Reinforcement and quantitative description of inorganic particulate-filled polymer composites

Composites: Part B 51 (2013) 224–232

Contents lists available at SciVerse ScienceDirect

Composites: Part B journal homepage: www.elsevier.com/locate/compositesb

Reinforcement and quantitative description of inorganic particulate-filled polymer composites Ji-Zhao Liang ⇑ Research Division of Green Function Materials and Equipment, College of Industrial Equipment and Control Engineering, South China University of Technology, Guangzhou 510640, PR China

a r t i c l e

i n f o

Article history: Received 25 May 2012 Received in revised form 11 September 2012 Accepted 8 March 2013 Available online 22 March 2013 Keywords: A. Polymer–matrix composites (PMCs) A. Particle-reinforcement B. Strength C. Analytical modelling

a b s t r a c t Understanding the reinforcing mechanisms should be meaningful for preparation of new polymer composites. The reinforcing mechanisms of the inorganic particulate-filled polymer composites were analyzed and discussed in the present paper, and concluded several reinforcing theories on the basis of the previous studies, such as interfacial adhesion reinforcing theory, filler inducing crystallization reinforcing theory, filler frame reinforcing theory, and synergistic reinforcing effect theory. The reinforcing effects should be related closely to the filler shape and size, in addition to the filler concentration and dispersion in the matrix. Consequently, to describe accurately the reinforcing mechanisms of the composites, two or more reinforcing theories should be used for the actual composite system, and one of among them should be usually as the major reinforcing mechanism. Finally, the quantitative characterization of the reinforcement was described. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction As is well known, mechanical strength is one of the main indexes of the performances for materials, it is very important for the materials used as a structure unit such as machine frame and automobile bumper. In general, mechanical strength includes tensile strength, flexural strength, compression strength, tear strength, etc. As to polymeric composites, the mechanical strength is usually required as high as possible under the premise of meeting the use function. Polymer filled with particulate including rigid organic and inorganic particles is an important modification method of polymeric materials [1–3]. The factors affecting the mechanical properties of the particulate-filled polymer composites are quite complicated [4–8]. The reinforcement of polymer composites is, therefore, one of important objectives of polymer modification [9–13]. The studies on reinforcing mechanisms of the particulate-filled polymer composites have been paid attention more and more, and these studies have become the focus and hot point in polymeric materials science. Because mechanical strength is related closely to modulus, the studies of the reinforcing mechanisms of particulate-filled polymer composites include increasing rigidity mechanisms. In general, there are a number of the factors affecting the mechanical properties of the particulate-filled polymer composites, such as the properties of the resin and filler and the compatibility between them, the filler shape, size, surface morphology and ⇑ Tel.: +86 02087114739. E-mail address: [email protected] 1359-8368/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2013.03.019

concentration, the dispersion and distribution of the particles in the matrix, as well as the interfacial status [11,14]. According to the shape of the filler particles, particulate fillers are mainly divided as three kinds of particles: sphere particle, sheet (block) particles, and needle (column) particles. It is found in researches that the rigid particles may increase not only the rigidity, but also the strength of filled polymeric composites, especially for sheet (block) particles and needle (column) particles. It is generally believed that the reinforcing mechanisms of the polymer composites filled with sheet (block) particles or needle (column) particles are somewhat different from the polymer composites filled with sphere particles. There are a number of the factors affecting the mechanical properties of the particulate-filled polymer composites, such as the properties of the resin and filler and the compatibility between them, the filler shape, size, surface morphology and concentration, the dispersion and distribution of the filler in the matrix, as well as the interfacial status. Consequently, there are differences in reinforcing mechanisms among various particulate-filled polymer composites. So far, the various interpretations on the reinforcing mechanisms and increasing rigidity of particulate-filled polymer composites have been proposed, but the reinforcing theories which are widely recognized have not been formed. In previous work, Liang and his colleagues measured the tensile strength several inorganic particulate-filled polymer composites, such as glass bead filled low density polyethylene composites [1–3], polypropylene composites filled with calcium carbonate (CaCO3) [4], glass bead filled polypropylene composites [5,6], acrylnitrile–butadiene–styrene copolymer (ABS) composites [7] and hollow glass bead filled

225

J.-Z. Liang / Composites: Part B 51 (2013) 224–232

polypropylene composites [8], high density polyethylene composites filled with mica [9], carbon black-filled high density polyethylene antistatic composites [10], diatomite filled polypropylene composites [11], polypropylene composites filled with aluminum hydroxide (Al(OH)3) and magnesium hydroxide (Mg(OH)2) [13]. They studied the characterization of the tensile mechanical properties of particulate-filled polymer composites [5,12,15], the interface and interfacial stress and characterization of particulate-filled polymer composites [16–22]. It is generally believed that the reinforcing effect of particulate filled polymer composites depends, to a great extent, upon whether the filler particles can modify the matrix resin to form the appropriate aggregation structure, such as the grain size and the crystallization degree. It was found in experiments that the crystallization degree of the composites increased with increasing the filler content, especially for crystalline polymers, and the mechanical strength and the Young’s modulus increased correspondingly in this case [23,24]. That is, the inorganic particles play a heterogeneous nucleation in the matrix resin, resulting in enhancing the crystallization capability of these filled systems [25,26]. This indicates that the aggregation structure of polymeric materials will be changed due to adding inorganic particles into the polymer. In addition, the filler particles in the matrix will hinder to a certain extent the movement of the macromolecular chains. Similarly, it will be beneficial to improving the strength and rigidity of the filled composite systems. In otherwards, the inorganic particles may also play the role of a framework in the matrix, leading to improving the strength and rigidity of the composites. The objectives of the present paper are to elucidate the reinforcing theories and mechanisms as well as to make the quantitative description of reinforcement for inorganic particulate-filled polymer composites. 2. General description of reinforcing theories On the basis of analyzing comprehensively the above studying results and the correlation literature, several reinforcing theories of particulate-filled polymer composites may be concluded as follows: (1) interfacial adhesion reinforcing theory; (2) filler inducing crystallization reinforcing theory; (3) filler frame reinforcing theory; and (4) synergistic reinforcing effect theory. 2.1. Interfacial adhesion reinforcing theory When polymer composite is bearing load, the stresses taken by the matrix and filler are transferred through the interface between them, especially for the particulate filled polymer composites. Therefore, interfacial adhesion reinforcing theory believes that the reinforcement of the particulate filled polymer composites depends upon the increase of the interfacial adhesion strength. In other words, the higher the interfacial adhesion strength, the better is the reinforcing effect of the polymer composites. Under the same interfacial adhesion strength, the larger the interfacial area of the fillers, the better is the reinforcing effect of the polymer composites. Turcsanyi and his co-workers [17] considered the filling property of inorganic particles and the case of weak interfacial adhesion, and proposed following expression:

