Composites: Part A 42 (2011) 1049–1059
Contents lists available at ScienceDirect
Composites: Part A journal homepage: www.elsevier.com/locate/compositesa
Influence of interfacial roughness and the hybrid filler microstructures on the properties of ternary elastomeric composites Pijush Kanti Chattopadhyay a, Narayan C. Das b, Santanu Chattopadhyay a,⇑ a b
Indian Institute of Technology, Kharagpur, India Indiana University Cyclotron Facility, Bloomington, IN 47408, USA
a r t i c l e
i n f o
Article history: Received 18 January 2011 Accepted 16 April 2011 Available online 22 April 2011 Keywords: SAXS B. Microstructures B. Electrical properties B. interface
a b s t r a c t Influences of microstructures upon the properties of epoxidized natural rubber (ENR) based composite containing nanoclay (NC) and different carbon black (CB) were analyzed based on SAXS, TEM, tensile properties, dynamic mechanical analysis, and electrical measurement. Tensile strength of CB–ENR composites depends directly on interfacial roughness of CB–ENR interfaces. In NC–CB–ENR composites, interfacial roughness was enhanced due to contribution from NC–CB interface. Such improved roughness was correlated with increased ‘Payne effect’ from binary to ternary composites. Connectivity in microstructures was realized through TEM and electrical properties (Maxwell–Wagner interfacial polarization, resistivity). In presence of NC, filler connectivity in all ternary composites was improved except for HAF–NC–elastomer composite which was due to intense ‘haloing effect’. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Various particulate polymer composites comprising of different types of fillers, such as, carbon black (CB), nanoclay (NC), silica, carbon nanotube etc., have been analyzed by different workers [1–5]. The purpose was to realize morphological characteristics in terms of interesting filler microstructure development that can be interrelated to notable electrical, mechanical, and rheological properties of the composites. Feller et al. pointed out the occurrence of the adsorption of montmorilonite platelet on CB aggregates that can be reflected in percolation threshold, storage and loss moduli [6]. Konishi and Cakmak established the formation of ‘nanounit’ comprising of primary particles of CB and NC platelets that contributes substantially in electrical properties of the composites [7]. Etika et al. put forward a theory based on ‘haloing effect’ that involves stabilization of the NC platelets by surrounding CB particles [8]. This unique microstructure development ultimately influences the electrical and mechanical properties of epoxy composites those contain both NC and CB particles. Small angle X-ray scattering (SAXS) coupled with microscopic techniques can be a better and quantitative way to determine the three dimensional filler microstructure as compared to the microscopic techniques used alone (HRTEM, SEM, Raman Imaging/Mapping etc.) [9]. Furthermore, electrical property evaluation can supplement this by providing more information about the topology of filler network structure, filler–filler connectivity etc.
⇑ Corresponding author. Tel.: +91 3222281759; fax: +91 3222282292. E-mail address:
[email protected] (S. Chattopadhyay). 1359-835X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2011.04.011
Epoxidized natural rubber (ENR), a kind of modified natural rubber, exhibits properties resembling those of polar rubbers rather than natural rubber due to polarity induced by epoxide groups. It has unique properties such as low gas permeability, good oil resistance, improved wet grip, lower rolling resistance, superior tensile and fatigue properties [10]. Therefore, ENR based composites filled with fillers like CB and NC can be utilized effectively in various industrial applications. Earlier, we reported preparation and characterization of ternary particulate ENR-25 (ENR containing 25 mol.% epoxy group) composites (CB and NC filled) which demonstrated synergistic mechanical and dynamic mechanical property development in certain compositions [11]. Moreover, judicious replacement of CB by suitable filler like NC in rubber composites is important from application point of views. In addition, the reinforcing effect of particulate fillers (CB, NC etc.) in rubber varies substantially due to different factors like size, surface characteristics, structure, and dispersion of the fillers in the rubber matrices. Rubber blends containing ENR–NC composites and variegated type of CB (ISAF and SRF) were compared based on thermal and mechanical properties. This revealed the best overall properties could be obtained for the composite containing SRF (N-774) and NC as particulate phases [12]. Outstanding interactions among ENR–NC and SRF had been proposed in favor of superior tensile strength of the system as compared to the system having ENR– NC and ISAF [12]. However, details investigation related to the possible complex microstructure development within those ternary elastomeric composites was not conducted. In the present work, ENR based binary and ternary composites have been analyzed to understand filler–filler, filler–elastomer interactions. Ternary ENR composites comprising of varying grades
1050
P.K. Chattopadhyay et al. / Composites: Part A 42 (2011) 1049–1059
of CB and particular type of NC have been analyzed by SAXS and TEM to evaluate filler microstructure characteristics including interfacial roughness and network structure. Finally, developed hybrid microstructures inside the composites and associated electrical, mechanical, dynamic mechanical properties have been interrelated. 2. Experimental 2.1. Materials Commercial grade ENR-25 (containing 25 mol.% epoxy group) used in this study was obtained from the Rubber Board, Kottayam, Kerala, India. NanomerÒ I.30E-sodium montmorillonite clay (organically modified with octadecyl amine, mean dry particle size 8–10 lm, specific gravity 1.71, minimum mineral purity 98.5%) was procured from Nanocor Corporation, USA. Different grades of furnace blacks [High abrasion furnace black, HAF (N330); Super abrasion furnace black, SAF (N110); Intermediate super abrasion furnace black (N220), and Fine extrusion furnace, FEF (N550)] were purchased from the Philips Carbon Black Ltd., Kolkata, India having the characteristics shown in Table 1. Other compounding and curing additives [e.g. N-cyclohexylbenzthiazyl sulphenamide (CBS), Tetramethyl thiuram di sulphide (TMTD), 2,2,4-trimethyl-1,2dihydroquinoline (TQ), sulphur, calcium stearate] were purchased from local suppliers (analytical grade). 2.2. Sample preparation All the rubber composites were prepared at room temperature ( 30 °C) in an open two roll mill (Schwabenthon, Berlin, Germany) of 300 mm length and 170 mm diameter. The speed of the slower roll was maintained at 18 revolutions per min with a friction ratio of 1:1.2. Initially, ENR-25 master batch was prepared by mixing calcium stearate (1.5 phr, parts per 100 g of rubber) to the raw rubber in 4 min. Thereafter, 1 phr antioxidant (TQ) was added. Later, NC, ZnO, stearic acid, CB were added in sequence. To achieve better state of dispersion, NC was added prior to the addition of CB. In fact, after NC addition, the compound was passed 3–4 times through the rollers having a tight nip gap of 1 mm. Finally, accelerators (CBS, TMTD) and sulphur were incorporated to obtain the desired rubber compounds. In all cases, the average mixing time was maintained at about 15 min. Optimum cure time (OCT) for all the composites were determined by using an Oscillating Disc Rheometer (Monsanto Rheometer 100, USA) having digital thermologger operated at 150 °C for 0.5 h maintaining a ±3° arc oscillation throughout the experiment. After mixing, the rubber compounds were left for 24 h at room temperature (25 °C) for maturation. Finally, these compounds were compression molded in the form of sheets in an electrically heated hydraulic press at 150 °C. For each
Table 1 Characteristics of various furnace blacks. Carbon black
Iodine absorption no. (g/kg)
DBP absorption no. (cm3/ (100 g))
Surface energy (cs)a
cds (mJ/m2)
Specific or polar (in benzene), Isp (mJ/m2)
270.4 235.2 196.9 134.4
120.0 103.9 85.9 75.0
Dispersive,
SAF (N110) ISAF(N220) HAF(N330) FEF (N550)
145.6 119.5 82.7 39.6
111.5 113.0 102.7 120.5
a =surface energy values were measured at 150 °C using inverse gas chromatography by Wang et al. [19].
