In-situ Cure and Cure Kinetic Analysis of a Liquid Rubber Modified

Article pubs.acs.org/IECR

In-situ Cure and Cure Kinetic Analysis of a Liquid Rubber Modified Epoxy Resin Raju Thomas,*,† Christophe Sinturel,‡ Jürgen Pionteck,§ Harinarayanan Puliyalil,∥ and Sabu Thomas⊥ †

Department of Chemistry, Mar Thoma College, Tiruvalla-689 103, Kerala, India Centre de Recherche Sur la Matiere Divisee, Universite d’Orleans, France § Leibniz- Institute of Polymer Research Dresden, 01069 Dresden, Germany ∥ School of Chemical Sciences, Mahatma Gandhi University, Priyadarshini Hills P.O., Kottayam, Kerala, 686 560, India ⊥ Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Priyadarshini Hills P.O., Kottayam, Kerala, 686 560, India ‡

ABSTRACT: The in-situ cure and cure kinetics of an epoxy resin based on diglycidyl ether of bisphenol A (DGEBA) polymerized with an anhydride hardener and its mixtures with a liquid polybutadiene rubber having hydroxyl functionality (HTPB) were studied using Fourier transform infrared spectroscopy (FTIR) and differential scanning calorimetry (DSC) in an isothermal mode. The cure reaction was monitored in-situ by FTIR spectroscopy by observing variation in intensity of epoxy, anhydride, and ester bands. The cure reaction mechanisms by which the network structure of epoxy was developed were discussed. Isothermal mode DSC measurements were performed at selected temperatures. The reaction followed an autocatalytic mechanism, and kinetic analysis was done by a phenomenological model developed by Kamal. Good fits were obtained between the autocatalytic model and the experimental data up to the vitrification state. Afterward, the reaction became diffusion controlled. The reaction during the later stages of cure was explained by introducing a diffusion factor, which agreed well with the kinetic data. The nature of the developing morphology of modified epoxies was analyzed by optical microscopy (OM) and small angle laser light scattering (SALLS) technique. The ultimate morphology of the cured blends was analyzed using scanning electron microscopy (SEM). The cure kinetics has been correlated with the developed morphology to get insight into the mechanism of reaction-induced microphase separation.

1. INTRODUCTION Epoxy resins are characterized with outstanding performance such as toughness, rigidity, high temperature performance, chemical resistance, adhesive properties, formulation latitude, and reactivity with a wide variety of chemical curing agents.1 However, the inherent toughness of the network polymer is low, and this restricts the material from many end-use applications. Low molecular weight elastomers are recommended to toughen epoxy matrix. Rubbers, when added to the liquid resin, undergo curing and precipitate out from the mixture in the form of dispersed particles and act as stress concentrators and are helpful in preventing crack growth that leads to catastrophic failure of the matrix.2,3 The properties of the epoxy resin depend on the extent of reaction. The knowledge of the mechanism and cure kinetics is necessary for assigning structure−property relationships and for the usage of the materials in various fields. Also, the knowledge of the cure kinetics can define the reaction process and subsequent engineering designs. Sun et al. have studied4 cure kinetics and mechanism of liquid lignin based epoxy resin− maleic anhydride (MA) system accelerated with benzyldimethylamine (BDMA) by Fourier transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC). Francis et al.5 have studied cure kinetics of hydroxyl terminated poly(ether ether ketone) based on tert-butyl hydroquinone (PEEKTOH) employing isothermal DSC measurements at different temperatures. Carrasco and Pagès6 have employed © 2012 American Chemical Society

FTIR spectroscopy to follow cure conversion (by selecting a suitable band for epoxide functional group) of nanocomposites consisting of a trifunctional epoxy resin, a hardener containing reactive primary amine group, and clay nanoparticles previously treated with octadecyl ammonium. In a recent study by Raman and Palmese,7 FTIR spectroscopy in the near-infrared (NIR) region was used to monitor cure kinetics of diglycidyl ether of bisphenol A (DGEBA) epoxy resin and 4,4′-methylenebiscyclohexanamine in the presence of tetrahydrofuran (THF) as a solvent. DSC is one of the main techniques for the study of the cure of epoxies.8,9 This calorimetric technique gives a quantitative measurement of the amount of reaction, which can determine the Tg of the material. Cure kinetics of the epoxy−anhydride system has been studied using various nonisothermal DSC scans, and the calculation of activation energy has been done by many authors.10,11 Certain studies deal with cure kinetics of a DGEBA epoxy resin in the presence of sulphanilamide (SAA) at different heating rates by nonisothermal DSC.12 Cure kinetics, using isothermal mode of DSC was employed to study a system composed of o-cresol formaldehyde epoxy resin (oCFER) using succinic anhydride (SA) as the curative and a Received: Revised: Accepted: Published: 12178

January 6, 2012 August 9, 2012 August 17, 2012 August 17, 2012 dx.doi.org/10.1021/ie2029927 | Ind. Eng. Chem. Res. 2012, 51, 12178−12191

