Weight Fraction Of Carbon Nanotubes Research Articles

Experimental free vibration and tensile test results of a five-layer sandwich plate by comparing various carbon nanostructure reinforcements with SMA

Considering to need for the sensitive and destructive industries for high stiffness and low weight, an experimental free vibration and tensile test results of a five-layer sandwich plate by comparing various carbon nano structures reinforcements with SMA is discussed. The effect of various reinforcements, including carbon nanostructures (carbon nanotubes (CNT), carbon nanorods (CNRs), Graphene platelets (GPLs)) and nitinol shape memory alloy (SMA) wire on the vibration behavior of a five-layer sandwich plate with a foam core is investigated. The purpose and novelty of this work are to compare the effect of different reinforcements on the vibrations of a five-layer plate so that by using this comparison, one can choose the best reinforcements according to the needs of the desired industry and more suitable economic conditions. Considering a 1 % weight fraction of epoxy resin, GPLs, CNTs, and CNRs increase Young's modulus of face sheets by 30 %, 25 %, and 5.8 %, respectively. In this work, a five-layer sandwich structure model can be suggested, and numerically analyzed. The special advantage novelty of this research compared to previous research is the construction of this five-layer model. This is a simple modeling structure for the construction and preliminary examination of structures with five layers experimentally. Also, the composite structure is made by the vacuum pump method, which does not have the disadvantages of the manual method, and the method is completely optimal. At first, the Young's and shear moduli of unidirectional glass fiber (UGF) are calculated by performing a tensile test. To examine all aspects of the construction of five-layer structures during construction, in this article first, the face sheets are made separately using resin, UGF, and various reinforcements, and then the layers of face sheets and the cores are connected using glue. In the following, the equations of motion for the sandwich plate are derived using refined first-order shear deformation theory (RFSDT) by employing Hamilton's principle. Using the Halpin-Tsai equation and the extended rule of mixture, the mechanical properties of the reinforced composite face sheets are obtained. According to the Brinson model, the constitutive equations of the SMA are presented. The influence of various parameters such as side ratio, thickness ratio, weight fraction of CNRs, CNTs, GPLs and SMA wire, fiber angle, and temperature changes on dimensionless fundamental frequency is also represented. Also, the natural frequency of orthotropic plates by considering reinforcements is higher than that without considering reinforcements. By increasing the aspect ratio (a/h), the dimensionless natural frequency increases, while the natural frequency decreases. For two-layer square angular asymmetric laminated sheets (-θ/θ), the minimum dimensionless natural frequency occurred at the fiber placement angle approximately equal to 26 and 64°. The highest frequency is related to the sandwich plate in that its face sheets have higher strength and stiffness because it is placed further from the middle plane. Also, the highest frequency is related to the sandwich plate, whose face sheets are reinforced with GPLs.

Nonlinear forced vibration of functionally graded hybrid three-phase nanocomposite toroidal shell segments reinforced by carbon nanotubes (CNTs) and graphene nanoplatelets (GPLs)

This study proposes a unique three-phase functionally graded (FG) hybrid nanocomposite material reinforcing the toroidal shell segments to investigate the nonlinear forced vibration using Reddy's higher-order shear deformation theory, von Karman geometrical nonlinearity and Stein-McElman's assumption along with the Hamilton principle. The examined toroidal shell's material consists of polymeric resin, carbon nanotubes (CNTs), and graphene platelets (GPLs) as nanocomposites. The material properties have been derived based on a modified Halpin-Tsai micromechanical model. Four distribution patterns have been studied: uniform (UD), FG-X, FG-O, and FG-V. The continuous distribution of GPLs and CNTs leads to inhomogeneous position-dependent properties throughout the shell thickness. The obtained differential equations of motion have been reduced to ordinary equations using Galerkin's technique. A multi-scales method (MSM) is used to estimate a closed-form solution representing the frequency-amplitude relation, and the state space representation is used along with numerical fourth-order Runge Kutta method (RK4) to obtain the nonlinear dynamic response of the toroidal shell. The accuracy of the current results obtained has been verified by comparing them with the relevant literature and numerical results using (RK4). In addition, the influence of both GPLs and CNTs weight fractions, nanofillers’ distribution types, longitudinal and circumferential wave numbers, elastic foundation parameters, static axial compression load, transverse excitation load, damping ratio, geometrical characteristics of the toroidal shell on the dimensionless natural frequency, nonlinear primary resonance (frequency-amplitude curve), and nonlinear dynamic response are carefully studied. The results found that combining (GPLs & CNTs) into the shell's matrix improves performance, especially in concave shells compared to convex ones. The FG-X pattern reduces peak resonance amplitude and improves natural frequency. A reduction of 12.3 % is observed for convex shells, and 21.5 % for concave shells compared to FG-O.

