Modeling of dynamic mechanical properties of vulcanized fluoroelastomer

The dynamic mechanical properties of a vulcanized fluoroelastomer (FKM) were studied over a range of temperatures and shear frequencies. Dynamic mechanical analysis and differential scanning calorimetry were used for the purpose of the study. A model was developed in order to describe FKM's viscoelastic behavior at various temperatures. The model was fitted to experimental data using an algorithm, which was developed for this purpose. As a result the FKM discrete relaxation spectrum at two reference temperatures was obtained, as well as the Williams‐Landel‐Ferry (WLF) equation parameters or the activation energy equivalent. Further on, the model was applied on storage modulus and loss tangent values obtained from the experiments, during which the temperature increased linearly. It was observed that the WLF equation fits well with the results during the glass transition, while the Arrhenius‐type relationship predicted too rapid decrease of the storage modulus during the glass transition. The master curves were constructed using the previously calculated WLF parameters and the activation energy equivalent. The developed model may be readily applied for the prediction of the numerous FKM compounds' frequency–temperature behavior using the dynamic mechanical properties obtained from either isothermal or low linear heating rate program measurements. POLYM. ENG. SCI., 47:2085–2094, 2007. © 2007 Society of Plastics Engineers     

Vitrification effect on the curing reaction of epoxy resin

Summary The curing reaction of diglycidyl ether of Bisphenol A(DGEBA) with triethylene tetramine(TETA) was studied by the differential scanning calorimetry(DSC). The reaction was affected as the vitrification occurred when the glass transition temperature(T_g) of the reaction mixture exceeded the curing temperature. In order to describe the curing reaction in the rubbery state as well as in the glassy state, the reaction kinetic equation containing the generalized WLF equation term was proposed and the parameters were determined from the DSC data.Nomenclature a_T time temperature shift factor, dimensionless - A_T temperature dependent frequency factor, /sec - A_Tg temperature dependent frequency factor at T_g, /sec - A_To temperature dependent frequency factor at T_g, /sec - A empirical parameter in temperature dependent frequency factor, dimensionless - B empirical parameter in temperature dependent frequency factor, K - C₁ empirical parameter in the generalized WLF equation, dimensionless - C₂ empirical parameter in the generalized WLF equation, K - D correction parameter in temperature dependent frequency factor, K - E activation energy, cal/mole - E_x/E_m ratio of lattice energies for crosslinked and uncrosslinked polymer, dimensionless - F_x/F_m ratio of segmental mobilities for crosslinked and uncrosslinked polymer, dimensionless - H_t cumulative heat generated up to time t, cal/g - H_RXN heat of reaction under complete conversion, cal/g - n reaction order, dimensionless - S _r scan rate of the DSC experiment, °C/sec - t time, second - T temperature, K - T_g glass transition temperature of the partially cured reaction mixture, K - T_go glass transition temperature of uncured reactant, 253 K - X conversion, dimensionless     

Cure and properties of unfoamed polyurethanes based on uretonimine modified methylene–diphenyl diisocyanate

The curing behaviour of a series of polyurethanes based on modified methylene–diphenyl diisocyanate (MDI) and poly(propylene oxide) polyols was studied using isothermal Fourier‐transform infrared spectroscopy (FTIR), temperature‐ramped differential scanning calorimetry (DSC) and adiabatic exotherm experiments. The effects of catalyst type and content, and of polyol molecular weight and functionality on the curing behaviour of the material were investigated. Increasing catalyst concentration or decreasing the polyol molecular weight raised the rate of reaction and shifted the DSC peak exotherm temperature to lower temperatures, but the heat of reaction was effectively constant. A marked increase in reaction rate was observed when a 1 °‐alcohol‐based polyol (from ethylene oxide end‐capping) was used in place of the standard poly(propylene oxide) end‐capped 2 °‐polyols. FTIR isocyanate conversion during polyurethane formation for a range of dibutyltin dilaurate (DBTDL) concentrations was satisfactorily fitted to second‐order kinetics. An approximately linear relationship between DBTDL catalyst concentration and reaction rate constant was found, but increasing the concentration of DBTDL was found to have no significant effect on the magnitude of the activation energy. The activation energy for polymerization was found to be independent of the molecular weight of the diol or triol systems. Dynamic mechanical thermal analysis revealed a linear increase of the glass transition temperature with decreasing triol weight fraction, and was in good agreement with a theoretical model based on copolymer and crosslinking effects. © 2000 Society of Chemical Industry     