Industrial & Engineering Chemistry Research

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tertiary amine as a catalyst.13 DGEBA and aniline modified with a low-Tg poly(ethylene glycol) (PEG) was used as a model system to study the importance of complex formation on the cure kinetics of multicomponent epoxy−amines.14 In a work done by Kalogeras et al.,15 aromatic amine-cured DGEBA epoxy resin and poly(ethylene oxide) (PEO) blends were analyzed by DSC and dielectric techniques to study the parameters controlling miscibility. In a recent work by Chen and Cook,16 the cure kinetics and morphology of interpenetrating polymer networks (IPNs) formed from a rigid epoxy resin thermally cured by an anhydride, and a photocured flexible dimethacrylate resin, have been studied by temperature ramping DSC, near infrared (NIR) spectroscopy, and dynamic mechanical thermal analysis (DMTA). Perrin et al.17 have reported the cure of epoxy−amine resins with bisphenol A (BPA) as an external catalyst employing DSC analyses in isothermal and dynamic modes. Both phenomenological and mechanistic models have been tested. Yoo et al.18 have investigated cure reactions of three cycloaliphatic epoxy resins with methyltetrahydrophthalic anhydride (MTHPA) by DSC at different heating rates. Activation energy was calculated based on the Kissinger method and varied in the range 67−72 kJ/mol depending on sample. In a very recent study by Tian et al.,19 a series of chain-extended ureas containing a hydroxyl-terminated polybutadiene (U-TPBn) spacer were used to modify epoxy resin based on a DGEBA and dicyanodiamide with a view to toughen the epoxy matrix. The cure behavior, viscoelastic properties, impact response, and fracture surface morphology of the systems were systematically investigated. In an interesting article by Zhou et al.,20 the effect of multiwalled carbon nanotubes (MWCNTs) on the cure behavior of DGEBA epoxy resin/2-ethyl-4-methylimidazole (EMI-2,4) system during the cure process was investigated with dynamic DSC. In a recent study, Qiu et al.21 reported the reaction kinetics of carbon nanotubes (CNTs) (modified by both chemical functionalization and mechanical shortening)−reinforced epoxy resins according to the DSC characterization. Since the cure reaction takes place between the epoxy and the curative, the kinetics depends on the nature of the hardener employed. Thus, each system can be considered as a separate entity depending on the type of curative used. The significance of the present study lies in the investigation of cure kinetics of the DGEBA-based epoxy resin with hydroxyl-terminated polybutadiene liquid rubber (HTPB) using an anhydride as the curative. The partial miscibility of the elastomer in the epoxy resin makes the system a novel one to report the cure kinetics, compared to the conventional elastomers, which are initially completely miscible. The cure reaction was monitored by FTIR spectroscopy by mainly following epoxy, anhydride, and ester bands. The suggested cure mechanisms are confirmed based on the intensity variations of absorption bands. The cure kinetics was followed calorimetrically by DSC, which is an important method for cure monitoring owing to the excellent results it can provide with a small amount of sample in a relatively short time span. The main advantages of using DSC include its reaction rate method of measurements by which the rate of reaction and degree of conversion can be estimated with great accuracy. Also, the cure reaction kinetics supplemented by in-situ morphology analysis by optical microscopy explains the mechanism of phase separation behavior supported by light scattering technique. The suggested mechanism is in agreement with the distribution of elastomer domains in modified blends, which are quantified by scanning electron microscopy (SEM)

analysis. To the best of our knowledge, no detailed in-situ cure and cure kinetic studies that extends to the analysis of phase separation behavior have been performed on HTPB-modified epoxy resin.

2. EXPERIMENTAL SECTION 2.1. Materials and Preparation of Blend Samples. The epoxy resin used was diglycidyl ether of bisphenol A (DGEBA, Gy-250). The curing agent was an anhydride, nadic methyl anhydride (NMA), trade name (Hy-906). A tertiary amine, N,N-dimethyl benzylamine (Dy-062) was used as an accelerator. Hydroxyl-terminated polybutadiene (HTPB) was used as the liquid rubber. All the chemicals except the liquid rubber were kindly supplied by Huntsmann, Mumbai, India, and were used as received without purification. HTPB was supplied by Vikram Sarabhai Space Centre, Thiruvananthapuram, India. The chemical structure of all the components and the characteristics of HTPB are represented in Figure 1 and Table 1, respectively.

Figure 1. Structure of components: (a) epoxy resin; (b) HTPB; (c) hardener; (d) accelerator.

Table 1. Characteristics of HTPB Propertiesa

HTPB

molecular weight (VPO) (g mol−1) hydroxyl value (mg KOH g−1) acid value (mg KOH g−1) viscosity at 30 °C, Brookfield (CP) specific gravity Tgb (K)

2710 42.4 0.3 6160 0.905 223

a

Material and data supplied by Vikram Sarabhai Space Centre, Thiruvananthapuram, India. bGlass transition temperature determined by DSC. 12179

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2.4.2. Scanning Electron Microscopy (SEM). The dimension of the samples from which the fracture surface is extracted for SEM analysis is 60 × 12 × 2 mm3. The cured samples were fractured under liquid nitrogen, and the dispersed rubber phase was extracted using toluene for 10 h at ambient temperature. The dried samples were sputter-coated with gold prior to SEM examination (JEOL JSM 5800 model) of specimens. Several micrographs were taken for each composition. The dimension of the dispersed phase was analyzed by image analyzer. The domain parameters such as the number (Dn), volume (Dv), weight (Dw) average domain diameters and polydispersity index (PI) were quantified using the following expressions.22,23

