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Physicochemical Effects in Aging Aqueous Laponite Suspensions

We study aging behavior of aqueous suspension of Laponite as a function of concentration of Laponite, concentration of salt, time elapsed since preparation of suspension (idle time) and temperature by carrying extensive rheological and conductivity experiments. We observe that temporal evolution of elastic modulus, which describes structural buildup and aging, shifts to low times for experiments carried out for higher concentration of Laponite, higher concentration of salt, greater temperature and on higher idle time while preserving the curvature of evolution in the solid regime. Consequently appropriate shifting of evolution of elastic modulus in the solid regime leads to aging time idle time salt concentration Laponite concentration temperature superposition. Existence of such superposition suggests generic nature of microstructure buildup irrespective of mentioned variables in the explored range. Behavior of shift factors needed to obtain the superposition indicate that energy barrier associated with structural buildup decreases with increase in idle time and temperature; and decreases linearly with increase in concentration of Laponite and that of salt. The conductivity experiments show that ionic conductivity of the suspension increases with increasing Laponite concentration, salt concentration, temperature and very importantly the idle time. We also analyze the interparticle interactions using DLVO theory that suggests increase in idle time, temperature and salt concentration increases height of repulsive energy barrier while decreases width of the same when particles approach each other in a parallel fashion. Analysis of rheological and conductivity experiments suggest strong influence of attractive interactions on the low energy structures in aqueous suspension of Laponite.


Abstract
We study aging behavior of aqueous suspension of Laponite as a function of concentration of Laponite, concentration of salt, time elapsed since preparation of suspension (idle time) and temperature by carrying extensive rheological and conductivity experiments. We observe that temporal evolution of elastic modulus, which describes structural build-up and aging, shifts to low

