POWDER OF SPHERICAL CROSSLINKABLE POLYAMIDE PARTICLES, PREPARATION PROCESS AND USE WITH THE SELECTIVE LASER SINTERING TECHNIQUE

Abstract

The present invention relates to a powder of spherical crosslinkable polyamide particles, which is suitable for the selective laser sintering (SLS) technique, and also to a process for obtaining such a powder of spherical crosslinkable polyamide particles. The present invention also relates to the production of articles by SLS, followed by a crosslinking step, using said powder of spherical crosslinkable polyamide particles.

Claims

1.-19. (canceled)

20. A powder of spherical particles of polyamide (I) functionalized by crosslinking functions Rt rendering it crosslinkable, wherein said crosslinking functions Rt are present at the surface and in the mass of said particles and in that said particles of crosslinkable polyamide (I) have a mean diameter d50 in the range 20 μm to 100 μm.

21. The powder of spherical particles of crosslinkable polyamide (I) according to claim 20, wherein the mean diameters d90 and d10 of said particles of crosslinkable polyamide (I) are such that (d90-d10) is in the range 10 μm to 80 μm.

22. The powder of spherical particles of crosslinkable polyamide (I) according to claim 20, wherein the polyamide is an aliphatic or semi-aromatic, semi-crystalline polyamide.

23. The powder of spherical particles of crosslinkable polyamide (I) according to claim 20, wherein the polyamide is selected from the group consisting of PA 6, PA 6.6, PA 10.10, PA 10.12, PA 11 and PA 12.

24. The powder of spherical particles of crosslinkable polyamide (I) according to claim 20, wherein the crosslinking functions Rt are selected from the group consisting of alkoxysilane, chlorosilane and acyloxysilane groups.

25. The powder of spherical particles of crosslinkable polyamide (I) according to claim 20, wherein the crosslinking functions Rt are introduced onto a polyamide (II) by grafting.

26. The powder of spherical particles of crosslinkable polyamide (I) according to claim 25, wherein the crosslinking functions Rt are supplied by grafting, directly onto the amine and/or carboxyl and/or amide functions of the polyamide (II), termed reactive functions Rr, of a crosslinking agent (III) with formula:
Rg-R1-Si(R2).sub.3-a(R3).sub.a  (III) in which: a=0, 1, or 2; Rg is a grafting function that is capable of reacting with Rr; R1 is a divalent hydrocarbon group or a covalent bond connecting Si directly to Rg; R2 is an alkoxy or acyl group or represents a halogen, the groups R2 being identical or different when a=0 or 1; R3 is an alkyl group, the groups R3 being identical or different when a=2.

27. The powder of spherical particles of crosslinkable polyamide (I) according to claim 26, wherein the grafting function Rg of the crosslinking agent (III) comprises at least one group selected from: the amino group —NH.sub.2; groups having an ethylenic unsaturation; epoxy groups; the thiol function —SH; halogen atoms; the isocyanate group —N═C═O; and the acylurea group —CO—NH—CO—NH.sub.2 or the alkylurea group R—NH—CO—NH.sub.2, with R representing a divalent hydrocarbon group.

28. A powder of spherical particles of crosslinkable polyamide (I) according to claim 26, wherein the crosslinking agent (III) is such that a=0, R1 is a divalent hydrocarbon group, R2 is an alkoxy group, Rg is an epoxy group.

29. A powder of spherical particles of crosslinkable polyamide (I) according to claim 20, wherein the crosslinkable polyamide (I) has a proportion of crosslinking functions Rt in the range 0.3% to 9% by weight relative to the total weight of crosslinkable polyamide.

30. A process for the preparation of an intermediate article from a powder of spherical particles of crosslinkable polyamide (I) according to claim 20, using a selective laser sintering technique.

31. A process for the preparation of an article, comprising: i. forming an intermediate article using a selective laser sintering technique, starting from a powder of spherical particles of crosslinkable polyamide (I) according to claim 20; and ii. crosslinking at least a portion of the crosslinkable functions Rt of said crosslinkable polyamide (I) of the intermediate article.

32. The process according to claim 31, wherein the crosslinking is carried out by hydrolysis in ambient air.

33. An article produced from a powder of spherical particles of crosslinkable polyamide (I) in accordance with the process of claim 31.

Description

A BRIEF DESCRIPTION OF THE FIGURES

[0165] FIG. 1 represents the IR spectra for Example 1.