The samples are prepared in the following method. Stoichiometric amount of epoxy resin and hardener (5:4) were taken and stirred for 10 min to ensure proper dispersion of hardener. Varying weights of HTPB are added followed by accelerator and stirred again for 20 min. The system was degassed to remove any issuing gases for 15 min. Small amounts of samples taken from freshly prepared blends were used for FTIR, DSC, optical microscopy (OM), and small angle laser light scattering (SALLS) analysis. For SEM investigations, cured samples were prepared by pouring the mixture into a steel mold, which was greased. The sample was then precured at 100 °C for 30 min followed by post curing at 180 °C for 2 h. The cure condition was chosen from DSC studies performed in the dynamic mode, which revealed that almost all curing processes took place before this time. 2.2. Fourier Transform Infrared Spectroscopy (FTIR). Samples were subjected to the analysis of characteristic absorptions in the range 4000−400 cm−1 using a PerkinElmer Spectrum GXA FTIR spectrometer. The instrument consists of a pyroelectric detector, which scan the samples in the form of KBr pellets or as a smear on NaCl plate. Each interferogram was generated by signal averaging 32 scans at a resolution of 4 cm−1, and the spectra were obtained as percentage transmittance against wavenumber. To normalize intensity changes of the reactive sites and reaction products in all spectra, the absorbance at 1605 cm−1 (C−C stretching aromatics) was set to be 0.5. 2.3. Differential Scanning Calorimetry (DSC). DSC measurements were performed using a Perkin-Elmer Pyris calorimeter supported by a Perkin-Elmer computer for data acquisition. Isothermal heating experiments were conducted in a nitrogen flow of 40 mL/min to study the kinetics of cure reaction. The instrument was calibrated with Indium and dry cyclohexane standards before recording the measurements. The heating was done from room temperature to the temperature of the isotherm at a heating rate of 100 °C/min. Samples of 5−10 mg were used for the measurements. The analysis was based on the assumption that the heat generated during the epoxy cure reaction is equal to the total area under the heat flow−time curve. The degree of cure was then determined from the heat of reaction. The cure reaction was assumed to be complete when the isothermal curve of the blends leveled off to the baseline. The areas of the peak under the isothermal curves at various times were used to determine the conversion (α) at various times. The conversion (α) at time, t was defined as

α=

ΔHt ΔHtotal

Dn =

Dv =

Dw =

∑ niDi ∑ ni

(2)

∑ niDi4 ∑ ni3

(3)

∑ niDi2 ∑ niDi

(4)

where ni is the number of particles within the diameter range Di. Polydispersity index, PI =

Dw Dn

(5)

2.5. Small Angle Laser Light Scattering (SALLS). The small angle laser light scattering (SALLS) set up was used to study the cloud point (CP) temperature as well as the phase separation behavior of modified epoxies during cure. The SALLS set up was used to measure the intensity of scattering profiles. The instrument consists of a 5 mW He−Ne laser of λ = 638.2 nm, a hot stage arrangement for keeping the sample, and a photo diode array composed of 86 diodes, which gives an intensity distribution that depends on the scattered angle. After necessary calibrations, a few milligrams of uncured blend samples were placed between two microscopic glass slides and placed in the hot stage at a specific temperature. The scattered intensity was recorded as a function of time on a PC. The data processing was performed using inbuilt software (custom-made TestPoint application).

3. RESULTS AND DISCUSSION 3.1. Cure ReactionFTIR Spectroscopy. FTIR analysis has been performed to follow the in-situ cure reaction. Also, this helps to check any significant chemical interactions involved between epoxy and the elastomer during the cure reaction. The spectra of virgin epoxy resin, HTPB elastomer, and the anhydride are depicted in Figure 2a with a briefing on important bands. The main peaks observed in pure epoxy resin occur at 913 and 826 cm−1 due to the oxirane group.24 A peak near 1220 cm−1 was also noted due to the stretching vibrations of C−O bond. The characteristic peaks of the anhydride hardener are observed at 1858 and 1780 cm−1. Other bands are C−H (str) due to methyl group observed near 2980 cm−1 and symmetric carbonyl group coupling stretching near 1770 cm−1. The main absorption peaks of HTPB are the broad O−H (str) band in the region of 3400−3500 cm−1 and bands at 1640 cm−1 ascribed to C−C (double bond) and vinylene group. The absorption bands near 2913 cm−1 and 2842 cm−1 are due to C−H stretching vibrations in CH2 groups. The band at 3004

(1)

where ΔHt is the heat of cure at time t and ΔHtotal is the total heat involved by the epoxy−anhydride reaction (without the inclusion of HTPB). It was taken as the average of the enthalpy values obtained from isothermal DSC measurements at the different curing temperatures. 2.4. Phase Morphology Studies. 2.4.1. Optical Microscopy (OM). An Olympus BH2 optical microscope was used to get information on the phase separation and overall morphology. Blend samples of a few milligrams were placed between two glass slides, and the temperature was controlled by a Mettler FP82-HT hot stage. Digital micrographs were taken using a JVC TK-C 1381 CCD camera, controlled by the program Qwin of the Leica Company at several temperatures during heating at 2 °C/min of rubber-modified samples. 12180



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hydroxyl groups are generated during the reaction as a result of the initiation step. The curing was analyzed by following the anhydride (1858 and 1780 cm−1), epoxy (913 cm−1), and ester (1744 cm−1) bands. During the cure reaction, the anhydride bands got reduced and a new CO band appeared at 1744 cm−1 due to ester group formation. The epoxide band also reduced, but it is overlapped with other bands. However, it is possible to analyze cure also by this band. The progress of the cure reaction of the neat epoxy was observed during the first 90 min by recording the variation in absorption units of epoxy, anhydride, and ester functionalities. The time interval for this measurement was 5 min. The kinetic chemigrams, Figure 2c, represent the changes in the intensities of the absorbance bands of the functionalities as cure time progresses. Similar spectra of modified epoxies with different weight content of HTPB were also analyzed; none of them showed significant variations from virgin epoxy and hence were omitted for brevity. Any chemical interaction between the elastomer and the resin is not evident from the spectra. In this respect, HTPB elastomer is found to be different from the conventional carboxyl terminated copolymer of butadiene and acrylonitrile (CTBN) rubber used for toughening epoxy resin. CTBN is miscible in the resin during cure and found to interact with the system chemically, which resulted in better interfacial adhesion with the resin matrix.27 On the other hand, HTPB is only partially miscible with the resin. However, a very slight amount of HTPB elastomer was observed to be dissolved in the resin at high temperature from OM, the discussion of which will follow, and DMTA analysis.28 Based on FTIR analysis, we can justify the proposed cure reaction mechanism of DGEBA/anhydride system. Scheme 1 explains the cure reaction mechanism between the epoxy resin and the anhydride. The reaction between the anhydride and the secondary hydroxyl group of the epoxy resin results in the Scheme 1. Cure Reaction Mechanism of Epoxy Resin and the Anhydride

