Colorimetric Evaluations and Characterization of Natural and Synthetic Dyes/Pigments and Dyed Textiles and Related Products

Abstract

This book chapter covers principles and few case studies on colorimetric Estimation of (i) determining purity/active ingredient % of selective dyes/pigments (ii) Identification of any colorants to distinguish from other similar compound, (iii) Measurement of surface colour strength of a dyed textile, (iv) Measurement of colour differences by estimating DE, DL*, Da*, Db*, DC and DH values, (v)Computer-aided colour match prediction for any standard shades, (vi) Estimation of compatibility of two dyes/colourants to use for compound shades, (vii) Determination of rate of dyeing, dyeing isotherm and dyeing kinetics to control dyeing, (viii) Optimization of dyeing process variables, (ix) Precession grading of Colour Fastness of dyed textiles on fading under different ways/agencies and (x) Estimation of Soil Removal efficacy of different detergent used for textiles. These colorimetric measurements are found to be very useful for effective process and product control of dyed textile materials. Selected Case studies on all the above colorimetric applications with specific example or experimented data are discussed for each of the method under reference. Finally, the other applications of colorimetric analysis besides textiles industry are also mentioned in concluding remarks.

1. Introduction

UV VIS Absorption spectrophotometer (applicable for coloured liquid) and UV VIS reflectance spectrophotometer (applicable for flat samples of coloured solids) are the two major equipment now being used in colorimetric evaluation related labs for textiles and other industries. Colour measurement of liquid dye solution or colorimetric titrations is known with the advent of UV Vis Absorption spectrophotometer. Colour measurement of solid substances was quantified by CIE internationally in 1923, which was further revised in 1976 and is continuing [1, 2, 3, 4]. Colour matching theory was made commercially applicable in 1950s. Till then, so many varied applications of colorimetric evaluations have made precision process control and product control possible for coloured textiles.

2. Principles of colorimetric/spectrophotometric evaluation of coloured substance using UV: VIS absorbance spectrophotometer

Beer’s Law states that the amount of light absorbed is directly proportional to the concentration of the colored solute in the solution.

$${\mathrm{Log}}_{10}\frac{{\mathrm{I}}_0}{{\mathrm{I}}_{\mathrm{t}}}=\mathrm{\epsilon }\mathrm{c}$$Ei

where, Ɛ = proportionality constant and c = concentration of the solute in solution.

Lambert’s Law states that the amount of light absorbed is directly proportional to the length and thickness of the solution (thorough which light is passed through) under analysis.

$${\mathrm{Log}}_{10}\frac{{\mathrm{I}}_0}{{\mathrm{I}}_{\mathrm{t}}}=\mathrm{\epsilon b}$$Eii

where Ɛ = proportionality constant and b = length/thickness of the quartz cell in which solution is tested.

So, combining these two laws, called Beer-Lambert Law [3, 4]:

$$\mathrm{A}\left(\text{Absorbivity or Absorbance}\right)={\mathrm{Log}}_{10}\frac{{\mathrm{I}}_0}{{\mathrm{I}}_{\mathrm{t}}}=\mathrm{\epsilon bc}$$Eiii

where I₀ = intensity of the incident light, It = intensity of the transmitted light, c = the concentration of absorbing substance/solute in the solution, b = the path length/the distance the light is passing through the absorbing solution, and A = absorptivity/Absorbance and Ɛ = proportionality constant dependent upon the absorbing substance, the wavelength of light used, and the units used to specify c and b.

In simple colorimetry, the entire visible spectrum (white light) is used to pass through the solution and consequently the complementary colour of the one absorbed, is observed as transmitted light. In UV VIS absorbance Spectrophotometer, a monochromatic light or a narrow band of light radiation is used, replaced the colorimeter and then this instrument is called Absorbance spectrophotometer or reflectance spectrophotometer, differentiating by measurement parameter i.e. measuring as absorbency or optical density of transmitted light intensity for colored solution.

Limitations and Cares for measuring absorbance/optical density parameter of liquids:

1. Beer-lambert law does not hold good for a concentrated solution. So sufficient dilution is necessary to obtain correct and reproducible results. Dilution to 50 to 100 times is preferably used.

2. Beer-lambert law does not hold good, if the solute/coloured liquid under measurement, has ionizing, dissociation or aggregation/association tendency or complex-forming tendency in the solution.

Example: Benzoic acid in Benzene solvent form dimer, i.e., aggregates as dimer, and Potassium dichromate on higher dilution, dichromate ions are ionizing or dissociating into chromate ions, which are the causes of deviation of correct reading in both these two cases.

1. If the colour liquid has fading tendency with time, then the sample is faded away due to instability of coloured molecules/solutes and hence incorrect results are obtained.

2. Presence of any impurities like fibre dust, residual dye bath additives/electrolyte etc. (comes to the coloured liquid solution during extraction of coloured substance/dyes/pigments from a dyed textiles or during measuring residual coloured liquor of exhausted dye bath effluent) and causes incorrect result.

3. Use of electrolyte at higher concentration usually shift the λmax values and changes the extinction coefficient/coefficient of absorption etc. and hence occur deviation in results.

4. Presence of any additives changes/makes alterations in the refractive index values of the coloured solution and hence it gives wrong results.

5. Changes in pH of solute/coloured liquid causes deviation in results.

While for Solid coloured samples, surface reflectance values are measured for any solid-coloured substance, the measurement parameter is reflectance (R values at different wavelengths user-chosen wavelength or preferably at maximum absorbance wavelength, i.e., λmax) and the instrument used for R values of solid coloured substance, is called UV-VIS Reflectance Spectro-photometer.

Thus, when it is required to measure colour from a solid dyed/printed surface, the measurement parameter is not absorbancevalues, but is Reflectance values (R), i.e., reflected light intensity from a solid surface of dyed textiles/coloured/coated polymeric film/plastics etc.${\mathrm{R}}_{\mathrm{L}}-\mathrm{Rs}$ UV-VIS reflectance spectrophotometer is used having different viewing angle with setting facility of measuring specular reflectance or diffused reflectance, with UV-in (On) and out (Off), with large viewing angle or small viewing angle, with D65 or other standard illuminant light ambience etc. having options of changed testing parameters. Both these spectrophotometers are not limited to the visible spectrum only and are often employed to make measurements in the ultraviolet and infrared regions too. So presence of any colored chemical agents/dyes/pigments can be thus calorimetrically or spectrophotometrically identified by absorbance spectrophotometer and can be quantitatively estimated frequently using a dilute solution at concentrations smaller than one part of the constituent in several hundred million parts of a selected coloured solution of specific solute. While by UV-VIS Reflectance Spectrophotometer, K/S values (i.e., surface colour strength) of any opaque coloured substance can be determined easily by Kubelka Munk Equation [2, 3] from the measured reflectance values at different wavelength by measuring intensity of reflected diffused light beam or intensity of specular reflected light beam.

Besides surface colour strength, the colour difference and other colour interaction parameters [2, 3, 5, 6] like Total colour differences (DE), Lightness/Darkness (DL*), Red-ness/Green-ness (Da*), Yellowness/Blueness (Db*), Changes in Chroma (DC) and Changes in hue (DH) can be calculated by CIE formulae [1, 2, 3, 4]. Also, non-coloured surface appearance properties of any flat sample including textile fabrics can be determined easily in terms of whiteness index, yellowness index, and brightness index values using appropriate and respective formulae of CIE/ASTM or other standards [1, 2, 3, 5, 6] to compare any changes in its surface texture for any chemical treatment or physical intervention on the sample, which is very useful for industry.

Limitations and Cares for measuring Reflectance/Surface Colour parameters of solids:

1. Calibration of the instruments and calibrated dyed samples: The UV VIS Reflectance spectrophotometer instrument need every day at the start calibration with standard white tiles to combat decayed power of illuminated lamp day by day for correct results. Also, for good colour matching results, the calibration dyeing samples must be prepared with great care at specific dyeing conditions in the laboratory and productions lab unit, which do not differ in various respects viz., checking purity of dye to give same exhaustion, pre-decided M:L ratio, dyeing additive and auxiliaries %, dyeing conditions, dyeing machines settings, exhaustion of dye etc.

2. Type of substrate and class of Dyes: Change of type of fibres or class of dyes changes surface colour strength (K/S Values) data. So, to compare K/S values, the type of fibres, fabric construction, type of dye and dye class should be same. But it is very difficult to maintain the required properties of the substrate from lot to lot as regards the quality of the fibres, yarn structure, fabric construction, colour, heat setting, pre-treatments and dyeing conditions etc. which in turn changes the dye uptake properties of the textiles and give variation in final colour yield/surface colour strength values. It is not at all advisory to prepare the basic calibration data of any particular type of textile fibres with a particular class/type of dyes under all such variations [7, 8]. Changes in dye even within the same class, due to change of groups and conjugation length etc., the dye colour is shifted either bathochromic shift (shift of absorption maxima to longer wavelength i.e., redshift) or hypochromic shift (shift of absorption maxima towards shorter wavelength i.e. blue shift) occurs. Similarly, changes in dye molecules with changes in auxo-chrome type may cause hyperchromic effect (i.e., increase in the intensity of absorption) or a hypochromic effect (decrease in the intensity of absorption) occurs.

