A logistic kinetic model for isothermal and nonisothermal cure reactions of thermosetting polymers

A model describing the low‐temperature crystallization kinetics observed for thermoplastic polymers from the melt by differential scanning calorimetry (DSC) was shown to accurately predict the cooling curves as a function of time and temperature. The model was successful for treating data for several cooling rates as well as for isothermal DSC data. In this article, we extended the model to cure reactions of thermosetting polymers. The parameters representing lower and upper exotherm reference temperatures in crystallization events have a different meaning for curing events. Thus, the model was modified to account for this change of context. The new model was tested for exothermic reactions of a Hysol® FP4527 epoxy adhesive system using data from DSC ramp heating experiments at several heating rates and also from isothermal experiments. Good fits were obtained for all the varied experimental conditions. The model made use of three fitting parameters with physical significance: a lower critical temperature (T_c) an activation energy (E_b), and a reaction order (τ + 1). Additionally, to complete the kinetic fitting, the dependence of the time to reach the reaction peak maximum for isothermal cure was considered. That dependence was found to follow a more simple model which is formally equivalent to that observed in isothermal crystallization, and which makes use of two parameters related to the limits of the temperature range in which the polymerization may occur. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40670.     

Toughened multiphase thermosetting polymers

In recent years a new generation of advanced structural adhesives has become available. They are typically based upon epoxy resins modified by the presence of a second phase of dispersed rubbery particles. This multiphase microstructure results in the material possessing a considerably higher toughness or crack resistance, compared to the unmodified, single-phase resin, but with only a minimal reduction in other important properties such as modulus and high-temperature and creep resistance. Even more recently, polyimide adhesives have also been toughened employing this principle. The present paper considers the following aspects:

• 1 The chemistry of rubbery-toughened thermosetting polymers developed for adhesive applications.
• 2 Structure-property relationships of multiphase adhesives which incorporate a dispersed rubbery phase or rigid particulate fillers. The mechanisms of toughening are discussed and related to the microstructure. The effects of volume fraction, particle size and particle size distribution on the polymer's fracture energy are also described
• 3 The particular problems encountered when using such toughened multiphase adhesives in structural joints are reviewed, including aspects of joint design and environmental effects.

     

Relationship between isothermal and dynamic cure of thermosets via the isoconversion representation

This study deals with the cure of thermoset resins used in the pultrusion of fiber reinforced composites. The objective was to predict the degree of cure under non‐uniform time‐temperature profiles. A simple procedure using differential scanning calorimetry results was developed for predicting the degree of cure vs. time under isothermal conditions from dynamic DSC tests and vice versa. The principal feature of the procedure is the transformation of the degree of cure vs. time curves obtained under isothermal or dynamic DSC conditions into isoconversion curves as time vs. temperature or time vs. heating rate diagrams. The proposed procedure is validated with isothermal and dynamic DSC results from epoxy and polyester resin formulations used in the pultrusion of fiber reinforced composites. The agreement between predictions and experiments was very good and the extension of the procedure for predicting the cure under non‐uniform temperature profiles as in pultrusion seems to be feasible.     

The application of ultra-violet microscopy to thermosetting polymers

Optical microscopy with ultra-violet illumination has been used to monitor the curing reactions and final structure of an amine-cured epoxy resin system. When low concentrations of u.v. absorbing additive are added to the resin before curing, the additive is usually completely uniformly distributed in the cured product. No density variations on a scale resolvable in optical microscopy are visible. Similarly when a u.v. absorbing eragent is allowed to diffuse into the cured resin its diffusion profile is normal and shows no detectable density fluctuations in the resin. Reaction of cured resins with a reagent which couples with amino groups to give u.v. absorbing adducts shows that conventional hand mixing techniques do not produce complete mixing of the resin components and spatially non-uniform concentrations of unreacted amines are found. This effect can only be removed by unusually thorough mixing techniques. Use of a water soluble u.v. absorber allows penetration of the epoxy by water to be followed. In particular, the penetration of fibre-matrix interfaces by water can be visualised.     

Critical surface tension of blends of thermosetting fluorochemical methacrylate polymers with thermosetting hydrocarbon acrylate polymers

Critical surface tensions (γ_c) for blends of thermosetting fluorochemical methacrylates and thermosetting acrylate polymers are measured in their cured thermoset condition. Values of γ_c depend on (1) the nature of the fluorochemical side chain and (2) the ratio of fluorochemical containing polymer to hydrocarbon polymer. The minimum value for γ_c is found to occur at a fluorocarbon to hydrocarbon polymer ratio of 0.10 to 0.001. At higher and lower ratios (>0.1 and <0.001), the value for γ_c increased. Thus, certain blends of fluorochemical methacrylate copolymer with hydrocarbon acrylate copolymer give lower γ_c than either the hydrocarbon acrylate or the fluorochemical methacrylate copolymer.     