Figure 2. (a) FTIR spectrum of epoxy resin, elastomer, and anhydride. (b) Neat epoxy before the cure reaction (dotted line) and after 2 h of cure reaction at 100 °C (solid line). (c) Kinetic chemigrams.

cm−1 is due to C−H stretching vibrations near C−C double bond. Figure 2b depicts the coupled spectra of neat epoxy at zero cure time and the system after 2 h of cure reaction at 100 °C. The dotted and solid lines represent the intensity variations of bands before and after the cure reaction, respectively. The appearance of a broad band near 3400 cm−1 in the spectrum is owing to the presence of certain number of hydroxyl groups on the surface of the sample that might establish intermolecular hydrogen bonds with other nucleophilic groups.25,26 These 12181



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reliable kinetic parameters. The significance of the present system is that it is phase separated initially, as observed by OM and SALLS. The study involves isothermal measurements at three different temperatures, 120, 140, and 150 °C, to compute the enthalpy, kinetic constants, and activation energies related to the cure process. Also, the reaction kinetic study has been employed to correlate the developed morphology during cure of the systems. Thus, the system is unique and needs prime attention. The heat evolved during the reaction of the mixture has been directly determined by integration of the exothermic peaks. The total heat of reaction (ΔHtotal) for the neat epoxy system was found to be 208 J/g. This is taken as the average value obtained for three different temperatures. The curves, obtained with the long-time isothermal scanning, were used to determine the degree of conversion and rate of cure using the traditional procedure of the reaction heat evaluation.34,35 Typical plots of conversion (α) versus time of the neat epoxy cured at various temperatures of study are shown in Figure 3a. The conversion (α) is calculated from the ratio of the heat of cure at time, t, over the total heat generated by the epoxy-anhydride reaction. The shape of the curve shows the autocatalytic nature of the reaction. Similar curves are obtained for other epoxy matrices, too.36 Epoxy cure is a thermally catalyzed one, and at higher cure temperature (Tcure), maximum conversion is attained speedily. A similar trend was observed during the kinetic study of the cure reaction for a system of bisphenol-S epoxy resin (BPSER) with DDS as a cure agent.37 Glass transition temperature, Tg, of the system increases during the cure process to form three-dimensional network structure. Usually, near maximum Tg, complete cure occurs. This is indicative of autocatalytic kinetics in the first stages of cure and diffusion controlled reaction, which is discussed later, as the Tg rises due to curing.37 From the curves, it is clear that maximum conversion occurs speedily at 140 °C compared to 120°. Also, it is to be noted that a decrease in the maximum conversion is obtained when Tcure = 150 °C, as compared to that of a lower cure temperature, Tcure = 140 °C. This is due to the Tg of the neat epoxy matrix. The Tg of the cured neat epoxy when Tcure = 140 °C, is 135 °C (from DMTA analysis),28 and the maximum degree of conversion is possible at this temperature, since it is near to the Tcure. However, a contradiction prevails here, as the Tg of the matrix is 140 °C at Tcure = 150 °C. Even if we neglect the difference of 5 units, this is (nature of the curve) normally not expected. This forced

formation of a monoester. The newly generated carboxyl group then reacts with the epoxide group and the secondary hydroxyl group to form a diester. Thus, the cure reaction initiates to form a network structure. It is a known fact that the interaction of epoxy compounds with anhydrides, amines, and other nucleophiles is promoted by the addition of hydroxylcontaining compounds such as water, alcohols, phenols, etc. Here, the reaction is supposed to proceed, initially, through a trimolecular transition state, as Smith29 has explained in the reaction of epoxy compounds with amines.

Also, the tertiary amine acts as a catalyst during the course of the reaction, and the reaction was initiated by the activation of the anhydride, as illustrated in the Scheme 2. The negative oxygen ion reacts with the epoxy group as well as with the anhydride. The mechanism is not a typical tertiary amine catalytic reaction, as the amine is not reformed in the reaction. Thus, an excellent network structure is formed in the epoxy− anhydride system.30 As the cure progresses, the cross-link density of the matrix increases and the liquid rubber became more and more insoluble in the epoxy, and ultimately, the rubber gets completely phase separated out as domains in the epoxy matrix, the details of which are portrayed in morphology analysis section. These domains hamper the cure reaction, and the system reaches to a vitrified statea physical transformation from liquid to glassy state via rubbery state. 3.2. Cure Kinetic AnalysisIsothermal DSC Method. The cure kinetic study and interpretation by isothermal DSC mode, compared to the dynamic method, is rather more informative31 and leads to better elucidations. For detailed investigation, this method is more applicable since cure polymerization involves many reactions such as etherification, esterification, homopolymerization, etc. Further, the heat of reaction obtained from dynamic DSC measurements is lower than that obtained from isothermal DSC measurements.32,33 It is also accepted that isothermal experiments generate more

Scheme 2. Cure Reaction Mechanism of Epoxy Resin and the Anhydride in the Presence of Tertiary Amine Catalyst

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Figure 4 shows the isothermal rate dα/dt versus time for the cure of the neat as well as HTPB-modified epoxies at 120, 140,

