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John Prausnitz
UC Berkeley and Lawrence Berkeley National Laboratory
Jianzhong Wu
Lawrence Berkeley National Laboratory
Dusan Bratko, Harvey Blanch
UC Berkeley


Wu, J., D. Bratko, H.W. Blanch and J.M. Prausnitz. 2000. Effect of Three-Body Forces on the Phase Behavior of Charged Colloids. J. Chem. Phys. 113(8): 3360-3365.

Wu, J., D. Bratko, H.W. Blanch and J.M. Prausnitz. 2000. Interaction between Oppositely Charged Micelles and Globular Proteins. Phys. Rev. E 62(4): in press.

Resolving a Mysterious Particle Attraction in Colloids

H igh school students are taught that, when two electrically charged objects are brought together, a positively charged object will be attracted to a negatively charged object, while two objects with the same charge will repel one another. However, in some everyday materials, it turns out that particles with the same charge can be attracted to one another. Jianzhong Wu, a postdoctoral researcher in John Prausnitz's group at Lawrence Berkeley National Laboratory, is using NPACI computers to understand why large charged molecules in colloids--mixtures of large and small charged particles in a water solution--are attracted to other molecules with the same charge. The findings may help engineers create improved materials and industrial processes.

Figure 1. An Attractive Force
The dip below zero in the total force curve shows that, at small separations, two similarly charged macroions will experience a small attraction (negative force). The graph shows average force (in kT/lB, where k is the Boltzmann constant, T is temperature and lB is Bjerrum length, which represents the separation between two electrons with the electrostatic energy equal to kT) between identical negatively charged macroions in a 2:2-electrolyte solution as a function of macroion separation (in units of macroion diameter). The diameter of macroions is 20 Ã…, while that for the smaller ions is 4 Ã…. The electrolyte concentration is 0.125 M, and lB is 7.14 Ã….

Colloids include materials as mundane as ink, paint, and soapy water, but are also used for high-tech applications in protein crystallography, industrial coatings, and even nanotechnology construction. In a general sense, colloids comprise two types of particles--large and small charged particles (ions)--suspended in a solvent such as water. The large ions, called macroions to distinguish them from their smaller cousins, are responsible for most of the useful and interesting properties of the colloidal material.


After attending Dusan Bratko's graduate course at UC Berkeley on molecular simulation for chemical engineering, Wu encountered several articles describing a peculiar experimental finding about the behavior of macroions in colloids, namely that like-charged macroions were attracted to one another. Because classical theories about interaction between colloidal particles could not explain this counterintuitive result, Wu initiated a class project that he has continued to pursue as a postdoctoral fellow in Prausnitz's group in the Chemical Sciences Division at Lawrence Berkeley National Laboratory.

"This study of colloids forms part of our research to interpret and correlate thermodynamic properties of a variety of mixtures for process and product design in the chemical and related industries, including biotechnology," said Prausnitz, also a professor in the Department of Chemical Engineering at UC Berkeley. "Toward that end, we obtain experimental data, perform Monte Carlo molecular simulations, and develop theoretical models of fluids and solids. Such insights can then be applied to industrial-scale chemical engineering design."

Instead of trying to examine every molecule in a colloid, Wu and the group are studying colloids through a subsystem containing two macroions and hundreds of smaller ions. The macroions are five times the size of the smaller ions, a limitation of the computational power available. In some real colloids, such as solutions of proteins used in crystallography, the macroions can be 100 times the size of the smaller ions. To keep the computation manageable, the surrounding water molecules of the solvent are treated as a continuum.

"We are calculating the phase diagram (liquid-liquid and solid-liquid) of the colloid and solvent. For this calculation we need quantitative information on the forces of attraction and repulsion between two macroions," Wu said. The group is using NPACI's Cray T3E systems at the University of Texas and SDSC, as well as the T3E at the National Energy Research Scientific Computing Center. The work, funded by the Department of Energy's Basic Energy Sciences program, has been under way for two years. "The phase diagram shows the structure of the material, which is crucial for the performance and properties of the material. We cannot use ab initio methods because we cannot afford to calculate all the interactions between the colloidal molecules."


