Thermosetting Polymers Part 9 pot

Then,some general criteria for an adequate selection of the cure conditionsinitial temperature, control of the temperature rise, influence of gelation,and vitrification, are analyzed.. The

Temperature and Conversion Profiles During Processing

The precursors of thermosetting polymers are usually one of the ingredients

of complex formulations They may be present in very small amounts, as inthe manufacture of abrasive disks where the thermoset acts as an aggluti-nant; in medium amounts, as in the case of filler-reinforced thermosets; or asthe only components, in formulations used for encapsulation purposes.Apart from fillers, fibers, pigments, etc., some formulations contain rubber

or thermoplastic modifiers that phase-separate upon the polymerizationreaction (cure)

The cure cycle is the temperature vs time schedule used to polymerizethe thermoset precursors The selection of an adequate cure cycle has severalpurposes What is desired is to obtain the final part without strains exceed-ing design tolerances, with a uniform conversion (usually close to the max-imum possible conversion), without degradation produced by the hightemperatures attained during the cure, with convenient morphologies (inthe case of heterogeneous materials), and all this, must be achieved in theminimum possible time for economic reasons

In this chapter, the evolution of conversion and temperature profilesduring typical cure processes is discussed This is useful for analyzing thepossibility of attaining the maximum conversion, avoiding undesired high

temperatures, and keeping the cycle time at practical values These tions are also necessary for estimating the distribution of stresses generatedduring the cure (Adolf et al., 1998) or the distribution of morphologiesgenerated in a rubber-modified thermoset (Williams et al., 1987; Fang etal., 1995) These two important problems will not be addressed here – thereferences mentioned will enable the reader to get acquainted with the com-plexities involved in the detailed analysis of these subjects.

calcula-A survey of typical processing technologies is first presented Then,some general criteria for an adequate selection of the cure conditions(initial temperature, control of the temperature rise, influence of gelation,and vitrification), are analyzed The remaining sections are devoted todiscussing the influence of selected cure conditions on temperature andconversion profiles generated in several types of processing technologies:cure in heated molds, autoclave molding of graphite/epoxy composites,foaming, and shell molding A range of adequate cure conditions arediscussed for each one of the selected examples A final design shouldconsider the distribution of stresses generated during the cure as well asthe corresponding strains

The processing of formulations containing thermosetting polymers involvesthe simultaneous development of the network structure together with themorphology and shaping of the final material Examples of processing tech-nologies are casting, coating, foaming, molding, pultrusion, filament wind-ing, etc Some of these technologies (e.g., autoclave molding, pultrusion,filament winding, etc.), are particularly suitable for processing compositesmade of continuous fibers (glass, carbon, etc.), impregnated with the pre-cursors of the thermosetting polymer

Casting may be used for encapsulation purposes or for small-volumeproductions of shaped parts Monomer casting is possibly the simplest pro-cessing technology It may be used both with bifunctional monomers, such

as methyl methacrylate and styrene, leading to linear polymers, as well aswith polyfunctional monomers such as those used in epoxy formulations.Parts made from bifunctional monomers made be reshaped by heatingbecause of their thermoplastic nature, while parts made from polyfunctionalmonomers reach the final shape during the polymerization Processingerrors in the case of thermoplastics may be repaired by reheating and recy-cling the material, but in the case of thermosets this is not possible.Therefore, cure cycles have to be analyzed in great detail to avoid processingproblems

Coating includes spread, roller, and spray processes for flat substrates,

as well as the coating of complex parts using liquid dipping and bed equipment

fluidized-Foaming requires thermosetting monomers that react very fast at themixing temperature The formulation is divided into two or more streamsthat circulate independently in the foaming machine and react at a fast ratewhen mixed together Usually monomers and comonomers are separated,and both a catalyst and a blowing agent are added to one of the streams.The blowing agent evaporates when the heat evolved in the polymerizationreaction increases the temperature to its boiling point in the mixture Fromthis time on, foaming takes place The end of the rise time is determined bygelation (in open molds) or by the filling time (in closed molds)