Method for time–temperature–transformation diagrams using DSC data: Linseed aliphatic epoxy resin

A novel method to generate time–temperature–transformation (TTT) diagrams from Differential Scanning Calorimetry (DSC) data is presented. The methodology starts with dynamical DSC information to obtain the total transformation heat, followed by an isothermal‐dynamic temperature ramp that allows the inclusion of diffusion‐controlled reaction kinetic. The cure kinetics is modeled using an auto‐catalytic Kamal–Sourour model, complemented with a Kissinger model that allows the direct prediction of one energy of activation, DiBenedetto's equation for the glass transition temperature as a function of the cure degree and adjusted reaction constants to include diffusion mechanisms. The methodology uses a nonlinear least‐squares regression method following J.P. Hernández‐Ortiz and T.A. Osswald's methodology (J. Polym. Eng. 2004, 25, 23). A typical linseed epoxy resin (EP) presents two different kinetics control mechanisms, thereby providing a good model to validate the proposed experimental and theoretical method. TTT diagrams for EPs at two different accelerator concentrations are calculated from direct integration of the kinetic model. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40566.     

Time–temperature–transformation cure diagrams of phenol–formaldehyde and lignin–phenol–formaldehyde novolac resins

In this study, the time–temperature– transformation (TTT) cure diagrams of the curing processes of several novolac resins were determined. Each diagram corresponded to a mixture of commercial phenol–formaldehyde novolac, lignin–phenol–formaldehyde novolac, and methylolated lignin–phenol–formaldehyde novolac resins with hexamethylenetetramine as a curing agent. Thermomechanical analysis and differential scanning calorimetry techniques were applied to study the resin gelation and the kinetics of the curing process to obtain the isoconversional curves. The temperature at which the material gelled and vitrified [the glass‐transition temperature at the gel point (_gelT_g)], the glass‐transition temperature of the uncured material (without crosslinking; T_g0), and the glass‐transition temperature with full crosslinking were also obtained. On the basis of the measured of conversion degree at gelation, the approximate glass‐transition temperature/conversion relationship, and the thermokinetic results of the curing process of the resins, TTT cure diagrams of the novolac samples were constructed. The TTT diagrams showed that the lignin–novolac and methylolated lignin–novolac resins presented lower T_g0 and _gelT_g values than the commercial resin. The TTT diagram is a suitable tool for understanding novolac resin behavior during the isothermal curing process. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Curing kinetics of epoxy‐urethane copolymers

The cure of the epoxy resin diglycidyl ether of bisphenol A (Araldyt GY9527) with a mixture of cycloaliphatic amines (Distraltec) was studied, and the focus was on the effect of the copolymerization with a commercial polyurethane (PU) elastomer (Desmocap 12). A simplified phenomenological model was proposed to represent the copolymerization reaction. It considered the effect of the temperature and the concentration of the elastomer on the reaction rate, and it was simple enough to be included in models of processing conditions. A nonlinear regression analysis of the experimental conversion data obtained from differential scanning calorimetry was utilized to find the best fitting parameters to Kamal's equation for the chemically controlled part of the reaction (short times) under isothermal and constant heating‐rate conditions. The Rabinowitch approach together with the Addam–Gibbs theory was utilized to introduce the effect of diffusion control at the end of the reaction on the overall constant for the reaction rate. The Di Benedetto equation was used to predict the conversion at which vitrification takes place for each run. Experimental results for conversions higher than this critical conversion were utilized to obtain information about the diffusion kinetic constant using a nonlinear regression analysis as previously. The overall model obtained was used to calculate a calorimetric conversion and reaction rate as functions of time, which was in excellent agreement with the experimental results. The addition of PU elastomers affected the values of the activation energies of the chemically and diffusion controlled parts of the reaction, as well as the final conversion reached by the epoxy–amine system. The proposed model allowed prediction of all the observed features using parameters that were independent of the temperature of the curing reaction. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 1771–1779, 2001     

