# On the Design of Aqueous Emulsions of Colophony Resin

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Equipment Characterization

#### 2.1. Materials

#### 2.2. Experimental Equipment and Procedure

#### 2.3. Quality Characterization Equipment

^{TM}pH meter, Mettler Toledo, Greifensee, Switzerland. The solid content was measured using gravimetric analysis with a precision balance. The particle size was measured using a Malvern Zetasizer Nano ZS, Malvern, Worcestershire, United Kingdom system, which provided both the particle size distribution (PSD) and the cumulative distribution curves.

## 3. Development Approach and Related Tools

#### 3.1. Overall Quality Performance Metric

#### 3.2. Design Procedure

`JMP`

^{®}can be used for the design and data analysis [43]. The results of Stage 1 included a set of primary factors and levels that could optimize quality performance and this combination of factors and levels was fixed in the second stage.

## 4. Results

#### 4.1. The Design Problem

#### 4.2. Screening of Primary Factors

#### 4.3. Optimization of Secondary Factors

#### 4.4. Formulations’ Repeatability

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**The state of the resin during the process (

**a**) as a (solid) raw material; (

**b**) after heating to the softening point; (

**c**) as a resin-in-water emulsion.

**Figure 2.**Systematic procedure for hierarchically organizing the experimental work in a customer-centric approach.

Resin Designation | ${\mathit{T}}_{\mathbf{soft}}$ (${}^{\circ}\mathbf{C}$) |
---|---|

A | 60 |

B | 70 |

C | 80 |

Quality Characteristic | Lower Specification | Upper Specification | Target Value | Loss Function |
---|---|---|---|---|

Viscosity (@ 25 ${}^{\circ}\mathrm{C}$) | ns${}^{\phantom{\rule{3.33333pt}{0ex}}\u2020}$ | 1000 cP | ns${}^{\phantom{\rule{3.33333pt}{0ex}}\u2020}$ | smaller-is-better |

pH | 7 | 9 | 8 | target-is-best |

Solid content | 54 %wt | 56 %wt | 55 %wt | target-is-best |

Particle diameter | ns${}^{\phantom{\rule{3.33333pt}{0ex}}\u2020}$ | 1000 nm${}^{\phantom{\rule{3.33333pt}{0ex}}\u2021}$ | ns${}^{\phantom{\rule{3.33333pt}{0ex}}\u2020}$ | smaller-is-better |

^{†}undefined;

^{‡}95% of particles below 1000 nm.

Quality Characteristic | Normalized Loss Function | Weight (${\mathit{w}}_{\mathit{i}}$) |
---|---|---|

Viscosity (@ 25 ${}^{\circ}\mathrm{C}$) | ${L}^{\mathrm{norm}}\left({C}_{1}\right)=1\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}{C}_{1}^{2}$ | 0.30 |

pH | ${L}^{\mathrm{norm}}\left({C}_{2}\right)={({C}_{2}-8)}^{2}$ | 0.15 |

Solid content | ${L}^{\mathrm{norm}}\left({C}_{3}\right)={({C}_{3}-55)}^{2}$ | 0.05 |

Particle diameter | ${L}^{\mathrm{norm}}\left({C}_{4}\right)=1\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}{C}_{4}^{2}$ | 0.50 |

Factor | Level | Characterization | Designat. |
---|---|---|---|

$-1$ | Resin with ${T}_{\mathrm{soft}}=60{}^{\circ}\mathrm{C}$ | A1 | |

${x}_{1}$ | 0 | Resin with ${T}_{\mathrm{soft}}=70{}^{\circ}\mathrm{C}$ | A2 |

$+1$ | Resin with ${T}_{\mathrm{soft}}=80{}^{\circ}\mathrm{C}$ | A3 | |

$-1$ | Surfactant from S1 | S1 | |

${x}_{2}$ | 0 | Surfactant from S2 | S2 |

$+1$ | Surfactant from S3 | S3 |

# Exper. | ${\mathit{x}}_{1}$ | ${\mathit{x}}_{2}$ | Designat. | ${\mathit{C}}_{1}$ (cP) | ${\mathit{C}}_{2}$ (-) | ${\mathit{C}}_{3}$ (%wt) | ${\mathit{C}}_{4}$ (nm) | ${\mathit{d}}_{95}$ (nm) | ${\mathit{C}}_{5}$ | O |
---|---|---|---|---|---|---|---|---|---|---|

1 | $-1$ | $-1$ | A1:S1_1 | 1562 | 11.04 | 54.36 | 209.6 | 310.45 | 0 | 2.161 |

2 | $-1$ | 0 | A1:S2_1 | 265 | 8.63 | 55.11 | 428.2 | 1029.93 | 0 | 0.173 |

3 | $-1$ | $+1$ | A1:S3_1 | 1292 | 11.19 | 54.58 | 614.9 | 1302.51 | 1 | 2.225 |

4 | 0 | $-1$ | A2:S1_1 | 187 | 10.28 | 55.62 | 444.3 | 4246.54 | 1 | 0.908 |

5 | 0 | 0 | A2:S2_1 | 339 | 8.46 | 54.34 | 262.7 | 695.22 | 0 | 0.123 |

6 | 0 | $+1$ | A2:S3_1 | - | - | - | - | - | - | ns${}^{\phantom{\rule{3.33333pt}{0ex}}\u2020}$ |

