Article pubs.acs.org/JPCB
Considerable Different Frequency Dependence of Dynamic Tensile Modulus between Self-Heating (Joule Heat) and External Heating for Polymer−Nickel-Coated Carbon Fiber Composites Rong Zhang,† Yuezhen Bin,† Enyuan Dong,‡ and Masaru Matsuo*,† †
Department of Polymer Material Science, Faculty of Chemical, Environmental and Biological Science, and ‡Department of Electrical and Electronics Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China S Supporting Information *
ABSTRACT: Dynamic tensile moduli of polyethylene−nickel-coated carbon fiber (NiCF) composites with 10 and 4 vol % NiCF contents under electrical field were measured by a homemade instrument in the frequency range of 100−0.01 Hz. The drastic descent of the storage modulus of the composite with 10 vol % was verified in lower frequency range with elevating surface temperature (Ts) by self-heating (Joule heat). The composite was cut when Ts was beyond 108 °C. On the other hand, the measurement of the composite with 4 vol % beyond 88 °C was impossible, since Ts did not elevate because of the disruption of current networks. Incidentally, the dynamic tensile moduli by external heating could be measured up to 130 and 115 °C for 10 and 4 vol %, respectively, but the two composites could be elongated beyond the above temperatures. Such different properties were analyzed in terms of crystal dispersions, electrical treeing, and thermal fluctuation-induced tunneling effect.
■
INTRODUCTION In the previous paper,1 a surprising phenomenon was reported. Without melting flow, the X-ray diffraction from linear ultrahigh molecular weight polyethylene (UHMWPE) provided only amorphous halo at 129.0 °C (surface temperature, Ts arisen by Joule heat) lower than the conventional known melting point 145.5 °C2 and the equilibrium melting point 141.6 ± 0.5 °C3 for PE, on applying electrical field to UHMWPE−nickel-coated carbon fiber (NiCF) composite. The appearance of only amorphous phase was attributed to three reasons: (1) the transferring electrons between overlapped adjacent NiCFs by tunneling effect struck together with X-ray photons, (2) some of the transferring electrons flown out from the gap to UHMWPE matrix collided against carbon atoms of UHMWPE, and (3) the impact by the collision caused disordering chain arrangement in crystal grains. Based on the above backgrounds, this paper deals with the mechanical properties of UHMWPE−NiCF composites by self-heating (Joule heat) and external heating. The comparison by the two heating modes is very important to investigate whether UHMWPE−NiCF composites can be adopted as positive temperature coefficient (PTC) materials. Certainly, PTC materials play important roles in promoting significant applications to floor-heating and loft-heating in order to get rid of snow removing by humans. To ensure comfortable daily living in winter, studies on the cost-effective floor-heating and loft-heating must be established.4−9 Obviously, light PTC materials as heating elements have advantages for saving construction cost of building circulation in addition to the © XXXX American Chemical Society
safety and cleanliness in comparison with heavy hot water tubes. Recently, PTC materials by floor-heating and loft-heating tend to be adopted on building isolated houses as well as apartments. Judging from the serious damage of bank building by low-frequency earthquake at Mexico in 1985, the horrors of low-frequency earthquake (0.1−2 Hz) must be taken into consideration for collapse of constructions. Different from topics of earthquake magnitude and the better prediction by magnetic field observation, there has no report about the damage of PTC materials against low-frequency earthquake, since no experimental method has been established for the frequency dependence of mechanical properties under applied electrical fields, which was different from usual external heating. This paper is concerned with frequency dependence of the dynamic tensile modulus of PTC materials under applied electrical field. Fine homemade attachments were fixed on a commercial viscoelastic spectrometer to measure the dynamic tensile modulus of UHMWPE−NiCF composites with different frequencies at the desired temperatures controlled by applied electrical field. As a result, the storage modulus decreased drastically with decreasing frequency. Before the present discussion, we must emphasize that the direction of the gap distance (D) between adjacent NiCFs in composites (see Figure 3f) is random, since the NiCFs are oriented randomly within the composites. Accordingly, when Received: March 29, 2014 Revised: May 28, 2014
A
