Quantitative Analysis ofDamping Enhancement andPiezoelectric Effect Mechanism of CNTs / PMN / EP Composites

New types of piezoelectric damping materials, including carbon nanotubes (CNTs)/lead magnesium niobate (PMN)/epoxy (EP) resin, are developed. +e tan δ area (TA) analysis method is selected to evaluate the damping properties which obviously clarifies the effect of maximum loss factor (tan δ) and effective temperature range on damping properties. Furthermore, the dominant factor of damping enhancement is quantitatively analyzed via the value of TA. Compared with PMN, the interfacial friction of CNTs acts as the dominant factor for the content less than 0.6wt.%. +e maximum damping percentage of CNTs reaches 29.14%. CNTs form loop circuits gradually with the content of CNTs increasing, and electrical energy generated via piezoelectric effect of PMN is efficiently dissipated through the conductive network. +us, PMN becomes the dominant factor as the content of CNTs exceeds 0.8 wt.%, and the damping percentage reaches 47.43% at the content of CNTs of 1.0 wt.%.


Introduction
In the past few decades, the viscoelastic material with an inherent high loss factor is widely applied in automobiles, aircraft, and military equipment to suppress vibration and impact noises [1].For example, soft viscoelastic layers in viscoelastic sandwich structures are provided as the damping component in order to improve dynamic response [2].A new type of damping enhancement with piezoelectric and conductive materials as fillers has been developed by Hagood and von Flotow [3,4].Electrical energy, generated by piezoelectric effect of piezoelectric ceramics, can be efficiently dissipated by external electronic circuits [5].Conductive fillers are introduced into piezoelectric-ceramic/polymer composites as passive electrical network, such as carbon nanotubes (CNTs), carbon black (CB), graphite, and aluminum particles [6][7][8][9][10][11][12][13].CNTs are widely used due to the high electric current carrying capacity (10 11 ∼10 12 A/cm 2 ) [14].It is revealed that the CNTs provide superior conductivity at very low concentrations which can transfer electrical energy into thermal energy efficiently [14].Tian et al. reported a type of CNTs/lead zirconate titanate (PZT)/EP composites.ey found that the generated electrical energy was well dissipated, and the loss factors of composites were improved by the incorporation of PZT and CNT at critical electrical percolation [7,8].Carponcin et al. studied the influence of piezoelectric on damping properties of CNTs/PZT/polyamide composites, and it was found that the polarization of piezoelectric ceramic particles improved the loss factor of 20% reaching to 0.052 [9].PMN as another piezoelectric material with perovskite structure also possess high piezoelectric coefficient and dielectric permittivity.PMN piezoelectric materials were used in 0-3 piezoelectric composites for damping enhancement gradually [10][11][12].Li and Du focused on damping properties of nitrilebutadiene rubber/phenolic resin/PMN/CB composite.Mechanical energy was converted efficiently via piezoelectric effect at PMN volume content of 50%, and the maximum loss factor reached 0.813 [10].Shamir et al. found that adding CB to the composites reduced the peak damping intensity but enhanced damping at higher temperature, and the effective damping temperature range was widened [15].Chang et al. investigated the damping property of polyurethane composites with different ultraviolet absorbents, and they found that the tan δ increased at the temperature range of higher than the glass transition temperature though the tan δ max was gradually reduced [16].us, in this study, tan δ area (TA) and loss modulus area (LA) values are selected as damping performance parameter of materials which obviously clarify the effect of maximum loss factor and effective temperature range on damping properties [17][18][19][20].Furthermore, TA analysis method can be used for quantitative analysis of damping enhancement.
In this study, conductive phase (CNTs) and piezoelectric phase (PMN) are introduced into epoxy matrix to fabricate piezoelectric damping composites.Electrical energy generated via piezoelectric effect of PMN is efficiently dissipated through conductive network.us, damping performance of CNTs/PMN/EP composites is effectively improved.e damping enhancement effect of each component is specifically clarified, and the damping percentage is quantitatively analyzed based on the TA analysis method.

Materials.
e lead magnesium niobate (PMN) ceramic powder was supplied by Baoding Hengsheng Acoustics Electron Apparatus Company with the mean particle size of 1-10 μm. e dimensions of CNTs (supplied by XFNANO) were 10-20 nm in diameter, and the purity of CNTs was >95%.Epoxy resin used in experiment was diglycidyl ether of bisphenol-A type with an epoxide equivalent weight of 185-200 g/eq.e curing agent used in experiment was polyethylene polyamine which was supplied by Aladdin.e molecular formula was C 2n H 5n N n .Epoxy resin was transferred into three-dimensional network structure by catalytic polymerization and addition polymerization reaction between molecular chains when polyethylene polyamine was introduced into epoxy, which resulted in the curing of composites.

