Carbon nanofibers possess characteristics that distin-guish them from other materials. These properties include thermal, mechanical, and electrical attributes. For example, CNFs may exhibit the high thermal conductivity, excellent mechanical strength, and superior electrical conductivity compared to other materials. The remarkable properties of CNFs have garnered significant attention from the scientific community. Researchers are interested in exploring and harnessing these properties for various appli-cations across different fields (Rahmat M. et al., 2011; Kenry et al., 2017) due to this it has been widely used to reinforce polymeric materials to improve their mechanical properties (high flexibility and light weight) and their thermal and electrical properties in an effort to achieve desirable properties such as high dielectric constant (Han C. et al., 2010; Shettar M. et al., 2020; Rathinavel S. et al., 2021; Kooti M. et al., 2021). The research into polymer/carbon nanofiber (CNF) nanocomposites has been extensive, particul-arly focusing on their dielectric properties and thermal stability and much emphasis has been placed on improving the dielectric properties by obtaining high dielectric constant and relatively low electrical loss (Jomaa M. et al., 2015; Begum S. et al., 2018). The epoxy resin is most often used as the polymer matrix due to its series of interesting properties like high specific strength, good stiffness, chemical resistance, dimensional stability and also strong adhesion to the embedded reinforcement (Chang J. et al., 2012; Zhang X. et al., 2012). Polyurethane coatings indeed offer several advantageous properties such as high hardness, wear resistance, radiation resistance, and peel strength, which make them suitable for various applications. However, its true that they may have limitations in terms of corrosion resistance and temperature resis-tance when compared to some other coating materials (Jianxin Zhang et al., 2022). Dielectric properties and thermal stability can be significantly improved by mixing epoxy and polyurethane resins with the addition of carbon nanofibers (CNFs) because of their ability to improve these properties (Ameli A. et al., 2014; Yang X et al., 2014). In light of the results of previous studies, the main objective of this research is to study the dielectric relaxation and thermal stability of epoxy/ polyurethane blends and their composites reinforced with carbon nanofibers (CNFs). During this experimental study, AC conductivity was exam-ined as a function of temperature, and over a frequ-ency range (102-107) Hz. The real and imaginary parts of the dielectric constant and the dissipation factor were also measured as a function of temperature and frequency. Furthermore, all blends and their comp-osites samples were scanned using DTA and TG to study the thermal stability of the blends and their composites. The composites fabricated in this study showed good dielectric properties and high thermal stability, which makes them useful materials in many manufacturing and electronic applications. 

The materials listed below were used according to the mention characteristics described in this study.

a) Epoxy Resins (DGEBA, YD-128).

Description: law molecular weight liquids with an epoxide equivalent weight of 176 G, supplied by Kukdo Chem. Co., Korea.

b) Curing agent pathalic anhydride (PA). 

Description: Phthalic anhydride is commonly used as a curing agent for epoxy resins, supplied by Kukdo Chem. Co., Korea.

c) Polyurethane (PU).

Description: A commercial resin type (TEK-CAST), supplied by TEKCAST- Industries, New Rochelle, NY 10801, USA

d) Curator Isocyanides (HYG)

Description: Isocyanides are likely used as curing agents for the polyurethane resins, supplied by TEKCAST- Industries, New Rochelle, NY 10801, USA

e) The Carbon nanofibers (CNFs) 

Description: purity 99.9, Diameter 1m and length less 100 m supplied by Nanoshell company, India was used in this study.

Samples Preparation

An open-mold casting technique was used to perform the epoxy/polyurethane blends and their composites in this study. Epoxy and polyurethane blends were prepared in this study with different weight fractions (90%-10%), (80%-20%), and (70%-30%), where the blend (80%-20%) was chosen to prepare the compo-site by adding a fixed weight fraction (10%) of carbon nanofiber of Diameter 1m and length less 100 m.

Measurements

Specimen Holder

The specimens of the epoxy/polyurethane blends and their composites, is fixed in a specimen holder. This holder ensures that the sample remains in place during testing.

Temperature Controller Oven

The temperature-controlled oven, manufactured by Heresies Electronic, is used to subject the specimen to controlled temperature conditions. This allows for testing the specimens electrical properties at different temperatures.

Dielectric Analyzer

The dielectric analyzer used in the experiment is of Hewlett Packard model, specifically HP4274A and HP4275A. These analyzers are designed to measure various electrical proper-ties of materials, including dielectric parameters.

