ANSI T 1214 SP-2012 Interrelation of reflectance R0 reflectivity R TAPPI opacity C0.89 scattering s and absorption k.pdf

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1、T 1214 sp-12 FORMERLY TIP 0804-03 STANDARD PRACTICE 1998 REVISED 2002 REVISED 2007 REVISED 2012 2012 TAPPI The information and data contained in this document were prepared by a technical committee of the Association. The committee and the Association assume no liability or responsibility in connect

2、ion with the use of such information or data, including but not limited to any liability under patent, copyright, or trade secret laws. The user is responsible for determining that this document is the most recent edition published. Approved by the Standard Specific Interest Group for this Test Meth

3、od TAPPI CAUTION: This Test Method may include safety precautions which are believed to be appropriate at the time of publication of the method. The intent of these is to alert the user of the method to safety issues related to such use. The user is responsible for determining that the safety precau

4、tions are complete and are appropriate to their use of the method, and for ensuring that suitable safety practices have not changed since publication of the method. This method may require the use, disposal, or both, of chemicals which may present serious health hazards to humans. Procedures for the

5、 handling of such substances are set forth on Material Safety Data Sheets which must be developed by all manufacturers and importers of potentially hazardous chemicals and maintained by all distributors of potentially hazardous chemicals. Prior to the use of this method, the user must determine whet

6、her any of the chemicals to be used or disposed of are potentially hazardous and, if so, must follow strictly the procedures specified by both the manufacturer, as well as local, state, and federal authorities for safe use and disposal of these chemicals. Interrelation of reflectance, R0; reflectivi

7、ty, R; TAPPI opacity, C0.89; scattering, s; and absorption, k 1. Scope The following interrelationships will be found particularly useful in predicting the effect upon opacity when a change occurs in either the basis weight or the reflectivity of a sheet of paper. These interrelationships can also b

8、e used to evaluate relative contributions of different pulps, fillers and pigments to optical properties. Extensions of these procedures that are cited in the references can be used to evaluate multilayer structures such as coated paper or coated board. 2. Significance The Kubelka and Munk (1) theor

9、y of light scattering was first published in 1931. The mathematical relationships between the optical properties of paper and the sheet thicknessbased on derivations of the Kubelka and Munk equations concerning the reflection of light from diffusing media were first shown by Steele (2) with a series

10、 of charts relating the various measurable properties. In a detailed study, Judd (3) later investigated the Kubelka and Munk theory as applied to paper to discover the magnitude of departures from theory, and concluded that “except for deviations of less than one percent, the Kubelka and Munk theory

11、 applies to paper; the two constants of the theory, reflectivity, R, and coefficient of scatter, S, yield a useful description of the material of which paper is made.” 3. Kubelka/Munk relationships 3.1 Judd prepared a number of graphical aids, including the reflectance-opacity charts in this Standar

12、d Practice relating the important optical properties of paper. Properties as defined by Robinson (4) are: R = reflectance of a layer (sheet, coating, ply) which has behind it a surface with a reflectance of RgRg= reflectance of the background behind the layer whose reflectance is being considered R0

13、= reflectance of the layer with ideal black background, Rg= 0 R= reflectivity = reflectance of a layer so thick that further increase in thickness does not change the reflectance - TAPPI Brightness when the reflectance is measured through the standard blue filter R0.89= reflectance of the layer whic

14、h has behind it a surface with reflectance of 0.89, i.e., Rg= 0.89 T 1214 sp-12 Interrelation of reflectance, R0; reflectivity, R; TAPPI / 2 opacity, C0.89; scattering, s; and absorption, k C0.89= R0/R0.89= TAPPI Opacity, as a fraction, when reflectances are measured through the standard green filte

15、r sW = scattering power, a function of composition and grammage which characterizes the ability of the paper to redirect light (formerly used as sx). kW = absorption power, which characterizes the ability of the paper to absorb light (formerly used as KX). W = grammage X = thickness S = sW/W = light

16、 scattering coefficient K = kW/W = light absorption coefficient 3.2 Note that opacity and scattering are normally characterized using the standard green filter. Therefore, the Rvalue in the following equations is the Rusing green light, not TAPPI Brightness which is measured using blue light. 3.3 R0

17、, R, C0.89, and SX are interrelated so that when the numerical values of any two of these properties are known, the other values may be calculated or read directly from the charts. With two optical measurements on a sample of known thickness, it is possible by calculation or reading of the chart to

18、determine the opacity of any sheet of the same fiber and filler composition but of different thickness. Another application for which an example is given allows determination of changes in opacity when absorption is changed by addition or removal of dye. 3.4 It was at once recognized that thickness,

