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Available online at www.sciencedirect.com

Journal of the European Ceramic Society 33 (2013) 1989–1994

Absorption effects in photopolymerized ceramic suspensions

Susan P. Gentry, John W. Halloran ∗University of Michigan, Department of Materials Science and Engineering, Ann Arbor, MI 48109, USA

Available online 3 April 2013

bstract

he effects of concentration of photoinitiator and concentration of an ultraviolet-absorbing dye on the cure depth and cure width of photopolymerizederamic suspensions were investigated. Both the cure depth and cure width have a semilogarithmic dependence on the energy dose, with theuspension characterized by the following parameters: the depth critical energy dose and depth sensitivity and width critical energy dose and widthensitivity. The values of these four parameters are highly dependent on the concentration of absorbers in the suspension. The depth sensitivities and

idth sensitivities are given by the absorption model, while the depth critical energy doses and width critical energy doses are given by the inhibitor

xhaustion model. Furthermore, the relationship between concentration of absorbers and the broadening depth was determined. The concentrationf photoinitiator did not significantly change the broadening depth, while the concentration of dye decreased the broadening depth.

2013 Elsevier Ltd. All rights reserved.

eywords: Photopolymerization; Stereolithography; Absorption; Ceramic suspensions

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. Introduction

Complex ceramic shapes can be produced from photopoly-erizable suspensions, made by suspending powders in aonomer solution containing ultraviolet (UV) photoactive com-

onents. These photoactive components include inert dyes,hich attenuate the UV radiation but do not participate in

hemical reactions, and photoinitiators, which attenuate the UVadiation by absorption while initiating polymerization. A com-ercially available stereolithography machine or novel devices

an be used with a photopolymerizable ceramic suspension toabricate ceramic green bodies.1 Stereolithography machinesontain ultra-violet lasers which are used to raster the surfacef the ceramic suspension, generating polymerized layers thatave a geometry specified by the design. The cured shape of aaser beam drawing a line in the suspension can be described byhe cross-sectional profile of this cured line. The cured profileill be dependent on composition of the resin that is used. For

eramic stereolithography, this is a particularly important issue,ince the ceramic particles act as scattering sites for the light.

Previous work with ceramic stereolithography suspensionshows that the dose dependence for the cured width andepth both depend on composition of the suspension. The

∗ Corresponding author. Tel.: +1 734 763 1051; fax: +1 734 763 4788.E-mail address: peterjon@umich.edu (J.W. Halloran).

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955-2219/$ – see front matter © 2013 Elsevier Ltd. All rights reserved.ttp://dx.doi.org/10.1016/j.jeurceramsoc.2013.03.004

oncentration of UV absorber and photoinitiator affect both theure width and the cure depth at constant energy dose.2,3 Theolume fraction of powders and the particle size will change theure response for both the cure width and cure depth.4–6 Thesebservations are limited in that they only measured the widtht two or three energy doses; they do not provide a comprehen-ive look at the relationship between the compositional factorsnd the changes that occur at a range of energy doses. Someeported on the process parameters, such as the illumination timer the drawing speed, which further limits their scope. A thor-ugh understanding of the compositional factors is needed, sohat these results can be applied broadly to photopolymerizationrocesses.

Stereolithography laser beams are usually modeled as havingaussian intensity distributions, which is the ideal spatial distri-ution for monomodal beams.7 The cured width is expected toepend on the beam width, energy dose, and suspension compo-ition. To study broadening in ceramic suspensions, it is simplero use a simple square wave beam. Unlike a stereolithographyaser, which has a Gaussian intensity distribution, a square waveas a uniform intensity distribution. A collimated slip apparatuss a convenient way to obtain a square wave beam where thentensity is uniform over a defined source width, which is theidth of the slit. Due to diffraction effects, a perfectly square

eam is not possible, but it produces a well-known intensity dis-ribution that can be used for suspension characterization.8 Theidth of a cured line can be broken into two components: the

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990 S.P. Gentry, J.W. Halloran / Journal of the E

idth of the source and the excess width (wex) on either side ofhe light source width. In the absence of broadening, the curedidth is simply equal to the width of the energy distribution that

s above the critical energy dose of the suspension. For a ste-eolithography beam, this width will be highly dependent on thenergy dose. In contrast, the cured width from the collimated slitpparatus will only have a slight dependence on energy dose.

