Cubic phases

Introduction to cubic phases

With any curved bilayer or topologically closed region such as single- or multi-walled vesicles, there is an inevitable conflict due to internal packing constraints (cf. Fig. 9.8 and 10.2).

In the energetically optimal configuration, lipids packed into the outer bilayer have normal curvature. The hydrocarbon chains are stretched. By contrast, the inner surfactants have reverse curvature. The chains are compressed. So although the interior of a bilayer can be considered fluid-like, above the Krafft (gel) temperature of the lipid it is asymmetric. As we have seen, and re-summarize, this necessary frustration has several consequences. The first is that when the radius becomes small enough, the interior layers of a multilamellar vesicle structure must collapse into aggregates different in structure to that of a bilayer. The interior can be micelles. Or it can be bicontinuous. This gives rise to supra-aggregation as a normal and expected state of self assembly. Or else the interior can be empty and surfactant-free. The second consequence is that a single-walled bilayer or vesicle has to have a radius (typically 100 nm) sufficiently large to accommodate this additional internal packing condition.

There is another way that the frustration can be relieved.

The bilayer-forming lipids or surfactants have a surfactant parameter around vH/(aPlH) ∼ 1, or <1. The average of the principal curvatures at the interface is zero for a flat bilayer.

Lifshitz theory and its extensions: an overview

Molecular recognition

The ideas behind the DLVO theory of long-range forces in colloidal particle interactions and of the electrical double layer that we have just outlined held centre stage in colloid science for at least 70 years. Quantitatively, as already remarked, agreement between experiment and theory was illusory, except at salt concentrations less than 10−2 M, or at most 10−1 M. It was illusory in the sense that while classical theory captured some essentials of the forces between ions and macromolecules, ion specificity was still missing. While the electrical double-layer forces decayed exponentially as predicted, the magnitude of the forces changed with a change in counterion or co-ion. Recall our typical examples. A change in counterion in a background electrolyte from Br− to OAc− could produce an increase in magnitude of the forces by a factor of 50 to 100! The same will be seen to occur with different surfaces with a change from Na+ to Li+. We will see much more of this specificity later. These differences depended on the nature of the charged interacting surfaces and, at the same electrolyte concentration, on the counterion. They occur even with a change in an apparently indifferent co-ion in an intervening electrolyte. The accommodation of such results could only be achieved by calling in more unquantified fitting parameters. This is unsatisfactory as predictability is lost. The attractive van der Waals forces were obscured by short-range effects due to solvent structure.

Ideas and defects of theories of self assembly

As already remarked, the first attempts to build such a unified molecular theory of self assembly that could embrace all possible aggregates began 30 years ago.

It began with Tanford's ideas on opposing intramolecular forces between surfactant molecules at interfaces.

A theory via statistical mechanics was developed based on minimal assumptions. This theory is just a characterization of self assembly. It is more complicated than, but at the same level as, nucleation theory for gas–liquid phase transitions. (Nucleation theory considers only the growth of spherical aggregates, droplets of liquid in a vapour. With surfactants we have to consider a multitude of possible aggregates of different shapes.) Nonetheless, as we have seen, the characterization that emerged gave out a set of simple design rules to predict microstructure for dilute systems.

In outline the ideas involved are these:

In the processes involved in formation of an aggregate there are several factors that can be identified.

There is a hydrophobic free energy of transfer of a monomer surfactant hydrocarbon tail, from water to the assumed bulk oil-like environment in its associated state. In an aggregate at its interface the forces between the hydrocarbon tails oppose the intra-aggregate headgroup interactions (see Fig. 10.1). These forces could be ionic, hydration, zwitterionic or steric forces. This competition at the interface sets the interfacial curvature. There is then an interfacial free energy contribution augmented by curvature contributions.

In collaboration with Drew F. Parsons.

(This chapter is more or less self-contained. It can be read independently of earlier chapters.)

