1

Theoretical Derivation and Experimental Result on Fabricating Ceramic Composite Reinforced with Aligned Discontinuous Fibers in Electric Field

Xiangzhen Sun1, Jinshan Yang1, Weiming Lu2, Chengying Xu1*

1Department of Mechanical Engineering, Florida State University

2UTC Aerospace Systems

*Email: cxu@fsu.edu, Tel: (850)410-6588

In this paper, electric field has been used to control and align the orientation of discontinuous carbon fibers

suspending in polysilazane. Induced by external electric field, random distributed carbon fibers were forced to

align in polysilazane. This field-induced alignment method is developed for fabricating ceramic composite

reinforced by discontinuous carbon fiber. The purpose of aligning carbon fiber reinforcements is to improve

mechanical and electrical properties of reinforced ceramic composite. Different from previous study on fiber

reinforced ceramic composites, theoretical derivation of estimating required field intensity is developed as a

guidance of aligning discontinuous carbon fibers in liquid environment. In the presented study, individual carbon

fiber is modeled as polarizable cylindrical suspension in liquid resin. The motion of carbon fiber inside DC electric

field is decomposed into polarization and rotation separately. The work DC field needs to do to align each piece

of carbon fiber is also calculated. Standing on energy view, the criterion for occurrence of alignment is presented

in order to solve the minimum required electric field intensity. A minimum field intensity is calculated from theory

and compared with experimental results. With respect to experimental result, a theoretical improvement method

on minimizing pearl-chain formation distribution among aligned chopped fibers was proposed in the last part.

Finally, discontinuous fibers were evenly dispersed in polysilazane and aligned in DC field afterwards. The

product of proposed experiment serves as a precursor of fiber-reinforced composite, which inherits promising

thermal, mechanical and dielectric properties from constitutive ingredients.

I. INTRODUCTION

Carbon fibers and carbon nanofibers (CNFs) have generated great interest in industries and scientific

communities due to their unique electrical, thermal, and mechanical properties when used as reinforcements in

polymer matrix composites. 1-5 Although generically different in sizes, the fact that CNFs are cylindrical structures

with diameters varying from a few to hundreds of nanometers and lengths ranging from less than a micron to

millimeters, 6 closely resembles that of short discontinuous carbon fibers in the presented research. It is worthwhile

combining their properties and applications in detailed discussion. The intrinsic conductivity of large diameter

vapor grown carbon fiber (VGCF) and the increased conductivity at temperatures approaching 3000 ºC was first

2

reported by Endo et al. 7 Heremans 8 measured resistance of VGCF vs. temperature as a function of heat treatment,

thus concluded factors regulating its electronic conduction band occupation. The properties of carbon fibers are

more obvious if combined with other materials to form a composite. 9,10 Extensive conductivity measurements for

VGCF/polypropylene and nylon composites was reported and interests in carbon fiber and CNFs reinforced

composites draw more and more attention. 11 A promising application of vapor grown carbon nanofibers

(VGVNGs) reinforced composites as sensors was made possible by its electrical resistivity property. 12

Additionally, the high thermal conductivity of carbon fiber or CNFs reinforced composites can be applied in

adhesives that provide sufficient thermal conductivity and electrical conductivity for aerospace applications. 13

Apart from high electrical and thermal conductivity, VGCFs have been reported to give values of 2.9 GPa for

tensile strength and 240 GPa for the tensile modulus, 14 which made it a desirable reinforcement of synthesizing

high strength composite materials.

Carbon structures such as vertically aligned carbon nanofibers (VACNFs) produced by chemical-vapor

deposition are of great interest due to their promising applications in areas such as scanning microscopy, field

emission devices, and biological probes. 15-17 However, most of these applications require carbon fibers to be

deposited on substrates in a uniformed pattern, such as horizontal or vertical relative to substrate, that result in

aligned pores. Similar to carbon nanotube (CNT) reinforced nanostructure, such architectures where CNF

reinforcements are deposited in aligned pattern prove to be very important for rapid ion transport, higher thermal

and electrical conductivity, longer life cycle, and structural uniformity. 18 Therefore, it is crucial to develop an

efficient method for fabricating aligned carbon fibers in polymer substrate. In literature, multiple ways have been

provided to align discontinuous carbon fibers, CNFs, even CNTs in polymer substrate. Techniques used in

alignment methods include but not confine to magnetic field, 19,20 gas flow, 21,22 electrical field, 23,24 shear flow of

