Self-consistent field modeling of mesomorphic phase changes of monoolein and phospholipids in response to additives.

Mapping the topological phase behaviour of lipids in aqueous solution is time consuming and finding the ideal lipid system for a desired application is often a matter of trial and error. Modelling techniques that can accurately predict the mesomorphic phase behaviour of lipid systems are therefore of paramount importance. Here, the self-consistent field theory of Scheutjens and Fleer (SF-SCF) in which a lattice refinement has been implemented, is used to scrutinize how various additives modify the self-assembled phase behaviour of monoolein (MO) and 1,2-dioleoyl-phosphatidylcholine (DOPC) lipids in water. The mesomorphic behaviour is inferred from trends in the mechanical properties of equilibrium lipid bilayers with increasing additive content. More specifically, we focus on the Helfrich parameters, that is, the mean and Gaussian bending rigidities (κ and [small kappa, Greek, macron], respectively) supplemented with the spontaneous curvature of the monolayer (Jm0). We use previously established interaction parameters that position the unperturbed DOPC system in the lamellar Lα phase ([small kappa, Greek, macron] < 0, κ > 0 and Jm0 ≈ 0). Similar interaction parameters position the MO system firmly in a bicontinuous cubic phase ([small kappa, Greek, macron] > 0). In line with experimental data, a mixture of MO and DOPC tends to be in one of these two phases, depending on the mixing ratio. Moreover we find good correlations between predicted trends and experimental data concerning the phase changes of MO in response to a wide range of additives. These correlations give credibility to the use of SF-SCF modelling as a valuable tool to quickly explore the mesomorphic phase space of (phospho)lipid bilayer systems including additives.

Structural and mechanical parameters of lipid bilayer membranes using a lattice refined self-consistent field theory.

The self-consistent field theory of Scheutjens and Fleer is implemented on a grid with (lattice) sites that are smaller than the segment size. In this quasi lattice-free implementation we consider united atom-like molecular models and study bilayer self-assembly of phospholipids in a selective solvent (water). We find structural as well as mechanical parameters for these bilayers. The mean (κ) and Gaussian ([small kappa, Greek, macron]) bending moduli, as well as the spontaneous curvature of the monolayer (Jm0), are computed for the first time following a grand canonical ensemble route. Results are in line with previous estimates for mechanical parameters that at the time could not be made following this correct route. This proves that the mean bending modulus is only a very weak function of the membrane tension. We performed a systematic study on the effects of model parameter variations. The mean bending modulus generally grows with increasing bilayer thickness. As expected Jm0 and [small kappa, Greek, macron] behave oppositely with respect to each other and for classical phospholipids assumes values near zero. As an example, an increase in the lipophilic to hydrophilic ratio in the lipids, may cause the Gaussian bending rigidity to switch sign from negative to positive, while - not necessarily at the same point - the spontaneous curvature of the monolayer may switch sign from positive to negative. Together with other investigated trends, these results point to mechanisms of how topological phase transitions of the lipid bilayer membranes may be regulated in the biological context, which correlates with known lipid phase behaviour.

Effects of feed composition on the fouling on cation-exchange membranes desalinating polymer-flooding produced water.

HYPOTHESIS: Cation exchange membranes (CEMs) are subject to fouling when utilized to desalinate wastewater from the oil and gas industry, hampering their performance. The kind and extent of the fouling are most likely dependent on the composition of the stream, which in practical applications can vary significantly. EXPERIMENTS: Fouling experiments were performed on commercial cation exchange membranes, which were used in electrodialysis runs to desalinate solutions of varying composition. The variations included ionic strength, type of ions, amount of viscosifying polyelectrolyte (partially hydrolyzed polyacrylamide), presence of crude oil, and surfactants. Performance parameters, like electric potential and pH, were monitored during the runs, after which the membranes were recovered and analyzed. FINDINGS: Fouling was detected on most CEMs and occurred mainly in the presence of the viscosifying polyelectrolyte. Under normal pH conditions (pH ~ 8), the polyelectrolyte fouled the concentrate side of the CEMs, as expected due to electrophoresis. However, by applying a current in the opposite direction, the polyelectrolyte layer could be removed. Precipitation occurred mostly on the opposite side of the membrane, with different morphology depending on the feed composition.

