US20120237856A1 - Selection method for additives in photopolymers - Google Patents

Abstract

The invention relates to a method for selecting compounds which can be used as additives in photopolymer formulations for producing light holographic media, and to photopolymer formulations which contain at least one softener which are selected according to the claimed method. The invention also relates to the use of photopolymer formulations for producing holographic media.

Description

• The invention relates to a method for selecting compounds which can be used as additives in photopolymer formulations for the production of light holographic media, and photopolymer formulations which contain at least one plasticizer which was selected by the method according to the invention.
• WO 2008/125229 A1 describes photopolymer formulations of the type mentioned at the outset. These comprise polyurethane-based matrix polymers, acrylate-based writing monomers and photoinitiators. In the cured state, the writing monomers and the photoinitiators are embedded with spatial distribution in the polyurethane matrix. The WO document likewise discloses the addition of dibutyl phthalate, a classical plasticizer for industrial plastics, to the photopolymer formulation.
• For uses of photopolymer formulations in the fields of use described below, the refractive index modulation Δn produced by the holographic exposure in the photopolymer plays the decisive role. During the holographic exposure, the interference field of signal and reference light beam (in the simplest case the two plane waves) is mapped by the local photopolymerization of, for example, highly refracting acrylates at sites of high intensity in the interference field into a refractive index grating. The refractive index grating in the photopolymer (the hologram) contains all information of the signal light beam. By illuminating the hologram only with the reference light beam, the signal can then be reconstructed. The strength of the signal thus reconstructed in relation to the strength of the reference light used is referred to as diffraction efficiency, DE below. In the simplest case of a hologram which forms from the superposition of two plane waves, the DE is obtained from the quotient of the intensity of the light diffracted on reconstruction and the sum of the intensities of incident reference light and diffracted light. The higher the DE, the more efficient is a hologram with respect to the necessary quantity of reference light which is required for making the signal visible with a fixed brightness. Highly refractive acrylates are capable of producing refractive index gratings having a high amplitude between regions having the lowest refractive index and regions having the highest refractive index and hence of permitting holograms having a high DE and high Δn in photopolymer formulations. It should be noted that the DE is dependent on the product of Δn and the photopolymer layer thickness d. The larger the product, the greater is the possible DE (for reflection holograms). The width of the angular range in which the hologram is visible (reconstructed), for example on monochromatic illumination, depends only on the layer thickness d. On illumination of the hologram with, for example, white light, the width of the spectral range which can contribute to the reconstruction of the hologram likewise depends only on the layer thickness d. It is true that the smaller d is the greater are the respective acceptance widths. It is therefore intended to produce bright and easily visible holograms, a high Δn·d and a small thickness d should be strived for in particular so that DE is as large as possible. This means that the higher Δn is, the more latitude is achieved for configuring bright holograms by adjusting d and without loss of DE. The optimization of Δn on the optimization of photopolymer formulations is therefore of outstanding importance (ref. Hariharan Optical Holography).
• One possibility for achieving as large a Δn as possible is the use of photopolymer formulations which contain plasticizers having no optical refraction, i.e. those having a low refractive index. In addition to the optical properties, a further important selection criterion for such plasticizers is that they must have sufficiently low volatility under typical production conditions for photopolymer formulations. Owing to an observed loss of mass in the production of the holographic film media, an obvious presumption is that evaporation of individual components might occur during the production, especially in the area of drying. However, on consideration of the boiling points and of the vapour pressures of the components used, it was not expected that these should be a cause for the evaporation at the respective drying temperatures and hence a reason for the substantially lower Δn values.
• However, the vapour pressure is a parameter with the aid of which the suitability of components for use in the industrial production of holographic media cannot be tested. This is because the vapour pressure of a chemical compound is a physical constant which describes how a pure substance or a mixture of substances is in thermodynamic equilibrium with its liquid or solid phase. For dynamic systems, however, the vapour pressure provides no guidance.
• Thus, the vapour pressure does not describe the situation which prevails, for example, in a continuously operated coating unit in which the material applied with a small layer thickness, distributed over a large surface by air circulation which ensures that the gaseous phase is constantly removed, is dried.
• Expediently, the volatility is considered instead of the vapour pressure. Since this value is difficult to determine experimentally, theoretical methods could be readily applied for this purpose.
• Methods in which, based on simple molecular descriptors, relationships between the molecular properties and the physical properties of substance, referred to below as Quantitative Structure Property Relationships (QSPR), are sought and known in principle from the literature. Thus, for example, Ha et al. (Energy & Fuels, 19, 152, (2005)) describe QSPR models which are suitable for estimating boiling points, relative densities and refractive indices of saturated and aromatic hydrocarbons without heteroatoms. Liu et al. have presented a QSPR model which is suitable primarily for fluorine and sulphur-containing hydrocarbons (J. Micro/Nanolith. MEMS MOEMS 7, 023001-1-023001-11, (2008)). These models are derived on the basis of a large set of experimental data and frequently permit a high degree of predictability for compounds which are sufficiently similar to the substances used for the preparation but have a significantly reduced accuracy when the similarity is not present.
• Further known methods for estimating molecular properties are group contribution methods which divide the given molecule into “groups” to which a certain incremental contribution to a given physical property is assigned. The physical properties are then obtained by summing the group contributions. An example is the method published in 2001 by Marrero and Gani (Fluid Phase Equilib. 183-184, 183-208 (2001)). However, a principle problem of this method is the fact that it is not possible to treat compounds whose molecular structure contains groups not covered by the method. Moreover, the accuracy is typically not sufficient for quantitative conclusions.
• WO 02/051263 and DE 10065443 describe QSPR methods which are based on descriptors derived from quantum chemical calculations. The method is used there to describe the phase behaviour of aromas or fragrances in multimaterial systems. These descriptors are suitable in particular for describing a versatile set of molecules, so that it is possible to find QSPR models with very few descriptors which can be used in a versatile manner.
• It was an object of the present invention to provide a selection method for additives in photopolymer formulations which permit production of holograms having a relatively high brightness.
• The object is achieved, in the method according to the invention if the refractive index and the volatility, expressed as TGA95 value, of a given still uncharacterized substance is estimated with the aid of a mathematical method in order to assess the suitability thereof as an additive in photopolymer formulations. A substance is considered to be suitable if its refractive index estimated by the method according to the invention is ≦1.4600 and its estimated TGA95 value is >100° C.
• For assessing the vaporization properties of a component with a small layer thickness during a drying process on open surfaces, the consideration of the volatility of this chemical component is important and is a measure of the tendency to evaporate. This volatility can preferably be determined by a thermogravimetric analysis (TGA).
• The TGA95 value of the individual components are then determined by weighing an amount of about 10 mg of the sample of the respective component into an aluminium pan having a volume of 70 μl, introducing the aluminium pan an oven of a thermobalance, preferably of a TG50 thermobalance from Mettler-Toledo, and measuring the loss of mass of the sample in the open aluminium pan at a constant oven heating rate of 20 K/min, the starting temperature being 30° C. and the end temperature of the oven 600° C., flushing the oven with a 200 ml/min nitrogen stream during the determination for determining as the TGA 95 value of the respective component, the temperature at which a loss of mass of the sample of 5% by weight, based on the originally weighed in amount of the sample, has occurred.
• In order to use the selection method according to the invention, first a substance to be tested is chosen (step a), a three-dimensional structure of which is created with the aid of a suitable software package. This structure is then subjected to a conformer analysis in a manner known per se with the aid of a force field method in order to determine the conformers of the substance which have the lowest energy (step b). The number of conformers is then further reduced by further optimization of the geometry by a force field method and a subsequent similarity analysis (step c). Steps a-c can be carried out, for example, with the conformers module of the Materials Studio programme package from Accelrys.
• The conformers generated in steps a-c are then optimized in terms of geometry by quantum chemical methods, ideally the B-P86 density functional and a triple C valence basis being used (step d). The optimization of the geometry is effected with the use of the continuum solvation model Conductor like Screening Model (COSMO), the element-specific COSMO radii optimized by Klamt being used if possible (AIChE Journal, 48, 369, (2002); Fluid Phase Equilibria, 172, 43 (2000); J. Chem. Soc. Perkin Trans. II, 799 (1993)). If elements for which no such optimized radii are available are present in the molecule, 1.17 times the Bondi valence radius is assumed.
• On the basis of the COSMO radii, a cavity outside which the molecule is ideally electrostatically shielded from the environment during the optimization of the geometry is calculated by the quantum chemistry software used. The surface (in Ų) and the volume of this cavity (in ų) are in each case descriptors in the context of the method according to the invention (step e).
• The third descriptor is derived from the shielding charge surface of the geometrically optimized molecule, which is obtained in the quantum chemical optimization of the geometry with COSMO. The surface is divided with the aid of a suitable computer programme, such as, for example, the COSMOtherm programme of COSMO/ogic, into segments whose mean shielding charge density (σ) is calculated. The third descriptor is then finally obtained as the second moment (M²) of the frequency distribution (P(σ)), the surface shielding charge densities of these segments (step f):
• ${\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">M</figure-callout>}}^2=10·\sum _iP\left({\sigma }_i\right)·{\mathrm{<figure-callout\; id="2"\; label="\sigma \; i"\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_i^{}·\mathrm{\Delta \sigma },$
• where Δσ is the interval width with which the discrete frequency distribution was generated. The charge densities σ are stated in the unit e/nm².
• The calculation of the descriptors A, V and M² used in the method according to the invention, carried out in the manner described, is effected in an identical manner for all conformers taken into account. Subsequently, the individual descriptors of the conformers are averaged according to their weight in the Boltzmann distribution (step g). The Boltzmann factors are determined using the energies which were obtained as the result of the quantum chemical optimization of the geometry by COSMO.
• Finally with the descriptors determined in this manner, the refractive index and the volatility of the substance to be tested are estimated. For this purpose, the molar polarizability (MP) of the compound to be tested is first determined with the aid of a QSPR approach known from the literature, for example by one of the methods of Crippen et al. (J. Comput. Chem., 7, 565, (1986) or Chem. Inf. Comput. Sci. 39, 868, (1999)). The volatility (TGA95) is estimated according to the invention on the basis of the QSPR approach (step h):
• $\mathrm{TGA}95\approx 207.015·\frac{M^2}{A}+41.405·\sqrt[3]{V}-253.2$
• The density is estimated according to the invention according to a second QSPR approach using (step i):
• $\rho =0.89·\frac{M}{V·N_A}-0.2·\frac{A}{V}+0.01·\sqrt{{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">M</figure-callout>}}^2}$
• and used to calculate the refractive index at 589 nm (n_D ²⁰) with the aid of the Lorentz-Lorenz equation (step j):
• $n_D=\sqrt{\frac{2·\frac{\rho ·\mathrm{MP}}{M}+1}{1-\frac{\rho ·\mathrm{MP}}{M}}}$
• In the last step, the suitability of the substance as an additive in photopolymer formulations is assessed according to the estimated n²⁰;_D and TGA95 value (step k).
• Suitable compounds in the context of the method according to the invention have a refractive index of ≦1.4600 and a TGA95 value of ≧100° C.
Preferred Embodiments
