## 1 Introduction  
Concrete is the most widely used construction material in modern civil engineering, and its performance directly impacts the safety and service life of building structures. Concrete's toughness, which measures its resistance to cracking and ability to maintain structural integrity, is particularly critical under complex conditions such as external impacts and structural deformation. This has received significant attention from researchers and engineers [1]. While concrete has an excellent compressive strength and durability compared with organic materials, its low tensile strength and toughness are major limitations, restricting its application in projects requiring high deformation and impact resistance. Building structures are evolving towards larger scales, greater complexity, and multifunctionality. To support this development trend, it has become a pressing issue to explore the mechanisms and optimization methods for enhancing concrete toughness [2]. Systematicstudies of concrete toughness can ensure the durability of traditional structures. Moreover, they can pave the way for the design and construction of new building structures. Researchers have explored various methods to improve the toughness of concrete; for example, optimizing the concrete mix design, adjusting aggregate grading, and using special mineral admixtures can improve the microstructure of concrete, thereby enhancing its toughness. Additionally, fiber reinforcement is a common approach, with steel fibers, basalt fibers, and synthetic fibers forming a three-dimensional reinforcement system within the concrete [3; 4; 5; 6; 7; 8].These fibers bridge cracks and prevent their propagation, significantly improving toughness. Polymers, as important chemical admixtures, can modify concrete by forming a continuous network structure that enhances adhesion, ductility, and durability, thereby improving crack resistance [9; 10; 11; 12; 13]. This enhances the deformation resistance and cracking performance of concrete. Commonly used polymers include styrene-acrylate (SA) emulsion [14], styrene-butadiene rubber (SBR) [15], and ethylene vinyl acetate (EVA) [16; 17]. Polymer modification is an effective method for toughening cementitious materials. It enhances toughness, viscosity, and impermeability without significantly affecting workability; thus, it has attracted considerable research interest [18; 19]. During the modification process, polymers adsorb onto the surface of hydrated cement particles and fill micropores after film formation [20], preventing crack expansion and improving toughness. However, most current studies focus on the effects of specific polymers on the toughness of cementitious materials. For example, [PERSON] et al. [21] investigated the fracture toughness of mortar modified with butylbenzene emulsion, finding that it changed the fracture behavior from brittle to ductile. [PERSON] et al. [22] compared the flexural strength, toughness, and impact resistance of cement concrete modified with styrene-butadiene emulsion, noting no significant correlation between these properties. [PERSON] et al. [23] combined polypropylene fibers and SBR polymer latex to enhance mortar toughness, achieving a compressive-flexural ratio as low as 2.17 and a JCI toughness index (the ratio of the energy absorbed by the concrete specimen during the failure process to the energy absorbed when the peak load is reached [24]) of 13.1, a 258% improvement over unmodified mortar [25]. Overall, research on the relationship between polymer structure, latex film properties, and modified cementitious material toughness remains limited and requires further exploration. In this study, five types of poly(styrene-co-butyl acrylate) (PSA) emulsions were synthesized with varying ratios of soft and hard monomers. These PSA emulsions exhibit different glass transition temperatures (T\({}_{\text{g}}\)), minimum film-forming temperatures (MFFTs), adhesive properties, and damping characteristics.