688
Ind. Eng. Chem. Res. 1995,34, 688-698
Buildup and Optimization of a Homogeneous Microwave Curing Process for Epoxy-Glass Composites Lhoussain Outifa, Henri Jullien,* Claude Mor& and Michel Delmotte CNRS, Organisation MolCculaire et MacromolCculaire, BP 28, F 94320 Thiais, France
To obtain homogeneously microwave cured epoxy-glass composite samples greater than the wavelength of radiation, physical considerations and mathematical calculations of the wave propagation in dielectric filled waveguides show that a single-mode travelling wave is required. According to this conclusion, a process is developed, using matched tapered transitions at airmaterial incoming and material-air outgoing interfaces, to reduce reflections and nonuniformities. Mould materials are selected with a permittivity less than that of the material to be cured. Experiments show that satisfactorily homogeneously cured samples can be obtained through this way. Introduction During the past 20-30 years, many scientific and industrial papers have appeared dealing with the use of microwave energy applied to organic chemical reactions reviewed, for instance, by Abramovitch, 1991, or Mingos and Baghurst, 1991, for organic synthesis, and by Mijovic and Wijaya, 1990, for polymerizations. In fact, because the energy is directly supplied inside materials, a microwave process offers the advantages of faster and more efficient heating. However, most of the papers are concerned with laboratory studies, applied to small samples, the size of which is generally smaller than the 2.45 GHz microwave half-wavelength (in free air, 6.1 cm; in a WR340 rectangular monomode standard waveguide, 8.7 cm), so that the electric field distribution in samples can be considered as uniform (Jullien and Petit, 1992). In many other cases reagents are either liquids or solutions contained in either flasks or balloons or sealed test tubes, the size of which is larger or of the order of magnitude of the wavelength, and put into a multimode oven (often an oven for domestic use), so that the electric field distribution is no more homogeneous; but a natural or forced agitation makes the temperature distribution somewhat homogeneous. The apparent simplicity of this approach often leads to misleading results due to the complexity of the electric field distribution inside the oven. Although multimode microwave ovens are largely used in industrial systems, many microwave processes require, because of the nature of the material to be transformed, special designs of applicators which call for theoretical treatments. An important field of application of this kind of process is the cross-linking reaction of thermosetting composite materials. Starting from a prepreg material, an object is preformed in a mould; then a thermal curing process has to be performed, with the application of pressure. For instance, a prepreg material made of an epoxy resin and a glass fiber cloth is inserted into a metallic mould which is heated through a conventional way (hot fluid, superheated water vapour, electric resistance, etc.) under a pressure of several bars. Additionally, such a composite material is a dielectric medium, which can also be heated by dielectric relaxation and therefore by microwaves as a transfer agent of the electric power. But an important drawback is the creation of standing waves inside the sample, due to
* To whom correspondence should be addressed. Present address: LM3, ENSAM, 151 boulevard de l’HBpita1, F 75013 Paris, France. 0888-588519512634-0688$09.00/0
wave reflections at the incoming air-material and outgoing material-air interfaces, so that the standing electric field distribution creates a heterogeneous temperature field, and therefore a heterogeneous structure and stress in cured samples. To prevent this situation, three solutions could be proposed. First, the sample, lying on a conveying belt for instance, could be moved in the electric field, so that every point in material could “see” every electric field configuration; but this solution is obviously inadequate for epoxy materials to be cured under pressure. A second solution would be to insert the sample into a monomode waveguide closed by a short-circuit generating a standing wave system and moving alternately in order to obtain the scanning of the sample by the standing wave system: this solution was found ineffective, because of wave reflections inside the sample itself, generating a stationary standing wave system, and because the power dissipated in the sample depends on the distance between the outgoing interface and the short circuit (Outifa et al., 1991). The third and consequently the best solution is to use a setup allowing the sample to be exposed to a monomode travelling wave. As the treatment of these materials must be performed under pressure, the process is based on the use of an applicator filled with dielectrics (mould). In such a microwave applicator, the electric field configuration must be known in every point at every time and should be controlled, in order to be as homogeneous as possible within the material, providing the homogeneity of cure. In fact, when the energy is carried by several propagation modes (see below), the electric field distribution within the applicator is difficult to control and the resulting microwave curing is clearly nonuniform (Manring and Asmussen, 19921, especially for materials with low thermal conductivity such as epoxy-glass composites. Consequently, only a monomode applicator allows a homogeneous electric field distribution to be obtained in a large volume, providing homogeneous microwave curing. The present paper deals with a homogeneous microwave curing process for epoxy-glass composites, based on the use of a travelling wave under the single fundamental mode TEol, inside a standard rectangular waveguide at 2.45 GHz.
