Håkan Wennerström

The cell model for polyelectrolyte systems. Exact statistical mechanical relations, Monte Carlo simulations, and the Poisson–Boltzmann approximation

Some exact statistical mechanical relations have been derived for polyelectrolyte systems within the primitive model. Using the cell model, the osmotic pressure is determined through an explicit evaluation of the derivative of the partition function. Planar, cylindrical, and spherical systems are considered and for a planar charged wall the contact value theorem [Henderson and Blum, J. Chem. Phys. 69, 5441 (1978)] is obtained as a special case. Analogous relations are derived for the cylindrical and spherical geometries. It is argued that the exact relations can be used as consistency tests for analytical approximations. It is pointed out that one merit of the Poisson–Boltzmann approximation is that the validity of the exact equations is retained. Finally, a simple method is devised for determining the osmotic pressure from Monte Carlo simulations. Results from such simulations are used to assess the accuracy of the osmotic pressure calculated using the Poisson–Boltzmann equation. For monovalent ions, the...

Self-diffusion of small molecules in colloidal systems

The self-diffusion of small molecules in colloidal systems is calculated using the cell model to describe the effect of varying concentration of colloidal particles. The relevant boundary conditions are found using arguments from the thermodynamics of irreversible processes. From a general description of the self-diffusion in systems with spherically symmetrical particles we derive expressions for the concentration dependence of the effective self-diffusion coefficientDeff for several cases of practical importance. It is shown that when the molecule studied is strongly attracted to the particle a minimum inDeff is expected around volume fractionΦ=0.35. It is also shown that the often made distinction between free and bound molecules is often problematic and a more general description is proposed. The obstruction effect generated by the excluded volume is discussed both for spherical and spheroidal systems. It is pointed out that the often used formula due to Wang ((1954) J Amer Chem Soc 76:4755) is incorrect for self-diffusion and for the obstruction factor for spheres we obtain (1+0.5Φ)−1. This expresion is tested both by experiments on water diffusion in systems containing latex particles and through computer simulations and it is found valid over a wide concentration range. For prolate ellipsoids the obstruction factor is not greatly different from that for spheres, while for oblate aggregates the limiting obstruction factor of 2/3 can be obtained at low concentrations. It is demonstrated that this effect can be used to distinguish between different aggregate shapes. It is also shown that the disorder present in a solution of colloidal particles leads to a decrease in the obstruction effect.

Nuclear spin relaxation in paramagnetic systems

A theory of nuclear spin relaxation in paramagnetic systems, allowing for the electron spin relaxation to be in the slow motion regime, is presented. The formulation is general and can, for example, be used to derive formally the modified Solomon-Bloembergen equations. The theory is applied to the specific problem of nuclear spin lattice relaxation caused by the dipole-dipole interaction between the nuclear spin and an electron spin (S = 1). The lattice is described in terms of the electron Zeeman interaction, a zero field splitting of cylindrical symmetry and isotropic rotational diffusion. The resulting equations are solved numerically for a range of parameter values of practical interest and limiting cases are discussed. In the slow motion regime for the electron spin relaxation (that is, where the zero field splitting is larger than the rotational diffusion constant), the behaviour of the nuclear spin-lattice relaxation rate predicted using the present formalism differs qualitatively from the predicti...

NMR lineshapes of I = 52 and I = 72 nuclei. Chemical exchange effects and dynamic shifts

Abstract Analytical expressions for NMR lineshapes of spin - 5 2 and - 7 2 nuclei are derived assuming quadrupolar relaxation and nonextreme narrowing conditions. The effects of both chemical exchange and dynamic shifts are included in the description. Also a fourth-order quadrupolar contribution to the relaxation is briefly discussed. The results are analyzed for some typical sets of parameters. It is found that the dynamic shifts can be substantial and sometimes account for experimentally observed shifts. In an intermediate range of correlation times the signal is slightly asymmetric. The linewidth at half-height Δν 1 2 , has a broad maximum as the correlation time is varied from long times to the extreme narrowing limit. With chemical exchange effects contributing to the transverse relaxation the behavior of Δν 1 2 is more complex. In general Δν 1 2 is less sensitive to the exchange rate than for a nucleus with an exponential relaxation in each site.

Nuclear magnetic relaxation induced by chemical exchange

A new method of treating chemical exchange in nuclear magnetic relaxation theory is proposed. The essence of the method is to introduce the exchange in the spin hamiltonian by writing , where fi (t) is a function of time and has the value unity if the nucleus considered is at site i at time t, and zero otherwise. The method is applied to cases where the chemical exchange is faster than the relaxation. Some previously derived results are re-derived and in some cases made more general. The case of very fast intramolecular exchange is also considered.

