POLIMERY 2000, 45, nr 11—12 759

JULITA JAKUBIAK*’, JAN F. RABEK** ***)’

Three-dimensional (3D) photopolymerization in stereolithography****

PART I. FUNDAMENTALS OF 3D PHOTOPOLYMERIZATION

"Stereolithography is like black art. You can build a part any num ber of ways, but the more you experience the process, the better you'll do" William J. Coleman

Summary — A review with 77 refs, covering the fundamentals of three-dimensional photopolymerization (3DP), viz., resin formulations (photoinitiators and monomers) for stereolithography, layer-by-layer space-resolved 3DP process, multiphotonic 3DP, optimization of 3DP parameters, volume contraction (shrinkage) and curl distortion in 3DP and applications of 3DP stereolithographic models. Key words: three-dimensional photopolymerization, photoinitiators for 3D polyme­ rization, layer-by-layer space-resolved 3 D photopolymerization, resin formulation for stereolithography.

Three-dimensional (3D) photopolymerization (stereo­ partment of Physical Chemistry, University of Techno­ lithography) is a new technology [1—18] linking the logy and Agriculture, Bydgoszcz, Poland) has develo­ computer models (Computer Aided Design (CAD) [13, ped a 3D photopolymerization program in Poland. Dr. 17—19]) and Computer Aided Manufacturing (CAM) J. Jakubiak of the Department of Chemistry, Jagiellonian processes [13,17—23] to the Rapid Prototyping and Ma­ University, Cracow, heads an international project on nufacturing (RPM) of a polymer solid, shaped product photopolymerization in cooperation with Prof. J. F. [13, 17—19]. In this method a laser beam, driven by a Rabek (Sweden). 3D-CAD-CAM system across an x,i/-surface, is used to form point by point, layer by layer a solid polymer ob­ ject by photopolymerizing an acrylate resin. Within the RESIN FORMULATIONS FOR STEREOLITHOGRAPHY last decade, several fully automated industrial 3D-CAD-CAM Solid Creation Systems (SCS) have been 3D photopolymerization requires a rapid photoche­ made available [13, 16—19, 24]. mical process [17, 25—27], and many photoinitiators In Europe, two research centers, viz., Ciba-Geigy Ltd. and monomers fail on these counts. The composition of Marly Works Research Center, CH-1701 Fribourg, Swi­ the resin formulation is the key factor in the 3D photo­ tzerland [15], and GRAPP-URA 328 CNRS, ENSIC-INPL, polymerization process since it directly determines the BP 451, 1 rue Grandville, F-54001 Nancy Cedex, France final product and the mechanical properties of the mo­ [17], are the centers most advanced in stereolithogra­ del. Current UV-sensitive formulations include a care­ phy. Professor J. P. Fouassier (Laboratoire de Photochi- fully selected UV-photoinitiator, a co-initiator, different mie Generale CNRS No. 431, ENSCMU, 3 rue Alfred monomers and oligomers, and additives. Werner, F-68200, Mulhouse Cedex, France) has been gu­ iding the fundamental research on laser photoinitiation, Photoinitiators for 3D polymerization photopolymerization, and photocuring, which are the basic techniques to evaluate resins to be used for stereo­ Three types of UV photoinitiators commonly used for lithographic purposes [25]. Professor J. Pączkowski (De­ initiation of 3D polymerization include: — photoinitiators which undergo an intramolecular *) Department of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Cracow, Poland. To whom all correspondence should be photocleavage into two radicals (Table 1) [15, 17, addressed. 26—32]: **) Polymer Research Group, Department of Dental Biomateriał Science, Karolińska Institute (Royal Academy of Medicine), Box CH3 СНз C -Ć -O H J™ . 4064, 141 04 Huddinge (Stockholm), Sweden, and Department of II I •ę-о н (1) Chemistry and Chemical Engineering Technical and Agricultural О CH3 ĆH3 University, Seminaryjna 3, 85-326 Bydgoszcz, Poland. ***) This paper was partially presented at the Chemical Forum orga­ — photoinitiators which produce free radicals by in- nized by Prof. M. Jarosz at the Technological University, War­ termolecular hydrogen abstraction from a hydrogen do­ saw, May 2000, and is dedicated by the Authors to Professor T. nor molecule (co-initiator) by the Electron/Proton Sikorski of the Department of Organic and Polymer Technology, Technical University, Wroclaw, Poland, on the occasion of his Transfer (EPT) [26—32]; this type of photoinitiators is 70th birthday. exemplified by benzophenones, diketones and thioxan- 760 POLIMERY 2000, 45, nr 11—12