Hofmeister effects in physical chemistry

Introduction

It will be clear by now that the theoretical edifice that deals with molecular forces in physical chemistry, built painstakingly over the past 150 years, is flawed. That there are defects and limitations in any theory we can live with. Of course there are. But the emerging picture from the preceding chapters is more disturbing. It seems that our intuition has become so seriously flawed that what ought to be the enabling discipline of physical chemistry has become impotent in the face of challenges posed by the biological sciences. To readers familiar with and schooled in the classical textbook literature, this claim is not easy to accept. And the burden of proof of a challenge to an established discipline lies with the proponent. So, in this chapter we recapitulate the standard literature ideas, and outline where they went off course. Then we revisit and pull together a number of examples from biology, some already mentioned, where it is clear that the standard theories fail. Then we outline our views on how it is that a reconciliation is on the way to being effected. How to fit Hofmeister effects into the scheme of things is a first issue.

This and succeeding chapters deal with how it is that molecular forces conspire with the size and shape of molecules called surfactants to associate spontaneously in solution into a myriad multimolecular aggregates. They can be ephemeral entities called micelles. Typical micelles formed by short-chained surfactants exist as entities for times of around 10−5 seconds. On the other hand they can be as long-lived as three or more months. That is so for membrane mimetic long-chained phospholipids that form complex single-walled vesicles and multi-bilayered structures. These self-assembled aggregates provide the organized microstructural scaffolding that forms the basis of biological cell membranes. Self-assembled entities direct biochemical cell traffic.

We have tried to identify conceptual developments in self assembly as they emerged over the past three decades. The result of a great deal of theorizing and experimentation is that some simple rules emerge. These allow the prediction of microstructure, as a function of components, component ratios and physicochemical solution conditions. This, combined with an understanding of how to change molecular forces via specific ion effects, gives some insights into the astonishingly complex background self-organization that occurs in biology. (The genius of DNA, RNA and proteins in biology is not in dispute. What is not generally recognized is that their work takes place within a hidden framework built from and involving the lipids, which are not just passive bystanders.)

This book outlines developments in physical and colloid chemistry over the last decade or two that have changed our understanding of molecular forces and the self assembly of amphiphilic molecules. Within the sciences, a subject or discipline is defined by a freemasonry, the members of which are united by a common lore. The received beliefs of adepts are reaffirmed by recitation and repetition of the lore, and reinforced by the weight of authority embodied in the literature of the discipline. The more venerable the literature, the more conservative is the freemasonry. Challengers to the canon are at first dismissed as heretics or apostates, but if, later, their claims are conceded to have validity, they and their theories are eventually accepted into the fold. The discipline moves on. So, the advocates of a once revolutionary Darwinism, wrongly defined by others by the trite aphorism ‘survival of the fittest’, retreated into convoluted defences of the dogma, represented by the elegant writings of Stephen J. Gould. Two decades ago the notion that environmental influences such as temperature could affect gene expression invited the ridicule attending to an earlier Lamarkism. Similarly for any questioning of the dogma of the Weissman barrier in immunology. Not any more.

The origins of the discipline of modern physical chemistry can probably be dated most conveniently to Napoleon's scientific expedition to Egypt 200 years ago. Berthelot, one of the expedition's scientists, observed on the receding flood plain of the Nile rocks that were covered with soda lime, sodium carbonate.

Emulsions

When a third component, ‘oil’, is added to a mixture of surfactants and water, the system can form an emulsion. The ‘oil’ can be any predominantly hydrophobic solution or solid paraffin particles that phase-separate from ‘water’ without surfactant. The ‘surfactant’ can include any amphiphilic materials like proteins or long-chain alcohols. The hydrophilic part can be water or another liquid, and can contain salts, sugars, whatever. So the term emulsion, including foods, cosmetics, lubricants, drug delivery, etc., embraces if we like an entire major phylum in the Chemical Kingdom.

Here the ‘surfactant’ adsorbs at the water–oil interface to segregate ‘oil’ from ‘water’ into macroscopic pools. The surfactant adsorbed can be a monolayer, or it can consist of multiple layers. Because of their size, emulsions usually scatter light and appear opaque. The pools of water in oil, or of oil in water, often contain within them smaller oil–water–surfactant microstructures. Sometimes they are bicontinuous. Emulsions are mostly thermodynamically unstable. That is, the droplets will coalesce with time. It used to be thought that the formation of emulsions always required work, such as stirring or sonication, but this is not so. Some, as we shall see, form spontaneously and are thermodynamically stable systems that exist as an apparent single ‘phase’ with complicated microstructure.