[0166] FIG. 2 represents the IR spectra for Example 2.

[0167] FIG. 3 represents the IR spectra for Example 3.

[0168] FIG. 4 represents the IR spectra for Example 4.

[0169] FIG. 5 represents graphs of the variation of the elastic modulus and the loss factor or damping factor corresponding to the tangent of the loss angle delta (Tan Delta) for Examples 5 and 6 compared with that for the reference PA 12 and for the comparative example.

[0170] FIG. 6 represents graphs of the variation of the elastic modulus and the loss factor or damping factor corresponding to the tangent of the loss angle delta (Tan Delta), for Example 7 compared with that for the reference PA 11

[0171] FIG. 7 represents optical microscope images for PA12, PA11, the polymers of Examples 1 to 4 and that for the comparative example.

[0172] In an embodiment, the polyamide (II) is a semi-aromatic, semi-crystalline polyamide. Examples of suitable semi-aromatic, semi-crystalline polyamides in the context of the present invention that may be cited are PA mXD.6 (polymetaxylylene adipamide) and PA mXD.10 (polymetaxylylene sebacamide). In one particular embodiment, the polyamide (II) is PA mXD.10.

[0173] In a preferred embodiment of the invention, the polyamide (II) is an aliphatic polyamide, preferably selected from PA 6, PA 6.6, PA 6.10, PA10.10, PA10.12, PA 11 and PA 12, and preferably PA 11 and PA 12.

[0174] In a first embodiment, the crosslinking functions Rt are introduced during the synthesis of the polyamide (II).

[0175] In another embodiment, the crosslinking functions Rt are provided by direct grafting onto the polyamide (II). In this regard, the polyamide (II) carries reactive functions on which a crosslinking agent reacts. In this embodiment, the crosslinking functions Rt are supplied by grafting, directly onto the amine and/or carboxyl and/or amide functions of the polyamide (II), termed reactive functions Rr, of a crosslinking agent (III). In other words, the crosslinkable polyamide (I) is characterized in that, when it is being produced, the functions Rg of the crosslinking agents (III) react with the reactive functions Rr of the polyamide (II) to result in grafting of the crosslinkable functions Rt.

[0176] Advantageously, the crosslinking agent (III) is as defined above.

[0177] The starting polyamides (II) and the crosslinking agents (III) are commercially available, in particular from Arkema and Momentive Performance Materials Inc respectively.

[0178] Advantageously, in accordance with the invention, the crosslinkable polyamide (I) differs from the starting polyamide (II) only in the presence of crosslinkable functions.

[0179] In an embodiment, the mixture in step c) is produced with a proportion of crosslinking agent (III) in the range 1% to 10% by weight, preferably 3% to 8% by weight, and even more preferably 4% to 6% by weight, relative to the total weight of crosslinking agent (III) and of polyamide (II).

[0180] Advantageously, the percentage of the crosslinking functions present in the crosslinking agent (III) represents 30% to 90% by weight of the crosslinking agent (III). Thus, when 1% to 10% by weight of crosslinking agent (III) is used to prepare the crosslinkable polyamide (I), this advantageously has a percentage of crosslinking functions Rt in the range 0.3% to 9% by weight, and preferably 1% to 5% by weight, relative to the total weight of crosslinkable polyamide (I).

[0181] Advantageously, the amount of grafting is in the range 50% to 100%, preferably 60% to 100% and even more preferably 70% to 100%. The amount of grafting here is the yield from the grafting step.

[0182] In an embodiment, the mixture in step c) is produced at a temperature in the range 20° C. to 30° C.

[0183] In an embodiment, the mixing in step c) is carried out dry, without a solvent, in particular in a container or a sealed mixer, in an inert atmosphere or otherwise.

[0184] In an embodiment, if Tg.sub.(II)+70° C.>Tcryst.sub.(II)−35° C., the heating in step d) is carried out at a temperature T1 in the range from Tg.sub.(II)+5° C. to Tcryst.sub.(II)−35° C., preferably from Tg.sub.(II)+10° C. to Tcryst.sub.(II)−40° C., and even more preferably from Tg.sub.(II)+20° C. to Tcryst.sub.(II)−45° C.