ryc ¼ rym

1  /f 1 þ 2:5/f

For the particulate filled polymer composites with certain interfacial adhesion strength, Turcsanyi and his co-workers [17] proposed an empirical formula with covering a wide range:

ryc ¼ rym

1  /f expðB/f Þ 1 þ 2:5/f

where B is the parameter related to interfacial adhesion strength. When B is less than 1, the interfacial adhesion is weak; when B is between 1 and 3, the composite has certain interfacial adhesion strength; the interfacial adhesion strength is strong as B is than 3, and the tensile strength increases with increasing the filler volume fraction in this case.For the particulate filled polymer composites with certain interfacial adhesion strength (1 < B < 3), the interfacial layer may transfer a part of stress, and the interfacial debonding phenomenon between the filler and matrix may be taken place in the meanwhile. Liang et al. [5,15,18] proposed an interfacial adhesion angle (h) concept, and established an interfacial debonding model based on the simple cubic stacking hypothesis, as shown in Fig. 1. On the basis of this model, they derived a new tensile strength equation of particulate filled polymer composites as follows:

ryc ¼ rym ð1  1:21 sin2 h  /2=3 f Þ

ð3Þ

Liang and Wu [19] investigated the effects of the glass bead (GB) surface treatment on the tensile strength of the filled polypropylene (PP) composites. In this work, the composite filled with the glass bead surface treated with silane coupling agent is called as PP/GB1, while composite filled with the glass bead surface untreated is called as PP/GB2. They found that the tensile strength of the PP/GB1 system decreased gently with an increase of the GB volume fraction, while the tensile strength of the PP/GB2 system decreased relatively obviously with increasing the GB volume fraction (see Fig. 2). Under the same concentration, the tensile strength of the PP/GB1 system is higher than that of the PP/GB2 system, and the difference between them is enlarged with the increase of the filler loading. This indicates that the surface treatment of the glass beads is beneficent to improve the interfacial adhesion status between the matrix and filler. As a result, the tensile strength of the PP/GB composite is enhanced properly. 2.2. Filler inducing crystallization reinforcing theory It was found in experiments that inorganic filler added to the polymer will play a heterogeneous nucleation [23–26]. Therefore, the crystallization properties of crystalline polymer will be changed after it is filled with inorganic particles. For example, the supercooled degree of particulate-filled polymer composites will

ð1Þ

where ryc and rym are the tensile yield strength of the composite and matrix, respectively. /f is the filler volume fraction.

ð2Þ

Fig. 1. Interfacial debonding model.

226

J.-Z. Liang / Composites: Part B 51 (2013) 224–232

The above discussion indicates that the reinforcement of polymer composites is closely related to the crystallinity of the matrix resin, while the crystallization degree of the matrix resin depends upon the competition between the filler particles taking the effect of heterogeneous nucleation in the matrix and the interaction between inorganic particles and the matrix such as polymer molecular chains restricting the macromolecules movement.

40 PP/GB1 PP/GB2

30

25

2.3. Filler frame reinforcing theory

20

15

0

2

4

6

8

10

12

14

16

18

20

φf (%) Fig. 2. Correlation between tensile strength and filler volume fraction of PP/GB composites.

increase with an increase of inorganic particles, but it is lower than that of unfilled resin, this indicates that the adding of inorganic particles will make the filled polymer to be easy crystallization. When polymer is filled with a small quantity of inorganic particles, the supercooled degree is low. This illustrates that as polymer is filled with small quantity inorganic particles, the melt is easy to form crystal nucleus during cooling, the crystallization accelerating effect of the polymer is maximum in this case, and the crystallization speed is the fastest. The crystallization speed of the composite decreases correspondingly with increasing gradually the filler content, but the crystallization speed is faster than the unfilled resin. Liang [24] investigated the nanometer calcium carbonate (nanoCaCO3) on the crystallization behavior of filled polyphenylene sulfide/glass fiber (PPS/GF) composites, and found that the crystallization degree of the composites increased with an increase of the nano-CaCO3 weight fraction; while the variation of the crystallization degree of the composites tended to smooth or somewhat reduction with further increasing the nano-CaCO3 weight fraction. This may be explained as follows: on the one hand, the interaction between inorganic particles and polymer molecular chains restricts the macromolecules movement, the molecular chains participated in the crystallization decrease relevantly, leading to reduction of the crystallinity of the composites; on the other hand, inorganic particles as a nucleating agent may improve the crystal structure of the polymer, resulting in increase of the crystallinity of the composites. It is generally believed that the increase of crystallinity is beneficial to improve the rigidity or to enhance the strength of polymer materials. Consequently, the filler inducing crystallization reinforcing theory of particulate-filled polymer composites may be described as follows: when crystal polymer is filled with inorganic particles, the filler particles take the effect of heterogeneous nucleation in the matrix, the crystallinity is increased correspondingly, resulting in the increase of the strength and rigidity of the composite systems and up to the effects of reinforcement and increasing rigidity. On the other hand, even though inorganic particles as nucleating agent may improve crystal structure and may increase crystallization degree, at the same time, due to the interaction between inorganic particles and polymer molecular chains restricts the macromolecules movement, the molecular chains participated in the crystallization decrease relevantly, leading to reduction of the crystallinity of the composites. Hence, this kind of the effects of reinforcement and increasing rigidity take place usually in the case of the polymer composites filled with low concentration of inorganic particles.

