Lichun Maa,
Linghui Menga,
Yuwei Wangab,
Guangshun Wua,
Dapeng Fanc,
Jiali Yua,
Meiwei Qia and
Yudong Huang*a
aSchool of Chemical Engineering and Technology, Harbin Institute of Technology, Harbin 150001, China. E-mail: ydhuang.hit1@yahoo.com.cn; Fax: +86 451 86221048; Tel: +86 451 86414806
bCollege of Materials Science and Engineering, Qiqihar University, Qiqihar 161006, China
cCollege of Material and Chemical Engineering, Heilongjiang Institute of Technology, Harbin 150001, China
First published on 11th August 2014
In order to understand the effects of chain length on the interfacial adhesion of PAN-based carbon fiber (CF)/epoxy composites, dendritic hexamethylenetetramine (HMTA) was functionalized on carbon fibers through quaternary ammonium salt reaction using alkyl dihalide of varying chain length [Cl(CH2)nCl, n = 2, 6 and 12]. Fourier transform infrared spectroscopy (FTIR), Raman spectra and X-ray photoelectron spectroscopy (XPS) confirmed the successful grafting of dendritic HMTA and alkyl dihalide. AFM images showed that dendritic HMTA modified CF surfaces enhanced roughness, and this effect was more pronounced with increasing alkyl dihalide chain length. The results of dynamic contact angle (DCA) and interfacial shear strength (IFSS) demonstrated that the surface energy and interfacial adhesion increased and then decreased with the chain length of alkyl dihalide. The tensile strength and impact roughness of the composites enhanced as the alkyl dihalide chain length grew. Moreover, the reinforcing and toughening mechanisms were also discussed.
Though people know the three main effective factors, it is not yet fully understood how these surface treatments ultimately influence the interfacial properties due to the difficulties in quantitatively defining and controlling both the interfacial thickness and chain length on carbon fibers.13,14 To further improve and develop advanced composite materials, a solid understanding of interface/interphase concepts is essential.15,16 So, it is necessary to look for a proper method that can simplify and model various complicated interfaces to obtain a better insight into the interfacial action mechanisms.
Grafting of polymer or micro-molecule to carbon fiber provides a means to obtain a controlled and ordered structure.17 The grafting method is based on attachment of premade end-functionalized polymer onto the tips and convex walls of the carbon fiber via chemical reactions such as etherification and amidization, or immobilization of reactive groups (initiators) onto the surface, followed by in situ polymerization of appropriate monomers to form polymer grafted carbon fiber. The advantages of this approach are that the mass and distribution of the grafted polymers or micro-molecule can be more precisely controlled and high grafting density can be achieved.18–22 In a previous study, we have investigated the chemical grafting approach, which involves the propagation of dendritic hexamethylenetetramine (HMTA) from carbon fiber surfaces by quaternary ammonium salt reaction in the presence of carbon fiber attached haloalkane,23 and dendritic HMTA is a kind of facile and effective coupling agents for increasing the interfacial adhesion of the composites by improving the wettability, enhancing chemical bonding and mechanical interlocking.
Although dendritic molecules are able to improve the interfacial properties between carbon fibers and epoxy matrix, the influence of alkyl chains lengths in the dendritic molecules on the interfacial performance has not been investigated. In this study, we further functionalized dendritic hexamethylenetetramine (HMTA) on carbon fibers through quaternary ammonium salt reaction using alkyl dihalide of varying chain lengths [Cl(CH2)nCl, Cn in short, n = 2, 6 and 12] to study the effect of chain length of alkyl dihalide on the interfacial adhesion of the composites. In addition, in order to understand the influence of chain lengths on the interface more clearly, we only adopt the second generation dendrimer. Fourier transform infrared spectroscopy (FTIR), Raman spectra and X-ray photoelectron spectroscopy (XPS) were carried out to confirm the alkyl dihalide successful grafting and generation buildup. The wettability of carbon fiber surface was studied by dynamic contact angle analysis (DCA). The effects of chain lengths on mechanical properties of the composites were investigated by micro-bond test, single fiber tensile testing and impact tests. The surface topographies of carbon fiber were observed by atomic force microscopy (AFM) and field emission scanning electron microscope (FESEM).
