Can More Nanoparticles Induce Larger Viscosities of Nanoparticle-Enhanced Wormlike Micellar System (NEWMS)?

There have been many reports about the thickening ability of nanoparticles on the wormlike micelles in the recent years. Through the addition of nanoparticles, the viscosity of wormlike micelles can be increased. There still exists a doubt: can viscosity be increased further by adding more nanoparticles? To answer this issue, in this work, the effects of silica nanoparticles and temperature on the nanoparticles-enhanced wormlike micellar system (NEWMS) were studied. The typical wormlike micelles (wormlike micelles) are prepared by 50 mM cetyltrimethyl ammonium bromide (CTAB) and 60 mM sodium salicylate (NaSal). The rheological results show the increase of viscoelasticity in NEWMS by adding nanoparticles, with the increase of zero-shear viscosity and relaxation time. However, with the further increase of nanoparticles, an interesting phenomenon appears. The zero-shear viscosity and relaxation time reach the maximum and begin to decrease. The results show a slight increasing trend for the contour length of wormlike micelles by adding nanoparticles, while no obvious effect on the entanglement and mesh size. In addition, with the increase of temperature, remarkable reduction of contour length and relaxation time can be observed from the calculation. NEWMS constantly retain better viscoelasticity compared with conventional wormlike micelles without silica nanoparticles. According to the Arrhenius equation, the activation energy Ea shows the same increase trend of NEWMS. Finally, a mechanism is proposed to explain this interesting phenomenon.


Introduction
Since 1980's nanocrystals have been firstly prepared by manual work, research studies and applications of nanostructured materials have received widespread attention [1,2]. Nanoparticles often refer to very small solid particles, which range from 1 to 100 nm [3]. Due to the small size, nanoparticles show special properties, such as large specific surface area and adsorption performance [4][5][6][7][8].
The study of materials modification by adding nanoparticles has been developed in the recent years, where enhancing the strength of wormlike micelles by adding nanoparticles is one of the focuses.
The rheological properties of samples were measured by using Haake Mars 60 rheometer (Thermo Fisher Scientific, Karlsruhe, Germany) with the cone plate system (diameter 35 mm; angle 1 • ). The range of shear rate is kept from 0.01 to 300 s −1 during the steady shear measurement. In oscillatory measurements, the frequency was kept at 6.28 rad·s −1 (1 Hz) with the variation of the stress (σ). When the linear viscoelastic region was confirmed, frequency sweep measurements were performed as a function of frequency at a constant stress. The temperature of measurements was regarded as the control variable in this work. These wormlike micelles samples were tested at different temperatures, such as 20, 30, and 40 • C.

Rheological Properties of NEWMS
In order to investigate the influence of added nanoparticles on NEWMS at elevated temperatures, the steady shear measurements are conducted firstly. Figure 1 shows the different shear-rate viscosities of NEWMS with different silica concentrations at 20, 30, and 40 • C. It can be observed that all viscosities keep constant at low shear rate, and this plateau value of shear viscosity can be regarded as the zero-shear viscosity (η 0 ), which is the significant assessment factor of rheological property. From Figure 1, it is clear that the addition of silica nanoparticles can promote the viscosity of wormlike micelles. After mixing for 1 h, NEWMS were prepared. In addition, wormlike micelle without silica nanoparticles was regarded as a contrast sample.

Rheological Measurements
The rheological properties of samples were measured by using Haake Mars 60 rheometer (Thermo Fisher Scientific, Karlsruhe, Germany) with the cone plate system (diameter 35 mm; angle 1°). The range of shear rate is kept from 0.01 to 300 s −1 during the steady shear measurement. In oscillatory measurements, the frequency was kept at 6.28 rad·s −1 (1 Hz) with the variation of the stress (σ). When the linear viscoelastic region was confirmed, frequency sweep measurements were performed as a function of frequency at a constant stress. The temperature of measurements was regarded as the control variable in this work. These wormlike micelles samples were tested at different temperatures, such as 20, 30, and 40 °C.