Dispersion mechanism of nanoparticles and its role on mechanical, thermal and electrical properties of epoxy nanocomposites - A Review

The combined effect of nano-reinforcements on the mechanical performance of nanocomposites, which are a novel class of epoxy matrix hybrid nanocomposites containing multiwall carbon nanotubes (MWCNT), graphene, and nanodiamonds (NDs), is drawing substantial attention from many research communities. The discussion concentrates on the dispersion techniques adopted for the preparation of epoxy composites containing different types of nanoparticles (3-D fillers, nanofibers, nanotubes, and plate-like fillers). This review paper covers the electrical, thermal, and mechanical properties of carbon nanotubes (CNTs), graphene, and nanodiamond-reinforced epoxy nanocomposites and correlates them with the topographical features, morphology, weight fraction, dispersion state, and surface functionalization of CNTs, graphene, and nanodiamond. This review paper also summarises recent developments in the dispersion method of different carbon nanoparticles in epoxy matrix.

Optimization of electrical and mechanical properties of a single-walled carbon nanotube composite using a three-roll milling method

In this study, the electrical and mechanical properties of carbon nanotube (CNT)/polydimethylsiloxane (PDMS) composites were optimized using a three-roll milling dispersion method. Depending on the number of CNT walls, such as single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs), the three-roll milling conditions required to optimize the electrical conductivity of CNT/PDMS composites are quite different. In addition, the mechanical properties of the CNT/PDMS composites depend on the dispersion time. These properties were improved under an appropriate three-roll milling time but gradually deteriorated after excessive processing time. To demonstrate and optimize this phenomenon, various mechanical, electrical, and thermal properties of the CNT/PDMS composites were measured with respect to the type of CNT, milling time, and filler weight fraction. Morphological and structural analyses were also conducted on the CNT fillers and composites after milling.

Study on Interfacial Interaction of Cement-Based Nanocomposite by Molecular Dynamic Analysis and an RVE Approach

There is an increased demand for cement nanocomposites in the twenty-first century due to their composition, higher strength, high efficiency, and multiscale nature. As carbon nanotubes (CNTs) possess extremely high strength, resilience, and stiffness, inclusion of carbon nanotubes in small quantities to the concrete mix makes them a multifunctional material. A molecular level understanding is significant to capacitate the macrolevel properties of these composites. In the proposed work, molecular dynamics (MD) simulations are used to understand the behaviour of the composites at the atomic level and continuum mechanics with representative volume element (RVE) homogenization modelling is carried out for interfacial interaction study of composites. The mechanical properties such as Young’s modulus, shear modulus, and poisons are evaluated using previous methods of simulations for different compositions of nanomaterials in cement matrix. The FORCITE module of MD simulation and square RVE model is used to determine the mechanical, electrical properties, and elastic constants of the cement nanocomposite. The MD simulation describes the linking effect of CNT into cement matric, and the RVE modelling study reveals the pull-out effect of CNT from matrix. From experimental and analytical studies, it is found that increase in CNT till 0.5% weight fraction increases the mechanical properties about 12% and further increasing of CNT weight fraction causes a reduction in mechanical properties about 5% due to the agglomeration of nanotubes. The density of states method in MD simulation indicates that mobility of the electrons increases with an increase in carbon nanotube proportion in the composites. The experimental test results substantiate the analytical studies, and the error obtained from both approaches is less than 20%. From the analytical study, the average maximum Young’s modulus, shear modulus, and bulk modulus are obtained as 46 GPa, 31 GPa, and 32 GPa for 0.5% weight fraction of CNT in cement matrix. Hence, it is concluded that 0.5% weight fraction of CNT is considered as optimum dosage to obtain better electrical and mechanical properties.