Alkyl dihalides | Molecular structure | |
---|---|---|
1 | 1,2-Dichloroethane | Cl(CH2)2Cl |
2 | 1,6-Dichlorohexane | Cl(CH2)6Cl |
3 | 1,12-Dichlorododecane | Cl(CH2)12Cl |
(i) The CFs were firstly extracted by Soxhlet with acetone in order to remove the polymer sizing and pollutants on the surface of CFs (denoted as untreated CF);24 second, the CFs were oxidized in AgNO3/K2S2O8 solution at 343 K for 1 h to introduce polar groups (such as hydroxyl groups, carboxyl groups);25 subsequently, the CF–COOH was reacted with SOCl2 for 48 h to yield acyl chloride functionalized CFs (CF–COCl);26–29 CF–COCl was reacted with 3-bromo-1-propanol in anhydrous pyridine solution in the ice water bath, and then at room temperature for 3 h to yield CF–Br;30–33 then 0.2 g CF–Br was reacted with 0.2 g hexamethylenetetramine (HMTA) in 30 mL trichloromethane at 333 K for 8 h to produce quaternary ammonium salt reaction and obtained functionalized CF containing the “first generation” amine groups (CF–N+Br−, CF-G1-HMTA).34,35 All reactions were extracted and washed by appropriate solvent. And every reaction step has been worked successfully by XPS.23
(ii) The grafting reaction and propagation of dendritic HMTA from the CF surface was accomplished by two processes:36,37 (1) quaternary ammonium salt reaction of alkyl dihalide [Cl(CH2)nCl, n = 2, 6 and 12] to peripheral amino groups. 0.2 g CF-G1-HMTA was reaction with 20 mL alkyl dihalide [Cl(CH2)nCl, n = 2, 6 and 12], respectively, the every reaction was maintained at 333 K for 8 h. Following this, carbon fibers were taken out and washed with ethanol for three times, respectively, and then used directly in the next procedure. And (2) quaternary ammonium salt reaction of terminal Cl group by HMTA. The carbon fiber was putted into 30 mL trichloromethane, followed by adding 0.2 g HMTA, respectively; the reaction was carried out 333 K for 8 h to obtain the functionalized CF containing the “second generation” amine groups (CF-G2(n)-HMTA, n = 2, 6 and 12). The resultant was extracted with trichloromethane to remove unreacted HMTA and dried.
A proposed mechanism for grafting dendritic HMTA (CF-G2-HMTA) onto CF surface by using alkyl dihalide of varying chain lengths is schematically represented below (Fig. 1).
The surface structures of the carbon fibers were analyzed by Raman spectrometer (Invia Renishaw 2000), the monochromatic light source was an Ar+ laser (514.5 nm). The laser beam, polarized parallel to the fibers axis, was focused on the samples with the 50× objective onto a spot 1–2 μm in diameter, the wavenumber range of Raman spectra was 800–2000 cm−1. The spectra acquired from experiment were analyzed using a Lorentzian curve fitting with a linear baseline to determine the peak areas in the software of WIRE3.3.
XPS (ESCALAB 220i-XL, VG, UK) was carried out to study grafting reaction procedure using a monochromated Al Ka source (1486.6 eV) at a base pressure of 2 × 10−9 mbar. The XPS was energy referenced to the C1s peak at 284.6 eV. The XPS peak version 4.1 program was used for data analysis.
Dynamic contact angle tests were measured by using a dynamic contact angle meter and tensiometer (DCAT21, Data Physics Instruments, Germany). Deionised water (γd = 21.8 mN m−1, γ = 72.8 mN m−1) and diiodomethane (γd = 50.8 mN m−1, γ = 50.8 mN m−1, 99% purity, Alfa Aesar, USA) were used as test liquids. The dispersive and polar components can be easily determined by solving the following equation:
γl(1 + cos![]() | (1) |
γf = γpf + γdf | (2) |
The interfacial shear strength (IFSS) was adopted to quantify the interfacial property between CFs and resin matrix by the interfacial evaluation equipment (FA620, Japan). The epoxy resin (E-51) and curing agent (H-256) were mixed at the weight ratio of 100:
32 to prepare microdroplets. The microdroplets were cured at 363 K for 2 h, 393 K for 2 h and 423 K for 3 h. The values of IFSS were calculated according to eqn (3),
![]() | (3) |
Single fiber tensile tests were performed on a universal testing machine (5569, Instron, USA) according to the ASTM D3379-75. The distance between the papers, i.e. the gauge length, was 20 mm. The samples were fixed and tested by the Instron at a cross-head speed of 1 mm min−1. At least 100 samples were tested for CF, the grafted CFs. The results were analyzed with Weibull statistical method.
