Impacts of filler covalent and non‐covalent modification on the network structure and mechanical properties of carbon–silica dual phase filler/natural rubber

The carbon–silica dual phase filler (CSDPF) was modified by bis (3‐triethoxy‐silylpropyl) tetrasulphane (Si69) and 1‐allyl‐3‐methyl‐imidazolium chloride (AMI), respectively. The natural rubber (NR) vulcanizates filled with modified CSDPF were fabricated through mechanical mixing followed by a high‐temperature cure process. The impacts of filler surface modification on the curing characters, crosslinked junctions, network structure, and mechanical properties of NR vulcanizates were investigated. The results showed that the Si69 interacted with CSDPF through covalent bond, while the interaction between AMI and CSDPF was hydrogen bond. Both modifications increased the cure rate of CSDPF/NR compounds as well as the crosslinked degree, compared with those of pristine CSDPF/NR compound. The modifications improved the dispersion of CSDPF in NR matrix. The covalent modification by Si69 caused a limited movement of NR chains in the CSDPF surface, which contributed to a greater tensile modulus of Si69‐modified CSDPF/NR. However, the higher content of mono‐sulfidic crosslink and the poorer content of strain‐induced crystallization in the NR matrix led to a slight increase of tensile strength and tear strength of Si69‐modified CSDPF/NR, compared with those of CSDPF/NR. The tensile modulus of AMI‐modified CSDPF/NR had a lower value due to a faster polymer chain motion on the CSDPF surface. However, the tensile and tear strength of AMI‐modified CSDPF/NR increased significantly because of the increase of mono‐sulfidic crosslink, strain‐induced crystallization, and the existed hydrogen bond between CSDPF and NR. Copyright © 2015 John Wiley & Sons, Ltd.     

Cure characteristics and properties of NBR composites filled with co‐precipitates of black liquor and montmorillonite

Acrylonitrile‐butadiene rubber (NBR) composites filled with co‐precipitates of black liquor and montmorillonite (CLM) were prepared by mechanical mixing on a two‐roll mill. The cure characteristics, mechanical properties, thermal properties, and thermo‐oxidative aging properties of NBR/CLM composites were evaluated. Scanning electron microscopy and transmission electron microscopy showed that the filler particles were well dispersed in the NBR/CLM composites. The scorch time and optimum cure time increase with increasing filler loading. A remarkable enhancement in tensile strength, elongation at break, 300% modulus, and shore “A” hardness was also observed. When the loading of CLM was 40 parts per hundred rubbers, it showed about seven times increase in tensile strength, about 1.8 times increase in elongation at break, about three times increase in 300% modulus, and about 1.3 times increase in shore A hardness, respectively, as compared with those of pure cured NBR. Thermal properties and thermal oxidative aging properties, in general, were also improved with loading of this novel filler. Copyright © 2011 John Wiley & Sons, Ltd.     

The effect of surface coating of CNTs on the mechanical properties of CF‐filled HDPE composites

Mechanical properties of carbon fiber (CF) and carbon nanotube (CNT)‐filled thermoplastic high‐density polyethylene (HDPE) composites were studied with particular interest on the effects of filler content and fiber surface treatment by coupling agent. Surface‐treated CF‐filled HDPE composites increased their tensile strength and impact strength, which is further increased with the addition of CNT. SEM showed that CNT‐coating‐treated CF‐HDPE composites show better dispersion of the filler into the matrix, which results in better interfacial adhesion between the filler and the matrix. Copyright © 2014 John Wiley & Sons, Ltd.     

Fabrication and characterization of composites composed of a bioresorbable polyester matrix and surface modified calcium carbonate whisker for bone regeneration

