METHOD FOR PRODUCING ZIRCONIUM DIOXIDE NANOPARTICLES IN THE PRESENCE OF AN AMINO ACID

Abstract

This invention relates to a process for preparing nanoparticles of zirconium dioxide, ZrO.sub.2, by hydrothermal treatment of a zirconium IV compound in the presence of water, at a pH below 7, and at least one amino acid comprising at least 4 carbon atoms, said amino acid exhibiting an acid function to amine function ratio greater than or equal to 1. The invention also relates to zirconium dioxide nanoparticles having a visible transmittance greater than or equal to 20% at 400 nm and greater than or equal to 95% at 800 nm measured in water at a concentration of 40% by weight

Claims

1. A process for preparing nanoparticles of zirconium dioxide, ZrO.sub.2, by hydrothermal treatment, said process comprising hydrothermally treating a zirconium IV compound in the presence of water, at a pH below 7, and at least one amino acid comprising at least 4 carbon atoms, said amino acid exhibiting an acid function to amine function ratio greater than or equal to 1.

2. The process according to claim 1, wherein the hydrothermal treatment is carried out at a temperature greater than or equal to 100° C., and at a pressure less than or equal to 2 MPa.

3. The process according to claim 1, wherein the zirconium IV compound is chosen from the group consisting of zirconium halides.

4. The process according to claim 1, wherein the amino acid is chosen from the group consisting of aminobutanoic acids, aminopentanoic acids and aminohexanoic acids.

5. The process according to claim 1, wherein the amino acid is formed in situ, by hydrolysis, from an amino acid precursor chosen from the group consisting of lactams.

6. The process according to claim 1, wherein the water in the hydrothermal treatment is obtained only from a hydrated form of the zirconium IV compound.

7. The process according to claim 1, wherein the hydrothermal treatment is carried out at a pressure of between 0.1 MPa and 0.6 MPa.

8. The process according to claim 1, wherein the amino acid is present in a molar ratio to the zirconium IV compound of between 1 and 50.

9. The process according to claim 1, wherein the hydrothermal treatment is carried out in the presence of one or more sources of dopant.

10. Zirconium dioxide nanoparticles, exhibiting a visible transmittance greater than or equal to 20% at 400 nm and greater than or equal to 95% at 800 nm, measured in water at a concentration of 40% by weight, at 20° C. with an optical path length of 10 mm.

11. The zirconium dioxide nanoparticles according to claim 10, wherein said nanoparticles exhibit, in water and at a concentration of 40% by weight, a viscosity of between 1 and 10 mPa.Math.s.

12. The zirconium dioxide nanoparticles according to claim 10, wherein said nanoparticles exhibit, in dispersion in water, a refractive index greater than or equal to 1.40 and less than or equal to 1.90 for a concentration at 40% by weight and greater than or equal to 1.50 and less than or equal to 2.00 for a concentration of 65% by weight.

13. The zirconium dioxide nanoparticles according to claim 10, wherein said nanoparticles exhibit, in dispersion in water, a dispersion index of between 1 and 7.

14. The zirconium dioxide nanoparticles according to claim 10, wherein said nanoparticles have a refractive index of between 2.0 and 2.2.

15. A dispersion comprising the zirconium dioxide nanoparticles according to one of claim 10.

16. The process according to claim 2, wherein: the zirconium IV compound is zirconium oxychloride; and the amino acid is chosen from the group consisting of 4-aminobutyric acid, norvaline, 5-aminovaleric acid and 6-aminocaproic acid.

17. The process according to claim 1, wherein the amino acid is formed in situ, by hydrolysis, from an amino acid precursor chosen from the group consisting of pyrrolidone and N-methylpyrrolidone, and wherein the zirconium IV compound is zirconium oxychloride.

18. The process according to claim 1, wherein the amino acid is present in a molar ratio to the zirconium IV compound of between 3 and 30.

19. The process according to claim 9, wherein at least one of the one or more sources of dopant is chosen from the group consisting of a source of yttrium and/or a source of cerium and/or a source of gadolinium.

20. The zirconium dioxide nanoparticles according to claim 10, wherein: said nanoparticles exhibit, in water and at a concentration of 40% by weight, a viscosity of between 2 and 6 mPa.Math.s; said nanoparticles exhibit, in dispersion in water, a dispersion index of between 1 and 1.5; and said nanoparticles have a refractive index of between 2.10 and 2.15.

