# Impact of Retention Agents on Functional Properties of Recycled Paper in Sustainable Manufacturing
## 3 Results and Discussion
However, excessive dosages of the agent can result in over-flocculation, creating large aggregates that disrupt the uniformity of the fiber network. This imbalance can weaken the tensile properties by introducing structural heterogeneity and reducing the effective load-bearing areas in the paper. The impact of a retention agent based on acrylamide and a cationic derivative of acrylic acid on the tensile properties of two types of wastewaterpaper (1.3 and 3.2) was analyzed. The results, summarized in Tables 2 and 3, reveal complex trends and highlight the non-linear relationship between retention aid concentration and paper strength. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Retention Agent Addition** & **I\({}_{\mathbf{B}}\)** & **F\({}_{\mathbf{B}}\)** & \(\sigma_{\mathbf{T}}\)\({}^{\mathbf{b}}\) & \(\sigma_{\mathbf{T}}\)\({}^{\mathbf{W}}\) & \(\varepsilon_{\mathbf{T}}\) & \(W_{\mathbf{T}}\)\({}^{\mathbf{b}}\) & \(W_{\mathbf{T}}\)\({}^{\mathbf{W}}\) & \(\mathbf{E}\)\({}^{\mathbf{b}}\) & \(\mathbf{E}\)\({}^{\mathbf{w}}\) & \(\mathbf{E}\)\({}^{\mathbf{*}}\) \\ \hline
**[\%]** & **[m]** & **[N]** & **[N/m]** & **[Nm/g]** & **[\%]** & **[J/m\({}^{2}\)]** & **[J/g]** & **[N/m]** & **[Nm/g]** & **[MPa]** \\ \hline Ref. & 2700 & 30.9 & 2095 & 26.4 & 1.60 & 22.1 & 0.278 & 320,667 & 4033 & 2915 \\
0.1 & 2300 & 27.5 & 1853 & 22.8 & 1.45 & 17.9 & 0.220 & 305,500 & 3753 & 2777 \\
0.2 & 1800 & 20.7 & 1425 & 17.9 & 0.92 & 8.4 & 0.105 & 295,167 & 3693 & 2683 \\
0.3 & 1800 & 21.3 & 1431 & 17.7 & 0.88 & 7.6 & 0.093 & 292,383 & 3611 & 2623 \\
0.4 & 1700 & 19.4 & 1338 & 16.5 & 0.78 & 7.2 & 0.089 & 289,817 & 3579 & 2600 \\
0.5 & 1750 & 19.3 & 1353 & 17.0 & 0.83 & 6.7 & 0.085 & 288,333 & 3622 & 2622 \\
0.6 & 1850 & 21.3 & 1465 & 18.1 & 1.08 & 11.0 & 0.136 & 283,483 & 3501 & 2543 \\
0.8 & 2000 & 22.9 & 1578 & 19.5 & 1.25 & 12.5 & 0.154 & 279,767 & 3455 & 2510 \\
1.0 & 2150 & 24.5 & 1685 & 21.2 & 1.40 & 15.5 & 0.194 & 276,833 & 3477 & 2515 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Tensile properties of paper from 1.3 white wastewater. For the 1.3 wastepaper, the reference sample exhibited the highest tensile strength values, with a breaking length of 2700 m. The addition of the retention aid resulted in an initial decrease in these values. At an addition rate of 0.2%, the breaking length dropped to 1800 m (a 33% reduction) and the force-at-break index decreased to 17.9 Nm/g (a 32% reduction). Further increasing the retention agent to 0.3% and 0.4% caused slight variations, but no significant improvement was observed. Interestingly, at concentrations above 0.8%, a reverse trend emerged, with strength values starting to recover. At 1.0% addition, the breaking length increased to 2150 m, and the force-at-break index reached 21.2 Nm/g. Despite this recovery, these values still did not exceed those of the reference sample. Other mechanical properties followed a similar trend. Strain at break decreased significantly at lower dosages, from 1.60% in the reference to 0.92% at 0.2%. However, it improved to 1.40% at 1.0%. The energy absorption index showed a marked drop at lower dosages but recovered to 0.194 J/g at 1.0%. The 3.2 wastepaper exhibited higher initial tensile properties compared to 1.3, likely due to differences in pulp composition and the heterogeneity of wastepaper. The reference sample had a breaking length of 3750 m, a breaking force of 42.6 N, and a tensile index of 36.2 Nm/g. However, the addition of the retention agent followed a similar decreasing trend. At 0.2% addition, the breaking length reduced to 2600 m (a 31% reduction), and the force-at-break index decreased to 24.9 Nm/g (a 31% reduction). As with the 1.3 type of wastepaper, increasing the retention agent concentration to 0.8% and 1.0% reversed the trend, with the force-at-break index reaching 29.6 Nm/g at 1.0%. Despite this recovery, the values remained lower than those of the reference. The strain at break and work of fracture also exhibited comparable trends.