Memory of Electric Field in Laponite and How It Affects Crack Formation

Subscriber access provided by Warwick University Library

Article

Memory of Electric Field in Laponite and how it affects Crack Formation: modelling through generalized calculus Somasri Hazra, Tapati Dutta, Shantanu Das, and Sujata Tarafdar Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02034 • Publication Date (Web): 02 Aug 2017 Downloaded from http://pubs.acs.org on August 5, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 30

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

Memory of Electric Field in Laponite and how it affects Crack Formation: modelling through generalized calculus Somasri Hazra1 , Tapati Dutta1,2 , Shantanu Das1,3 and Sujata Tarafdar1∗ 1

Condensed Matter Physics Research Centre, Physics Department, Jadavpur University, Kolkata 700032, India 2

3

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

Reactor Control System Design Section (E & I Group), Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India Sujata Tarafdar∗ : Corresponding author, sujata [email protected], Phone 913324146666(Ex. 2760), Fax: 913324138917

Abstract Desiccation crack formation is affected by the presence of electric fields. We show here that the field effect is not only at work while the power supply is on, but leaves a memory even after switching off. The time required for first appearance of cracks is shown to depend on the voltage of the field as well as the time duration of exposure. We model the system as a leaky capacitor described by a fractional order derivative in the constitutive equation. This gives a good fit to experimental data and explains the memory effect. Keywords: Desiccation, Laponite, Electric field, Memory

1 ACS Paragon Plus Environment

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

1

Page 2 of 30

Introduction

A material such as clay develops cracks when an aqueous slurry is left to dry. These desiccation cracks form characteristic patterns depending on ambient conditions such as temperature and relative humidity, besides nature of the drying material and the substrate [1]. Energy is required to create new surfaces during crack formation. Normally this energy is derived from thermal energy of the surroundings, leading to evaporation and hence fracture. However, an external stimulus can provide extra energy, speeding up the cracking process and also changing the crack patterns significantly. Examples of such stimuli are external electric [1, 2] or magnetic fields [1, 3]. When no voltage is applied during desiccation, cracks appear after a time t0 following deposition. When drying takes place under a voltage V , the time of crack appearance is much reduced to tc (V ). A ‘memory’ effect has been observed in the case of static electric fields [2]. In this case the field is applied for a certain time interval τ and then switched off before cracks start to form. The time of appearance of cracks tτ (V ) is a function of τ and the applied voltage, where t0 > tτ (V ) > tc (V ). We show that the effect of the field is felt even after the external supply is switched off. In the present work we try to understand the memory effect employing ideas based on generalized calculus. It is well known that dependence of a system on its earlier history, in other words its memory, can be treated elegantly using generalized calculus [4], where the order of derivatives in constitutive equations is allowed to take fractional values. We build upon the following concept: a real system behaves


Page 3 of 30

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

like a leaky capacitor on charging and subsequent discharging. An ideal capacitor of capacitance C, connected to a voltage source V is expected to get fully charged to CV in a short time and henceforth retain that charge indefinitely. However it has been observed for many systems that ‘dielectric absorption’ continues as long as the voltage source is connected [5] and on discharge, voltage is retained for a time ∼ τ and then falls off very slowly. This implies that if we consider our drying clay drop as a real capacitor, electrical energy dissipated in the system does not go to zero as soon as the external voltage supply is switched off. This is clearly demonstrated in our experiment as a non-zero voltage measured across the system, which falls slowly to zero during a time much larger than τ . In our experiment a droplet of colloidal Laponite solution is allowed to dry under different conditions: (A) with no applied field, (B) with a voltage V applied continuously until cracks appear and (C) with voltage V applied for different time intervals τ . The time of first appearance of cracks is noted in all cases. We analyse our results, assuming the clay drop to behave like a real capacitor. The experimental details are described in the next section, the results, analysis, discussion and conclusions follow in subsequent sections.

2

Experimental

Our set up is similar to that of Khatun et al. [2] but here we conduct a new set of experiments, where the electrodes are of platinum instead of aluminium, to avoid interaction with the colloid. Details are given below.


