PHYSICAL REVIEW E 86, 016114 (2012) Electric-field-induced crack patterns: Experiments and simulation Tajkera Khatun, 1 Moutushi Dutta Choudhury, 1 Tapati Dutta, 2 and Sujata Tarafdar 1 1 Condensed Matter Physics Research Centre, Physics Department, Jadavpur University, Kolkata 700032, India 2 Physics Department, St. Xavier’s College, Kolkata 700016, India (Received 25 February 2012; revised manuscript received 28 May 2012; published 30 July 2012) We report a study of crack patterns formed in laponite gel drying in an electric field. The sample dries in a circular petri dish and the field is radial, acting inward or outward. A system of radial cracks forms in the setup with the center terminal positive, while predominantly cross-radial cracks form when the center is at a negative potential. The laponite accumulates near the negative terminal making the layer thicker at this end. A spring model on a square lattice is used to simulate the desiccation crack formation, with an additional radial force acting due to the electric field. With the radial force acting outward, radial cracks form and for the reversed field cross-radial cracks form. This conforms to the observation that laponite platelets become effectively positive due to overcharging and are attracted towards the negative terminal. DOI: 10.1103/PhysRevE.86.016114 PACS number(s): 62.20.mt I. INTRODUCTION The patterns created by the network of desiccation cracks formed under different conditions has been a subject of research for a long time [1–3] and is still an active field [4–6]. Of particular interest are typical reproducible patterns formed when certain external perturbations are imposed: for example, the memory of mechanical vibration or rotation retained by pastes—the “Nakahara effect”—producing circular or linear cracks [7,8], the patterns produced in laponite gels under an electric field [9,10] and magnetic field [11], and miniature columnar joints grown in the laboratory by desiccating starch [12]. Other interesting papers have reported on spiral cracks [13] and cracks due to directional drying [14] and maturation of crack patterns [15]. In the present work we report further studies on des- iccation crack patterns formed by clay gels subjected to a radial electric field during drying. We show that typical crack patterns which depend on the field direction and strength [9,10] can be reproduced by a simple model using a spring network. This model has been applied earlier to explain crack patterns in composites [16] and peeling effects [17]. The experiments show that in radial geometry, when an electric field is directed outward from the center, radial cracks are formed, whereas when the field is directed inward, cross- radial cracks are formed. Our simulation algorithm is very sim- ple, based principally on symmetry considerations. With the assumption of an electric field strength following a cylindrical Laplacian potential distribution, we find that the experimental observations are reproduced quite well. We thus show that the complex environment of charged laponite macroions together with counterions and water molecule dipoles can be repre- sented simply by an effective radial force on the clay particles during drying. The present observations lead us to infer that laponite particles are overcharged by Al 3+ ions entering from the Al anode and become effectively positively charged. Such effects are commonly found in colloids under similar conditions [18,19]. II. EXPERIMENTS A. Experimental method and setup In the present experiments 2.5 g of laponite (Rockwood additives) is mixed with 40 ml of distilled water. The mixture is stirred and poured in circular petri dishes of 10 cm diameter and allowed to dry. The thick suspension just before formation of the gel is mildly alkaline with a pH of 9.5. Two electrodes constructed from aluminum foil were fitted to the petri dishes. One electrode is in the form of a thin rod placed at the center of the dish and the counterelectrode consists of an aluminum strip placed along the edge of the petri dish in the form of a short cylinder. A static field is applied from a constant voltage power supply, between the two electrodes. For comparison we dry a set of samples in an identical arrangement but without the applied voltage. We refer to the setup with central electrode positive as CP and the central negative as CN. In the present set of experiments the voltage is 120 V. Figure 1 shows a schematic diagram of the experimental setup in radial geometry. B. Experimental results Figures 2 and 3 show respectively the experimental results with the two different field directions. In the CP setup, cracks always start from the center and proceed towards the periphery. For CN, on the other hand, some very small cracks appear at the outer boundary of the petri dish and develop radially inwards, but the dominant feature is a system of cross-radial cracks concentric with the center of the setup. In earlier reports [9,10] the cross-radial cracks were supposed to be due to naturally appearing stochastic disorder. However, on carefully repeating the experiment several times, we find that the cross-radial cracks are a typical feature of this setup, with the negative electrode at the center. Our simulation algorithm also reproduces this observation. We observe that the thickness of the laponite layer near the outer periphery in CP configuration is much greater than it is nearer the center after the sample is exposed to the field for one or two days. This is shown in Fig. 4. It is to be noted that initial gel solidification occurs within a few minutes 016114-1 1539-3755/2012/86(1)/016114(8) ©2012 American Physical Society