Mechanical Properties Of Epoxy Resin Research Articles

A DOPO Derivative Constructed by Sulfaguanidine and Thiophene toward Enhancing Fire Safety, Smoke Suppression, and Mechanical Properties of Epoxy Resin

AbstractIn order to eliminate the negative effect of traditional 9,10‐dihydro‐9‐oxa‐10‐phosphaphenanthrene‐10‐oxide (DOPO) ‐based flame retardants on heat resistance, mechanical properties, and curing process of epoxy resin (EP), a DOPO derivative (DST) constructed by sulfaguanidine and thiophene is designed and used as co‐cured agent for EP. Compared with EP, the maximum decrease of glass transition temperature (Tg) in all EP/DST samples is less than 5%, indicating EP modified by DST maintains good heat resistance. Encouragingly, DST shows satisfactory flame‐retardant efficiency and excellent smoke suppressing effects. EP containing barely 5 wt% of DST (P content: 0.37 wt%) achieves a UL‐94 V‐0 rating and 32.8% limited oxygen index (LOI) value. Its peak heat release rate (PHRR), total heat release (THR), and total smoke production (TSP) are also decreased by 31.2%, 18.8%, and 30.2% . Further, DST significantly improves mechanical properties of the EP/DDM/DST system. The tensile strength and modulus increase by 37.2% and 14.6%, respectively, as DST content is 7.5 wt%. It is revealed that DST has positive quenching and diluting effects in the gas phase, as well as promoting the formation of a compact char layer in the condensed phase.

Effect of casting and curing temperature on the interfacial bond strength of epoxy bonded concretes

The effect of casting and curing temperature on concrete-epoxy-concrete interfacial bond strength was evaluated. To cover a wide range of climatic conditions, six different temperature values from 5 to 55 °C were considered. The interfacial bond strength of the composites was experimentally assessed using pull-off, wedge splitting and bi-surface shear tests. The individual materials, epoxy and cement paste, were also characterized by means of viscosity, shore D hardness and setting time measurements. Results show that the casting and curing temperature dramatically impacts the mechanical properties of the epoxy bonded concretes. Indeed, increasing temperature from 5 to 55 °C leads to a decrease in bond strength up to 65%. The significant drop in setting time of epoxy compared to cement at high temperature, the inferior epoxy mechanical properties, as well as the reduction in epoxy thickness due to material loss in pores and microcracks can explain this decrease.

Self-compatibilization effect of phosphonate with cyano group on flame retardancy and mechanical properties of epoxy

A phosphonate flame retardant containing cyano group (CPDPO) was synthesized by using diphenylphosphinyl chloride and 4-cyanophenol and used to modify the flame retardancy epoxy (EP). The curing process, flame retardant performance and mechanism of EP/CPDPO were investigated. The cyano is a strong electron-withdrawing group which makes some CPDPO to react with EP via transesterification, thus about 17% diphenyl phosphine oxide (DPO) and 4-cyanophenol group will be grafted onto the chain of EP. Therefore CPDPO plays a self-compatibilization role in the system. The EP with 6 wt% CPDPO achieves the UL-94 V-0 rating and a LOI value of 36.6%. The peak of heat release rate and total heat release of EP with 6 wt% CPDPO are decreased by 47% and 24% compared with EP, respectively. The DPO grafted on the EP network tends to work in the condensed phase, while the free CPDPO is easy to work in the gas phase. The latter is far more than the former. Therefore, the effect of gas phase is obviously greater than that of condensed phase, which matches the structure of EP which has good charring ability itself. Moreover, the EP/CPDPO has better mechanical properties than that of EP and transparency equivalent to itself. This work suggests that the phosphonate containing strong electron-withdrawing group not only has self-compatibilization effect, but also regulates the properties and flame retardant mechanism.