sample, molding time was maintained according to the respective OCTs. The formulations and designations of all the ENR-25 composites are compiled in Table 2. 2.3. Small angle X-ray scattering (SAXS) SAXS was performed on compression-molded composite sheets of 1 cm 1 cm dimension having thicknesses of 1.5–2.0 mm at room temperature. X-ray (beam size = 0.2 mm in diameter) was generated with CuKa radiation from a 1.2 kW rotating anode Xray generator (007 HF, Rigaku Denki Co. Ltd., Japan) using twodimensional multi-wire detector. The sample to detector distance of 1.5 m allowed a ‘‘q range’’ from 0.0065–0.12 Å1 [q = 4p/k sin(h/2), where k is X-ray wavelength (0.1545 nm) and h is scattering angle]. The scattering intensity after subtraction of the background was circularly averaged. Finally, the unified model fitment on the experimental results was done using Igor software, USA, choosing q value within a range from 0.0065 to 0.12 Å1. 2.4. High resolution transmission electron microscopy The rubber composite samples for TEM analysis were prepared by ultra cryomicrotomy using Leica Ultracut EM FCS, Gmbh, Austria. Freshly sharpened glass knives with cutting edge of 45° were used to get cryo-sections of 50 nm thickness. Since the composites are elastomeric in nature, the sample temperature during ultramicrotomy was maintained at – 60 °C, which was well below the glass transition temperature (Tg) of ENR composites. The cryo-sections were collected and directly supported on a copper grid of 300-mesh size. The microscopic examination was performed later using a transmission electron microscope (JEOL JEM-2100, Japan) operated at an acceleration voltage of 200 kV and with a beam current of 145 lA. 2.5. Dynamic contact angle measurement To measure the contact angle and the respective surface energies of the powder sample (clay), clay pellets of 13 mm diameter were prepared using a hydraulic press. Thereafter, the pellets were undergone dynamic contact angle measurement by surface tensiometer (Dataphysics DCAT 11, Germany) at 24 °C using benzene (surface tension = 28.65 mN/m). For the polymer sample, pieces having dimensions of 7 mm 20 mm 1.8 mm were cut out from the molded sheet, and then the sample is undergone contact angle measurement. The percentage error in the measurements was limited to ±5%. 2.6. Dielectric measurement The dielectric and electrical properties of the circular composite samples were measured using a computer-controlled impedance analyzer (PSM 1735), United Kingdom. In this experiment, an alternating electric field was applied across the sample cell with a blocking electrode (aluminum foil) at a frequency range (102– 106 Hz) and temperature ranging from 30 to 100 °C. The dielectric permittivity (e0 ) were obtained as a function of frequency and temperature, respectively. The dielectric constant or dielectric permittivity (e0 ) was determined by using the following equation:
e0 ¼ C p =C 0
ð1Þ
where Cp is the observed capacitance of the sample (in parallel mode), and Co is the capacitance of the cell. The value of Co was calculated using the expression (eoA)/d, where d and A are the thickness and area of the sample, respectively. eo is the dielectric
1051
P.K. Chattopadhyay et al. / Composites: Part A 42 (2011) 1049–1059 Table 2 Designations and formulations of the ENR-25 compounds (all ingredients are measured in phr, parts per 100 g of rubber). Ingredients
ENR-25 Calcium stearate Clay ZnO Stearic acid HAF(N330) SAF (N110) ISAF (N220) FEF (N550) CBS TMTD TQ Sulphur a
Sample namea EH0N0C
EH20N0C
ES20N0C
EI20N0C
EF20N0C
EH20N15C
ES20N15C
EI20N15C
EF20N15C
EH0N35C
100.0 1.5 – 5.0 2.0 – – – – 1.0 0.2 1.0 2.2
100.0 1.5 – 5.0 2.0 20.0 – – – 1.0 0.2 1.0 2.2
100.0 1.5 – 5.0 2.0 – 20.0 – – 1.0 0.2 1.0 2.2
100.0 1.5 – 5.0 2.0 – – 20.0 – 1.0 0.2 1.0 2.2
100.0 1.5 – 5.0 2.0 – – – 20.0 1.0 0.2 1.0 2.2
100.0 1.5 15.0 5.0 2.0 20.0 – – – 1.0 0.2 1.0 2.2
100.0 1.5 15.0 5.0 2.0 – 20.0 – – 1.0 0.2 1.0 2.2
100.0 1.5 15.0 5.0 2.0 – – 20.0 – 1.0 0.2 1.0 2.2
100.0 1.5 15.0 5.0 2.0 – – – 20.0 1.0 0.2 1.0 2.2
100.0 1.5 35.0 5.0 2.0 – – – – 1.0 0.2 1.0 2.2
Sample designations are given according to the following: E = ENR, H = HAF, S = SAF, I = ISAF, F = FEF, N = Nanoclay, and C = Conventional cure.
constant of vacuum, and the value of e0 is 8.85 1012 F/m. The percentage error in the measurements was limited to ±2%.
temperature of 1 Hz and 35 °C, respectively, with the applied strain varying from 0.01% to 20%.
2.7. AC resistance
3. Results and discussion
The AC resistance was measured at 35 °C using QuadTech 7600 precision LCR meter, USA, over the frequency range 100– 2 106 Hz. The percentage error in the measurements was limited to ±4%.
