By analyzing Figure 2, it was found that speed factor, when increased, also causes increased amounts of response variables tensile strength (MPa) and hardness (BH). Also, the increased speed affects yield response variable reduction (%) and desirability (D) composite reduction.

Regarding the lead temperature factor, with increasing temperature, one realizes values reduction of response variables tensile strength (MPa), Hardness (BH) and desirability

By observing increase in polymer concentration factor, one can see that there will be decrease in response variables values called tensile strength (MPa) and hardness (BH), yield increase

In Table 10, it is shown specifications (minimum, nominal and maximum) relative to 6.50 mm diameter. Also one searches nominal values (target) for mechanical properties called tensile strength and hardness, and for mechanical property called yield, one seeks maximization.

> **Yield (%)**

1770 1875 1980 40 48 ≥ 56 500 530 560

As shown in Figure 3, for obtaining the highest possible value for *desirability* composite (D),

Maximum (target)

Minimum

Maximum Minimum Nominal

**Hardness (BH)**

Nominal (target)

Maximum

**•** For response variable called hardness, d=0.96916.

**•** For response variable called yield, d=1.0;

with required specifications and are: **•** For tensile strength (y= 2029.5 MPa);

**•** For yield (y= 54.8182 %);

74 Design of Experiments - Applications

**•** For hardness (y= 572.8636 BH).

(%) and desirability composite (D).

**Traction resistance limit (MPa)**

Nominal (target)

**Table 10.** Specifications for 6.50 mm gauge

the best factors adjustments are:

**•** Lead temperature, fit at -0.1919;

**•** Polymer concentration, fit at 1.0.

**•** Speed, fit at -1.0;

Minimum

**•** For hardness, (y= 529.7879 BH);

Regarding the speed factor, by increasing the speed one obtains values increase of response variable called tensile strength (MPa) and hardness (BH). Also, with increasing speed factor, it is observed a response variable reduction called yield (%) and desirability composite reduction (D).

Regarding the lead temperature factor, the increase means that there is all response variables decrease, including the desirability composite (D). By observing the polymer concentration factor, it is found that the increase will cause decrease of response variables tensile strength and hardness, increasing yield and desirability composite (D).

**References**

483-496.

editora LTC, (2002). , 589.

[1] Benyounis, K. Y, & Olabi, A. G. Optimization of different welding processes using statistical and numerical approaches- A reference guide, *Science Direct*, (2008). , 39,

Optimization of Multiple Responses in Quench Hardening and…

http://dx.doi.org/10.5772/56544

77

[2] Callister, J. R. W. D. *Uma introdução a engenharia e a ciências dos materiais*, 5ª edição,

[3] Derringer, G, & Suich, R. Simultaneous Optimization of Several Response Variables,

[4] Granato, D, Branco, G. F, & Calado, V. M. A. Experimental design and application of response surface methodology for process modeling and optimization: A review,

[5] Lima, V. B. S, Balestrassi, P. P, & Paiva, A. P. Otimização do desempenho de amplifi‐ cadores de radio frequência banda larga: uma abordagem experimental, *Produção*, n.

[6] Mayers, A. M, & Chawla, K. K. *Princípios de metalurgia mecânica,* 2ª edição, Edgard

[8] Montgomery, D. C, & Runger, G. C. *Estatística aplicada e probabilidade para engenheiros*,

[9] Paiva, E. J. *Otimização de Manufatura com Múltiplas Respostas baseadas em índices de ca‐*

[10] Silva, H. A, & Silva, M. B. Aplicação de um projeto de Experiments (DOE) na solda‐ gem de tubos de zircaloy-4; *Produção & Engenharia*, n. 1, set./dez. (2008). , 1, 41-52. [11] Wang, J, & Wan, W. Application of desirability function based on neural network for optimizing biohydrogen production process, *international journal o f hydrogen energy*,

[12] Wu, F. C. optimization of correlated multiple quality characteristics using desirabili‐

*pacidade,* Dissertação, Universidade Federal de Itajubá, (2008). p.

ty function. *Quality engineering*, n 1, (2005). , 17, 119-126.

th edition, John Wiley & Sons,

Journal of Quality Technology, n 4, (1980). , 12, 214-219.

[7] Montgomery, C. D. *Design and analysis of experiments,* 7

2ª edição, editora LTC, (2003). p., 2003, 230-320.

*Food Research International*, (2011). , 1, 0-14.

1, jan/mar, (2011). , 21, 118-131.

Blucher, (1982). p.

(2009). , 34, 1253-1259.

(2010). p.

The red line (vertical) contained in Figure 3, can be interpreted as follows: in case it is moved, it will change the response values, and this will directly affect the composite desirability (D) values and individual desirability (d). For instance, by moving the red line, contained in the space relative to the lead temperature factor to the right, it will provide drop in the desirability composite (D), and all response variables (shown in Figure 3). It is possible to realize the drop in desirability composite (D) by observing the slope of straight contained in the location indicated previously. This decrease in D would represent optimization reduction of multiple responses and consequently no use of responses at their best factors adjustment conditions.

### **5. Conclusions**

The design of experiments methodology with analysis in blocks applied to quench hardening and tempering process in SAE 9254 drawn steel wires with 2.00 mm and 6.50 mm diameters provided a wide understanding of factors influence in mechanical properties called tensile strength, hardness and yield.

By means of significance test (through of the Minitab Statistical Software), it was possible to find that factors such as diameter, speed, tempering temperature and polymer concentration have a significant influence on the studied mechanical properties and by statistical methods application it was possible to model the process, obtaining the best factors adjustment condition, which in turn, provided simultaneously multiple responses optimization.

Through the findings generated by this study, one seeks to fit in a planned way the quench hardening furnace set-up in a productive environment, obtaining, this way, reduction of initial laboratory tests amount and waiting time of these results, whose cost impacts directly the company financial indicators.

### **Author details**

Cristie Diego Pimenta1 , Messias Borges Silva1 , Rosinei Batista Ribeiro2 , Roberto Campos Leoni1 , Ricardo Batista Penteado1 , Fabrício Maciel Gomes1 and Valério Antonio Pamplona Salomon1

\*Address all correspondence to<EMAIL_ADDRESS>
1 FEG UNESP – SP / Brasil, Guaratinguetá-SP, Brasil

2 FATEA – SP / Brasil, Lorena – SP, Brasil

### **References**

Regarding the lead temperature factor, the increase means that there is all response variables decrease, including the desirability composite (D). By observing the polymer concentration factor, it is found that the increase will cause decrease of response variables tensile strength

The red line (vertical) contained in Figure 3, can be interpreted as follows: in case it is moved, it will change the response values, and this will directly affect the composite desirability (D) values and individual desirability (d). For instance, by moving the red line, contained in the space relative to the lead temperature factor to the right, it will provide drop in the desirability composite (D), and all response variables (shown in Figure 3). It is possible to realize the drop in desirability composite (D) by observing the slope of straight contained in the location indicated previously. This decrease in D would represent optimization reduction of multiple responses and consequently no use of responses at their best factors adjustment conditions.

The design of experiments methodology with analysis in blocks applied to quench hardening and tempering process in SAE 9254 drawn steel wires with 2.00 mm and 6.50 mm diameters provided a wide understanding of factors influence in mechanical properties called tensile

By means of significance test (through of the Minitab Statistical Software), it was possible to find that factors such as diameter, speed, tempering temperature and polymer concentration have a significant influence on the studied mechanical properties and by statistical methods application it was possible to model the process, obtaining the best factors adjustment

Through the findings generated by this study, one seeks to fit in a planned way the quench hardening furnace set-up in a productive environment, obtaining, this way, reduction of initial laboratory tests amount and waiting time of these results, whose cost impacts directly the

, Rosinei Batista Ribeiro2

, Roberto Campos Leoni1

and Valério Antonio Pamplona Salomon1

,

condition, which in turn, provided simultaneously multiple responses optimization.

, Messias Borges Silva1

\*Address all correspondence to<EMAIL_ADDRESS>
1 FEG UNESP – SP / Brasil, Guaratinguetá-SP, Brasil

2 FATEA – SP / Brasil, Lorena – SP, Brasil

, Fabrício Maciel Gomes1

and hardness, increasing yield and desirability composite (D).

**5. Conclusions**

76 Design of Experiments - Applications

strength, hardness and yield.

company financial indicators.

**Author details**

Cristie Diego Pimenta1

Ricardo Batista Penteado1

**Chapter 5**

**Taguchi Method Applied to Environmental Engineering**

Over the last decades, environmental concerns have become more critical and frequent. This is, mainly, due to population growth and the increase of industrial activities in which anthro‐ pogenic actions have reached catastrophic proportions resulting in changes of soil, air, and

Environmental pollution by industrial effluent is being characterized as one of the major causes of the aggravation of this problem. Residues, in general, produce diversified compounds, containing, frequently, pollutants that are toxic and resistant to conventional treatments such as coagulation/flocculation or biodegradation [2], and they are eventually discharged, in most of the cases, in an inadequate way causing severe damages. Regarding the environmental problem, researchers were driven to study the feasibility of new techniques and methodolo‐ gies, as well as, the emission and pollutant discharge control. In order to apply the pollution control and to attend environmental legislation, patterns and quality indicators were estab‐ lished. In terms of water quality: oxygen concentration, phenols, Hg, pH, temperature, among

Companies search for new environmental alternatives to treat generated residuals. The environmental reality is demanding for further actions to mitigate industrial impacts on water. Therefore, water treatment has become a mandatory investment to industries, institutions, and

> © 2013 de Freitas et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 de Freitas et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

others with the aim to attending environmental laws, as well as ISO 14000 series.

Ana Paula Barbosa Rodrigues de Freitas, Leandro Valim de Freitas,

Carla Cristina Almeida Loures, Marco Aurélio Reis dos Santos,

Geisylene Diniz Ricardo, Fernando Augusto Silva Marins, Hilton Túlio Lima dos Santos, Gisella Lamas Samanamud,

Mateus Souza Amaral and Messias Borges Silva

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/56531

**1. Introduction**

water quality [1].

other requirements [3].

### **Taguchi Method Applied to Environmental Engineering**

Ana Paula Barbosa Rodrigues de Freitas, Leandro Valim de Freitas, Carla Cristina Almeida Loures, Marco Aurélio Reis dos Santos, Geisylene Diniz Ricardo, Fernando Augusto Silva Marins, Hilton Túlio Lima dos Santos, Gisella Lamas Samanamud, Mateus Souza Amaral and Messias Borges Silva

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/56531

### **1. Introduction**

Over the last decades, environmental concerns have become more critical and frequent. This is, mainly, due to population growth and the increase of industrial activities in which anthro‐ pogenic actions have reached catastrophic proportions resulting in changes of soil, air, and water quality [1].

Environmental pollution by industrial effluent is being characterized as one of the major causes of the aggravation of this problem. Residues, in general, produce diversified compounds, containing, frequently, pollutants that are toxic and resistant to conventional treatments such as coagulation/flocculation or biodegradation [2], and they are eventually discharged, in most of the cases, in an inadequate way causing severe damages. Regarding the environmental problem, researchers were driven to study the feasibility of new techniques and methodolo‐ gies, as well as, the emission and pollutant discharge control. In order to apply the pollution control and to attend environmental legislation, patterns and quality indicators were estab‐ lished. In terms of water quality: oxygen concentration, phenols, Hg, pH, temperature, among other requirements [3].

Companies search for new environmental alternatives to treat generated residuals. The environmental reality is demanding for further actions to mitigate industrial impacts on water. Therefore, water treatment has become a mandatory investment to industries, institutions, and others with the aim to attending environmental laws, as well as ISO 14000 series.

© 2013 de Freitas et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 de Freitas et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this context, textile sector can be referred because of its great industrial area that gener‐ ates a high volume of effluent deeply colored and containing high concentration of organ‐ ic compounds, which if not treated, may cause serious damage to environmental contamination [4].

•OH + OM Intermediates ® (2)

Taguchi Method Applied to Environmental Engineering

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BC,

81

The several AOPs are split into two groups: Homogenous Processes and Heterogeneous Processes. The former occur in one single phase and use ozone, H2O2 or Fenton reagent (mixture of H2O2 with salts of Fe2+) as hydroxyl radical generators. The latter uses semicon‐

Practical studies using TiO2 have been developed; however, the reaction mechanism is not totally understandable, yet. Nevertheless, most of researchers agree on some mechanisms steps such as: the excitation of semiconductors species and the formation of h+BV and e-

the recombination process among them, O2, H2O adsorption and organic species on the semiconductor surface, "trapping" where chemical species donate or accept a pair of electrons e-/h+ preventing the recombination. It is believed that O2 is the main responsible specie to give continuity to the reactions started during the photo-oxidation process, reacting as a formed organic radical and promoting a complete mineralization [15-16]. Figure 1 shows the excitation

**Figure 1.** Schematic illustration of electricity generation and hydrogen production by solar energy conversion using

Direct oxidation process occurs when a photogerated gap in the valence band of semiconductor

Indirect oxidation process occurs when a photogerated gap in the valence band of semicon‐ ductor reacts with H2O molecule adsorbed on the semiconductor surface producing hydroxyl

( ) ( ) R ads + h+BV R ads 1 1 ® (3)

semiconducting materials. CB: Conduction band, VB: Valence band Source: [17].

reacts directly with the organic compound (Equation 3) [18].

radical that will oxide the organic material (Equation 4) [18-19].

ductors as catalysts (titanium dioxide, zinc oxide, etc.)[14].

**3. Heterogeneous photocatalysis**

scheme of the semiconductors.

Hazardous waste treatment and the presence of organic pollutants in water have increased the use of alternatives to environmental matrixes such as the use of Advanced Oxidation Processes (AOPs) to residual water treatment [5].

This work features the application of Design of Experiments; Taguchi L9 Orthogonal Array; in the effluent treatment of polyester resin that is originated from textile industries and through the application of Advanced Oxidation Processes (Heterogeneous Photocatalysis - UV/TiO2) in the study of chemical oxygen demand.

### **2. Advanced oxidation processes**

Advanced Oxidation Processes (AOP's) and electrochemical methodologies are developed to treat the contaminants of drinking water and industrial effluents. The oxidation processes are based on reactive species generation that degrades a great variety of organic pollutants, in a quick and non-selective way. Reactive species are unstable and must be generated continu‐ ously *"in situ*", through chemical or photochemical reactions [6].