3. Instrumental colour value vs Human perceived colour: For colour measurement and matching, formulations generated by the computer-aided colour measuring system are based on minimum colour difference value within given tolerance & least metamerism value in CIELAB scales. But always instrumentally obtained CIELAB tolerances do not confirm exactly with human perceived colour differences and variation persists.

4. Failure of Kubelka-Munk Equation in some specific cases: The measurement of K/s values following kubelka–munk equation does not holds good strictly on extra glossy or fluorescent samples. For too Dull shade or too bright shade sometimes behave differently and do not follow K-M(Kubelka-Munk) theory.

5. Linearity of Plots between K/S values vs. concentration of dyes sometimes deviates from linearity and therefore must be checked beforehand. For practical purposes, if non-linear curve appears in the plots between K/S values vs. concentration of dyes, it is needed to re-dye to recheck linearity or to modify the curve by simply eliminating data of one or two erroneous dyed samples to make it linear for precision colour measuring and match prediction. Also, some mordanted textile samples dyed with a variety of natural dyes, do not show linearity for plots between K/S values vs. concentration of dyes.

6. Instrumental settings and type of Illuminate sources used: Test results of instrumental colour values and matching precision varies with changes of instrumental settings for type of CIE standard illuminate used, viewing area (large or small) used, choice of Specular or diffused reflectance measurement, Choice of UV Light on or Off (either UV or VIS or both UV and VIS range of wavelength, Choice of user-chosen wavelength or at deterministic maximum absorbance wavelength, i.e. λmax which are not same for all type of dyes/pigments and hence, there is instrument to instrument metamerism results, which with respect to illuminate type varies too large. Moreover, Instrumental accuracy is to be checked on a daily basis or at least periodically in a week or month.

7. Some special cares needed during measurement of colour values of solid dyed textiles

1. If the dye uniformity is not up to the acceptable level, the measurement of K/S values will vary a large resulting higher coefficient of variation of K/S data for non-uniform dyeing i.e., Un level dyeing (in general more than 5% coefficient of variation of K/S data is taken as un-level dyeing for all type of dyed textiles).

2. During mounting of solid coloured textile yarns or fabrics, background opaqueness of the sample is to be assured for correct results (So, nos. of folds required in the sample to obtain opaqueness, are to be pre-decided and to be kept constant in all the measurements).

3. During mounting of solid coloured textile yarns or fabrics, changes in the sample orientation (warp wise or weft wise vertical or horizontal measurement or changes of side of the textile fabrics (Colour value in one face of fabric usually differ from other face) differs colour strength values. So, warp or weft wise orientations/and face or backside facing measurements of colour values are to be pre-decided and not to be changed throughout all the colour value measurements of all samples to compare.

4. Some chemical/biochemical treatment before dyeing may alter the surface texture and hence changes scattering value of the sample and hence deviations in K/S value measurement occurs. So, care should be taken to avoid such treatments which changes texture of the sample and alter K/S values to a large extent.

5. Defects in fabric (Any defect of the fabric on surface may cause variation in colour value) like Slabbing/snarls, patchy dyeing, dyeing warp or weft bar etc. causes such variations. So defective fabrics must be avoided during measurements of surface colour values.

3. Colourimetric evaluations for process/product control of dyed textiles

Different types of selective colorimetric evaluation methods are described one by one in brief with examples/case studies with experimental data below mentioning the importance of each method.

3.1 Colorimetric identification and estimation of purity/concentrations of any colorants/dyes/pigments using UV: VIS absorbance spectrophotometer

An optical UV-VIS absorbance spectrophotometer records the absorbance values at different wavelength range at which absorption occurs, together with the degree of absorption at each wavelength and thus a pictorial curve of wavelength (X-axis) vs. Absorbance (Y-axis) called UV-VIS spectrum of that solute from its very dilute solution (preferably 1/100th dilution). The resulting UV VIS spectrum is presented as a graph of absorbance (A) versus wavelength showing maxima (λmax) and minima (λmin) of absorbance at different wavelength in both UV and visible region.

Solute molecules absorb ultraviolet or visible light from a monochromatic beam of incident light beam and the rest are transmitted through the solutions of fixed path length (b or d) in a cuvvete/quartz cell holding the sample solution. As optical density or absorbance is directly proportional to the Path length, b, and the concentration, c, of the solute/absorbing species of the coloured solution, Beer’s -Lambert Law stands here as, A = Ɛbc, (where Ɛ is a constant of Proportionality, called the absorbtivity Constant) and is Optical density/Absorbance.

Different solute molecules absorb UV-VIS light/radiation of different wavelengths depending on its chemical nature and structure with or without interference, if any, as depicted by corresponding absorption spectrum showing absorption peaks and troughs/bands according to the chemical structural groups present in the respective solute molecules present in the coloured dilute solution. Thus, the UV-VIS spectral scan (For absorption or optical density) of a particular-coloured compound/dyes/pigment at a particular wavelength (at λmax₎ is deterministic and identifiable instrumentally, which is the basis of the identification and estimation of purity/concentrations of any colourants/dyes/pigments by UV VIS spectrophotometric (Absorbance) evaluation.

CASE STUDY 1: As a case study, UV–VIS Absorbance spectrophotometric method of determination of purity and concentrations of rubia/madder as a natural colorant is discussed:

Calibration curve (Figure 1) is prepared by using 1,2,3,4,5,6 to maximum of 10 mg of natural Rubia/madder (Madder or Manjistha) containing manjishthin and purpurin as natural colourant powder per ml of methanol, after extracted in aqueous solution and purified by Soxhlet extraction under methanol. The solutions were filtered through Whatman filter paper-40 and then used for UV Calibration method and the absorbance was measured at 426 or 430 nm as λmax.

Figure 1.

Calibration curve for the Rubia dye natural colorant for determining concentration of a solution of unknown concentration of colour component extracted from Rubia/Madder.

Once the calibration curve is ready in UV VIS absorbance spectrophotometer screen or manual graph paper, the unknown solution of the same compound having unknown quantity of solution is placed in UV VIS scanning taking 10 ml of sample solution of unknown concentration, diluted to known times i.e. say 50 to 100 times until a very fent colour appears in the solution and from that dilute solution 2–3 cc is poured in quartz cell of sample solution and mounted in UV-VIS absorbance Spectro, to measure its Optical density/absorptivity values. Once the absorptivity/Optical density values of sample of unknown concentration are obtained, the concentration can now be easily obtained by putting measured absorbance or OD (optical density) values in calibration curve of Figure 1, to find the Concentration/purity of the content of rubia/madder coloured component in it in specific unit, after correcting the value with dilution factor and converted into proper unit like % or g/lit etc. as per requirement. .

3.2 Identification of colorants/dyes/pigments powder or from its dyed textiles by using UV: VIS absorbance spectrophotometer

CASE STUDY 2: Identification of Natural dye Madder/Rubia as a natural colorant is discussed below and is also compared with the synthetic Alizarin coloured compound to distinguish them by UV-VIS Spectrophotometric evaluation method.

The two red dyes-- [(i) Natural Rubia (Manjishtha/Madder) which contains manjisthin (similar to alizarin as coloured compounds) in its natural extract and (ii) synthetic alizarin coloured compounds as synthetic same coloured dye] were weighed separately (0.1 gm) and dissolved in 1000 ml dichloromethane/methanol and then wavelength scan under UV-Visible absorbance spectrophotometer was taken for both. For visible spectral analysis, this solution may be used, but for UV spectral analysis this solution needs to be further diluted by 5−10 times for better results. Comparative Identification of Synthetic alizarin and madder (Rubia) as natural colourant/dye, by this UV VIS spectral analysis, involves a comparison of the minute details of UV–VIS peaks/bands of UV VIS spectrum (at λmax) of Rubia/Madder as natural colourant and synthetic alizarin red colour. Such a Comparative spectral analysis of both with corresponding UV-VIS peaks is compared in Figure 2. The details method of identification of rubia/madder as natural colourant is available in new IS standards 17,085:2019 [9] in Annexure-E as one of the confirmatory tests.

Figure 2.

UV spectrum of Rubia and Alizarin dyes: [Source -IS standard- 17,085: 2019 [9]].

Thus from Figure 2 Comparative analysis of UV-Vis Spectrum of Natural Rubia/Madder extract and Synthetic alizarin (as shown in Figure 2 indicate that Natural Rubia/Madder colourant shows uv–vis peaks at 250 nm (with 0.954 OD) and at 491 nm (with 0.171 OD), while Synthetic Red alizarin shows uv–vis peaks at 250 nm (with 1.38 OD) and 426 nm (with 0.309 OD). This different OD at 250 nm in UV zone and Peaks in Visible Zone at two different wavelengths (at 491 nm with 0.171 OD for Rubia/madder natural colourant and at 426 nm with 0.309 OD) are identifying factors confirming presence or absence of them, as shown Figure 2 and Table 1.

Specific Wavelength (nm) and Sample	Peak Reading at Specific wavelength (nm)		Results with inference (describing difference in UV VIS spectra between the two samples taken)
	For Synthetic Red Alizarin	For Natural Rubia/Madder colorant
250 nm and 426 nm for synthetic alizarin	250 nm (1.38 OD) and 426 nm (0.309 OD)	—	The pattern of the peaks in UV and Visible region are very different for the two samples indicating and confirming their presence/absence in corresponding samples.; (natural Rubia/Madder colourant and synthetic alizarin)
250 nm and at 491 nm for rubia/madder as natural colourant	—	250 nm (0.954 OD) and 491 nm (0.171 OD)

Table 1.