Fundamentals of the Microwave Processing Propagation of Microwaves in Waveguides. The propagation of electromagnetic energy in waveguides is described by Maxwell’s equations: 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34,No. 2, 1995 689 rot E = -p dWdt
(1)
rot H = E dE/dt
(2)
The resolution of these equations shows that the energy is transmitted through modes of propagation. Each mode is characterized by a distinctive field configuration, its propagation wavelength (Ag), and cutoff frequency These two parameters are functions of cross-sectionaldimensions of the guide, the permittivity of the load materials and of the frequency of the incident wave ($0). The mode of which the cutoff frequency is the lowest is called the dominant or the fundamental mode. The next lowest is the first higher mode, etc. The modes by which the energy is carried are determined according to the condition of the propagation:
xt
vc).
f, < fo:
f, > fo:
the mode can exist in the waveguide
in a waveguide in fundamental propagation mode TEol.
L
the mode cannot exist in the waveguide
The dominant mode in a standard rectangular waveguide is the TEol mode, indicating that the wave is of the transverse electric type, and there is no variation of transverse electric along the x axis, and there is a single half-sinusoid variation along the y axis with its maximum in the middle of the guide (at y = a/2). This distribution is shown in Figure 1 for an air-filled rectangular waveguide. Microwave Heating. Microwave heating involves the conversion of electromagneticenergy into heat. The fundamental property of nonmagnetic materials for interaction between microwaves and organic materials is the complex permittivity E*. The real part E’ is related to the energy stored in the material. The imaginary part is the loss factor E”, to which the energy dissipated as heat in the material is related. The volumetric density of absorbed electromagnetic power P (W/m3)in a material is dependent on the frequencyfo, the material loss factor E” and the squared electric field strength Eint inside the material as described in the following equation (see also eq 7):
P = JGfoe0~”lE,I
a
Figure 1. Transverse distribution of the electric field intensity
(3)
Thermosetting polymers have polar groups to interact with electromagnetic fields and exhibit dielectric relaxation at microwave frequencies. So that these materials can be heated by microwaves and irreversibly converted from fusible materials to infusible, rigid, and crosslinked solids. Physical Background. The complete description of the experimental setup including calculations is to be given elsewhere (Outifa et al., in preparation). Nevertheless it is necessary to present here the principal features which make the process comprehensive. Matched Transitions. As said in the Introduction, when an electromagnetic wave penetrates from air into a dielectric substance, a wave reflection takes place at the incoming interface. Considering an infinite medium, the wave continues travelling in the dielectric, according to conditions related with the complex dielectric constant E* of the substance. To prevent a partial reflection of the wave at the interface from air to dielectric filled waveguide, it is necessary to insert a matched transition between air and dielectric.
Figure 2. Tapered transition between two dielectrics GI and G2.
A transition between two uniform waveguides is made of a nonuniform waveguide section (Figure 2). To match this transition means that the wave reflection is 0, i.e., the wave energy is totally transmitted from the empty part to the dielectric filled part through the transition section. In terms of electric impedance, it means that the impedance continuously and smoothly varies from the guide G1 (characteristic impedance 21)to the guide G2 (characteristic impedance 22). Without any matching transition (L = 0 in Figure 2) the reflection coefficient r is given by (4)
Inside the uniform waveguides G1 and G2 the propagation laws are known, while in the transition part the mathematical resolution of the propagation equations is not simple, because of the variations of dielectric properties in the propagation axis (nonuniform waveguide) and because of the coupling of different possible propagation modes. According to Hord (1966), the matching by means of linear tapers can be obtained through the three ways shown in Figure 3. The determinant factor is the reflection coefficient at the incoming cross section of the applicator: r(0) a t z = 0. Assuming the coupling between the fundamental mode and upper modes is negligible, i.e., the fundamental mode is the only mode to be considered (first-orderapproximation according to Hord), the problem can be solved accordingto the theory of nonuniform lines described by the telegraphists’ equations (Schelkunof, 1952). For an unlossy dielectric, and assuming that
i.e., the taper slope is weak, the input reflection coefficient is given (Moreno, 1989) by
For every kind of taper selected, and with the indicated conditions (E’ = 4, frequency 8.2 GHz), he gives the
690 Ind. Eng. Chem. Res., Vol. 34,No. 2, 1995 Cut-off freauencies
a Standard waveguide
6
Y
1ba ==4 3 mmmm
4 0420 13
2 45 2
11
TE02 10
TEOl ,111,
Figure 3. Three different types of tapered transitions between empty and filled sections in waveguide: linear unsymmetrical continuous taper (UCT); linear symmetrical center continuous taper (SCCT); linear symmetrical side continuous taper (SSCT); (from Hord, 1966).
