Showing papers on "Polymer nanocomposite published in 2017"
TL;DR: In this paper, an electrostatic assembly approach for fabricating highly conductive MXene@polystyrene nanocomposites by electrostatic assembling of negative MXene nanosheets on positive polystyrene microspheres is demonstrated, followed by compression molding.
Abstract: Highly conductive polymer nanocomposites are greatly desired for electromagnetic interference (EMI) shielding applications. Although transition metal carbide/carbonitride (MXene) has shown its huge potential for producing highly conductive films and bulk materials, it still remains a great challenge to fabricate extremely conductive polymer nanocomposites with outstanding EMI shielding performance at minimal amounts of MXenes. Herein, an electrostatic assembly approach for fabricating highly conductive MXene@polystyrene nanocomposites by electrostatic assembling of negative MXene nanosheets on positive polystyrene microspheres is demonstrated, followed by compression molding. Thanks to the high conductivity of MXenes and their highly efficient conducting network within polystyrene matrix, the resultant nanocomposites exhibit not only a low percolation threshold of 0.26 vol% but also a superb conductivity of 1081 S m−1 and an outstanding EMI shielding performance of >54 dB over the whole X-band with a maximum of 62 dB at the low MXene loading of 1.90 vol%, which are among the best performances for electrically conductive polymer nanocomposites by far. Moreover, the same nanocomposite has a highly enhanced storage modulus, 54% and 56% higher than those of neat polystyrene and conventional MXene@polystyrene nanocomposite, respectively. This work provides a novel methodology to produce highly conductive polymer nanocomposites for highly efficient EMI shielding applications.
562 citations
TL;DR: In this paper, a review article collectively introduces a variety of reactions for functionalization of CNTs and graphene and fabrication of their polymer nanocomposites and compares the significance of different functionalization approaches on their composite properties.
465 citations
TL;DR: In this paper, a desktop 3D printer was used to print CNT and graphene-based polybutylene terephthalate (PBT) structures for electrical conductivity and mechanical stability.
407 citations
TL;DR: In this paper, the authors used poly(2-butylaniline) (P2BA) as a dispersing agent to achieve stable dispersion of graphene in organic solvents via non-covalent π-π interactions between P2BA and graphene.
336 citations
TL;DR: In this paper, a trilayered polymer nanocomposite with an optimized filler content displays a discharged energy density of 20.5 J cm−3 at Weibull breakdown strength of 588 MV m−1, which is among the highest discharged energy densities reported so far.
Abstract: The development of advanced dielectric materials with high electric energy densities is of crucial importance in modern electronics and electric power systems. Here, a new class of multilayer-structured polymer nanocomposites with high energy and power densities is presented. The outer layers of the trilayered structure are composed of boron nitride nanosheets dispersed in poly(vinylidene fluoride) (PVDF) matrix to provide high breakdown strength, while PVDF with barium strontium titanate nanowires forms the central layer to offer high dielectric constant of the resulting composites. The influence of the filler contents on the electrical polarization, breakdown strength, and energy density is examined. Simulations are carried out to model the electrical tree formation in the layered nanocomposites and to verify the experimental breakdown results. The trilayered polymer nanocomposite with an optimized filler content displays a discharged energy density of 20.5 J cm−3 at Weibull breakdown strength of 588 MV m−1, which is among the highest discharged energy densities reported so far. Moreover, the nanocomposite exhibits a superior power density of 0.91 MW cm−3, more than nine times that of the commercially available biaxially oriented polypropylene. The findings of this research provide a new design paradigm for high-performance dielectric polymer nanocomposites.
328 citations
TL;DR: In this article, the effect of nanoparticle fraction on the microstructure and dielectric properties of composite films is investigated, which confirms that these ultimate sized nanocrystals can perform as superior high permittivity fillers in the nanocomposites for energy storage applications.
298 citations
TL;DR: This study demonstrates the fused deposition modeling (FDM) 3D printing of TPU/PLA/GO nanocomposites and its potential application as biocompatible materials and found that the mechanical response is highly dependent on printing orientation.