[0185] In an embodiment, if Tg.sub.(II)+70° C.<Tcryst.sub.(II)−35° C., the heating in step d) is carried out at a temperature T1 in the range from Tg.sub.(II)+5° C. to Tg.sub.(II)+70° C., preferably Tg.sub.(II)+10° C. to Tg.sub.(II)+70° C., preferably from Tg.sub.(II)+20° C. to Tg.sub.(II)+70° C.

[0186] In an embodiment, the heating step d) is carried out in a sealed container, which may or may not be stirred, preferably in an inert atmosphere, in particular nitrogen or argon.

[0187] In an embodiment, the heating in step e) is carried out at a temperature T2 greater than or equal to T1+10° C. and lower than Tcryst.sub.(II), preferably from T1+20° C. to Tcryst.sub.(II)−5° C., and even more preferably from T1+30° C. to Tcryst.sub.(II)−10° C.

[0188] In general, the heating of step d) to the temperature T1 is maintained for a period of 1 hour (h) to 4 h and the heating of step e) to the temperature T2 is maintained for a period of 3 h to 12 h.

[0189] In a particular embodiment of the invention, the preparation process comprises a step f), which is subsequent to step e), for adding a flow agent, preferably selected from silicas or fumed silicas, a reinforcing filler, preferably selected from solid or hollow glass beads, carbon fibers, wollastonite fibers or aluminas, a flame retardant, a thermal stabilizer, an antistatic agent or conductive agent, or a colorant.

Use of a Powder of Spherical Particles of Crosslinkable Polyamide (I)

[0190] Formation of an Intermediate Article with the SLS Technique

[0191] The present invention also provides the use of a powder of spherical particles of crosslinkable polyamide (I) as defined in the context of the invention for the preparation of articles, termed intermediate articles, using the selective laser sintering technique (SLS). The present invention also provides a process for the preparation of articles, known as intermediate articles, using the selective laser sintering technique (SLS), from a powder of spherical particles of crosslinkable polymer (I) of the present invention.

[0192] The three-dimensional shape of the article, termed the intermediate article, is then produced by the SLS technique, i.e. by forming superimposed layers of elements that are bonded together in succession by repeating the following steps:

[0193] a) depositing a continuous bed of powder comprising or exclusively constituted by a powder of spherical particles of crosslinkable polyamide (I) as defined in the context of the invention;

[0194] b) carrying out localized consolidation of a portion of the deposited powder of the spherical particles of crosslinkable polyamide (I) by applying a laser beam in accordance with a predetermined pattern for each layer, in order to generate the layer element, and simultaneously bonding the layer element that has been formed thereby to the preceding layer, in a manner such as to cause the desired three-dimensional shape of the intermediate article to grow progressively.

[0195] Advantageously, the continuous bed of powder of step a) has a constant thickness and extends as a surface above the section of the desired intermediate article taken at the level of the layer, in order to guarantee precision at the ends of the article. The thickness of the bed of powder is advantageously in the range 40 μm to 120 μm.

[0196] The consolidation of step b) is carried out by laser treatment.

[0197] To this end, it is in particular possible to use any SLS printing machine that is known to the person skilled in the art such as, for example a 3D printer of the SnowWhite type from Sharebot, of the Vanguard HS type 3D Systems or of the P396 type from EOS.

[0198] When a SnowWhite type printer is used, the power of the laser is advantageously in the range 4 watts (W) to 8 W.

[0199] The movement rate of the laser is advantageously in the range 0.2 meters per second (m/s) to 2.5 m/s, preferably 0.8 m/s to 2 m/s.

[0200] The parameters of the SLS printing machine are selected in a manner such that the surface temperature of the bed of powder is in the sintering range, i.e. comprised between the offset crystallization temperature and the onset fusion temperature, and preferably is in the range from Tcryst.sub.(I)offset+10° C. to Tfus.sub.(I)onset−5° C.

[0201] Advantageously, the powder of particles of crosslinkable polyamide (I) does not crosslink during the passage of the laser and the parts obtained are still thermoplastic.

[0202] Once the three-dimensional structure of the intermediate article has been formed, the non-consolidated material is then eliminated.

[0203] Advantageously, the powder of particles of crosslinkable polyamide (I) employed but that has not been subjected to laser impact is not agglomerated under the action of the heat and does not undergo any modification at all, and particularly advantageously can be used again for the preparation of articles by SLS, and in particular at least 5 times.