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

2.1

Page 4 of 30

Sample and Set-up

The experimental material Laponite RD has been procured from Rockwood Additives. It has the formula Si8 M g5.5 Li0.4 H4 O24 N a0.7 [6]. Laponite is a synthetic clay which consists of disc-like platelets of diameter ∼ 25 nm and thickness ∼ 0.92 nm. The structure of Laponite consists of octahedrally coordinated magnesium oxide sandwiched between two sheets of tetrahedrally coordinated silica. For concentrations above 2 wt% it forms a gel when stirred in deionised water [7]. At concentration ∼ 7 wt%, lumps appear in the film and its homogeneity is lost [7, 8]. At lower concentrations i.e. below 6 wt%, it takes a very long time to gel. The concentration is chosen such that gelation can occur and the gel formed is of homogeneous nature. Laponite platelets acquire a surface charge in aqueous environment. The negative surface charge of Laponite RD, defined as cation exchange capacity(CEC), is equal to 0.75 meq/g [9]. The positive charges are generally screened by the diffuse part of the electric double layer [10]. The magnitude of the positive charge decreases with increasing pH and gets neutralized at pH > 11 [11, 12].


Page 5 of 30

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

Figure 1: (A) Schematic diagram of set-up. Laponite gel is placed within the circular platinum anode and the platinum wire at centre is the cathode. (B) This shows the initial shape of the sessile drop like a spherical cap. Our experimental set up consists of one circular platinum ring of diameter 18 mm forming the outer boundary of the drop and acting as the cathode. At the centre of the ring a straight platinum wire of diameter 0.75 mm is suspended which acts as the anode. This set up is placed on a perspex sheet. The experimental set up is shown in Figure 1 A. The central electrode is connected to the positive terminal of a power supply and the outer i.e. the peripheral electrode to the negative. Figure 1 B shows the initial shape of the droplet. 0.625 g of Laponite RD is added to 10 ml of deionized water while it is on a magnetic stirrer. The suspension is stirred carefully for 45 s. It was observed that gel forms after stirring for 30 s, so a slightly longer stirring time of 45 s was chosen for the experiment. A longer time of more than 60 s would make the sample lose its pouring consistency. A droplet of Laponite gel of volume 1.1 ml is deposited within the platinum ring placed on a perspex sheet. A time interval of 2 min is allowed for the drop to spread evenly before any experiment is started. 5 ACS Paragon Plus Environment

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

2.2

Page 6 of 30

Crack formation study

(A) Desiccation effect

Figure 2: A, B1, B2 show cracks forming for V = 0V. A and B show separate sets. Photographs taken at 274 min, 254 min, 263 min for A, B1 and B2 respectively. C shows cracks forming for V = 4V. C1 shows the appearance of bubbles on both electrodes. C1, C2 and C3 show photographs taken at 3 min, 225 min, 418 min respectively .

To see the purely desiccation effect on the crack pattern of Laponite gel, the droplet is allowed to dry and the time of first appearance of a crack t0 is noted. The procedure is repeated 6 times. During our experiment, ambient temperature and relative humidity (RH) varied between 20◦ C to 27◦ , and ∼ 38 to 51 % respectively. Figure 2 (A, B1, B2) shows typical desiccation cracking of a droplet. Figures 2 A and 2 B (B1 and B2) show two different sets of experiments. In the absence of a


Page 7 of 30

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

field, the first crack always appears from the outer electrode. (B) Continuously applied field

Figure 3: All sets for τ = 15 s. All times are measured starting from switching on the power supply. Photographs of A1, A2 taken at 20 s, 344 min respectively for 4 V. Photographs of B1, B2 taken at 10 min, 251 min respectively for 8 V. C1, C2 show the photograph for 10 V after 179 min and 261 min respectively. Bubbles are seen prominently nearby inner electrode in all figures.

