WO2003020445A1 - Method of predicting optical properties and physical characteristics to formulate optimum coating system - Google Patents
Method of predicting optical properties and physical characteristics to formulate optimum coating system Download PDFInfo
- Publication number
- WO2003020445A1 WO2003020445A1 PCT/US2002/027976 US0227976W WO03020445A1 WO 2003020445 A1 WO2003020445 A1 WO 2003020445A1 US 0227976 W US0227976 W US 0227976W WO 03020445 A1 WO03020445 A1 WO 03020445A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- coating
- optical property
- pigment
- physical characteristics
- sheet
- Prior art date
Links
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B05—SPRAYING OR ATOMISING IN GENERAL; APPLYING FLUENT MATERIALS TO SURFACES, IN GENERAL
- B05D—PROCESSES FOR APPLYING FLUENT MATERIALS TO SURFACES, IN GENERAL
- B05D1/00—Processes for applying liquids or other fluent materials
-
- D—TEXTILES; PAPER
- D21—PAPER-MAKING; PRODUCTION OF CELLULOSE
- D21H—PULP COMPOSITIONS; PREPARATION THEREOF NOT COVERED BY SUBCLASSES D21C OR D21D; IMPREGNATING OR COATING OF PAPER; TREATMENT OF FINISHED PAPER NOT COVERED BY CLASS B31 OR SUBCLASS D21G; PAPER NOT OTHERWISE PROVIDED FOR
- D21H19/00—Coated paper; Coating material
- D21H19/36—Coatings with pigments
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/0205—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system
- G05B13/026—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system using a predictor
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B05—SPRAYING OR ATOMISING IN GENERAL; APPLYING FLUENT MATERIALS TO SURFACES, IN GENERAL
- B05D—PROCESSES FOR APPLYING FLUENT MATERIALS TO SURFACES, IN GENERAL
- B05D5/00—Processes for applying liquids or other fluent materials to surfaces to obtain special surface effects, finishes or structures
- B05D5/06—Processes for applying liquids or other fluent materials to surfaces to obtain special surface effects, finishes or structures to obtain multicolour or other optical effects
Definitions
- the present invention is directed to a method of predicting optical properties and physical characteristics of coated paper products for the purpose of formulating enhanced coating systems, and in particular to a method, which uses a diffusion approximation model derived from a radiative transfer theory employing various inputs of the properties and/or characteristics to predict coating system performance.
- K-M Kubelka-Munk
- the principal advantage of using the K-M theory is its mathematical simplicity, but this simplicity is in effect a tradeoff for a loss of explicit connection with the optical properties of the individual components within a diffusive layer that are part of a coating system.
- One particular problem with the use of the K-M theory as an aid to assessing performance of coating systems is its treatment of scattering as being caused by a homogenous medium, rather than a collection of individual scattering centers. Under the K-M approach, isotropic scattering of light is considered to occur, 'but in real systems, light is scattered anisotropically.
- K-M theory Another problem with the K-M theory is its limited number of degrees of freedom and the inability to address all of the other variables that exist in a pigmented coating system, e.g., coating thickness, properties of the base sheet, certain properties of the pigment, both physical and optical, the boundary layer conditions associated with the coating layer, etc.
- the K-M approach while sometimes a reasonable approximation depending on the homogeneity of the medium, is deficient in predicting the actual light scattering effects in non-homogenous coating systems having multiple scattering centers as well as boundary layer effects and can therefore only predict performance properties to a certain extent.
- the present invention solves this need through the utilization of a diffusion approximation model and its adaptation through the identification of various inputs to the model that relate to both the physical characteristics and the optical properties of coating systems. Using selected inputs and the diffusion approximation model, one can predict the performance of a coating system. This ability is especially useful when making predictions for coating systems being designed to meet certain targeted optical or physical characteristics for a particular end-use application.
- the model can determine what physical characteristics are needed to meet specific coating performance targets in the form of optical properties such as brightness, gloss, and opacity.
- United States Patent No. 6,064,487 to Kettler et al discloses a process for calculating a color formulation of a pigmented special effect shade that include determining optical reflection factors using a radiation transport model, particularly an azimuth-independent form thereof.
- Kettler et al . are primarily concerned with developing a paint formulation to match that of an existing automobile.