Figure 3. (a) Conversion of neat epoxy at different cure temperatures. (b) Conversion of neat and HTPB−epoxy blends at 120 °C.

us to conclude that almost maximum cure takes place even at 140 °C. However, when cure temperature is low, the reaction practically stops after attaining the vitrified state. Therefore, in practice, to alleviate these doubts, samples for mechanical properties and SEM analysis are precured at 100 °C for 30 min and then postcured at 180 °C for 2 h. Conversion versus time of neat and modified epoxies with varying weight content of HTPB, at the selected cure temperatures mentioned above, were determined and the Figure 3b is a representative case. At a particular cure temperature, there was slight reduction in conversion with respect to the addition of rubber, which can be ascribed mainly to the physical changes like dilution effect and/or viscosity increase as a result of the liquid rubber addition38−40 or by the reduction in the density of the reactive groups.41 For example, the conversion at an instant of 30 min for neat and modified samples (5, 10, 15, and 20 phr) is 0.74, 0.70, 0.69, 0.68, and 0.66, respectively, at a Tcure of 120 °C. A similar change in conversion, with a varying extent, was observed at all cure temperatures. Also the curves show the thermal accelerating effect of the thermoset reactions. Similar trends in conversions after isothermal cure were observed by Fernandez et al.42 for other epoxy systems too.

Figure 4. Rate of HTPB-modified epoxies at (a) 120 °C, (b) 140 °C, (c) 150 °C.

and 150 °C. The velocities represent the conversion kinetics, which is obtained experimentally by the derivative of the conversion with respect to time. The curves illustrate that the rate of cure increases with increase in cure temperatures. The reaction rate increases with time at a particular temperature, 12183



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and it attains a maximum after the start of the reaction, showing autocatalytic nature. The reaction mechanism remained the same even after the inclusion of the liquid rubber. The maximum peak value of the rate of the reaction is higher as the isothermal temperature is higher, shifting to shorter time with increase in isothermal temperature. The curves show that the reaction rate decreased after attaining a maximum. The simple nth order kinetics is not pertinent here as the cure kinetics of neat as well as modified epoxies show a maximum reaction rate at t > 0. Also, it is worth to remind the cure mechanism at this context. The decrease in the rate of the reaction indicates the incipient formation of the network structure due to the mechanisms discussed previously. As cure progresses, molecular weight and viscosity of the system increase. As a result, the rubber and epoxy becomes less compatible and a phase separation state is reached. Rubber became completely phase separated from the epoxy matrix (discussed in the morphology section). Thus, ultimately, in the later stage of the cure process, the sample approaches a solid state. The movement of the reacting groups and the products is greatly diminished, and the rate of reaction, which was previously controlled by the chemical kinetics, now becomes diffusion controlled. Typical plots of the rate of cure versus conversion for the neat and modified systems at all cure temperatures are depicted in Figure 5. From the figures, it is evident that the reaction rate for higher modified systems and the extent of conversion for all modified systems decreased with increase in elastomer content at a particular temperature. The rate of conversion significantly increases with increase in temperature for neat, as well as modified systems, once again showing the thermal effect of the cure reaction. An enhancement in the reaction rate with conversion was indicated for all modified systems during the initial stages of cure at all temperatures, which leads to a state of deviation due to the diffusion controlled reaction (the diffusion controlled model is discussed in the later part of the text). 3.3. Kinetic Model and Activation Energies. Even though an nth order kinetic model has been employed43−45 to explain the cure reactions of a thermoset, the lack of prediction of the peak observed in the isothermal rate of reaction curve or the sigmoidal shape of the heat of reaction curve make it less significant for the thermoset cure analysis. Also, such a kinetic model could not explain the conversion from gelation to vitrification due to network formation, which is characteristic for thermosets. As we observed previously, the maximum reaction rates are attained at time t > 0, hence negating the nth order kinetics and supporting the autocatalytic model. The nth order kinetic model is applicable only if the maximum reaction rate is observed at t = 0. The autocatalytic kinetics, expressed by Kamal,46 as given in the following, is suitable to explain the isothermal cure behavior. dα = (k1 + k 2α m)(1 − α)n dt

Figure 5. Rate versus conversion (epoxy/HTPB) at (a) 120 °C, (b) 140 °C, (c) 150 °C.

(6)

where α is the extent of the reaction, obtained by the partial area under a DSC trace versus time, t. k1 and k2 are the specific rate constants of the models and are functions of temperature; m and n are the reaction orders and (m + n) is the overall reaction order. Equation 6 represents the experimental observations. The experimental value of the rate of reaction (dα/dt) and conversion (α) for the complete course of the reaction were computed at all cure temperatures and adjusted with the kinetic equation. In the present study, the kinetic parameters k1, k2, m, and n were estimated without any

constraints on them by fitting the experimental data of dα/dt versus α at different temperatures using a nonlinear least-square procedure. This is different from other methods47−50 used to compute the kinetic parameters, where many of them assume the total reaction order, (m + n) as 2, restraining the range of application of the proposed model. The typical representative plots of the experimental data and the data obtained by autocatalytic model for the neat as well as modified epoxies at 120 and 150 °C are shown in Figure 6a and 12184