1
4
3
5
Permittivity (E’ )
Figure 5. Determination of the propagation modes which can exist in a filled Wl3340 waveguide as a function of the dielectric permittivity. X
-4oi
2
t
d
I
n f, = 8.2GHz E, =
4.0
First order approximation
0
.5
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
LI a Figure 4. Variation of the reflection coefficient of a dielectric tapered transition Ir(0)l(length L, guide width a ) as a function of Llu (from Hord, 1966).
variations of Ir(0)las a function of the taper angle (in fact the ratio Lla, a being the size of the waveguide larger side) as shown in Figure 4 (the numerical values for 2.45 GHz are a bit higher, but not very different). Three important remarks become obvious: 1. For higher values of the permittivity for dielectric, matching is more difficult since the reflection coefficientincreases with E’. 2. The variation of r(0)shows oscillations due to the exponential factor in eq 2, as exhibited by the SSCT line. 3. The SCCT gives relatively higher reflections, due to the fact that the double slope begins in the middle of the waveguide, where the electric field intensity is a maximum; nevertheless, this particularity of the SCCT line helps the stabilization of the fundamental mode, so that this one is easily maintained from the air-filled waveguide to the dielectric filled waveguide. In conclusion, we can say that the matching by means of linear tapers provides the transmission of almost all of the input energy if using a convenient value for the taper angle. As our main objective is to maintain the dominant mode in the applicator (monomodeapplicator, see below: selection of the fundamental mode), the SSCT dielectric transition is used in the process for matching as well as the incoming and outgoing interfaces of the applicator. $
Figure 6. Cross section of the applicator loaded with two dielectrics.
Buildup of the Process Homogeneously Filled Waveguide. However, the fundamental mode can be conserved only in the dielectric filled part when the permittivity E’ is not too high. Considering a rectangular 2.45 GHz standard waveguide filled with a dielectric substance, the permittivity of which is E’, the cutoff frequency f’, of a selected mode is given by
in which f, is the cutoff frequency of the mode in an airfilled waveguide. Figure 5 gives the variation of the cutoff frequencies of several propagation modes versus E’ in a 2.45 GHz standard waveguide WR340. According to the conditions of the wave propagation, a mode can exist only in the guide when its cutoff frequency is lower than 2.45 GHz. It appears that the fundamental mode can only be conserved in a dielectrically filled waveguide when the permittivity E’ is lower than 2. When E’ is higher than 2, the modes TElo, TEo2, and TEll are successively appearing. In fact hybrid modes combiningthe possible modes are experimentally observed, with irregular distributions of the electric field and finally of temperature inside the material being cured. Three-Layer Dielectric System. The material to be cured is lying in a mould material, the dielectric constant of which is generally different. Thus we must
Ind. Eng. Chem. Res., Vol. 34,No. 2, 1995 691
a
d2E,(r)ldy2
Maxwell's Equations
+ (Erik: - P2)E,(r)= 0
for parts I and 111in Figure 6
verified by E and H
I
Resolution ( sin or sh form)
+
(9)
for part I1 in Figure 6
Continuity of E and H at intetfaces between dielectrics
I
1 v
25
expressions in which ko is the propagation constant of the wave in the empty waveguide. Following many authors (as for instance Chambers, 1953, Vartanian et al., 1958, Eberhardt, 1967, ElShandwily and El-Dinary, 19721, we introduce the transverse propagation constants parameters p and q (p in I and 111, q in 11), determined by the following equations:
(pld)2= d l k ;
- P2
Computer resolution
p is a positive real number, 0, or an imaginary number, while q always is a real positive number; pld and 2qlc are the standardized constant of transversal propagation in parts I and I11 or 11, respectively. The solution which we propose for the differential equations is detailed elsewhere (Outifa, 1992). It leads to the following expressions:
Ex licit e ressions d:end% fields in every area of the applicator L
(tanp
e -)=Ocla
cla + eq 1- cla
q 1 - cla
(13)
that is to say:
now examine methods to maintain the fundamental mode propagating inside a three-layer system, as shown in Figure 6. This figure represents the cross section of a waveguide WR340 filled with two dielectrics, E'I and ~ ' 2 ,in three layers (E'Z > ~ ' 1 ) . The width of the central part (containing the material t o be cured) being c and the total interior width of the waveguide being a, we must find the conditions for ~ ' 1 ~, ' 2 , and cla to prevent the propagation of upper order modes in the guide, so that the whole microwave energy is travelling with the fundamental mode TEol. As done for a waveguide homogeneously filled with a lone dielectric, to know whether a mode can travel in the guide is necessary to determine its cutoff frequency, in order to compare it with the frequency fo of the microwave beam (2.45 GHz). Maxwell's equations describe the spatial distribution of the electric field inside a loaded waveguide. As functions of z and t, the variations of the electric and magnetic fields are expressed by formulas in expvwt yz), leading t o the differential equation governing Ex: d2EJdy2
+ (w2ep+ y2)E, = 0
(7)
The whole expression for E, is
