Crack Patterns in Drying LaponiteâNaCl Suspension: Role of the

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Crack patterns in drying Laponite®- NaCl suspension : Role of the substrate and a static electric field Sudeshna Sircar, Moutushi Dutta Choudhury, Sanat Karmakar, Sujata Tarafdar, and Tapati Dutta Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00501 • Publication Date (Web): 11 May 2018 Downloaded from http://pubs.acs.org on May 14, 2018

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R - NaCl suspension : Role Crack patterns in drying Laponite

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of the substrate and a static electric field

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Sudeshna Sircar1 , Moutushi D. Choudhury2,1 , Sanat Karmakar1 , Sujata Tarafdar1

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and Tapati Dutta3,1,∗

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Condensed Matter Physics Research Centre,Physics Department, Jadavpur University, Kolkata 700032, India

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Centre for Advanced Studies in Condensed Matter and Solid State Physics,

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Department of Physics, Savitribai Phule Pune University, Pune 411007, India 3

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Physics Department, St. Xavier’s College, Kolkata 700016, India

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Abstract

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R -NaCl soluWe report the formation of crack patterns in drying films of Laponite

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R tion. Crack patterns that develop upon drying aqueous Laponite - NaCl solution

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change drastically as the amount of NaCl is varied in the solution. In this work we

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R have investigated the effect of NaCl on drying films of aqueous solution of Laponite

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under two conditions - (i) when the film is bounded by a wall as in petri dish ex-

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periments, (ii) when the film does not have any boundary as in experiments with

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droplets. In order to obtain insights into the effect of substrate, the experiments

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have been done with two different substrates, of different hydrophobicity, polypropy-

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lene and glass. The formation of crack patterns have been explained on the basis

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of the wetting and spreading properties of the solution on these substrates and the

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effect of salt on colloidal aggregation. In this work, we have shown that the presence 1

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R solution can induce crack patterns depending on the of salt to aqueous Laponite

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nature of the substrate. Another important aspect of this work is the role of NaCl

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R in crack inhibition in desiccating films of aqueous Laponite , in the presence of DC

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electric field. This effect can be utilized to suppress undesirable crack formation in

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many applications.

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Keywords: desiccation cracking, salt-colloid interactions, crack induction

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Introduction

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The effect of salt on aqueous solutions of colloids has been an active area of research

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for the past decade having wide applications in medical diagnostics, ink-jet print-

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ing and cement industry, to name a few [1, 2]. Some colloids, in particular clays,

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belonging to the smectic and montmorillonite groups, swell in contact with water.

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This property of swelling clay is utilized to seal micro-cracks in concrete and cement.

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However, the swelling property of the clay is inhibited when exposed to saline water

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[3, 4]. Therefore, it is important to study in a systematic manner the effect of salt

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on crack patterns that develop in desiccating colloids like clay. In this work we

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report the effect of adding NaCl on the crack patterns developed during desiccation

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R , under different conditions. of aqueous solution of the synthetic clay Laponite

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R Crack patterns of desiccating aqueous Laponite in the presence of electric field

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have been an area of ongoing research [5, 6]. The third aspect of this paper reports

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R solutions of different salinities are the interesting effects observed when Laponite

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allowed to dry in a static electric field.

2


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The final crack pattern in all the three cases is determined by the combined effect

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of salt concentration, substrate, the wetting and spreading property of the solution

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on the substrate and the evaporation rate determined by the curvature of the film

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interface, apart from the usual ambient conditions of temperature and humidity.

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In order to analyze the crack patterns observed in desiccating films of aque-

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R R , it is necessary to understand the behaviour of Laponite in water. ous Laponite

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R particles are highly anisotropic oblate particles that develop a net negaLaponite

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tive charge on their flat faces and a small positive charge on the rim of the particles

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[7] when dissolved in deionised water to form an aqueous solution. The charged state

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of the particles is dependant on the pH of the solution [8, 9] and can change with

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ageing [10, 11]. An electric double layer of counterions develops around the particles.

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When subject to direct (DC) or alternating (AC) fields, the colloidal particles exhibit

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a wide range of phenomena [6, 12] which arise from particle polarization, motion

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of the ions in the electric double layer coupled with fluid flow, and forces resulting

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from gradients in the electric field. In aqueous medium, the particles share complex

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interactions among themselves due to their anisotropic shape, electrophoretic mo-

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bility, dissimilar charges on the edges and the faces, and screening of the charges

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due to the presence of the ions in the liquid media. These interactions may lead to

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repulsion between the faces and attraction between the edges and the faces of the

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particles. In addition, there could be van der Waal’s attraction among the particles.

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All these interactions and shape effects are responsible for the microstructure of

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R Laponite suspension, which evolves as a function of time, causing changes in its

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R particles acquire charges in solution viscoelastic character. Also, as the Laponite

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it is expected that they will respond to the application of an external electric field.