• According to a first embodiment, the conformer with the lowest energy which is found in the conformer analysis, preferably all conformers which are up to 4 kJ/mol and particularly preferably all conformers which are up to 8 kJ/mol above the lowest conformer, are taken into account for the method.
• In a particularly preferred embodiment of the method according to the invention, a check is carried out in step k) to determine whether the volatility of the compound to be tested is >120° C. and the refractive index n¹⁰;_D thereof is ≦1.4500, preferably ≦1.4400, particularly preferably ≦1.4300.
• A further aspect of the invention relates to a photopolymer formulation comprising matrix polymers, writing monomers and photoinitiators, said photopolymer formulation containing at least one plasticizer which is selected by the method according to the invention.
• The matrix polymers may be in particular polyurethanes. Preferably, the polyurethanes are obtained by reacting an isocyanate component a) with an isocyanate-reactive component b).
• The isocyanate component a) preferably comprises polyisocyanates. Polyisocyanates which may be used are all compounds well known to the person skilled in the art or mixtures thereof, which on average have two or more NCO functions per molecule. These may have an aromatic, araliphatic, aliphatic or cycloaliphatic basis. In minor amounts, it is also possible concomitantly to use monoisocyanates and/or polyisocyanates containing unsaturated groups.
• For example, butylene diisocyanate, hexamethylene diisocyanate (HDI), isophorone diisocyanate (IPDI), 1,8-diisocyanato-4-(isocyanatomethyl)octane, 2,2,4- and/or 2,4,4-trimethylhexamethylene diisocyanate, the isomeric bis(4,4′-isocyanatocyclohexyl)methanes and mixtures thereof having any desired isomer content, isocyanatomethyl-1,8-octane diisocyanate, 1,4-cyclohexylene diisocyanate, the isomeric cyclohexanedimethylene diisocyanates, 1,4-phenylene diisocyanate, 2,4- and/or 2,6-toluoylene diisocyanate, 1,5-naphthylene diisocyanate, 2,4′- or 4,4′-diphenylmethane diisocyanate and/or triphenylmethane 4,4′,4″-triisocyanate.
• The use of derivatives and monomeric di- or triisocyanates having urethane, urea, carbodiimide, acylurea, isocyanurate, allophanate, biuret, oxadiazinetrione, uretdione and/or iminooxadiazinedione structures is likewise possible.
• The use of polyisocyanates based on aliphatic and/or cycloaliphatic di- or triisocyanates is preferred.
• The polyisocyanates of component a) are particularly preferably dimerized or oligomerized aliphatic and/or cycloaliphatic di- or triisocyanates.
• Isocyanurates, uretdiones and/or iminooxadiazinediones based on HDI, 1,8-diisocyanato-4-(isocyanatomethyl)octane or mixtures thereof are very particularly preferred.
• NCO-functional prepolymers having urethane, allophanate, biuret and/or amide groups can likewise be used as component a). Prepolymers of component a) are obtained in a manner well known per se to the person skilled in the art by reacting monomeric, oligomeric or polyisocyanates a1) with isocyanate-reactive compounds a2) in suitable stoichiometry with optional use of catalysts and solvents.
• Suitable polyisocyanates a1) are all aliphatic, cycloaliphatic, aromatic or araliphatic di- and triisocyanates know per se to the person skilled in the art, it being unimportant whether these were obtained by means of phosgenation or by phosgene-free processes. In addition, the higher molecular weight secondary products of monomeric di- and/or triisocyanates having a urethane, urea, carbodiimide, acylurea, isocyanurate, allophanate, biuret, oxadiazinetrione, uretdione or iminooxadiazinedione structure, which are known per se to the person skilled in the art, can also be used, in each case individually or as any desired mixtures with one another.
• Examples of suitable monomeric di- or triisocyanates which can be used as component a1) are butylene diisocyanate, hexamethylene diisocyanate (IMO, isophorone diisocyanate (IPDI), trimethylhexamethylene diisocyanate (TMDI), 1,8-diisocyanato-4-(isocyanatomethyl)octane, isocyanatomethyl-1,8-octane diisocyanate (TIN), 2,4- and/or 2,6-toluene diisocyanate.
• OH-functional compounds are preferably used as isocyanate-reactive compounds a2) for the synthesis of the prepolymers. These are analogous to the OH-functional compounds as described below for the component b).
• The use of amines for the prepolymer preparation is also possible. For example, ethylenediamine, diethylenetriamine, triethylenetetramine, propylenediamine, diaminocyclohexane, diaminobenzene, diaminobisphenyl, difunctional polyamines, such as, for example, Jeffamine®, amine-terminated polymers having number average molar masses of up to 10 000 g/mol or any desired mixtures thereof with one another are suitable.
• For the preparation of prepolymers containing biuret groups, isocyanate is reacted in excess with amine, a biuret group forming. Suitable amines in this case for the reaction with the di-, tri- and polyisocyanates mentioned are all oligomeric or polymeric, primary or secondary, difunctional amines of the abovementioned type.
• Preferred prepolymers are urethanes, allophanates or biurets of aliphatic isocyanate-functional compounds and oligomeric or polymeric isocyanate-reactive compounds having number average molar masses of 200 to 10 000 g/mol; urethanes, allophanates or biurets of aliphatic isocyanate-functional compounds and oligomeric or polymeric polyols or polyamines having number average molar masses of 500 to 8500 g/mol are particularly preferred and allophanates of HDI or TMDI and difunctional polyetherpolyols having number average molar masses of 1000 to 8200 g/mol are very particularly preferred.
• The prepolymers described above preferably have residual contents of free monomeric isocyanate of less than 1% by weight, particularly preferably less than 0.5% by weight, very particularly preferably less than 0.2% by weight.
• Of course, the isocyanate component may contain further isocyanate components proportionately in addition to the prepolymers described. Aromatic, araliphatic, aliphatic and cycloaliphatic di-, tri- or polyisocyanates are suitable for this purpose. It is also possible to use mixtures of said di-, tri- or polyisocyanates. Examples of suitable di-, tri- or polyisocyanates are butylene diisocyanate, hexamethylene diisocyanate (HDI), isophorone diisocyanate (IPDI), 1,8-diisocyanato-4-(isocyanatomethyl)octane, 2,2,4- and/or 2,4,4-trimethylhexamethy lene diisocyanate (TMDI), the isomeric bis(4,4′-isocyanatocyclo-hexyl)methanes and mixtures thereof having any desired isomer content, isocyanatomethyl 1,8-octane diisocyanate, 1,4-cyclohexylene diisocyanate, the isomeric cyclohexanedimethylene diisocyanates, 1,4-phenylene diisocyanate, 2,4- and/or 2,6-toluoylene diisocyanate, 1,5-naphthylene diisocyanate, 2,4′- or 4,4′-diphenylmethane diisocyanate, triphenylmethane 4,4′,4″-triisocyanate or derivatives thereof having a urethane, urea, carbodiimide, acylurea, isocyanurate, allophanate, biuret, oxadiazinetrione, uretdione, iminooxadiazinedione structure and mixtures thereof. Polyisocyanates based on oligomerized and/or derivatized diisocyanates which were freed from excess diisocyanate by suitable methods, in particular those of hexamethylene diisocyanate, are preferred. The oligomeric isocyanurates, uretdiones and iminooxadiazinediones of HDI and mixtures thereof are particularly preferred.
• It is optionally also possible for the isocyanate component a) proportionately to contain isocyanates which are partly reacted with isocyanate-reactive ethylenically unsaturated compounds. α,β-Unsaturated carboxylic acid derivatives, such as acrylates, methacrylates, maleates, fumarates, maleimides, acrylamides, and vinyl ethers, propenyl ethers, allyl ethers and compounds which contain dicyclopentadienyl units and have at least one group reactive towards isocyanates are preferably used here as isocyanate-reactive ethylenically unsaturated compounds; these are particularly preferably acrylates and methacrylates having at least one isocyanate-reactive group. Suitable hydroxy-functional acrylates or methacrylates are, for example, compounds such as 2-hydroxyethyl(meth)acrylate, polyethylene oxide mono(meth)acrylates, polypropylene oxide mono(meth)acrylates, polyalkylene oxide mono(meth)acrylates, poly(ε-caprolactone)mono(meth)acrylates, such as, for example, Tone® M100 (Dow, USA), 2-hydroxypropyl(meth)acrylate, 4-hydroxybutyl(meth)acrylate, 3-hydroxy-2,2-dimethylpropyl(meth)acrylate, the hydroxy-functional mono-, di- or tetra(meth)acrylates of polyhydric alcohols, such as trimethylolpropane, glycerol, pentaerythritol, dipentaerythritol, ethoxylated, propoxylated or alkoxylated trimethylolpropane, glycerol, pentaerythritol, dipentaerythritol or the industrial mixtures thereof. In addition, isocyanate-reactive oligomeric or polymeric unsaturated compounds containing acrylate and/or methacrylate groups are suitable alone or in combination with the abovementioned monomeric compounds. The proportion of isocyanates which are partly reacted with isocyanate-reactive ethylenically unsaturated compounds, based on the isocyanate component a) is 0 to 99%, preferably 0 to 50%, particularly preferably 0 to 25% and very particularly preferably 0 to 15%.
• It is optionally also possible for the abovementioned isocyanate component a) completely or proportionately to contain isocyanates, which are completely or partly reacted with blocking agents known to the person skilled in the art from coating technology. The following may be mentioned as an example of blocking agents: alcohols, lactams, oximes, malonic esters, alkyl acetoacetates, triazoles, phenols, imidazoles, pyrazoles and amines, such as, for example, butanone oxime, diisopropylamine, 1,2,4-triazole, dimethyl-1,2,4-triazole, imidazole, diethyl malonate, ethyl acetoacetate, acetone oxime, 3,5-dimethylpyrazole, ε-caprolactam, N-tert-butylbenzylamine, cyclopentanone carboxyethyl ester or any desired mixtures of these blocking agents.
• All polyfunctional, isocyanate-reactive compounds which have on average at least 1.5 isocyanate-reactive groups per molecule can in principle be used as component b).
• Isocyanate-reactive groups in the context of the present invention are preferably hydroxy, amino or thio groups; hydroxy compounds are particularly preferred.
• Suitable polyfunctional, isocyanate-reactive compounds are, for example, polyester-, polyether-, polycarbonate-, poly(meth)acrylate- and/or polyurethanepolyols.
• Suitable polyesterpolyols are, for example, linear polyesterdiols or branched polyester polyols, as are obtained in a known manner from aliphatic, cycloaliphatic or aromatic di- or polycarboxylic acids or their anhydrides with polyhydric alcohols having an OH functionality of ≧2.
• Examples of such di- or polycarboxylic acids or anhydrides are succinic, glutaric, adipic, pimelic, suberic, azelaic, sebaccic, nonanedicarboxylic, decanedicarboxylic, terephthalic, isophthalic, o-phthalic, tetrahydrophthalic, hexahydrophthalic or trimellitic acid and acid anhydrides such as o-phthalic, trimellitic or succinic anhydride, or any desired mixtures thereof with one another.
• Examples of such suitable alcohols are ethanediol, di-, tri- and tetraethylene glycol, 1,2-propanediol, di-, tri- and tetrapropylene glycol, 1,3-propanediol, 1,4-butanediol, 1,3-butanediol, 2,3-butanediol, 1,5-pentanediol, 1,6-hexanediol, 2,2-dimethyl-1,3-propanediol, 1,4-dihydroxycyclohexane, 1,4-dimethylolcyclohexane, 1,8-octanediol, 1,10-decanediol, 1,12-dodecanediol, trimethylolpropane, glycerol or any desired mixtures thereof with one another.
• The polyesterpolyols may also be based on natural or raw materials, such as castor oil. It is also possible for the polyesterpolyols to be based on homo- or copolymers of lactones, as can preferably be obtained by an addition reaction of lactones or lactone mixtures, such as butyrolactone, ε-caprolactone and/or methyl-ε-caprolactone, with hydroxy-functional compounds, such as polyhydric alcohols having an OH functionality of ≧2, for example of the abovementioned type.
• Such polyesterpolyols preferably have number average molar masses of 400 to 4000 g/mol, particularly preferably of 500 to 2000 g/mol. Their OH functionality is preferably 1.5 to 3.5, particularly preferably 1.8 to 3.0.
• Suitable polycarbonatepolyols are obtainable in a manner known per se by reacting organic carbonates or phosgene with diols or diol mixtures.
• Suitable organic carbonates are dimethyl, diethyl and diphenyl carbonate.
• Suitable diols or mixtures comprise the polyhydric alcohols mentioned per se in connection with the polyester segments and having an OH functionality of ≧2, preferably 1,4-butanediol, 1,6-hexanediol and/or 3-methylpentanediol, or polyesterpolyols can be converted into polycarbonatepolyols.
• Such polycarbonatepolyols preferably have number average molar masses of 400 to 4000 g/mol, particularly preferably of 500 to 2000 g/mol. The OH functionality of these polyols is preferably 1.8 to 3.2, particularly preferably 1.9 to 3.0.
• Suitable polyetherpolyols are polyadducts of cyclic ethers with OH- or NH-functional starter molecules, said polyadducts optionally having a block structure.
• Suitable cyclic ethers are, for example, styrene oxides, ethylene oxide, propylene oxide, tetrahydrofuran, butylene oxide, epichlorohydrin and any desired mixtures thereof.
• Starters which may be used are the polyhydric alcohols mentioned per se in connection with the polyesterpolyols and having an OH functionality of ≧2 and primary or secondary amines and amino alcohols.
• Preferred polyetherpolyols are those of the abovementioned type, exclusively based on propylene oxide, or random or block copolymers based on propylene oxide with further 1-alkylene oxides, the proportion of the 1-alkylene oxide not being higher than 80% by weight. In addition, poly(trimethylene oxides) and mixtures of the polyols mentioned as being preferred are preferred. Propylene oxide homopolymers and random or block copolymers which have oxyethylene, oxypropylene and/or oxybutylene units are particularly preferred, the proportion of oxypropylene units, based on the total amount of all oxyethylene, oxypropylene and oxybutylene units, accounting for at least 20% by weight, preferably at least 45% by weight. Here, oxypropylene and oxybutylene comprise all respective linear and branched C3- and C4-isomers.