Considering only the real part E' of the complex dielectric constant E*, E&) is given by the expressions
for a TE,, mode with n even
tanp= p
cla
tanq
(15)
1 - c/a q
for a TE,, mode with n odd
1
This final transcendental equation gives the wavelengLh in guide A, as a function of 6'1, E'Z, and cla. It is solved by means of Turbo-Pascal computer code, the chart of which is presented in Figure 7. The wavelength in guide A, being then known, the values ofp and q can be computed, and also the values of the electric and magnetic field intensity. Selection of the Fundamental Mode To obtain only one possible energy distribution inside the waveguide, it is necessary to use the single fundamental mode TEol, for if several modes could simultaneously propagate in the guide, the electric field distribution would become a complex combination of the modes, so that the energy distribution would be uncontrollable. Now we are able t o determine the conditions for 6'1, 6'2, and cla (giving c ) to prevent other modes than the
692 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 Elp
=4
E'*
= 1.5
4.5
0.0
0.2
0.4
0.6
0.8
1.5 0.0
1.0
cia Figure 8. Cutoff frequency versus cia for the propagation modes TEol, TEo2, and TEo3 in a three layer system, with 6'1 = 1.5 and €?2 = 4.
fundamental mode TEol to propagate in the waveguide; that is t o say we have now to determine the cutoff frequency of every mode and to compare it with the microwave frequency, 2.45 GHz. A propagation mode is in cutoff conditions when the wavelength in guide & becomes infinite, so that /3 = 0. Equations 11 and 12 become
I
,
0.2
,
I
0.4
0.6
I
I
I
0.8
I
1.0
cla
Figure 9. Cutoff frequency versus clu and E'I for the first upper propagation mode TEo2, with 6'2 = 4.
(c/a) crit
E'p =
4
0.40 \
I
0.20
(17) 0.10
( 2 q l ~=) ~ d2k:
(18)
in which k, is the propagation constant in cutoff conditions. For eqs 14 and 15 it follows
0.0 E'1
Figure 10. Variation of (cla)c,.jtas a function of 6'1, with 6'2 = 4.
TEO2mode
TE,, or TE,, mode The cutoff wavelengths (or frequencies) of the fundamental mode TEol and of the next modes TEoz and TE03 are obtained by the numerical resolution of expressions 19 and 20 by means of another Turbo-Pascal computer code. Figure 8 shows the variation of the cutoff frequencies for three propagation modes, as a function of the dimensional ratio cla, in a standard 2.45 GHz waveguide filled with two dielectrics, the permittivity of which are 1.5 (41, external parts I and I11 in Figure 6) and 4 (6'2, central part 11). These values are realistic, related to the substances used and hereafter presented in the experimental part. In such a case, the fundamental mode TEol can always travel in the filled waveguide, the TE03 mode will never propagate, while the TEo2 mode can propagate when the ratio cla becomes higher than a critical value obtained as the TEoz curve intersects the horizontal line 2.45 GHz, i.e., cla = 0.32. That is t o say it is possible to obtain the single fundamental mode propagating in such a system with a value of the cla ratio up to 0.32. In fact 6'2 will always be about 4, the usual value for epoxy-glass composites and also for mould materials in the central part. Figure 9 exhibits the variation of the cutoff frequency for the first upper mode TEoz as a
function of the ratio cla and for several values of permittivity 6'1 for the external dielectric. This diagram gives, for each value of 6'1, the critical value of cla, (cl fit, over which the TEoz mode can travel in the waveguide. Figure 10 shows the variation of (clu),fitas a function of 6'1, with E'Z = 4. The curve is a border separating two areas: the inner area in which the lone fundamental mode TED1 can propagate, the outer area in which the both modes TEol and TEoz can simultaneously propagate in the loaded waveguide. It follows that the permittivity 6'1 of the external dielectric must be smaller than 1.5. This value is a good compromise: (i)When 1 < 6'1 < 1.5 the critical value for cla decreases from 0.37 to 0.31 only: the thickness of the central part does not decrease drastically. (ii) When 6'1 > 1.5 the variation with 6'1 of (cla),fiit is very fast; a slight error in the experimental determination of 6'1 can induce the propagation conditions of the TEoz mode or drastically decreases the thickness of the central part of the waveguide, containing the composite to be cured, in which the lone fundamental mode must be obtained. Electric Field Focusing in the Central Part of the Applicator. Using the wave propagation equations determined above and taking into account the boundary conditions, we can describe the transversal variations of the electric field in waveguide. Considering the same values for the permittivity and for the width of the central part containing the material to be cured (6'2 = 4, cla = 0.321, Figure 11exhibits the transversal profile of the electric field intensity in a filled waveguide. The three curves are related to three
Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 693 1.o
normalized electric field E(y)IE,
0.81
A ,
E'*
=4
I
0.6
of diglycidyl ether of bisphenol-A (DGEBA, Dow Chemical DER 332) with either dicyanodiamide (DDA)or ( 3 3 dimethyl-4,4' diaminodicyclohexy1)methane (3DCM, BASF Laromin C 260) as a curing agent. The impregnation of glass fibers is made by the filament winding technique, providing plates of 25 x 3.3 x 0.3 cm, with an average glass fiber content of 70 w t %.