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The work reports three aspects of our findings. The first part of the paper reports

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R and the substrate effect on the crack patterns when aqueous solution of Laponite

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NaCl is allowed to dry in the form of films. Petri dishes of polypropylene (PP) and

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glass are used for this purpose. It is observed that the substrate has a strong role

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R in determining the final crack pattern of aqueous Laponite of different salinity.

Figure 1: (a) Experimental set up for application of direct field (DC) to the petridish systems with centre positive (CP) configuration; (b) Experimental set up for applying DC field to the droplet system with CP configuration as well. In both the cases the substrate is of PP.

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In the second part of this work, we report crack patterns that develop on droplets

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R R of different salinity as they desiccate. Laponite is a synthetic of aqueous Laponite

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nano clay which when dissolved in deionized water forms a gel. This gel when left to

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dry in a petri dish of PP or glass, cracks around the edges in a random manner. But

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R gel dries to form a transparent, brittle without the bounding wall the Laponite

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sheet that does not crack at all. In our current work we report the remarkable crack

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patterns produced with the addition of small amounts of sodium chloride (NaCl) to 4


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R gel, with or without the presence of a bounding wall. The role of the Laponite

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salt on crack patterns in drying droplets has been earlier reported by Pauchard et

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al. [13] who worked on droplets of silica solution of different salinities. No report is

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however available on the role of salt concentration on crack pattern in clay droplets,

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though the effect of salt on evaporating droplets of PEO polymer [14] and PTFE

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particles [15] have been reported. It is expected that the droplet shape along with

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the ionised state of colloid particles in solution shall affect the final crack pattern.

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Experimental Section

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Desiccation Experiments

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R We observe desiccation cracks in films of aqueous Laponite gel containing different

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concentrations of NaCl under two situations − (i) when the film is enclosed by a

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boundary which we call the ‘petri dish experiments’ (PD), and − (ii)without

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the presence of a boundary which we call the ‘droplet experiments (DE)’.

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Figure 2: Variation of (a) aggregate diameter; (b) zeta potential; (c) conductivity and (d) mobility with NaCl concentration. The error bars are indicated in the graphs.

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R (LP) gel is formed by the addition of For PD experiments, pure Laponite

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R powder to 40ml of deionized water and stirred by a magnetic 2.5gm of Laponite

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stirrer for about 30 seconds. The solution is immediately poured into a petri dish

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R -NaCl (LN) solutions of and allowed to dry for 4−5 days. To prepare the Laponite

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varying salt concentrations (0.1%, 0.2%, 0.3%, 0.4%, 0.6%, 0.8% and 1.0%), we first

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prepare the salt solution by adding the required amount of NaCl to 40ml of deionized

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water, for example, for 0.2% LN solution we add 0.08gms of Laponite to 40ml of

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R powder and stir it for deionised water, etc. To this we add 2.5gm of Laponite

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about 1 minute before pouring the solution into the petri dish. Instrumental errors

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in the measurement of mass and volume of the samples is in the limit of ±0.001gm

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and ±2ml, respectively. To check for substrate effects, we use petri dishes of PP

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and glass, each of diameter 9 cm.

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With an increase in salt concentration in the Laponite solutions, the time re-

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quired for complete gelation to occur increases considerably. For the DC field ex-

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periments, complete gelation of the solution is required before the electric field can

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be switched on. As the cracking process is very sensitive to temperature and hu-

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midity, the measurements for all the different salt concentrations need to be taken

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within a single day so as to keep the ambient conditions identical. So, with a gela-

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tion time increasing from about 30 min for 0.05% of salt to 4-5 hours for 0.3% salt,

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it becomes difficult to perform the experiment for higher salt concentrations within

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a single day.

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For DE experiments, the LP and LN solutions are prepared in the same manner

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as above and deposited on both the substrates as drops, each drop of volume 0.5 ml.

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To check for the effect of droplet volume on crack pattern, the droplet experiments

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on PP substrate were also performed with 1.0 ml volume. The error in volume

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measurements for droplets is about ±0.001ml.

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Figure 3: Variation with NaCl concentration of: (a) contact angle, θ; (b) adhesion, ∆W; (c) spreading coefficient, S; (d) surface tension, γ; (e) pH; Error bars are indicated within graphs; (f) Time evolution of a drop of 0.4% LN solution while contact angle measurements are done by the pendant drop method, at time instants of: (i) t=0mins, (ii) t=20mins, (iii) t=40mins, (iv) t=45mins.

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The temperature and relative humidity during desiccation vary between 24◦ C

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R RD is procured from Rockwood - 31◦ C and 45% - 66%, respectively. Laponite

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additives and Sodium chloride from Merck, India.