Table 1. Typical UV photoinitiators used in the 3D photopolymerization

Commercial name Chemical name Chemical structure Absorption, nm and supplier

Substituted alkyl aryl ketones Sandoray 100 240—360 (Sandoz)

Phenyl-2-hydroxy-2-propyl ketone Darocure 1173 250—350 (Ciba-Geigy) N----/ CH3

2,2-Dimethoxy-2-phenyl acetophenone (benzyl- o O-CH, Irgacure 651 250—350 dimethyl ketal) (2,2-dimethoxy-l,2-diphenyl- (Ciba-Geigy) ethan-l-one) O-CHj

2-Methyl-l-(4-methylthiophenyl)-2-morpholino ---- 0 CH3 /----4 Irgacure 907 230—360 propan-l-one CH3 -S 4 Q V C - c - N 0 (Ciba-Geigy) '— ' a-i3 ^— /

1-Hydroxy-cyclohexyl-phenyl ketone о он Irgacure 184 331 (Ciba-Geigy)

l-Phenyl-l,2-propanedione-2-o-ethoxycarbonyl ,----ч 0 CH3 0 Quantacure PDO 275—400 ii i и oxime (X))— c—c= n- o- c- c2h5 (AcetoChemical)

Bis(2,6-dimethoxybenzoyl)-2,4,4-trimethyIpen- OCH3 H3CO BAPO 380 O O O tyl-phosphine oxide ,----/ \----- (Ciba-Geigy)

OCH3 H2CO/ thones (Table 2); the most common hydrogen-atom do­ Table 2. Photoinitiators which produce free radicals by intermole- nors are amines: cular hydrogen abstraction from a hydrogen donor molecule (coini­ tiator)

Chemical name Structure Absorption, nm

Benzophenone 220—300

CH3 Camphorquinone 1 480 _ -C -^ н2сI Т H3C—C—CH3 Г г г гчГ'О i ^ 0 h2c^ ^ h___ c^o

Thioxanthone о 260 OĆO

CH3 — cationic photoinitiators (Table 3) [15, 25, 26, C-он H- ’ę -он 33—36]. сн 3 The primary step in the photolysis of the diaryliodo- nium cation is the homolytic bond cleavage to yield the aryliodonium radical cation, АгГ», and an aryl radical о о /__ ^ (Ar«). Пае H-atom abstraction from the monomer (MH) , c 2H5 is postulated to result in the radical М» and in the pro- + h3c- ch2- n C2H5 tonated aryl iodide which dissociates into H+X' and Arl [33—36]: \hv Аг,ГХ“ ,lv > Arł .X' + Ar • (4) о OH C2H5 c - c + H3C-CH-N' A d »X~ + M H -> А гГ H X“ + M (5) . - o C2H5 POLIMERY 2000, 45, nr 11—12 761

Table 3. Cationic photoinitiators Table 5. Examples dye visible light photoinitiators used in the 3D photopolymerization [47] Absolute maxima, Cation Anion nm Absorption Chemical structure Chemical name nm S b F 6 238, 358 Ж Xanthene dyes: в 246 сн^сЧ0 ^ 'ч 0>

p u 6 237

b f 4 230 -S +

3

AsF 6 225, 280

b f 4 258, 266, 275 -Se+ н 3

АгГ HX' -» Ari + FTX' (6)

