Cure Kinetics of Nanodiamond-Filled Epoxy Resin - American

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Cure kinetics of nanodiamond filled epoxy resin: Influence of nanodiamind surface functionality Atousa Aris, Akbar Shojaei, and Reza Bagheri Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b01858 • Publication Date (Web): 13 Aug 2015 Downloaded from http://pubs.acs.org on August 19, 2015

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Industrial & Engineering Chemistry Research

Cure kinetics of nanodiamond filled epoxy resin: Influence of nanodiamond surface functionality

Atousa Aris1, Akbar Shojaei∗, 1, Reza Bagheri2

1

Department of Chemical and Petroleum Engineering, Sharif University of Technology, P. O. Box 11155-9465, Tehran, Iran 2

Department of Materials Science and Engineering, Sharif University of Technology, P. O. Box 11155-9466, Tehran, Iran

∗

Corresponding author. Tel./fax: +98-21-66166432 E-Mail address: [email protected] (A. Shojaei)

1

ACS Paragon Plus Environment


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Abstract Thermally oxidized nanodiamond (OND), amine functionalized ND (AND) and untreated ND (UND) were added to epoxy/TETA at 1 wt% loading. NDs enhanced dynamic storage modulus of epoxy while decreased glass transition temperature due to increment of free volume in vicinity of ND surfaces. NDs induced acceleration effect on curing reaction which could be due to functional groups of NDs and lack of any steric hindrance on molecules by ND particles themselves. Vyazovkin model-free isoconversional method indicated that all NDs decreased the activation energy, among them, AND showed the lowest value because of significant promotion of epoxide ring opening reaction by polar amino groups. Sestak-Berggren kinetics model was used to predict successfully the cure kinetics of epoxy/ND.

Keywords: Nanodiamonds; Cure kinetics; Epoxy resin

2


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1. Introduction Epoxy resins are the widely used thermosetting matrices in polymer composites, structural adhesives and protective coatings, because of their high mechanical properties, low shrinkage, remarkable chemical/corrosion resistance and good adhesion. In order to further improve the performance of epoxy resins for advanced applications (especially toughness, electrical conductivity and thermal stability), incorporation of various reinforcing particles, either in nano or micro-scale, into that resin has been the subject of many research investigations1-5. Recent studies have shown that the carbon based nanoparticles such as carbon nanotube (CNT), carbon nanofiber (CNF) and graphene are extremely effective reinforcements for epoxy resins even at very low concentrations due to their extremely large specific surface area, exceptional performance and multifunctional features6-9. Nanoscale dispersion of the nanoparticles and strong polymer-nanoparticle interaction are of prime importance to obtain full potential reinforcing aptitude of the nanoparticles in the epoxy matrix. It is well explored that the suitable surface functionalization of the nanoparticles has an essential influence on both interfacial interaction and uniform dispersion, however the functional groups can involve in the curing reaction and change the curing process accordingly7, 10, 11. Nanodiamond (ND) is a kind of carbon based nanoparticle bringing diamond properties into nanoscale world. ND is first discovered in the 1960s by the Russian scientists12; however, extensive researches on polymer nanocomposites filled with ND are 3



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back to the past decade. ND produced by detonation process is economically viable nanoparticle having spherical shape with average diameter of 4-6 nm and very large specific surface area, typically around 400 m2/g 13. Furthermore, the outer surface of ND is originally covered by many functional groups such as hydroxyl, carboxyl and ketone12, 14-19, making the ND surface tailorable for sophisticated functionalizations without compromising the core properties of ND. Spherical shape of ND (a geometrical feature offering entanglement free nanoparticle) with maximum interfacial area compared to platelet- and rod-like nanoparticles and rich surface chemistry along with high mechanical properties, excellent biocompatibility and high thermal conductivity19-21 have motivated researchers to look for polymer/ND nanocomposites with multifunctional features for advanced applications. Recent studies have shown that ND (either in functionalized or unfunctionalized forms) is able to improve the mechanical properties of various polymers22-29. The influence of ND on the performance of epoxy resin has also been addressed in literature3, 30-36. Zhai et al.35 observed that in presence of 0.3 wt% ND, Vicker’s hardness, tensile strength and modulus increased by 24%, 52% and 54% respectively. Mochalin et al.37 reported that the right surface modification of ND (amine functionality in their study) leads to a significant improvement in mechanical properties, i.e. 150% and 50% in hardness and Young’s modulus, respectively; thanks to the formation of covalent bonding between ND and epoxy. Rakha36 observed that by adding 0.4 wt% of acid treated ND, hardness, storage modulus and loss modulus enhanced by 86%, 68% and 55%, respectively, as a result of the electrostatic interaction between carboxylic acid group of ND surface and epoxide groups. 4