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Electric Field Experiments

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The effect of a static electric field on the crack patterns in LN experiments is studied

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by applying a radial field to the PP petri dish system. The outer and inner electrodes

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are made by wrapping the vertical walls of the petri dish with Al foil and placing

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a small Al rod at the centre, respectively (Figure 1). The crack pattern formed on 8


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the application of a direct electric field (DC) of 100 V for the centre positive (CP)

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configuration of the system, is observed for the different concentrations of NaCl.

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The electric field is applied only after complete gelation occurs and is kept on for a

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continuous period of about 24 hours. The LN solutions for this set of experiments

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are prepared in the same manner as stated above in Section .

R -NaCl solution in a petri dish. The Figure 4: A. Crack pattern of dry Laponite

R salt percentage is mentioned along the horizontal axis; 0.3% Laponite -NaCl shows

hierarchical cracking; B. The time evolution of the crack patterns for 0.2% LN solutions are shown for PP substrate, after (i) 50 hours and (ii) 70 hours of desiccation and glass substrate, after (iii) 24 hours and (iv) 30 hours of desiccation.

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Electric field (DC) of 10 V is also applied to droplets of different concentrations

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of LN solution on PP substrate. A circular ring of Al wire surrounding the outer

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edge of the droplet forms the peripheral electrode. The inner electrode is formed 9


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from an Al wire placed vertically at the centre of the droplet, (Figure 1b).

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Characterization Measurements

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R A pendant drop technique was employed to analyze surface tension of Laponite

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gel with different concentrations of salt in ambient air at 25◦ C and relative humidity

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of 45%. The measurements for the adhesion and spreading coefficient have been

139

calculated from the contact angle measurements of the LN solutions from equations

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(3) and (4). The contact angle is measured using the pendant drop method using

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automated optical contact angle (OCA) goniometer and the data analyzed using

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software SCA 20 (Data Physics Instruments, GmbH, Germany). The measurement

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of the contact angle is taken at a point where the solution has already gelled, so

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that it is equivalent to measuring the contact angle of the gelled film used in our

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cracking experiments.

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R The pH of Laponite solution with different concentrations of salt were mea-

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sured by Digital pH meter (MIFA systems, India) maintaining same physical condi-

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tions of the room.

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Figure 5: Variation of crack ped number with NaCl concentration for: (a) PD systems for different substrates and (b) DE systems of two different volumes, on PP substrate.

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Figure 6: A. (a) and (g) show droplets of pure Laponite on PP and glass substrate respectively, without any formation of cracks; (b)-(f) Crack patterns of dry LN solutions for 0.5ml droplet on PP; (h)-(j) Zoomed portions of crack patterns for LN droplets on glass substrate. Salt percentages are mentioned for each figure. For figures (a) - (g) one small green box has the dimension of 1mm x 1mm; B. Appearanace of cracks on 0.2% LN solution droplets on PP substrate after (i) 1 hour 50 minutes, (ii) 3 hours and (iii) 3 hours, 15 minutes, and on glass substrate after (iv) 2hours 50 minutes, (v) 3hours, 20 minutes and (vi) 3 hours, 50 minutes. 12


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R -NaCl solutions were prepared in molar ratios of 0.2, 0.4, 0.6, Dilute Laponite

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0.8 and 1.0. These solutions were used to measure the Hydrodynamic radius,

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Zeta potential, Conductivity and Mobility of the samples using Zetasizer Nano

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ZS (Malvern Instrument, UK). The experiments were repeated three times and their

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average values were plotted against the molar ratios (Figure 2).

Figure 7: Crack pattern of dry LN solution in a droplet of 1.0 ml, on PP for different salt concentrations. Salt concentrations are mentioned in Figures (a-e). For each figure, one small green box has the dimension of 1mm x 1mm

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Results and Discussion

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Characterizations

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R Figures 2a, b, c and d, show the effect of salt concentration in aqueous Laponite

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solution on colloidal particle diameter, the zeta potential, conductivity and mobil-

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ity, respectively. These measurements were done on dilute solutions with different

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R molar ratios of Laponite and NaCl. Although, zeta potential and DLS experi-

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ments are performed at much lower concentrations than those used in dessication

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experiments, it is useful to know the electrostatic behaviour as well as the hydro-

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R dynamic radius of Laponite particles in an aqueous solution. Individual smectite

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R aggregate or flocculate into colloidal particles. The colloidal platelets of Laponite

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particle size decreases with decrease in salt concentration as is evident from Figure

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2a. Though this is a pointer to greater flocculation of the particles with increase

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in NaCl concentration, it may be mentioned that the NaCl crystals grow on the

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flocs adding to their total size. If the thickness of the double layer is very small

168

compared to the particle size, i.e. κa >> 1, the von Smoluchowski equation relates

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the electrophoretic mobility, µ to the electrical potential at the shear plane of every

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colloidal particle, i.e. the zeta potential, ζ, by ǫ µ= ζ η

(1)

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Here κ is the inverse of the Debye length, a, the particle radius, η, the dynamic

172

viscosity and ǫ is the dielectric constant of solvent. For small particles in low dielec-

173

tric constant, Equation (1) becomes µ=

2ǫ ζ 3η

(2)

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This is the Huckel approximation generally used for non-aqueous measurements.