dx.doi.org/10.1021/jp5031202 | J. Phys. Chem. B XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry B
■
Article
EXPERIMENTAL SECTION Sample Preparation. In this study, UHMWPE (Mitsui Chemicals, Hizex) powders with a viscosity average molecular weight of 6.3 × 106 (M̅ W/M̅ N ca. 4.2 measured by GPC and degree of short chain branching (1/1000C) ≪ 1) were used as matrix. For the original NiCF, average diameter of CF was ca. 7.5 μm, thickness of Ni coating layer was ca. 0.25 μm, density of NiCF was 2.7 g/cm3, and specific resistivity was 7.50 × 10−5 Ω· cm, which was a little bit higher than the intrinsic resistivity of nickel (6.84 × 10−6 Ω·cm). The composites were prepared by the gelation/crystallization method, and the details of the preparation were described elsewhere.1 Measurements. Simultaneous measurements concerning dynamic tensile modulus, electrical conductivity, and surface temperature (Ts) were carried out for the UHMWPE−NiCF composite as a function of frequency at several temperatures. The complex dynamic tensile modulus functions were measured continuously as a function of frequency under decreasing process from 100 to 0.01 Hz or from 100 to 8 Hz by using a viscoelastic spectrometer (VES-F, Iwamoto Machine Co. Ltd.). The specimens with a length of 40 mm and a width of 4 mm were used, and the length of the specimen between the jaws was 30 mm. On measuring the dynamic modulus under applied electrical field, the special homemade holders were prepared and insulated medium was set between the electrodes and the clamps body to avoid the current flow to the main body of the spectrometer as shown in Figure 1. That is,
the bulk strain is applied along one direction, the strain of a number of D existed in the composite appears as stretching, shear, and compression. Such detailed analyses are described elsewhere.10−12 Different from the cases reported by other papers,13−16 the external bulk strain to place the sample in tension ensuring axial sinusoidal oscillation which had a peak deformation of 0.067% to ensure linearity for measuring correct dynamic tensile modulus, and then the strain of D is negligible small to change conductivity of the composite. Considering the crystal dispersion of PE in terms of viscoelastic studies, the disordering of UHMWPE chains in crystal grains has been thought to be due to α2 dispersion associated with intracrystal lattice retardation phenomenon relating to smearing-out effect of the crystal lattice potential at the onset of rotational and transitional oscillations of polymer chains within the crystal grains.12,17−20 Recently, from theoretical consideration by computer simulation for 40 chains with each consisting 400 CH2 segments, Zhang and Luo21 pointed out that the segmental rotations along PE chains could significantly scatter phonons and thus reduce the thermal conductivity, but the rotation is limited to the dihedral angle of the chain backbone because of stiffness for the bond stretching and bond bending. Their theoretical analysis justified a number of reports published already.12,17−20 Based on the above backgrounds, this paper is concentrated on the frequency−temperature dependence of UHMWPE− NiCF composites with 10 and 4 vol % NiCF contents measured under self-heating (by Joule heat) and external heating. The master curves of the storage modulus (E′) and the loss modulus (E″) were obtained by shifting horizontally and then vertically until good superposition was achieved. From the horizontal shift of the E″ curves, the two kinds of activation energies could be obtained, indicating the existence of two relaxations α1 and α2, as have been reported by a number of papers.12,17−20,22,23 The large difference of activation energy of α2 between self-heating and external heating was confirmed, although the values of α1 associated with intercrystal mosaic block relaxation12,17−20,22,23 were independent of heating modes. Different from usual external heating in the frequency range of 100−0.01 Hz, Ts beyond 108 °C by self-heating did not realize by cutting of the composite with a 10 vol % content and Ts did not elevate beyond 88 °C for the composite with a 4 vol % content when raising electrical field. The drastic decrease of E′ at low frequency range (20 °C, which were calculated at A = 1.17 nm2. (c) Logarithmic plots of the resistivity (open circles) versus temperature for a 10 vol % NiCF content in the range from −146 to 140 °C and the calculated results. (d) Temperature dependence of D at different K. (e) Open circle plots of resistivity and calculated values of D versus Ts arisen by Joule heat. (f) Arrangement model (I) of NiCFs through junction gaps; (II) enlargement of the gap between neighboring NiCFs with distance D and A in model I.