• Such polyetherpolyols preferably have number average molar masses of 250 to 10 000 g/mol, particularly preferably of 500 to 8500 g/mol and very particularly preferably of 600 to 4500 g/mol. The OH functionality is preferably 1.5 to 4.0, particularly preferably 1.8 to 3.1.
• In addition, aliphatic, araliphatic or cycloaliphatic di-, tri- or polyfunctional alcohols which have a low molecular weight, i.e. having molecular weights of less than 500 g/mol, and a short chain, i.e. containing 2 to 20 carbon atoms, are also suitable as polyfunctional, isocyanate-reactive compounds as constituents of component c).
• These may be, for example, ethylene glycol, diethylene glycol, triethylene glycol, tetraethylene glycol, dipropylene glycol, tripropylene glycol, 1,2-propanediol, 1,3-propanediol, 1,4-butanediol, neopentylglycol, 2-ethyl-2-butylpropanediol, trimethylpentanediol, positional isomers of diethyloctanediol, 1,3-butylene glycol, cyclohexanediol, 1,4-cyclohexanedimethanol, 1,6-hexanediol, 1,2- and 1,4-cyclohexanediol, hydrogenated bisphenol A (2,2-bis(4-hydroxycyclohexyl)propane), 2,2-dimethyl-3-hydroxy-propionic acid (2,2-dimethyl-3-hydroxypropyl ester). Examples of suitable triols are trimethylolethane, trimethylolpropane or glycerol. Suitable higher-functional alcohols are ditrimethylolpropane, pentaerythritol, dipentaerythritol or sorbitol.
• One or more photoinitiators are used as component c). These are usually initiators which can be activated by actinic radiation and initiate a polymerization of the corresponding polymerizable groups. Photoinitiators are commercially distributed compounds known per se, a distinction being made between monomolecular (type I) and bimolecular (type II) initiators. Furthermore, these initiators are used for free radical, anionic (or), cationic (or mixed) forms of the abovementioned polymerizations, depending on the chemical nature.
• (Type I) systems for the free radical photopolymerization are, for example, aromatic ketone compounds, e.g. benzophenones, in combination with tertiary amines, alkylbenzophenones, 4,4′-bis(dimethylamino)benzophenone (Michlers ketone), anthrone and halogenated benzophenones or mixtures of said types. (Type II) initiators, such as, benzoin and its derivatives, benzil ketals, acylphosphine oxides, e.g. 2,4,6-trimethylbenzoyl-diphenylphosphine oxide, bisacylophosphine oxides, phenylglyoxylic esters, campherquinone, alpha-aminoalkylphenones, alpha-,alpha-dialkoxyacetophenones, 1-[4-(phenylthio)phenyl]octane-1,2-dione 2-(O-benzoy loxime), differently substituted hexarylbisimidazoles (HABI) with suitable coinitiators, such as, for example, mercaptobenzoxazole and alpha-hydroxyalkylphenones are furthermore suitable. The photoinitiator systems described in EP-A 0223587 and consisting of a mixture of an ammonium aryl borate and one or more dyes can also be used as a photoinitiator. For example, tetrabutylammonium triphenylhexylborate, tetrabutylammonium triphenylbutylborate, tetrabutylammonium trinaphthylbutylborate, tetramethylammonium triphenylbenzylborate, tetra(n-hexyl)ammonium (sec-butyl)triphenylborate, 1-methyl-3-octylimidazolium dipentyldiphenylborate, tetrabutylammonium tris(4-tert-butyl)phenyl-butylborate, tetrabutylammonium tris(3-fluorophenyl)hexylborate and tetrabutylammonium tris(3-chloro-4-methylphenyl)hexylborate are suitable as the ammonium aryl borate. Suitable dyes are, for example, new methylene blue, thionine, basic yellow, pinacynol chloride, rhodamine 6G, gallocyanine, ethylviolet, Victoria blue R, celestine blue, quinaldine red, crystal violet, brilliant green, astrazone orange G, darrow red, pyronine Y, basic red 29, pyrillium I, safranine O, cyanine and methylene blue, azure A (Cunningham et al., RadTech'98 North America UV/EB Conference Proceedings, Chicago, Apr. 19-22, 1998).
• The photoinitiators used for the anionic polymerization are as a rule (type I) systems and are derived from transition metal complexes of the first series. Here are chromium salts, such as, for example, trans-Cr(NH₃)₂(NCS)₄— (Kutal et al, Macromolecules 1991, 24, 6872) or ferrocenyl compounds (Yamaguchi et al., Macromolecules 2000, 33, 1152). A further possibility of anionic polymerization consists in the use of dyes, such as crystal violet leuconitrile or malchite green leuconitrile, which can polymerize cyanoacrylates by photolytic decomposition (Neckers et al., Macromolecules 2000, 33, 7761). However, the chromophore is incorporated thereby into the polymer so that the resulting polymers are coloured throughout.
• The photoinitiators used for the cationic polymerization substantially comprise three classes: aryldiazonium salts, onium salts (here specifically: iodonium, sulphonium and selenonium salts) and organometallic compounds. On irradiation both in the presence and in the absence of a hydrogen donor, phenyldiazonium salts can produced a cation that initiates the polymerization. The efficiency of the overall system is determined by the nature of the counterion used for the diazonium compound. The not very reactive but very expensive SbF₆ ⁻, AsF₆ ⁻ or PF₆ are preferred here. These compounds are as a rule not very suitable for use in coating of the thin films since the nitrogen liberated after the exposure reduces the surface quality (pinholes) (Li et al., Polymeric Materials Science and Engineering, 2001, 84, 139). Very widely used and commercially available in many forms are onium salts, especially sulphonium and iodonium salts. The photochemistry of these compounds has been investigated for a long time. After excitation, the iodonium salts initially decompose homolytically and thus produce a free radical and a radical anion which is stabilized by H abstraction and releases a proton and then initiates the cationic polymerization (Dektar et al. J. Org. Chem. 1990, 55, 639; J. Org. Chem., 1991, 56, 1838). This mechanism permits the use of iodonium salts also for free radical photopolymerization. The choice of the counterion is once again of considerable importance here; SbF₆ ⁻, AsF₆ ⁻ or PF₆ are likewise preferred. Otherwise, this choice of the substitution of the aromatic is completely free in this structure class and is determined substantially by the availability of suitable starting building blocks for the synthesis. The sulphonium salts are compounds which decompose in according to Norrish(II) (Crivello et al., Macromolecules, 2000, 33, 825). In the case of the sulphonium salts, too, the choice of the counterion is of critical importance and manifests itself substantially in the curing rate of the polymers. The best results are as a rule obtained with SbF₆ ⁻ salts. Since the self-absorption of iodonium and sulphonium salts is at <300 nm, these compounds must be appropriately sensitized for the photopolymerization with near UV or short-wave visible light. This is effected by the use of more highly absorbing aromatics such as, for example, anthracene and derivatives (Gu et al., Am. Chem. Soc. Polymer Preprints, 2000, 41 (2), 1266) or phenothiazine or derivatives thereof (Hua et al, Macromolecules 2001, 34, 2488-2494).
• It may also be advantageous to use mixtures of these compounds. Depending on the radiation source used for the curing, type and concentration of photoinitiator must be adapted in a manner known to a person skilled in the art. Further details are described, for example, in P. K. T. Oldring (Ed.), Chemistry & Technology of UV & EB Formulations For Coatings, Inks & Paints, Vol. 3, 1991, SITA Technology, London, pages 61-328.
• Preferred photoinitiators c) are mixtures of tetrabutylammonium triphenylhexylborate, tetrabutylammonium triphenylbutylborate, tetrabutylammonium trinaphthylbutylborate, tetrabutylammonium tris-(4-tert-butyl)phenylbutylborate, tetrabutylammonium tris-(3-fluorophenyl)hexylborate and tetrabutylammonium tris-(3-chloro-4-methylphenyl)hexyl-borate with dyes, such as, for example, astrazone orange G, methylene blue, new methylene blue, azure A, pyrillium I, safranine O, cyanine, gallocyanine, brilliant green, crystal violet, ethyl violet and thionine.
• The photopolymer formulation may additionally contain urethanes as plasticizers, it being possible for the urethanes preferably to be substituted by at least one fluorine atom.
• The urethanes are preferably compounds which have a structural element of the general formula I.
• 
• They can be obtained from monofunctional alcohols and monofunctional isocyanates. These are preferably substituted by at least one fluorine atom.
• It is more preferable if the fluorourethanes have the general formula II
• 
• in which n is >1 and n is <8 and R¹, R², R³ are hydrogen and/or, independently of one another, linear, branched, cyclic or heterocyclic organic radicals which are unsubstituted or optionally also substituted by heteroatoms, at least one of the radicals R¹, R², R³ being substituted by at least one fluorine atom. Here, R¹ is particularly preferably an organic radical having at least one fluorine atom.
• According to a further embodiment, R¹ may comprise 1-20 CF₂ groups and/or one or more CF₃ groups, particularly preferably 1-15 CF₂ groups and/or one or more CF₃ groups, particularly preferably 1-10 CF₂ groups and/or one or more CF₃ groups, very particularly preferably 1-8 CF₂ groups and/or one or more CF₃ groups, R² may comprise a C1-C20 alkyl radical, preferably a C1-C15 alkyl radical, particularly preferably a C1-C10 alkyl radical or hydrogen, and/or R³ may comprise a C1-C20 alkyl radical, preferably a C1-C15 alkyl radical, particularly preferably a C1-C10 alkyl radical or hydrogen.
• The fluorourethanes may have a fluorine content of 10-80% by weight of fluorine, preferably of 13-70% by weight of fluorine and particularly preferably 17.5-65% by weight of fluorine.
• According to a further preferred embodiment of the invention, it is envisaged that the photopolymer formulation contains 10 to 89.999% by weight, preferably 25 to 70% by weight, of matrix polymers, 10 to 60% by weight, preferably 25 to 50% by weight, of writing monomers, 0.001 to 5% by weight of photoinitiators and optionally 0 to 4% by weight, preferably 0 to 2% by weight, of catalyst, 0 to 5% by weight, preferably 0.001 to 1% by weight, of free radical stabilizers, 0 to 30% by weight, preferably 0 to 25% by weight, of plasticizers and 0 to 5% by weight, preferably 0.1 to 5% by weight, of further additives, the sum of all constituents being 100% by weight.
• Photopolymer formulations having 25 to 70% by weight of matrix polymers consisting of compounds of component a) and of component b), 25 to 50% by weight of writing monomers, 0.001 to 5% by weight of photoinitiators, 0 to 2% by weight of catalyst, 0.001 to 1% by weight of free radical stabilizers, optionally 0 to 25% by weight of the urethanes described above and optionally 0.1 to 5% by weight of further additives are particularly preferably used.
• A further preferred embodiment of the invention envisages that the photopolymer formulation contains urethanes having a number average molecular weight of ≦250 g/mol, preferably of ≦200 g/mol and particularly preferably of ≦190 g/mol.
• The photopolymer formulation therefore advantageously contains aliphatic urethanes. In this case, the aliphatic urethanes may have in particular the general formula (III)
• 
• in which R⁴, R⁵, R⁶, independently of one another, are linear or branched (C1-C20)-alkyl radicals optionally substituted by heteroatoms. It is particularly preferable if R⁴ is a linear or branched (C1-C8)-alkyl radical, R⁵ is a linear or branched (C1-C8)-alkyl radical and/or R⁶ is a linear or branched (C1-C8)-alkyl radical, it being particularly preferable if R⁴ is a linear or branched (C1-C4)-alkyl radical and R⁵ is a linear or branched (C1-C6)-alkyl radical and R⁶ is hydrogen. In this case, it was in fact found that the urethanes thus obtained are very compatible with the polyurethane matrix and show the effect described here.
• According to a further preferred embodiment, it is envisaged that the urethanes have substantially no free NCO groups.
• The writing monomers can preferably comprise a monofunctional acrylate of the general formula (IV)
• 
• in which R⁷, R⁸ are hydrogen and/or, independently of one another, linear, branched, cyclic or heterocyclic unsubstituted organic radicals.
• It is also possible for the writing monomers to comprise a polyfunctional writing monomer, it being possible for this to be in particular a polyfunctional acrylate.
• The polyfunctional acrylate can preferably have the general formula (V)
• 
• in which n is ≧2 and n is ≦4 and R⁹, R¹⁰ are hydrogen and/Or, independently of one another, linear, branched, cyclic or heterocyclic organic radicals which are unsubstituted or optionally also substituted by heteroatoms.
• The present invention furthermore relates to the use of a photopolymer formulation according to the invention for the production of holographic media, in particular for the production of in-line holograms, off-axis holograms, full-aperture transfer holograms, white light transmission holograms, Denisyuk holograms, off-axis reflection holograms, edge-lit holograms and holographic stereograms.
EXAMPLES
• The invention is explained in more detail below with reference to examples. First, the synthesis and characterization of the example molecules are described and thereafter the handling thereof in the method according to the invention.
• Unless noted otherwise, all stated percentages relate to percent by weight.
Determination of the Refractive Index
• Measurement of the refractive index n²⁰;_D at a wavelength of 589 nm: a sample of the example compound was introduced into an Abbe refractometer and n²⁰;_D was measured.
Determination of the Vapour Pressure
• For Examples 2 and 7, the synthesis of which is described further below, the vapour pressures were determined under a nitrogen atmosphere in a circulation apparatus (isobar in an Ebulliometer) by the Röck method according to the OECD guideline for the testing of chemicals, No. 104. The resulting vapour pressure curves are shown in FIG. 5 in the temperature range from 90 to 180° C. The resulting parameters of the Antoine equation
• $\lg \frac{P^{\mathrm{Sat}}}{\mathrm{hPa}}=A-\frac{B}{C+T\left(°C.\right)}$
• are accordingly:

• TABLE 1
  Physical data of Examples 2 and 7

  Vapour

  Vapour

  	Parameters of the	pressure	pressure	TGA
  	Antoine equation	at 80° C.	at 100° C.	95

  Example	A	B	C	[hPa]	[hPa]	[° C.]

  2	15.6189	2616.075	90.3596	1.30	7.30	72.5
  7	6.5466	1053.404	42.458	0.13	0.42	111.8

• It is evident from this that the equilibrium vapour pressure, for example for a temperature of 100° C. in both Examples 2 and 7, is <10 hPa, so that it would be expected that the two components have sufficient stability in the formulation. The TGA95 values of the two two Examples 2 and 7 on the other hand correlate substantially better with the observed behaviour during the film coating.
• FIG. 1 shows the measured vapour pressure curves of Examples 2 and 7.
Determination of the TGA95 Value
• The TGA95 values of the individual components are determined by weighing an amount of about 10 mg of the respective component into an aluminium pan having a volume of 70 introducing the aluminium pan into an oven of a thermobalance, preferably a TG50 thermobalance from Mettler-Toledo, and measuring the loss of mass (of the sample) in the open aluminium pan at a constant oven heating rate of 20 K/min, the starting temperature being 30° C. and the end temperature of the oven being 600° C., the oven being flushed with a 200 ml/min nitrogen stream during the determination and the temperature at which a loss of mass of the sample of 5% by weight, based on the originally weighed in amount of the sample, has occurred being determined as the TGA95 value of the respective component.
Measurement of the Holographic Properties DE and Δn of the Holographic Media by Means of Two-Beam Interference in Reflection Arrangement
• For the measurement of the holographic performance, the protective foil of the holographic film is peeled off and the holographic film is laminated on the photopolymer side with a 1 mm thick glass plate of suitable length and width using a rubber roller with gentle pressure. This sandwich of glass and photopolymer film can now be used for determining the holographic performance parameters DE and Δn.
• The holographic media produced as described below were then tested with regard to the holographic properties by means of a measurement arrangement according to FIG. 3, as follows:
• The beam of an He—Ne laser (emission wavelength 633 nm) was converted with the aid of the spatial filter (SF) and together with the collimation lens (CL) into a parallel homogeneous beam. The final cross sections of the signal and reference beam are established by the iris diaphragm (I). The diameter of the iris diaphragm opening is 0.4 cm. The polarization-dependent beam splitters (PBS) split the laser beam into two coherent equally polarized beams. Via the λ/2 plates, the power of the reference beam was adjusted to 0.5 mW and the power of the signal beam to 0.65 mW. The powers were determined using the semiconductor detectors (D) with sample removed. The angle of incidence (α₀) of the reference beam is −21.8° and the angle of incidence (β₀) of the signal beam is 41.8°. The angles are measured starting from the sample normal to the beam direction. According to FIG. 3, α₀ therefore has a negative sign and β₀ a positive sign. At the location of the sample (medium), the interference field of the two overlapping beams produced a grating of lighter and darker strips which are perpendicular to the angle dissectors of the two beams incident on the sample (reflection hologram). The strip spacing Λ, also referred to as grating period, in the medium is ˜225 nm (the refractive index of the medium is seen to be ˜1.504).
• FIG. 3 shows the holographic experimental setup with which the diffraction efficiency (DE) of the media was measured.
• Holograms were recorded in the medium in the following manner:
• • both shutters (S) are opened for the exposure time t.
  • thereafter, with closed shutters (S), the medium was allowed a time of 5 minutes for diffusion of the still unpolymerized writing monomers.
• The holograms recorded were now read in the following manner. The shutter of the signal beam remained closed. The shutter of the reference beam was opened. The iris diaphragm of the reference beam was closed to a diameter of <1 mm. This ensured that the beam was always completely in the previously recorded hologram for all angles of rotation (Ω) of the medium. The turntable, now computer controlled, covered the angle range from Ω_min to Ω_max with an angle step width of 0.05°. Ω is measured from the sample normal to the reference direction of the turntable. The reference direction of the turntable is obtained when the angle of incidence of the reference beam and that of the signal beam have the same absolute value during recording of the hologram, i.e. α₀=−31.8° and β₀=31.8°. Ω_recording is then 0°. For α₀=−21.8° and β₀=41.8°, Ω_recording is therefore 10°. In general, the following is true for the interference field during recording of the hologram:
• 
  α₀θ₀+Ω_recording.
• θ₀ is the semiangle on the laboratory system outside the medium and the following is true during recording of the hologram:
• ${\mathrm{<figure-callout\; id="0"\; label="\theta "\; filenames="US20120237856A1-20120920-D00002.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_0=\frac{{\alpha }_0-{\mathrm{<figure-callout\; id="0"\; label="\beta "\; filenames="US20120237856A1-20120920-D00002.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_0}{2}.$
• In this case, θ₀ is therefore −31.8°. At each angle of rotation Ω approached, the powers of the beam transmitted in the zeroth order were measured by means of the corresponding detector D and the powers of the beam diffracted in the first order were measured by means of the detector D. The diffraction efficiency was obtained at each angle Ω approached as a quotient of:
• $\eta =\frac{P_D}{P_D+P_T}$
• P_D is the power in the detector of the diffracted beam and P_T is the power in the detector of the transmitted beam.
• By means of the method described above, the Bragg curve (it describes the diffraction efficiency η as a function of the angle of rotation Ω of the recorded hologram) was measured and was stored in a computer. In addition, the intensity transmitted in the zeroth order was plotted against the angle of rotation Ω and stored in a computer.
• The maximum diffraction efficiency (DE=η_max) of the hologram, i.e. its peak value, was determined at Ω_{reconstruction}. It may have been necessary for this purpose to change the position of the detector of the diffracted beam in order to determine this maximum value.
• The refractive index Δn and the thickness d of the photopolymer layer was now determined by means of the coupled wave theory (cf. H. Kogelnik, The Bell System Technical Journal, Volume 48, November 1969, Number 9, page 2909-page 2947) from the measured Bragg curve and variation of the transmitted intensity as a function of angle. It should be noted that, owing to the thickness shrinkage occurring as result of the photopolymerization, the strip spacing Λ′ of the hologram and the orientation of the strips (slant) may differ from the strip spacing Λ of the interference pattern and the orientation thereof. Accordingly, the angle α₀′ and the corresponding angle of the turntable Ω_{reconstruction}, at which maximum diffraction efficiency is reached will also differ from α₀ and from the corresponding Ω_recording, respectively. The Bragg condition changes as a result. This change is taken into account in the evaluation method. The evaluation method is described below:
• All geometrical quantities which relate to the recorded hologram and not to the interference pattern are shown as quantities represented by a dashed line.
• According to Kogelnik, the following is true for the Bragg curve η(Ω) of reflection hologram:
• $\eta =\{\begin{array}{c}\frac{1}{1-\frac{1-{\left(\xi /v\right)}^2}{{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\left(\sqrt{{\xi }^2-v^2}\right)}},\mathrm{for}v^2-{\mathrm{<figure-callout\; id="2"\; label="\xi "\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">\xi </figure-callout>}}^2<0\\ \frac{1}{1+\frac{1-{\left(\xi /v\right)}^2}{{\mathrm{<figure-callout\; id="2"\; label="sinh"\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">sinh</figure-callout>}}^2\left(\sqrt{v^2-{\xi }^2}\right)}},\mathrm{for}v^2-{\mathrm{<figure-callout\; id="2"\; label="\xi "\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">\xi </figure-callout>}}^2\ge 0\end{array}$