The theory of filler frame reinforcing and increasing rigidity in particulate filled polymer composites is similar to the theory of filler frame reinforcing and increasing rigidity of the sandstone in concrete. In general, the modulus of inorganic particles is higher or much higher than that of resins [27,28]. When polymer is filled with inorganic particles, the fillers will limit, to a certain extent, the movement of macromolecular chains, leading to increase of deformation difficulty of the composite systems. When the composite materials are under loading, the stresses are shared and transferred by the matrix and filler, resulting in enhancing obviously the strength and rigidity of polymer composites. In other words, inorganic particles in the matrix play the role of cytoskeleton. Liang and Wu [19] investigated the influence of the surface treatment of glass beads (GBs) on the tensile elastic modulus of the filled polypropylene (PP) composites, and found that the relative Young’s modulus of the PP/GB composites increased nonlinearly with the glass bead volume fraction, even though for the glass bead with untreated surface filled PP composite system, as shown in Fig. 3. 2.4. Synergistic reinforcing effect theory As mentioned above, the studies on the reinforcing theories are relatively weaker than the toughening theories of the particulate filled polymer composites. Hence, there have been fewer comprehensive descriptions on reinforcing mechanisms so far, even though various explanations for reinforcing mechanisms of the particulate filled polymer composites have been proposed. On the basis of the previous studies, the above three reinforcing theories are induced. That is, interfacial adhesion reinforcing theory, filler inducing crystallization reinforcing theory and filler frame reinforcing theory. These reinforcing theories may explain better the reinforcing mechanisms of the particulate-filled polymer composites under given conditions.

1.25 1.20

PP/GB1 PP/GB2

1.15 1.10

ER

σ yc (MPa)

35

1.05 1.00 0.95 0.90 0.85

0

2

4

6

8

10

12

14

16

18

20

φf (%) Fig. 3. Relationship between relative elastic modulus and filler volume fraction PP/ GB composites.

227

J.-Z. Liang / Composites: Part B 51 (2013) 224–232

However, the factors affecting the reinforcing mechanisms of the particulate-filled polymer composites are complex. In fact, the reinforcing mechanisms of the particulate-filled polymer composites is usually not singular, while the reinforcing mechanisms are possible twice even triple. In other words, the reinforcing effects may be provided by multiple factors, this is the synergistic reinforcing effect theory. For instance, as to spherical particle filled polymer composite, owing to the interfacial adhesion between the filler and matrix is relatively weak, the major reinforcing mechanisms should be the results of joint actions by the filler inducing crystallization reinforcing effect and the filler frame reinforcing effect, while the interfacial adhesion reinforcing mechanism might be less important. For polymer composites filled with sheet (block) particles or needle (column) particles, owing to relative strong the interfacial adhesion between the resin matrix and particles, the major reinforcing mechanisms should be the results of joint actions by the filler inducing crystallization reinforcing effect and interfacial adhesion reinforcing effect, while the filler frame reinforcing mechanism might be subordinate importance. It is, therefore, usually difficult to explained perfectly the reinforcing effect of inorganic particles to polymer materials only using singular reinforcing theory in fact. In other words, the above reinforcing theories can be combined according to specific situation including composite type, so as to interpret more accurately the reinforcing mechanisms of the composite system. In view of this, to realize the synergistic reinforcing effect of the filler in the resin matrix, different type of inorganic particles can be selected according to the requirement of engineering application when polymer composite is designed, to play each reinforcing effect of these fillers, thus to reach synergistic reinforcing effects. Liang [29–31] prepared respectively PPS/GF binary composite and PPS/GF/ nano-CaCO3 ternary composite, and measured the mechanical properties including tensile, impact and flexural properties at room temperature. The results showed that the mechanical properties of the PPS/GF/nano-CaCO3 ternary composite were better than those of the PPS/GF binary composite. Pei and his colleagues [32] found that there were strong nanocomposite reinforcement effects in polyurethane elastomer even though at low volume fraction of cellulose nanocrystal. 3. Characterization of reinforcing mechanisms In general, rigid particles including two kinds: rigid organic particles and rigid inorganic particles. The reinforcing mechanisms and increasing rigidity mechanisms of both rigid organic particles and rigid in organic particles are similar. As most inorganic particle are rigid, the reinforcing mechanisms and increasing rigidity of polymer/inorganic particles composites are emphasized to discuss in the present paper. As mentioned above, on the particle shape, the inorganic particles used usually as filler in polymer industry have sphere particles, sheet (block) particles, needle (column) particles, etc. In general, there are somewhat differences in reinforcing mechanisms for filled polymer composites among these fillers. 3.1. Polymer/inorganic spherical particle composites Inorganic spherical particle is a kind of common filler used in polymer industry. Glass bead, including solid and hollow, is a typical inorganic spherical particle, some ultra fine or nanometer inorganic particles may be considered roughly as spherical particles. It is generally believed that under the same interfacial adhesion strength, the larger the interfacial area of the filler is, the better is the reinforcing effect of the filled polymer composites. When the dispersion of the inclusions in the matrix is uniform, the interfacial area is equal to the sum of the surface area of the filler

particles.Suppose that d is as the diameter of sphere particle, then the surface area (AS) of the spherical particle can be expressed as: 2