Step-wise linking of vesicles by combining reversible and irreversible linkers - towards total control on vesicle aggregate sizes.

Small vesicle aggregates as a model for primitive cellular assemblies or for application as multi-compartment drug delivery systems recently received a lot of interest, yet controlling the aggregation of vesicles to predetermined aggregate sizes remains quite a challenge. We show that this type of control is possible by using a combination of two different linker systems: streptavidin-biotin and C18-pNIPAm. The latter linker is a thermoresponsive surfactant, which below its lower critical solution temperature (LCST) of 32 °C acts as barrier on the outside of the vesicles preventing aggregation, even in the presence of other linkers. Above the LCST however, C18-pNIPAm collapses, becomes sticky and thus acts as a linker inducing aggregation. By working at low vesicle concentrations and tuning the C18-pNIPAm/lipid ratio, the aggregation is by design limited. When the temperature drops below the LCST again, the aggregation is reversed. However, this is not the case if other linkers are present. The collapse of C18-pNIPAm above the LCST provides close contact between vesicles, allowing other linker molecules to connect them. By combining the reversible 'switch-like' aggregation properties of C18-pNIPAm, with the irreversible linkage between biotinylated lipids and streptavidin, it is possible to control the size of the aggregates step by step using a simple temperature program.

Entropy estimates of a hard sphere system by data compression of Monte Carlo simulation data.

Data compression algorithms remove redundant information from a file. The extent to which a file size is reduced is a measure of the entropy. Recently, it has been suggested to use this technique to find the entropy from a simulation of a physical system. Here, we apply this technique to estimate the entropy from Monte Carlo simulations of the hard sphere system. Numerical results compare well with the limited available entropy estimates from the laborious thermodynamic integration method, while this new algorithm is much faster. Our results show the phase transition by calculation of the entropy for a large number of densities. A common tangent method is used to find the coexistence densities for the fluid-solid phase transition. The upper density deviates from the established density from the literature, while the lower density compares very well.

Self-limiting aggregation of phospholipid vesicles.

Lipid vesicles are widely used as model systems to study biological membranes. The self-assembly of such vesicles into vesicle pairs provides further opportunity to study interactions between membranes. However, formation of vesicle pairs, while subsequently keeping their colloidal stability intact, is challenging. Here, we report on three strategies that lead to stable finite-sized aggregates of phospholipid vesicles: (i) vesicles containing biotinylated lipids are coupled together with streptavidin, (ii) bridging attraction is exploited by adding cationic polymers (polylysine) to negatively charged vesicles, and (iii) temperature as a control parameter is used for the aggregation of vesicles mixed with a thermo-sensitive surfactant. While each strategy has its own advantages and disadvantages for vesicle pair formation, the latter strategy additionally shows reversible limited aggregation: above the LCST of pNIPAm, vesicle pairs are formed, while below the LCST, single vesicles prevail. Mixing protocols were assessed by dynamic and static light scattering as well as fluorescence correlation spectroscopy to determine under which conditions vesicle pairs dominate the aggregate size distribution. We have strong indications that without subsequent perturbation, the individual vesicles remain intact and no fusion or leakage between vesicles occurs after vesicle pairs have formed.

Influence of solution composition on fouling of anion exchange membranes desalinating polymer-flooding produced water.

HYPOTHESIS: Anion exchange membranes (AEMS) are particularly prone to fouling when employed to desalinate polymer flooding produced water (PFPW), an abundant sub-product from the oil and gas industry. The formation of fouling on an AEM will be affected by the composition of the solution, which includes various dissolved salts, partially hydrolyzed polyacrylamide (HPAM), crude oil, and surfactants. EXPERIMENTS: Electrodialysis experiments were performed to desalinate feed solutions with different compositions, aiming to distinguish between their individual and combined effects. The solutions contained diverse mono- and divalent ions. The analysis included data collected during the desalination and characterization of the fouled AEMs by diverse analytical techniques. FINDINGS: HPAM produced the most severe effects in terms of visible fouling and increase of resistance. This polyelectrolyte fouls the AEM by adsorbing on its surface and by forming a viscous gel layer that hampers the replenishment of ions from the bulk solution. Ca and Mg have a large influence on the formation of thick HPAM gel layers, while the oily compounds have only a minimal influence acting mainly as a destabilizing agent. The membranes also presented scaling consisting of calcium precipitates. The effects of the gel layer were minimized by applying current reversal and foulant-free solution.