polymer matrix, 25-27 mechanical shear press, 28,29 and mechanical stretch alignment. 30 Flow induced alignment is

often used for aligning fibers in injection molded parts. Although high levels of alignment are possible in this

method, fiber length largely affects alignment of individual fibers, with shorter fibers being easier to align in the

shear flow. 31 Magnetic field alignment takes effect by inducing a torque that rotates and anisotropic material in

order to minimize the magnetic energy. 32,33 The advantage of aligning by magnetic field is free control of

alignment direction even in a thin film substrate. Increased thermal and electrical properties along the magnetic

alignment direction were observed by Choi et al 34 using 25 T magnetic field for alignment. However, due to the

low magnetic susceptibility of carbon fibers and carbon nanostructures, 35 alignment comes with a price of high

intensity of magnetic field, let alone inaccessibility of such demanding devices. Electrospinning-induced

3

alignment was also employed for fabrication of organic fibers. 36 Specifically, CNTs were successfully aligned in

polymer nanofibers by electrospinning mixture. This method requires a high DC voltage (e.g. 25kV) generated

between negatively charged polymer fluid and fiber collector. Bradford and Wang 29 reported a method to quickly

produce aligned composites with a high volume fraction of reinforcements. Specifically, shear pressing was

employed to process millimeter long, well aligned CNT arrays into densely aligned ones. Due to its high density,

composites made by sheer pressing procedure might not be the best morphology for products such as battery

anodes that need to be low in density. Besides, sheer pressing takes more complicated process than aligning carbon

fibers with simply electric field. Electrical method has low experimental requirements on devices, and does not

produce by products during the whole process. Relying on fiber conductivity, 37 electric field induces dipole that

leads to torque acting on fiber. The torque combats viscous drag of surrounding medium in the direction of electric

field. 23 Besides DC electric field, AC field-induced method that allows for control over degree of alignment, was

also reported to align CNT-polymer composites. 24 Although influence of AC field strength varying from 10 to

250 Vp-p was fully researched, a mathematical description on aligning criteria and required field strength has not

been explicitly derived.

This proposed research focuses on using electrical field to align short fiber in liquid resin. The liquid resin

used in experiment is polysilazane, which is versatile, low viscosity (50-200 cps at room temperature) liquid

thermosetting resins containing repeat units in which silicon and nitrogen atoms are bonded in an alternating

sequence. Because of the high ceramic yields (>80 wt%), polysilazanes have been used as precursors of silicon-

based ceramics. For composite fabrication, an ultraviolet setup was used to cure the resin. The fibers and resin are

mixed in prescribed proportion. Treated by ultrasonic, short fibers are fully dispersed in polysilazane. Power

supply is applied to the suspension until fibers in suspension are thoroughly aligned. Figure 1 shows the conceptual

setup of the process. On prediction of motions performed by short carbon fiber suspensions, individual fibers were

FIG. 1. Schematic of apparatus for short carbon fiber alignment

4

ideally constructed as dielectric cylindrical aggregation of molecules. Thus, it is reasonable to assume the

polarization of short carbon fiber induced by electric field should observe all principles of normal polar particles

in electric field. Unlike previous models on analysis of motions during alignment, the behavior of short fibers was

decomposed into polarization and rotation, which is a simplified version of more complicated dielectrophoresis.

Prior work studying electro-kinetics of nanomaterial inclusions in various aqueous and organic solutions found

that particle dynamics is mainly affected by dipole forces, induced charge electro-osmosis (ICEO), and Brownian

motion. 38-43 Standing on energy view, effective minimum field strength was derived based on proposed model.

Through overcoming an energy barrier, carbon fibers are redirected in parallel to field direction by electric field.

Observation of head-to-toe (pearl-chain) formation among aligned short fibers inspires our effort on eliminating

the undesired formation to acquire better properties on composite product. A succinct way of improvement is by

adjusting weight ratio of fiber inclusions so that average distance among short carbon fibers are critically large

enough to attenuate attraction. The assumption was proved by both theoretical proof and experimental results.