The broadening behavior of individual cured lines of ceramicuspension can be quantified in terms of a quasi-Beer-Lambertehavior of the excess width and the cure depth.8 The cure depth,d, is given by

d = Sd ln

(E0

Ed

)(1)

here E0 is the incident energy dose, Sd is the sensitivity inhe depth direction (with units of length), and Ed is the criticalnergy dose in the depth direction. The size of the excess widthwex) follows a similar expression as the cure depth,

ex = Sw ln

(E0

Ew

)(2)

here Sw is the resin sensitivity in the horizontal directionunits of length) and Ew is the critical energy dose in the widthirection. The cure depth where excess broadening becomesmportant can be quantified by a “broadening depth” Db, whichnvolves both the width and depth critical energy doses as:

b = Sd ln

(Ew

Ed

)(3)

This describes the depth at which broadening becomes sig-ificant, which occurs at the energy dose where E = Ew. A largealue for Db indicates that a suspension can be cured deeperefore beginning to broaden, while a small Db indicates thatroadening will occur at shallower cure depths. This has a prac-ical consequence, since deep and narrow features cannot beured using suspensions with a small broadening depth.

The resin sensitivity (Sd) has been shown to be due to theffects of the absorption coefficients of each of the individualomponents as well as the scattering from the ceramic particles.ssuming the ceramic is UV transparent, the sensitivity can beredicted in terms of the concentrations of the components andheir extinction coefficients, ε,

1

Sd

= 1

lsc+ (1 − Φ)(cPεP + cDεD) (4)

here lsc is the scattering length of the suspension, Φ is theolume fraction of ceramic powder in the suspension, cP is thehotoinitiator concentration, εP is the extinction coefficient ofhe photoinitiator, cD is the dye concentration, and εD is thextinction coefficient of the dye.9,10 It can be seen that there arewo additive effects: the scattering effects which are character-zed by 1/lsc and the absorption effects which are characterizedy (1 − Φ)(cPεP + cDεD). This allows the behavior of the recip-

ocal of sensitivity to be broken down into a scattering dominatedegime and an absorption dominated regime.

Similar to the behavior of the resin sensitivity, theritical energy dose (Ed) can be predicted from the

2

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ean Ceramic Society 33 (2013) 1989–1994

ndividual components in the suspension using the inhibitor-xhaustion model. Photons are either absorbed by the inert dyer react with the photoinitiator to release free radicals. Theseadicals can either be annihilated by the inhibitors in the sys-em or can contribute to free radical polymerization. In orderor polymerization to take place, all of the inhibitor must beonsumed by free radicals so that there are excess radicals toropagate the reaction. The inhibitor is exhausted at the criticalnergy dose, Ed, which is dependent on the composition of theuspension as

d = (γinhcinh + γDcD)hv

Ω

×[

1/lsc + (1 − Φ)(cPεP + cDεD)

c2Pε2

P

](5)

here cinh is the concentration of the inhibitors (such as oxygenr added quinones, etc.), γ inh is the number of radicals removeder inhibitor, γD is the number of radicals that were not generatedue to the presence of the dye, h is Plank’s constant, ν is therequency of the light, and Ω is the number of free radicalsiven off per photon absorbed.10,11 The critical energy dose ofq. (5) can be approximated to a linear form as10

d = (1 − Φ)hv

Ω(γinhcinh + γDcD)

1

cPεP

(6)

Below this energy dose, the inhibitors and dye absorb freeadicals and no curing occurs. Above this energy dose, free radi-als are available to cause propagation of the polymerizationeaction and curing occurs.

For absorption-dominated systems, the key compositionalactors are the concentration of photoinitiator and the concen-ration of the UV dye. The behavior of scattering-dominatedystems is much more complex. The refraction of light athe interfaces of the powder and monomer cause the photonirection to become randomized. The particle sizes for stereo-ithography are around 1–5 �m and the wavelength of ultravioletight is typically 355 or 365 nm, so the scattering is best describedy Mie theory. For suspensions containing homogeneous parti-les in dilute solution, the angular distribution of the scatteringan be easily predicted using computational methods. However,eramic green bodies require a high solids loading (ceramicolume fractions of 50–65%) to ensure sufficient mechanicaltrength after the binder is removed. These volume fractionsequire accounting for the correlation effects between the par-icles. Furthermore, the broad particle size distributions alsoomplicate the calculations. The result is that scattering dom-nated systems do not have a closed form solution due to theomplexities of scattering in turbid suspensions. This paperocuses on the effects of absorption within ceramic suspensions,o extrapolated values are used for the scattering length. Theffect of scattering can be found elsewhere.12