A Hybrid Monte Carlo Self-Consistent Field Model of Physical Gels of Telechelic Polymers.

We developed a hybrid Monte Carlo self-consistent field technique to model physical gels composed of ABA triblock copolymers and gain insight into the structure and interactions in such gels. The associative A blocks of the polymers are confined to small volumes called nodes, while the B block can move freely as long as it is connected to the A blocks. A Monte Carlo algorithm is used to sample the node configurations on a lattice, and Scheutjens-Fleer self-consistent field (SF-SCF) equations are used to determine the change in free energy. The advantage of this approach over more coarse grained methods is that we do not need to predefine an interaction potential between the nodes. Using this MC-SCF hybrid simulation, we determined the radial distribution functions of the nodes and structure factors and osmotic compressibilities of the gels. For a high number of polymers per node and a solvent-B Flory-Huggins interaction parameter of 0.5, phase separation is predicted. Because of limitations in the simulation volume, we did however not establish the full phase diagram. For comparison, we performed some coarse-grained MC simulations in which the nodes are modeled as single particles with pair potentials extracted from SF-SCF calculations. At intermediate concentrations, these simulations gave qualitatively similar results as the MC-SCF hybrid. However, at relatively low and high polymer volume fractions, the structure of the coarse-grained gels is significantly different because higher-order interactions between the nodes are not accounted for. Finally, we compare the predictions of the MC-SCF simulations with experimental and modeling data on telechelic polymer networks from literature.

Self-Assembly of Lysine-Based Dendritic Surfactants Modeled by the Self-Consistent Field Approach.

Implementing a united atom model, we apply self-consistent field theory to study structure and thermodynamic properties of spherical micelles composed of surfactants that combine an alkyl tail with a charged lysine-based dendritic headgroup. Following experiments, the focus was on dendron surfactants with varying tail length and dendron generations G0, G1, G2. The heads are subject to acetylation modification which reduces the charge and hydrophilicity. We establish a reasonable parameter set which results in semiquantitative agreement with the available experiments. The critical micellization concentration, aggregation number, and micelle size are discussed. The strongly charged dendronic surfactants micelles are stable for generation numbers G0 and G1, for progressively higher ionic strengths. Associates of G2 surfactants are very small and can only be found at extreme surfactant concentration and salt strengths. Micelles of corresponding weaker charged acetylated variants exist up to G2, tolerate significantly lower salt concentrations, but lose the spherical micelle topology for G0 at high ionic strengths.

Complex coacervates formed across liquid interfaces: A self-consistent field analysis.

The Scheutjens-Fleer self-consistent field (SF-SCF) theory is used to study complexation between two oppositely charged polyelectrolytes across an interface formed by two solvents, here called oil and water. The focus is on the composition and the lateral stability of such interfacial coacervate. One polyelectrolyte is chosen to be oil soluble and the other one prefers water, whereas the counter and salt ions are taken to distribute ideally over all phases. There exists an electrostatic associative driving force for the formation of the coacervate phase which increases with decreasing ionic strength and may be assisted by some specific affinity between the associating units and an effective poor solvency for the coacervate. As with respect to the lateral stability an unusual wetting scenario, called pseudo-partial wetting, presents itself, which results from interactions on two different length scales. On the segmental length the screening of oil-water contacts promotes the wetting by the coacervate: a pre-wetting jump-like transition takes place off-coexistence from a microscopically thin to a mesoscopically thin film. Usually this implies complete wetting. However, the mesoscopically thin film is exposed to long-ranged attractive electrostatic interactions and therefore cannot grow to macroscopic dimensions upon approach towards coexistence. Hence the system remains partial wet. The bulk correlation length controls the thickness of the mesoscopically thin film and as a result the wetting transition occurs extremely close to the bulk critical point. We therefore expect that a thick coacervate film typically is laterally inhomogeneous: there are drops on top of a mesoscopically thin coacervate film. This conclusion qualitatively explains the experimental observation that such a coacervate film scatters visible light.