This work aims to evaluate the potential of a bioresorbable composite as material for bone regeneration. Surface‐modified calcium carbonate whiskers (CCWs) were prepared by grafting of ethylene glycol (EG) using 1,6‐hexamethylene diisocyanate as coupling agent, followed by ring‐opening polymerization of l ‐lactide initiated by the hydroxyl group of EG. The resulting PLLA‐EG‐g‐CCW was used as filler to reinforce a bioresorbable terpolymer, poly(l ‐lactide‐co‐trimethylene carbonate‐co‐glycolide) (PLTG). The mechanical properties and thermal stability of the PLTG/PLLA‐EG‐g‐CCW composites were greatly improved. Compared with neat PLTG, a 39.3% increase in tensile strength and 26.7% increase in elongation at break were obtained for the composite with 2 wt% PLLA‐EG‐g‐CCW filler. This was assigned to the reinforcement effect of evenly dispersed PLLA‐EG‐g‐CCW in the polymeric matrix. In fact, entanglement of PLLA grafts at the surface of PLLA‐EG‐g‐CCW with PLTG chains results in a homogeneous distribution of the filler in the matrix. Thus, the composites are simultaneously strengthened and toughened. The cytocompatibility of the materials was evaluated from cell morphology and 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide assay using L929 mouse fibroblast cell line. The results indicate that the composite presents very low cytotoxicity. Copyright © 2017 John Wiley & Sons, Ltd.     

Influence of filler type and content on properties of styrene‐butadiene rubber (SBR) compound reinforced with carbon black or silica

Rubber compounds are filled with reinforcing fillers to improve their physical properties. Carbon black and silica have different surface chemistries to each other. Differences in properties of carbon black‐ and silica‐reinforced styrene‐butadiene rubber (SBR) compounds were studied. Variation of properties of carbon black‐ or silica‐filled compounds with the filler content was also investigated. The silica‐filled compounds without any coupling agent and dispering agent were prepared to investigate the influence of polar materials‐adsorption on the silica surface. Viscosity and crosslink density increased with increase of the filler content. Hardness, modulus, tensile strength, and wear property were improved more and more by increasing the filler content. Viscosity of the silica‐filled compound was higher than that of the carbon black‐filled one. Cure rate of the silica‐filled compound became slower as the filler content increased, while that of the carbon black‐filled one became faster. Difference in properties between the carbon black‐ and silica‐filled compounds were explained by the poor silica dispersion and the adsorption of cure accelerator on the silica surface. Copyright © 2004 John Wiley & Sons, Ltd.     

Mechanical properties of clay‐reinforced polyamide

Intercalated and exfoliated nanocomposites were prepared by extrusion and injection of polyamide‐6 and highly swollen or slightly swollen montmorillonite, respectively. The microstructure of the nanocomposites has been studied previously. In this article, we investigated the influence of the preferential orientation of the montmorillonite sheets on the mechanical properties of the nanocomposites. Dynamic mechanical analysis and tensile tests showed that the elastic modulus depends mainly on the filler loading. A parallel coupling could well account for the behavior of the nanocomposites. The calculated elastic and storage moduli of montmorillonite were set to 140 and 40 GPa, respectively. Compression tests were performed to study the anisotropy of the mechanical properties. The elastic modulus and flow strain were sensitive to the filler orientation. A Tandon–Weng approach was applied to consider the geometry of the filler. In all low‐deformation tests, no significant difference between intercalated and exfoliated systems was observed. Finally, the influence of the dispersion and exfoliation state of the filler on the ultimate properties of the nanocomposites (tensile tests) is discussed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 272–283, 2002     

Effect of silane coupling agent on the polymer‐filler interaction and mechanical properties of silica‐filled NR

The effects of filler loading and a new silane coupling agent 3‐octanoylthio‐1‐ propyltriethoxysilane (NXT silane) on the polymer‐filler interaction and mechanical properties of silica‐filled and carbon black‐filled natural rubber (NR) compounds were studied. Silica (high dispersion silica7000GR, VN2, and VN3) and carbon black (N330) were used as the fillers, and the loading range was from 0 to 50 phr. The loading of NXT silane was from 0 to 6 phr. Experimental results show that the maximum and minimum torques of silica and carbon black‐filled NR increase with increasing filler loading. With increasing filler loading, the scorch time and optimum cure time decrease for carbon black‐filled NR, but increase for silica‐filled NR. The minimum torque, scorch time, and optimum cure time decrease because of the presence of NXT silane. For the carbon black and silica‐filled NR, the tensile strength and elongation at break have maximum values, but the hardness, M300, M100, and tear strength keep increasing with filler loading. The mechanical properties of silica‐filled NR were improved in the presence of NXT silane. With increasing filler loading, the storage modulus of filled NR increases, but the loss factor decreases. Carbon black shows the strongest polymer‐filler interaction, followed by VN3, 7000GR, and VN2. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 573–584, 2005     