CO‐Free Hydrogen Production by Ethanol Steam Reforming in a Pd–Ag Membrane Reactor

In this work, the ethanol steam reforming (ESR) reaction has been studied by using a dense Pd–Ag membrane reactor (MR) by varying the water/ethanol molar ratio between 3:1 and 9:1 in a temperature range of 300–400 °C and at 1.3 bar as reaction pressure. The MR was packed with a commercial Ru‐based catalyst and a constant sweep gas flow rate in counter current mode was used. The influence of the temperature and the feed molar ratio on different parameters such as the ethanol conversion, the hydrogen production, the hydrogen yield and the CO‐free hydrogen recovery has been evaluated.     

Prediction of solvent‐diffusion coefficient in polymer by a modified free‐volume theory

Several versions of free‐volume theory have been proposed to correlate or predict the solvent diffusion coefficient of a polymer/solvent system. The quantity of free volume is usually determined by the Williams–Landel–Ferry (WLF) equation from viscosity data of the pure component in these theories. Free volume has been extensively discussed in different equation‐of‐state models for a polymer. Among these models, the Simha–Somcynsky (SS) hole model is the best one to describe the crystalline polymer, because it describes it very approximately close to the real structure of a crystalline polymer. In this article, we calculated the fractions of the hole free volume for several different polymers at the glass transition temperature and found that they are very close to a constant 0.025 by the SS equation of state. It is quite consistent with the value that is determined from the WLF equation. Therefore, the free volume of a crystalline polymer below the glass transition temperature (T_g) is available from the SS equation. When above the T_g, it is assumed that the volume added in thermal expansion is the only contribution of the hole free volume. Thus, a new predictive free‐volume theory was proposed. The free volume of a polymer in the new predictive equation can be estimated by the SS equation of state and the thermal expansion coefficient of a polymer instead of by the viscosity of a polymer. The new predictive theory is applied to calculate the solvent self‐diffusion coefficient and the solvent mutual‐diffusion coefficient at different temperatures and over most of the concentration range. The results show that the predicted values are in good agreement with the experimental data in most cases. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 428–436, 2000     

Optimization of the coordination–insertion ring‐opening polymerization of poly(p‐dioxanone) by programmed decreasing reaction temperatures

The optimization of the synthesis of poly(p‐dioxanone), by ring‐opening polymerization with tin II bis(2‐ethylhexanoic acid) as the catalyst, was conducted by a new method in which programmed decreasing reaction temperatures were employed. The results were compared with those obtained for polymerization reactions performed at constant temperatures in the 80–180°C range. In the novel method, the temperature was gradually reduced, as the reaction proceeded, to maintain a maximum polymerization rate and monomer conversion as the monomer was consumed. The experiments performed at constant temperatures confirmed previous reports that the bulk polymerization of 1,4‐dioxan‐2‐one is an equilibrium polymerization reaction. With increasing polymerization temperature, the initial rate of polymerization increased, but the monomer conversion, reaching equilibrium, decreased. High conversions were obtained at low temperatures and long reaction times. Therefore, reducing the reaction temperature, to ensure working conditions that guaranteed the maximum polymerization rate and monomer conversion, could optimize the polymerization process. These conditions were calculated under the assumption of equilibrium polymerization reaction kinetics. With our proposed method, a 71% conversion was achieved in half the time needed when the polymerization was performed at a constant temperature of 120°C. Similarly, a 78% conversion was obtained with our proposed method in only a third of the time employed when the reaction was carried out at a constant temperature of 80°C. Our method guarantees high conversions in shorter times and a gradual reduction of the polymerization temperature. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 659–665, 2005     

Curing kinetics and thermal property characterization of an o‐cresol formaldehyde epoxy resin and 4,4′‐diaminodiphenyl ether system