Persistence length of dendronized polymers: the self-consistent field theory.

We present numerical results for the thermodynamic rigidity and induced persistence length of dendronized polymers with systematically varied topology of their grafts obtained by the Scheutjens-Fleer self-consistent field method. The results were compared to predictions of an analytical mean-field theory. The two approaches have marked different predictions. In particular, the analytical theory predicts that the induced persistence length and the effective segment aspect ratio of dendronized polymers are increasing functions of the degree of branching of their side chains, whereas numerical calculations provide evidence of the opposite dependences. This discrepancy is argued to be due to the ability of side chains to repartition from the compressed to the dilated regions of a curved bottle brush, which is accounted for by the numerical, but not by the analytical method. The difference is most crucial in the light of the expected ability of dendronized polymers to have a liquid crystalline ordering in semi-dilute solutions.

Interactions between nodes in a physical gel network of telechelic polymers; self-consistent field calculations beyond the cell model.

Triblock copolymers, with associative end-groups and a soluble middle block, form flower-like micelles in dilute solutions and a physical gel at higher concentrations. In a gel the middle blocks form bridges between domains/nodes that contain the ends. We combine the self-consistent field theory with a simple molecular model to evaluate the pair potential between the nodes. In this model the end-groups are forced to remain in nodes and the soluble middle blocks are in solution. When the distance between the centres of the nodes is approximately the corona diameter, loops can transform into bridges, and the pair potential is attractive. Due to steric hindrance, the interaction is repulsive at smaller distances. Till now a cell-model has been used wherein a central node interacts through reflecting boundary conditions with its images in a spherical geometry. This artificial approach to estimate pair potentials is here complemented by more realistic three-gradient SCF models. We consider the pair interactions for (i) two isolated nodes, (ii) nodes positioned on a line (iii) a central node surrounded by its neighbours in simple cubic ordering, and (iv) a central node in a face centred cubic configuration of its neighbours. Qualitatively, the cell model is in line with the more refined models, but quantitative differences are significant. We also notice qualitative differences for the pair potentials in the specified geometries, which we interpret as a breakdown of the pairwise additivity of the pair potential. This implies that for course grained Monte Carlo or molecular dynamics simulations the best choice for the pair potentials depends on the expected node density.

Surfactant-polymer interactions: molecular architecture does matter.

Polymer-surfactant mixtures are found in many industrial formulations, and hence there is a significant interest in understanding, at a molecular level, how the self-assembly of surfactant is affected by oppositely-charged polyelectrolytes (PEs). We use self-consistent field modeling and show that the modes of interaction of PEs strongly depend on the architecture of the PE on the segmental level. Hydrophilic cationic PEs with their charge proximal to the linear backbone are expected to bind electrostatically to the outsides of the coronas of the spherical micelles of anionic surfactants, such as sodium laureth sulphate (SLES). As a result, the surfactant aggregation number increases, but at the same time the colloidal stability deteriorates, due to bridging of the PEs between micelles. PEs with their charge somewhat displaced from the backbone by way of short hydrophobic spacers, are expected to be present inside a micelle at the core-corona boundary. In this case the aggregation number decreases, yet the colloidal stability is retained. Hence, SLES tends to remove hydrophilic PEs from an aqueous solution, whereas it solubilizes more hydrophobic ones. The binding isotherm shows that the uptake of PEs remains typically below charge compensation and in this case the spherical micelle topology remains the preferred state.

On the edge energy of lipid membranes and the thermodynamic stability of pores.