- the method disclosed in this patent is totally unrelated to modeling the coating systems and coating performance properties that are relevant to the paper industry.
- Another object of the present invention is a method that identifies one or more target properties of a coating system, generates a predictive value of the coating system based on a number of inputs . These inputs are related to various optical or physical characteristics of the coating system as well as its boundary conditions for comparison to the targeted value (s), and by altering these inputs enables additional predictive values to be generated until the target property is attained.
- Another object of the present invention is the use of a diffusion approximation model, which incorporates a number of inputs of coating system variables to generate the predictive values .
- One further object of the invention is a method of predicting the performance properties or physical characteristics of coating systems that use kaolin clay or calcium carbonate as one of the coating pigments as well as various combinations of kaolin clay and calcium carbonate .
- the invention entails the use of radiative transfer theory to predict optical properties and/or physical characteristics in paper coating systems that employ a base sheet and/or a coating comprised of one or more pigments and/or fillers.
- a base sheet and/or a coating comprised of one or more pigments and/or fillers.
- any one of the fine particle kaolin clays produced by J. M. Huber Corporation from middle Georgia cretaceous clay crudes or east Georgia tertiary clay crudes can be used as one of the coating pigments.
- Representative examples of coating grade, kaolin clays produced by J. M. Huber Corporation include
- Other coating pigments include calcined kaolin clays, ground or precipitated calcium carbonates, synthetic amorphous silicas, precipitated metal silicates such as the sodium magnesium aluminosilicates, talc, titanium dioxide, carbon black, etc.
- Examples of the optical properties for the coating systems that can serve as inputs, targets, or outputs include TAPPI brightness, gloss, opacity and its reflectance spectrum over the visible wavelength range.
- Exemplary physical characteristics of the coating pigment or coated paper product for use in the invention include absorption coefficient, scattering coefficient, anisotropic light scattering, pigment refractive index, coating porosity characteristics such as the pore diameter size and total pore volume, the coating pigment's median particle size and its particle size distribution, coating thickness, surface roughness of the coating, characteristics associated with the interfacial region between the pigmented coating layer and the base sheet, the optical properties of the base sheet, the physical characteristics of the base sheet and the like.
- This list is not a complete list and other variables of the coating system that may affect performance can also be used as would be within the skill of the artisan and the level of predictive accuracy desired.
- the diffusion approximation model is in the form of a mathematical expression for which a computer program can be written.
- the required computations using the diffusion equation are preferably carried out by a computer so that predictions of coating performance properties and physical characteristics can be efficiently done.
- the method entails providing a radiative transfer equation that relates a number of physical characteristics of the coating system selected from coating thickness, the coating pigment's median particle size, the coating pigment's particle size distribution, the coating median pore size, pore size distribution, the coating pore volume, surface roughness of the coating, scattering coefficient, absorption coefficient, anisotropy factor, and optical properties of a base sheet to one or more optical properties for a coating system selected from the group consisting of gloss, TAPPI brightness, opacity and its reflectance spectrum over the visible wavelength range of 450 - 700 nm.
- the diffusion equation is solved by inputting a number of the physical characteristics of the coating system to obtain at least one optical property output of the coating system.
- This method is especially useful when first selecting at least one target optical property and comparing the output of the solved diffusion equation to the target optical property. If the predicted output does not match, one or more of the physical characteristics are adjusted and the solving step is repeated to obtain another optical property output. This output is then compared to the target, and the process is repeated again with another adjustment until the output matches the desired target. As previously discussed, the computations needed for this process are best carried out via a computer program to efficiently obtain the results.
- the method is particularly adapted for coating systems that use a kaolin clay or a calcium carbonate as one of the coating pigments
- the substrate to be coated is a paper product which serves as the base sheet and where formulating a pigmented coating using the inputted optical properties or physical characteristics for application onto said paper base sheet to form a coated paper product.
- the diffusion equation can be solved using the scattering coefficient, the absorption coefficient, and the anisotropy factor for scattering as inputs to obtain a brightness output of the coating system.
- the method predicts or identifies at least one physical characteristic of the coating system.
- the same diffusion equation is used, but the inputs are changed.
- the equation is solved by inputting a number of the physical characteristics and at least one optical property to obtain at least one physical characteristic output.
