particles
shape, l/d > 1
fraction
composition
formation of the
skeleton structure
opal in
epoxy resin
F < Fs
F > Fs
F < Fs
F = 0.60
Vf
Vp
Fs = 0.64
17
Experimental measurements of the value of packing-factor
Ye.P.Mamunya, V.V.Davydenko, P.Pissis, E.V.Lebedev.
Europ. Polym. J., 38 (2002) 1887-1897.
Vibrational compression
method
Ye.P.Mamunya, V.F.Shumskii, E.V.Lebedev.
Polym. Sci., 36B (1994) 835-838.
Rheological method
P
F=
ρ ⋅V
η ⎛ 1.25 ⋅ ϕ ⎞
⎟⎟
= ⎜⎜1 +
ηp ⎝
F −ϕ ⎠
For the portion
of powder:
P – weight
V – volume
ρ – density
f
2
η is viscosity of composite
ηp is viscosity of polymer
ϕ is volume fraction of filler
F is value of packing-factor
15
1 – PP+CB, F=0.24
2
2 – PE+CB, F=0.28
For monodispersed
spherical particles F = 0.64.
In any system the volume
occupated by filler can not
be higher than 64 %.
c
p
ηη/η/η p
10
1
5
0
0,00
0,05
0,10
0,15
Filler content, ϕ
ϕ
0,20
18
Influence of aspect ration l/d on the value
of packing-factor F
D.M.Bigg.
Advanc. Polym. Sci., 119 (1995) 2-29.
Ye.P.Mamunya, V.D.Myshak, E.V.Lebedev.
Compos. Polym. Mater., 20/1 (1998) 14-20.
• Computer simulation gives the
graphical
form of relationship
between ratio l/d and
value of
packing-factor F for the anisotropic
filler.
1
• This relation can be presented in
analytical form by empiric equation:
0.1
F
F=
0.01
0.001
1
10
100
l/d
1000
5
75
+l/d
10 + l / d
• In turn, the value of F is joined with
value of percolation threshold ϕc
19
Correlation between values of packing factor F and
percolation thrshold ϕc
Ye.P.Mamunya, V.V.Davydenko, E.V.Lebedev.
Doklady AN USSR., 5B (1991) 124-127.
ϕc = Xc·F
ϕc
Xc
Ye.P.Mamunya, V.V.Davydenko, P.Pissis, E.V.Lebedev.
Europ. Polym. J., 38 (2002) 1887-1897.
If to measure or to calculate the value of F,
possible to predict the value of ϕc of composite with any shape of particles because the
value of ϕc is defined by values of F.
F
0.16 0.25 0.64
-0,5
-1,0
5
6-7
8-9
– theoretical value
– dispersed metals
– carbon black
6
98
10
11
c
log
lg ϕϕc*
Critical parameter Xc is constant in the case
of lack of interaction between conductive and
nonconductive phases in the polymer
composite.
5
7
-1,5
12
-2,0
-2,5
-3,0
-2,0
13
14
15
-1,5
10-15 – carbon fibers
with l / d = 20 for 10
40 for 11
110 for 12
150 for 13
230 for 14
290 for 15
-1,0
log
lg FF
-0,5
Packing-factor F is
key parameter
of filled composites
0,0
20
Relationship between packing-factor F and
parameters of conductive lattices
A.L.Efros. Physics and geometry of disorder.
Moscow: Nauka, 1982.
• This relation exists for all types of
co
nd
uc
tiv
e
ve
nducti
nonco
conductivity
lattices
ϕc = Xc·F
• For any type of lattice the values
Xc and F are changed such a way
that the value ϕc is constant and
equal ϕc = 0.16 :
ϕc
percolation
threshold, ϕc
ϕc=0.16
conductive volume, ϕ
Xc
F
Type of lattice:
0.16 0.31 0.52
cubic
0.16 0.24 0.68
centered cubic
0.15 0.43 0.34
diamond
21
Influence of the packing-factor F values on
physical-mechanical properties of PWC
Ye.Mamunya, M.Zanoaga, V.Myshak, F.Tanasa,
E.Lebedev, C.Grigoras, V.Semynog.