Description

[0105] The invention and the advantages which result therefrom will emerge more clearly from the following figures and examples given in order to illustrate the invention and not in a limiting manner.

[0106] FIG. 1 is a TEM image of the zirconium dioxide nanoparticles from Example 16.

[0107] FIG. 2 is a photograph of various samples of dispersions according to the invention.

EXAMPLES OF EMBODIMENT OF THE INVENTION

Examples 1 to 23 (Invention)

[0108] Unless otherwise indicated, the percentages of the constituents of a dispersion are expressed by weight.

[0109] The doping is for its part expressed as a molar percentage relative to the molar quantity of zirconium. This is generally the content of yttrium oxide (Y.sub.2O.sub.3), cerium oxide (CeO.sub.2) or gadolinium oxide (Gd.sub.2O.sub.3). Thus, 3 mol % of yttrium corresponds to a doping of 3 mol % of Y.sub.2O.sub.3.

[0110] In an autoclave, the zirconium IV compound, the amino acid, its precursor or a mixture of several amino acids and, if necessary, water are introduced and/or a doping agent. The autoclave is then sealed, and the desired temperature and pressure is applied.

[0111] The process conditions are listed in Table 1 below. The pH before hydrothermal treatment of Examples 1 to 23 is between 1 and 5.

TABLE-US-00001 TABLE 1 ZrIV Amino Temperature Pressure Duration Example (36 mmol) acid/precursor Doping Solvent (° C.) (bar) (hour) 1 ZrOCl.sub.2 pyrrolidone No Water 180-200 10-12 3 (119 mmol) 2 ZrOCl.sub.2 Pyrrolidone Yttrium Water 200 10-12 3 (236 mmol) (3 mol %) 3 ZrOCl.sub.2 Pyrrolidone Yttrium Water 200 10-12 3 (236 mmol) (6 mol %) 4 ZrOCl.sub.2 Pyrrolidone No — 200 <3 3 (944 mmol) 5 ZrOCl.sub.2 Pyrrolidone Yttrium — 200 <3 3 (944 mmol) (3 mol) 6 ZrOCl.sub.2 NMP No — 200 <3 3 (747 mmol) 7 ZrOCl.sub.2 ACA4 No Water 200 12-15 3 (119 mmol) 8 ZrOCl.sub.2 ACA4 Yttrium Water 200 12-15 1 (119 mmol) (3 mol %) 9 ZrOCl.sub.2 ACA4 Yttrium Water 200 12-15 3 (119 mmol) (6 mol %) 10 ZrOCl.sub.2 ACA4 No — 220 <3 3 (119 mmol) 11 ZrOCl.sub.2 ACA4 Yttrium — 220 <3 3 (119 mmol) (3 mol %) 12 ZrOCl.sub.2 ACA6(119 mmol) No Water 200 12-15 3 13 ZrOCl.sub.2 ACA6(119 mmol) Yttrium Water 200 12-15 3 (3 mol %) 14 ZrOCl.sub.2 ACA6(119 mmol) Yttrium Water 200 12-15 3 (6 mol %) 15 ZrOCl.sub.2 ACA6(119 mmol) Yttrium Water 200 12-15 3 (8 mol) 16 ZrOCl.sub.2 ACA6(119 mmol) Yttrium Water 200 12-15 3 (10 mol) 17 ZrOCl.sub.2 ACA6(119 mmol) No — 220 <3 3 18 ZrOCl.sub.2 ACA6(119 mmol) Yttrium — 220 <3 3 (3 mol %) 19 ZrOCl.sub.2 Pyrrolidone + ACA6 Yttrium — 200 <3 3 (944 mmol + 119 mmol) (3 mol %) 20 ZrOCl.sub.2 NMP + ACA6 Yttrium — 200 <3 3 (944 mmol + 119 mmol) (3 mol %) 21 ZrOCl.sub.2 ACA4 + ACA6 Yttrium — 220 <3 3 (119 mmol + 119 mmol) (3 mol %) 22 ZrOCl.sub.2 ACA6 Gadolinium Water 200 12-15 3 (119 mmol) (2 mol %) 23 ZrOCl.sub.2 ACA6 Cerium Water 200 12-15 3 (119 mmol) (15 mol) ACA4 = 4-Aminobutyric acid ACA6 = 6-Aminocaproic acid