. Materials and methods

Photopolymerizable ceramic suspensions were prepared byolling in plastic bottles. A difunctional monomer was used (1,6

S.P. Gentry, J.W. Halloran / Journal of the European Ceramic Society 33 (2013) 1989–1994 1991

0.000

0.001

0.002

0.003

0.004

0.005

0 0.05 0.1 0.15 0.2

1/S

(1/μ

m)

cp (mol /L)

1/Sw

1/Sd

Fig. 1. Depth sensitivity (Sd) and width sensitivity (Sw) as a function of pho-toinitiator concentration for suspensions containing a volume fraction of 60%sm

htAvM(rlktCtasomQ

3

3

dtrcemtdt(rt

Table 1Fitting constants from the absorption model for photoinitiator extinctioncoefficient.

lsc (�m) εP, L/(mol �m)

From Tomeckova and Halloran9 0.0020Measured depth sensitivity (Sd) 410 0.0265M

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ilica. Note that the reciprocals are plotted for comparison to the absorptionodel.

exanediol diacrylate, SR 238B, Sartomer) with a ketone pho-oinitiator (Irgacure 184, Ciba, molecular weight = 204.3 g/mol).bsorption-dominated suspensions were prepared containingolume fractions of 60% silica powder (Tecosphere-A, CEinerals, density = 2.2 g/cm3, nD = 1.4603). The dispersant

Variquat CC-59, Evonik, density = 1.1 g/cm3) was used at aatio of 4.17 ml per 100 ml of powder. For each liter of totaliquids, the silica suspensions contained 0.046–0.18 mol of aetone photoinitiator with no dye or 0.092 mol of photoinitia-or and 0–0.00283 mol of an inert triazole dye (Tinuvin 171,iba, molecular weight = 395 g/mol). Suspensions were allowed

o mix for 24 h prior to use. Ceramic suspension was cured using collimated slit apparatus, which uses a 365 nm collimated lightource illuminating a 200 �m wide slit to result in a cured linef ceramic/polymer green body.8 Specimen dimensions wereeasured from optical micrographs taken with a camera (Go-3,Imaging) attached to a stereomicroscope (SMZ 1000, Nikon).

. Results and discussion

.1. Effect of photoinitiator concentration

Cure width and depth were measured as a function of energyose for silica suspensions containing 0.046–0.18 mol/L pho-oinitiator with no UV absorber. As predicted by Eq. (4), theeciprocal of the sensitivity should increase linearly with con-entration of photoinitiator. The slope of the best fit line isxpected to be equal to the volume fraction liquids (1 − Φ)ultiplied by the extinction coefficient (ε), or (1 − Φ) * ε. For

hese suspensions, the best fit line can also be used to pre-ict the scattering length of the suspension, as 1/lsc is equalo 1/S for a composition with no dye (cD = 0). It can be seen

Fig. 1) that the reciprocal of the width sensitivity and theeciprocal of the depth sensitivity are both linear with pho-oinitiator concentration, as predicted by the absorption model.

tsd

easured width sensitivity (Sw) 1040 0.0043

his is significant, as the relationship between photoinitiatoroncentration and cure width had not previously been estab-ished. Fitting the sensitivities to a linear equation allows thextinction coefficients to be determined for the suspension, asiven by Eq. (4). The measured extinction coefficients and scat-ering lengths for the absorption model are given in Table 1,long with the literature value of the extinction coefficient (at aavelength of 365 nm) for comparison. The measured extinc-

ion coefficients are 2–13 times larger than the literature valuef 0.0020 L/(mol �m). The extinction coefficient from the depthensitivity is 0.0265 L/(mol �m) and the extinction coefficientrom the width sensitivity is 0.0043 L/(mol �m). The scatter-ng lengths were 410 �m for the width direction and 1040 �mor the depth direction. The physics of the absorption modelredict that the scattering length and extinction coefficient wille the same in both the depth and width directions, but thisas not observed. The differences between the depth and widtharameters can be attributed to the path length traveled by thehoton within a low-scattering medium.12 Although the physicsf absorption are constant in both directions, the small scatter-ng angles cause the sensitivity and critical energy dose to haveirectional dependencies.

