Natural Rubber Vulcanizates Research Articles

Aging of natural rubber studied via Fourier-transform rheology and double quantum NMR to correlate local chain dynamics with macroscopic mechanical response

Nowadays mainly the linear rheological properties of natural rubber (NR) vulcanizate during aging are studied, even though NR is rheologically nonlinear under most application conditions. Here, the nonlinearity was quantified via Fourier transform rheology (FT-Rheology) using I3/1, the relative intensity of the 3rd harmonic. The crosslink density and the content of defects were investigated by the 1H double quantum nuclear magnetic resonance (DQ-NMR). For aerobic aging at 120 °C, the crosslink density increases, but later turns into a broader mesh size distribution with more defects. Accordingly, the rheological nonlinearity of the material increases in the earlier stage and then decreases. For mechanical aging, the nonlinearity continuously decreases as a function of the fatigue cycle numbers, whereas the local crosslink density of the polymer network remains constant. This behavior can be assigned to the micro-cracks generated along adjacent network defects, which are larger than the detection scale of DQ-NMR. Compared to the linear rheological parameters, storage modulus G′ and loss factor tanδ, I3/1 exhibits higher sensitivity to the aging of crosslinked NR under both high temperature aerobic and mechanical fatigue conditions.

Synthesis of Natural Composite of Natural Rubber Filling Chitosan Nanoparticles

Mechanical properties of natural rubber composite were improved by adding chitosan nanoparticles in this work. The chitosan nanoparticles were prepared by ionotropic gelation method. The effect of chitosan nanoparticle content in natural rubber at 0, 3, 6 and 9 phr were studied. Size of the synthesized chitosan nanoparticles was 282 ± 96 nm. Natural rubber vulcanization was by electron irradiation at intensity 200 kGy. The morphology of composite was investigated by scanning electron microscopy (SEM). The mechanical properties (tensile strength and modulus) were determined by tensile testing. The interaction of filler-rubber was illustrated by Fourier transform-infrared (FTIR) and dynamic mechanical analysis (DMA). It was found that chitosan nanoparticles was well dispersed within natural rubber matrix. The optimum filler content was affected to mechanicals properties of natural rubber composites. The chitosan nanoparticles at 3 phr in natural rubber composites was found to have the highest mechanical properties. The dispersion and immobilization of chitosan nanoparticles at 3 phr was the best among all loading. In addition, 3 phr chitosan nanoparticles / natural rubber composite had filler-rubber higher interaction than those of other loading.

Enhanced electromechanical properties of natural rubber using highly efficient and cost-effective mussel-inspired modification of TiO2 nanoparticles

Recently, dopamine and its secondary function are being used as the intermediate to tailor the surface molecular structure of high-dielectric-constant nanoparticles, which improves interfacial interaction of dielectric elastomer (DE) composites, due to their versatile adhesion properties. However, the high-cost of dopamine limits the large-scale applications of DE. Herein, a mussel-inspired modification of TiO2 nanoparticles is presented to prepare high-performance natural rubber (NR) DE composites by replacing dopamine with cheaper poly(catechol/polyamine) (PCPA). First, the TiO2 nanoparticles were deposited with PCPA. Then, the PCPA-coated TiO2 nanoparticles were further grafted with γ-methacryloxypropyl trimethoxy silane (KH570), which contains double bonds and denoted as TiO2-PCPA-KH570. Owing to the presence of CC bonds, the TiO2-PCPA-KH570 nanoparticles participated in the vulcanization of NR and the TiO2-PCPA-KH570/NR composites exhibited enhanced filler dispersion and interfacial interaction, leading to the improved mechanical, dielectric, and electromechanical properties. Furthermore, the 10 phr TiO2-PCPA-KH570/NR composite resulted in the largest actuated strain of 12.3%, which is ~2 times higher than that of the largest actuated strain of pure NR (6.0%). The present study provides a high-efficient and cost-effective route to obtain DEAs with enhanced electromechanical properties.