Examples CE1 to CE6 (Comparative Examples)

[0112] According to the method indicated for Examples 1 to 23, comparative tests were carried out (Table 2) in the presence of the following compounds or mixtures: [0113] Butanoic acid+butylamine (example CE1). [0114] Amino acid having two amine functions and an acid function (example CE2). [0115] Butanoic acid (example CE3). [0116] Butylamine (example CE4). [0117] Aminocaproic acid+NH.sub.4OH added gradually, leading to a pH of 12 before the hydrothermal treatment (example CE5). [0118] Addition of NaOH, formation of a precipitate purified with water (to a conductivity less than 250 μS/cm), addition of acetic acid, the final pH being less than 7 (example CE6, carried out according to EP 2,371,768).

TABLE-US-00002 TABLE 2 ZrIV Functionalizing Doping Temperature Pressure Duration Example (36 mmol) Agent (mol %) Solvent (° C.) (bar) (hour) CE1 ZrOCl.sub.2 Butanoic acid + Yttrium Water 200 12-15 3 butyl amine (3) (119 mmol + 119 mmol) CE2 ZrOCl.sub.2 DL-lysine Yttrium Water 200 12-15 3 (119 mmol) (3) CE3 ZrOCl.sub.2 Butanoic acid Yttrium Water 200 12-15 3 (119 mmol) (3) CE4 ZrOCl.sub.2 1.6-diaminohexane Yttrium Water 200 12-15 3 (119 mmol) (3) CE5 ZrOCl.sub.2 ACA6 Yttrium Water 200 12-15 3 (119 mmol) + NH.sub.4OH (3) CE6 ZrOCl.sub.2 Acetic Acid Yttrium Water 200 12-15 3 (0.108 mmol) + NaOH (3)

[0119] Once the hydrothermal treatment is complete, the temperature and pressure are lowered so that the autoclave may be opened in a safe manner. The reaction media are then optionally washed and/or diluted or concentrated in order to obtain dispersions in water, fluids, having a concentration of 40% or 65% by weight of zirconium dioxide nanoparticles.

[0120] Each of the dispersions obtained is then analyzed. The state of agglomeration of the dispersion is determined by DLS. The stability of the dispersion at different concentrations is determined visually by the appearance or not of a precipitate after waiting for 10 days, without disturbance, at 20° C. The index of dispersion (ID) is determined by the ratio between the hydrodynamic size of the particle in volume measured by DLS and the primary size of the particle measured by TEM, only in the examples showing a single crystal phase with a spherical morphology, which may correspond to the monoclinic phase (M) when the particle size is less than 10 nm or to the quadratic/cubic phase (Q). In the case where the dispersion has different crystalline phases, including a monoclinic phase (M) exhibiting anisotropic particles with a primary size greater than 10 nm, the ID is not calculated. The primary size measured by TEM, on particles of monoclinic phase and anisotropic shape of more than 10 nm, corresponds to the length of the major axis of the particle. The viscosity is determined with a Malvern Instrument, model Kinexus Pro+, using geometry cone/plan 40 mm in diameter and 4° tilt at 20° C. The refractive index of the dispersion is determined at 20° C., at 589 nm, with an Anton Paar apparatus, model Abbemat 200.

[0121] As such, a Bruker D8 Advance diffractometer with Cu K-alpha radiation was used for 2-theta angles between 10-75° and the characteristic peaks were identified and attributed to either quadratic/cubic (Q) phase or in the monoclinic phase (M) by comparison with the X-ray diffraction database of the International Center for Diffraction Data. The relative intensity of peak 111 of phase Q and the sum of the relative intensities of peaks −111 and 111 of phase M were used to determine the majority phase (Table 3).

