Jan Forsman

Perspective: Coulomb fluids—Weak coupling, strong coupling, in between and beyond

We present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are introduced for a (primitive) counterion-only system in the presence of macroscopic, uniformly charged boundaries, where they can be derived systematically. Later we show how this formalism can be generalized to the cases with additional characteristic length scales that introduce new coupling parameters into the problem. These cases most notably include asymmetric ionic mixtures with mono- and multivalent ions that couple differently to charged surfaces, ions with internal charge (multipolar) structure and finite static polarizability, where weak and strong coupling limits can be constructed by analogy with the counterion-only case and lead to important new insights into their properties that cannot be derived by any other means.

A Classical Density Functional Theory of Ionic Liquids

We present a simple, classical density functional approach to the study of simple models of room temperature ionic liquids. Dispersion attractions as well as ion correlation effects and excluded volume packing are taken into account. The oligomeric structure, common to many ionic liquid molecules, is handled by a polymer density functional treatment. The theory is evaluated by comparisons with simulations, with an emphasis on the differential capacitance, an experimentally measurable quantity of significant practical interest.

Weak- and strong-coupling electrostatic interactions between asymmetrically charged planar surfaces.

We compare weak- and strong-coupling theory of counterion-mediated electrostatic interactions between two asymmetrically charged plates with extensive Monte Carlo simulations. Analytical results in both weak- and strong-coupling limits compare excellently with simulations in their respective regimes of validity. The system shows a surprisingly rich structure in terms of interactions between the surfaces as well as fundamental qualitative differences in behavior in the weak- and the strong-coupling limits.

Monte Carlo simulations of hydrophobic interactions: A test particle approach

By use of the Widom particle insertion method we have evaluated the hydrophobic force and free energy of solvation for both two Lennard‐Jones as well as two hard sphere particles in water as a function of their separation. The entropy, energy, and free energy of a single hydrophobic particle were also calculated. By simulating water confined between two hard walls, we were able to obtain the free energy of interaction between a small nonpolar particle and a nonpolar wall. The results show ‘‘contact separation’’ to be the most stable configuration in all cases studied, but the free energy barrier of separation for two nonpolar particles is rather small, of the order of kT. For a nonpolar solute in contact with a hydrophobic wall the barrier is significantly larger, of the order of 4 kT. The effect of system size and geometry on the free energy was investigated. The insertion method produces satisfactory accuracy, provided that the inserted particles are not too large, that a sufficient number of uncorrelat...

Dressed counterions: Strong electrostatic coupling in the presence of salt

We reformulate the theory of strong electrostatic coupling in order to describe an asymmetric electrolyte solution of monovalent salt ions and polyvalent counterions using field-theoretical techniques and Monte Carlo simulations. The theory is based on an asymmetric treatment of the different components of the electrolyte solution. The weak coupling Debye-Hückel approach is used in order to describe the monovalent salt ions while a strong coupling approach is used to tackle the polyvalent counterions. This combined weak-strong coupling approach effectively leads to dressed interactions between polyvalent counterions and thus directly affects the correlation attraction mediated by polyvalent counterions between like-charged objects. The general theory is specifically applied to a system composed of two uniformly charged plane-parallel surfaces in the presence of salt and polyvalent counterions. In the strong coupling limit for polyvalent counterions, the comparison with Monte Carlo simulations shows good agreement for large enough values of the electrostatic coupling parameter. We delineate two limiting laws that in fact encompass all the Monte Carlo data.

Anisotropic Interactions in Protein Mixtures: Self Assembly and Phase Behavior in Aqueous Solution

Recent experimental studies show that oppositely charged proteins can self-assemble to form seemingly stable microspheres in aqueous salt solutions. We here use parallel tempering Monte Carlo simulations to study protein phase separation of lysozyme/α-lactalbumin mixtures and show that anisotropic electrostatic interactions are important for driving protein self-assembly. In both dilute and concentrated protein phases, the proteins strongly align according to their charge distribution. While this alignment can be greatly diminished by a single point mutation, phase separation is completely suppressed when neglecting electrostatic anisotropy. The results highlight the importance of subtle electrostatic interactions even in crowded biomolecular environments where other short-ranged forces are often thought to dominate.

Attraction between neutral dielectrics mediated by multivalent ions in an asymmetric ionic fluid

We study the interaction between two neutral plane-parallel dielectric bodies in the presence of a highly asymmetric ionic fluid, containing multivalent as well as monovalent (salt) ions. Image charge interactions, due to dielectric discontinuities at the boundaries, as well as effects from ion confinement in the slit region between the surfaces are taken fully into account, leading to image-generated depletion attraction, ion correlation attraction, and steric-like repulsive interactions. We investigate these effects by employing a combination of Monte Carlo simulation methods, including explicit-ion simulations (where all electrostatic interactions are simulated explicitly) and implicit-ion simulations (where monovalent ions are replaced by an effective screened electrostatic potential between multivalent ions), as well as an approximate analytical theory. The latter incorporates strong ion-image charge correlations, which develop in the presence of high valency ions in the mixture. We show that the implicit-ion simulations and the proposed analytical theory can describe the explicit simulation results on a qualitative level, while excellent quantitative agreement can be obtained for sufficiently large monovalent salt concentrations. The resultant attractive interaction between the neutral surfaces is shown to be significant, as compared with the usual van der Waals interactions between semi-infinite dielectrics, and can thus play an important role at the nano scale.

