## 2 Materials and Methods
### The Performance Characterization of PSA Emulsion-Modified Mortar  
The properties of PSA emulsion-modified mortar were characterized by testing physical properties (air content and dry density), hydration heat, and mechanical properties (flexural and compressive strength, and three-point bending test) and observing microscopic morphology. The air content was measured directly using the air content meter (Tianjin Think Line Test Instrument Technology Co., Ltd., Tianjin, China, LS-546). The mortar was dried for 24 h at 60 \({}^{\circ}\)C, then for 24 h at 80 \({}^{\circ}\)C, and finally for 105 days. The PSA emulsion-modified mortar was cured for 28 days. It was dried at 60 \({}^{\circ}\)C for 24 h, then at 80 \({}^{\circ}\)C for 24 h, and finally at 105 \({}^{\circ}\)C until it reached a constant weight. After this, the density of the dry mortar was tested. The heat of hydration of the PSA emulsion-modified mortar was tested using a microcalorimeter (TA Instruments Co., Ltd., New Castle, DE, USA, TAM-air); the instrument and test materials were kept at a constant temperature for 24 h before the test. Suitable proportions of cement, deionized water, and PSA emulsions were mixed to form a cement slurry bottle, and the water-cement ratios and polymer-cement ratios were the same as those of the modified mortar. The mixed cement slurry bottle was quickly placed into the calorimeter channel, and the heat dissipation was recorded for 7 days. The microscopic morphology of the PSA emulsion-modified mortar was observed using a scanning electron microscope (SEM) (JEOL, Co., Ltd., Tokyo, Japan, SM-7800F). To better observe the morphology of the polymer film, the mortar was soaked in 5% hydrochloric acid for 3 h before the test. The flexural and compressive strengths of the PSA emulsion-modified mortar were tested. The specimen was 40 mm \(\times\) 40 mm \(\times\) 160 mm. After the flexural specimens were broken, the compressive strength test was conducted. The test process is shown in Figure 2a,b. According to the recommendation of the RILEM technical committee [27], the fracture toughness of PSA emulsion-modified mortar was tested using a three-point bending test with a notch. Before the test, a notch with a width of 2 mm and a depth of 13.3 mm was cut out on the bottom surface of the sample with a cutting machine. Then, two 1 mm pointed iron plates were used to fix the clamp extender on both sides of the notch to measure the crack mouth opening displacement (CMOD), and the loading speed was set to 0.5 mm/min. The test process is shown in Figure 2c. The fracture energy (\(G_{f}\)) of notched mortar strips was calculated using Equation (1) when performing the three-point bending test, as follows  
\[G_{f}=\frac{W_{0}-mg\partial_{0}}{A_{lig}} \tag{1}\]where \(W_{0}\) is the area of the load-deflection curve, \(mg\) is the self-weight of the mortar strip, \(\partial_{0}\) is its deflection corresponding to the maximum load, and \(A_{lig}\) is the area of the fracture surface [\(B(W-a_{0})\)], where \(B\) is the width of the mortar strip, \(W\) is the height of the mortar strip, and \(a_{0}\) is the initial crack length. The two-parameter method [28] was used to calculate the fracture toughness of the modified mortar, as shown in Equation (2). This method can directly calculate the critical stress intensity factor; that is, the fracture toughness (\(K_{IC}\)), which can be used to measure the crack propagation resistance of the material, as follows:  
\[K_{IC}=\frac{3P_{max}S}{2W^{2}B}\sqrt{\pi a}F(\alpha) \tag{2}\]  
where \(P_{max}\) is the maximum load, \(S\) is the distance between the two support points at the bottom of the specimen, \(a\) is the effective crack length, and \(F(\alpha)\) is calculated as in Equation (3):  
\[F(\alpha)=\frac{1}{\sqrt{\pi}}\frac{1.99-\alpha(1-\alpha)\left(2.15-3.95\alpha +2.7\alpha^{2}\right)}{(1+2\alpha)(1-\alpha)^{\frac{3}{2}}} \tag{3}\]  
where \(\alpha\) is \(a_{0}/W\).