TABLE-US-00003 TABLE 3 DLS volume Viscosity Refractive D.sub.V (nm) TEM (mPa .Math. s) index D.sub.V50 (nm) Majority phase 40 wt % 40 wt % Dispersion Example D.sub.V90 (nm) (nm) 65 wt % 65 wt % Index 1 22.8 26.8 ± 10 — — — 20.4 (M) + — — 35.9 (Q) 2 25.8 8.6 ± 2 — — 3.00 22.8 (Q) — — 41.0 3 11.8 8.0 ± 2 — — 1.48 9.8 (Q) — — 19.5 4 9.9 4.0 ± 1 — — 2.48 9.1 (M) — — 15.0 5 5.2 .sup. 4.0 ± 0.8 — — 1.30 4.7 (M) — — 7.9 6 7.3 .sup. 3.0 ± 0.6 — — 2.43 6.4 (M) — — 11.5 7 31.6 41.5 ± 8  — — — 29.2 (M) + (Q) — — 47.2 8 25.1 15.2 ± 4  — — — 23.0 (Q) + (M) — — 37.7 9 29.1 20.2 ± 3  — — — 27.0 (Q) + (M) — — 42.4 10 41.7 52.1 ± 11 — — — 38.8 (M) — — 61.0 11 41.7 53.4 ± 12 — — — 39.1 (M) — — 60.5 12 8.4 6.0 ± 1 — — — 7.5 (Q) + (M) — — 13.1 13 6.0 5.0 ± 1 5.7 1.4123 1.2  5.4 (Q) — — 9.2 14 5.5 .sup. 5 ± 1 4.8 1.4104 1.10 4.9 (Q) 3900.2   1.5175 8.5 15 5.5 4.7 ± 1 5.0 1.4086 1.17 4.7 (Q) 3100.4   1.5086 8.0 16 4.6 4.6 ± 1 4.9 1.4019 1.00 4.9 (Q) 2500.1   1.5045 6.9 17 28.6 5.0 ± 1 — — 5.72 25.5 (M) — — 44.3 18 9.5 .sup. 3.0 ± 0.7 — — 3.17 8.6 (Q) — — 14.5 19 6.3 .sup. 2.0 ± 0.4 — — 3.15 5.5 (Q) — — 9.6 20 6.5 .sup. 2.8 ± 0.6 — — 2.32 5.8 (Q) — — 9.8 21 16.0 .sup. 3.3 ± 0.6 — — — 14.6 (Q) + (M) — — 23.8 22 7.6 6.1 ± 1 2.9 1.4091 1.25 6.9 (Q) — — 11.6 23 6.3 6.2 ± 1 3.1 — 1.02 5.7 (Q) — — 9.7 D.sub.V = hydrodynamic diameter in volume T % = transmittance in percent Q = quadratic/cubic phase particles M = monoclinic phase particles

[0122] According to the invention, a stable dispersion of ZrO.sub.2 nanoparticles at each of the concentrations was obtained in all of Examples 1 to 23.

TABLE-US-00004 TABLE 4 DLS volume D.sub.V (nm) D.sub.V50 (nm) Example D.sub.V90 (nm) TEM (nm) Stability CE1 105.3 3 ± 1 Unstable.sup.(1) 99.6 152.2 CE2 111.4 5 ± 1 Unstable.sup.(1) 104.4 165.3 CE3 85.4 >50 Unstable.sup.(1) 77.5 137.0 CE4 108.4 9 ± 2 Unstable.sup.(1) 105.1 175.3 CE5 1465.1 8 ± 1 Unstable.sup.(1) 1220.4 4730.7 CE6 7.8 5 ± 1 Stable.sup.(2) 7.1 11.8 .sup.(1)formation of a precipitate at all concentrations .sup.(2)dispersion at a concentration less than or equal to 40% by weight; formation of a solid at a concentration greater than 40% by weight

[0123] In the absence of amino acid, or when the amino acid does not correspond to that used in the invention, or when a mixture of acid and amine is used, or when in the presence of amino acid used in the invention, the pH is greater than 7, the dispersions obtained are not stable, in particular due to the presence of particle agglomerates.

[0124] Thus, among the counter-examples, only CE6 makes it possible to obtain a stable dispersion when the concentration is less than or equal to 40% by weight. On the other hand, beyond 40% by weight of nanoparticles, the dispersion becomes very viscous and begins to solidify and to dry. Thus, it is not possible to obtain a dispersion at a concentration greater than 40% by weight of nanoparticles in the case of the counterexample CE6.

[0125] The transmittances at a concentration of 40% by weight of a dispersion of nanoparticles according to Examples 6, 12 to 16, 19 and 22 and according to counterexample CE6 were measured. The transmittance, in the range 400 to 800 nm, was determined with a Jasco Model V-670 apparatus. These are listed in Table 5.