Enhanced mechanical and damping properties of epoxy using aggregated nanoparticles organic-inorganic hybrid as a filler

ABSTRACT Graphene, with high strength and ultra-high specific surface area, is an excellent filler to improve the mechanical properties of epoxy resin. However, due to the strong interface interaction between graphene and epoxy resin, it always negatively affects the damping performance of the matrix. Besides, the dispersibility of graphene in the epoxy matrix is also a problem that needs to be solved. To enhance the dispersibility of graphene and adjust the interface strength between graphene and epoxy matrix, one kind of organic-inorganic hybrid, which contains polyether amine as shell and aggregated nanoparticles of reduced graphene oxide (r-GO) and ZnO nanocrystalline as core, was synthesized. The morphology, chemical structure, physical characteristics and dispersity of the hybrid were investigated. The mechanical properties of the nanocomposites with different weight fractions of the hybrid were studied. The free vibration tests were conducted on these nanocomposites to obtain the natural frequency and damping ratio, and the Euler-Bernoulli beam theory was employed to calculate the storage modulus and loss modulus of the nanocomposites. The dynamic thermomechanical analysis (DMA) was employed to study the damping properties of neat epoxy and nanocomposite. The results showed that the hybrid filler can improve the mechanical and damping properties simultaneously.

Influence of the size of walnut shell particulates on mechanical properties of epoxy-based composites

In the present work, a new class of polymer composite is developed using walnut shell powder (WSP) as particulate filler in the epoxy matrix. Three different sizes of WSP are used for preparing three different sets of composites. The particle size selected is 50-micron, 75-micron, and 100-micron. In each set of composites with different particle size, four compositions i.e., 5 wt. %, 10 wt. %, 15 wt. % and 20 wt. % of the WSP is fabricated. All prepared composites have undergone testing to study the behavior of the material under mechanical loading. The different mechanical tests performed are the tensile test, flexural test, compressive test and hardness test. From the experimentation, the inclusion of WSP appreciably alters the different mechanical properties of epoxy. With the increase in the content of filler, an appreciable increase in the value of hardness and compressive strength is observed. Though, it has been seen that the tensile strength and flexural strength of the material is compromised slightly when the content of WSP increases beyond a certain limit. Further, it is observed that composites fabricated with smaller size particles give improved mechanical properties as compared to their counterparts.

Improving the Antimicrobial and Mechanical Properties of Epoxy Resins via Nanomodification: An Overview.

The main purpose of this work is to provide a comprehensive overview on the preparation of multifunctional epoxies, with improved antimicrobial activity and enhanced mechanical properties through nanomodification. In the first section, we focus on the approaches to achieve antimicrobial activity, as well as on the methods used to evaluate their efficacy against bacteria and fungi. Relevant application examples are also discussed, with particular reference to antifouling and anticorrosion coatings for marine environments, dental applications, antimicrobial fibers and fabrics, and others. Subsequently, we discuss the mechanical behaviors of nanomodified epoxies with improved antimicrobial properties, analyzing the typical damage mechanisms leading to the significant toughening effect of nanomodification. Some examples of mechanical properties of nanomodified polymers are provided. Eventually, the possibility of achieving, at the same time, antimicrobial and mechanical improvement capabilities by nanomodification with nanoclay is discussed, with reference to both nanomodified epoxies and glass/epoxy composite laminates. According to the literature, a nanomodified epoxy can successfully exhibit antibacterial properties, while increasing its fracture toughness, even though its tensile strength may decrease. As for laminates—obtaining antibacterial properties is not followed by improved interlaminar properties.

Complex structures formed by combination of polymer-grafted GO and impact modifier in epoxy

Parameters of epoxy can be effectively improved using polymer-grafted GO. This study reveals so far unknown structure-directing performance of single- and bimodally-grafted GO in impact-modified epoxy. Bimodal grafting leads to formation of lamellae with less ordered more distant GO and fair mobility of grafted dissimilar chains due to their repulsive interactions, resulting in favourable effect on mechanical properties of epoxy . Unlike single-grafted GO with aligned plates, this ordering is not disturbed by added rubber which is more markedly incorporated even as layered domains into lamellae. Formation of more complex structures controlled by grafting geometry was also found. Structure–properties relationships indicate low contribution of added rubber, both as single inclusions or incorporated into ordered GO domains, which confirms high effectivity of lamellar structure with linked polymer chains of relatively high mobility.