AOPs are defined as processes with great capacity of producing hydroxyl radicals (•OH), that are reactive species. The high standard potential of radical's reduction is demonstrated by Equation 1. This radical is capable of oxidizing a great variety of organic compounds to CO2, H2O and inorganic ions originated from heteroatoms [7-8].

$$\bullet \text{OH} + \text{e}^\cdot + \text{H} + \rightarrow \text{H}\_2\text{O} \tag{1}$$

$$\text{E}\_o = 2.730 \text{ V} \tag{1}$$

Its destructive process is one of its great advantages. Contaminants are chemically destroyed instead of undergoing a phase change that happens, for instance, in physical-chemical processes of adsorption, filtration, precipitation, coagulation, flocculation, sedimentation, flotation, membrane use, organic and inorganic adsorption, centrifugation, reverse osmosis, extraction, distillation and evaporation [9]. The final disposition of solid phases continues being a problem without any solution; therefore, a passive agent [10]. This reagent is very few selective, electrophilic character, easy to produce and detains kinetic reaction control [11].

The hydroxyl radicals can be obtained from strong oxidants, as H2O2 and O3 combined or not with UV radiation, with salts of Iron II or III, combined or not, with radiation, photocatalysis with TiO2 or water photolosys with UV radiation [12].

The organic matter (OM) present in the system is attacked by hydroxyl radical at the moment that it is generated, and as a consequence of this process, the effluent is degraded to other intermediate products described in Equation 2[13].

$$\bullet \text{OH} + \bullet \text{M} \to \text{Intermediate} \tag{2}$$

The several AOPs are split into two groups: Homogenous Processes and Heterogeneous Processes. The former occur in one single phase and use ozone, H2O2 or Fenton reagent (mixture of H2O2 with salts of Fe2+) as hydroxyl radical generators. The latter uses semicon‐ ductors as catalysts (titanium dioxide, zinc oxide, etc.)[14].

### **3. Heterogeneous photocatalysis**

In this context, textile sector can be referred because of its great industrial area that gener‐ ates a high volume of effluent deeply colored and containing high concentration of organ‐ ic compounds, which if not treated, may cause serious damage to environmental

Hazardous waste treatment and the presence of organic pollutants in water have increased the use of alternatives to environmental matrixes such as the use of Advanced Oxidation

This work features the application of Design of Experiments; Taguchi L9 Orthogonal Array; in the effluent treatment of polyester resin that is originated from textile industries and through the application of Advanced Oxidation Processes (Heterogeneous Photocatalysis - UV/TiO2)

Advanced Oxidation Processes (AOP's) and electrochemical methodologies are developed to treat the contaminants of drinking water and industrial effluents. The oxidation processes are based on reactive species generation that degrades a great variety of organic pollutants, in a quick and non-selective way. Reactive species are unstable and must be generated continu‐

AOPs are defined as processes with great capacity of producing hydroxyl radicals (•OH), that are reactive species. The high standard potential of radical's reduction is demonstrated by Equation 1. This radical is capable of oxidizing a great variety of organic compounds to CO2,

Its destructive process is one of its great advantages. Contaminants are chemically destroyed instead of undergoing a phase change that happens, for instance, in physical-chemical processes of adsorption, filtration, precipitation, coagulation, flocculation, sedimentation, flotation, membrane use, organic and inorganic adsorption, centrifugation, reverse osmosis, extraction, distillation and evaporation [9]. The final disposition of solid phases continues being a problem without any solution; therefore, a passive agent [10]. This reagent is very few selective, electrophilic character, easy to produce and detains kinetic reaction control [11].

The hydroxyl radicals can be obtained from strong oxidants, as H2O2 and O3 combined or not with UV radiation, with salts of Iron II or III, combined or not, with radiation, photocatalysis

The organic matter (OM) present in the system is attacked by hydroxyl radical at the moment that it is generated, and as a consequence of this process, the effluent is degraded to other

2 o •OH + e + H+ H O E = 2,730 V ® (1)

contamination [4].

80 Design of Experiments - Applications

Processes (AOPs) to residual water treatment [5].

in the study of chemical oxygen demand.

**2. Advanced oxidation processes**

ously *"in situ*", through chemical or photochemical reactions [6].

H2O and inorganic ions originated from heteroatoms [7-8].

with TiO2 or water photolosys with UV radiation [12].

intermediate products described in Equation 2[13].

Practical studies using TiO2 have been developed; however, the reaction mechanism is not totally understandable, yet. Nevertheless, most of researchers agree on some mechanisms steps such as: the excitation of semiconductors species and the formation of h+BV and e-BC, the recombination process among them, O2, H2O adsorption and organic species on the semiconductor surface, "trapping" where chemical species donate or accept a pair of electrons e-/h+ preventing the recombination. It is believed that O2 is the main responsible specie to give continuity to the reactions started during the photo-oxidation process, reacting as a formed organic radical and promoting a complete mineralization [15-16]. Figure 1 shows the excitation scheme of the semiconductors.

**Figure 1.** Schematic illustration of electricity generation and hydrogen production by solar energy conversion using semiconducting materials. CB: Conduction band, VB: Valence band Source: [17].

Direct oxidation process occurs when a photogerated gap in the valence band of semiconductor reacts directly with the organic compound (Equation 3) [18].

$$\text{R}\_1\text{(ads)} + \text{h} + \text{BV} \rightarrow \text{R}\_1\text{(ads)}\tag{3}$$

Indirect oxidation process occurs when a photogerated gap in the valence band of semicon‐ ductor reacts with H2O molecule adsorbed on the semiconductor surface producing hydroxyl radical that will oxide the organic material (Equation 4) [18-19].

$$\bullet \text{OH} \bullet \text{R}\_1 \rightarrow \text{R}\_2 \tag{4}$$

**6. Design of Experiments (DOE)**

eters in multivariable systems [28].

21 W.

resin effluent.

**7. Taguchi method**

Design of Experiments has been widely used to optimize processes parameters and to improve the quality of products with the application of engineering concepts and statistics [26].

Taguchi Method Applied to Environmental Engineering

http://dx.doi.org/10.5772/56531

83

Design of Experiments is defined as a set of applied statistical planning techniques, conducting, analyzing and interpreting controlled tests with the aim to find and define factors that may

DOE considers interaction among variables and may be used to optimize operational param‐

According to [29], design of experiments was studied as a relevant mathematical tool in the area of Advanced Oxidation Processes. Taguchi's Orthogonal Array L9 was used in this work for the degradation of organic material of the polyester resin effluent and the percentage reduction of the total organic carbon obtained in the treatment was 39.489%. This removal of organic load corresponds to an average ratio of TOC removal. This condition is inclusive of the weight ratio of hydrogen peroxide at 183g, pH = 3, TiO2 = 0.250 g/L and lamp intensity =

Design of experiments was used by [30] in the degradation of organic material of the polyester resin effluent by advanced oxidation processes. Taguchi's Orthogonal Array L16 was used to select statistically the most significant factors in the process; being optimized, lately. It was concluded that more influent variables permitted a reduction of 34% COD of the polyester

According to [31], Taguchi's method is a powerful mathematical tool capable to find significant

**•** Analyzing results by using signal-to-noise ratio (S/N) and analysis of variance (ANOVA);

There are independent variables or entries in the signal-to-noise ratio that compromises the performance of a process. For this reason, two categories are defined: controllable and non-

parameters of an ideal process through multiple qualitative aspects.

**•** Identifying factors (entry variables) and choosing the levels;

**•** Performing random experiments to avoid systematic errors;

**•** Selecting the appropriate orthogonal array according to literature [33];

The application of Taguchi's method [32] consists of:

**•** Selecting the variable response to be optimized;

**•** Finding the best parameter settings.

controllable factors [34].

influence values of a parameter or of a group of parameters [27].

Photocatalytic process has been efficiently used to degrade innumerable recalcitrant substan‐ ces prior to the biological treatment.

### **4. Benefits of advanced oxidation processes**

Advanced Oxidation Processes offer several advantages when compared to conventional oxidation processes [20-21].

### **5. Chemical Oxygen Demand (COD)**

Chemical Oxygen Demand (COD) measures the amount of oxygen consumed through the organic material in water and, also represents an essential parameter in the characterization study of sanitary wastewater and industrial effluents. COD is crucial when used along with BOD to analyze and evaluate wastewater biodegradability [22].

By determining COD, the oxidation-reduction reaction is performed in a closed system using potassium dichromate due to its high oxidative capacity and to its application in a large variety of samples and operational feasibility [23].

Sample results of COD using potassium dichromate as an oxidation agent are superior to BOD, because the high oxidative power of the potassium dichromate is greater if compared to the action of micro-organisms, except in rarely cases, as aromatic hydrocarbonetes and pyridine. BOD measures only the biodegradable fraction. The more this value approximates to COD more easily biodegradable the effluent is [22, 24-25].

### **6. Design of Experiments (DOE)**

1 2 •OH + R R ® (4)

Photocatalytic process has been efficiently used to degrade innumerable recalcitrant substan‐

Advanced Oxidation Processes offer several advantages when compared to conventional

**•** Destroy resistant refractory compounds to other treatments, as for example, biological

**•** Used in effluents with high toxicity that can entail a certain difficulty in the biological process

Chemical Oxygen Demand (COD) measures the amount of oxygen consumed through the organic material in water and, also represents an essential parameter in the characterization study of sanitary wastewater and industrial effluents. COD is crucial when used along with

By determining COD, the oxidation-reduction reaction is performed in a closed system using potassium dichromate due to its high oxidative capacity and to its application in a large variety

Sample results of COD using potassium dichromate as an oxidation agent are superior to BOD, because the high oxidative power of the potassium dichromate is greater if compared to the action of micro-organisms, except in rarely cases, as aromatic hydrocarbonetes and pyridine. BOD measures only the biodegradable fraction. The more this value approximates to COD

ces prior to the biological treatment.

oxidation processes [20-21].

82 Design of Experiments - Applications

treatment;

treatment;

**•** Enable *in situ* treatment;

**•** Do not create reaction by-products;

**5. Chemical Oxygen Demand (COD)**

of samples and operational feasibility [23].

more easily biodegradable the effluent is [22, 24-25].

**4. Benefits of advanced oxidation processes**

**•** Assimilate a large variety of organic compounds;

**•** May be used in other processes as a pre or post-treatment;

**•** Improve the organoleptic properties of the treated water; **•** Contain oxidizing power with elevated kinetic reaction.

BOD to analyze and evaluate wastewater biodegradability [22].

**•** Complete mineralization of pollutants;

Design of Experiments has been widely used to optimize processes parameters and to improve the quality of products with the application of engineering concepts and statistics [26].

Design of Experiments is defined as a set of applied statistical planning techniques, conducting, analyzing and interpreting controlled tests with the aim to find and define factors that may influence values of a parameter or of a group of parameters [27].

DOE considers interaction among variables and may be used to optimize operational param‐ eters in multivariable systems [28].

According to [29], design of experiments was studied as a relevant mathematical tool in the area of Advanced Oxidation Processes. Taguchi's Orthogonal Array L9 was used in this work for the degradation of organic material of the polyester resin effluent and the percentage reduction of the total organic carbon obtained in the treatment was 39.489%. This removal of organic load corresponds to an average ratio of TOC removal. This condition is inclusive of the weight ratio of hydrogen peroxide at 183g, pH = 3, TiO2 = 0.250 g/L and lamp intensity = 21 W.

Design of experiments was used by [30] in the degradation of organic material of the polyester resin effluent by advanced oxidation processes. Taguchi's Orthogonal Array L16 was used to select statistically the most significant factors in the process; being optimized, lately. It was concluded that more influent variables permitted a reduction of 34% COD of the polyester resin effluent.

### **7. Taguchi method**

According to [31], Taguchi's method is a powerful mathematical tool capable to find significant parameters of an ideal process through multiple qualitative aspects.

The application of Taguchi's method [32] consists of:

There are independent variables or entries in the signal-to-noise ratio that compromises the performance of a process. For this reason, two categories are defined: controllable and noncontrollable factors [34].

**•** H2O2 was added, and

**Controlled Variables (Factors)**

C- H2O2 \*

**Table 1.** Controlled Variables and Levels

**Experiment pH**

**Factor A**

**Table 2.** Taguchi's Orthogonal Array L9, with 4 factors and 3 levels each

**9. Results and discussion**

**•** Simultaneously, the UV lamp was turned on.

variables and levels used in the degradation process.

were performed on each experimental condition.

The design of experiments of polyester resin effluent was performed in a Taguchi's Orthogonal Array L9. pH, titanium dioxide (TiO2), ultraviolet lamp and hydrogen peroxide with concen‐ tration of 30% w/w were used in this process as controlled variables. Table 1 shows the

Table 2 shows Taguchi's Orthogonal Array L9, where experimental procedures were per‐ formed at random and, after each experimental procedure, chemical oxygen demand analysis

A- Ph 3.0 5.0 7.0 B- TiO2 [g/L] 0.083 0.167 0.25

D- UV [W] Without 15 21

[g] 120.0 151.0 182.0

**TiO2 Factor B**

1 1 1 1 1 2 1 2 2 2 3 1 3 3 3 4 2 1 2 3 5 2 2 3 1 6 2 3 1 2 7 3 1 3 2 8 3 2 1 3 9 3 3 2 1

**Level 1 Level 2 Level 3**

**H2O2 Factor C**

Taguchi Method Applied to Environmental Engineering

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85

**UV Factor D**

**Figure 2.** Tubular reactor used for photochemical treatment Source: [28]

Taguchi's method uses orthogonal arrays to study diverse factors with a reduced number of experiments [35]. Besides that, the method can offer other advantages as: process variability reduction, conformity of the expected result and, consequently, operational cost reduction [36].

The analysis of variance (ANOVA) is applied to Taguchi's statistical method to evaluate the significance of parameters used in the process [37].

### **8. Materials**

The polyester resin effluent was conditioned in a chamber at 4 ºC. The oxidation reaction of the effluent was performed in a tubular reactor of Germetec brand, Model GPJ-463/1, with nominal volume of approximately 1L, receiving radiation from a low-pressure mercury lamp type GPH-463T5L emitting UV radiation of 254 mm intensity of 15 W and 21 W, protected by a quartz pipe according to Figure 2.

