## 1 Introduction  
A plant-based diet has been a growing trend in recent years. This causes an increased production of food without any animal products. One of them can be vegan mayonnaise, which is a healthy alternative to traditional mayonnaise containing 65-85% of fat [1]. Due to high oil content, oil-in-water emulsions such as mayonnaisees are vulnerable to the oxidation processes of the unsaturated fats in the oil phase. These undesirable reactions lead to the formation of unpleasant flavor, rancid odor, degradation of color or texture, and the generation of potentially toxic compounds [2, 3]. Recently, a wide variety of natural and synthetic antioxidants have been used to reduce the rancidity of emulsions. It is well known that plant materials are natural sources of different antioxidants, such as phenolic acids and their derivatives, that can inhibit the oxidative degradation of lipids. For this reason, various essential oils, plant extracts, and spices such as _Carum copticum_ essential oil [4], rosmears essential oil, _Ferulago angulata_ extract [2], _Rosa canina_ fruit extract [5], and ginger [6] were successfully incorporated into mayonnaise samples to enhance their oxidative stability. Furthermore, by-products of the food industries, such as beetroot peel [7], pistachio green hull [8], grape seed extract [9], and purple corn husk extract [10] demonstrated high antioxidant potential; thus, they were used as antioxidant agents in food emulsions to reduce their rancidity. This application of by-products is promissory to reduce industrial waste, assure safety against rancidity and extend shelf-life, i.e., the period during which oil-based food products maintain satisfactory quality. Lately, to retard or inhibit the oxidative process and the prolongation of emulsions' shelf life, the addition of synthetic additives named phenolipids has been widely used. Interestingly, phenolipids as phenolic compounds modified with aliphatic chains using lipophilization have health benefits due to phenolic motif and amphiphilic and antioxidant properties [11]. The choice of antioxidants is based on their effectiveness in multiphase systems and depends on many factors, such as molecular structure, the reactivity of antioxidants, their physical location, and the presence of other compounds. Among them, the partitioning of the antioxidant into the different phases is the most important factor [12]. It is noteworthy that lipid oxidation in emulsion is initiated at the interface between oil and water phases. Therefore, the antioxidant should be placed at the surface of oil droplets in an oil-in-water emulsion. There are two hypotheses describing the efficiency of antioxidants in emulsion: the cut-off effect and the polar paradox theory. According to the second theory, non-polar antioxidants tend to be located in the interfacial region, whereas polar antioxidants have a tendency to accumulate in the water phase. Therefore, lipophilic/amphiphilic antioxidants should be desired to protect mayonnaise from oxidation [12; 13]. Unfortunately, phenolic compounds, which mainly occur in plants, are very water-soluble antioxidants. Nevertheless, the esterification of phenolic acids with various alkyl alcohols was widely used to enhance the hydrophobicity of the synthesized phenolipids. However, alcohols with different carbon chain lengths affected the degree of lipophilization, which was associated with the antioxidant properties of phenolipids. This phenomenon is called the cut-off effect, and it is an extension of the polar paradox hypothesis [12; 13]. Previous research demonstrated that phenolic acid alkyl esters added to oil-in-water emulsions increased their oxidative stability and antioxidant potential [11; 14; 15]. The addition of different caffeic acid esters to oil-in-water emulsions indicated the enhancement of their antioxidant activity up to octyl caffeine incorporation, whereas further elongation of the alkyl carbon chain caused a decrease in the antioxidant properties of the emulsions [11; 16].