Influence of CNT fillers on the thermal, mechanical and shape memory properties of TPI shape memory polymer composites

TPI, also known as artificial eucommia rubber, is a thermo-responsive SMP created by molecular recombination and modification with contemporary polymer synthesis and modification techniques. In this paper, TPI shape memory polymer is reinforced with different weight proportions (0, 0.2%, 0.4%, 0.6%, 0.8% and 1%) of carbon nanotube (CNT) and specimens were fabricated with the aim of enhancing the properties of neat TPI polymer composites. Some thermo-mechanical characteristics were investigated and interpreted, including the differential scanning calorimeter (DSC) test, dynamic mechanical analysis (DMA) test, thermal conductivity test, compression test, and a few shape memory properties such as shape recovery ratio and shape recovery rate. TPI shape memory polymers exhibit strong shape memory capabilities and the best mechanical properties based on the testing results for the specimen TPI with 0.8% CNT weight fraction.

Size-dependent linear and nonlinear vibration of functionally graded CNT reinforced imperfect microplates submerged in fluid medium

The linear and nonlinear vibrations of functionally graded carbon nanotubes reinforced microplate (FGCNTRM) submerged in fluid medium have been studied analytically. The primary novelty of this research is to take into consideration the effects of using carbon nanotubes (CNT) and geometric imperfection on the vibrational behavior of microplates submerged in the fluid. Equations of motion are obtained by first-order shear deformation theory of plates and considering the size effects and large deformations. Effective mechanical properties have been determined using the rule of mixtures for four various types of CNT distributions. The nonlinear equations of motion are discretized using the Galerkin method, and the equation response is acquired applying the method of multiple time scales. After verifying the results, the effect of microplate geometric characteristics, small size parameter, fluid height, geometrical imperfection amplitude, weight fraction, and distribution of CNT on linear and nonlinear frequencies as well as amplitude-frequency curves have been studied. The results demonstrate that an increase in fluid height leads to a decrease in the natural frequency. Also, geometric imperfection causes the stiffening behavior of the softening spring and substantially bends the response curve to the right. This bending can induce jump instabilities as the frequency slowly varies.

Effect of interphase thickness and fiber diameter on elastic properties of composites using multi-scale modelling

Composite materials are the largely used engineering materials in aerospace and automobile industries due to their high specific strength and high specific stiffness. The composites’ properties are essential for the design and development of the machine parts. They vary with fiber content, fiber properties, matrix properties, and type of manufacturing process. More experiments are required to obtain the properties and the best combination of fibers and matrices. However, several analytical methods are available to find the properties of the composite to avoid the number of experiments. In the present study, the properties of CFRP, GFRP, Amino-functional multi-walled carbon nano-tubes (CNT) added CFRP, CNT added GFRP composites have been calculated using the properties of fiber, interphase between fiber and matrix, matrix, and CNT. The properties of CNT added epoxy are obtained using the Halpin-Tsai equation in the first stage. In the second stage, the properties of interphase are calculated using the properties of CNT added epoxy and fiber properties. In the third stage, the properties of CFRP and GFRP are calculated using three phase constitutive model by considering the properties of fiber, interphase, and CNT added matrix. The properties are calculated at fiber diameters: 8 μm and 14 μm while varying the fiber volume fraction (%): 0 to 70%, interphase thickness: 50 nm to 500 nm, the weight fraction of CNT (%) added in epoxy: 0 to 5%. The addition of CNT has improved the elastic properties of CFRP and GFRP. The elastic properties of the composites are improved significantly with an increase in the interphase thickness.

The experimental assessment of carbon nanotubes incorporation on the tensile and impact properties of fiber metal laminate fabricated by jute/basalt fabrics-aluminum layers: As hybrid structures

In this work, the simultaneous effect of different stacking sequences of basalt/jute fibers and adding the various weight fractions of carbon nanotubes (CNTs) on the mechanical features of fiber metal laminates (FMLs) under the tensile and impact conditions was assessed. According to the results, the FML had the highest performance under the mechanical tests, when the jute layers were sandwiched by the basalt fibers. In contrast, by sandwiching the basalt fibers with the jute fibers, the FML showed the weakest performance just under the tensile test. This configuration had the moderate performance under the impact test. Incorporating 0.3 wt.% CNTs in all configurations caused to reach the highest improvement in the tensile strength, elastic modulus and impact energy, which were 301 MPa, 50.9 GPa, and 12.3 J, respectively. Reinforcing an adhesion between skin/core and enhancing the mechanical properties of composite core were the effective factors for improving the tensile properties. The delamination of layers, fibrillation of jute fibers, creation of imprint phenomenon, and pull out the basalt fibers were the characterized wasting mechanisms under the impact conditions.