The design of experiments followed these steps:

### **9. Results and discussion**

The design of experiments of polyester resin effluent was performed in a Taguchi's Orthogonal Array L9. pH, titanium dioxide (TiO2), ultraviolet lamp and hydrogen peroxide with concen‐ tration of 30% w/w were used in this process as controlled variables. Table 1 shows the variables and levels used in the degradation process.

Table 2 shows Taguchi's Orthogonal Array L9, where experimental procedures were per‐ formed at random and, after each experimental procedure, chemical oxygen demand analysis were performed on each experimental condition.

Taguchi's method uses orthogonal arrays to study diverse factors with a reduced number of experiments [35]. Besides that, the method can offer other advantages as: process variability reduction, conformity of the expected result and, consequently, operational cost reduction [36]. The analysis of variance (ANOVA) is applied to Taguchi's statistical method to evaluate the

The polyester resin effluent was conditioned in a chamber at 4 ºC. The oxidation reaction of the effluent was performed in a tubular reactor of Germetec brand, Model GPJ-463/1, with nominal volume of approximately 1L, receiving radiation from a low-pressure mercury lamp type GPH-463T5L emitting UV radiation of 254 mm intensity of 15 W and 21 W, protected by

significance of parameters used in the process [37].

**Figure 2.** Tubular reactor used for photochemical treatment Source: [28]

a quartz pipe according to Figure 2.

**•** Then, it was added TiO2,

The design of experiments followed these steps:

**•** 1L of effluent for 2L of distilled water was firstly added,

**•** The system for the effluent recirculation was turned on,

**8. Materials**

84 Design of Experiments - Applications

**Table 2.** Taguchi's Orthogonal Array L9, with 4 factors and 3 levels each

The COD of the effluent sample *in natura* was initially calculated with a mean value of 49990mg/L and, lately submitted to a pre-treatment. For each experiment, the COD of each sample *in natura* was calculated to an equal period of 60-minute-reaction. Then, the percentage of reduction of COD was calculated for each experiment and the results are shown in Table 3 and 4.

For experiments performed in the first replica, it is noticeable that oxidative processes reduced COD until 82.345% of the initial amount, being experiment 4 the one with best experimental condition for the degradation experiment, consisting of pH of 5, titanium dioxide of 0.083

Taguchi Method Applied to Environmental Engineering

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87

The design experiments of the second replica featured that advanced oxidation processes reduced COD until 83.34% of the initial amount, being experiment 6 the one with best experimental variables conditions at pH of 5, titanium dioxide of 0.25g/L, titanium peroxide

**Factors Sum of Squares DF Mean Sum Fisher Test P-Value** Intercept 101741.1 1 101741.1 33172.66 0.000000 pH 40.2 2 20.1 6.56 0.017495 TiO2 0.2 2 0.1 0.03 0.975085 H2O2 264.7 2 132.3 43.15 0.000024 UV 149.6 2 74.8 24.39 0.000232

Table 5 shows ANOVA factor involved in the polyester resin effluent treatment with the Heterogeneous Photocatalytic Process. The analysis of variance with 95% trust, critical F equal to 4.26 and p-value lower than 5% demonstrated that hydrogen peroxide (F= 6.56 and P-value= 1,7%), temperature (F= 43,15 and P-value= 0,0024%) and lamp intensity(F= 24,39 and P-value=

Taguchi's L9 statistical design of experiment (Figure 3) showed more significant parameters for the organic material degradation of the effluent, corresponding to pH=5 adjusted to medium level, TiO2 adjusted to any level, H2O2 concentration = 120g and the ultraviolet lamp

According to [38], the influence of peroxide and temperature is related to the efficiency ratio in the use of this compound and its accelerated decomposition in the reactional medium. Figure 4 shows the most significant factors to a percentage reduction of Chemical Oxygen Demand. The graph of surface response shows an increase in the degradation of polyester resin compounds by the increase in the UV lamp intensity for lower hydrogen peroxide ratio.

Advanced Oxidation Process (Heterogeneous Photocatalysis) for the Taguchi design of this work was evaluated, in which values are found to be significant to the chemical oxygen

g/L, hydrogen peroxide of 151 g and ultraviolet lamp intensity of 21 watts.

of 120 g and ultraviolet lamp intensity of 15 Watts.

Error 27.6 9 3.1

**Table 5.** Analysis of Variance for polyester resin effluent degradation

0,0232%), were significant in the COD removal process.

intensity adjusted to maximum level of 21 W.

The highest percentage reduction is of 83%.

**10. Conclusions**

**Table 3.** Result of replica 1 - percentage reduction obtained by experiments for an initial COD amount of 49990 mg/l.

**Table 4.** Results of replica 2 – percentage reduction obtained by experiments, for an initial COD amount of 49990 mg/l.

For experiments performed in the first replica, it is noticeable that oxidative processes reduced COD until 82.345% of the initial amount, being experiment 4 the one with best experimental condition for the degradation experiment, consisting of pH of 5, titanium dioxide of 0.083 g/L, hydrogen peroxide of 151 g and ultraviolet lamp intensity of 21 watts.

The design experiments of the second replica featured that advanced oxidation processes reduced COD until 83.34% of the initial amount, being experiment 6 the one with best experimental variables conditions at pH of 5, titanium dioxide of 0.25g/L, titanium peroxide of 120 g and ultraviolet lamp intensity of 15 Watts.

**Table 5.** Analysis of Variance for polyester resin effluent degradation

Table 5 shows ANOVA factor involved in the polyester resin effluent treatment with the Heterogeneous Photocatalytic Process. The analysis of variance with 95% trust, critical F equal to 4.26 and p-value lower than 5% demonstrated that hydrogen peroxide (F= 6.56 and P-value= 1,7%), temperature (F= 43,15 and P-value= 0,0024%) and lamp intensity(F= 24,39 and P-value= 0,0232%), were significant in the COD removal process.

Taguchi's L9 statistical design of experiment (Figure 3) showed more significant parameters for the organic material degradation of the effluent, corresponding to pH=5 adjusted to medium level, TiO2 adjusted to any level, H2O2 concentration = 120g and the ultraviolet lamp intensity adjusted to maximum level of 21 W.

According to [38], the influence of peroxide and temperature is related to the efficiency ratio in the use of this compound and its accelerated decomposition in the reactional medium.

Figure 4 shows the most significant factors to a percentage reduction of Chemical Oxygen Demand. The graph of surface response shows an increase in the degradation of polyester resin compounds by the increase in the UV lamp intensity for lower hydrogen peroxide ratio. The highest percentage reduction is of 83%.

### **10. Conclusions**

The COD of the effluent sample *in natura* was initially calculated with a mean value of 49990mg/L and, lately submitted to a pre-treatment. For each experiment, the COD of each sample *in natura* was calculated to an equal period of 60-minute-reaction. Then, the percentage of reduction of COD was calculated for each experiment and the results are shown in Table

> **H2O2 Factor C**

1 1 1 1 1 73.44

2 1 2 2 2 78.39

3 1 3 3 3 72.77

4 2 1 2 3 82.35

5 2 2 3 1 69.81

6 2 3 1 2 80.70

7 3 1 3 2 71.13

8 3 2 1 3 78.71

9 3 3 2 1 71.13

**Table 3.** Result of replica 1 - percentage reduction obtained by experiments for an initial COD amount of 49990 mg/l.

 1 1 1 1 73.11 1 2 2 2 76.08 1 3 3 3 70.14 2 1 2 3 81.69 2 2 3 1 65.85 2 3 1 2 83.34 3 1 3 2 69.15 3 2 1 3 81.69 3 3 2 1 73.77

**Table 4.** Results of replica 2 – percentage reduction obtained by experiments, for an initial COD amount of 49990

**H2O2 Factor C**

**TiO2 Factor B**

**UV Factor D**

**UV Factor D** **Replica 1 reduction of chemical oxygen demand (%)**

**Replica 2 reduction of chemical oxygen demand (%)**

3 and 4.

**Experiment pH**

86 Design of Experiments - Applications

**Experiment pH**

mg/l.

**Factor A**

**Factor A**

**TiO2 Factor B**

> Advanced Oxidation Process (Heterogeneous Photocatalysis) for the Taguchi design of this work was evaluated, in which values are found to be significant to the chemical oxygen

**Figure 3.** Graphic of Average Impact Factors

demand removal. This design of experiment verified that the highest COD reduction is related to the increase in peroxide hydrogen concentration of 120g, pH=5 and use of UV lamp, since the mechanism of photocatalysis requires energy to the degradation of organic matter of the effluent. Taguchi L9 Orthogonal Array found was 83%, which demonstrates efficiency on the use of design of experiments and alternative methodologies to the degradation of organic load of polyester resin effluents.

**Author details**

Fernando Augusto Silva Marins2

1 Petróleo Brasileiro SA (PETROBRAS), Brasil

**Figure 4.** Graphic of influential factors on COD removal

2 São Paulo State University (UNESP), Brasil

4 University of Texas at San Antonio (UTSA), Brasil

3 University of São Paulo (USP), Brasil

Mateus Souza Amaral3

**References**

Ana Paula Barbosa Rodrigues de Freitas2,3, Leandro Valim de Freitas1,2, Carla Cristina Almeida Loures2,3, Marco Aurélio Reis dos Santos2

and Messias Borges Silva2,3

, Hilton Túlio Lima dos Santos3

[1] Mulbry, W.; Kondrad, S.; Pizarro, C.; Kebede-Westhead, E. Treatment of dairy man‐ ure effluent using freshwater algae: Algal productivity and recovery of manure nu‐

, Geisylene Diniz Ricardo2

Taguchi Method Applied to Environmental Engineering

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89

, Gisella Lamas Samanamud4

,

,

### **Acknowledgements**

The authors would like to thank Fundação para o Desenvolvimento Científico e Tecnológico (FDCT) for translation support.

**Figure 4.** Graphic of influential factors on COD removal

### **Author details**

Ana Paula Barbosa Rodrigues de Freitas2,3, Leandro Valim de Freitas1,2, Carla Cristina Almeida Loures2,3, Marco Aurélio Reis dos Santos2 , Geisylene Diniz Ricardo2 , Fernando Augusto Silva Marins2 , Hilton Túlio Lima dos Santos3 , Gisella Lamas Samanamud4 , Mateus Souza Amaral3 and Messias Borges Silva2,3

### **References**

demand removal. This design of experiment verified that the highest COD reduction is related to the increase in peroxide hydrogen concentration of 120g, pH=5 and use of UV lamp, since the mechanism of photocatalysis requires energy to the degradation of organic matter of the effluent. Taguchi L9 Orthogonal Array found was 83%, which demonstrates efficiency on the use of design of experiments and alternative methodologies to the degradation of organic load

The authors would like to thank Fundação para o Desenvolvimento Científico e Tecnológico

of polyester resin effluents.

**Figure 3.** Graphic of Average Impact Factors

88 Design of Experiments - Applications

**Acknowledgements**

(FDCT) for translation support.

[1] Mulbry, W.; Kondrad, S.; Pizarro, C.; Kebede-Westhead, E. Treatment of dairy man‐ ure effluent using freshwater algae: Algal productivity and recovery of manure nu‐ trients using pilot-scale algal turf scrubbers. Bioresource Technology, v. 99, p. 8137 – 8142, 2008.

[14] Tobaldi, D. M.; Tucci, A.; Camera-Roda, G.; Baldi d, G.; Esposito, L. Photocatalytic activity for exposed building materials. Journal of the European Ceramic Society, v.

Taguchi Method Applied to Environmental Engineering

http://dx.doi.org/10.5772/56531

91

[15] Choi, W.; Hoffmann, M. R. Novel Photocatalytic Mechanisms of CHCl3, CHBr3, and CCl3CO2- Degradation and the Fate of Photogenerated Trihalomethyl Radicals on

[16] Chen, J.; Ollis, D. F.; Rulkens, W. H.; Bruning, H. Photocatalyzed oxidation of alco‐ hols and organochlorides in the presence of native TiO2 and metalized TiO2 suspen‐ sions. Part (II): Photocatalytic mechanisms. Water Research, v. 33, n. 3, p. 669 – 676,

[17] López, C. M.; Choi, K.-S. "Enhancement of electrochemical and photoelectrochemica properties of Fibrous Zn and ZnO electrodes" Chem. Commun. 2005, 3328-3330.

[20] Gabardo Filho,H. Estudo e projeto de reatores fotoquímicos para o tratamento de efluentes químicos. 2005. Dissertação (Mestrado em Engenharia Química) –Facul‐ dade de Engenharia Química, Universidade Estadual de Campinas, Campinas. [21] Domènech, X.; Jardim, W. F.; Litter, M. I. Procesos avanzados de oxidación para La eliminación de contaminantes. In: Eliminacion de Contaminantes. La Plata: Rede CY‐

[22] HU, Z.; GRASSO, D. Chemical Oxygen Demand. In: Water Analysis. 2nd ed. New

[23] Peixoto, A. L. C.; Brito, R. A.; Salazar, R. F. S.; Guimarães, O. L. C.; Izário Filho, H. J. Predição da demanda química de oxigênio no chorume maduro contend reagents de fenton, por meio de modelo matemático emprírico gerado com planejamento factori‐

[24] Piveli, R. P.; Morita, D.M. Caracterização de águas Residuárias / Sólidos. São Paulo:

[25] Aquino, S. F.; Silva, S. Q.; Chernicharo, C. A. L. Considerações práticas sobre o teste de demanda química de oxigênio (DQO) aplicado a análise de efluentes anaeróbicos

[26] Wang, T. Y., Huang, C.Y. Improving forecasting performance by employing the Ta‐ guchi method. European Journal of Operational Research, p. 1052-1065, 2007.

[27] Bruns, R. E.; Neto, B. B.; Scarminio, I. S. Como Fazer Experimentos. 4. ed. Porto Ale‐

(nota técnica). Engenharia Sanitária e Ambiental, v. 11, p. 295-304, 2006.

[18] Hoffmann, M.; Martin, S.T.; Choi, W; Bahnemann. Chem. Rev., v. 95, p. 69, 1995.

[19] Linsebigler, A. L.; Lu, G.; Yates Jr, J. T. Chem. Rev., v. 95, p. 735, 1995.

York: Elsevier Academic Press, 2005. p. 325-330.

