ELECTRICAL PROPERTIES AND ELECTRICAL PROPERTIES AND STRUCTURE OF POLYMER COMPOSITES STRUCTURE OF POLYMER COMPOSITES

WITH CONDUCTIVE FILLERSWITH CONDUCTIVE FILLERSI. Influence of filler geometry I. Influence of filler geometry

and spatial distributionand spatial distribution

Ye. P. MamunyaInstitute of Macromolecular Chemistry

National Academy of Sciences of Ukraine Kiev, Ukraine

yemamun@i.kiev.ua

Director of the Instituteacademician, professorE. Lebedev

Associate directors on scienceProfessor Yu. KerchaDSc Yu. Savelyev

Academic secretaryPhD V. Myshak

Chief engineerV. KrulitskiyAccountant-generalM. Kolchenko

A d m i n i s t r a t i o n of the I n s t i t u t eA d m i n i s t r a t i o n of the I n s t i t u t e

National Academy of Sciences of UkraineInstitute of Macromolecular Chemistry

S c i e n t i f i c d e p a r t m e n t sS c i e n t i f i c d e p a r t m e n t s

2. Physical chemistry of polymersPhysical chemistry of multi-com-ponent polymer systems, polymer blends and melts, structure of multicomponent systems (personnel - 28)DSc T. Todosiychuk

1. Chemistry of heterochainpolymers and interpenetraitingnetworks 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

4. Polymers for medical purposesElaboration of biocompatible polymer materials for medical applications and medical-biological testing of polymer materials (personnel - 25)DSc N. Galatenko

3. Polymer modificationStructural, chemical and physical modification of heterogeneous polymers and related systems (personnel - 22)DSc, professor Yu. Kercha

5. Polymer compositesStructure and properties of polymer composites based on conventional polymers and organic-inorganic systems (personnel - 33)Academician, professorE. Lebedev

6. Chemistry of oligomers and cross-linked polymersSynthesis reactive oligomers and creation of polymer systems based on synthesized oligomers. Development of functional polymers (personnel - 17)DSc, professor V. Shevchenko

7. Physics of polymersPhysics of polymer systems and nanocomposites. Characterization of microheterogeneous state of polymer systems and composites (personnel - 10)DSc V. Klepko

General informationGeneral informationGeneral numbers of personnel General numbers of personnel -- 253253Scientific personnel Scientific personnel -- 9292

including:including: DSc DSc -- 1717PhD PhD -- 7575

PhD students PhD students -- 2323

G e n e r a lG e n e r a ld e p a r t m e n t sd e p a r t m e n t s

Scientific-technical information, patent-license and publishing activities (personnel - 7)A. Dyakova

Standards and metrology(personnel - 6)V. Krulitskiy

Ancillary technical department(personnel - 37)V. Krulitskiy

Personnel management(personnel - 2)E. Kazina

www.macromol.kiev.ua

Scope of the Institute for the application of new polymer materials and technologies

Pilot plant(personnel - 23)

N. Gladyreva

Adhesives

Mastics

Lacquers

Paints

Polymer composites

Produced materials

Technical laboratory

“MONOLITH”(personnel - 9)

PhD V.Kolyada

Materials and technologies Protective dampproofing of concrete constructions based on elaborated materials:

- water protection in the metro tubes and stations- breakdown elimination of the concrete pipelines- moisture protection of the concrete bridges- protection and insulating of the nuclear station constructions

- soil solidification- flooding floors in the special factory sections

3

New polymer materials elaborated in the Institute

New film materials

New lacquer and paint compositions

New protective composite materials and technologies of their use

4

The topics proposed: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 electricalproperties

• filled conductive polymer blends: structure and properties

• phase inversion in filled polymer blends

• conductive composites with carbon nanotubes: technology, structure, conductivity, dielectric properties

5

Electrical characteristics of materialsElectrical characteristics of materials6

Polymer materials

Antistatic materials

Organic conductors,ionic conductors

Polymers with intrinsicconductivity

Carbon materials

MetalsConductors

Semi-conductors

Insulators

σ, S/cm

106

104

102

100

10-2

10-4

10-6

10-8

10-10

10-12

10-14

10-16

MetalsCarbon materials: carbon black,carbon fibers and tissue, carbonnanotubesConductive ceramicPolymers with intrinsic conductivity(polyaniline, polypyrol, polythiophenand others)

Types of conductive and insulating materialsTypes of conductive and insulating materials

7

Disadvantages• high conductivity

• metals – high density, high weight

• carbon – low mechanical characteristics

• rest – impossibility of processing byhighly productive industrial methods

• high cost

Conductive Nonconductive

Advantages

Polymer materials

Advantages

Disadvantages

• low density, low weight

• high mechanical characteristics• procesability by highly

productive industrial methods• low cost

• no conductivity

• impossible to use at hightemperatures

polymer-insulator + conductive filler

Conductive polymer compositesConductive polymer composites

8

Advantages• presence of conductivity

• low density, low weight• high mechanical characteristics• possible to process by highly

productive industrial methods• low cost

TwoTwo--phase systemphase system

Types of conductive fillersTypes of conductive fillers

• Conductive composite is two-phase system with insulatingphase (polymer matrix) and conductive phase (filler).