Molding processes include compression molding, resin transfer ing (RTM), injection molding and reaction injection molding (RIM), auto-clave molding, and several types of specific processes such as shell molding,which is used in foundries

mold-Compression molding involves the use of preforms (bulk moldingcompounds, sheets of glass fibers impregnated with the thermoset precur-sors, etc.) that are placed in a heated mold When the mold is closed, theplastified preform flows to fill the mold and cure takes place in about 1–2min Then, the mold is opened and the final part ejected

RTM involves the pumping of the thermoset precursors into a heatedmold cavity containing preplaced fiber mats Mold filling and fiber impreg-nation may be assisted by partial evacuation of the mold

Conventional injection molding has been adapted for the production

of thermosets In this case, the volume of the ducts between the exit die andthe mold cavity is minimized to reduce the scrap as much as possible.Capital investment and operational costs are much less in the case ofRIM In this process, two or more low-viscosity streams are accuratelymetered, mixed by impingement at high pressures (20–30 MPa) in a hydrau-lically operated mixhead, and injected into the mold cavity Mold-fill timesare in the order of 1 s and cycle times in the order of 1 min Although thereaction is activated by mixing, the mold is heated to increase the cure ratefor the material located close to the wall Polyurethanes and polyurethanes–copolyureas are typically processed by RIM Short glass fibers may beintroduced in one of the streams, in which case the process is known asreinforced-reaction injection molding (RRIM) Difficulties associated withthis process are the control of both the stability of the suspension of glassfibers and the abrasion that it generates during its flow in the moldingmachine

Autoclave molding has been particularly adapted for the cure of nates of preimpregnated plies of continuous fibers (prepregs) A lay-up of

lami-preimpregnated plies with fibers oriented according to the mechanical design

of the final part is covered by a porous release film, bleeder cloths, a porous release film, and a pressure plate The ensemble is enclosed in avacuum bag, which is placed in an autoclave While a vacuum is beingmade inside the bag, the temperature is increased up to a particular value,where it is held constant for a predetermined period At this particulartemperature, which must be high enough to lower the viscosity of the ther-moset precursors but no so high as to begin the cure, pressure is applied toconsolidate the part This step provokes the elimination of resin, which isabsorbed by the bleeder plies, and the increase in the fiber volume fractionfrom about 50% to about 65% Then, the temperature is increased again toanother plateau value, leading to the cure of the laminated panel

non-In the pultrusion process, continuous fibers are impregnated by thethermoset precursors and are pulled through a heated die where the curetakes place: this produces continuous profiles of different shapes at a rate ofthe order of 1 m min
1

Filament winding also involves the impregnation of continuous fibers

by the thermosetting formulation, and the winding of fibers onto a mandrelwith angles that are previously determined in the mechanical design of thepart When the desired thickness is obtained, cure of the composite is per-formed by heating the ensemble using different procedures This process isuseful for producing tubes and tanks, but it may also be adapted to producemore complex shapes with a computer controlling the winding process usingseveral axes

Epoxies, unsaturated polyesters, and vinyl esters are typical setting polymers used in pultrusion and filament winding applications

9.3.1 Selection of the Initial Temperature

Usually it is desired to start with a low-viscosity formulation to permit theshaping of the part (for example, the filling of a mold) This puts a con-straint on the initial temperature, T0, which must be high enough to obtain

a low initial viscosity but not so high as to advance the cure during theshaping stage and cause premature gelation (in the case of mold filling, thiswill cause a ‘‘short shot’’)

Figure 9.1shows a qualitative plot of the viscosity variation producedduring the heating of a thermosetting polymer Initially, viscosity decreaseswith the increase in temperature, but as cure progresses, an abrupt increase

in viscosity is observed The processability window is the range of T values

where both the viscosity and the polymerization rate are low enough tofacilitate shaping of the part.

9.3.2 Control of the Temperature Rise

One of the main problems in the selection of a cure cycle is to achievecontrol of the exothermic polymerization reaction, particularly for thecase of large parts The exothermic character of the polymerization reactionarises from the evolution of the Gibbs free energy:

For the polymerization to proceed spontaneously,
G < 0 But
S <

0, because the system evolves to a more ordered state (the number of figurations in which free monomers may be placed in space decreases by theintroduction of covalent bonds among themselves); thus, the entropy changedoes not favor polymerization Then, the only possibility of getting
G < 0

con-is to have a significantly exothermic reaction (
H < 0) to counterbalancethe unfavorable entropy change

The actual temperature variation at a particular location of the partdepends on the ratio of the heat dissipation rate to the heat generation rate.This ratio must be kept high enough to control the temperature increase andtherefore avoid degradation reactions As most polymers exhibit a very lowthermal conductivity, heat dissipation can only be increased by using largesurface areas per unit volume (thin parts) or fillers with high thermal con-ductivities (aluminum powder, graphite fibers, etc.)