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Our measurements show that the zeta potential and mobility, Figures 2b and d,

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show exactly the same variation with salt concentration. The zeta potential shows

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R : NaCl = 0.6. It is well known [16] a maximum of -52 mV for the ratio Laponite

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that a higher magnitude of ζ, whether positive or negative, points to greater stability

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of the colloidal solution. The zeta potential reaches a minimum of 0 mV for the ratio

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R Laponite : NaCl = 0.2. Thus, it is clear that increase in salt concentration leads

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to aggregation or flocculation of the particles, thus destroying the stability of the

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colloidal solution.

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R -NaCl solution Figure 3a displays the variation of contact angle of the Laponite

184

of different salt concentrations on PP and glass. On glass substrate the contact angle

185

is acute ∼ 35◦ , whereas for PP the contact angle is ∼ 98◦ . Increasing the salinity

186

has almost no effect on the contact angle. Figures 3b and c display the adhesion and

187

spreading of the solution of different salinities for each of the substrates. Knowing

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R the contact angle, θ, of the Laponite -NaCl solutions on both the substrates, glass

189

and PP and the surface tension, γ, the spreading parameter, S, and the adhesion

190

energy per unit area, ∆W , can be calculated as follows:

S = γ(cosθ − 1)

(3)

∆W = γ(cosθ + 1)

(4)

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On both glass and PP, adhesion shows a general tendency to increase with salt

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concentration reaching a maximum at 0.6% salt concentration on glass. The spread-

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ing of the solution on glass substrate shows a slow decrease with increasing salinity.

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On PP substrate, the spreading shows a minimum at 0.6% salt concentration.

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Figure 8: (a-e) SEM images of crack ped surface of films of LN solutions of different concentrations after complete drying, i.e. no further crack production. The concentrations are indicated on the images; (f) The pyramidal growth of NaCl crystals on crack peds for 0.6% salt concentration.

195

R of different salinities increases steadily The surface tension of aqueous Laponite

196

to a maximum ∼ 57 N/m at a salt concentration of 0.6% (Figure 3d). Thereafter it

197

remains almost constant with increasing salinity. Figure 3e displays the variation in

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the pH of the solution at different salinities. Figure 3f(i-iv) shows the time evolution

199

of a drop of LN solution during the measurement of surface tension by the pendant

200

drop method.

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Petri Dish Experiments

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R The experiments were performed on petri dishes of PP and glass. Pure Laponite

203

gel on desiccation cracks randomly, starting at the edges of its bounding walls for

204

both PP and glass. However, the scenario changes completely once salt i.e. NaCl is

205

added to the system. As the gel dries, cracks start to appear in a specific manner

206

with increasing salt concentration. With the rise in the salt level, the gelation time

207

of the system increases as well, ranging from a few seconds for LP to several hours

208

R for 1% LN solution. Laponite gel with no salt is completely transparent, even

209

after drying. Even though 0.2% LN solution retains the transparent nature, it

210

turns opaque for all higher concentrations of salt.

211

Complete desiccation takes about 5 − 6 days, at the end of which the crack

212

patterns are formed (Figure 4). Comparison of the crack peds formed for the two

213

substrates show that the peds formed on the glass substrate tend to curl up at the

214

edges on complete drying. Further, at the particular concentration of 0.6% NaCl,

215

there is a minimum in the number of crack peds, i.e. the tendency to crack decreases.

216

This occurs for both PP and glass as seen in the graph of Figure 5a. A comparison

217

between the plots for the two substrates show that at 0.3% concentration of salt,

218

the number of crack peds, Np , peak for both, though Np for glass is far higher than

219

that of PP. It is noteworthy that at this concentration, the crack pattern shows a

220

distinct hierarchical pattern for both the substrates. For all other concentrations,

221

the variation of Np shows the same nature for both surfaces, with ped numbers

222

always being higher in case of glass.

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Droplet Experiments

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R when allowed to dessicate on a glass or PP Pure droplets of aqueous Laponite

225

substrate dries without cracking. The addition of even a small percentage of salt

226

produces crack patterns on both substrates. Figure 6 shows the final crack patterns

227

R obtained by desiccating 0.5 ml by volume of aqueous Laponite with different con-

228

centrations of NaCl. The droplets on PP, Figures 6(a-e), show a coffee-ring effect

229

[17] at salt concentrations greater than 0.4%, followed by a transparent border. The

230

number of peds, Nd , decrease and become more irregular in shape as the salt con-

231

centration increases. With increase in salt concentration, the opacity of the peds

232

increases too.

