MULTILAYER MATERIAL FOR SCREENING OUT ULTRAVIOLET, COMPOSITION COMPRISING SAME, PROCESS FOR TREATING KERATIN MATERIALS USING SAME, AND PROCESS FOR PREPARING THE MATERIAL

Abstract

The invention relates to i) a multilayer material; ii) a process for preparing said multilayer materials; iii) a cosmetic composition comprising one or more multilayer materials; iv) a process for treating keratin materials, notably human keratin materials such as the skin; v) the use of multilayer material for screening out ultraviolet (UV) rays. Said multilayer material has an odd number N of layers: .square-solid.comprising at least three layers, each layer of which consists of a material A or of a material B different from A, said successive layers A and B being alternated and two adjacent layers having different refractive indices; .square-solid.for which the thickness of each layer obeys the mathematical formula (I) below: [x/y/(αx/y).sub.a/x] in which formula (I): x is the thickness of the inner and outer layer; y is the thickness of the layer adjacent to the inner layer αx or the outer layer x; α is an integer or fraction and α=2±0 to 15%, preferably α=2±0 to 10%, more preferentially α=2±0 to 5%, the intermediate odd layers (αx) have a double thickness±0 to 15% of the thickness of said outer layers x; and a represents an integer greater than or equal to 0, connected to the number of alternated layers N such that a=(N−3)/2; it being understood that: .square-solid.preferably, x has a different thickness from y; .square-solid.when several layers are of thickness x, this means that each layer has a thickness x±0 to 15%, preferably±0 to 10%, more preferentially±0 to 5%; .square-solid.when several layers are of thickness y, this means that each layer has a thickness y±0 to 15%, preferably±0 to 10%, more preferentially±0 to 5%; and .square-solid.when several layers are of thickness α x, this means that each layer has a thickness α x±0 to 15%, preferably±0 to 10%, more preferentially±0 to 5%.

Claims

1. A multilayer material with an odd number N of layers: comprising at least three layers, each layer of which consists of a material A or of a material B different from A, said successive layers A and B being alternated and two adjacent layers having different refractive indices; for which the thickness of each layer obeys the mathematical formula (I) below: [x/y/(αx/y)/x] in which formula (I): x is the thickness of the inner and outer layer; y is the thickness of the layer adjacent to the inner layer αx or the outer layer x; α is an integer or fraction and α=2±0 to 15%, the intermediate odd layers (αx) have a double thickness±0 to 15% of the thickness of said outer layers x; and a represents an integer greater than or equal to 0, connected to the number of alternated layers N such that a=(N−3)/2; it being understood that: has a different thickness from y; when several layers are of thickness x, this means that each layer has a thickness x±0 to 15%; when several layers are of thickness y, this means that each layer has a thickness y±0 to 15%; and when several layers are of thickness α x, this means that each layer has a thickness α x±0 to 15%.

2. The material as claimed in claim 1, which is free of substrate.

3. The material as claimed in claim 1, in which the adjacent layers x and y consist of (in)organic compounds with different refractive indices.

4. The material as claimed in claim 1, in which the materials A and B consist of inorganic materials that are pure or as a mixture; these inorganic compounds constituting A and B are chosen from: germanium (Ge), gallium antimonide (GaSb), tellurium (Te), indium arsenide (InAs), silicon (Si), gallium arsenide (GaAs), indium phosphide (InP), gallium phosphide (GaP), graphite (C), chromium (Cr), zinc telluride (ZnTe), zinc sulfate (ZnSO.sub.4), vanadium (V), arsenic selenide (As.sub.2Se.sub.3), rutile titanium dioxide (TiO.sub.2), copper aluminum diselenide (CuAlSe.sub.2), perovskite calcium titanate (CaTiO.sub.3), tin sulfide (SnS), zinc selenide (ZnSe), anatase titanium dioxide (TiO.sub.2), cerium oxide (CeO.sub.2), gallium nitride (GaN), tungsten (W), manganese (Mn), titanium dioxide notably vacuum-deposited (TiO.sub.2), diamond (C), niobium oxide (Nb.sub.2O.sub.3), niobium pentoxide (Nb.sub.2O.sub.5), zirconium oxide (ZrO.sub.2), sol-gel titanium dioxide (TiO.sub.2), zinc sulfide (ZnS), silicon nitride (SiN), zinc oxide (ZnO), aluminum (Al), hafnium oxide (HfO.sub.2), corundum aluminum oxide or corundum (Al.sub.2O), aluminum oxide (Al.sub.2O.sub.3), yttrium oxide (Y.sub.2O.sub.3), periclase magnesium oxide (MgO), polysulfone, sodium aluminum fluoride (Na.sub.3AlF), lead fluoride (PbF.sub.2), mica, aluminum arsenide (AlAs), sodium chloride (NaCl), sodium fluoride (NaF), silica (SiO.sub.2), barium fluoride (BaF.sub.2), potassium fluoride (KF), vacuum-deposited silica (SiO.sub.2), indium tin oxide (ITO), strontium fluoride (SrF.sub.2), calcium fluoride (CaF.sub.2), lithium fluoride (LiF), magnesium fluoride (MgF.sub.2), bismuth oxychloride (BiOCl), bismuth ferrite (BiFeO.sub.3), and boron nitride (NB), and (bi)carbonate such as calcium carbonate (CaCO.sub.3); compounds constituting A and B are more particularly chosen from particularly (TiO.sub.2 or Nb.sub.2O.sub.5)+(SiO.sub.2 or MgF.sub.2 or BaF.sub.2 or MgO or CaCO.sub.3) and (ZnO or ZnS)+MgF.sub.2.