YIa
Figure 11. Transverse distribution of the electric field intensity in a three-layer system, as functions of the permittivity in the external dielectric (6'2 = 4;c/u = 0.27; 6'1 = 1.1,2.5, or 4).
different values of 6'1 for the external parts I and 111: 1.1,2.5, or 4. It becomes clear that the highest concentration of energy in the central part is obtained when the value of 6'1 is as low as possible. In conclusion, we can say that the selection of the fundamental propagation mode and the concentration of the energy in the material to be cured have the same requirements, providing the optimization of the process: to put the dielectric material t o be cured in the central part of the waveguide and to fill the external parts with dielectrics with very low permittivity. E'~=
Experimental Section General Features. We consider now a finite medium, with incoming and outgoing interfaces. The wave, which is assumed t o be incompletely absorbed by the dielectric, can partially reflect waves a t all of the interfaces, creating a standing wave, so that energy is spatially inhomogeneously transferred to the dielectric substance. In a standard rectangular waveguide (WR340) this wave is uniformly propagating according to the fundamental mode TEol. Inserting the dielectric substance to be cured into an equivalent dielectric ("mould"), the problem is t o maintain the single fundamental mode travelling wave in the sample. To prevent reflections, matched tapered transitions are added both at the incoming and outgoing interfaces. It follows that the incoming wave can travel under the fundamental mode all along the setup, in air, then in dielectrics, in air again, to be finally absorbed in a dummy water load. Figure 12 shows a general and simplified scheme of the setup. The 2.45 GHz microwave energy supplied by the generator (3 kW) travels through an empty WR340 standard waveguide with the fundamental mode TEol. In the microwave applicator, the sample to be cured, 3, is inserted between two layers of a similar cured dielectric substance, 2, so that 2 and 3 constitute part I1 in Figure 6. This central dielectric is inserted between two layers of an external dielectric 1, so that in this section the waveguide is filled with dielectric materials. Parts 4 are matched transitions, which are t o be precisely described hereafter. Going out of this microwave applicator, the energy which is not absorbed travels through an empty waveguide to a dummy water load, in order to be absorbed without any reflection. Composite To Be Cured. The composite material to be cured is made of an epoxy resin reinforced with glass fibers. The epoxy resin is a stoichiometricmixture
In Figure 13 are shown the variations of the dielectric constants of the DGEBADDA-based composite, as a function of temperature during cure, measured by means of a microwave method (Ollivon, 1985; Ollivon et al, 1988). The average value of the permittivity of the composite is about 4. Mould Materials. The dielectric material for the part 2 in Figure 12 must satisfy t o four conditions: (i) permittivity about 4; (ii) very good resistance to heat up t o 250 "C, because the curing temperature can rise up to 200 "C; (iii) good mechanical resistance, for the process is performed under pressure (10 bars); (iv)very small absorption factor E". The most appropriate material is a silicone-glass composite called Silirite Silicone. Figure 14 shows the temperature dependence of the dielectric constants of this material. At 2.45 GHz and 25 "C, the dielectric constants are E' = 3.7 and E" = 0.03 and are almost independent of temperature. Moreover, the mechanical properties and resistance to heat are high (20 000 h at 230 "C; UDD-FIM, Delle, France). As has been demonstrated in the buildup section, the external dielectric material 1must be with a dielectric constant as low as possible, so that the microwave energy is focused into the central part. A convenient solution is provided by a honeycomb polyimide material (E' = 1.1,E" = 0) which is provided by Hexcel (HRH). Matched Transitions. To maintain the travelling wave under fundamental mode TED1 from the waveguide into the applicator, the above-described operating part is inserted between two matched transitions. According to the considerations and the mathematical calculations given in the physical background section, these transitions are symmetrical center continuously tapered (SCCT) transitions, made of Silirite Silicone, as described in Figure 15. The external dielectric material, HRH honeycomb, being with very low dielectric constants, it follows that the transitions cover only the central part of the guide, including mould material (Silirite) and the piece to be cured. The length of these transitions is 110 mm. Operating Conditions. The mechanical pressure applied to the sample was 10 bars. The microwave power supplied by the generator was settled to 400 W for 20 min. In fact, relatively to the small size of samples, only 56 W were absorbed by the samples, as shown by a balance calculated from the temperaturehime data provided by the results below. Temperature Measurements. Temperature measurements were made by means of a four-way Luxtron Fluoroptic temperature probe. The probes were inserted at four points into the curing material, protected by quartz tubes, along the median line of the plates.