Thermal conductivities and mechanical properties of epoxy resin as a function of the degree of cross-linking

Epoxy resins are widely used polymer matrices for numerous applications. Despite substantial advances, the molecular-level knowledge-base required to exploit these materials to their full potential remains limited. A deeper comprehension of structure/property relationships in epoxy resins at the molecular level is critical to progressing these efforts. It can be laborious, if not impractical, to elucidate these relationships based on experiments alone, particularly in aiding the search for new, multi-functional resins. Here, molecular dynamics simulations are used to calculate, compare, and elucidate connections between both thermal conductivities and mechanical properties of an exemplar epoxy resin, Bisphenol F cross-linked with Diethyl Toluene Diamine, as a function of degree of cross-linking. Both the elastic modulus and thermal transport of the resin show an increase with greater cross-linking. Specifically, decomposition of the thermal conductivity into different force contributions suggests that although the bonded term contributes to an increase in the heat flux as a function of cross-linking, the contributions from non-bonded interactions suggest a less predictable trend. These outcomes provide a foundation for designing customized epoxy resins with both desirable thermal and mechanical attributes.

Glass fiber/Carbon nanotube/Epoxy hybrid composites: Achieving superior mechanical properties

Owing to their excellent physical and mechanical properties, polymer-matrix hybrid nanocomposites have found extensive applications in various fields. In this study, different parameters such as materials characteristics and processing parameters are investigated and optimally selected for composite fabrication. The purpose of selecting the optimal parameters and fabricating different types of composite samples was to achieve simultaneous and high improvement in various mechanical properties of epoxy resin. As a result, the process of this study was designed in such a way that by making epoxy-matrix composites reinforced with carbon nanotubes (CNTs) in different CNT weight percentages (0.1, 0.5, and 1 wt%) via solution casting method and using optimal values for material characteristics and processing parameters, the improvement of epoxy mechanical properties for each CNT weight percentage was investigated. Results indicated that the highest improvement in mechanical properties of CNT/epoxy composite was observed in 0.5 wt% CNT sample which had a tensile strength of 61 MPa and Young's modulus of 1.8 GPa. Then, CNT/epoxy composites with the highest improvement in mechanical properties were selected to fabricate the matrix phase of glass fiber/CNT/epoxy hybrid composite. Hybrid composite samples with fiber to matrix ratio of 45:55 were fabricated via the hand lay-up technique. To achieve maximum improvement of mechanical properties for the hybrid composite, the optimal parameters were selected which led to the maximum tensile strength of 300 MPa and Young's modulus of 24.9 GPa. Mechanical properties of the glass fiber/CNT/epoxy hybrid composites showed an identical trend to the CNT/epoxy composite. Moreover, all the fracture mechanisms of CNT/epoxy and glass fiber/CNT/epoxy composites were precisely investigated by scanning electron microscopy.

Effect of Egg Shell Composition on the Flexural and Hardness Properties of Epoxy Resin/ Egg Shell Particles Composite

The effect of calcined egg shell particles on the mechanical properties of epoxy resin had been studied. The egg shell was sun dried for 3 days and calcined at 800oC in an electrically fired furnace model KGVB. The calcined egg shell was ground in a locally fabricated pulverized machine and sieved using Sieve Model 567924/173281Endecotts in accordance with ASTM standard. Microwave digestion system and an inductively coupled plasma mass spectrometer (ICP-MS) were used to determine the chemical composition of the egg shell. The egg shell particles were mixed with epoxy resin to develop a composite casted by open mold casting. The flexural and hardness properties of the developed composite was determined using Universal Testing Machine model TUE-C-100, observing ASTM D790 standard and Rockwell Scale K hardness testing machine according to ASTM D785 respectively. The results showed that the calcined egg shell contained mostly CaO. Maximum flexural strength of 12MPa was observed at 25 wt. % egg shell particles. The highest hardness value of HRN 393 was observed at 20 wt. % egg shell particles. The produced composites may be applied where moderate strength is required.

Bioderived Bilayer Shell Modification β‐FeOOH Nanorods via Self‐Assembly Technique as Sustainable Flame Retardants for Enhancing Flame Retardancy of Epoxy Resin

AbstractThe design and application of bioderived flame retardants have been widely conducted to meet the concept of green and sustainable development. Here, self‐assembly technique is used to prepare core–shell bioderived additives by using β‐FeOOH as the core and polydopamine (PDA)/tannic acid (TA) bilayer as the shell, following adsorption of nickel ions to enhance the thermal stability, flame retardancy, and mechanical properties of epoxy resin (EP). The molecular structure of biobased resources is rich in hydroxyl groups and carbon content, which can be dehydrated and carbonized during combustion and promote the formation of robust protective char layer. With the addition of 5 wt% β‐FeOOH@PTNi, the EP composites can pass V‐0 rating in the UL‐94 test. The peak heat release rate and total heat release decrease by 28.4% and 17.4% compared with pure EP. The bioderived nanorods can capture the oxygen free radicals, contributing to flame retarding in gaseous phase. Thus, the release of high‐toxic CO and flammable gaseous is significantly suppressed. Besides, the storage modulus of EP composites increases by 16.0% with the addition of 5% β‐FeOOH@PTNi compared with pure EP. This work provides a sustainable methodology for the design of bioderived flame retardants for EP.