Plasma polymerization of acetylene onto silica: an approach to control the distribution of silica in single elastomers and immiscible blends

Surface modification of silica by acetylene plasma polymerization is applied in order to improve the dispersion in and compatibility with single rubbers and their blends. Silica, used as a reinforcing filler for elastomers, is coated with a polyacetylene (PA) film under vacuum conditions. Water penetration measurements show a change in surface energy due to the PA‐film deposition. The weight loss measured by thermo‐gravimetric analysis (TGA) is higher for the PA‐coated silica compared to the untreated filler, confirming the deposition of the PA film on the silica surface. Time of flight‐secondary ion mass spectrometry (ToF‐SIMS) shows the well‐defined PA cluster peaks in the high mass region. Scanning electron microscopy (SEM) measurements show silica aggregates, coalesced by the coating with smooth and uniform surfaces, but without significant change in specific surface area. Elemental analysis by energy dispersive X‐ray spectroscopy (EDX) measurements also confirms the deposition of the polymeric film on the silica surface, as the carbon content is increased. The performance of single polymers and their incompatible blends based on S‐SBR and EPDM, filled with untreated, PA‐ and silane‐treated silica, is investigated by measurements of the bound rubber content, weight loss related to bound rubber, cure kinetics, reinforcement parameter, Payne effect, and mechanical properties. The PA‐ and silane‐modified silica‐filled pure S‐SBR and EPDM samples show a lower filler–filler networking compared to the unmodified silica‐filled elastomers. Decrease in the reinforcement parameter (α_F) for the plasma‐polymerized silica‐filled samples also proves a better dispersion compared to silane‐modified and untreated silica‐filled samples. On the other hand, the PA‐silica‐filled samples show a higher bound rubber content due to stronger filler–polymer interactions. Finally, the PA‐silica‐filled pure EPDM and S‐SBR/EPDM blends show high tensile strength and elongation at break values, considered to be the result of best dispersion and compatibilization with EPDM. Copyright © 2008 John Wiley & Sons, Ltd.     

Microstructure and properties of styrene‐butadiene rubber based nanocomposites prepared from an aminosilane modified synthetic lamellar nanofiller

In this work, a novel nanocomposite series based on styrene‐butadiene rubber (SBR latex) and alpha‐zirconium phosphate(α‐ZrP) lamellar nanofillers is successfully prepared. The α‐ZrP lamellar filler is modified at the cation exchange capacity by γ‐aminopropyltrimethoxysilane and the filler surface modification is first discussed. A significant improvement of the mechanical properties is obtained by using the surface modified nanofillers. However, no modification of the gas barrier properties is observed. The impact of addition of bis(triethoxysilylpropyl)tetrasulfide (TESPT) as coupling agent in the system is discussed on the nanofiller dispersion state and on the filler–matrix interfacial bonding. Simultaneous use of modified nanofillers and TESPT coupling agent is found out with extraordinary reinforcing effects on both mechanical and gas barrier properties and the key factors at the origin of the improvement of these properties are identified. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 1051–1059     

Investigation of sub‐micron size cenosphere fillers and filler loading on the mechanical and tribological peculiarity of polyester composites

This paper investigates the effect of sub‐micron size cenosphere filler and filler loading on mechanical and dry sliding wear property of polyester composites. Composites are fabricated by filling with 10 and 20 wt% of 800 and 200‐nm size of cenosphere filler particles. Neat polyester composite is also prepared for comparison analysis. Dry sliding wear test is conducted for these composites over a range of sliding distance with different sliding velocities and applied loads on a pin‐on‐disc wear test machine. Taguchi methodology and analysis of variance (ANOVA) is used to analyze the friction and wear characteristics of the composites. The artificial neural network (ANN) approach is implemented to the friction and wear data for corroboration. In this work, mechanical properties of composites such as hardness, tensile strength, tensile modulus, flexural strength, and compressive strength revealed that mechanical properties and wear resistance of the composites increase with a decrease in the particle size. The measured Young's moduli are comparable to standard theoretical prediction models. The morphology of worn composite specimens has been examined by scanning electron microscopy to understand the dominant wear mechanisms. Finally, optimal factor settings are determined using a genetic algorithm (GA). Copyright © 2017 John Wiley & Sons, Ltd.     