J. Appl. Polym. Sci. 101 (2006) 1700-1710.
Model system: composite of polymer/wood = 60/40
Wood particles size,
L, mm
F
σt,
MPa
ΔW,
ΔS,
%
%
M,
g⋅m
1.00
0.20
particles mixture
0.57
0.58
0.71
5.2
5.9
7.9
3.4
2.4
0.9
2.5
2.0
0.6
1200
1350
1000
0,6
0.6
F
F
0,4
0.4
0,2
0.2
0,0
0.0 0
0
2
2
4
4
66
L , mm
L,
mm
8
8
10
10
If to use the wood filler with higher value of F (0.71
versus 0.57-0.58), the sharp increase of the composite
properties takes place.
What is a reason of characteristics improvement?
⎛ F
⎞
− 1⎟⎟
R = L⎜⎜ 3
⎝ ϕ
⎠
R
L
ϕ
F1 > F2
is a distance between particles;
is a size of particles;
is volume filler content in composite
ϕ1 = ϕ2
The increase of F value determines the increase of R value, i.e. the polymer layers between
wood particles become thicker, which is equivalent to the decrease of wood content.
22
How to take into account the packing-factor F and
other parameters of composites ?
Well-know equation joins the
values of conductivity σ, volume
fraction of filler ϕ and value of
percolation threshold ϕc:
σ = σ 0 (ϕ - ϕ
Ye.P.Mamunya, V.V.Davydenko, E.V.Lebedev.
Polym. Compos., 16 (1995) 319-324.
Ye.Mamunya, Yu.Musychenko, P.Pissis, E.V.Lebedev,
M.Shut. Polym. Eng. Sci, 42 (2002) 90-100.
The generalized equation can be obtained by
t
c)
introducing the parameters of conductivity into eq. 1
σ0 is parameter of conductivity;
Conductivity, log σ
t
σm
σ − σ c ⎛ ϕ − ϕc ⎞
⎟⎟
= ⎜⎜
σ m − σ c ⎝ F − ϕc ⎠
σc
σp
⎛ ϕ − ϕc
σ = σ c + (σ m − σ c )⎜⎜
⎝ F − ϕc
t is critical exponent, t = 1.7-2.0
ϕc
Filler volume fraction, ϕ
F
⎞
⎟⎟
⎠
t
Correlations between parameters l/d, F and ϕc
in the real fillers
Filler
l /d
F
ϕc
0.16
0.64
1
Ideal spheres
0.08-0.12
0.30-0.50
5-13
Dispersed metals
0.050-0.090
0.22-0.36
10-20
Carbon black
0.005-0.025
0.02-0.10
50-200
Carbon fibers
Carbon nanotubes 500-3000 0.0017-0.01 0.0004-0.0025
50 μm
100 μm
50 μm
3 nm
100 nm
23
The
lowest
values
of
percolation threshold and
packing factor exist for the
carbon nanotubes because
of their highest value of l/d.
80 μm
70 μm
500 nm
45 μm
24
Spatial distribution of filler in the polymer matrix
It is possible to create the skeleton structure of filler in
the volume of polymer matrix.
The real local concentration of particles into skeleton
(ϕloc) is much higher than the average concentration (ϕ)
related to the whole volume of composite, ϕloc >> ϕ.
Skeleton structure can be arranged by technological
methods in two ways:
• compacting of powder-powder mixtures;
• using the polymer blends as the composite matrix.
skeleton
structure
of filler
(segregated
structure)
25
Creation of segregated structure by compacting method
D – polymer particle
d – filler particle
D>d
d
D
Ye.P.Mamunya, E.G.Privalko, E.V.Lebedev, V.P.Privalko.
Macrom. Sympos. 169 (2001) 297-306.
Ye.P.Mamunya, V.V.Davydenko, H.Zois, L.Apekis, A.A.Snarskii,
K.V.Slipchenko. Polym. & Polym. Comp. 10 (2002) 219-227.
Evolution of the skeleton structure with filling
powderpowder
mixture
Temperature
of polymer
softening
hot pressing
(compacting)
PVC-Ni composites:
D=100 μm, d=10 μm
26
Geometrical model of segregated structure
Ye.P.Mamunya, V.V.Davydenko, P.Pissis, E.V.Lebedev.
Europ. Polym. J., 38 (2002) 1887-1897.