Effect of Reactive and Non-Reactive Diluent on Mechanical Properties of Epoxy Resin

Epoxy resins, which are frequently preferred among thermoset plastics in the industry, are materials with high viscosity, and good mechanical performance. The biggest disadvantage of epoxy resins is that they encounter difficulties in application alone due to their high viscosity. For this reason, various diluents are added to reduce their viscosity and applications are conducted. In this study, the mechanical properties of the epoxy resin, which is used in many fields, were observed with the addition of certain sizes of reactive and non-reactive diluents. Diglycidyl ether was used as the reactive diluents, and benzyl alcohol was used as the non-reactive diluent. In addition, ethylene diamine and diethylene triamine were used as curing agents. It was tried to determine the optimum modification of the hardened epoxy resin by measuring the mechanical strengths in the electromechanical test device. The results indicated the optimum composition that does not dramatically affect the mechanical performance of the epoxy resin is the composition containing 7.5% DE and 10% EDA, its tensile strength measured as 53.27 N/mm2.

Synergistic effect of piperazine pyrophosphate and epoxy-octavinyl silsesquioxane on flame retardancy and mechanical properties of epoxy resin

In order to solve the contradiction between the flame retardancy and mechanical properties of epoxy resin, piperazine pyrophosphate (PAPP) and epoxy-octavinyl silsesquioxane (EOVS) are applied as flame retardants for epoxy resin (EP). With the introduction of PAPP and EOVS, the properties of the EP composites about flame retardancy, mechanical properties and smoke suppression are significantly improved. EP/9 wt% PAPP/1 wt% EOVS (EP3) passes a vertical burning (UL-94) test V-0 rating and acquires the limiting oxygen index (LOI) test value of 32.4%. The results of cone calorimeter (CC) tests confirm that the incorporation of PAPP and EOVS significantly reduces the total heat release (THR), peak heat release (PHRR), total smoke production (TSP) and peak smoke produce rate (PSPR) values, which are respectively decreased by 25%, 81%, 57% and 63% compared with those of pure EP. Scanning electron microscope (SEM), energy dispersive spectrometry (EDS), Laser Raman spectroscopy (LRS), X-ray photoelectron spectroscopy (XPS) and Thermogravimetry-Fourier transform infrared (TG-FTIR) spectroscopy are adopted to analyze the flame-retardant mechanism of PAPP/EOVS flame retardants. These results reveal that the flame retardancy of EP3 is attributed to the excellent charring ability, the dilution effect of non-combustible gases and the flame inhibition of gaseous phosphorous compounds. Besides, the tensile and impact strength of EP3 increase benefitting from the presence of epoxy groups and Si-O bonds in EOVS. This work proposes a new method to prepare the mechanically reinforced and flame-retardant epoxy resin.

Efficient reinforcement of epoxy resin with amine‐rich rigid short‐chain grafted graphene oxide

AbstractFor improving the mechanical properties of epoxy resin (EP), it is an effective strategy to utilize surface‐modified graphene oxide (GO) as a reinforcement. However, there is nearly no report on surface modification using rigid short‐chain grafted GO, especially with multiple reactive sites. In this work, a novel surface functionalization of GO with an amine‐rich rigid short‐chain was successfully prepared and applied as a filler for EP with simultaneously high toughness and mechanical strength. Superior toughness and mechanical strength of the resultant epoxy nanocomposite can be obtained by grafting amine‐rich rigid short‐chain onto GO (DHN‐GO) owing to the enhanced interface binding ability with the EP and the optimized dispersibility in the matrix. Compared with the pure EP, the epoxy nanocomposites at an extremely low loading (0.75 wt‰) of DHN‐GO showed excellent mechanical properties. The tensile strength, elongation at break, and bending strength are increased by 28%, 37%, and 29%, respectively. This work is expected to provide more inspiration for the preparation of GO/EP composites with high toughness and mechanical strength.