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model predictions slightly deviated from that of the experiment. Thus, in the later stages of cure, the reaction was controlled by diffusion mechanism rather than by kinetic parameters. Differences between model predictions and experimental data are observed to be greater at higher cure temperature. This is related to the Tg of the fully cured material. The free volume is reduced, if the cure temperature is close to the glass transition region of the highly cured material. The higher cross-linked structure makes the reaction diffusion controlled. There are two kinetic constants, k1 and k2; hence, two activation energies, Ea1 and Ea2, are possible. This could be obtained by plotting ln k1 and ln k2 versus 1/T. The slopes of the plots were used to estimate the activation energies Ea1 and Ea2. The kinetic parameters obtained for the HTPB systems at all cure temperatures after a large number of iteration are given in Tables 2, 3, and 4. The values of m and n were in the range Table 2. Epoxy−HTPB Blends, Autocatalytic Model Constants at 120 °C blend systems neat epoxy 5 phr HTPB 10 phr HTPB 15 phr HTPB 20 phr HTPB

m

n

(m + n)

k1 × 10−3 (min−1)

k2 × 10−3 (min−1)

0.23 0.51 0.82

1.15 0.92 1.09

1.38 1.43 1.91

2.4 18.6 23.4

68.2 93.6 94.7

0.49

1.45

1.94

31.6

90.6

0.61

1.71

2.32

15.2

114.8

Table 3. Epoxy−HTPB Blends, Autocatalytic Model Constants at 140 °C blend systems neat epoxy 5 phr HTPB 10 phr HTPB 15 phr HTPB

m

n

(m + n)

k1 × 10−3 (min−1)

k2 × 10−3 (min−1)

0.24 0.48 0.43

1.35 1.83 1.39

1.59 2.31 1.82

16.1 21.2 30.4

285.0 361.0 244.0

0.41

1.35

1.76

13.8

271.0

Table 4. Epoxy−HTPB Blends, Autocatalytic Model Constants at 150 °C blend systems neat epoxy 5 phr HTPB 10 phr HTPB 15 phr HTPB 20 phr HTPB

m

n

(m + n)

k1 × 10−3 (min−1)

k2 × 10−3 (min−1)

0.41 0.65 1.03

1.66 2.97 2.78

2.07 3.62 3.81

22.8 48.6 91.3

528.0 1172.0 1910.0

1.40

2.50

3.90

68.2

3722.0

1.60

2.60

4.20

74.2

472.0

0.50−1.00 for the neat resin, and the overall order of the reaction for HTPB-modified blends is in the range 1.00−2.00 at 120 and 140 °C. However, the order increased up to 4.00 for high Tcure systems (150 °C). This is attributed to the trimolecular mechanism reported earlier for epoxy systems.51 Few of the hydroxyl groups in the molecular chain of the epoxy resin participate in the reaction. However, this cure reaction is not a standard nth order reaction. The −OH group in the molecular chain of the epoxy resin can become proton donor and participate in the reaction with increasing cure temperature.

Figure 6. HTPB−epoxy blends: Experimental and autocatalytic conversion at (a) 120 °C and (b) 150 °C. (c) Plots of f (α) versus conversion, α, at different curing temperatures for a 10 phr HTPBmodified system.

b, respectively. At both cure temperatures, the data of experimental as well as model predictions were well in agreement at lower conversions, which represent the initial stages of the cure reaction. However, in the later stages of the cure reaction, that is, at higher conversions, the data of the 12185



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1 1 1 = + ke kd kc

The reaction should follow a trimolecular mechanism with the participation of the proton. This is the reason for the increase in the (m + n) value with the temperature. Similar results in the cure of epoxies are reported elsewhere.13 The k1 values showed an increasing trend, whereas no regular tendency in k2 values was noticed. This is probably due to the variations in the extent of chemical and diffusion kinetics for each system during cure. However, the values increased with elastomer content in most cases. The correlation for k1 values was found to be poor compared with that for k2. This is because k1 is computed only with the two or three first experimental data that may lead to imprecise calculated values. It was observed that, generally, the k1 values of neat and modified epoxies are low compared with those obtained for k2. Based on Arrhenius relationship, the reaction constants k1 and k2 depend on temperature, as per the relation ⎛ −E ⎞ k = A exp⎜ a ⎟ ⎝ RT ⎠

From these equations, the diffusion factor, f(α), f (α ) =

Table 5. Activation Energy Values for Epoxy−HTPB Blend Systems Ea1 (kJ/mol)

Ea2 (kJ/mol)

71.2 72.1 74.3 79.4 96.3

96.0 110.4 116.5 120.3 137.4

systems exhibited higher activation energies compared to the neat resin and the values showed an increasing order with the inclusion of elastomer content. The phase separated elastomer domains will definitely obstruct the cure polymerization reaction between epoxide and anhydride. In this context, it is worth to remind the study of CTBN-modified DGEBA epoxy resin by Thomas et al.,27 which was mentioned earlier. For a 10 phr CTBN at a temperature of 120 °C, the reported values for m and n are 0.88 and 1.07, respectively. For the same system, the kinetic constants k1 and k2 are reported as 25.3 × 10−3 and 93.6 × 10−3 min−1, respectively, whereas activation energies, Ea1 and Ea2, are obtained as 75.4 and 118.6 kJ mol−1, respectively. 3.4. Diffusion Factor. A semi-empirical relationship based on free volume considerations was used to explain diffusion control in epoxy cure reaction.52,53 The conversion becomes diffusion controlled after attaining a critical value, αc, and the corresponding rate constant, kd, is given by kd = kc e(−C(a − aC))

ke 1 = ( − kc 1 + e C(α − αC))

