4. Effect of shear and ionic strength on the SAP-AP systems

Previous research has demonstrated that the mechanical degradation of polymers is path independent; thus, the effect of shear on the mechanical stability of polymers can be evaluated using any kind of degrading geometry [26]. In this work, the mechanical stability of the SAP-AP systems was determined through thixotropic behavior analysis using oscillatory rheology as recommended in Ref. [22]. Table 3 summarizes the dynamic-mechanical conditions employed during the thixotropic analysis. The percentage of regeneration method was used to analyze the thixotropic behavior of the samples. In this method, the percentage of regeneration that takes place at the end of the third interval is read off and the percentage is calculated in relation to the reference value G<sup>0</sup> -at-rest at the end of the first interval which was taken as the 100% value [22]. These analyses were conducted for the baseline polymers and for the SAP-AP systems prepared at different salinity concentrations: 1.4, 2.1, 4.2, 6.3, and 8.4 wt% (see Table 1). The objective was to determine the simultaneous effect of shear and ionic strength on the structural and shear stability of the different systems.

Figures 8–10 summarize the time-dependent function of G<sup>0</sup> and G<sup>00</sup> for Step 1 and Step 3 for polymers AP1 and SAP-AP1, AP2 and SAP-AP2, and AP3 and SAP-AP3, respectively. Likewise, Tables 4 and 5 summarize the structural strength of the baseline polymers and the corresponding SAP-AP systems in terms of the G<sup>0</sup> - or G00-values taken at the end of Step 1, and the G<sup>0</sup> - or G00-values taken at the end of Step 3, and the percentage (%) of structural regeneration of the respective samples.


LVE refers to the linear viscoelastic range.

Table 3. Preset of the dynamic-mechanical conditions for each of the intervals used during the thixotropic behavior analysis.

Figure 8 demonstrates that the optimum SAP-AP1 shows higher structural strength (> G<sup>0</sup>

with a regeneration of G<sup>00</sup> > 100%.

and > G00-values) relative to polymer AP1. The second important result is that there is no complete regeneration of the initial structural strength. The first two rows of Table 5 show that the percentage of structural regeneration for polymer AP1 in terms of G<sup>0</sup> > 95% for all brine salinities (1.4, 4.2, 6.3 wt%) except for the 8.4 wt% brine with a structural regeneration of 91%. In terms of G<sup>00</sup> (see Table 5), both systems: AP1 and SAP-AP1 show a structural regeneration > 96%, excluding the baseline polymer AP1 in 1.4% brine that shows a gain in structural strength

The minor loss of structural strength observed for both systems might be related to macromolecular shear degradation under the high-shear forces applied during Step 2 causing the

Figure 9 presents the time-dependent behavior of polymer AP2 and the SAP-AP2 system in terms of G<sup>0</sup> and G<sup>00</sup> for the low-shear interval (Step 1) and for the regeneration interval (Step 3).

breaking of carbon/carbon bonds of some of the polymer chains [5].

Figure 10. log10 G<sup>0</sup> and log10 G<sup>00</sup> for steps 1 and 3 vs. time for polymer AP3 and SAP-AP3.

Figure 9. log10 G<sup>0</sup> and log10 G<sup>00</sup> for steps 1 and 3 vs. time for polymer AP2 and SAP-AP2.

Experimental trends observed from Figure 9 and Tables 4 and 5 are as follows:


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Figure 8. log10 G<sup>0</sup> and log10 G<sup>00</sup> for steps 1 and 3 vs. time for polymer AP1 and SAP-AP1.


Figure 9. log10 G<sup>0</sup> and log10 G<sup>00</sup> for steps 1 and 3 vs. time for polymer AP2 and SAP-AP2.

4. Effect of shear and ionic strength on the SAP-AP systems

reference value G<sup>0</sup>

212 Cyclodextrin - A Versatile Ingredient

the G<sup>0</sup>

stability of the different systems.

of the respective samples.

LVE refers to the linear viscoelastic range.

corresponding SAP-AP systems in terms of the G<sup>0</sup>

Previous research has demonstrated that the mechanical degradation of polymers is path independent; thus, the effect of shear on the mechanical stability of polymers can be evaluated using any kind of degrading geometry [26]. In this work, the mechanical stability of the SAP-AP systems was determined through thixotropic behavior analysis using oscillatory rheology as recommended in Ref. [22]. Table 3 summarizes the dynamic-mechanical conditions employed during the thixotropic analysis. The percentage of regeneration method was used to analyze the thixotropic behavior of the samples. In this method, the percentage of regeneration that takes place at the end of the third interval is read off and the percentage is calculated in relation to the

These analyses were conducted for the baseline polymers and for the SAP-AP systems prepared at different salinity concentrations: 1.4, 2.1, 4.2, 6.3, and 8.4 wt% (see Table 1). The objective was to determine the simultaneous effect of shear and ionic strength on the structural and shear

Figures 8–10 summarize the time-dependent function of G<sup>0</sup> and G<sup>00</sup> for Step 1 and Step 3 for polymers AP1 and SAP-AP1, AP2 and SAP-AP2, and AP3 and SAP-AP3, respectively. Likewise, Tables 4 and 5 summarize the structural strength of the baseline polymers and the

Steps Oscillation test ω (rad/s) Strain (%) Number of samples Test time (s)

Table 3. Preset of the dynamic-mechanical conditions for each of the intervals used during the thixotropic behavior analysis.