It is also possible to act over the heat generation factor This can bedecreased by diluting the formulation with fillers or fibers But this depends

FIGURE9.1 Variation of viscosity during the heating of a thermosetting mer

poly-on the desired mechanical properties, which will be significantly modified bytheir presence One method of decreasing the heat generation is to dilute themonomers with partially cured polymer, a procedure used in the manufac-ture of organic glasses based on diethylene glycol bis (allyl carbonate)(DADC or CR-39)(Fig 9.2).The polymerization of this monomer can bestopped at the soluble, fusible stage The dried polymers may be ground intopowder, mixed with monomer and peroxide initiator, and molded by heat-ing to give a glasslike hard, clear, thermoset plastic.

9.3.3 Influence of Gelation and Vitrification

Both gelation and vitrification have to be taken into account in the analysis

of a cure cycle As already mentioned, gelation must be avoided during moldfilling In some processing technologies such as in free-rise foaming, gelationdetermines the maximum height and the apparent density of the final foam(Sec 9.6)

The influence of vitrification on the thermoset cure is very important,because once the material enters the glassy region the polymerizationkinetics is severely retarded On occasions one can take advantage of thissituation, as in the once-in-the-life cure of large structures By operatingclose to the vitrification curve(Chapter 4),any thermal excursion following

an adiabatic trajectory is arrested by vitrification.Figure 9.3 shows a sible trajectory where periodic increases in the external temperature arefollowed by adiabatic heatings, ending in the vitrification curve The cureproceeds until T reaches Tg1 and full cure of the part is achieved

pos-But vitrification may be a problem when the cure is started at roomtemperature and no external heat source is provided (the only source of heatgeneration is the polymerization reaction) This is the case of UV (ultra-violet radiation), EB (electron beam), or X-ray curing processes

In the cure with high-energy EB irradiation, polymerization proceedsvia a free-radical mechanism, where the initiating species are formed bybond cleavage of monomers or other components of the formulation EBcuring of epoxy monomers via a cationic mechanism using onium salts asinitiators(Chapter 2)is also possible In every case, the irradiation is per-formed at room temperature, but a fast temperature increase usually occursdue to the very high polymerization rate (Glauser et al., 1999)

F 9.2 Structure of diethylene glycol bis (allyl carbonate)

The EB cure of vinyl ester resins (VE) based on acrylic and methacrylicend groups was reported by Glauser et al., (1999) Both thin (2 mm thick-ness) and thick (20 mm diameter) specimens were cured using one to foursweeps of 2.5 Mrad each After the first dose, the maximum temperaturerecorded in thick specimens was Tmax ¼1508C for the acrylate-VE and Tmax

¼1108C for the methacrylate-VE Subsequent doses did not increase Tmaxbeyond these values The higher value obtained for the acrylate resin is due

to the larger values of both the heat of polymerization and the propagationrate Glass transition temperatures after the first dose, defined as the max-imum in tan d measured by dynamic-mechanical thermal analysis, were

Ta ¼1508C for the acrylate-VE and Ta ¼1568C for the methacrylate-VE.Subsequent doses increase these values to 1598C and 1778C, respectively.But complete cure could not be attained After the four doses, 7% and 15%

of residual unsaturations remained in the acrylate-VE and methacrylate-VE,respectively The temperature increase in thin specimens was significantlyless important, as indirectly shown by the resulting Ta values After fourdoses, Tawas equal to 1178C for the acrylate-VE and Ta ¼1418C for themethacrylate-VE Thin samples dissipated the heat generated in the poly-merization in a more efficient way, so that vitrification took place at lowertemperatures (and conversions)