II. Theoretical Derivation Modeling on Discontinuous Fiber Alignment

Charged particles are driven by electrical force in an electric field, while the case is more complicated if a

neutral particle or molecule is positioned in the field. Basically, motion of neutral particle suspensions in an

electric field falls into two categories: dielectrophoresis and electrophoresis. The latter phenomenon requires

responses to free charge on a body in an electric field. Thus, electrophoresis is not distinguished in this case at all

due to restrained charge in neutral body and polymer resin. Carbon fiber, CNFs and other carbon nanostructures

are anisotropic, polarizable aggregates and their structures determine that dielectrophoresis, a translational motion

of neutral matter caused by polarization effects in electric field, 44 characterizes suspension behaviors. It should

be noted that neutral polarizable particles do not perform translational motion in uniform field, but they can still

be polarized and therefore, be oriented in uniform field. When a neutral particle is positioned in electric field, the

polarization responses to the field in the form as an instant torque on the positive and negative charges of its atom.

The distributions of electrons are moved by external field. Such a process is explained in Figure 2. The physical

quantity used to describe polarization is polarizability.

When a neutral particle is positioned in electric field, the polarization responses to the field in the form of an

instant distortion of the centers of positive and negative charges of its atoms. The distributions of electrons are

distorted by external field. In electrical potential aspect, the polarization process is aimed at minimizing the

5

potential of every atoms inside the neutral particle so that the electrical distribution of these atoms has to be

realigned. The process is more directly shown in Figure 2. The physical quantity used to describe polarization is

polarizability, usually a three dimensional tensor, correlates electric field and induced dipole moment p :

p Ea= (1)

Since the fiber tube can be regarded as a tiny capacitor, the local electric field inside this “capacitor” should not

be omitted in most cases. Due to an opposite direction of inner electric field innE , the total electric field across a

short carbon fiber is:

ext innE E E= - (2)

FIG. 2. Carbon fiber kinetics diagram in electrical field

Suppose the 3 dimensional tensor can be diagonalized by appropriately choosing principal axis ( , , k)i j , and the

induced dipole moment should be:

0 0 0xx x yy y zz zp E i E j E ka a a= + + (3)

From quantum mechanics view, the components of polarizability tensor of every material are capable of being

calculated, yet it is quite difficult to quantify the accurate value of these components. For this reason, researchers

have provided different approximations to polarizability components. Benedict et al. 45 rigorously discussed the

calculation of longitude polarizability 0zza and traverse polarizability 0xxa separately . In his paper, the direction

6

of polarization does not depend on the positional relationship of CNT and electric field. The longitude

polarizability is proportional to g

RE

, where gE is the average band gap of CNT and R is the radius of nanotube.

Specifically, 2 2

08

zzg

e RmA Epa

æ öé ù= ç ÷ê úç ÷ë ûè ø

, and 0xxa is negligible compared with 0xxa . An alternative

interpretation46 gives general consideration of the polarizability of all spheroid dielectrics immersed in liquid

solvents as 3

0 24 log(2 ) 1s

zzlR

ka =-

, where sk is dielectric constant of liquid solvent and l is the axial length

of spheroid inclusion. Once again, the traverse polarizability was considered to be trivial in this situation.

In particular, Pohl’s 44 research on dielectric sphere in a non-uniform field referred that the induced dipole of

neutral particle should be:

3 2 10 1

2 1

42

p a Ek kp e kk kæ ö-

= ç ÷+è ø (4)

, where 1k is the dielectric constant of liquid resin, 2k is the dielectric constant of solid inclusion, a is the radius

of the sphere, 0e is the dielectric constant of vacuum and is equal to 8.85× 10−12 F/m. In this study, Pohl’s principle

is applied to short carbon fibers for gauging induced dipole considering accessibility of parameters and well-suited

conditions.

The work needed in the whole process of alignment consists of two parts: 1) producing the dipole; and 2)

aligning the dipole along the direction of electrical field. The required amount of work is described and presented

in the following:

(1) Producing the dipole

To evaluate the work to produce the dipole, it is necessary to introduce a pair of forces, F+ and F-, acting on

two opposite ends of fiber during the process of polarization. Assuming the charge of the entire fiber is 2q and the

length of the fiber is 2d, the force pair exerting at a distance of s from the center can be represented as:

sF qEd± = (5)

In order to pull all the electrical charges to the ends of the fiber, the work to produce dipole moment is derived by

integrating the force along d, we have:

7

10 0

1 12 2

d dqEW F ds sds qEd pEd±= = = =ò ò (6)

(2) Aligning the dipole along the direction of electrical field

The second part of work concerns the torque exerted on fibers and the angle fibers rotate. Specifically, right

after the process mentioned above, the fibers, under impact of electrical force, rotate to position described in

