OPTIMIZATION ASPECTS ON MODIFICATION OF STARCH USING ELECTRON BEAM IRRADIATION FOR THE SYNTHESIS OF WATER-SOLUBLE COPOLYMERS
M. BRASOVEANU1, E. KOLEVA2,3, K. VUTOVA2, L. KOLEVA3, M.R. NEMȚANU1 1
National Institute for Lasers, Plasma and Radiation Physics, Electron Accelerators Laboratory, P.O. Box MG-36, RO-071125, Bucharest-Măgurele, Romania, E-mail:
[email protected], E-mail:
[email protected] 2 Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko shossee blvd., Sofia 1784, Bulgaria, E-mail:
[email protected],
[email protected] 3 University of Chemical Technology and Metallurgy, 8 Kl. Ohridski blvd., Sofia 1756, Bulgaria, E-mail:
[email protected] Received February 2, 2016
The acrylamide grafting onto starch by electron beam (EB) irradiation in order to synthesize water-soluble copolymers having flocculation abilities was optimized by implementation of the Response surface methodology (RSM) and robust engineering design. The results showed different optimal regions of EB irradiation dose and dose rate depending on acrylamide/starch weight ratio. Key words: Grafting parameters optimization, electron beam irradiation, starch, acrylamide, response surface methodology.
1. INTRODUCTION
The current environmental considerations impose rigorous protection rules and sustainable progress that minimize the impact of wastes on the environment. Accordingly, there is a strong demand to develop economically viable and ecofriendly replacements of conventional synthetic flocculants, based upon the renewable organic materials that are low cost and degrade naturally when are released in the environment [1]. Grafting is the most effective way of regulating the properties of natural polysaccharides, which can be tailor-made according to the needs and produce high efficient graft copolymers [2], having application as flocculating agents for treatment of different wastewaters. Rom. Journ. Phys., Vol. 61, Nos. 9–10, P. 1519–1529, Bucharest, 2016
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Electron beam (EB) grafting (modification of polymer substrates using electron beam induced graft copolymerization) is an important process for creation of new functional materials with different applications [3]. EB irradiation grafting is used to develop a wide variety of ion exchangers, polymer-ligand exchangers, chelating copolymers, hydrogels, affinity graft copolymers and polymer electrolytes, having various applications in water treatment, chemical industry, biotechnology, biomedicine, etc. [4]. The advantages of electron beam induced grafting process are connected with the ability to ionize polymers with limited reactivity in chemical processes, generation of polymer radicals is performed by clean non-chemical method, which can be precisely controlled and uses low energy. The electron beam irradiation can be easily modified and integrated into complete process lines. Electron beam irradiation can be implemented also in other processes with different effects resulting from the formation of free radicals besides grafting like curing, crosslinking and scission [5]. During the electron beam graft process the depth of EB energy deposition into materials can be controlled by the accelerating potential of the equipment and the elemental composition and density of the material being irradiated. Acrylamide monomer gives a polar graft side chain resulting in hydrophilic copolymer. In order to estimate models, giving the relationship between the process parameters and the performance characteristics, a properly planned experimental design should be performed. There are experiments during which the variance is non-homogeneous over the factor (process parameters’) space and when the noise factors cannot be identified nor an experiment to study them can be conducted. The observations in this case are called heteroscedastic (variance varies with the factor levels). In this case regression models for the mean and the variance of the quality characteristics of the product, based on repeated observations, can be estimated. This circumstance gives possibility to implement robust (not sensitive to noises and errors) engineering approach for parameter optimization in terms of obtaining repeatability and quality improvement by minimization of variations in the quality characteristics. In this paper multi-criteria optimization involving requirements for economic efficiency, assurance of low toxicity, high copolymer efficiency in flocculation process and good solubility in water is presented. The optimization applies estimated regression models, describing the dependencies of the quality characteristics: y1 – monomer conversion coefficient (Conv, %), y2 – residual monomer concentration (Mr, %), y3 – apparent viscosity (ηa, mPa·s) and y4 – intrinsic viscosity ([η], dL/g) and y5 – Huggins’ constant (kH) on the variation
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of the process parameters: acrylamide/starch (AMD/St) weight ratio, concentration of AMD and St, respectively, electron beam irradiation dose and dose rate.