3.1. SAXS
2.8. Volume resistivity The DC volume resistivity (X cm) of the sheets was measured at 35 °C using a Hewlett–Packard high resistance meter (Model 43294) coupled with a Hewlett–Packard (Model 160084) resistivity cell manufactured in USA. In this test, the applied pressure and voltage was maintained at 0.49 MPa and 1 V, respectively. The charge time for each experiment was maintained at 30 s. The percentage error in the measurement of volume resistivity was limited to ±1.5%. 2.9. Mechanical properties The usual dog-bone shaped specimens for the measurement of the mechanical (tensile) properties were punched out from the moulded sheets with ASTM Die-C. The measurement was carried out in a Hioks-Hounsfield universal testing machine (Test Equipment Ltd., Surrey, United Kingdom) with a crosshead speed of 500 mm/min at 35 °C. The stress–strain curve was plotted with Lab Tensile software, from which the tensile modulus, tensile strength, and elongation-at-break (EB) were calculated. In each case, the error corresponding to tensile modulus, tensile strength, and EB measurement were limited to ±1%, ±2%, and ±2%, respectively. 2.10. Dynamic mechanical analyses Dynamic temperature sweep experiment of all the composites was conducted under dynamic tensile mode at the frequency of 1 Hz and amplitude of about 11.0 lm using TA instruments (DMA 2980 V 1.7B) manufactured in Lukens drive, New Castle, DE. Rectangular specimens of 19 mm 6 mm 1.5 mm were subjected to sinusoidal stress (about 4 MPa), and were heated from 70 to +120 °C at a rate of 2 °C/min. Using the same instrument, dynamic strain sweep experiment of all the composites were conducted under dynamic tensile mode at a constant frequency and
All the SAXS derived plots are analyzed based on unified approach which can take into account the overlap of various morphological features in a general way. Beaucage and Schaefer described how Guinier’s law and structurally limited power laws can be derived from mutually exclusive scattering events [13]. In the simplest case, the observed scattering is a summation of two components, and the equation is the following:
q2 R2g IðqÞ G exp 3
!
" pffiffiffi #P ferf ðqRg = 6Þg3 þB q
ð2Þ
In the equation, G is called the Guinier prefactor, Rg is the radius of gyration, erf is the error function, and B is the power-law prefactor, described by the regime in which the power-law slope (P) falls. As noted above, for surface fractals, P is (6 ds), and ds is the surface fractal dimension. For a two-dimensional (2D), smooth, sharp surface, the power-law follows Porod’s law [14]. In this case, the slope of a log I, intensity, versus log q, scattering vector, plot is ‘4’. For a fractally rough surface, the power-law slope is shallower than ‘4’ following a slope of (ds 6), as described by Bale and Schmidt [15]. In Fig. 1, Eq. (2) was used to fit the experimental data from 0.006568 Å1 to about 0.12689 Å1. In this way, SAXS data for all the samples were put up for unified equation fitment, and the corresponding parameter values are depicted in Table 3. For unfilled sample (EH0N0C), the ds is recorded at 2.42. This is the lowest among all the samples. As the sample contains only 5 phr ZnO (microscopically measured average particle diameter = 50 ± 10 nm), the filler polymer interfacial area should be the lowest giving rise to the highest interfacial smoothness in the sample. Additionally, the result also signifies poor ENR–ZnO interaction and hence non-reinforcing characteristics of ZnO particles. Among solely CB filled samples, the ds value maintains the following order: ES20N0C > EH20N0C > EI20N0C > EF20N0C (Table 3). As interfacial roughness can be correlated to interaction of CB with polymer molecules [16], the lowest ds value for FEF filled sample signifies semireinforcing characteristics of FEF. In this regard, SAF offers the highest reinforcement in ES20N0C. Interestingly, though ISAF particles have the greater surface area density, HAF filled sample shows the higher interfacial roughness as compared to ISAF filled one. In
1052
P.K. Chattopadhyay et al. / Composites: Part A 42 (2011) 1049–1059
Fig. 1. Single level unified model fitment to the SAXS result for a representative sample (EH0N0C).
fact, two counteracting factors (e.g. surface area density and structure of CB) are responsible for such observation. Theoretically, both low structure and high surface area are disadvantageous in relation to degree of dispersion of CB in the composite. DBP (Di-butyl-pthalate) adsorption numbers (Table 1) reveal that ISAF contains the greater void volume and hence contains higher structure with many nodules as compared to HAF. On the contrary, ISAF has the higher surface area density as against HAF. Thus, a combined effect of two counteracting factors (e.g. surface area density and structure of CB) contributes to the dispersion of CB in the polymer. In this regard, EH20N0C can have slightly better CB dispersion as compared to EI20N0C, which results in slightly higher interfacial roughness (Table 3). It is well known that the surface roughness of CB particle is governed mainly by the population of higher energy sites like crystallite edges and slit shaped cavities. HAF (N330) has 10% of type II (amorphous carbon), III (crystallite edges) and IV (slit shaped cavities) sites, and the remaining 90% of the surface consists of graphitic planes (sp2) [17]. ISAF (N220) bears 16% of types II–IV sites, and the rest 84% constituted of graphitic planes. On the contrary, SAF has 23% of types II–IV sites, and the rest 77% constituted of graphitic planes [18]. Such energy site distribution is reflected in their respective dispersive and polar components of surface energy values (Table 1) obtained by inverse gas chromatography at 150 °C [19]. In this regard, ISAF particles (in the powder form) have a higher surface energy than HAF particles. Thus, in a composite, ISAF should be more difficult to disperse as compared HAF, which leads to more uniform HAF dispersion in the ENR matrix as compared to ISAF. This ultimately gives rise to higher interfacial roughness for EH20N0C in SAXS (Table 3).