Formation of an Article by Crosslinking an Intermediate Article

[0204] The present invention also provides an article formed by a first step for selective laser sintering (SLS) of a powder of spherical particles of crosslinkable polyamide (I) such as that defined in the context of the invention, followed by a step for crosslinking the crosslinking functions of said crosslinkable polyamide (I).

[0205] The present invention provides the preparation of a polyamide article, comprising:

[0206] i. forming an intermediate article using the selective laser sintering technique, starting from a powder of spherical particles of crosslinkable polyamide (I) such as that defined in the context of the invention, and in particular in accordance with the process described in the context of the invention;

[0207] ii. crosslinking at least a portion of the crosslinkable functions Rt of said crosslinkable polyamide of the intermediate article.

[0208] In an embodiment, the crosslinking of step ii) is carried out in the presence of water, preferably by take-up of moisture from the open air or in a controlled atmosphere, for example at 40° C. with a relative humidity of 80%, or by immersion in water.

[0209] In a particular embodiment, the crosslinking of step ii) is carried out by immersing the intermediate article in water, preferably at a temperature in the range 20° C. to 100° C., preferably 50° C. to 95° C., for 1 h to 24 h, preferably 6 h to 18 h and more preferably 9 h to 15 h.

[0210] In an embodiment, the amount of crosslinking is in the range 70% to 100%, preferably 100%.

[0211] The “amount of crosslinking” of the present invention should be understood to mean the proportion of crosslinkable functions in the crosslinkable polyamide that has been crosslinked. This proportion is expressed as the percentage by weight relative to the initial weight of the crosslinking functions.

[0212] In an embodiment, the process for the preparation of a polyamide article as mentioned above furthermore comprises a step iii), which is subsequent to step ii), for drying the article that has been formed. Preferably, this drying step is carried out at a temperature in the range 20° C. to 100° C., preferably 50° C. to 95° C., in particular for 1 h to 12 h, preferably 3 h to 6 h.

[0213] The present invention is illustrated in the examples below, which are given purely by way of illustration without in any way limiting the scope. The examples make reference to the accompanying figures.

[0214] FIG. 1 represents the IR spectra for Example 1, with: [0215] 1: glycidoxypropyl trimethoxysilane (Silquest A 187 marketed by Momentive Performance Materials Inc); [0216] 2: PA 12 (Orgasol invent smooth marketed by Arkema); [0217] 3: mixture of 95% of PA 12 (Orgasol invent smooth marketed by Arkema)+5% of glycidoxypropyl trimethoxysilane (Silquest A 187 marketed by Momentive Performance Materials Inc); [0218] 4: PA 12 (Orgasol invent smooth marketed by Arkema) impregnated with glycidoxypropyl trimethoxysilane (Silquest A 187 marketed by Momentive

[0219] Performance Materials Inc) after the impregnation phase at 80° C.; and [0220] 5: PA 12 grafted with 5% of glycidoxypropyl trimethoxysilane.

[0221] FIG. 2 represents the IR spectra for Example 2, with: [0222] 1: glycidoxypropyl triethoxysilane (Silquest A1871 marketed by Momentive Performance Materials Inc); [0223] 2: PA 12 (Orgasol invent smooth marketed by Arkema); [0224] 3: mixture of 95% PA 12 (Orgasol invent smooth marketed by Arkema)+5% of glycidoxypropyl triethoxysilane (Silquest A1871 marketed by Momentive Performance Materials Inc); and [0225] 4: PA 12 grafted with 5% of glycidoxypropyl triethoxysilane.

[0226] FIG. 3 represents the IR spectra for Example 3, with: [0227] 1: glycidoxypropyl triethoxysilane (Silquest A1871 marketed by Momentive Performance Materials Inc); [0228] 2: PA 12 (Orgasol invent smooth marketed by Arkema); [0229] 3: mixture of 92% PA 12 (Orgasol invent smooth marketed by Arkema)+8% of glycidoxypropyl triethoxysilane (Silquest A1871 marketed by Momentive Performance Materials Inc); and [0230] 4: PA 12 grafted with 8% of glycidoxypropyl triethoxysilane.

[0231] FIG. 4 represents the IR spectra for Example 4, with: [0232] 1: glycidoxypropyl triethoxysilane (Silquest A1871 marketed by Momentive Performance Materials Inc); [0233] 2: PA 11 (Rilsan Invent Natural marketed by Arkema); [0234] 3: mixture of 94% PA 11 (Rilsan Invent Natural marketed by Arkema)+6% of glycidoxypropyl triethoxysilane (Silquest A1871 marketed by Momentive Performance Materials Inc); and [0235] 4: PA 11 grafted with 6% of glycidoxypropyl triethoxysilane.