Abstract: Blending thermoplastic polyurethane (TPU) with poly(lactic acid) (PLA) is a proven method to achieve a much more mechanically robust material, whereas the addition of graphene oxide (GO) is increasingly applied in polymer nanocomposites to tailor further their properties. On the other hand, additive manufacturing has high flexibility of structure design which can significantly expand the application of materials in many fields. This study demonstrates the fused deposition modeling (FDM) 3D printing of TPU/PLA/GO nanocomposites and its potential application as biocompatible materials. Nanocomposites are prepared by solvent-based mixing process and extruded into filaments for FDM printing. The addition of GO largely enhanced the mechanical property and thermal stability of the nanocomposites. Interestingly, we found that the mechanical response is highly dependent on printing orientation. Furthermore, the 3D printed nanocomposites exhibit good biocompatibility with NIH3T3 cells, indicating promise as biomat...
286 citations
TL;DR: The nanocomposite TIMs not only exhibit a superhigh through-plane thermal conductivity enhancement of about 10 times at a low BNNS loading of 15.6 vol % in comparison with the pristine PDMS but also show excellent electrical insulating property (i.e., high volume electrical resistivity).
Abstract: The continuous evolution toward semiconductor technology in the “more-than-Moore” era and rapidly increasing power density of modern electronic devices call for advanced thermal interface materials (TIMs). Here, we report a novel strategy to construct flexible polymer nanocomposite TIMs for advanced thermal management applications. First, aligned polyvinyl alcohol (PVA) supported and interconnected 2D boron nitride nanosheets (BNNSs) composite fiber membranes were fabricated by electrospinning. Then, the nanocomposite TIMs were constructed by rolling the PVA/BNNS composite fiber membranes to form cylinders and subsequently vacuum-assisted impregnation of polydimethylsiloxane (PDMS) into the porous cylinders. The nanocomposite TIMs not only exhibit a superhigh through-plane thermal conductivity enhancement of about 10 times at a low BNNS loading of 15.6 vol % in comparison with the pristine PDMS but also show excellent electrical insulating property (i.e., high volume electrical resistivity). The outstandi...
255 citations
TL;DR: In this article, the authors focus on cellulose materials as filler in polymer nanocomposites and their properties depend on the type of nanomaterial used, but the crucial point is the processing technique.
Abstract: Several forms of cellulose nanomaterials, notably cellulose nanocrystals and cellulose nanofibrils, exhibit attractive properties and are potentially useful for a large number of industrial applications. These include the paper and cardboard industry, use as reinforcing filler in polymer nanocomposites, basis for low-density foams, additive in adhesives and paints, as well as a wide variety of filtration, electronic, food, hygiene, cosmetic, and medical products. This entry focuses on cellulose materials as filler in polymer nanocomposites. The ensuing mechanical properties obviously depend on the type of nanomaterial used, but the crucial point is the processing technique. The emphasis is on the melt processing of such nanocomposite materials that has not yet been properly resolved and remains a challenge.
247 citations
TL;DR: In this paper, the Young's and shear moduli of the composites with different graphene volume fractions under different temperatures are simulated and discussed, and large discrepancies between the results from the MD simulations and the rule of mixture are observed.
Abstract: This paper investigates the mechanical properties of graphene/PMMA nanocomposite system by using the molecular dynamics simulations. The graphene nanoplates are assumed to be fully exfoliated in the PMMA matrix and are all planar orientated, which are similar to the ones assembled using layer-by-layer technique. The Young's modulus and shear modulus of the composites with different graphene volume fractions under different temperatures are simulated and discussed. The results show that the Young's and shear moduli increase with the increase of graphene volume fraction and decrease as the temperature rises from 300 K to 500 K, while the efficiency of the reinforcement is reduced as the graphene content becomes higher. Simulations of single layer graphene under uniaxial tension, in-plane pure shear and uniformly distributed transverse load are performed and the effective thickness and the elastic moduli of graphene are subsequently determined uniquely. The obtained stiffnesses of graphene are then substituted into the simple rule of mixture to predict the overall mechanical properties of the composite. Large discrepancies between the results from the MD simulations and the rule of mixture are observed.
232 citations
TL;DR: The large extractable energy density and high dielectric breakdown strength suggest the potential applications of the BT@AO-DA NFs/PVDF nanocomposite films in electrostatic capacitors and embedded devices.