UV VIS spectral peaks analysis of natural Rubia colorant and synthetic alizarin.

[Source-IS standard- 17,085: 2019 [9]].

Individual UV VIS absorbance Spectrum at visible region only at 390–700 nm, when is partly enlarged for 390–450 nm, it is also observed that the UV–Vis absorbance spectrum of aqueous solution of natural Rubia/Madder extract (extract of Indian Madder i.e., natural manjishthin) also shows small hump like peaks at 398 nm (with 0.801 OD) and also indicating large hump like peak at also 426 nm (with 0.838 OD), which are vivid from Figure 3. Therefore, the appearance of the above said two respective peaks in the said wavelength region lead to indicate the presence of natural Rubia/Madder with manjisthin (not synthetic alizarin), which is more clearly understandable in the enlarged peak of highlighted part of UV–VIS Spectrum (Figure 3) of extracted solution of Rubia-cordifolia (used as Natural dye) dyed cotton textiles. Thus, even if Rubia/Madder shows peak at 426−430 nm showing λmax at around 426 nm (with 0.838 OD) i.e., at the same wavelength where synthetic alizarin has also shown its peak at 426 nm (with 0.309 OD), but OD values are different and thus these two red dyes are easily distinguishable by this method.

Figure 3.

Part of enlarged UV-Vis Spectrum of Natural Rubia/Madder colorant (containing manjisthin).

3.2.1 Confirmation of identification of natural RUBIA/madder as compared to synthetic alizarin from UV: VIS spectral scan analysis

Optical density/absorbance at λmax for extract of natural Rubia/Madder colourant and synthetic alizarin dyes are thus found to be quite different from UV VIS Spectral analysis. In the UV–VIS spectrum, although the peaks are at 250 nm, they have shown different optical densities/absorbance values (Figure 2 and Table 1). In the visible region, peaks at 426 nm for alizarin and peaks at 398 nm (0.801) and 426 nm (0.838) for Natural Rubia/madder dye-containing manjishthin (a natural coloured compound similar to alizarin, but bio synthesised as natural colorant in Madder/Rubia plant in association with other natural ingredients) are the characteristic peaks of differentiating alizarin and manjisthin (from natural rubia/madder). There are other different methods available for identification of natural Madder/Rubia colourant by either HPLC-DAD analysis or LC–Ms/UPLC-MS analysis or also by FTIR analysis and NMR analysis, some of which are detailed in IS standards-17,085:2019 [9] and International ISO Standard: ISO/Standards-22,195-1-2019 [10] published in recent past in 2019.

3.3 Colour quantification and measurement of surface colour strength (K/S values) of any dyed textiles using UV–VIS-reflectance spectrophotometer

Colour quantification in mathematical term is necessary to develop a systematic understanding of the principles of colour perception and measurement for understanding the differences between colours of two samples i.e., match and mismatch for any method of colour encoding/imaging and communications, to give a more realistic picture for colour reproduction. Hence, TRISTIMULUS VALUES (X, Y, Z) are defined as three coordinates to define any colour for communications, where X, Y and Z values are as follows:

Thus, Tristimulus values X, Y, Z can be calculated from measured total reflectance of a textile or similar flat surface with its derivative formula function as shown below [2–3, 6–8]:

$$\mathrm{X}=\sum {\mathrm{P}}_{\mathrm{\lambda }}{\mathrm{x}}_{\mathrm{\lambda }}{\mathrm{R}}_{\mathrm{\lambda }}$$E1

$$\mathrm{Y}=\sum {\mathrm{P}}_{\mathrm{\lambda }}{\mathrm{y}}_{\mathrm{\lambda }}{\mathrm{R}}_{\mathrm{\lambda }}$$E2

$$\mathrm{Z}=\sum {\mathrm{P}}_{\mathrm{\lambda }}{\mathrm{z}}_{\mathrm{\lambda }}{\mathrm{R}}_{\mathrm{\lambda }}$$E3

where P_λ=Spectral power distribution of standard source, R_{λ =} Spectral reflectance of substrate and x_λ. y_λ. z_λ=colour coordinates/factor of standard observer for red, blue and green.

For ease of working, colours are redefined from TRISTIMULUS values to CIE Chromaticity coordinates (x, y and z instead of Capital X, Y, Z as tristimulus values), which can be plotted in two-dimensional plot. These new CIE chromatically coordinates (x, y, z) can be defined as follows.

$$\mathrm{x}=\frac{\mathrm{X}}{\mathrm{X}+\mathrm{Y}+\mathrm{Z}}$$E4

$$\mathrm{y}=\frac{\mathrm{Y}}{\mathrm{X}+\mathrm{Y}+\mathrm{Z}}$$E5

$$\mathrm{z}=\frac{\mathrm{Z}}{\mathrm{X}+\mathrm{Y}+\mathrm{Z}}$$E6

and

$$\mathrm{x}+\mathrm{y}+\mathrm{z}=1$$E7

From Eq. (22), i.e., x + y + z = 1, the value of anyone CIE chromaticity coordinate can be determined from the values of other two CIE chromaticity coordinates, i.e., the third one can be determined easily from first two.

Still, as Plot of Dye Concentrations Vs Reflectance (R) are non-linear and non-additive, Tristimulus values X, Y, and Z are interdependent on one another, and CIE chromaticity coordinates are still two factors dependent variables to get third one. HUE, value chroma are also 3 coordinates based, it is difficult in practice to control all those multivariate/factors/colour parameters simultaneously to get a precision match of colour.

So, quantification of colour was finally made by Kubelka and Munk [2, 3, 6, 7, 8], where K/S value (surface colour strength) is defined as follows:

$$\text{Surface colour strength}\left(\frac{\mathrm{K}}{\mathrm{S}}\right)=\frac{\mathrm{Co}–\text{efficient of absorption}}{\mathrm{Co}–\text{efficient of scattering}}=\frac{{\left(1-{\mathrm{R}}_{\text{λmax}}\right)}^2}{2{\mathrm{R}}_{\text{λmax}}}=\mathrm{\alpha }{\mathrm{C}}_{\mathrm{D}}$$E8

where K is the coefficient of absorption; S, the coefficient of scattering; and R_ʎmax, is the Reflectance value at maximum absorbance wavelength (λmax) and C_D is the dye concentration and α is the constant. Moreover, K/S Vs Dye concentration plots are linear, and K/S is additive in nature.

For Additive nature of K/S value, for use of mixture of colourants/dyes at different concentrations c1, c2 and c3 respectively for dye1, dye2 and dye3 K/S values of resultant fabric may be written as:

$${\left(\mathrm{K}/\mathrm{S}\right)}_{\mathrm{MAX}}={\left(\mathrm{K}/\mathrm{S}\right)}_{\text{subs}}+{\left(\mathrm{K}/\mathrm{S}\right)}_1+{\left(\mathrm{K}/\mathrm{S}\right)}_2+{\left(\mathrm{K}/\mathrm{S}\right)}_3+\cdots +$$E9

$$={\left(\mathrm{K}/\mathrm{S}\right)}_{\text{subs}}+{\mathrm{\lambda }}_1{\mathrm{C}}_1+{\mathrm{\lambda }}_2{\mathrm{C}}_2+{\mathrm{\lambda }}_3{\mathrm{C}}_3$$E10

Thus, handling of K/S values become much easy to match colour, as because K/S is treated as a single variable i.e., it operates on a single constant theory (scattering remaining constant for same fabric and dye sample) and K/S is directly proportional to dye concentration in linear and additive relationship.

For dyed textiles/clothes, it is pre-assumed that dyes on specific textile fabric do not add or substract, i.e., change scattering and K is the sum of absorption of dye stuff on dyed textiles and therefore, it is only dye absorption values of dyed textile substrate (if textile substrate remained unaltered/fixed). So, it may be considered that for dyed textiles, K/S directly varies with concentration of dyes linearly and scattering of dyed textile substrate is independent of dye concentration (which is not the case for pigments in paints for wall colours). So, in textile it is single constant theory of colourmatch prediction through K/S values, as most widely applicable colour parameter for colour quantification, measurement and colour matching of textiles. So, for the particular dyed textile sample (with same fibre material, yarn parameter and fabric construction/surface finish remain unaltered) scattering value is assumed to be constant.

Thus, higher is the K/S value, meant higher is the dye absorption in textiles, meant higher absorption value of dye thus signifying or indicating higher dye uptake, but this measurement is surface colour strength, not bulk dye uptake, which can only be determined by extraction of colour from dyed textile samples and then analysis of optical density or absorbance values in absorption spectrophotometric analysis of coloured liquid.

Dye Uniformity in terms of CV % of K/s values at minimum 10 different points may be expressed for deciding factor for level/unlevel dyeing. CV % of K/S values within 5% value is considered as acceptable for level dyeing and more than 5% values (CV % of K/S values) is considered as un-level dyeing leading to rejection of the sample.

