Indian Journal of Textile ResearchVol. 12, June 1987, pp. 88-92

Optimization of a Low-Temperature Combined Scouring and BleachingProcess for Polyester/Cotton Blend Fabrics Using Penalty Function Method

R VENKATRAJ, M L GULRAJANI and P CHANDRASEKARANaDepartment of Textile Technology.Tndian Institute of Technology, New Delhi 110016, India

Received 19 January 1987; revised and accepted 10 April 1987

A low-temperature single-stage scouring and bleaching process has been worked out using an emulsified solvent-basedscouring agent and sodium dichloroisocyanurate-activated sodium chlorite bleaching agent. The process parameters wereoptimized by factorial design and penalty function method. The total treatment cost for the proposed process worked outto be a little less than that of the conventionally prepared fabric.

Keywords: Bleaching, Penalty function method, Polyster / cotton blend fabrics, Scouring

1 IntroductionWith the popularization of Tex/Tex polyester fa-

brics, extensive use of sodium chlorite is being madeto bleach this fabric. Bleaching with sodium chloriteat boil results in the liberation of large volumes ofchlorine dioxide gas. Instances of acute toxicityamong the workers due to the inhalation of chlorinedi-oxide are becoming more frequent.

Various organic compounds have been patented 1-4,

which can activate sodium chlorite at low tempera-tures. These compounds either get oxidized into acidsby the action of sodium chlorite or liberate acids onhydrolysis. One such compound which has been veryrecently patented for this purpose is sodium dichloro-isocyanurate". This compund gets hydrolyzed atlow temperatures to yield hydrochloric acid.

The present study was undertaken to work outa process for the combined scouring and bleaching ofa polyester/cotton blend fabric using a solvent-assist-ed scouring agent and sodium dichloroisocyanurate-activated sodium chlorite. The experiments wereconducted according to the response surface metho-dology, and regression analysis was carried out to es-tablish the relationship between the various processparameters and the whiteness index of the bleachedsamples. The optimized recipe was worked out bya penalty function method.

2 Materials and Methods

2.1 FabricPolyester/cotton (52: 48) blend fabric obtained

from Mis East India Cotton Manufacturing Co. Ltd,

"Department of Computer Science and Engineering, lIT,New Delhi.

88

with the following quality particulars, was selected forthe study:

Warp count, 2/40s; weft count, 2/40s;ends/m, 2560; picks/m, 2400; Wt/m-, 250g.The grey fabric contains starch as a major compo-

nent of size. The fabric was desized using alkaline po-tassium persulphate solution (about 12 pH) at 40°Cfor 3 h. After desizing, the fabric was given cold- andhot-wash followed by dilute acetic acid souring to re-move the residual alkali. The fabric was drip-driedbefore padding.

2.2 ChemicalsSodium chlorite of 80% strength (solid) was used as

bleaching agent; sodium dichloroisocyanurate sup-plied by Aldrich Chemicals Co., USA, was used as theactivator for chlorite. An already standardized" self-emulsifiable solvent-based scouring agent consistingof perchloroethylene as solvent, a nonionic (nonylphenol lOEO condensate) emulsifier and pine oil aswetting agent mixed in the proportion 1 : 4 : 5 wasused as scouring agent. The scouring/bleaching bathwas prepared by mixing the scouring agent, thebleaching agent and the activator and buffering it topH 4.6 by adding sodium acetate (0.1 mol) and aceticacid (0.1 mol).

2.3 Fabric TreatmentThe fabrics were padded with the scouring/bleach-

ing formulation and kept at the specified temperaturefor 5 h. After the treatment, the fabrics were givena cold rinsing followed by an antichlor treatment withsodium thiosulphate and a final cold rinsing.

2.4 TestingTo evaluate the whiteness of treated fabrics, an

ACS 1600 computer colour matching system was

VENKATRAJ et al: LOW-TEMPERATURE COMBINED SCOURING AND BLEACHING PROCESS

used. The observed values have been reported inHunter Whiteness Index(H), computed by using theformulaH= L- 3b, where Land bare Hunter coord-inates.