Effect of crosslinking on the properties of composites based on LDPE and conducting organic filler

New types of composites were prepared using low-density polyethylene (LDPE) filled with modified organic filler, Canadian switch grass coated with polypyrrole (PPy). The grass surface was entirely covered when 10 wt.% of pyrrole was used for the modification, as confirmed by scanning electron microscopy and infrared spectroscopy. LDPE composites filled with modified grass were prepared by melt mixing and their properties were compared with the properties of the composites filled with unmodified grass. The influence of crosslinking, induced by 1 wt.% of peroxide, on mechanical, thermal and electrical properties of the composites was investigated. Crosslinking enhanced the tensile strength of the prepared composites in the entire range of the filler content. The Young’s modulus of the composites prepared by crosslinking is slightly lowered when compared with the uncrosslinked composites if the filler content is less than 60 wt.%, for higher filler content it is increased. The conductivity of the uncrosslinked composites containing 40 wt.% of grass modified by PPy was in the range 1 × 10⁻⁶ S cm⁻¹, which is a value by 5 orders of magnitude higher than the conductivity of the crosslinked materials. The presence of PPy on grass surface leads to a reduction of crosslinking of the LDPE matrix.     

Comparison of the effect of mica and talc and chemical coupling on the rheology,morphology, and mechanical properties of polypropylene composites

The effect of filler types of mica and talc on the oscillatory shear rheological properties, mechanical performance, and morphology of the chemically coupled polypropylene composites is studied in this work. The Maleic Anhydride grafted Polypropylene (MAPP) was used as an adhesion promoter for coupling mineral particles with the polypropylene matrix. The samples were prepared by a co‐rotating, L/D = 40, 25 mm twin screw extruder. The tensile tests carried out on the injection molded samples showed a reinforcing effect of talc up to 20 wt% on the Polypropylene (PP). The tensile strength of PP‐mica composites showed a slight decrease at all percentages of mica. The effect of chemical coupling by using MAPP on the tensile strength was more pronounced in increasing the tensile strength for PP‐mica than PP‐talc composites. The complex viscosity curve of pure PP and the composites, showed a Newtonian plateau (η₀) up to 30 wt% at low frequency terminal zone. By increasing the filler content to 40 and 50 wt%, the complex viscosity at very low shear rates sharply increased and showed yield behavior that can be due to the formation of filler particles networks in the melt. At the optimum amount of coupling agent, a minimum in cross over frequency curve against MAPP content is observed. The optimum amount of coupling agent for PP‐talc composites is about 1.5%, and about 3% for PP‐mica formulations. The analysis of viscosity behavior at power‐law high region, revealed the more shear thinning effect of mica than talc on the PP matrix resin. Copyright © 2009 John Wiley & Sons, Ltd.     

Properties of rubber filled with montmorillonite with various surface modifications

Layered silicate/natural rubber composites were prepared by direct polymer melt intercalation. Na‐montmorillonite Kunipia‐F and its organic derivates (organo‐clays) prepared by ion exchange were used as clay fillers. Silica (SiO₂) Ultrasil VN3, a filler commonly used in the rubber industry, was used in combination with clay fillers. The effect of clay or organo‐clay loading from 1 up to 10 phr without (0 phr) or with silica (15 phr) showed significant improvement of the tensile properties (stress at break, strain at break and modulus M100). Modification of montmorillonite by three alkylammonium cations with the same length of alkylammonium chain (18 carbons) and different structure resulted in altered reinforcing and plasticizing effects of the filler in composites with rubber matrix. Copyright © 2011 John Wiley & Sons, Ltd.     