Results Qualitative Observations. Figure 16 exhibits two epoxy-glass samples cured according to a conventional monomode microwave process, without any matched tapered transition. Overheated parts are regularly distributed all along samples, with steps corresponding
694 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995
Water 4
2.45 GHz Generator
Waveguide
Applicator Dummy water load
1 , 2 : mould dielectrics
3 : composite to be cured
4: matched transitions
Figure 12. Experimental setup. E' 51
4 /E/==-
3
E" r 2.0
-
1I 0
11.0
10.8
50
100
150
200
Temperature ("C) Figure 13. Temperature variations of the dielectric constants c' and c" of a DGEBA/DDA/glass fiber system during curing with 2.45 GHz microwaves. E"
E'
r 2.0
51 4
3
2
1
1
1
!
E'
1::: 1.0
1 0
50
100
150
E!m
0.4 0.2
,
0.0
200
Temperature ("C) Figure 14. Temperature variations of the dielectric constants E' and c" of the Silirite-Silicone a t 2.45 GHz.
to the half-wavelength in guide of a standing wave system. In Figure 17 are shown three replicas, obtained on temperature-sensitive papers, cured according to different microwave processes (but with the same treatment time). The first one (up) is the same as described in Figure 16, without tapered transition; the second one (middle) was cured with nonmatched transitions: a hybrid mode of wave propagation provided an irregular distribution of curing; the third one (down) exhibits a homogeneous thermal treatment obtained by means of matched tapered transitions designed as described above. Thus it has qualitatively become clear that a microwave process generally provides a nonhomogeneous thermal treatment of long epoxy-based composite samples, unless a conveniently designed matched transition system makes it homogeneous. Moreover because the treatment durations were identical, it is obvious that
thermal homogeneity is obtained by using matched transitions and not because of heat diffision in samples. Temperature-Time Variations. On Figure 18 are represented the temperature-time variations in four points along the longitudinal axis of a DGEBA/DDA/ glass fiber composite sample; the abscissas of these points were 5, 10, 18, and 21 cm, respectively. Figure 19 shows the time variation of the temperature difference between the first and the last probe, giving an idea of the longitudinal temperature gradient. These two diagrams can be understood with the aid of Figure 13, giving the temperature variation of the dielectric constants in the composite. At the beginning of cure and because of the highenergy absorption due to a high (and increasing) E" value, the head of the piece was the seat of an important degradation of energy into heat, so that the temperature increased faster than further in the sample (the reaction exothermy appeared after some minutes and was also taken into account); the longitudinal gradient largely increased in Figure 19. As the chemical reaction progresses, the value of c" in the head of the sample decreased, this part of the sample became transparent to microwaves, so that energy transfer and temperature increased in the second part of the sample: the temperature distribution became uniform in the whole sample, and the temperature gradient decreased to 0. That is to say, the temperature distribution in the sample was heterogeneous at the beginning of cure and became homogeneous at the end of cure. Similar variations of temperature are observed in every experiment of microwave elaboration of epoxyglass composite samples: first an increase of temperature before the macromolecular network starts t o crosslink, then a faster increase of temperature related to the exothermy of the epoxyamine reaction, and at last a temperature plateau as dielectric loss heat production is balanced by heat loss due t o diffusion and convection. Figures 20 and 21 show such temperature-time variations for large samples (500 x 100 x 3 mm and 500 x 100 x 10 mm, respectively) with a double microwave energy input: every extremity of samples is alternately an incoming and an outgoing interface. On Figure 20 every point of the whole sample follows the same temperature-time law, for the wave attenuation is weak, because of the small thickness of the sample. In Figure 21 are shown the temperature-time variations in a thicker composite material: consequently the
Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 695
waveguide 0)
(E;=%', &;
oo2
-..- z=2lcm
- z=l8cm 0
4
8
12
16
20
Time (min)
Figure 18. Temperature-time variations in four points along the longitudinal axis of a DGEBA/DDA/glass fiber composite sample during microwave curing.