19、 X, was an awkward variable with which to work from a practical standpoint. Workers in the field immediately began to divide SX by W, the grammage, to obtain the “scattering coefficient” with “grammage substituted for X.” One of the reasons given for this practice was the fact that grammage was usua

20、lly more accurately known than was thickness. Van den Akker (5) pointed out that this substitution is perfectly justified and, in fact, allows additional benefits not immediately recognizable to the casual user of the Kubelka and Munk theory. In view of this, TAPPI has now adopted the term sW as the

21、 preferred nomenclature for scattering powerrather than the original SX. For additional information on terminology for optical measurements, see TAPPI T 1213 “Optical Measurements Terminology (Related to Appearance Evaluation of Paper).” 3.5 When one considers a mixture of two or more components in

22、film or sheet, the specific scattering coefficient, s, of each of the constituents may be calculated on the basis of their relative grammages. Thus, the contribution of an individual component of a film or sheet is the product of its specific scattering coefficient and the grammage of the component

23、in the reference unit of area (one ream, for example). This relationship is expressed as: sW = s1W1+ s2W2+ . . . + snWnwhere W1W2, and Wnare the grammages of the individual components and s1, s2, and snare their respective scattering coefficients; s is then the coefficient for the mixture, and W is

24、the total grammage. The above relationship is based upon three assumptions: 1. Light scattering in a pulp-filler mixture is directly proportional to filler content. 2. Reduction in scattering through internal bonding is negligible. 3. The degree of optical contact between particles remains unchanged

25、 with changing density, and, therefore, s is independent of density. 3.6 While none of the above assumptions is entirely true, the deviations are slight in low-loading systems and the contributory scattering power concept has been used by many workers to establish specific scattering coefficients of

26、 various pulps and filler materials. Steele (6) was one of the first to do this and establish the s values for the more common pulps of the day. He arrived at the scattering coefficients of pigments by difference, thus: spigment= spaper- (1 - y)spulp / y where y = the fraction of pigment in the pape

27、r. 3.7 It was immediately apparent that the s values of pigments in sheets, as obtained by Steele, would provide an excellent clue to pigment efficiency if the true (absolute) s values of the pigments were also known. Davis (7) attempted this by making sheets containing varied percentages of loading

28、. He then plotted the s value of each sheet against filler content and extrapolated to the hypothetical sheet containing 100% filler and no pulp. His results were questioned because of assumptions 1 and 2 above. In high loadings the scattering of light in a sheet by a filler is not 3 / Interrelation

29、 of reflectance, R0; reflectivity, R; TAPPI T 1214 sp-12 opacity, C0.89; scattering, s; and absorption, k directly proportional to the filler content by reason of the attendant materials which are used in flocculating the filler upon the cellulose fibers. 3.8 Adrian (8) developed a method for obtain

30、ing the absolute s values of pigments which he called the “film” method, as distinguished from the more commonly employed handsheet method. One of the most interesting aspects of his work is that he found this method particularly useful for measuring the influence of the compacting of pigment partic

31、les, particle size variations, and admixtures with other materials on the light scattering properties of pigment films. (See entire Adrian Thesis, Institute of Paper Chemistry, May 1942). 3.9 Recently, Biermann (10) has described how a computer spreadsheet can be used to customize the charts in this

32、 Standard Practice to focus on a small area for precise, graphical solutions that may apply to a particular grade of paper. 4. Example applications of the interrelationships 4.1 The interrelationships of the above optical properties can be used in a number of different ways. With ready access to com

33、puters, the use of the charts has largely been replaced by direct calculations. However, one useful application of the charts is to estimate sensitivity to measurement errors when working in different regions of the chart. Each of Figures 1 to 6 show that there are regions where the contour lines fo

34、r R or sW get very close together. In these areas, result is sensitive to measurement errors and computer output should be used carefully. 4.2 Examples of two specific applications are described in the following sections: (1) opacity changes related to grammage changes, and (2) use of dye addition o

35、r removal to optimize the tradeoff between opacity and reflectivity. Another important application is the determination of optical performance of the coating layer for samples of coated paper. Clark and Ramsey (11) have provided procedures for that case. 4.3 With an opacimeter meeting the requiremen

36、ts of TAPPI T 425, measure any two of the following optical properties of a paper specimen of predetermined grammage: C0.89TAPPI Opacity (see TAPPI T 425). R0, the reflectance of a specimen backed with a black body (with the instrument adjusted to read zero with the black body in position and absolu

37、te reflectance with an absolute reflectance standard in position (see TAPPI T 425). R, the reflectance (reflectivity) of an opaque pile of the specimen using the same distribution of light wavelengths as in T 425 (standard green filter). 4.4 With any two of these measurements, the third parameter ca