After even spreading of the drop, the power source with voltage V is switched on, with the centre terminal positive. Observations for V = 4, 6, 8 and 10 V are recorded. At time tc (V ) after switching on the field, cracks are observed to appear 7 ACS Paragon Plus Environment

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 8 of 30

at the +ve terminal. The cracks proceed radially towards the -ve terminal, which is the periphery of the drop. Small bubbles are seen to appear near the +ve terminal during the drying process. For higher V bubbles appear at the -ve terminal as well. Figure 2 C1 as well as Figure 3 show the cracks formed and the bubbles appearing. The current across the sample is measured. The current as function of time for different V , up to the time of appearance of the 1st crack, is shown in Figure 4 A. The fluctuations in the current graph are due to the bursting of the bubbles which release water, particularly at higher voltages. As voltage increases, more and more bubbles appear at the central electrode. As the bubbles coalesce, water is released, which momentarily forms a conducting path across the electrodes, so the current increases. For 4 and 6 V the current falls slowly with time and the cracks appear later. For 8 V there is an initial rise in the current, before it falls. At 10 V where the maximum number of bubbles appears, the current rises significantly, and cracks appear before the current starts to fall again. With increase in applied voltage, the time of appearance of the 1st crack decreases. In all the graphs experimental error is less than symbol size.


Page 9 of 30

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

Figure 4: (A)The figure shows the current-time data upto the appearance of first crack time for each voltage. There are fluctuations in current due to bursting of bubbles during measurement. The error in current measurement is 0.1 mA, which is less than symbol size. (B) Time of first appearance of cracks is plotted against applied voltage, red circles are experimental points and the line is an exponential fit as discussed in section 3.2. In this graph the standard deviation is calculated which is within the symbol size. (C) Field applied for time τ 2 min after deposition of the drop the power supply is switched on. After τ s, the supply is switched off and the time of crack appearance tτ (V ), measured from the time when V is applied, is noted. The experiment is conducted for τ = 15, 30, 45 and 60 s and V = 4, 6, 8, 10 V. The cracks appear from outer electrode and move towards the inner. Time of appearance of the cracks for varying V and τ are tabulated in Table 1.


Langmuir

2.3

Voltage measured after switching off source

3

10

A

B

2

10

6V

4V

τ = 15 s τ = 30 s τ = 45 s τ = 60 s

1

10

Vd(t, τ) (mV)

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 10 of 30

τ = 15 s τ = 30 s τ = 45 s τ = 60 s

1 3

10

D

C

2

10

8V

1

10

1

10V

τ = 15 s τ = 30 s τ = 45 s τ = 60 s 1

1

10

τ = 15 s τ = 30 s τ = 45 s τ = 60 s

2

10

3

10

4

10

1

1

10

2

10

3

10

4

10

Time (s)

Figure 5: The graph represents variation of discharge voltage (Vd (t, τ )) with time after the field is switched off at t = τ for different applied voltage, V . Figures A, B, C, D represent 4V, 6V, 8V and 10V respectively. The error in all graphs is less than symbol size.

A multimeter is connected across the droplet and the voltage Vd (t, τ ) is measured, starting immediately after switch-off until it falls to zero. The results are shown in Figure 5. We find that as expected for a real capacitor the voltage across it does not reach zero as soon as the supply is cut off, but falls slowly reaching 0 after about 1 hour depending on τ and on V .


Page 11 of 30

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

2.4

SEM imaging of the cracks

Figure 6: The photographs A, B, C1 represent the SEM images for 0V, 4V and 10V respectively. Nano cracks and smooth cracks are seen in A and B. C2 shows the marked portion of C1 where striations are present on the crack surface.

To see details of the micro-structure, scanning micrograph images of the cracked samples are taken using SEM,configuration no. QUO-35357-0614 funded by FIST-2, DST Government of India, at the Physics Department, Jadavpur University. SEM has been performed for samples dried under continuously applied voltages of 4, 6, 8, 10 V and also for samples dried without applying electric field. There are no


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 12 of 30

distinct differences in the films of Laponite gel dried with and without field. Some nano cracks can be seen in the films (Figure 6 A). For the sample dried under 10 V (Figure 6 C1), the crack surface has striations as shown in Hazra et al. [13], whereas below this voltage the cracks surfaces are smooth as shown in Figure 6 B. The striations (Figure 6 C2) are prominent where the crack is bending.

3

Results

When a Laponite drop is deposited on the perspex sheet as a sessile drop, with no imposed boundary, no cracks are formed. But when we deposit the drop within a boundary e.g. in a petri-dish, cracks form randomly. In our experiment, the circular electrode acts as the outer boundary and there is also a straight wire at the centre, so random cracks form even without applied electric field.