Figure 3c shows temperature dependence of the resistivity for the composite with a 10 vol % NiCF content in the temperature range from −146 to 140 °C. The resistivity increased slightly from −146 to 125 °C like metal. The resistivity increased suddenly in the temperature range from 125 to 140 °C like the PTC phenomenon, but the maximum was ca. 0.12 Ω·cm. Such behavior is quite different from the thermal behavior of the composite with a 4 vol % NiCF content beyond 106 Ω·cm at 140 °C, which was due to high conductivity of the composite with a 10 vol % NiCF content. The best fitting up to 120 °C could be obtained at D = 0.185 nm, A = 500 nm2, and λ = 0.235. Sheng’s equation assured the good agreement for the increase of resistivity with elevating temperature at very narrow gap distance D. The problem is that the gap, 0.185 nm, is too narrow to allow the existence of UHMWPE between overlapped adjacent NiCFs. The electron transfer between the narrow gap by the tunneling effect is similar to the current flow along continuous Ni layer. This means that many conjunctions of NiCFs are thought to be continuous polygonal line for electrical current. However, the current transfer between very narrow Ni surfaces by tunneling effect is not equal to usual electrical transfer along continuous surface. The value of D to give the best fitting as a function of temperature was given at A = 500 nm2 and λ = 0.235, which is shown in Figure 3d.
composites. Figure 3a shows logarithmic plots of resistivity versus temperature for a 4 vol % content, in which the resistivity (plotted as open circles) decreased gradually with increasing temperature from ca. −145 to ca. 20 °C and increased clearly beyond ca. 50 °C associated with the beginning temperature of α dispersion (crystal dispersion).12 The logarithmic plots of resistivity increased drastically beyond ca. 120 °C and reached the maximum at ca. 140 °C. The increase of resistivity with elevating temperature was obviously attributed to the powerless tunneling effect of electrons. Namely, the increase of resistivity beyond 20 °C is probably thought to be due to the fact that the thermal expansion of UHMWPE matrix with elevating temperature was more predominant than promotion by direct tunneling effect with elevating temperature.32−35 The red curve below 20 °C and blue curve above 20 °C were calculated by using the fluctuation probability function based on the Sheng’s theory.24 The outline is described in the Supporting Information. By using eqs S1 and S2 in the Supporting Information, the parameters D, A, and λ (= 0.795e2/4DKU0, K: permittivity of insulating barrier = 2.3 for UHMWPE36) to achieve the best fitting between experimental and theoretical results were obtained as a function of temperature by computer simulation. The results are shown in Figure 3b, in which A and λ were 1.17 nm2 and 0.080, respectively. At temperature ≤20 °C, D was 1.24 nm, and D increased with increasing temperature at temperature >20 °C. D
dx.doi.org/10.1021/jp5031202 | J. Phys. Chem. B XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry B
Article
Figure 4. Frequency dependence of storage modulus E′ and loss modulus E″ of the composite with 10 vol % in the range (100−0.01 Hz): (a) E′ and (b) E″ at the indicated Ts by self-heating; (c) E′ and (d) E″ at the indicated T by external heating.
composites with 4 and 10 vol % contents provided quite different tunneling effect power under self-heating. Incidentally, for the composite with a 4 vol % content with high resistivity (low conductivity), the maximum Ts (92.0 °C) decreased with elapsing time under 6 V/cm, which was due to descent of corresponding current by cutting of current paths. As discussed in the previous paper,1 drastic decrease of Ts and current (I) beyond 6 V/cm were thought to be attributed to the chain scission of adhesive UHMWPE between overlapped adjacent NiCFs as breakdown by high electrical field as well as appearance of airspaces (voids) by the breakdown. The mechanism shall be discussed later in Figure 6. Based on the information for D and A with 10 and 4 vol % contents in Figure 3, the different behaviors of dynamic tensile modulus under electrical field and usual external heating (no electrical field) are discussed in the present paper. That is, the following discussion is mainly focused on the difference of dynamic tensile modulus measured by self-heating and traditional external heating. Figures 4a and 4b show frequency dependence of storage modulus (E′) and loss modulus (E″), respectively, at the indicated surface temperature (Ts) by self-heating under the indicated electrical field for the composite with a 10 vol % content, while Figures 4c and 4d show frequency dependence of E′ and E″, respectively, at the indicated temperatures by external heating. In comparison with Figures 