The kinetics of the curing reaction for a system of o‐cresol formaldehyde epoxy resin (o‐CFER) with 4,4′‐diaminodiphenyl ether (DDE) as a curing agent were investigated with differential scanning calorimetry (DSC). An analysis of the DSC data indicated that an autocatalytic behavior appeared in the first stages of the cure for the system, and this could be well described by the model proposed by Kamal, which includes two rate constants and two reaction orders (m and n). The overall reaction order (m + n) was 2.7–3.1, and the activation energies were 66.79 and 49.29 kJ mol^?1, respectively. In the later stages, a crosslinked network was formed, and the reaction was mainly controlled by diffusion. For a more precise consideration of the diffusion effect, a diffusion factor was added to Kamal's equation. In this way, the curing kinetics were predicted well over the entire range of conversions, covering both the previtrification and postvitrification stages. The glass‐transition temperatures of the o‐CFER/DDE samples were determined via torsional braid analysis. The results showed that the glass‐transition temperatures increased with the curing temperature and conversion up to a constant value of approximately 370 K. The thermal degradation kinetics of the system were investigated with thermogravimetric analysis, which revealed two decomposition steps. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 182–188, 2004     

Photocure properties of high‐heat‐resistant photoreactive polymers with cinnamate groups

New high‐heat‐resistant photoreactive polymers with cinnamate groups were synthesized by the reaction of cinnamic acid (CA) and epoxy resins. Their photocure properties were investigated with Fourier transform infrared spectroscopy, UV–visible spectroscopy, and thermogravimetric analysis (TGA). Their photocure reaction rates and the extent of reaction conversion increased with the intensity of UV irradiation. To investigate their photocure reaction kinetics, their reaction conversion rates were plotted against reaction conversion so that their photocure reactions could be analyzed in terms of an nth‐order kinetics reaction equation. The YX4000H–CA photoreactive polymer with a biphenyl moiety, which was expected to have strong molecular interactions, showed a lower reaction conversion rate and reaction constant, and the highest reaction conversion rate and reaction constant was observed in XP2030–CA with an optimum cure reaction space and a reduction of molecular interactions compared with the other photoreactive polymers. Thermal stability was studied by observation of the changes in the transmittance of the photocured polymer films upon heating and by measurement of the weight loss with temperature with TGA. These photoreactive polymers showed good thermal properties, with almost no transmittance change in the visible range even after they were heated at 250°C for 1 h, and they exhibited little weight loss up to about 250°C. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Master curve and time–temperature–transformation cure diagram of lignin–phenolic and phenolic resol resins

The aim of this work is to generate both a master curve of resol resins based on the time–temperature superposition principle and their TTT cure diagrams. The samples used for this purpose were lignin–phenolic and phenol–formaldehyde resol resins. A TMA technique was employed to study the gelation of resol resins. In addition, a DSC technique was employed to determine the kinetic parameters through the Ozawa method, which allowed us to obtain isoconversional curves from the data fit to the Arrhenius expression. Establishing the relationship between the glass‐transition temperature and curing degree allowed the determination of the vitrification lines of the resol resins. Thus, using the experimental data obtained by TMA and DSC, we generated a TTT cure diagram for each of resins studied. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3362–3369, 2007     

Dielectric analysis of the cure of thermosetting epoxy/amine systems

A low molecular weight epoxy resin is cured isothermally with an aromatic amine hardener, and the dielectric properties are measured as a function of the frequency, reaction time, and cure temperature. At specific stages in the cure, small samples from the reacting mixture are quenched and subsequently analyzed for the glass transition temperature and epoxy group conversion by differential scanning calorimetry. In this manner, the change In dielectric properties can be directly correlated with the network structure. The ionic conductivity is modeled as a function of the cure temperature and the cure-dependent glass transition temperature using a Williams-Landel-Ferry (WLF) relation. Combining this WLF relation with the DiBenedetto equation, a comprehensive model relating conductivity with the extent of reaction and cure temperature has been developed.     