Investigating The Effect of Magnetite (Fe3O4) Nanoparticles on Mechanical Properties of Epoxy Resin

In this paper, study the effects of magnetite nanomaterial Fe3O4 on the mechanical properties of epoxy. Dispersion of Fe3O4 nanoparticles in the epoxy resin was performed by ultrasonication. The samples of the nanocomposites were prepared using the casting method. The nanocomposites contain epoxy resins as a matrix material incorporated by different weight percentages of magnetite Fe3O4 that varies from 0wt.% to 15wt.% as a reinforcing material. The epoxy with the additive reinforcement materials Fe3O4 was slowly mixed in a sonication bath for 15 minutes, then the mixture poured into silicon molds. Field Emission Scanning Electron Microscopy FESEM and X-ray diffraction spectra XRD were used to characterize the morphological and structural properties of preparing samples and the distribution of Fe3O4 nanoparticles to the epoxy resin. Mechanical testing consists of tensile, hardness shore, and three-point flexural tests were performed on the samples at room temperature according to ASTM standards. The results showed that reinforcement by 15wt.% of Fe3O4 nanoparticles maximizes these mechanical properties of nanocomposites compared with pure epoxy except for the young modulus's preferred weight at 9 wt.%, this is due to aggregation of the additives nanomaterials in epoxy resin above 9 wt.%.

Thermal and Mechanical Properties of Epoxy Resin Functionalized Copper and Graphene Hybrids using In-situ Polymerization Method

Objective: In this work, graphene (Gr) or/and Cu particles are used to improve the thermal and mechanical properties of epoxy resin. Methods: Various contents of Gr powder (0.1, 0.3, and 0.5 wt%), and Cu powder (10, 30, and 50 wt%) were loaded to epoxy to form Gr/epoxy and Cu/epoxy composites, respectively. In addition, hybrids epoxy/Cu/Gr samples were prepared with a selection of the lowest (0.1 and 10) and the highest (0.5 and 50) ratios of Gr, and Cu, respectively. Results: The thermal conductivity increased with the increasing weight ratio of Gr and Cu as compared to the pure epoxy. The thermogravimetric analysis (TGA) of epoxy composites and hybrid composites revealed an improvement in the thermal stability. In addition, the mechanical properties such as hardness shore D and the wear resistance were enhanced for both the epoxy composites and hybrids composites. However, the Ep+0.5wt%Gr+50wt%Cu hybrid composite was found to have the maximum hardness 84, with the thermal conductivity of 3.84 W/m.K. It showed the lowest wear resistance 2.7×10-6 mm3/Nm at loading 10 N. Conclusion: The hybrid composite containing 0.5wt%Gr and 50wt%Cu shows the maximum hardness and thermal conductivity, as well as the lowest wear resistance when compared to other composites. The physical properties of the hybrid composite can be controlled by the host blend, and hence the morphology, and interfacial characteristics.

Effect of polyhedral oligomeric silsesquioxanes with different structures on dielectric and mechanical properties of epoxy resin

AbstractPolyhedral oligomeric silsesquioxane (POSS) is a hybrid material composed of an organic substituent shell and inorganic skeleton core. To study the influence of different shells and cage‐shaped cores on dielectric and mechanical properties, four kinds of epoxy resin composites (EPs) fabricated with 9,10‐dihydro‐9‐oxa‐10‐phosphaphenanthrene‐10‐oxide (DOPO), DOPO‐containing polyhedral oligomeric silsesquioxane (DOPOPOSS), octaphenyl polyhedral oligomeric silsesquioxane (OPS), and epoxy phenyl polyhedral oligomeric silsesquioxane (EPOSS) with the addition of 5 and 10 wt% were prepared, respectively. The dispersion, transparency, glass transition, dielectric, mechanical tensile, flexural, and impact properties of these epoxy resins were studied. Dielectric constant and loss of EPs were significantly reduced through introduction of three POSSs owing to their inherent hollow cores, and dielectric constant of the resins was further decreased with additional increase. Compared with three POSSs, DOPOPOSS had the best compatible shell, and its composites exhibited favorable transparency similar to pure EP and the obvious reduction in dielectric constant and loss, due to its nano‐dispersion in matrix. EPOSS was dispersed in a perfect spherical shape and uniformly embedded in matrix, and the composites showed good mechanical tensile, flexural, and impact strength. OPS was disorderly dispersed in resins, but its eight phenyl rings symmetrical shell had the advantage of nonpolar molecule structure, which endowed epoxy resin lower dielectric loss over the high‐frequency range (105–106 Hz). Compared with DOPOPOSS, DOPO was effective in reducing dielectric constant and loss of epoxy resin due to its reactive addition, however, it decreased the glass transition temperature, mechanical tensile, flexural, and impact strength of epoxy resin either.