3.1

Drying under no electric field

There is some variation in the crack appearance time t0 , even under similar ambient conditions. Cracks appear after 274 min, 254 min, 263 min from the periphery in experiments shown in Figures 2 (A, B1, B2). The time of the appearance of the 1st crack is dependent on temperature and humidity. Two sets of experiments were done to see the pure desiccation effect, (i.e. when there is no electric field) on the Laponite droplet. The times required for the appearance of 1st crack are displayed in Table 1.


Page 13 of 30

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

3.2

Drying under continuously applied voltage V

We apply 4, 6, 8 and 10 V across the drop during drying. The central electrode is always positive and the outer is negative. A time interval of 2 min is allowed for the drop to spread uniformly, before the power supply is switched on. When we switch on the power supply, small bubbles are observed to form near both electrodes. After ∼ 5 min, the bubbles near the negative electrode disappear and after ∼ 1 hour the gel recedes slightly from the boundary forming a ring-shaped void (Figure 2 C2, C3). Under constant DC voltage, the time of appearance of 1st crack decreases with increasing V as shown in Figure 1 B. In all the four cases, the 1st crack appears from central positive electrode and proceeds towards the negative (outer) electrode. After several hours, Figure (2 C3), the Laponite gel separates into 5 to 6 disjoint pieces. In the present report we focus only on the time of appearance tc (V ) of the 1st crack for different continuously applied voltages. The time tc (V ) for 4, 6, 8, 10 V are 900, 318, 183, 88 s respectively. This data along with the case of no field, and the best fit exponential curve are shown in Figure 4 B. The data can be best fit by the expression t = t0 exp(−V /V0 ), where t0 = 267 min and the parameter V0 = 1.5V . The observations have been averaged over 3-6 trials.


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

3.3

Page 14 of 30

Crack appearance when field is switched off after τ

The time taken for cracks to appear texpt (τ, V ) when the field is switched off after τ s, is tabulated for various V and τ in Table 1. Obviously t0 > texpt (τ, V ) > tc (V ), for τ < tc 10V . Even at 10 V the results appear somewhat erratic, for example, the variation of ∆t with τ shows an increasing trend except for one data point in the 10 V result. The current here (Figure 4 A) increases first as a function of time. This is due to the larger and more copious bubbles formed. On bursting, each bubble creates a conducting path of fluid across the drop, which causes a momentary increase in current. After a certain time, when the bubbles disappear, the current falls as expected. But for the 10 V set, the cracks appear within the time when the current 25 ACS Paragon Plus Environment

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 26 of 30

is on the rise. Comparing with the earlier results of Khatun et al.[2] the following differences may be noted. Firstly, the time of appearance of cracks is in general much larger compared to Khatun et al. In particular in case when the field is switched off at τ . This may be due to the chemical reactions which occurred with the aluminium electrodes, in the earlier experiments providing more energy in addition to the electrical energy. Secondly, in absence of electric field (after τ ) cracks appear first from the periphery in the present experiment, whereas they appeared from the center in case of the experiment by Khatun et al. However the two experiments show identical scaling behaviour (Figure 9). The presence of memory in visco-elastic systems has been reported for various stimuli, such as mechanically vibrating or rotating the system [19]. However, such effects for electric fields are being observed and reported only recently. With applications of desiccation crack patterns coming up in nano-patterning, we may expect that memory effects will also be of practical use in producing ‘designer cracks’ [1, 20, 21] in future.

Acknowledgements Somasri Hazra is grateful to Jadavpur University, Alumni Association for financial support through a research scholarship. Authors gratefully acknowledge DST Government of India, for providing Scanning Electron Microscope,configuration no. QUO-35357-0614 funded by FIST-2, at the Physics Department, Jadavpur Univer-


Page 27 of 30

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

sity.