The effect of photoinitiator concentration on the criticalnergy doses was also measured for these ceramic suspensions.rom the inhibitor exhaustion model (Eq. (6)), the critical energyose is expected to increase linearly with the inverse of the con-entration of photoinitiator, with the critical energy dose goingo infinity in the absence of photoinitiator. It was found thatoth the depth critical energy dose (Fig. 2A) and width criticalnergy dose (Fig. 2B) increase linearly with the reciprocal ofhotoinitiator concentration. Thus, these results are consistentith the predicted behavior of the inhibitor-exhaustion model.owever, it is important to note that the width critical energyoses are more than an order of magnitude larger than the com-arable depth critical energy doses. This large difference is likelyue to the small scattering angles in the nearly index-matchedilica suspensions (�n = 0.0043). Increasing the energy doseffectively increases the path length traveled by the photons,o they can begin propagating sideways. Below the width crit-cal energy dose, there is expected to be some scattering to theide, but its effect is minimal. The large width critical energyoses are advantageous for ceramic stereolithography and otherhotopolymerization systems, because a significant portion ofepth can be cured prior to the broadening depth.

It was found that changing the concentration of the photoini-

iator has no effect on the broadening depth (Fig. 3). This isurprising, as there was a clear dependence of the width andepth parameters with the concentration of photoinitiator. The

1992 S.P. Gentry, J.W. Halloran / Journal of the European Ceramic Society 33 (2013) 1989–1994

A) Dep th Critical Ene rgy Dose B) Wid th Critical Ene rgy Dose

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25

E d( m

J/cm

2 )

1/c (L/ mol )

0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25

E w(m

J /cm

2 )

1/c (L/ mol )

h crit

rcttstdieco

3

twi0apc

iteEitoAinfTF1dtaFig. 4 are equal to (1 − Φ) * εD. The literature value of the dyeextinction coefficient is 0.868 L/(mol �m) at a wavelength of

p

Fig. 2. Effect of photoinitiator concentration on the dept

eciprocal sensitivities both increased with photoinitiator con-entration (Fig. 1) and the critical energy doses increased withhe reciprocal of photoinitiator concentration (Fig. 2). However,he uniform broadening depths indicate that these changes off-et each other. This is a beneficial finding, because it allowshe concentration of photoinitiator to be tailored to the inci-ent energy source without contributing to broadening. Fornstance, concentration of photoinitiator can be increased tonsure that polymerization occurs rapidly, increasing the effi-iency of the process. This change will not affect the broadeningf the ceramic suspension.

.2. Effect of dye concentration

The effect of dye concentration on the photocuring proper-ies of the suspension was also determined. The resin sensitivityas measured as a function of the dye concentration, as shown

n Fig. 4. The silica suspensions contained 60% powder and.092 mol/L photoinitiator, with 0–0.00283 mol/L dye. The dye

cts by absorbing photons that are propagating through the sus-ension, so that they cannot penetrate deeper or participate in theuring reaction. Note that the extinction coefficient of the dye

0

200

400

600

800

1000

1200

0 0.05 0.1 0.15 0.2

Db (

μm)

cP (mol/L)

Fig. 3. Effect of photoinitiator concentration on the broadening depth.

Fca

p

ical energy dose (A) and width critical energy dose (B).

s high (0.868 L/(mol �m)), so only small concentrations (onhe order of mmol/L) are required to change the curing prop-rties of the suspensions. The absorption model (as given byq. (4)) predicts that the reciprocal of the sensitivity should

ncrease linearly with concentration of dye, when the photoini-iator concentration is held constant. This linear behavior wasbserved for both the width sensitivity and the depth sensitivity.gain, it is significant that the reciprocal of the width sensitiv-

ty increases with the dye concentration, as this relationship hadot previously been established. The linear fitting parametersor Eq. (4) (1/S(cP = 0.092 mol/L, cD = 0) and εD) are given inable 2, along with the dye extinction coefficient from literature.urthermore, the absorption model predicts that the behavior of/S versus dye concentration (Fig. 4) for suspensions containingye (cD > 0) can be extrapolated to give the behavior of composi-ions without dye (cD = 0). This was observed for both the widthnd depth parameters. Finally, it is predicted that the slopes in

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.010

0 0.00 1 0.002 0.00 3

1/S

(1/μ

m)

cD (mol /L)

1/Sw

1/Sd

ig. 4. Depth sensitivity (Sd) and width sensitivity (Sw) as a function of dyeoncentration. Note that the reciprocals (1/S) are plotted for comparison to thebsorption model.