Figure 2 (shown as dashed lines). According to the definition, in a three-dimensional space, the torque equals to

the cross-product of moment and force:

sinp E pEt q= ´ = (7)

Assuming the current position of carbon fiber in electrical field starts from an arbitrary angle q , by integrating

torque with respect to angular increment, we have:

0

02 ( ) cos | cos (0) ( )W d pE pE pE U Uq

q

t q q q q q= = - = - + = -ò (8)

, where ( )U q is the electrical potential, according to definition

( ) cosU pEq q= - (9)

In extreme case, when all the fibers initially are perpendicular to the electrical field, the maximum work to bring

all carbon fiber aligned is when we choose the initial angle q as2p

.

(3) Total work required by carbon fiber

Adding W1 and W2, and after substitution q =2p

, the final expression of work needed to be done to realize

alignment is:

1 21 1cos( )

2 2 2W W W pE pE pE pEp= + = - + + = - (10)

Thus, the static mechanical analysis of carbon fiber subjected to electrical field is completed. A concise and

accurate method was proposed by Pohl 44 who provided the expression of local electric field inside the neutral

particle as:

1

2 1

32inn extE Ee

e e=

+ (11)

Effective field intensity is acquired by subtracting the local electric field with external field in equation (3):

8

2 1

2 12extE Ee e

e e-

=+

(12)

Combining equations (4), (10) and (12), the final work needed to align carbon fiber under required electric field

strength is:

23 2 10 1

2 1

22

W a Ek kp e kk kæ ö-

= - ç ÷+è ø (13)

, where a is the radius of spherical particle. With regard to carbon fiber, a should be replaced by fiber’s radius of

gyration 48:

2 2 1/2 2 1/2((R / 2) ( /12)) ( /12)a l l= + » (14)

If a sinusoidal electric field was applied, the scalar value of electric field should be:

22

2 0

0

( sin( ))

2

T

T

A t dtAE

dt

w= =ò

ò (15)

where A is the amplitude of sinusoidal electric field strength. Applying into equation (13), we have:

22 3/2 2 1

0 12 1

( /12)2

W l Ak kp e kk kæ ö-

= - ç ÷+è ø (16)

Now suppose the dimension of carbon fiber and relative electrical constants (effective dielectric constant,

conductivity etc.) are known, by employing estimation equation (12) and equation (13), the required electrical

work W can be solved. Based on Reference 49 , the required electric field used to align carbon fibers has to be

larger than a value as:

BW K T³ (17)

where KB is Boltzmann’s constant (1.38×10-23 JK-1), T is absolute temperature (K).

Comparing equation (16) with equation (17), we calculated the required electric field strength. By solving

equation (17), it is obvious that the influencing parameters include the length and diameter of discontinuous fibers,

dielectric constants of fibers and liquid resin, and fabrication temperature during experiment. Viscosity of liquid

resin does not affect the value of minimum electric field intensity, but smaller viscosity facilitates faster alignment.

In this research, the length of carbon fiber l is assumed to be 0.15 mm (in average), and the radius of carbon fiber

9

is 8 µm. The dielectric constant is chosen as 1 2.85k = . The dielectric constant of liquid resin (polymer precursor

in this research) is 2 3.45k = . The vacuum permittivity 0e is taken as 8.85× 10−12 F/m. The experimental

temperature was controlled around 160。C (433K). Using the liquid resin, the value of required electric field is at

least 46.6V/mm. It can be seen that the larger the aspect ratio of carbon fiber is, theoretically the smaller electrical

field we need to align carbon fiber.

Assuming the tank in Figure 1 is 2 mm in length (which is the distance between the two electrodes), the total

required power supply for alignment is 93.2 volts, in regardless of the width and depth of the tank, and the volume

fraction of fibers in the solution. All judging conditions are based on the fact that the summation of electrical

potential and the energy used to induce molecular dipole should compete thermal agitations.

III. Experimental procedure and results

During experiment, two parallel metal electrodes were attached to glass substrate to form the mixture tank as

conceptually presented in Figure 1. Both Copper electrodes and Zinc electrodes were applied and bound to glass

substrate by glue tape. The setup has to be sealed airtight, otherwise liquid spreads to crevices around during

experiment. Glue tapes are used to envelope two parallel lateral sides of metal electrodes so that liquid solutions

are prevented from contacting metal directly and conducting electro-chemical reaction consequently. Also, Double

(a) Copper electrode (bird view) (b) Copper electrode (bottom view)

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(c) Copper electrode (bird view) (d) Copper electrode (bottom view)

FIG. 3. Copper and Zinc electrodes formulate reaction sink by attaching to glass substrate

sided adhesive tapes were used to attach metal electrodes to glass substrate. Figure 3 illustrates both the bird view

and bottom view of the attachment of the Copper/Zinc electrodes onto glass substrate, where the tiny space

between the two metal electrodes represents the length of the mixture tank (2 mm).