Rheological Properties of NEWMS
In order to investigate the influence of added nanoparticles on NEWMS at elevated temperatures, the steady shear measurements are conducted firstly. Figure 1 shows the different shear-rate viscosities of NEWMS with different silica concentrations at 20, 30, and 40 °C. It can be observed that all viscosities keep constant at low shear rate, and this plateau value of shear viscosity can be regarded as the zero-shear viscosity (η0), which is the significant assessment factor of rheological property. From Figure 1, it is clear that the addition of silica nanoparticles can promote the viscosity of wormlike micelles. As can be seen from Figure 1, with the further increase of shear rate, viscosities become smaller and show remarkable shear thinning phenomenon, which is the representative symbol of wormlike micelles formation [12,[22][23][24]. The high shear rates lead to the alignment of aggregates in micelles, and make shear banding phenomenon eventually. At low shear rates, NEWMS with 0.1 wt % nanoparticles has the highest zero-shear viscosity (η0) through comparison. This phenomenon illustrates that the addition of silica nanoparticles can indeed improve the viscosity of NEWMS. However, with further increase of nanoparticles, the zero-shear viscosity begins to decrease. As can be seen from Figure 1, with the further increase of shear rate, viscosities become smaller and show remarkable shear thinning phenomenon, which is the representative symbol of wormlike micelles formation [12,[22][23][24]. The high shear rates lead to the alignment of aggregates in micelles, and make shear banding phenomenon eventually. At low shear rates, NEWMS with 0.1 wt % nanoparticles has the highest zero-shear viscosity (η 0 ) through comparison. This phenomenon illustrates that the addition of silica nanoparticles can indeed improve the viscosity of NEWMS. However, with further increase of nanoparticles, the zero-shear viscosity begins to decrease.
From Figure 2, it can be seen clearly that with the increase of temperature, steady shear viscosities become smaller dramatically, which can be interpreted as the acceleration of the dynamic process of breaking and recombination of micelles with temperature increasing [25]. Similarly, even at different temperatures, NEWMS still have larger viscosities than wormlike micelles without nanoparticles. The NEWMS with the addition of 0.1 wt % silica nanoparticles still retain the highest η 0 at different temperatures. From Figure 2, it can be seen clearly that with the increase of temperature, steady shear viscosities become smaller dramatically, which can be interpreted as the acceleration of the dynamic process of breaking and recombination of micelles with temperature increasing [25]. Similarly, even at different temperatures, NEWMS still have larger viscosities than wormlike micelles without nanoparticles. The NEWMS with the addition of 0.1 wt % silica nanoparticles still retain the highest η0 at different temperatures. To further study the effects of nanoparticle concentrations and elevated temperatures on micellar viscoelasticity, dynamic oscillatory measurements were conducted. As can be seen from Figure 3, the storage modulus G′ and loss modulus G″ vary with oscillation frequencies, and all NEWMS exhibit typical features of wormlike micelles at elevated temperatures. G′ and G″ increase with the increase of frequency. At low shear frequencies, G″ is larger than G′, showing that NEWMS have more viscous properties, while at high shear frequencies, G′ is larger than G″, showing to be more elastic. It can be observed that G′ reaches a constant value, which is the plateau modulus G0, and G″ can reach the minimum value, which is determined as G″min. To further study the effects of nanoparticle concentrations and elevated temperatures on micellar viscoelasticity, dynamic oscillatory measurements were conducted. As can be seen from Figure 3, the storage modulus G and loss modulus G" vary with oscillation frequencies, and all NEWMS exhibit typical features of wormlike micelles at elevated temperatures. G and G" increase with the increase of frequency. At low shear frequencies, G" is larger than G , showing that NEWMS have more viscous properties, while at high shear frequencies, G is larger than G", showing to be more elastic. It can be observed that G reaches a constant value, which is the plateau modulus G 0 , and G" can reach the minimum value, which is determined as G" min . From Figure 2, it can be seen clearly that with the increase of temperature, steady shear viscosities become smaller dramatically, which can be interpreted as the acceleration of the dynamic process of breaking and recombination of micelles with temperature increasing [25]. Similarly, even at different temperatures, NEWMS still have larger viscosities than wormlike micelles without nanoparticles. The NEWMS with the addition of 0.1 wt % silica nanoparticles still retain the highest η0 at different temperatures. To further study the effects of nanoparticle concentrations and elevated temperatures on micellar viscoelasticity, dynamic oscillatory measurements were conducted. As can be seen from Figure 3, the storage modulus G′ and loss modulus G″ vary with oscillation frequencies, and all NEWMS exhibit typical features of wormlike micelles at elevated temperatures. G′ and G″ increase with the increase of frequency. At low shear frequencies, G″ is larger than G′, showing that NEWMS have more viscous properties, while at high shear frequencies, G′ is larger than G″, showing to be more elastic. It can be observed that G′ reaches a constant value, which is the plateau modulus G0, and G″ can reach the minimum value, which is determined as G″min.  