Vol. 20 No. 1

Jom~al of Wuhan University of Technology- Mater. Sci. Ed.

Mar. 2005

Percolation Model of Graphite-modified Asphalt Concrete MO Liantong WU Shaopeng LIU Xiaoming CHEN Zheng (Key Laboratory for Silicate Materials Science and Engineering of Ministry of Education, Wuhan University of Technology, Wuhan 430070, China)

Abstract: The addition of graphite powder in conventional asphalt mixture can produced asphalt concrete with excellent electrical peoCormance. Percolation theory was employed to discuss the relation between the conductivity and graphite content of graphite- modified asphalt concrete. It was found that the results of percolation model are consistent with experimental values. The percolation threshold of graphite-modified asphalt concrete is 10.94% graphite content account for the total volume of the binder phase consisting of asphalt and graphite. The critical exponent is 3.16, beyond the range of 1.6- 2.1 for the standard lattice continuous percolation problem. Its reason is that the tuurwl conduction mechanism originates near the critical percent content, which causes this system to be not universal. Tunnel mechanism is demonstrated by the nonlinear voltage-current characteristic near percolation threshold. The percolation model is able to well predict the formation and development of conductive network in graphite-modified asphalt concrete. Key words: asphalt concrete; electrical conduction; graphite; percolation model

1 Introduction

2 Experimental

The addition of graphite in conventional asphalt mixture has produced asphalt concrete with an excellent electrical performance I1'21 , which is expected to be applied due to its electrothermal behavior as an efficient, convenient, safe and environmental conservative method to melt and remove snow or ice on pavements, bridge decks and airfield runways. In general, percolation theoryI3-61 has been usually employed to explain the insulating-conductive transition of irregular mixing conductive composites. The relation between the conductivity and the volume percentage of a conductive additive often meets the following equation: aoc(P-Pe) t (1) where, a denotes the conductivity; P and Pc express the volume percentage and the critical percent content of the conductive additive respectively; t the critical exponent and t = 1.6-2.0 the universal in three-dimensional systems [3~ . The percolation theory mentioned above is suitable for the conductive composite of two phases, but the application in multi-phase conductive systems filled with different Sizes (0. 075-19turn) of fillers (stone aggregate) has not been reported. This study discussed the percolating conduction behavior of graphite-modified conductive asphalt concrete, and then established its percolation model employed to predict the formation and development of conductive path and to guide the material design of graphite conductive asphalt concrete.

2. l

( Received:May 18,2004; Accepted:Nov. 12,2004) MO Liantong(~'~ ~ ): E-mail: molt@mail: whut. edu. cn * Funded by the Outstanding Youth Foundation of Hubei Province of China (No. 2004ABBOt9)

Materials Bitumen: a heavy-duty type (AH-70) produced by Koch Asphalt Co. Ltd in Hubei province, China, with a penetration of 65 (0. lmm at 25~ 100 & 5 seconds), ductility 167.3cm (at 5 ~ ) and softening point 51.5 ~ Aggregate: crushed basalt mineral, with a density of 2. 930g/cm 3 and maximal size of 16ram. Combined gradation of aggregate mixture is listed in Table 1. Mineral filler: limestone type, with a density of 2. 830g/cm3 , some major chemical compounds which included 5 1 . 5 % CaO content and 1.76% SiO2 content. The passed percentage on sieve is 100%, 9 7 . 3 % and 8 3 . 7 % for the sieve openings 0.3ram, 0.15mm and 0.075mm, respectively. Graphite: particle size 150gin, carbon content 98.9 %, ash content 0 . 2 % , iron content 0.03 % , the electrical resistivity 10-4~2 9 cm, obtained from Xingtai Graphite Ore Factory in Hubei province, China. Graphite content accounts for the volume percentage of the binder phase of the combination of the bitumen and the conductive filler,ranging from 8vo1% to 20vo1%. 2.2 Methods The gradation of aggregate mix design employed Superpave 12.5 E7'83 , listed in Table 1. The size of graphite is smaller than 0. 075mm, which can replace some part of limestone powder, serving as mineral filler. Graphite absorbs asphalt liquid easily at high temperature greater than 135~ so asphalt content(4wt%-6wt%) increases with the increase of graphite content. When the air void percentage of specimens is 4 % , the corresponding asphalt content is the optimum asphalt content. The mixing procedure is shown in the Reference [ 1 ] in details. A full-automatic asphalt mixture mixer (HB-10model, Huida instru-

112

Journal of Wuhan Universityof Technology- Mater.Sci. Ed.

