BSI Standards Publication BS ISO 18314-2:2015 Analytical colorimetry Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, hiding powerBS ISO 18314-2:2015 BRITISH STANDARD National foreword This British Standard is the UK implementation of ISO 18314-2:2015. The UK participation in its preparation was entrusted to Technical Committee STI/1, Pigments. A list of organizations represented on this committee can be obtained on request to its secretary. This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. © The British Standards Institution 2015. Published by BSI Standards Limited 2015 ISBN 978 0 580 86040 9 ICS 87.060.10 Compliance with a British Standard cannot confer immunity from legal obligations. This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 June 2015. Amendments/corrigenda issued since publication Date T e x t a f f e c t e dBS ISO 18314-2:2015 © ISO 2015 Analytical colorimetry — Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, hiding power Analyse colorimétrique — Partie 2: Correction de Saunderson, solutions de l’équation de Kubelka-Munk, force colorante, pouvoir couvrant INTERNATIONAL STANDARD ISO 18314-2 First edition 2015-06-01 Reference number ISO 18314-2:2015(E)BS ISO 18314-2:2015ISO 18314-2:2015(E)ii © ISO 2015 – All rights reserved COPYRIGHT PROTECTED DOCUMENT © ISO 2015, Published in Switzerland All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of the requester. ISO copyright office Ch. de Blandonnet 8 • CP 401 CH-1214 Vernier, Geneva, Switzerland Tel. +41 22 749 01 11 Fax +41 22 749 09 47

[email protected] www.iso.orgBS ISO 18314-2:2015ISO 18314-2:2015(E)Foreword iv 1 Scope . 1 2 T erms, definitions, s ymbols, and abbr e viat ed t erms . 1 2.1 Terms and definitions . 1 2.2 Symbols and abbreviated terms. 2 3 Saunderson correction . 4 3.1 General . 4 3.2 Incidence diffuse, observation 0° (d/0°) 4 3.3 Incidence 45°, observation 0° (45°: 0°) . 4 4 Solution of the Kubelka-Munk equations . 5 5 Determination of relative tinting strength and residual colour difference of coloured pigments 6 5.1 General . 6 5.2 Principle 6 5.3 Procedure 6 5.3.1 General 6 5.3.2 Evaluation of absorption at the absorption maximum . 7 5.3.3 Evaluation of the weighted K/S sum 7 5.3.4 Evaluation by equalizing the tristimulus value, Y .8 5.3.5 Evaluation by equalizing the smallest of the tristimulus values X, Y, and Z .8 5.3.6 Evaluation by equalizing the shade depth . 9 6 Determination of hiding power of pigmented media 10 6.1 General 10 6.2 Example for white or light coloured paints with a contrast ratio of 0,98 as hiding power criterion 11 7 Repeatability and reproducibility .12 8 Test report 12 Annex A (normative) T ables of c oefficients for calculating a(φ) v alues (standar d illuminant D65 and 10° standard observer) 13 Annex B (normative) T ables of c oefficients for calculating a(φ) v alues (standar d illuminant C and 2° standard observer) 15 Bibliography .17 © ISO 2015 – All rights reserved iii Contents PageBS ISO 18314-2:2015ISO 18314-2:2015(E) Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives). Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents). Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement. For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information The committee responsible for this document is ISO/TC 256, Pigments, dyestuffs and fillers. ISO 18314 consists of the following parts, under the general title Analytical colorimetry: — Part 1: Practical colour measurement — Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, hiding power — Part 3: Special indicesiv © ISO 2015 – All rights reservedBS ISO 18314-2:2015Analytical colorimetry — Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, hiding power 1 Scope This part of ISO 18314 specifies the Saunderson correction for different measurement geometries and the solutions of the Kubelka-Munk equation for hiding and transparent layers. It also specifies methods for the calculations of the tinting strength including the residual colour difference with different criteria and of the hiding power. The procedures for preparing the samples for these measurements are not part of this part of I S O 18314. They are agreed between the contracting parties or are described in other national or International Standards. 2 T erms, d efinitions , s ymbols, and abbr e viat ed t erms 2.1 T erms and definiti ons For the purposes of this document, the following terms and definitions apply. 2.1.1 tinting strength measure of the ability of a colorant, based on its absorption, to impart colour to other materials 2.1.2 relative tinting strength C rel percentage ratio of those mass fractions of the coloured pigment reference and test samples (m rand m t , respectively) that cause the particular tinting strength criterion used to have identical values for the reference and test samples 2.1.3 tinting strength criterion parameter that describes the colouring effect of a colorant, based on its absorption Note 1 to entry: The tinting strength criteria used in this part of ISO 18314 are the following: — value of the Kubelka-Munk function at the absorption maximum; — weighted sum of the Kubelka-Munk function values; — tristimulus value Y; — the smallest of the tristimulus values X, Y, Z; — shade depth parameter B. Examples of other tinting strength parameters not used in this part of ISO 18314 are the following: — unweighted sum of the Kubelka-Munk function values; — chromaticity given by the three colour coordinates (L*, a*, b*); INTERNATIONAL ST ANDARD ISO 18314-2:2015(E) © ISO 2015 – All rights reserved 1BS ISO 18314-2:2015ISO 18314-2:2015(E) — reflectance factor at the absorption maximum. 2.1.4 residual colour difference colour difference that remains between the white reductions of the reference and test samples when the tinting strength criterion values are the same or have been equalized EXAMPLE Given by ΔE*. 