Dynamic Light Scattering (DLS)

The aging behavior in soft matter systems is usually probed by scattering experiments through dynamic-structure factor and correlation-curve analysis. The correlation function (Fig. 1) showed the emergence of non-ergodic behavior of Laponite® RD (3% w/v) in a water–methanol binary solvent as a function of methanol content and aging time.

Fig. 1

Intensity autocorrelation curve of 3% w/v Laponite® RD in a water–methanol binary solvent for various W:M ratios: a 1:0, b 5:1, c 2:1, and d 1:1

The issue of non-ergodicity in DLS experiments is understood by scanning the entire phase space of the sample cell via rotation (Coviello et al., Reference Coviello, Burchard, Geissler and Maier1997). Nevertheless, the heterodyne approach (Coviello et al., Reference Coviello, Burchard, Geissler and Maier1997) can also be implemented to understand the non-ergodic system using Eq. 2. The value of X = 1 in Eq. 2 transforms it into Eq. 1 where the Siegert relation holds; whereas, for the non-ergodic phase, the value of X < 1 and the term 2X(1 − X) makes a finite contribution to g ₂(τ). The pre-factor of the linear term for g ₁(τ) in Eq. 2 was observed to be much larger than the quadratic second term in most of the cases and thus $g_1\left(\tau \right)$ can be written as Eq. 3:

(3) $g_1\left(\tau \right)\approx [g_2\left(\tau \right)-1]/\left[2{\beta }^{{}^{\prime }}\left(X(1-X)\right)\right]$

The intercept of the plot of $\left(g_2,\left(\tau \right),-,1\right)$ vs. delay time, τ, at τ → 0 gives β′[2X − X ²] from which the value of X was calculated.

The calculated value of the ergodic parameter, X, was plotted (Fig. 2) and the value of X for Laponite® RD in the binary solvent decreased with aging as well as with the increase in methanol content. The plot of X (Fig. 2) suggested that the sample with a W:M = 1:0 ratio remained ergodic until 165 min whereas samples with a larger methanol content became non-ergodic at a much earlier time.

Fig. 2

Variation of the ergodic parameter (X) as a function of time for 3% w/v Laponite® RD in various W:M ratios: a 1:0, b 5:1, c 2:1, and d 1:1

Viscosity Measurement

Viscosity studies were used to determine the evolution of the non-ergodic behavior of Laponite® RD in the binary solvent. The viscosity data (Fig. 3a) showed that initially (t ≈ 0 min) the relative viscosity was very small for Laponite® RD in W:M = 1:0; with aging, however, the viscosity increased. The increase in viscosity led to the formation of a gel with a house-of-cards arrangement. As discussed in various previous studies (Cummins, Reference Cummins2007; Martin et al., Reference Martin, Pignon, Piau, Magnin, Lindner and Cabane2002; Mongondry et al., Reference Mongondry, Tassin and Nicolai2005; Ruzicka et al., Reference Ruzicka, Zulian and Ruocco2004; Shahin & Joshi, Reference Shahin and Joshi2010), the house-of-cards arrangement was formed due to the interaction between the negatively charged surfaces and positively charged edges of Laponite® RD in a high ionic-strength solution. The assertion of the house-of-cards arrangement, however, was derived from the work of Shahin and Joshi (Reference Shahin and Joshi2010) who suggested that the aging that occurs over a long period of time in a low salt-concentration system is qualitatively similar to that occurring in high salt-concentration systems over a short period of time.

Fig. 3

Time-dependent viscosity of 3% w/v Laponite® RD in a water–methanol binary solvent for various W:M ratios: a 1:0, b 5:1, c 2:1, and d 1:1. The arrow indicates the time, t*, where viscosity fluctuation was observed

The plot of viscosity vs time (Fig. 3) suggested that the relative viscosity (at t ≈ 0 min) for 3% w/v Laponite® RD in the binary solvent increased with the increase in methanol content. This increase was attributed to the aggregation of Laponite® RD particles owing to the limited availability of water for hydration. Note that the viscosity trend of Laponite® RD for W:M ratios of 1:0 and 5:1 (Fig. 3a,b) was evolving whereas the saturated viscosity profile was observed for W:M ratios of 2:1 and 1:1 (Fig. 3c,d). The data indicated that the large viscosity value and the plateau region may have evolved due to the aggregation of particles because of jamming and limited access to water for hydration.

Nevertheless, in the viscosity profile (Fig. 3b, c, d), an anomaly was noted at time t* at which a reduction in viscosity was observed. The anomalous fluctuation in viscosity at t* and a plateau region for large alcohol contents in binary solvents was not an artefact; in fact, the anomalous fluctuation and plateau region could invariably be seen in binary mixtures when ethanol was used instead of methanol (Fig. 4). An anomalous viscosity fluctuation by Laponite XLG in a water-alcohol binary mixture was also observed by Kimura and Haraguchi (Reference Kimura and Haraguchi2017).