233

By contrast, the same volume of droplets having identical salt concentrations

234

as before when placed on a glass substrate, have a larger average diameter. Each

235

droplet shows an opaque border. At lower salt concentrations of ∼0.2%, the dry

236

droplets show a hierarchical crack pattern with larger peds at the centre that branch

237

into smaller peds at the periphery. The peds are polygonal structures with straight

238

edges. At salt concentrations > 0.4%, this hierarchical structure of cracks is de-

239

stroyed. The peds have irregular edges, become more opaque and move towards a

240

uniform size distribution with increasing salt concentration.

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Figure 9: Optical microscope images of different aspects of crack pattern for 0.4% NaCl concentration developed on PP substrate. (a) Particles stick to substrate between cracks; (b) Dendritic growth of NaCl crystal growth on film surface; (c) The periphery of the dried droplet showing particles constituting the coffee ring.

241

Figure 7 shows the final crack pattern when the experiment was repeated on the

242

PP substrate with a higher volume of 1 ml. The coffee-ring effect is not discernible

243

till concentrations are > than 0.8%. The transparent border observed in the case of

244

smaller droplet volume of 0.5 ml, is absent. Nd shows a maximum at ∼0.4% of salt

245

concentration as compared to 0.2% for 0.5ml of the solution. Figure 5b displays the

246

effect of droplet volume on the variation of ped number with salt concentration. At

247

every salt concentration, the nature of the variation is similar with the number of

248

peds always higher for 1ml than 0.5ml.

249

Figure 8a-e shows SEM images of the dried film with different salt concentra-

250

R tions. The increase in the average size of the aggregates indicate that the Laponite

251

particles have flocculated with crystals of NaCl on the surface. It appears that the

252

average size of a floc is the largest for 0.6% of NaCl concentration. While the cubic

253

crystals of NaCl is clearly visible on the surface of aggregates for all salt concentra-

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tions, the SEM image for 0.6% also shows pyramidal crystal structures of NaCl on

255

the film surface (Figure 8f).

R solution containing Figure 10: Desiccation crack pattern on aqueous Laponite

different concentration of NaCl, in the presence of DC electric field. The central electrode is anode, the peripheral electrode is cathode. The different concentrations of NaCl are: (a) 0.05%, (b) 0.15%, (c) 0.2% and (d) 0.25%, where the direction of propagation of cracks has been marked by red arrows; (e) Variation of time of appearance of first crack versus salt concentration. The experimental data is denoted by symbols. The dotted line denotes the best-fit line.

256

Figure 9 shows optical microscope images of different aspects of the dried film

257

ped for the case of 0.4% NaCl concentrated film on PP substrate, as a case study.

258

The cracks that develop are not ‘clean’ as particle deposits stick to the substrate

259

between crack walls (Figure 9a). The dendritic aggregation of NaCl crystals on the

260

surface of the crack peds is visible in Figure 9b. Figure 9c shows the deposition

261

of particles at the periphery of the droplet forming the ‘coffee ring’ effect. The 20


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transparent zone between the ‘coffee ring’ and the peds indicate that the droplet on

263

PP dried following a stick-slip movement.

264

R Desiccation cracks of Laponite and NaCl solution in DC

265

field

266

R containThe crack patterns obtained on desiccating aqueous solution of Laponite

267

ing different concentrations of NaCl are displayed in Figures 10(a-d). In the absence

268

of any salt, desiccation cracks in the presence of a DC electric field emerges from

269

the central anode and proceeds radially to the cathode. However, the addition of

270

as little as 0.05% of NaCl changes the crack pattern drastically. A displacement of

271

mass of the gel which is still soft, occurs from around the anode. This displace-

272

ment proceeds outward towards the cathode in the manner of a circular wave. The

273

opacity of the outer region increases with increase in salt concentration. The inner

274

depressed region is translucent in nature. Cracks that emerge from the anode are

275

only confined to the inner depressed region. As the salt concentration increases, the

276

mass displacement wave pushes towards the peripheral cathode making the outer

277

elevated region thicker. It is observed that the rate of increase in area of the inner

278

depressed region coincides with the increase in the voltage drop across the system

279

(Figure 11a). We calculated the electrical energy supplied to the system during this

280

time (Figure 11b) from measurements of current and voltage. It is evident that the

281

energy is utilized in the displacement wave that propagates from the central anode

282

to the peripheral cathode. Figures 12a and b show SEM images of the regions near

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the anode and the opaque outer ring, respectively. While almost no NaCl crystals

284

are seen in the inner ring region, these are clearly visible in the outer region. An

285

interesting observation is that with an increase in the salt concentration of the LN

286

solution, the length of the crack propagating from the anode is inhibited, (Figures

287

10a-d). Another noteworthy point is that with increasing salt concentration the

288

time of appearance of first crack increases exponentially (Figure 10e), until crack

289

growth is suppressed as is evident from Figure 10d.

