VOLUME 84, NUMBER 16 PHYSICAL REVIEW LETTERS 17 APRIL 2000 Gas-Liquid Transition in a Two-Dimensional System of Millimeter-Sized Like-Charged Metal Balls B. V. R. Tata, 1,2 P. V. Rajamani, 1,2 J. Chakrabarti, 1,2 Alex Nikolov, 1 and D.T. Wasan 1, * 1 Department of Chemical Engineering, Illinois Institute of Technology, Chicago, Illinois 60616 1 Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamil Nadu, India (Received 13 July 1999) Metal balls with a diameter of 1.59 mm, gently rubbed against a dielectric surface using a shaker, are seen to spontaneously exhibit a two-dimensional liquidlike order with macroscopic dimensions, viz., interball distances of several millimeters. This liquidlike order transforms to a gaslike order through coexistence upon decreasing the area fraction of the balls. The measured pair interaction of like-charged balls surprisingly exhibits a long-range attractive term analogous to that in charged colloids. PACS numbers: 61.20.Qg, 64.70.Fx, 82.70.Dd Electrostatic interactions play a crucial role in many chemical, physical, and biological processes [1,2]. Such interactions have been used with much success recently in the organization of nanoscale materials: deposition of col- loidal particles on surfaces with patterned surface charge [3], Langmuir-Blodgett assemblies of alternating layers of polyelectrolytes with opposite charges [4], and in making photonic band gap materials [5]. Electrostatically stabi- lized polymer latex particles have been found very useful for some of these applied studies as well as for understand- ing the ordering at micrometer length scales due to the easy tunability of the interparticle interaction among the particles. Here we report a novel electrostatically interact- ing two-dimensional (2D) system of macroscopic length scales, consisting of millimeter-sized metal balls charged by gentle rubbing against a dielectric surface. Structural ordering is an interesting cooperative phe- nomenon that occurs mainly due to the competition be- tween the interaction energy (U) and thermal energy k B T , k B being the Boltzmann constant and T the temperature, of a system [6]. Atomic systems order with length scales of angstroms, whereas ordering at several micrometer length scales [2] has been realized using charged colloidal particles of submicron size. Systems of charged particles of larger size offer convenient length and time scales [2]. These convenient length scales ( micrometers) result in the elastic constants being about 10–12 orders of magnitude less than conventional solids’, which has been exploited for the investigation of many exotic nonequi- librium phenomena [7]. Given this background, it is of interest to ask an intriguing question: Is it possible to have an ordering at macroscopic length scales using macrosized particles? In fact, Bragg and Nye have shown that ordering of millimeter-sized bubbles [8] mimics the crystalline order in metals. Recently there have been reports of crystallinelike order by large particles of granular media [9]. Since these particles are of hard-sphere type and temperature has no role to play in ordering, it is rather difficult to achieve vari- ous structural orders in granular systems. However if the interaction between two macroparticles is strong enough and tunable it might be possible to have different struc- tural orders in an assembly of such particles. Motivated by this, we make an attempt to bring out ordering in a sys- tem of millimeter-sized charged balls. We report in this Letter the change in the ordering behavior as a function of area fraction f of such large charged balls. The extracted pair potential UR at very low values of f shows the ex- istence of a long-range attraction between the like-charged balls and its origin is understood by performing ab initio Monte Carlo (MC) simulations on a scaled down system. We prepare a novel 2D system by spreading a monolayer of a few thousand stainless steel balls (Thompson preci- sion ball company, USA) of diameter d  1.59 mm on the bottom surface of a plug sealed polystyrene box (Corning coster corporation, USA) of size, 16.5 3 13.5 3 4.5 cm 3 (Fig. 1A). The metal balls are allowed to rub gently against the bottom surface of the box using a reciprocal shaker at a frequency n of 1.5 Hz for about 5 to 8 min. Upon rubbing under low humidity (,50%) conditions, the balls acquire positive charge leaving the countercharges on the polystyrene surface (Fig. 1B). In order to charge the entire dielectric surface and the metal balls as uniformly as possible, the balls are brought together by tilting the box and then spread again several times. We estimate the charge Ze, Z being the charge number and e the electronic charge, on the ball by gently tilting the box using a go- niometer to an angle of 15 ± , where the like-charged balls touch due to the gravitational force balancing the Coulom- bic repulsion. The charge on the balls is estimated to be of the order of 10 9 e and is seen to remain the same even on further shaking at the same or slightly higher frequencies. Besides charging the balls, the horizontal shaking at a constant frequency serves another important purpose, viz., it creates motion of the balls only on the polystyrene sur- face (xy plane) and enables them to explore the configu- ration space. The friction between the ball and the surface sets the lower limit in the shaking frequency n for moving the balls on the surface which determines the energy scale, viz., G  mv 2 d 2 2, where m is the mass of the metal ball 3626 0031-9007 00  84(16)  3626(4)$15.00 © 2000 The American Physical Society