- This method allows for the identification of a certain physical characteristic necessary to achieve the inputted optical property.
- a target optical property can be selected as the input in order to predict what physical characteristic is necessary to obtain such an optical property. For example, in the case of targeting a desired opacity value, a particular coating pore size distribution or particle size distribution could be predicted.
- Figure 1 is a schematic flowsheet identifying various inputs and outputs used to obtain predictive properties of coating systems
- Figure 2 shows a schematic of a coating system and identifies certain boundary conditions
- Figure 3 is a graph relating experimental and simulated reflectance data for one coating formulation (Coating B) ;
- Figure 4 is a graph relating experimental and simulated reflectance data for a second coating formulation (Coating A) ;
- Figure 5 shows predicted pore size distribution curves using the diffusion approximation model
- Figure 6 compares mean optical path distance for two coating formulations.
- Figure 7 is an illustrative schematic of the light path through a coated product .
- the present invention is a significant advance in the field of modeling coating systems, particularly paper coating systems that use such parameters as TAPPI brightness, gloss, and opacity as performance guidelines for determining the coating system components to be employed.
- the invention provides a much improved technique for selecting the right combination of materials and variables making up a coating system so that that improved performance is realized.
- the ability to predict the optical performance properties of coating systems in the paper industry particularly those employing a fine particle size kaolin clay or calcium carbonate as well as combinations thereof as the coating pigments.
- the predictive capability of the invention with respect to the use of fine particle kaolin clay and calcium carbonate pigments in coating systems is independent of whether these coating pigments have a broad or narrow particle size distribution.
- a diffusion approximation model as a more comprehensive treatment of light propagation is being utilized to better describe the optical properties of coating systems, particularly systems employing and calcium carbonate-based coatings and to correlate the coating system's observed reflectance spectra over the visible wavelength range with coating microstructure .
- the diffusion approximation describes light propagation inside a highly scattering medium having very low absorption. Unlike K-M theory that only considers isotropic scattering, the diffusion approximation is able to model anisotropic scattering as well. Also, using the diffusion approximation, the optical characteristics of the medium are related directly to the physical parameters of the scattering centers .
- the diffuse reflectance from a scattering medium denoted as R(Q)
- R(Q) the diffuse reflectance from a scattering medium
- ⁇ s is the scattering coefficient
- ⁇ a is the absorption coefficient
- g is the anisotropy factor
- the average radiance U (r, t) is a directly measurable quantity that equates to the diffuse energy density.
- the above equation for R (Q) is but one solution of the differential equation defining the diffusion approximation approach to the transport of light , as other solutions arising from the use of different boundary conditions are possible as described below .
- the differential equation for the diffusion approximation is solved subject to boundary conditions and source specifics, and analytical solutions can be obtained for reflectance and transmittance calculations .
- the phase function is characterized as a single anisotropy factor
- the diffusion approximation provides mathematical convenience. Through renormalization, an asymmetry-corrected scattering cross-section that depends only on the average cosine of scattering angle defines the diffusion coefficient D, and therefore, an- essentially anisotropic propagation problem is mapped into an almost isotropic one.
- the absorption length l a ⁇ a -1 , which is the distance traveled by a photon before it is absorbed
- the scattering length l s ⁇ s ⁇ 1 , which is the average distance between successive events
- the transport mean free path 1 * - I s (l-g) that defines the distance traveled before the direction of propagation is randomized.
- the differential equation for the diffusion approximation can have a number of solutions depending on the conditions imposed upon it when solving it.
- the equation R(Q) noted above is one of the simplest solutions for reflectance based on using only the absorption coefficient, scattering coefficient and anisotropy factor as inputs while assuming smooth boundary layers.
- the porosity and pore size distribution properties of the coating can be optically determined and the values so determined can be compared with those derived from mercury intrusion porosimetry analysis to assure that the optically determined properties are in good agreement with physically measured values.
- Figure 1 is a flowsheet representing a number of variable inputs/outputs that have utility with the diffusion approximation model 100 as applied to coating systems. Variables relating to the coating, the base sheet, and the interface between these two materials can be inputted into the diffusion model 100 to obtain one or more optical properties such as TAPPI brightness (reflectance) , gloss, and opacity. It is believed that at least the inputs of pigment composition, particle size distribution and coating thickness are necessary to obtain one performance output such as TAPPI brightness or reflectance.