3 Experimental Plan and ResultsTo study the effect of variables, namely scouring

agent concentration, bleaching agent concentration,activator concentration and treatment temperature,a four-variable five-level response surface design wasused. The selected levels of variables are given in

Table 1.As per Yeate's standard, 31 treatments weregiven to the desized polyester/cotton blend fabric.The measured and computed responses, namelyHunter Whiteness Index, for the treated fabrics arereported in Table 2. The computation of f3 coeffi-cients and variance analysis were done using Micro-stat statistical software (Ecosoft USA) on an IBM per-sonal computer and an indigenously developed pro-gram processed in an ICL 2960 mainframe compu-ter. The values are reported in Table 3. The multiplecorrelation coefficient R and F-ratio computed for

Table 1- Variables and Their Levels Used in Experimental PlanVariable Level

-2 -1 0 1 2Scouring agent cone. (% owf) (Xl) 0.0 1.0 2.0 3.0 4.0Bleachingagent cone, (% owf) (X2) 0.0 0.6 1.2 1.8 2.4Activator conc. (% owf) (X3) 0.000 0.025 0.050 0.075 0.100Temperature, °C (X4) 20.0 30.0 40.0 50.0 60.0

Table 2-Experimental Plan for a Low-Temperature Scouring-Bleaching Process forPolyester/Cotton (52 : 48) Blend Fabric

Expt. Scouring Bleaching Activator Temp. Whiteness indexNo. agent agent %owf °C

%owf %owf Actual Predicted1 1.0 0.6 0.Q25 30 75.48 76.4882 3.0 0.6 0.025 30 76.69 76.4883 1.0 1.8 0.025 30 80.30 78.134·4 3.0 1.8 0.025 30 80.09 78.1345 1.0 0.6 0.075 30 75.26 77.5606 3.0 0.6 0.075 30 77.36 77.5607 1.0 1.8 0.075 30 79.37 79.2068 3.0 1.8 0.075 30 79.37 79.2069 1.0 0.6 0.025 50 81.77 81.162

10 3.0 0.6 0.025 50 79.68 81.16211 1.0 1.8 0.025 50 84.06 82.80712 3.0 1.8 0.025 50 83.14 82.80713 1.0 0.6 0.075 50 82.88 82.23314 3.0 0.6 0.075 50 82.07 82.23315 1.0 1.8 0.075 50 84.81 83.87916 3.0 1.8 0.075 50 84.29 83.87917 0.0 1.2 0.050 40 80.89 80.18418 4.0 1.2 0.050 40 79.20 80.18419 2.0 0.0 0.050 40 72.29 73.60120 2.0 2.4 0.050 40 84.07 86.76621 2.0 1.2 0.000 40 74.17 75.87922 2.0 1.2 0.100 40 83.29 84.47923 2.0 1.2 0.050 20 76.05 75.51124 2.0 1.2 0.050 60 84.70 84.85725 2.0 1.2 0.050 40 81.55 80.18426 2.0 1.2 0.050 40 80.52 80.18427 2.0 1.2 0.050 40 76.24 80.18428 2.0 1.2 0.050 40 80.74 80.18429 2.0 1.2 0.050 40 82.45 80.18430 2.0 1.2 0.050 40 81.87 80.18431 2.0 1.2 0.050 40 81.05 80.184

Conventionally treated fabric 85.00

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INDIAN J. TEXT. RES., VOL. 12, JUNE 1987

Table 3-Coefficients of Regression EquationCoefficient Whiteness index

f30f31f32f33f34flllfl22fl33s:e:fl222fl333fl444«.fll3e;fl23fl24e;R2

MultipleRF ratio

2nd order(full Eq.)80.631*

-0.1931.949*0.978*2.337*0.034

-0.433-0.295

0.116

3rd order(full Eq.)80.631 *0.Q380.971

-0.3422.511 *0.034

-0.433- 0.29S

0.116-0.115

0.494*0.656*

- 0.087-0.078

0.123-0.465-0.231-0.203

0.4630.8980.9485.863

0.8120.901

38.920

2nd order(sig. coef.)80.184

3rd order(sig. coef.)