2. EXPERIMENTAL
Experiments for the modification of starch by grafting acrylamide using electron beam irradiation were performed in order to synthesize water-soluble copolymers having flocculation abilities. The synthesis of graft copolymers was performed by two steps: (1) preparation of solutions containing starch and monomer; (2) irradiation of solutions by electron beam. 1. Starch aqueous solutions were prepared by dissolving corn starch in distilled water. Acrylamide was added to starch aqueous solution with further stirring, resulting in various acrylamide/starch (AMD/St weight ratios) homogenous aqueous solutions. 2. Therefore, homogenous aqueous solutions prepared in step 1 were exposed to electron beam irradiation. The irradiations were carried out at ambient temperature and pressure by using linear electron accelerators of mean energy of 6.23 MeV with different irradiation doses and dose rates. The synthesized graft copolymers were characterized by monomer conversion coefficient, Conv [%]; residual monomer concentration, Mr [%]; apparent viscosity, ηa [mPa·s] and intrinsic viscosity, [η] [dL/g]; and Huggins’ constant, kH. The variation regions [zmin–zmax] of the process parameters were: for EB irradiation dose (z1) – [0.65–5.50 kGy]; the dose rate (z2) – [0.41– –1.50 kGy/min] and the concentration of AMD (z3) – [9.8–19.6 %]. The concentration of St for this experiment was constant and is 1.8%. The (AMD/St) weight ratio varies from 5.56 to 11.11. There were 19 process parameter experimental sets and for each set the means yu and the variances su2 of the quality characteristics of graft copolymers: monomer conversion coefficient, residual monomer concentration, apparent viscosity, intrinsic viscosity and Huggins’ constant were estimated using three measurements and the following equations:
yu
1 n yui n i 1
su2
1 n yui yu 2 n 1 i 1
u 1, 2, ..., N ,
(1)
where n is the number of replications, N is the number of experimental sets (N = 19).
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3. MODELS OF THE MEAN AND THE VARIANCE OF THE QUALITY CHARACTERISTICS
The estimated values of the means yu and the variances su2 can be considered as two responses at the design points and ordinary least squares method can be used to fit two polynomial regression models for each quality characteristic [6]: Model of the mean value: k
y ~ y ( x ) ˆyi f yi ( x )
(2)
i 1
Model of the variance:
k 2 ~ ln s x ˆi fi x
(3)
i 1
where ˆyi and ˆi are estimates of the regression coefficients, and f yi and f i are known functions of the process parameters. The variance of normally distributed observations has a 2 – distribution. The use of the logarithm transformation of the variance function makes it approximately normally distributed, which improves the efficiency of the estimates of the regression coefficients. The models are estimated for coded in the region [–11] values of the process parameters, using the following equation:
xi (2 zi zi ,max zi ,min ) /( zi ,max zi ,min ) ,
(4)
where xi and zi are the coded and the natural values of the process parameter, correspondingly, zi,min and zi,max are the minimal and the maximal values of the parameter experimental region. The (AMD/St) weight ratio and the concentration of AMD, when coded, have equal levels, since St concentration was constant during the experiment. Their influence on the variation of the quality characteristics cannot be distinguished in this case and only one of these factors should be used in the estimated models. The dependencies of the means and the variances of the product quality characteristics: y1 – residual monomer concentration (Mr, %), y2 – monomer conversion coefficient (Conv, %), y3 – apparent viscosity (η, mPa·s) and y4 – intrinsic viscosity ([η], dL/g) and y5 – Huggins’ constant (kH) on the variation of the process parameters: x1 – electron beam irradiation dose, x2 – electron beam
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irradiation dose rate and x3 – concentration of AMD are estimated. The obtained regression models are presented in Table 1 and Table 2, together with the values of the corresponding multiple correlation coefficients R. These coefficients are tested for significance and their values are measures of the accuracy of the estimated models (the closer to 1 is the value of R, the better the model describes the variations of the quality characteristics as a function of the process parameters). Table 1 Models for the means of the product quality characteristics ~ y1 ( x ) ~ y2 ( x ) ~ y3 ( x )
~ y4 ( x ) ~ ln y5 ( x )
Model 0.2201–2.9960x1+1.3525x2+8.1993x12+3.4525x12x3+ + 0.5287x2x3 99.7648+30.9220x1–8.8640x2+3.8197x3–46.4803x12 4.3536+2.2769x1+0.6985x2+0.9575x3–5.3920x13–2.0758x13x3– –1.5789x13x2 3.3567+2.6973x3+3.8957x12–1.4537x1x2+0.6490x2x3 –1.5068+0.6948x3+1.3320x22+2.6242538x14
R 0.9173 0.9287 0.8499 0.8724 0.7396
Figure 1 shows the contour plots of the variation of the investigated quality characteristics, depending on the EB irradiation dose (x1) and the dose rate (x2) at constant AMD concentration z3 = 14.7% (or AMD/St weight ratio 8.335), which are calculated by the implementation of the estimated models in Table 1. Table 2 Models for the variance of the product quality characteristics
ln ~ s12 x ln ~ s22 x 2 ~ ln s3 x ln ~ s42 x
Model –3.8165–1.8301x1–1.8470x2+2.4135x3– –2.7529x1x2+0.2421x2x3+0.7634x1x3 1.0867–1.3932x2+1.2312x3–0.8401x1x2+0.9424x2x3–0.2723x1x3 –3.8243–0.7520x2+1.6698x3+3.1626x12-2.0835x22–1.7126x1x2 –6.2547–0.1703x1–0.9083x2+1.0830x3+3.4344x12–1.8865x1x2– –0.5980x1x3
R 0.7819 0.8590 0.8009 0.8251
The standard deviations of the product characteristics are calculated by the equation: ~2 ~ si x eln(si ) .