Assessment of Carbonised Wood-Flour Fillers on the Mechanical Properties of Natural Rubber Vulcanisates

In view of the need to enhance the mechanical properties of vulcanisates, this study evaluated the potentials of carbonised wood-flour in this regard. Samples of wood-flour were carbonised at 600 ℃ and 700 ℃. The characterisation results revealed an increase in the pH (7.14 to 8.99) and loss on ignition (76.32 to 82.04%) of the carbonised wood-flour with increase in the carbonisation temperature. There was also a significant decrease in moisture content (0.21 to 0.15%) and bulk density (0.63 to 0.51 g/ml) with increasing temperature. The mechanical properties of the carbonised wood-flour filled vulcanisates were improved in the domain of tensile strength (6.08 to 10.38 MPa and 7.19 to 12.65 MPa), tensile modulus (2.53 to 3.78 MPa and 2.68 to 3.96 MPa) and hardness (48.25 to 60.55 Shore A and 50.88 to 63.92 Shore A) as carbonisation temperature increases from 600 ℃ to 700 ℃ respectively. Meanwhile, other properties investigated decreased with increased filler loading and carbonisation temperature and these were EAB (501.03 to 312.58% and 460.28 to 309.56%), compression set (18.43 to 12.07% and 15.35 to 8.99%), abrasion resistance (28.65 to 20.53% and 38.24 to 23.06%) and flex fatigue (8.02 to 5.84% and 8.63 to 6.04%) from 600 ℃ to 700 ℃ respectively. The results revealed that carbonised wood-flour is an excellent filler for natural rubber vulcanisates to improve the mechanical properties for specialised applications.

Study on the effect of modified and unmodified silica on the properties of natural rubber vulcanizates

AbstractIn the article, the effects of silica (silicon oxide) on some properties of natural rubber (NR) were studied. Silica used are unmodified (SiKBT) and modified with triethoxi silane propyl tetrasunfite (SiBT). It is shown SiBT increases vulcanization network density (VND), so it enhances strength and elastic properties of NR. In contrary, SiKBT decreases VND and reduces, but has almost no effect on strength of NR. Silica, both modified and unmodified, are assumed to improve network regularity of NR that change thermal degradation behavior of materials and keep the strength of NR‐SiKBT compound unchanged.

Effect of Ingredient Loading and Temperature on Tensile Properties of Surfactant-Loaded Natural Rubber Vulcanizates

Tensile properties are among the measures that give rubber products value. In this study, the effect of ingredient loading and temperature on the tensile properties of surfactant-loaded natural rubber vulcanizates (NRV) are investigated. Rubber dogbone samples are compounded using an L12 orthogonal array of Taguchi design of experiment, where ingredients are treated as factors varied at low and high loadings. Rubber specimens for each formulation are thermally aged for 20 days in ovens with temperatures of 40, 50, and 60 °C. Results show that zinc oxide (ZnO), paraffin wax, sulfur, mercaptobenzothiazole (MBT), and diphenylguanidine (DPG) significantly have the highest effect on increasing the elastic modulus while decreasing the tensile strength, tensile strain, and tensile set. Used oil has the highest effect on decreasing the elastic modulus but has the highest effect on increasing tensile strength, tensile strain, and tensile set. High loading of cocamide diethanolamide (coca DEA) significantly increases tensile strength at 60 °C. High loading of glycerol monostearate (GMS) significantly decreases tensile strength and strain at 40 °C. Highest elastic modulus, tensile strength, strain, and set are achieved when NRV are thermally aged at 50 °C.

Tensile and rheometric properties of calcium carbonate-filled natural rubber compounds without/with lauryl alcohol

The tensile and rheometric properties of CaCO3, calcium carbonate-filled natural rubber (NR) compounds without and with lauryl alcohol (LA) as a new rubber additive were examined. The NR was filled by CaCO3 with a certain addition, thirty phr. The LA was synthesized from palm kernel oil and incorporated into CaCO3-filled NR compounds at 1, 3, 5 and 7 phr. From the overall results, the LA was a curative and also plasticizing material. As a curative material, LA enhanced both tensile strength and difference in torque up to a five phr of addition. As a plasticizing material, LA reduced tensile moduli but enhanced elongation at break of CaCO3-filled NR vulcanizates. A five phr of LA was an optimum addition.