5. The material as claimed in claim 1, in which materials A and/or B contain organic compounds chosen from polystyrene (PS), polycarbonate, urea formaldehyde, styrene-acrylonitrile copolymers, polyether sulfone (PES), polyvinyl chloride (PVC), polyamide nylons, styrene-butadiene copolymers, type II polyamide nylons, multiacrylic polymers, ionomers, polyethylene, polybutylene, polypropylene, cellulose nitrate, acetal homopolymers, methylpentene polymers, ethylcellulose, cellulose acetatebutyrate, cellulose propionate, cellulose acetate, chlorotrifluoroethylene (CTFE), polytetrafluoroethylene (PTFE), fluorocarbon or polyvinylidene fluoride (FEP).

6. The material as claimed in claim 1, in which the layers x consist of compounds with a higher refractive index than y being inorganic compounds.

7. The material as claimed in claim 1, in which the layers y consist of compounds with a lower refractive index than x chosen from metal oxides, halides and carbonates.

8. The material as claimed in claim 1, in which the layers y consist of compounds with a higher refractive index than x, and being inorganic compounds and are preferably chosen from metal oxides, particularly metal oxides of metals which are in the Periodic Table of the Elements in columns IIIA, IVA, VA, IIIB and lanthanides, more particularly chosen from the following metal oxides: TiO.sub.2, CeO.sub.2, Nb.sub.2O.sub.3, Nb.sub.2O.sub.5, HfO.sub.2, Al.sub.2O.sub.3, Y.sub.2O.sub.3 and ZrO.sub.2, more particularly TiO.sub.2, Nb.sub.2O.sub.5, CeO.sub.2 and preferentially TiO.sub.2, Nb.sub.2O.sub.5 or TiO.sub.2, CeO.sub.2 and even more preferentially TiO.sub.2.

9. The material as claimed in claim 1, in which the layers x consist of compounds with a lower refractive index than y chosen from metal oxides and halides.

10. The material as claimed in claim 1, in which the maximum thickness of each layer of the multilayer material is 120 nm.

11. The material as claimed in claim 1, in which a ranges from 0 to 7, (0≤a≤7; 3≤N≤17 it being understood that: x has a different thickness from y; when several layers are of thickness x, this means that each layer has a thickness x±0 to 15%; when several layers are of thickness y, this means that each layer has a thickness y±0 to 15; and when several layers are of thickness αx, this means that each layer has a thickness αx±0 to 15%.

12. (canceled)

13. (canceled)

14. A process for manufacturing the material as claimed claim 1, comprising the following steps: 1. preparing a substrate and optionally applying to the substrate at least one nonstick layer, also known as a sacrificial layer, onto said substrate; 2. depositing an odd number N of alternated layers of materials A and B consisting of (in)organic compounds of high and lower refractive index, or of low and higher refractive index, onto the substrate optionally coated with sacrificial layer; 3. detaching the multilayer material from the substrate optionally coated with sacrificial layer; 4. if necessary, adjusting the size of the multilayer material to obtain multilayer material particles; and 5. optionally performing a post-treatment optionally followed by a (re)adjustment.

15. The process as claimed in claim 14, in which the substrate consists of an inorganic compound.

16. The process as claimed in claim 11, which uses a nonstick or sacrificial layer, which is inert with respect to the substrate.

17. A composition comprising one or more multilayer materials as defined in claim 1.

18. A process for treating keratin materials by application to said materials of a composition as defined in claim 17, leaving to dry between the layers, the application(s) being sprayed or otherwise.

19. A process for protecting keratin materials against UVA and UVB which comprises applying to the keratin materials one or more multilayer materials as defined in claim 1.

20. The material as claimed in claim 1 in which the adjacent layers x and y consist of (in)organic compounds with different refractive indices differ by at least 0.3.

21. The material as claimed in claim 1, which includes between 3 and 17 layers and which is such that: TABLE-US-00027 Material Thickness of the layers x, y 3 5 7 9 13 17 Layers layers layers layers layers layers layers 1 A x x x x x x 2 B y y y y y y 3 A x αx αx αx αx αx 4 B y y y y y 5 A x αx αx αx αx 6 B y y y y 7 A x αx αx αx 8 B y y y 9 A x αx αx 10 B y y 11 A αx αx 12 B y y 13 A x αx 14 B y 15 A αx 16 B y 17 A x it being understood that: x has a different thickness from y; when several layers are of thickness x, this means that each layer has a thickness x±0 to 15%; when several layers are of thickness y, this means that each layer has a thickness y±0 to 15%; and when several layers have a thickness α x, this means that each layer a has a thickness α x±0 to 15%; and x and y are the thicknesses of the layers of the material with x<y; it being understood that the thicknesses of the layers x between each other, αx between each other and y between each other are identical, α being as defined previously.

22. The material as claimed in claim 1, which includes between 3 and 17 layers and which is such that: TABLE-US-00028 Material Thickness of the layers x, y 3 5 7 9 13 17 Layers layers layers layers layers layers layers 1 B x x x x x x 2 A y y y y y y 3 B x αx αx αx αx αx 4 A y y y y y 5 B x αx αx αx αx 6 A y y y y 7 B x αx αx αx 8 A y y y 9 B x αx αx 10 A y y 11 B αx αx 12 A y y 13 B x αx 14 A y 15 B αx 16 A y 17 B x Multilayer materials in which: A and B are inorganic or organic materials of the adjacent layers with A having a higher refractive index than that of B; and x and y are the thicknesses of the layers of the material such that x<y it being understood that: x is a different thickness from y; the thicknesses of layers x between each other, α x between each other and y between each other are identical, α being as defined previously; when several layers are of thickness x, this means that each layer has a thickness x±0 to 15%; when several layers are of thickness y, this means that each layer has a thickness y±0 to 15%; and when several layers are of thickness α x, this means that each layer has a thickness α x±0 to 15%.