From the previous calculation, the larger the supplied electrical field is, the better alignment results in. During

our experiment, one series circuit consisting four 12V Pb-batteries, one digital power supply (30V) and one analog

power supply (30V) were connected in series to provide in total 108V power supply.

Experimental materials were selected as 0.5wt% chopped fiber and 1.0wt% chopped fiber, both included in

polymer precursor. During experiment, electrode sink was placed right under an optical microscope for real time

observation. In average, the distance between electrodes is calculated as 2 mm. Figure 4 shows the experiment

process.

(a) The least distance between electrodes (b) Conducting observation using optical microscope

FIG. 4. Real time observation of chopped fiber alignment

The alignment process was recorded in time sequence. Before adding electric field, all chopped carbon fiber

in sight were randomly dispersed by mechanical stirring and supersonic vibrational homogenization. Polymer

11

precursor serves as the liquid resin where chopped carbon fibers are used as reinforcement for the composites.

Instantaneously starting from adding the DC field, chopped fibers started to rotate. As expected, electrical force

exerts on each individual fiber and each carbon fiber was aligned to a direction parallel to electrical field

(perpendicular to the electrodes plane). The whole alignment process ends in 12 minutes. Figure 5 shows

alignment results during the time span.

(a) 0 sec (b) 15 sec

(c) 30 sec (d) 1 min

(e) 5 min (f) 10 min

12

(g) 12 min

FIG. 5. Time sequence of aligning carbon fiber in polymer precursor

IV. Improvement on Alignment Effect

In previous model, carbon fibers were supposed to align in uniform electric field and all theoretical

calculations were conducted on that premise. It is noticed that the alignment of carbon fibers comes with chain-

like structure along electric field lines. This pearl chain formation 50 can be explained by self-induced non-uniform

electric field near the ends of fibers. Figure 6 presents a conceptual diagram with respect to pearl chain formation

phenomenon. Due to the existence of local non-uniform electric field, fibers are subject to dielectrophoretic force

at two sides, thus moving to connect each other.

FIG. 6. Pear chain formation caused by self-induced field

Dielectrophoretic force is directly correlated with gradient of nonuniform electric field 51:

2

22 11

12DEPR lF Es sp e

s-

= Ñ (18)

where 1s and 2s are conductivity of carbon fiber and liquid resin separately. Ideally, carbon fibers should align

in electric field and disperse evenly in solvent. To minimize the extent of pearl-chain aggregation, it is reasonable

to control the volume fraction of carbon fiber in liquid resin so that the work done by non-uniform field to bring

the ends two separate fibers in touch is less than average translational energy (integral energy associated with 3

degree of freedom) 32BK T 44..

E

Non-uniform Field

13

The calculation of induced dipole need to be reconsidered due to addition of non-uniform local field.

Individual fibers can be modeled as large circular, polarizable particles. At a distance d, both fibers in Figure 7 are

subject to the external uniform field as well as the local induced non-uniform field. The dipole of each fiber

induced by external field has been calculated in equation (4). Based on the same pattern with equation (1), (4), it

is easy to derive the induced dipole caused by local field Eloc:

3 2 11 0 1

2 1

42 loc locp a E Ek kp e k a

k kæ ö-

= =ç ÷+è ø (19)

The field at a distance d from a dipole of moment p0 is 52:

03

1

ˆ4locpE edpe

= (20)

By adding newly induced dipole to previous one, the current dipole of each carbon fiber is:

0 1 locp p p p Ea= + = + (21)

FIG. 7. Force diagram of carbon fiber pairs in uniform field, with induced local electric field

Combining equation (19), (20), current dipole is derived as:

10

31

12

pp

dape

=-

(22)

To calculate the work non-uniform electric field does to bring a pair of fiber dipoles from a distance of d to

contact, it is necessary to analyze the motion of fiber pairs during the whole process. As illustrated in Figure 8,

random placed fibers were modeled to take a space of a sphere in liquid resin. Ideally, if carbon fibers were

dispersed evenly, the size of these sphere spaces should be equal. On adding external electric field, carbon fibers

were forced to polarize and orient to a direction parallel to field line. After alignment, adjacent carbon fibers were