of the standing waves would generate cold and hot points in material. The homogeneous look of the third temperature-sensitive card in Figure 17 and the homogeneous distribution of Tgshow that a travelling wave is obtained all along the sample, by means of convenient matched taper transitions, at both the incoming and outgoing interfaces. The second requirement is to maintain the fundamental mode TEol travelling along the applicator and along the curing sample and to prevent the creation of higher order &odes. This is obtained both by the geometric shape of transitions and by means of a convenient selection of the dielectric characteristics for mould materials. However, if the permittivity of materials to be cured is about 4, the permittivity of mould materials must be less than this value, limiting the choice of mould materials. Moreover, if the electric field distribution is an essential factor in the process, thermal considerations
0
1
2
3
4
5
6
7
8
9
10
Time (min)
Figure 19. Time variation of the temperature difference between the first and the last probe, giving an idea of the longitudinal temperature gradient during the experiment of Figure 16.
must also be taken into account. A whole description of the balance of energy and heat should be done, related to many factors: (i) The heat sources due to both the microwave energy converted into heat and to the chemical reaction exothermy; (ii)the variation in time of the heat source intensity due to 6’’ variations as functions of both temperature and chemical structure; (iii) the wave attenuation due to dielectric loss in mould materials and in curing materials, decreasing energy dissipation and thus the heat source intensity along samples; (iv) the heat transfers outside materials and applicator (thermal conduction and convection)and inside materials (anisotropic transfers due to glass fiber orientation, Outifa et al, 1993). Therefore, the homogeneity of cure and the optimization of the process require a better appreciation of the heat source evolution and heat transfer both in composite materials itself and in the applicator, including mould materials, matched transitions, and waveguide.
Ind. Eng. Chem. Res., Vol. 34, No. 2,1995 697 de YEnergie (ADEME), Peugeot SA, Renault SA, and Electricit6 de France (EDF). Special thanks to Dr. J. Galy and Dr. C. Jordan (INSA, Lyon, France) for DSC measurements, and to Dr. D. Lewis (IBMT. J. Watson Research Center, Yorktown Heights, NY)for his help in the revision of the manuscript.
2*200w 3*100*500mm 4 probes on longitudinal axis
r
20 1 250
-__.,
____---
. ...._.....,..........
_,,i)
f/
.I..
,,
d)
-20"
front 60mm front - _ _ _ _25-0" (middle) .......... 20mm back
50
'
100
'
200
3bO
'
4b0
'
'
500
'
6bO '
Time (s) Figure 20. Temperature-time variations in a large and thin (3 mm) epoxy-glass sample, with a double alternate microwave input. For four points no difference is observed. 250
200
r
1
2*1OOw 10*37*500mm 4 probes on longitudinal axis
I
c I I'
,
.." ,.'
g 100
-20mm front
______
60mm front
250" (middle) ...... ... 20mm back 200
Ob
"
" 400
600
"
'
800 I
" 1000
Time (s) Figure 21. Temperature-time variations in a large and thick (10mm) epoxy-glass sample, with a double alternate microwave input. The kinetic differences are due to dielectric loss in material, but the final temperature is the same in every point.
Table 1. Glass Transition Temperature All along the Median Line of a DGEBNSDCWGlass Fiber Composite Plate after Microwave Curing and before Postcure z(cm)
T,("C)
3 147
6 142
9 144
12 142
15 144
18 144.5
It becomes clear that heat modelling is necessary, taking into account the thermal properties of materials and the kinetics of the chemical cross-linking reaction. This will be the subject of a future paper.
