Mechanisms of carbon dioxide laser stereolithography

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Applied Surface Science 106 (1996) 275-281

Mechanisms of carbon dioxide laser stereolithography M.A.F. Scarparo a,*, Q.j. Chen

b, A.S. Miller b, C.J. Li b, H. Leary b, S.D. Allen b

a Unicamp, lnstituto de Fisica-DEQ, 13083-970 Campinas, SP, Brazil b Tulane Uni~,ersit3,, 103 Stanley Thomas Hall, New Orleans. LA 70118, USA

Received 17 September 1995; accepted 31 December 1995

Abstract Using a carbon dioxide (CO 2) laser focused onto a sample composed of epoxy, diethylene triamine and silica powder, the results showed that we were able to confine the heating in the material and, therefore, curing in all three dimensions. We solved the time-dependent heat equation in cylindrical coordinates using the Crank-Nicholson finite-difference method to predict the curing behavior of the resin as a function of the laser radiation conditions and devised a physical and chemical model that describes the process. The data show the curing rate as a function of temperature. Activation energy results were derived from differential scanning calorimetry.

1. Introduction Lasers have been used in materials processing applications of a wide variety of materials. Stereolithography is one such application which has proved to be a powerful means of producing three dimensional models or prototypes. Conventional stereolithography uses ultraviolet (UV) lasers, typically operated at a wavelength of 352 nm, to cure photosensitive polymers, by computer control of the direction and power of the laser beam to build a desired 3D shape [1,2]. W e believe that the application of IR laser radiation to thermosensitive materials, such as resins, may provide a novel, reliable and cost-effective means of manufacturing industrial prototypes [3]. It has been reported in the literature, for example, that the automobile industry plans to incorporate new light weight materials into automobiles.

* Corresponding author. Tel.: + 504-862-8678; fax: + 504-8655274; e-mail: [email protected].

Our results showed we can confine the CO 2 laser heating in the epoxy resin based material and, therefore, its curing in all three dimensions. We present a simple physical description of the localized curing process. We also solved the time-dependent heat equation in cylindrical coordinates using the C r a n k Nicholson finite-difference method to allow us to predict the curing behavior of the sample as a function of the laser irradiation conditions. By means of differential scanning calorimetry (DSC), we have obtained the activation energy of the curing reaction as a function of temperature. There is good qualitative agreement between the calculated and observed behavior of the resin.

2. Laser processing for localized curing of resins: physical and technical considerations In previous work [4], we have presented the resuits of a method for spatially selective solidification

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M.A.F. Sc~trparo et al./ Applied Surface Science 106 (1996) 275-281

of a high-viscosity resin mixed with diethylene triamine and silica powder, using a carbon dioxide (CO 2) laser. The resulting structures did not shrink significantly after curing. In the current work, we have examined some of the physics of the process, with an emphasis on understanding the parameters which affect our ability to restrict or localize curing to a small region. We found that the amount of silica, relative to the amounts of epoxy and diethylene triamine, is critical for confining the curing process to a localized volume. If the amount of silica is too small, curing is not localized. Conversely, if the amount of silica is too large, the sample does not cure properly. The formula for our sample represents a balance between these competing concerns. We have constructed a simple model to describe the flow of energy in laser-induced curing, so that we may predict both localization and curing rates. We achieved localized curing by scanning a continuous wave (cw) CO 2 laser repeatedly over a circular path on the sample's surface with a scan speed u. By dividing the beam diameter 26o by the scanning speed, one obtains the dwell time,

t~ = Zoo~v,

(2)

and where w is the 1 / e radius of the laser beam. The energy deposited in volume V is the product of the cw laser power and the dwell time

E,, = Ptd.

El, = mCpAT.

