Distribution Of Carbon Nanotubes Research Articles

Free vibration analysis of laminated anisotropic doubly-curved shell structures reinforced with three-phase polymer/CNT/fiber material

The present work investigates the vibrational response of laminated anisotropic doubly-curved shell structures reinforced with Carbon Nanotubes (CNTs) short fibers. The fundamental equations are derived from a curvilinear reference system of principal coordinates, employing the Equivalent Single Layer (ESL) methodology. Furthermore, a general variation in laminate thickness is considered. The unknown field variable is described using higher order theories through the unified formulation, taking into account a general interpolation of the unknown variables with Lagrange polynomials across the physical domain. The Hamiltonian Principle is adopted for the derivation of the dynamic equilibrium equations, which arediscretized numerically by using the Generalized Differential Quadrature (GDQ) method. In addition, an efficient isogeometric NURBS-based mapping is adopted for the distortion of the physical domain. The boundary conditions of the differential problem are modelled through a general distribution of linear elastic springs along the lateral surfaces of the three-dimensional doubly-curved solid. The theory is then applied to study the vibrational modes of structures with different curvatures and lamination schemes, taking into account a general distribution of CNTs along the thickness direction. The homogenized properties of CNTs layers are obtained from the Mori-Tanaka procedure, which accounts for the agglomeration effects of the dispersed nanofibers within the matrix. Unlike previous studies focusing on doubly-curved shells reinforced with composite materials and CNTs, the present formulation enables to derive the vibration characteristics of structures made of generally anisotropic materials with general orientations. Furthermore, the calibration of the parameters for the linear elastic springs’ distribution leads to general external constraints within a single element, thus reducing the computational cost of the problem.

Vibration analysis of a sandwich Timoshenko beam reinforced by GOAM/CNT with various boundary conditions using VIM

In the present study, a sandwich beam reinforced by carbon nanotubes (CNTs)/graphene origami auxetic metamaterials (GOAM) and porous cores is studied. Various distributions of CNTs in facesheets and porosity in the core are stated in terms of thickness. The equations of motion for a sandwich beam are derived and solved under various boundary conditions using variational iteration method (VIM), in which, it is a powerful technique with higher convergence with the computational method that gives analytical response to a linear problem. The effect of the types of CNT distributions, porosity coefficient, types of porous cores, porosity parameter, weight fraction and folding degree of GOAM, different geometric dimensions and different B.C.’s on the natural frequency is investigated. The obtained results are compared with the other literature, that there is a good agreement between them. On the other hands, the maximum error percentage of the present work (VIM) with Civalek and Kiracioglu [66] (Discrete singular convolution method) for the first five frequencies is equal to 0.3% according to Table 2, while in Table 3, the maximum error percentage of the present work (VIM) with Yas and Samadi [67] (differential quadrature method) for the first frequency with various boundary conditions and nanocomposite material is equal to 0.22%. In this regard, the present study can be a suitable platform to find the natural frequency and prevent the phenomenon of resonance and increase the life of the structure. Moreover, it is seen that with enhancing of weight fraction of GOAM, frequency increases because increasing the stiffness of structures. The importance of this research is to extract the formulation of sandwich beam structure for GOAM under different boundary conditions and compare the results between them by repeating the changes.

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.

Effect of carbon nanotube content and annealing temperature on corrosion performance of carbon nanotube/Ni composite layer

Adding carbon nanotubes (CNTs) to metal composites changes their corrosion resistance, which is significantly affected by the distribution of CNTs. In this study, the effect of the content and distribution of CNTs on the corrosion resistance of composites was investigated by changing the electrodeposition process. The results indicated that could inhibit grain growth and act as an elemental channel for passivation film formation, which positively enhanced the corrosion resistance of the material. However, the annealing used to improve the bonding strength of CNTs to the matrix increased the grain size of the material, which had a weakening effect on the corrosion resistance. Using ultrasonic in electrodeposition had an obvious promoting effect on the uniform distribution of CNTs. The composites with 0.1 g/l CNT showed the best corrosion resistance after annealing for 30 min at 600 °C.