1 Single frequency/strain controlled 6.283 20 within the LVE 200 ≈960 2 Single frequency/strain controlled 6.283 100 outside the LVE 100 ≈480 3 Single frequency/strain controlled 6.283 20 within the LVE 200 ≈960

Figure 8. log10 G<sup>0</sup> and log10 G<sup>00</sup> for steps 1 and 3 vs. time for polymer AP1 and SAP-AP1.




Figure 10. log10 G<sup>0</sup> and log10 G<sup>00</sup> for steps 1 and 3 vs. time for polymer AP3 and SAP-AP3.

Figure 8 demonstrates that the optimum SAP-AP1 shows higher structural strength (> G<sup>0</sup> -values and > G00-values) relative to polymer AP1. The second important result is that there is no complete regeneration of the initial structural strength. The first two rows of Table 5 show that the percentage of structural regeneration for polymer AP1 in terms of G<sup>0</sup> > 95% for all brine salinities (1.4, 4.2, 6.3 wt%) except for the 8.4 wt% brine with a structural regeneration of 91%. In terms of G<sup>00</sup> (see Table 5), both systems: AP1 and SAP-AP1 show a structural regeneration > 96%, excluding the baseline polymer AP1 in 1.4% brine that shows a gain in structural strength with a regeneration of G<sup>00</sup> > 100%.

The minor loss of structural strength observed for both systems might be related to macromolecular shear degradation under the high-shear forces applied during Step 2 causing the breaking of carbon/carbon bonds of some of the polymer chains [5].

Figure 9 presents the time-dependent behavior of polymer AP2 and the SAP-AP2 system in terms of G<sup>0</sup> and G<sup>00</sup> for the low-shear interval (Step 1) and for the regeneration interval (Step 3). Experimental trends observed from Figure 9 and Tables 4 and 5 are as follows:


The objective of bold numbers in Table 4 is to emphasize the percentage of regeneration in each system.

Table 4. G<sup>0</sup> -values and percentage of regeneration.

• The SAP-AP2 system formulated at different ionic strengths displays significantly higher structural strength, G<sup>0</sup> and G00, than the baseline AP2 polymer.

The mechanical stability shown by the SAP-AP2 system might result from the increased rigidity of the polymeric network due to self-aggregation with the bulky structure of the β-CD and the long-chain alkyl branched anionic surfactant [3, 5]. Supramolecular aggregates based on physical bonding are considerably more rigid compared to the superstructures of the thread-like macro-

1.4 2.1 4.2 6.3 8.4

Step 3 1.371 >100 1.10 96.92 1.25 97.66 1.04 98.89 1.02 99.03

Step 3 1.46 99.25 1.21 98.17 1.26 99.2 1.12 98.29 1.17 99.07

Step 3 1.447 98.2 1.28 98.54 1.27 100 — — 1.29 96.26

Step 3 4.64 >100 2.91 >100 2.99 >100 — — 1.72 87.26

Step 3 — — 1.155 98.55 1.21 98.27 1.07 100 1.27 >100

Step 3 — — 3.16 >100 1.381 >100 2.28 >100 3.67 >100

Step 1 1.311 1.14 1.28 1.05 1.03

Step 1 1.47 1.23 1.27 1.14 1.18

Step 1 1.476 1.39 1.27 — 1.34

Step 1 3.96 2.72 2.45 — 1.97

Step 1 — 1.172 1.22 1.07 1.26

Step 1 — 2.39 1.209 1.97 3.30

G<sup>00</sup> (Pa) Reg (%) G<sup>00</sup> (Pa) Reg (%) G<sup>00</sup> (Pa) Reg (%) G<sup>00</sup> (Pa) Reg (%) G<sup>00</sup> (Pa) Reg (%)

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Figure 10 indicates that the SAP-AP3 system displays higher structural strength in terms of G<sup>0</sup> and G<sup>00</sup> relative to the baseline polymer. In low-salinity brines (≤ 4.2 wt%), the SAP-AP3 systems

The gain in structural strength displayed by the SAP-AP2 and the SAP-AP3 systems in salinity concentrations ≤ 4.2 wt% demonstrates the self-healing character of these self-assemblies. As stated by Yang, "supramolecular self-healing materials [rely] on the use of noncovalent bonds to generate reversibility and dynamic networks, which are able to heal the damaged sites" [10]. According to Mezger, (this self-healing or self-repairing effect occurs because) "the structural development aims at achieving a balance or equilibrium of the active forces or energies …

salinities ≥ 4.2 wt%, there is no complete structural regeneration as shown by the G<sup>0</sup>



molecules of synthetic polymers [22].

Table 5. G00-values and percentage of regeneration.