The surface topography and roughness of samples before and after being treated was examined by atomic force microscope (AFM, NT-MDT Co., Zelenograd Research Institute of Physical Problems, Moscow, Russia). The observed area was 4 mm × 4 mm. Images were obtained in non-contact mode with a silicon cantilever (nominal spring constant of 3 N m−1, minimum tip radius of 10 nm). Each datum was obtained from the average value of 15 different positions on three different fibers.
The unidirectional prepreg of carbon fibers and epoxy resin was put into a mold to manufacture composites. The resin content of the composites was controlled at 35 ± 1.5 mass%. The curing process was at 363 K for 2 h under 5 MPa, 393 K for 2 h under 10 MPa and 423 K for 4 h under 10 MPa.
Impact tests were carried out on a drop weight impact test system (9250HV, Instron, USA). The specimen dimensions were 55 mm × 6.5 mm × 2 mm. The impact span is 40 mm. The drop weight was 3 kg and the velocity was 1 m s−1. Each date was obtained from the average value of 5 specimens.
The morphologies of the CF, and the grafted CFs after de-bonded and impacted were observed by FESEM (Quanta 200FEG, Hitachi Instrument, Inc. Japan). The samples were coated with a thin conducted gold layer by sputtering prior to the FESEM observation in order to capture a stable and clear image.
To further analyze the surface structures of the CF and grafted CFs, Raman spectroscopy was adopted. The Raman spectra of carbonaceous materials have two characteristic bands including: (1) “D-band”, centered at the wavenumber of 1330–1350 cm−1 that is attributed to defects and disordered carbonaceous structure, and (2) “G-band”, located at the wavenumber of 1580–1600 cm−1 that is related to ordered graphitic structures. The integral area ratio of the “D-band” to the “G-band” (ID/IG, known as the “R-value”) indicates the amount of structurally ordered graphite crystallites in the carbonaceous materials.40
In addition, the overlap between D and G peak is serious, which is not conducive to analyze thoroughly, therefore, the spectra must be fitted. “A-band” around 1500–1550 cm−1 has been observed in some carbon materials with lower ordered structure (such as glassy carbon, carbon black and so on), it is associated with amorphous carbonaceous structures, some hetero atoms on the surfaces of CFs or some original functional groups.41–43 The integral area ratio of the “A-band” to the “G band” (IA/IG) indicates the proportion of amorphous carbonaceous structures as well as some oxygen-containing and/or nitrogen containing functional groups on the CFs surface.
The Raman spectra and curve fitting using the Lorentzian–Gaussian method with the software of WIRE3.3 for untreated CF, CF-G1-HMTA, and CF-G2(n)-HMTA (n = 2, 6 and 12) are shown in Fig. 3. The wave numbers of three bands and the calculated values of “ID/IG” and “IA/IG” are shown in Table 2. It indicated that the micro-structure of carbon fibers surface changed after grafting.
![]() | ||
Fig. 3 Raman spectra (a) and curve fitting for all the samples (b) CF, (c) CF-G1-HMTA, (d–f) CF-G2(n)-HMTA (n = 2, 6 and 12). |
Samples | D | G | A | R = ID/IG | IA/IG |
---|---|---|---|---|---|
W (cm−1) | W (cm−1) | W (cm−1) | |||
CF | 1340 | 1590 | 1500 | 1.46 | 0.69 |
CF-G1-HMTA | 1340 | 1590 | 1508 | 2.05 | 0.87 |
CF-G2(2)-HMTA | 1340 | 1590 | 1505 | 2.06 | 0.93 |
CF-G2(6)-HMTA | 1336 | 1590 | 1505 | 2.03 | 1.06 |
CF-G2(12)-HMTA | 1339 | 1592 | 1508 | 2.02 | 1.11 |
Compared to the untreated CF, the “R(ID/IG)” value of CFs after being grafted HMTA (CF-G1-HMTA) increased to 2.05 from 1.46, which indicated that the oxidation in the process of grafting partially damaged the structurally ordered sheath region of CFs, a suitable etching would preferably remove the carbonaceous structures on the fiber surface, the disordered carbonaceous components on the surface of CFs was improved, and the crystalline structure of the CFs was reduced. And as the dendritic generation and chain lengths increased, the “R(ID/IG)” values were slightly affected.