[0236] FIG. 5 represents graphs of the variation of the elastic modulus and the loss factor or damping factor corresponding to the tangent of the loss angle delta (Tan Delta) for Examples 5 and 6 compared with that for the reference PA 12 and for the comparative example, with: [0237] graph 1: Example 5; [0238] graph 2: Example 6; [0239] graph 3: PA 12 (Orgasol invent smooth marketed by Arkema); and [0240] graph 4: comparative example.

[0241] FIG. 6 represents graphs of the variation of the elastic modulus and the loss factor or damping factor corresponding to the tangent of the loss angle delta (Tan Delta), for Example 7 compared with that for the reference PA 11, with: [0242] graph 1: PA 11 (Rilsan Invent Natural from Arkema); and [0243] graph 2: Example 7.

[0244] FIG. 7 represents optical microscope images for PA12, PA11, the polymers of Examples 1 to 4 and that for the comparative example.

EXAMPLES

[0245] Materials and Methods

[0246] DSC analysis: The differential scanning analyses (DSC) were carried out with a DSC Q20 instrument from TA instruments. The thermal cycle applied was as follows: 1.sup.st ramp-up from ambient temperature to 240° C. at 10° C./min, temperature ramp-down 240° C. to −20° C. at 10° C./min, 2.sup.nd ramp-up from a temperature of −20° C. to 240° C. at 10° C./min.

[0247] Grain size and shape of particles: The grain size for powders of polymer particles was measured by dry laser granulometry with the aid of a Malvern Instruments Mastersizer 2000 granulometer. The shape of the particles was observed by optical microscopy with the aid of a USB microscope from Andonstar.

[0248] Thermoplasticity: The thermoplasticity of the polymers was validated by producing a thin film by thermocompression with a thermoregulated hydraulic press (40 grams (g) of powder deposited between the press plates heated to 220° C., pressed at 10 bar with a holding period of 2 minutes).

[0249] Preparation of a powder of spherical particles of crosslinkable polyamide of the invention: 1 kilogram (k) of powder of polyamide (II) was dry mixed with the crosslinking agent (III) until a sticky paste was obtained which did not flow. The mixture (II+III) was then introduced into a sealed stainless steel container that was then placed in a programmable oven. The following thermal cycle was applied: isothermal at 80° C. for 3 h in order to carry out impregnation of the powder, followed by isothermal at 130° C. for 8 h in order to carry out grafting.

[0250] Infrared analysis: Infrared spectroscopy was carried out in reflection with a Nicolet IS10 spectrometer equipped with a Smart ITR cell.

[0251] Thermogravimetric analysis (TGA): the TGA analysis was carried out under an inert atmosphere (nitrogen) by applying a temperature ramp-up of 10° C./min up to 650° C. with a TGA Q500 instrument from TA instruments.

Example 1: Preparation of a Powder of Spherical Particles of Crosslinkable Polyamide of Type PA 12 Grafted with 5% w/w of Glycidoxypropyl Trimethoxysilane

[0252] A PA 12 powder suitable for laser sintering (Orgasol invent smooth marketed by Arkema) (d50=38 μm, spherical grain, fusion temperature equal to 182° C., glass transition temperature equal to 40° C.) was modified according to the invention. The grafting agent was glycidoxypropyl trimethoxysilane (Silquest A 187 marketed by Momentive Performance Materials Inc) in a proportion of 5% w/w. A container of crosslinkable polyamide of the invention was prepared in accordance with the process described in the “Materials and method” section.

[0253] Another container of powder of particles de PA 12 (Orgasol smooth invent marketed by Arkema), impregnated with 5% w/w of glycidoxypropyl trimethoxysilane (Silquest A 187 marketed by Momentive Performance Materials Inc) was also prepared in the same manner, but removed from the oven after the impregnation phase at 80° C. before the grafting phase.

[0254] After cooling, the powder of particles of crosslinkable polyamide obtained was dried and regained flow properties that were close to that of the unmodified PA 12 (Orgasol invent smooth marketed by Arkema).