M »+M H —> polymerization (7) In these onium salts, typical non-nucleophilic anions are BF4", C104', CF3S03~, PF6‘, AsF6‘ and SbF6‘. Anions СГ, Br', or Г, bases, water and hydroxyl-containing com­ pounds quench the cation formation and inhibit polyme­ rization. Unlike radical polymerizations, oxygen does not inhibit cationic polymerization. Dyes like acridine orange and benzoflavin efficiently sensitize cationic polymerization in the visible light range [37]. Visible light 3D photopolymerization is mainly based on: — fluorinated diaryltitanocene [38] and a chlorome- thyl substituted triazine [39] (Table 4); co-initiators (Table 6 ) [28, 40—46]. Most visible photo­ — dye photoinitiators, e.g. xanthenes, modified xan- initiators function by the EPT mechanism in which the thenes, fluorones (Table 5) in the presence of different light absorbing dye is either oxidized or reduced in the

Table 4. Typical visible light photoinitiators used in the 3D photopolymerization

Chemical name Chemical structure Commercial name and supplier Absorption, nm

Fluorinated diaryltitanocene Irgacure 784 (Ciba-Geigy) 450—500

Methyl substituted triazine CH, (Hoechst) 488

CH3- 0 —/(~)VcH=CH-(/ N

CH3 762 POLIMERY 2000, 45, nr 11—12

Table 6 . Coinitiators for photoreducible dyes [28] Monomers and formulated resins

Type Chemical structure Chemical name Resins for 3D photopolymerization consist of combi­ Amines N(C2H2OH)3 Triethanolamine nations of mono- (Table 7), di-(Table 8 ), multi- (Table 9), oligomeric and polymeric multifunctional (Table 10) Aminoacids N-Phenylglycine O - N K ^ C monomers [15, 17]. Recently epoxy, epoxyacrylates and urethane acrylates have also been used [27, 48]. A typi­ OH cal formulation for the He-Cd laser induced 3D photo­ Phosphi- Triphenylpho- polymerization is shown in Table 11. nes/Arsines sphine Tripheny- _ p larsine Table 7. Monofunctional monomers [15] X-P.A, Chemical name Chemical structure

о 2-Phenoxyethyl acrylate 0 Sulphinates Sodium p-tolyl- sulphinate

Tetrahydrofurfuryl acrylate Enolates Dimedone enola- ,p HjC ,— к te

H3C '— ^ N-Vinylpyrrolidone 4o ф р

Carboxylates CHlOH Ascorbic acid i " „ e x / 0 N-Vinylcaprolactam and/or lactones HO-CH—

CN i o HO/ 4 OH 1=

Organotin com­ СНз ,----- Benzyltrimethyl- pounds H3C - Sn - CH2p Q ) stannane CH3 Multifunctional acrylate resin formulations are gene­ rally 1 , 0 0 0 centipoise or more in viscosity at room tem­ Borates Triphenylbutyl- perature (25—30°C). At these viscosities, the resins be­ borate 0 have as thick syrups that flow very slowly. For 3D pho­ <0 > - * с л topolymerization, moderately high viscosity (>1,000 cP) results in lower throughput, longer recoating times, and more difficult removal of unwanted air bubbles from и the resin. To lower the viscosity of the resins, monofunc­ Miscellaneous s Diallyl thiourea tional monomers (most commonly N-vinylpyrrolidone II CH2=CHCH2NH-C- nhch2ch= ch2 (Table 8 )) are added. After laser irradiation, the resin forms an insoluble, highly crosslinked gel. The newly 2,4,5-Triphenyli- formed part is chan cterized as being "green", in the midazole sense that it still has unchanged monomers that can be cured in a post-irradiation or in post-thermal steps. The strength of the green part is related to the cross-link density of the part. It must be sufficiently high to [49]: — permit detailed product formation; excited singlet or triplet state and EPT occurs in the pre­ — minimize swelling; sence of a hydrogen atom donor co-initiators according — permit handling prior to the post curing processes. to the mechanisms [47]: The acrylate-based systems also require a high green strength (or high crosslink density) in the green part, to dye— ——>' dye* -»3dye* (8 ) minimize post-cure distortion effect. A high crosslink