Dielectric cure determination of a thermosetting epoxy composite prepreg

Evaluation of degree of cure (DoC) of a glass reinforced epoxy composite prepreg used for manufacturing of printed circuit board (PCB) is an intensive issue because of its practical importance and cost reduction in industry. Typical techniques such as differential scanning calorimetry (DSC) and fourier transform infrared spectroscopy (FTIR) are destructive and require curing a material during a chosen time, quenching the sample to stop cure before performing analysis. Thus, it is necessary to remove the temperature influence on the determination of DoC. In this study, the feasibility of nondestructive dielectric sensing method as an in situ DoC measuring technique through cure monitoring of prepreg is presented, where a vacuum packing configuration has been established so as for the prepreg to evaluate accurately the DoC in a quenched state at an ambient temperature. The optimal curing condition to get the fully cured state of a prepreg material is determined by the dielectric cure monitoring based on the behavior of ion viscosity. The temperature effect compensated DoC of prepreg is correlated and compared with that evaluated by DSC and FTIR. The correlated DoC with ion viscosity has identified the curing behavior of prepreg by determining cure kinetic parameters. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44707.     

The interface between glass and carbon fibers and thermosetting polymers

The interface between the fibers and the polymer matrix controls the properties of fiber composites and has been the subject of much study. Recently, special techniques have been developed for single fiber pull-out experiments on production fibers, which make it possible to obtain data on the frictional forces which govern sliding after the interface has fractured, as well as the adhesion strength of the interface. Tests on glass in polyester and epoxy resins show that the work of fracture of the interface is much smaller than that of the resin, and that the shrinkage pressures of these matrices, when fully postcured, are approximately the same (about 20 MPa). Coefficients of friction at the interface are 0.6 for the polyester and 1.0 to 1.6 for the epoxy. The carbon-epoxy interface yields at shear stresses as high as 60 MPa, instead of fracturing, and the coefficient of friction during sliding is about 0.4.     

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.     

The examination of some thermosetting polymers by inelastic electron tunnelling spectroscopy

This paper first discusses the principles of Inelastic Electron Tunnelling Spectroscopy (IETS) and describes the experimental procedures needed to obtain spectra. Spectra are presented for an epoxide resin and two aliphatic amine-hardeners, and for epoxideamine mixtures both before and after a heat curing schedule. From the latter it can be seen that the normal curing reaction between amine and epoxide groups does not take place within an IETS junction. A possible reason for this is the adsoprtion of amines onto the aluminium oxide surface of the substrate.     

Molecular simulations of crosslinking process of thermosetting polymers

We use molecular dynamics (MD) with a procedure to describe chemical reactions to predict the atomic structure and properties of the thermosetting polymer epoxy EPON-862 and curing agent DETDA. The DREIDING force field is employed with environment-dependent atomic charges obtained self consistently during the dynamics. We propose a computationally efficient method to describe charge evolution based on the observation that atomic charges evolve significantly only during chemical reactions and in a repeatable manner. Two chemistry models with different relative rates for primary and secondary amine reactions are used to mimic the curing process in two extreme cases of processing conditions. The simulations show that differences in chemical reaction rates affect properties for intermediate conversion degrees (∼40-70%) but not for the higher conversion rates of interest in most applications. We also find that performing the polymerization at high temperatures leads to networks with lower internal strain energy due to increased molecular mobility. The predicted density, coefficient of thermal expansion, glass transition temperature and elastic constants of the resulting polymers are in excellent agreement with experiments.     

Curing of thermosetting polymers by an external fluid

A theoretical model is proposed for curing thermosetting polymers. The following heat transfer mechanisms are taken into account: convection through the heated fluid-mold interface, conduction through the resin, and heat generated by chemical reaction. To study the influence of the convective heat in the curing step of the polymers, different external heating fluids are considered. Several chemical systems are used in the simulation. The results show that an apoxy requires precise control of thermal runaway. Criteria for processability are established and they provide a cycle time without promoting a damaging exotherm.     

Some mechanical properties of particulate-filled thermosetting and thermoplastic polymers

A semiempirical, single-parameter equation describes the modulus of particulate systems This equation has been found applicable for thermoplastic/glass bead systems, and it is further verified for particulate thermosetting systems (epoxy and polyester matrices). The temperature effect on the modulus of epoxy/glass bead composites is also analyzed. Crazing characteristics calculated from tensile data of thermoplastic/glass bead composites are summarized and compared with literature results on the corresponding unfilled polymers. The effect of coupling agents and preliminary results on rigid foams are also presented.     