With ionic surfactants, electrostatic double-layer forces act to oppose coalescence of droplets. Depletion forces (see Chapter 4) due to micelles in water are probably even more effective in stabilizing emulsions.

Inclusion of electrolytes and Hofmeister effects in the theory

We have seen that the classical theories of electrolytes are limiting laws that are strictly valid, if at all, at very low concentrations. That is so for the Born self energy, the correlation free energy of Debye–Hückel theory, the interfacial tension of electrolytes represented by Onsager's theory, and the double-layer theory of interactions between charged colloidal particles. These theories ignore water structure, hydration, induced by ions. They also ignore dispersion interactions between ions and between ions and surfaces. In reality, with moderate salt concentrations of interest in biology (> 0.1 M) strong specific ion effects emerge. These effects can be taken into account by introducing more (unquantified) parameters that attempt to build in hard core interactions, local ‘water structure’ and overlap of hydration shells. But even with such extensions, the parameters vary from one situation to another. For example, the double-layer forces between the cationic bilayers of Chapter 4 differ by more than an order of magnitude with sodium bromide or sodium acetate at concentrations as low as 10−3 M! This is entirely unsatisfactory. A theory of electrolytes that deserves the name ought to work predictively for all electrolytes.

As a first step to throwing some light on the problem, we here address how to build a theory that includes the missing dispersion forces together with electrostatics.

Bubble–bubble coalescence

Effect of electrolytes

The Hofmeister effects we have just discussed required a complete revision of theoretical ideas, and a revision of the way we interpret measurements that date back a century or more. We come now to some neglected phenomena that throw the entire theoretical applecart upside down again.

It is an extraordinary fact that an explanation of what appears the simplest conceivable experiment remains elusive. Breaking waves in the ocean are foamy, those in fresh water are not. Bubbles in salt water do not fuse, those in fresh water do. The experiment – illustrated in Figs. 8.1 and 8.2 – quantifies this effect, which is quite dramatic.

Bubbles of nitrogen pass through a glass frit, as in a fish tank, and ascend a column. As they do they collide and fuse, and the column stays clear. (There is no problem with impurities that might affect matters. The column is self-cleaning.)

If salt is added, nothing much occurs until around 0.1 M. Suddenly the bubbles do not fuse, they remain small and the column becomes a mass of small bubbles. The change can be monitored by a laser diode that measures transmission of light through the column, and the scale gives per cent coalescence vs. salt concentration. (The same experiments can be done with single bubble–bubble interactions.)

Forces in the DLVO theory of colloidal stability

For over 50 years the theory of the stability of colloid suspensions due independently to Deryaguin and Landau and Verwey and Overbeek held centre stage in the field. Following the derivation from quantum mechanics of the attractive force between two molecules, it was a straightforward matter to add these forces up to arrive at a force between two model colloidal particles. This potential of interaction per unit area behaves, for two particles modelled as planar interfaces a distance l apart as, V(l) ≈ −A/(12πl2) where A is the Hamaker constant (see Chapter 2).

The double-layer force of repulsion between the (charged) surfaces behaves at large distances of separation as V(l) ≈ f · exp(−κDl). Here κD is the Debye length, which depends on salt concentration, and the prefactor is a complicated function of the surface charge or potential (see Chapter 3). Then a combination of these forces gives rise to a predicted net force of attraction like that shown schematically in Fig. 4.1.

These forces depend on geometry assumed for the particles (see Chapter 2). The insertion of this potential into a theory of coagulation of particles predicted whether the particles would stay in suspension or flocculate. The particles could flocculate into a ‘secondary minimum’, with a barrier usually at l ∼ 1/κD.

Or in the absence of such a barrier they could (theoretically) adhere into a deep ‘primary’ minimum at a distance of a few molecular diameters.