As 15 phr NC has been added to each CB filled samples, ds values for all the CB filled samples are increased after NC addition (Table 3). In addition to ENR–CB, there exists two additional interfaces (e.g. NC–polymer and NC–CB) which can contribute to the improved ds values of the ternary particulate samples. Such improvement can be originated from difference in the surface energy values of individual components. In this regard, using dynamic contact angle measurement method, the total surface energy per unit area for NC and unfilled ENR matrix was obtained as 38.7 and 53.8 mJ/m2, respectively (with respect to benzene). Using inverse gas chromatography at 150 °C, M. Mravcakova et al. reported that the dispersive contribution to the surface energy for organomodified montmorillonite is 34.0 mJ/m2 [20]. It is known that the values of surface tensions of polymers range from 20 mJ/m2 for Teflon to 46 mJ/m2 for nylon [21]. Of course, these surface tension data was obtained using contact angle measurement (ASTM D2578). Though the surface energy measurement method is different, the results obtained are comparable to the results obtained by the earlier workers. Since, other ingredients are present in the unfilled ENR sample, the surface tension of the unfilled ENR sample may be elevated as compared to pristine ENR. As a whole, surface energy measurement for ENR, CB and NC suggests the difference in wettability of component surfaces. The difference in surface energy between NC and CB is the highest which is followed by the differences in surface energy between ENR and CB. Finally, the difference in surface energy between ENR and NC (53.8–38.7 = 15.1 mJ/m2) is observed to be the lowest among all. Since, all the system thermodynamically tends to attain minimum energy levels, the stability of the NC–CB attachment should be the highest followed by ENR–CB and ENR–NC. Therefore, in the ternary systems, the contributions of the NC–CB interface towards the total ds values (Table 3) of the composites are the highest followed by the contribution of ENR–CB and ENR–NC interfaces. Such variable extent of NC–CB interactions in ternary composites can depend on the following factors: (1) extent of ‘nanounit’ and ‘halo’ formation, (2) state of exfoliation, intercalation or aggregation of NC, (3) mutual interaction possibilities of free functional groups present both on NC and on CB surfaces, and (4) competitive adsorption potential among different phases. The higher ds values for EH20N15C and ES20N15C (2.8) can be attributed to formation of the greater interfacial area. This is again possible if more uniform dispersion of fillers can be achieved. Thus, the possibility of ‘nanounit’ and ‘halo’ formation as well as extent of exfoliation is the highest in case of EH20N15C, followed by ES20N15C. In addition, radius of gyration (Rg) values (Table 3) shows the following order: EF20N0C > EH20N0C > ES20N0C > EI20N0C. The order is almost in accordance with the decreasing CB particle sizes. The exception is the greater value for ES20N0C as compared to EI20N0C. This may be due to the higher degree of aggregation owing to the higher surface energy density in case of ES20N0C, which leads to the
Table 3 SAXS results of various composites. Sample
Rg 0
(Å A)
Rg error
G value (cm1)
G error (cm1)
Slope (P)
P Error
B value (cm1 ÅP)
B (error) (cm1 ÅP)
ds = 6 P (surface fractal dimension)
Radius of particle (assuming spherical), R
Diameter,
1.56 103 2.55 103 1.54 103 1.45 103 2.81 103 3.6 103 2.7 103 1.8 103 5.92 103 3.48 103
0.02 103 0.08 103 0.08 103 0.08 103 0.15 103 0.13 103 0.09 103 0.14 103 0.3 103 0.83 103
3.58 3.33 3.32 3.37 3.4 3.18 3.2 3.27 3.24 3.43
0.01 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
3.1 1005 11 1005 7.5 1005 6.6 1005 7.1 1005 3.8 1004 3.2 1004 1.8 1004 3.8 1004 1.1 1004
0.08 1005 0.1 1005 0.2 1005 0.2 1005 0.2 1005 0.1 1004 0.1 1004 0.1 1004 0.1 1004 0.0
2.42 2.67 2.69 2.63 2.60 2.82 2.80 2.73 2.76 2.57
320 297 290 282 312 264 257 249 288 329
640 594 580 564 624 528 514 498 576 658
0
0
2R (Å A)
(Å A) EH0N0C EH20N0C ES20N0C EI20N0C EF20N0C EH20N15C ES20N15C EI20N15C EF20N15C EH0N35C
248 230 224 219 242 205 199 193 223 255
2 0 1 1 1 0 0 1 1 1
1053
P.K. Chattopadhyay et al. / Composites: Part A 42 (2011) 1049–1059
lesser extent of void spaces within the aggregates (Table 1). Moreover, such a high level of mismatch between the microscopically measured diameter (Fig. 2) and SAXS derived diameter (Table 3) can be originated owing to the differences in moments. Theoretically, Rg is expressed as the second moment of inertia, whereas the microscopically derived diameter is dependent on the fourth moment of inertia [13]. A second possible source for the discrepancy pertains to the microstructure as well as the structure of the primary particles. For primary particles having a core and shell structure with an external graphitic shell covering an internal amorphous domain, the observed radius of gyration might be different than that for a homogeneous structure since the electron density for the core and shell would be different [22]. Above all, single level of fitment does not necessarily show the carbon black primary particle sizes (Fig. 2 and Table 3). Interestingly, SAXS overestimates the primary particle radius of SAF and strongly underestimates the size of FEF. This is possible as the surface or shell characteristics of SAF are different than that of FEF. Moreover, SAF shell bears different extent and characteristics of functional groups as compared to FEF shell. Therefore, the electron density difference between core and shell cannot be the same for both CBs. In this regard, Rieker et al. observed similar kind of mismatch between TEM derived primary particle diameter and SAXS derived primary particle size [23]. Interestingly, as 15 phr NC was incorporated in each CB filled samples, the corresponding Rg values were reduced such that Rg value for EH20N15C < EH20N0C, ES20N15C < ES20N0C, EI20N15C < EI20N0C, EF20N15C < EF20N0C (Table 3). In a separate experiment, the Rg value of EH0N35C can be observed as 255. The value is the highest among all the samples. Therefore, in a ternary particulate sample, the reduction of overall Rg value for the hybrid fillers as compared to the Rg value of individual fillers signifies changes in (1) second moment of area or moment of inertia (I) and/or (2) total cross-sectional area (A). Theoretically, the radius of gyration can be expressed as:
R2g ¼
I A
ð3Þ
Moment of inertia for sphere and cylinder can be expressed as:
Is ¼
2mr2 ðfor solid sphereÞ 5
Icx ¼ Icy ¼
1 2 mc 3r 2c þ h ðfor solid cylinder measured around 12
ð4Þ
X=Y axisÞ
ð5Þ
where, r and rc is the radii of the sphere and the cylinder respectively; h is the height of the cylinder; m and mc are the masses of the spherical (CB primary particle) and cylindrical particles (NC aggregates). For exfoliated clay platelets, the h ? 0, and these are assumed as discs. For CB filled composites, with the increase of r, Is increases which ultimately gives rise to the highest Rg for EF20N0C (Table 3). For ternary particulate composites, the change of Rg can be possible owing to the following reasons: (1) reduction in ‘h’ leading to increase in ‘A’ due to partial/ full exfoliation of the NC (Eqs. (3) and (5)) (2) breakdown of NC particles leading to reduction in rc (Eqs. (3) and (5)) (3) formation of ‘nanounit’ or hybrid structure due to ‘haloing effect’ (Fig. 3). First two factors can contribute significantly as CB may assist in breakdown of NC platelets by improvement of viscosity of the matrix which can ultimately impart more shearing force upon NC tactoids/platelets. The third factor is a complicated one since a change of radius of curvature for NC can be possible leading to bending of NC around carbon black in a ‘nanounit’ (Fig. 3) [7,11]. Such deformation in shape can bring about change in the I, and hence the Rg value of the hybrid system can be altered (Table 3). 3.2. High resolution transmission electron microscopy Filler distributions of all the TEM photomicrographs of binary (CB filled) and ternary (CB and NC filled) composite samples are undergone statistical measurements including the inter-aggregate distances and the bending of NCs. For all the samples, at least five photomicrographs are analyzed. The average inter-aggregate distance reported here is the data corresponding to the range having maximum frequency distributions in the generated histograms (not shown here). In the photomicrographs, the appeared bending of NC (Fig. 4) may be due to specific arrangement of NC platelets within a thin tactoid in space wherein the projection of individual platelet slightly deviates from the others. Altogether, the analyses show the following remarkable features:
Fig. 2. TEM photomicrographs of (a) ES20N0C, (b) EI20N0C, (c) EH20N0C and (d) EF20N0C.