Abstract: Flexible electrostatic capacitors are potentially applicable in modern electrical and electric power systems. In this study, flexible nanocomposites containing newly structured one-dimensional (1D) BaTiO3@Al2O3 nanofibers (BT@AO NFs) and the ferroelectric polymer poly(vinylidene fluoride) (PVDF) matrix were prepared and systematically studied. The 1D BT@AO NFs, where BaTiO3 nanoparticles (BT NPs) were embedded and homogeneously dispersed into the AO nanofibers, were successfully synthesized via an improved electrospinning technique. The additional AO layer, which has moderating dielectric constant, was introduced between BT NPs and PVDF matrixes. To improve the compatibility and distributional homogeneity of the nanofiller/matrix, dopamine was coated onto the nanofiller. The results show that the energy density due to high dielectric polarization is about 10.58 J cm–3 at 420 MV m–1 and the fast charge–discharge time is 0.126 μs of 3.6 vol % BT@AO-DA NFs/PVDF nanocomposite. A finite element simulation of t...
TL;DR: In this article, double-shell structure of BaTiO3@TiO2@Al2O3 nanofibers (BT@TO@AO NFs) was proposed to improve the energy efficiency of polymer nanocomposites.
Abstract: Polymer nanocomposites with high energy density have potential applications in advanced electronics and electric power systems. The inevitable electrical mismatch between nanofillers and the polymer matrix could compromise the energy storage capability and dielectric properties of the polymer nanocomposites. Herein, novel core–double-shell structured BaTiO3@TiO2@Al2O3 nanofibers (BT@TO@AO NFs) were prepared via a one step method, and were incorporated into poly(vinylidene fluoride) (PVDF). The novel design of gradually varying the multilayer hierarchical interface was advantageous to alleviating the local electric field and electric current density intensification in the filler/polymer system. As compared with the nanocomposites loaded with BT NFs and BT@TO NFs, the nanocomposites filled with BT@TO@AO NFs exhibit much decreased dielectric loss, enhanced breakdown strength, and suppressed leakage current densities. Simulations were carried out to verify that the new core–double-shell structure significantly enhances the breakdown strength and energy density. As a result, the nanocomposite films loaded with 3.6 vol% BT@TO@AO NFs show a maximum energy storage density (Ue) of 14.84 J cm−3 at 450 MV m−1, which is about twelve times greater than that of biaxially oriented polypropylene (BOPP) (≈1.2 J cm−3 at 640 MV m−1). Moreover, the nanocomposite exhibits a superior power density of 4.7 MW cm−3 and an ultra-fast discharge speed of 0.37 μs. This research opens up a convenient and effective way for designing high-performance dielectric polymer nanocomposites.
TL;DR: In this paper, a systematic study of the sandwich-structured ceramic/polymer nanocomposites composed of pristine poly(vinylidene fluoride) (PVDF) as the middle layer and barium titanate (BT)/pVDF nan composites as two outer layers has been presented.
Abstract: Compared to conventional single-layered thin films, spatial organization of the polymer matrix and ceramic nanofillers into three-dimensional sandwich structures is a promising route to dielectric materials for enhanced energy storage properties (ESPs) that enable the dielectric capacitors for a number of applications in advanced electronic and electrical power systems. In this study, a systematic study of the sandwich-structured ceramic/polymer nanocomposites composed of pristine poly(vinylidene fluoride) (PVDF) as the middle layer and barium titanate (BT)/PVDF nanocomposites as two outer layers has been presented. Experimental results indicate that the ESP of the sandwich BT/PVDF composites, including breakdown strength, discharge efficiency, and energy density, can be significantly improved by tailoring the BT content. As verified by finite element simulations, the ESP of sandwich films is mainly governed by the electric field distribution owing to the introduction of high-dielectric-constant BT into the layered structures. The rational design of BT content leads to the electric field distribution capable of enhancing the dielectric strength and reducing the electrical conductivity for high energy density and improved discharge efficiency. An ultrahigh energy density of 16.2 J cm−3 has been achieved at the breakdown strength of 410 MV m−1 in the optimized sandwich-structured nanocomposites. The understanding of the influence of filler content on electric field distribution achieved in this work provides a viable way for exploiting novel layered dielectrics with exceptional ESPs for energy storage devices.
TL;DR: Large-scale biomimetic organic/inorganic hybrid nanocoatings with a nacre-like microstructure were prepared via a facile coassembly process and contain a high concentration of nanosheets, which can be well aligned along the substrate surface.