To perform its barrier function, the lipid bilayer membrane requires a robust resistance against pore formation. Using a self-consistent field (SCF) theory and a molecularly detailed model for membranes composed of charged or zwitterionic lipids, it is possible to predict structural, mechanical, and thermodynamical parameters for relevant lipid bilayer membranes. We argue that the edge energy in membranes is a function of the spontaneous lipid monolayer curvature, the mean bending modulus, and the membrane thickness. An analytical Helfrich-like model suggests that most bilayers should have a positive edge energy. This means that there is a natural resistance against pore formation. Edge energies evaluated explicitly in a two-gradient SCF model are consistent with this. Remarkably, the edge energy can become negative for phosphatidylglycerol (e.g., dioleoylphosphoglycerol) bilayers at a sufficiently low ionic strength. Such bilayers become unstable against the formation of pores or the formation of lipid disks. In the weakly curved limit, we study the curvature dependence of the edge energy and evaluate the preferred edge curvature and the edge bending modulus. The latter is always positive, and the former increases with increasing ionic strength. These results point to a small window of ionic strengths for which stable pores can form as too low ionic strengths give rise to lipid disks. Higher order curvature terms are necessary to accurately predict relevant pore sizes in bilayers. The electric double layer overlap across a small pore widens the window of ionic strengths for which pores are stable.

Dendron brushes and dendronized polymers: a theoretical outlook.

Dendron brushes are molecular structures built up of treelike macromolecules, with multiple generations of branches, grafted with a root segment to a surface (particle) or to a backbone chain (dendronized polymer) with a sufficiently high grafting density so that the dendrons interact laterally. Recent advances in the theory of dendron brushes are highlighted and complemented by insights from numerical self-consistent field modelling. Our focus is on controversial issues, which are still under debate, such as, the strain distribution in individual dendrons and the appearance of distinct populations with a different extent of stretching for dendrons in planar brushes. We anticipate that dendritic brushes (i) show a strong resistance against bending, which may manifest in a high apparent persistence length of dendronized polymers, and (ii) have an unusually large beneficial effect on the colloidal stability due to the sharp steric repulsive interaction observed when these surface layers are pushed towards the overlap.

Linking lipid architecture to bilayer structure and mechanics using self-consistent field modelling.

To understand how lipid architecture determines the lipid bilayer structure and its mechanics, we implement a molecularly detailed model that uses the self-consistent field theory. This numerical model accurately predicts parameters such as Helfrichs mean and Gaussian bending modulus kc and k̄ and the preferred monolayer curvature J(0)(m), and also delivers structural membrane properties like the core thickness, and head group position and orientation. We studied how these mechanical parameters vary with system variations, such as lipid tail length, membrane composition, and those parameters that control the lipid tail and head group solvent quality. For the membrane composition, negatively charged phosphatidylglycerol (PG) or zwitterionic, phosphatidylcholine (PC), and -ethanolamine (PE) lipids were used. In line with experimental findings, we find that the values of kc and the area compression modulus kA are always positive. They respond similarly to parameters that affect the core thickness, but differently to parameters that affect the head group properties. We found that the trends for k̄ and J(0)(m) can be rationalised by the concept of Israelachivili's surfactant packing parameter, and that both k̄ and J(0)(m) change sign with relevant parameter changes. Although typically k̄ < 0, membranes can form stable cubic phases when the Gaussian bending modulus becomes positive, which occurs with membranes composed of PC lipids with long tails. Similarly, negative monolayer curvatures appear when a small head group such as PE is combined with long lipid tails, which hints towards the stability of inverse hexagonal phases at the cost of the bilayer topology. To prevent the destabilisation of bilayers, PG lipids can be mixed into these PC or PE lipid membranes. Progressive loading of bilayers with PG lipids lead to highly charged membranes, resulting in J(0)(m) >> 0, especially at low ionic strengths. We anticipate that these changes lead to unstable membranes as these become vulnerable to pore formation or disintegration into lipid disks.

Particles decorated by an ionizable thermoresponsive polymer brush in water: experiments and self-consistent field modeling.