1054
P.K. Chattopadhyay et al. / Composites: Part A 42 (2011) 1049–1059
(D) In EF20N0C, almost no connectivity among CB aggregates can be observed with very high average inter-aggregate distance (400–600 nm) (Fig. 2d). (E) In presence of nanoclay, in ES20N15C, the following interesting features can be observed: (a) ‘Haloing effect’ in which NC platelets are at least partly surrounded by CB primary particles (b) bending of NCs (angle of bending 20–25°) very thin NC platelets which raises a possibility of ‘nanounit’ formation (Fig. 4a). (F) In case of EI20N15C, the characteristics are as follows: (a) ‘Haloing effect’ is almost absent (b) bending of thin NCs around ISAF (angle 20°) to form ‘nanounit’ can be detected (c) NC appears to have improved the overall network connectivity (Fig. 4b). (G) In EH20N15C, the following are the important characteristics: (a) Intense ‘Haloing effect’ with lesser available free HAF to maintain overall filler network connectivity (b) appreciable quantity of ‘nanounit’ formation with intense bending of nanoclay platelets around CB particles (angle 25–40°) and (c) presence of holes in the HAF network as it is observed in Fig. 4c. (H) Finally, for EF20N15C, the following features can be observed: (a) association of FEF and NC without ‘halo’ formation (b) bending of NC (10–20°) with small extent of ‘nanounit’ formation (c) improved overall filler connectivity (Fig. 4d). Fig. 3. Typical hybrid microstructures in ternary particulate composites: (I) ‘nanounit’ (II) ‘Halo’.
(A) Filler microstructures formation in ES20N0C showing primary particle size of SAF (16 nm) with prominent lack of connectivity with considerably high inter-aggregate distance (75–200 nm) (Fig. 2a). (B) For EI20N0C, the connectivity of the filler network is better than ES20N0C (Fig. 2b). The measured average inter-aggregate distance is found as 80 ± 30 nm. (C) For EH20N0C, the connectivity of the filler network is appeared to be at the highest level among all the CB filled composites (Fig. 2c) with the measured average inter-aggregate distance of 60 ± 20 nm.
3.3. Dielectric measurement Fig. 5 shows the change of relative permittivity over increasing frequency at 35 °C, 65 °C and 80 °C. It shows a general tendency of reduction of permittivity with the increasing frequency levels. This is possible since lesser time is available for polarization (either interfacial or orientation) to occur. According to Maxwell [24], the charges will accumulate in time at the interfaces between the layers whenever, e01 r2 – e02 r1 (e01 and e02 are the relative permittivity of the polymer and filler; r1 and r2 are the conductivities of the polymer and filler phases respectively). Theoretically, relative permittivity of the composite contributed by interfacial polarization is inversely related to the relaxation time. The permittivity
Fig. 4. TEM photomicrographs of (a) ES20N0C, (b) EI20N0C, (c) EH20N0C and (d) EF20N0C.
P.K. Chattopadhyay et al. / Composites: Part A 42 (2011) 1049–1059
1055
Fig. 5. Variation of relative permittivity over the range of frequencies at (a) 35°C, (b) 65°C and (c) 80°C.
of the samples is also directly proportional to the volume fraction and the conductivity of the fillers. Moreover, permittivity is dependent on the shape of the fillers. Fig. 5 shows that a sudden drop and subsequent recovery of relative permittivity occurred for all the solely CB filled composites within 100–100,000 Hz at three different temperatures. The phenomenon is the most pronounced for EF20N0C followed by ES20N0C. Such recovery can be due to contribution of interfacial polarization as space charge accumulation at the interface takes place within these frequency ranges. Such type of interfacial polarization within 100–100,000 Hz has been noticed by Liu et al. in case of BiFeO3 thin film capacitors [25]. This type of prominent changes in relative permittivity within that particular frequency ranges have not been noticed in case of EI20N0C and EH20N0C. This suggests that the charge accumulation at space of the CB–ENR interface is lesser as polarized interfaces are close enough (Fig. 2b and c) to interact with ease (Fig. 6). In fact, within the range, in case of ES20N0C (Fig. 2a) and EF20N0C (Fig. 2d), average interparticle or inter-aggregate distance is still sufficiently large (Fig. 6) and local fields created by the particles through interfacial polarization do not interact [26]. Addition of clay is accompanied by two facts: (1) sudden drop of relative permittivity at a definite frequency zone (100,000 Hz and 500,000 Hz) and (2) the formation of three types of interfaces (e.g. NC–ENR, NC–CB, and ENR–CB). Since, NC has a lower electrical conductivity as compared to CB and ENR, the attainment of the inequality (e01 r2 – e02 r1) in case of NC–polymer and NC–CB interfaces can be possible much easily and at a lesser time interval. The conductivity of pristine montmorillonite has been reported near about 4 108 S cm1[27], and the octadecyl amine modification can reduce the conductivity furthermore. This can be possible
as the ionic conduction would be hampered if increasing amount of Na+ ion is replaced by alkyl amine cations. Therefore, in addition to the permittivity drop at lower frequency ranges (100–100,000 Hz), sharp drop of relative permittivity at the higher frequency level (100,000 Hz and 500,000 Hz) can be possible in case of ternary composites owing to contribution from both the NC–polymer and NC–CB interfaces. Surprisingly, in case of EH20N15C, drop of relative permittivity are minimum in both the frequency ranges. Hence, the lowest interfacial polarization has been occurred in EH20N15C. Here, space charge at the interface cannot be accumulated owing to electron tunneling through well connected network (Fig. 3c). At higher level of temperatures, (at 65 °C and at 80 °C), similar type of permittivity drop can be noticed in those particular frequency ranges (Fig. 5b and c). 3.4. AC resistance Table 4 shows the resistance of all the composites measured at varying frequencies. In the lower frequency ranges, the order of resistance is the following: EF20N0C > ES20N0C > EI20N0C > EH0N0C > EH20N0C. At higher frequency ranges, the order of resistance changed to the following: ES20N0C EH20N0C > EH0N0C > EI20N0C > EF20N0C. These observations can be governed by two main factors: (1) Characteristics of the microstructure (network formation, interconnectivity, quality of interparticle contacts, shape and size of the conductive particles and (2) polarization effect (orientational polarization at higher frequency level and interfacial polarization at lower frequency level). In the lower frequency ranges, owing to interfacial polarization, the interparticle contacts are assumed to have a substantial influence. Due to charge accumulation at
1056
P.K. Chattopadhyay et al. / Composites: Part A 42 (2011) 1049–1059
Fig. 6. Possible filler microstructures in CB filled composites: (a) ES20N0C, (b) EI20N0C, (c) EH20N0C and (d) EF20N0C.