• with:
• $v=\frac{\pi ·\Delta n·d^{\prime }}{\lambda ·\sqrt{c_s·c_r}}$ $\xi =-\frac{d^{\prime }}{2·c_s}·\mathrm{DP}$ $c_s=\cos \left({\vartheta }^{\prime }\right)-\cos \left({\psi }^{\prime }\right)·\frac{\lambda }{n·{\Lambda }^{\prime }}$ $c_r=\cos \left({\vartheta }^{\prime }\right)$ $\mathrm{DP}=\frac{\pi }{{\Lambda }^{\prime }}·\left(2·\cos \left({\psi }^{\prime }-{\vartheta }^{\prime }\right)-\frac{\lambda }{n·{\Lambda }^{\prime }}\right)$ ${\psi }^{\prime }=\frac{{\beta }^{\prime }+{\alpha }^{\prime }}{2}$ ${\Lambda }^{\prime }=\frac{\mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}{2·n·\cos \left({\psi }^{\prime }-{\alpha }^{\prime }\right)}$
• On reading the hologram (“reconstruction”), the following is true, as shown analogously above:
• 
  ∂′₀=θ₀+Ω
• 
  sin(∂′₀)=n·sin(∂′)
• Under the Bragg condition, the “dephasing” DP is 0. Accordingly, the following is true:
• 
  α′₀=θ₀+Ω_{reconstruction}
• 
  sin(α′₀)=n·sin(α′)
• The still unknown angle β′ can be determined from the comparison of the Bragg condition of the interference field on recording of the hologram and the Bragg condition on reading the hologram, assuming that only thickness shrinkage takes place. Then follows:
• $\sin \left({\beta }^{\prime }\right)=\frac{1}{n}·\left[\sin \left({\alpha }_0\right)+\sin \left({\beta }_0\right)-\sin \left({\mathrm{<figure-callout\; id="0"\; label="\theta "\; filenames="US20120237856A1-20120920-D00002.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_0+{\Omega }_{\mathrm{reconstruction}}\right)\right]$
• v is the grating thickness, ξ is the detuning parameter and ψ′ is the orientation (slant) of the refractive index grating which was recorded. α′ and β′ correspond to the angles α₀ and β₀ of the interference field on recording of the hologram, but measured in the medium and applicable to the grating of the hologram (after thickness shrinkage). n is the mean refractive index of the photopolymer and was set at 1.504. λ is the wavelength of the laser light in vacuo.
• The maximum diffraction efficiency (DE=η_max) is then obtained for ξ=0 as:
• $\mathrm{DE}={\mathrm{<figure-callout\; id="2"\; label="tanh"\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">tanh</figure-callout>}}^2\left(v\right)={\mathrm{<figure-callout\; id="2"\; label="tanh"\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">tanh</figure-callout>}}^2\left(\frac{\pi ·\Delta n·d^{\prime }}{\lambda ·\sqrt{\cos \left({\alpha }^{\prime }\right)·\cos \left({\alpha }^{\prime }-2\psi \right)}}\right)$
• The measured data of the diffraction efficiency, the theoretical Bragg curve and the transmitted intensity are, as shown in FIG. 4, plotted against the centred angle of rotation ΔΩ≡Ω_{reconstruction}−Ω=α′₀−∂′₀, also referred to as angle detuning.
• Since DE is known, the shape of the theoretical Bragg curve according to Kogelnik is determined only by the thickness d′ of the photopolymer layer. Δn is subsequently corrected via DE for a given thickness d′ so that measurement and theory of DE always agree. d′ is now adapted until the angle positions of the first secondary minima of the theoretical Bragg curve agree with the angle positions of the first secondary maxima of the transmitted intensity and additionally the full width at half maximum (FWHM) for the theoretical Bragg curve and the transmitted intensity agree.
• Since the direction in which a reflection hologram concomitantly rotates on reconstruction by means of an Ω scan, but the detector for the diffracted light can detect only a finite angle range, the Bragg curve of broad holograms (small d′) is not completely detected in an Ω scan, but only the central region, with suitable detector positioning. That shape of the transmitted intensity which is complementary to the Bragg curve is therefore additionally used for adapting the layer thickness d′.
• FIG. 4 shows the plot of the Bragg curve η according to the coupled wave theory (dashed line), of the measured diffraction efficiency (solid circles) and of the transmitted power (black solid line) against the angle detuning ΔΩ.
• For a formulation, this procedure was possibly repeated several times for different exposure times t on different media in order to determine the average energy dose of the incident laser beam at which DE reaches the saturation value during recording of the hologram. The average energy dose E is obtained from the powers of the two part-beams coordinated with the angles α₀ and β₀ (reference beam with P_r=0.50 mW and signal beam with P_s=0.63 mW), the exposure time t and the diameter of the iris diaphragm (0.4 cm), as follows:
• $E\left(\mathrm{mJ}/{\mathrm{cm}}^2\right)=\frac{2·\left[P_r+P_s\right]·t\left(s\right)}{\pi ·{0.4}^2{\mathrm{<figure-callout\; id="2"\; label="cm"\; filenames="US20120237856A1-20120920-D00005.png"\; state="\{\{state\}\}">cm</figure-callout>}}^2}$
• The powers of the part-beams were adapted so that the same power density is achieved in the medium at the angles α₀ and β₀ used.
• In examples, respectively the maximum value in Δn is reported, and the doses used are between 4 and 64 ml/cm² per arm.
Substances Used
• CGI-909 (tetrabutylammonium tris(3-chloro-4-methylphenyl)(hexyl)borate, [1147315-11-4]) is an experimental product produced by CIBA Inc., Basle, Switzerland.
• The (fluorinated) alcohols and monofunctional isocyanates used were obtained in the chemicals trade.
• 1,8-Diisocyanato-4-(isocyanatomethyl)octane (TIN) was prepared as described in EP 749958.
• 2,4,4-Trimethylhexane 1,6-diisocyanate, Vestanat TMDI, is a product of Evonik Degussa GmbH, Marl, Germany.
Preparation of the Polyol Component:
• In a 11 flask, 0.18 g of tin octoate, 374.8 g of ε-caprolactone and 374.8 g of a difunctional polytetrahydrofuranpolyetherpolyol (equivalent weight 500 g/mol OH) were initially introduced and heated to 120° C. and kept at this temperature until the solids content (proportion of nonvolatile constituents) was 99.5% by weight or more. Thereafter, cooling was effected and the product was obtained as a waxy solid.
• Preparation of Urethane Acrylate 1: phosphorothioyltris(oxybenzene-4,1-diylcarbamoyloxyethane-2,1-diyl)trisacrylate
• In a 500 ml round-bottomed flask, 0.1 g of 2,6-di-tert-butyl-4-methylphenol, 0.05 g of dibutyltin dilaurate (Desmorapid Z, Bayer MaterialScience AG, Leverkusen, Germany) and 213.07 g of a 27% strength solution of tris(p-isocyanatophenyl)thiophosphate in ethyl acetate (Desmodur® RFE, product of Bayer MaterialScience AG, Leverkusen, Germany) were initially introduced and heated to 60° C. Thereafter, 42.37 g of 2-hydroxyethyl acrylate were added dropwise and the mixture was further kept at 60° C. until the isocyanate content had fallen below 0.1%. Thereafter, cooling was effected and the ethyl acetate was completely removed in vacuo. The product was obtained as a semicrystalline solid.
• Preparation of Urethane Acrylate 2: 2-({[3-(methylsulphanyl)phenyl]carbamoyl}oxy)-ethyl prop-2-enoate):
• In a 100 ml round-bottomed flask, 0.02 g of 2,6-di-tert-butyl-4-methylphenol, 0.01 g of Desmorapid® Z, 11.7 g of 3-(methylthio)phenyl isocyanate were initially introduced and heated to 60° C. Thereafter, 8.2 g of 2-hydroxyethyl acrylate were added dropwise and the mixture was further kept at 60° C. until the isocyanate content had fallen below 0.1%. Thereafter, cooling was effected. The product was obtained as a light yellow liquid.
Example 1 Trifluoroethyl butylcarbamatez
• In a 2 l round-bottomed flask, 0.50 g of Desmorapid Z and 498 g of n-butyl isocyanate were initially introduced and heated to 60° C. Thereafter, 502 g of trifluoroethanol were added dropwise and the mixture was further kept at 60° C. until the isocyanate content had fallen below 0.1%. Thereafter, cooling was effected. The product was obtained as a colourless solid. The refractive index n²⁰;_D determined by method B is 1.3900 and the measured TGA95 value is 63.7° C.
Further Examples
• Examples 2-25 were prepared in the manner described for Example 1, in the compositions stated in Table 2. The associated n²⁰;_D and TGA95 values for all examples were measured as described in the above correspondingly named sections.

• TABLE 2
  Preparation and characterization of Examples 2-35

  Exam-		Isocyanate and		Catalyst and	Temp	Descrip-
  ple	Name	amount	Alcohol and amount	amount	[° C.]	tion