Mar. 2005

RS/tt, where, p denotes the resistivity of conductive asphalt-based composite; R the resistance-measured value of specimen; S the cross section area of the specimen and H the height of the specimen. Scanning electron microscopy images was analyzed on the fracture surfaces of the specimens coated in vacuum with a thin layer of gold and observed with an SEM-Model Hitachi S-2500, made in Japan.

ment plant, Tianjin province, China) was used to blend asphalt mixtures. Stone aggregate was heated in an oven at 165'12 for two hours previously, then blended with graphite and asphalt liquid at 165~ for 90 seconds respectively in the mixer. Specimens were prepared by a superpave gyratory compactor ( EP-31111 model, America) at the temperature of (145 _ 1 ) ~ . Gyratory number is Ni~ = 9, Na,~ = 125, and N.~, = 205. TaMe 1 Combined gradation of aggregate mixture Sieve /him

19 12.5 9.5

4.75 2.36 1.18 0.6

0.3

3

0.15 0.075

Percentage. 100 95.677.3 49.5 29.7 21.7 15.7 10.5 /%

7.9

Results and Discussion

The conductive medium of conductive asphalt concrete is the conductive binder phase, consisting of asphalt and graphite in voids of mineral aggregate. The particles of mineral aggregate are insulators and the size is far larger than graphite, so they functioned just as fillers, shown in Fig. 1. Graphite particles disperse randomly in asphalt base, forming two-phase conductive composites. With the increase of graphite content, the isolated particles as~mble and take shape to continuous conductive path, shown in Fig. 2. It is well known that the graphite has a good chemical stability, for instance, acidproof, alkali resisting and is able to boar corrosion of the organic solvent, etc. Therefore, no chemical reactions will ari~ with asphalt, only physical combination exists at the interface of asphalt and graphite, so no different insulating pha.~ exists on the graphite surface.

5.7

The electrical resistance was measured by two-probe method at room temperature 25~ The electrodes were made by stainless steel with a diameter of 150ram, thickness of 20ram and a total wcight of 3000g. Dry Graphite powders smaller than 0. 075ram in dispersion form were used to fill the gap between the electrodes and specimens in order to ensure perfect contact botwcen the electrodes and specimcns to minimi~ the measurement error. A resistance tester (type ZC-43) was used to measure the resistance, which was higher than 106~. Otherwise., a digital muhi-meter (type 1)'I"-830) was used for the measurement in ca.~ of resistance bolow 106~. The resistance value was the average measured on four specimens of each group. The correlation coefficient was above 95 %. Volume resistivity calculation used the formula followed, p =

-2 -3 -4 ,

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Image of cross-section for compacted conductive asphalt mixture

Fig.2 Scanning electron microscopy image of conductive asphalt concrete (graphite content: 16%)

The relation between the volume conductivity an(l graphite content of conductive asphalt concrete is displayed in Fig. 3. The curve trend is similar to that of other two-phase in'egular conductive composites. A sudden change takes place at a certain critical value, called percolation threshold p r3~sl in the conductivity. The conductivity is 8.7 x 10- ~ S/em with the addition of 10% graphite, exhibiting as an insulating material. According to percolation theory, graphite partMes disperse in asphalt existing in the form of limited-size clusters, and are unable to form the continuous conductive path with h)w graphite content less than P< ; hence the conductivity of the system is similar to that of asphah ( 1.0 x 10 -13 S / e r a ) . When the graphite content reaches 13%, the conductivity increases to 6.7. x 10 -6 S/era tempestuously. A sudden

I

10

5 20 25 P/vol% Fig.3 Relation between volume conductivity and graphite content

change in the conductivity occurs near 11% ~aphite content, increasing by about 5 orders of magnitude. This indicates the formation of conductive network, which is demonstrated by SEM microstmcture of conductive asphalt concrete, just like that in Fig. 2. The image reveals that conductive particles contact each other to form a three-dimensional conductive network in asphah concrete. The analysis mentioned 'above indicates that the conductive asphalt concrete exhibits the general conductive behavior of percolation model as the amount of graphite increases. When fitting Eq. ( I ) with least square method, the results are t = 3.16 and P<, = 10.94%, which are consistent with Pc = 12%, t = 6.27 for graphite filling polymer in the Reference [9]. As Eq. ( I ) is conducted by logarithm transition, one obtains Eq. (2) as

Vol. 20 No. 1

MO Liantong et a/: Percolation Model of (,raphite-modified Asphalt Concrete. . . .