Table 4 Results of AC resistance of the samples at varying frequency levels. Frequency (Hz)
1000 5000 10,000 50,000 100,000 500,000 10,00,000
AC resistance (k X) measured at 35 °C EH0N0C
EH20N0C
ES20N0C
EI20N0C
EF20N0C
EH20N15C
ES20N15C
EI20N15C
EF20N15C
1349.857 259.534 133.581 31.467 13.107 – –
760.778 216.482 126.6 44.361 23.980 8.136 4.133
3090.995 415.510 178.308 44.082 24.190 4.08 –
1653.202 217.726 96.438 25.295 12.793 3.447 0.155
4801.474 505.073 169.69 25.415 7.05 – –
1548.958 360.841 181.562 46.792 23.95 16.982 11.46
1264.972 323.529 169.444 42.793 18.987 8.152 4.823
1306.279 316.745 161.959 39.958 18.609 9.124 5.838
2034.316 463.448 230.033 53.989 23.407 18.359 12.787
the ENR–CB interfaces, the resistance of EF20N0C, ES20N0C, and EI20N0C exceeds the resistance offered by EH0N0C. In EF20N0C, lesser number of available CB particles can form CB network with a number of discontinuities in the filler microstructure. Moreover, bigger size spherical particle will be more inefficient at imparting conductivity, since most of the material in the spheres is wasted as far as electrical conduction is considered [24]. In ES20N0C, such type of wastage of conduction is the least owing to minimum average particle size for SAF (16 nm). Of course, the higher aggregating tendency for SAF can form discontinuous network formation (Fig. 6). In EI20N0C, such aggregating tendency will be reduced leading to greater possibility of formation of continuous filler microstructure (Fig. 6). In EH20N0C, both the network continuity and the interparticle conduction become optimized. Conversely, in the higher frequency ranges, the orientational polarization is effectively arrested in case of ES20N0C and EH20N0C. It is reflected in higher ENR–CB interaction or higher ENR–CB interfacial roughness/friction (Table 3). EI20N0C and EF20N0C show the lower polymer–CB interaction as orientation polarization remains least affected. As NC is added to CB filled system, dramatic change in the order of resistivity (EF20N15C > EH20N15C > EI20N15C > ES20N15C) can be observed at lower frequency levels. Interestingly, the increase of resistivity can only be noticed in case of EH20N15C as compared to corresponding 20 phr CB filled system (Table 4). This can be possible owing to ‘haloing effect’ (Figs. 3, 4c and 7c) leading to lesser availability of free HAF to form nanochannels (bridge) between
the associated CB [8]. In all other cases, the incorporated NC improves connectivity among CB particles (Figs. 4 and 7). Primary particle size can play a substantial role in this regard. At higher frequency ranges, a similar observation can be noted in which both the network characteristics and the CB particle size contribute significantly.
3.5. Volume resistivity In the absence of NC, volume resistivity depicts the following order: EH0N0C > EF20N0C > EH20N0C > EI20N0C > ES20N0C (Table 5). Since, the resistivity is measured under a pressure of 0.49 MPa, only the primary particle size of the CB plays the major role in determining the volume resistivity of the filled samples. The applied pressure significantly can reduce the inter-aggregate distance in all CB filled samples. Thus, the conductivity is improved as favorable interaggregate distance (<5 nm) may be attained to suffice tunneling of electrons [24]. As NC (less conductive than CB) is incorporated, the volume resistivity is improved for all CB filled samples (Table 5), and the order constitutes the following: EF20N15C > EH20N15C > EI20N15C > ES20N15C. This order is similar to the order corresponding to binary samples. Thus, in the ternary samples, the CB primary particle size becomes the major factor. Again the applied pressure is responsible for reduction of the inter-aggregate distances, and the ‘haloing effect’(Fig. 3) cannot play a dominant role as the number of available free CB primary particles is sufficient
1057
P.K. Chattopadhyay et al. / Composites: Part A 42 (2011) 1049–1059
Fig. 7. Possible filler microstructures in CB and NC filled ternary composites: (a) ES20N15C, (b) EI20N15C, (c) EH20N15C ad (d) EF20N15C.