It is surprising to realize how often the undercure produced by fication is completely ignored when performing the thermosetting polymer-ization by irradiation (UV, EB, X-ray) at room temperature As there is noexternal heat source, once vitrification sets in conversion may only increasethrough the continuation of reaction in the glassy state However, as wehave discussed in Chapter 5, polymerization in the glassy state is a self-retarded and very slow process

vitri-FIGURE9.3 Temperature vs conversion transformation diagram representing

a cure cycle along the vitrification curve

Vitrification also has a bearing on the microwave cure of ting polymers The use of microwave radiation has the potential advantage

thermoset-of significantly reducing cure times, because the polymerization begins atthe same time in all the specimen (it is not necessary to wait for thermalenergy to diffuse inside the sample) Energy transfer in microwave heatingoccurs by electrical dipolar coupling of the radiation to permanent dipolemoments in the polymer The rate of conversion of electrical energy intothermal energy is primarily determined by the dielectric loss factor of thematerial

Srinivasan et al (1997) analyzed the feasibility for microwave cure ofcyanate ester resins(Chapter 2).They observed that when the temperatureapproached 1608C, polymerization took place at a very fast rate, and theconsequent exothermic heat resulted in a tremendous acceleration of theheating rate The sharp temperature rise was very hard to control by eitherdetuning the cavity or by lowering the input power Such an uncontrolledprocess resulted in a charred product If microwave radiation was turned off

at an early stage, reactions were arrested by vitrification, resulting in apartially cured material As the magnitude of the dielectric loss peaks wasvery small, it was not possible to reheat the material by microwave radia-tion Therefore, vitrification has a significant influence on microwave pro-cessing of thermosetting polymers

An interesting method of eliminating the undercure caused by cation when using microwave radiation is to modify the formulation, includ-ing the use of polar thermoplastic that phase-separates during cure(Chapter8) The thermoplastic material can convert microwave energy into heat,which enables the thermosetting polymer to devitrify and reach full cure

vitrifi-An aspect that has not received enough attention is the influence ofpressure on the vitrification curve (Chapter 10) For some processes thatoperate at very high pressures there is a significant shift of the vitrificationcurve to lower temperatures: for example, in the processing of phenolicmolding compounds, where the polymerization may be arrested by vitrifica-tion at much lower temperatures than those predicted using Tgvs conver-sion values determined at ambient pressure

Most thermosetting materials are polymerized in heated molds Figure 9.4

shows a schematic diagram of the mold; L is the part thickness, which isassumed to be much less than the other two dimensions Therefore, thesystem may be modeled as a case of unidimensional heat transfer withsimultaneous heat generation

The thermal energy balance for this case may be written as

where r, cp, and kT, are, respectively, density, specific heat and thermalconductivity (in the z-direction if the material is anisotropic) These para-meters may vary with temperature (T) and conversion (x) Rc is the poly-merization rate in time
1 units, which may be expressed by a set of kineticequations or by a simple rate equation, Rc(x,T), for single-path reactions

(Chapter 5).The factor (

H) is the reaction heat evolved at full sion, which is expressed per unit mass of the formulation

conver-The rate at which conversion increases at any point is given by

Equation (9.2) simply states that the rate of heat accumulation in adifferential volume (first term) is the difference between the heat flow thatenters and leaves the volume element by thermal conduction (second term)plus the rate of heat generation by the polymerization reaction (third term)

To illustrate the system’s behavior it will be assumed that r, cp, kT, and(

H) are constant, and that the polymerization rate may be described by asimple second-order equation:

FIGURE9.4 Schematic diagram of the heated mold (Tw¼wall temperature,

T0¼initial temperature, L ¼ part thickness)

(Tw) remains constant during the cure, and no reaction occurs during themold-filling stage Therefore, the following conditions are stated for T(t,z)and x(t,z):

Equation (9.2) may be rewritten in terms of the thermal diffusivity,

aT¼kT=rcp, and the adiabatic temperature rise (Chapters 4 and 5),

Tad¼ð

HÞ=cp,

For generalization purposes, the system of differential equations withthe initial and boundary conditions may be conveniently rewritten in terms

of dimensionless variables: z* ¼ z=L; t* ¼ A expð
E=RT0Þt; T* ¼ ðT
T0Þ=

Tad Substituting in Eqs (9.3) to (9.9) leads to

¼W ) When W ! 0, the material behaves as a thermal insulator and

an adiabatic cure takes place Dividing Eq (9.10) with W1 ¼0 by Eq (9.11),and integrating, leads to