• Several kinds of materials can be used as conductivefillers:

• dispersed metals; • carbon black;• metallized mineral particles;• carbon and metallic fibers; • carbon nanotubes; • conductive ceramic;• polymers with instrinsic conductivity

9

Why such materials are attractive for researchWhy such materials are attractive for researchand application ?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 invarious 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.

10

11Correlation of structure with conductive Correlation of structure with conductive

properties of compositeproperties of composite

Region 1 – the composite is non-conductive, the matrix includes the separate particles of conductive filler.Region 2 – the region of percola-tion, the conductive cluster is created, the conductivity sharply increases at ϕ > ϕc.Region 3 – the conductivity slowly increases because of growth of conductive cluster.

Conductivity of composite is a function of the filler content and reflects the structure of composite.

Filler volume fraction, ϕ

Con

duct

ivity

, log

σ

conductivenonconductive

ϕc

10-16

10 1

10 4

percolation threshold

Region 1

Region 2

Region 3

12

Methods of definition of the percolationMethods of definition of the percolation thresholdthreshold

3. At maximum of the derivative function d(log σ)/dϕ, it is close to method 1.

1. Start of creation of the conductive cluster and sharp growth of conductivity of the composite.

4. At value of conductivity

fpc σσσ ⋅=

2. When conductive cluster is completed and the composite is conductive.

5. By fitting of equation( )tcϕϕσ −∝

Filler volume fraction, ϕ

Con

duct

ivity

, log

σ

ϕc

1

2

4

3

log (ϕ-ϕc)

log σ5

5 methods of definition of the percolation threshold

Main factors that define the conductive properties Main factors that define the conductive properties of polymer composites with conductive fillersof 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;

13

Influence of shape of conductive particles and their Influence of shape of conductive particles and their distribution on the percolation thresholddistribution on the percolation threshold

Statistical distribution of the sperical particles, theoretical value of percolation threshold,ϕc = 0.16

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 distributionof the filler particles arevery importantfor the value of percolation threshold.

14

ϕc = 0.16 ϕ

log σ

ϕc < 0.16 ϕ

log σ

ϕc << 0.16 ϕ

log σ

What parameter can take into accout the What parameter can take into accout the shape and spatial distribution of the filler shape and spatial distribution of the filler

particles?particles?

15

It is the packing-factor F.

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:

pf

f

VVV

F+

=Vf – volume occupied by the filler particles; Vp – volume occupied by the polymer

(space among filler particles).

What is the packingWhat is the packing--factor of filler?factor of filler?

For statistically packed monodispersed spherical particles of any size, Fs = 0.64

The value of F depends on:

monodispersed particles

Fs = 0.64

particles shape, l/d > 1

F < Fs

fraction composition

F > Fs

formation of the skeleton structure

F < Fs

16

Vf

Vp

opal inepoxy resin

F = 0.60

Experimental measurements of the value of packingExperimental measurements of the value of packing--factor factor

Vibrational compression method

VPF⋅

=ρ

For the portion of powder:P – weightV – volume ρ – density

f

Rheological method

225.11 ⎟⎟

⎠

⎞⎜⎜⎝

⎛−⋅

+=ϕϕ

ηη

Fp

η is viscosity of compositeηp is viscosity of polymerϕ is volume fraction of fillerF is value of packing-factor

17

For monodispersed spherical particles F = 0.64.In any system the volume occupated by filler can not be higher than 64 %. 0,00 0,05 0,10 0,15 0,20

0

5

10

15

21

η c /η

p

ϕFiller content, ϕ

η/η p

1 – PP+CB, F=0.24

2 – PE+CB, F=0.28

Ye.P.Mamunya, V.V.Davydenko, P.Pissis, E.V.Lebedev.Europ. Polym. J., 38 (2002) 1887-1897.Ye.P.Mamunya, V.F.Shumskii, E.V.Lebedev.Polym. Sci., 36B (1994) 835-838.