Interactions among colloidal particles have been studied for more than 50 years. For most of that time, colloids have been seen as complex multi-body systems described by highly approximate relations from classical physics. However, the finding of like-charged macroions being attracted to one another cannot be explained by the conventional theories. Previous computational studies of colloids by other groups have focused on the multi-body interactions of many macroions.

"In such an approach, you calculate only the average probability distribution of the macroion behavior," Wu said. "In ours, we have to calculate the forces directly, including both the interactions between the macroions and that due to the smaller ions." In a sense, the computations by Prausnitz's group look at the problem at much higher resolution, allowing them to isolate the behavior of two macroions (Figure 1).

To calculate the potential of mean force, or the strength of the attraction, between two macroions in such an environment, the group devised a novel simulation method based on a Monte Carlo algorithm, which uses statistical sampling to improve the precision of a calculation. The first component of the program calculates the collisions between particles as if they were hard spheres, while the second component computes the electrostatic interactions between the particles.

"Our method for sampling hard-sphere collision force saves computing time by at least an order of magnitude relative to conventional methods," Wu said. "The Ewald-sum method [for calculating electrostatic interactions] is a well established algorithm, but our modification has improved its efficiency significantly."

To calculate the attractive force between the macroions as a function of distance and to obtain the phase diagram, Wu must calculate the potential of mean force between the two macroions, for a given set of solution conditions, at seven to 10 distances between the macroions. Each calculation takes about a week on 10 T3E processors, which produces one point on the phase diagram. Further calculations must be made for variations in salt concentration, ion valence, and macroion size. To investigate the contributions of factors such as ion concentration and macroion charge, at least 50 different computations are required.

Figure 2. Small Ion Distribution
Top: Distribution of divalent positively charged ions around two isolated, negatively charged macroions, with peaks showing the ions clustering around the macroions. Bottom: Distribution around two neutral hard spheres of the same size as the macroions. The lack of peaks indicates an even distribution throughout the solvent. The diameter of the small ions is 4 Ã… and the macroions 20 Ã…; the electrolyte concentration is 0.125 M. The x-y plane reflects the distance from the macroions.


The project's initial success was to confirm and provide a theoretical explanation for the unexpected attraction between two macroions that had been demonstrated in experiments. According to Wu's computations, it turns out that the smaller ions, and more specifically their movements, play a major role in the attraction between the macroions.

"The fluctuation of the charge distribution by the small ions causes the attraction between the macroions," Wu said. "The movement of the charge creates an attractive force. It's similar to the attraction between two neutral argon atoms." In argon atoms, the constant movement of the electrons around the nucleus parallels the role of the smaller ions in a colloid. The attraction is greatest at intermediate concentrations of the smaller ions (Figure 2).

Wu has also examined the potential of mean force between oppositely charged macroions. As expected, such oppositely charged macroions are always attracted to one another. However, in addition to classical electrostatic attraction, part of the attraction arises from the hard-sphere collisions with the small ions; at some conditions, the macroions can weakly repel each other at close range.

The next step for Prausnitz's group is to study the multi-body interactions between three macroions and identify how the smaller ions contribute to the structure of the phase diagram. In addition, they are working to extend their model to investigate how the distribution of the electrical charge on the macroion surface affects the behavior. Introducing this complexity makes the calculations much more demanding.

A better understanding of the behavior of macroions could lead to improved industrial processes, more effective materials, and even new classes of applications. Such materials might include paints with better stability or solvents with greater cleaning ability. (The active molecules in soaps, for example, cluster together into colloidal particles called micelles.) Colloids may also one day be used in nanotechnology applications to build structures such as tiny crystals or advanced membranes. Colloidal crystals have potential application as photonic crystals for improved light emission and for photon-based communication systems.

The group's ultimate goal is to contribute to a better theoretical model, which will be tested against simulation results for various conditions, to describe the interaction of macroions in colloids. The interaction, in turn, affects the properties of the material, Wu said. Engineers need an accurate theoretical model to predict whether the characteristics of a particular colloidal composition will lead to the desired property. With accurate predictions, engineers can much more quickly and efficiently design and develop more advanced materials and processes. --DH *