80.184

1.9920.9352.337 2.337

0.8230.536

-0.0640.109

-0.465-0.231-0.258

0.4770.7980.8934.507

0.7440.863

26.161

the second-order regression equation showeda poor fit of the model. Hence the computation wasextended for calculating the coefficients of the thirdorder polynomial. We observed a considerable im-provement in the fit of the model (higher R and higherF-ratio). The third-order polynomial with significantf3 coefficients (recalculated) showed a better fit of themodel for this treatment plan and subsequently thispolynomial, viz.y(W.I) = 80.184 + 2.337 x 4 + 0.823

X23+0.536X33 ... (1)was considered for the interior penalty functionmethod.

3.1 Optimization Procedure 7

The better fitted model for this plan is the third or-der polynomial. The solution to this equation cannotbe obtained by transforming the equation into its ca-nonical form. But the solution can be obtained by se-lecting any of the nonlinear optimization procedures.Among the nonlinear optimization methods, interiorpenalty function method is best suited for this plan.This is because we specify various constraints to beimposed on the range of selected variables so that theoptimum lies within the feasible region. Also, we canspecify any nonlinear functions of the independentvariables as constraints.

In the penalty function method the basic con-strained optimization problem is transformed into

90

alternative formulations such that numerical solu-tions are sought by solving a sequence of uncon-strained minimization problems. Let the basic opti-mization problem be of the form 'Find X which mini-mizesf(X) subjectto the constraints gj.Y) < O,j= 1,2,... m'. This problem is converted into an unconstraintminimization problem by constructing a function ofthe form

m

¢ = ¢(X,rk) = f(X) + r, I Gj{gj(X)}i= 1

... (2)

where G is some function of the constraint gj and r k isJ

a positive constant known as penalty parameter. Thesecond term on the right-hand side ofEq. (2) is calledpenalty term. The optimization of ¢ function is re-peated for a sequence of values of the penalty parame-ter r k (k = 1, 2, ... ) until the solution is brought toconverge to that of the original problem, i.e. f(X) inEq. (1).The advantages claimed in this method are (i)the minima lie within the feasible region of the levels ofthe variables chosen, (ii) there is no limitation in se-lecting the number of constraints, and (iii) the startingpoint for the optimization can be chosen from practi-cal experience. The basic steps involved in the com-puter programming are as follows:

(1) Start with an initial feasible point X satisfyingall the constraints with strict inequalities sign, that is,f5J(X)< 0 for j= 1,2, ... m and initial value if r> O. Setk= 1.

(2) Minimize ¢(X,rk) by using interior penaltyfunction minimization method and obtain the solu-tionXk*'

(3) Test whether x; is the optimum solution of theproblem, i.e. x; - Xk'-l becomes very small. If x; isfound to be the optimum, terminate the process.Otherwise, go to the next step.

(4) Find the value of the next penalty parameterrk+ 1 as rk+ I = eX rk, where e < 1.

(5) Set the value of k = k + 1, take the new startingpoint as XI = X; and go to step 2.

The penalty function optimization procedure wasoriginally designed for positive function so that theglobal minima can be obtained within the feasible re-gion. But in the preset optimization, as the whitenessindex is higher the better is the result and hence the ne-gative function of X is taken as the objective function.

4 DiscussionThe effectiveness of a scouring/bleaching treatment

is normally assessed in terms of the wettability of thefabric, its retained tensile strength and the whitenessindex of the fabric.

In an earlier study" on the low-temperature scour-ing/bleaching of polyester/cotton, we used a light-weight fabric, whereas in this optimization we have

VENKATRAJ et al.: LOW-TEMPERATURE COMBINED SCOURING AND BLEACHING PROCESS

used a heavy weight polyester/cotton (52: 48) blendfabric and hence we decided to include the scouringagent as one of the variables to study the effect of wett-ing characteristics of the fabric. However, we couldnot observe any specific trend owing to this variableand we did ohserve 40s of wetting time (average) forthis fabric, which is acceptable. Also, the coefficientof scouring agent is not significant at any level, so wedid not include this variable in the objective function.