Influence of aspect ration Influence of aspect ration ll//dd on the value on the value of packingof packing--factor factor FF

18

0.001

0.01

0.1

1

1 10 100 1000

F

l / d

dldl

F/

/1075

5

++

=

• Computer simulation gives the graphical form of relationship between ratio l/d and value of packing-factor F for the anisotropic filler.

• This relation can be presented in analytical form by empiric equation:

• In turn, the value of F is joined with value of percolation threshold ϕc

Ye.P.Mamunya, V.D.Myshak, E.V.Lebedev.Compos. Polym. Mater., 20/1 (1998) 14-20.

D.M.Bigg. Advanc. Polym. Sci., 119 (1995) 2-29.

Critical parameter Xc is constant in the case of lack of interaction between conductive and nonconductive phases in the polymer composite.

Correlation between values of packing factor Correlation between values of packing factor FF and and percolation thrshold percolation thrshold ϕϕcc

19

ϕc = Xc·F

ϕc Xc F

0.16 0.25 0.64

-2,0 -1,5 -1,0 -0,5 0,0-3,0

-2,5

-2,0

-1,5

-1,0

-0,5

11

10

14

13

15

12

7

896 5

lg ϕ

c*

lg Flog F

log ϕ c

10-15 – carbon fibers with l / d = 20 for 10

40 for 11110 for 12150 for 13230 for 14290 for 15

5 – theoretical value6-7 – dispersed metals8-9 – carbon black

If to measure or to calculate the value of F, possible to predict the value of ϕc of compo-site with any shape of particles because the value of ϕc is defined by values of F.

Packing-factor F iskey parameter

of filled composites

Ye.P.Mamunya, V.V.Davydenko, E.V.Lebedev.Doklady AN USSR., 5B (1991) 124-127.

Ye.P.Mamunya, V.V.Davydenko, P.Pissis, E.V.Lebedev.Europ. Polym. J., 38 (2002) 1887-1897.

20Relationship between packingRelationship between packing--factor factor FF and and

parameters of conductive latticesparameters of conductive lattices

nonconductive

cond

uctiv

e

percolation threshold, ϕc

conductive volume, ϕ

cond

uctiv

it y

ϕc=0.16

• This relation exists for all types of lattices

• 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 = Xc·F

ϕc Xc F

0.16 0.31 0.52

0.16 0.24 0.68

0.15 0.43 0.34

Type of lattice:cubic

centered cubic

diamond

A.L.Efros. Physics and geometry of disorder. Moscow: Nauka, 1982.

Wood particles size, L, mm F σt,

MPaΔW, %

ΔS, %

M, g⋅m

1.000.20

particles mixture

0.570.580.71

5.25.97.9

3.42.40.9

2.52.00.6

120013501000

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 13

ϕFLR

R is a distance between particles;L is a size of particles;ϕ is volume filler content in composite

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.

0,0

0,2

0,4

0,6

0 2 4 6 8 10

L , m m

F

0 2 4 6 8 10L, mm

0.6

0.4

0.2

0.0

F

Model system: composite of polymer/wood = 60/40

What is a reason of characteristics improvement?

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.

Influence of the packingInfluence of the packing--factor factor FF values on values on physicalphysical--mechanical properties of PWC mechanical properties of PWC

ϕ1 = ϕ2

F1 > F2

21

Ye.Mamunya, M.Zanoaga, V.Myshak, F.Tanasa, E.Lebedev, C.Grigoras, V.Semynog. J. Appl. Polym. Sci. 101 (2006) 1700-1710.

How to take into account the packingHow to take into account the packing--factor factor FF and and other parameters of composites ?other parameters of composites ?

σ= σ0 (ϕ - ϕc)t

σ0 is parameter of conductivity;t is critical exponent, t = 1.7-2.0

ϕc

Filler volume fraction, ϕ

Co n

d uct

ivit y

, lo g

σ

F

σm

σcσp

The generalized equation can be obtained by introducing the parameters of conductivity into eq. 1

t

c

c

cm

c

F ⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=−−

ϕϕϕ

σσσσ

( )t

c

ccmc F ⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

−+=ϕϕϕ

σσσσ

22

Well-know equation joins the values of conductivity σ, volume fraction of filler ϕ and value of percolation threshold ϕc:

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.