For typical wormlike micelles, a simple Maxwell model is generally used to investigate rheological properties [26,27]. As to the Maxwell fluid, G′ and G″ can be calculated according to Equations (1) and (2) [22]: In these equations, ω is the angular frequency and τR is the micelle relaxation time. The relaxation time τR is an significant factor for estimating rheological properties of wormlike micelles, which can be calculated according to Equation (3) proposed by Cates [22]: where ωco is the angular frequency of crossover point while storage modulus G′ is the same as the value of loss modulus G″.
The Cole-Cole plot is usually used to evaluate whether the data of G′ and G″ fit the Maxwell model well [12,28]. As for this work, Cole-Cole plots (a curve of G″ as a function of G′) are studied from the following Equation (4) [22]: Figure 4 shows the plots of G″ versus G′ of NEWMS. It is observed that Cole-Cole plots of these NEWMS fit well with the calculated results at low shear frequencies. While at high shear frequencies, practical data begin to deviate from theoretical semicircle in the Cole-Cole plot. This phenomenon can be explained by the appearance of Rouse modes or "breather modes" [14,26], which is usually observed in other wormlike micelles reported before [16,25]. For typical wormlike micelles, a simple Maxwell model is generally used to investigate rheological properties [26,27]. As to the Maxwell fluid, G and G" can be calculated according to Equations (1) and (2) [22]: In these equations, ω is the angular frequency and τ R is the micelle relaxation time. The relaxation time τ R is an significant factor for estimating rheological properties of wormlike micelles, which can be calculated according to Equation (3) proposed by Cates [22]: where ω co is the angular frequency of crossover point while storage modulus G is the same as the value of loss modulus G". The Cole-Cole plot is usually used to evaluate whether the data of G and G" fit the Maxwell model well [12,28]. As for this work, Cole-Cole plots (a curve of G" as a function of G ) are studied from the following Equation (4) [22]: Figure 4 shows the plots of G" versus G of NEWMS. It is observed that Cole-Cole plots of these NEWMS fit well with the calculated results at low shear frequencies. While at high shear frequencies, practical data begin to deviate from theoretical semicircle in the Cole-Cole plot. This phenomenon can be explained by the appearance of Rouse modes or "breather modes" [14,26], which is usually observed in other wormlike micelles reported before [16,25]. To further investigate the rheological properties of NEWMS with the addition of nanoparticles at different temperatures, some important parameters of NEWMS were calculated. As mentioned before, G0 is a practical plateau value of storage modulus. However, sometimes in actual experiments, it is hard to test this value or get it inaccurately. Researchers often use Equation (5) to calculate the plateau modulus G′∞ [22]: Here, the modulus G″max is the value of intersection point where G′ is equal to G″. In addition, some important parameters of NEWMS are dependent on their structures, such as the mesh size ξM, the entanglement length le, the persistence length lp, and the contour length L. These parameters can be calculated from Equations (6)-(8) [22,29]: Here, the modulus G″min is the minimum of the loss modulus G″ at high shear frequencies, as shown in Figure 3. The parameters L, le, and ξM decide the rheological properties of NEWMS. The value of kB is 1.38 × 10 −23 J/K as the Boltzman constant and the persistence length lp is set to 15-25 nm according to previous studies [25,29]. According to the above information, these parameters of NEWMS are listed in Table 1. To further investigate the rheological properties of NEWMS with the addition of nanoparticles at different temperatures, some important parameters of NEWMS were calculated. As mentioned before, G 0 is a practical plateau value of storage modulus. However, sometimes in actual experiments, it is hard to test this value or get it inaccurately. Researchers often use Equation (5) to calculate the plateau modulus G ∞ [22]: Here, the modulus G" max is the value of intersection point where G is equal to G". In addition, some important parameters of NEWMS are dependent on their structures, such as the mesh size ξ M , the entanglement length l e , the persistence length l p , and the contour length L. These parameters can be calculated from Equations (6)-(8) [22,29]: Here, the modulus G" min is the minimum of the loss modulus G" at high shear frequencies, as shown in Figure 3. The parameters L, l e , and ξ M decide the rheological properties of NEWMS. The value of k B is 1.38 × 10 −23 J/K as the Boltzman constant and the persistence length l p is set to 15-25 nm according to previous studies [25,29]. According to the above information, these parameters of NEWMS are listed in Table 1.