7 | $+1$ | $-1$ | A3:S1_1 | - | - | - | - | - | - | ns${}^{\phantom{\rule{3.33333pt}{0ex}}\u2020}$ |

8 | $+1$ | 0 | A3:S2_1 | 112 | 8.55 | 54.44 | 615.5 | 1064 | 1 | 0.254 |

9 | $+1$ | $+1$ | A3:S3_1 | - | - | - | - | - | - | ns${}^{\phantom{\rule{3.33333pt}{0ex}}\u2020}$ |

^{†}non-dispersed formulations.

Optimization of Emulsion A1:S1 (${\mathit{x}}_{1}=-1$, ${\mathit{x}}_{2}=-1$) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

# Exper. | ${\mathit{x}}_{\mathbf{3}}$ (%wt) | ${\mathit{x}}_{\mathbf{4}}$ (rpm) | ${\mathit{x}}_{\mathbf{5}}$ (%wt) | Designat. | ${\mathit{C}}_{\mathbf{1}}$ (cP) | ${\mathit{C}}_{\mathbf{2}}$ (-) | ${\mathit{C}}_{\mathbf{3}}$ (%wt) | ${\mathit{C}}_{\mathbf{4}}$ (nm) | ${\mathit{C}}_{\mathbf{5}}$ | $\mathit{O}$ |

1 | 2.0 | 100 | 7.0 | A1:S1_1 | 1562 | 11.04 | 54.36 | 209.6 | 0 | 2.161 |

10 | 2.5 | 100 | 7.0 | A1:S1_2 | 5967 | 10.11 | 55.02 | 150.0 | 0 | 11.361 |

11 | 0.0 | 100 | 7.0 | A1:S1_3 | - | - | - | - | - | ns${}^{\phantom{\rule{3.33333pt}{0ex}}\u2020}$ |

12 | 1.0 | 100 | 7.0 | A1:S1_4 | 440 | 10.19 | 54.44 | 261.1 | 0 | 0.827 |

13 | 1.0 | 100 | 6.0 | A1:S1_5 | 429 | 10.14 | 55.92 | 319.0 | 0 | 0.835 |

14 | 0.5 | 100 | 7.0 | A1:S1_6 | - | - | - | - | - | ns${}^{\phantom{\rule{3.33333pt}{0ex}}\u2020}$ |

15 | 0.5 | 100 | 10.5 | A1:S1_7 | 235 | 8.99 | 54.68 | 1007.7 | 1 | 0.676 |

16 | 0.5 | 100 | 14.0 | A1:S1_8 | 172 | 8.28 | 55.46 | 209.4 | 0 | 0.053 |

Optimization of emulsion A1:S2 (${x}_{1}=-1$, ${x}_{2}=0$) | ||||||||||

2 | 2 | 100 | 7.0 | A1:S2_1 | 265 | 8.63 | 55.11 | 428.2 | 0 | 0.173 |

17 | 2.5 | 100 | 7.0 | A1:S2_2 | 352 | 8.36 | 54.30 | 236.2 | 0 | 0.109 |

18 | 2.0 | 50 | 7.0 | A1:S2_3 | 392 | 8.62 | 55.92 | 231.1 | 0 | 0.173 |

19 | 1.0 | 50 | 7.0 | A1:S2_4 | - | - | - | - | - | ns${}^{\phantom{\rule{3.33333pt}{0ex}}\u2020}$ |

20 | 1.5 | 50 | 7.0 | A1:S2_5 | 131 | 8.05 | 54.91 | 205.53 | 0 | 0.027 |

Optimization of emulsion A2:S2 (${x}_{1}=0$, ${x}_{2}=0$) | ||||||||||

5 | 2.0 | 100 | 7.0 | A2:S2_1 | 339 | 8.46 | 54.34 | 262.7 | 0 | 0.123 |

21 | 2.5 | 100 | 7.0 | A2:S2_2 | 308 | 8.35 | 54.58 | 341.3 | 0 | 0.114 |

22 | 2.0 | 50 | 7.0 | A2:S2_3 | 337 | 8.70 | 54.96 | 350.6 | 0 | 0.169 |

23 | 1.0 | 50 | 7.0 | A2:S2_4 | 87 | 6.96 | 54.94 | 245.5 | 0 | 0.195 |

24 | 1.5 | 50 | 7.0 | A2:S2_5 | 118 | 7.94 | 54.98 | 210.5 | 0 | 0.027 |

^{†}non-dispersed formulations.

