## 3 Results and Discussion
### Viscoelastic Behavior of CPC-Stabilized Emulsions
#### 3.3.1 Emulsions Stabilized by Gelling CPC
During the cooling step, G\({}^{\prime}\) decreased but further deviated from G\({}^{\prime\prime}\), indicating the maintenance of the structural change in which the sample transitioned into an elastically dominated system (G\({}^{\prime}\)? G\({}^{\prime\prime}\)). When the temperature returned to 20 \({}^{\circ}\)C, a significant difference in the initial and final G\({}^{\prime}\) values was clearly evident (Figure 2b), suggesting that permanent heat-induced conformational changes of the protein had occurred. The increase in elasticity of the system (denoted by the rise in G\({}^{\prime}\)) was most likely due to the non-covalent interactions such as hydrogen bonds and hydrophobic interactions [59; 62; 63]. Nevertheless, the observed decrease in viscoelasticity as the temperature decreased suggests the formation of a fine-stranded gel in which heat-induced protein gelation involved unfolding followed by protein aggregation but not spatial cross-linking (covalent bonds were not significantly involved in the gel structure). Under these conditions, biopolymer molecules built up thin filaments and had a low tendency to aggregate further; protein molecules did not undergo extensive aggregation owing to the strong electrostatic repulsion between them. In the case of the C\({}_{\text{g}}\), changes in G\({}^{\prime}\) and G\({}^{\prime\prime}\) were also observed during the temperature ramp-up, hold, and ramp-down procedure (Figure 2a). The increase in G\({}^{\prime}\) and G\({}^{\prime\prime}\) started when the temperature reached \(\sim\)82 \({}^{\circ}\)C (14 min) and continued when the temperature was held constant at 95 \({}^{\circ}\)C, indicating molecular unfolding (denaturation). Then, when lowering the temperature back to 20 \({}^{\circ}\)C, the G\({}^{\prime}\) and G\({}^{\prime\prime}\) also decreased. Finally, once the temperature returned to 20 \({}^{\circ}\)C, the decrease in moduli plateaued, and the specimen reached its final G\({}^{\prime}\)! G\({}^{\prime\prime}\), suggesting its liquid state remains similar to before heating. It should be mentioned that a higher denaturation temperature of proteins in their water dispersion compared to the denaturation temperature in emulsion has also been demonstrated for other protein systems, because proteins undergoing surface denaturation during adsorption at the water-oil interface are more susceptible to thermal denaturation [33; 34; 64]. For eC\({}_{\text{g}}\) with 0.1M NaCl, peaks of G\({}^{\prime}\) and G\({}^{\prime\prime}\) moduli were observed at \(\sim\)72 \({}^{\circ}\)C (12 min) during heating (Figure 2c). As the temperature was further ramped, G\({}^{\prime}\) was now significantly greater than G\({}^{\prime\prime}\) (i.e., a crossover was observed), and the increase in G\({}^{\prime\prime}\) began to slow down. Then, during the isothermal hold step at 95 \({}^{\circ}\)C, G\({}^{\prime}\) increased until the end of the ramp, and G\({}^{\prime\prime}\) remained fairly constant. The increase in G\({}^{\prime}\) upon heating suggests that the observed rheological behavior was driven by conformational changes and aggregation of the protein molecules. During the cooling step, a sudden increase in both G\({}^{\prime}\) and G\({}^{\prime\prime}\) initiated at 80 \({}^{\circ}\)C, and then rapid jumps in the rheological responses were observed. It suggests that protein aggregation and the growth and rearrangement of aggregates were induced and further accentuated when the temperature was reached and lowered. In the presence of NaCl, aggregation was more random leading to particulate aggregates linked together in a spatial network (Figure S4c).