3 dye* + DH -V[dye... DH]* (9) density yields strong parts; the acrylates lack toughness, CT - complex however. The lack of toughness can also give rise to part fracture when stress is relieved in large and com­ 3[dye... DHf -> dye • + D H • (10) plicated parts during a post-cure step. Since acrylate systems are highly crosslinked in the green state (to mi­ dye»+ DH»—» dye H«+ D« nimize post cure distortion), large or complex geometry D •+monomer —> polymerization (12) parts exhibit variability in the degree of cure. In addi­ dye H • + monomer polymerization (if occurs) (13) tion, the UV post cure irradiation is not isotropic, owing POLIMERY 2000, 45, nr 11—12 763

Table 8. Difunctional monomers [15]

Chemical name Chemical structure

Aliphatic diacrylates (linear)

Hexanedioldiacrylate 0

0

Triethyleneglycol diacrylate 0

d Aliphatic diacrylates (branched)

Neopentylglycol diacrylate ° ' y ^ ' о 0

Ethoxylated neopentylglycol diacrylate о

0

Aromatic diacrylates

Table 9. Multifunctional monomers [15] to a non-uniform light flux, resulting from variable thickness throughout the part. Acrylate resins are brittle due to the nature of their chemical structure. Formula­ tions are limited in improving the mechanical proper­ ties without sacrificing viscosity, cure speed and strength. For photocationic polymerization mainly epoxides (Table 12), vinyl ethers and urethane vinyl ethers have been used [15]. These monomers allow the mechanical end properties of 3D models to be finely designed. It goes beyond the scope of this review to describe in any details all the resin formulations available for pho- topolymerization; this subject has been amply reviewed [15, 27, 40, 50] and approached in monographs [25, 26, 29]. The kinetic modelling of linear and crosslinking photopolymerization has been discussed in detail [51, 52]. The computerized kinetic model of the 3D laser photopolymeriztion, which takes the viscosity pheno­ mena and gel point into special account, has been de­ scribed elsewhere [53]. 764 POLIMERY 2000, 45, nr 11—12

Table 10. Oligomeric and polymeric multifunctional monomers [15]

Table 11. Resin formulation for HeCd laser 3D photopolymeri­ 1 2 zation [15] 0 CV 184 Part by weight Component 46 Bisphenol-A-diglycidyl-diacrylate r V 4 0 ^ 23 Ethoxyla ted bisphenol-A-dimethacryla te D ° 0 17 Dipentaerythritol pentaacrylate о DY 026 5 2-Phenoxyethyl acrylate c r 5 N-Vinylpyrrolidone CY 177 4 1-Hydroxycyclohexyl-phenylketone < Г Л ~ П Г ' С > о о Table 12. Epoxy resins for photocationic polymerization [15] о О MY 720 p b

PT 810

o r

N ^ sN

о о POLIMERY 2000, 45, nr 11—12 765

LAYER-BY-LAYER SPACE-RESOLVED 3D where I0 is the intensity of incident laser beam, is the PHOTOPOLYMERIZATION monophotonic absorption (molar extinction) coefficient of a photoinitiator at wavelength X, [A] is the concentration of ab­ In this 3D photopolymerization, a portion of the open sorbing species (photoinitiator), and Dt, is the light penetra­ layer of a monomer is irradiated by a UV laser (excimer tion depth at the laser wavelength (X). In practice, the poly­ or YAG lasers), where upon a new layer of the mono­ merization does not proceed beyond a limited depth mer is added and polymerized and so on, until a com­ where laser intensity is below a threshold value. plete object is manufactured (Fig. 1) [5, 17, 53, 54]. Poly­

p, Laser 2.5 mm ^ -5 * 1 0 '19

i LFirst voxel Monomer/oligomer + photoinitiator 2*10‘ 18 ^-5*1CT18 ^ — 1x10'17 у-— 2*1СГ17 ! V -—5*1Cf^7 1 — 1x1 O'16 ^fууууууууууууууууууууууууууууууууу / у / — 2x1Cf18 At t=0 ■. polymerization of the first voxel 2 2 Resin surface Laser Fig. 2. The distribution of photon absorption [55]