TABLE-US-00005 TABLE 5 T % at 400 nm T % at 800 nm Example 40 wt % 40 wt % 6 31.4 95.0 12 28.1 91.6 13 46.9 95.4 14 59.9 97.6 15 74.0 99.2 16 82.9 99.9 19 32.8 91.5 22 41.0 96.4 CE6 17.5 85.5

[0126] Thus, at the maximum concentration making it possible to obtain a stable dispersion according to counterexample CE6, namely 40% by weight of nanoparticles, the dispersions according to the invention exhibit better total transmittance at 400 nm and at 800 nm.

[0127] On the other hand, excellent transmittances even at 65% by weight can be obtained. The transmittance of dispersions with the nanoparticles of Examples 14, 15 and 16 were measured according to the above method at different concentrations. The results are listed in Table 6 below.

TABLE-US-00006 TABLE 6 T % at T % at T % at 400 nm 600 nm 800 nm 10 wt % 10 wt % 10 wt % 30 wt % 30 wt % 30 wt % TMO 40 wt % 40 wt % 40 wt % 160-600° C. Example 65 wt % 65 wt % 65 wt % (%) 14 79.2 95.9 99.2 3.1 65.2 91.2 97.7 59.9 89.2 97.6 46.3 82.8 96.9 15 85.5 97.8 99.6 3.3 77.4 95.9 99.1 74.0 94.6 99.2 68.2 93.8 98.5 16 89.7 98.6 99.9 3.4 84.7 97.8 99.9 82.9 97.6 99.9 74.7 94.9 98.5

[0128] FIG. 2 visually illustrates the transmittance of dispersions according to the invention. Three samples 1, 2 and 3 of dispersions according to the invention are positioned in front of an image 4. Sample 1 is a dispersion comprising 50% by weight of nanoparticles from Example 16. Sample 2 is a dispersion comprising 65% by weight of nanoparticles from Example 16. Sample 3 is a dispersion comprising 40% by weight of nanoparticles from Example 9.

[0129] The dispersion of sample 3 has a lower transmittance than the dispersions of the two samples 1 and 2. The transmittance of sample 3 is still very satisfactory, since one can effortlessly distinguish image 4 positioned behind the samples, despite a slight coloration of sample 3. p The two samples 1 and 2 have, for their part, a very high transmittance which makes it possible to perceive the image 4 very clearly without modification of the color. The magnifying effect that may be seen in FIG. 2 is due to the containers and not the dispersions.

Examples 24 and 25

[0130] The particles from Examples 12 and 16 were redispersed in acetone using a precipitation and functionalization procedure with a molecule endowed with a phosphate function. Stable and transparent dispersions of particles in acetone were obtained.

Examples 26 and 27

[0131] The particles from Examples 12 and 16 dispersed in acetone, after replacement of the amino acid by a molecule endowed with a phosphate function, were redispersed in a monomer, such as 1,10-decanediol dimethacrylate (D3MA), using a procedure of incorporation and evaporation of the initial solvent. Stable and transparent dispersions of particles in D3MA were obtained.

Example 28

[0132] The particles resulting from Example 16 were redispersed in propylene glycol, without substitution of the amino acid, using a procedure of precipitation and redispersion in the final solvent. A stable and transparent dispersion of particles in propylene glycol was obtained.

[0133] The total transmittances at different concentrations of the dispersions of Examples 24 to 28 were measured. The total transmittance value is described as a percentage relative to the transmittance measured on the tank filled with the corresponding pure solvent. These are listed in Table 7.

TABLE-US-00007 TABLE 7 Example No. Initial Transmittance Transmittance Example Particles Solvent 400 nm 800 nm 24 12 Acetone 45.2 (10 wt %) 94.6 (10 wt %) 11.6 (40 wt %) 83.5 (40 wt %) 4.2 (72 wt %) 68.3 (72 wt %) 25 16 Acetone 78 (10 wt %) 97.2 (10 wt %) 53.9 (40 wt %) 95.7 (40 wt %) 12.8 (67 wt %) 57.4 (67 wt %) 26 12 D3MA 8.8 (10 wt %) 73.9 (10 wt %) 3.9 (40 wt %) 63.9 (40 wt %) 3.7 (50 wt %) 68.2 (50 wt %) 5.0 (60 wt %) 74.5 (60 wt %) 27 16 D3MA 33.8 (10 wt %) 73.3 (10 wt %) 27.9 (40 wt %) 83.9 (40 wt %) 27.4 (50 wt %) 80.6 (50 wt %) 4.8 (70 wt %) 58.9 (70 wt %) 3.2 (80 wt %) 33.0 (80 wt %) 28 16 Propylene glycol 70.8 (60 wt %) 94.7 (60 wt %)

[0134] It is thus possible to redisperse the zirconium nanoparticles obtained according to the invention in a solvent other than water and to retain excellent transmittance at high concentration, as well as low viscosity and high stability over time.