3.4 Measurement of colour differences by estimating DE, DL*, Da*, Db*, DC and DH

Colour attributes of a human perception consisting of any combination of chromatic and achromatic content in terms of differences in combination of red, blue and green sensation of human eye (as shown in Figure 4) alters change in predominating hue which can be described by chromatic hue names such as yellow, orange, brown, red, pink, green, blue, purple, etc., or by achromatic colour names such as white, grey, black, etc., and is associated with some other attributes like bright, light, dark etc., hence colour differences in between two samples arises by value of these attributes of human perception or instrumental measurements. Measurement of colour differences is important for judging two nearer coloured samples as match with degree of matching or mismatch. It is Judged by differences in light and dark (∆L*), Redness or Greenness (∆a*) and Blueness or yellowness (∆b^*) as CIELab* colour difference coordinates in CIE colour difference space diagram to determine the total colour difference values (in terms of ∆E*) from respective CIE-Lab equations following CIELab* standard-1976, which are measurable in UV VIS Reflectance Spectrophotometer and Associated software attached to computer aided colour measurement and matching system.

Figure 4.

Red-Blue-Green perception of colour.

Thus, according to CIE (Commission International de eclairase, Paris) 1976, total colour difference values (in terms of DE* or ∆E*) as obtained from individual DL* or ∆L^* (Light or dark), Da* or ∆a* (Redness or greenness), and Db* or ∆b^* (Blueness and yellowness) values makes it easy to compare the colour difference values in between two nearer match samples (standards and produced) and this gives a degree of matching according to tolerances set for these attributes of colour as well as gives opportunity to correct shade by adding exactly required colour/dyes to improve less red, less green, less yellow or less blue sample to solve its light and dark by adding white or black as well during dyeing production.

The above said terms DE* or ∆E* represent total colour difference, DL* or ∆L^* by 0–100 scale representing lightness and darkness, Da* or ∆a*, if positive represents redness and if negative represent greenness and Db* or ∆b^*, if positive represents yellowness and if negative represent blueness by their positive and negative values respectively, as shown in Eqs. 5 to 8 and pictorially is shown in Figure 5.

Figure 5.

CIE L*a*b* colour difference space diagram. By human eye (wavelength vs. intensity).

The above said CIE colour differences equations are depicted below for ease of understanding:

$$∆E={\left[{\left(∆L^{\ast }\right)}^2+{\left(∆a^{\ast }\right)}^2+{\left(∆{\mathit{Lb}}^{\ast }\right)}^2\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$E11

where,

$${\mathrm{L}}^{\ast }=116{\left(\mathrm{Y}/{\mathrm{Y}}_{\mathrm{a}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}-16$$E12

$$∆{\mathrm{L}}^{\ast }={\mathrm{L}}_1^{\ast }-{\mathrm{L}}_2^{\ast }$$E13

$${\mathrm{a}}^{\ast }=500[{\left(\mathrm{X}/{\mathrm{X}}_{\mathrm{a}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}-{\left(\mathrm{Y}/{\mathrm{Y}}_{\mathrm{a}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$$E14

$$∆{\mathrm{a}}^{\ast }={\mathrm{a}}_1^{\ast }-{\mathrm{a}}_2^{\ast }$$E15

$${\mathrm{b}}^{\ast }=200[{\left(\mathrm{Y}/{\mathrm{Y}}_{\mathrm{a}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}-{\left(\mathrm{Z}/{\mathrm{Z}}_{\mathrm{a}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$$E16

$$∆{\mathrm{b}}^{\ast }={\mathrm{b}}_1^{\ast }-{\mathrm{b}}_2^{\ast }$$E17

Chroma, (psychometric chroma) values in CIELAB colour space can be calculated as follows:

$${\mathrm{C}}_{\left(\mathrm{ab}\right)}^{\ast }={\left({\mathrm{a}}^{\ast 2}+{\mathrm{b}}^{\ast 2}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$E18

$$∆{\mathrm{C}}^{\ast }={\mathrm{C}}_{1\left(\mathrm{ab}\right)}^{\ast }-{\mathrm{C}}_{2\left(\mathrm{ab}\right)}^{\ast }$$E19

where, ${\mathrm{C}}_{1\left(\mathrm{ab}\right)}^{\ast }$ and ${\mathrm{C}}_{2\left(\mathrm{ab}\right)}^{\ast }$ are the chroma values for standard and produced sample.

CIE 1976 metric Hue-Difference (ΔH) for CIELAB system can be calculated as follows:

$$∆{\mathrm{H}}_{\mathrm{ab}}={\left[{\left(∆{\mathrm{E}}_{\mathrm{ab}}^{\ast }\right)}^2-{\left(∆{\mathrm{L}}^{\ast }\right)}^2-{\left({\mathrm{C}}_{\mathrm{ab}}^{\ast }\right)}^2\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$E20

Moreover, Brightness is another additional colour attribute associated with perception of colour differences. This attribute of visual sensation of colour gives an additional visual perception that appears to be more or less intense or luminescence i.e., this visual stimulus appears to emit more or less light from specific hue of colour and differs from one another.

Brightness Index (BI) as per ISO-2469/2470–1977 method [11] can be calculated by following ISO formula for this:

$$\text{Brightness Index}=\begin{array}{l}\frac{\text{Reflectance Value of the Sample}\mathrm{at}457\mathrm{nm}}{\mathrm{\text{Reflectance Value of the Standard white diffuser(white tiles)}}\mathrm{at}457\mathrm{nm}}\\ \times 100\end{array}$$E21

Application of fluorescent brightening agents to white textiles show an additional higher reflectance value more than 100 and up to 150. Though the sample appears to be still whiter as usual, there is emitting of more reflectance of incident light in the bluer zone and the appearance thus changes its chroma towards blue increasing its more whiteness and brightness, where brightness value may be represented or expressed in quantitative term by ISO standard method. Conversely, yellowing of white textiles by chemical treatment or by heat scorching or by any type of degradation by exposure to light or by gas fading etc. can blur the brightness value of the white or dyed sample. Thus, along with colour differences like DE, DL, Da, Db, this Brightness index (BI) as another additional colour attributes related to surface appearance properties of textiles have immense important role and simply high or low BI values an important colour surface appearance parameter too in defining the colour quality of any textile fabric.

A recent newer concept of defining colour differences by Colour Difference Index (CDI) values as a measure of dispersion of colour values at different points from all angle of instrumental measured variation, depending on dyeing process variables, to understand the combined effects of different dyeing process variables by a single parameter, is defined [12] taking only the magnitudes of the respective ΔE, ΔC, ΔH and MI values (irrespective of their sign and direction), to calculate CDI values using the following empirical formula (Eq. 22).

$$\text{Colour Difference Index}\left(\mathrm{CDI}\right)=\frac{∆E\mathrm{X}∆H}{∆C\mathrm{X}\mathrm{MI}}$$E22

Higher the differences in between maximum and minimum CDI values, higher is the dispersion of colour values at different points i.e., colour values are more widely dispersed, and that variable become critical for reproducibility for such dyeing. So, lower the differences in between maximum and minimum CDI value in one set of dyeing for particular dyeing process variables or use of mixture of same set of binary mixture of dyes, better is the match with lower dye dispersion in such cases of colour match CDI value below 5 is acceptable and good and below 1.0 is considered as excellent.

CASE STUDY 3:

The above shown data in Table 2 on colour parameters, obtained in a study on use of different mordant concentration yields different surface colour strength(K/S) showing reasonable differences of Colour values in terms of ∆E, ∆L, ∆a, ∆b, ∆C, ∆H, MI (LABD) and CDI values indicating the inter-dependence of colour strength and other colour interaction parameters of tesu dyed silk fabric, clearly showing the role of increasing mordant concentrations up to 15% for higher K/S values, with maximum ∆E, and medium CDI, while increase of Mordant concentration beyond 15–25%, gradually reduces colour strength but increases colour dispersion with lowering of CDI.

Mordant Concn. (%)	K/S At λmax	∆L	∆a	∆b	∆C	∆H	∆E	MI (LABD)	CDI
5	2.24	−12.52	3.77	8.25	8.95	−1.49	23.35	1.19	3.26
10	2.65	−15.61	4.29	8.24	9.07	−2.00	22.87	1.34	3.75
15	3.89	−20.90	4.73	7.53	8.56	−2.42	17.97	2.11	2.41
20	3.15	−16.51	4.84	12.09	12.92	−1.64	18.06	1.69	1.35
25	2.45	−12.90	4.53	10.81	11.60	−1.68	20.57	1.54	1.94

Table 2.

Effect of Mordant concentration on Colour Strength and Colour Differences for dyeing silk fabric with tesu (containing butein) extract as natural colourant.

3.5 Computer aided colour match prediction of textiles and others by using UV: VIS reflectance spectrophotometer and colour measuring/matching software for producing any standard shades

Colour matching of two samples are considered as fully satisfactory, if any one of the following 3 conditions are achieved with plus-minus mutually accepted tolerances values of their colour differences in CIELab attributes as follows:

Thus, to become colour of produced sample = colour of given standard sample, following should be the conditions be satisfied - i.e., below given conditions (1)–(3).