290

R has the effect Thus, it appears that the addition of NaCl to aqueous Laponite

291

R of suppressing crack formation in desiccating Laponite films in the presence of

292

DC electric field. We restricted our experiments to 0.3% NaCl concentration as the

293

gelling time required for higher salt concentration increases hugely. The DC field

294

cannot be switched on until the film has gelled.

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Discussions

Figure 11: (a) The black line shows the variation in the square of the radius (cm2 ) ∼ area of the crack ring for different LN solutions formed by the application of a DC field in the PD system. The red plot shows the time instant, tN (min) at which the system attains the maximum applied DC voltage and the current drops to zero. Both the sets of data have been normalized by their maximum values for a better comparison of their nature of variation ; (b) The energy supplied by the direct electric field to the system has been calculated from the current-voltage data recorded for the different salt concentrations of the LN solutions in the PD system. The variation of the electrical energy, the ring area and the time show a similarity in nature.

296

For identical salt concentration, the crack pattern and characteristics of desiccating

297

R solution are different for petri dishes of PP and glass (Figure 4). films of Laponite

298

This difference is attributed to the different spreading and wetting of the solutions

299

on the different substrates. The addition of NaCl increases the number of cations

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300

in the solution which is responsible for neutralizing part of the negative surface

301

R particles. This reduces the repulsion between charge on the faces of the Laponite

302

R Laponite particles. The particles start forming aggregates through flocculation

303

and the solution loses its stability as is evident from the decreased value of the

304

zeta potential. The SEM images of Figure 8 show the aggregates increasing in size

305

with increasing salinity upto 0.6% of salt concentration, after which they appear

306

to decrease a little in size. This is responsible for the maximum in ped number at

307

0.2% where aggregate size is seen to be minimum because cracks can develop only

308

along the aggregate boundaries. By the similar argument, the maximum size of the

309

aggregate corresponding to 0.6%, yields the minimum number of crack peds. The

310

excess NaCl in solution starts crystallizing on ped surface as tiny cubes following the

311

dendritic growth pattern (Figure 9b), as reported by Dutta Choudhury et.al. [18].

312

Xu et al.[19] suggest that the effects of added salts are twofold: (1) compressing the

313

double-layer between the particles and the substrate leading to increased number

314

of adsorbed particles and (2) reducing the electrokinetic effect and hence the radial

315

R velocity of the mobile particles. The spreading coefficient of aqueous Laponite

316

with 0.6% NaCl on PP is a minimum (Figure 2c). This may be responsible for the

317

supersaturation of the solution which in turn causes unequal and rapid crystallisa-

318

tion of the salt about the edges rather than the faces of a crystal cube leading to

319

the pyramidal crystals. Figure 2d shows that a maximum of surface tension value

320

is reached at 0.6% NaCl concentration. A higher value of surface tension is likely

321

to suppress evaporation. It is possible that this affects the rate of crystallization

322

in the solution allowing greater time for the NaCl crystal to grow around a nucle24


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ating centre. This probably explains the occurrence of the pyramidal NaCl crystal

324

aggregates that are found only at the salt concentration of 0.6%.

325

For any given salinity, the adhesion and spreading of the solution is far greater

326

on glass than on PP (Figures 3b and c). With contact angle between glass and

327

the different solutions much < 90◦ , the glass substrate behaves like a hydrophilic

328

substrate to the solution unlike the PP substrate that tends to be hydrophobic with

329

its contact angle > 90◦ . The adhesion between the substrate and the solution in the

330

case of glass, generates shear stress between consecutive layers of the film that dries

331

top down. It is well established that thin films generate more cracks than thicker

332

films [20]. Lazarus [21] has shown that cracks interact mutually as soon as the

333

spacing between them is smaller than ten times the thickness of the layer. A simple

334

Griffith-type balance between the elastic deformation energy and the fracture bulk,

335

and debonding, captures a broad number of observations. The observations range

336

from square-root or linear increase of the spacing with the thickness, to its decrease

337

with loading until saturation. Adhesion is identified as playing a key role in these

338

behaviour changes. In this context, the greater spreading ability of the same volume

339

of solution, makes a thinner film on glass than on PP. The greater number of peds

340

observed on glass substrate than on PP, Figure 5a, is therefore explained.

341

Examination of the crack peds on glass reveal that their edges curl upwards as

342

they dry. This happens because once the peds are formed, drying also commences

343

from along the edges of the thin peds while the central part of the peds remain

344

attached to the substrate. If the drying rate is faster than the rate at which the

345

system relaxes, the threshold strain can be reached faster and peeling can happen 25


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346

from along the edges as is observed. As spreading is lower on PP, the peds are

347

relatively thick. The rate of drying is slower than the rate at which the system

348

relaxes and this curling up of the edges is absent.