AS ¼ p d

ð4Þ

Comparing to other inorganic particles, the surface area of sphere particle is the smallest. That is, the interfacial area between the resin matrix and sphere particle is the smallest. In addition, it can be seen from Fig. 1 that the tensile stress in the sphere particle-filled polymer composite is transferred through the interface between the arc surface of the particle and the matrix, and the interface is roughly perpendicular to tensile load, and the interfacial debonding will be relatively easy to take place. Hence, the reinforcing effect of inorganic sphere particles in polymer composites is relatively weak. It was found in researches that the increasing rigidity effect of inorganic sphere particles to polymer was significant, such as glass bead filled polypropylene [5,6,15,18], glass bead filled low density polyethylene [1–3], hollow glass bead filled polyvinyl chloride resin (PVC) [33], and hollow glass bead filled acrylonitrile butadiene styrene (ABS) [7]. Moreover, after the surface of inorganic sphere particles was treated suitably, the tensile strength of the filled composite system was some improved at low filler concentration [9]. Considering the factors affecting the Young’s modulus of sphere particulate filled polymer composites, such as the particle diameter distribution and shape as well as interfacial adhesion, Liang et al. [5,15,18] proposed following equation:

" Ec ¼ Em 1 þ

s¼

k/f ðm  1Þ 1 þ ð1  /f Þðm  1Þs

#

7  5m m 15ð1  mm Þ

ð5Þ

ð6Þ

Ef , Em

where m ¼ Ef, Em and Ec are respectively the Young’s modulus of the filler, matrix and composite, k is the parameter related to the particle diameter distribution and shape as well as interfacial adhesion. Summary of above mentioned, the reinforcing effect of the inorganic sphere particle-filled polymer composites is relatively weak, especially when the interfacial adhesion strength between the filler and matrix is weak. In this case, the reinforcing effect and increasing rigidity effect are mainly attributed to the induced crystallization effect and frame effect of the particles in the matrix. In other words, when the interfacial adhesion strength between the filler and matrix is weak, the reinforcing mechanisms of the inorganic sphere particle-filled polymer composites may be explained using the filler inducing crystallization reinforcing theory and the filler frame reinforcing theory. As stated above, there is certain influence of inorganic filler size on the mechanical properties of the filled polymer composites. Landon et al. [34] considered the effect of the particle size on the tensile strength of the filled systems, and proposed a semi-empirical expression:

ryc ¼ rym ð1  /f Þ  kð/f Þd

ð7Þ

where k is the slope of the curves of the tensile strength of composite versus average filler diameter (d), ryc and rym are the yield tensile strength of the composite and the matrix, respectively. On the basis of the previous studies and the predecessors’ work, Liang and Li [11] derived a new tensile strength formula of the inorganic sphere particle-filled polymer composites as follows:

h i nh i 1  /f 1 exp 1 þ r f ð1  /fc Þ3  1 qf Af 1 þ 2:5/f " # ) 2 1 þ 2:5/fc /f  lnð1  1:21/3fc Þ þ ln 1  /fc

ryc ¼ rym

ð8Þ

228

J.-Z. Liang / Composites: Part B 51 (2013) 224–232

where qf is the filler particle density, Af is the specific surface area of the filler particles, /fc is the critical volume fraction of the filler particles, rf is the particle radius. It may be found by comparing Eqs. (7) and (8) that Eq. (7) is simple but it contains a parameter k which is determined through experiments; while Eq. (8) may be directly used to estimate the tensile strength of composites as soon as the property parameters of the materials are known. 3.2. Polymer/inorganic sheet particle composites Inorganic sheet (block) particle or flaky particle is also a kind of common filler used in polymer industry. The typical inorganic sheet (block) particles are mica, talcum powder, clay, etc. Fig. 4 shows the element mechanical model of the flaky particle filled polymer composites. It may be observed that when inorganic flaky particle is oriented along the loading direction, the stress transferred of the interface between the four side wall of the particle and matrix is the maximum. In other words, the reinforcing effect along this direction should be the best. If the length, width and thickness of inorganic flaky particle are respectively set as l, w and d, then the surface area of the particle may be expressed as:

AS ¼ 2ðld þ wd þ lwÞ

ð9Þ

To compare conveniently, if suppose d = d and l = w, then Eq. (9) can be rewritten as

AS ¼ 4ld þ 2l

2

ð10Þ

If further, let l = 2d, then Eq. (10) may be adapted as 2

AS ¼ 16d

ð11Þ

It can be seen by comparing Figs. 1 and 4 that the stress transfer way through the interface of the two polymer composite systems is different: the stress transfer of the inorganic sphere particle filled polymer composite system is made through the interface between the arc surface of the particle and the matrix, and the interface is roughly perpendicular to tensile load direction; while the stress transfer of the inorganic flaky particle filled polymer composite system is made through the interface between the four side walls of the particle and matrix, and the interfaces are parallel to the tensile load direction, in addition to the stress transfer is made through the interface between the top and bottom surfaces of the particle which is perpendicular to tensile load direction and the matrix. It may be known by comparing Eqs. (4) and (11) that the surface area of flaky particle is more than that of spherical particle under the same particle volume. That is, the interfacial area between the flaky particle and the resin matrix is relatively large. Consequently, the reinforcing effect of the inorganic flaky particles in polymer composites is relatively strong under the same interfacial

Fig. 4. Element mechanical model of polymer/flaky particle composites.

Fig. 5. Dependence of tensile strength on filler weight fraction of PAEK/mica composite [37].

adhesion status. Moreover, the difference in strength at the direction between length and breadth is insignificant due to both two sides of the flaky particle is relatively large, while there is some different in strength with the width direction. The experimental results showed that the reinforcing effect and increasing rigidity effect of the inorganic flaky particles in polymer composites are significant [35,36]. Gan and his colleagues [37] studied the mechanical properties and friction behavior of a mica-filled polyaryl ether ketone (PAEK) composite, they found that the tensile strength of the composite with mica surface treatment is higher than that of the mica surface untreated composite system, as shown in Fig. 5. Osman and his co-workers [38] investigated the reinforcement of polydimethylsiloxane (PDMS) networks by mica flake, and compared the reinforcing effect of the fillers with different shape and size, the result is shown in Fig. 6. Where, the mica particle size: mica fines > R180 > SX400. It may be found that the tensile strength of the reinforced PDMS composites increases nonlinearly with an increase of the filler volume fraction. Relatively, the reinforcing effect of the glass bead filled system is insignificant. On the basis of the hypothesis of uniform dispersion of inorganic flaky particles in resin matrix, the concept of the interfacial strength factor is introduced, a relative tensile strength equation of inorganic flaky particulate filled polymer composites can be derived [39,40]:

rR ¼ 1 þ

 1=3 1 2=3 ½2K I ðf þ 1Þ  1/f f

ð12Þ

Fig. 6. Ultimate strength of PDMS composite filled with different fillers [38].