- Figure 2 is illustrative of the boundary conditions imposed by the coating system, i.e., a base sheet 21, an interfacial region or boundary layer 22 between the base sheet 21 and coating 23 having thickness 24, and the surface 25 of the coating 23, each having their own set of variables that affect light scattering and performance.
- the diffusion model can produce outputs of the variables too, e.g., reflectance as an input into the model with particle size distribution as an output.
- other conditions can be described for use in the diffusion equation. Examples include internal reflection and boundary effects as a result of interfacial properties between the pigmented coating and the base sheet.
- the diffusion equation can also be solved for different geometries using modified Green's functions to take into account the reflection at the boundary. This solution can therefore account for the effective reflectivity at the interface. This can be important as the effect of reflection is the lowering of the effective diffusion coefficient of the medium.
- the diffusion model can also be modified to take into account coating systems having a dense suspension of particles or large volumes of scattering particles. This situation results in multiple light scattering and diffusion of light waves is characterized by the number density of scatterers in the medium and by their scattering strength. In this system the particles are close enough that the scattering centers are not independent and collective scattering has to be considered. This is because the scattering centers are sufficiently close together that the fields scattered by the different centers are partially in phase .
- Coating A employed a narrow size distribution for both the clay and calcium carbonate pigments
- Coating B employing a broader size distribution for both types of mineral pigment particles.
- This distinction was used since it is well established that pigmented coatings employing pigments having a narrow particle size distribution give higher performance in terms of optical properties because of the change in the amount and in the size of the microvoids formed (i.e., scattering centers) resulting from their poor particle packing characteristics. In contrast, coating pigments having a broad particle size distribution tend to particle pack extremely well thereby creating fewer and smaller scattering centers in the coating.
- using the physical and optical characteristics of these two sets of materials would provide a good comparison between actual characteristics, and the characteristics predicted using the diffusion model.
- Coatings formulations A and B per above were applied to a Mylar® film using a band viscometer and then air-dried. Three coat weights (approximately 10, 20 and 30 g/m 2 ) were applied for each test formulation and the strips were double side coated. Standard optical measurements were made on the coated strips using a Technidyne BNL-3 Opacimeter and scattering coefficients (determined via Kubelka-Munk) were calculated.
- Porosity analysis via mercury intrusion porosimetry measurements on the coated strips was carried out with a Micromeritics AutoPore II 9220 Porosimeter. Reflectance measurements over the wavelength range from 450 nm to 700 nm were made with a Cary 500 Spectrophotometer equipped with an integrating sphere.
- the plot for data "A” represents 5A-experimental; the plot for data " ⁇ ” represents 4A-experimental; and the plot for data " ⁇ ” represents 3A-experimental .
- the respective predicted or simulated plot lines 5A, 4A and 3A are identified in Figure 4.
- the simulated- values are used to generate pore size distributions for Coating B and Coating A as plotted as normalized probability density and particle radius as shown in Figure 5.
- the "s" value for Coating B is 1, while the "s" value of for Coating A is 4.
- a comparison of actual and predicted peak pore radii is shown in Table III.
- Pore volume predictions using the simulated reflectance data are detailed in Table IV and V.
- the volume fraction of the coating pores (p) , the pore size distribution and the absorption coefficient ⁇ a are the input parameters for the diffusion model relative to getting a good fit to a reflectance spectrum; hence, when the absorption coefficient is known the volume fraction and pore distribution can both be optically determined.
- pore size distribution curves for Coatings A and B were generated (see Figure 5) . Inspection of Figure 5, where the "s" parameter is a distribution parameter that increases as the pore size distribution is narrower, shows that Coating A has a much more narrow pore size distribution than for the pores present in Coating B.
- Pore volume information on Coatings A and B was also obtained from reflectance-based determinations using the diffusion model.
- Various normalized pore volume ratios are compared in Tables IV and V for the A and B coatings .
- Table IV shows that the increase in pore volume fraction is proportionally similar between the A and B coatings as the applied coat weight is increased.
- the trends and volume ratios are also similar whether using pore volume data from mercury porosimetry or from the diffusion model.