14

dragged together by induced field at two ends. To simplify the whole process, motion of fiber pairs was divided

into three categories: rotation, translation and approaching, corresponding to stage 2, 3, and 4 separately, as

indicated in Figure 8. Starting from alignment status, suppose the average distance of every two carbon fibers is

d. Then in an ununiform field Eloc , the electric potential of two adjacent fiber pairs is totally:

2

210 3

13

1

1( )2 1

2

d locpU p Ed

dapepe

= =-

(23)

FIG. 8. The influence of external and induced field on the motion of carbon fiber pairs

If a pair of carbon fibers were forced to contact head-to-toe by dielectrophoretic force FDEP, the distance between

their center is l then, and the current potential is:

2

213

13

1

1( )2 1

2

lpUl

lapepe

=-

(24)

The work done by FDEP during the process is:

2

2 213 3

13 3

1 1

1 1 1 1( ) ( )2 1 1

2 2

DEP l dpW U U

l dl d

a apepe pe

é ùê úê ú= - = -ê ú- -ê úë û

(25)

By solving 32B

DEPK TW £ , the minimum average distance of carbon fibers dmin can be calculated. Assuming the

15

mass of liquid resin is m, the weight percentage of carbon fiber in liquid resin is w , the density ratio of carbon

fiber and liquid resin is 1

2

rnr

= , then it is possible to calculate the number of fibers inside liquid resin by

combining the following equations:

21

mwnR lr p

= (26)

3

2

43 avg

mV n rpr

= = (27)

This method of calculation 53 is based the assumption that if particles are ideally dispersed in solvent, each particle

takes a space of sphere with an average radius of ravg:

13

234avgr R lwnæ ö= ç ÷

è ø (28)

By establishing inequality that equation (25) is less than 32BK T , and substituting 2 avgr d= as well as equation

(28) into this inequality, the following inequality can be derived:

2

22 2

3 2 11 13 2

1 1

1 16 324 (1 )2

Bw R l K TR l w l

l p

a an peape n pepe

+ £ +- -

(29)

which is a 21w C

wkk + £ type inequality. Equation (29) provides an approximate evaluation that can help decide

the least weight percentage of carbon fiber inclusions for aligning carbon fibers in liquid resin with minimized

pearl-chain phenomenon.

In response to proposed analysis on improvement, short carbon fiber – polysilazane mixtures were prepared

with the weight ratio of carbon fiber ranging from 0.1wt% to 1.0wt%. The voltage on electrodes was uniformly

107.8V. Figure 9 illustrate a decreasing pearl-chain extent as weight ratio of carbon fiber reduced from high to

low. The experimental results indicates inversely proportional relation between weight ratio of carbon fiber

16

(a) 1.0wt% (b) 0.5wt%

(c) 0.2wt% (d) 0.1wt%

FIG. 9. Carbon fiber aligning effect vs. varying weight ratio

inclusions and the extent of local aggregation.

V. Conclusion

On expectation of aligned carbon fiber-reinforced composites having better performance than composited

reinforced by random oriented carbon fibers, a novel theoretical deduction was developed to support experiment

deployment. Minimum required electrical field intensity was calculated. Applying 0.15 mm as average length of

fibers in experiment, the desired dc field intensity was calculated as no less than 46.6V/mm. This theoretical value

proved to be a little less than actual dc field intensity in following experiment. Discontinuous carbon fiber

suspensions with 0.5wt% and 1.0wt% weight ratio were aligned in dc field around 58V/mm. The duration of

alignment process lasts as long as 12 minutes, although aligning action occurs within 15 seconds as indicated. The

experiment results in this paper proved DC electric field’s influential function in aligning neutral polarizable

dielectric inclusions in liquid environment. Theoretical estimation overall matches actual field intensity applied

in experiment. Experimental result also justifies the proposed method to align discontinuous fibers in electrical

field. On observing local concatenation of carbon fibers head-to-tail, namely pearl-chain formation as proposed

in this paper, a theoretical optimal weight ratio was presented in inequality form in order to minimize the content

17

of undesired concatenation. The significance of optimal weight ratio estimation is especially obvious in making

well-performed ceramic composite reinforced by discontinuous carbon fiber

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