Mussel-inspired modification of boron nitride for natural rubber composites with high thermal conductivity and low dielectric constant

Owing to the development of modern micro-electronic devices, polymer composites with high thermal conductivity and low dielectric constant have become increasingly important. Herein, a combination of covalent and non-covalent modification was used to functionalize boron nitride (BN) platelets via first deposition with poly(dopamine) (PDA) followed by grafting with γ-methacryloxypropyl trimethoxy silane (KH570) (denoted as BN-PDA-KH570). The as-prepared BN-PDA-KH570 platelets were incorporated into the natural rubber (NR) matrix to prepare thermal conductive composites. After modification with PDA-KH570, the BN platelets were uniformly dispersed into the NR matrix, which is beneficial for improving the thermal conductivity of NR. The interfacial thermal resistance of the composites was also reduced due to the stronger interfacial interaction via vulcanization of NR with double bonds in KH570. Thus, the NR composites filled with 30 vol% BN-PDA-KH570 platelets exhibited a relatively high thermal conductivity of 0.39 W/mK, which is about 1.5 times and 4 times of 30 vol% BN/NR composite (0.26 W/mK) and pure NR (0.10 W/mK), respectively. In addition, the BN-PDA-KH570/NR composites exhibited a low dielectric constant (3.51 at 100 Hz) and a low dielectric loss tangent (0.25 at 100 Hz), which holds promising applications as thermal management materials for electronic devices.

The Influence of Trans-1,4-poly(butadiene-co-isoprene) Copolymer Rubbers (TBIR) with Different Molecular Weights on the NR/TBIR Blends

The molecular weight of a polymer is of prime importance and greatly influences the processing and mechanical properties of the polymer. Trans-1,4-poly(butadiene-co-isoprene) multi-block copolymer rubbers (TBIR) exhibit outstanding fatigue resistance, low heat build-up and good abrasion resistance, and are expected to be desirable candidate for high performance tire. Study on the influence of TBIR with different molecular weights on the structure and properties of TBIR and natural rubber (NR)/TBIR blends is essential to understand its contribution to the greatly improved dynamic properties of the rubber vulcanizates. TBIR with different molecular weights characterized by 1H-NMR, 13C-NMR, GPC, and DSC were highly trans-1,4-copolymers with similar chain sequence distribution and crystalline trans-1,4-polyisoprene (TPI) blocks. The green strength and modulus of TBIR increased with the increasing molecular weight. The NR/TBIR compounds filled with 40 phr carbon black were chemically cured by sulfur for the preparation of NR/TBIR vulcanizates. The compatibility between NR and TBIR, filler distribution, crosslinking bond and density, and properties of NR/TBIR vulcanizates were studied. The NR/TBIR vulcanizates showed increasing tensile strength, hardness, modulus, rebound, abrasion resistance, and flexural fatigue properties with increasing molecular weight of TBIR. Furthermore, they presented significant improvement in flexural fatigue resistance when compared with that of NR vulcanizate. The contribution mechanism of TBIR on the NR/TBIR blends was discussed. The TBIR with a wide range of molecular weight are ideal rubbers for high performance tires.

Equivalent strain failure criterion for multiaxially loaded incompressible hyperelastic elastomers

An analysis of distortional, i.e. constant volume, bulk material failure of incompressible hyperelastic elastomers in multiaxial loading conditions is presented. The present work describes deformation-based failure surfaces in terms of strain and stretch because stress-based descriptions render impractical. Classical as well as generalized strain and stretch-based failure criteria are reviewed regarding their suitability for hyperelastic polymers in their entropy-elastic regime. Classical criteria, such as the normal strain hypothesis or a von Mises-like strain criterion, prove inadequate for hyperelastic elastomers. Instead, the present work proposes a strain-based formulation of the generalized Podgórski–Bigoni–Piccolroaz criterion. This reformulation allows for an accurate description of failure surfaces of natural and synthetic rubber, filled and unfilled vulcanizates as well as silicones. It describes the failure surface in a single equation and can be readily implemented in finite element codes. For parameter identification, standard tests of soft polymers such as bulge test, uniaxial tension or planar tension test can be used.