Preparation of CNTs/PMN/EP Composites.
CNTs were functionalized by 3 : 1 H 2 SO 4 (98%)/HNO 3 (70%) acid treatment to obtain carboxyl and hydroxyl groups.Matrices of epoxy resin (EP) with different contents of acid-treated CNTs were made.en, PMN ceramic was preprocessed by silane coupling agents KH-560 to improve interfacial contact performance and then added to CNT/EP solution.e solution was stirred at 60 °C for 12 h with magnetic stirrer and then placed in vacuum drying oven for gas evaporation.Finally, solution with curing agent was cast into a mold and cured for 5 h at room temperature, with a subsequent step at 105 °C for 2 h.e fracture surface analysis was performed by field emission scanning electron microscope (FE-SEM, Hitachi S-4800).
e investigation of viscoelastic behavior was performed by dynamic mechanical thermal analysis (DMA, PYRIS-7e).Resistivity was tested by impedance analyzer (HP4294A).

TA Analysis Method.
e TA analysis method is selected to evaluate the damping properties, which obviously clarifies the effect of maximum loss factor and effective temperature range on damping properties.Fradkin et al. proposed the definition of damping functions [21]: where E ″ is the loss modulus, tan δ is the loss factor, T g is the glass transition temperature, E ′ G and E ′ R are the storage modulus in glassy and rubbery states, T G and T R are the initial and final temperature of glass transition, (E a ) avg is the activation energy of the relaxation process, and R is the gas constant.Materials show obvious damping performances for the loss factor reaching 0.3 around damping peak, which means composites reach effective loss factor.us, in this research, we choose effective damping temperature range (tan δ ≥ 0.3) as integral region.T G and T R in formulas (1) and ( 2) are replaced with the initial and final temperature of which tan δ reaches 0.3.en, TA values are obtained through integral calculation of loss factor curves over the temperature range.Toshio Ogawa proposed that loss factor had more practical significance than loss modulus in noise control and damping analysis [17].Amorphous polymer, semicrystalline polymer, and single damping peak copolymer were used as research objects, and the functional relation between TA values and group numbers was shown as follows: where X i is the number of group i, a i is the regression coefficient which means the contribution of TA values by each group, and a 0 is a constant.e group contribution analysis method is used to calculate theoretical TA values and develop a relation between the contribution of each functional group and damping properties.
us, TA values can be used for quantitative analysis of damping enhancement.e damping percentage of each component is quantitatively analyzed based on following formulas: where D i is the damping percentage of component i, TA i and TA c are the TA value of component i and composite, and TA c,0 is the TA value of composite at 0 wt.% content of component i.