  2	2,2,2-Trifluoroethyl hexylcarbamate	n-Hexyl isocyanate	Trifluoroethanol	Desmorapid Z	60° C.	colourless
  		55.9 g	44.0 g	0.05 g		liquid
  3	2,2,3,3-Tetrafluoropropyl butylcarbamate	n-Butyl isocyanate	2,2,3,3-Tetra-	Desmorapid Z	60° C.	colourless
  		10.7 g	fluoropropan-1-ol	0.01 g		liquid
  			14.3 g
  4	Bis(2,2,2-trifluoroethyl)-(2,2,4-	2,4,4-Trimethylhexane	Trifluoroethanol	Desmorapid Z	60° C.	colourless
  	trimethylhexane-1,6-diyl) biscarbamate	1,6-diisocyanate	463 g	0.48 G		liquid
  		(TMDI)
  		496 g
  5	Bis(2,2,2-trifluoroethyl)-[4-	1,8-Diisocyanato-4-(iso-	Trifluoroethanol	Desmorapid Z	60° C.	colourless
  	({[(2,2,2-trifluoroethoxy)-	cyanatomethyl)octane	272 g	0.48 g		liquid
  	carbonyl]amino}methyl)octane-	(TIN)
  	1,8-diyl] biscarbamate	228 g
  6	2,2,3,3,4,4,4-Heptafluorobutyl	n-Butyl isocyanate	2,2,3,3,4,4,4-Hepta-	Desmorapid Z	60° C.	colourless
  	butylcarbamate	24.8 g	fluorobutanol	0.04 g		solid
  			50.1 g
  7	2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9-	n-Butyl isocyanate	2,2,3,3,4,4,5,5,6,6,7,7,8,	Desmorapid Z	60° C.	colourless
  	Hexadecafluorononyl butylcarbamate	186 g	8,9,9-Hexadecafluoro-	0.50 g		liquid
  			nonanol
  			813 g
  8	Bis(2,2,3,3,4,4,4-heptafluorobutyl)-	2,4,4-Trimethylhexane	2,2,3,3,4,4,4-Hepta-	Desmorapid Z	60° C.	colourless
  	(2,2,4-trimethylhexane-1,6-diyl)	1,6-diisocyanate	fluorobutanol	0.01 g		liquid
  	biscarbamate	(TMDI)	13.1 g
  		6.88 g
  9	Bis(2,2,3,3,4,4,4-heptafluorobutyl)-[4-	1,8-Diisocyanato-4-(iso-	2,2,3,3,4,4,4-Hepta-	Desmorapid Z	60° C.	colourless
  	({[(2,2,3,3,4,4,4-heptafluoro-	cyanatomethyl)octane	fluorobutanol	0.01 g		oil
  	butoxy)carbonyl]amino}methyl)octane-1,8-	(TIN)	14.1 g
  	diyl] biscarbamate	5.91 g
  10	2,2,3,3,4,4,5,5,5-Nonafluoropentyl	n-Butyl isocyanate	2,2,3,3,4,4,5,5,5-Nona-	Desmorapid Z	70° C.	colourless
  	butylcarbamate	4.25 g	fluoropentan-1-ol	0.02 g		liquid
  			10.7 g
  11	Bis(2,2,3,3,4,4,5,5,5-nonafluoropentyl)-	2,4,4-Trimethylhexane	2,2,3,3,4,4,5,5,5-Nona-	Desmorapid Z	70° C.	colourless
  	(2,2,4-trimethylhexane-1,6-diyl)	1,6-diisocyanate	fluoropentan-1-ol	0.02 g		liquid
  	biscarbamate	(TMDI)	10.6 g
  		4.43 g
  12	2,2,3,3,4,4,5,5,5-Nonafluoropentyl	n-Hexyl isocyanate	2,2,3,3,4,4,5,5,5-Nona-	Desmorapid Z	70° C.	colourless
  	hexylcarbamate	5.05 g	fluoropentan-1-ol	0.02 g		liquid
  			9.94 g
  13	2,2,3,3,4,4,5,5,5-Nonafluoropentyl	i-Propyl isocyanate	2,2,3,3,4,4,5,5,5-Nona-	Desmorapid Z	70° C.	colourless
  	propan-2-yl carbamate	3.81 g	fluoropentan-1-ol	0.02 g		liquid
  			11.2 g
  14	2,2,3,3,4,4,5,5,6,6,6-Undecafluorohexyl	n-Butyl isocyanate	2,2,3,3,4,4,5,5,6,6,6-	Desmorapid Z	70° C.	colourless
  	butylcarbamate	3.72 g	Undecafluorohexan-1-ol	0.02 g		liquid
  			11.3 g
  15	Bis(2,2,3,3,4,4,5,5,6,6,6-undecafluoro-	2,4,4-Trimethylhexane	2,2,3,3,4,4,5,5,6,6,6-	Desmorapid Z	70° C.	colourless
  	hexyl)-(2,2,4-trimethylhexane-1,6-diyl)	1,6-diisocyanate	Undecafluorohexan-1-ol	0.02 g		oil
  	biscarbamate	(TMDI)	11.1 g
  		3.88 g
  16	2,2,3,3,4,4,5,5,6,6,6-Undecafluorohexyl	n-Hexyl isocyanate	2,2,3,3,4,4,5,5,6,6,6-	Desmorapid Z	70° C.	colourless
  	hexylcarbamate	4.46 g	Undecafluorohexan-1-ol	0.02 g		liquid
  			10.5 g
  17	Bis(2,2,3,3,4,4,5,5,6,6,7,7-dodecafluoro-	2,4,4-Trimethylhexane	2,2,3,3,4,4,5,5,6,6,7,7-	Desmorapid Z	70° C.	colourless
  	heptyl)-(2,2,4-trimethylhexane-1,6-diyl)	1,6-diisocyanate	Dodecafluoroheptan-1-ol	0.02 g		oil
  	biscarbamate	(TMDI)	11.4 g
  		3.60 g
  18	2,2,3,3,4,4,5,5,6,6,7,7-Dodecafluoroheptyl	n-Hexyl isocyanate	2,2,3,3,4,4,5,5,6,6,7,7-	Desmorapid Z	70° C.	colourless
  	hexylcarbamate	4.15 g	Dodecafluoroheptan-1-ol	0.02 g		liquid
  			10.8 g
  19	2,2,3,3,4,4,5,5,6,6,7,7-Dodecafluoroheptyl	i-Propyl isocyanate	2,2,3,3,4,4,5,5,6,6,7,7-	Desmorapid Z	70° C.	colourless
  	propan-2-ylcarbamate	3.06 g	Dodecafluoroheptan-1-ol	0.02 g		liquid
  			11.93 g
  20	2,2,3,3,4,4,5,5,6,6,7,7-Dodecafluoroheptyl	Cyclohexyl isocyanate	2,2,3,3,4,4,5,5,6,6,7,7-	Desmorapid Z	70° C.	colourless
  	cyclohexylcarbamate	4.10 g	Dodecafluoroheptan-1-ol	0.02 g		liquid
  			10.9 g
  21	2,2,3,4,4,4-Hexafluorobutyl butylcarbamate	n-Butyl isocyanate	2,2,3,4,4,4-	Desmorapid Z	70° C.	colourless
  		5.28 g	Hexafluorobutan-1-ol	0.02 g		liquid
  			9.71 g
  22	2,2,3,4,4,4-Hexafluorobutyl hexylcarbamate	n-Hexyl isocyanate	2,2,3,4,4,4-Hexafluoro-	Desmorapid Z	70° C.	colourless
  		6.16 g	butan-1-ol	0.02 g		liquid
  			8.83 g
  23	2,2,3,4,4,4-Hexafluorobutyl propan-2-	i-Propyl isocyanate	2,2,3,4,4,4-Hexafluoro-	Desmorapid Z	70° C.	colourless
  	ylcarbamate	4.77 g	butan-1-ol	0.02 g		oil
  			10.2 g
  24	2,2,3,3,4,4,5,5-Octafluoropentyl	n-Butyl isocyanate	2,2,3,3,4,4,5,5-Octa-	Desmorapid Z	70° C.	colourless
  	butylcarbamate	4.48 g	fluoropentan-1-ol	0.02 g		liquid
  			10.5 g
  25	Bis(2,2,3,3,4,4,5,5-octafluoropentyl)-{4-	1,8-Diisocyanato-4-	2,2,3,3,4,4,5,5-Octa-	Desmorapid Z	70° C.	colourless
  	[({[(2,2,3,3,4,4,5,5-octafluoropentyl)-	(isocyanatomethyl)octane	fluoropentan-1-ol	0.02 g		oil
  	oxy]carbonyl}amino)methyl]octane 1,8-	(TIN)	11.0 g
  	diyl}biscarbamate	3.98 g
  26	Bis(2,2,3,3,4,4,5,5-octafluoropentyl)-(2,2,4-	2,4,4-Trimethylhexane	2,2,3,3,4,4,5,5-Octa-	Desmorapid Z	70° C.	colourless
  	trimethylhexane-1,6-diyl) biscarbamate	1,6-diisocyanate	fluoropentan-1-ol	0.02 g		oil
  		(TMDI)	10.3 g
  		4.67 g
  27	2,2,3,3,4,4,5,5-Octafluoropentyl propan-	i-Propyl isocyanate	2,2,3,3,4,4,5,5-Octa-	Desmorapid Z	70° C.	colourless
  	2-ylcarbamate	4.02 g	fluoropentan-1-ol	0.02 g		liquid
  			10.9 g
  28	2,2,3,3,4,4,5,5-Octafluoropentyl	Cyclohexyl isocyanate	2,2,3,3,4,4,5,5-Octa-	Desmorapid Z	70° C.	colourless
  	cyclohexylcarbamate	5.25 g	fluoropentan-1-ol	0.02 g		liquid
  			9.73 g
  29	Bis(2,2,3,3-tetrafluoropropyl)-[4-	1,8-Diisocyanato-4-	2,2,3,3-Tetrafluoro-1-	Desmorapid Z	70° C.	colourless
  	({[(2,2,3,3-tetrafluoro-	(isocyanatomethyl)octane	propanol	0.02 g		oil
  	propoxy)carbonyl]amino}methyl)octan-1,8-	(TIN)	9.16 g
  	diyl] biscarbamate	5.83 g
  30	Bis(2,2,3,3-tetrafluoropropyl)-(2,2,4-	2,4,4-Trimethylhexane	2,2,3,3-Tetrafluoro-1-	Desmorapid Z	70° C.	colourless
  	trimethylhexane-1,6-diyl) biscarbamate	1,6-diisocyanate	propanol	0.02 g		liquid
  		(TMDI)	8.35 g
  		6.64 g
  31	2,2,3,3-Tetrafluoropropyl propan-	i-Propyl isocyanate	2,2,3,3-Tetrafluoro-	Desmorapid Z	70° C.	colourless
  	2-ylcarbamate	5.87 g	propan-1-ol	0.02 g		liquid
  			9.11 g
  32	Ethyl hexylcarbamate	n-Hexyl isocyanate	Ethanol	Desmorapid Z	60° C.	colourless
  		36.7 g	13.3 g	0.02 g		liquid
  33	iso-Propyl hexylcarbamate	n-Hexyl isocyanate	iso-Propanol	Desmorapid Z	60° C.	colourless
  		34.0 g	16.0 g	0.02 g		liquid
  34	3-Ethyl butylcarbamate	n-Butyl isocyanate	Ethanol	Desmorapid Z	60° C.	colourless
  		34.1 g	15.9 g	0.02 g		liquid
  35	iso-Propyl butylcarbamate	n-Butyl isocyanate	iso-Propanol	Desmorapid Z	60° C.	colourless
  		31.1 g	18.9 g	0.02 g		liquid

Estimation of the Refractive Index (n_D ²⁰) and of the volatility (TGA95) of 2,2,2-trifluoroethyl butylcarbamate Example 1
• The three-dimensional structure of the abovementioned compound (Example 1) was generated and preoptimized with the aid of the graphic user interface of the molecular modelling package Materials Studio of Accelrys. This preoptimized structure was then used as input for the conformer analysis, for which a Monte Carlo algorithm was used, which, in each case starting from the conformer generated just beforehand, changes all dihedral angles within the molecule according to the random principle. In this way, 1000 random conformers were generated and directly preoptimized. In the procedure, all conformers which have a relative energy of >8.37 kJ/mol were directly discarded.
• After this procedure, all 90 conformers obtained was subsequently optimized using a more stringent convergence criterion and then subjected to a similarity analysis, very similar conformers being discarded. The remaining 34 conformers were then optimized geometrically using the quantum chemistry package TURBOMOLE with the aid of the density functional theory. The B-P86 density functional and the triple ξ valence basis set TZVP, which was taken from the TURBOMOLE basis set library, were used and the COSMO option, using the optimized COSMO radii, was switched on.
• For the 22 conformers whose relative DFT/COSMO Energy was <8 kJ/mol, the individual descriptors V_i, A_i, and M² _i were subsequently calculated according to steps e and f of the method according to the invention. For this purpose, the COSMOtherm of COSMOlogic was used. The results are listed in Table 3.

• TABLE 3
  	Rel. energy	Boltzmann
  Conformer	in kJ/mol	Weight in %	V (Å3)	A (Å2)	M2

  1	0.00	15.92	224.534	224.129	69.717
  2	0.14	15.02	224.692	224.472	69.698
  3	0.46	13.21	223.745	228.546	74.656
  4	0.95	10.86	222.437	228.836	74.314
  5	1.80	7.70	224.267	226.684	73.407
  6	1.90	7.39	224.614	226.738	73.401
  7	3.86	3.35	222.143	224.595	74.151
  8	3.96	3.22	223.430	227.027	74.845
  9	4.09	3.06	224.181	220.790	73.732
  10	4.24	2.88	226.841	218.562	73.464
  11	5.07	2.06	222.067	227.356	72.800
  12	5.08	2.05	224.635	224.359	72.785
  13	5.35	1.84	225.926	217.658	76.949
  14	5.58	1.68	227.028	216.153	72.131
  15	6.32	1.24	222.207	226.866	74.032
  16	6.39	1.21	224.162	220.368	71.597
  17	6.97	0.95	224.831	226.248	75.008
  18	7.55	0.76	224.889	222.006	71.440
  19	7.60	0.74	225.386	223.325	75.264
  20	7.72	0.71	225.336	225.147	74.730
  21	7.88	0.66	221.676	224.815	72.557
  22	7.88	0.66	226.532	216.022	73.523
  This gives the following as Boltzmann-weighted mean values:
  A = 225.308 Å2,
  V = 224.137 Å3,
  M2 = 72.609

• It results in the values 85.0° C. and 1.197 g/mol for the volatility (TGA95) and the density.
• The molar polarizability was estimated as 40.310 m³/mol with the aid of the QSPR approach published in 1986 by Crippen and implemented in the Materials Studio QSAR module, which, in combination with the density, results in a refractive index of (n_D ²⁰)=1.3999. The substance, with a TGA95 value of 85.0° C. and a refractive index of 1.3999, is therefore not suitable overall in the context of the selection method according to the invention as an additive for photopolymer formulations since its estimated volatility is clearly too high. As shown by the comparison with experimental values, this evaluation is correct.
• The volatilities and refractive indices of Examples 2-39 were calculated in a manner analogous to that of Example 1 and the results were summarized in Table 4. A further 30 fluorinated urethanes (Examples 2-31), 4 unfluorinated urethanes (Examples 32-35) and four commercial plasticizers (Examples 36-39) are contained therein.