Terminal connections and measurements

The specimen holder has high and low terminals, which are connected to the dielectric analyzer for electrical measurements. The third grade is connected to the earth, for grounding purposes to prevent elec-trical interference. Three dielectric parameters were measured directly from above setup total resistance (RT), total capacitance (CT) and dissipation factor tan (δ). Thermal stability was performed by thermos-gravimetric analysis (TG) and deferential thermal analysis (DTA) (NETZSCHSTA 409PG/PC) the mea-surement performed under heating rate of 20 C0/min over the range (0-800) C0.

A.C Conductivity (σac ()

Fig. 1 shows the variation of AC conductivity (σ ()) as a function of frequency ( ) at various temperatures (T/K0) for A) EP8%/PU20%B) EP/PU-CNFs have revealed that AC conductivity (σ ()) increased with increasing frequency and temperature for all tested samples. Hence, there are two factors that affect σ () for the EP80%/PU20% mixture, namely the mobility of the ions and the mobility of the polymer backbone (main chain). Moreover, the movement of ions contributes only at high frequencies and temperatures (T. Jeevanada. Siddaramaiah, 2003). Therefor the increase in the σ () at law frequencies over the range (100-400) Hz is attributed to interfacial polarization (T. Jeevanada et al., 2002) while the rapid increase in σ () with increasing frequency at frequencies greater than (103) Hz indicates the effect of electronic polarization, and the conductivity is pure ac conduc-tivity σ ()) in this region.  The composite (EP/PU-CNFs) shows a big jump in  (), which is increased by three orders to reach (9.11×10-4 Scm-1) at frequency of 1MHz. Thus the discussion is truly changed into a semiconducting case. This jump in  () was achieved by incorporating (10%) weight fraction of CFNs to EP/PU blends, which can be used to dissipate the static charges. This behavior occurs because all fiber molecules in the composite network are connected to each other forming tri-phase continuity, and all are contributed to the transport of charges (Maffezzoli A et al., 1994). 

Fig. 2 shows the variation of exponent (s) of EP/PU blend and EP/PU-CNFs composites as the function of temperature. The result reveals that the exponent values are less than unity for EP/PU blend and EP/PU-CNFs composites. Also these values are decreased with temperature increasing. This behavior of the exponent (s) can be explain with the correlated barrier hopping model (CBH) model which proposed by Elliot (Maffezzoli A et al., 1994). 

Fig. 3 shows the variation of activation energy (Eac) of (A) EP/PU blend (B) EP/PU-CNFs Composites as a function of frequency, the activation energy is esti-mated by Arrhenius equation. Each sample reveals three activation energies, the values of (Eac) were decreased with increasing frequency, such result com-plies with the theory of CBH model. In light of the published literature, these results are in good agree-ment with published results for both epoxy bends and epoxy-based composites (Carmona F. et al., 2017). The first critical temperature coincides approximately with glass transition temperature (Tg) of polymers. This phenomenon was observed in the epoxy resin by Warfield and Petree (Warfield R.W. & Petree M.C., 1962). The change in the slope at Tg can be explained by increases in the free volume and active diffusion motions of the chain segment (Saito S. et al., 1968). The free volume would also make possible great incre-ase in the mobility of the charge carriers. The com-posite reinforced by carbon nanofiber show smallest values of (Eac), this result supports the changing of this composite into a semiconducting phase.

Dielectric Study

Fig. 4 shows the real part of dielectric constant (r) as a function of frequency () at various temperatures for the A) EP/PU blend and B) EP/PU-CNFs composite. The results show that the values of (r)  in EP/PU blend  samples decreases with increasing frequency to reach a lower values at high frequency which represent the onset frequency. This result can be explained by the fact that the electrode blocking layers is dominated mechanism at low frequency region (Maffezzoli A. et al., 1994). Thus the dielectric behavior is affected by electrode polarization in the range of (102- 104) Hz. Likewise, the value of the real part of the dielectric constant increases slowly with increasing temperature until it reaches the highest value, this behavior was consistent with Debye- type dielectric dispersion characterized a long relaxation time  (Radzuan. N. A et al., 1989). Fig. 5B shows that the values of (εr) are affected by the adding of reinforcement material (CNFs). However; the real part of dielectric constant revels highly frequency dependence at the frequency range over (102-107) Hz. This result can be explained by an intra-chain transport mechanism involving polarons is exist, this mechanism allows an explan-ation of high dielectric constant values due to nomadic polarization which is observed in many polymer composites (Pohl H. A. & Pollok. M., 1975).  