Description

EXAMPLES

Preparation of the Multilayer Materials

[0266] Measurement of the UV-screening properties of the multilayer materials of the invention and outside the invention

Comparison between a 5-Layer Material According to the Invention and Outside the Invention

[0267] Two 5-layer samples were manufactured via standard methods by vapor deposition (CVD/PVD, S5) on 9×9 cm transparent glass substrates. A thin layer of water-soluble PVA polymer (JP-05® Japan Vam and Poval Co) was applied to the surface of the glass plates as nonstick (sacrificial) layer before the vapor deposition. The multilayer materials were prepared by detachment of the abovementioned films from the glass substrate after immersion in hot water (50° C.) for 6 hours. Once detached, the multilayer materials were recovered by filtration and redispersed in deionized water. The first multilayer material ML1 is according to the invention. The second multilayer material ML2 outside the invention was designed as comparative.

[0268] The thicknesses detailed and compositions of each layer are given in the following table:

TABLE-US-00007 TABLE 7 Chemical ML1 (invention) ML2 (outside the invention) Layers composition Layer thickness (nm) Layer thickness (nm) 1 TiO.sub.2 21 32 2 SiO.sub.2 37 34 3 TiO.sub.2 42 67 4 SiO.sub.2 37 38 5 TiO.sub.2 21 22

[0269] The measurements of transmittance between the 5-layer materials ML1 and ML2 were performed as follows:

Saturated Application:

[0270] A drop of a dispersion of multilayer material at 1.7% by weight in deionized water was deposited onto a quartz substrate. After total evaporation of the water, the transmittance measurement was performed.

Successive Multiple Applications:

[0271] A brush was immersed in the dispersion of multilayer materials (1.7% by weight) and the excess multilayer material was removed, followed by applying a continuous coat to the quartz substrate. After evaporation of the water under room temperature conditions (20° C.), the operation was performed three times with measurement of the transmittance and microscopy in each step in order to see the influence of the surface covering and of the amount of material on the optical properties.

Application by Spraying:

[0272] In order to vary the study on the applications of the multilayer material, coating by spraying was tested. Before applying the material to the substrate, the size of ML1 was reduced by treatment with an Ultra-Turrax® machine for 5 minutes at 15 000 rpm, giving rise to sML1. The size comparison is found in the table below:

TABLE-US-00008 TABLE 8 Sample D50 μm (volume) ML1 107.7 ± 3.15 sML1   33.5 ± 0.07 ML2 103.1 ± 2.26

[0273] The particle size distributions were determined by laser scattering using a Malvern Instruments Ltd Master Size 2000 granulometer. This laser scattering particle size analyzer uses a blue light (wavelength of 488.0 μm) and a red light (He-Ne wavelength of 633.8 μm).

Double-Wavelength and Single-Lens Detection System.

[0274] An Ecospray rechargeable micro-sprayer with a disposable gas-pressure tank was used to apply a dispersion sML1 of inorganic compounds onto the substrate. The application was performed on a hot substrate so as to accelerate the evaporation of the water, while maintaining a distance of about 25 cm between the sprayer and the substrate. This procedure was repeated three more times, waiting 5 minutes between each application.

Optical Performance of the 5-Layer Materials According to the Invention Versus Outside the Invention

[0275] The transmittance measurements were taken with a USB4000-UV-VIS spectrophotometer (Ocean Optic) equipped with a reflectance-transmittance integration sphere (Oriel Instruments, model 70491). The transmittance data were recorded on a quartz substrate as foundation; its effect was subtracted by using an identical uncoated quartz as blank in the double beam. The light source was established between 200 and 800 nm, DH-2000-BAL Ocean Optics.

Transmission Analysis:

[0276]

TABLE-US-00009 TABLE 9 (nm) Application UV UVB UVA Visible process 250-400 290-320 320-400 421-700 400-500 1 application ML1 (Invention) 0.43 0.36 0.50 0.84 0.78 2 applications ML1 0.22 0.15 0.28 0.77 0.66 3 applications ML1 0.15 0.10 0.20 0.72 0.60 4 sprayed applications ML1 spray 0.15 0.06 0.23 0.75 0.66 1 application ML2 (Comparative) 0.18 0.10 0.25 0.67 0.46 2 applications ML2 0.13 0.07 0.19 0.62 0.39 3 applications ML2 0.09 0.05 0.14 0.56 0.32

Saturated Application (Drop):

[0277] The overall transmission is higher for the multilayer material according to the invention ML1, in particular in the blue wavelength range; 57% as opposed to 39% for ML1 relative to the comparative ML2.

[0278] The multilayer material ML1 according to the invention functions better in terms of capacity for protecting against UV and of overall visible transparency than the material ML2 outside the invention.

Multiple Applications, Comparison between 1 Application and 3 Applications:

[0279] The overall UV transmission decreases greatly, notably for UVA; the transmission passes from 50% to 20% (reduction by a factor of 2.5) for the multilayer material ML1 according to the invention and from 25% to 13% (reduction by a factor of 1.9) for the comparative material ML2.

[0280] The overall visible transmission is significantly less impacted for the multilayer material ML1 of the invention than for the comparative multilayer material ML2, notably in the blue wavelength range: the transmission reduction is 1.3 for ML1 relative to a factor of 1.46 for ML2.

[0281] It follows that the multilayer material ML1 according to the invention has a better capacity for protecting against UV and better overall visible transparency than the multilayer material ML2 outside the invention.

Sprayed Application:

[0282] It is seen that ML1 has good UV-screening properties and also high visible transmission.