References [1] Goehring, L.; Nakahara, A.; Dutta, T.; Kitsunezaki, S.; Tarafdar, S. Desiccation Cracks and their Patterns. Wiley, VCH, Germany, 2015. [2] Khatun, T.; Dutta, T.; Tarafdar, S. Crack Formation under an Electric Field in Droplets of Laponite Gel: Memory effect and scaling relations. Langmuir, 2013, 29, 15535-15542. [3] Pauchard, L.; Elias, F.; Boltenhagen, P.; Cebers, A.; Bacri, J. C. When a crack is oriented by a magnetic field. Physical Review E, 2008, 77, 021402. [4] Das, S. Functional Fractional Calculus, 2nd edn, Springer-Verlag, Berlin, 2011. [5] Westerlund, S.; Ekstam, L. Capacitor Theory, IEEE Transactions on Dielectrics and Electrical Insulation, 1994, 1, 826-839. [6] Ramsay, J. D. F. Colloidal properties of synthetic hectorite clay dispersions:I. Rheology, J. Colloid and Interface Sci., 1986, 109, 441-447. [7] Cummins, H. Z. Liquid, glass, gel: the phases of Colloidal Laponite, J. NonCryst. Solids, 2007, 353, 3891-3905. [8] Website: http://www.laponite.com/faqs.asp [9] Ruzicka, B.; Zaccarelli, E. A fresh look at the laponite phase diagram, Soft Matter, 2011, 7, 1268. 27 ACS Paragon Plus Environment

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 28 of 30

[10] Negrete-Herrera, N.; Jean-Luc, P.; Bourgeat-Lami, E. Synthesis of polymer /laponite nanocomposite latex particles via emulsion polymerization using silylated and cation-exchanged laponite clay platelets. Progress in Solid State Chemistry, 2006, 34, 121-137. [11] Tawari, S. L.; Kochi, D. L.; Cohen, C. Electrical double-layer effects on the brownian diffusivity and aggregation rate of laponite clay particles. J. Colloid Interf. Sci., 2001, 240, 5466. [12] Martin, C.; Pignon, F.; Jean-Michel, P.; Magnin, A.; Lindner, P.; Cabane, B. Dissociation of thixotropic clay gels. Phys. Rev. E, 2002, 66, 021401. [13] Hazra, S.; Sircar, S.; Khatun, T.; Choudhury, M. D.; Giri, A.; Karmakar, S.; Dutta, T.; Das, S.; Tarafdar, S. Unstable crack propagation in LAPONITE gels:selection of a sinusoidal mode in an electric field. RSC Adv., 2016, 6, 64297. [14] Dijkstra, M.; Hansen, J. P.; Madden, P. A. Gelation of a Clay Colloid Suspension. Phys. Rev. Lett., 1995, 75, 2236. [15] Mourchid, A.; Delville, A.; Lambard, J.; LeColier, E.; Levitz, P. Phase Diagram of Colloidal Dispersions of Anisotropic Charged Particles: Equilibrium Properties, Structure, and Rheology of Laponite Suspensions. Langmuir, 1995, 11, 1942.


Page 29 of 30

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

[16] Odriozola, G.; Romero-Bastida, M.; Guevara-Rodriguez, F. de J. Brownian dynamics simulations of Laponite colloid suspensions. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2004, 70 (2), 021405. [17] Kuenen, J. C.; Meijer, G. M. Measurement of dielectric absorption of capacitors and analysis of its effects on VCOs. IEEE Transactions on Instrumentation and Measurement, 1996, 45, 89-97. [18] Du, M.; Wang, Z.; Hu, H. Measuring memory with the order of fractional derivative. Scientific Reports, 2013, 3, 3431. [19] Nakahara, A.; Matsuo, Y. Imprinting memory into paste and its visual- ization as crack patterns in drying process. J. Phys. Soc. Jpn., 2005, 74, 1362-1365. [20] Kumar, A.; Kulkarni, G. U. Evaluating conducting network based transparent electrodes from geometrical considerations. Journal Of Applied Physics, 2016, 119, 015102. [21] Rao, K. D. M.; Gupta, R.; Kulkarni, G. U. Transparent Conducting Electrodes Using a Spontaneously Formed Crackle Network as Template. Adv. Mater. Interfaces, 2014, 1, 1400090.


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

Graphic for TOC


Page 30 of 30

Memory of Electric Field in Laponite and How It Affects Crack Formation

Recommend Documents