Hydration forces and phase equilibria in the dipalmitoyl phosphatidylcholine—water system

Abstract The hydration force recently studied by Rand, Parsegian, and co-workers is suggested to be the main factor governing the phase equilibria between different lamellar phospholipid phases, when water is not present in excess. A procedure for calculating the phase equilibria is developed and applied to the dipalmitoyl phosphatidylcholine—water system. The calculated phase diagram, using experimentally determined hydration forces and transition enthalpies, is in good qualitative agreement with experimental observations. The relative stability of the gel and liquid-crystalline phases changes as the water content is decreased. The repulsive hydration force is weakest in the Lβ′ phase, and this phase dominates at the lowest water contents. An explanation of the molecular origin of the hydration force is also outlined on the basis of a continuum electrostatic description of the system. The solvation of the zwitterionic groups has a long-range character, and repulsive image charges will be induced as a second bilayer is approaching the polar group, giving rise to a repulsive interaction.

Dipole-dipole nuclear spin relaxation: A cross correlation correction to the Solomon-Bloembergen equation forT2

The transverse spin relaxation of a spin I in a IS pair is analysed for the dipole-dipole relaxation mechanism. It is shown that, when for the S-spin there is an additional efficient relaxation mechanism, which is of a second order tensorial rank, there can exist substantial corrections to the Solomon-Bloembergen equation for T 2. The correction terms are found to be non-negligible in the non-extreme narrowing limit. The correction terms are due to a cross correlation effect between the dipole-dipole interaction and the interaction causing the efficient relaxation of the S spin. As shown in the Appendix the correction appears as a near divergence of a fourth order term in the Redfield type expansion of the equation of motion of the density matrix. The explicit expressions for T 2 are, however, derived using a Liouville operator formalism combined with a perturbation expansion. For the relaxation of the S-spin a zero field splitting term is considered for a paramagnetic system with S ≥ 1. Similarly for a n...

Nuclear spin-lattice and spin-spin relaxation in paramagnetic systems in the slow-motion regime for the electron spin. III. Dipole-dipole and scalar spin-spin interaction for S = 32 and S = 52

Abstract The theory for nuclear spin relaxation in paramagnetic complexes, where the electron spin relaxation is allowed to be in the slow-motion regime, [Mol. Phys. 48, 329 (1983)] is generalized to spin states of multiplicity higher than triplet. Numerical calculations of nuclear spin-spin and nuclear spin-lattice relaxation rates are reported for electron spin systems ( S = 3 2 , S = 5 2 ), coupled to the nuclear spin system via dipole-dipole and scalar spin-spin interaction. Analogous to the S = 1 case, in the region when the zero-field splitting interaction is larger than the electron Zeeman interaction, the spectral densities show qualitatively different behavior than that described by the Solomon-Bloembergen (SB) theory. Furthermore, the spectral densities show an additional structure, a “soft plateau,” compared to the S = 1 case. This extra structure is a characteristic feature for half-integer electron spin systems ( S ⩾ 3 2 ). It is shown that this structure is mainly due to the lifting of the Kramers degeneracy of the |S ± 1 2 〉 level. The results show that the interference spectral density at zero frequency K0,0DD-SC(0), i.e., the contribution to the nuclear spin-spin relaxation due to the interference term when both dipole-dipole and scalar coupling are present, does not vanish in the Redfield region for the electron spin system.

Nuclear spin relaxation in paramagnetic systems (S = 1) in the slow-motion regime for the electron spin. II. The dipolar T2 and the role of scalar interaction

The previously presented theory (Mol. Phys. 48, 329 (1983)) for the dipolar contribution to the spin-lattice relaxation in paramagnetic systems is extended. The theory, which allows the electron spin relaxation to be in the slow motion regime, is generalized to cover both the longitudinal and the transverse relaxation and to include both the dipole-dipole (DD) and the scalar interaction in the Hamiltonian coupling the nuclear spin to the lattice. The lattice is described in terms of the electron Zeeman interaction, a zero-field splitting (ZFS) of cylindrical symmetry and the isotropic rotational diffusion. It is shown that the spectral densities at the nuclear Larmor frequency and at zero frequency consist of three terms. Besides the usual DD and scalar components, a cross-term is shown to contribute to nuclear spin relaxation rates for certain parameter ranges. In the absence of exchange, the numerical calculations for S = 1 show that the DD and cross term spectral densities at zero frequency are independent of the magnetic field and the ZFS parameter. This is traced to the cross correlation between the DD and ZFS interactions. A formal way to include chemical exchange in the model is sketched. The effect of including exchange is that the DD-ZFS cross correlation is reduced.

The Association of Ionic Surfactants to Micelles and Liquid Crystalline Phases: A Thermodynamic Model

A model for the association behaviour of ionic surfactants is presented, in which it is emphasized that the formation of micelles in a dilute aqueous solution is but a first step in a continuing association process leading to liquid crystalline phases and also to reversed micellar solutions. Using an expression for the free energy, which contains contributions due to the hydrophobic effect and the electrostatic free energy, chemical potentials for all the components are derived. In particular the electrostatic contributions are treated in detail using the Poisson-Boltzmann equation and the cell model. Spherical, cylindrical, and planar aggregates are considered. The calculated chemical potentials are compared with experiments relating to monomer and counterion activities, phase equilibria and CMC values. In all cases it is found that there is good agreement between theory and experiment. It is particularly gratifying that the phase boundaries (including two phase regions) are predicted with good accuracy.