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However, the research work conducted by, Ayatollahi3 exhibited that amine grafted ND shows a limited improvement in the mechanical properties of epoxy resin (15% and 6% increment in young’s modulus and tensile strength). Study of cure kinetics for any thermosetting polymer nanocomposites is of great importance not only from the viewpoint of design of the processing operations, but also it can shed light on the microstructure of nanocomposites. This latter benefit can be postulated by the fact that the possible role of nanoparticle on cure behavior of the thermosetting matrix is normally dominated by its external surface, a fact that can be correlated to the extent of nanoscale dispersion and surface functionality. Although the research works dedicated to the mechanical properties of epoxy-ND composites have increasingly been appeared in recent literature, the research works dealing with the role of ND on the cure kinetics of epoxy resin is still very sparse. As the surface functionalization of ND is shown to be essential for achieving highly improved epoxy-ND nanocomposites3,30,35-37, the cure kinetics investigation considering surface functionality in this nanocomposite can provide deeper insight into the microstructure of epoxy-ND nanocomposites. Literature shows some researches on the cure kinetics analysis of carbon based nanoparticle like carbon nanotube (CNT) filled epoxy nanocomposites reporting on the influence of various aspects of the nanoparticles on the cure kinetics such as surface functionality, thermal conductivity and surface area/state of dispersion38-40. These investigations have shown that the CNT based nanocomposites might play different roles in the cure kinetics behavior such as acceleration (catalytic) 5


39,41-43

or even retardation44


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effects. For instance, Qiu45 observed an increase in activation energy of untreated CNTepoxy nanocomposite compared to neat resin while amine treated CNT facilitated the cure reaction of epoxy resin leading to a decrease in the activation energy. The application of suitable cure kinetic models and even modelling techniques has also taken special attentions in cure kinetics investigation of epoxy-CNT systems38. These investigations have shown that the surface functionality can have a great influence on the cure kinetics parameters of carbon based epoxy nanocomposites. In this paper, the cure kinetics behavior of epoxy-ND composites is investigated using dynamic differential scanning calorimetry (DSC). To take into account the role of surface functionality on the cure kinetics of the composites, as received ND is further functionalized to enhance the carboxylic group and attach the amine functionality. Then the isoconversional method was employed to determine the activation energy and the cure kinetics model parameters. 2. Theoretical Background There are different techniques to analyze cure behavior of thermosetting resins. DSC is an efficient instrument that traces the variation of heat flow with temperature (or time) in the course of curing reaction. The basic assumption in this technique is that the degree of cure ( α ) is proportional to the heat of reaction. Therefore, the degree of cure at any time during the curing process can be correlated with the heat of reaction released until that time. Based on this assumption Vyazovkin46 minimized the following equation, Eq. (1), to obtain activation energy at any conversion: 6


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n

Φ(E α ) =

n

(

) = min α , Tα , j ) βi

I E α , Tα ,i β j

∑∑ I ( E i =1 j≠ i

(1)

where i and j are the number of DSC experiments, and β , T and E α stand for heating rate, temperature and I(E, T) =

∫

α

0

activation

exp(−E / RT)dT .