‘‘large’’ thickness to an adiabatic behavior But how small is ‘‘small’’ andhow large is ‘‘large’’ depends on the values of the four dimensionless groupsthat determine the system’s behavior

The parameter W2 is called the Arrhenius number It varies fromvalues of about 15 for low-activation energy systems (e.g., thermosettingpolyurethanes), to values of about 40 for high-activation energy systems(e.g., phenolic molding compounds)

The parameter W3depends strongly on the presence of fillers, fibers, orany inert modifier in the formulation For unfilled thermosetting polymerswith high values of
Tad, W3may take values of about 1–2 For formula-tions including a large fraction of fillers and moderate values of
Tad, W3may increase to between 4 and 8

Finally, W4depends on the value selected for the wall temperature,which is usually determined by the need to reduce the molding time as much

as possible without leading to thermal degradation of the part Values of W4are usually in the range of 0–0.7 Low values are used for systems that reactvery fast at the mixing temperature (T0), such as formulations used in RIMapplications High values correspond to the usual case, where the polymer-ization is activated by heat transfer from the wall

Depending on the shape of temperature vs conversion trajectories,vitrification may take place at particular locations in the part If this hap-pens, the constitutive equations describing the kinetics must include thediffusional resistance that characterizes the sharp decrease in the polymer-ization rate when entering the vitrification region In particular, vitrificationcan occur at the wall if Tw < Tg1 In the examples that illustrate thissection, it will be assumed that vitrification does not take place, but in thefollowing section the influence of vitrification on the cure in a heated moldwill be discussed

Differential Eqs (9.10) and (9.11), with initial and boundary tions (9.12) and (9.13), may be numerically solved for different sets of values

condi-of the four dimensionless parameters, W1–W4 (Williams et al., 1985) Toillustrate the evolution of temperature and conversion profiles during thecure, values of W2–W4 will be kept constant and W1 will be varied tosimulate the influence of the part thickness The particular case of W2

¼40, W3 ¼1.5, and W4 ¼0.125 will be analyzed This represents a processcharacterized by high values of both the activation energy and the adiabatictemperature rise

Figure 9.5shows the evolution of temperature and conversion profilesfor W1¼0.01 (a relatively thick part) As a result of the heat flow from thewall and the high value of the activation energy, the cure takes place first inthe proximity of the wall, followed by the material located at the core But

as the material close to the wall is kept at Tw, it cures at a relatively slow rateand determines the molding time (cycle time) The maximum temperature isattained at an intermediate position and is slightly higher than the adiabaticvalue, Tmax > T0þ
Tad This results from the extra heating arising fromthe presence of a boundary at Tw The material located at the core under-goes a strictly adiabatic cure, leading to a maximum temperature of T0þ

Tad

Figure 9.6shows the evolution of temperature and conversion profileswhen the specimen thickness is reduced; i.e., for W1 ¼0.1 Again, thematerial located close to the wall polymerizes at a fast rate, originatingthermal and conversion fronts that travel to the core and to the wall Themaximum temperature is obtained at an intermediate location and is higherthan that attained in the previous case: T0þ
Tad< Tmax< Twþ
Tad.When the thickness is further reduced, giving W1 ¼1, a similar situa-tion is observed(Fig 9.7).But now the maximum temperature takes place atthe core and its value is Tmax> Twþ
Tad This is because the cure of thismaterial is not directly affected by the wall at Twbut by the high-tempera-ture moving front that travels at a fast rate to the core of the part.Decreasing the part thickness to obtain W1 ¼10 produces a dramaticchange in the way in which the part cures, as observed in Fig 9.8 Thematerial located at the core cures first, generating conversion and tempera-ture fronts advancing at a very fast rate to the wall, which acts as a heat sink(notice the short period of time in which most of the material is cured) Themaximum temperature is observed at an intermediate position and is lowerthan in the previous case: T0þ
Tad< Tmax < Twþ
Tad

For very thin parts (W1 ¼100), the cure proceeds almost isothermally

at the wall temperature(Fig 9.9) A slight temperature increase is rapidlydissipated to the wall, and conversion profiles are almost uniform in thewhole specimen