To study the effect of variables on the whiteness in-dex, spatial diagrams were drawn (Figs 1-3) from thefitted regression equation. It is evident from these dia-grams that the effect of the bleaching agent on the white-ness index is relatively more than that of the other var-iables. The temperature shows a linear effect onwhiteness index. Considerable improvement inwhiteness index of the fabric has been observed be-tween - 2 and - 1 levels, followed by a slow increasetill + 1 level of the bleaching agent concentration andactivator concentration. The maximum attainablewhiteness index (85.00) was obtained within + llevel(bleaching agent 1.80%, activator 0.075% and tem-perature of treatment 50°C) of the variables. Thesteep increase in the whiteness index beyond + 1 to+ 2 level is indicated in the spatial diagram. However,obtaining a whiteness index beyond 85.00 is of theor-etical importance, since that is the limiting whitenessindex attainable on this fabric. Moreover, increasingthe concentration of activator beyond + 1 level (i.e.0.075%) leads to excessive liberation of chlorine di-oxide gas, which is undesirable.

95

90

85

'"-oc

'"ec 75~i::"!

70

Temperature, ·c

Fig. I-Spatial diagram showing the effect of bleaching agent con-centration, activator concentration and treatment temperature on

whiteness index

5 OptimisationThe above-mentioned observations give valuable

information about fixing the maximum limits of thevariables to be selected as constraints and also thestarting points of optimization. For example, to avoidexcessive liberation of chlorine dioxide, the concen-

~"'0E.

:::"c~s:"!

70

Temperature 1 C

Fig. 2-Spatial diagram showing the effect of activator concentra-tion, bleaching agent concentration and treatment temperature on

whiteness index -

95

90

85

60~~~ __ ~~~~~~0.0 0·025 0.050 0.075

Acti vo tor , -I. owf

Fig. 3 -Spatial diagram showing the effect of treatment tempera-ture, activator concentration and bleaching agent concentration

on whiteness index

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INDIAN J. TEXT. RES., VOL. 12, JUNE 1987

Table 4-Treatment Conditions Selected from Penalty Function Optimisation Output

Treatment Bleaching agent Activator Temp. Whiteness indexcondition computed

No. Coded Actual Coded Actual Coded Actual%owf %owf °C

1 -0.155 1.107 -1.216 0.020 1.050 50.5 81.6722 -0.356 0.986 -0.707 0.032 0.855 48.6 81.9553 0.214 1.328 -1.099 0.023 1.131 48.6 82.1244 -0.208 1.075 -0.348 0.041 0.856 48.6 82.1535 -0.360 0.984 -0.717 0.032 1.358 54.0 83.1216 -0.117 1.130 -0.829 0.029 1.586 55.9 83.5827 1.234 1.940 -0.396 0.040 0.857 48.6 83.7008 1.351 2.011 -1.051 0.024 1.005 50.1 83.9399 -0.074 1.156 -0.647 0.034 1.725 57.3 84.068

10 -0.046 1.172 -0.554 0.036 1.780 57.8 84.27211 1.451 2.071 -1.051 0.024 1.005 50.1 84.42412 1.250 1.950 0.717 0.068 1.358 53.6 85.161

Table 5 - Comparative Cost Analysis of Conventionaland Single-Stage Scouring-Bleaching Process?

Conventional Single-stagepaise/kg paise/kg

72.00 145.0Q100.00 20.0032.00 16.0033.00 10.00

237.00 191.00

ChemicalSteam cost'ElectricityWagesTotal

'Steam cost, 20 paise/kg.

tration of the the activator should not exceed beyond0.075% (+ 1 level) and hence the maximum limit ofthis variable is fixed at + 1 level. Since the optimiza-tion program has the flexibility of choosinga different starting point, we can optimize the treat-ment conditions within the feasible region. Amongthe 100's of computed treatment combinations, onlythose having a whiteness index between 81 and 85were chosen and these are reported in Table 4. Thetreatment condition No.12 seems to be nearer to theconventionally prepared fabric (85.00) and this canbe considered as the optimum treatment conditionfor this activator system.

Based on the optimum recipe the cost of a single-stage scouring and bleaching preparatory process

92

was worked out and it is reported in Table 5. Thisshows that the preparation cost of the proposed single-stage process works out to be a little less than that ofthe conventional process.

AcknowledgementThe authors acknowledge the financial grant re-

ceived from the Department of Science and Techno-logy, Government of India.

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4 Stoffel Max, Br Pat, 864230,29 March 1961.

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