energy and

I is

an

integral

equation

In cases that E α is strongly conversion-dependent,

given

as

I(E, T) is

supposed to be integrated at a small fractional conversion increment, i.e. between α − ∆α and α corresponding with the temperatures Tα−∆α and Tα in a dynamic run, where activation energy can be considered to be constant. Knowing the value of activation energy, Malek47 introduced two functions of y(α) and z(α ) , expressed as follows, to choose the most suitable kinetics models:

(

y ( α ) = dα

dt

) exp ( x )

(

dt

z ( α ) = π ( x ) dα

where x =

(2)

) Tβ

(3)

E is the reduced activation energy and π ( x ) can be described by the following RT

expression:

π(x) =

x 3 + 18x 2 + 88x + 96

(4)

x 4 + 20x 2 + 240x + 120

7



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3. Experiment 3.1. Materials and methods Detonated ND with average diameter of 4-6 nm and purity of 98-99% was obtained from Nabond Co., China. Epoxy Epon828 with average molecular weight of 185- 192 gr/eq was supplied by Shell Co. Triethylenetetramine (TETA) produced by Huntsman was used as hardener of epoxy resin. Oleylamine (70% Sigma-Aldrich) was used for amine functionalization of ND. As-received untreated ND, denoted here as UND, was first oxidized in air atmosphere at 420 °C for 1.5 hr according to literature48, to enhance the surface carboxylic groups of ND. Then, the oxidized ND (so called OND) was utilized to further surface functionalization by Oleylamine to obtain aminated ND, i.e. denoted by AND in this study, according to the procedure mentioned in literature48. To accomplish this functionalization, OND (1 wt%) was added to a solution containing acetone (99% Merk) and Oleylamine (30 wt% based on OND weight in the suspension). Then the mixture was put in an ultrasonic bath with the power of 70 W for 15 min48. All three NDs including UND, OND and AND were used to prepare ND filled epoxy composites by employing solution mixing method. To prepare epoxy-UND nanocomposite, the required amount of epoxy resin was added to the mixture of UND/acetone, which was sonicated for 15 min in advance. The obtained solution, i.e. epoxy resin/UND/acetone, was mixed mechanically at 2000 rpm for 30 min at ambient temperature followed by one hour at 100 ̊C to evaporate the acetone entirely while the system is under mixing. Then the mixture was exposed to vacuum condition in order to 8


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ensure the removal of acetone entirely. Thereafter, TETA hardener was added to epoxyUND mixture at off stoichiometric amount of 15 phr to avoid the participation of secondary amine in cure reaction49. The amount of UND in final mixture was set to be 1 wt% (compared to the resin/hardener) and the corresponding epoxy-UND nanocomposite was called EUND. The same solution mixing procedure was employed to obtain epoxy nanocomposite with OND, i.e. so called EOND, and AND, i.e. named EAND, as well. To prepare specimens for investigating dynamic-mechanical properties, the samples were first degassed in a vacuum for 30 min at 45 ̊C and then cured at room temperature for 24 hr. The cured samples were then post cured at 100 °C for 1 hr. 3.2. Characterization Surface characterization of nanoparticles was performed by fourier transform infrared spectroscopy (FTIR) analysis (Bomem MB100) and thermogravimetric analysis (TGA) (Mettler Toledo DSC-TGA). FTIR was performed using a KBr pellet in a transmission mode within the wavelength of 4000-400 cm-1. TGA was carried out on almost 10 mg samples over the temperature range of 100-600 ̊ C with heating rate of 10 °C min under the nitrogen atmosphere. The carboxylic acid conversion due to thermal

oxidation was estimated using Boehm titration method50 for both UND and OND. DSC measurements were carried out utilizing TA-Q100 (TA instruments) under dynamic conditions. This equipment was first calibrated by standard indium. Samples of about 20 mg were placed in an aluminum pan and heated from room temperature to 200 ̊C at different heating rates of 4, 8, 12, 16 °C min . The experimental data were analyzed with the TA Universal Analysis software. The temperature-dependent elastic moduli were 9



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measured by dynamic mechanical analysis (DMA) 8000 (Perkin-Elmer) at a frequency of 1 Hz and a rate of 5 °C min for rectangular samples with size of 30mm × 10mm × 5mm. DMA tests were conducted with three point bending mode at a strain rate of 0.04%.

