D. John Mitchell

Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers

A simple theory is developed that accounts for many of the observed physical properties of micelles, both globular and rod-like, and of bilayer vesicles composed of ionic or zwitterionic amphiphiles. The main point of departure from previous theories lies in the recognition and elucidation of the role of geometric constraints in self-assembly. The linking together of thermodynamics, interaction free energies and geometry results in a general framework which permits extension to more complicated self-assembly problems.

Theory of self-assembly of lipid bilayers and vesicles

A simple theory is developed that explains the formation of bilayers and vesicles and accounts quantitatively for many of their physical properties: Properties including vesicle size distributions and bilayer elasticity emerge from a unified theory that links thermodynamics, interaction free energy, and molecular geometry. The theory may be applied to the analysis of more complicated membrane structures and mechanisms.

Micelles, vesicles and microemulsions

A theory of self-assembly of surfactant molecules into micelles and bilayers is critically examined and extended to include vesicles and microemulsions. The notion of hydrophilic–lipophilic balance is quantified. The theory gives a unified account of type, size and shape of the aggregates which form under various conditions. Observed trends due to change in salt concentration, temperature and oil type, and due to the addition of cosurfactants, are correlated and emerge from a simple global framework.

Phase behaviour of polyoxyethylene surfactants with water. Mesophase structures and partial miscibility (cloud points)

From a review of the major factors responsible for surfactant mesophase structure, a model phase diagram is deduced which shows phase structure as a function of surfactant volume fraction and micelle curvature. To test this model the phase behaviour of a series of pure polyoxyethylene surfactants (CnEOm) with water has been studied using optical microscopy over the temperature range 0–100 °C. The compounds studied were C8EO3, C8EO4, C8EO8, C8EO12, C10EO3, C12EO3-C12EO6, C12EO8, C12EO12, C14EO3, C14EO6, C16EO3, C16EO4, C16EO6, C16EO8, C16EO12, C9PhEO8 and C12(2-C10)EO10. Phase diagrams were determined for C8EO4, C12EO3-C12EO6, C12EO8, C16EO4, C16EO8 and C16EO12. With the other compounds optical microscopy was used to determine the number, sequence and type of mesophases.The mesophases observed were cubic–spherical-micelles (I1), hexagonal (H1), normal-cubic–bicontinuous (V1), lamellar (Lα) and reversed-cubic–bicontinuous (V2). Large head groups and low temperatures favour I1 and H1 phases, while Lα and reversed phases occur for small head groups and higher temperatures.There is agreement between experiment and theory for low to medium temperatures if increasing temperature is assumed to lead to a decreased surface area per molecule at the micelle surface (a). At high temperatures and low water content theoretical concepts were reconciled to practical behaviour only by assuming that increased interactions between EO groups occur at a critical water concentration. Two separate mechanisms are proposed for the lower consolute behaviour of surfactant + water solutions (the cloud point). One, involving van der Waals attractions between micelle cores, operates at low temperatures, while the second, involving intermicellar EO—EO attractions occurs at high temperatures. These two mechanisms can account for the ‘double’ cloud point phenomenon observed for surfactants with short EO groups.

A model of solvent structure around ions

The nature of solvent structure around ions is considered using a model of hard spheres with embedded point charges in a solvent of hard spheres with embedded point dipoles. The statistical mechanics of this model is treated in the mean spherical approximation which is a natural extension of the Debye–Huckel theory of electrolytes to include discrete charges and dipoles of finite size. Our results include (i) a modified expression for the Born energy which had been used empirically to fit solubility data, (ii) explicit forms for the polarization density about an ion from which we can deduce the orientation order of the dipolar solvents and the validity or otherwise of the concept of a ’’local’’ dielectric constant near charged bodies, and (iii) the form of the interaction free energy (potential of mean force) between ions at separations comparable to the solvent size. In presenting these results which are given in detail in Section IV only a familiarity with the general description of this model given in ...

The electrostatic interaction in colloidal systems with low added electrolyte

Abstract In a colloidal system in which the amount of added electrolyte is sufficiently low (e.g., nonaqueous dispersions or aqueous dispersions that have been treated by ion-exchange resins or micellar systems with no added electrolyte) conventional double-layer theory cannot be used to describe the electrostatic interaction between the particles. A theoretical treatment of such systems which takes into account the contribution of the counterions derived from the colloidal particles in screening the coulombic repulsion, is proposed. This leads to an effective colloid-colloid pair potential which varies with the volume fraction of the colloidal particles present in the system. A striking consequence of the theory is that under certain conditions, correlations in the spatial distribution of particles can persist over four orders of magnitude of the volume fraction. Moreover, these correlations, as measured by the height of the first peak of the structure factor, may not be a monotonically increasing function of the particle charge. These theoretical predictions are compared with neutron and light-scattering studies on the structure of colloidal systems.

The structure of electrolytes at charged surfaces: The primitive model

The effects of ion size on the structure of a primitive model electrical double layer at a charged surface is considered using the integral equation method based on a combined hypernetted chain and mean spherical approximation (HNC/MSA). The HNC/MSA is shown to be a nonlinear weak field approximation. The contact values of the surface ion distribution functions are shown to have the correct quadratic dependence on the surface charge density, An analytical comparison between the HNC/MSA and earlier work based on the modified Poisson–Boltzmann equation is given.

Dressed‐ion theory for electrolyte solutions: A Debye–Hückel‐like reformulation of the exact theory for the primitive model

A detailed derivation of the dressed‐ion theory—a formally exact theory for primitive model Coulomb fluids—is presented for the case of bulk electrolyte solutions. It is shown that the exact average electrostatic potential, ψ av(r), in the ion atmosphere around each ion satisfies a linear Poisson–Boltzmann (PB) equation for ‘‘dressed ions,’’ each of which consists of a central ion together with a specific part of the surrounding ion cloud. The dressed‐ion charge distribution—a renormalized charge for each ion—takes the role that the bare ionic charge has in the usual PB equation. Apart from this, virtually the only difference between the exact dressed‐ion and the approximate Debye–Huckel (DH) theories for the pair distribution function is that the former theory is nonlocal; the spread‐out nature of the dressed‐ion charge distribution gives rise to a nonlocal polarization response to the average potential. The linear response function relating the polarization and the average potential is investigated in t...

Beyond Poisson-Boltzmann: Images and correlations in the electric double layer. I. Counterions only

The general solution to the zero size mean spherical model is found for an inhomogeneous electrolyte (with specified profile) between charged planar surfaces. The analysis includes the effects of images and correlations. It provides the primary correction to the classical mean field theory of the double layer and allows the error in that theory to be easily estimated over experimental regimes. The relationship between Lifshitz theory and primitive model theories of electrolytes is made explicit. Results obtained for the one component double layer are accurate for systems with low coupling.

Beyond Poisson–Boltzmann: Images and correlations in the electric double layer. II. Symmetric electrolyte

An extension of the Poisson–Boltzmann theory of the electric double layer is applied to a symmetric electrolyte between two charged planar surfaces. This analytic treatment includes the effects of images and of ion correlations via the Debye–Huckel closure for the direct correlation function. It is demonstrated that at large separations the corrections to Poisson–Boltzmann theory appear as an effective surface charge. A means of correcting the apparent ion binding inferred from fitting experimental force data is also given. The extended theory shows good agreement with accurate numerical calculations for systems with low coupling. The generalization of the Onsager–Samaras limiting result to higher concentrations and to the case of the surface free energy of a charged dielectric interface is also presented.