Fig. 5 shows the imaginary part of dielectric constant (i) as a function of frequency () at various tempe-ratures for the (A) EP/PU blend and (B) EP/PU-CNFs composite. Fig. 6A show the decrease in values of (i) with increasing the frequency further 103 Hz, where strong relaxation contributions prevail (Narula  A. K. et al., 2000). In the frequency greater than 103Hz the values of (i) are grown up and the loss peak is exist at a constant position, where the migrating charges play the major role in dielectric polarization (Butta E. et al., 1995). At high frequencies the values of (i) are decreased rapidly with the frequency this behavior is referred to an electrode blocking layers polarization dominancy (Han C. et al., 2010). Fig. 6B shows that the values of (εi) are affected by the adding of reinfor-cement material (CNFs). However the result shows that the (εi) was decreased with increasing the frequ-ency and the strong dispersion exhibited at (4×103) Hz the composite. At the strong dispersion region, the migrating charges play a major role and the space charge polarization is dominant mechanism, while at high frequency the relaxation contribution prevail (Ming Qin. et al., 2022).

Fig. 6 shows the variation of dissipation factor (tan (δ)) as a function of frequency at various temperatures for (A)- EP/ PU blends and (B) EP/PU-CNFs composites. Fig. 6A shows that the loss peak occurs at the region of strong dispersion (10×103) Hz. This behavior is typical of many dielectric materials, the common feature of which is presence of strong carrier polarization rising from high densities of low mobility charge carriers (Ming Qin et al., 2022). At low tempe-ratures the tan (δ) show weak frequency dependent, while at high temperatures greater than 353K the strong frequency dependence phenomenon is existing. This result supports the discussion present on σac (). Also this result consistent with Debye- type disper-sion, which is suggest that the Debye relaxation had being adequate to explain the dielectric data (Papa-thanassiou A. N. et al., 2007). Fig. 6B shows a strong dispersion occurs in EP/PU-CNFs composites, over the frequency range (102- 103) Hz and the loss peaks does not show any significant shift with increasing temperature. This result has been attributed to strong carrier polarization a rising from high densities of low mobility charge carriers (Ming Qin et al., 2022).

The thermodynamic parameters Gibbs free energy of activation (ΔG), and entropy (ΔS) are estimated from dielectric relaxation measurements according to Eyrings theory (Eyring H. 1936). Fig. 7 shows the variation of thermo-dynamic parameters (ΔG), and (ΔS) as function of temperature. The results revile that the values of free energy of activation (ΔG) and the entropy (ΔS) are increased with increasing tempe-rature. The physical reason of this result can be related to the amount of thermal energy which is absorbed by the polymer chains, which a rise the segmental motion of molecules (Alshammari A. H et al., 2023). While the CNFs composite appears high values of energy of activation ΔG to reach (67KJ) at 443K0, and this result confirms a strong intermolecular interaction. Such resultant composites possess a high degree of cross linking (Eyring H., 1936). 

Fig. 7:  The Gibbs free energy of activation (ΔG), and entropy (ΔS) EP/PU blend and EP/PU-CNFs Composites at different temperatures.

Fig. 8:  The dielectric relaxation parameters (,α,s, ) of (A) EP/PU blend (B) EP/PU-CNFs Composites at different temperatures.

Fig. 8 shows the values of static dielectric constant (s) and optical dielectric constant (∞) distribution para-meter (α) and relaxation time of (A) EP/PU blend (B) EP/PU-CNFs Composites at different temperatures. The values of relaxation time () and distribution para-meter (α) EP/ PU blends and composites are system-atically decreased with increasing temperature. This result due to the orientation polarization, since this type of polarization is very sensitive to the temperature (Afiqah N. A. et al., 2017). The result shows that the values of molecular relaxation time () decreased with increasing temperature. Also result shows that the static and optical dielectric constants are systematical increase with increasing temperature. This can be explained as; the temperature increases the dipoles slowly get activated and attain freedom of rotation while the dielectric remains in the solid phase (Afiqah N. A. et al., 2017).