Analysis of the Transmittance-to-Wavelength Slope:

[0283] Transmittance-to-wavelength curves for the multilayer material according to the invention with λ the wavelength axis (nanometers) and t the transmittance axis (nm.sup.−1): [0284] t=0.0056λ−1.9155 (linear 1 drop ML1) [0285] t=0.0034λ−0.7037 (linear 1 application ML1) [0286] t=0.0048λ−1.4557 (linear 2 applications ML1) [0287] t=0.0050λ−1.6315 (linear 3 applications ML1) [0288] t=0.0055λ−1.765 (linear 4 applications as spray ML1)

[0289] Transmittance-to-wavelength curves for the multilayer material outside the invention: [0290] t=0.0021λ−0.5468 (linear 1 drop ML2) [0291] t=0.0019λ−0.4012 (linear 1 application ML2) [0292] t=0.0017λ−0.3864 (linear 2 applications ML2) [0293] t=0.0017λ−0.4491 (linear 3 applications ML2)

TABLE-US-00010 TABLE 10 Slope of the curves ML1 (Invention) ML2 (outside the invention) Application 1 saturated ″drop″ 0.0056 0.0021 1 application 0.0034 0.0019 2 applications 0.0048 0.0017 3 applications 0.0050 0.0017 Sprayed 4 times 0.0055 /

[0294] Values of ML1 and ML2 in table 10 are given in nm.sup.−1

[0295] The UV and Visible transmittance-to-wavelength slope is obtained by linear regression; it is markedly higher for the multilayer material ML1 according to the invention than for the material ML2 outside the invention:

[0296] More than twice as high for ML1 in the saturated application and for an application versus ML2.

[0297] The slope parameter increases significantly with the number of applications for ML1, unlike ML2. The sprayed application also improves the slope parameter.

[0298] Multiple application of the comparative multilayer material ML2 affords little improvement as regards the slope parameter.

[0299] Besides the high transmittance in the visible range, of high transmittance-to-wavelength slope (greater than 3×10.sup.−3), the multilayer material of the invention has, as another noteworthy optical property, a narrow filtration front between UV and the visible range.

Cut-Off Position

[0300]

TABLE-US-00011 TABLE 11 Cut-off position (nm) ML1 (Invention) ML2 (outside the invention) Application 1 saturated ″drop″ 405 481 1 application 390 450 2 applications 399 477 3 applications 402 488 Sprayed 4 times 401 /

[0301] The cut-off position is well defined in the case of the multilayer material ML1 according to the invention at 400 nm±10 nm, independently of the application method. Conversely, in the case of the multilayer material ML2 outside the invention, the shift passes from 450 nm to 488 nm, which shows high dependence of the cut-off position as a function of the application method for the comparative ML2.

Design and Simulation of Multilayer Materials

[0302] The following simulations will demonstrate designs fitting the invention description with other materials than the combination TiO.sub.2/SiO.sub.2.

Description of the Silico Approach for the Design and Performance Evaluation

[0303] All designs composed of a material A and B presented in the following were achieved thanks to transfer matrix calculations coupled with a particle swarm optimization algorithm.

[0304] More precisely, the relationships between the refractive indices of materials A and B used and the thicknesses of the layers of each of these materials define the “cut-off position” of the transition profile of the transmission between the UVA wavelength range (320 nm to 400 nm) and the visible range (400 nm to 780 nm).

[0305] It is possible to model the thickness of the layers to optimize the optical properties.

[0306] The calculations linking the thicknesses and the refractive index of the (in)organic compounds A and B constituting the layers of the multilayer material of the invention with the optical properties (transmission, reflection, absorption) may notably be performed via the “Transfer Matrix Method” such as the one in the “open source” algorithms that are available, for example, at the address

https://fr.mathworks.com/matlabcentral/fileexchanpe/47637-transmittance-and-reflectance-spectra-of-multilavered-dielectric-stack-usinp-transfer-transfer-transfer-mansx-method.

[0307] According to a particular embodiment of the invention, the iterative calculations for optimizing the “cut-off” position are performed via a “particle swarm algorithm” from the optimization toolbox of the software Matlab from Mathworks company.

[0308] The refractive index data needed to model the optical properties of multilayers (real refractive index n and imaginary refractive index k) can be found in the open source database https://refractiveindex.info/. The specific references are reported in the following tabulation.

TABLE-US-00012 TABLE 12 Material Bibliographic references BaF.sub.2 M. R. Querry. “Optical constants of minerals and other materials from the millimeter to the ultraviolet”, Contractor Report CRDEC-CR-88009 (1987) CaCO.sub.3 G. Ghosh. “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals”, Opt. Commun. 163, 95-102 (1999) Additional comment: Since the material is berinfringent, the average of both extraordinary and ordinary refractive index is taken into account. Both data can be found in the previous reference. MgF.sub.2 L. V. Rodríguez-de Marcos, J. I. Larruquert, J. A. Méndez, J. A. Aznárez. “Self-consistent optical constants of MgF2, LaF3, and CeF3 films”, Opt. Mater. Express 7, 989-1006 (2017) (Numerical data kindly provided by Juan Larruquert) MgO R. E. Stephens and I. H. Malitson. “Index of refraction of magnesium oxide”, J. Res. Natl. Bur. Stand. 49 249-252 (1952) PS: N. Sultanova, S. Kasarova and I. Nikolov. “Dispersion properties of optical polystyrene polymers”, Acta Physica Polonica A 116, 585-587 (2009) TiO.sub.2 S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P.T. Probst, J. Joseph, T.A.F. König, “Hybridized guided-mode resonances via colloidal plasmonic self- assembled grating”, ACS Appl. Mater. Interfaces, 11, 13752-13760 (2019) (Numerical data kindly provided by Dr. Tobias König) SiO.sub.2 F. Lemarchand, private communications (2013). ZnO C. Stelling, C. R. Singh, M. Karg, T. A. F. König, M. Thelakkat, M. Retsch. “Plasmonic nanomeshes: their ambivalent role as transparent electrodes in organic solar cells”, Sci. Rep. 7, 42530 (2017)-see Supplementary information (Numerical data kindly provided by Tobias König) ZnS S. Ozaki and S. Adachi. “Optical constants of cubic ZnS”, Jpn. J. Appl. Phys. 32, 5008-5013 (1993)

[0309] The surrounding medium simulates a cosmetic base of constant refractive index of value 1.45.