J.-Z. Liang / Composites: Part B 51 (2013) 224–232

229

3.0 by treated mica by mica

2.5 2.0

Equation (12)

σR

1.5 1.0 0.5 0.0

0

4

8

12

16

20

24

28

32

φf (%) Fig. 7. Relative tensile strength of PAEK/mica composite.

Fig. 9. Sketch of mechanical element of polymer/inorganic needle (column) particle composite.

where KI is the interfacial strength factor, f is the particle width-tothickness ratio, f = l/d. Evidently, when the particle width-to-thickness ratio is constant, the higher the interfacial strength is, the more significant is the reinforcing effect of the filled polymer composites. As the interfacial strength is constant, the tensile strength of the inorganic sheet (block) like particulate-filled polymer composites increases with an increase of the particle width-to-thickness ratio. According to the physical property data provided in Ref. [37], the relative tensile strength of the PAEK/mica composites is estimated using Eq. (12), then the estimations are compared with the experimental measurement from Ref. [37], and the results are shown in Fig. 7. It can be seen that the relative tensile strength of composites increases nonlinearly with increasing the mica volume fraction, and good agreement is showed between the predictions and the measured data. According to the physical property data provided in Ref. [38], the relative tensile strength of the PDMS/mica composites is estimated using Eq. (12), then the estimations are compared with the experimental measurement from Ref. [38], and the results are shown in Fig. 8. It can be seen that the relative tensile strength of composites increases nonlinearly with increasing the mica volume fraction, and good agreement is showed between the predictions and the measured data. Summary of above mentioned, the reinforcing mechanisms and increasing rigidity mechanisms of sheet (block) particulate filled polymer composites may be explained using the above theories,

6 mica fines R180 SX400

5

σR

4 Equation (12)

3 2 1 0

0

5

10

15

20

25

30

φ f (%) Fig. 8. Relative tensile strength of PDMS/mica composite.

35

that is, the interfacial adhesion reinforcing theory, the filler inducing crystallization reinforcing theory, and filler frame reinforcing theory. Among them, the reinforcing effect in the sheet (block) particulate filled polymer composites should be the interfacial adhesion reinforcement between the particle and matrix, and should be as the major reinforcing mechanism. 3.3. Polymer/inorganic needle particle composites Similarly, inorganic needle (column) particle is also a kind of common filler used in polymer industry. Typical inorganic needle (column) particles have wollastonite, tremolite, asbestos, fibrous sepiolite, short fiber, etc. Fig. 9 shows the sketch of mechanical element of polymer/inorganic needle (column) particle composite. If the length and diameter of inorganic needle (column) particle are respectively denoted as l and d, then the surface area of the particle may be expressed as: 2

AS ¼ p d



l 1 þ d 4

 ð13Þ

In general, the length-to-diameter ratio of inorganic needle (column) particle is more than 1 (l/d > 1). Similarly, if let l = 2d, the Eq. (13) can be rewritten as

AS ¼

9 2 pd 4

ð14Þ

It is known by comparing with Eq. (4) that the surface area of the inorganic needle (column) particle is larger than that of the inorganic sphere particle under the same particle diameter. That is, the interface between the inorganic needle (column) particle and matrix is relatively large. If the inorganic needle (column) particle orients along the tensile load direction, then the stress transfer of the filled polymer composite system is made through the interface between the side walls of the particle and matrix, and the interfaces are parallel to the tensile load direction, besides the stress transfer is made through the interface between the top and bottom surfaces of the particle which is perpendicular to tensile load direction and the matrix, as shown in Fig. 9. Therefore, the reinforcing effect of the polymer composites is relatively strong at the orientation direction of the inorganic needle (column) particles, while the reinforcing effect is relatively weak at the direction is perpendicular to tensile load direction. In other words, the physical and mechanical properties of the inorganic needle (column) particulate filled polymer composites present obvious anisotropy.

230

J.-Z. Liang / Composites: Part B 51 (2013) 224–232

It was found in researches that the reinforcing effect and increasing rigidity effect of the inorganic needle (column) particulate filled polymer composites were significant [41,42]. Wang and his colleagues [41] studied properties of PA6-PP-wollastonite composite compatibilised by PP-graft-maleic anhydride prepared via pan milling, and found that the mechanical properties of the composite were better when the weight fraction of the surface treated wollastonite particles was 30%. Comparing with the particle surface untreated composite system, the tensile strength increased from 54.6 MPa to 58.6 MPa, the notched impact strength increased from 29.4 J/m to 48.7 J/m. Li and Dou [42] investigated the effects of malonic acid treatment on crystal structure, melting behavior, morphology, and mechanical properties of isotactic poly(propylene)/wollastonite composites, the results showed that the compatibility between the matrix and filler was good, and the b-crystal type increased, hence the tensile strength, flexural modulus and impact strength of the composite systems were improved. From the above discussed, comparing with the inorganic sphere particles and needle (column) particles, the surface area of the inorganic sheet (block) particles or flaky particles is the largest, i.e. the interfacial area between the particle and matrix is the largest. Hence the reinforcing effect of the inorganic sheet (block) particulate filled polymer composites is the most significant under the same conditions, while the inorganic needle (column) particulate filled polymer composites is the second. 4. Characterization of interfacial adhesion strength As stated above, the mechanical properties of polymer composites depend, to a certain extent, upon the interfacial adhesion strength. That is, the interfacial strength depends majorly upon the interfacial adhesion strength. The interfacial adhesion strength is an important parameter for characterization of the interfacial properties of particulate-filled polymer composites, and it may be characterized by the interaction parameter and interfacial adhesion angle.