4. Results and discussion 4.1. Characterization of surface functionalization of ND FTIR analysis was carried out to characterize the surface chemistry of as-received and surface treated NDs. Fig.1 compares the FTIR spectra of UND, OND, AND and Oleylamine. Main characteristic peaks for UND is the absorption peaks for bonds C=O (1724 cm-1), C-H (2851 cm-1, 2927 cm-1 bending), N-H (1627 cm-1) and O-H (3414 cm-1 stretching and 2927 cm-1 bending). For OND, absorption peak of C=O is shifted to 1780 cm-1 because of the conversion of some oxygen containing groups like ketone, alcohol and ester to carboxylic

group. The carboxylic acid group content determined by Boehm

titration method exhibited also an increment from 0.229 mmol/g for UND to 1.657 mmol/g for OND confirming the conversion of some functional groups on UND to carboxylic group on OND. Prominent peaks of AND are assigned to C-H (2819-2955 cm-1 stretching), N-H (3402 cm-1 stretching and 1538 cm-1 bending) and C=C (1639 cm-1) which are relevant to the Oleyleamine attached on the AND surface48. Attachment of Oleyleamine onto the surface of AND was further investigated by TGA. Fig. 2 compares the TGA curves of both OND and AND. It is revealed that there is no any sensible mass loss for carboxylated ND up to 500 ̊ C, while AND shows almost 5 wt% mass losses over the temperature range of 250-300 ̊ C with a differential TGA (DTGA) peak at 300 ̊ C which is correspondent with 10


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the thermal decomposition of neat Oleyleamine as mentioned in literature51. It is believed that amino group of Oleyleamine acts as electron donors for carboxylic acid (Lewis acid) sites of nanodiamonds52 leading to OND/Oleyleamine complexes containing –NH3+ group anchored on the OND surfaces48, as shown in Fig. 3. However, Liu et al.51 observed that Oleyleamine can be interacted with carboxylated surfaces via covalent and ionic-bonding. 4.2. Dynamic mechanical analysis DMA was utilized to trace the molecular mobility of epoxy matrix and interfacial interactions in epoxy/NDs composites. Fig. 4 shows the storage modulus versus temperature for neat epoxy resin and the composites. As can be seen, incorporation of all NDs leads to the enhancement of storage modulus at temperatures below Tg, i.e. glass transition temperature, indicating the reinforcing effects of all three NDs on epoxy matrix. This can be ascribed to the high stiffness of ND itself19, fine dispersion of NDs and good interfacial interaction with matrix51. EOND exhibits slightly higher improvement in storage modulus with respect to EUND probably because of the effectiveness of carboxylic group in promoting higher effective covalent bond with epoxide groups of epoxy resin53. However, EAND shows slightly lower improvement compared to other NDs. Presence of nonpolar alkyl chain of Oleyleamine, which is arranged towards outside the nanoparticle48, may provide regions with higher free volumes around the AND surfaces36. Furthermore, it was found that that the alkylamine molecules can play plasticizing role on the network structure of crosslinked polymers54. Cross linking density estimated by rubber elasticity theory55,56 showed no improvement in presence of NDs (as can also be inferred by inspection of storage modulus in rubbery state shown in Fig. 4). This suggests that the 11