1 13

follows :

those in many other continuous ~rcolation systems 15'9'~~ lg a ~ t l g ( P - P,) (2) The higher critical exponent is related to the characteristic The relation of lg a - lg ( P - P,. ) exhibits a good of complex system of conductive asphalt concrete9 In this system, graphite particles disperse in'egulady in asphalt linearity shown in Fig. 4. According to Eq. ( 1 ), percolabinder, especially near P , , the electrical conduction is tion model of a ( P ) - P is fitted using t = 3 . 1 6 and controlled by tunnel mechamsm 31 through the narrow inP,, = 10.94% ,shown as the curve in Fig.4. The results sulating gaps t~tween graphite particles. The local conof pewolation model are corrsistent with ex~rimental valduction correlates with gap width between graphite partiues well. t value is higher than the prot~t'tion coeffieient cles and tunnel probability, hence it has some certain dis( t = 1 . 6 - 2 . 0 ) of W,reolation theory, which shows that tribution, which leads to the non-universality of critical the continuous percolation problem of this system does not exponent 3..s~ belong to the same universality class as the standard lattice percolation problem. This phenomenon is similar to -A -2.5 0.7 -3.0 0.6 -3.5 -10% 0.5 -4.0 "~ 0.4 -4.5 <~ -20% "~ -5.0 0.3 o -5.5 ~-~ 0.2 -30% -6.0 0.1 A A -6.5 i i -40% -7.0 5 tO 15 20 25 30 35 5 1~0 1~5 20 259149 3~5 -2.20 -I.70 -I.20 -0.70 Voltage/V log(P-P,.) Voltage/V Fig.4 Relationbetween lgtrand lg (P-P~) Fig.5 Voltage-current characteristic (a) and V-A R relation (b)(P=12.1%)

9

0%

A/~

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t

i

The voltage-cum'nt (V-I) characteristic I~0~ of direct

graphite-modified asphalt concrcte.

4

-7~

The continuous pereolation problem of graphite-modified conductive asphah concrete doe.s not belong to the ,same universality class as the standard lattice percolation problem. The percolation thr~hold and critical extx)nent is P,. = 1 0 . 9 4 % , t = 3.16,respectively. The higher critical exponent is related to the electrical conduction controlled by tunnel mechanism near P,., which is demonstratext by the nonlinear V-I characteristic. The fitting l~.suhs of percolation model arc consistent with experimental values well. The percolation model is able to predict the

l

fommtion and development of conductive network in

cun~nt (DC) exhibits a nonlinearity and the resistanc, e reduces obviously with the increase of DC voltage near the critical content ( P = 12.1% ), shown in Fig.5. Because the graphite accords with Ohm's law and the contact conduction of graphite particles a l ~ meets the linear V-I characteristic, so the nonlinearity originates from the nonlinear conduction of tunnel mechanism through the narrow gap ~tween graphite particles. The nonlinear V-I characteristic demonstrates the conductive mechanism is controlled by tunnel mechanism near P~, which is the evidence for the analysis mentioned above about the non-universality of t value. Therefore, the percolation model of graphite-modified asphalt concrete is given as following: a~(P10.94v~ ) s~6 (3) where, P > 1 0 . 9 4 % .

Conclusions

l

References "1]

2]

~3] [d~5]

[6]

8]

.9 j

~10]

Wu Shaopeng,Mo lJantolug,Shni 7Jaonghc.An hnprovement of Electrical Propertir of Asphalt Concrete. Journal of Wuhan Unioersity qf Technolog3. - Mater. Sci. Ed. ,2002, 17(4):69-72 Wu S P, Mo L T, Shui Z H. Piezoresistivityof Graphite Modifi~xl Asphah-based Composites. Key Engineerirug Material,s, 2002,249: 391-396 Nan C W. Physics tff lnhomogeneous Inorganic Materials. Progress in Materials Science, 1993,37 : 1-116 Nan Ccwen, Chcn Xinzheng. Pe,colation Model of Ti-AI:O3 cemlet. ACTA Phys. SINICA , 1987,36:511-514 Grimaldi C, Mat~ter T, Ry,~r P, Strassler S. ~grcgated Tun,leling-tx'rcolation Model fi~rTransl:x~rlNonuniversality.Phys. Rely. B, 2003.68 (2) : 2420-2427 Xue Q z. A Percolation Model of Metal-insulato, Composites. Ptos . B- r Material ,2003,325(1-4) : 195-198 -'Kar~lhalP S. Gx~lcy 1. A. Gnrse-versLts Fine-g~aded Superpave Mixtures. Transporuaion research Reeord,~lY2 (1789):216-224 Yildirim Y, N)laimanian M, McGemfis 1'/B. Conq~trativc analysis of Valmnetric l~)w.rties for Superpave Gyratory Compactors. Tramportatkm research Record, 2002, ( 1712) : 44-52 Ez~luerraT A, Connor M T, Roy S. Alternating-current Prow.rties of Graphite, Cm'bon-black and Cadxm-fil~r Polymeric ComI~sitcs. Comt~sites S~'&nce and Technology, 2001.61: 903-1001 Guohua Chen,Wengui Wen, Dajma Wu,Cuiling Wu. Nonlinear Conduction in Nylon-6/FoliatextGraphite Nanocomposires above the Percolation Threshold. Journal ( f Polymer Science, Part B: Pol)mer Pbysics,2004,42:155-162