End-Use Properties of Pineapple Leaf Fibre Filled Natural Rubber

The effects of incorporating pineapple leaf fibre (PLF) as a filler on the end-end properties of natural rubber vulcanizates were studied at different filler contents and particle sizes. The pineapple leaf fibre was used within filler contents, 0 to 40 phr at the following filler particle sizes, 75, 150 and 300 μm. The PLF was characterized for filler properties while carbon black (N330) served as the reference filler. The natural rubber vulcanizates were compounded on a two-roll mill. Results showed that the abrasion resistance of filled natural rubber vulcanizates was generally higher than that of the unfilled natural rubber vulcanizate at filler content, 5 phr, and for PLF (150 and 300 μm) and carbon black filled natural rubber vulcanizates, the abrasion resistance decreased within filler content, 5 to 20 phr after which it increased with filler content. CB exhibited better abrasion resistance in the vulcanizates than PLF at filler contents greater than 20 phr. The hardness of filled natural rubber vulccanizates was generally greater than that of unfilled vulcanizate and increased with increases in filler particle size at filler contents, 10 and 20 phr. The specific gravity of the rubber vulcanizates increased gradually with the increase in filler content at filler content greater than 5 phr, and increased with increases in filler particle size at any filler content considered. The swelling index of filled natural rubber vulcanizates in toluene generally decreased with increasing filler particle size at filler contents, 5, 10 and 40 phr whereas the swelling index for PLF (150 μm) filled natural rubber decreased with increases in filler content. CB filled vulcanizates absorbed the highest amount of toluene (2.5%) in the vulcanizates at filler content, 40 phr. PLF (150 and 300 μm) generally gave optimum performances in the end-use properties of the rubber vulcanizates determined within filler contents, 30 and 40 phr. The incorporation of pineapple leaf fibre into natural rubber was found to improve the end-use properties of natural rubber vulcanizates and therefore, has potential in the formulation of natural rubber products.

Influence of sulphur crosslink type on the strain-induced crystallization of natural rubber vulcanizates during uniaxial stretching by in situ WAXD using a synchrotron radiation

Abstract Strain-induced crystallization (SIC) of varied crosslink structures of vulcanized natural rubber (NR) are compared by using synchrotron X-ray. The sulphur crosslink type (mono-, di- and poly-sulphidic) was controlled by changing the sulphur to accelerator ratio (2.67, 0.50 and 0.10) using CBS as an accelerator. The onsets of SIC occurred at the strain of 2.24 for NR vulcanizates which contain mainly monosulphidic and disulphidic crosslinks (the EV-cured and the SEV-cured system). For the CV-cured NR vulcanizate, the crosslinks of which are dominated by polysulphidic type, SIC began to appear at the higher strain of 2.63. Thus, it appears that short sulphidic crosslinks favour the initiation of SIC. The rate of SIC was found to be slightly higher for the NR vulcanizate which contains a large amount of polysulphidic crosslinks (the CV-cured system) than for the samples which contain mainly monosulphidic and disulphidic crosslinks (the SEV-cured and the EV-cured systems). However, the CV-cured system showed the smaller development of crystallinity during deformation than did the SEV- and EV-cured samples but the final crystalline fraction at the rupture point was higher.

Effect of Different Vulcanizing Systems on SMR-L/Waste Latex Compound Blends

Abstract Natural rubber (NR) is widely used in the industry to produce various products. It requires excellent physical, mechanical and thermal properties to prolong its performance for indoor and outdoor applications. Different sulphur vulcanization systems such as conventional vulcanization (CV), semi-efficient vulcanization (SEV) and efficient vulcanization (EV) systems have different sulphur intake thus give different cross-link density (CLD) and subsequently end properties of the NR vulcanizate. To conserve natural resources, industrial waste such as waste latex compound (WLC) can be utilized to form rubber-rubber blend with the NR. In this study, the effect of different vulcanizing system on the properties of SMR-L/WLC blend was investigated. By comparing the properties of 75:25 SMR-L/WLC blend with 100:0 SMR-L/WLC blend, the effect of WLC loading was also studied. Generally, 100:0 and 75:25 SMR-L/WLC blend with CV system has the best physical and mechanical properties in tensile strength, elongation at break, M100, M300 and hardness. This is due to higher polysulphidic cross-links in CV system which facilitate structural networks rearrangement. This enable the test specimens to withstand higher force. For heat retention properties, both blends showed EV system has better heat retention properties. EV system consists of mainly monosulphidic cross-links with higher thermal stability because the monosulphidic bond is stronger than the polysulphidic bond. The loading of WLC has affect the end properties of rubber vulcanizate. In general, WLC improved the physical and mechanical of vulcanizate but may improve or deteriorate the heat retention. WLC is partially vulcanized rubber thus, presence of WLC lead to higher crosslink density. However, during heat ageing test, the structural changes of the blend vulcanizate results in lesser changes in M100 and M300 but more changes in tensile strength and elongation at break. As conclusion, there is an optimum rubber vulcanizate properties need to be obtained by either using different sulphur vulcanization system or the WLC to have a balance in physical, mechanical and thermal properties.

