Changes In Phase Behavior Research Articles

A New 3D Compositional Model for Hydraulic Fracturing With Energized Fluids

Summary While several 3D fracturing models exist for incompressible water-based fluids, none are able to capture the thermal and compositional effects that are important when using energized fluids such as CO2, N2, LPG, and foams. This paper introduces a new 3D, compositional, non-isothermal fracturing model. The new model predicts changes in temperature and fluid density. These changes are treated on a firm theoretical basis by using an energy-balance equation and an equation of state, both in the fracture and in the wellbore. The model is capable of handling any multicomponent mixture of fluids and chemicals. Changes in phase behavior with temperature, pressure, and composition can be modeled. A new simulator has been developed based on the compositional model presented in this paper. The simulator is validated for traditional fluid formulations against known analytical solutions and against a well-established commercial fracturing simulator. Results from the new simulator are then presented for energized fluids such as CO2 and LPG. In particular, the compositional model shows how fluid expansion and viscosity reduction impact fracture growth. These effects are not captured by traditional fracturing simulators. The compositional tool is specifically suited for fracture design in formations in which energized fluids constitute a viable alternative to traditional fracturing fluids.

Interplay of pH and Binding of Multivalent Metal Ions: Charge Inversion and Reentrant Condensation in Protein Solutions

Tuning of protein surface charge is a fundamental mechanism in biological systems. Protein charge is regulated in a physiological context by pH and interaction with counterions. We report on charge inversion and the related reentrant condensation in solutions of globular proteins with different multivalent metal cations. In particular, we focus on the changes in phase behavior and charge regulation due to pH effects caused by hydrolysis of metal ions. For several proteins and metal salts, charge inversion as measured by electrophoretic light scattering is found to be a universal phenomenon, the extent of which is dependent on the specific protein-salt combination. Reentrant phase diagrams show a much narrower phase-separated regime for acidic salts such as AlCl3 and FeCl3 compared to neutral salts such as YCl3 or LaCl3. The differences between acidic and neutral salts can be explained by the interplay of pH effects and binding of the multivalent counterions. The experimental findings are reproduced with good agreement by an analytical model for protein charging taking into account ion condensation, metal ion hydrolysis, and interaction with charged amino acid side chains on the protein surface. Finally, the relationship of charge inversion and reentrant condensation is discussed, suggesting that pH variation in combination with multivalent cations provides control over both attractive and repulsive interactions between proteins.

Effects of phase behaviour on mass transfer in micellar liquid/liquid systems

Transport limitations often occur in liquid/liquid systems and, for instance, are responsible for low reaction rates in homogeneous catalysed liquid/liquid reactions with water soluble catalysts. By using surfactants the water solubility of the reactants can be increased, which results in an increase of the reaction rate. Surfactants adsorb at liquid/liquid interfaces, but this is the place where the important transport processes occur. Therefore, an influence by surfactant molecules on the transport processes is obvious. In this work the focus lies on the effects of surfactants on liquid/liquid mass transfer. An increase of surfactant concentrations leads to a decrease in the mass transfer rate. In the literature this reduction is described by two effects, but as the experimental results show, the effects describe this reduction of the mass transfer rate incompletely. Furthermore, the effects exerted by the change in phase behaviour must be taken into consideration.