• TABLE 4
  Comparison of estimated and experimental refractive indices and TGA95 values.

  Exam-					M/	MP/	ρ	(nD 20)	TGA95	(nD 20)	TGA95
  ple	Name	V/Å3	A/Å2	M2	(g/mol)	(m3/mol)	(QSPR)	(QSPR)	(QSPR)	(Exp.)	(Exp.)

  2	2,2,2-Trifluoroethyl hexylcarbamate	266.609	268.162	76.273	227.23	49.51	1.146	1.4136	72.2	1.3984	72.5
  3	2,2,3,3-Tetrafluoropropyl butylcarbamate	254.440	253.494	94.734	231.19	44.09	1.241	1.3893	86.5	1.3879	71.6
  4	Bis(2,2,2-trifluoroethyl)-(2,2,4-	449.384	412.813	142.624	410.35	83.03	1.285	1.4333	135.5	1.4202	167.1
  	trimethylhexane-1,6-diyl) biscarbamate
  5	Bis(2,2,2-trifluoroethyl)-[4-({[(2,2,2-	571.236	540.825	214.491	551.40	103.39	1.384	1.4322	172.5	1.4213	174.9
  	trifluoroethoxy)carbonyl]amino}methyl)-
  	octane-1,8-diyl] biscarbamate
  6	2,2,3,3,4,4,4-Heptafluorobutyl	299.099	285.161	71.344	299.19	49.65	1.372	1.3727	75.5	1.3625	69.8
  	butylcarbamate
  7	2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9-	476.888	415.268	92.904	531.23	72.10	1.569	1.3459	116.6	1.3555	111.8
  	Hexadecafluorononyl butylcarbamate
  8	Bis(2,2,3,3,4,4,4-heptafluorobutyl)-	606.335	522.310	136.852	610.38	101.71	1.432	1.3930	151.5	1.3887	139.1
  	(2,2,4-trimethylhexane-1,6-diyl)
  	biscarbamate
  9	Bis(2,2,3,3,4,4,4-heptafluorobutyl)-[4-	813.142	689.703	193.478	851.44	131.40	1.517	1.3846	191.3	1.3876	159.7
  	({[(2,2,3,3,4,4,4-heptafluorobutoxy)-
  	carbonyl]amino}methyl)octane-
  	1,8-diyl] biscarbamate
  10	2,2,3,3,4,4,5,5,5-Nonafluoropentyl	336.687	311.927	73.341	349.19	54.31	1.433	1.3640	83.5	1.3580	72.8
  	butylcarbamate
  11	Bis(2,2,3,3,4,4,5,5,5-nonafluoropentyl)-	683.549	574.484	135.816	710.40	111.04	1.484	1.3807	160.5	1.3820	157
  	(2,2,4-trimethylhexane-1,6-diyl)
  	biscarbamate
  12	2,2,3,3,4,4,5,5,5-Nonafluoropentyl	379.492	352.267	73.741	377.25	63.52	1.369	1.3780	89.9	1.3690	83.5
  	hexylcarbamate
  13	2,2,3,3,4,4,5,5,5-Nonafluoropentyl	315.705	289.954	70.340	335.17	49.61	1.469	1.3541	79.0	1.3497	58.5
  	propan-2-ylcarbamate
  14	2,2,3,3,4,4,5,5,6,6,6-Undecafluorohexyl	374.581	335.864	68.869	399.20	58.98	1.479	1.3560	87.7	1.3538	82.6
  	butylcarbamate
  15	Bis(2,2,3,3,4,4,5,5,6,6,6-	757.048	613.121	134.098	810.41	120.38	1.536	1.3736	169.4	1.3750	152.7
  	undecafluorohexyl)-(2,2,4-trimethyl-
  	hexane-1,6-diyl) biscarbamate
  16	2,2,3,3,4,4,5,5,6,6,6-Undecafluorohexyl	416.853	379.371	73.759	427.25	68.18	1.419	1.3704	96.4	1.3640	90
  	hexylcarbamate
  17	Bis(2,2,3,3,4,4,5,5,6,6,7,7-	811.336	671.039	176.795	874.44	127.93	1.560	1.3739	187.5	1.3839	158.6
  	dodecafluoroheptyl)-(2,2,4-
  	trimethylhexane-1,6-diyl) biscarbamate
  18	2,2,3,3,4,4,5,5,6,6,7,7-Dodecafluoroheptyl	445.778	401.101	94.859	459.27	71.96	1.440	1.3690	112.1	1.3716	117.6
  	hexylcarbamate
  19	2,2,3,3,4,4,5,5,6,6,7,7-Dodecafluoro-	381.492	338.779	91.463	417.19	58.05	1.534	1.3470	103.0	1.3563	93.3
  	heptylpropan-2-yl carbamate
  20	2,2,3,3,4,4,5,5,6,6,7,7-Dodecafluoroheptyl	430.049	369.790	83.268	457.25	69.90	1.491	1.3731	105.9	1.3830	123.7
  	cyclohexylcarbamate
  21	2,2,3,4,4,4-Hexafluorobutyl	291.826	273.825	90.643	281.20	49.25	1.332	1.3829	90.0	1.3775	73.8
  	butylcarbamate
  22	2,2,3,4,4,4-Hexafluorobutyl	335.639	313.390	92.270	309.25	58.45	1.271	1.3959	95.5	1.3876	89.5
  	hexylcarbamate
  23	2,2,3,4,4,4-Hexafluorobutyl propan-2-	269.738	259.029	91.749	267.17	44.54	1.368	1.3733	87.7	1.3682	71.5
  	ylcarbamate
  24	2,2,3,3,4,4,5,5-Octafluoropentyl	330.134	303.188	88.913	331.20	53.42	1.393	1.3674	93.7	1.3731	80.5
  	butylcarbamate
  25	Bis(2,2,3,3,4,4,5,5-octafluoropentyl)-{4-	895.878	763.826	254.799	947.50	142.73	1.552	1.3840	215.0	1.3955	172.5
  	[({[(2,2,3,3,4,4,5,5-octafluoropentyl)-
  	oxy]carbonyl}amino)methyl]octane-1,8-
  	diyl} biscarbamate
  26	Bis(2,2,3,3,4,4,5,5-octafluoropentyl)-	667.015	566.787	174.890	674.42	109.26	1.457	1.3880	172.4	1.3971	163.9
  	(2,2,4-trimethylhexane-1,6-diyl)
  	biscarbamate
  27	2,2,3,3,4,4,5,5-Octafluoropentyl propan-2-	308.600	286.261	90.842	317.18	48.72	1.429	1.3577	92.3	1.3654	74.4
  	ylcarbamate
  28	2,2,3,3,4,4,5,5-Octafluoropentyl-	355.202	319.977	87.653	357.24	60.56	1.400	1.3905	96.7	1.3977	110.5
  	cyclohexylcarbamate
  29	Bis(2,2,3,3-tetrafluoropropyl)-[4-	668.003	606.741	275.686	647.45	114.73	1.417	1.4162	202.8	1.4240	197.9
  	({[(2,2,3,3-tetrafluoropropoxy)-
  	carbonyl]amino}methyl)octane-1,8-
  	diyl]biscarbamate
  30	Bis(2,2,3,3-tetrafluoropropyl)-(2,2,4-	517.127	461.959	184.103	474.39	90.59	1.313	1.4155	161.6	1.4229	185.3
  	trimethylhexane-1,6-diyl) biscarbamate
  31	2,2,3,3-Tetrafluoropropyl propan-2-	234.335	231.845	93.129	217.16	39.38	1.268	1.3770	85.2	1.3831	78.1
  	ylcarbamate
  32	Ethyl hexylcarbamate	241.340	247.593	72.851	173.26	48.81	0.941	1.4431	65.5	1.4376	83.9
  33	iso-Propyl hexylcarbamate	264.827	264.082	70.384	187.28	53.23	0.930	1.4413	67.9	1.4336	84.9
  34	3 Ethyl butylcarbamate	197.717	207.505	71.325	145.20	39.61	0.960	1.4367	59.2	1.4313	66.1
  35	iso-Propyl butylcarbamate	220.538	224.943	68.619	159.23	44.03	0.946	1.4361	60.1	1.4284	63.9
  36	Propylene carbonate	115.733	128.139	71.612	102.09	21.49	1.167	1.4059	64.3	1.4210	87
  37	Dimethyl adipate	221.881	226.334	97.343	174.20	42.28	1.055	1.4256	86.5	1.4280	80.4
  38	Diethylene glycol diacetate	231.636	242.845	113.550	190.19	43.90	1.110	1.4261	97.9	1.4300	99.1
  39	Triethyl citrate	328.385	305.298	134.859	276.28	64.18	1.174	1.4575	123.9	1.4420	131

  
  Comparison between Experimental and Estimated TGA95 and Refractive Index Values
• The comparison between the experimental refractive indices and TGA95 values of Examples 1-39 and those estimated by the selection method according to the invention (Table 4), which is illustrated in the correlation diagrams in FIG. 3 and FIG. 4, clearly show the suitability of the method. The refractive indices could be determined with a standard deviation of 0.0082, the maximum error over the total set, with an absolute value of 0.0155 for Example 39, likewise being very small. The standard deviation for the TGA95 values is 15.8° C., with an absolute maximum error of 42.5° C. for the fluorinated urethane of Example 25. However, this comparatively large error is not significant since both the experimental value of 172.5° C. and the estimated value of 215.0° C. are substantially above the suitability limit of 100° C. Thus, in spite of the error, the compound is correctly classed by the method according to the invention as being suitable as an additive for photopolymer formulations. In general, it may be stated that very large differences between predicted and experimental TGA95 typically occur in the case of comparatively high absolute values (typically >150° C.), which is attributable to incipient decomposition of the substances. This fact does not imply any limitation of the informative power of the selection method according to the invention since the threshold value for the suitability of the substance at 100° C. is typically well below the decomposition temperature of customary additive molecules.
Selection of the Example Molecules on the Basis of the Method According to the Invention
• The refractive indices of Examples 1-39 are all below 1.4600. In this case, the TGA95 estimated by the method according to the invention are therefore decisive regarding the suitability as additives in photopolymer formulations. All examples whose estimated volatility, according to TGA95, is greater than 100° C. are summarized in Table 5.

• TABLE 5
  Additives selected according to the invention.

  	(nD 20)	TGA95	(nD 20)	TGA95
  Example	(QSPR)	(QSPR)	(Exp.)	(Exp.)