(5)
Visualization of the standard deviation dependence on the process parameter values for each one of the product characteristics is presented in Figure 2. It can be seen that the standard deviation ~s2 x of the process parameter monomer conversion coefficient (y2, %) has the highest values within the experimental region.
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a) y1 f ( z1 , z 2 )
b) ~ y2 f ( z1 , z2 )
c) ~y3 f ( z1 , z2 )
d) y4 f ( z1 , z2 )
~
~
e) y5 f ( z1 , z2 ) Fig. 1 – Contour plots of the mean values of the quality characteristics at z3 = 14.7% (or AMD/St weight ratio 8.335).
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a)
b)
c)
d)
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Fig. 2 – Contour plots of the standard deviations of product characteristics depending on EB irradiation dose (x1) and the dose rate (x2) at constant AMD concentration z3 = 14.7% ~ (or AMD/St weight ratio 8.335): a) ~ s2 x ; c) ~ s1 x ; b) ~ s3 x ; d) s4 x .
4. OPTIMIZATION
Multi-criteria optimization unifying requirements for economic efficiency, assurance of low toxicity, high copolymer efficiency in flocculation process, good solubility in water, as well as the repeatability of the obtained results is performed. Methods based on graphical optimization and on Pareto-optimization are implemented for solving this task. The set of requirements is the following: ~ residual monomer concentration: y1 ( x) < 5% => assurance of low toxicity; ~ monomer conversion coefficient: y 2 ( x) > 90% => economic efficiency; apparent viscosity: ~y3 ( x) > 3 mPa·s => copolymer efficiency in flocculation process;
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intrinsic viscosity: ~y 4 ( x) > 6 dL/g => copolymer efficiency in flocculation process; Huggins’ constant: 0.3 ~y5 ( x) 1 (or –1.20397 ln ~y5 ( x) 0) => good solubility in water. Graphical optimization is a method for multi-criteria optimization, applicable in cases with formulated one- or two-sided constrains for the product quality characteristics. It is conducted in order to find the regions of the process parameters, working at which the requirements for the quality characteristics are fulfilled simultaneously. The optimal regions are obtained by superimposing the contour plots of the calculated limit values of the characteristics, thus finding the section of all the admissible values of the process parameters. In Fig. 3 the optimal regions of the process parameters values EB irradiation dose (z1) and dose rate (z2), for different concentrations of AMD (z3): 14.7% and 19.6% (or AMD/St weight ratio correspondingly equal to 8.335 and 11.11) are presented. For the lowest AMD concentration z3 = 9.8% (or AMD/St weight ratio 5.56) there is no allowable region for the process parameters, where the optimization requirements are simultaneously fulfilled. It can be seen that at lower concentration of acrylamide z3 = 14.7% (or lower acrylamide/starch (AMD/St) weight ratio), the EB irradiation doses should be chosen in the region 4.8–5.2 kGy and the dose rates should be between 0.5 and 1.0 kGy/min. The increase of the AMD concentration to z3 = 19.6 % requires EB irradiation doses in a wider range from 2.3 to 4.8 kGy and dose rates higher than 0.6 and less than 1.3 kGy/min. Critical restrictions are connected with Huggins’ constant (y5) and good solubility in water; intrinsic (y4) viscosity and copolymer efficiency in flocculation process; as well as monomer conversion coefficient (y2) and economic efficiency. The requirements for the quality characteristics residual monomer concentration ~y1 ( x) < 5% connected with the assurance of low toxicity as well as the apparent viscosity (y3) are fulfilled for wider regime conditions within the experimental region. For improving the reproducibility of the obtained results the variation of the product quality characteristics should be minimized. This puts additional requirements for the solutions that are obtained through graphical optimization. In order to minimize the variances of the product parameters, multi-criterion optimization is performed and compromise Pareto-optimal solutions are obtained (Table 3 and Table 4). If these compromise solutions are compared two by two, one can note the property of these solutions – some of the obtained optimal values are better but at least one value is worse than that in another compromise solution. Every variance function has its minimum at different set of process parameters and a compromise can be chosen among many by some additional criteria. In the tables are presented only six Pareto-optimal solutions. The minimal values for each standard deviation are bolded.