[0310] An ideal multi-application process was modelled to demonstrate the improvement of the optical performance as described in the invention. That is to say, we assume the stacking to be perfect so that a given multi-application of a given multilayer from the invention would be equivalent to another multilayer of higher number of layer from the invention. The equivalency tabulation is reported in the following table:

TABLE-US-00013 TABLE 13 Type of multi-application Multilayer equivalency 3 layer multilayer applied once 3 layers multilayer 3 layers multilayer applied twice 5 layers multilayer 3 layers multilayer applied three times 7 layers multilayer 3 layers multilayer applied four times 9 layers multilayer 3 layers multilayer applied five times 11 layers multilayer 3 layers multilayer applied six times 13 layers multilayer 3 layers multilayer applied seven times 15 layers multilayer 3 layers multilayer applied eight times 17 layers multilayer 5 layers multilayer applied once 5 layers multilayer 5 layers multilayer applied twice 9 layers multilayer 5 layers multilayer applied three times 13 layers multilayer 5 layers multilayer applied four times 17 layers multilayer

[0311] Therefore, in order to demonstrate the optical performance improvement thanks to a simulated multi-application process, we will in the following directly compare the optical performances of 5, 9, 13, multilayers. The conclusions can be extrapolated from 3 to 17 layers.

Validation of the Silico Performance Prediction

[0312] This section reproduces in simulation with the procedure described above the two experimental examples ML1 and ML2. Since the refractive index of the real and simulated materials are likely to be slightly different, the optimization of the ML S1 is slightly different from ML1

TABLE-US-00014 TABLE 14 Simulated Experimental ML S1 ML S2 ML 1 ML 2 (invention) (Outside invention) (invention) (Outside invention) Chemical Layer Thickness Layer Thickness Layer Thickness Layer Thickness Layers composition (nm) (nm) (nm) (nm) 1 TiO.sub.2 18 32 21 32 2 SiO.sub.2 50 34 37 34 3 TiO.sub.2 36 67 42 67 4 SiO.sub.2 50 38 37 38 5 TiO.sub.2 18 22 21 22

Results of Simulation

[0313]

TABLE-US-00015 TABLE 15 Cut off UV UVB UVA Visible Slope position 290-400 nm 290-320 nm 320-400 nm 400-800 nm (nm.sup.−1) (nm) 1 application Equivalent 0.2895 0.0493 0.3757 0.9855 0.0082 380 ML S1 5 layers 2 applications Equivalent 0.0899 0.0075 0.1193 0.9736 0.0129 404 ML S1 9 layers 3 applications Equivalent 0.0338 0.0013 0.0454 0.9726 0.0226 405 ML S1 13 layers  1 application Equivalent 0.2948 0.0353 0.3901 0.9682 0.0058 380 ML S2 5 layers 2 applications Equivalent 0.1371 0.0036 0.1849 0.9274 0.0047 425 ML S2 9 layers 3 applications Equivalent 0.0897 0.0005 0.1213 0.9064 0.0041 435 ML S2 13 layers 
Equation of Transition between UV and Visible Domain: [0314] ML S1 x1 application: t(λ)=0.0082λ−2.5987 Spectral interval of validity: [325:450 nm] [0315] ML S1 x2 applications: t(λ)=0.0129λ−4.6693 Spectral interval of validity: [355:445 nm] [0316] ML S1 x3 applications: t(λ)=0.0226λ−8.6225 Spectral interval of validity : [375:425 nm] [0317] ML S2 x1 application: t(λ)=0.0058λ−1.8847 Spectral interval of validity: [320:465 nm] [0318] ML S2 x2 applications: t(λ)=0.0047λ−1.5688 Spectral interval of validity: [320:450 nm] [0319] ML S2 x3 applications: t(λ)=0.0041λ−1.3972 Spectral interval of validity: [320:450 nm]

[0320] Both designs have similar performances for the simulation of an ideal application once, with [0321] UV mean transmission respectively of 28.95% and 29.48% for ML S1 and MLS2, [0322] UVA mean transmission respectively of 37.57% and 39.01% for ML S1 and MLS2, [0323] UVB mean transmission respectively of 4.93% and 3.53% for ML S1 and MLS2, [0324] Visible mean transmission respectively of 98.55% and 96.82% for ML S1 and MLS2,
Multiple Applications, Comparison between 1 Application and 3 Applications:

[0325] The simulation of 3 applications in comparison to 1 application for each ML demonstrates: [0326] Less impact in the visible range with a decrease of transmission of 1.3% for ML 51 against 6.3% for ML S2, [0327] More efficiency In the UV with a decrease of transmission by a factor 8.6 for ML S1 against 3.3 for ML S2, [0328] More efficiency In the UVA with a decrease of transmission by a factor 8.3 for ML S1 against 3.2 for ML S2, [0329] More efficiency in the UVB with a decrease of transmission by a factor 70.6 for ML S2 against 38 for ML S21 [0330] The slope of the transition increases by a factor 2.8 for ML S1 and is quite constant for the design ML S2. It even slightly decreases by a factor 0.7. [0331] The cut-off position stabilizes around 405 nm for ML S1 against 435 nm for ML S2.

[0332] Therefore, the first design (invention) is more efficient than the second (outside the invention). Regarding the diminution of the UV transmission, the constant behavior in the visible range, the respect of the cut-off position around 400 nm+/−10 nm and at last the augmentation of the transition slope between UV and visible domains.