The Effect of Particle Size of Palm Kernel Shell on the Mechanical Properties and Physical Properties of Filled Natural Rubber Vulcanizates

Abstract The production of crude palm oil resulting in large amounts of by-product called oil palm wastes (OPW) which can be transformed to biochar via pyrolysis. Utilizing the Palm Kernel Shell based biochar had been studied by researches in thermoplastic area but limited studies in rubber area. In rubber application, the particle size plays an important role in governing the properties of the filled vulcanizate. Finer particle size is results in better reinforcement. In this study, the effect of PKS size on the biochar size and the filled vulcanizate were studies. PKS size of 300 μm, 250 μm and 100 μm were pyrolyzed at 500°C for six hours. The biochar obtained showed that the PKS of size 300 μm has finer median particle size; 40 mm but broader distribution as compare to the other two PKS sizes. The PKS of size 200 μm and 100 μm have the same median particle size; 50 μm and similar particle size distribution. The mean size for all the PKS sizes is however similar; i.e. 60 μm. Thermogravimetric Analysis (TGA) performed on these PKS sizes showed that the PKS of size 100 μm has the highest amount of residue: 14.96% followed by 250 μm and 300 μm which are 5.09% and 3.21%, respectively. The tensile properties and hardness show that there is no significant difference on the PKS size to these properties. However, the PKS size which is 100 μm contributes to the lowest value in tear strength. The result suggests that the high amount of ash contents contributed to highest tear strength among the rubber vulcanizates.

Multiple Structural Changes Found around Crack Tip of Carbon Black-filled Natural Rubber Vulcanizate

Multiple Structural Changes Found around Crack Tip of Carbon Black-filled Natural Rubber Vulcanizate

Surface treated natural rubber latex sludge as a potential filler for natural rubber compounds

Natural rubber (NR) latex sludge, a byproduct generated from centrifuged latex manufacturing industry, contains a large portion of inorganic materials and presently treated as a waste material. In this study, the sludge was converted to a powdery material through drying and grinding processes followed by a surface modification with a long chain fatty acid with a view improving its compatibility with rubber composites. Composition and structure analysis of the latex sludge powder showed that it is mainly a crystalline material of phosphate mineral with approximately 8% of trapped rubber particles within the sludge material. Processed NR latex sludge powder was surface treated with a long chain fatty acid to offer organophilic character to the sludge. FTIR analysis confirmed that latex sludge was successfully modified with the long chain fatty acid. A series of NR compounds were prepared with different loading levels of the surface treated sludge using a laboratory scale internal mixer to study the effect of the surface modified sludge on curing and mechanical properties in comparison to unmodified latex sludge filled NR compounds. Curing characteristics measured under low shear strain rate have shown that surface modification improves the processing safety without a significant impact on other curing characteristics. Mechanical properties of surface treated sludge filled NR vulcnizates have shown an improvement in tensile properties, especially strength and elongation at break, in comparison to untreated counterparts. However, on the other hand, stiffness as measured with hardness was reduced at higher loadings of surface treated sludge filled NR vulcanizates. Both surface treatment and the increase of filler loading increased the compression strength and abrasion weight loss of the compounds.

Cereal straw and their physical modifications with hydrophilic and hydrophobic silica – The influence of functional hybrid material on natural rubber biocomposites

Unmodified and silanized cereal straw and two types of silica (hydrophilic and hydrophobic) were chosen to produce functional hybrid fillers. The method of mechanical grinding with simultaneous mixing was used to combine the applied compounds. The obtained materials were subjected to thermal, morphological and dispersive analysis as well as surface wettability. The introduction of an inorganic phase into the lignocellulosic material improved the thermal stability of the systems. A new functional additive with significantly lower polarity was obtained by combining hydrophobic silica and silanized straw. The prepared organic-inorganic hybrid materials were used as fillers of natural rubber (NR). The determined processing and usage properties indicate the beneficial effect of newly formed additives on the parameters of crosslinking, rheometry characteristics and aging resistance. In addition, organic-inorganic hybrid additives are capable of producing a more developed filler structure in the elastomer matrix, which results in an increase in crosslinking density and mechanical strength of the vulcanizates. The presence of the straw-silica hybrid system has a significant influence on the barrier properties and flammability of the NR vulcanizates.