Escola Politécnica/USP, 1998, 11p. (apostila).

gre: Editora Artmed, 2010. 401p.

al complete. Química Nova, v. 31, n.7, p. 1641-1647, 2008.

TiO2. Environmental Science Technology, v. 31, p. 89 – 95, 1997.

28, p. 2645–2652, 2008.

1999.

TED, 2001. Cap. 1.

[14] Tobaldi, D. M.; Tucci, A.; Camera-Roda, G.; Baldi d, G.; Esposito, L. Photocatalytic activity for exposed building materials. Journal of the European Ceramic Society, v. 28, p. 2645–2652, 2008.

trients using pilot-scale algal turf scrubbers. Bioresource Technology, v. 99, p. 8137 –

[2] Al-Momani, F.; Touraud, E.; Degorce-Dumas, J.R.; ROUSSY, J.; THOMAS, O. Biode‐ gradability enhancement of texile dyes and textile wastewater by VUV photolysis. Journal of Photochemistry and Photobiology, A: Chemistry, v. 153, p. 191– 197, 2007.

[3] Braga, B.; Hespanhol, I.; Lotufo, C.; Conejo, J. G.; Mierzwa, J. C.; De Barros, M. T. L.; Spencer, M.; Porto, M.; Nucci, N.; Juliano, N.; Eiger, S. Introdução à Engenharia Am‐

[4] Pelegrini, R., Peralta-Zamora, P., Andrade, A.R., Reyes, J., Duran, N., Appl. Catal. B:

[5] Segura,Y.; Molina, R.; Martínez, F.; Melero, J. A. Integrated heterogeneous sono–pho‐ to Fenton processes for the degradation of phenolic aqueous solutions. Ultrasonics

[6] Oliver, J. H.; Hynook, K.; Pen-Chi, C. Decolorization of wastewater, Crit. Rev.Envi‐

[7] Poulopoulos, S.G.; Arvanitakis, F.; Philippopoulos, C.J. Photochemical treatment of phenol aqueous solutions using ultraviolet radiation and hydrogen peroxide. Journal

[8] Kusic, H.; Koprivanac, N.; Srsan, L. Azo dye degradation using Fenton type process‐ es assisted by UV irradiation: A kinetic study. Journal of Photochemistry and Photo‐

[9] Teixeira, C.P.A.B.; Jardim, W.F. Processos Oxidativos Avançados – Conceitos Teóri‐ cos. Campinas: Instituto de Química (IQ) e Laboratório de Química Ambiental

[10] Kunz, A., Peralta-Zamora, P. de Moraes, S. G., Duran, N., Novas Tendências no Tra‐ tamento de Efluentes Têxteis, Química Nova. v. 25, n. 1, p. 78-82, 2002. Disponível

[11] Oppenlander, T. Photochemical Purification of Water and Air. Weinheim: Wiley-Vch

[12] Ferreira, I. V. L.; Daniel, L. A. Fotocatálise heterogênea com TiO2 aplicada no trata‐ mento de esgoto sanitário secundário. Engenharia Sanitária Ambiental, v. 9, n. 4, p.

[13] Khataee, A. R.; Vatanpour, V.; Ghadim, A. R. A. Decolorization of C.I. Acid Blue 9 solution by UV/Nano-TiO2, Fenton, Fenton-like, electro-Fenton and electrocoagula‐ tion processes: A comparative study. Journal of Hazardous Materials, v. 161, p. 1225–

em: http://www.scielo.br/pdf/qn/v25n1/10428.pdf Acesso em: 04/jan/2013.

(LQA). Universidade de Campinas. (Caderno Temático, v. 3, 2004).

biental. 2ª ed. São Paulo: Pearson Prentice Hall, 2005.

ronmental Science Technology, v. 30, n.4, p. 499–505, 2000.

Sonochemistry, v. 16, p. 417–424, 2009.

of Hazardous Materials, v. 129, p. 64–68, 2006.

biology A: Chemistry, v. 181 p. 195–202, 2007.

8142, 2008.

90 Design of Experiments - Applications

Envorn.22 (1999) 83.

Verlag, Germany, 2003.

335-342, 2004.

1233, 2009.

[28] Ay, F.; Catalkaya, E.C.; Kargi, F. A statistical experiment design approach for ad‐ vanced oxidation of Direct Red azo-dye by photo-Fenton treatment. Journal of Haz‐ ardous Materials, v. 162, p. 230-236, 2009.

**Chapter 6**

**Application of 2K Experimental Design and Response**

**Mass Reduction of Poly (3-Hydroxybutyrate-***co***-3-**

Amilton Martins Santos, Messias Borges Silva and Marli Luiza Tebaldi

Biodegradable and biocompatible polymers have attracted great attention, both from scientific and technological fields. Developing new biodegradable materials to replace petrochemical derivatives is demanding and also a challenge for chemists worldwide as well as to developing more efficient synthesis processes with the aim to reduce their production cost. Besides environmental effects due to plastic wastes, there is great interest in the development of biocompatible and biodegradable materials for biomedical applications or in other biomate‐ rials. Regarding such materials, polyhydroxyalkanoates (PHAs) are good examples among them. They are polyesters of hydroxyalkanoic acid, globally manufactured in industrial scale using microbial biosynthesis deriving from renewable carbon sources, in form of storage materials as shows Figure 1. The accumulation of such polymers in granules shape are found in the cell´s cytoplasm, their diameter show a wide range variation, from 0.2-0.5μm and they

Awareness of PHAs physical, chemical and biological properties is important, mainly in regards to the development of controlled release systems, once they directly influence, among other factors, microencapsulation processes selection and drug release mechanisms [4-5].

> © 2013 Montoro et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Montoro et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Sérgio Roberto Montoro, Simone de Fátima Medeiros,

work as glycogen synthesizers and are stored by mammals [1-3].

Additional information is available at the end of the chapter

**Hydroxyvalerate) (PHBHV)**

http://dx.doi.org/10.5772/56532

**1.1. General PHAs properties**

**1. Introduction**

**Surface Methodology in the Optimization of the Molar**

**Application of 2K Experimental Design and Response Surface Methodology in the Optimization of the Molar Mass Reduction of Poly (3-Hydroxybutyrate-***co***-3- Hydroxyvalerate) (PHBHV)**

Sérgio Roberto Montoro, Simone de Fátima Medeiros, Amilton Martins Santos, Messias Borges Silva and Marli Luiza Tebaldi

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/56532

### **1. Introduction**

[28] Ay, F.; Catalkaya, E.C.; Kargi, F. A statistical experiment design approach for ad‐ vanced oxidation of Direct Red azo-dye by photo-Fenton treatment. Journal of Haz‐

[29] Freitas, A. P. B. R. de.; Freitas, L. V. de.; Samanamud, G. L.; Marins, F. A. S.; Loures, C. C. A.; Salman, F.; Santos, H. T. L. dos.; Silva, M. B. Book: Multivariate Analysis in

[30] Carneiro, L. M. Utilização de Processos Oxidativos Avançados na degradação de efluentes provenientes das indústrias de tintas. 2007, 118 f. Dissertação (Mestrado em Engenharia química) – Escola de Engenharia de Lorena, Universidade de São Paulo,

[31] Chiang, Y. M.; Hsieh, H.H. The use of the Taguchi method with grey relational anal‐ ysis to optimize the thin-film sputtering process with multiple quality characteristic in color filter manufacturing. Computers & Industrial Engineering, v. 56, p. 648-661,

[32] Barrado, E.; Vega, M.; Grande, P.; Del Valle, J.L. Optimization of a purification meth‐ od for metal-containing wastewater by use of a Taguchi experimental design. Water

[33] Taguchi, G.; Konish, S. Taguchi Methods: Orthogonal Arrays and Linear Graphs.

[34] Yang, H.J.; Hwang, P.J.; Lee, S.H. A study on shrinkage compensation of the SLS process by using the Taguchi method. International Journal of Machine Tools &

[35] Sharma, P., Verma, A.; Sidhu, R. K.; Pandey, O. P. Process parameter selection for strontium ferrite sintered magnets using Taguchi L9 orthogonal design. Journal of

[36] Barros, N.; Bruns, R.E.; Scarminio, I. S. Otimização e planejamento de Experimentos.

[37] Rosa, J. L.; Robin, A.; Silva, M.B.; Baldan, C. A.; Peres, M. P. Electrodeposition of cop‐ per on titanium wires: Taguchi Experimental Design Approach. Journal of Materials

[38] Malik, P. K., Saha, S.K. Oxidation of direct dyes with hydrogen peroxide using fer‐ rous ion as catalyst. Separation and Purification Technology, v. 31, p. 241-250, 2003.

ardous Materials, v. 162, p. 230-236, 2009.

Research, v. 30, p. 2309–2314, 1996.

American Supplier Institute, 1987.

Manufacture, v.42, p. 1203–1212, 2002.

Materials Processing Technology, p.147-151, 2005.

Campinas : Editora da Unicamp, 1995, p.291.

Processing Technology, p. II8I-II88, 2009.

Lorena 2007.

92 Design of Experiments - Applications

2009.

Advanced Oxidation Process. Ed:Intech, p. 73-90, 2012.

Biodegradable and biocompatible polymers have attracted great attention, both from scientific and technological fields. Developing new biodegradable materials to replace petrochemical derivatives is demanding and also a challenge for chemists worldwide as well as to developing more efficient synthesis processes with the aim to reduce their production cost. Besides environmental effects due to plastic wastes, there is great interest in the development of biocompatible and biodegradable materials for biomedical applications or in other biomate‐ rials. Regarding such materials, polyhydroxyalkanoates (PHAs) are good examples among them. They are polyesters of hydroxyalkanoic acid, globally manufactured in industrial scale using microbial biosynthesis deriving from renewable carbon sources, in form of storage materials as shows Figure 1. The accumulation of such polymers in granules shape are found in the cell´s cytoplasm, their diameter show a wide range variation, from 0.2-0.5μm and they work as glycogen synthesizers and are stored by mammals [1-3].

### **1.1. General PHAs properties**

Awareness of PHAs physical, chemical and biological properties is important, mainly in regards to the development of controlled release systems, once they directly influence, among other factors, microencapsulation processes selection and drug release mechanisms [4-5].

indicated to be used in animal´s controlled drug release tests [18]. The PHBHV structure is

**O**

Polymers used as carrier agents play a very important role in active ingredients controlled delivery systems, determining, among other factors, drug release rates. In fact, drug release can be performed by different mechanisms: diffusion throught the swelled polymer network, erosion/biodegradation of polymer chains as well as a combination of mechanisms. Basically, the difference between erosion and biodegradation mechanisms is established based on the macromolecule degradation ones. Polymer matrix erosion results, in a macroscopic level, in mass loss, with no modifications on macromolecular units. It can happen in two different ways: either by breaking intermolecular bonds in cross-linked systems, where matrixes are gradually eroded from the external surface, or by main chain´s side group hydrolysis, resulting in

According to such context, biodegradable polymers are those where chain´s breaking results in monomeric units in which molar masses are small enough to be eliminated by normal metabolic pathways. Such breakage can occur by hydrolysis (hydrolytic degradation) or enzymatic attack (enzymatic degradation). Erosive or degradable systems, particularly those that degrade in biological mediums (biodegradable) have found great utility in controlled

Polymers natural elimination, after total drug release, is an advantage once it avoids the inconvenience of surgical interventions to remove it. Thus, micro and nano-structured as well as biodegradable and biocompatible systems (microspheres, microcapsules, nano-capsules,

The role that polymers play during the formulation (modulation) of these controlled release systems is very different if compared to an inert conventional excipient for pharmaceutical formulations. Polymers influence not only drug kinetics release, as expected, but also the drug

Innumerous techniques have been proposed in literature, regarding polymeric micro and

The most common method used for systems based on PHAs, such as PHB and PHBHV, is called micellization, i.e., - preparation of small micelles through self-assemblage of amphiphilic chains in water [7]. Inside amphiphilic structures of polymeric micelles, hydrophobic drug molecules are distributed within the hydrophobic cores, whereas the shell keeps a hydration

´s stability, toxicity and the compatibility between biopolymers and living organism.

nanostructured materials for drug controlled delivery systems preparation [21].

n m

**O**

Application of 2K Experimental Design and Response Surface Methodology…

**O H**

http://dx.doi.org/10.5772/56532

95

**O**

shown in Figure 2.

**H O**

polymers dissolution, without reducing its molar mass [19].

nano-spheres) have been developed for drug controlled release [20].

**Figure 2.** Illustration of PHBHV chemical structure.

release systems development.

**Figure 1.** Exponential growth phase containing about 40 - 50% PHB (left) and final accumulation phase containing about 93% PHB (right).

Usually, PHAs are crystalline structures, so their brittleness and low flexibility set limits their application in some biomedical procedures. Thus, lack of superior mechanical proprieties, require modifications, mainly, for medical applications [6].

PHAs molar mass is a crucial factor, once such parameter directly affects mechanical strength, swelling capacity and the ability to undergo hydrolysis, as well as polymers biodegradation rates. Molar mass is related to PHA´s crystallinity. Therefore, developing a controlled drug delivery system using PHAs requires an essential preliminary molar mass reduction step. An important factor showing molar mass dependence of biodegradable polymers degradation rates dues to a direct proportionality between this parameter and the polymers Tg, i.e., the lower the polymer molar mass, the lower the Tg value. In addition, degradation rates increasing leads to complex ingredients release rates increasing, having these polymers as polymeric matrixes, they will be promptly absorbed by the body [4]. Moreover, low molar mass PHAs can be used as components on several architecture constructions, such as block and grafted copolymers [7].

### **1.2. PHB and PHBHV copolymers**

Poly(3-hydroxybutirate) (PHB) and its copolymers with hydroxyvalerate (HV) are the most studied PHAs in literature [8]. PHB and PHBHV are completely biodegradable and produced by a variety of bacteria´s fermentation, [1] degrading throughout natural biological processes, turning them into excellent candidates for bioactive molecules release system´s production [9-15]. Both poly(3-hydroxybutyrate) (PHB) and poly(3-hydroxybutyrate-*co*-3-hydroxyvaler‐ ate) (PHBHV) are biodegradable thermoplastic polyesters produced by a bacteria known as *Ralstonia eutropha* or *Alcaligenes latus* [16]. PHBHV has emerged as a new generation of PHA in which the surface morphology combined with its lower crystallinity when compared to PHB homopolymers fastens degradation processes. Furthermore, copolymers physical properties can be manipulated by varying the HB and HV's composition [17]. Such advantages make the use of PHBHV copolymers suitable for many applications, once compared to PHB homopol‐ ymers. Nevertheless, ISO 10993 highlighted such polymers as safe and non toxic materials indicated to be used in animal´s controlled drug release tests [18]. The PHBHV structure is shown in Figure 2.