Application of the CUF–EFG method for buckling analysis of the multilayer GPLs–CNTs-reinforced FG plates with cutout

In this article, the element free Galerkin (EFG) method and Carrera’s Unified Formulation (CUF) are employed as the CUF–EFG method for the buckling analysis of multilayer GPLs–CNTs-reinforced functionally graded (FG) plates with cutout. The radial basis shape functions which possess the Kronecker delta function property are used as the shape functions. In CUF, a Taylor expansion with first to 4th order is employed as the thickness function. In the proposed method, the stretching effect (effect of thickness extension ‘ ε zz ≠ 0 ’) is taken into account. The plate is under axial, biaxial, shear and combined loadings and composed of a number of layers stacked up in the thickness direction. The carbon nanotubes (CNTs) and graphene platelets (GPLs) uniformly distributed in each individual layer but their weight fractions gradually vary in each layer to achieve functionally graded properties. Four types of distribution patterns with the same average GPLs and CNTs weight fraction are considered in the problem. The mechanical properties of plates with various grading patterns of GPLs and CNTs distributions are estimated using the modified Halpin-Tsai method and the rule of mixture. A comparison between the obtained results with both analytical solution and other shear deformation theories given in the published literatures is performed to show the accuracy and efficiency of the proposed CUF–EFG method. A parametric study is carried out to evaluate the influences of the boundary conditions, aspect ratio, CNT and GPLs weight fraction, number of layers, stacking sequences of layers, dimension and location of circular cutout on the buckling capacity of plates.

Towards optimized carbon nanotubes (CNTs) reinforced polyetherimide (PEI) 3D printed structures: A comparative study on testing standards

Tailoring the properties of high-performance polymers through reinforcing will bring multifunctionality and expand their use in additive manufacturing (AM). However, machine and material-based challenges exist, eventually resulting in low-quality end products. When expensive polymers are considered, it is still challenging to tailor their properties and print them for high-quality multifunctional structures. Here, polymer composites of polyetherimide (PEI) and carbon nanotubes (CNTs) with varying CNT weight fractions are produced in filament form by melt-processing. Neat PEI, 1 wt% and 3 wt% CNTs/PEI are additively manufactured in two different raster orientations (Rectilinear and Concentric), and two most proposed testing geometries, ASTM D638 and D3039. Through effective melt-processing, CNTs-reinforced PEI filaments were achieved, printing parameters and testing protocols were discussed. As a result, ASTM D3039 showed superior coherence with filaments’ mechanical properties. Moreover, based on failure modes, ASTM D3039 provided better compatibility to AM, owing to its simple rectangular form yielding well-adhered layers.

Hybrid effect of nanoparticles presence on low‐velocity impact resistance in sandwich panels

AbstractConsidering the massive employment of sandwich panels in multifarious applications, numerous research studies have been conducted on their impact resistance enhancement, one of which, is via simultaneous nanoparticles incorporation including various amounts of silica nanoparticles, clay nanoparticles and carbon nanotubes (CNTs) in to sandwich panels, composed of two glass fiber epoxy composite face sheet and polyvinyl chloride core to render them reinforced. The research objective is to experimentally scrutinize the behavior of nano reinforced sandwich panels under low‐velocity impact test conducted at different energy levels. The damaged areas of the panels were investigated via scanning electron microscopy, the result of which demonstrated that the impact resistance of the sandwich panel can be improved by the integration of nanoparticles. The incorporation of 0.3% of CNT, 1% of nano clay, and 3% of nano silica enhanced maximum contact force by 18.6%, compared to the unreinforced equivalent. Increasing the weight fraction of both CNTs and silica nanoparticles, made contribution to sandwich panels impact resistance increase. The presence of nano clay up to 1 wt% improved the maximum contact force; however, the integration of it into matrix more than 1 wt% led to the reduction of maximum contact force, thus weakened the impact resistance of sandwich panel.