Effects of Silica Nanoparticle Concentration
According to results listed in Table 1, at the same temperature, the addition of nanoparticles indeed improves the viscosities of wormlike micelles. With the further increase of silica nanoparticle concentrations, the viscosities of NEWMS reach the maximum and begin to decrease. In addition, the changes of relaxation time τ R and contour length L can be used to investigate the effect of nanoparticle concentration on NEWMS. As shown in Table 1, the contour length L is closely linked with the zero-shear viscosity η 0 . With the addition of nanoparticles, L gets increase, indicating that nanoparticles induce micellar growth. However, with the further addition, L decreases, suggesting that redundant nanoparticles destroy the original structure of wormlike micelles and shorten the micellar length. As shown in Figure 5, it can be observed that the relaxation time τ R is increased with the addition of silica nanoparticles, which has the same changing trend as that of the zero-shear viscosity η 0 . The plateau modulus G ∞ , mesh size ξ M and entanglement length l e do not show variation distinctly, suggesting that the entangled network structure of NEWMS keeps integrated with the addition of nanoparticles. NEWMS with the addition of 0.1 wt % silica nanoparticles have the longest contour length L.

Effects of Silica Nanoparticle Concentration
According to results listed in Table 1, at the same temperature, the addition of nanoparticles indeed improves the viscosities of wormlike micelles. With the further increase of silica nanoparticle concentrations, the viscosities of NEWMS reach the maximum and begin to decrease. In addition, the changes of relaxation time τR and contour length L can be used to investigate the effect of nanoparticle concentration on NEWMS. As shown in Table 1, the contour length L is closely linked with the zero-shear viscosity η0. With the addition of nanoparticles, L gets increase, indicating that nanoparticles induce micellar growth. However, with the further addition, L decreases, suggesting that redundant nanoparticles destroy the original structure of wormlike micelles and shorten the micellar length. As shown in Figure 5, it can be observed that the relaxation time τR is increased with the addition of silica nanoparticles, which has the same changing trend as that of the zero-shear viscosity η0. The plateau modulus G′∞, mesh size ξM and entanglement length le do not show variation distinctly, suggesting that the entangled network structure of NEWMS keeps integrated with the addition of nanoparticles. NEWMS with the addition of 0.1 wt % silica nanoparticles have the longest contour length L.