In-depth investigation of how carbon nanofiller dispersion affects microcellular foaming behavior in poly(butylene succinate) nanocomposites

This study explores the impact of carbon nanotubes (CNTs) dispersion on the microcellular foaming characteristics of poly(butylene succinate) (PBS) matrices. Two distinct dispersion methods, primary (PD) and secondary (SD), were employed to fabricate PBS/CNT nanocomposites, resulting in different filler dispersion states. The PD technique involves the conventional method of direct melt blending PBS with CNTs, while the SD technique adopts a more advanced strategy by integrating the Pickering emulsion template with melt blending, achieving finer CNTs distribution within the PBS matrix. The results reveal that the SD technique leads to significantly more uniform distribution of CNTs, which in turn enhances the melt strength and crystallization of the polymer matrix, thereby broadening the window for microcellular foaming. Notably, foams developed through the SD method exhibited a decrease in cell size to 10.4 μm and an increase in cell density to 1.8×1010 cells·cm‐3. Moreover, this uniform distribution of CNTs contributed to superior cell stability and an increase in compressive strength to 14.0 MPa. These findings highlight the pivotal role of nanofiller dispersion in determining foam properties and establish foundational knowledge for designing PBS foams with consistent and uniform cell structures. Such advancements are crucial for enhancing the applicability and performance of PBS-based materials across a spectrum of industries.

Carbon nanotubes used to enhance the wear properties of AlSi10Mg/CNTs nanocomposites prepared through additive manufacturing

In this work, varying weight percentages of carbon nanotubes (CNTs) were reinforced in the AlSi10Mg alloy, and prepared nanocomposites through additive manufacturing. The distribution of CNTs in the metal matrix were achieved through functionalization and ball milling. The dispersion of CNTs were investigated through FESEM, TEM, and Raman spectroscopy. To study the wear properties, the prepared samples underwent wear tests at various loads and speeds. The wear properties, worn surfaces, and microhardness were thoroughly investigated. The results unveiled that the incorporation of CNTs led to a decrease in the wear rate and a reduction in the coefficient of friction. It was observed that CNTs functioned as a solid lubricant, resulting in a significant reduction in both the coefficient of friction and wear rate. The microstructures of the worn surfaces and wear channels became smaller and smoother after the addition of CNTs, and smaller-sized debris was produced.

Vibration analysis of functionally graded carbon nanotubes reinforced composite nanoplates

This work presents the analytical analysis for free linear vibration behavior of functionally graded-carbon nanotubes reinforced composite (FG-CNTRC) nanoplates in the framework of nonlocal strain gradient theory (NSGT) and the first-order shear deformation plate theory (FSDPT). The nanoplate is considered made of a mixture of an isotropic polymer matrix and reinforced carbon nanotubes (CNTs). Four different distributions of CNTs are examined including uniformly distributed and FG reinforcements (FG-O, FG-X, and FG-V). The governing equations of motion are established based on the Hamilton’s principle. The closed-form analytical solution for the natural frequency of FG-CNTRC nanoplates with simply supported all edges is carried out by using the Navier-type solution. The impact of some key parameters on the natural frequencies of FG-CNTRC nanoplates is also studied and discussed. The result shows that FG-CNTRC nanoplates reveal the softening- or hardening-stiffness effects depending on the relationship between the nonlocal parameter and the material length scale parameter. The aspect ratios of FG-CNTRC nanoplates, the volume fraction, and the distribution pattern of CNTs have also an important impact on the vibration behavior of FG-CNTRC nanoplates.