**Figure 2.** Illustration of PHBHV chemical structure.

Usually, PHAs are crystalline structures, so their brittleness and low flexibility set limits their application in some biomedical procedures. Thus, lack of superior mechanical proprieties,

**Figure 1.** Exponential growth phase containing about 40 - 50% PHB (left) and final accumulation phase containing

PHAs molar mass is a crucial factor, once such parameter directly affects mechanical strength, swelling capacity and the ability to undergo hydrolysis, as well as polymers biodegradation rates. Molar mass is related to PHA´s crystallinity. Therefore, developing a controlled drug delivery system using PHAs requires an essential preliminary molar mass reduction step. An important factor showing molar mass dependence of biodegradable polymers degradation rates dues to a direct proportionality between this parameter and the polymers Tg, i.e., the lower the polymer molar mass, the lower the Tg value. In addition, degradation rates increasing leads to complex ingredients release rates increasing, having these polymers as polymeric matrixes, they will be promptly absorbed by the body [4]. Moreover, low molar mass PHAs can be used as components on several architecture constructions, such as block and grafted

Poly(3-hydroxybutirate) (PHB) and its copolymers with hydroxyvalerate (HV) are the most studied PHAs in literature [8]. PHB and PHBHV are completely biodegradable and produced by a variety of bacteria´s fermentation, [1] degrading throughout natural biological processes, turning them into excellent candidates for bioactive molecules release system´s production [9-15]. Both poly(3-hydroxybutyrate) (PHB) and poly(3-hydroxybutyrate-*co*-3-hydroxyvaler‐ ate) (PHBHV) are biodegradable thermoplastic polyesters produced by a bacteria known as *Ralstonia eutropha* or *Alcaligenes latus* [16]. PHBHV has emerged as a new generation of PHA in which the surface morphology combined with its lower crystallinity when compared to PHB homopolymers fastens degradation processes. Furthermore, copolymers physical properties can be manipulated by varying the HB and HV's composition [17]. Such advantages make the use of PHBHV copolymers suitable for many applications, once compared to PHB homopol‐ ymers. Nevertheless, ISO 10993 highlighted such polymers as safe and non toxic materials

require modifications, mainly, for medical applications [6].

copolymers [7].

about 93% PHB (right).

94 Design of Experiments - Applications

**1.2. PHB and PHBHV copolymers**

Polymers used as carrier agents play a very important role in active ingredients controlled delivery systems, determining, among other factors, drug release rates. In fact, drug release can be performed by different mechanisms: diffusion throught the swelled polymer network, erosion/biodegradation of polymer chains as well as a combination of mechanisms. Basically, the difference between erosion and biodegradation mechanisms is established based on the macromolecule degradation ones. Polymer matrix erosion results, in a macroscopic level, in mass loss, with no modifications on macromolecular units. It can happen in two different ways: either by breaking intermolecular bonds in cross-linked systems, where matrixes are gradually eroded from the external surface, or by main chain´s side group hydrolysis, resulting in polymers dissolution, without reducing its molar mass [19].

According to such context, biodegradable polymers are those where chain´s breaking results in monomeric units in which molar masses are small enough to be eliminated by normal metabolic pathways. Such breakage can occur by hydrolysis (hydrolytic degradation) or enzymatic attack (enzymatic degradation). Erosive or degradable systems, particularly those that degrade in biological mediums (biodegradable) have found great utility in controlled release systems development.

Polymers natural elimination, after total drug release, is an advantage once it avoids the inconvenience of surgical interventions to remove it. Thus, micro and nano-structured as well as biodegradable and biocompatible systems (microspheres, microcapsules, nano-capsules, nano-spheres) have been developed for drug controlled release [20].

The role that polymers play during the formulation (modulation) of these controlled release systems is very different if compared to an inert conventional excipient for pharmaceutical formulations. Polymers influence not only drug kinetics release, as expected, but also the drug ´s stability, toxicity and the compatibility between biopolymers and living organism.

Innumerous techniques have been proposed in literature, regarding polymeric micro and nanostructured materials for drug controlled delivery systems preparation [21].

The most common method used for systems based on PHAs, such as PHB and PHBHV, is called micellization, i.e., - preparation of small micelles through self-assemblage of amphiphilic chains in water [7]. Inside amphiphilic structures of polymeric micelles, hydrophobic drug molecules are distributed within the hydrophobic cores, whereas the shell keeps a hydration barrier that protects the integrity of each micelle. The use of amphiphilic block copolymers is advantageous because they possess unique physicochemical features such as self-assembly and thermodynamic stability in aqueous solution [22]. In order to get amphiphilic structures, surface changes on the hydrophobic segment with a hydrophilic, which is able to stabilize particles, nontoxic and blood compatible materials essential to avoid macrophages recogni‐ tion, prolonging blood circulation time and sustaining encapsulated drugs release. Many hydrophilic polymers have been suggested for such application. Poly(ethylene glycol) (PEG), for example, is widely used as a hydrophilic nontoxic segment once combined with hydro‐ phobic biodegradable aliphatic polyesters. It was found that incorporated hydrophilic mPEG groups, showing resistance against opsonization and phagocytosis, also presenting prolonged residence time in blood if compared to nanoparticles prepared without mPEG. Nevertheless, it has been demonstrated that surface modifications of a polymer with this nontoxic material reduces side effects risk in comparison to the non-modified polymers [15].

were modified with triarylsulfonium salts upon UV irradiation. The process forms species that abstract hydrogen atoms from the PHBHV surface, generating primary radicals which are able to initiate monomer's polymerization by UV-mediation allowing wettability control of produced films, improving their ability for cellular interaction [32]. Vergnol G. *et al.* [10] described the use of PHAs as stent coatings containing the sirolimus drug. Natural PHBHV, poly(3-hydroxyoctanoate) functionalized with carboxylic groups,PHO75COOH25, and diblock copolymer PHBHV-*b*-(lactic acid) were sprayed onto metallic stents. P(HBHV-*b*-LA) as coating, enhanced the drug release profile by limiting sirolimus release. Bilayer systems were proposed, it seemed to be very promising, especially in systems with PHBHV and P(HBHV*b*-LA). Gracida J. *et al.* [24] studied blends of PHBHV/PHEMA´s degradation by fungal activity using the ASTM method and CO2 measurements to determine biodegrability. Studies showed

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As previously mentioned, to tailor PHB thermal and mechanical proprieties, its copolymeri‐ zation with 3HV is commonly performed. Currently, much research work has been published reporting various methods of obtaining a range of PHBHV copolymers with different 3HV content using different carbon nutrition conditions [1,38]. However, molar mass in biosyn‐ thesis is typically high and not suitable for systems of drug controlled release. Moreover, commercial PHBHV shows some disadvantages, such as poor thermal stability and high melting temperature. PHBHV´s thermal degradation temperature is close to 160°C and their

In addition, in PHBHV´s biosynthesis only highly hydrophobic polymers are produced and this is unfavorable to the interaction between a biomaterial surface and cells or some other *in vivo* applications. Such polymers need much more versatile modifications in order to obtain new materials with improved mechanical and thermal properties, besides increasing the

To achieve this goal, the main procedure aims to perform PHBHV molar mass reduction.

In this context, aiming to solve the aforementioned problems, polymers molar mass reduction is a fundamental requirement. Such procedure offers, as its main advantage, the possibility to carry a series of modifications including polymer functionalization with terminal vinyl groups,

Many efforts have been made in order to provide PHB molar mass reduction and to improve

PHB and PHBHV molar mass reductions can be obtained by thermal degradation [34,41], acid hydrolysis [4, 42-43], transesterification with glycols [44] reduction with NaBH4 [6, 45] or also

One promising approach to improve their physical properties, adjusting degradation rates, dues to synthesizing block copolymers using telechelic PHB or PHBHV of low molar mass through chemical routes. These modifications involve reactions with bromide or chloride

its copolymers properties or to prepare the material for further modifications.

that PHBHV/PHEMA blends are biodegradable in a ASTM method context.

melting temperature is around 150°C, resulting in a small processing window [39].

hydrophilic character [1].

*in vivo* esterification with PEG [46].

*1.3.1. Molar mass reduction and further modifications*

which are highly reactive, in further modification reactions [40].

Low molar mass biodegradable block copolymers, in form of amphiphilic micro and nano‐ particles, were a suggestion of use as sustained release for a variety of hydrophobic drugs [22]. Encapsulate active ingredients in polymeric nanoparticles aims to turn the delivery of effective doses of pharmacologically active substance to a particular site possible, mainly in tumors, for a sustained period of time, avoiding innumerous side effects associated with multiple drug dosing. The defective and leaky structure of tumor vessels and impaired lymphatic system facilitates internalization of polymeric nanoparticles containing drugs, which enhances active agent local effects and protects healthy cells [4].

### **1.3. Why PHB and PHBHV need modifications?**

Besides PHBHV lower cristallinity when compared to other PHAs, its crystalline percentage (55–80%) also needs to be considered. Moreover, it may suffer degradation by conventional melt processing, which limits its use in many specific applications [15]. In order to minimize such problems, PHB and PHBHV are often blended [13-14, 23-26] or used with a mixture of substances such as natural rubber, it is also used in the preparation of composites, [27] or it can be changed through a number of strategies such as using click chemistry [28-29] or modifying the surface and subsequent graftization in a series of monomers [30-35] as well as along with agents: plasticizers, lubricants, antioxidants, photostabilizers and other miscible polymers [36]. PHBHV were modified with natural rubber producing composites with enhanced mechanical proprieties [27]. Ke *et al*. [33] studied thermal properties and in vitro degradation of amide, amine, and collagen-modified PHBHV films aiming to improve biodegradation rates on cytocompatible biomaterials. Biodegradation rates of modified PHBHV were greater than pure PHBHV, offering an alternative to improve such materials properties.

Linhart and *co-authors* [37] showed that amorphous calcium phosphate (ACP) composites and PHB or PHBHV (PHB-ACP or PHBHV-ACP) would be potential bone substitution materials. As it is known, PHAs intrinsic hydrophobic properties restrict some of their applications *in vivo*. Consequently, these materials could be improved by either chemical modification with functional group's introduction or by modifying the topographic surface. PHBHV surfaces were modified with triarylsulfonium salts upon UV irradiation. The process forms species that abstract hydrogen atoms from the PHBHV surface, generating primary radicals which are able to initiate monomer's polymerization by UV-mediation allowing wettability control of produced films, improving their ability for cellular interaction [32]. Vergnol G. *et al.* [10] described the use of PHAs as stent coatings containing the sirolimus drug. Natural PHBHV, poly(3-hydroxyoctanoate) functionalized with carboxylic groups,PHO75COOH25, and diblock copolymer PHBHV-*b*-(lactic acid) were sprayed onto metallic stents. P(HBHV-*b*-LA) as coating, enhanced the drug release profile by limiting sirolimus release. Bilayer systems were proposed, it seemed to be very promising, especially in systems with PHBHV and P(HBHV*b*-LA). Gracida J. *et al.* [24] studied blends of PHBHV/PHEMA´s degradation by fungal activity using the ASTM method and CO2 measurements to determine biodegrability. Studies showed that PHBHV/PHEMA blends are biodegradable in a ASTM method context.

As previously mentioned, to tailor PHB thermal and mechanical proprieties, its copolymeri‐ zation with 3HV is commonly performed. Currently, much research work has been published reporting various methods of obtaining a range of PHBHV copolymers with different 3HV content using different carbon nutrition conditions [1,38]. However, molar mass in biosyn‐ thesis is typically high and not suitable for systems of drug controlled release. Moreover, commercial PHBHV shows some disadvantages, such as poor thermal stability and high melting temperature. PHBHV´s thermal degradation temperature is close to 160°C and their melting temperature is around 150°C, resulting in a small processing window [39].

In addition, in PHBHV´s biosynthesis only highly hydrophobic polymers are produced and this is unfavorable to the interaction between a biomaterial surface and cells or some other *in vivo* applications. Such polymers need much more versatile modifications in order to obtain new materials with improved mechanical and thermal properties, besides increasing the hydrophilic character [1].

To achieve this goal, the main procedure aims to perform PHBHV molar mass reduction.

### *1.3.1. Molar mass reduction and further modifications*

barrier that protects the integrity of each micelle. The use of amphiphilic block copolymers is advantageous because they possess unique physicochemical features such as self-assembly and thermodynamic stability in aqueous solution [22]. In order to get amphiphilic structures, surface changes on the hydrophobic segment with a hydrophilic, which is able to stabilize particles, nontoxic and blood compatible materials essential to avoid macrophages recogni‐ tion, prolonging blood circulation time and sustaining encapsulated drugs release. Many hydrophilic polymers have been suggested for such application. Poly(ethylene glycol) (PEG), for example, is widely used as a hydrophilic nontoxic segment once combined with hydro‐ phobic biodegradable aliphatic polyesters. It was found that incorporated hydrophilic mPEG groups, showing resistance against opsonization and phagocytosis, also presenting prolonged residence time in blood if compared to nanoparticles prepared without mPEG. Nevertheless, it has been demonstrated that surface modifications of a polymer with this nontoxic material

Low molar mass biodegradable block copolymers, in form of amphiphilic micro and nano‐ particles, were a suggestion of use as sustained release for a variety of hydrophobic drugs [22]. Encapsulate active ingredients in polymeric nanoparticles aims to turn the delivery of effective doses of pharmacologically active substance to a particular site possible, mainly in tumors, for a sustained period of time, avoiding innumerous side effects associated with multiple drug dosing. The defective and leaky structure of tumor vessels and impaired lymphatic system facilitates internalization of polymeric nanoparticles containing drugs, which enhances active

Besides PHBHV lower cristallinity when compared to other PHAs, its crystalline percentage (55–80%) also needs to be considered. Moreover, it may suffer degradation by conventional melt processing, which limits its use in many specific applications [15]. In order to minimize such problems, PHB and PHBHV are often blended [13-14, 23-26] or used with a mixture of substances such as natural rubber, it is also used in the preparation of composites, [27] or it can be changed through a number of strategies such as using click chemistry [28-29] or modifying the surface and subsequent graftization in a series of monomers [30-35] as well as along with agents: plasticizers, lubricants, antioxidants, photostabilizers and other miscible polymers [36]. PHBHV were modified with natural rubber producing composites with enhanced mechanical proprieties [27]. Ke *et al*. [33] studied thermal properties and in vitro degradation of amide, amine, and collagen-modified PHBHV films aiming to improve biodegradation rates on cytocompatible biomaterials. Biodegradation rates of modified PHBHV were greater than pure PHBHV, offering an alternative to improve such materials

Linhart and *co-authors* [37] showed that amorphous calcium phosphate (ACP) composites and PHB or PHBHV (PHB-ACP or PHBHV-ACP) would be potential bone substitution materials. As it is known, PHAs intrinsic hydrophobic properties restrict some of their applications *in vivo*. Consequently, these materials could be improved by either chemical modification with functional group's introduction or by modifying the topographic surface. PHBHV surfaces

reduces side effects risk in comparison to the non-modified polymers [15].

agent local effects and protects healthy cells [4].