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crosslinking density is not responsible for the difference in the extent of improvement in storage modulus. Loss factor (tanδ) versus temperature curve is shown in Fig 4. It is revealed that the Tg (corresponding to the tanδ peak) shows a slight decrease, particularly for EOND and EAND, compared to neat epoxy resin, from 116 ̊ C to 111.5 ̊ C. As the Tg value actually reflects the molecular motion, this result indicates that the molecules has easier movement in presence of NDs. The similar observation was reported by Rakha et al36 who ascribed such behavior to the increment of free volume in the vicinity of ND surfaces. 4.3. Dynamic DSC data Cure behavior of neat epoxy resin and epoxy/ND composites was investigated using dynamic DSC at different heating rates. Basically, epoxy/amine curing reaction is initiated by ring opening of epoxide group by primary amine resulting in hydroxyl group and secondary amine. Secondary amine itself opens the epoxide group leading to tertiary amine as well. In cases that the reaction temperature is high, side reactions such as etherification can also be promoted57. Fig. 5 shows the DSC thermograms of all samples. As can be inferred, neat epoxy resin and all three composites show a single peak at all heating rates. This suggests that the presence of ND in epoxy resin does not change the cure reaction mechanism, although it is speculated that the functional groups present on the surface of NDs might be able to involve in the cure reaction. Therefore, it is supposed that the cure reaction in all samples proceeds mainly with the epoxy-amine ring opening addition reaction58-60. 12


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As expected, Tp (the temperature corresponding with the maximum heat flow curve) increased by increasing heating rates for both neat epoxy resin and its composites with NDs (see Fig. 6). Furthermore, total heat of reaction ( ∆H0 ) exhibited a maximum value at the heating rate (β) of 8 °C min and then it deceased steadily with heating rate. Almost the same trend was found for all NDs filled epoxy resin except EAND that showed a steadily decreasing trend with heating rate for ∆H0 probably due to the shift of maximum value to lower heating rates. As the heat of reaction is directly correlated with the extent of reaction, it can be concluded that the final extent of reaction decreases at higher heating rates (above 8 °C min ). This might be attributed to development of diffusion controlled mechanisms such as gelation and vitrification which are believed to be met faster at higher heating rates. Such phenomena prevent the completion of reaction due to the limited molecular diffusion and mobility of reactants. For EAND, presence of polar amino groups more probably facilitates the cure reaction resulting in domination of diffusion controlled mechanism even at lower heating rates. Overall trend observed in Fig. 6b reveals that Tp decreases by adding NDs, particularly with the modified one, suggesting the acceleration role of NDs on the cure reaction, which is basically associated with the acceleration of epoxide ring opening in presence of functional groups of NDs as ascribed in literature for carbon based nanoparticles as well42, 43, 61. For the CNT filled epoxy resin, it was reported that the overall influence of CNT on the cure reaction of epoxy resin is the competition between the acceleration role of functional groups and the retardation effect due to the steric hindrance of CNT itself39, 44. Whenever the steric hindrance of CNT is dominant, the cure reaction is 13



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sensibly retarded. As all NDs in our system exhibited acceleration role on the cure reaction of epoxy resin, it can be speculated that the steric hindrance is not effective in the ND filled epoxy resin possibly due to the spherical shape of ND providing entanglement free reinforcing particle. The lower Tg value of epoxy/ND systems compared to neat epoxy resin, as shown in Fig. 4, corroborates ineffectiveness of NDs themselves on promotion of steric hindrance, because steric hindrance normally reduces the molecular motion. According to Fig. 6b, higher reduction of Tp for the modified NDs, i.e. OND and AND, compared to UND might be ascribed to better dispersion of such modified NDs providing higher exposed external surface as well as presence of highly reactive functional groups like carboxylic group in OND and polar amino group in AND. It is also deduced that the ∆H0 shows increment in presence of modified NDs, i.e. OND and AND, suggesting the increment of final degree of cure. Acceleration role of OND and AND on the epoxide/amine reaction, as mentioned above, more probably promotes the crosslinking reaction leading to higher degree of reaction in these cases. Lower heat of reaction of EAND compared to EOND can be explained by the fact that the Tp for this sample is reduced to lower temperatures that makes possible the diffusion controlled mechanisms of sample earlier resulting in prevention of further reactions. The tanδ curve obtained by DMA (shown in Fig. 4) emphasizes the lower Tg value of this sample compared to OND as well. Lower ∆H0 of EUND compared to neat epoxy will be discussed in later section based on model free activation energy.