Reaction kinetics modeling and thermal properties of epoxy–amines as measured by modulated‐temperature DSC. II. Network‐forming DGEBA + MDA

Reaction‐induced vitrification takes place in the network‐forming epoxy–amine system diglycidyl ether of bisphenol A (DGEBA) + methylenedianiline (MDA) when the glass‐transition temperature (T_g) rises above the cure temperature (T_cure). This chemorheological transition results in diffusion‐controlled reaction and can be followed simultaneously with the reaction rate in modulated‐temperature DSC (MTDSC). To predict the effect of T_cure and the NH/epoxy molar mixing ratio (r) on the reaction rate in chemically controlled conditions, a mechanistic approach was used based on the nonreversing heat flow and heat capacity MTDSC signals, in which the reaction steps of primary (E_1OH = 44 kJ mol^?1) and secondary amine (E_2OH = 48 kJ mol^?1) with the epoxy–hydroxyl complex predominating. The diffusion factor DF as defined by the Rabinowitch approach expresses whether the chemical reaction rate or the diffusion rate determines the overall reaction rate. A model based on the free volume theory together with an Arrhenius temperature dependency was used to calculate the diffusion rate constant in DF as a function of conversion (x) and T_cure. The relation between x, r, and T_g, needed in this model, can be predicted with the Couchman equation. An experimental approximation for DF is the mobility factor DF* obtained from the heat capacity signal at a modulation frequency of 1/60 Hz, normalized for the effect of the reaction heat capacity in the liquid state and the change in C_p in the glassy region with x and T_cure. In this way, an optimized set of diffusion parameters was obtained that, together with the optimized kinetic parameters set, can predict the reaction rate for different cure schedules and for stoichiometric and off‐stoichiometric mixtures. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 91: 2814–2833, 2004     

Rheological cure characterization of phosphazene–triazine polymers

Cyclomatrix phosphazene–triazine network polymers were synthesized by co‐curing a blend of tris(2‐allylphenoxy), triphenoxy cyclotriphosphazene (TAP), and tris(2‐allylphenoxy) s‐triazine (TAT) with bis(4‐maleimido phenyl) methane (BMM). The co‐curing of the three‐component resin was investigated by dynamic mechanical analysis using rheometry. The cure kinetics of the Diels–Alder step was studied by examining the evolution of the rheological parameters, such as storage modulus (G′), loss modulus (G″), and complex viscosity (η*), for resins of varying compositions at different temperatures. The curing conformed to an overall second‐order phenomenological equation, taking into account a self‐acceleration effect. The kinetic parameters were evaluated by multiple‐regression analysis. The absence of a definite trend in the cure process with blend composition ratio was attributed to the occurrence of a multitude of competitive reactions whose relative rates depend on the reactant ratio and the concentration of the products formed from the initial phase of reaction. The cure was accelerated by temperature for a given composition, whereas the self‐acceleration became less prominent at higher temperature. Gelation was accelerated by temperature. The gel conversion decreased with increase in maleimide concentration and, for a given composition, it was independent of the cure temperature. The activation energy for the initial reaction and the crosslinking process were estimated for a composition with a maleimide‐to‐allyl ratio of 2 : 1. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 908–914, 2003     

Effect of blending polyethersulfone on the cure kinetics and physical properties of dicyanate resin

The curing behavior and thermomechanical properties of dicyanate/polyethersulfone (PES) blends were investigated. Differential scanning calorimetry (DSC) was used to study the curing behavior of the dicyanate/PES blends. A second‐order autocatalytic reaction mechanism was used to describe the cure kinetics of the blends. The reaction kinetic parameters were determined by fitting DSC conversion data to the kinetic equation. The main glass‐transition temperatures of the blends decreased with increasing PES content. Two glass‐transition temperatures indicating phase‐separated morphology of the blends were observed. The thermal decomposition behavior of the blends was measured using thermogravimetric analysis. Mechanical and electrical properties of the blends were investigated. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1952–1962, 2001     

Study of the nonlinear phase‐separation behavior of a polystyrene/poly(vinyl methyl ether) blend using small‐angle light scattering