Modeling of Pressure and Solution Gas for Chemical Floods

Summary The goal of surfactant/polymer (SP) flooding is to reduce interfacial tension (IFT) between oil and water so that residual oil is mobilized and high recovery is achieved. The optimal salinity and optimal solubilization ratios that correspond to ultralow IFT have recently been shown, in some cases, to be a strong function of the methane mole fraction in the oil at reservoir pressure. We incorporate a recently developed methodology to determine the optimal salinity and solubilization ratio at reservoir pressure into a chemical-flooding simulator (UTCHEM). The proposed method determines the optimal conditions on the basis of density estimates by use of a cubic equation of state (EOS) and measured phase-behavior data at atmospheric pressure. The microemulsion phase-behavior (Winsor I, II, and III) are adjusted on the basis of this predicted optimal salinity and solubilization ratio in the simulator. Parameters for the surfactant phase-behavior equation are modified to account for these changes, and the trend in the equivalent alkane carbon number (EACN) is automatically adjusted for pressure and methane content in each simulation gridblock. We use phase-behavior data from several potential SP floods to demonstrate the new implementation. The implementation of the new phase-behavior model into a chemical-flooding simulator allows for a better design of SP floods and more-accurate estimations of oil recovery. The new approach could also be used to handle free gas that may form in the reservoir; however, the SP-flood simulation when free gas is present is not the focus of this paper. We show that not accounting for the phase-behavior changes that occur when methane is present at reservoir pressure can greatly affect the oil recovery of SP floods. Improper design of an SP flood can lead to production of more oil as a microemulsion phase than as an oil bank. This paper describes the procedure to implement the effect of pressure and solution gas on microemulsion phase behavior in a chemical-flooding simulator, which requires the phase-behavior data measured at atmospheric pressure.

Influence of Counterions on Lauric Acid Vesicles and Theoretical Consideration of Vesicle Stability

The counterions, including inorganic cations, Na(+) and Cs(+), and organic cation, (C(2)H(5))(4)N(+), influence the phase behavior and self-assembled structures of the lauric acid (LA) in water. Dissolving LA in NaOH, CsOH, and (C(2)H(5))(4)NOH (tetraethylammonium hydroxide, TeAOH) solutions, respectively, we observed that the three systems totally exhibited the same phase behavior, from birefringent L(α) phase/precipitates (P) → L(α) phase → L(α) phase/L(1) (micelles) → L(1). The temperature influence on phase behavior was investigated, and with an increase of temperature, we observed that less phase behavior change occurred in the systems of LA/CsOH/H(2)O and LA/TeAOH/H(2)O, while the phase behavior of the LA/NaOH/H(2)O system exhibited an obvious change. Cryogenic transmission electron microscopy (cryo-TEM) images demonstrated that the different microstructures of L(α) phase samples in the three systems existed. For the systems of LA/NaOH/H(2)O and LA/TeAOH/H(2)O, uni- and multilamellar vesicles coexist for L(α) phase samples, as both the morphology and size of these vesicles are polydisperse. The curvatures of the bilayer membranes of the two systems are considered to vary from positive, zero, and even negative. However, only spherically unilamellar vesicles exist in the system of LA/CsOH/H(2)O, indicating that the bilayers are more rigid than those in the LA/NaOH/H(2)O and LA/TeAOH/H(2)O systems. Through the combination of the Helfrich curvature energy theory and the mass-action model, the effective bending constant K = 0.5 k(B)T in the LA/CsOH/H(2)O system was obtained, demonstrating that the unilamellar vesicles are stabilized by thermal fluctuations. A primary discussion for the effect of the nature of counterions on the stability and deformation of the vesicles is presented.

A New Method To Model Relative Permeability in Compositional Simulators To Avoid Discontinuous Changes Caused by Phase-Identification Problems

Summary Simple methods, such as the use of density during compositional simulations, often fail to identify the phases correctly, and this can cause discontinuities in the computed relative permeability values. The results are then physically incorrect. Furthermore, numerical simulators often slow down or even stop because of discontinuities. There are many important applications in which the phase behavior can be single phase, gas/liquid, liquid/liquid, gas/ liquid/liquid, or gas/liquid/solid at different times in different gridblocks. Assigning physically correct phase identities during a compositional simulation turns out to be a difficult problem that has resisted a general solution for decades. We know that the intensive thermodynamic properties, such as molar Gibbs free energy, must be continuous, assuming local equilibrium, but this condition is difficult to impose in numerical simulators because of the discrete nature of the calculations. An alternative approach is to develop a relative permeability model that is continuous and independent of the phase numbers assigned by the flash calculation. Relative permeability is a function of saturation, but also composition, because composition affects the phase distribution in the pores (i.e., the wettability). The equilibrium distribution of fluids in pores corresponds to the minimum in the Gibbs free energy for the entire fluid/rock system, including interfaces. In general, however, this relationship is difficult to model from first principles. What we can easily do is calculate the molar Gibbs free energy (G) of each phase at reference compositions where the relative permeabilities are known or assumed to be known and then interpolate between these values by use of the G calculated during each timestep of the simulation. Relative permeability values calculated this way are unconditionally continuous for all possible phase-behavior changes, including even critical points. We tested the new relative permeability model on a variety of extremely difficult simulation problems with up to four phases, and it has not failed yet. We illustrate several of these applications.