Abstract: Large-scale biomimetic organic/inorganic hybrid nanocoatings with a nacre-like microstructure were prepared via a facile coassembly process. Different from conventional polymer nanocomposites, these nanocoatings contain a high concentration of nanosheets, which can be well aligned along the substrate surface. Moreover, the nanosheets and polymer matrix can be chemically co-cross-linked. As a result, the nanocoatings exhibit exceptional mechanical properties (high stiffness and strength), barrier properties (to both oxygen and water vapor), and flame retardancy, but they are also highly transparent (maintaining more than 85% of their original transmittance to visible light). The nanocoatings can be applied to various substrates and regular or irregular surfaces (for example, films and foams). Because of their excellent performance and high versatility, these nanocoatings are expected to find widespread application.
TL;DR: It is shown that a significant increase in the dielectric constant can be achieved in polyetherimide nanocomposites with nanofillers whose dielectrics can be similar to that of the matrix.
Abstract: In order to increase the dielectric constants of polymer-based dielectrics, composite approaches, in which inorganic fillers with much higher dielectric constants are added to the polar polymer matrix, have been investigated. However, high dielectric constant fillers cause high local electric fields in the polymer, resulting in a large reduction of the electric breakdown strength. We show that a significant increase in the dielectric constant can be achieved in polyetherimide nanocomposites with nanofillers whose dielectric constant can be similar to that of the matrix. The presence of nanofillers reduces the constraints on the dipole response to the applied electric field, thus enhancing the dielectric constant. Our results demonstrate that through nanostructure engineering, the dielectric constant of nanocomposites can be enhanced markedly without using high dielectric constant nanofillers.
TL;DR: In this paper, the CNTs are functionalized by attaching melamine to improve the dispersibility in epoxy matrix and to enhance the interfacial bonding between CNT and matrix, and a significant increase of fracture toughness was observed for 2wt% M-CNT/Epoxy nanocomposite.
Abstract: Carbon nanotubes (CNTs) are considered as high potential filler material to improve the mechanical properties of epoxy nanocomposites. The CNTs are functionalized by attaching melamine to improve the dispersibility in epoxy matrix and to enhance the interfacial bonding between CNTs and matrix. The tensile tests and single edge notch bending (SENB) tests were performed for CNT/Epoxy and M-CNT/Epoxy nanocomposites at various weight fraction of functionalized CNTs. The M-CNT/Epoxy nanocomposites with addition of 2wt% functionalized CNTs exhibited enhancements of Young's modulus by 64% and ultimate tensile strength by 22%. Furthermore, a significant increase of fracture toughness by 95% was observed for 2wt% M-CNT/Epoxy nanocomposite. The homogeneity of CNTs in epoxy matrix has been analyzed and related to the improvement of modulus and strength. The phenomena of crack propagation has been investigated and related to the improvement of fracture toughness.
19 Jun 2017
TL;DR: In recent years, polymer nanocomposites (PNCs) have attracted the attention of scientists and technologists in water purification due to improved processability, surface area, stability, and tunable properties as discussed by the authors.
Abstract: In recent years, polymer nanocomposites (PNCs) have attracted the attention of scientists and technologists in water purification due to improved processability, surface area, stability, tunable pr...
TL;DR: It is demonstrated that well-dispersed, small (diameter ∼1.8 nm) nanoparticles with attractive interactions lead to unexpectedly large and qualitatively different changes in PNC structural dynamics in comparison to conventional nanocomposites based on particles of diameters ∼10-50 nm.
Abstract: Polymer nanocomposites (PNCs) are important materials that are widely used in many current technologies and potentially have broader applications in the future due to their excellent property tunability, light weight, and low cost. However, expanding the limits in property enhancement remains a fundamental scientific challenge. Here, we demonstrate that well-dispersed, small (diameter ∼1.8 nm) nanoparticles with attractive interactions lead to unexpectedly large and qualitatively different changes in PNC structural dynamics in comparison to conventional nanocomposites based on particles of diameters ∼10–50 nm. At the same time, the zero-shear viscosity at high temperatures remains comparable to that of the neat polymer, thereby retaining good processability and resolving a major challenge in PNC applications. Our results suggest that the nanoparticle mobility and relatively short lifetimes of nanoparticle-polymer associations open qualitatively different horizons in the tunability of macroscopic propertie...