(4)

3. Temperature calculation heating of the polymer

for

laser-induced

In order to model the flow of heat in laser-induced curing, we used a finite-difference approach to solve the time-dependent heat equation. We assumed that each time the laser passes over a point on the epoxy surface, the irradiated volume absorbs the energy of the pulse and experiences a temperature increase. The time-dependent heat equation is

1 ST

G

v2;r= D

(5)

where D is the thermal diffusivity of the sample, K is the thermal conductivity, and G describes the rate at which heat is delivered from the laser, expressed by:

(1)

which is the average time any spot on the laser scanning path is irradiated. We determined the absorption depth 6 by measuring the transmittance of an 25 /~m thick sample of uncured material over a wavelength range which included that of the CO 2 laser at 10.6 /xm, and found that 6 = 37 /~m. We assumed that a small cylindrical volume V absorbed an energy E during the dwell time, where V is given by

V = 7rw28,

capacity Cp and the mass m of material contained in the volume V according to

(3)

The rate d / 3 / d t at which the polymer cures (where 13 is the fractional extent of the reaction) is a function of the temperature imposed upon it. For the short irradiation times utilized in the previous experiments, the change in temperature, AT, is directly proportional to the energy deposited through the heat

a =

\ 7rco~ /

exp

w2

8

,

(6)

where r is the distance from the center of the beam, z is the depth from the surface of the sample, 8 is the absorption depth, P is the power input, and ce is the optical absorption coefficient. The scanning period was 35 ms, the scanning speed u = 160 c m / s and dwell time was 0.6 ms for the beam focused to a l,/e radius of 0.5 mm [5]. The radial and axial thermal transient constant ~- are defined as

= d2/D,

(7)

where D for our sample is 22.5 × 10 5 cmZ/s and d is the appropriate characteristic length. Thus ~- is about 10 s for the radial transient ( d = o9 = 500 /xm) and about 60 ms for the axial transient (d = 8 = 37 /zm). We employed the Crank-Nicholson finite-difference algorithm to solve the heat equation with the appropriate periodic heat source term G defined above [6]. The thermal conductivity of our epoxy sample is close to that of air (0.24 m W / c m • K), so that a significant fraction of the heat dissipation will occur into the air. We assumed that the thermal

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M.A.F. Scarparo et al. / Applied Surface Science 106 (1996) 275-281

properties, K and D, and the optical properties, and R (the surface reflectivity ~ 5%), are all temperature-independent and we ignore the silica and the change in the optical and thermal properties of the sample as it cures.

4. E x p e r i m e n t a l p r o c e d u r e

We chose the epoxy resin (#D.E.R. 330) on the basis of its viscosity, thermosensitivity and stability during the curing process. We determined by trial and error an appropriate mixture of reactants which provided the best results for localized curing. The optimum sample was composed of 10 parts (by weight) epoxy resin, 1.4 parts diethylene triamine, and 0.7 parts silica powder. In order to predict more accurately the rate at which the reaction occurs as a function of temperature, we used a standard DSC method [7]. We determined the activation energy E A using the general equation, d/3/dt = Ke

EA/kr,

(8)

where k is the Boltzmann constant, T is the absolute temperature, and K is a pre-exponential constant.

5. R e s u l t s

The first tests performed with the DSC used a linearly increasing (or scanned) temperature (within _+0.5°C), where we monitored the flow of heat to the sample. The average value obtained for the enthalpy of the reaction over several differential temperature scans was 65.5 _+ 1 k J / m o l . We also utilized isothermal scans, where a small amount of the sample is heated quickly to a prescribed temperature, and maintained at that temperature for the duration of the reaction. A typical plot is shown in Fig. 1 where the initial increase in power flow represents the energy required to heat the sample to the desired temperature. Integrating the difference of the two curves from time t = 0 s to t gives the amount of energy released by the reaction prior to t. As t ~ ~c the energy released in the isothermal scan approaches A H. The ratio of the energy re-

Heat flow for curing process & non-reactive sample 300

L

i

i

i

250

200

~v.150 -i-

loo non-reactive sample 50

"500

[

[

I

[

5

10

15

20

25

Time (rain)

Fig. 1. Results of DSC isothermal scan of the polymer curing process and comparison with the heat flow into a non-reactive sample at 90°C.