96 Design of Experiments - Applications

**1.3. Why PHB and PHBHV need modifications?**

properties.

In this context, aiming to solve the aforementioned problems, polymers molar mass reduction is a fundamental requirement. Such procedure offers, as its main advantage, the possibility to carry a series of modifications including polymer functionalization with terminal vinyl groups, which are highly reactive, in further modification reactions [40].

Many efforts have been made in order to provide PHB molar mass reduction and to improve its copolymers properties or to prepare the material for further modifications.

PHB and PHBHV molar mass reductions can be obtained by thermal degradation [34,41], acid hydrolysis [4, 42-43], transesterification with glycols [44] reduction with NaBH4 [6, 45] or also *in vivo* esterification with PEG [46].

One promising approach to improve their physical properties, adjusting degradation rates, dues to synthesizing block copolymers using telechelic PHB or PHBHV of low molar mass through chemical routes. These modifications involve reactions with bromide or chloride

(HEMA) to form macro-monomers with two unsaturated end groups and afterwards graftized with methyl methacrylate to obtain materials that can be used as constituents in acrylic bone cements for use in orthopaedic applications [34]. Oliveira, AM. and *co-authors* synthesized PHBHV-*b*-PNIPAAm block copolymers reacting hydroxyl-caped PHBHV of low molar mass and carboxyl-caped PNIPAAm obtained via reversible addition-fragmentation chain transfer (RAFT) polymerization. The thermo-responsive particles were loaded with dexametasone acetate (DexAc) and showed drug delivery behaviour dependent of temperature, suggesting that these polymeric micelles can be utilized as drug delivery systems [12]. Baran, ET. *et al.* [45] prepared PHBHV of low molar mass via mechanisms of degradation by sodium borohydride (NaBH4). Nanocapsules of PHBHV of low molar mass was prepared and tested for the entrapment of therapeutically active proteins such as those used in cancer therapy. The studies indicated that the use of low molar mass PHBHV was more favorable in increasing entrapment and entrapment efficiency and enzyme activity [46]. Montoro, SR. *et al.* [42] used the methods of acid hydrolysis and trans-esterification with ethylene and hexyleneglycol and also by reductions with sodium borohydride [4,6] to obtain PHBHV with molar mass reduced in order to develop materials suitable to be used as carriers in active systems. Liu,Q. *et al.* [39] synthe‐ sized telechelic PHBHV-diols with various molar mass by trans-esterification with ethylene glycol. The results showed that PHBHV-diol was more stable than original PHBHV and the

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melt-processing window increase gradually with molar mass decrease.

click chemistry reaction conducting to graphitization with MeO-PEG [29].

products of P3HB-PEG diblock copolymers type with reduced molar mass.

Lemechko, P*. at al.* prepared dextran-*graft-*PHBHV amphiphilic copolymers using two ''grafting onto'' methods. In the first one, PHBHV oligomers were reacted with SOCl2 to obtain chloride terminated PHBHV with subsequent esterification with dextran. In the second method, PHBHV oligomers were functionalized with alkyne end groups and graftized onto functionalized dextran via click chemistry reaction. The presence of reactive groups could be interesting to bind bioactive molecules in order to develop heterofunctional nanoparticles [28]. Babinot, J. *at al*. synthesized amphiphilic diblock copolymers with different PHAs of low molar mass. The authors firstly prepared the PHAs oligomers by thermal treatment (190°C) varying the time of reaction and after that, the oligomers were functionalized with alkine function by

The reduction of PHB´s molar mass *in vivo* is another strategy, which was used by Ashby RD*. et al.* [46]. The authors controlled PHB´s molar mass by adding PEG segments in the incubation medium. PEG interacts with the cellular biosynthetic system which is responsible for P3HB synthesis and regulates the molar mass. A series of PEGs with different molar mass were added to the *Alcaligenes latus* DSM 1122 incubation medium. Such strategy resulted in

Shah *et al.* [15], synthesized amphiphilic biodegradable core–shell nanoparticles by emul‐ sification–solvent evaporation technique using poly(3-hydroxybutyrate-*co*-3-hydroxyvaler‐ ate) or poly(3-hydroxybutyrate-*co*-4hydroxybutyrate) diblock copolymers. Copolymers were coupled to monomethoxy poly(ethylene glycol) (mPEG) via trans-esterification reactions. Nanoparticles were found to be assembled in aqueous solution into an outer hydrophilic shell of mPEG, connected to the interior hydrophobic polyhydroxyalkanoate (PHA) copolymer core. Moreover, the morphological examination, by means of atomic force microscope,

**Figure 3.** Possible modification reactions in PHBHV with low molar mass.

molecules turning these polymers macro-initiators, which can trigger a new polymerization with various monomers in order to obtain new materials type graft [30-31] or block [12,29,47-48] copolymers with specific properties, for example, amphiphilic systems for drug carrier. Figure 3 shows some possible modifications that can be done to improve PHBHV with low molar mass proprieties.

Arslan H. and *co-authors* prepared lower molar mass PHB-Cl by using a depolymerization process (heating it under reflux with 1,2-dichlorobenzene) and by subsequent choration by means of passing chlorine gas through PHB solutions. The chlorinated PHB (PHB-Cl) were used as macro-initiators in methyl methacrylate (MMA) polymerization aiming to obtain PHB*g-*PMMA graft copolymers by the atom transfer radical polymerization (ATRP) method [31]. ABA triblock copolymers were prepared trough three consecutive steps. Firstly, natural PHB with high molar mass, was converted into low molar mass PHB-diol by trans-esterification with diethylene glycol. In the next step, PBH-diol pre-polymers were reacted with 2-bromo-2 methylpropionylbromide to obtain PHB-Br macro-initiators which were used to carry out the *tert*-butyl acrylate (*t*BA) polymerization by ATRP. The degradation rate was adjusted accord‐ ing to PHB contents [48]. Spitalský, Z. *et al.* [44] prepared PHB oligomers by alcoholysis using two types of alcohol in the presence of *p*-toluene sulfonic acid as catalyst, which can be used for further crosslinking and chain-extension reactions. Reeve, MS. *et al.* [49] synthesized PHB macro-initiators of low molar mass by methanolysis followed by reactions with AlEt3, which were used to obtain biodegradable diblock copolymers. Hirt, TD. *et al.* [50] obtained telechelic OH- termined PHB and PHBHV by trans-esterification in order to prepare precursors with reactive end groups which were used to synthesize high-molar mass block copolymers by chain extension. PHB oligomers were prepared and reacted with 2-hydroxyethyl methacrylate (HEMA) to form macro-monomers with two unsaturated end groups and afterwards graftized with methyl methacrylate to obtain materials that can be used as constituents in acrylic bone cements for use in orthopaedic applications [34]. Oliveira, AM. and *co-authors* synthesized PHBHV-*b*-PNIPAAm block copolymers reacting hydroxyl-caped PHBHV of low molar mass and carboxyl-caped PNIPAAm obtained via reversible addition-fragmentation chain transfer (RAFT) polymerization. The thermo-responsive particles were loaded with dexametasone acetate (DexAc) and showed drug delivery behaviour dependent of temperature, suggesting that these polymeric micelles can be utilized as drug delivery systems [12]. Baran, ET. *et al.* [45] prepared PHBHV of low molar mass via mechanisms of degradation by sodium borohydride (NaBH4). Nanocapsules of PHBHV of low molar mass was prepared and tested for the entrapment of therapeutically active proteins such as those used in cancer therapy. The studies indicated that the use of low molar mass PHBHV was more favorable in increasing entrapment and entrapment efficiency and enzyme activity [46]. Montoro, SR. *et al.* [42] used the methods of acid hydrolysis and trans-esterification with ethylene and hexyleneglycol and also by reductions with sodium borohydride [4,6] to obtain PHBHV with molar mass reduced in order to develop materials suitable to be used as carriers in active systems. Liu,Q. *et al.* [39] synthe‐ sized telechelic PHBHV-diols with various molar mass by trans-esterification with ethylene glycol. The results showed that PHBHV-diol was more stable than original PHBHV and the melt-processing window increase gradually with molar mass decrease.

Lemechko, P*. at al.* prepared dextran-*graft-*PHBHV amphiphilic copolymers using two ''grafting onto'' methods. In the first one, PHBHV oligomers were reacted with SOCl2 to obtain chloride terminated PHBHV with subsequent esterification with dextran. In the second method, PHBHV oligomers were functionalized with alkyne end groups and graftized onto functionalized dextran via click chemistry reaction. The presence of reactive groups could be interesting to bind bioactive molecules in order to develop heterofunctional nanoparticles [28]. Babinot, J. *at al*. synthesized amphiphilic diblock copolymers with different PHAs of low molar mass. The authors firstly prepared the PHAs oligomers by thermal treatment (190°C) varying the time of reaction and after that, the oligomers were functionalized with alkine function by click chemistry reaction conducting to graphitization with MeO-PEG [29].

molecules turning these polymers macro-initiators, which can trigger a new polymerization with various monomers in order to obtain new materials type graft [30-31] or block [12,29,47-48] copolymers with specific properties, for example, amphiphilic systems for drug carrier. Figure 3 shows some possible modifications that can be done to improve PHBHV with

**O**

m n

CH2Cl2

**O O**

**O**

BPO/H2O

HEMA

EDC/NHS/CH2Cl click reaction <sup>2</sup>

**H**

OH OH

HO

OH

OH

OH

**Figure 3.** Possible modification reactions in PHBHV with low molar mass.

O Br

**O O**

Sn(oct)2

**OH**

TEA, DMAP CH2Cl2/ 50ºC-24h

CH3OH,H2SO4

**H3C**

Br

**H**

PHBHV

O O O

**O**

**<sup>O</sup> <sup>m</sup> <sup>n</sup>**

O

R

**OH**

PHBHV-Br

**O O O**

> O O

**O**

ATRP

<sup>m</sup> <sup>n</sup> **<sup>O</sup>**

conditions

R

**O**

\*

**Br**

Arslan H. and *co-authors* prepared lower molar mass PHB-Cl by using a depolymerization process (heating it under reflux with 1,2-dichlorobenzene) and by subsequent choration by means of passing chlorine gas through PHB solutions. The chlorinated PHB (PHB-Cl) were used as macro-initiators in methyl methacrylate (MMA) polymerization aiming to obtain PHB*g-*PMMA graft copolymers by the atom transfer radical polymerization (ATRP) method [31]. ABA triblock copolymers were prepared trough three consecutive steps. Firstly, natural PHB with high molar mass, was converted into low molar mass PHB-diol by trans-esterification with diethylene glycol. In the next step, PBH-diol pre-polymers were reacted with 2-bromo-2 methylpropionylbromide to obtain PHB-Br macro-initiators which were used to carry out the *tert*-butyl acrylate (*t*BA) polymerization by ATRP. The degradation rate was adjusted accord‐ ing to PHB contents [48]. Spitalský, Z. *et al.* [44] prepared PHB oligomers by alcoholysis using two types of alcohol in the presence of *p*-toluene sulfonic acid as catalyst, which can be used for further crosslinking and chain-extension reactions. Reeve, MS. *et al.* [49] synthesized PHB macro-initiators of low molar mass by methanolysis followed by reactions with AlEt3, which were used to obtain biodegradable diblock copolymers. Hirt, TD. *et al.* [50] obtained telechelic OH- termined PHB and PHBHV by trans-esterification in order to prepare precursors with reactive end groups which were used to synthesize high-molar mass block copolymers by chain extension. PHB oligomers were prepared and reacted with 2-hydroxyethyl methacrylate

low molar mass proprieties.

 The authors controlled PHB´s molar mass by adding PEG segments in the incubation medium. PEG interacts with the cellular biosynthetic system which is responsible for P3HB synthesis and regulates the molar mass. A series of PEGs with different molar mass were added to the *Alcaligenes latus* DSM 1122 incubation medium. Such strategy resulted in products of P3HB-PEG diblock copolymers type with reduced molar mass.

Shah *et al.* [15], synthesized amphiphilic biodegradable core–shell nanoparticles by emul‐ sification–solvent evaporation technique using poly(3-hydroxybutyrate-*co*-3-hydroxyvaler‐ ate) or poly(3-hydroxybutyrate-*co*-4hydroxybutyrate) diblock copolymers. Copolymers were coupled to monomethoxy poly(ethylene glycol) (mPEG) via trans-esterification reactions. Nanoparticles were found to be assembled in aqueous solution into an outer hydrophilic shell of mPEG, connected to the interior hydrophobic polyhydroxyalkanoate (PHA) copolymer core. Moreover, the morphological examination, by means of atomic force microscope, revealed the nanoparticle's smooth spherically shape. The average particle sizes and zeta potentials of amphiphilic nanoparticles were in the range of 112–162 nm and -18 to -27 mV, respectively. Finally, a hydrophobic drug (thymoquinone) was encapsulated in the nanopar‐ ticles and its release kinetics was studied.

level and that factor *B* is at low level. The treatment combination using both factors at low level is represented by (1). Such notation will be used throughout the whole 2k design's series. For

treatment, having *A* and *C* at high level, as well as *B* and *D* at low level, is

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Treatment

factorial design's effects regards *A* and *B* effects, as well as *AB* second order's

( ) ( ) <sup>1</sup> <sup>1</sup> <sup>1</sup>

( ) ( ) <sup>1</sup> <sup>1</sup> <sup>1</sup>

= - = - = + -- é ù ë û (2)

= - = - = + -- é ù ë û (1)

interaction factor. According to cases in which fonts (1), *a*, *b*, *ab* are the total of all (*n)* observa‐ tions performed over these planning points. It is easy to estimate such factor's effects. In order to estimate *A* factor's main effect, it is necessary to find the observation's average on the right side of the square (Figure 4), - having *A* at high level – and subtract such average from the

Similarly, *B's* main effect is found taking the comments' average at the top of the square, being - having *B* at high level -, and subtract the observations' average at the bottom of the square -

observation's average on the left side of the square, where *A* is at low level, or:

2 22 *A A a ab b Ay y a ab b n nn* + - + +

2 22 *B B b ab a By y b ab a n nn* + - + +

Factorial design

Factorial design

combination A B (1) - a + b - + ab + +

example, a 24

The interest in 22

A factor's main effect: 22

having *B* at low level:

B factor's main effect: 22

highlighted by (*ac)* [51,52].