Effects of Temperature
In order to further investigate the rheological properties of NEWMS, the temperature effect is studied in the range of 20-40 • C and the corresponding parameters of NEWMS are listed in Table 1. At different temperatures, NEWMS show remarkable viscoelastic properties. With the increase of temperature, the viscosities of NEWMS begin to decrease dramatically.
In addition, it can be observed that the contour length L decreases sharply with the increase of temperature, which results in the reduction of viscosities at higher temperature. This changing trend is consistent with the results of τ R , while the values of l e and ξ M keep nearly constant with the change of temperature, suggesting that the entangled network structure of NEWMS keeps integrated within the temperature range. The relationship between lnτ R and the reciprocal of the absolute temperature of NEWMS are plotted in Figure 6. The experimental data accords well to a linear relationship, indicating that the main relaxation time fits the Arrhenius relationships [22,29]: In order to further investigate the rheological properties of NEWMS, the temperature effect is studied in the range of 20-40 °C and the corresponding parameters of NEWMS are listed in Table 1. At different temperatures, NEWMS show remarkable viscoelastic properties. With the increase of temperature, the viscosities of NEWMS begin to decrease dramatically.
In addition, it can be observed that the contour length L decreases sharply with the increase of temperature, which results in the reduction of viscosities at higher temperature. This changing trend is consistent with the results of τR, while the values of le and ξM keep nearly constant with the change of temperature, suggesting that the entangled network structure of NEWMS keeps integrated within the temperature range. The relationship between lnτR and the reciprocal of the absolute temperature of NEWMS are plotted in Figure 6. The experimental data accords well to a linear relationship, indicating that the main relaxation time fits the Arrhenius relationships [22,29]: Here, Ea is the activation energy that describes the energy of individual micelles moving into an environment of surrounding micelles [23,30,31]. R is the gas constant and A is a constant. According to this Equation, Ea values of NEWMS can be calculated and are listed in Table 2. By adding silica nanoparticles, Ea values are larger than those of conventional wormlike micelles, indicating the influence of nanoparticles on micellar rheology.   Here, E a is the activation energy that describes the energy of individual micelles moving into an environment of surrounding micelles [23,30,31]. R is the gas constant and A is a constant. According to this Equation, E a values of NEWMS can be calculated and are listed in Table 2. By adding silica nanoparticles, E a values are larger than those of conventional wormlike micelles, indicating the influence of nanoparticles on micellar rheology.

Mechanism Discussion
According to previous work [3,15,20,21], there are many different thickening mechanisms of wormlike micelles with the addition of nanoparticles. Bandyopadhyay et al. proposed that the viscosity of wormlike micelles was increased because of additional electrostatic screening through contributions of silica nanoparticles to the bulk ion concentration [15]. Helgeson et al. found that the presence of nanoparticles does not significantly alter the electrostatic interactions between micelles [21]. They proposed that the addition of nanoparticles not only changes the surface electrical behavior of micellar molecules, but also forms a new kind of physical cross-link micellar structure, which can also be called a "double network".
In this work, the improvement of wormlike micelle rheological properties is obvious, and micellar solution with addition of 0.1 wt % silica shows the highest zero-shear viscosity. As for this phenomenon, the hydrophilic silica nanoparticles have negative charges with high surface area. Cationic CTAB surfactant molecules can adsorb on the surface of nanoparticles due to electrostatic attraction and hydrophilic interaction, forming a bilayer circular structure. With the addition of NaSal, the counter-ion can improve the aggregation of CTAB molecules. Meanwhile, bilayer circular structures would regroup and be involved in the formation of wormlike micelles, forming a new micelle-particle junction. This junction behaves as a bridging joint, improving micelles entangling with each other, causing the strength to increase and lead to the growth of micelles. With the increase in temperature, the contour length L of NEWMS begins to decrease sharply. At the same temperature, the contour length L and entanglement of NEWMS are larger than those of conventional wormlike micelles without nanoparticles. As can be seen in Figure 7, dilute silica concentrations can improve the aggregation of micelles and induce micellar growth. With the further increase of nanoparticle addition, excessive micelle-nanoparticle junctions make the network structure unconsolidated and weak. Redundant nanoparticles gather and aggregate due to surface energy. Such effects of aggregation improvement unexpectedly destroy the original network structure and form larger micellar molecular aggregates from overlapping and entanglement, which results in the decrease of viscosity.