Table 5 DC volume resistivity of the samples (35 °C and 0.49 MPa pressure). Sample
Volume resistivity (X Cm)
EH0N0C EH20N0C ES20N0C EI20N0C EF20N0C EH20N15C ES20N15C EI20N15C EF20N15C EH0N35C
5.0856 1010 9.8781 109 8.7581 108 2.5163 109 1.3625 1010 5.5911 1011 2.3839 109 4.6054 1011 7.7117 1011 2.6456 1012
to form conductive nanochannel (bridge) connecting the associated CBs of the halo. 3.6. Mechanical properties In solely CB filled samples (Table 6), the stress levels at different strain percentages can be observed in the following order: EH20N0C > EF20N0C > EI20N0C > ES20N0C. In fact, the increasing tendency of aggregate formation in the ISAF and SAF filled samples can be responsible for substantial lowering of ENR–CB interfacial area leading to lower stress level at lower strain percentages. Of course, if the tensile strength values are compared, then the order changes to the following: ES20N0C > EH20N0C > EI20N0C > EF20N0C. The order
is exactly identical with the order of the ds values recorded in the SAXS analyses (Table 3). The superior tensile strength of ES20N0C and EH20N0C over EI20N0C and EF20N0C was also reflected in the AC resistance results (Section 3.4). Therefore, failure property like tensile strength is highly dependent on the surface fractal values of the interfaces. This is again dependent on the roughness of the CB surface originating from the relative population of high energy sites (types III and IV) of the CB surface [18]. Interestingly, EB values follow the identical order as observed in case of tensile strength values. On the contrary, after NC addition, the order of the modulus values changes dramatically to the following: EH20N15C > ES20N15C > EI20N15C > EF20N15C. In addition, the sequence tensile strength values are not the same as the order observed in the surface fractal analyses. In fact, the higher ds values in EF20N15C can be responsible largely due to roughness of the NC–FEF interfaces. The tendency of formation of considerably greater amount of NC–FEF interfaces may reduce the extent of filler-polymer interfaces, which can be responsible for such lower tensile strength than that of EI20N15C. Such reduction of NC–FEF interfaces is indicated earlier in the respective SAXS results (Table 3). 3.7. Dynamic mechanical properties 3.7.1. Strain sweep The slope values corresponding to the modulus drop (Table 7) at lower strain percentages show the following order: ES20N0C > EI20N0C > EH20N0C > EF20N0C, which indicates tendency of
Table 6 Tensile properties of the composites. Sample
EH0N0C EH20N0C ES20N0C EI20N0C EF20N0C EH20N15C ES20N15C EI20N15C EF20N15C EH0N35C
Stress different strain levels (MPa) 10%
100%
200%
300%
400%
500%
0.15 0.36 0.23 0.23 0.24 0.59 0.54 0.52 0.36 0.19
0.99 1.74 1.37 1.45 1.48 2.64 2.34 2.26 2.04 2.25
1.36 3.34 2.73 3.01 3.28 5.18 3.89 3.86 3.68 2.96
– – – – NA 8.27 5.97 5.91 5.77 3.75
– – – – NA 12.35 8.23 8.28 8.04 6.02
– – – – NA 17.26 10.96 11.31 10.91 7.92
Tensile strength (MPa)
EB (%)
1.8 7.8 8.7 6.2 4.5 20.6 19.0 18.9 14.7 12.1
221 399 500 365 263 556 715 680 610 828
1058
P.K. Chattopadhyay et al. / Composites: Part A 42 (2011) 1049–1059
Table 7 Results showing the contribution of interfacial roughness in the low strain ‘Payne effect’ for ternary composites. Sample
EH20N0C ES20N0C EI20N0C EF20N0C EH20N15C ES20N15C EI20N15C EF20N15C
Moduli (MPa) at different strain (%) 0.2%
2%
4.65 4.15 4.41 3.49 10.43 9.97 10.16 8.09
4.18 3.61 3.90 3.36 7.79 7.77 8.22 6.64
a
of strain sweep plot for NC=CB filled ternary composite Sf ¼ Slope . Slope of strain sweep plot for CB filled binary composite
b
fractal values for NC=CB filled ternary composite Rf ¼ Surface . Surface fractal values for CB filled binary composite
Slope
Slope improvement factor, Sfa
Roughness improvement factor (Table 3), Rfb
0.2597 0.2983 0.2818 0.0718 1.4586 1.2155 1.0718 0.8011
– – – – 5.62 4.07 3.80 11.15
– – – – 1.0556 1.0444 1.0385 1.0609
Table 8 Dynamic mechanical properties of various samples. Sample
EH0N0C EH20N0C ES20N0C EI20N0C EF20N0C EH20N15C ES20N15C EI20N15C EF20N15C
Tan dmax
2.315 1.364 1.453 1.470 1.727 1.051 1.052 1.008 1.234
Tg (°C)
28.36 29.40 28.69 28.93 28.27 30.41 30.39 28.09 29.41
Storage modulus at diff temperatures (MPa) 30 °C
40 °C
50 °C
60 °C
80 °C
100 °C
2.09 5.65 4.25 4.93 3.64 15.15 14.52 14.89 9.48
2.07 5.22 4.09 4.76 3.55 14.00 13.36 13.71 8.96
2.06 5.13 4.00 4.68 3.51 13.00 12.11 12.61 8.25
2.07 4.98 3.82 4.56 3.53 11.81 11.06 11.28 7.75
2.10 4.74 3.65 4.37 3.54 9.21 8.96 8.66 6.71
2.13 4.38 3.36 4.11 3.36 7.53 7.70 7.56 5.97
aggregate formation for the CB filled samples. As NC is added, the slopes corresponding to modulus drop have been improved substantially for all the samples. At the lower strain level, the improvement of slope after the addition of clay to the CB filled samples has been summarized in Table 7. The ‘slope improvement factor’s after NC addition stay in the following order: EF20N0C > EH20N0C > ES20N0C > EI20N0C. In addition, ‘interfacial roughness improvement factor’s for all the ternary samples have been calculated as mentioned in Table 7. Surprisingly, the sequence of ‘roughness improvement factor’ is exactly same with the sequence of ‘slope improvement factor’. In fact, ‘slope improvement factor’s can express the extent of low strain ‘Payne effect’ in a quantitative way. Therefore, improvement in the ‘Payne effect’ after NC addition can be well correlated with the improvement of the interfacial roughness values obtained from SAXS analyses (Tables 3 and 7). Since, CB–NC interface play a substantial role in improvement of overall interfacial roughness in ternary samples, the extent of CB–NC interface is the dominating factor behind intense aggregate break down at the lower strain values. 3.7.2. Temperature sweep Table 8 shows the storage moduli of different samples ranging from 30 °C to 100 °C (i.e. plateau region). All the CB filled samples show the modulus improvement as compared to the unfilled samples in the following order: EH20N0C > EI20N0C > ES20N0C > EF20N0C. The modulus improvement for ES20N0C and EI20N0C is less as compared to that of EH20N0C. This is because the applied strain in the temperature sweep is not sufficient to cause breakdown of the intense CB aggregates particularly in case of EI20N0C and ES20N0C. Such intense aggregate formation in case of EI20N0C and ES20N0C can be noted earlier from the slope of low strain storage modulus drop in the strain sweep analyses (Table 7). It can also be noted that with the increase in temperature, the modulus drop is more intense in case of ternary samples as compared to CB filled samples. Among the ternary samples, such modulus drop is less prominent in case of EF20N15C. With the increase in temperature,
the relatively greater volume expansion of ENR as compared to the fillers can cause separation among filler particles. Such separation can be easier if the ternary sample contains hybrid microstructures of lesser strength. In EF20N15C, the extent of strong hybrid filler microstructure is appeared to be less as compared to other samples. Therefore, the sample shows less intense storage modulus drop as compared to other ternary samples. In this regard, the modulus drop is the highest for EH20N15C, which signifies formation of higher number of strong NC–CB hybrid microstructures (‘nanounit’) (Fig. 3). As 15 phr NC is added to each sample, appreciable improvement in storage moduli at all temperature levels can be noticed. Such improvement factors in the ternary samples with respect to the CB filled samples are noted to be in the following order: ES20N15C > EI20N15C > EH20N15C > EF20N15C. It can be speculated that the added clay helps in breaking down the CB aggregates particularly present within ES20N0C and EI20N0C. Such breakdown results in rearrangement of the overall microstructure and thereby formation of improved CB network (Figs. 6 and 7). As a result of clay addition, breakdown of CB aggregates and subsequent rearrangement in ES20N0C and EI20N0C is also reflected in the improvement of connectivity of the filler network during electrical property measurements. 4. Conclusions 1. Reinforcing effect of CB upon ENR chains can be realized through interfacial roughness values of solely CB filled composites. This is verified later through tensile strength of the CB composites. The superior tensile strength of ES20N0C and EH20N0C over EI20N0C and EF20N0C was also reflected in the AC resistance results. In ternary systems, the improved interfacial roughness values as compared to CB filled composites are mainly due to contribution of CB–NC interfaces and hybrid microstructures. Formation of hybrid microstructures is reflected in the reduction of Rg value for ternary composites in contrast to CB filled ones.