- Table V shows good agreement between A/B pore volume ratios determined by mercury intrusion porosimetry versus those obtained from the diffusion model at the three different coat weights.
- the A coatings consistently contain about 30% more pore volume that the B coatings independent of the applied coat weight.
- the higher pore volume content of the A coatings is consistent with the creation of more scattering centers as a consequence of the poor particle packing obtained with the combination of clay and calcium carbonate pigments having a narrow particle size distribution .
- V total intrusion pore volumes determined by Hg Porosimetry.
- the coating surface topographies were observed by AFM for Coatings A and B.
- a visual inspection of these two topographies demonstrates that the surface of Coating A is rougher and more open or porous than the surface of Coating B. Given these topographies, one can hypothesize that A has the sharply defined geographical features that would scatter light to a greater extent than B.
- Figure 6 shows the mean optical path-length distances that were measured for Coatings A and B over the range of coat weights applied in this study.
- the values plotted in Figure 6 are the combined path-lengths for both sides of applied coating minus the thickness of the Mylar® film (which was 57 microns) .
- the significantly greater mean optical path-length for Coating A is observed over the entire range of coat weights explored and is a direct consequence of its greater light scattering ability.
- the greater scattering ability of Coating A translates on average to a longer transport path for light through the coating medium as graphically illustrated in Figure 7.
- the magnitude of difference in mean optical path-length seen between Coatings A and B cannot be accounted for on the basis of their small difference in physical coating thickness as measured by SEM.
- Figure 7 provides an illustrative comparison of mean optical path-length for coating A (70) and coating B (71) , in which incident light 72 and respective optical light paths 73 and 74 are depicted. The transmitted light 75 and 76 also is shown .
- the solution of the diffusion approximation model used to obtain the reflectance data, and pore size distribution data is one that is based on a smooth boundary layer, i.e., a Mylar® film, and an assumption of an infinitely small coating thickness (zero thickness).
- the pore volume fractions, the peak pore diameters and the pore size distributions within pigmented coatings can be determined that correlate well with values obtained from more traditional porosity measurements, such as mercury intrusion porosimetry, on a global scale.
- the diffusion approximation model easily elucidates the structural characteristics of a coated surface that yields more scattering of light.
- a coated paper manufacturer may have a product that has a certain, brightness, gloss, and opacity.
- the company could expand its market if the coated paper product had two more points of opacity.
- the diffusion approximation model can be used to determine what is needed to gain the two points of opacity without the need for extensive experimental testing.
- the physical characteristics of the pigment as well as other conditions pertaining to the coating system could be used as inputs into the diffusion approximation model, with one variable, e.g., size distribution, being changed to produce a predictive opacity output.
- the predictive value can then be compared to the target opacity value.
- the selected size distribution does not predict the desired increase in opacity
- another particle size distribution can be used, or another variable can be changed, such as increasing the coating thickness, increasing the pore volume, etc.
- the computational process can continue until a system is predicted that would meet the manufacturer's goal, i.e., an increase in opacity of two points .
- the diffusion approximation model can be used to generate optical properties of coating systems for a specific combination of inputs .
- parameters XI, X2, X3, and X4 can be used as inputs to get one or more of Yl, Y2, and Y3 as outputs.
- one or more of Yl, Y2, and Y3, along with Xl, X3, and X4 can be used as inputs to get X2 as an output.
- optical performance properties In the first scenario, physical characteristics are used to predict optical performance properties. In the second scenario, optical properties and physical characteristics are used to get another physical characteristic. As in the opacity example discussed above, reflectance data and a targeted opacity value could be used along with certain physical parameters to predict the required particle size and particle size distribution of the pigment.
- the diffusion approximation model as a mathematical expression with input variables is used as part of a computer program. This quickly enables the user to predictably calculate the optical performance of coatings or one or more physical characteristics, which thereby aids the formulator in the development of coating systems with optimal end-use properties.
- the noninvasive diffusion approximation model based approach as described herein is not limited merely to predicting and formulating coating systems for substrates such as paper, but also has application to self- supporting sheets per se that contain pigments for adjusting the optical attributes thereof. Using the same basic methodology described above via the example of paper coating systems, a sheet-forming composition containing the pigment and including the enhanced physical characteristic output obtained via the above-described diffusion approximation model can be provided.