TL;DR: In this paper, a new physical-assisted casting method was developed to tune the orientation of elongated BaTiO3 nanowires in a P(VDF-CTFE) matrix.
Abstract: In practical application, new dielectric capacitors with greater energy density at lower operating voltage will be promising candidates for high-performance electrical devices. Theoretically, it is possible to achieve large electric polarization at a low electric field via embedding aligned ferroelectric nanowires in a polymer matrix, which could release high energy density. However, in terms of practice, the design of nanocomposites with aligned nanowires poses a great technical challenge. Here, a new physical-assisted casting method was developed to tune the orientation of elongated BaTiO3 nanowires in a P(VDF-CTFE) matrix. In the Z-aligned nanocomposites, a large (Dmax − Pr) value of 9.93 μC cm−2 can be induced at a low electric field of 2400 kV cm−1 by aligning 3 vol% ferroelectric BaTiO3 nanowires in the poling direction. Compared with X–Y-aligned nanocomposites even at a high electric field of 3400 kV cm−1, the Z-aligned nanocomposites could exhibit simultaneously an enhanced energy density of 10.8 J cm−3 and a discharge efficiency of 61.4% at 2400 kV cm−1. To the best of our knowledge, among ferroelectric nanocomposites, this is the highest energy density ever obtained at such a low electric field. This work is of critical significance in making dielectric nanocomposites viable for energy storage devices in current electrical and electronic applications.
TL;DR: In this paper, the roles of nanoparticles aggregation/agglomeration in the interfacial/interphase and tensile properties of polymer nanocomposites are discussed and quantitatively characterized in some samples using known models.
Abstract: In this article, the roles of nanoparticles aggregation/agglomeration in the interfacial/interphase and tensile properties of polymer nanocomposites are discussed. The interfacial/interphase and tensile levels are quantitatively characterized in some samples using known models assuming the aggregation/agglomeration phenomena by the effective volume fraction of nanoparticles. The findings show that the nanoparticles aggregation/agglomeration significantly reduces the interfacial/interphase and tensile properties of nanocomposites via decreasing the specific surface area and effective volume fraction of nanoparticles. Additionally, Kerner and Paul models suggest the accurate predictions compared to the experimental data considering the aggregated/agglomerated nanoparticles. However, assumption of well-dispersed nanoparticles over-predicts the modulus in the reported samples.
TL;DR: In this paper, lead-free ferroelectric nanofibers with a high aspect ratio (>200) are synthesized by a hydrothermal method and dispersed in a polyvinylidene difluoride-co-hexafluoropropylene (P(VDF-HFP)) matrix.
Abstract: Ceramic/polymer nanocomposites are attractive for energy storage applications due to their ability to exploit the high permittivity of ceramic fillers and high breakdown strength of the polymer matrix. One challenge for the development of high performance nanocomposites based on ceramic particulates or fibers in a polymer matrix is that they often require a high volume fraction (>50%) to achieve a high permittivity, which is often at the expense of a reduction in dielectric strength and mechanical flexibility. In this paper we demonstrate by both experiment and finite element simulation that high aspect ratio nanofiber fillers offer an effective approach to achieve high energy density and dielectric strength. Lead-free ferroelectric Na0.5Bi0.5TiO3 (BNT) nanofibers with a high aspect ratio (>200) are synthesized by a hydrothermal method and dispersed in a poly(vinylidene difluoride-co-hexafluoropropylene) (P(VDF-HFP)) matrix. The increased fraction of β-phase and the alignment of BNT nanofibers perpendicular to the direction of the applied electric field lead to an enhanced dielectric strength, compared to spherical BNT/P(VDF-FHP) nanoparticles and pure P(VDF-HFP), and experimental measurements are compared with numerical simulations. The results demonstrate that the nanofiber nanocomposites exhibited an ultra-high discharged energy density (12.7 J cm−3) and provide an innovative approach to produce high-energy storage density materials.
TL;DR: In this article, an extrusion based 3D printing graphene oxide (GO)/geopolymer (GOGP) nanocomposite was reported for the first time, and the addition of GO in geopolymeric aqueous mixture (alumiosilicate and alkaline-source particles) dramatically changes its rheology properties.
TL;DR: In this paper, the incorporation of uniformly dispersed nanosheets into polymer matrix as charge-blocking barrier paves a way to significant reduction of conduction loss in high temperature dielectrics.