Now, the effect of varying W2, W3to W4will be discussed.Figure 9.10

shows the maximum dimensionless temperature that is attained during thecure as a function of W1, and different sets of W2, W3, and W4 The thick-ness increases to the left (W1 L
2) Cases 4 and 5 correspond to poly-merization kinetics exhibiting high values of the activation energy (as in theexample illustrated by Figs 9.5–9.9) For these cases, Tmax exceeds T0 þ

Tad significantly However, for systems characterized by a low value ofthe activation energy (cases 1 and 2), the maximum temperature rise varies

FIGURE9.5 Temperature (a)and conversion (b)profiles for W1¼0.01; (1)t*=0.0312, (2)t* ¼ 0.0417, (3)t* ¼ 0.0432, and (4)t* ¼ 0.0434 (Reprinted fromWilliams et al., 1985 by courtesy of Marcel Dekker, Inc.)

smoothly from the adiabatic limit (for a large thickness) to the isothermallimit (for thin specimens) This is a typical behavior for the cure of poly-urethane formulations.

When applying the mathematical model to analyze the cure of a ticular system, one has to be aware of the following issues:

par-1 The quality of the available kinetic equation to fit experimentaldata in a wide range of isothermal and scanning rate conditions(the numerical solution exhibits a very high parametric sensitivity

on the values of the activation energies)

FIGURE 9.6 Temperature (a)and conversion (b)profiles for W1¼0.1; (1)t* ¼ 0.0198, (2)t* ¼ 0.0228, (3)t* ¼ 0.0284, and (4)t* ¼ 0.0365 (Reprintedfrom Williams et al., 1985 by courtesy of Marcel Dekker Inc.)

2 The actual boundary condition at the wall (it is very difficult toget a true isothermal condition at the wall; a better boundarycondition arises by stating the continuity of the heat flux at thewall) (Gorovaya and Korotkov, 1996).

3 The possibility of vitrifying part of the material during the curecycle and the availability of the vitrification curve and of consti-tutive equations to represent the kinetics in the glassy state.With these concepts in mind, good predictions of cure cycles may beachieved

FIGURE 9.7 Temperature (a)and conversion (b)profiles for W1¼1; (1)t* ¼ 0.0179, (2)t* ¼ 0.0186, (3)t* ¼ 0.0202, and (4)t* ¼ 0.0216 (Reprintedfrom Williams et al., 1985 by courtesy of Marcel Dekker Inc.)

9.5 AUTOCLAVE MOLDING OF GRAPHITE/EPOXY

COMPOSITES

The autoclave molding of graphite/epoxy composites based on tetraglycidyl4,40-diaminodiphenylmethane (TGDDM), crosslinked with 4,40-diaminodi-phenylsulfone (DDS), is analyzed in this section (Williams et al., 1990)

Figure 9.11 shows a scheme of the mold configuration with the lay-up ofpreimpregnated plies (prepregs) placed between a heated plaque and thebleeder cloth

A typical cure cycle is shown inFig 9.12.Somewhere in the plateau at1358C the autoclave pressure is applied This step provokes the elimination

of resin, which is absorbed by the bleeder cloth, and the increase in the fiber

FIGURE 9.8 Temperature (a)and conversion (b)profiles for W1¼10; (1)t* ¼ 0.01251, (2)t* ¼ 0.01255, (3)t* ¼ 0.01268, and (4)t* ¼ 0.01291.(Reprinted from Williams et al., 1985 by courtesy of Marcel Dekker Inc.)

volume fraction from its initial value in the prepreg (close to 50%) to itsfinal value in the composite (close to 65%) The slow increase of the walltemperature after the plateau favors the partial dissipation of the reactionheat The slow cooling at the end of cure enables the partial relaxation ofresidual stresses In this case, the quality of the molded part is by far moreimportant than the length of the cure cycle.

The evolution of temperature and conversion profiles in the part may

be simulated by solving Eqs (9.2) and (9.3), with the following initial andboundary conditions:

t ¼ 0; x ¼ 0; T ¼ 298K; Vf ¼0:50

FIGURE 9.9 Temperature (a)and conversion (b)profiles for W1¼100; (1)t* ¼ 0.0019, (2)t* ¼ 0.0069, (3)t* ¼ 0.0257, and (4)t* ¼ 0.1043 (Reprintedfrom Williams et al., 1985 by courtesy of Marcel Dekker Inc.)