Effect of Mechanical Stresses on Lipid Membrane Phase Properties

We currently investigate how membrane tension modifies the miscibility properties of model lipid bilayers, namely giant unilamellar vesicles. We use fluorescence microscopy to observe coexisting liquid phases within temperature-controlled vesicles under surface tension induced by micropipette aspiration. We measure shifts in liquid/liquid miscibility temperatures as a function of applied tension.We compare our experimental data to the theoretical prediction of [1], by which a surface tension of ∼1mN/m should cause a decrease in miscibility temperature of ∼1K. This prediction may explain why Giant Plasma Membrane Vesicles (GPMVs) show large-scale liquid/liquid phase coexistence [2,3] whereas undisturbed cell membranes do not. GPMV's, which are detached from the cytoskeleton, are hypothesized to have lower surface tensions than cell membranes.[1] Uline, Schick and Szleifer. Changes in phase behavior of lipid bilayers under tension. Submitted.[2] Baumgart, Hammond, Sengupta, Hess, Holowka, Baird and Webb. Large-scale fluid/fluid phase separation of proteins and lipids in giant plasma membrane vesicles. Proc. Natl. Acad. Sci. USA, 104:3165-3170, 2007.[3] Veatch, Cicuta, Sengupta, Honerkamp-Smith, Holowka and Baird. Critical fluctuations in plasma membrane vesicles. ACS Chem Biol., 3:287-293, 2008.

Probing molecular interactions of poly(styrene-co-maleic acid) with lipid matrix models to interpret the therapeutic potential of the co-polymer

To understand and maximize the therapeutic potential of poly(styrene-co-maleic acid) (SMA), a synthetic, pharmacologically-active co-polymer, its effect on conformation, phase behavior and stability of lipid matrix models of cell membranes were investigated. The modes of interaction between SMA and lipid molecules were also studied. While, attenuated total reflection-Fourier-transform infrared (ATR-FTIR) and static 31P nuclear magnetic resonance (NMR) experiments detected SMA-induced conformational changes in the headgroup region, differential scanning calorimetry (DSC) studies revealed thermotropic phase behavior changes of the membranes. 1H NMR results indicated weak immobilization of SMA within the bilayers. Molecular interpretation of the results indicated the role of hydrogen-bond formation and hydrophobic forces between SMA and zwitterionic phospholipid bilayers. The extent of membrane fluidization and generation of isotropic phases were affected by the surface charge of the liposomes, and hence suggested the role of electrostatic interactions between SMA and charged lipid headgroups. SMA was thus found to directly affect the structural integrity of model membranes.