Structure and properties of star‐shaped solution‐polymerized styrene‐butadiene rubber and its co‐coagulated rubber filled with silica/carbon black‐I: morphological structure and mechanical properties

The morphological structure and mechanical properties of the star‐shaped solution‐polymerized styrene‐butadiene rubber (SSBR) and organically modified nanosilica powder/star‐shaped SSBR co‐coagulated rubber (N‐SSBR) both filled with silica/carbon black (CB) were studied. The results showed that, compared with SSBR, silica powder could be mixed into N‐SSBR much more rapidly, and N‐SSBR/SiO₂ nanocomposite had better filler‐dispersion and processability. N‐SSBR/SiO₂/CB vulcanizates displayed higher glass‐transition temperature and lower peak value of internal friction loss than SSBR/SiO₂/CB vulcanizates. In the N‐SSBR/SiO₂/CB vulcanizates, filler was dispersed in nano‐scale resulting in good mechanical properties. Composites filled with silica/CB doped filler exhibited more excellent mechanical properties than those filled with a single filler because of the better filler‐dispersion and stronger interfacial interaction with macromolecular chains. N‐SSBR/SiO₂/CB vulcanizates exhibited preferable performance in abrasion resistance and higher bound rubber content as the blending ratio of silica to CB was 20:30. Copyright © 2008 John Wiley & Sons, Ltd.     

The effect of shear on mechanical properties and orientation of HDPE/mica composites obtained via dynamic packing injection molding (DPIM)

The interfacial interaction and orientation of filler play important roles in the enhancement of mechanical performances for polymer/inorganic filler composites. Shear has been found to be a very effective way for the enhancement of interfacial interaction and orientation. In this work, we will report our recent efforts on exploring the development of microstructure of high density polyethylene (HDPE)/mica composites in the injection‐molded bars obtained by so‐called dynamic packing injection molding (DPIM), which imposed oscillatory shear on the melt during the solidification stage. The mechanical properties were evaluated by tensile testing and dynamic mechanical analysis (DMA), and the crystal morphology, orientation, and the dispersion of mica were characterized by scanning electron microscopy and two‐dimensional wide‐angle X‐ray scattering. Compared with conventional injection molding, DPIM caused an obvious increase in orientation for both HDPE and mica. More importantly, better dispersion and epitaxial crystallization of HDPE was observed on the edge of the mica in the injection‐molded bar. As a result, increased tensile strength and modulus were obtained, accompanied with a decrease of elongation at break. The obtained data were treated by Halpin–Tsai model, and it turned out that this model could be also used to predict the stiffness of oriented polymer/filler composites. Copyright © 2009 John Wiley & Sons, Ltd.     

Reinforcement effect of MAA on nano‐CaCo3‐filled EPDM vulcanizates and possible mechanism

Methacrylic acid (MAA) was used as in situ surface modifier to improve the interface interaction between nano‐CaCO₃ particle and ethylene–propylene–diene monomer (EPDM) matrix, and hence the mechanical properties of nano‐CaCO₃‐filled EPDM vulcanizates. The results showed that the incorporation of MAA improved the filler–matrix interaction, which was proved by Fourier transformation infrared spectrometer (FTIR), Kraus equation, crosslink density determination, and scanning electron microscope (SEM). The formation of carboxylate and the participation of MAA in the crosslinking of EPDM indicated the strong filler–matrix interaction from the aspect of chemical reaction. The results of Kraus equation showed that the presence of MAA enhanced the reinforcement extent of nano‐CaCO₃ on EPDM vulcanizates. Crosslink density determination proved the formation of the ionic crosslinks in EPDM vulcanizates with the existence of MAA. The filler particles on tensile fracture were embedded in the matrix and could not be observed obviously, indicating that a strong interfacial interaction between the filler and the matrix had been achieved with the incorporation of MAA. Meanwhile, the presence of MAA remarkably increased the modulus and tensile strength of the vulcanizates, without negative effect on the high elongation at break. Furthermore, the ionic bond was thought to be formed only on filler surface because of the absolute deficiency of MAA, which resulted in the possible structure where filler particles were considered as crosslink points. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1226–1236, 2006     

Synthesis and characterization of compatibilized poly(ϵ‐caprolactone)/granular starch composites