D
Model in a form
nd
of cubic lattice
Structural
coefficient
Ks =
For PVC-Ni composites with D/d=10
the model predicts the value of
percolation threshold ϕcs two times
lower comparing with ϕc at random
distribution of filler
0,20
5
0,16
6
ϕϕcccs
0,12
ϕ loc F
=
ϕ
Fs
1
⎛ nd ⎞
= 1 − ⎜1 −
⎟
Ks
D⎠
⎝
3
Relationship between value of
percolation threshold and
parameters of model
0,08
4
3
2
1
0,04
0,00
0
4
8
12
D/d
D/d
16
20
⎛ ⎛ nd ⎞ 3 ⎞
ϕ cs = ϕ c ⎜1 − ⎜ ⎟ ⎟
⎜ ⎝D⎠ ⎟
⎝
⎠
27
Computer simulated model of segregated structure
N.Lebovka, M.Lisunova, Ye.Mamunya, N.Vygornitskii.
J. Phys. D: Appl. Phys., 39 (2006) 1-8.
R
r
n=2
A composite was simulated as
the lattice containing small
conductive particles distributed
in the channels between large
insulative particles
PVC-Cu
PC-Cu
⎡ ⎛ nr ⎞ − d ⎤
∞
ϕ cs ( R / r , n) = ϕ c ⎢1 − ⎜1 + ⎟ ⎥
R ⎠ ⎥⎦
⎢⎣ ⎝
ϕcs
L
R/(r⋅n)
Composites
R
r
R/r
n
ϕc teor
ϕc exp
PVC-Cu
PC-Cu
120
315
4.8
23
25
13.7
3.64
3.73
0.055±0.001
0.084±0.001
0.065
0.095
28
PVC/CNT and PE/CNT composites with ultralow
value of percolation threshold
l/2r ≈ 1000
Ye.P.Mamunya, N.I.Lebovka, M.O.Lisunova, E.V.Lebedev,
A.Rybak, G.Boiteux. J. Nanostr. Polym. Nanocomp., in print.
D = 100 μm
M.O.Lisunova, Ye.P.Mamunya, N.I.Lebovka, A.V.Melezhyk.
Europ. Polym. J. 43 (2007) 949-958.
MWCNT:
l =10-20 μm, 2r = 10-20 nm,
l/2r =1000.
100 μm
100 nm
The model equation
3n
ϕ cs =
l D
⋅
2r d
-2
-4
-4
predicts the value of ϕcs=3·10-5.
-6
log ( , S/cm)
log ( , S/cm)
-6
-8
-1 0
P VC /C NT
-1 2
P E/C NT
ϕc=0.00036
-14
-1 6
0,000
-10
-12
ϕc=0.00047
-1 4
-8
-16
0,002
0,004
0,006
Volume fra c tion, ϕ
0,008
0
0,001
0,002
0,003
Volume fra c tion, ϕ
0,004
0,005
The real value of ϕcs is
sufficiently higher because of
non-ideal distribution of filler
29
What advantages have the composites with anisotropic
filler and ordered spatial distribution of particles ?
• Fillers with high aspect ratio l/d (for example, carbon nanotubes
with l/d ~1000) enable to reach very low percolation threshold in
the composites, hence the composites can be conductive at very
low filler content.
• The change of spatial filler distribution from the random to the
ordered distribution, can essentially reduce the percolation
threshold for isotropic fillers.
It allows to obtain the conductive material with low
content of filler and with mechanical and rheological
properties close to the pure polymer.
30
Experimental methods of the conductivity
measurements on DC
D
h
Rv
h
Rv
l
Rs
d
V πD 2
ρv = ⋅
I 4h
D2
V
ρv =
I
D1
ρ <105-106
Rc
Rv
Rv
V
Rc
I
V πD22
ρv = ⋅
I 4h
R
V/I
Rs
V π ( D1 + D2 )
ρs = ⋅
I ( D1 − D2 )
V d ⋅l
⋅
I h
h
Rc
h
31
Conclusions
• Combination of conductive filler and non-conductive polymer
gives the two-phase system which can be in two states:
conductive and non-conductive. Transition between two states
takes place at percolation threshold ϕ = ϕc.
• Geometric characteristics of filler are very important and enables
to regulate the value of percolation threshold and physicalmechanical properties of composites.
• Change of the spatial distribution of filler is effective method to
obtain the conductive composites with low value of percolation
threshold.
• Combination of strongly anisotropic filler and its segregated
spatial distribution for composites polymer/MWCNT enables to
obtain ultralow percolation threshold.