On the wave propagation in a higher-order multi-phase curved porous system

The porosity affecting the vibrational characteristics of structures should be considered due to the fact that these porosities can happen during the manufacturing process. The solid body and the liquid or gas compose the porous materials. In this regard, for the first time, wave propagation corresponding to the curved panel made of reinforced porous composites is investigated. Higher-order shear deformable theory (HSDT) is employed in order to extract the formulation. The effective material is attained by employing the rule of the mixture as well as the modified Halpin–Tsai model. Also, equations of motions that are solved analytically are extracted via Hamilton’s principle. The impacts of radius-to-total thickness ratio, the weight fraction of carbon nanotubes (CNTs), porosity factor, that different composite patterns, the pattern of porosity, as well as carbon fibers on phase velocity behavior corresponded with a reinforced curved porous panel are studied. The presented results can be employed in ultrasonic inspection techniques as well as structural health monitoring.

Hybrid sintering of CNT/PZT ceramics using microwave oven

Piezoelectric materials play a major role in a variety of applications such as sensing, actuation and energy harvesting. Lead Zirconate Titanate (PZT) is a commonly used piezoelectric material because of its superior piezoelectric properties. One of the key elements to optimize the manufacturing process of this group of piezoelectric materials is minimizing the processing time and energy required to prepare ceramic parts. Among the production steps, the sintering process needs the most time and consumes the most energy. In this study, a rapid sintering method of bulk PZT elements is proposed based on microwaves. Carbon nanotubes (CNTs) are added to the material as an absorption aid. The effects of different sintering temperatures, microwave (MW) power and CNT weight fraction on the grain size, physical, mechanical and piezoelectric properties are investigated. The results show that higher MW powers lead to smaller grain sizes, higher mechanical properties but lower densities and electromechanical properties. The introduction of CNTs to the PZT material results in higher heating rates at the initial portion of the sintering process as well as smaller and more uniform grains while decreasing the density. The ceramic parts with 1 wt% CNTs concentration have the highest piezoelectric coefficient after sintering and poling. Generally, the proposed method is more environmentally friendly than the conventional method because not only does it require a lower processing time and energy, but also it leads to the formation of a single-phase perovskite structure without the need for additional amounts of lead.

One‐step fabrication of bulk nanocomposites reinforced by carbon nanotube array fragments

AbstractVertically aligned carbon nanotube (VACNT) array growth is an established process where high aspect ratio carbon nanotubes (CNTs) are produced. This work demonstrates one‐step approach to fabricate bulk polymer nanocomposites using CNT array fragments'. Here, 4.5 mm long CNTs were collected post VACNTs synthesis. Next, CNT array fragments were coated with pyrolytic carbon (PyC) and infused with polydimethylsiloxane (PDMS) matrix to create porous CNT/PDMS nanocomposite with a CNT weight fraction of 20%. Achieving similar weight fraction with super long bundled CNTs using dispersion techniques is extremely difficult. The compression and dynamic mechanical behaviors and piezoresistive response of the PDMS filled nanocomposite were assessed. The results revealed the potential of the synthesized structure to serve as fatigue‐resistant pressure sensors with high damping and self‐sensing capabilities. The proposed fabrication technique is versatile, as it can work with thermosetting and thermoplastic polymers in addition to allowing for mass production of PDMS filled nanocomposites.

Qualifying carbon nanotube reinforced polyurethane foam as helmet inner liner through in-situ, static and low velocity impact testing

Helmet inner liner (HIL) is a critical component of helmets which ensures safety and comfort of the wearer. Efforts are made in this work to qualify polyurethane (PU) foams for HIL application. Processing temperature and weight fraction of carbon nanotubes (CNTs) nanofillers is varied to optimize the microstructure and hence average properties of PU foams. Experimental results show that PU foam processed at −5 °C and reinforced with 1.6 wt% of oxidized CNTs shows 40% higher specific elastic modulus and 11% better recovery under compression testing, absorbs 97% more energy per unit volume in comparison to EPS under low velocity impact in drop weight tests. The 34% higher thermal conductivity than EPS implies that it will provide better comfort by efficiently dissipating the heat generated in helmet. The superior combination of properties makes CNT reinforced PU foams a better alternative as HIL in comparison to currently used EPS foam.