Mechanism Discussion
According to previous work [3,15,20,21], there are many different thickening mechanisms of wormlike micelles with the addition of nanoparticles. Bandyopadhyay et al. proposed that the viscosity of wormlike micelles was increased because of additional electrostatic screening through contributions of silica nanoparticles to the bulk ion concentration [15]. Helgeson et al. found that the presence of nanoparticles does not significantly alter the electrostatic interactions between micelles [21]. They proposed that the addition of nanoparticles not only changes the surface electrical behavior of micellar molecules, but also forms a new kind of physical cross-link micellar structure, which can also be called a "double network".
In this work, the improvement of wormlike micelle rheological properties is obvious, and micellar solution with addition of 0.1 wt % silica shows the highest zero-shear viscosity. As for this phenomenon, the hydrophilic silica nanoparticles have negative charges with high surface area. Cationic CTAB surfactant molecules can adsorb on the surface of nanoparticles due to electrostatic attraction and hydrophilic interaction, forming a bilayer circular structure. With the addition of NaSal, the counter-ion can improve the aggregation of CTAB molecules. Meanwhile, bilayer circular structures would regroup and be involved in the formation of wormlike micelles, forming a new micelle-particle junction. This junction behaves as a bridging joint, improving micelles entangling with each other, causing the strength to increase and lead to the growth of micelles. With the increase in temperature, the contour length L of NEWMS begins to decrease sharply. At the same temperature, the contour length L and entanglement of NEWMS are larger than those of conventional wormlike micelles without nanoparticles. As can be seen in Figure 7, dilute silica concentrations can improve the aggregation of micelles and induce micellar growth. With the further increase of nanoparticle addition, excessive micelle-nanoparticle junctions make the network structure unconsolidated and weak. Redundant nanoparticles gather and aggregate due to surface energy. Such effects of aggregation improvement unexpectedly destroy the original network structure and form larger micellar molecular aggregates from overlapping and entanglement, which results in the decrease of viscosity.

Conclusions
In conclusion, a doubt about the effect of nanoparticles on the wormlike micelles has been clarified. With the addition of nanoparticles, viscosities of wormlike micelles cannot be continually increased. The viscosity of NEWMS can reach the maximum with the addition of nanoparticles. NEWMS have higher viscosity and better viscoelasticity than conventional wormlike micelles without

Conclusions
In conclusion, a doubt about the effect of nanoparticles on the wormlike micelles has been clarified. With the addition of nanoparticles, viscosities of wormlike micelles cannot be continually increased.
The viscosity of NEWMS can reach the maximum with the addition of nanoparticles. NEWMS have higher viscosity and better viscoelasticity than conventional wormlike micelles without silica nanoparticles. The added silica nanoparticles are attracted by hydrophilic headgroups of surfactant, forming a new micelle-particle junction. In addition, it can be observed that the viscosity of NEWMS is associated with values of τ R and L, indicating that nanoparticles lead to micellar growth and enhance bridging attractions between nanoparticles and micelles. However, with the further increase of nanoparticle concentration, the viscosity of NEWMS begins to decrease, which also reflects in values of τ R and L. Since the effects of aggregation improvement unexpectedly destroy the original network structure and form larger micellar molecular aggregates for overlapping and entanglement. Experimental results show that NEWMS with the addition of 0.1 wt % nanoparticles has the highest values of η 0 , τ R , and L. In addition, the temperature can cause a remarkable change for the contour length of NEWMS, while no effect on the entanglement length l e and mesh size ξ M . We expect this work can enrich the knowledge of NEWMS and widen their applications.