(10)

where C is the diffusion coefficient, an empirical parameter that depends on temperature, and αc is the critical conversion. C denotes the ratio of rate of diffusion reaction at two different stages in the diffusion controlled region. When α is much smaller than the critical value, α ≪ αC, e(−C(α−αC)) ≈ 0, then ke ≈ kc, f(α) approximates unity, the reaction is kinetically controlled and the effect of diffusion is negligible. When α increases, and approaches to αc, f(x) begins to decrease. At α = αc, f(x) becomes 0.5 and beyond this point, approaches zero as the reaction effectively stops, where both factors are controlling. The effective reaction rate at any conversion is given by the chemical reaction rate multiplied by f(α).55 The value of f(α) is considered as the ratio of the experimental reaction rate to the reaction rate predicted by the autocatalytic model. During the early stages of cure, the value of f(α) is near unity. As the cure reaction proceeds, the value decreases due to the onset of diffusion control. Figure 6c depicts the plots of f(α) versus conversion, α, at different cure temperatures for a 10 phr epoxy−HTPB system. 3.5. Morphological Analysis. Cryogenically fractured surface of the neat (Tcure= 150 °C) and rubber-modified epoxies (Tcure= 120 °C and 150 °C) was examined. The SEM micrograph of the neat resin is shown in Figure 7a. The glassy fracture surface shows ripples that are due to the brittle fracture. The initial transparency of the blend of the neat epoxy sample indicates a high degree of miscibility between DGEBA and the hardener. The cryogenically fractured surfaces of blends cured at 120 and 150 °C are depicted in Figure 7b [i, ii, iii, and iv] and Figure 7c [i, ii, iii, and iv], respectively, in which the particle size region is 10 μm. The figures represent 5 to 20 phr HTPBmodified epoxies, which clearly show two distinct phases: a continuous epoxy matrix and dispersed rubber phase. The samples were opaque due to heterogeneous morphology. The holes developed in the SEM micrographs were due to the extracted particles from the surface of the samples after treatment with toluene for 12 h. The domain parameters of the phase separated blends were quantified (refer to eqs 2−5) to find the number average (Dn), volume average (Dv), and weight average (Dw) of the domain sizes and to compute the polydispersity index (PI). The results are furnished in Table 6. The results showed that at a particular cure temperature the size of the precipitated rubbery domains increased with increase in elastomer content of the formulations. Number and area average domain diameters were found to have increased with respect to rubber content. The increase in domain size with the incorporation of rubber is attributed to the coalescence of the dispersed rubber particles, which depends on viscosity and elasticity ratio. This becomes more prominent in higher weight content of the dispersed rubber phase. Also, the particle size decreased with increase in cure temperature. The rate of epoxy cure reaction is high at higher temperatures attaining onset of gelation at a shorter time, which is obvious from kinetic analysis. This ultimately resulted in the suppression of the degree of coalescence of particles and formation of smaller phase separated structures. Other prominent factors that

The activation energy values, Ea1 and Ea2, obtained for the neat epoxy and modified epoxies are tabulated in Table 5. All

neat system 5 phr HTPB 10 phr HTPB 15 phr HTPB 20 phr HTPB

is defined

as

(7)

epoxy compositions

(9) 54

(8)

where kc = rate constant for chemical kinetics and C is a parameter. An abrupt change of diffusion control from chemical control for the cure reaction after the conversion reaches the critical value of αc is illustrated in eq 8. However, this change is gradual, and there is a region where both factors control the kinetics. The overall effective rate constant, ke, can be expressed in terms of kd and kc. 12186



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defined particle nature. Figure 8a [i, ii, iii and iv] depicts the representative morphologies of a 15 phr HTPB system, at time intervals of 0, 2, 4, and 6 min, respectively, during dynamic cure to 120 °C. The particle size region in these images is 2 μm. Even though the initial morphology [Figure 8a(i)] of the system appears homogeneous, some immiscible particles can be observed, suggesting that HTPB is not completely miscible in epoxy−hardener system. However, when curing initiates, more transparent and homogeneous nature appears [Figure 8a(ii)], and shortly, domains are found to be developed in the system [Figure 8a(iii)]. These grow gradually but slowly in size and ultimately change to well-defined shapes of elastomeric domains [Figure 8a(iv)]. Also, we have tried to analyze these systems using the SALLS set up in dynamic as well as isothermal mode to view the phase growth behavior from the transmitted light at the time of phase separation. The SALLS technique is effectively employed to analyze the phase separation nature of certain elastomer modified epoxies, in which the elastomers are initially completely miscible and structure growth takes place during cure.57 In such systems, the intensity of the scattering profile reflects the evolution of particles during the demixing phenomenon. The isothermal light scattering profile of 15 phr blend system at 120 °C is depicted in Figure 8b, in which the dynamic profile of the same system is inscribed. The dynamic profile clearly shows a cloud point region near 90 °C, which is reminiscent of Figure 8a(iii) in OM. Particle growth starts at this region. However, the isothermal light scattering profile does not show any indication of demixing phenomenon, suggesting that the system is already phase separated before it attains the isothermal temperature. Similar profiles were obtained at other isothermal temperatures too, suggesting that the particles appear to be too large to contribute to the scattering in the experimental q-windows. Thus, OM seems to be the most reliable source to study the phase growth behavior of developed morphologies of the system rather than the light scattering studies, as the scattering profile fails to signify any hint. Therefore, we believe that the development of phase separated morphology is via a nucleation and growth (NG) mechanism. Some immiscible elastomeric particles in the system are themselves acting as nuclei for further growth of elastomeric domains in the network of epoxy matrix. The mechanism supplemented with other prime factors, which are mentioned already, is believed to be the reason for the development of bigger elastomer domains in the system at both cure temperatures. Figure 8c[i, ii, iii and iv] is a schematic representation of the NG mechanism, which is believed to be operating in the present system. Figure 8c(i) represent few immiscible elastomer particles in a homogeneous system of epoxy resin and hardener. As curing initiates, the system becomes more transparent as some of these elastomer particles get dissolved in the system. This state is represented by Figure 8c(ii). As curing proceeds, coalescence of particles takes place