Synthesis of thermosetting polymers from the by-products of coal conversion processes

The use of coal conversion by-products as raw materials in the synthesis of thermosetting polyesters has been investigated. Heavy tar residues were oxidized by gaseous oxygen in an alkaline medium, yielding a complex mixture of benzenecarboxylic acids and smaller amounts of aliphatic carboxylic acids. The mixture was polymerized by condensation with tetraethylene glycol “bottoms,” a by-product of the synthesis of ethylene glycol. The resultant polyesters were cured by reacting them with epoxy resins in the presence of basic catalysts. Molded sheets and laminates were fabricated and tested. Tensile strength was found to increase with increasing curing time and with increasing concentration of epoxy crosslinking agent. Glass-reinforced composites fabricated by the autoclave process showed an increase in flexural and shear strength with decreasing autoclave pressure.     

Simultaneous dielectric and dynamic mechanical analysis of thermosetting polymers

This work presents a new method to measure simultaneously the dielectric loss factor and viscosity of thermosetting polymers during various cure cycles. A microdielectric sensor was mounted in the bottom plate of a parallel plate rheometer. Three types of high performance laminating resins were investigated. During non-isothermal curing, dipole peaks were found to correspond to softening/devitrification, the maximum in the loss factor followed the same heating rate dependence as the minimum in the viscosity, and dipole peaks were observed to correlate with vitrification when the cure temperature was below the ultimate glass transition temperature of the resin.     

Nanohole volume dependence on the cure schedule in epoxy thermosetting networks: A PALS study

A systematic study on the dependence of the volumes at nanoscale in epoxy systems cured with two selected aminic hardeners at different pre-cure temperatures is presented. Nanohole volumes were measured by positron annihilation lifetime spectroscopy. Additional information regarding the structure of the thermosets was obtained using dynamic mechanical analysis. Volume results obtained are discussed in terms of the cure schedule applied to the epoxy systems, their characteristic glass transition temperatures and their crosslink density. The pre-cure temperature and the structure of the hardeners govern the packing of the molecular chains of the epoxy network. Using together positron and mechanical experimental techniques allows to conclude that a strong change in the volume and number density of the nanoholes takes place when the pre-cure temperature crosses the glass transition temperature of the systems.     

Cure kinetics modeling and cure shrinkage behavior of a thermosetting composite

In this work, the cure kinetics and through‐the‐thickness cure shrinkage upon curing of a carbon fiber‐epoxy composite (AS4/8552) were studied. The study is composed of two major parts. Firstly, dynamic and isothermal Differential Scanning Calorimeter (DSC) scans were performed to develop a new cure kinetics model. The most appropriate kinetic model that produces a nearly perfect fit of all data sets corresponds to a process with two single‐step parallel autocatalytic reactions with diffusion control. Multivariate kinetic analysis was used to evaluate the parameters. In the second part of the study, the coefficients of thermal expansion (CTEs), the glass transition temperatures (T_g), and the through‐the‐thickness cure shrinkage strain values of the partially cured unidirectional and cross‐ply composite samples were measured by using a dynamic mechanical analyzer (DMA). Cure strains were measured throughout the Manufacturer's Recommended Cure Cycle (MRCC) with the same method. Results indicate that glass transition temperatures of partially cured samples can be measured very closely by the two methods (DSC and DMA). The methods proposed were proved to be very reliable to predict the degree of cure and to measure the through‐the‐thickness strains during the cure cycle. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Settling behavior of fillers in thermosetting epoxy casting resins during cure

Using a theory based on a modified Stokes' law equation, the settling behavior of fillers was investigated (glass beads and silica powder) in thermosetting epoxy casting resins during cure. In this study a suspension (a thermosetting epoxy casting resin) containing a large amount of filler particles is assumed to be a homogeneous fluid, and the settling phenomena are treated such that one or more particles of the filler settle into the homogeneous fluid under gravity without interference from other particles. The viscosity increase of the fluid during cure is taken into consideration. The experimental results agree well with the theoretical predictions when the settling distances are small and the particle size distribution is narrow. When these conditions are not satisfied, various effects are observed such as convection, filtering, combination, bottom effect, and a broad particle size distribution. In addition, the formation of a compression zone and of a compaction zone are clearly observed.     

The evolution of thermosetting polymers in a conversion–temperature phase diagram

A conversion–temperature phase diagram for thermosetting polymers is analyzed. The curing under different external conditions—isothermal, at a constant heating rate, adiabatic, and in a mold at constant wall temperature—is represented by definite trajectories in the phase diagram. Conditions related to incomplete curing or falsification of kinetic parameters are stated.     

Evolution of the coefficient of thermal expansion of a thermosetting polymer during cure reaction

The evolution of the coefficient of thermal expansion (CTE) of a thermosetting polymer during cure reaction is an important parameter for industrial applications such as composite processing since it influences the development of internal stresses in the material. The CTE being almost impossible to measure on a reacting thermoset, we propose to use an indirect method based on the modelling of ionic conductivity by a modified WLF equation, allowing to calculate the evolution of CTE from dielectric spectroscopy measurements. This method is applied to a dicyanate ester thermosetting polymer, leading to encouraging results both qualitatively and quantitatively.