278

M.A.F. Scarparo et al./ Applied Surface Science 106 (1996) 275-281

Fractional Conversion at Different Temperatures 1.0 0.9 0.8 "N

0.7

~

0.6

r..)

0.5 . ~

~

0A

Lt~

0.3

o.2

."

0.1

.....~ / /

0.0 0

1

2

3

4

5

6

7

In[t(sec)] Fig. 2. Plot of fractional completion of the reaction (or conversion) versus In(t) for various temperature

Arrhenius Plot -2.0 -2.5 -3.0

* •

°~ 'ca-3.5

~

•

atlO% Caring at20% Curing at30% Caring at40% Cttring atSO% Caring at60% Curing at70%Curing

~-4.o ~-4.5 -5.0 -5.5

Average Activation Energy Ea=50.1 kJ/mol

-6.0 0.0024

0.0025

0.0026

0.0027

0.0028

0.0029

1/T (OK) Fig. 3. The Arrhenius plots of the curing process taken from the results of Fig. 4.

M.A.F. Scarparo et al./ Applied Surface Science 106 (1996) 275-281

time was deposited in a volume of 29 × 10-3 mm 3. With a cw operating power of 20 W, the energy deposited per dwell time is approximately 13 mJ. The thickness of the uncured sample for each layer of the cylinder grown by stereolithography was 80100 /zm. In Fig. 4 we show the temperature evolution in time given by simulation of the heat equation. Because of the low thermal conductivity of the sample, each irradiation of the site results in an essentially adiabatic rise in the temperature which does not decay to ambient between irradiations. As the total AT increases, however, the 1 / e decay time decreases, varying from 225 ms for the first heating cycle to 35 ms for the 7th. At steady state, the temporal behavior of the temperature of an irradiated site would be a series of temperature spikes on a constant background with a decay time equal to the cycle time. Because of the simplifying assumption of temperature independent thermal properties, each adiabatic temperature spike is the same. For our experimental adiabatic conditions AT = 253 K from Eq. (4) while the time dependent calculation yields AT finite-difference = 260 K. As shown in Fig. 4,

leased at t to A H is the fractional conversion, /3, of the reactants at time t. A standard procedure [8,9] to obtain E A is by using the following equation:

ln(t't~)-ln(t2~)=

1,

T,

(9)

T2 '

where t 1~ and t 2~ are the times required to reach a given fractional conversion at two different temperatures TI and T2, and R is the molar gas constant (R = 8.314 J / K . tool). We have performed several isothermal scans of the epoxy sample and the semilog plots of /3 versus ln(t) are shown together in Fig. 2. The corresponding Arrhenius plots are shown in Fig. 3, where each of the lines represents one specific fractional conversion /3. The results show that the activation energy for the curing process is E A = 50.1 _+ 0.9 kJ/mol. Numerical simulation of heat flow in the sample induced by the laser is accomplished with the heat equation (Eq. (5)). Using an absorption depth of 37 /~m, we assumed that the laser energy of each dwell

800/

.

.

.

279

Time Evolution of Surface Temperature

.

.

.

.

700I 600~500 ,=

~ 400 ~.3oo E

1-

200 100 0 0

01

012

013

014

01,

018

Time (second)

017

o18

Fig. 4. Calculated T(0, 0) as function of time for seven pulses.

I

0.9

M.A.F. Scarparo et al. /Applied Surface Science 106 (1996) 275-281

280

Cross-Section Isothermal Profile

(a)

g 0.5 O3 E o c

e~ 0

z

-0.5

I

-1

I

I

I

I

-0.5 0 0.5 1 Lateral Position on Surface Relative to Beam Center (mm) Cross-Section Isothermal Profile at 1/e of Tmax

0.5

(b) 0.4

A E

0.3

8

0.a

g

E 0.1 o

~m

0

-~ -0.1 0

z

-0.2

-0.3

-0-'-0.8

-o18

-oi,

-0'.2

o

o'.2

o'.,

o18

0.8

Lateral Position on Surface Relative to Beam Center (mm) Fig. 5. (a) Isotherms representing 10% increments from maximum temperature at the center (T---- 760 K) after 6 revolutions. (b) Isotherm enclosing the region where the surface temperature is within 1/e of the maximum temperature ( ~ T = 600 K).