Figure 2 shows the distribution of photon absorption, and indicates the cross-sectional progress in the poly­ merization of a solidified cell. Parameter p means the probability that a photon is absorbed in a unit volume per one photon input: t>0 : polymerization of successive voxels f - r m <17> dx Fig. 1. Principle of layer-by-layer spacse-resolved 3D photo­ polymerization by a laser beam [5, 54] Tire absorption p of n identical photons by a molecule A is proportional to the nth power of the excitation laser flux (I) (photon • cm-2 ■ s'1) [15]. merization occurs in a volume element called the voxel. Every laser pulse polymerizes a voxel. Successive poly- Multiphotonic 3D photopolymerization merizaton occurs by polymerizing voxel after voxel. Multiphotonic 3D photopolymerization is based on the absorption of two photons (differing in energies, E, Absorption of the laser radiation = /zv, and E2 = /zv2) by a photoinitiating system [3, 5, Tire laser radiation passing through the resin compo­ 56—58]. The energies of the two photons must satisfy site layer should be completely absorbed by photoinitia­ the following conditions: tors. However, only very small amounts of photons are /zv, + /zv, > El( (18) absorbed in the micro-layer of the resin composite, and with /zv, < Erf and hv2 < Eti, where Erf is the energy of disso­ most of the exposure light passes straight through the ciation of a photoinitiator into free radicals. material. The laser light is not absorbed homogeneously by the composite layer but, according to the exponential The photoinitiator molecule (A) absorbs first photon Beer-Lambert law, decreases exponentially with depth E, and is excited to the singlet excited state ‘S, and by (x) [5, 15, 55]: inter system crossing (ISC) to the triplet excited state 3T, (14) (Fig. 3): j r = Io exp(-XE. [A]) cLy A(S0)+ /zv,—>'A*(' S,) (19) or 'A * ISC > M * f T ,) (20) (15) "7 “ = L exp(-.vD ) d.x One of this "intermediate" states, 'A* (’S,) or 3A* (3T,), where absorbs the second photon E2 (singlet-singlet absorption or triplet-triplet absorption) and is excited to higher D„ = E ; [ A ] (16) zz-states, 1 S„ or 3T„, whose excitation energy is higher 766 POLIMERY 2000, 45, nr 11—12

Optimization of the 3D polymerization parameters

The CAD models [17, 20—23] for a laser induced 3D photopolymerization process couple the irradiation pa­ dissociation rameters [16—18], chemical and polymerization reac­ state tions kinetics, and heat transfer equations. Quantities which should be predicted include: spatial variations in light intensity, absorbed light, conversion of monomer to polymer, depletion of photoinitiator, and local varia­ tions of temperature in and around the spot contacted by the laser (heat of polymerization). In addition, physi­ cal data such as: rate constants of photoinitiation, pro­ pagation and termination (temperature dependent) for polymerization, heat of polymerization, heat capacity, thermal conductivity, density of monomer/polymer are Fig. 3. Energy diagram of a biphotonic reaction: S0 is the required. This allows predictions to be made about the initial ground state of a photoinitiator molecule, 1S1 or ’T, laser dwell time, depth penetration, and uniformity of are the singlet or triplet "intermediate" excited states formed the photopolymer formed in the 3D process. after absorption of a photon with energy E, = hv,; ,S„ or 1 TM The relationship between the cure depth (thickness of are higher singlet and triplet excited states formed after anb- the exposed layer) (Crf) for a single laser cured line and sorption of a second photon with energy E, = hv2 and E,( is the applied laser maximum energy (E,„„r) is called the the energy of the dissociation state of a photoinitiator into "working curve", and is given by the equation: free radicals