Development of dynamic constitutive model of epoxy resin considering temperature and strain rate effects using experimental methods

Epoxy resin composite materials are increasingly used in the aerospace field. The dynamic mechanical behavior of the resin matrix is of great significance in studying the impact response of composites. In the current study, the quasi-static and dynamic compression properties of TDE86 epoxy are studied at different temperatures, and the influence of the temperature and strain rate on the mechanical properties of epoxy are analyzed. The quasi-static and dynamic compression stress–strain curves are used to fit the parameters of the Zhu–Wang–Tang (ZWT) constitutive equation at different temperatures. A subroutine for the ZWT constitutive model is developed in ABAQUS, and numerical simulations of split Hopkinson pressure bar tests are performed. The results show that, at low strain rates, the elastic modulus, yield stress, and yield strain of the epoxy increase as the strain rate increases and decrease as the temperature increases. The dynamic stress–strain curve of the epoxy can be divided into four stages, namely the initial elastic, yield, strain softening, and unloading stages. There is no distinct relationship between the yield strain and the logarithmic strain rate under high strain rates, although the yield strain is generally smaller than that under low strain rates. The yield stress increases linearly with the logarithmic strain rate. Under the same strain rate, the yield stress decreases as the temperature increases, whereas the yield strain does not change monotonically. By comparing the stress–strain curves obtained by simulations with the test results, the developed subroutine is validated and the applicability of the ZWT constitutive model at different temperatures is verified.

Investigation of the functional network modifier loading on the stoichiometric ratio of epoxy resins and their dielectric properties

Reactive molecular additives have often been employed to tailor the mechanical properties of epoxy resins. In addition, several studies have reported improved electrical properties in such systems, where the network architecture and included function groups have been modified through the use of so-called functional network modifier (FNM) molecules. The study reported here set out to investigate the effect of a glycidyl polyhedral oligomeric silsesquioxane (GPOSS) FNM on the cross-linking reactions, glass transition, breakdown strength and dielectric properties of an amine-cured epoxy resin system. Since many previous studies have considered POSS to act as an inorganic filler, a key aim was to consider the impact of GPOSS addition on the stoichiometry of curing. Fourier transform infrared spectroscopy revealed significant changes in the cross-linking reactions that occur if appropriate stoichiometric compensation is not made for the additional epoxide groups present on the GPOSS. These changes, in concert with the direct effect of the GPOSS itself, influence the glass transition temperature, dielectric breakdown behaviour and dielectric response of the system. Specifically, the work shows that the inclusion of GPOSS can result in beneficial changes in electrical properties, but that these gains are easily lost if consequential changes in the matrix polymer are not appropriately counteracted. Nevertheless, if the system is appropriately optimized, materials with pronounced improvements in technologically important characteristics can be designed.

A study on the mechanical properties of graphene oxide/epoxy nanocomposites

The aims of this research are to elucidate the role of graphene oxide on the mechanical properties of epoxy and also to obtain an equation for the modeling of its behavior. Accordingly, graphene oxide/epoxy nanocomposite samples are fabricated using the solution casting method. Tensile, flexural, SEM and FTIR tests are conducted on epoxy and the nanocomposite samples afterwards. The obtained results show that the tensile strength of epoxy improves even at low contents of graphene oxide such that 0.3 wt.% of GO yields an improvement of approximately 11.5%. The flexural strength of epoxy is also enhanced by 5.8% with 0.5 wt.% GO. Then, it decreases due to the agglomeration with increasing the GO content. In order to predict the tensile strength of GO/epoxy nanocomposites, a modified Halpin–Tsai equation is obtained with a new introduced correction factor as K = 39.5 Vf1.135exp(2.9−1644.6 Vf). The obtained equation is in good agreement with the experimental data.