Conclusion
To obtain homogeneously cured samples, a microwave curing process for epoxy-glass composites requires a monomode travelling wave inside the material to be cured. By means of basic considerations about the electric field distribution in multilayer dielectrics filling a standard waveguide and about the energy transfer through matched transitions from air to material and from material to air, we have calculated and realized a process providing satisfactorily and homogeneously cured composites plates. However, a better result will be obtained by taking into account the heat production and transfers inside and outside materials and applicators. Acknowledgment The work was supported by the Centre National de la Recherche Scientifique (CNRSPIRSEM-ECOTECH), the Agence FranGaise de 1'Environnement et la Maitrise
Glossary a: wave attenuation coefficient p: phase constant (J= 2d1,) y : propagation constant ( y = a + j p ) EO: electrical permittivity in vacuum e*: complex relative dielectric constant (E* = E' - jc") E': relative permittivity in a material E": relative absorption factor (or loss factor) in a material r: complex reflection coefficient 10: wavelength in free space (122 mm for 2.45 GHz) 1,: wavelength in guide (dependingon wave frequency and material permittivity) PO: magnetic permeability in vacuum w : wave pulsation a: length of the larger side of the waveguide cross section b: length of the smaller side of the waveguide cross section e: central part width in the dielectric filling of waveguide d : d = (a - c)/2 E: electric field intensity Ei: incident electric field intensity at interface E,: reflected electric field intensity at interface Eint: internal electric field intensity (in a material) E,, Ey,E,: electric field components in Ox, Oy, Oz directions fo: operating frequency (2.45 GHz) fc: cutoff frequency H magnetic field intensity H,, Hy, H,: magnetic field components in Ox, Oy, Oz directions ko: wave propagation constant (ko = 2n/10) k,: cutoff wave propagation constant (K, = 2n/1,) L: taper length P: volumetric density of electromagnetic power absorbed in a material p : transverse propagation constant in I and I11 q: transverse propagation constant in I1 u : wave propagation celerity in dielectric WR340: standard rectangular waveguide (a = 3.40 in. or 86.36 mm, b = a/2) TE,,: transverse electric propagation mode, in which m and n are the number of half-period variations in transverse field intensity along the x and y dimensions of the guide, respectively Zi: characteristic impedance in waveguide Gi Literature Cited Abramovitch, R. A. Applications of microwave energy in organic chemistry. A review. Org. Prep. Proc. Znt. 1991, 6, 685. Chambers, L. G. Propagation in waveguides filled longitudinally with two or more dielectrics. Brit. J.Appl. Phys. 1963, 39. Eberhardt, N. Propagation in the off center E-plane dielectrically loaded wave guide. IRE Trans. Microwave Theory Techn. 1967, MTT-15, 282. El-Shandwily, M. E.; El-Dinary, S. M. Travelling-wave coherent light-phase modulator. ZEEE Trans. Microwave Theory Techn. 1972, MTT-20 (2), 132. Hord, W. E. Continuously tapered dielectric matching transitions for waveguides. Ph.D. Dissertation, University of Missouri, Rolla, 1966. Jullien, H.; Petit, A. The microwave reaction of phenylglycidylether with aniline on inorganic supports as a model for the microwave crosslinking of epoxy resins. Polym. Mater. Sei. Eng. 1992, 66, 378. Manring, E. B.; Asmussen, Jr., J. Numerical calculations for singlemode, continuous processing for rods and filaments. Polym. Mater. Sei. Eng. 1992, 66, 476.
698 Ind. Eng. Chem. Res., Vol. 34,No.2, 1995 Mijovic, J.; Wijaya, J. Review of cure of polymers and composites by microwave energy. Polym. Compos. 1990,11, 184. Mingos, D. M.; Baghurst, D. R. Applications of microwave dielectric heating effects to synthetic problems in chemistry. Chem. Ssc. Rev. 1991, 20, 1. Moreno, T. Waveguides filled with dielectric materials. In Microwave Transmission Design Data; Artech House Inc.: Boston, MA, 1989; Chapter 11. Ollivon, M. Dynamic measurement of complex permittivity and temperature during microwave heating. IEEE-MTT-S Digest Int. Microwave Symp., St Louis, MO, 1985; p 645. Ollivon, M.; Quinquenet, S.; Seras, M.; Delmotte, M.; More, C. Microwave dielectric measurements during thermal analysis. Thermochim. Acta 1988, 125, 141. Outifa, L.Contribution a u genie de l’elaboration par microondes de materiaux composites a matrice polymere de dimensions superieures a la longueur d’onde. Aspects Blectromagdtique et thermique. Ph.D. Dissertation, University Pierre et Marie Curie, Paris, France, 1992. Outifa, L.; More, C.; Urro, P.; Jullien, H.; Delmotte, M. Approche experimentale de la propagation electromagnetique en milieu dielectrique dense. R6le des interfaces. Microwave and High Frequency Intern. Conf., Nice, Oct 1991 (published by CFE, Tour Atlantique, Cedex 06, Paris La Defense, France), 1991; VOl. 11, p 393.
Outifa, L.; Guyonvarch, G.; Delaunay, D.; More, C. Thermal modelling and optimisation of a microwave curing process of thermoset composites. Microwave and High Freq. 1993 Intern. Congr., Gijteborg, 1993; Vol. I (Proceedings), E4 (SIK publ.). Outifa, L.; Delmotte, M.; Jullien, H. The dielectric and geometric dependence of the electric field and microwave power spatial distribution in a waveguide completely loaded with lossy dielectrics. IEEE Trans. Microw. Theory Techn., in press. Schelkunof, S. A. Generalized telegraphist’s equations for waveguides. Bell Syst. Techn. J . 1952, 31, 784. Vartanian, P. H.; Ayres, W. P.; Helgesson, A. L. Propagation in dielectric slab loaded rectangular waveguide. IRE Trans. Microwave Theory Techn. 1958, MTT-6, 215. Receiued for review September 21, 1994 Accepted October 30,1994 @
IE940002Q Abstract published in Advance ACS Abstracts, January 15, 1995. @