We have synthesized anionic multistimuli responsive core-shell polymer nanoparticles with low size dispersity composed of glassy poly(methyl methacrylate) (PMMA) cores of ca. 40 nm radius and poly(N-isopropylacrylamide) (PNIPAM) anionic brush-like shells with methacrylic acid comonomers. Using dynamic light scattering, we observed a volume phase transition upon an increase in temperature and this response was pH and ionic strength dependent. Already at room temperature we observed a pronounced polyelectrolyte effect, that is, a shift of the apparent pKa extracted from the degree of dissociation of the acids as a function of the pH. The multiresponsive behavior of the hydrophobic polyelectrolyte brush has been modeled using the Scheutjens-Fleer self-consistent field (SF-SCF) approach. Using a phenomenological relation between the Flory-Huggins χ parameter and the temperature, we confront the predicted change in the brush height with the observed change of the hydrodynamic radius and degree of dissociation and obtain estimates for the average chain lengths (number of Kuhn segments) of the corona chains, the grafting density and charge density distributions. The theory reveals a rich internal structure of the hydrophobic polyelectrolyte brush, especially near the collapse transition, where we find a microphase segregated structure. Considering this complexity, it is fair to state that the theoretical predictions follow the experimental data semiquantitatively, and it is attractive to attribute the observed disparity between theory and experiments to the unknown polydispersity of the chains, the unknown distribution of the charges, or other experimental complications. More likely, however, the deviations point to significant problems of the mean field theory, which focuses solely on the radial distributions and ignores the possibility of the formation of lateral (local) inhomogeneities in partially collapsed polyelectrolyte brushes. We argue that the PNIPAM brush at room temperature is already behaving nonideally.

Equivalence of chain conformations in the surface region of a polymer melt and a single Gaussian chain under critical conditions.

In the melt polymer conformations are nearly ideal according to Flory's ideality hypothesis. Silberberg generalized this statement for chains in the interfacial region. We check the Silberberg argument by analyzing the conformations of a probe chain end-grafted at a solid surface in a sea of floating free chains of concentration φ by the self-consistent field (SCF) method. Apart from the grafting, probe chain and floating chains are identical. Most of the results were obtained for a standard SCF model with freely jointed chains on a six-choice lattice, where immediate step reversals are allowed. A few data were generated for a five-choice lattice, where such step reversals are forbidden. These coarse-grained models describe the equilibrium properties of flexible atactic polymer chains at the scale of the segment length. The concentration was varied over the whole range from φ = 0 (single grafted chain) to φ = 1 (probe chain in the melt). The number of contacts with the surface, average height of the free end and its dispersion, average loop and train length, tail size distribution, end-point and overall segment distributions were calculated for a grafted probe chain as a function of φ, for several chain lengths and substrate∕polymer interactions, which were varied from strong repulsion to strong adsorption. The computations show that the conformations of the probe chain in the melt do not depend on substrate∕polymer interactions and are very similar to the conformations of a single end-grafted chain under critical conditions, and can thus be described analytically. When the substrate∕polymer interaction is fixed at the value corresponding to critical conditions, all equilibrium properties of a probe chain are independent of φ, over the whole range from a dilute solution to the melt. We believe that the conformations of all flexible chains in the surface region of the melt are close to those of an appropriate single chain in critical conditions, provided that one end of the single chain is fixed at the same point as a chain in the melt.

Bending rigidities of surfactant bilayers using self-consistent field theory.

Self-consistent field (SCF) theory is used to find bending moduli of surfactant and lipid bilayers. Recently, we successfully applied low-memory search methods to solve the SCF equations. Using these we are now able to directly evaluate the Gaussian bending modulus for molecularly detailed models of bilayers by evaluating the excess Helmholtz energy of tensionless bilayers in a (part of the) Im3m cubic phase. The result prompted us to reconsider the protocol that has been used thus far to find the mean bending modulus kc and Gaussian bending modulus k[overline]. With respect to previous predictions, the value of kc is reduced by a factor of two and the Gaussian bending modulus is less negative and much closer to zero. In line with experimental data we now find that k[overline] can also become positive. In this paper we use the non-ionic surfactants series of the type CnEm for illustration.

Direct evaluation of the saddle splay modulus of a liquid-liquid interface using the classical mean field lattice model.

We study the curvature dependence of the liquid-liquid (liquid-gas) interface using the well-known mean field lattice model to estimate its rigidity parameters. The gaussian or saddle-splay modulus is found by evaluating the curvature energy of an interface onto which a saddle shape is imposed as this occurs in an Im3m cubic phase. The resulting values are consistent with those found by the classical indirect route, wherein the gaussian bending modulus results from combining the curvature dependences of the interfacial tension in cylindrical and spherical geometries.