Nonlinear bending examination of nanocomposite cylindrical shell exposed to mechanical loads using dynamic relaxation method

In the current context, the nonlinear bending examination of a carbon nanotube reinforced composite (CNTRC) shell exposed to mechanical loading using the first-order shear deformation shell model via the dynamic relaxation (DR) procedure, is perused. The composite shell is assumed to be reinforced in the longitudinal axis. The curved morphology distribution of CNTs is considered to be functionally graded (FG) or uniform along the shell thickness. Mechanical properties of the constituents are gathered based on the modified rule of the mixture. For verification, the present numeric outcomes are compared with available references and ABAQUS finite element package. Finally, the roles of effective items including carbon nanotubes (CNTs) distributions, thickness-to-radius and length-to-radius ratios, boundary conditions, and the volume fraction of CNTs are investigated on the maximum non-dimension deflection.

Detection of compatibilizer efficiency in conductive polymer blends by impedance spectroscopy: Microstructure evaluation approach

AbstractA novel approach of electrical impedance spectroscopy (EIS) is proposed to investigate the role of a compatibilizer on nanoparticle distribution in polymer blends with a co‐continuous morphology. Polypropylene/poly(ethylene‐co‐vinyl acetate) PP/EVA blends containing 3 vol% carbon nanotubes (CNT) with varying contents of polypropylene‐grafted‐ maleic anhydride (PP‐g‐MA) as compatibilizer were directly melt mixed. Microscopy, rheology, and thermodynamic analyses confirmed the distribution of CNTs in PP, EVA, and their interface. The EIS behavior of the blend nanocomposites was remarkably changed due to the formation of interphase by PP‐g‐MA/CNT. It was found that as the efficiency of compatibilizer increases the frequency dependency of the impedance diminishes showing a significant shift in the frequency cutoff from 104 Hz to 5 × 105 Hz. The EIS results also showed that compatibilizer can affect the loss factor. Incorporating 5 vol% or 10 vol% of the compatibilizer slightly reduced the loss factor, but a considerable reduction was observed at 20 vol% at which a conductive continuous interphase of compatibilizer formed at the interface. Moreover, the presence of compatibilizer led to a remarkable increase in dielectric constant by four orders of magnitude. EIS can effectively and comfortably trace the performance of a compatibilizer in a conductive polymer blend nanocomposite.Highlights EIS measurements describe microstructure of conductive polymer blend. EIS detects morphology development of a compatibilizer at varying contents. Migration of compatibilizer intensifies the Nyquist diameter decrement. Compatibilizer decreases dielectric relaxation time.

Carbon Nanotubes (CNT) as an additive towards crack-free catalyst coated membranes (CCM)

In this study, carbon nanotubes (CNT) were used as an additive in coating inks for catalyst layers for PEM electrolyzers and fuel cells. Catalyst layers with and without CNT were prepared by direct membrane coating and analyzed for cracking behavior. The influence of CNT on crack prevention is discussed by varying the film thickness. Layers with CNT show no or less cracks at the same film thickness. Increasing the drying rate by raising the film temperature has no effect on crack formation, which allows shorter production times. The distribution and interaction of CNT in the microporous system are also discussed.

Natural Frequency Response of FG-CNT Coupled Curved Beams in Thermal Conditions

This study investigates the sensitivity of dynamic properties in coupled curved beams reinforced with carbon nanotubes (CNTs) to thermal variations. Temperature-dependent (TD) mechanical properties are considered for poly methyl methacrylate (PMMA) to be strengthened with single-walled CNTs (SWCNTs), employing the basic rule of mixture to define the equivalent mechanical properties of nanocomposites. The governing equations of motion are derived using a first-order shear deformation theory (FSDT) and Hamilton’s principle, accounting for elastic interfaces modeled using elastic springs. A meshfree solution method based on a generalized differential quadrature (GDQ) approach is employed to discretize the eigenvalue problem and to obtain the frequency response of the structure. The proposed numerical procedure’s accuracy is verified against predictions in the literature for homogeneous structural cases under a fixed environmental temperature. The systematic investigation assesses the impact of various geometric and material properties, including curvature, boundary conditions, interfacial stiffness, and CNT distribution patterns, on the vibrational behavior.