[0255] In order to verify grafting of the glycidoxypropyl trimethoxysilane, an analysis by infrared spectroscopy and thermogravimetric analysis (TGA) was carried out (i) on the powder of particles of crosslinkable polyamide and (ii) on the powder of particles of non-grafted PA 12 impregnated with glycidoxypropyl trimethoxysilane.

[0256] The infrared analysis showed that the absorbance peak at 760 cm.sup.−1, which is characteristic of the epoxy function of silane, present in the initial mixture and in the sample removed at the end of the impregnation phase (see FIG. 1, graphs 3 and 4), had disappeared after the grafting phase (see FIG. 1, graph 5). These epoxy functions were consumed by the grafting reaction.

[0257] The absorbance peak at 1072 cm.sup.−1, which is characteristic of —O—CH— bonds, was shifted to 1110 cm.sup.−1 (see FIG. 1).

[0258] Regarding the powder removed at the end of the impregnation phase, the two peaks coincided: grafting had already commenced during the impregnation phase. The TGA analysis provided a proportion of volatiles of 4% to 4.5%.

[0259] Regarding the powder of particles of polyamide removed at the end of the grafting phase, the peak at 1070 cm.sup.−1 had disappeared. The proportion of volatiles measured by TGA was less than 0.2%, which indicated that grafting was almost complete.

[0260] The thermal profile of the powder of particles of crosslinkable polyamide was determined by DSC analysis. The results prove that the thermal profile of the PA 12 powder was not modified by the grafting (see Table 1).

[0261] The grain size of the powder obtained was almost unmodified (see Table 2 and FIG. 7). The spherical shape of the particles was retained. The particle size remained homogeneous: the (d90-d10) value was 26 μm, and was comparable to that of PA 12 (23 μm).

[0262] The thermoplasticity of the grafted PA powder was validated by producing a thin film by thermocompression with a thermoregulated hydraulic press. The film obtained was perfectly homogeneous, thereby indicating that the PA 12 powder grafted with 5% w/w of glycidoxypropyl trimethoxysilane was still thermoplastic.

[0263] Thus, the PA 12 particles grafted with 5% w/w of glycidoxypropyl trimethoxysilane of the invention were spherical and homogeneous in size and suitable for the SLS technique. The powder obtained thereby was dry and had good flow properties. In addition, the thermal profile of the powder of spherical particles of PA 12 grafted with 5% w/w of glycidoxypropyl trimethoxysilane of the invention had not been modified by the grafting and thus retained thermal properties that are suitable for the SLS technique.

TABLE-US-00001 TABLE 1 Thermal characteristics measured by DSC 1.sup.st heating ramp-up Cooling ramp-down 2.sup.nd heating ramp-up Tfus Tfus Tcryst Tcryst Tfus Tfus Onset peak ΔHfus Offset peak ΔHcryst Onset Peak ΔHfus Polymer (° C.) (° C.) (J/g) (° C.) (° C.) (J/g) (° C.) (° C.) (J/g) PA 12 (Orgasol Invent 174 182 −98 154 151 54.5 167 172/178 −52.8 Smooth from Arkema) PA 11 (Rilsan Invent 198 202 −106.4 164 160 45.0 178 183/189 −46.0 Natural from Arkema) Example 1 174 181 −86.5 151 148 48.9 170 172/178 −48 Example 2 175 184 −93.5 152 148 51.8 165  −/179 −53.5 Example 3 178 183 −86.5 151 148 48.9 170 172/178 −48.0 Example 4 199 205 −103.6 161 156 44.6 176  −/186 −48.0 Example 5 168 179 −42.3 151 147 58.6 168 179 −51.3 Example 6 169 179 −51 151 148 44.7 170  −/180 −53.0 Example 7 177 191 −40.5 157 162 47.2 174 183/190 −48.0 Comparative example 168 179 −41 159 152 44.6 169 179 −49

TABLE-US-00002 TABLE 2 Grain size of powders Grain size distribution (μm) By volume By number Polymer D10 d50 D90 D90-D10 D10 d50 D90 PA 12 (Orgasol 28 38 51 23 24 32 44 Invent Smooth) PA 11 (Rilsan 15 37 71 56 6 9 22 Invent Natural) Example 1 26 37 52 26 22 33 44 Example 2 28 38 53 25 24 33 45 Example 3 27 41 54 27 23 35 46 Example 4 16 40 74 58 8 12 24 Comparative 35 71 121 86 5 10 35 example