" h ¼ arcsin

1  rrmc

#1=2 ð17Þ

1:21/2=3 f

The value of h may be estimated applying Eq. (17) from the tensile experimental data. Similarly, the values of h may also be determined by means of the diagram method. Let

P¼

ryc 1 rym

ð18Þ

where the parameter P describes the correlation between the tensile strengths of the composite and matrix, and it can be determined from the tensile tests of the composites. Thus one may plot P against /2=3 and construct these lines to estimate the value of h. If f parameter a represents the line slope, then

h ¼ arcsin

rffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a ¼ arcsin 0:83a 1:21

ð19Þ

4.3. Relationship between measured B and h On the basis of the theoretical model as discussed above, one might conclude that the relationship between the interfacial interaction parameter and the interfacial adhesion angle is a negative interrelation. To investigate further the correlation between the two interfacial adhesion strength parameters, the interfacial interaction parameter and the interfacial adhesion angle are calculated based on the mechanical property data of PP/nano-CaCO3 composites reported respectively by Chan et al. [44] and Yang et al. [45]. To describe directly the relationship between the theoretical calculated and measured for B and h, we plot B against h, namely B is as the ordinate and h is as the abscissa, and the results are shown in Fig. 10. It may be seen that the B decreases roughly linearly with increasing h, namely the relationship between them is negative interrelation. According to the least square theory, it is found by means of the linear regression analysis of the data that the relationship between the B and h may be expressed as follows:

B ¼ 3:75  0:04h

ð20Þ

4.1. Interfacial interaction parameter

where the correlation coefficient R is equal to 0.9826.

From Eq. (2), the interfacial interaction parameter can be expressed as [43]:

4.4. Contact angle

1 B¼ ln /f

"

ryc ð1 þ 2:5/f Þ rym ð1  /f Þ

# ð15Þ

Thus, the interfacial interaction parameter may be estimated using Eq. (15) based on the tensile experiments of polymer composites. Moreover, the interfacial interaction parameter may be estimated using the graphic method. That is, one may define a parameter Q according to Eq. (2), which is given by:

Q¼

ryc

In addition to the interfacial adhesion strength, the contact angle between the filler and matrix is also an important parameter charactering the interfacial adhesion strength of polymer composite. The bigger the contact angle between the filler and matrix, the better is the invasion. Yusoff and his colleagues [46] researched the

3.0 2.5

where the parameter Q describes the correlation among the tensile strengths of the composite and matrix, as well as the filler volume fraction, and it can be determined from the tensile tests of the composites. Thus one may plot ln Q against /f and construct these lines to estimate the value of B, namely, the slope of the lines is the interfacial interaction parameter under the experimental conditions.

2.0

rym ½ð1 þ 2:5/f Þ=ð1  /f Þ

B

ð16Þ

Reference [45] Data of the study Theoritical data Reference [44]

1.5 1.0 0.5 0.0

4.2. Interfacial adhesion angle

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 ο

From Eq. (3), the interfacial interaction parameter can be expressed as [43]:

θ() Fig. 10. Relationship between B and h .

J.-Z. Liang / Composites: Part B 51 (2013) 224–232

effect of contact angle and surface free energy on the mechanical properties of chemically treated and untreated kaolin filler polypropylene composites. They found that the treated samples had stronger mechanical properties than untreated PP-kaolin composite. That is, high contact angle will have lower surface energy which will then lead to an increase in compatibility of kaolin filler in the composite, and increase in compatibility will increase the mechanical property, which is portrayed by treated PP-kaolin composite samples.

5. Characterization of interfacial layer 5.1. Effect of interfacial layer on reinforcement The interfacial layer between the filler and matrix is related closely with the mechanical properties of polymer composites, and the interfacial layer thickness is one of major parameters for characterizing the interlayer structure and plays an important role for the mechanical properties of composites. Esmaeili et al. [47] studied a ternary composite system by presenting an interface layer around the particle, and demonstrated that a soft interlayer changes the shear band pattern around a hard particle and therefore, leading to changes in macroscopic resistance, mean stress and normal stress. The results obtained suggested that a suitable combination of the stiffness of the particles and interfaces leaded to an improvement in the mechanical characteristics of the blended polymer. Therefore, the mechanisms of interlayer generation as well as the structure and property of the interlayer in polymer composites have been paid extensively attention during the past 20 years [48–50]. 5.2. Determination of interfacial layer thickness Because the interlayer thickness is very thin, how to determine it is one of major questions faced by the scientists and engineers of polymer materials today. The determination methods of the interlayer thickness are mainly divided as three kinds: (1) instrument measurement; (2) fractal analysis based on electron micrograph photograph; and (3) estimation by using mathematical model. In 1999, several researchers applied some advanced instruments and techniques to measure or observe the interlayer of polymer composites, such as attenuated total reflectance FTIR technique [51], atomic force microscope (AFM) [52] and pressing trace instrument, and so on. However, the measurement precision for the interlayer by these apparatus should be further studied. Kozlov and Lipatov [53] investigated two types of composites based on poly(hydroxy ether) and graphite with various amounts of a filler, and estimated the characteristics of adhesion and interfacial layer, including its thickness and tensile strength and interdependence between these values and adhesion, on the basis of the theory of irreversible aggregation, cluster theory of the polymer structure and fractal analysis. The results showed that all important characteristics of adhesion, interfacial layer and mechanical properties were interconnected with the difference between fractal dimensions of the surface of the aggregates of filler particles and of a polymer matrix, whose structure was distorted under the influence of the filler surface. 5.3. Characterization of interfacial layer thickness Because the factors affecting the interlayer are quite complicated, it is difficultly to measure accurately the interfacial layer thickness under general conditions. Therefore, most of the studies on the quantitative analysis or prediction of the layer thickness are