To improve the mechanical properties of granular corn starch‐filled poly(ϵ‐caprolactone) (PCL) compositions, three strategies were investigated including the hydrophobic coating of starch granules by reaction with n‐butyl isocyanate, the addition of PCL‐grafted dextran (PGD) as an amphiphilic compatibilizer, and the use of PCL‐grafted granular starch (PGS). Except for the chemical modification of granular starch by reaction with n‐butyl isocyanate, the synthesis of both PGD and PGS relies upon the controlled ring‐opening polymerization (ROP) of ϵ‐caprolactone (CL) initiated by Al‐alkoxides generated onto the polysaccharide, either dextran or starch particles. While the hydrophobic coating of starch only provides higher tensile strength and elongation at break, these properties as well as Young's modulus and strength at yield of the PCL/starch blends were remarkably increased by locating the PCL‐grafted dextran at the filler/matrix interface. It is however worth pointing out that a tougher and stiffer material was obtained by melt blending PGS and pure PCL. These property changes were analyzed and clearly related to parameters such as filler dispersion, interfacial tension, interfacial adhesion and reinforcement by PCL crystallites.     

Polypropylene/layered double hydroxide nanocomposites: Synergistic effect of designed filler modification and compatibilizing agent on the morphology,thermal, and mechanical properties

This work addresses the optimization of the morphology, thermal, and mechanical properties of polypropylene/layered double hydroxide (LDH) nanocomposites. For this, the nanofillers were modified by a calcination rehydration process using two surfactants, sodium dodecylsulfate (SDS) and sodium dodecylbenzenesulfonate, respectively. The nanofillers were characterized at each step of the modification process by thermal gravimetry, X‐ray diffraction, and Infra red spectroscopy. Furthermore, the impact of anionic modifiers on the filler surface energy and on the interactions toward water was analyzed. Polypropylene (PP)/LDH nanocomposites were then prepared by a melt intercalation process and a high molar mass maleic anhydride functionalized polypropylene (PPgMA) was introduced as a compatibilizer. The dispersion of LDH in the PP matrix was characterized and the thermal and mechanical properties of the corresponding nanocomposites were determined and discussed as a function of the filler modification, of the nanocomposite morphology, and of the filler/matrix interfacial properties. The nanocomposites prepared from SDS modified LDH and PPgMA exhibited superior properties thanks to an optimized filler dispersion state and improved interfacial interactions. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 782–794     

The influence of matrix crystallinity,filler grain size and modification on properties of PLA/calcium carbonate composites

Thermal and mechanical properties of polylactide (PLA) composites with different grades of calcium carbonate, 40 nm and 90 nm nanoparticles, and also with submicron particles, unmodified and modified with calcium stearate or stearic acid, obtained by melt mixing, were compared. Films with amorphous and crystalline matrices were prepared and examined.T_g of PLA in the composites remained unaffected whereas its cold crystallization was enhanced by the fillers and predominantly depended on filler content. Filling decreased thermal stability of the materials but their 5% weight loss temperatures well exceeded 250 °C, evidencing stability in the temperature range of PLA processing. The amorphous nanocomposites with modified nanoparticles exhibited improved drawability and toughness without a significant decrease of tensile strength; nearly two-fold increase of the elongation at break and tensile toughness was achieved at 5 wt% content of the modified nanofiller. Lack of surface modification of the filler, larger grain size with an average of 0.9 μm, and matrix crystallinity had a detrimental effect on the drawability. However, the presence of nanofillers and crystallinity improved tensile modulus of the materials by up to 15% compared to neat amorphous PLA.     

Magnetic composites based on natural rubber prepared by using peroxide and sulfur curing system

In this work, rubber magnetic composites were prepared by incorporation of strontium ferrite into elastomeric matrix based on natural rubber. Cross‐linking of the rubber matrix was performed by using sulfur and peroxide curing system. The study was aimed at the investigation of the type of curing system and magnetic filler content on curing process and cross‐link density of prepared materials. Then, the influence of both factors on physical–mechanical and magnetic properties was observed. The obtained results demonstrate that sulfur‐cured composites show better physical–mechanical properties, especially at lower content of strontium ferrite. With increasing amount of ferrite, the differences between the characteristics of both types of composites became less visible, while peroxide‐cured sample with maximum ferrite content showed superior tensile strength in comparison with tensile strength of maximally filled sample cured with sulfur system. The obtained results demonstrate better compatibility between the rubber and the filler when peroxide system was introduced for cross‐linking of the rubber matrix. Copyright © 2014 John Wiley & Sons, Ltd.