38、n be determined by reference to the charts or by calculation with the equations below. Scattering power, sW, and absorption power, kW, can also be determined. Scattering and absorption power are dimensionless parameters. Dividing each by the grammage , W, gives the specific scattering coefficient, s

39、, or specific absorption coefficient, k, which will have units of reciprocal grammage. 5. Procedure 5.1 Equations 5.1.1 From measurement of R0and REqn 1. a = 0.5 (1/R+ R) Eqn 2. b = 0.5 (1/ R- R) Eqn 3. x = (1 - aR0)/(bR0) Eqn 4. R0.89= R0+ 0.89(R- R0) (1 - R0R)/ R(1 - 0.89 R0) Eqn 5. C0.89= TAPPI O

40、pacity = R0/R0.89Eqn 6. sW = (0.5/b) ln(x + 1)/(x - 1) s = sW/W Eqn 7. kW = sW (a-1) k = kW/W T 1214 sp-12 Interrelation of reflectance, R0; reflectivity, R; TAPPI / 4 opacity, C0.89; scattering, s; and absorption, k 5 / Interrelation of reflectance, R0; reflectivity, R; TAPPI T 1214 sp-12 opacity,

41、C0.89; scattering, s; and absorption, k T 1214 sp-12 Interrelation of reflectance, R0; reflectivity, R; TAPPI / 6 opacity, C0.89; scattering, s; and absorption, k 7 / Interrelation of reflectance, R0; reflectivity, R; TAPPI T 1214 sp-12 opacity, C0.89; scattering, s; and absorption, k T 1214 sp-12 I

42、nterrelation of reflectance, R0; reflectivity, R; TAPPI / 8 opacity, C0.89; scattering, s; and absorption, k 9 / Interrelation of reflectance, R0; reflectivity, R; TAPPI T 1214 sp-12 opacity, C0.89; scattering, s; and absorption, k T 1214 sp-12 Interrelation of reflectance, R0; reflectivity, R; TAPP

43、I / 10 opacity, C0.89; scattering, s; and absorption, k NOTE 1: The units of scattering coefficient (s) and absorption coefficient (k) are m2/g. The multiplier (1000) is used to convert m2/g to the more convenient and standard units m2/kg. 5.1.2 From measurement of R0 and C0.89Eqn 8. R0.89= R0/C0.89

44、Eqn 9. a = 0.5R0.89+ (R0- R0.89+ 0.89)/(0.89 R0) Eqn 10. R= a - (a2- 1)Calculate sW, kW using Eqns 3, 6, 7 5.1.3 From measurements of Rand C0.89 Eqn 11. = C0.891/ R+ R- 1.1236 + 1.1236 Eqn 12. R0= 0.5 - ( 2- 4 C0.89) Calculate sW, kW using Eqns 6, 7 5.2 Example 1. Determine the expected opacity of a

45、 paper specimen of the same composition but of a new grammage 5.2.1 Graphical method 5.2.1.1 With the instrument adjusted to read correctly on the absolute scale and properly zeroed, measure the reflectance over black R0 of the specimen of grammage W. 5.2.1.2 Measure the TAPPI opacity, C0.89value of

46、 the specimen in the normal manner. 5.2.1.3 Locate the intersect of these values on the accompanying charts. (Figure 1 is a general chart to locate proper area. Figures, 2, 3, 4, 5, and 6 show expanded view of areas A, B, C, D, and E, respectively). Determine the reflectivity, R and the scattering p

47、ower, sW. 5.2.1.4 The scattering power, sW, is the product of the specific scattering coefficient, s (which remains constant for any weight of sheet of the same composition), and the grammage, W. Thus, changing the basis weight from W to W changes the scattering power by W/W. New sW = (sW) (W) / W =

48、 (old sW) (new grammage) / (old grammage) Calculate the new sW by using the chart-obtained value of sW and the ratio of grammages. 5.2.1.5 On the chart, locate the intersect point of this new sW and the previously obtained R (reflectivity) value, since Rdoes not change with changing grammage 5.2.1.6

49、 Read the new (anticipated) TAPPI opacity by projecting this intersect point down to the abscissa scale (C0.89scale). 5.2.1.7 Example: A 50.5-lb. (25 x 38500) bleached sulfite sheet containing 0.6% titanium dioxide filler was found by measurement with an opacimeter to have a reflectance over black (R0) value of 0.30. It has a TAPPI opacity (C0.89) value of 0.37. At the intersection of these lines on the accompanying chart, it will be found that this sheet has a reflectivity (R) value of 0.62 and scattering power (sW) of