Filler l /d F ϕc

Ideal spheresDispersed metalsCarbon blackCarbon fibersCarbon nanotubes

15-13

10-2050-200

500-3000

0.640.30-0.500.22-0.360.02-0.10

0.0017-0.01

0.160.08-0.12

0.050-0.0900.005-0.025

0.0004-0.0025

Correlations between parameters Correlations between parameters ll//dd, , FF and and ϕϕccin the real fillersin the real fillers

3 nm 100 nm500 nm

80 μm50 μm

The lowest values of percolation threshold and packing factor exist for the carbon nanotubes because of their highest value of l/d.

70 μm

45 μm

23

50 μm 100 μm

24

Spatial distribution of filler in the polymer matrixSpatial 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 structureof filler

(segregatedstructure)

25

Creation of segregated structure by compacting methodCreation of segregated structure by compacting method

dD

powder-powder mixture

Evolution of the skeleton structure with filling

hot pressing(compacting)

D > dYe.P.Mamunya, V.V.Davydenko, H.Zois, L.Apekis, A.A.Snarskii, K.V.Slipchenko. Polym. & Polym. Comp. 10 (2002) 219-227.

D – polymer particled – filler particle

PVC-Ni composites: D=100 μm, d=10 μm

Ye.P.Mamunya, E.G.Privalko, E.V.Lebedev, V.P.Privalko.Macrom. Sympos. 169 (2001) 297-306.

Temperature of polymer softening

26

Geometrical model of segregated structureGeometrical model of segregated structure

nd

D

0 4 8 12 16 200,00

0,04

0,08

0,12

0,16

0,20

65

4321

ϕ cc

D/dD/d

ϕ cs

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−=

3

1Dnd

ccs ϕϕ

s

locs F

FK ==ϕϕ

3

111⎟⎠⎞

⎜⎝⎛ −−=

Dnd

Ks

Structural coefficient

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

Model in a formof cubic lattice

Ye.P.Mamunya, V.V.Davydenko, P.Pissis, E.V.Lebedev.Europ. Polym. J., 38 (2002) 1887-1897.

Relationship between value of percolation threshold and

parameters of model

Computer simulated model of segregated structureComputer simulated model of segregated structure

L

R n=2r

R/(r⋅n)

ϕ cs

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +−=

−∞

d

ccs RnrnrR 11),/( ϕϕ

A composite was simulated asthe lattice containing smallconductive particles distributedin the channels between largeinsulative particles

PVC-Cu

PC-Cu

Composites R r R/r n ϕc teor ϕc exp

PVC-CuPC-Cu

120315

4.823

2513.7

3.643.73

0.055±0.0010.084±0.001

0.0650.095

N.Lebovka, M.Lisunova, Ye.Mamunya, N.Vygornitskii.J. Phys. D: Appl. Phys., 39 (2006) 1-8.

27

PVC/CNT and PE/CNT composites with ultralow PVC/CNT and PE/CNT composites with ultralow value of percolation thresholdvalue of percolation threshold

28

100 nm 100 μm

-16

-14

-12

-10

-8

-6

-4

0,000 0,002 0,004 0,006 0,008

Volume fraction, ϕ

log

(, S

/cm

)

PVC/CNT

-16

-14

-12

-10

-8

-6

-4

-2

0 0,001 0,002 0,003 0,004 0,005

Volume fraction, ϕ

log

(, S

/cm

)

PE/CNT

ϕc=0.00047 ϕc=0.00036

The model equation

predicts the value of ϕcs=3·10-5.

dD

rl

ncs

⋅=

2

3ϕ

MWCNT:l =10-20 μm, 2r = 10-20 nm, l/2r =1000.

The real value of ϕcs is sufficiently higher because of non-ideal distribution of filler

l/2r ≈ 1000 D = 100 μm Ye.P.Mamunya, N.I.Lebovka, M.O.Lisunova, E.V.Lebedev, A.Rybak, G.Boiteux. J. Nanostr. Polym. Nanocomp., in print.

M.O.Lisunova, Ye.P.Mamunya, N.I.Lebovka, A.V.Melezhyk.Europ. Polym. J. 43 (2007) 949-958.

29

What advantages have the composites with anisotropic What advantages have the composites with anisotropic filler and ordered spatial distribution of particles ?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.

Experimental methods of the conductivity Experimental methods of the conductivity measurements on DC measurements on DC

Rs

Rv h

D

Rv

D2 D1

hD

IV

v 4

2πρ ⋅=

hD

IV

v 4

22πρ ⋅=

)()(

21

21

DDDD

IV

s −+

⋅=πρ

hld

IV

v⋅

⋅=ρV

ld

h

I

V

I

Rc

h

R

h

V/I

30

Rc

Rc

RsRv

Rv

ρ <105-106

C o n c l u s i o n sC o n c l u s i o n s

• 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 physical-mechanical 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.

31