14


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4.4. Model-free isoconversional analysis of cure behavior Fig. 7 exhibits the α − T and cure rate versus the degree of cure of a typical sample (EUND) at various heating rates. It is evident that the cure reaction exhibits an autocatalytic behavior in which the reaction rate versus the degree of cure shows a maximum. It is believed that in autocatalytic reactions, one of the intermediate products catalyzes the reaction38. In our case, the degree of cure corresponding to maximum reaction rate, i.e. α p , remains almost unchanged at α p ≈ 50% with increasing the heating rate suggesting a negligible side reactions59; however, the value of maximum reaction rate increases steadily with the heating rate. Model-free kinetics analysis based on Eq. (1) was used to determine the variation of activation energy ( E α ) versus α . This makes possible to explore the role of NDs on the cure reaction mechanisms more accurately. Fig. 8 illustrates the E α − α curve for neat epoxy resin and the corresponding composites. For the neat epoxy resin, E α varies in the range of 66-77 kJ/mol in the course of curing process which is typically in the range of epoxy-amine reaction reported in literature59, 62, 63. Actually, E α shows a step loss from 77 to 70 kJ/mol at the early stage of curing process followed by a gradual decrease, until it remains almost unchanged at 66 kJ/mol in a wide range of degree of cure at latter stage of cure reaction. Such an initial reduction in E α is often observed in model-free kinetics analysis based on the dynamic runs which is associated with the viscosity reduction by increasing temperature in nonisothermal experiments20,49,59. The constant activation energy exhibits that the reaction mechanisms do not change during the cure process. One possible reason may be 15



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the off-stoichiometric hardener ratio used in this study making possible presence of sufficient primary amine to involve in the reaction throughout the cure process49,

64

.

Basically, at the stoichiometric ratio, by reducing primary amine content during the curing process, secondary amine finds opportunity to react with epoxy molecules reflecting in the decrease of E α . Other possibility may be due to the lack of significant diffusion controlled phenomena in this case. As shown in Fig. 8, the activation energy decreases and the trend of variation of E α with the degree of cure alters with incorporation of NDs. EAND shows the lowest activation energy during the whole curing process in comparison with other NDs filled epoxy resin studied in this research. Indeed, it exhibits a rapid loss at the early stage of curing process, i.e. from 80 to 60 kJ/mol at the degrees of cure below 10%, followed by almost a constant value of 55 kJ/mol for a large range of cure degree. As the variation of activation energy at the early stage of curing process was attributed to the amount of viscosity and the variation of viscosity with temperature, it can be inferred that AND has increased the viscosity of epoxy but it is sensitive to temperature resulting in rapid loss by increasing temperature65. The same behavior (higher activation energy at the beginning and a rapid loss in E α at the early stage of cure) is also observable for OND which is of course a surface functionalized ND. Our viscosity measurement performed by Anton Paar, model MCR300 at room temperature exhibited that the complex dynamic viscosity (at low frequency) of epoxy resin increased from 4.53 Pa.s to 5.7 Pa.s for END and 7.46 Pa.s for OEND. This suggests that the improvement of interfacial interaction between epoxy-ND