The Analysis of Gas Productivity by the Influence of Condensate Bank near Well

ABSTRACT While producing gas from the reservoir to the surface, there exists a unavoidable pressure drop near the wellbore. Due to excessive pressure drops, a condensate drops out from gas and flows with gas towards a well because of compositional changes in PVT phase behavior. Since these all make a productivity of reservoir worse and reduce an overall recovery, many studies of condensate bank phenomena have been performed for a long time. In this study, a reservoir simulation has been conducted to investigate the effect of well's productivity due to the behavior of condensate bank near well. Also this study presents the effects of heterogeneity on condensate banking and conformance control methods to minimize condensate bank problems effectively. From simulational results of condensate bank phenomena in a gas-condensate reservoir, the condensate forms rapidly in the vicinity of the well as soon as gas production begins since the bottom-hole pressure is much lower than the dew-point pressure. The accumulated condensate causes a blockage effect on the movement of reservoir fluids and reduce the effective permeability to gas appreciably, and also causes the decline of well's productivity. The trend of producing GOR shows the abrupt changes which represents typical complex behaviors of gas-condensate reservoirs. In a very heterogeneous reservoir, the bank radius expands up to 100 ft in a day and the maximum saturation of condensate reaches 0.61. Therefore, the mobility of gas is dropped and the overall recovery of oil and gas is decreased. While oil saturation has a highest value near the well in general, in case of reservoir with a strong heterogeneity, some regions away from the wellbore show high level of oil saturation according to local distributions of permeability. To increase the productivity, a different producing strategy was conducted by changing the manner in which the well is brought into flowing condition. The maximum gas and oil production can be achieved by lowering the BHP slowly in the first step of operation period instead of dropping the BHP quickly. The large pressure drops from the beginning of operation makes the formation of condensate bank earlier and increases the producing GOR due to the growth of condensate bank. Accordingly, the implementation of optimal production strategy is essential by considering the condensate content, technical factors, economics depending on market price as well as gas and condensate production profiles in long term.

The co-micelle/emulsion templating route to tailor nano-engineered hierarchically porous macrospheres

Here we present a new class of nano-engineered hierarchically porous materials in which the entire framework is mesoporous. This material is engineered into macrospheres of controllable size with a highly interconnected macropore network to facilitate molecular diffusion access. To achieve this, a new co-micelle/emulsion templating (co-MET) technique was developed. In this technique a block copolymer plays the dual roles of emulsion stabilization and micelle formation within the aqueous phase of that emulsion to produce the hierarchical structures. The emulsion templating provides the macroporous structure while the mesoporous structure is formed by hydrolyzation of silica around block copolymer micelles. Increasing the copolymer concentration improves the mesoporosity up to a certain concentration where the emulsion phase behavior changes and the macroporosity is affected. Unlike other hierarchically porous materials, the walls of the co-MET macrospheres are entirely mesoporous, which provides high surface areas (>500 m 2 g −1) and pore volumes (>1 cm 3 g −1) and narrow mesopore size distributions (∼10 nm). This interconnected hierarchical meso/macroporous structure combined with the controlled particle size makes this new class of materials promising for applications requiring high diffusion and throughput rates, alleviating the problems of using typical fine particle mesoporous materials.

Fluorescence and ESR spectroscopy studies on the interaction of isoflavone genistein with biological and model membranes

Genistein (5,7,4′-trihydroxyisoflavone) the common soy beans isoflavone has attracted scientific interest due to its antioxidant, estrogenic, antiangiogenic and aniticancer activities. The aim of the present study was to investigate the interaction of genistein with biological (erythrocyte) and model membranes (dimyristoyl- and dipalmitoylphosphatidylcholine). Using Laurdan and Prodan as fluorescent probes, we demonstrated phase behavior and membrane fluidity changes induced by genistein. ESR spectroscopy revealed alterations caused by genistein in membrane domains structure and mobility of spin probes with free radicals located at different depths of membrane. The method of ESR spectra decomposition and computer simulation of the recorded spectra were used in order to visualize domain coexistence by GHOST condensation method. Fluorescence and ESR spectroscopy experiments performed at different temperatures enabled us to observe the effect of isoflavone on phospholipid bilayers in either gel or liquid crystalline phase. It was concluded that genistein preferentially intercalated into lipid headgroup region, to some extent into polar–apolar interface and only in minimal degree into hydrophobic core of the membrane. According to our best knowledge this is the first study on modification of domain structure of membranes by genistein.

Could the energy cost of using supercritical fluids be mitigated by using CO2 from carbon capture and storage (CCS)?