  4	1.4333	135.5	1.4202	167.1
  5	1.4322	172.5	1.4213	174.9
  7	1.3459	116.6	1.3555	111.8
  8	1.3930	151.5	1.3887	139.1
  9	1.3846	191.3	1.3876	159.7
  11	1.3807	160.5	1.3820	157.0
  15	1.3736	169.4	1.3750	152.7
  17	1.3739	187.5	1.3839	158.6
  18	1.3690	112.1	1.3716	117.6
  19	1.3470	103.0	1.3563	93.3
  20	1.3731	105.9	1.3830	123.7
  25	1.3840	215.0	1.3955	172.5
  26	1.3880	172.4	1.3971	163.9
  29	1.4162	202.8	1.4240	197.9
  30	1.4155	161.6	1.4229	185.3
  39	1.4575	123.9	1.4420	131.0

• Examples 7 and 17 which, owing to their low refractive indices and the sufficiently high volatility, should be very efficient are selected for an experimental investigation of the holographic activity. The compound 2 which, with an estimated volatility of 72.2° C., is substantially outside the limits of the method according to the invention is selected as a comparative example.
Preparation of the Photopolymer Formulation for the Production of Holographic Films Film Example 1
• 6.77 g of the polyol component prepared as described above were mixed with 4.00 g of phosphorothioyltris(oxybenzene-4,1-diylcarbamoyloxyethane-2,1-diyl)trisacrylate (urethane acrylate 1), 4.00 g of 2-({[3-(methylsulphanyl)phenyl]carbamoyl}oxy)propylprop-2-enoate (urethane acrylate 2) 3.00 g of 2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9-hexadecafluorononyl butylcarbamate (Example 7), 0.02 g of Fomrez UL 28 (urethanization catalyst, commercial product of Momentive Performance Chemicals, Wilton, Conn., USA), 0.30 g of CGI 909 (experimental product of Ciba Inc, Basle, Switzerland), 0.03 g of new methylene blue, 0.06 g of BYK 310 and 1.02 g of N-ethylpyrrolidone at 60° C. so that a clear solution was obtained. Thereafter, cooling to 30° C. was effected, 1.25 g of Desmodur® N3900 (commercial product of Bayer MaterialScience AG, Leverkusen, Germany, hexane diisocyanate-based polyisocyanate, proportion of iminooxadiazinedione at least 30%, NCO content: 23.5%) were added and mixing was effected again. The liquid material obtained is then applied by means of a knife coater to a 36 μm thick polyethylene terephthalate film and dried for 4.5 minutes at 80° C. in an air circulation dryer. Thereafter, the photopolymer layer is covered with a 40 μm thick polyethylene film and rolled up.
Film Example 2
• 6.77 g of the polyol component prepared as described above were mixed with 4.00 g of phosphorothioyltris(oxybenzene-4,1-diylcarbamoyloxyethane-2,1-diyl)trisacrylate (urethane acrylate 1), 4.00 g of 2-[({3-(methylsulphanyl)phenyl]carbamoyl}oxy)propylprop-2-enoate (urethane acrylate 2) 3.00 g of bis(2,2,3,3,4,4,5,5,6,6,7,7-dodecafluoroheptyl)-(2,2,4-trimethylhexane-1,6-diyl)biscarbamate (Example 17), 0.02 g of Fomrez UL 28 (urethanization catalyst, commercial product of Momentive Performance Chemicals, Wilton, Conn., USA), 0.30 g of CGI 909 (experimental product of Ciba Inc, Basle, Switzerland), 0.03 g of new methylene blue, 0.06 g of BYK 310 and 1.02 g of N-ethylpyrrolidone at 60° C. so that a clear solution was obtained. Thereafter, cooling to 30° C. was effected, 1.25 g of Desmodur® N3900 (commercial product of Bayer MaterialScience AG, Leverkusen, Germany, hexane diisocyanate-based polyisocyanate, proportion of iminooxadiazinedione at least 30%, NCO content: 23.5%) were added and mixing was effected again. The liquid material obtained is then applied by means of a knife coater to a 36 μm thick polyethylene terephthalate film and dried for 4.5 minutes at 80° C. in an air circulation dryer. Thereafter, the photopolymer layer is covered with a 40 μm thick polyethylene film and rolled up.
Comparative Film Example I
• 6.77 g of the polyol component prepared as described above were mixed with 4.00 g of phosphorothioyltris(oxybenzene-4,1-diylcarbamoyloxyethane-2,1-diyl)trisacrylate (urethane acrylate 1), 4.00 g of 2-({[3-(methylsulphanyl)phenyl]carbamoyl}oxy)propylprop-2-enoate (urethane acrylate 2) 3.00 g of 2,2,2-trifluoroethyl butylcarbamate (Example 1), 0.02 g of Fomrez UL 28 (urethanization catalyst, commercial product of Momentive Performance Chemicals, Wilton, Conn., USA), 0.30 g of CGI 909 (experimental product of Ciba Inc, Basle, Switzerland), 0.03 g of new methylene blue, 0.06 g of BYK 310 and 1.02 g of N-ethylpyrrolidone at 60° C. so that a clear solution was obtained. Thereafter, cooling to 30° C. was effected, 1.25 g of Desmodur® N3900 (commercial product of Bayer MaterialScience AG, Leverkusen, Germany, hexane diisocyanate-based polyisocyanate, proportion of iminooxadiazinedione at least 30%, NCO content: 23.5%) were added and mixing was effected again. The liquid material obtained is then applied by means of a knife coater to a 36 μm thick polyethylene terephthalate film and dried for 4.5 minutes at 80° C. in an air circulation dryer. Thereafter, the photopolymer layer is covered with a 40 μm thick polyethylene film and rolled up.

• TABLE 6
  Holographic evaluation of film examples

  	Example, [% by weight]	Δn

  Film Example
  1	7, 15	0.038
  2	17, 15	0.032
  Comparative film example
  1	2, 15	0.012

• The values described by Δn were obtained at doses of 4-32 ml/cm².
• The values found for the holographic property Δn of the holographic media show that the additives selected by the method according to the invention are better suited for use in holographic photopolymer films.

Claims (21)

1.-11. (canceled)

12. A method for selecting compounds which can be used as plasticizers in photopolymer formulations for the production of light holographic media, wherein the method comprises:

a) selecting a compound to be tested,

b) carrying out a conformer analysis of the compound to be tested using a suitable computer programme, c) generating an optimization of the geometry of all conformers with the aid of a force field method and the conformer space is then further reduced with the aid of a similarity analysis,

d) effecting a quantum chemical optimization of the geometry of the conformers which are energetically most favourable according to the force field optimization with the use of the B-P86 density functional and a triple □ valence basis set, and of the Conductor Like Screening Model (COSMO) in combination with the optimized COSMO radii or, if these do not exist for a given element, with 1.17 times the Bondi valence radius,

e) calculating the area (A) in Ų and the enclosed volume (V) in ų of the three-dimensional COSMO shielding charge density surfaces of the conformers having the lowest energy, which are obtained as result of the quantum chemical optimization of the geometry,

f) dividing into segments, the COSMO shielding charge density surfaces of the conformers having the lowest energy with the aid of a suitable software package, the mean surface shielding charge density (□) of these segments are plotted in the form of a frequency distribution P(□) and the second moments (M²) of this distribution, defined according to the equation:

$M^2=10·\sum _iP\left({\sigma }_i\right)·{\sigma }_i^2·\mathrm{\Delta \sigma }$

 are determined, □□ being the interval width of the discrete frequency distribution and the charge densities □ being stated in the unit e/nm²,

g) averaging the volumes, areas and second moments of all conformers considered according to their weight in the Boltzmann distribution on the basis of the energies obtained from the quantum chemical optimizations of the geometries,

h) estimating the volatility of the substance according to the computational rule:

$\mathrm{TGA}95\approx 207.015·\frac{M^2}{A}+41.405·\sqrt[3]{V}-253.2,$

i) estimating the density of the compound at room temperature with the aid of the equation:

$\rho =0.89·\frac{M}{V·N_A}-0.2·\frac{A}{V}+0.01·\sqrt{M^2}$

 □ being the density of the pure substance in g/cm³, M being the molar mass in g/mol, N_A being the Avogadro number, A being the COSMO shielding charge density surface in Ų, V being the volume in ų enclosed by the surface and M² being the second moment of the surface shielding charge density frequency distribution,

j) using the estimated density in order, with the aid of the Lorentz-Lorenz equation:

$n_D=\sqrt{\frac{2·\frac{\rho ·\mathrm{MP}}{M}+1}{1-\frac{\rho ·\mathrm{MP}}{M}}},$

 to convert the molar polarizability (MP) estimated according to a QSPR approach as accurately as possible into a refractive index at 589 nm (n_D ²⁰)

k) determining whether the volatility of the compound to be tested is >100° C. and the refractive index thereof is ≦1.4600, the compound to be tested being classed as being suitable if both conditions are fulfilled.

13. The method according to claim 12, wherein, in step b), the computer program used to carry out the conformer analysis is the conformers module of the Materials Studio program package of Accelrys.

14. The method according to claim 12, wherein, in step f), the suitable software package is the program COSMOtherm of COSMOlogic.

15. The method according to claim 12, wherein, in step d), a quantum chemical optimization of the geometry of the conformer having the lowest energy according to the force field optimization is effected.

16. The method according to claim 12, wherein, in step d), a quantum chemical optimization of the geometry of all conformers in an energy window of 0-4 kJ/mol according to the force field optimization is effected.

17. The method according to claim 12, wherein, in step d), a quantum chemical optimization of the geometry of all conformers in an energy window of 0-8 kJ/mol according to the force field optimization is effected.

18. The method according to claim 12, wherein, in step k), a check is carried out to determine whether the volatility of the compound to be tested is >120° C. and the refractive index thereof nD is ≦1.4500.

19. The method according to claim 12, wherein, in step k), a check is carried out to determine whether the volatility of the compound to be tested is >120° C. and the refractive index thereof nD is ≦1.4400.

20. The method according to claim 12, wherein, in step k), a check is carried out to determine whether the volatility of the compound to be tested is >120° C. and the refractive index thereof nD is ≦1.4300.

21. A photopolymer formulation comprising matrix polymers, writing monomers and photoinitiators, wherein the photopolymer formulation further comprises at least one plasticizer which is selected by the method according to claim 12 and wherein the matrix polymers comprise polyurethanes.

22. The photopolymer formulation according to claim 21, wherein the photoinitiators comprise an anionic, cationic or neutral dye and a coinitiator.

23. The photopolymer formulation according to claim 21, wherein the at least one plasticizer comprises urethanes, and wherein the urethane is capable of being substituted by at least one fluorine atom.

24. The photopolymer formulation according to claim 23, wherein the urethanes have the formula (II)

wherein

n is from 1 to 8 and

R¹, R², R³ represent, independently of one another, hydrogen or linear, branched, cyclic or heterocyclic organic radicals which are unsubstituted or optionally also substituted by heteroatoms.

25. The photopolymer formulation according to claim 24, wherein at least one of the radicals R1, R2, R3 is substituted by at least one fluorine atom.

26. The photopolymer formulation according to claim 24, wherein R1 represents an organic radical having at least one fluorine atom.

27. The photopolymer formulation according to claim 21, wherein the writing monomers comprise a monofunctional acrylate of the formula (IV)

wherein

R⁷, R⁸, independently of one another, represent hydrogen or linear, branched, cyclic or heterocyclic organic radicals which are unsubstituted or optionally also substituted by heteroatoms.

28. The photopolymer formulation according to claim 21, wherein the writing monomers comprise a polyfunctional writing monomer.

29. The photopolymer formulation according to claim 21, wherein, the writing monomers comprise a polyfunctional acrylate.

30. The photopolymer formulation according to claim 29, wherein the polyfunctional acrylate has the formula (V)

wherein

n is from 2 to 4 and

R⁹, R¹⁹, independently of one another, represent hydrogen or linear, branched, cyclic or heterocyclic organic radicals which are unsubstituted or optionally also substituted by heteroatoms.

31. A method comprising producing in-line holograms, off-axis holograms, full-aperture transfer holograms, white light transmission holograms, Denisyuk holograms, off-axis reflection holograms, edge-lit holograms or holographic stereograms, wherein the holograms or stereograms are produced with the photopolymer formulation according to claim 21.

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