I. Introduction:
Smectite clay minerals are important class of colloidal materials with immense academic importance and wide ranging applications. 1, 2 Smectite clays have oblate shape (layered like) with aspect ratio in the range 25 to 1000. 1 Particularly clays embedded in aqueous media are used in petroleum, healthcare, cosmetic, etc. industries, as rheology modifiers. 3 Therefore, it is not surprising that rheological and phase behaviors of clays have been very active areas of research over past several decades. 1,2,[4][5][6][7][8][9][10][11][12][13][14][15][16][17] In the recent literature synthetic clay mineral called Laponite has received significant attention due to its rich physical behavior and industrial applications. In addition, aqueous Laponite suspension shows time dependence evolution of its microstructure and physical properties that is reminiscent to physical aging in molecular, spin and colloidal glasses. 18,19 In this work we carry out extensive rheological and conductivity studies on aqueous suspension of Laponite and analyze various distinct characteristic features of aging observed in this system. Physical aging is a natural tendency of those materials that, owing to kinetic constraints, have fallen out of thermodynamic equilibrium. 20 In a physical aging process material explores its phase space and undergoes time dependent evolution in order to progressively attain lower energy microstructures. 21 There are many soft materials such as concentrated suspensions and emulsions, cosmetic and pharmaceutical pastes, colloidal gels, clay suspensions, foams, etc. that demonstrate physical aging and have enormous academic and industrial importance. 22 Physical aging is, in principle, a reversible phenomenon. Application of deformation field reverses the effects of aging by rejuvenating the material to higher energy levels. 23,24 Physical aging is analyzed by monitoring affected physical properties of the material that show time dependent change. In soft materials, the light scattering techniques are commonly used to probe structure and evolution of the mobility of the constituents of materials, [25][26][27][28][29][30] which also leads to the relaxation time of the same. Bulk rheological techniques are also used to monitor evolution of viscoelastic properties such as elastic and viscous modulus which get strongly affected by physical aging. [31][32][33] Recently microrheological techniques have also been used to analyze soft glassy materials. [34][35][36] For various soft materials that are thermodynamically out of equilibrium, including aqueous Laponite suspension, ample literature is available that employs scattering as well as rheological techniques to study the aging behavior. However, since effect of aging in soft glassy materials can be reversed by application of deformation field alone, rheological techniques are crucial for studying these phenomena. 18 Laponite particles are present in stacks with sodium ions residing in the interparticle gallery. When dispersed in aqueous medium sodium ions dissociate rendering the faces of Laponite disk a permanent negative charge. The edge of Laponite particle, which is composed of hydrous oxides of magnesium and silica, is reported to acquire a positive charge at low pH (below the pH of around 11). 41 Overall Laponite particles share edge -to -face attractive interactions while face -to -face repulsive interactions among each other.
Addition of salt such as NaCl enhances concentration of cations and anions in the suspension which shield the charges on the particle thereby reducing repulsion among the particles. Addition of Laponite in water, typically beyond 2 weight %, increases its viscosity and elastic modulus by several orders of magnitude over a short duration. 31 Microstructure of Laponite suspension and its time dependency that is responsible for such enormous increase in viscosity is, however, not completely understood even after more than fifteen years of research on this topic. [42][43][44] Issue of contention is whether microstructure of Laponite is an attractive gel (interconnected particles through positive edgenegative face contact) 16,30,42,[45][46][47] or a repulsive glass (particles in a selfsuspended state in a liquid media owing to repulsion among them). 15,[48][49][50] Some reports claim existence of both the states over a certain concentration regime. 51 Interestingly, several groups have observed Laponite disks to show anisotropic orientation in a suspended state. [6][7][8][9]13 Recently our group reported that anisotropy originates at air -suspension interface and percolates into the bulk as a function of time. 52 Aging behavior of Laponite suspension can be rheologically monitored by applying small amplitude oscillatory shear to shear melted suspension so as to record evolution of elastic ( G′ ) and viscous ( G′′ ) modulus as a function of time. 39,44,53,54 However, it has been observed that, unlike many soft materials that show complete reversal of aging when strong deformation field is applied, In the liquid regime G′ shows a stronger enhancement as a function of aging time compared to that of G′′ , and eventually crosses the same. The point of crossover ( G′ = G′′ ) is represented as a liquid -solid transition in the literature. 32 It should be noted that this point of transition does depend on applied frequency (or a timescale of probe), 39 as also observed for glass transition in molecular glasses. 59 In solid state ( G′ > G′′ ), G′ increases with a weaker dependence on aging time and G′′ decreases after showing a maxima. We also perform aging experiments at different frequencies.
Interestingly, G′ does not show any dependence on frequency beyond G′ > G′′ .
However G′′ shows weak decrease with frequency in the solid state.
As mentioned before, evolution of G′ and G′′ for experiments on Laponite suspension carried out at higher idle times and with greater concentration of salt shift to lower aging times. The representative behavior for a 3.5 weight % suspension is plotted in figure 2. It can be seen that the curvature of the evolution of G′ beyond the cross-over is self-similar, which leads to aging time   with time dependent elasticity and viscosity. For a Maxwell model, where ω is frequency of oscillations and τ is characteristic (or dominating) relaxation time. 59 The relaxation time, which is very small in the liquid regime increases as a function of time (typically relaxation time shows exponential dependence on aging time in the liquid regime). 19 where 0 ε is permittivity of free space, r ε is relative permittivity, B k is Boltzmann constant, i z is the ionic charge number for i th ion (NaCl is a 1:1 electrolyte), e is the electron charge, and i n is the total number density of i th ion. In order to evaluate the denominator we need to calculate the number density of Cland Na + ions. Since Clions are present in the suspension only through externally added NaCl, its concentration is same as that of NaCl. On the other hand, concentration of Na + ions can be estimated from ionic conductivity and is given  66 Under such situation, mere thermal energy is not sufficient for the particle to escape the cages. 60 where β is a proportionality constant. If we assume that viscoelastic behavior of suspension is given by single mode Maxwell model, viscous modulus of the same can be written as: 53 Equation (2) , where U is energy barrier related to microscopic movement within the cage (It should be noted that E is depth of energy well associated with the cage while U is activation barrier associated with microscopic timescale. In figure 15 we have represented this scenario using a schematic).
In the glassy domain, evolution of G′ can usually be described by, as shown by curvature of the superposition described in figure 10. Therefore, the power law index µ can be represented by: 53 where parameter 0 G does not depend on either concentration of Laponite or temperature as no vertical shifting is required with respect to both these variables to get the comprehensive superposition of G′ as shown in figure 10 (Vertical shift factor based on Laponite concentration used is figure 4 is just to show the respective superpositions more clearly. This shift factor has not been used in figure 10). Equation ( where v φ is volume fraction of Laponite in suspension, R is radius ( ≈ 12 to 15 nm) and h is thickness ( ≈ 1 nm) of Laponite particle, 44 where n are number of ions per unit volume, d is half distance between the two plates, H A is Hamaker constant (1.06×10 −20 J for Laponite 71 ) and ∆ is thickness of unit layers between the same plates (6.6 A). 1 Furthermore, where z is valence of ion, and 0 Φ is electric potential on the surface. In equation (5), the first term on the right hand side represents double layer repulsion while the second term represents van der Waals attraction between the two layers.
In order to compute free energy using equation (5), we assume complete delamination of all the Laponite particles. The number of sodium ions dissociated per particle is given by: , where 0 n is concentration of Na + ions due to external sources (externally added NaOH or NaCl) and P n is number of particles per unit volume. In equation (5) Figure S1. Evolution of storage (closed symbols) and loss (open symbols) modulus for 2.8 weight % no salt system having idle time i