Fig. 4

Time-dependent viscosity of 3% w/v Laponite® RD in a water–ethanol binary solvent with various water:ethanol ratios: a 5:1, b 2:1, and c 1:1

Small-angle X-ray Scattering (SAXS)

Viscosity measurements revealed the occurrence of aggregation in Laponite® RD particles with the passage of time and increasing methanol concentration in the binary solvent. Nothing definitive could be stated about the viscosity fluctuations, i.e. the reduction in the viscosity measurements. This suggests that the reduction was due to repulsion between negatively charged Laponite® RD surfaces within the aggregates. This hypothesis of aggregation and repulsion behavior within aggregates was supported by results from the SAXS study. The plot (Fig. 5) depicted the scattering intensity (I) profile of Laponite® RD in a water–methanol binary solvent as a function of scattering vector (q) for various W:M ratios immediately after sample preparation, i.e. t = 0. The SAXS data (Fig. 5) revealed that the scattering profile could be split into two regions, referred to here as I and II. The data points in region II for all samples could be fitted with the power law I ≈ q ^–α where the value of α = 2.07 ± 0.04. The value of 2 for α in the high-q region (region II) suggested that the Laponite® RD particle is disc-shaped (Cui et al., Reference Cui, Pizzey and van Duijneveldt2013). Data from the low-q region (region I) revealed that scattering intensity from Laponite® RD increased with the increase in methanol concentration in the binary solvent (see inset in Fig. 5). The increase in scattering intensity suggested enhanced aggregation of Laponite® RD in samples with increasing methanol content (Chatani et al., Reference Chatani, Inoue, Imamura, Sugiyama, Kato, Yamamoto, Nishida and Kanaya2015; Kikhney & Svergun, Reference Kikhney and Svergun2015; Lecomte et al., Reference Lecomte, Dauger and Lenormand2000; Londoño et al., Reference Londoño, Tancredi, Rivas, Muraca, Socolovsky, Knobel and Sharma2018).

Fig. 5

SAXS scattering intensity (I) profile of 3% w/v Laponite® RD in a water–methanol binary solvent as a function of scattering vector (q) for various W:M ratios at the initial time (t = 0). Inset is a close-up image of region I

The data (Fig. 5) showed a variation (immediately after sample preparation, i.e. t = 0) of scattering intensity as a function of the scattering vector; the data, however, revealed nothing about the anomalous fluctuation that occurred with the passage of time. The aging behavior was observed from the time-dependent scattering intensity of the SAXS profile of each individual sample (Fig. 6); apparently the scattering profile was the same with aging for larger q values; at smaller q values, however, some variations were noticed.

Fig. 6

SAXS intensity (I) profile as a function of the scattering vector (q) and aging time for 3% w/v Laponite® RD in a water–methanol binary mixture at various W:M ratios

The explicit variation of the scattering profile with aging time at low q (0.0627 nm^–1) revealed the interactions between Laponite® RD particles in the water–methanol binary solvents. The variation of scattering intensity for each sample at q = 0.0627 nm^–1 as a function of time (Fig. 7b, c, d) revealed that the scattering intensity decreased with aging in all the samples with methanol, which suggests a repulsive interaction (Franke et al., Reference Franke, Kikhney and Svergun2012; Kikhney & Svergun, Reference Kikhney and Svergun2015) between Laponite® RD particles. The repulsive force within aggregates might be the reason for the observed anomalous fluctuation (reduction in viscosity) as mentioned in the viscosity section (Fig. 3).

Fig. 7

SAXS intensity (I) profile of Laponite® RD as a function of time at the lowest scattering vector (q = 0.0627 nm^–1) for various W:M ratios

The sample without methanol (W:M = 1:0) showed an increase in scattering intensity with time (Fig. 7a), which suggested an attractive interaction (Franke et al., Reference Franke, Kikhney and Svergun2012; Kikhney & Svergun, Reference Kikhney and Svergun2015) between the negatively charged basal surface and the positively charged edge of the Laponite® RD, thus forming the house-of-cards arrangement discussed above.

Note that the rise in viscosity of Laponite® RD in water–methanol binary solvent as observed in this work was not in accord with the results obtained by Kimura and Haraguchi (Reference Kimura and Haraguchi2017); those authors did not note an anomalous increase in the viscosity of Laponite XLG in water–methanol binary solvents. Although both Laponite® RD and Laponite XLG are structurally similar and have gel-forming properties, the difference in the results may be attributed to the sample preparation. Kimura and Haraguchi (Reference Kimura and Haraguchi2017) prepared samples by adding alcohol in a dropwise manner whereas in the current study methanol was added immediately during the preparation of samples. The sudden and immediate addition of methanol may have contributed to the sudden flocculation and aggregation of Laponite® RD, which was responsible for the anomalous increase in the viscosity. The occurrence of dissimilar anomalous behavior among different grades of Laponite in water-alcohol binary solvents needs meticulous investigation, considering various parameters, such as purity, heavy-metal content, extent of exfoliation, and hydration behavior, as mentioned by Kimura and Haraguchi (Reference Kimura and Haraguchi2017).

