**4. Dynamic mechanical analysis (DMA)**

The structural strength of a material is usually determined through the reestablishment of the storage modulus, *G*', of the disrupted network after the shear deformation driven by high shear rates has been lifted [5, 45]. In this study, the structural strength of the SAP system was established through thixotropic behavior analysis by applying an oscillatory rheological test consisting of three steps, each one at constant dynamic mechanical conditions, as recommended in Ref. [45]. The first or *reference* step is carried out at low-shear conditions (strain = 20%, *ω* = 6.283 rad/s, time ≈ 960 s) within the LVE range. The *G*'-value at the end of the first step is taken as the reference value of *G*'-at-rest to be compared to the *G*'-value occurring at the end of the third step [45]. The second or *high shear* step is conducted at high shear conditions (strain = 1000%, *ω* = 6.283 rad/s, time ≈ 480 s) outside the LVE range with the purpose of breaking the internal structure of the sample. The third or *regeneration* step is performed at the same shear conditions (strain = 20%, *ω* = 6.283 rad/s, time ≈ 960 s) of the first step within the LVE range to facilitate the regeneration of the sample's structure. The percentage of structural regeneration is calculated by taking the *G*'-value at the end of the third step in relation to the reference value of *G*'-at-rest of the first step [45].

**Figure 8** displays the curves of *G*' and *G*" as a function of time [s], brine concentration (2.1 and 8.4 wt%), and polymer systems for the *reference* step (step 1) and for the *regeneration* step (step 3).

**Figure 8** shows that at low salinity (i.e., brine 2.1 wt%), the baseline displays a complete structural regeneration (i.e., thixotropic behavior), while the SAP system exhibits a 5% increase in the structural strength relative to the reference value of *G*' obtained from step 1. The *G*'-values (empty square symbols) gathered during the regeneration step are consistently higher than the *G*'-values (solid square symbols) obtained during the reference step. Furthermore, **Figure 8** indicates that the structural regeneration of both systems takes place immediately after the high shear step ends. The corresponding *G*"-curves for both systems show a similar behavior. The mechanical response for both systems is dominated by *G*' (tan*δ* < 1) during the entire testing period, thus displaying a network-like character. The upsurge in the structural strength exhibited by the SAP network is due to the increase in the number and strength of noncovalent interchain associations that reconnect the polymer chains in the network very quickly, causing the rapid regain and enhancement of the mechanical structural strength and solution viscosity [3, 5, 36, 45].

At high brine concentration (i.e., 8.4 wt%), the baseline does not show complete structural regeneration (**Figure 8**). The *G*'-values obtained in step 3 are below the *G*'-values obtained in step 1 during the entire testing period. The decrease in the structural strength might be related to the weakening of the interchain noncovalent interactions for this system. On the contrary, the SAP system demonstrates full recovery after extension under load. The *G*'-values in step 3 show an immediate 100% structural strength regeneration. Again, for the SAP system, *G*' > *G*" showing network-like properties during the total testing period.

These results verify the reversibility of the interpolymer interactions of the SAP system involving the instant recovery of the noncovalent associations following shear thinning [58]. This demonstrates the self-healing advantage of supramolecular polymer networks due to the reversibility of the physical associations and high-chain mobility in water [3, 6, 58].

**Figure 8.** Thixotropic analysis: *G*' and *G*" as a function of time.

**Figure 7** demonstrates the significant effect of ionic strength on the SAP system. At the highest ionic strength (i.e., brine 8.4 wt%), the SAP system displays the highest elasticity and viscosity. The curves in **Figure 7** show *G*' values that are markedly larger than *G*" at all frequencies. A tan*δ* < 1 in the entire range of angular frequency is consistent with a gel (physical network)-like behavior [45]. **Figure 7** also reveals a negligible effect of ionic strength on the viscoelasticity of the baseline or PB # 1, which consists of a mixture of 0.2 wt% polymer **B and** 

These rheological data indicate that the higher the ionic strength the higher the suppression of the electrostatic repulsion among polymer chains through cation bridging (i.e., Ca2+), which results in more and stronger intra- and specially interpolymer complexations and associations that reinforce the polymer network and enhances the viscosity of the solution [36]. Previous research has also demonstrated that the addition of inorganic salts to interpolymer mixtures (e.g., anionic and nonionic polymers) in aqueous solutions deteriorates the thermodynamic quality of the solvent (e.g., water) with respect to the polymers, which promotes the strengthening of the interchain

The main difference between the SAP system and the baseline shown in **Figure 7** is that the SAP system contains 0.1 wt% of AP polymer (i.e., hydrophobically modified polymer); therefore, the addition of inorganic salts shelters the charged groups in the associating polymer side chains and uncovers the hydrophobic moieties, making these associating groups more accessible for intra- and interpolymer hydrophobic interactions [31, 36]. These observations

These experimental findings indicate that the viscoelastic functionality of the SAP formulation is improved as the ionic strength in the aqueous solution increases. This performance makes the SAP system suitable for EOR applications involving brines containing high salinity

The structural strength of a material is usually determined through the reestablishment of the storage modulus, *G*', of the disrupted network after the shear deformation driven by high shear rates has been lifted [5, 45]. In this study, the structural strength of the SAP system was established through thixotropic behavior analysis by applying an oscillatory rheological test consisting of three steps, each one at constant dynamic mechanical conditions, as recommended in Ref. [45]. The first or *reference* step is carried out at low-shear conditions

complexation through hydrophobic interactions and hydrogen bonding [57].

**Figure 7.** Curves of tan*δ*, *G*', *G*", and |*η*\*| versus *ω* and brine concentration.

**at 0.2 wt% of HPAM.**

104 Polymer Rheology

agree with previous work [51].

and hardness concentrations.

**4. Dynamic mechanical analysis (DMA)**