Nonlinear vibration behavior of hybrid multi-scale cylindrical panels via semi numerical method

Based on differential quadrature method (DQM), a nonlinear vibrational analysis of hybrid multi-scale cylindrical panels has been performed in this article. The mechanical properties of hybrid composites have been formulated within the framework of three-dimensional Mori-Tanaka model taking into consideration the effects of unidirectional oriented fibers and randomly dispersed carbon nanotubes (CNTs). The governing equations for cylindrical panels have been established with respect to thin shell assumptions taking into account geometrical non-linearity. Next, DQM has been used to solve the governing equations for establishing the frequency-deflection curves of the cylindrical panel. It will be exhibited that frequency-deflection curves change by the varying of CNT weight fractions, fiber orientations, fiberglass volume, panel radius and dimension of CNTs.

A solution to free vibration of rotating pretwisted hybrid CNTs multiscale functionally graded conical shell

In the present study, the free vibration analysis of multiscale functionally graded (FG) carbon nanotube (CNT)–metal–ceramic composite conical shells is conducted using finite element methodology. Using first-order shear deformation theory (FSDT) strains are computed and an eight noded isoparametric shell element is used in the present formulation. Dynamic equation is derived using Lagrange’s equation of motion for moderate rotational speeds wherein Coriolis effect is neglected. The finite element code is developed and validated with the existing literature to analyze the effects of power law index, weight fraction of CNTs, length to thickness ratio, aspect ratio, twist angle and rotational speeds on fundamental natural frequency. Mode shapes of both twisted and untwisted conical shells under varying rotating conditions are also presented.

Using ultra-thin interlaminar carbon nanotube sheets to enhance the mechanical and electrical properties of carbon fiber reinforced polymer composites

A major shortcoming of carbon fiber reinforced polymer composites (CFRP) is their interlaminar performance. This study provides an inexpensive and readily scalable solution to this problem by incorporating ultra-thin sheets of carbon nanotubes (CNT) between the plies (laminates) of CFRPs. To this end, dry carbon fiber fabrics are first sandwiched between CNT sheets. The fabrics are then stacked and infused with epoxy to form a CFRP with interlaminar CNT sheets. Contrary to the typical approach where microns-long CNTs are distributed randomly within a CFRP for reinforcement, this study uses ~100 nm thick CNT sheets consisting of aligned and ultra-long (0.3 mm) nanotubes. Despite their negligible weight fraction of only 0.016%, the interlaminar CNT sheets enhanced the CFRP's flexural strength by 49%, interlaminar shear strength by 30%, and mode I fracture toughness by 30%. X-ray micro-tomography revealed that samples with interlaminar CNTs are significantly resistant to delamination and crack propagation. Moreover, the in-plane electrical conductivity of these composites increased commensurate with the weight fraction of CNTs, providing a maximum enhancement of 278% over the reference sample for 0.048 wt% of CNT sheets. This study reveals that for almost no change in weight and thickness, interlaminar CNT sheets can enhance the electrical conductivity and interlaminar performance of CFRPs.

Molecular dynamics predictions of thermo-mechanical properties of carbon nanotube/polymeric composites

In this study, the mechanical and thermal properties of carbon nanotube-reinforced polymeric nano-composite have been predicted by simulating molecular dynamics (MD). The polymer matrix is of epoxy polymer type with EPON828 resin along with EpiCure Curing Agent-3234 hardener which is reinforced with a single-walled carbon nanotube (SWCNT). Mechanical and thermal properties such as density, elastic modulus, Poisson’s ratio, and coefficient of thermal expansion (CTE) for various states, including the cross-linking degree of resin and hardener molecules 10–65%, carbon nanotubes (CNTs) with different diameters, and weight fraction of carbon nanotubes of 0.5, 1 and 2% have been estimated. The cell’s stiffness matrix in all cases was extracted, and thermo-mechanical properties were obtained using it. The placement of carbon nanotubes in a representative cell is completely random which has a random orientation, and the cell is dynamically analyzed separately under constant temperature and constant pressure conditions at the specified time, and after equilibration, its properties are extracted. The results show an obvious increase in the elastic modulus by increasing cross-linking degrees and an increase in the elastic modulus, and a significant decrease in the nano-composite CTE when the weight fraction of CNTs has increased. The experimental studies and simulation of other researchers were examined to validate the simulation that, the results are in good agreement with each other.