This article explores the possibility of utilising supercritical CO2 obtained from carbon capture and storage (CCS) as a solvent and examines the hydrogenation of isophorone to 3,3,5-trimethylcyclohexanone using supercritical CO2 with added N2, CO or H2O to emulate the contaminants expected in CO2 from CCS. None of the impurities appear to cause insuperable problems in the hydrogenation of isophorone when present at concentrations likely to be found in CO2 from CCS. N2 introduces modest changes in phase behaviour at some pressures, while CO and H2O reduce the activity of the catalyst. However, the activity can be largely regained by increasing the reaction temperature.

Correlated AFM and NanoSIMS imaging to probe cholesterol-induced changes in phase behavior and non-ideal mixing in ternary lipid membranes

Cholesterol is believed to be an important component in compositionally distinct lipid domains in the cellular plasma membrane, which are referred to as lipid rafts. Insight into how cholesterol influences the interactions that contribute to plasma membrane organization can be acquired from model lipid membranes. Here we characterize the lipid mixing and phase behavior exhibited by 15N-dilaurolyphosphatidycholine (15N-DLPC)/deuterated distearoylphosphatiylcholine (D70-DSPC) membranes with various amounts of cholesterol (0, 3, 7, 15 or 19mol%) at room temperature. The microstructures and compositions of individual membrane domains were determined by imaging the same membrane locations with both atomic force microscopy (AFM) and high-resolution secondary ion mass spectrometry (SIMS) performed with a Cameca NanoSIMS 50. As the cholesterol composition increased from 0 to 19mol%, the circular ordered domains became more elongated, and the amount of 15N-DLPC in the gel-phase domains remained constant at 6–7mol%. Individual and micron-sized clusters of nanoscopic domains enriched in D70-DSPC were abundant in the 19mol% cholesterol membrane. AFM imaging showed that these lipid domains had irregular borders, indicating that they were gel-phase domains, and not non-ideally mixed lipid clusters or nanoscopic liquid-ordered domains.

The influence of dipalmitoyl phosphatidylserine on phase behaviour of and cellular response to lyotropic liquid crystalline dispersions

Lyotropic liquid crystalline nanoparticles (cubosomes) have the potential to act as amphiphilic scaffolds for the presentation of lipids and subsequent application in, for example, bioseparations and therapeutic delivery. In this work we have formulated lyotropic liquid crystalline systems based on the synthetic amphiphile 1,2,3-trihydroxy-3,7,11,15-tetramethylhexadecane (phytantriol) and containing the lipid dipalmitoyl phosphatidylserine (DPPS). We have prepared a range of DPPS-containing phytantriol cubosome formulations and characterized them using Small Angle X-ray Scattering and Cryo-transmission electron microscopy. These techniques show that increased DPPS content induces marked changes in lyotropic liquid crystalline phase behaviour, characterized by changes in crystallographic dimensions and increases in vesicle content. Furthermore, in vitro cell culture studies indicate that these changes correlate with lipid/surfactant cellular uptake and cytotoxicity. A model cell membrane based on a surface supported phospholipid bilayer was used to gain insights into cubosome–bilayer interactions using Quartz Crystal Microgravimetry. The data show that mass uptake at the supported bilayer increased with DPPS content. We propose that the cytotoxicity of the DPPS-containing dispersions results from changes in lipid/surfactant phase behaviour and the preferential attachment and fusion of vesicles at the cell membrane.

Convulsant agent pentylenetetrazol does not alter the structural and dynamical properties of dipalmitoylphosphatidylcholine model membranes

Pentylenetetrazol (PTZ) is an epileptogenic agent, which is widely used in the determination of epilepsy-induced alterations and in the assessment of anticonvulsant agents in epileptic studies. Even though PTZ is suggested to induce repetitive firing of nerve fibers and shorten the refractory, its mechanism of action is only partially understood. In the literature there are discrepancies for its action mechanism. While some studies stated that primary sites of PTZ are membrane proteins, some reports indicated that PTZ acts on membrane lipids. In order to gain new insight for this we tested the possibility of interaction of PTZ with a simplified model system called dipalmitoylphosphatidylcholine (DPPC) multilamellar vesicles (MLVs) at agent concentrations (0–24 mol%) using differential scanning calorimetry (DSC), Fourier transform infrared (FTIR), electron spin resonance (ESR) and steady-state fluorescence spectroscopy. The results showed that PTZ at concentrations used (1–24 mol%), does not cause any significant change in lipid phase behavior, lipid dynamics (fluidity), lipid acyl chain flexibility (order), hydration state of the head group and/or the region near the head group of DPPC MLVs. These results clearly revealed that PTZ does not change the structural and dynamical parameters of neutral DPPC lipid vesicles and does not locate within the bilayer.