P.K. Chattopadhyay et al. / Composites: Part A 42 (2011) 1049–1059
2. TEM observation depicts prominent lack in interconnectivity among CB aggregates in SAF and FEF filled samples, which is substantiated by permittivity values at lower frequency levels. Improved connectivity after NC addition is realized through TEM and AC conductivity results. ‘Nanounit’/‘halo’ formation played an important role in the conductivity changes from binary to ternary samples. 3. Filler microstructure breakdown at low strain (‘Payne effect’) for ternary composites has an intimate relationship with the SAXS results corresponding to interfacial roughness (ds) data obtained through single level unified model fitment. Dynamic temperature sweep results reveal the possible changes in microstructures due to clay addition which was predicted earlier by SAXS, TEM and electrical property measurement.
References [1] Zhang W, Richard SB, Dehghani-Sanij AA. Effect of silica concentration on electrical conductivity of epoxy resin–carbon black–silica nanocomposites. Scr Mater 2007;56:581–4. [2] Bao HD, Guo ZX, Yu J. Effect of electrically inert particulate filler on electrical resistivity of polymer/multi-walled carbon nanotube composites. Polymer 2008;49:3826–31. [3] Praveen S, Chattopadhyay PK, Albert P, Dalvi VG, Chakraborty BC, Chattopadhyay S. Synergistic effect of carbon black and nanoclay fillers in styrene butadiene rubber matrix: development of dual structure. Composites: Part A 2009;40:309–16. [4] Valentı´n JL, Mora-Barrantes I, Carretero-Gonzalez J, Lopez-Manchado MA, Sotta P, Long DR, et al. Novel experimental approach to evaluate filler– elastomer interactions. Macromolecules 2010;43:334–46. [5] Praveen S, Chattopadhyay PK, Jayendran S, Chakraborty BC, Chattopadhyay S. Effect of nanoclay on themechanical and damping properties of aramid short fibre-filled styrene butadiene rubber composites. Polym Int 2010;59:187–97. [6] Feller JF, Bruzaud S, Grohens Y. Influence of clay nanofiller on electrical and rheological properties of conductive polymer composite. Mater Lett 2004;58:739–45. [7] Konishi Y, Cakmak M. Nanoparticle induced network self-assembly in polymer–carbon black composites. Polymer 2006;47:5371–91. [8] Etika KC, Liu L, Hess LA, Grunlan JC. The influence of synergistic stabilization of carbon black and clay on the electrical and mechanical properties of epoxy composites. Carbon 2009;47:3128–36.
1059
[9] Justice RS. Small-angle scattering from composite: elucidation of hierarchical morphology/property relationships. Ph.D. thesis, University of Cincinnati; 2007. [10] Gelling IR. Epoxidised natural rubber. In: Salamone JC, editor. Polymeric materials encyclopedia, vol. 3, no. D–E. CRC Press; 1996. p. 2192–7. [11] Chattopadhyay PK, Basuli U, Chattopadhyay S. Studies on Novel Dual Filler Based Epoxidized Natural Rubber Nanocomposite. Polym Compos 2010;31:835–46. [12] Pal K, Rajasekar R, Kang DJ, Zhang ZX, Kim JK, Das CK. Effect of epoxidized natural rubber–organoclay nanocomposites on NR/high styrene rubber blends with fillers. Mater Des 2009;30:4035–42. [13] Beaucage G, Schaefer DW. Structural studies of complex systems using smallangle scattering: a unified Guinier/power-law approach. J Non-Cryst Solids 1994;172–174:797–805. [14] Porod G. General theory. In: Glatter O, Kratky O, editors. Small angle X-ray scattering. London: Academic Press; 1982. p. 17–52. [15] Bale HD, Schmidt PW. Small angle X-ray scattering investigation of submicroscopic porosity with fractal properties. Phys Rev Lett 1984;53:596–9. [16] Vilgis TA, Heinrich G. Disorder-induced enhancement of polymer adsorption – a model for the rubber–polymer interaction in filled rubbers. Macromolecules 1994;27:7846–54. [17] Mathew T, Datta RN, Dierkes WK, Noordermeer JWM, Van Ooij WJ. Mechanistic investigations of surface modification of carbon black and silica by plasma polymerisation. Plasm Chem Plasm Process 2008;28:273–87. } ppel M, Schuster RH, Heidberg J. Surface energy distribution of [18] Schröder A, Klu carbon black measured by static gas adsorption. Carbon 2002;40:207–10. [19] Wang MJ, Wolff S, Donnet JB. Filler–elastomer interactions: carbon-blacksurface energies and interactions with elastomer analogs. Rubber Chem Technol 1991;64:714–36. [20] Mravcˇa´kova´ M, Boukerma K, Omastova´ M, Chehimi MM. Montmorillonite/ polypyrrole nanocomposites: the effect of organic modification of clay on the chemical and electrical properties. Mater Sci Eng C 2006;26:306–13. [21] Charles A. Harper handbook of plastics, elastomers, and composites. 4th ed. New York: McGraw-Hill Professional; 2002. [22] Beaucage G, Rane S, Schaefer DW, Long G, Fischer DJ. Morphology of polyethylene–carbon black composites. Polym Sci Part B: Polym Phys 1999;37:1105–19. [23] Rieker TP, Misono S, Dolle FE. Small-angle X-ray scattering from carbon blacks: crossover between the fractal and Porod regimes. Langmuir 1999;15:914–7. [24] Blythe T, Bloor D. Electrical properties of polymers. 2nd ed. New York: Cambridge University Press; 2005. [25] Liu GZ, Wang C, Wang CC, Qiu J, He M, Xing J, et al. Effects of interfacial polarization on the dielectric properties of BiFeO3 thin film capacitors. Appl Phys Lett 2008;92:122903–13. [26] Yacubowicz J, Narkis M, Benguigui L. Dielectric properties of medium thermal black-polyethylene systems. Polym Eng Sci 1988;28:1581–5. [27] Han Y. Synthesis and characterization of montmorillonite/polypyrrole nanocomposite. Polym Compos 2009;30:66–9.