Brine concentration (wt%)

Polymer AP1

SAP-AP1

Polymer AP2

SAP-AP2

Polymer AP3

SAP-AP3

show a gain in the structural strength (see G<sup>0</sup>


The gain in structural strength is significant for the SAP-AP2 prepared in low brine salinity with a 15% gain of the G<sup>0</sup> -value and 17% gain of the G00-value (see Figure 9). Although at brine salinity concentrations up to 4.2 wt%, the gain in structural strength is ≥ 100%, it decreases as salinity increases, which demonstrates the negative effect of increased ionic strength on the shear stability of the SAP-AP2 system.


Table 5. G00-values and percentage of regeneration.

• The SAP-AP2 system formulated at different ionic strengths displays significantly higher

1.4 2.1 4.2 6.3 8.4

Step 3 2.34 98.84 1.85 96.51 1.80 98.82 1.57 98.59 1.36 91.03

Step 3 3.01 98.49 2.42 96.75 2.25 98.34 1.99 97.72 2.17 99.7

Step 3 2.41 98.16 1.72 92.47 1.82 100 — — 1.04 97.70

Step 3 11.82 >100 6.20 >100 3.61 100 — — 3.79 77.01

Step 3 — — 2.41 100 2.79 98.27 2.75 98.82 4.33 98.68

Step 3 — — 13.86 >100 6.81 >100 5.45 97.23 12.68 85.39

Step 1 2.47 1.92 1.82 1.59 1.49

Step 1 3.05 2.50 2.28 2.04 2.18

Step 1 2.45 1.86 1.82 — 1.07

Step 1 10.26 6.05 3.61 — 4.92

Step 1 — 2.41 2.84 2.79 4.38

Step 1 — 13.22 6.17 5.60 14.85

The objective of bold numbers in Table 4 is to emphasize the percentage of regeneration in each system.

G<sup>0</sup> (Pa) Reg (%) G<sup>0</sup> (Pa) Reg (%) G<sup>0</sup> (Pa) Reg (%) G<sup>0</sup> (Pa) Reg (%) G<sup>0</sup> (Pa) Reg (%)

• As the ionic strength increases, the structural strength of the AP2 polymer and the SAP-

• The baseline polymer AP2 shows structural regeneration G<sup>0</sup> and G<sup>00</sup> > 92% but < 100% in the range of salinity concentration studied. While the SAP-AP2 systems prepared in 1.4, 2.1, and 4.2 wt% brines display gain in structural strength with regenerations ≥ 100%. In 8.4 wt% brine, the structural regeneration SAP-AP2 system falls to 77% and to 87.26% in

The gain in structural strength is significant for the SAP-AP2 prepared in low brine salinity

salinity concentrations up to 4.2 wt%, the gain in structural strength is ≥ 100%, it decreases as salinity increases, which demonstrates the negative effect of increased ionic strength on the


structural strength, G<sup>0</sup> and G00, than the baseline AP2 polymer.

AP2 system decreases.

Brine concentration (wt%)

214 Cyclodextrin - A Versatile Ingredient

Polymer AP1

SAP-AP1

Polymer AP2

SAP-AP2

Polymer AP3

SAP-AP3

Table 4. G<sup>0</sup>

with a 15% gain of the G<sup>0</sup>

terms of G<sup>0</sup> and G00, respectively.


shear stability of the SAP-AP2 system.

The mechanical stability shown by the SAP-AP2 system might result from the increased rigidity of the polymeric network due to self-aggregation with the bulky structure of the β-CD and the long-chain alkyl branched anionic surfactant [3, 5]. Supramolecular aggregates based on physical bonding are considerably more rigid compared to the superstructures of the thread-like macromolecules of synthetic polymers [22].

Figure 10 indicates that the SAP-AP3 system displays higher structural strength in terms of G<sup>0</sup> and G<sup>00</sup> relative to the baseline polymer. In low-salinity brines (≤ 4.2 wt%), the SAP-AP3 systems show a gain in the structural strength (see G<sup>0</sup> - and G00-curves in Figure 10). However, for brine salinities ≥ 4.2 wt%, there is no complete structural regeneration as shown by the G<sup>0</sup> -curve.

The gain in structural strength displayed by the SAP-AP2 and the SAP-AP3 systems in salinity concentrations ≤ 4.2 wt% demonstrates the self-healing character of these self-assemblies. As stated by Yang, "supramolecular self-healing materials [rely] on the use of noncovalent bonds to generate reversibility and dynamic networks, which are able to heal the damaged sites" [10]. According to Mezger, (this self-healing or self-repairing effect occurs because) "the structural development aims at achieving a balance or equilibrium of the active forces or energies … based on the very fast connection, disconnection, and re-connection" of the physical bonds such as the decomplexation and complexation of host-guest interactions [7, 22], that results in improved structural strength. "Therefore, when tension is imparted on these networks, the force is distributed homogeneously across the whole network [due to the dynamic disassembling and re-assembling of the physical interactions]" protecting the macromolecules in the network from permanent shear degradation [7].