M.A.F. Scarparo et al. / Applied Surface Science 106 (1996) 275-281

the temperature at the surface of the sample is sufficiently high to ensure that curing occurs quite rapidly with a small number of pulses. Very little curing occurs during the first pulses, but after the 4th pulse, the curing rate increases rapidly with all of the sample surface, 70% or greater, cured during the 6th pulse. The challenge is to maintain the temperature of the sample at a temperature that results in rapid curing without significant sample degradation. It is well known that the degradation of this sample occurs at temperatures above 550 K. The temperature calculation indicates that the sample does exceed the degradation limit but only for very short times. Fig. 5a shows a temperature profile across the epoxy-air interface after about seven pulses, where the various curves are surfaces of constant temperature. In Fig. 5b, we show the isotherm for 1 / e of Tmax. We compared the size of the isotherm with the size of the laser beam, and observed that they are nearly identical. The fact that the temperature increase is confined roughly to within a lateral radius of 0.6 mm and a depth of 0.3 mm is attributable to the relatively short exposure to the laser and the low thermal conductivity of the sample. This gives us hope that we may confine the cured volume to approximately the width of the beam.

6. Conclusion

We showed a novel use of infrared laser as a localized heat source in a polymer material system. We have found that localized curing occurs only for optimized processing and that the final product obtained with CO 2 laser curing is hard and stable, showing no significant shrinkage and requiring no post-cure treatment. Depth resolution is determined by the thickness of the uncured liquid layer. With smaller CO 2 laser beam sizes, the technique should be capable of producing structures with a lateral spatial resolution of tens of microns. In order to adapt the infrared laser curing process to geometries other than a thin ring, one must account for the effect of several experimental parameters, including laser

281

power, dwell time or pulse duration, scanning frequency and speed, size of the laser beam, thermal conductivity of the sample, and the mixture of reactants. Variations in any of the above parameters will affect both the geometry of the cured sample and its material quality. Localizing the curing process to a desired (presumably small) region in all three dimensions requires that the laser energy be deposited in a well-defined volume and that the heat will not be conducted away to regions where we do not wish to cure the epoxy. Because our sample has a relatively low thermal conductivity and is strongly absorptive of the CO 2 laser irradiation, curing is restricted to the desired region. We were able to show by numerical simulation that, in the time required for curing to occur, we can successfully confine curing laterally to dimensions less than or equal to the diameter of the laser beam and vertically to less than twice the absorption depth.

References [1] R. Kaplan, Photonics Spectra (June 1990) 74. [2] D.A. Belfore, Laser Focus World (June 1993) 126. [3] A.B. Lovins and L.H. Lovins, Atlantic Monthly (January 1995) 75. [4] M.A.F. Scarparo, M.L. Barros, A. Kiel, E. Gerck and J.J. Hurtak, J. Appl. Polymer Sci. 54 (1994) 1575. [5] H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, Vol. 10, 2nd ed. (Oxford University, New York, 1959). [6] W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipies in C (Cambridge University Press, 1992) pp. 222-259. [7] G. Wisanrakkit and J.K. Gilham, The Glass Transition Temperature as a Parameter for Monitoring the Isothermal Cure of an Amine-cure Epoxy System, from Polymer Characterization: Physical Properties, Spectroscopic and Chromatographic Methods, Advances in Chemistry Series, Vol. 227, Eds. C.D. Craver and T. Provder (ACS, Washington, DC, 1990) ch. 9. [8] P.E. Willard, Polym. Eng. Sci. 12(2) (1972) 120. [9] B. Fuller, J.T. Gotro and G.C. Martin, Analyses of the Glass Transition Temperature, Conversion and Viscosity During Epoxy Resin Curing, from Polymer Characterization: Physical Properties and Chromatographic Methods, Advances in Chemistry Series, Vol. 277, Eds. C.D. Craver and T. Provder (ACS, Washington, DC, 1990) ch. 12.