Experimental Data on Slope Parameter and Cut-Off Position Gathered on ML1 and ML2:

[0333]

TABLE-US-00016 TABLE 16 Slope parameter (nm.sup.−1) Cut-off position 1 application ML 1 0.0034 390 2 applications ML 1 0.0048 399 3 applications ML 1 0.0050 402 1 application ML 1 0.0019 450 2 applications ML 1 0.0017 477 3 applications ML 1 0.0017 488

Between 1 Application and 3 Applications

[0334] The slope parameters increases by a factor 1.5 experimentally compared to a factor 2.8 in simulation respectively for ML1 and its simulated counterpart ML S1, [0335] The slope parameter is quite constant both for ML2 and its simulated counterpart ML S2, [0336] The cut-off position lies at 402 nm and 405 nm respectively for ML1 and its simulated counterpart ML S1. [0337] The cut-off position of ML2 and its simulated counterpart ML S2 are both out of the invention specification respectively with values of 435 nm and 488 nm.

[0338] Although the values may be slightly different between simulated and experimental values due mainly to uncertainties on the true refractive index of the materials, the trends of performance are similar. Therefore we demonstrate that this performance prediction by simulation is in agreement with the experimental evaluation.

Exemplification with Other Materials than the Association TiO.sub.2/SiO.sub.2
Family A—with TiO.sub.2

[0339] The thicknesses detailed and compositions of each layer are given in the following table:

TABLE-US-00017 TABLE 17 ML A1 ML A2 ML A3 ML A4 Thicknesses In the In the In the In the (nm) invention invention invention invention x TiO.sub.2 18 TiO.sub.2 17 TiO.sub.2 17 TiO.sub.2 15 y MgF.sub.2 54 BaF.sub.2 62 MgO 55 CaCO.sub.3 60 2*x TiO.sub.2 36 TiO.sub.2 34 TiO.sub.2 34 TiO.sub.2 30

Results of Simulation

[0340]

TABLE-US-00018 TABLE 18 Cut off UV UVB UVA Visible Slope position 290-400 nm 290-320 nm 320-400 nm 400-800 nm (nm.sup.−1) (nm) 1 application Equivalent 0.2847 0.0401 0.3724 0.9849 0.0089 375 ML A1 5 layers 2 applications Equivalent 0.0930 0.0041 0.1246 0.9760 0.0131 400 ML A1 9 layers 3 applications Equivalent 0.0424 0.0005 0.0572 0.9764 0.0249 400 ML A1 13 layers  1 application Equivalent 0.2939 0.3763 0.0642 0.9830 0.0077 380 ML A2 5 layers 2 application Equivalent 0.0863 0.1126 0.0126 0.9703 0.0115 405 ML A2 9 layers 3 application Equivalent 0.0292 0.0386 0.0028 0.9690 0.0211 406 ML A2 13 layers  1 application Equivalent 0.4229 0.1071 0.5367 0.9902 0.0093 360 ML A3 5 layers 2 applications Equivalent 0. 2191 0.0387 0.2846 0.9809 0.0122 385 ML A3 9 layers 3 applications Equivalent 0.1281 0.0151 0.1696 0.9771 0.0145 395 ML A3 13 layers  1 application Equivalent 0.3376 0.0845 0.4285 0.9883 0.0077 370 ML A4 5 layers 2 applications Equivalent 0.1210 0.0243 0.1557 0.9756 0.0104 400 ML A4 9 layers 3 applications Equivalent 0.0482 0.0079 0.0629 0.9730 0.0169 405 ML A4 13 layers 
Equation of Transition between UV and Visible Domain: [0341] ML A1 x1 application: t(λ)=0.0089λ−2.8287 Spectral interval of validity: [325:440 nm] [0342] ML A1 x2 applications: t(λ)=0.0131λ−4.7046 Spectral interval of validity: [350:440 nm] [0343] ML A1 x3 applications: t(λ)=0.0249λ−9.4683 Spectral interval of validity: [375:420 nm] [0344] ML A2 x1 application: t(λ)=0.0077λ−2.4018 Spectral interval of validity: [325:455 nm] [0345] ML A2 x2 applications: t(λ)=0.0115λ−4.1129 Spectral interval of validity: [350:455 nm] [0346] ML A2 x3 applications: t(λ)=0.0211λ−8.0554 Spectral interval of validity: [375:430 nm] [0347] ML A3 x1 application: t(λ)=0.0093λ−2.8171 Spectral interval of validity: [300:415 nm] [0348] ML A3 x2 applications: t(λ)=0.0122λ−4.1372 Spectral interval of validity: [330:415 nm] [0349] ML A3 x3 applications: t(λ)=0.0145λ−5.0091 Spectral interval of validity: [345:415 nm] [0350] ML A4 x1 application: t(λ)=0.0077λ−2.3296 Spectral interval of validity: [300:465 nm] [0351] ML A4 x2 applications: t(λ)=0.0104λ−3.5811 Spectral interval of validity: [330:450 nm] [0352] ML A4 x3 applications: t(λ)=0.0169λ−6.2607 Spectral interval of validity: [360:425 nm]
Multiple Applications, Comparison between 1 Application and 3 Applications:

[0353] In each example ML A1, A2, A3, A4 between one application and 3 applications: [0354] The transmission in the visible range has a variation within a 2% range, [0355] The transmission in UV, decreases by a factor 6.7, 10.1, 3.3, 7 respectively for ML A1, A2, A3 and A4. [0356] The transmission in UVB, decreases by a factor 80.2, 9.7, 7.1, 10.7 respectively for ML A1, A2, A3 and A4. [0357] The transmission in UVA, decreases by a factor 6.5, 23, 3.2, 6.8 respectively for ML A1, A2, A3 and A4, [0358] The slope parameter increases by a factor 2.8, 2.7, 1.56, 2.2 respectively for ML A1, A2, A3 and A4, [0359] The cut-off position stabilizes for each design at 400 nm+/−6 nm.