Example 29 (Invention)

[0135] Example 29 may be compared to Example 9, only two synthesis parameters are modified. The amounts of zirconium precursors, yttrium, aminobutyric acid and water are the same, 6-aminocaproic acid is added. The procedure for dissolving solids is different. The zirconium precursor is dissolved in water together with 4-aminobutyric acid. The yttrium precursor is dissolved in water in the presence of 6-aminocaproic acid. After complete dissolution, the two solutions are mixed.

[0136] 36 mmol of zirconium oxychloride, 119 mmol of 4-aminobutyric acid (ACA4) and 36 ml of water are introduced into a beaker. In a second beaker, yttrium chloride (doped with 6 mol % Y.sub.2O.sub.3), 23.8 mmol of 6-aminocaproic acid (ACA6) and 36 mL of water are introduced. After complete dissolution, the 2 solutions are mixed and introduced into a 100 mL autoclave. The autoclave is then sealed and heated to 200° C. for 3 hours, the pressure is between 12 and 15 bar.

[0137] In Example 29, a stable dispersion of ZrO.sub.2 nanoparticles was obtained.

[0138] Unlike Example 9, the diffractogram obtained by X-ray diffraction analysis reveals the unique presence of the quadratic/cubic phase. Image analysis from TEM images of the nanoparticles obtained in Example 29 only reveals the presence of spherical particles with an average primary size of 20 nm.

Example 30

[0139] Nanoparticles obtained according to Examples 12 and 15 were washed with water and concentrated to different concentrations. The level of amino acid present on the surface of the nanoparticles was measured by TGA (thermogravimetric analysis). The refractive index of the resulting dispersions was measured using a refractometer (Anton Paar, Abbemat 200) at a wavelength of 589 nm and a temperature of 20° C. The density of nanoparticles having an amino acid on the surface (or functionalized) was calculated by linear approximation. The refractive index of the functionalized nanoparticles was calculated by linear regression from the refractive index values of the dispersions measured as a function of the volume fraction of the functionalized nanoparticles according to the linear approximation model. Taking into account the level of functionalizer present at the surface, the refractive index of non-functionalized (or bare) nanoparticles was calculated. The results of these measurements and calculations are presented in Table 8:

TABLE-US-00008 TABLE 8 Example No. % Volume Refractive Initial functionalized index measured Particles nanoparticles at 20° C. 12 0.021 1.3471 0.046 1.3651 0.077 1.3864 0.114 1.4121 0.162 1.4470 0.225 1.4845 15 0.023 1.3472 0.050 1.3629 0.083 1.3824 0.123 1.4066 0.174 1.4382 0.241 1.4794

[0140] For the nanoparticles from Example 12, after washing, the level of amino acid present on the surface and measured by TGA is 4.3% by mass on the total mass of the nanoparticles after drying, the density of the non-functionalized nanoparticles is 6.14 g/cm.sup.3. The density of the functionalized nanoparticles is 5.16 g/cm.sup.3. The density of the medium is 0.998 and its refractive index is 1.3330. The density of the functionalizer (ACA6) is 1.13 g/cm.sup.3 and its index is 1.4870. The refractive index of the resulting unfunctionalized nanoparticles is 2.1434 and the associated coefficient of determination is 0.9990.

[0141] After washing the nanoparticles from Example 15, the level of amino acid present on the surface and measured by TGA is 4.3% by mass on the total mass of the nanoparticles after drying, the density of the non-functionalized nanoparticles is 6.00 g/cm.sup.3. The density of the functionalized nanoparticles is 4.72 g/cm.sup.3. The density of the medium is 0.998 and its refractive index is 1.3330. The density of the functionalizer (ACA6) is 1.13 g/cm.sup.3 and its index is 1.4870. The refractive index of the resulting unfunctionalized nanoparticles is 2.1011 and the associated coefficient of determination is 0.9999.

[0142] It should be noted that the linear approximation model underestimates the refractive index of nanoparticles. Consequently, the non-functionalized nanoparticles have a refractive index greater than or equal to that calculated.