349

In the case of droplet drying of the solution on PP substrate, a ring of particles

350

marks the initial boundary of the droplet. The triple line of contact is not pinned

351

to the substrate. This is not unexpected given the high angle of contact and low

352

adhesion between substrate and solution. With increase in salt concentration, the

353

transparent quality of the gel observed at 0.2% concentration turns opaque due to

354

R particles. As the droplet dries, the contact line aggregation between Laponite

355

contracts, drawing the particles to the thickening central region. As a result, the

356

number of cracks become fewer.

357

The droplet on glass substrate has a larger average radius following its greater

358

spreading coefficient on glass. This ensures that the droplet height is much less

359

than that on PP. Further the pinned triple line of contact ensures a pronounced

360

‘coffee ring’ effect manifested by the thick opaque outer boundary. For lower salt

361

concentration, ∼0.2%, the peds follow a hierarchical pattern being smaller in size

362

along the periphery, and joining to form larger peds at the centre. The low amount

363

of NaCl is not sufficient to form a thick gelled ‘foot’ at the periphery. The natural

364

curvature of the droplet ensures that the edge remains thinner than the central part

365

of the droplet. This enables smaller and more numerous cracks to develop along the

366

edges, while the cracks at the centre remain thicker and fewer in number. However,

367

with increase in salt concentration, the thick ’gelled foot’ advances inwards creating

368

a thinner film at the central part of the drying droplet. The central thinner film 26


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breaks up into numerous tiny peds as the film dries to release the shear stress that

370

builds up because of the greater adhesion between glass and solution.

371

For both PP and glass substrates it is noted that as the salt concentration in-

372

creases, the crack ped edges change from straight lines to a more irregular line as

373

cracking now occurs along the aggregate boundaries.

Figure 12: (a) SEM micrographs of LN solutions placed in an external electric field (DC) of 100V near the central positive electrode; (b) SEM micrographs of a portion the same system that is just outside the crack ring formed due to the electric field. The NaCl crystals can be clearly seen in (b), which are completely absent in (a).

374

R -NaCl solution in DC The most remarkable effect of desiccation of Laponite

375

electric field is the inhibition effect that increasing salinity has on crack formation

376

(Figure 10). The difference between Figure 10a and the other images of Figure 10 is

377

testimony that even a small percentage of NaCl has a drastic effect on crack pattern.

378

Figure 10e indicates that the time of appearance of the first crack increases with

379

salt concentration. This is supportive of the fact that cracking in the presence of 27


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DC electric field seems to be inhibited with increased salinity.

381

Summary and Conclusions

382

R has In this work the effect of NaCl on drying film of aqueous solution of Laponite

383

been investigated under two conditions - when the film is bounded by a wall as in

384

petri dish experiments, and when the film does not have any boundary as in droplet

385

experiments. The experiments have been done with two different substrates, PP

386

and glass. The former is less wetted than the latter by the solution. The crack

387

patterns have been explained on the basis of the wetting and spreading properties

388

of the solution on these substrates and the effect of salt on colloidal aggregation.

389

R It is worth recalling that aqueous Laponite droplet shows no cracking and can

390

R crack only when bound by a boundary [22]. The strong cohesion between Laponite

391

particles enables drying of the droplet while shrinking as a whole. The force of

392

adhesion between solution and substrate is weaker than cohesion. We show in this

393

R work that the addition of salt to aqueous Laponite solution destabilizes the solution

394

and weakens cohesion considerably. Crack patterns now develop depending on the

395

substrate type.

396

The third important aspect of this work is the role of NaCl in crack inhibition

397

R in the presence of DC electric field. This in desiccating films of aqueous Laponite

398

effect can be utilized to suppress undesirable crack formation in many applications.

399

This effect is quite drastic though we have not yet been able to propose a clear

400

understanding of the reason. We hope to be able to provide a suitable answer in

28


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our future work.

402

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403

Acknowledgement

404

The authors would like to acknowledge the SEM facility of the Physics Department

405

of Jadavpur University, Kolkata (Configuration no. QUO-35357-0614 funded by

406

FIST-2, DST Govt. of India). M.D.C. thanks SERB, India, for providing financial

407

support through NPDF (PDF/2016/001151/PMS).

408

References

409

[1] van Hameren, R. et al. Macroscopic Hierarchical Surface Patterning of Por-

410

phyrin Trimers via Self-Assembly and dewetting, Science 2006, 314 ,14331436.

411

[2] Norbert, R. et al., Electrospray Crystallization for Nanosized Pharmaceuticals

412

413

with Improved Properties, Cryst. Growth Des. 2012, 12, 35143520. [3] Jones Jr., F.O., Influence of Chemical Composition of Water on Clay

414

Blocking of Permeability. J Pet Technol. 1964,

415

http://dx.doi.org/10.2118/631-PA

416

[4] Mungan,

N.,

Salinity.