1. (X_SL, Y_SL, Z_SL) values of produced sample = (X_SD, Y_SD, Z_SD) values of given standard sample where X, Y & Z are the tristimulus value of Sample (SL) and Standard (SD)

2. (Reflectance)_SL value at 400 to 700 nm of produced sample = (Reflectance)_SD value at 400 to 700 nm of given standard sample

3. (K/S) _SL value of produced Sample = (K/S) _SD value of given standard sample, where K/S = α C.

3rd Conditions are easy to check and achieve, as it is additive in nature and Dye Concentration vs. K/s values plot are linear and is predictable from sample database by computerised algorithm.

For computer aided colour matching theory [2, 6, 7, 8], for a shade from mixture of multiple colourants (say 3 colourants), following three equations are to be solved as a function of dye concentrations of the colourants (1, 2,3 or n) and to be checked by measuring tristimulus values or reflectance values or K/s values with measurement of DE*, DL*, Da* and Db* values under different standard illuminants.

$$\begin{array}{c}\mathrm{f}\left({\mathrm{c}}_1,{\mathrm{c}}_2,{\mathrm{c}}_3\right)=\mathrm{x}\\ \mathrm{f}\left({\mathrm{c}}_1,{\mathrm{c}}_2,{\mathrm{c}}_3\right)=\mathrm{y}\\ \mathrm{f}\left({\mathrm{c}}_1,{\mathrm{c}}_2,{\mathrm{c}}_3\right)=\mathrm{z}\end{array}$$

where x, y, z tristimulus values of standard given sample are to be matched with the matched dyed textile sample to be produced, by using say 3 different dyes with respective concentrations of those 3 selective dyes indicated by c₁, c₂ and c₃. For determining/predicting these selective concentrations of specific dyes to get a specific match of colour, In practice, the reflectance values of standard sample at 400 to 700 nm are initially measured from standard dyed textile substrate and those reflectance data are processed through computer aided software to generate matched K/S Values, within tolerance set for specific L, a and b colour difference parameters and DE total colour difference parameter to match for the predicted/produced sample. As K/S values vs. concentration of dyes is linear & additive, so this is used as basic data for handling colour match prediction by computer aided colour measuring cum matching instrument from different companies with application software in built in the system.

Colour matching is always associated with Some practicable values of DE*, DL*, Da* and Db* values, within acceptable tolerances, but is also associated another factor/term called metamerism index (MI), due to measurement of colour values under different conditions of measuring colour values i.e. within varying illuminates or varying observers or varying instruments etc. [2, 6, 7, 8].

Thus, only colour difference values do not represent true differences of perceived colour in human eye due to observer’s metamerism or even instrumental metamerism or illuminate metamerism etc. An ideal or perfect colour match is called isomeric match i.e., which are always match under all illuminates or under all observers or under all instruments in all the ranges of wavelength values in visible region and then that ideal match is called true isomeric match. While Most of the given standard of colour and produced samples are not at all show isomeric match, there is always some differences in their colour difference results at different wavelength range or otherwise i.e. when two coloured sample (standard and produced sample for colour matching) show match under one illuminant/one observer or one instrument but do not match under any other illuminant/other observer or other instrument at different wave length values is termed as a metameric match. So, it is a challenge to produce a Least metameric match instead of ideal isomeric match. A general metamerism index (MI) value can be calculated using Eq. 23, as follows:

$$\text{General metamerism Index}=\frac{\sum {\left(∆\mathrm{R}\overline{x}\right)}^2}{{\mathrm{X}}^2}+\frac{\sum {\left(∆\mathrm{R}\overline{y}\right)}^2}{{\mathrm{Y}}^2}+\frac{\sum {\left(∆\mathrm{R}\overline{z}\right)}^2}{{\mathrm{Z}}^2},$$E23

where ∆R = Difference in reflectance between pair of metamer samples; $\overline{x}$, $\overline{y}$, $\overline{z}$ = CIE standard observer colour function X, Y, Z = CIE tristimulus value normally taken for illuminate C. It is average value of colour differences of two specimens under two different measuring conditions.

The Metamerism-Index (MI) indicate the probability of any two near match or matched two samples when show the different colour difference values under changed conditions of measurements like if measured under two different illuminants (represented by the first and second illuminant) or under two different make reflectance spectrophotometer instruments or under any other two different conditions of measuring colour parameters of the said two specific samples by calculating. CIE LAB i.e., LABD metamerism index [2, 6, 7, 8], which is represented below in Eq. 24:

$${\mathrm{MI}}_{\left(\text{LABD}\right)}=[{\left(∆L_1^{\ast }-∆L_2^{\ast }\right)}^2+(∆a_1^{\ast }-{\left(∆a_2^{\ast }\right)}^2+(∆b_1^{\ast }-{\left(∆b_2^{\ast }\right)}^2]{}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$E24

∆L₁*, ∆a₁*, and ∆b₁*are the Delta CIELab* colour coordinates between standard and sample for the first illuminate and ∆L₂*, ∆a₂*, and ∆b₂* are the Delta CIELab* colour coordinates between standard and sample for the second illuminate interpretation:

If MI is low, the colour difference between the sample pair is the closer and more similar for different conditions of measurement, even under different illuminates or observers or instruments. So, matching of two-coloured samples produced at comparable conditions are to always to minimize to obtain least metameric match for control of colour by using computer aided colour measuring and matching system [7, 13].

CASE STUDY 4: Computer aided colour match prediction for dyeing of textiles: as an Example

Practical Guideline for Colour Match prediction: it is necessary to prepare Company wise Dye Class type and Sample type (Substrate fibre type) database by calibration dyeing [7, 14, 15] of 0.25, 0.50, 0.75, 1.00, 1,25, 1.50, 1.75. and 2, 2.5, 3 percent dyed sample of specific fabric (based on type of fibre) i.e., say- bleached cotton fabric and their reflectance or X, Y and Z Data are to be measured and to be saved as library of database for use for formulation prediction of dye weight % required for colour matching from time to time for given standard sample.

Colour matching tolerances against Standard daylight D65 illuminate, Artificial Tube light -TL84 (A) and fluorescent light (F) are to be set as maximum 1.00 for each light or to be mutually fixed between buyers and sellers in order agreement. If dye cost from lot to lot regular purchase is updated in this system, cost of dyes for different formulations are also calculated and available at fingertips, other dyeing process and utility cost remaining same. Not only it helps to reduce dye inventory and it saves matching time for lab to production trial time with reasonable known combination of dyes and cost involved along with average predicted dE*, dL*, da*, db* values to know the degree of precision of colour matching, below is the example of one colour match prediction formulation using computer aided colour matching system with database for different class of textile dyes already fed in (the present example is colour matching formulation of cotton fabric with reactive dyes database, as given in Table 3.

	Standard Id = Coloured Cotton Fabric-C 12
	RFl; DATA; For Std.	3.65	3.90	4.46	5.87	7.44	8.77	9.32	10.61	11.56	12.71
		12.33	11.14	10.33	9.34	8.10	7.82	6.98	6.53	5.39	4.34
	Dye class used		= Reactive Dye database for white cotton
	Dye ID# used		1,3,4, 6, 7,9,10, 11and 12 from data base
	Substrate ID#		3, Enzyme pre-treated Bleached Cotton
	TOLERENCES		dE* for D65 Light = 1.00						dE* for Artificial Light = 1.00
			dE* for Fluorescent Light = 1.00
	ID# Colorant			Amount	Per cent			da*	db*	dL*	dE*	Rs
	Matching Formulation Generated by computer Aided Color Matching System
	Formula#1
	3	R Red M3B		0.15	0.15		D	−0.0	−0.0	0.0	0.0	56.51
	6	R Brown 5R		0.68	0.68		A	−0.42	0.2	0.10	0.23	227.73
	10	R Procian Blue 2R		1.41	1.41		F	−0.62	0.4	0.33	0.66	495.00
				2.14	2.14							778.24
	Formula # 2
	3	R Red M 6B		0.13	0.13		D	−0.0	−0.0	0.1	0.01′	48.53
	11	R Grey 2R		0.54	0.54		A	−0.52	0.3	0.0	0.36	188.26
	10	R Procian Blue 2R		1.28	1.28		F	−0.71	0.5	0.11	0.78	449.36
				1.95	1.95							686.15

Table 3.

Example of a colour match predicted from the database of direct dye for cotton.

Dye combination	CDI			Difference in CDI max & CDI min	RCR*	Compatibility grade
	75:25a	50:50a	25:75a
M11(D Red: D Green)	0.131	0.589	0.039	0.550	2–3	Fair
M12(D Red: D Yellow)	0.149	0.089	0.036	0.113	4	Good
M13(D Red: D T. Blue)	0.037	0.408	0.056	0.371	3	Average

Table 4.

Colour Difference Index (CDI) and Relative Compatibility Rating (RCR) for application of selected binary pairs of synthetic dyes of jute fabric.

^*

Based on chart values of differences in max and Min. CDI values [12, 19].

^a

Proportion of dyes.