Low speed impact on sandwich beam with flexible core and face sheets reinforced with FG-CNTs

Purpose The purpose of this study is to model the theory of the low-velocity impact (LVI) process on sandwich beams consisting of flexible cores and face sheets reinforced with functionally graded carbon nanotubes (CNTs). Design/methodology/approach A series of parameters derived from molecular dynamics are used to consider the size scale in the mixture rule for the combination of CNTs and resin. A procedure involving the use of the first-order shear deformation theory of the beam is used to provide the displacement field of the sandwich beam. The energy method and subsequently the generalized Lagrange method are used to derive the motion equations. Due to the use of Hertz’s nonlinear theory to calculate the contact force, the equations of motion are nonlinear. Validation of the problem is carried out by comparing natural frequencies with other papers. Findings The influence of a series of parameters such as CNTs distributions pattern in the face sheets, the influence of the CNTs volume fraction and the influence of the core thickness to the face sheets thickness ratio in the issue of LVI on sandwich beams with clamped-clamped boundary conditions is investigated. The result shows that the type of CNTs pattern in the face sheet and the CNTs volume fraction have a very important effect on the answer to the problem, which is caused by the change in the value of the Young’s modulus of the beam at the contact surface. Changes in the core thickness to the face sheets thickness ratio has little effect on the impact response. Originality/value Considering the important application of sandwich structures in vehicles, aviation and ships, in this research, sandwich beams consisting of flexible core and CNTs-reinforced face sheets are investigated under LVI.

Flutter investigation and deep learning prediction of FG composite wing reinforced with carbon nanotube

Abstract The flutter of a composite wing reinforced with functionally graded carbon nanotubes (CNTs) has been investigated. A rectangular plate models a supersonic wing with cantilever boundary conditions. To determine displacement fields of a moderately thick plate, shear deformation theory is used. Using the Hamilton principle, a first-order piston theory was used to simulate supersonic airflow. This study examines four types of CNT thickness. Also, four different CNT distribution patterns are investigated. In a two-layer asymmetric composite, the effects of patch mass, mass distribution, fiber orientation angle, and distribution of CNTs were examined. Moreover, the results are compared and verified with other studies. A greater mass ratio led to a smaller flutter boundary, while a longer added mass increased the flutter boundary. A variation in the distribution pattern in CNT fiber orientation results in a distinct behavior of the flutter boundary for asymmetric composites with increasing orientation angles. The artificial neural network is utilized to predict the damping ratio, and the results showed great accuracy compared to the study results. Hyperparameter tuning is employed for better optimizing the predictive models.

Flexible Piezoresistive Polystyrene Composite Sensors Filled with Hollow 3D Graphitic Shells.

The objective of this research was to develop highly effective conductive polymer composite (CPC) materials for flexible piezoresistive sensors, utilizing hollow three-dimensional graphitic shells as a highly conductive particulate component. Polystyrene (PS), a cost-effective and robust polymer widely used in various applications such as household appliances, electronics, automotive parts, packaging, and thermal insulation materials, was chosen as the polymer matrix. The hollow spherical three-dimensional graphitic shells (GS) were synthesized through chemical vapor deposition (CVD) with magnesium oxide (MgO) nanoparticles serving as a support, which was removed post-synthesis and employed as the conductive filler. Commercial multi-walled carbon nanotubes (CNTs) were used as a reference one-dimensional graphene material. The main focus of this study was to investigate the impact of the GS on the piezoresistive response of carbon/polymer composite thin films. The distribution and arrangement of GS and CNTs in the polymer matrix were analyzed using techniques such as X-ray diffraction and scanning electron microscopy, while the electrical, thermal, and mechanical properties of the composites were also evaluated. The results revealed that the PS composite films filled with GS exhibited a more pronounced piezoresistive response as compared to the CNT-based composites, despite their lower mechanical and thermal performance.