However, “IA/IG” value of the CF after being grafted HMTA increased significantly, from 0.69 for un-treated CF to 0.87 for CF-G1-HMTA, which proved that the amorphous carbonaceous structures (C–C, C–H bond) as well as nitrogen-containing functional groups (HMTA) were grafted on the surface of CFs, and the “IA/IG” values gradually increased as the dendritic generation and chain lengths increased, which would mean that the more nitrogen-containing functional groups will provide more activity sites to improve the interfacial strength of the composites.
XPS is a very sensitive and surface specific analytical tool. To further present enough evidence of HMTA and alkyl dihalide grafted onto carbon fiber surface, we used high-resolution XPS to detect the surface composition and the chemical environment of CF-G2(n)-HMTA (n = 2, 6 and 12), The survey spectrum of CFs and C1s peak positions derived from peak deconvolution and fitting to data are listed in Fig. 4 and Table 3. The XPS C1s core-level spectrum of untreated CF (Fig. 4a) was resolved into three component peaks: Csp2 and Csp3 in the fiber structure (peak C1s (1), 284.4 eV), C–C bonding of amorphous carbon (peak C1s (2), 285.6 eV) and C–O bond (peak C1s (3), 286.3 eV).44–46 As shown in Table 3, the content is 74.5%, 18.44%, 7.06%, respectively. The C1s peak of CF-G1-HMTA (Fig. 4b) shows a peak assigned to –CO (C1s (4), 287.3 eV) generated on the CF through AgNO3/K2S2O8 oxidation. What's more, there were two additional binding energy peaks at 286.3 eV and 285.8 eV, which is assigned to new generated bond C–N+ by quaternary ammonium salt reaction and C–N bond existence in the HMTA,47,48 and the content of C–N and C–N+ bond increased with the dendritic generation number as shown in Table 3. These amine groups grafted onto the fiber surface would effectively increase the polarity of the carbon fiber surface and make the fibers more easily further react with epoxy matrix and enhance the interfacial strength of the composites. In addition, compare the CF-G2(n)-HMTA (n = 2, 6 and 12), as the chain lengths of alkyl dihalide increased, the peak areas of C–C (peak C1s(1) 284.4 eV) increased, indicating the alkyl dihalide has been grafted to the HMTA through quaternary ammonium salt reaction, which was consistent with the results of the FTIR discussed above. Moreover, the content of C–N and C–N+ increased, this is due to the growth of molecular chain, the steric hindrance effect between rigid HMTAs reduced, thereby more HMTA molecules could be grafted to alkyl dihalide. While as n = 12, the content of C–N and C–N+ decreased, this is possibly because that the long chain alkyl dihalide has good flexibility, molecular chain curls and wraps the polar functional groups from being exposed outside, and the G2-HMTA can not be grafted, which lead to the content of C–N and C–N+ decreased. From the survey spectrum of CFs, we also found that the content of nitrogen element (N1s, 400.5 eV) increased greatly and then decreased.
![]() | ||
Fig. 4 XPS survey spectrum and curve fitting for C1s peak (a) CF, (b) CF-G1-HMTA, (c–e) CF-G2(n)-HMTA (n = 2, 6 and 12). |
Samples | The relative content of functional group (%) | ||||
---|---|---|---|---|---|
C1s (1), C–C | C1s (2), C–C/C–N/C–N+ | C1s (3), C–O | C1s (4), C![]() |
C1s (5), –COOH | |
CF | 74.50 | 18.44/—/— | 7.06 | — | — |
CF-G1-HMTA | 67.50 | 10.00/12.85/4.05 | — | 5.60 | — |
CF-G2(2)-HMTA | 61.52 | 10.59/17.19/8.03 | — | 2.67 | — |
CF-G2(6)-HMTA | 63.26 | 7.99/16.93/10.51 | — | 1.31 | — |
CF-G2(12)-HMTA | 65.20 | 9.41/15.25/9.52 | — | 0.62 | — |
In short, through the analysis of FTIR, Raman and XPS, it could be concluded that alkyl dihalide and dendritic HMTA are well organized and grafted to the CF surfaces.