Thus, the above predicted 2 formulations indicate that formaulation#1 is less metameric as understood from comparison of their dE*, dL*, da*, db* values, and cost wise Formulation#2 is least cost match,

3.6 Estimation of compatibility between two colorants to use for compound binary shades

Compatibility between any two same class of dyes can be judged by different methods, such as (i) comparative subjective visual assessment of the degree of on-tone build up by carrying out a series of dyeing for both dyes to same substrate and checking gradual colour build up by visual assessment, (ii) theoretical prediction of compatibility [16] by comparison of rates of dye by rate of diffusion of dyes by determining diffusion coefficients or by determining time of half dyeing for each individual dye at comparable dyeing conditions (iii) by quantitative assessment of change in hue angle(∆H) for increasing dyeing time and temperature or increasing dye concentrations [16] under two sets of dyeing for colour built up on specific textile substrate (iv) by comparing the nature of plots of ∆C vs. ∆L or K/S vs. ∆L values for two sets of progressive built up shades as said in point -no (iii) obtained by dyeing with varying dye concentration and also with varing dyeing time and temperature as said in point no-3 using 50:50 of two dyes [17] and (v) quantitative compatibility rating for the mixtures of more than two dyes by colorimetric analysis of actual colour strength developed (not on the basis of dye absorbed) for mixture dyeing in different proportions following Relative compatibility rating (RCR) method [12] by calculating differences of CDI (Colour difference Index) values [17, 18] as a newer empirical index of overall colour differences for dyeing different proportions of two dyes of different pairs of synthetic or natural dyes applied on any textiles.

CASE STUDY 5: Comparison of compatibility of two dyes by comparing the nature of plots of ∆C vs. ∆L or K/S vs. ∆L values for two sets of progressive built up shades by dyeing with variation of dye concentrations (SET-1) and dyeing with variation of Time and temperature (SET-2) using 50:50 of two dyes as well as also Determining compatibility of 2 dyes by Relative compatibility rating (RCR) method by calculating differences of CDI values for dyeing different proportions of any two dyes.

Dyes Selected are: Direct dyestuffs (make: Atul Ltd. (Tuladir)) of four different colours, i.e., Direct Turquoise blue (CI Direct Blue 199), Direct Red (CI Direct Red 31), Direct Yellow (CI Direct yellow 44), Direct Green (CI Direct Green 513).

Dyeing carried out for Conventional methods of determining compatibility, for obtaining plots of ∆C vs. ∆L or K/S vs. ∆L values for two sets of progressive built up shades following selected binary pairs (50:50) of synthetic direct dyes were applied on the 6% H₂O₂ (50%) bleached Jute fine hessian fabric using three pair of following combination of binary pair of direct dyes such as M-11 -Direct Red + Direct Green, b) M-12-Direct Red + Direct Yellow and c) M-13-Direct Red + Direct T. Blue taken in 50:50 ratio in two sets.

In Set I, the progressive depth of colour was gradually built up by varying dyeing time and temperature profile for each pair of dyes (M11, M-12 and M13), three jute fabric samples were dyed laboratory beaker dyeing machine with temperature controller for 10–60 min varying dyeing time period. The said dyed fabric samples were one by one taken out from the respective dye bath at equal interval of 10 min from dyeing temperature of 60°C onwards up to 100°C, maintaining the constant heating rate of 2–5°C/min. The final and ultimate dyed sample was taken out from dye bath after 60 min dyeing time at 100°C dyeing temperature.

In Set II, the progressive depth of shade was obtained by varying total concentration of dye mixture in 50:50 ratio but varying percent application from 20–100% of 1% shade for each pair of dyes, for 3 separate samples of jute fabrics, which were dyed at the at the increments of 20% points of dye concentration at pre-fixed dyeing conditions at 100°C for 60 min. Taking two dyes in equal proportions (50:50).

The colour difference values in terms of ∆E* and ∆L*, ∆a*, ∆b* and ∆C* for all the above said dyed fabrics using Set I and Set II conditions, against undyed fabric sample as standard for reference, were obtained by individually separate measurement of the colour difference parameters Using UV–VIS reflectance spectrophotometer within built software and computer attached. The compatibility of a selected pair of dyes was judged [16, 17, 18, 19] from the degree of closeness and overlapping of two curves ∆C vs. ∆L or K/S vs. ∆L observed using the two sets of dyeing (Set I and Set II) as shown in Figure 6.

Figure 6.

Plots showing K/S Vs ∆L curves of (a) M11-D Red: D Green (b)M-12 -D Red: D yellow and (c)M-!3 -D Red: D T. Blue for two sets of each showing M-12 -D Red: D yellow combination has good compatibility, while M11-D Red: D Green combination ahs not so good compatibility or has fair compatibility and M-!3 -D Red: D T. Blue has more or less average compatibility at higher time (Table 4).

For Relative Compatibility Rating Newer method of Determining Compatibility of two dyes, 6% H₂O₂ (50%) bleached jute fabric samples were dyed with four direct dyes taken from Atul direct dye of either single or selected binary pairs of direct dyes in varying proportions (100:0, 75:25,50:50,25:75 and 0:100) under specific fixed and comparable dyeing conditions. The results are shown in Table 4.

Thus, both of these methods show a similar results, while the method −2 of RCR compatibility rating method is easier and less time consuming and hence has advantages over plotting of K/S Vs DL.

3.7 Optimization of dyeing process variables for dyeing textiles with any synthetic or natural dyes

Dyeing of any textiles, say cotton or jute or any other fibres to be dyed with specific class of synthetic dyes like reactive dye (or even for any natural dyes) need to be optimised [14, 15] to derive standard dyeing conditions to obtain maximum surface colour strength (K/S values).

So, it need to have experiments on varying dyeing time, temperature, dye concentration, salt concentrations, MLR and pH etc., so that reproduced and uniform dyeing can be achieved easily.

However, for reactive dyes, Dyeing time has two type -Dye exhaustion time and Dyeing fixation time and similarly dyeing temperature has two dimensions, i.e., Dye exhaustion temperature and Dye Fixation temperature and also for last stage of alkali fixation of reactive dye, addition of soda ash is to be considered, also, besides addition of salt for exhaustion as evident from earlier references [20].

UV VIS reflectance spectrophotometer thus helps by colorimetric analysis of Surface colour strength and other colour parameters, for dyeing of any fibre with specific class of dye by varying conditions of dyeing.

|CASE STUDY 6: Optimization of dyeing process variables for jute dyeing with reactive dyes.

Fabric used: 3% H₂O₂ bleached fine hessian jute fabric having 215 tex jute yarns as warp and 285 tex jute yarns as weft, 64 ends/dm and 58 picks/dm, fabric area density 320 g/m² and fabric thickness 0.70 mm, obtained from M/s Gloster Jute Mills Ltd., Bauria, Howrah, was used.

Dyes Selected: (i) Hot brand Reactive Green HE4BD (CI Reactive Green 19), (ii) Hot brand Reactive Orange CN (C.I. Reactive Orange 84) and (iii) Cold brand Magenta (C.I. Reactive Red 11) were used.

Measurement of Colour Parameter: K/S values of differently dyed jute fabrics under varying conditions of dyeing were determined by using computer-aided UV VIS Reflectance spectrophotometer [Premier Colour Scan Instrument Ltd. Mumbai Make Model SC 5100A] along with associated Colour-Lab plus software employing Kubelka Munk [2, 6, 7, 8] equation and CIE-Lab equations against a particular undyed (bleached) sample set as standard followed by calculating the K/S values with the help of relevant software.

The relevant color parameters measured for each sample of varying dyeing conditions are detailed in Table 5 and plots of each dyeing process variables vs. K/S values are shown in Figure 7 for 3 selected reactive dyes applied on jute under varying conditions of dyeing, to optimize dyeing conditions of each dye.

Name of variable parameter of dyeing	Parameter varied unit	K/S (Orange CN)	K/S(Green HE4BD)	K/S(Magenta Cold)
Dye concentration (%)	1	7.44	11.9	2.43
	2	7.69	14.98	3.6
	3	9.57	15.31	5.05
	4	9.87	15.70	7.51
	5	9.13	15.53	7.12
Salt (g/L)	30	9.25	8.35	3.08
	40	9.68	11.37	4.26
	50	9.73	11.97	3.55
	60	9.82	10.52	3.89
	70	7.68	11.34	3.67
	80	7.89	12.17	3.97
Dye exhaustion time (Min.)	30	6.69	5.76	2.46
	40	7.07	5.46	2.69
	50	9.46	7.00	3.10
	60	6.33	7.43	3.49
	70	8.00	8.44	2.99
	80	7.79	9.44	3.17
Dye exhaustion temp (°C)	60	6.20	7.35	—
	70	7.65	8.37	—
	80	8.77	7.03	—
	90	6.81	6.35	—
	100	5.38	5.97	—
Soda Ash(gpl)	10	7.04	2.53	3.34
	12	7.27	3.66	4.65
	15	7.82	4.09	4.42
	18	8.43	5.69	3.94
	20	8.16	5.84	3.66
pH	8	6.39	4.41	3.05
	9	6.42	4.96	3.22
	10	6.78	5.12	3.29
	11	6.95	5.75	3.38
	12	7.25	6.01	2.87
MLR	1:10	10.78	6.30	3.42
	1:20	11.71	8.35	4.05
	1:30	10.63	4.17	3.69
	1:40	9.68	3.38	3.09
	1:50	9.35	3.24	2.41

Table 5.

Surface colour strength (K/S) data showing the effects of dyeing process variables on colour yield of different reactive dyed jute fabric.

Plots of dyeing process variables Vs K/S values for three reactive dyed jute fabric dyed with varying dyeing conditions as per Table 5.