# Exper. | Designat. | ${\mathit{x}}_{1}$ (-) | ${\mathit{x}}_{2}$ (-) | ${\mathit{x}}_{3}$ (%wt) | ${\mathit{x}}_{4}$ (rpm) | ${\mathit{x}}_{5}$ (%wt) |
---|---|---|---|---|---|---|

16 | A1:S1_8 | $-1$ | $-1$ | 0.5 | 100 | 14.0 |

20 | A1:S2_5 | $-1$ | 0 | 1.5 | 50 | 7.0 |

24 | A2:S2_5 | 0 | 0 | 1.5 | 50 | 7.0 |

Repeatability of Emulsion A1:S1 (${\mathit{x}}_{1}=-1$, ${\mathit{x}}_{2}=-1$, ${\mathit{x}}_{3}=$ $0.5$ %wt, ${\mathit{x}}_{4}=$ 100 rpm, ${\mathit{x}}_{5}=$ $14.0$ %wt) | |||||||
---|---|---|---|---|---|---|---|

# Exper. | Designat. | ${\mathit{C}}_{\mathbf{1}}$ (cP) | ${\mathit{C}}_{\mathbf{2}}$ (-) | ${\mathit{C}}_{\mathbf{3}}$ (%wt) | ${\mathit{C}}_{\mathbf{4}}$ (nm) | ${\mathit{C}}_{\mathbf{5}}$ | $\mathit{O}$ |

16 | A1:S1_8 | 172 | 8.25 | 55.46 | 209.43 | 0 | 0.051 |

25 | A1:S1_9 | 236 | 8.61 | 54.27 | 460.97 | 0 | 0.205 |

26 | A1:S1_10 | 231 | 8.42 | 54.43 | 448.80 | 0 | 0.159 |

27 | A1:S1_11 | 237 | 8.39 | 55.07 | 449.25 | 0 | 0.141 |

${\overline{x}}_{{C}_{i}}$ | 219.00 | 8.42 | 54.81 | 392.11 | |||

${s}_{{C}_{i}}$ | 31.44 | 0.15 | 0.56 | 121.92 | |||

${C}_{v,i}\phantom{\rule{3.33333pt}{0ex}}(\%)$ | 14.36 | 1.76 | 1.01 | 31.09 | |||

Repeatability of emulsion A1:S2 (${x}_{1}=-1$, ${x}_{2}=0$, ${x}_{3}=$ $1.5$ %wt, ${x}_{4}=$ 50 rpm, ${x}_{5}=$ $7.0$ %wt) | |||||||

20 | A1:S2_5 | 131 | 8.05 | 54.91 | 205.53 | 0 | 0.027 |

28 | A1:S2_6 | 132 | 7.96 | 55.26 | 206.35 | 0 | 0.030 |

29 | A1:S2_7 | 132 | 8.04 | 54.84 | 202.35 | 0 | 0.027 |

30 | A1:S2_8 | 128 | 8.01 | 54.87 | 196.25 | 0 | 0.025 |

${\overline{x}}_{{C}_{i}}$ | 130.75 | 8.02 | 54.97 | 202.62 | |||

${s}_{{C}_{i}}$ | 1.89 | 0.04 | 0.20 | 4.58 | |||

${C}_{v,i}\phantom{\rule{3.33333pt}{0ex}}(\%)$ | 1.45 | 0.50 | 0.36 | 2.26 | |||

Repeatability of emulsion A2:S2 (${x}_{1}=0$, ${x}_{2}=0$, ${x}_{3}=$ $1.5$ %wt, ${x}_{4}=$ 50 rpm, ${x}_{5}=$ $7.0$ %wt) | |||||||

24 | A2:S2_5 | 118 | 7.94 | 54.98 | 210.5 | 0 | 0.027 |

31 | A2:S2_6 | 108 | 7.89 | 55.31 | 208.57 | 0 | 0.032 |

32 | A2:S2_7 | 112 | 7.95 | 54.66 | 219.48 | 0 | 0.034 |

33 | A2:S2_8 | 106 | 7.82 | 54.15 | 215.65 | 0 | 0.068 |

${\overline{x}}_{{C}_{i}}$ | 111.00 | 7.90 | 54.78 | 213.55 | |||

${s}_{{C}_{i}}$ | 5.29 | 0.06 | 0.49 | 4.96 | |||

${C}_{v,i}\phantom{\rule{3.33333pt}{0ex}}(\%)$ | 4.77 | 0.75 | 0.90 | 2.32 |

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## Share and Cite

**MDPI and ACS Style**

Ingrez, I.B.D.; Ferreira, P.C.N.; Gameiro, D.; Duarte, B.P.M.
On the Design of Aqueous Emulsions of Colophony Resin. *Polymers* **2023**, *15*, 1691.
https://doi.org/10.3390/polym15071691

**AMA Style**

Ingrez IBD, Ferreira PCN, Gameiro D, Duarte BPM.
On the Design of Aqueous Emulsions of Colophony Resin. *Polymers*. 2023; 15(7):1691.
https://doi.org/10.3390/polym15071691

**Chicago/Turabian Style**

Ingrez, Isa B. D., Paula C. N. Ferreira, Davide Gameiro, and Belmiro P. M. Duarte.
2023. "On the Design of Aqueous Emulsions of Colophony Resin" *Polymers* 15, no. 7: 1691.
https://doi.org/10.3390/polym15071691