Figure 7. (a) SEM image of neat epoxy resin. (b) [i, ii, iii, and iv]: SEM micrographs of epoxy−HTPB (5−20 phr) blends Tcure = 120 °C [(i) 5 phr (ii) 10 phr (iii) 15 phr (iv) 20 phr]. (c) [i, ii, iii, and iv]: SEM micrographs of epoxy−HTPB (5−20 phr) blends Tcure = 150 °C [(i) 5 phr (ii) 10 phr (iii) 15 phr (iv) 20 phr].

resulted in the formation of particles are the increase in the viscosity of the system and differences in solubility parameters and surface tension of the elastomeric phase during the cure process.56 The cure of the blend systems, at both curing temperatures, were analyzed by time- resolved optical microscope with an automated time scale set up. A series of photographs of the phase separating systems at different time intervals were obtained. All systems showed almost similar trends of phase separation nature during curing before attaining the well-

Table 6. Dispersed Particle Size and Polydispersity of the Modified Epoxies Cured at Different Temperatures curing temperature (°C) 120

150

HTPB composition (phr)

Dn

Dv

Dw

PI

Dn

Dv

Dw

PI

5 10 15 20

0.84 0.92 1.30 1.60

1.49 1.55 2.50 3.10

0.93 1.10 2.00 2.52

1.11 1.20 1.54 1.58

0.83 0.90 1.20 1.50

1.46 1.52 2.31 2.81

0.91 1.07 1.70 2.20

1.09 1.18 1.41 1.46

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phase separated elastomer domains in the network of epoxy resin system as depicted in Figure 8c(iv). Rubber-modified samples containing higher weight content of elastomer are characterized by a heterogeneous particle size distribution. A wide range of particle size distribution is observed in these samples. The particle size distribution in a blend containing 20 phr HTPB is illustrated in Figure 9a after computing the size of the particles in more than 50 samples.

Figure 8. (a) [i,ii,iii and iv]: Optical photographs of 15 phr HTPB system at 150 °C (i) before the initiation of cure (ii) cure time, t = 2 min, (iii) cure time t = 4 min, (iv) cure time t = 6 min. (b) Isothermal light scattering profile of 15 phr blend system at 120 °C (inset: dynamic profile of the system). (c) [i, ii, iii and iv]: Schematic representation of the NG mechanism.

targeting the immiscible particles as nuclei which is denoted by Figure 8c(iii). Finally, the coalescence and the growth of the particles attain a stagnation point, so as to form well-defined

Figure 9. (a) Particle size distributions in 20 phr rubber-epoxy blend. (b) Interfacial areas per unit volume as a function of the weight % of HTPB. (c) Interparticle distances in HTPB−epoxy blends. 12188



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the reaction followed an autocatalytic mechanism, which was analyzed by Kamal model to find out kinetic parameters and activation energies. The reaction became diffusion controlled after the vitrification stage, which was explained by introducing a diffusion factor. Cure and the generated morphology were correlated. The morphology of the phase separated elastomeric domains in cured blends (Tcure = 120 and 150 °C) were quantified. The lower particle size at the higher cure temperature has been correlated with the formation of gelation at a lower time, which suppresses the degree of coalescence and results in smaller particles. The investigation of cure using OM and SALLS led to the conclusion that a nucleation and phase growth mechanism is responsible for the phase separation behavior. A schematic phase separation model has also suggested. The mechanism also supports the heterogeneous morphology developed in higher elastomer modified epoxies.

The particle size distribution has a wide range from 0.1 to 58 μm. A large number of particles were present in the range 15− 28 μm. The percentage of particles having large sizes was predominant in modified epoxies containing higher weight content of the elastomer. The heterogeneous morphology developed in blends having high weight contents of rubber can be correlated with gelation time and the nature of the phase separation mechanism. The gelation time increases as the concentration of the rubber increases, due to viscosity and reduced reactivity. During the polymerization reaction, small particles agglomerated and increased in size to form bigger particles. Thus, there is enormous chance for coalescence of particles having varying size distribution. Nucleation and growth mechanism of phase separation also causes wide distribution of particle size, especially when cure reactions are sufficiently low. The poor mechanical performance of high rubber filled systems28 shall be attributed to this heterogeneous nature of particle size distribution. The interfacial area per unit volume and the interparticle distance (δ) were computed from the following expressions.58 Interfacial area per unit volume =

3Φ r

⎡⎛ π ⎞1/3 ⎤ ⎟ Inter particle distance, δ = D⎢⎜ − 1⎥ ⎢⎣⎝ 6Φ ⎠ ⎥⎦

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +91-469-2630888. Fax: +91-469-2605843. E-mail: [email protected].

(11)

Notes

The authors declare no competing financial interest.

■

(12)

where D is the diameter of domains, r is the radius of the domains, and Φ is the volume fraction of the dispersed phase, which can be estimated56 from the equation Φ = (π/4)(∑nD2/ Aref), where Aref is the area of micrographs region under analysis. Interfacial area per unit volume in HTPB−epoxy blends are represented in Figure 9b. The value increased up to 10 phr rubber concentration and then showed a decreasing trend. The lower values of interfacial area showed that the interaction of HTPB rubber with the epoxy matrix was poor. When the HTPB content was more, the phase separated elastomer domains were bigger due to the tendency of agglomeration of particles. This further reduced the interaction with the matrix, and as a result, the values were low. Furthermore, the interparticle distances decreased [Figure 9c] with the introduction of higher elastomer content. Since the elastomer is not well miscible in the resin, agglomeration of phase separated structures leads to comparatively bigger elastomer domains.

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