Thermal analysis and Thermal Stability 

Fig. 9 shows the differential thermal analysis (DTA) thermograms of EP/PU blend and their composites. The glass transition temperature (Tg) values as exhibited by DTA and estimated by dielectric measurements (DM) are shown in Table 2. The results show that the blend had only one (Tg) while the composites exhibited two values of (Tg). These two values of Tg of the composites probably reflected the fact that permanent compatibility of composites networks was impossible (Alshammari A. H. et al., 2023). DTA and DM values of Tg show small variation 0.78%-1.6% for EP/PU blends this result attributed to high compatibility between two networks. The two components of the blend are cross-linked networks, hence the single Tg may be attributed to the permanent interpenetration of the polymer networks and well give arise to improve compatibility and less phase separation (Venkatesh M. et al., 2023). The values of Tg for CNFs composites are strongly influenced by the adding of the dispersed phases. The composites reveal two glass transition values the first can be referred to the polymer blends and the second one may be referred to the interface between the polymers and the CNFs. 

Table 2: The values of glass transition temperature ( Tg ) of EP/PU blend and EP/PU-CNFs composite which are estimated by  DTA and dielectric measurements (DM). 

Fig. 10A shows TGA thermograms of EP/PU blend and EP/PU-CNFs composite. Table 3 summarizes the result of onset (initial weight losses) temperature (Ti), the T50% value represents the temperature at which the sample has lost 50% of its initial weight due to decomposition, volatilization, or other thermal proce-sses, the sample lost 80% of its initial weight called (Tf) and weight fraction of char yield at 800 C (wt% char at 800 ﻩC). The EP/PU blend the adding of PU resin reduces the char yield and (Tf) of the blend. This result agrees with the nature of PU which possess two steps of degradation, the first one is well correlated with the hard segment concentration; polyol, while the second step is correlated with degradation of the soft segment; isocyanate, (Shokralla S. A. and Al Muikel. N. S., 2010). The TGA thermo-grams show that the EP/PU blend is stable up to 341C and completely degrades around 600C in three steps, the first step weight loss occurs over the temperature range 220-350 C, due to the loss of bound dopant and the degra-dation of segment (polyol) referred to PU and EP resins [32]. The major weight loss occurs in the range 377-500C corresponds mainly to the loss of main chain degradation include the bisphenol-A and isocyanate (A. Maffezzoli et al., 1994). The degradation takes place at temperatures above 500C through thermo-oxidative reactions (Venkatesh M., 2023). Fig. 10B illustrates TGA curves of EP/PU-CNFs composites. TGA curves reveal that the composite is stable up to 200C0 and then completely degra-ded around 600C in three steps. The first step weight loss occurs at 220C0 is due to the loss of bound dopant and the degradation of segment (polyol). The second weight loss represent the major loss is exhibited at temperature of 371C0 this is due to the degradation of main chain includes the bisphenol-A and isocyanate (Venkatesh M. et al., 2023). The final step is located at temperatures above 700C, and this loss refers to thermo-oxidative reactions (Shokralla S. A. & Al Muikel N. S., 2010; Abubakre O. K. et al., 2023). Table 3 shows that the char yield at 800C of the blend and its composite are strongly affected by the reinforcement phases. Thus the reinforcement materials enhance the char yield. Since the rate of degradation of the composite reduces by adding the reinforcement materials. The thermal stability enhances by reinforcement materials at high temper-ature region, Tf increases rapidly to equal 711.6C. 

Table 3: The experimental data of thermal stability (Ti, T50%, Tf, and wt% char at 800C).

Based on the information provided about the study involving the EP/Polyurethane blend and EP/ Polyure-thane -CNFs composites, several conclusions and observations can be drawn:

• The addition of dispersive phases such as poly-urethane resin type novolac and embedding CNFs into the EP resin leads to improvements in various electrical properties.

• The dielectric properties of the materials, including parameters like distribution parameter (α), macroscopic relaxation time (τ0), and static dielectric constant (εs), are sensitive to tempe-rature variations. This indicates that temperature plays a significant role in influencing the mole-cular dynamics and polarization mechanisms within the materials.

• The estimation of thermodynamic parameters using dielectric measurements provides valuable insights into the energy dynamics and molecular interactions within the blends and composites. Understanding these parameters is essential for optimizing material compositions and processing

• Tg values are determined using both dielectric measurements (DM) and differential thermal analysis (DTA) techniques. These methods are commonly used to analyze the thermal properties of materials, including their glass transition temperatures

• Char yield at 800°C and Tf improve with the inclusion of reinforcement materials

• Conditions, particularly in applications where thermal stability and energy management are critical factors.

The author thanks the Chair of the Department of Physics at the College of Science Al-Baha University and fellow faculty members for their unlimited cooperation.

The author thanks the Chair of the Department of Physics at the College of Science Al-Baha University and fellow faculty members for their unlimited cooperation.