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a)
b) Fig. 3 – Contour plot of the optimal regions of the process parameters EB irradiation dose (z1) and dose rate (z2), for different concentrations of AMD: a) z3 =14.7 % (or AMD/St weight ratio 8.335); b) z3 = 19.6 % (or AMD/St weight ratio 11.11). Table 3 Pareto-optimization – optimal process parameters and standard deviations ~ si x of product characteristics
1 2 3 4 5 6
z1
z2
z3
~ s1 x
~ s2 x
~ s3 x
~ s4 x
4.7815 4.2628 4.3872 4.7686 4.5346 4.3741
1.3038 1.3887 1.3811 1.3066 1.3604 1.3790
16.8766 18.1727 17.9708 16.9291 17.6355 17.9746
0.0463 0.0764 0.0671 0.0470 0.0580 0.0683
1.3142 1.6162 1.5350 1.3228 1.4430 1.5435
0.1635 0.1071 0.1125 0.1615 0.1251 0.1130
0.0547 0.0405 0.0419 0.0541 0.0450 0.0419
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Table 4 ~ Pareto-optimization – optimal process parameters and the values of the constrained means yi ( x) of product characteristics
1 2 3 4 5 6
z1
z2
z3
~ y1 ( x)
~ y 2 ( x)
~ y 3 ( x)
~ y 4 ( x)
~ y 5 ( x)
4.7815 4.2628 4.3872 4.7686 4.5346 4.3741
1.3038 1.3887 1.3811 1.3066 1.3604 1.3790
16.8766 18.1727 17.9708 16.9291 17.6355 17.9746
3.9473 2.6813 3.0080 3.9206 3.3787 2.9572
94.5323 99.4131 98.5060 94.7094 97.2313 98.6489
4.2759 5.7490 5.5014 4.3248 5.1139 5.5255
6.0138 6.0024 6.0214 6.0193 6.0225 6.0089
0.9909 0.9803 0.9963 0.9881 0.9910 0.9798
5. CONCLUSIONS
Regression models for the mean values and the variances of the investigated product quality characteristics depending on the variations of the grafting process parameters during the modification of starch by grafting acrylamide using electron beam irradiation in order to synthesize water-soluble copolymers having flocculation properties were estimated. Optimal regions of the grafting process parameters that satisfy specified optimization criteria based on the estimated models for the mean values of the product parameters were obtained by implementation of graphical optimization. Thus, different optimal regions of EB irradiation dose and dose rate depending on AMD/St weight ratio were identified. The optimal regions were found to be 4.8–5.2 kGy for irradiation doses and 0.5–1.0 kGy/min for dose rates, at AMD/St weight ratio of 8.335. Increase of acrylamide concentration (AMD/St weight ratio of 11.11) required different regions of irradiation doses (2.3–4.8 kGy) and dose rates (0.6–1.3 kGy/min). Compromise Pareto-optimal solutions fulfilling the formulated restrictions and at the same time simultaneously minimizing all the variances of the quality characteristics were received. This additional requirement for robustness (insensitivity) in respect of variations in input parameters and noise factors of the process lead to better reproducibility of the results, together with the implementation of the requirements for economic efficiency, low toxicity, efficient copolymer in flocculation processes and good water solubility. Acknowledgements. Bilateral joint research project between Bulgarian Academy of Sciences (BAS) and Romanian Academy (RA) is acknowledged. Bulgarian co-authors would like to acknowledge the support of the BNF Scientific Investigations under the project DO02-127 (BIn5/2009). This work was also partially supported by a grant of the Romanian National Authority for Scientific Research, CNDI–UEFISCDI, project number 64/2012.
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