C,i = D (, ln(EIIIl)v / E ,) (24) than the energy of dissociation of a photoinitiator into where D;, is the light "penetration depth", and Ec is the free radicals (Ef): "critical exposure" at which solidification starts to occur [16, 64]. Equation (24) states, in the mathematical form, the 1 A * (' S,) + /;v2-» 'A ,* (' S„) (21) following basic points [16, 65]: — the cure depth is proportional to the natural loga­ (2 2 ) rithm of the maximum exposure on the centerline of the scanned laser beam; Tire "intermediate" states ’A* (’S,) or 3A*(3T,) must be — a semilog plot of Q versus E„,„v should be a stra­ in long-lived photochemically unreactive excited states ight line; and have a high quantum efficiency. For that reason the — the slope ACrf/AlnE of the "working curve" is pre­ triplet-triplet absorption is the most acceptable photo­ cisely D(„ the penetration depth of a resin, at a given la­ chemical process. ser wavelength; In this two-beam process, originating from upper — the intercept of the "working curve", specifically excited states, a few photoinitiators like ketones (ben- the value of the exposure at which the cure depth is zophenone), diketones (benzil) and 9-halofluorenones, zero, is simply Ec, the critical exposure of a resin, at a can be activated only after they absorb two photons of given laser wavelength; different but well-known wavelengths [58—63]. Poly­ — since D;, and E, are resin parameters, then both the merization will be initiated only in the volume in which slope and the intercept of the "working curve" are inde­ two light beams of the proper wavelengths intersect. pendent of laser power. The amount of the radiations of two lasers absorbed A higher exposure will gradually increase the degree by a photoinitiating system is given by the modified of cure, but the cure depth is given by the thickness of Beer-Lambert equation: the layer. The accurate determination of the variables (23) that define the "working curve" for the resin mixture is £ = 5 W 0(.,)M the most important factor in controlling the accuracy of where 5 is the biphotonic absorption coefficient I0iv<)and the stereolithographic process. l0(ls) are intensities of two lasers beams 1 and 2, and [A ] is The "maximum cured linewidth" (L„,„v) is defined as the concentration of absorbing species (photoinitiator). [16]:

Tire problem which can limit multiphotonic initiation EIf„.v = B(Ctl / 2D (,) 1/2 (25) of polymerization is the differences in the refractive in­ where В is the laser spot diameter. This "maximum cured dices of resin composite: monomers, oligomers and fi­ linewidth" function shows that for a Gaussian laser nally crosslinked polymer, which are not equal and uni­ scanned in a straight line across a photopolymerizing form during the polymerization reactions. The refrac­ layer obeying the Beer-Lambert Law of absorption: tive index can change locally due to temperature rise, as each photopolymerization is an exothermic reaction. POLIMERY 2000, 45, nr 11—12 767

— the cured linewidth, (L„„„), is directly proportional and resin composition (type of photoinitiator, mono­ to the laser spot diameter (B); mers and their ratio) [5, 15, 53, 54]. — the cured linewidth is also proportional to the The linear and volume shrinkage (3—15%) [67], cau­ square root of the ratio of the cure depth to the resin ses distortion such as curl (Fig. 4) [6 8 , 69] and internal penetration depth (Crf/Dp); stress in final products. The solidification process occurs — thus, a deeper curing will result in an increased after the passage of the laser beam (Fig. 5). The shrin­ linewidth; for that reason, it is very important to deter­ kage continues after the layer has become attached to mine "the line width compensation factor" (algorithm the layer below. This shrinkage generates the stress per­ in software) for the photosensitive material used; pendicular to the beam path, which cause the attached — the line width in the stereolithographic process is, layer to curl. in part, influenced by the amount of light scattering present in the resin mixture. Light scattering is the con­ sequence of certain additives that can be added to pho­ topolymer to achieve the desired balance of imaging and/or physical properties (e.g ., fillers [6 6 ]).

Volume contraction (shrinkage) and curl distortion in the 3D photopolymerization

Polymerization cause linear and volume contractions (shrinkages). Tire shrinkage that occurs during polyme­ rization arises from different causes: ■— The major factor relates to the fact that monomers Fig. 5. Schematic side view of moving laser beam incident are located at Van der Waals distances from one on resin (postirradiation shrinkage area is shown crossha- another, while in the corresponding polymer the tched) [69] (mono)mer units have moved to within a covalent ra­ dius which is approximately 1/3 of the Van der Waals Liquid photopolymer radius. This causes the shrinkage that is roughly related Solidified part to the number of mono(mer) units per unit volume converted to polymer. -I — Tire change in entropy and the relative free volu­ mes of monomer and polymer. Free volume is primarily _.—)/?////////}//////£ ////i-*- — Platform determined by the packing efficiency of the macromole­ cules. Crystalline (and to some extent semi-crystalline) Liquid resin polymers are, for example, more closely packed than the corresponding amorphous polymers. The shrinkage depends on various parameters such as: laser flux intensity, irradiation time, curing depth