**Figure 4.** Treatment combinations in a 22 design [*adapted* 51]

In this context, this section presents a study on optimization of ideal PHBHV molar mass reduction due to temperature changes and in concentration of the reducing agent (NaBH4). From a statistical experimental design (2k Full Factorial) and Response Surface Methodology (RSM), it was determined which of these variables had a greater influence in reducing the molar mass of PHBHV.

Actually, these PHAs are produced in Brazil (pilot-scale), and are considered one of the most promising alternatives due to its properties and low cost.

### **2. 2k factorial design**

Factorial designs are often used in experiments involving several factors that demand the study of their total effects over a certain response. However, special cases regarding factorial design - in general - are important due to the fact that they are widely used by researchers and because they represent the basis for other considerably valorous planning.

K factor's case is the most important one among them all. Each one presents only two levels. Such levels may be quantitative - two temperature, pressure or time values, etc. - or qualitative - two machines, two operators, a factor's "high" and "low" level-, or, yet the presence and absence of a factor. A complete replication of planning requires 2 x 2 x... x 2 = 2k observations and is known as 2k factorial design.

2k design is particularly useful in some experiment's early stages, when many factors are, probably, observed. It provides a lower amount of turns in which k factors can be studied - by means of a complete factorial design - once there are only two levels of each factor. We must assume that the response is basically linear, considering the chosen factor's ranges [51-54].

#### **2.1. 22 design**

2k factorial design simplest type is the 22 – two factors, *A* and *B*, each one of them holding two levels. We usually think about such levels as "low" and "high" values. Figure 4 illustrates the 22 planning. Note that "plans" can be geometrically represented as squares in which 22 = 4 runs - or treatment combinations, forming the square's vertices. Regarding 22 planning, it is usual to highlight A and B factors as "low" and "high" levels, using ( - ) and ( + ) signs to demonstrate them, respectively. Sometimes it is called "geometric concept for planning".

A special concept is used to underline treatment combinations. In general, a treatment combination is represented by a series of lowercase fonts. If a certain font is shown, the corresponding factor is ran at that treatment combination's high level; if it is absent, the factor is ran at its low level. For example, treatment combination (a) indicates that factor *A* is at high level and that factor *B* is at low level. The treatment combination using both factors at low level is represented by (1). Such notation will be used throughout the whole 2k design's series. For example, a 24 treatment, having *A* and *C* at high level, as well as *B* and *D* at low level, is highlighted by (*ac)* [51,52].

revealed the nanoparticle's smooth spherically shape. The average particle sizes and zeta potentials of amphiphilic nanoparticles were in the range of 112–162 nm and -18 to -27 mV, respectively. Finally, a hydrophobic drug (thymoquinone) was encapsulated in the nanopar‐

In this context, this section presents a study on optimization of ideal PHBHV molar mass reduction due to temperature changes and in concentration of the reducing agent (NaBH4). From a statistical experimental design (2k Full Factorial) and Response Surface Methodology (RSM), it was determined which of these variables had a greater influence in reducing the

Actually, these PHAs are produced in Brazil (pilot-scale), and are considered one of the most

Factorial designs are often used in experiments involving several factors that demand the study of their total effects over a certain response. However, special cases regarding factorial design - in general - are important due to the fact that they are widely used by researchers and because

K factor's case is the most important one among them all. Each one presents only two levels. Such levels may be quantitative - two temperature, pressure or time values, etc. - or qualitative - two machines, two operators, a factor's "high" and "low" level-, or, yet the presence and absence of a factor. A complete replication of planning requires 2 x 2 x... x 2 = 2k observations

2k design is particularly useful in some experiment's early stages, when many factors are, probably, observed. It provides a lower amount of turns in which k factors can be studied - by means of a complete factorial design - once there are only two levels of each factor. We must assume that the response is basically linear, considering the chosen factor's ranges [51-54].

2k factorial design simplest type is the 22 – two factors, *A* and *B*, each one of them holding two levels. We usually think about such levels as "low" and "high" values. Figure 4 illustrates the

A special concept is used to underline treatment combinations. In general, a treatment combination is represented by a series of lowercase fonts. If a certain font is shown, the corresponding factor is ran at that treatment combination's high level; if it is absent, the factor is ran at its low level. For example, treatment combination (a) indicates that factor *A* is at high

= 4 runs

planning. Note that "plans" can be geometrically represented as squares in which 22

them, respectively. Sometimes it is called "geometric concept for planning".

ticles and its release kinetics was studied.

promising alternatives due to its properties and low cost.

they represent the basis for other considerably valorous planning.

molar mass of PHBHV.

100 Design of Experiments - Applications

**2. 2k factorial design**

and is known as 2k factorial design.

**2.1. 22**

22

 **design**

**Figure 4.** Treatment combinations in a 22 design [*adapted* 51]

The interest in 22 factorial design's effects regards *A* and *B* effects, as well as *AB* second order's interaction factor. According to cases in which fonts (1), *a*, *b*, *ab* are the total of all (*n)* observa‐ tions performed over these planning points. It is easy to estimate such factor's effects. In order to estimate *A* factor's main effect, it is necessary to find the observation's average on the right side of the square (Figure 4), - having *A* at high level – and subtract such average from the observation's average on the left side of the square, where *A* is at low level, or:

A factor's main effect: 22 Factorial design

$$A = \overline{y}\_{A+} - \overline{y}\_{A-} = \frac{a+ab}{2n} - \frac{b+\begin{pmatrix} 1 \\ \end{pmatrix}}{2n} = \frac{1}{2n} \left[ a + ab - b - \begin{pmatrix} 1 \\ \end{pmatrix} \right] \tag{1}$$

Similarly, *B's* main effect is found taking the comments' average at the top of the square, being - having *B* at high level -, and subtract the observations' average at the bottom of the square having *B* at low level:

B factor's main effect: 22 Factorial design

$$\overline{y}\_B = \overline{y}\_{B+} - \overline{y}\_{B-} = \frac{b+ab}{2n} - \frac{a+\begin{pmatrix} 1 \\ \end{pmatrix}}{2n} = \frac{1}{2n} \left[ b + ab - a - \begin{pmatrix} 1 \\ \end{pmatrix} \right] \tag{2}$$

Finally, *AB* interaction is estimated by finding the difference from diagonal's averages seen on Figure 4, or:

AB effect's interaction: 22 Factorial design

$$AB = \frac{ab + \begin{pmatrix} 1 \\ \end{pmatrix}}{2n} - \frac{a+b}{2n} = \frac{1}{2n} \left[ ab + \begin{pmatrix} 1 \\ \end{pmatrix} - a - b \right] \tag{3}$$

The equations quantities in brackets (1), (2) and (3) are called contrasts. For example, *A* contrast is: ContrastA = a + ab - b - (1).

According to such equations, the contrasts' coefficients are always (+1) or (-1). A plus (+) and minus (-) signs table, such as on Table 1, can be used to determine the sign of each treatment combination for a particular contrast. The columns names on Table 1 are *A* and *B* main effects, *AB* interaction and *I* - representing the total. The lines names are treatment combinations. Note that signs on the *AB* column are the product of *A* and *B* columns. In order to generate the contrast from this table, it is demanding to multiply the signals from the appropriate column on Table 1 by the treatment combinations listed on the lines and add. For example, con‐ trastAB = [(1)] + [a] + [b] + [ab] = ab + (1) - a - b [51,52].

**Table 1.** Algebraic signs for calculating effects in 22 Design.

Contrasts are used to calculate effects estimations and the squares sums for *A*, *B* and *AB* interaction. Regarding any 2k design with (*n)* replications, effects estimations are calculated from:

Relation between a contrast and an effect

$$Effect = \frac{Contrust}{n2^{k-1}} \tag{4}$$

( )

*SS*

points and *y*¯*C* is the average of *<sup>n</sup> <sup>C</sup>* runs at the midpoint [51,52]

**2.2. Adding central points to 2k designs**

**Figure 5.** Design with central points [51].

2*k Contrast*

There is a level of freedom associated to each effect (two levels minus one), so that the error's mean square to each effect is equal to the sum of the squares. The variance analysis is completed by calculating the total sum of squares SST (with 4n - 1 level of freedom), as usual, and by getting the squares' error sum SSE (with (4n - 1) levels of freedom) by subtraction means [51,52].

A potential concern in the use of two levels factorial designs is the linearity assumption of linearity in factors effects. Naturally, perfect linearity is unnecessary and the 2k system will work out well, even when linearity's assumption is approximately kept. However, there is a method to replicate certain points in the 2k factor. It avoids bending as well as allows estima‐ tion, regardless the errors that can be obtained. The method consists in adding points to the 2k central planning. They consist on replicas races *n <sup>C</sup>* = 0 at point *x <sup>i</sup>* (*i* = 1, 2,..., *k*). An important reason to add replicated races to the planning's center, due to the fact that the central point do not affect usual estimations regarding 2k planning effects. We consider *k* factors as quantitative ones. Aiming to illustrate the approach, it was considered a 22 plan, with one observation on each one of the factorial points (-,-), (+,-), (-,+) and (+,+) and (*n <sup>C</sup>*) observations on the central points (0,0). Figure 5 illustrates the situation. *y*¯ *<sup>F</sup>* is the average of four runs on the four factorial

2

*<sup>n</sup>* <sup>=</sup> (5)

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And, the sum of any effect's square is:

Any effect's square sum

**Figure 5.** Design with central points [51].

Finally, *AB* interaction is estimated by finding the difference from diagonal's averages seen on

( ) ( ) <sup>1</sup> <sup>1</sup> <sup>1</sup>

= - = + -- é ù

The equations quantities in brackets (1), (2) and (3) are called contrasts. For example, *A* contrast

According to such equations, the contrasts' coefficients are always (+1) or (-1). A plus (+) and minus (-) signs table, such as on Table 1, can be used to determine the sign of each treatment combination for a particular contrast. The columns names on Table 1 are *A* and *B* main effects, *AB* interaction and *I* - representing the total. The lines names are treatment combinations. Note that signs on the *AB* column are the product of *A* and *B* columns. In order to generate the contrast from this table, it is demanding to multiply the signals from the appropriate column on Table 1 by the treatment combinations listed on the lines and add. For example, con‐

(1) + - - + a + + - b + - + ab + + + +

Contrasts are used to calculate effects estimations and the squares sums for *A*, *B* and *AB* interaction. Regarding any 2k design with (*n)* replications, effects estimations are calculated

<sup>1</sup> 2*<sup>k</sup>*

*<sup>n</sup>* - <sup>=</sup> (4)

*Contrast Effect*

**Factorial Effects** *I A B AB*

ë û (3)

*ab a b AB ab a b n nn*

2 22

+ +

Factorial design

trastAB = [(1)] + [a] + [b] + [ab] = ab + (1) - a - b [51,52].

**Table 1.** Algebraic signs for calculating effects in 22 Design.

Relation between a contrast and an effect

And, the sum of any effect's square is:

Any effect's square sum

Figure 4, or:

AB effect's interaction: 22

102 Design of Experiments - Applications

is: ContrastA = a + ab - b - (1).

**Treatment Combination**

from:

$$SS = \frac{\left(Contrast\right)^2}{n2^k} \tag{5}$$

There is a level of freedom associated to each effect (two levels minus one), so that the error's mean square to each effect is equal to the sum of the squares. The variance analysis is completed by calculating the total sum of squares SST (with 4n - 1 level of freedom), as usual, and by getting the squares' error sum SSE (with (4n - 1) levels of freedom) by subtraction means [51,52].

### **2.2. Adding central points to 2k designs**

A potential concern in the use of two levels factorial designs is the linearity assumption of linearity in factors effects. Naturally, perfect linearity is unnecessary and the 2k system will work out well, even when linearity's assumption is approximately kept. However, there is a method to replicate certain points in the 2k factor. It avoids bending as well as allows estima‐ tion, regardless the errors that can be obtained. The method consists in adding points to the 2k central planning. They consist on replicas races *n <sup>C</sup>* = 0 at point *x <sup>i</sup>* (*i* = 1, 2,..., *k*). An important reason to add replicated races to the planning's center, due to the fact that the central point do not affect usual estimations regarding 2k planning effects. We consider *k* factors as quantitative ones. Aiming to illustrate the approach, it was considered a 22 plan, with one observation on each one of the factorial points (-,-), (+,-), (-,+) and (+,+) and (*n <sup>C</sup>*) observations on the central points (0,0). Figure 5 illustrates the situation. *y*¯ *<sup>F</sup>* is the average of four runs on the four factorial points and *y*¯*C* is the average of *<sup>n</sup> <sup>C</sup>* runs at the midpoint [51,52]

If the difference *y*¯ *<sup>F</sup>* <sup>−</sup> *<sup>y</sup>*¯*C* is small, the central point will be at or near the flat plane passing through the factorial points and, therefore, there will be no quadratic curve. On the other hand, if *y*¯ *<sup>F</sup>* <sup>−</sup> *<sup>y</sup>*¯*C* is large, then a quadratic curve will be present. Squares sums –with an unique freedom degree – to a curve is given by:

Sum of squares sums for curves

$$SS\_{Pure\\_quadratic} = \frac{n\_F n\_C \left(\overline{y}\_F - \overline{y}\_C\right)^2}{n\_F + n\_C} = \left(\frac{\overline{y}\_F - \overline{y}\_C}{\sqrt{\frac{1}{n\_F} + \frac{1}{n\_C}}}\right)^2\tag{6}$$

(x2) to maximize a process' performance (y). The process performance is a function between

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where ε represents the noise or the observed error in the response Y. If we denote the expected response by E(Y) = ƒ(x1,x2) = η, then the surface represented by η = ƒ(x1,x2) is called "response

We usually, graphically, represent "response surface" as shown on Figure 6, where η is plotted against the x1 and x2 levels. Such response surface plots were seen represented on a surface

**Figure 6.** A three-dimensional response surface showing the expected performance (η) as a function between tem‐

Aiming to observe a response surface plot - particularly in the chapters on factorial designs to help visualizing its shape, we often plot the response surface's contour, as shown on Figure 7. Regarding the contour's plot, constant response lines are drawn in the x1,x2 plane. Each contour corresponds to a response surface particular height. We have seen the utility of

In most of RSM problems, the relation between response and independent variables is unknown. Thus, RSM's first step means finding an adequate rapprochement to the real relationship between Y and the independent variables. Generally, a polynomial of low degree is applied to some independent variables areas. If the answer is well modeled by independent variables linear functions, then the rapprochement function will be the first-order model:

temperature degrees and pressure, such as in:

graph in a three dimensional environ.

perature (x1) and pressure (x2) [52].

contours plots already.