418

http://dx.doi.org/10.2118/1283-PA

420

441-446.

Permeability Reduction Through Changes in pH and

417

419

J

16 (4):

Pet

Technol

1965

17

(12):

14491453.

SPE-1283-PA.

[5] Khatun, T.; Dutta, T.; Tarafdar, S. Crack formation in Laponite gel under AC fields. Appl. Clay Sc. 2013, 86, 125-128.

30


Page 31 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

421

[6] Sircar, S.; Khatun, T.; Dutta, T.; Tarafdar, S. Alternating field induced crack

422

patterns in desiccating Laponite solutions: experiment and simulation. Indian

423

J. Phys. 2016, 90(12), 1355-1366.

424

425

426

427

[7] Kroon, M.; Vos, W. L.; Wegdam, G. H. Structure and formation of a gel of colloidal disks. Phys. Rev. E. 1998, 57, 1962-1970. [8] Thompson, D. W.; Butterworth, J. T. The nature of laponite and its aqueous dispersion. J. Colloid Interface Sci. 1992, 151, 236-243.

428

[9] Tawari, S. L.; Koch, D.L.; Cohen, C. Electrical double-layer effects on the

429

Brownian diffusivity and aggregation rate of Laponite clay particles. J. Colloid

430

Interface Sci. 2001, 240, 54-66.

431

[10] Bandyopadhyay, R.; Liang, D.; Yardimci, H.; Sessoms, D. A.; Borthwick, M.

432

A.; Mochrie, S. G. J.; Harden, J. L.; Leheny, R. L. Evolution of particle-scale

433

dynamics in an aging clay suspension. Phys. Rev. Lett. 2004, 93, 228302.

434

[11] Mourchid, A.; Levitz, P. Long-term gelation of laponite aqueous dispersions.

435

436

437

Phys. Rev. E. 1998, 57, R4887-R4890. [12] Khatun, T.; Choudhury, M.D.; Dutta, T.; Tarafdar, S. Electric-field- induced crack patterns: Experiments and simulation. Phys. Rev. E. 2012, 86, 016114.

438

[13] Pauchard, L.; Parisse, F.; Allain, C. Influence of salt content on crack patterns

439

formed through colloidal suspension desiccation. Phys. Rev. E. 1999, 59(3),

440

3737-3740.

31


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 34

441

[14] Msambwa, Y.; Shackleford, A.S.D.; Ouali, F.F.; Fairhurst, D.J. Controlling and

442

characterising the deposits from polymer droplets containing microparticles and

443

salt. The European Physical Journal E. 2016, 39(2), 21.

444

[15] Zhang, Y.; Liu, Z.; Qian, Y.; Li, Z.; Zang, D. Pattern Formation Mechanism via

445

Evaporation of Colloidal Droplet Containing PTFE Particles and NaCl. KAO

446

TENG HSUEH HSIAO HUA HEUSH HSUEH PAO. 2014, 35(6):1258-66.

447

[16] Gibson, N.; Shenderova, O.; Luo, T. J. M.; Moseenkov, S.; Bondar, V.; Puzyr,

448

A.; Purtov, K.; Fitzgerald, Z.; Brenner, D.W. Colloidal stability of modified

449

nanodiamond particles. Diamond and Related Materials 2009, 18, 620-626.

450

[17] Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten,

451

T. A. Capillary flow as the cause of ring stains from dried liquid drops. Nature

452

1997, 389(6653): 827.

453

[18] Choudhury, M. D.; Dutta, T.; Tarafdar, S. Pattern formation in droplets

454

of starch gels containing NaCl dried on different surfaces. Colloids Surf. A:

455

Physic0-chem. Eng. Asp. 2013, 432, 110118.

456

[19] Xu, G.; Hong, W.; Sun,W.; Wang, T.; Tong, Z. Effect of Salt Concentration on

457

the Motion of Particles near the Substrate in Drying Sessile Colloidal Droplets.

458

Langmuir 2017, 33 (3), 685695.

459

460

[20] Groisman, A. and Kaplan, E., An Experimental Study of Cracking Induced by Desiccation. EPL (Europhysics Letters) 1994,25 (6), 415.

32


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Langmuir

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[21] Lazarus V´eronique., Fracture spacing in tensile brittle layers adhering to a rigid

462

substrate. EPL (Europhysics Letters) 2017 117, 24002. doi: 10.1209/0295-

463

5075/117/24002

464

[22] Khatun, T.; Dutta, T.; Tarafdar, S. Crack Formation under an Electric Field

465

in Droplets of Laponite Gel: Memory Effect and Scaling Relations. Langmuir

466

2013, 29 (50), 1553515542.

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Graphical Abstract

34


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