Thermo-electrical postbuckling behavior of carbon nanotubes-reinforced composite beams with piezoelectric layers and tangentially restrained ends

An analytical investigation on the buckling and postbuckling behavior of carbon nanotube-reinforced composite beams integrated with surface-bonded piezoelectric layers under uniform temperature rise is presented in this paper. Carbon nanotubes (CNTs) are reinforced into isotropic matrix through uniform distribution and functionally graded distributions. The properties of material constituents are assumed to be temperature-dependent and effective properties of CNT-reinforced composite are estimated using an extended rule of mixture. Equilibrium equations of the beams are established based on Euler-Bernoulli theory including von Kármán nonlinearity and solved using analytical solutions and Galerkin method. Critical temperatures and postbuckling load-deflection paths are determined using an iteration algorithm. Parametric studies are performed to examine the influences of CNT distribution and volume fraction, applied voltage, in-plane and out-of-plane conditions of the ends, slenderness, and thickness ratio of layers on the critical loads and postbuckling load carrying capacity of beams. Results reveal that CNT volume fraction and degree of in-plane ends constraint have slight and significant influences on the critical temperatures and thermal postbuckling paths, respectively. The study also finds that negative and positive voltages increase and decrease the thermal buckling temperatures of piezoelectric CNT-reinforced composite beams.

Electrochemical performance of TiNb2O7/graphene/CNTs hybrid nanocomposites as anode materials for Li-ion batteries

In this study, the titanium niobium oxide (TiNb2O7)/ electrochemically exfoliated graphene/ carbon nanotubes (CNTs) hybrid nanocomposites with different hybrid ratios are synthesized by the solvothermal method for application as anode materials for lithium-ion batteries. Results indicated that the graphene sheets act as a substrate for the distribution of both TiNb2O7 nanoparticles and CNTs. Morphological studies showed the effective distribution of CNTs and TiNb2O7 nanoparticles on the surfaces and between the few-layered graphene in hybrid nanocomposites. Electrochemical studies showed the synergic effects of graphene and CNTs in improving the high-rate capacity and cyclic stability of the TiNb2O7. This study revealed that the electrochemical performance of hybrid nanocomposites is influenced by the mass ratio of graphene to CNTs. As the optimal sample, the samples with 1 wt% graphene and 2 wt% CNTs presented enhanced-cyclic stability (161 mAh/g after 200 cycles at a current density of 387 mA/g) and rate performance (74.4 mAh/g at a high current density of 7740 mA/g).

Influences of External Magnetic Field on Thermo-Mechanical Vibration Analysis of Nanocomposite Beam using Higher-Order Strain Gradient Theory

Composite nanobeams with carbon nanotube (CNT) reinforcement are crucial components in various applications due to their unique mechanical and thermal properties. The present work investigates the frequency–aspect ratio relationship in composite nanobeams with CNT reinforcement, particularly under varying temperatures, magnetic field strengths, and Winkler elastic stiffnesses. The non-dimensional frequency variation with aspect ratio, influenced by temperature differences, reveals distinct behavior patterns. The introduction of a magnetic field alters frequency characteristics, with uniform distribution (UD) nanobeams displaying higher frequencies. The impact of Winkler elastic stiffness, temperature differences, and magnetic field strengths on frequency elucidates differing responses between UD, [Formula: see text]-type distribution (XD), and [Formula: see text]-type distribution (VD) nanobeams. Nonlocal strain gradient theory proves essential in capturing dynamic characteristics influenced by CNT distribution. These findings shed light on the intricate dynamics of composite nanobeams, providing valuable insights for the design of future nano-devices employing CNT-reinforced composite beams as fundamental elements.

