Like-charged macroions in aqueous electrolyte solution can attract each other because of the presence of inter- and/or intramolecular correlations. Poisson-Boltzmann theory is able to predict attractive interactions if the spatially extended structure (which reflects the presence of intramolecular correlations) of the mobile ions in the electrolyte is accounted for. We demonstrate this for the case of divalent, mobile ions where each ion consists of two individual charges separated by a fixed distance. Variational theory applied to this symmetric 2:2 electrolyte of rodlike ions leads to an integro-differential equation, valid for arbitrary rod length. Numerical solutions reveal the existence of a critical rod length above which electrostatic attraction starts to emerge. This electrostatic attraction is distinct from nonelectrostatic depletion forces. Analysis of the orientational distribution functions suggests a bridging mechanism of the rodlike ions to hold the two macroions together. For sufficiently large rod length, we also observe "overcharging", that is, an over-compensation of the macroion charges by the diffuse layer of mobile rodlike ions. Our results emphasize the importance of the often rodlike internal structure that condensing agents such as polyamines, peptides, or polymer segments exhibit. The results were compared with Monte Carlo simulations.

It is well-known that the addition of salts influences the properties of proteins in solution. The essential nature of this phenomenon is far from being fully understood, partly due to the absence of the relevant thermodynamic information. To help fill this gap, in this work isothermal titration calorimetry (ITC) was employed to study the ion-lysozyme association in aqueous buffer solutions at pH = 4.0. ITC curves measured for NaCl, NaBr, NaI, NaNO3, NaSCN, KCl, CaCl2, and BaCl2 salts at three different temperatures were described by a model assuming two sets of independent binding sites on the lysozyme. The resulting thermodynamic parameters of binding of anions (counterions) to the first class of sites (N approximately 7) indicate that the binding constant (K approximately 102 M-1) increases in the order Cl- < Br- < I- < NO3- < SCN-. The anion-lysozyme association is entropy driven, accompanied by a small favorable enthalpy contribution and a positive change in heat capacity. It seems that the entropy and heat capacity increase is due to the water released upon binding, while the net exothermic effect originates from the anion-NH3+ pair formation. Moreover, the results reveal that the nature of the cation has little effect on the thermodynamics of the anion-lysozyme association under the given experimental conditions. Taken together, it seems that the observed thermodynamics of association is a result of a combination of both electrostatic and short-range interactions. The anion ordering reflects the strength of water mediated interactions between anions and lysozyme.

We consider the interaction between two equally charged surfaces in an electrolyte solution composed of long divalent rigid rod-like counterions of arbitrary length. Further, we study the influence of orientational ordering of rigid rod-like counterions on the interaction between charged surfaces. Density functional theory is introduced, where the spatial distribution of charge within the divalent rod-like counterions is represented by two effective charges at a fixed distance. The result of variational procedure gives an integral differential equation for the electrostatic potential which was solved numerically. From the electrostatic potential and the concentration of counterions, the free energy of two charged surfaces interacting in a solution of rod-like counterions is calculated. For large surface charge densities and for long enough divalent rod-like counterions the minimum of the free energy is obtained at a distance between the surfaces which equals the counterion length. This indicates that a bridging mechanism might be responsible for the attraction between like-charged surfaces. The analysis of the orientational distribution function confirms that, at the minimum of the free energy, the rod-like counterions are oriented perpendicularly and thus connect the like-charged surfaces. Finally, canonical Monte-Carlo simulations confirm the theoretical calculations of the osmotic pressure between like-charged surfaces for long enough rod-like counterions.

The solubility of aqueous solutions of lysozyme in the presence of polyethylene glycol and various alkaline salts was studied experimentally. The protein-electrolyte mixture was titrated with polyethylene glycol, and when precipitation of the protein occurred, a strong increase of the absorbance at 340 nm was observed. The solubility data were obtained as a function of experimental variables such as protein and electrolyte concentrations, electrolyte type, degree of polymerization of polyethylene glycol, and pH of the solution; the last defines the net charge of the lysozyme. The results indicate that the solubility of lysozyme decreases with the addition of polyethylene glycol; the solubility is lower for a polyethylene glycol with a higher degree of polymerization. Further, the logarithm of the protein solubility is a linear function of the polyethylene glycol concentration. The process is reversible and the protein remains in its native form. An increase of the electrolyte (NaCl) concentration decreases the solubility of lysozyme in the presence and absence of polyethylene glycol. The effect can be explained by the screening of the charged amino residues of the protein. The solubility experiments were performed at two different pH values (pH = 4.0 and 6.0), where the lysozyme net charge was +11 and +8, respectively. Ion-specific effects were systematically investigated. Anions such as Br(-), Cl(-), F(-), and H(2)PO(4)(-) (all in combination with Na(+)), when acting as counterions to a protein with positive net charge, exhibit a strong effect on the lysozyme solubility. The differences in protein solubility for chloride solutions with different cations Cs(+), K(+), and Na(+) (coions) were much smaller. The results at pH = 4.0 show that anions decrease the lysozyme solubility in the order F(-) < H(2)PO(4)(-) < Cl(-) < Br(-) (the inverse Hofmeister series), whereas cations follow the direct Hofmeister series (Cs(+) < K(+) < Na(+)) in this situation.