Figure 7.

Plots (a-i) showing dyeing process variables vs. K/S curves for three reactive dyes-for varying. (a) Dye concentration; (b) Salt concentration; (c) Dye Exhaustion Time (Min); (d) Dye Exhaustion Temp (^oc); (e) Soda Ash (gpl); (f) Dye fixing time (Min); (g) Dye fixing Temp (^oc); (h) pH; and (i)MLR.

Finally, data in Table 6 indicate the relevant optimised dyeing parameters for each reactive dyes studied and reported here as optimised dyeing conditions for those respective dyes applied on Jute fabric by conventional reactive dyeing method.

Name of Dye; Process Parameters	Re Orange CN	Re Green HE4BD	Re Magenta Cold
Dye Concentration (%)	4	4	4
Salt Conc (gpl)	60	60	40
Dye Exhaustion Time(Min)	50	50	40
Dye Exhaustion Temp(^0C)	80	70	-
Soda Ash(gpl)	18	18	12
Dye Fixing Time(Min)	45	55	45
Dye Fixing Temp(^0C)	80	70	-
pH	12	12	11
MLR	1:20	1:20	1:20

Table 6.

Optimised conditions of dyeing process variables by conventional method of reactive dyeing of jute fabric using three selected reactive dyes.

3.8 Precession grading of colour fastness of dyed textiles by colorimetric measurement of total colour difference (dE*) values after fading/staining in colour fastness test procedure

In color fastness test for washing, rubbing or crocking or perspiration, or gas fading or any other agencies, the assessment is done two ways—(i) assessing change of colour/loss of depth of shade and (ii) assessing staining on a same or multifiber white fabric after colour fastness test s by fading under different agencies/conditions as per standard test method and followed by assessing colour loss or staining amount by comparing with two types of grey scale as said. But this assessment is sometimes misleading to one grade upper or lower and is debatable unless quantitative measurement of amount of colour change or amount of staining occur is done and checked not fully depending on visual assessment with the said two types of grey scale.

Colour changing grey scale card consists of colour fastness rating for the colour change with a corresponding decreasing scale of grey chroma, which is standardised in 5-grade levels or nine grades system including half grades, where grade 5 representing the best Colour Fastness and grade 1 representing the worst colour fastness. The middle levels are assessed as half grade: like grade 4−5 and grade 3−4 and then it consists of nine levels.

Similarly, stained grey scale card consists of standard scale of white with a corresponding group of increasing grey chroma having standardised mainly by five grades (1–5), or nine grades system including half grades, where grade 5 implies virtually no staining representing best colour fastness while grade 1 signifies the worst colour fastness, and the middle grade are assessed as half grade, like grade 4–5 and grade 3–4. But these grey scale grading is comparative visual assessment of grades and may not always be true.

Hence later, as per ISO-105-A02—1993 Textiles- Test for Color fastness test -part -A02, Grey scale for assessing change in color and ISO-105-A03–2019 - Textiles- Test for Color fastness test- part-A03, Grey scale for assessing staining, the quantitative data for dE* values for both types of grey scale are shown in Table 7 with given tolerances. So precision and correct color fastness grading is now possible matching with the values of measured DE* values after fading/staining on each type of colour fastness tests under different agencies instead of using visual comparative assessment by grey scales only. Thus, colorimetric measurement of these cases is found to be useful for correct/precision color fastness grading.

Grey scale for assessing change in color
Fastness Grade	CIELAB difference	Tolerance
5	0	0.2
4.5	0.8	±0.2
4	1.7	±0.3
3–4	2.5	±0.35
3	3.4	±0.4
2–3	4.8	±0.5
2	6.8	±0.6
1–2	9.6	±0.7
1	13.6	±1.0
Grey scale for assessing staining
Fastness grade	CIEIAB difference	Tolerance
5	0	0.2
4–5	2.2	±0.3
4	4.3	±0.3
3–4	6.0	±0.4
3	8.5	±0.5
2–3	12.0	±0.7
2	16.9	±1.0
1–2	24.0	±1.5
1	34.1	±2.0

Table 7.

Colour fastness grading in terms of colour difference values (dE*) as equivalent to grades of grey scale with tolerances for precision grading of colour fastness assessment.

3.9 Determination of rate of dyeing, dyeing isotherm and dyeing kinetics parameters by colorimetric analysis

Rate of dyeing can be understood by colorimetric analysis of dye in fibre (rest are dye in solution) at specific dyeing time and its temperature dependence and dyeing isotherm is understood by Din Fibre vs. Dye in solution plots and dye in fibre with respect to different dyeing temperature indicates its bearing on heat of dyeing. All these can be easily calculated by colorimetric analysis of dye absorbed in fibre (out of total dye added in bath) by analysis of dye concentration left in dyeing bath at any time span and even after different dyeing time and temperature, if dye% added in bath solution before dyeing is known. This must be done in UV VIS absorbance spectrophotometer after obtaining calibrated dye concentrations curve for specific dye. Discussion of a case study will bring more clarity in it to understand it practically. Hence, an example of determining rate of dyeing, dyeing isotherm and dyeing kinetics are briefly mentioned as a case study facilitating both offline and on line colour control in relation to computer aided colour control and matching [21] for textiles.

CASE STUDY 9: An example of determining rate of dyeing, dyeing isotherm [Dye in fibre vs. Dye in Solution curves] and dyeing kinetics (determining half dyeing time, heat of dyeing or dyeing enthalpy, bond energy etc] are briefly mentioned here as case study. Relevant data and the rate of dyeing curve [D_f (amount of Dye exhausted to the fibre) vs. t_d (time of dyeing)] for jute fabric for dyeing with madder (also known as Manjistha/Rubia) after double pre-mordanting with 20% harda (myrobolan) and 20% Al₂(S0₄)₃ applied in sequence followed by subsequent dyeing with madder/Manjishtha under a pre-optimized conditions of dyeing are shown in Table 8 and Figure 8.

Time (min)	[D] f, g/kg at 50°C	[D] f, g/kg at 90°C
15	1.5	2.6
30	2.7	4.0
45	3.8	5.2
60	4.8	6.1
75	5.5	6.5
90	5.9	6.6
120	6.1	6.6

Table 8.

Dye exhaustion to the fibre [Df] for different dyeing time indicating rate of dyeing for application of Madder/manjistha as natural dye on double pre-mordanted bleached jute fabric.

Figure 8.

Rate of dyeing plot as function of time for dyeing of pre-mordanted jute fabric with Madder at 50 and 90°C.

Relevant Data in Table 8 also shows the dye exhaustion to the fibre for different dyeing temperature indicating rate of dyeing for application of madder extract on the said double pre-mordanted jute at lower temperature (at 50°C) and at higher temperature (at 90°C), where differences of dye up take at these two temperature are found to be higher at lower dyeing temperature of dyeing and gradually the differences reduces for use of higher temperature, viz. data in Table 8.

Relevant curves in Figure 8, using data of Table 8, indicate that with increase in dyeing time, the dye uptake (D_f) increases measurably up to 60 min of dyeing time and then gradually slows down and almost levels off in between 90 and 120 min. Since, purpurin and manjistin are present as the two main colouring components of in Indian Madder [a natural dye], both these colouring components [having -OH and -COOH functional groups] gradually starts reacting by attachment to mordant with increasing of dyeing time and temperature, while its exhaustion to the mordanted fibre might have levelled off after possible saturation of such dye-mordant-fibre complex forming reaction and possible hydrogen bonding etc. for dye fixation is completed and no further increase in temperature or time can increase dye up take further.

While, Figure 9 is the Plot between Dye in solution (Ds) Vs Dye in Fibre (Df) at a particular time and temperature (here at 90°C) represent at saturation or equilibrium as corresponding dyeing isotherm.

Figure 9.

Plot showing the dyeing isotherm for pre-mordanted jute fabric dyed with Madder/Manjistha at 90°C.

The chemical affinity (−∆μ) for the dye molecule or dyeing affinity for Madder/Rubia/Manjistha towards mordants for pre-mordanted bleached jute fabric when dyed at optimized dyeing conditions for different durations at two different dyeing temperatures (50 and 90°C) is shown in Table 5.2.9. Low but measurable increase in chemical affinity of the said colourant is observed for increase in dyeing temperature from 50–90°C, albeit, higher increase in chemical affinity is expected for increase of dyeing temperature. This moderate value and low increase of chemical affinity for enhancement of dyeing temperature showed that dyeing of bleached and mordanted jute fabric with madder/manjistha do not occur as rapidly as expected and maybe there is low extent of formation of Fibre-Mordant-Dye coordinated complex, while it may be presumed that dyeing occur through weak hydrogen bonding formation in a slower speed. While it is reported in earlier literature [22] that some synergistic effects for application of double pre mordanting with 10% natural potash alum and 10% harda (myrobolan) on cotton before dyeing with madder (Manjistha) due to additional coordinating power of chebulinic acid of harda as a mordanting assistant, facilitates more number of strong and giant bigger complex formation amongst the said fibre (cotton)-mordanting assistants (harda)—metallic mordant (natural alum)—natural dye (madder) to develop higher colour strength and higher Colour fastness to wash as an optimised and better option, which however do not happen in case of dyeing jute fabric with madder/manjistha, after double pre-mordanting with 20% harda (myrobolan) and 20% Al₂(S0₄)₃ applied in sequence in this case, may be due to acidity of jute do not allow chebulinic acid of harad (myrobolan) to be attracted/absorbed to jute fibre, as required.