[0360] In conclusion these four designs belonging to the definition of the invention demonstrates improvements of their optical properties (mean UV, UVA, UVB transmissions, slope of transition between UV and visible region and cut-off position) by a simulated multi-application process.

Family B—with Nb2O5

[0361] The thicknesses detailed and compositions of each layer are given in the following table:

TABLE-US-00019 TABLE 19 ML B1 ML B2 ML B3 ML B4 Thicknesses In the In the In the In the (nm) invention invention invention invention x Nb.sub.2O.sub.5 13 Nb.sub.2O.sub.5 16 Nb.sub.2O.sub.5 14 Nb.sub.2O.sub.5 14 y SiO.sub.2 63 MgF.sub.2 57 MgO 57 CaCO.sub.3 63 2*x Nb.sub.2O.sub.5 26 Nb.sub.2O.sub.5 32 Nb.sub.2O.sub.5 28 Nb.sub.2O.sub.5 28

Results of Simulation

[0362]

TABLE-US-00020 TABLE 20 Cut off UV UVB UVA Visible Slope position 290-400 nm 290-320 nm 320-400 nm 400-800 nm (nm.sup.−1) (nm) 1 application Equivalent 0.2846 0.0663 0.3628 0.9817 0.0076 380 ML B1 5 layers 2 applications Equivalent 0.0804 0.0092 0.1055 0.9723 0.0128 404 ML B1 9 layers 3 applications Equivalent 0.0317 0.0017 0.0422 0.9732 0.0212 405 ML B1 13 layers  1 application Equivalent 0.2517 0.0467 0.3252 0.9787 0.0087 380 ML B2 5 layers 2 applications Equivalent 0.0648 0.0046 0.0861 0.9670 0.0135 404 ML B2 9 layers 3 applications Equivalent 0.0232 0.0005 0.0313 0.9662 0.0174 405 ML B2 13 layers  1 application Equivalent 0.4066 0.1246 0.5078 0.9892 0.0085 365 ML B3 5 layers 2 applications Equivalent 0.1885 0.0557 0.2345 0.9770 0.0114 395 ML B3 9 layers 3 applications Equivalent 0.1060 0.0281 0.1327 0.9733 0.0184 395 ML B3 13 layers  1 application Equivalent 0.3132 0.0990 0.3898 0.9837 0.0094 380 ML B4 5 layers 2 applications Equivalent 0.0954 0.0359 0.1155 0.9684 0.0163 404 ML B4 9 layers 3 applications Equivalent 0.0335 0.0150 0.0394 0.9654 0.0281 405 ML B4 13 layers 
Equation of Transition between UV and Visible Domain: [0363] ML B1 x1 application: t(λ)=0.0076λ−2.3661 Spectral interval of validity: [315:455 nm] [0364] ML B1 x2 applications: t(λ)=0.0128λ−4.6086 Spectral interval of validity: [350:440 nm] [0365] ML B1 x3 applications: t(λ)=0.0212λ−8.0269 Spectral interval of validity: [370:425 nm] [0366] ML B2 x1 application: t(λ)=0.0087λ−2.8169 Spectral interval of validity: [325:455 nm] [0367] ML B2 x2 applications: t(λ)=0.0135λ−4.9227 Spectral interval of validity: [350:455 nm] [0368] ML B2 x3 applications: t(λ)=0.0174λ−6.5164 Spectral interval of validity: [375:430 nm] [0369] ML B3 x1 application: t(λ)=0.0085λ−2.5457 Spectral interval of validity: [300:425 nm] [0370] ML B3 x2 applications: t(λ)=0.0114λ−3.854 Spectral interval of validity: [325:425 nm] [0371] ML B3 x3 applications: t(λ)=0.0184λ−6.318 Spectral interval of validity: [355:415 nm] [0372] ML B4 x1 application: t(λ)=0.0094λ−3.002 Spectral interval of validity: [335:410 nm] [0373] ML B4 x2 applications: t(λ)=0.0163λ−6.0363 Spectral interval of validity: [375:430 nm] [0374] ML B4 x3 applications: t(λ)=0.0281λ−10.951 Spectral interval of validity: [325:455 nm]
Multiple Applications, Comparison between 1 Application and 3 Applications:

[0375] In each example ML B1, B2, B3, B4 between one application and 3 applications: [0376] The transmission in the visible range has a variation within a 2% range, [0377] The transmission in UV, decreases by a factor 10.0, 10.8, 3.83, 9.34 respectively for ML B1, B2, B3 and B4. [0378] The transmission in UVB, decreases by a factor 39, 93.4, 4.43, 6.6 respectively for ML B1, B2, B3 and B4. [0379] The transmission in UVA, decreases by a factor 8.6, 10.4, 3.83, 9.89 respectively for ML B1, B2, B3 and B4, [0380] The slope parameter increases by a factor 2.8, 2, 2.2, 3 respectively for ML B1, B2, B3 and B4, [0381] The cut-off position stabilizes for each design at 400 nm +/−5 nm.

[0382] In conclusion these four designs belonging to the definition of the invention demonstrates improvements of their optical properties (mean UV, UVA, UVB transmissions, slope of transition between UV and visible region and cut-off position) by a simulated multi-application process.