The Nonsteroidal Anti-Inflammatory Drug Indomethacin Induces Heterogeneity in Lipid Membranes: Potential Implication for Its Diverse Biological Action

BackgroundThe nonsteroidal anti-inflammatory drug (NSAID), indomethacin (Indo), has a large number of divergent biological effects, the molecular mechanism(s) for which have yet to be fully elucidated. Interestingly, Indo is highly amphiphilic and associates strongly with lipid membranes, which influence localization, structure and function of membrane-associating proteins and actively regulate cell signaling events. Thus, it is possible that Indo regulates diverse cell functions by altering micro-environments within the membrane. Here we explored the effect of Indo on the nature of the segregated domains in a mixed model membrane composed of dipalmitoyl phosphatidyl-choline (di16∶0 PC, or DPPC) and dioleoyl phosphatidyl-choline (di18∶1 PC or DOPC) and cholesterol that mimics biomembranes.Methodology/Principal FindingsUsing a series of fluorescent probes in a fluorescence resonance energy transfer (FRET) study, we found that Indo induced separation between gel domains and fluid domains in the mixed model membrane, possibly by enhancing the formation of gel-phase domains. This effect originated from the ability of Indo to specifically target the ordered domains in the mixed membrane. These findings were further confirmed by measuring the ability of Indo to affect the fluidity-dependent fluorescence quenching and the level of detergent resistance of membranes.Conclusion/SignificanceBecause the tested lipids are the main lipid constituents in cell membranes, the observed formation of gel phase domains induced by Indo potentially occurs in biomembranes. This marked Indo-induced change in phase behavior potentially alters membrane protein functions, which contribute to the wide variety of biological activities of Indo and other NSAIDs.

Effect of calcium neutralization on elastic and swelling properties of crosslinked poly(acrylic acid) - correlation to inhomogeneities and phase behaviour

AbstractCrosslinked hydrogels of poly(acrylic acid) neutralized with calcium hydroxide were synthesized using free radical co-polymerization. The effects of the amount added calcium on the elastic modulus and swelling properties of the gels and the correlation to phase behaviour and structural changes within the gels were studied using texture analysis, gravimetric analysis, scanning electron microscopy (SEM), energy dispersive X-ray (EDX) analysis and atomic force microscopy (AFM). It was found that the elastic modulus decreased nonlinearly with increasing amount of added calcium and that the swelling’s dependence on the amount of added calcium was complicated. The maximum swelling increased with increasing amount of added calcium until a critical calcium content was reached, upon which the gels phase separated, with a strong decrease in swelling as a result. The changes in properties are explained by the fact that calcium affects the structure of the polymer network during synthesis and by the phase behaviour of the gels. Changes in the gel structure with the addition of calcium were detected with AFM. Furthermore, AFM revealed different phases on the nanometre scale for the sample with a calcium content around which phase separation is macroscopically observed. Finally, it was shown that the sulphur from the initiator potassium persulfate formed crystal like regions with high sulphur and calcium content upon drying of the hydrogels.