231

limited to numerical analysis or under critical conditions [48,50– 52,54,55]. More recently, on the basis of a simplified model of interlayer, Liang [56] derived an expression for estimating the interlayer thickness (di) as follows:

di ¼

o  1=3 df n 1 1  /f ð1  aÞ =ð1  /f Þ 2

ð21Þ

where df is the diameter of the filler particle. Parameter a represents the weigh constant of the interlayer volume fraction. Eq. (21) describes quantitatively the relationship among the interlayer thickness, filler particle diameter and the fraction of the interlayer. 6. Conclusions The studies on the reinforcing theory were weak relatively to the studies on the toughening theory for the inorganic particulate filled polymer composites. There have been a few comprehensive descriptions of reinforcing mechanisms so far, even though various explanations for reinforcing mechanisms of the inorganic particulate filled polymer composites have been proposed. On the basis of the previous studies, the reinforcing mechanisms of the inorganic particulate-filled polymer composites were analyzed in the present paper, and several reinforcing theories were concluded as follows: (1) interfacial adhesion reinforcing theory; (2) filler inducing crystallization reinforcing theory; (3) filler frame reinforcing theory; and (4) synergistic reinforcing effect theory. The filler shape and size would affect directly the reinforcing effects of the filled polymer composites, in addition to the filler concentration and dispersion in the matrix as well as interlayer. In general, using singular reinforcing theory was not enough to explain correctly the reinforcing mechanisms of the inorganic particulate filled polymer composites. Hence, to describe accurately the reinforcing mechanisms, two or more reinforcing theories should be usually used, and one of among them should be as the major reinforcing mechanism. References [1] Liang JZ, Li RKY, Tjong SC. Tensile fracture behaviour and morphological analysis of glass bead filled low density polyethylene composites. Plast Rubber Compos Process Appl 1997;26:278–82. [2] Liang JZ, Li RKY, Tjong SC. Morphology and tensile properties of glass bead filled low density polyethylene composites. Polym Test 1997;16:529–48. [3] Liang JZ, Li RKY, Tang CY, Wong TT. Tensile yield behaviour of glass bead filled LDPE composites. Met Mater 1998;4:265–8. [4] Liang JZ, Tang CY, Li RKY, Wong TT. Mechanical properties of polypropylene/ CaCO3 composites. Met Mater 1998;4:616–9. [5] Liang JZ, Li RKY. Mechanical properties and morphology of glass bead filled polypropylene composites. Polym Compos 1998;19:698–703. [6] Tang CY, Liang JZ, Yung KC, Li RKY, Tjong SC. Mechanical properties of glass beads filled polypropylene composites. Key Eng Mater 1998;145–148:823–8. [7] Liang JZ. Tensile and flexural properties of hollow spheres-filled ABS composites. J Elast Plast 2005;37:361–70. [8] Liang JZ. Tensile properties of hollow glass bead-filled polypropylene composites. J Appl Polym Sci 2007;104:1697–701. [9] Liang JZ, Yang QQ. Studies of mechanical, thermal and flow properties of HDPE/ mica composites. J Thermoplast Comput Mater 2007;20:225–36. [10] Liang JZ, Yang QQ. Mechanical properties of carbon black-filled high density polyethylene antistatic composites. J Reinf Plast Compos 2009;28:295–304. [11] Liang JZ, Li A. Inorganic particle size and content effects on tensile strength of polymer composites. J Reinf Plast Compos 2010;29:2744–52. [12] Liang JZ, Li RKY. Prediction of tensile yield strength of rigid inorganic particulate filled thermoplastic composites. J Mater Process Technol 1998;83:127–30. [13] Liang JZ. Tensile properties of polypropylene flame retardant composites. Polym Bull 2012;68:803–13. [14] Liang JZ, Li RKY. Measurement of dispersion of glass beads in PP matrix. J Reinf Plast Compos 2001;20:630–8. [15] Liang JZ, Li RKY, Tjong SC. Tensile properties and morphology of PP/EPDM/ glass bead ternary composites. Polym Compos 1999;20:413–22. [16] Pukanszky B, Van Es M, Maurer FHJ, Vörös G. Micromechanical deformations in particulate filled thermoplastics: volume strain measurements. J Mater Sci 1994;29:2350–8.