Y = *f* (x1,x2) +ε

surface".

when, in general, *n <sup>F</sup>* is the amount of factorial design points. Such quantity can be compared to error's mean square error in order to test the curve. Note that when the Equation (6) is divided by *σ*̑<sup>2</sup> <sup>=</sup>*<sup>M</sup> SE* the result will be similar to *t*-statistic's square, used to compare two means. To be more specific, when points are added to the center of 2k design, the model that can be found is:

$$Y = \beta\_0 + \sum\_{j=1}^k \beta\_j \boldsymbol{\chi}\_j + \sum\_{i$$

once βjj are the pure quadratic effects.

Such squares sum may be incorporated to ANOVA and may be compared to error's mean square, aiming to test pure quadratic curves. When points are added to the center of the 2k design the matrix for curve (using equation 6) actually tests the hypotheses:

$$H\_0: \sum\_{j=1}^k \mathcal{B}\_{ji} = 0$$

$$H\_1: \sum\_{j=1}^k \mathcal{B}\_{ji} \neq 0$$

Furthermore, if the factorial design points are not replicated, *n <sup>C</sup>* central point can be used in order to find an error estimation with *n <sup>C</sup>* - 1 level of freedom. A *t-test* can also be used to test curves [51,52].

### **3. Response surface planning and methods (RSM)**

Response surface methodology, or RSM, is a collection of mathematical and statistical techniques that are useful for modeling and analyzing applications in which the interest response is influenced by several variables and the target is to optimize this response. For example, think of a chemical engineer willing to find temperature degrees (x1) and pressure (x2) to maximize a process' performance (y). The process performance is a function between temperature degrees and pressure, such as in:

$$\mathbf{Y} = f\left(\mathbf{x}\_1, \mathbf{x}\_2\right) \star \mathbf{z}$$

If the difference *y*¯ *<sup>F</sup>* <sup>−</sup> *<sup>y</sup>*¯*C* is small, the central point will be at or near the flat plane passing through the factorial points and, therefore, there will be no quadratic curve. On the other hand, if *y*¯ *<sup>F</sup>* <sup>−</sup> *<sup>y</sup>*¯*C* is large, then a quadratic curve will be present. Squares sums –with an unique

( )

\_ 1 1

when, in general, *n <sup>F</sup>* is the amount of factorial design points. Such quantity can be compared to error's mean square error in order to test the curve. Note that when the Equation (6) is divided by *σ*̑<sup>2</sup> <sup>=</sup>*<sup>M</sup> SE* the result will be similar to *t*-statistic's square, used to compare two means. To be more specific, when points are added to the center of 2k design, the model that can be

Such squares sum may be incorporated to ANOVA and may be compared to error's mean square, aiming to test pure quadratic curves. When points are added to the center of the 2k

Furthermore, if the factorial design points are not replicated, *n <sup>C</sup>* central point can be used in order to find an error estimation with *n <sup>C</sup>* - 1 level of freedom. A *t-test* can also be used to test

Response surface methodology, or RSM, is a collection of mathematical and statistical techniques that are useful for modeling and analyzing applications in which the interest response is influenced by several variables and the target is to optimize this response. For example, think of a chemical engineer willing to find temperature degrees (x1) and pressure

design the matrix for curve (using equation 6) actually tests the hypotheses:

**3. Response surface planning and methods (RSM)**

*F C*

*nn y y y y SS n n*

2

*F C F C F C*

ç ÷ - ç ÷ - = = ç ÷ <sup>+</sup> ç ÷ <sup>+</sup> ç ÷

2

(6)

*F C*

*n n*

è ø

æ ö

freedom degree – to a curve is given by:

*Pure quadratic*

*<sup>β</sup>ijxixj* <sup>+</sup> ∑ *j*=1 *k β jjxj* 2 + *ε*

Sum of squares sums for curves

104 Design of Experiments - Applications

*<sup>β</sup>jxj* <sup>+</sup> ∑ ∑ *i*< *j*

once βjj are the pure quadratic effects.

found is:

*<sup>Y</sup>* <sup>=</sup>*β*<sup>0</sup> <sup>+</sup> ∑ *j*=1 *k*

*<sup>H</sup>*<sup>0</sup> :∑ *j*=1 *k*

*<sup>H</sup>*<sup>1</sup> :∑ *j*=1 *k*

*β jj* =0

*β jj* ≠0

curves [51,52].

where ε represents the noise or the observed error in the response Y. If we denote the expected response by E(Y) = ƒ(x1,x2) = η, then the surface represented by η = ƒ(x1,x2) is called "response surface".

We usually, graphically, represent "response surface" as shown on Figure 6, where η is plotted against the x1 and x2 levels. Such response surface plots were seen represented on a surface graph in a three dimensional environ.

**Figure 6.** A three-dimensional response surface showing the expected performance (η) as a function between tem‐ perature (x1) and pressure (x2) [52].

Aiming to observe a response surface plot - particularly in the chapters on factorial designs to help visualizing its shape, we often plot the response surface's contour, as shown on Figure 7. Regarding the contour's plot, constant response lines are drawn in the x1,x2 plane. Each contour corresponds to a response surface particular height. We have seen the utility of contours plots already.

In most of RSM problems, the relation between response and independent variables is unknown. Thus, RSM's first step means finding an adequate rapprochement to the real relationship between Y and the independent variables. Generally, a polynomial of low degree is applied to some independent variables areas. If the answer is well modeled by independent variables linear functions, then the rapprochement function will be the first-order model:

**Figure 7.** A contour plot of a response surface [52].

$$\mathbf{Y} = \boldsymbol{\beta}\_0 + \boldsymbol{\beta}\_1 \mathbf{x}\_1 + \boldsymbol{\beta}\_2 \mathbf{x}\_2 + \dots + \boldsymbol{\beta}\_k \mathbf{x}\_k + \varepsilon \tag{7}$$

in the system and the first-order model will be appropriate. Our goal here is to fast and efficiently lead the experimentalist to optimum's surroundings. Once optimum's region has been found, a more elaborate model - such as the second-order model -, may be applied, and an analysis may be performed to locate the optimum. On Figure 8, we see that the analysis of a response surface can be seen as "climbing a hill" - the top of the hill represents the point of maximum response. If a real optimum is a point of minimum response, then we may think of

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RSM further goal dues to determine optimum operating conditions for systems far from the real optimum or to determine an area in the factorial environ, in which operating requirements are fulfilled. Also note that the word "optimum" in RSM is used in a particular sense. "Climbing a hill" RSM procedures aiming to ensure convergence only to an "optimum" place [51,52].

More extensive RSM presentations can be found in Myers and Montgomery (2002), Khuri and Cornell (1996), and Box and Draper (1987). And review paper by Myers et al. (2004) is also a

Frequently, optimal operating conditions initial estimation to the system will be far from real optimum. In such circumstances, the experimentalist's goal is to rapidly move to optimum's general surroundings. We wish to use a simple and economically efficient experimental procedure. When we are away from the optimum, we usually assume that a first-order model

is an adequate rapprochement to the true surface in X's small region [51,52].

it as "going down a valley".

**Figure 8.** The sequential nature of RSM [52].

**3.1. Steepest ascent method**

useful reference.

If there is curve in the system, then a higher degree polynomial must be used, such as in the second-order model:

$$Y = \beta\_0 + \sum\_{i=1}^{k} \beta\_i \mathbf{x}\_i + \sum\_{i=1}^{k} \beta\_{ii} \mathbf{x}\_i^2 + \sum\_{i$$

Almost all RSM problems use one or both of these models. Of course, it is not feasible that a polynomial model could be a reasonable rapprochement to a real functional relationship regarding the whole independent variables environ. However, regarding a relatively small area, they usually work out quite well.

The minimum squares method is used to estimate parameters to polynomial rapprochements. Response surface analysis is then performed in terms of adjusted surfaces. If the adjusted surface is an adequate rapprochement of the response's true functions, the adjusted surfaces will be almost equivalent to the real system analysis. The model parameters can be estimated most effectively if proper experimental design is used in order to collect data. A design for adjusted response surface is called response surface design [51,52].

RSM is a sequential procedure. Often, whenever we are located on a point on a response surface far from optimum - such as the current operating conditions in Figure 8 -, there is little curving

**Figure 8.** The sequential nature of RSM [52].

0 11 22 ... *Y xx xk k* = + + ++ +

*i i i j Y x x xx*

== <

 b

If there is curve in the system, then a higher degree polynomial must be used, such as in the

2

Almost all RSM problems use one or both of these models. Of course, it is not feasible that a polynomial model could be a reasonable rapprochement to a real functional relationship regarding the whole independent variables environ. However, regarding a relatively small

The minimum squares method is used to estimate parameters to polynomial rapprochements. Response surface analysis is then performed in terms of adjusted surfaces. If the adjusted surface is an adequate rapprochement of the response's true functions, the adjusted surfaces will be almost equivalent to the real system analysis. The model parameters can be estimated most effectively if proper experimental design is used in order to collect data. A design for

RSM is a sequential procedure. Often, whenever we are located on a point on a response surface far from optimum - such as the current operating conditions in Figure 8 -, there is little curving

*i i ii i ij i j*

 b

> b

=+ + + + å å åå (8)

 e

 e

(7)

 b

bb

1 1

adjusted response surface is called response surface design [51,52].

*k k*

0

area, they usually work out quite well.

**Figure 7.** A contour plot of a response surface [52].

bb

second-order model:

106 Design of Experiments - Applications

in the system and the first-order model will be appropriate. Our goal here is to fast and efficiently lead the experimentalist to optimum's surroundings. Once optimum's region has been found, a more elaborate model - such as the second-order model -, may be applied, and an analysis may be performed to locate the optimum. On Figure 8, we see that the analysis of a response surface can be seen as "climbing a hill" - the top of the hill represents the point of maximum response. If a real optimum is a point of minimum response, then we may think of it as "going down a valley".

RSM further goal dues to determine optimum operating conditions for systems far from the real optimum or to determine an area in the factorial environ, in which operating requirements are fulfilled. Also note that the word "optimum" in RSM is used in a particular sense. "Climbing a hill" RSM procedures aiming to ensure convergence only to an "optimum" place [51,52].

More extensive RSM presentations can be found in Myers and Montgomery (2002), Khuri and Cornell (1996), and Box and Draper (1987). And review paper by Myers et al. (2004) is also a useful reference.

### **3.1. Steepest ascent method**

Frequently, optimal operating conditions initial estimation to the system will be far from real optimum. In such circumstances, the experimentalist's goal is to rapidly move to optimum's general surroundings. We wish to use a simple and economically efficient experimental procedure. When we are away from the optimum, we usually assume that a first-order model is an adequate rapprochement to the true surface in X's small region [51,52].

**Figure 9.** First-order response surface and path of steepest ascent [51,52].

The steepest ascent method is a procedure to sequentially move towards a maximum increase in the response. Of course, if minimization is desired, then we call the technique "steepest descent" method. The adjusted first-order model is:

$$
\hat{y} = \hat{\beta}\_0 + \sum\_{i=1}^k \hat{\beta}\_i x\_i \tag{9}
$$

ascent is determined, and the procedure continues. Eventually, the experimentalist will reach optimum's surroundings. It is usually indicated by first-order model's lack of adjustment. At this point, additional experiments are performed in order to obtain a more precise optimum

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PHBHV (Biocycle®) was the PHA used in the current work, containing 6% HV. The used polymer had a weight average (Mw) and number average (Mn) molar masses of 294.275 and 198.168, respectively, polydispersity index (PI) of the 1,48, melting temperature of 164°C and crystallinity of 55%. The reducing agent used was sodium borohydride, NaBH4 (Colleman) with 97% purity. Solvent chloroform was used as PA (purity > 99%) and to polymer purification it was used methyl alcohol PA (Anidrol) (~ 96% purity). All solvents and other chemicals were

Reducing PHBHV molar mass was done by NaBH4 reduction. The methodology used in the

To optimize the conditions of the current process, we used an experimental design, which

Molar mass and the polydispersity index (PI) were determined by means of Gel Permeation

The experimental matrix for the factorial design is illustrated in Table 4. It is noteworthy that the experiments were performed randomly and an error experimental design was obtained

A: NaBH4 concentration (%) 2 4 6 B: Temperature (ºC) 50 52,5 55

factorial design, with high (+) and low (-) levels, three central points (average)

**Factors Low Level (-) Medium level (0) High level (+)**

used without prior purification by presenting analytical purity.

**4.2. General methodology to reduce PHBHV molar mass**

(Table 2), resulting in seven experiments (Table 3).

**Table 2.** Factors and their respective control levels.

**5. Results and analysis**

procedure was described in Montoro's, SR *et al.* work [4,6,55]

Chromatography (GPC) in a Waters Breeze System equipment.

estimation [51,52]

**4. Experimental methods**

**4.1. Solvents and reagents**

**4.3. Statistical design**

included a 22