S.P. Gentry, J.W. Halloran / Journal of the European Ceramic Society 33 (2013) 1989–1994 1993

A) Depth Critical Energy Dose

0

1

2

3

4

5

6

7

8

0 0.000 5 0.001 0.001 5 0.002 0.002 5 0.003

E d (m

J/cm

2 )

cD (mol /L)

B) Wid th Critical Ene rgy Dose

0

50

100

150

200

250

300

350

400

0 0.001 0.002 0.003

E w (m

J/cm

2 )

cD (mol/L)

Fs

34ictattfwdt

dcesT

TF

FMM

0

200

400

600

800

1000

1200

0 0.001 0.002 0.003

Db (

μm)

cD (mol /L)

Fs

tadcwas

wesodwattot

4

dmSib

ig. 5. Effect of dye concentration on the critical energy dose of the ceramicuspensions for both the depth (A) and width (B).

65 nm,9 whereas the measured depth extinction coefficient is.72 L/(mol �m) and the measured width extinction coefficients 2.04 L/(mol �m). The measured depth and width extinctionoefficients were 5.4 and 2.4 times larger, respectively, thanhe predicted extinction coefficient, indicating that the energy isttenuating more rapidly than expected. Similar to the photoini-iator extinction coefficients, the dye extinction coefficient fromhe depth direction was larger than the extinction coefficientrom the width direction, and both dye extinction coefficientsere larger than the literature value. Again the source of thisiscrepancy can be attributed to the path length effects of scat-ering.

The effect of the dye concentration on the critical energyose was also determined. As shown in Fig. 5A, increasing theoncentration of the dye had little effect on the depth critical

nergy dose. The width critical energy dose (Fig. 5B) increasedtrongly with the concentration of the dye in the composition.his shows that the inhibitor exhaustion model, which predicts

able 2itting constants for absorption model as the concentration of dye is varied.

1/S(cP = 0.092 mol/L,cD = 0) (1/�m)

εD,L/(mol �m)

rom Tomeckova and Halloran9 0.868easured depth sensitivity (Sd) 0.00316 4.72easured width sensitivity (Sw) 0.00123 2.04

rlptwwTmawiT

ig. 6. Change in broadening depth as a function of the dye concentration forilica suspensions containing 0.092 mol/L photoinitiator.

he effect of composition on the depth critical energy dose, canlso be used to predict the effect on the width critical energyose. Similar to the effect of photoinitiator concentration, theritical energy dose is over an order of magnitude larger in theidth direction than in the depth direction. Again, this discrep-

ncy is attributed to the small Mie scattering angles in the silicauspensions.

The effect of the dye concentration on the broadening depthas also determined (Fig. 6). It was found that the broad-

ning depth decreased with the concentration of dye in theystem. The suspension without dye had a broadening depthf 940 ± 140 �m, while the suspension with 0.00283 mol/L ofye had a broadening depth of 480 ± 60 �m. For applicationsith cure depths of 100–200 �m, there will be no broadening for

ny of these suspensions. However, if deeper curing is required,hen the broadening depth must be accounted for. Additionally,hese results suggest that it is important to account for the effectf the concentration of dye on the broadening depth, to ensurehat optimal resolution is attained.

. Conclusions

The relation between UV energy dose and the resulting cureepth and excess width can be fit to a quasi-Beer Lambertodel involving cure parameters Sd and Ed for the depth and

w and Ew for the excess width. The effect of UV absorb-ng photoinitiators and inert dyes were observed and found toe in accord with expectations from theoretical models. Theeciprocals of the width and the depth sensitivities increasedinearly with the concentration of the photoactive species, asredicted by the absorption model. The apparent photoinitia-or extinction coefficient inferred from the absorption modelas larger when measured in the depth direction than in theidth direction. Both were larger than the values reported byomeckova. The dye extinction coefficient was larger wheneasured in the depth direction than in the width direction,

nd again both were larger than expected from Tomeckova. Theidth critical energy dose and depth critical energy dose exhib-

ted the behavior predicted by the inhibitor-exhaustion model.he critical energy dose increased linearly with the reciprocal

1 urop

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994 S.P. Gentry, J.W. Halloran / Journal of the E

f the photoinitiator concentration in the suspension. For thenert absorbing dye, the width critical energy dose increasedith 1/cD, but the depth critical energy dose had no systematic

hange.The change in the broadening depth with concentration of

hotoinitiator and dye was also determined. When the amountf photoinitiator was varied, it was found that the changes in theidth and depth parameters offset each other and the broadeningepth did not change. However, the dye concentration does affecthe broadening depth, with broadening depth decreasing linearlyith inert dye concentration.

cknowledgements

This work was funded primarily by a sponsored researchroject of Honeywell and partially by the United States Defensedvanced Research Projects Agency (DARPA) under HR0011-7-1-0034.

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