4a and 4c at the similar temperatures up to 108 °C, the change in E′ by Joule heat became much larger than that by external heating. Further measurement beyond Ts = 108 °C could not be achieved, since the specimen was cut beyond 108 °C on the measuring process above 1.1 V/cm. For external heating, the measurement could be done up to 130 °C, and further increase in temperature caused sample elongation by initial load needed to set up axial sinusoidal oscillation.20 In preliminary experiment,12 the measurement of pristine undrawn UHMWPE by external heating reached a limit at 110 °C because of sample elongation. The measurement up to 130 °C for the composite with 10 vol % was due to the increase in elastic stiffness associated with the reinforced effect of a 10 vol % NiCF content. The large
Despite increasing electron transfer power between adjacent NiCFs by the tunneling effect with elevating temperature, the increasing power is considered to be less effective than the growth of collision frequency of free electrons against Ni atoms along NiCF axis associated with an increase in resistivity. Accordingly, the tunneling effect associated with the decrease of resistivity with temperature was not observed in Figure 3c. Even so, it is obvious that movement of free electrons along the fiber direction by the tunneling effect can be realized through the narrow air gap between overlapped adjacent NiCFs ensuring high conductivity of the composite with a 10 vol % NiCF content. Actually, the temperature dependence of conductivity calculated at K = 1 for the air provided good fitting with the experimental results as shown in Figures 3c and 3d. Different from external heating shown in Figures 3a and 3c, Figure 3e shows resistivity against surface temperature (Ts) arisen by Joule heat. The resistivity increased with elevating Ts. The black curve calculated by eqs S1 and S2 in the Supporting Information shows the best agreement with experimental results, when selecting K = 2.3 in addition to A = 500 nm2 and λ = 0.235, where the values of D (shown as black dashed curve) increase slightly with elevating Ts. The values of D were 0.155− 0.192 nm in the given Ts, which is similar to the 0.185 nm estimated by external heating as discussed already in Figure 3d. Anyway, such narrow gap between overlapped adjacent NiCFs indicates no existence of UHMWPE. Accordingly, the numerical recalculation was done again by using λ, which is given by 0.795e2/4DKU0 (K: permittivity of insulating barrier = 1 for air). The red curve in Figure 3e shows the best fitting of resistivity (ρ) for self-heating, which was calculated by using the parameters A = 500 nm2 and λ = 0.235. The values of D at K = 1 become 0.220−0.260 nm, which are longer than the values (0.155−0.192 nm) calculated at K = 2.3 and slightly longer than 0.185 nm calculated at K = 2.3 in the case of external heating. Of course, the gap 0.220−0.260 nm is also too narrow to allow the existence of UHMWPE between overlapped adjacent NiCFs. This indicates that the gap difference between overlapped adjacent NiCFs for the E
dx.doi.org/10.1021/jp5031202 | J. Phys. Chem. B XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry B
Article
Figure 5. Frequency dependence of storage modulus E′ and loss modulus E″ of the composite with a 4 vol % in the range (100−0.01 Hz): (a) E′ and (b) E″ at the indicated Ts by self-heating; (c) E′ and (d) E″ at the indicated T by external heating.
difference value of E′ between self-heating up to 108 °C and external heating up to 110 °C is attributed to the damage against the composite by electrical current flow. This tendency was considerable at lower frequency range (115 °C because of initial load needed to set up axial sinusoidal oscillation. This indicates that the reinforced effect by mixing a 4 vol % NiCF content was less effective than that by mixing a 10 vol % NiCF content. As for E″ in Figures 5c and 5d, the dispersion peak appeared clearly at 0.1 Hz beyond ca. 78 °C, while the broad peak profile by self-heating appeared beyond 40 °C and shifted to higher frequency side with increasing temperature. To investigate the dispersion behaviors of E″, the master curves were proposed in Figure 7. Figures 7a and 7b show the master curves of E′ and E″, respectively, reduced to the common reference temperature of 60 °C under self-heating for a 10 vol % NiCF content, and Figures 7c and 7d show the corresponding master curves for E′ and E″, respectively, under external heating. The reference temperature was determined by considering that Joule heat generated in PTC plate as heater transfer to decollated floor surface through innocent wooden plate. Judging from heat conductivity of the innocent wooden plate with a thickness of 30 mm, the desired setting temperature of PTC plate was about 60 °C at outdoor air