![]() | ||
Fig. 5 3D AFM images of CF surface: (a) untreated, (b) CF-G1-HMTA, (c–e) CF-G2(n)-HMTA ( n = 2, 6 and 12). |
![]() | ||
Fig. 6 Contact angles and surface energy of untreated CF, CF-G1-HMTA and CF-G2(n)-HMTA (n = 2, 6 and 12). |
Compare the CF-G2(n)-HMTA (n = 2, 6 and 12), as n = 6, the contact angles decreased from 33.08 to 25.10° for water and from 24.56 to 22.78° for diiodomethane. The increased polar component of surface energy could be interpreted by the increase of amine groups caused by more HMTA grafted on the fiber surface. In addition, the increased dispersion component could be attributed to the increased fiber surface roughness caused by the longer chain of alkyl dihalide, so both the dispersion component (γd) and polar component (γp) make it have the highest surface energy. As n = 12, the contact angle increased for water, this could also be due to the fact that the long alkyl dihalide chain curls and blocks the polar functional groups from being exposed on the entire system surface, which lead to the reduction of polar groups. But the contact angle still decrease for diiodomethane as the growth of carbon chain. Owing to the extent of increment of dispersive component is higher than the extent of decrement of polar component, the CF-G2(12)-HMTA which has the highest dispersion component owns the higher surface energy compared CF-G2(2)-HMTA and lower surface energy compared CF-G2(6)-HMTA. In short, the higher surface energy could lead to a better wettability especially for the polar matrices, which is beneficial to the subsequent formation of covalent bonding, van der Waals interaction and physical entanglement, and could greatly enhance the interfacial properties of composites.
Furthermore, after the carbon chain (C2) of CF-G2(2)-HMTA surfaces were replaced with C6, the composite also showed significant improvement in IFSS, improved by 82.90% compared to untreated composite, at the same time, the value of IFSS is also higher than that of CF-G3-HMTA obtained in previous study.23 This may be because the longer alkyl chain in CF-G2(6)-HMTA make the distance between HMTAs of generation 1 and 2 increase, and the steric hindrance effect of rigid molecules reduced, thereby more HMTA molecules could be easily grafted to alkyl dihalide. In addition, there are much broad space in the molecular interior and exterior, epoxy matrix can infiltrate into molecular interior and exterior to form a strong mechanical interlocking with CF, which result a better adhesion at the interface, therefore the stress transfer more efficiency from the matrix to CF increased.
Whereas the longest alkyl chains of C12, due to the flexibility, it is easily to curl and block a part of polar functional groups from being exposed on outermost surface, making the G2-HMTA can not be grafted. Meanwhile, the end of chains itself may not be able to graft new active group, so the value of IFSS lower. Although polar group has less contribution to the improvement of interfacial properties, the interaction physical entanglement between the long chain and the chain of epoxy at the interface is responsible for the improvement of interfacial performances to some extent, therefore the IFSS value is still higher than CF-G2(2)-HMTA.
In order to further confirm the reason for such an enhancement, the surface morphologies of CFs de-bonding from the matrix were examined by FESEM, as shown in Fig. 8. In the case of untreated CF, the de-bonded CF surface (Fig. 8b) is almost neat. Scilicet, there is almost no epoxy remained on the CF surface, which indicates that the interface is easily de-bonded due to the weak van der Waals force reaction between CF and epoxy.53 In the case of HMTA functionalized CF, the CF surface (Fig. 8c) is not as smooth as that for the CF-G1-HMTA, that is to say that some epoxy have remained on the CF surface, which signifies the interface between CF and epoxy becomes so strong that fracture is not restricted to the interface only. As mentioned above, the HMTA not only links to the CF by the chemical interactions, but also reacts with epoxy matrix as curing agent. As a result, the bonding between CF and epoxy is not the van der Waals interaction but chemical interaction. Fig. 8d presents the surface morphology of CF-G2(2)-HMTA, the remained epoxy is more than the case of CF-G1-HMTA, which further conformed that the interfacial performance greatly improved as the growth of dendritic generation.