- the sheet-forming composition containing the pigment can be selected, for example, from paper, paperboard, or plastic, and so forth.
- the coating technique of the present invention is applicable to the coating of nonporous, non- absorbent substrate materials such as coating (e.g., painting) metal surfaces (e.g., aluminum bodies or sheets), or plastic surfaces (e.g., vinyl bodies or sheets), or other coatable materials having surfaces receptive to the coating system of the present invention described herein.
Abstract
Description
Claims
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
EP02775740A EP1423207A4 (en) | 2001-09-04 | 2002-09-04 | Method of predicting optical properties and physical characteristics to formulate optimum coating system |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US31710001P | 2001-09-04 | 2001-09-04 | |
US60/317,100 | 2001-09-04 |
Publications (1)
Publication Number | Publication Date |
---|---|
WO2003020445A1 true WO2003020445A1 (en) | 2003-03-13 |
Family
ID=23232117
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/US2002/027976 WO2003020445A1 (en) | 2001-09-04 | 2002-09-04 | Method of predicting optical properties and physical characteristics to formulate optimum coating system |
Country Status (2)
Country | Link |
---|---|
EP (1) | EP1423207A4 (en) |
WO (1) | WO2003020445A1 (en) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US7465948B2 (en) | 2003-09-16 | 2008-12-16 | Paper Australia Pty Ltd. | Sheet-surface analyser and method of analysing a sheet-surface |
CN114535033A (en) * | 2022-04-27 | 2022-05-27 | 河南银金达新材料股份有限公司 | Processing method of polyester film with coating on surface |
Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5231472A (en) * | 1991-09-16 | 1993-07-27 | Ppg Industries, Inc. | Color matching and characterization of surface coatings |
US5929998A (en) * | 1996-09-10 | 1999-07-27 | Herbert Gmbh | Method for matching a colour formulation |
US6064487A (en) * | 1997-05-17 | 2000-05-16 | Herberts Gmbh | Method for calculating dye formulations of pigmented effect dyeing tones |
US6246416B1 (en) * | 1998-12-01 | 2001-06-12 | Silicon Graphics, Inc. | Method for modeling reflection of light from an anisotropic surface |
-
2002
- 2002-09-04 EP EP02775740A patent/EP1423207A4/en not_active Withdrawn
- 2002-09-04 WO PCT/US2002/027976 patent/WO2003020445A1/en not_active Application Discontinuation
Patent Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5231472A (en) * | 1991-09-16 | 1993-07-27 | Ppg Industries, Inc. | Color matching and characterization of surface coatings |
US5929998A (en) * | 1996-09-10 | 1999-07-27 | Herbert Gmbh | Method for matching a colour formulation |
US6064487A (en) * | 1997-05-17 | 2000-05-16 | Herberts Gmbh | Method for calculating dye formulations of pigmented effect dyeing tones |
US6246416B1 (en) * | 1998-12-01 | 2001-06-12 | Silicon Graphics, Inc. | Method for modeling reflection of light from an anisotropic surface |
Non-Patent Citations (1)
Title |
---|
See also references of EP1423207A4 * |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US7465948B2 (en) | 2003-09-16 | 2008-12-16 | Paper Australia Pty Ltd. | Sheet-surface analyser and method of analysing a sheet-surface |
CN114535033A (en) * | 2022-04-27 | 2022-05-27 | 河南银金达新材料股份有限公司 | Processing method of polyester film with coating on surface |
CN114535033B (en) * | 2022-04-27 | 2022-07-19 | 河南银金达新材料股份有限公司 | Processing method of polyester film with coating on surface |
Also Published As
Publication number | Publication date |
---|---|
EP1423207A4 (en) | 2004-10-20 |
EP1423207A1 (en) | 2004-06-02 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
US7045169B2 (en) | Method of predicting optical properties and physical characteristics to formulate optimum coating system | |
Brown et al. | Multiscale analyses and characterizations of surface topographies | |
Hwang et al. | Designing angle-independent structural colors using Monte Carlo simulations of multiple scattering | |
Sung et al. | Optical reflectance of metallic coatings: Effect of aluminum flake orientation | |
US20140327912A1 (en) | Method for determining the surface gloss of a colour standard | |
