Colloquium: The physics of charge inversion in chemical and biological systems A. Yu. Grosberg, T. T. Nguyen, and B. I. Shklovskii Department of Physics, University of Minnesota, Minneapolis, Minnesota 55455 (Published 19 April 2002) The authors review recent advances in the physics of strongly interacting charged systems functioning in water at room temperature. In these systems, many phenomena go beyond the framework of mean-field theories, whether linear Debye-Hu ¨ ckel or nonlinear Poisson-Boltzmann, culminating in charge inversion—a counterintuitive phenomenon in which a strongly charged particle, called a macroion, binds so many counterions that its net charge changes sign. The review discusses the universal theory of charge inversion based on the idea of a strongly correlated liquid of adsorbed counterions, similar to a Wigner crystal. This theory has a vast array of applications, particularly in biology and chemistry; for example, in the presence of positive multivalent ions (e.g., polycations), the DNA double helix acquires a net positive charge and drifts as a positive particle in an electric field. This simplifies DNA uptake by the cell as needed for gene therapy, because the cell membrane is negatively charged. Analogies of charge inversion to other fields of physics are also discussed. CONTENTS I. Introduction 329 II. Historical Remarks: Mean-Field Theories 331 III. Strongly Correlated Liquid of Multivalent Ions 332 IV. Correlation-Induced Charge Inversion 333 V. Enhancement of Charge Inversion by a Monovalent Salt 334 VI. Screening of a Charged Plane By Polyelectrolytes 335 VII. Polyelectrolytes Wrapping Around Charged Particles 336 VIII. Multilayer Adsorption 337 IX. Correlation-Induced Attraction of Like Charges 338 X. Experimental Evidence of Charge Inversion 339 XI. Correlations ‘‘in Sheep’s Clothing’’ 341 XII. Charge Inversion in a Broader Physics Context 342 XIII. Conclusions and Outlook 343 Acknowledgments 343 References 343 I. INTRODUCTION Molecular biological machinery functions in water at around room temperature. For a physicist, this very lim- ited temperature range contrasts unfavorably with the richness of low-temperature physics, where one can change the temperature and scan vastly different energy scales in an orderly manner. In this Colloquium, we re- view the recently developed understanding of highly charged molecular systems in which Coulomb interac- tions are so strong that we are effectively in the realm of low-temperature physics. More specifically, imagine a problem in which one big ion, called a macroion, is screened by much smaller but still multivalent ions, each with a large charge Ze , where e is the proton charge; for brevity, we call them Z -ions. A variety of macroions are of importance in chemistry and biology, ranging from the charged surface of mica or charged solid particles to charged lipid membranes, col- loids, DNA, actin, and even cells and viruses. Multiva- lent metal ions, charged micelles, dendrimers, short or long polyelectrolytes including DNA—to name but a few—can play the role of the screening Z -ions. The central idea of this Colloquium is that of correla- tions: due to strong interactions with the macroion sur- face and with each other, screening Z -ions do not posi- tion themselves randomly in three-dimensional space, but form a strongly correlated liquid on the surface of the macroion. Moreover, in terms of short-range order, this liquid is reminiscent of a Wigner crystal, as Fig. 1 depicts. Depending on the system geometry and other circum- stances, correlations between screening ions may appear in many different ways. To create some simple images in the reader’s mind, it is useful to begin with a few ex- amples. One example is that shown in Fig. 1, which could be the surface, say, of a latex particle screened by some compact ions. With a modest leap of the imagina- tion, we could also envision the same picture as the sur- face of a DNA double helix screened by multivalent counterions, such as spermine with Z =4 (Bloomfield, 1996). Here, we imagine DNA as a long, thick cylinder, of diameter 2 nm and charge -e per 1.7 nm along the cylinder, or, in other words, with a huge negative surface charge density -0.9e /nm 2 . We study correlations be- tween pointlike Z -ions in Secs. III – V. One obvious problem with the model in Fig. 1 is that it ignores the FIG. 1. Strongly correlated liquid—almost a Wigner crystal—of Z-ions on the oppositely charged macroion surface. The figure is characteristic in showing the degree to which we are willing to ignore the microscopic details. REVIEWS OF MODERN PHYSICS, VOLUME 74, APRIL 2002 0034-6861/2002/74(2)/329(17)/$35.00 ©2002 The American Physical Society 329