Results and Discussion
As shown in Figure 1, CNTs dispersed well in the chemically functionalized CNTs/EP composites at 0.2 wt.% CNT content, which improves interfacial frictional energy dissipation of CNTs.As we can see from the magni ed SEM image, the interparticle distance between carbon nanotubes is very close.When CNT content is up to 1.0 wt.%, no obvious agglomeration is observed in the matrix, and the dispersion state in the whole region still keeps well.With the content of CNTs increasing, some matrix-rich (not containing CNTs) regions appear, and some CNTs entangle with each other as shown in Figure 1(c).As we can see from the magni ed SEM image, the agglomeration of CNTs weakens the interfacial contact between CNT llers and epoxy matrix.Dynamic mechanical analysis (DMA) of CNTs/EP composites are shown in Figure 2(a).In general, damping materials reach maximum loss factor (tan δ max ) at glass transition temperature (T g ).T g of CNTs/EP composites is in correspondence with pure epoxy materials.tan δ max at T g increases sharply and reaches optimal value at the CNT content of 0.2 wt.%, due to the interfacial friction when CNTs uniformly dispersed in epoxy matrix.High content of CNTs widens e ective temperature range, while tan δ max decreases due to agglomeration of llers and high viscosity of composites.
us, TA values are selected as damping performance parameter which obviously clari es the e ect of maximum loss factor and wide temperature range on damping properties.Based on loss factor curves of CNTs/EP composites, TA values of composites with di erent contents of CNTs are obtained as shown in Figure 2(b).e frictional energy dissipation between conductive phase and epoxy matrix rises as the content of CNTs increases.e TA value of CNTs/EP composites increases correspondingly and reaches the maximum value at 0.6 wt.% content of CNTs, for the reason that CNTs widen e ective temperature range at 0.6 wt.% content of CNTs compared to 0.2 wt.% CNTs/EP composite.As the CNT content increases gradually, CNTs/EP composites show higher viscosity.
e e ective temperature range keeps constant when the content of CNTs exceeds 0.8 wt.%.
e entanglement of CNTs in epoxy matrix results in the decrease of TA value.However, the e ective temperature range is widened signi cantly when the content of conductive phase exceeds percolation threshold.e TA value of CNTs/EP composites increases at CNT content of 2.0 wt.% consequently.Damping percentage of CNTs and epoxy matrix can be calculated by formulas ( 4) and ( 5).
e damping percentage of CNTs shows the same trend with TA values and reaches 32.22% at the CNT content of 0.6 wt.%.For the reason that CNTs are uniformly dispersed in epoxy matrix without obvious agglomeration behavior, the interfacial friction is e ectively promoted for damping enhancement.
As shown in Figure 3, PMN is uniformly dispersed in epoxy matrix without obvious agglomeration.Composites show strong interfacial compatibility between PMN and epoxy.
ough the viscosity of PMN/EP composites increases at 60 wt.% content of PMN, the dispersion state in the whole region can still keep well.e viscosity increases signi cantly when the content of PMN reaches 80 wt.%.As a result, cohesive force between PMN and epoxy becomes weaker, which causes the agglomeration of PMN ceramic powders and even some holes show up in composites.
As shown in Figure 4(a), T g of PMN/EP composites is a ected obviously by the addition of PMN ceramics.T g shifts toward high temperature region for the content less than 40 wt.%.T g of PMN/EP composite is lower than pure epoxy material, and the e ective temperature range is e ciently widened.Based on loss factor curves of PMN/EP composites, TA values of composites with di erent contents of PMN are obtained as shown in Figure 4(b).Piezoelectric e ect of PMN ceramic is generated by external force.Bound charge exists on the crystal surface which cannot be transferred into other forms of energy.As a result, the enhancement of damping properties is mainly achieved by the interfacial friction of PMN ceramics.TA values of PMN/EP composites increase with the increase in the content of PMN and reach 14.4 at 40 wt.% content of PMN.On the one hand, the interfacial friction between llers and polymer chains over Advances in Materials Science and Engineering the transition range is enhanced with the increase in the content of PMN.On the other hand, llers reduce the free volume of elastic polymers which results in the decrease of viscoelastic damping.It means that the increase in frictional energy dissipation can be massively o set by the decrease in viscoelastic damping of matrix; thus, TA values of PMN/EP composites decrease correspondingly.Damping percentage of PMN and EP can be calculated by ( 4) and ( 5). e damping percentage of PMN shows the similar trend with TA values and reaches 33.95% at PMN content of 40 wt.%.PMN llers are uniformly dispersed in the matrix and improve damping properties through frictional energy dissipation e ciently while maintaining the inherent viscoelastic damping of epoxy.However, damping properties cannot be improved obviously with the content of PMN exceeding 60 wt.%. e increase in frictional energy dissipation is massively o set by the decrease in viscoelastic damping of epoxy matrix, so the damping percentage of PMN is merely 4.28% at 60 wt.%PMN content.
Loss factor curves of CNTs/60 wt.% PMN/EP composites are shown in Figure 5(a).e increase in frictional energy dissipation can be massively o set by the decrease in free volume of matrix at 60 wt.% content of PMN, and the impact of piezoelectric e ect on damping properties can be signi cantly indicated.As shown in Figure 5(a), tan δ max increases sharply at 1.0 wt.% content of CNTs.Combined with TA values of CNTs/EP composites, the damping percentage of each component is shown in Figure 5(b).TA values of CNTs/60 wt.% PMN/EP composites increase gradually with the increasing content of CNTs and reach 21.26 at 1.0 wt.% CNT content.e e ect of piezoelectric phase (PMN) and conductive phase (CNTs) on damping properties can be explained from two aspects.On the one hand, the interfacial friction between llers and epoxy matrix promotes energy dissipation e ciently.On the other hand, piezoelectric e ect of PMN results in the enrichment of positive and negative charge on crystal surface.
en, electrical energy converted from mechanical energy is dissipated through continuous conductive network (CNTs).When the content of CNTs is less than 0.6 wt.%, CNT llers exist as independent units rather than conductive network.us, bound charge on the crystal surface cannot be transferred into other forms of energy.e interfacial e ect of CNTs is the dominant factor of damping enhancement  4 Advances in Materials Science and Engineering through frictional energy dissipation.
e damping percentage of CNTs reaches 29.14% at CNT content of 0.6 wt.%. e conductive network generates gradually for the content exceeding 0.8 wt.%.Electrical energy generated via piezoelectric e ect of PMN is dissipated in the form of thermal energy; thus, piezoelectric phase (PMN) becomes the dominant factor of damping enhancement.Damping percentage of PMN increases obviously and reaches 47.43% at 1.0 wt.% CNT content.When the content of CNTs reaches percolation threshold (1.0 wt.%), the conversion e ciency of electrical energy is the highest.When the CNT content increases to 2.0 wt.%, the high viscosity of composites results in the agglomeration behavior of llers which reduces functional energy dissipation.Furthermore, high content of CNTs forms short circuit network which decreases energy conversion e ciency.As a result, TA values of CNTs/60 wt.% PMN/EP composites and the damping percentage of PMN decrease.
e damping percentage of PMN shows the similar trend with TA values.It is indicated that damping properties of composites are signi cantly improved by piezoelectric e ect of PMN.us, the e ective method for damping enhancement of piezoelectric damping materials is to realize e cient energy conversion by improving piezoelectric e ect.As shown in Figure 6, the R v value decreases apparently for the content of CNTs exceeding 0.8 wt.%, which implies that CNT particles gradually contact with each other at 0.8 wt.% CNT content.e R v value is lower than 10 7 when the CNT content reaches 2.0 wt.%. e formation status of CNT conductive network at di erent CNT contents is shown in Figure 7.When the content of CNTs is small (Figure 7(a)), less than 0.6 wt.%, the electrical network cannot form.us, the piezoelectric e ect of PMN has no signi cant e ect on damping enhancement.With the increase in CNT content, carbon nanotubes start to form small loops around PMN particles (Figure 7(b)).
ose loop circuits are taken as conversion units to convert electrical energy into thermal