The thermally induced phase‐separation behavior of a polystyrene/poly(vinyl methyl ether) (PS/PVME) blend was studied mainly using time‐resolved small‐angle light scattering, as a function of temperature and heating rate. Under a non‐isothermal field, the dependence of the critical temperature on heating rate deviated obviously from linearity, even at very low heating rates. Such a nonlinear dependence was consistent with the deviation from linearity of the temperature dependence of the isothermal phase‐separation behavior in a wider temperature range from 100 to 140 °C. It was also found that a Williams–Landel–Ferry (WLF)‐like equation could be employed to describe the temperature dependence of the apparent diffusion coefficient (D_app) and the relaxation time (τ) of normalized scattering intensity at the early stage of spinodal decomposition (SD), as well as τ of phase behavior at the late stage of SD for the PS/PVME blend. The equilibrium phase‐separation temperature could hardly be established through the conventional linear extrapolation of heating rate or D_app to zero at the early stage of SD. The successful use of the WLF‐like function for PS/PVME blends extends the applicability of the time–temperature superposition principle for describing the phase‐separation behavior of binary polymer mixtures over a relatively large temperature range. Copyright © 2010 Society of Chemical Industry     

Noncatalytic Hydrolysis of Iminodiacetonitrile in Near‐Critical Water – A Green Process for the Manufacture of Iminodiacetic Acid

The hydrolysis of iminodiacetonitrile (IDAN) in near‐critical water, without added catalysts, has been successfully conducted with temperature and residence time ranges of 200–260 °C and 10–60 min, respectively. The effects of temperature, pressure, and initial reactant/water ratio on the reaction rate and yield have been investigated. The final reaction products primarily included iminodiacetic acid (IDA) and ammonia associated with other by‐products; gas formation was negligible. The maximum yield of IDA was 92.3 mol.‐% at 210 °C and 10 MPa, with a conversion of almost 100 %.The apparent activation energy and ln A of IDAN hydrolysis were evaluated as 45.77 ± 5.26 kJ/mol and 8.6 ± 0.1 min^–1, respectively, based on the assumption of first‐order reaction. The reaction mechanism and scheme were similar to those of base‐catalyzed reactions of nitriles examined in less severe conditions.     

Kinetics study of an acrylic tetrapolymer: Poly(IBMA–MMA–MAA–TBMA)

In this study, the polymerization kinetics and the molecular structure of the tetrapolymer poly[isobornyl methacrylate (IBMA)–methyl methacrylate (MMA)–methacrylic acid (MAA)–tert‐butyl methacrylate (TBMA)] were investigated. The relationships among the tetrapolymer composition, monomer conversion, and reaction time were studied. Kinetic equations of the four‐component copolymerization related to the mean sequence length, the run number, the reactivity ratio, and the monomer concentration were derived. The mean sequence length of the monomer IBMA increases with the reaction time and monomer conversion. However, those of the other three monomers remain an insignificant variation. Furthermore, the run number decreases rapidly at the end of polymerization. These results suggest that the slow polymerization rate of IBMA is due to its bulky side group. The mean sequence lengths of IBMA, MMA, MAA, and TBMA at the end of polymerization are 1.772, 1.304, 1.169, and 1.229, respectively. On the other hand, the run number of the prepared tetrapolymer is 70.25. The results of the mean sequence length, run number, and the single glass transition temperature suggest that the prepared tetrapolymer is a random copolymer. The molecular weight distribution of the prepared tetrapolymer is significantly affected by polymerization conditions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 853–863, 2001     

Three‐dimensional thermorheological behavior of isotactic polypropylene across glass transition temperature

The aim of this work was to determine the three‐dimensional thermorheological behavior of isotactic polypropylene (i‐PP) in the region of its glass transition temperature (T_g) by a master curve. The i‐PP is a widespread polymer with a T_g ～ 0°C. Dynamic mechanical analysis (DMA) at varying frequencies and temperatures and bulk tests at varying temperatures and times are carried out to obtain the relaxation spectra. Traditionally, the combination of time and temperature is done for thermorheological simple material by the creation of a master curve based on the Arrhenius or William–Landel–Ferry (WLF) equation. This investigation shows that these equations do not fit the behavior across the glass transition of i‐PP. Instead, a new arc tangent function is derived. Additionally, it can be shown that the shifting factors differ from shear to bulk load. Therefore, the mode of mechanical stress seems to have an influence on the thermorheological behavior. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 877–880, 2004