TL;DR: The elaborate functionalization of BaTiO3 NWs with fluoro-polydopamine has guaranteed both the increase of k and the maintenance of breakdown strength, resulting in significantly enhanced energy storage capability.
Abstract: Rapid evolution of energy storage devices expedites the development of high-energy-density materials with excellent flexibility and easy processing. The search for such materials has triggered the development of high-dielectric-constant (high-k) polymer nanocomposites. However, the enhancement of k usually suffers from sharp reduction of breakdown strength, which is detrimental to substantial increase of energy storage capability. Herein, the combination of bio-inspired fluoro-polydopamine functionalized BaTiO3 nanowires (NWs) and a fluoropolymer matrix offers a new thought to prepare polymer nanocomposites. The elaborate functionalization of BaTiO3 NWs with fluoro-polydopamine has guaranteed both the increase of k and the maintenance of breakdown strength, resulting in significantly enhanced energy storage capability. The nanocomposite with 5 vol % functionalized BaTiO3 NWs discharges an ultrahigh energy density of 12.87 J cm–3 at a relatively low electric field of 480 MV m–1, more than three and a half ...
TL;DR: Inspired by spider silk with multiscale hierarchical architectures, this article used aramid nanofibers F-3 (ANFs-3) to reinforce polyvinyl alcohol (PVA) via hydrogen bonding assembly.
TL;DR: In this article, 1-3 type nanocomposites combining BaTiO3 nanotubes (BT NTs) and polyvinylidene fluoride (PVDF) were prepared by a solution cast method.
TL;DR: In this paper, the effects of Al2O3 shell and the arising interfaces on the dielectric and electric properties in comparison with bare BaTiO3 (BT) nanoparticles were studied.
Abstract: Design of core–shell nanoarchitectures is powerful approach to obtain advanced high-k polymer nanocomposites. Core–shell nanoparticles with uniform amorphous Al2O3 shell layer encapsulating BaTiO3 (BT) particles were fabricated through an effective, facile and low-cost heterogeneous nucleation method. The dielectric behaviors of the polyvinylidene fluoride (PVDF) nanocomposite films were adjusted by varying BT@Al2O3 nanoparticles loadings. The effects of Al2O3 shell and the arising interfaces on the dielectric and electric properties in comparison with bare BT nanoparticles were studied. Due to the highly insulating Al2O3 shell with proper dielectric constant, the local electric field distribution around interfaces between polar BT nanoparticles and PVDF were greatly modified leading to obvious dielectric loss suppression yet maintaining high dielectric constant. The study provides a solution for obtaining high-k dielectric composite with low loss and high breakdown strength, which is highly desired in high power systems.
TL;DR: In this article, homogeneous dispersion of graphene nanosheets in epoxy is achieved via chemical functionalization of graphene oxide with 4-nitrobenzenediazonium salt.
TL;DR: In this article, the roles of nanoparticle geometry, loading, dispersion and temperature on the thermal conductivity of poly(2-vinylpyridine) (P2VP) matrices are investigated.
TL;DR: The finite element simulation of electric potential and electric current density distribution revealed that the PATP grafted into the surface of BCZT NFs surface could significantly improve the dielectric performances.
Abstract: One-dimensional (1D) materials as fillers introduced into polymer matrixes have shown great potential in achieving high energy storage capacity because of their large dipole moments. In this article, 1D lead-free 0.5(Ba0.7Ca0.3)TiO3–0.5Ba(Zr0.2Ti0.8)O3 nanofibers (BCZT NFs) were prepared via electrospinning, and their formation mechanism was systematically studied. Polypropylene acyl tetraethylene pentamine (PATP) grafted into the surface of BCZT NFs was embedded in the polymer matrixes, which effectively improved the distribution and compatibility of the fillers via chemical bonding and confined the movement of the charge carriers in the interface filler–matrix. The energy density at a relatively low electric field 380 MV m–1 was increased to 8.23 J cm–3 by small loading of fillers, far more than that of biaxially oriented polypropylene (BOPP) (≈ 1.2 J cm–3 at 640 MV m–1). Moreover, the nanocomposite loaded with 2.1 vol % BCZT@PATP NFs exhibits a superior discharge speed of ≈0.189 μs, which indicates the...