Investigation on Electron Absorbed Dose in a Mixture of Natural Rubber Latex and Cross-linking Agents

Natural rubber vulcanization using electron beam is one of interesting applications of electron accelerators with an energy in a range of a few hundred keV to a few MeV. At the Plasma and Beam Physics (PBP) Research Facility, Chiang Mai University, a 4-MeV radio-frequency (RF) linear accelerator is developed for utilizing in natural rubber vulcanization. To accelerate the vulcanization process, cross-linking agents are added in a natural rubber latex to increase the bonding probability between the chains of rubber molecules. This research used a Monte Carlo based program GEANT4 to simulate the electron absorbed dose in a mixture of natural rubber latex and cross-linking agents. The initial electron energy distributions were obtained from the beam dynamic simulation in the accelerator, which were done with program ASTRA. The initial electron beams have average energy in the range of 0.70 to 4.02 MeV at the position 6 cm prior the 50μm titanium vacuum window foil. The air gap between the vacuum window to the natural rubber latex was set at 18 cm. The electron beam transportation in the titanium foil, air gap and a mixture of natural rubber latex were simulated. The cross-linking agents that are added in the natural rubber latex are ethylene glycol dimethacrylate (EDMA) and 1,6-hexanediol-diacrylate (HDDA). Finally, electron absorbed dose distributions in both transverse direction and along the depth of the natural rubber latex mixed with each cross-linking agent were calculated and analyzed. The results from this work can be used for experimental planning of electron beam irradiation on the natural rubber latex with appropriate cross-linking agents and electron absorbed dose.

Study on Penetration of 4-MeV Electron Beam in Natural Rubber Latex

Vulcanization with electron beam irradiation provides unique and high efficient processing for natural rubber latex. It is one of very interesting and effective industrial applications of particle accelerators. A radio-frequency (RF) linear accelerator (linac) and electron beam irradiation system have been developed for natural rubber vulcanization at the PBP-CMU Electron Linac Laboratory of the Plasma and Beam Physics (PBP) Research Facility, Chiang Mai University (CMU). This accelerator will be able to produce electron beams with maximum energy up to about 4 MeV. In this research, we used a Monte Carlo simulation program called GEANT4 to study transportation of 4-MeV electron beam with Gaussian transverse distribution through a vacuum window, an air gap and natural rubber latex. The vacuum window is made of 50-micron titanium foil and the natural rubber was placed 18 cm downstream the foil exit. Simulations of electron depth dose and transverse distribution in these media were conducted. In addition, calculation on the irradiation throughput was performed. The study results revealed that for the electron beam with Gaussian transverse distribution and an average energy of 4.06 MeV, the irradiation area should be 2.8 mm×2.8 mm with the depth of 8 mm. With this condition, the irradiation time of 0.02 second will provide the dose of at least 50 kGy per irradiated point, which is enough for the rubber vulcanization process. The overall irradiation throughput rate is 6.865 kg/hr.

Simulations and measurements of the dipole magnet using in the 4-MeV electron spectrometer

A dipole magnet is one of important components in particle accelerators. It can be used to transport a charged particle beam with desired deflecting angle and direction. Moreover, it is often utilized as a part of an energy spectrometer. This research focuses on simulations and measurements of the dipole magnet, which will be used to measure the electron beam energy produced from the 4-MeV radio-frequency (RF) linear accelerator (linac) for natural rubber vulcanization at the PBP-CMU Electron Linac Laboratory of the Plasma and Beam Physics (PBP) Research Facility in Chiang Mai University (CMU). The research activities are divided into three main parts. The first part focuses on three-dimensional (3D) simulation of the dipole magnet by using the RADIA program. The 3D field map of the magnetic field can be derived from the RADIA model. The second past is the magnetic field measurements of the magnet after the construction. The maximum magnetic field of 248.6 mT can be obtained with an excitation current of 3 A. The last part focuses on the electron beam dynamic study by using the program called ASTRA to track the particles though the 3D magnetic field distribution. The simulation data provides six-dimensional coordinates of the particles at the considered position downstream the dipole magnet. The optimal bending angle of the 4-MeV electron beam in the magnetic field of 0.22 T is 50° with an energy spread of 0.827 MeV.