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Fig. 8 SEM micrographs of before de-bonding (a) and after de-bonding samples: (b) untreated CF, (c) CF-G1-HMTA, (d–f) CF-G2(n)-HMTA (n = 2, 6 and 12). |
Compare the surface morphologies of CF-G2(n)-HMTA (n = 2, 6 and 12) de-bonding from the matrix. It can be seen that the surface CF-G2(6)-HMTA was almost covered by remained epoxy and the de-bonding took place in the matrix (Fig. 8e). In addition to the active functional groups increased, the longer chain of alkyl dihalide grafting must lead to increased roughness of the CF surface, which enhances the mechanical interlocking effect between the CF and matrix. The pullout of CF from the epoxy matrix certainly consumes some more energy thus enhancing the interfacial strength. Fig. 8f presents the surface morphology of CF-G2(12)-HMTA, the remained epoxy is more than the case of CF-G2(2)-HMTA, but less than the case of CF-G2(6)-HMTA. The longest chains of alkyl dihalide make the interaction physical entanglement with the chain of epoxy increase, but the active groups which exposed in the outside surface and take part in the chemical interactions with epoxy matrix may reduce, so remained epoxy is less than the surface of CF-G2(6)-HMTA. These observations are consistent with the IFSS results. The stronger the interfacial shear strength, the more epoxy remained on the CF surface.
Sample | Ra | m | Σ0 | Expectation (GPa) |
---|---|---|---|---|
CF | 0.99 | −4.98 | 3.91 | 3.80 |
CF-G1-HMTA | 0.99 | −4.96 | 3.86 | 3.78 |
CF-G2(2)-HMTA | 0.97 | −5.16 | 3.87 | 3.83 |
CF-G2(6)-HMTA | 0.99 | −5.23 | 3.88 | 3.92 |
CF-G2(12)-HMTA | 0.98 | −5.38 | 3.96 | 3.98 |
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Fig. 9 Impact test results of the composites (a) and SEM micrographs of fracture surface of composites (b) untreated CF, (c) CF-G1-HMTA, (d–f) CF-G2(n)-HMTA (n = 2, 6 and 12). |
FESEM observations of the fractured surfaces of the composites are also demonstrated in Fig. 9. For the untreated carbon fiber composites (Fig. 9b), a large number of fibers were pulled out from the matrix, the pulled-out fibers were clean and there were almost no resin fragments adhered on the fiber surface, which indicates the adhesion between fibers and matrix is poor. Compared with Fig. 8b, for the HMTA grafted fiber sample (Fig. 9c), the interfacial adhesion was obviously improved and the number of pulled-out fibers decreased. For the CF-G2-HMTA (Fig. 9d), the flat fracture surface could be observed, the combination is so close that there is no gap between fiber and resin. And as chain length of alkyl dihalide growth, fracture surface is more flat, but a part of the cross section was covered with the broken fragments of the resin and fiber. This may be because that the introduction of HMTA molecules and the alkyl dihalide of long chain in the interface phase formed a crack network structure during the process of crack induction and dispersion, which make matrix resin and fiber nearby form a large number of fragments under the action of a large number of cracks. Thus large amounts of energy were consumed and the impact resistance of composite improved with the chain length of alkyl dihalide.
To summarize, the influence of the different chain lengths on the interfacial adhesion is illustrated in Fig. 10. We can see that the active sites HMTA (indicated by red dot) increases evidently as the dendrimer generation number increases, compare the schematic illustration of CF-G2(n)-HMTA (n = 2, 6 and 12), as the alkyl dihalide chain length increases, the active sites first increases and then decreases, and the entanglements between the chains become more obvious.
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Fig. 10 Schematic of the interaction of matrix with CF grafted different chain lengths at the surface. |
Maximum IFSS is expected for a large number of polar groups of HMTA reaction with matrix, combined with strong penetration of the long alkyl dihalide chains into the matrix. But the longest chain length leaded to a lowering of IFSS due to the decrease of polar groups, so the chemical interaction is also play an important role for the improvement of the interfacial adhesion. Here, we have to consider that the mechanical interlocking is not the only parameter responsible for the interface adhesion. The highest interfacial adhesion can be expected to result from a combination of sufficient chain space, length and polar groups.57 In addition, dendritic HMTA effectively increased the tensile strength and impact toughness of the composites through increasing the alkyl dihalide chain length. Therefore, according to different applications, a balance of the resulting composite properties among the interfacial adhesion, tensile strength and impact resistance should be considered.
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