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reflects in enhancement of viscosity, supporting the literature report on the role of viscosity on reaction mechanism at early stage of curing. The considerably lower E α for EAND compared to neat epoxy resin suggests the effective role of polar amino group on the promotion of epoxide ring opening reaction. This is consistent with the report by Jagtap et al.66 who described the significant role of polar amine group on catalyzation of the epoxy/amine reaction in clay filled epoxy composites. Both UND and OND, having almost similar functional groups, have decreased the activation energy compared with neat epoxy resin but with different trends of variation. These two NDs have the same functional groups, but with different carboxylic acid group contents. Indeed, hydroxyl and carboxylic acid groups present on the surface of these NDs, can share their electron pairs with epoxide group leading to acceleration of ring opening reactions and reduction of activation energy36. Comparing E α of EOND and EUND, it is deduced that the EOND having higher carboxylic acid content shows higher E α at the beginning of reactions, i.e. α < 0.05 , it is speculated that the interfacial interaction and the degree of dispersion, dominating the viscosity of the system, is higher in the case of OND. As shown in Fig. 8, activation energy of EUND undergoes considerable alterations in the degrees of cure above 0.2, while EOND shows almost constant activation energy up to very latter stage of curing process, i.e. up to 0.9, similar to EP and EAND. This suggests that the reaction mechanism in the case of EUND is more likely influenced by some chemical spices, because, physically dominated processes are not observed for EP and other NDs filled epoxy resin, e.g. EAND and EOND, in this range of cure degree. As the 17



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carboxylation reduces the moisture content as mentioned in literature64,66, this behavior is more likely attributable to the higher content of moisture in UND which is able to promote the ring opening reaction at the early stage of reaction where the chemical species play the critical roles on the reaction rate. The lower ∆H0 of EUND compared to even neat epoxy resin, see Fig. 6a, can also be mentioned based on the involvement of moisture in the cure reaction. At the higher degrees of cure, i.e. α > 0.7 , where moisture is significantly consumed, activation energy of both OND and UND becomes almost the same. At the latter stage of cure, α > 0.9 , the activation energy of EOND becomes higher than that of EUND. As in this region, the cure process is mainly dominated by the physical phenomena like molecular diffusion of reactants and decrease of the mobility of the reactive groups67, such difference is understandable. Higher total heat of reaction of EOND compared to EUND, see Fig. 6a, suggests that higher degree of reaction for EOND is achievable which could be responsible for domination of physical phenomena in this range of cure degree. 4.5. Cure kinetics modeling Using activation energy values presented above, Malek functions can be calculated. As illustrated in Fig. 9, all normalized y(α) s for a specific sample at various heating rates have a similar behavior, and the degrees of cure at which y(α) reaches the maximum value, i.e. α M , are the same. It is to be noted that y(α) is strongly dependent on activation energy so its precise value is an important parameter to find the best rate equation. z(α) shows a C

( )

shape curve with maximum values α ∞p of 0.5 (Fig. 9). Since 0 < α M < α∞p and α∞p ≠ 0.632 , based on Malek’s graph Sestak- Berggren (SM(m,n) given by Eq. (5), was chosen as the 18


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kinetics model68 in this study. This model is often used for epoxy system to consider the complexity of hydroxyl catalytic effect on the cure process. SB ( m, n ) = α m (1 − α )

n

(5)

where m and n are the constants of SB model and their ratio (m/n) can be replaced by p = α M (1 − α M )

47,69

. The final form of the rate equation is expressed as follows:

dα  E  m n = A exp  −  α (1 − α ) dt RT  

(6)

where A and R are the pre-exponential factor and universal gas constant, respectively. Taking logarithm of Eq. (6), giving Eq. (7), then plotting ln ( dα dt ) exp ( x )  versus ln  α p (1 − α )  gives the n value from the slope. Then the m value is calculated using m=pn.  

ln ( dα dt ) exp ( x )  = ln A + n ln  α p (1 − α )   

(7)

The model parameters of samples are summarized in Table 1. The overall order of reaction (m+n) of EP is 1.86. The overall order of reaction in epoxy/Epicure system analyzed by Abdalla et al.38 was reported to be 1.69 and in epoxy/polypropylenimine octaamine dendrimer investigated by Zabihi et al.62, it was calculated to be 1.23 which are properly consistent with the value obtained in this study. For the composites, overall order of reaction varies between 1.81 to 2.05 depending on the ND type used. This exhibits a slight increase in the overall reaction rate for the case of EUND and EAND. To investigate the appropriateness of the rate equations, experimental results and the model predictions are compared in Fig. 10 for a typical sample, i.e. EUND, at different heating rates. It is revealed that the model is able to predict the reaction rate reliably. 19