Stochastic free vibration analysis of FG-CNTRC plates based on a new stochastic computational scheme

Stochastic analysis can provide more accurate results compared to deterministic analysis. In this study, the spatial variability of material parameters is introduced into the free vibration analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates to achieve a higher degree of accuracy, and a new stochastic computational scheme is proposed to handle the low-level uncertainties. First-order shear deformation theory (FSDT) is employed to establish the displacement field of the plates. The Young's moduli of carbon nanotube (CNT) and matrix are regarded as one-dimensional (1D) and two-dimensional (2D) random fields, respectively, which is discretized by Karhunen-Loève (K-L) expansion. The obtained random variables are substituted into modified perturbation stochastic method (MPSM) and radial point interpolation method (RPIM) to calculate the first two order estimates of the stochastic non-dimensional natural frequencies ω¯. The sensitivity of the first to fourth ω¯ to the random fields is analyzed, and the corresponding stochastic bands are plotted. The results indicate that the presented approach can accurately solve the generalized eigenvalue problem in stochastic free vibration; ω¯ is sensitive to random fields E11CNT and Em, and insensitive to random field E22CNT; the CNT distribution mode also affects the sensitivity.

Atomic insights into the tensile behavior of carbon nanotube with different geometrical characteristics embedded in nickel matrix

Carbon nanotubes (CNTs) extensively serve as reinforcements in metal matrix nanocomposites because of their superior mechanical properties. In this paper, we have performed a qualitative analysis of carbon nanotubes with different geometrical properties embedded in a nickel matrix to predict tensile behavior and mechanical properties via molecular dynamics simulations. The effects of CNT rotate angle, long-short CNT and CNT number on the deformation mechanism, Young's modulus and ultimate tensile strength (UTS) were investigated. The different rotation angles of CNTs significantly affect the deformation mechanisms and mechanical properties of CNT/Ni nanocomposites. For the long CNT/Ni composites, when the rotate angle is 0°, the Young's modulus and UTS are the smallest, which are 233.03 GPa and 10.68 GPa, respectively. When the rotate angle is 15°, the elastic modulus and UTS are the largest, which are 252.9 GPa and 15.63 GPa, which increase by 8.5 % and 46.3 %, respectively. For the short CNT/Ni composites, when the rotate angle is increased from 0°to 90°, its mechanical properties first decrease and then increase. The distribution of long and short CNTs significantly modifies the deformation pattern of the nickel matrix. Increasing number of CNTs improves Young's modulus and UTS of CNT/Ni nanocomposites.

Effect of CNT on the Physical and Electrical Properties of CNT/UHMWPE Nanocomposite Sensor

Nano Composites Polymer represents a class of multifunctional sensors that can effectively respond to changes in electrical properties when subjected to external forces acting on their physical characteristics. The research aims to develop nanocomposite polymer sensors that can respond well and be easily molded. The experimental process involved mixing Ultra-high-molecular-weight polyethylene (UHMWPE) with 1%, 4%, and 7wt% of carbon nanotubes (CNT) using the hot pressing method, leading to remarkable improvements in the electrical and mechanical properties of the composite polymers. The distribution patterns of CNT at different weight ratios showed that 4 wt% exhibited a more desirable and uniform distribution. However, at 1 wt%, the amount of CNT was insufficient, resulting in scattering and disconnection. On the other hand, at 7 wt%, the CNT distribution appeared to be densely bundled in some areas, leading to detrimental effects on the mechanical and electrical properties, as well as the electrical percolation threshold of the composites. Regarding the mechanical properties test, significant improvements were found at 4 wt% for the tensile strength, but when the filler content exceeded 4 wt%, there was a reduction in the tensile strength of the CNT/UHMWPE composites. Additionally, the change in electrical resistance based on the physical characteristics was examined by varying the percentage of CNT added to UHMWPE through compression and bending tests. The compression tests were conducted using weights ranging from 0 to 10 kg, and the bending tests were performed with angles from 0° to 40° degrees. In terms of the test results, however, with 4% and 7% wt% CNT filler, the electrical resistance values could be successfully measured by a multimeter. The electrical percolation threshold was found to be very good at 4 wt%. For the compression testing results, the resistance values ranged from approximately 27.329 to 32.389 KΩ for the 4 wt% filler and from 0.504 to 0.552 KΩ for the 7 wt% filler. As for the bending testing, the resistance values ranged from approximately 4.019 to 4.044 KΩ for the 4 wt% filler and from 0.427 to 0.432 KΩ for the 7 wt% filler.