To understand the chemistry of attachment of this particular natural colorant specifically whether the dye molecules from madder or manjistha has been bonded to the fibre-mordant system through pre-dominant H-bonding or through coordinate/chelating complex formation, dyeing isotherm indicate that there is formation of more intermolecular H-bonding between dimeric association of – OH groups of madder component and mordanting assistant like harda (myrobolan) used in double mordant attached through metallic mordant of aluminium sulphate and the jute fibre forming intermolecular H-bonds, and less or no Dye-Mordant Fibre Complex formation occur predominantly as expected. Hence the dyeing isotherm observed is Nernst type (and not Langmuir type) is observed in Figure 9 like dyeing of non-polar disperse dyes to hydrophobic polyester fibre. However, some metallic chelate formation cannot be excluded fully and need to be explored by FTIR scan etc.

For dyeing of bleached jute after double pre-mordanting with harda (myrobolan) and Al₂(SO₄)₃, applied in sequence, heat (enthalpy) of dyeing is found to be positive, showing medium magnitudes of positive values. Thus, this dyeing process may be considered as endothermic and therefore more dye would be adsorbed with increase of dyeing temperature up to equilibrium. In case of double pre-mordanting with harda (myrobolan) and Al₂(SO₄)₃ applied in sequence and subsequent dyeing at pH 11.0, K/S value initially increases with increase in dyeing temperature up to 90°C, and above which, the K/S value levelled off. From observed data in Table 9, it is indicated that at dyeing temperature between 50–90°C, the ∆H values (required heat of dyeing, as a measure of bond energy/forces of attraction responsible to bind natural dye molecules to the fibre by bridging through the metallic mordant) are always positive in this case but showing lower magnitude of ∆H values within 6.91 to 29.52 kJ/mol. This bond energy values nearly matches with the usual range of bond energy (10–40 kJ/mol) [23] of hydrogen bond formation indicating formation of a weaker dye-fibre bond that has been taken place instead of coordinated co-valent bonds. The +ve sign of ∆H values might have indicated this dyeing process as an endothermic process, which actually occur for hydrogen bond formation between the dye and mordanted fibre. However, metallic mordanting is also essential to increase the attraction of the dye to the fibre in the dye bath during dyeing to increase their chemical affinity and exhaustion of this natural dye towards jute.

[D]f; g/kg		[D]s; g/l		—∆μ; kJ/mol		∆H; kJ/mol	∆S; J/mol/°K
at T1	at T2	at T1	at T2	at T1	at T2	for (T2—T1)	at T2
1.5	2.6	0.031	0.016	13.31	18.62	29.52	132.62
2.7	4	0.038	0.026	14.35	18.45	18.83	102.70
3.8	5.2	0.043	0.034	14.93	18.44	13.37	87.61
4.8	6.1	0.047	0.041	15.32	18.35	9.17	75.82
5.5	6.5	0.051	0.043	15.47	18.40	8.23	73.36
5.9	6.6	0.053	0.044	15.55	18.38	7.27	70.65
6.1	6.6	0.054	0.044	15.59	18.38	6.91	69.67

Table 9.

Thermodynamic parameters for dyeing pre-mordanted jute with Madder/Manjistha after double premordanting with harda plus Aluminium sulphate.

Changes in dyeing entropy (∆S) and dyeing enthalpy (heat of dyeing) are the main indicator of dye absorption and dye fixation force. From observed results in Table 9, it is indicated that for different D_f (dye in Fibe) and D_s (dye in solution) values, there is some changes in dyeing entropy at the initial stage of dyeing, with measurable small changes in ∆H values (heat of dyeing), as dyeing time progresses. Df values continues to increase slowly with increase in dyeing time from 30 to 60 min at 90°C in case of said double mordanting system using harda and Al₂(SO₄)₃ in pre-mordanting. This slow increase in K/S value, for increase in dyeing time may be due to only physical absorption of dye molecules in fibre by hydrogen bonding with less possibility of Fibre -Mordant-dye co-ordinated complex formation for the dye fixation even on the pre-mordanted fibre, thus without much affecting ∆H and ∆S values.

3.10 Estimation of soil removal efficacy of different detergents used for textiles

For estimation of degree of soiling and soil removal efficiency by standard domestic laundering by selective detergent [24], first the clean white or light coloured fabrics are to be artificially soiled under standard conditions by dipping and running the clean fabric under an oil in water emulsion with water+ coconut oil/carbon tetrachloride with addition of recommended dosages of graphite powder or carbon black powder and the changes in reflectance value after artificial soiling gives degree of soiling as depicted in the following Eq. 25;

$$\text{Degree of Soiling}\left(\%\text{Soiling}\right)=\frac{{\mathrm{R}}_0-\mathrm{Rs}}{\mathrm{Rs}}\times 100$$E25

Where R₀ is the Initial Reflectance value of clean (unsoiled) white/light coloured fabric and Rs is the Reflectance value of artificially soiled white or light coloured fabric.

Further, estimation of soil removal efficacy % of any detergent, can be similarly calculated by change of Reflectance of corresponding soiled fabric sample before and after washing at specified standard conditions in launder-o-meter, represented by following Eq. 26:

$$\begin{array}{c}\text{Degree of Soil removal efficacy}\left(\%\right)\\ \text{Or Percent soil removal Efficiency}\end{array}=\frac{{\mathrm{R}}_{\mathrm{L}}-\mathrm{Rs}}{{\mathrm{R}}_0-\mathrm{Rs}}\times 100$$E26

where Rs is the Reflectance value of artificially soiled white or light coloured fabric before laundering and R_L is Reflectance values of the standard soiled fabric after Laundering for given numbers of cycles of wash under specified washing conditions of domestic wash under lauder-o-meter. Also, to determine degree of soil redeposition %, AATCC Test Method 151 can be used to estimate the degree of soil redeposition likely to occur during laundering as soil removal efficiency is never 100% and gradual redeposition of soil on fabrics under wash always occurs. The fabrics to be tested are exposed to initially to a standard soiling method (preferably taking fabric swatches with both dry soiling followed by fabric pretreated with a standard oily soil) and then subjected to laundering to determine both soil removal efficacy and soil redeposition during a laundering simulated with a standard domestic wash with selective detergent. The change in reflectance of the fabric before and after laundering for the soiled fabric under testing is an indication of the % soil redeposition potential of the fabric as well as soil removal efficacy percent of the corresponding detergent.

4. Concluding remarks

The application of above said colorimetric analysis with few case studies for textile industry are a small glimpse only considering this vast subject of colorimetry and hence, this can be applied in makeshift way to other different industry as well. In the colorimetric analysis, besides conventional old model of colorimeter (which is almost abandoned) UV VIS absorbance spectrophotometer and UV VIS Reflectance spectrophotometer, both took major role for colorimetric analyses of all types of Liquid and solid coloured samples used in textile industry, paint industry, food industry, chemical industry, cosmetic industry, pharmaceutical industry etc., where colour information could be obtained with different type of sensor/detector to quantify the colour variation in different colour spaces such as CIE L*a*b* colour space and other recent few more colour space used such as CIE-LUV, RGB, CMC etc., Besides the conventional approaches of colorimetric analysis, non-conventional approaches are now being applied on liquid samples for detection of chlorine in water, to check ripeness estimation of different fruits, to check colour differences in blood to determine blood shading date (or age) for forensic purpose, to determine efficacy of UV active agents like Bluing agents or optical brighteners/UV absorbers used in textile industry etc., where quantification of required colour parameters are calculated using analytical formulas extracted from different colour space concepts defined and measured using UV VIS absorbance spectrophotometer and UV VIS Reflectance spectrophotometer. Presently Portable Reflectance spectrophotometer are the industry’s major choice due to its handy use and carrying capability from one place to other.

As an alternative to UV-VIS spectrophotometric analysis, colorimetry is also widely used in many applications including food allergen testing, albumin testing in urine analysis, blood analysis, pH quantification and water monitoring in different industry.

Over the last decade, scientist has made possible that smartphones may also be used in a variety of scientific fields as spectrometers or as colorimeters, if provided with optical sensor. Smartphone optical spectrometers uses the wavelength scan components, which give spectral information at 400 to 700 nm for the collimated light from the optical source which is dispersed after interaction with samples and corresponding results are recorded. The colour spectrum image of the sample taken in a smart phone is transformed into various colour spaces for the extraction of quantitative colour data. The wavelength of the spectrum generally changes between 400 and 700 nm because of the optical filters set in front of the camera in the manufacturing process which serves the purpose of using this Spectral information in many applications from smart phone.

Smartphone-based spectrometer and colorimetry have been gaining popularity and current relevance due to the widespread advances of these type of small sized and multipurpose smart devices with increasing computational and spectral recording power having relatively low cost and portable designs with very much user-friendly interfaces, and compatibility with data acquisition and processing facility. They find applications in interdisciplinary fields, including but not limited to textiles or paints or pharmaceutical industry, agriculture industry chemical industry and biological and medical purposes too.