A New Compositional Model for Hydraulic Fracturing With Energized Fluids

Summary Traditional fracturing models regard fracturing fluids as a single-component, single-phase fluid. This assumption is clearly incorrect for energized fluids where phase changes and mass transfer between phases play important roles in controlling fluid rheology, leakoff, and fracture geometry. A model is developed to simulate hydraulic fracturing with energized fluids. Compositional balances allow tracking of the changes in phase behavior and fluid properties, such as rheology and multiphase leakoff. An energy balance is implemented in order to consider temperature changes during fracturing. Phase behavior has been taken into account through an equation-of-state (EOS) formulation. These compositional- and phase-behavior effects are coupled with a geomechanical model for fracture propagation. It is shown that phase behavior and leakoff can change the composition and fluid rheology in the fracture significantly. This has a dramatic effect on the fracture geometry. Phase-behavior changes are coupled closely to the temperature and pressure changes in the fracture. The temperature, phase behavior, and partitioning of components in the liquid and gas phases have a significant effect on fracture dimensions. For example, shorter and wider fractures can be obtained by foaming an energized fluid. With the model presented, these temperature, pressure, and composition changes can now be modeled accurately and incorporated into the fracture growth and geometry.

Polydispersity effects in poly(isoprene-b-styrene-b-ethylene oxide) triblock terpolymers

Four hydroxyl-terminated poly(isoprene-b-styrene) diblock copolymers with comparable molecular weights and compositions (equivalent volume fractions of polyisoprene and polystyrene) but different polystyrene block polydispersity indices (M(w)/M(n)=1.06,1.16,1.31,1.44) were synthesized by anionic polymerization using either sec-butyllithium or the functional organolithium 3-triisopropylsilyloxy-1-propyllithium. Poly(ethylene oxide) (PEO) blocks were grown from the end of each of these parent diblocks to yield four series of poly(isoprene-b-styrene-b-ethylene oxide) (ISO) triblock terpolymers that were used to interrogate the effects of varying the polydispersity of the middle bridged polystyrene block. In addition to the neat triblock samples, 13 multicomponent blends were prepared at four different compositions from the ISO materials containing a polystyrene segment with M(w)/M(n)=1.06; these blends were used to probe the effects of increasing the polydispersity of the terminal PEO block. The melt-phase behavior of all samples was characterized using small-angle X-ray scattering and dynamic mechanical spectroscopy. Numerous polydispersity-driven morphological transitions are reported, including transitions from lamellae to core-shell gyroid, from core-shell gyroid to hexagonally packed cylinders, and from network morphologies [either O(70) (the orthorhombic Fddd network) or core-shell gyroid] to lamellae. Domain periodicities and order-disorder transition temperatures also vary with block polydispersities. Self-consistent field theory calculations were performed to supplement the experimental investigations and help elucidate the molecular factors underlying the polydispersity effects. The consequences of varying the polydispersity of the terminal PEO block are comparable to the polydispersity effects previously reported in AB diblock copolymers. Namely, domain periodicities increase with increasing polydispersity and domain interfaces tend to curve toward polydisperse blocks. The changes in phase behavior that are associated with variations in the polydispersity of the middle bridged polystyrene block, however, are not analogous to those reported in AB diblock copolymers, as increases in this middle block polydispersity are not always accompanied by (i) increased domain periodicities and (ii) a tendency for domain interfaces to curve toward the polydisperse domain. These results highlight the utility of polydispersity as a tool to tune the phase behavior of ABC block terpolymers.

Theory of Raft Formation by the Cross-Linking of Saturated or Unsaturated Lipids in Model Lipid Bilayers

We consider the effect of cross-linking a small fraction of lipids, either saturated or unsaturated, in a mixture of saturated and unsaturated lipids and cholesterol. The change in phase behavior is examined utilizing a recent phenomenological model of the ternary system, which is extended to include a fourth component representing the cross-linked lipids. These lipids are taken to be identical to monomeric ones except for their reduced entropy of mixing. We find that even a relatively small amount of cross-linked lipids, less than 5 mol %, is sufficient to significantly expand the range of compositions within which there is coexistence between liquid-ordered and liquid-disordered phases. Equivalently, the cross-linking of lipids increases the liquid-liquid miscibility transition temperature, and therefore could bring about phase separation at a temperature at which, before cross-linking, there was only a single liquid phase.