Evaluating Force Fields for the Computational Prediction of Ionized Arginine and Lysine Side-Chains Partitioning into Lipid Bilayers and Octanol

Abundant peptides and proteins containing arginine (Arg) and lysine (Lys) amino acids can apparently permeate cell membranes with ease. However, the mechanisms by which these peptides and proteins succeed in traversing the free energy barrier imposed by cell membranes remain largely unestablished. Precise thermodynamic studies (both theoretical and experimental) on the interactions of Arg and Lys residues with model lipid bilayers can provide valuable clues to the efficacy of these cationic peptides and proteins. We have carried out molecular dynamics simulations to calculate the interactions of ionized Arg and Lys side-chains with the zwitterionic 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipid bilayer for 10 widely used lipid/protein force fields: CHARMM36/CHARMM36, SLIPID/AMBER99SB-ILDN, OPLS-AA/OPLS-AA, Berger/OPLS-AA, Berger/GROMOS87, Berger/GROMOS53A6, GROMOS53A6/GROMOS53A6, nonpolarizable MARTINI, polarizable MARTINI, and BMW MARTINI. We performed umbrella sampling simulations to obtain the potential of mean force for Arg and Lys side-chains partitioning from water to the bilayer interior. We found significant differences between the force fields, both for the interactions between side-chains and bilayer surface, as well as the free energy cost for placing the side-chain at the center of the bilayer. These simulation results were compared with the Wimley-White interfacial scale. We also calculated the free energy cost for transferring ionized Arg and Lys side-chains from water to both dry and wet octanol. Our simulations reveal rapid diffusion of water molecules into octanol whereby the equilibrium mole fraction of water in the wet octanol phase was ∼25%. Surprisingly, our free energy calculations found that the high water content in wet octanol lowered the water-to-octanol partitioning free energies for cationic residues by only 0.6 to 0.7 kcal/mol.

Polyelectrolyte adsorption on solid surfaces: theoretical predictions and experimental measurements.

This work utilizes a combination of theory and experiments to explore the adsorption of two different cationic polyelectrolytes onto oppositely charged silica surfaces at pH 9. Both polymers, poly(diallyldimethylammonium chloride), PDADMAC, and poly(4-vinyl N-methylpyridinium iodide), PVNP, are highly charged and highly soluble in water. Another important aspect is that a silica surface carries a relatively high surface charge density at this pH level. This means that we have specifically chosen to investigate adsorption under conditions where electrostatics can be expected to dominate the interactions. Of specific focus in this work is the response of the adsorption to the addition of simple salt (i.e., a process where electrostatics is gradually screened out). Theoretical predictions from a recently developed correlation-corrected classical density functional theory for polyelectrolytes are evaluated by direct quantitative comparisons with corresponding experimental data, as obtained by ellipsometry measurements. We find that, at low concentrations of simple salt, the adsorption increases with ionic strength, reaching a maximum at intermediate levels (about 200 mM). The adsorption then drops but retains a finite level even at very high salt concentrations, indicating the presence of nonelectrostatic contributions to the adsorption. In the theoretical treatment, the strength of this relatively modest but otherwise largely unknown nonelectrostatic surface affinity was estimated by matching predicted and experimental slopes of adsorption curves at high ionic strength. Given these estimates for the nonelectrostatic part, experimental adsorption data are essentially captured with quantitative accuracy by the classical density functional theory.

Polyelectrolyte adsorption: electrostatic mechanisms and nonmonotonic responses to salt addition.

The main question addressed in this work is as follows: Under pure electrosorption conditions, that is, disregarding nonelectrostatic effects, how does the net adsorption of a polyelectrolyte at an oppositely charged surface respond to the addition of simple salt? Previous simulations and mean-field calculations have suggested that the polymers will desorb. However, we will demonstrate that an increased adsorption also is possible, even for pure electrosorption, at low and intermediate levels of salt. As this is a correlation-driven effect, mean field approaches will fail to capture it. Using simulations, one will in general need to simulate large systems and relatively long polymers. Also important is the presence of a proper bulk solution, with a finite and well-defined polyelectrolyte concentration. We have performed a theoretical study of polyelectrolyte adsorption, assuming screened Coulomb interactions between monomers; that is, the salt is implicit. This work focuses on the effects from ionic screening and polymer length. Specifically, the adsorption at a weakly charged colloidal particle, with a diameter of 200 nm, is monitored for various salt concentrations, in the presence of highly charged chains. Using simulations, we investigate polymers with two different degrees of polymerization: 40 and 160, respectively. These simulations are complemented by predictions from classical polymer density functional theory, utilizing a recently developed correlation-correction (Forsman, J.; Nordholm, S. Langmuir, in press). The agreement with corresponding simulations is semiquantitative, and because the calculations run many orders of magnitude faster than the simulations, longer and more realistic polymers could be studied with this approach. However, switching off the correlation-correction leads to a mean-field theory, which fails to even qualitatively reproduce the simulated response to screening.