232

J.-Z. Liang / Composites: Part B 51 (2013) 224–232

[17] Turcsanyi B, Pukanszky B, Tudos F. Composition dependence of tensile yield stress in filled polymers. J Mater Sci Lett 1988;7:160–2. [18] Liang JZ, Li RKY. Effect of filler content and surface treatment on the tensile properties of glass-bead-filled polypropylene composites. Polym Int 2000;49: 170–4. [19] Liang JZ, Wu CB. Effects of glass bead content and surface treatment on mechanical properties of polypropylene composites. J Appl Polym Sci 2012;123:3054–63. [20] Fu SY, Feng XQ, Lauke B, Mai YW. Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate-polymer composites. Compos Part B: Eng 2008;39:933–61. [21] Tsui CP, Chen DZ, Tang CY, Uskokovic PS, Fan JP, Xie XL. Prediction for debonding damage process and effective elastic properties of glass-beadfilled modified polyphenylene oxide. Compos Sci Technol 2006;66(11–12): 1521–31. [22] Fan JP, Tsui CP, Tang CY. Modeling of the mechanical behavior of HA/PEEK biocomposite under quasi-static tensile load. Mater Sci Eng A 2004;382: 341–50. [23] Liang JZ, Li RKY, Tjong SC. Crystallization behaviour of glass bead filled low density polyethylene composites. J Appl Polym Sci 1999;71:687–92. [24] Liang JZ. Crystallization properties of glass fiber-reinforced poly(p-phenylene sulfide) nanocomposites. Polym Int 2012;61:160–5. [25] Ariffin A, Ariff ZM, Jikan SS. Evaluation on nonisothermal crystallization kinetics of polypropylene/kaolin composites by employing Dobreva and Kissinger methods. J Therm Anal Calorim 2011;103:171–7. [26] Bouza R, Marco C, Naffakh M, Barral L, Ellis G. Effect of particle size and a processing aid on the crystallization and melting behavior of iPP/red pine wood flour composites. Compos Part A – Appl Sci Manuf 2011;42:935–49. [27] Saad ALG, Dimitry OIH. Studies of particle dispersion in plasticized poly(vinyl chloride)/montmorillonite nanocomposites. J Appl Polym Sci 2012;123:1407–20. [28] Afrooz IE, Ochsner A, Rahmandoust M. Effects of the carbon nanotube distribution on the macroscopic stiffness of composite materials. Comput Mater Sci 2012;51:422–9. [29] Liang JZ. Impact toughness and flexural properties of PPS/GF/nano-CaCO3 ternary composites. Polym–Plast Technol Eng 2008;47:1227–30. [30] Liang JZ. Mechanical properties of PPS/PC/GF/nano-CaCO3 hybrid composites. Polym–Plast Technol Eng 2009;48:292–6. [31] Liang JZ, Liu GS. Effects of nano-CaCO3 content and surface treatment on tensile properties of PPS/GF ternary composites. Polym–Plast Technol Eng 2009;48:1025–9. [32] Pei AH, Malho JM, Ruokolainen J, Zhou Q, Berglund LA. Strong nanocomposite reinforcement effects in polyurethane elastomer with low volume fraction of cellulose nanocrystals. Macromol 2011;44:4422–7. [33] Liang JZ. Tensile and impact properties of hollow glass bead-filled PVC composites. Maclom Mater Eng 2002;287:588–91. [34] Landon G, Lewis G, Boden GF. The influence of particle size on the tensile strength of particulate-filled polymers. J Mater Sci 1977;12:1605–13. [35] Bose S, Mahanwar PA. Effects of titanate coupling agent on the properties of mica-reinforced nylon-6 composites. Polym Eng Sci 2005;45:1479–86. [36] García-Martínez JM, Areso S, Collar EP. The role of a novel p-phenylen-bismaleamic acid grafted atactic polypropylene interfacial modifier in

[37] [38] [39] [40]

[41]

[42]

[43] [44] [45]

[46]

[47]

[48] [49] [50]

[51]

[52]

[53] [54]

[55]

[56]

polypropylene/mica composites as evidenced by tensile properties. J Appl Polym Sci 2009;113:3929–43. Gan D, Lu S, Song C, Wang Z. Mechanical properties and friction behavior of a mica-filled poly(aryl ether ketone) composite. Euro Polym J 2001;37:1359–65. Osman MA, Atallah A, Müller M, Suter UW. Reinforcement of poly(dimethylsiloxane) networks by mica flakes. Polymer 2001;42:6545–56. Liang JZ. Reinforcing and toughening theories of polymer composites. Guangzhou: South China University of Technology Press; 2012. Liang JZ. Estimation of tensile strength of inorganic plate-like particulate reinforced polymer composites. Polym Eng Sci 2013. http://dx.doi.org/10. 1002/pen. Wang Q, Liu CS, Chen YH. Studies on PA6-PP-wollastonite composite compatibilised by PP-graft-maleic anhydride prepared via pan milling. Plast Compos 2001;30:363–9. Li L, Dou Q. Effects of malonic acid treatment on crystal structure, melting behavior, morphology, and mechanical properties of isotactic poly(propylene)/ wollastonite composites. Polym Compos 2010;31:966–73. Liang JZ. Quantitative description of interfacial strength in polypropylene/ inorganic particle composites. Polym Compos 2011;32:821–8. Chan CM, Wu JS, Li JX, Cheung YK. Polypropylene/calcium carbonate nanocomposites. Polymer 2002;43:2981-. Yang K, Yang Q, Li GX, Sun YJ, Feng DC. Morphology and mechanical properties of polypropylene calcium carbonate nanocomposites. Mater Lett 2006;60:805. Yusoff NSM, Ahmad MSB, Akil HM, Ariffin KS, Ariffin A. Contact angle of untreated/treated kaolin and its correlation with the mechanical properties of PP-kaolin composites. J Reinf Plast Compos 2010;29:3442–9. Esmaeili N, Lu W, Tomita Y. Characterization of micro- to macroscopic responses of ternary polymer-based composite system. Adv Eng Plast Appl Pts, 1–2 Key Eng Mater 2004;274–276:313–8. Wu QS, Chen XB, Son HC. Interlayer in particulate-reinforced composite materials. J Compos Mater 1985;2:41–5. Lipatov YS. Polymer reinforcement. Toronto: Chem. Tec. Publishing; 1995. Liu ZH, Li J, Liang NG, Liu HQ. On the influence zone and the prediction of tensile strength of particulate polymer composites. J Reinf Plast Compos 1997;16:1523–33. Pangelinan AB, Mccullough RL, Keylley MJ. Attenuated total reflectance FTIR analysis of surface induced molecular weight segregation. Composites, Part A 1999;30:67–74. VanLandingham MR, Dagastine RR, Eduljee RF, McCullough RL, Gillespie JW. Characterization of nanoscale property variation in polymer composite systems: 1. Experimental results. Composites Part A 1999;30:75–83. Kozlov GV, Lipatov YS. Fractal and structural aspects of adhesion in particulate-filled polymer composites. Compos Interf 2002;9:509–27. Yung KC, Wang J, Yue TM. Modeling Young’s modulus of polymer-layered silicate nanocomposites using a modified Halpin–Tsai micromechanical model. J Reinf Plast Comps 2006;25:847–61. Bogetti TA, Wang T, Vanladingham MR, Gillespie JW. Characterization of nanoscale property variation in polymer composite systems: 2. Numerical modeling. Composites Part A 1999;30:85–94. Liang JZ. Estimation of interlayer thickness in inorganic particulate-filled polymer composites. J Thermoplast Compos Mater 2011;24:777–88.