Seubert et al. | The characterization and effects of microstructure on the appearance of platelet–polymer composite coatings | |
WO2003020445A1 (en) | Method of predicting optical properties and physical characteristics to formulate optimum coating system | |
Lee et al. | Characterization of the paper coating structure using focused ion beam and field-emission scanning electron microscopy. 2. Structural variation depending on the glass transition temperature of an S/B latex | |
JP7363589B2 (en) | Paint quality prediction device and trained model generation method | |
Dullaert et al. | A mechanistic study of the effect of pigment loading on the appearance of powder coatings: The effect of surface topography on the optical properties of powder coatings: Modelling and experimental results | |
Latour et al. | Determination of the absorption and scattering coefficients of pigments: application to the identification of the components of pigment mixtures | |
Coppel et al. | Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures | |
Icart et al. | A physically-based BRDF model for multilayer systems with uncorrelated rough boundaries | |
Flys et al. | Characterization of surface topography of a newly developed metrological gloss scale | |
Elton | Optical measurement of microroughness of pigment coatings on rough substrates | |
Elton et al. | Wavelength dependence of Kubelka–Munk scattering spectra for studies of TiO2 microstructure and aggregation in paints | |
Farnood | Optical properties of paper: Theory and practice | |
JP5644069B2 (en) | Coating film reflectance estimation method | |
Modrić et al. | Modeling light dispersion in the printing substrate within the Monte Carlo method | |
Seubert et al. | A hybrid ray-wave optics model to study the scattering behavior of silver metallic paint systems | |
Elton | A two-scale roughness model for the gloss of coated paper | |
Gamonal-Repiso et al. | Influence of topographical features on the surface appearance measurement of injection moulded components | |
Martinez-Hermosilla | Model based design of barrier coatings for paper based materials: a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Bioprocess Engineering at Massey University, Manawatu campus, New Zealand | |
Granberg et al. | Forward scattering of fiber-containing surfaces studied by 3-D reflectance distribution simulations and measurements | |
Gate et al. | The specular reflection of polarized light from coated paper |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
AK | Designated states |
Kind code of ref document: A1 Designated state(s): AE AG AL AM AT AU AZ BA BB BG BR BY BZ CA CH CN CO CR CU CZ DE DK DM DZ EC EE ES FI GB GD GE GH GM HR HU ID IL IN IS JP KE KG KP KR KZ LC LK LR LS LT LU LV MA MD MG MK MN MW MX MZ NO NZ OM PH PL PT RO RU SD SE SG SI SK SL TJ TM TN TR TT TZ UA UG UZ VN YU ZA ZM ZW Kind code of ref document: A1 Designated state(s): AE AG AL AM AT AU AZ BA BB BG BY BZ CA CH CN CO CR CU CZ DE DM DZ EC EE ES FI GB GD GE GH HR HU ID IL IN IS JP KE KG KP KR LC LK LR LS LT LU LV MA MD MG MN MW MX MZ NO NZ OM PH PL PT RU SD SE SG SI SK SL TJ TM TN TR TZ UA UG UZ VN YU ZA ZM |
|
AL | Designated countries for regional patents |
Kind code of ref document: A1 Designated state(s): GH GM KE LS MW MZ SD SL SZ TZ UG ZM ZW AM AZ BY KG KZ MD RU TJ TM AT BE BG CH CY CZ DE DK EE ES FI FR GB GR IE IT LU MC NL PT SE SK TR BF BJ CF CG CI CM GA GN GQ GW ML MR NE SN TD TG Kind code of ref document: A1 Designated state(s): GH GM KE LS MW MZ SD SL SZ UG ZM ZW AM AZ BY KG KZ RU TJ TM AT BE BG CH CY CZ DK EE ES FI FR GB GR IE IT LU MC PT SE SK TR BF BJ CF CG CI GA GN GQ GW ML MR NE SN TD TG |
|
121 | Ep: the epo has been informed by wipo that ep was designated in this application | ||
WWE | Wipo information: entry into national phase |
Ref document number: 2002775740 Country of ref document: EP |
|
WWP | Wipo information: published in national office |
Ref document number: 2002775740 Country of ref document: EP |
|
NENP | Non-entry into the national phase |
Ref country code: JP |
|
WWW | Wipo information: withdrawn in national office |
Country of ref document: JP |