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5. Conclusion The present article examined the influence of ND on cure kinetics of epoxy/TETA resin for the first time. Both untreated ND (UND) and surface treated NDs including thermal oxidized ND (OND) and amine functionalized ND (AND) were considered in this investigation. Cure kinetics experiments performed by DSC technique revealed that both neat epoxy resin and ND filled epoxy showed autocatalytic reaction. It was also deduced that ND did not change the cure reaction mechanism; however, it influenced the cure kinetics characteristics of epoxy resin. According to DSC data, maximum heat flow peak shifted to lower temperatures by incorporating all NDs indicating the acceleration role of NDs on the cure kinetics of epoxy/amine resin. It was postulated to the role of organic groups of NDs in promoting epoxide ring opening without any restriction (steric hindrance) from ND particles on molecular motion probably due to its structures (spherical structure). Model-free isoconversional method exhibited that NDs decreased the activation energy of curing reaction of epoxy resin. Among the NDs, AND containing polar amino groups showed the lowest activation energy suggesting that the amine functionality accelerated considerably the epoxide ring opening reaction with amine hardener. Using Malek method, Sestak- Berggren kinetics model was adopted to model the cure kinetics. The model was able to predict experimental kinetics charactristics reasonably.

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Acknowledgements The authors acknowledge the financial supports received from Iranian nanotechnology initiative and research deputy of Sharif University of Technology.

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Figure captions Fig. 1. FTIR spectra of (a) UND, (b) OND, (c) AND, (d) Oleylamine. Fig. 2. TGA and DTGA results of OND and AND. Fig. 3. Schematic representation of a) OND and b) AND. Fig. 4. DMA results including variation of storage modulus and tanδ versus temperature. Fig. 5. Dynamic DSC thermograms at different heating rates; a) EP, b) EUND, c) EOND, d) EAND. Fig. 6, a) Total heat of reaction and b) peak temperature (Tp) versus DSC heating rate. Fig. 7. Cure kinetics data for EUND, (a) the degree of cure versus temperature and (b) reaction versus the degree of cure. Fig. 8. Activation energy of EP, EUND, EOND and EAND versus the degree of cure. Fig. 9. a)

( ) and b) z(α ) for EUND system.

y α

Fig. 10. Comparison of experimental data (symbols) and prediction of kinetic model (solid line) for EUND.

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Table 1. Pre-exponential factor and parameters of SB model. Sample

m

n

A (s-1)

EP

0.26

1 .6

EUND

0.35

1 .7

EOND

0.11

1 .7

EAND

0.25

1 .7

6 2.2 × 10 6 2.1 × 10 6 4.1 × 10 6 2.7 × 10

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Fig. 1. FTIR spectra of (a) UND, (b) OND, (c) AND, (d) Oleylamine.

Fig. 2. TGA and DTGA results of OND and AND.

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b)

a)

-+

-C(=O)OH

-C(=O)O NH3(CH2)8CH=CH(CH2)7CH3

Fig. 3. Schematic representation of a) OND and b) AND.

Fig. 4. DMA results including variations of storage modulus and tanδ versus temperature.

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Fig. 5. Dynamic DSC thermograms at different heating rates; a) EP, b) EUND, c) EOND, d) EAND.

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Fig. 6, a) Total heat of reaction and b) peak temperature (Tp) versus DSC heating rate.

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a)

b)

Fig. 7. Cure kinetics data for EUND, (a) the degree of cure versus temperature and (b) reaction versus the degree of cure.

Fig. 8. Activation energy of EP, EUND, EOND and EAND versus the degree of cure.

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a)

b)

Fig. 9. a) y(α ) and b) z(α ) for EUND system.

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Fig. 10. Comparison of experimental data (symbols) and prediction of kinetic model (solid line) for EUND.

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Cure Kinetics of Nanodiamond-Filled Epoxy Resin - American

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