Shrinkage Ł Distortion

s >7 Liquid -----► Solid J

H ► Force -«—I

I Layer 2 ] Normal layer I Layer 1~] < S >

Curl

c ^

__ Cantilever Fig. 6. Schematic side view of part building leading the curl: Fig. 4. Physical representation of geometric distortion resul­ (a) first layer of cantilever, (b) second layer of cantilever and ting from anisotropic shrinkage [70] (c) after many layers [69] 768 POLIMERY 2000, 45, nr 11—12

Curl distortion, is a phenomenon characterized by Successively irradiated voxels bending of multiple unsupported cantilevered parts where the solidifying resin undergoes shrinkage (Fig. 6 ) [5, 53, 54, 69, 70]. Curl distortion can be manifested in a variety of forms (Fig. 7). It is desirable to minimize curl 1 st distortion, because higher part accuracy can then be 2 nd 3 rd achieved. A high curl distortion requires ancillary support structures of the photofabricated parts. Polymerized voxels

CAD model Distorted part

Fig. 9. Warping of a polymerized bar resulting from shrinka­ Upward distortion ge [53]

□ 0 У voxel

Iteration 800 (t = 0.25 sf

Fig. 7. Comparison of CAD models with distorted parts by the curl [69]

Surface of the laser beam Iteration 1200 (t=0.37 s) I I I I I IU V laser Fig. 10. Computer simulation of the polymer shrinkage at different times in the case of a parallelepipedic laser beam [5, 54] Irradiated Maximum voxel depth absorption Solid The deformation can be strongly decreased by several of light polymer ways [5]: — employing as high-molecular as possible oligome­ ric components, consistent with maintaining a relatively Fig. 8. The shrinkage of a voxel vs. irradiation depth [53] low formulation viscosity (however, the high viscosity of the resin composite can act as a support); The total deformation in the layer-by-layer space-re- — using monomers with very low shrinkage; solved 3D photopolymerization depends on the defor­ — the internal part of the object, should be polymeri­ mation of every polymerized volume element (voxel) zed, so that deformation will concern only a small volu­ (Fig. 8 ) and on the way these elementary deformations me of a polymer; combine with themselves (memory effect) to give a war­ — using a pulsed rather than a continuous laser irra­ ping effect (Fig. 9) [5, 53]. A simulation model of geome­ diation; trical deformations, based on the hypothesis of homoge­ — controlling the intensity of the photon flux and ir­ neous shrinkage and viscoelastic properties of the poly­ radiation time or the light displacement (dashed poly­ merizing medium, has been developed [53]. Figure 10 merization); shows the computer simulations of polymer shrinkage. — adding porous fillers [6 6 ]. POLIMERY 2000, 45, nr 11—12 769

APPLICATIONS OF 3D-SL MODELS land, and Ms. Mary Woods, Public Relations Mgr, 3D Sys­ tems, Valencia, CA, USA and European Office, 3D Systems, 3D-stereolithographic models (3D-SL) are readily sca­ GmbH, Germany, for providing excellent materials, photo­ led, quickly produced, and some 3D-SL models provide graphs and reference books enabling this review paper to be final parts with mechanical properties well suited for written. dynamic testing [71, 72]. Model testing has long been used to validate, augment, or replace structural analy­ sis. Experimental modelling is performed for three basic REFERENCES reasons: to validate analysis, to augment analysis, or to replace analysis. Experimental models can have a num­ [I] US Patent 2 755 758 (1956). [2] Herbert A. J.: J. ber of characteristics that make them attractive, compa­ Appl. Photogr. Eng. 1982, 8 , 185. [3] Schwerzel R. E., red to testing actual components. Table 13 lists several Wood V. E., McGinness V. D., Weber C. M. 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