Conclusions
e present paper has provided a comprehensive study about quantitative analysis of damping properties based on the TA analysis method.e addition of high content of conductive phase would reduce the damping peak intensity but enhance damping at higher temperatures, and the effective damping temperature range is widened.It is di cult to evaluate the comprehensive damping properties of materials by choosing tan δ max as the only performance index.us, in this research, the TA value is selected to evaluate damping properties.
e TA analysis method obviously clari es the e ect of maximum loss factor (tan δ) and effective temperature range on damping properties.And synergies of piezoelectric phase and conductive phase are further researched.Data Availability e data used to support the ndings of this study are available from the corresponding author upon request.Advances in Materials Science and Engineering

Figure 5 :Figure 4 :
Figure 5: Damping properties of CNTs/PMN/EP composites as a function of CNT content: (a) loss factor curves; (b) TA values and damping percentage.

( 1 )
e damping percentage of CNTs in CNTs/EP composites reaches 32.22% at CNT content of 0.6 wt.%. e maximum loss factor reaches 0.56, and the e ective temperature range is widened.(2) e damping percentage of PMN ceramics in PMN/EP composites reaches 33.95% at 40 wt.%PMN content.e increase in frictional energy dissipation can be massively o set by the decrease in viscoelastic damping of matrix when the content of PMN exceeds 60 wt.%.So damping properties of PMN/EP composites cannot be improved obviously, and the damping percentage of PMN is merely 4.28%.(3) e interfacial e ect of CNTs acts as the dominant factor of damping enhancement for the content less than 0.6 wt.% in CNTs/PMN/EP composites, and the maximum damping percentage reaches 29.14%.However, PMN becomes the dominant factor of damping enhancement with the content of CNTs increasing, and the damping percentage reaches 47.43% for the content of CNTs reaching percolation threshold.Synergies of piezoelectric phase and conductive phase result in the damping enhancement of CNTs/PMN/EP composites.

Figure 7 :
Figure 7: Formation status of CNT conductive network at di erent CNT contents.

Figure 6 :
Figure 6: Resistivity of composites as a function of CNT content.