Family C—with ZnO

[0383] The thicknesses detailed and compositions of each layer are given in the following table:

TABLE-US-00021 TABLE 21 Thicknesses (nm) ML C1 In the invention x ZnO 28 y MgF.sub.2 62 2*x ZnO 56

Results of Simulation

[0384]

TABLE-US-00022 TABLE 22 Cut off UV UVB UvA Visible Slope position 290-400 nm 290-320 nm 320-400 nm 400-800 nm (nm.sup.−1) (nm) 1 application Equivalent 0.5653 0.4166 0.6205 0.9730 0.0043 375 ML C1 5 layers 2 applications Equivalent 0.3359 0.2168 0.3809 0.9474 0.0054 385 ML C1 9 layers 3 applications Equivalent 0.2010 0.1096 0.2363 0.9260 0.0076 400 ML C1 13 layers 
Equation of Transition between UV and Visible Domain: [0385] ML C1 x1 application: t(λ)=0.004λ−0.09309 Spectral interval of validity: [290:465 nm] [0386] ML C1 x2 applications: t(λ)=0.0054λ−1.4895 Spectral interval of validity: [290:470 nm] [0387] ML C1 x3 applications: t(λ)=0.00076λ−2.5319 Spectral interval of validity: [350:480 nm]
Multiple Applications, Comparison between 1 Application and 3 Applications:

[0388] For example ML C1 between one application and 3 applications: [0389] The transmission in the visible range stays above 96%, [0390] The transmission in UV, decreases by a factor 1.7, [0391] The transmission in UVB, decreases by a factor 3.8, [0392] The transmission in UVA, decreases by a factor 2.6, [0393] The slope parameter increases by a factor 1.77, [0394] The Cut off stabilizes at 400 nm.

[0395] In conclusion this design belonging to the definition of the invention demonstrates improvements of its optical properties by a simulated multi-application process.

Family D—with ZnS

[0396] The thicknesses detailed and compositions of each layer are given in the following table:

TABLE-US-00023 TABLE 23 Thicknesses (nm) ML D1 In the invention x ZnS 7 y MgF.sub.2 93 2*x ZnS 14

Results of Simulation

[0397]

TABLE-US-00024 TABLE 24 Cut off UV UVB UVA Visible Slope position 290-400 nm 290-320 nm 320-400 nm 400-800 nm (nm.sup.−1) (nm) 1 application Equivalent 0.4161 0.3031 0.4561 0.9332 0.0037 380 ML D1 5 layers 2 applications Equivalent 0.1573 0.1494 0.1563 0.8846 0.0074 405 ML D1 9 layers 3 applications Equivalent 0.0764 0.1042 0.0620 0.8442 0.0076 405 ML D1 13 layers 
Equation of Transition between UV and Visible Domain: [0398] ML D1 x1 application: t(λ)=0.0037λ−0.8667 Spectral interval of validity: [335:510 nm] [0399] ML D1 x2 applications: t(λ)=0.0074λ−2.5171 Spectral interval of validity: [335:465 nm] [0400] ML D1 x3 applications: t(λ)=0.0076λ−2.7247 Spectral interval of validity: [355:480 nm]
Multiple Applications, Comparison between 1 Application and 3 Applications:

[0401] For example ML D1 between one application and 3 applications: [0402] The transmission in the visible range stays above 84%, [0403] The transmission in UV, decreases by a factor 5.4, [0404] The transmission in UVB, decreases by a factor 2.9, [0405] The transmission in UVA, decreases by a factor 7.35, [0406] The slope parameter increases by a factor 2, [0407] The Cut off stabilizes at 405 nm.

[0408] In conclusion this design belonging to the definition of the invention demonstrates improvements of its optical properties by a simulated multi-application process.

Family E—TiO.sub.2 with Mix SiO.sub.2/PS

[0409] In the particular case of a mix of organic and inorganic materials we simulated a mix of SiO.sub.2 and polystyrene (PS) at a 10% wt concentration (mass fraction).

[0410] In order to simulate this mix we calculated the resulted n and k values of the new material:

n.sub.SIO290%PS10%=0.9*n.sub.SiO2+0.1*n.sub.PS

k.sub.SIO290%PS10%=0.9*k.sub.SiO2+0.1*k.sub.PS

[0411] The thicknesses detailed and compositions of each layer are given in the following table:

TABLE-US-00025 TABLE 25 Thicknesses (nm) ML E1 In the invention x TiO.sub.2 16 y SiO.sub.2 (90%)/PS (10%) 62 2*x TiO2 32

Results of Simulation

[0412]

TABLE-US-00026 TABLE 26 Cut off UV UVB UVA Visible Slope position 290-400 nm 290-320 nm 320-400 nm 400-800 nm (nm.sup.−1) (nm) 1 application Equivalent 0.3234 0.0637 0.4164 0.9878 0.0088 370 ML E1 5 layers 2 applications Equivalent 0.1165 0.0099 0.1542 0.9815 0.0125 395 ML E1 9 layers 3 applications Equivalent 0.0588 0.0017 0.0790 0.9836 0.0210 400 ML E1 13 layers 
Equation of Transition between UV and Visible Domain: [0413] ML E1 x1 application: t(λ)=0.0088λ−2.7329 Spectral interval of validity: [305:415 nm] [0414] ML E1 x2 applications: t(λ)=0.0125λ−4.415 Spectral interval of validity: [345:440 nm] [0415] ML E1 x3 applications: t(λ)=0.0210λ−7.8267 Spectral interval of validity: [365:420 nm]
Multiple Applications, Comparison between 1 Application and 3 Applications:

[0416] For example ML E1 between one application and 3 applications: [0417] The transmission in the visible range stays above 98%, [0418] The transmission in UV, decreases by a factor 5.5, [0419] The transmission in UVB, decreases by a factor 37.5, [0420] The transmission in UVA, decreases by a factor 5.3, [0421] The slope parameter increases by a factor 2.4, [0422] The Cut off stabilizes at 400 nm.

[0423] In conclusion this design belonging to the definition of the invention demonstrates improvements of its optical properties by a simulated multi-application process.