The observed time-dependent fluctuation in the viscosity of Laponite® RD in a water-alcohol binary solvent was, however, in accord with the results obtained by Kimura and Haraguchi (Reference Kimura and Haraguchi2017). The SAXS data revealed that the repulsive forces due to negatively charged Laponite® RD platelets within aggregates were the reason for such anomalous viscosity fluctuations.

Rheology

The viscoelastic properties of the samples were characterized using rheology. The samples were allowed to mature for 30 h before performing the rheological experiments. The storage modulus (Gˈ(ω)) and loss modulus (Gˈˈ(ω)) of the samples were plotted (Fig. 8) to characterize the viscoelastic properties. The explicit frequency dependence of the storage modulus was determined by fitting Gˈ(ω) to the power-law function given by Eq. 4 (Barnes, Reference Barnes2000).

(4) $G^{{}^{\prime }}\left(\omega \right)\sim {\omega }^n$

where ω is the angular frequency.

Fig. 8

Variation of storage modulus (Gˈ(ω)) and loss modulus (Gˈˈ(ω)) as a function of frequency for 3% w/v Laponite® RD in a water–methanol binary solvent with various W:M ratios: a 1:0, b 5:1, c 2:1, and d 1:1. The arrow indicates the frequency at which the slope of the storage modulus changed

The data (Fig. 8) showed the frequency-dependent storage and loss modulus of 3% w/v Laponite® RD in a binary solvent with W:M ratios of 1:0, 5:1, 2:1, and 1:1. The data (Fig. 8) revealed that the interaction between Laponite® RD particles increased with high methanol concentrations, which gave rise to a large storage modulus. Furthermore, the storage modulus exhibited two regions (indicated by the arrow) based on the slope of the graph except for the case when W:M = 1:1. The two regions were fitted to Eq. 4 which gave two power law exponents n ₁ and n ₂.

The linear viscoelastic model (Barnes, Reference Barnes2000) predicts that the power-law frequency dependence behavior given by Eq. 4 with 0 < n < 1 will be followed. The number of crosslinks (excess crosslinks, n < 1/2 and lack of crosslinks, n > 1/2) defines stoichiometric balanced and unbalanced networks strictly for chemically crosslinked gels. The data (Fig. 8) were, however, fitted to Eq. 4 and the value of n was determined in order to understand the strength of the samples.

The power law exponents (n ₁ and n ₂) were obtained and plotted (Fig. 9) by fitting the storage modulus data (Fig. 8) using Eq. 4. From the large storage modulus (Fig. 8) and almost zero frequency dependence (Fig. 9) for W:M = 1:1, the present authors concluded that a high concentration of methanol provided greater physical interaction between Laponite® RD particles.

Fig. 9

Variation in the power law exponents (n ₁ and n ₂) for 3% w/v Laponite® RD in a water–methanol binary solvent with various W:M ratios: a 1:0, b 5:1, c 2:1, and d 1:1

Furthermore, understanding whether Laponite® RD in the binary solvent has gel or melt-like behavior is important. In order to understand the arrested phase, a plot of the loss tangent (tan δ = Gˈˈ(ω)/Gˈ(ω)) as a function of frequency (Fig. 10) for various W:M ratios yielded a straight-line equation (tan δ = 0.07 – 0.001 ω) of almost zero slope, indicating that Laponite® RD aggregates in binary solvent behaved almost like a gel in all the samples.

Fig. 10

Variation of the loss tangent (tan δ) as a function of frequency for Laponite® RD in a water–methanol binary solvent with W:M ratios of 1:0, 5:1, 2:1, and 1:1. The straight line in the graph shows a single fitting to all the data points

The low-frequency storage modulus, G ₀, defined as G ₀ = $\underset{\omega \to 0}{\lim }{G}^{{}^{\prime }}\left(\omega \right)$ was determined explicitly using Eq. 5 (Arfin et al., Reference Arfin, Aswal and Bohidar2014; Barnes, Reference Barnes2000). The equation gave the measure of elastic free energy stored per unit volume of a characteristic viscoelastic network of size ζ (Barnes, Reference Barnes2000).

(5) ${\zeta }^3\approx k_{B}T/G_0$

The value of G ₀ for each sample in this work was determined at 0.1 rad/s. The values for G ₀ and viscoelastic length (ζ) obtained from Eq. 5 were plotted (Fig. 11) and indicated that the rigidity of the Laponite® RD network increased with the increase in methanol concentration in the binary solvent.

Fig. 11

Variation of the storage modulus (G ₀ (ω)) at 0.1 rad/s and viscoelastic length (ζ) for 3% w/v Laponite® RD in a water–methanol binary solvent with various W:M ratios: a 1:0, b 5:1, c 2:1, and d 1:1