2.1.5 standard shade depth shade depth measure of the intensity of a colour sensation, which increases with increasing chroma and decreases with increasing lightness Note 1 to entry: Standard shade depths are values set by convention. For colourimetric purposes, the standard shade depth is defined by the shade depth parameter B = 0, which is calculated from the tristimulus value, Y, and the chromaticity coordinates, x and y. 2.1.6 hiding power ability of a pigmented medium to hide the colour or the colour differences of a substrate 2.2 Symbols and abbreviated terms a constant α* CIELAB colour coordinate a(φ) factor a(λ) auxiliary variable b* CIELAB colour coordinate b(λ) auxiliary variable B shade depth parameter C rel relative tinting strength D m hiding power value indicating the area of the contrast substrate concerned, in m 2 , which can be coated with 1 kg D v hiding power value indicating the area of the contrast substrate concerned, in m 2 , which can be coated with 1 l F(λ) Kubelka-Munk function F′(λ) modified Kubelka-Munk function g(λ) weighting function (defined as the sum of the colour matching functions x , y , and z for a 10° standard observer) h thickness K coefficient2 © ISO 2015 – All rights reservedBS ISO 18314-2:2015ISO 18314-2:2015(E) K(λ) absorption coefficient (K/S) r Kubelka-Munk value of reference sample (K/S) t Kubelka-Munk value of test sample L* CIELAB lightness m r mass fraction of coloured pigment reference sample m t mass fraction of coloured pigment test sample n refractive index r 0 reflection coefficient at the surface for directional light incident perpendicular from outside r 0 reflection coefficient at the surface for directional light incident parallel under 45° from out- side r 2 reflection coefficient for light incident diffusely from the inside of the specimen R λ reflectance spectrum R λ reflectance of infinitely thick layer R λ reflectance of the sample λ Saunderson-corrected reflectance of the black substrate λ Saunderson-corrected reflectance of the white substrate R λ b Saunderson-corrected reflectance of the sample on black substrate λ w Saunderson-corrected reflectance of the sample on white substrate R´ λ modified reflectance spectrum including surface effects s saturation S λ scattering coefficient T weighted sum x, y chromaticity coordinates X, Y, Z tristimulus values E * residual colour difference© ISO 2015 – All rights reserved 3BS ISO 18314-2:2015ISO 18314-2:2015(E) E * CIELAB colour difference φ hue angle φ o closest angle in the table below the hue angle 3 Saunderson correction 3.1 General For colourimetric calculation it is necessary to account for surface phenomena to obtain viable results. The formulas are known as Saunderson correction, their derivation can be found in References [1] and [2] The necessary coefficients are solutions of the Fresnel formulae [3]depending on the index of refraction for the given binder. The formulae are derived assuming an ideal surface, a perfectly hiding layer and a perfectly diffuse scattering of light inside the interior of the specimen. Any deviation from these assumptions shall lead to consideration of the usefulness of the following calculations. The formulae given here are for two of the most widespread geometries: diffuse incidence, 0° observation (d/0°) and 45° incidence, 0° observation (45°/0°). In nearly every colourimeter used, the measurement angle is not 0° but 8°. This deviation is not considered problematic. The constants necessary for the calculation are the following: r 0 : reflection coefficient at the surface for directional light incident perpendicular from outside. For n = 1,5 r 0= 0,040. r 0 : reflection coefficient at the surface for directional light incident parallel under 45° from outside. For n = 1,5, r 0 = 0,050. r 2 : reflection coefficient for light incident diffusely from the inside of the specimen. For n = 1,5, r 2= 0,596. 3.2 Incidence diffuse, observation 0° (d/0°) The constant a = 1 if a gloss trap is closed and a = 0 if the gloss trap is open and the specular reflection is excluded. λ λ λ * *(1) : λ λ λ(2) : λ λ λ(3) 3.3 Incidence 45°, observation 0° (45°: 0°) λ λ λ (4)4 © ISO 2015 – All rights reservedBS ISO 18314-2:2015ISO 18314-2:2015(E) λ λ λ (5) 4 Solution of the Kubelka-Munk equations The Kubelka-Munk theory describes the reflection of a pigmented layer by two constants: absorption [K(λ)] and scattering [S(λ)]. It is based on the following assumptions: a) ideally diffuse radiation distribution on the irradiation side; b) ideally diffuse radiation distribution in the interior of the layer; c) no consideration of surface phenomena resulting from the discontinuity in refractive index. For an infinitely thick, respectively hiding layer with a reflectance of R(λ) ∞ , the following solutions are found, which allow the determination of the relation between the scattering and the absorption coefficient: λ λ λ λ λ (6) respectively the inverse: λ λ λ λ λ λ λ (7) For the determination of the scattering and absorption coefficient two different methods can be applied (the Saunderson correction shall be used): Method 1 Measurement of the reflectance of an infinite thick (respectively hiding) layer and the reflectance R * of a coating of the thickness, h, on a substrate of the reflection R . λ λ λ (8) λλ λ λ λ (9) λ λ λλλλ λ λλ λ (10) λλ λ 1 (11) Method 2 This method applies two layers of equal thickness (h) on black and white substances. After the determination of the auxiliary variables a(λ), b(λ) according to Formulae (12) and (13), either Formula (14) or (15) may be used to calculate the scattering coefficient S(λ). The possibility with the least experimental uncertainty should be chosen. λ λλλλ λλ λλ λλ λλ (12)© ISO 2015 – All rights reserved 5BS ISO 18314-2:2015ISO 18314-2:2015(E) λλ (13) λ λ λλλλ λ λ ** ** λλ ** (14) λ λ λλλλ λ λ ** ** λλ ** (15)