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At least 73 records · Page 4

Molecular dynamics studies of simple membrane-water interfaces: Structure and functions in the beginnings of cellular life

Molecular dynamics computer simulations of the structure and functions of a simple membrane are performed in order to examine whether membranes provide an environment capable of promoting protobiological evolution. Our model membrane is composed of glycerol 1-monooleate. It is found that the bilayer surface fluctuates in time and space, occasionally creating thinning defects in the membrane. These defects are essential for passive transport of simple ions across membranes because they reduce the Born barrier to this process by approximately 40%. Negative ions are transferred across the bilayer more readily than positive ions due to favorable interactions with the electric field at the membrane-water interface. Passive transport of neutral molecules is, in general, more complex than predicted by the solubility-diffusion model. In particular, molecules which exhibit sufficient hydrophilicity and lipophilicity concentrate near membrane surfaces and experience 'interfacial resistance' to transport. The membrane-water interface forms an environment suitable for heterogeneous catalysis. Several possible mechanisms leading to an increase of reaction rates at the interface are discussed. We conclude that vesicles have many properties that make them very good candidates for earliest protocells. Some potentially fruitful directions of experimental and theoretical research on this subject are proposed.

Pohorille, Andrew↗

Durability of Membrane Electrode Assemblies (MEAs) in PEM Fuel Cells Operated on Pure Hydrogen and Oxygen

Proton exchange membrane (PEM) fuel cells are energy sources that have the potential to replace alkaline fuel cells for space programs. Broad power ranges, high peak-to-nominal power capabilities, low maintenance costs, and the promise of increased life are the major advantages of PEM technology in comparison to alkaline technology. The probability of PEM fuel cells replacing alkaline fuel cells for space applications will increase if the promise of increased life is verified by achieving a minimum of 10,000 hours of operating life. Durability plays an important role in the process of evaluation and selection of MEAs for Teledyne s Phase I contract with the NASA Glenn Research Center entitled Proton Exchange Membrane Fuel cell (PEMFC) Power Plant Technology Development for 2nd Generation Reusable Launch Vehicles (RLVs). For this contract, MEAs that are typically used for H2/air operation were selected as potential candidates for H2/O2 PEM fuel cells because their catalysts have properties suitable for O2 operation. They were purchased from several well-established MEA manufacturers who are world leaders in the manufacturing of diverse products and have committed extensive resources in an attempt to develop and fully commercialize MEA technology. A total of twelve MEAs used in H2/air operation were initially identified from these manufacturers. Based on the manufacturers specifications, nine of these were selected for evaluation. Since 10,000 hours is almost equivalent to 14 months, it was not possible to perform continuous testing with each MEA selected during Phase I of the contract. Because of the lack of time, a screening test on each MEA was performed for 400 hours under accelerated test conditions. The major criterion for an MEA pass or fail of the screening test was the gas crossover rate. If the gas crossover rate was higher than the membrane intrinsic permeability after 400 hours of testing, it was considered that the MEA had failed the test. Three types of MEAs out of the nine total membranes failed the test. The evaluation results showed that fuel cell operating conditions (current, pressure, stoichiometric flow rates) were the parameters that influenced the durability of MEAs. In addition, the durability test results indicated that the type of membrane was also an important parameter for MEA durability. At accelerated test conditions, the MEAs with casted membranes failed during the 400 hour test. However, the MEAs prepared from the casted membrane with support as well as extruded membranes, both passed the 400h durability test at accelerated operating test conditions. As a result of the MEA accelerated durability tests, four MEAs were selected for further endurance testing. These tests are being carried out with four-cell stacks under nominal fuel cell operating conditions.

Stanic, Vesna↗

Specific photoaffinity labeling of two plasma membrane polypeptides with an azido auxin

Plasma membrane vesicles were isolated from zucchini (Cucurbita pepo) hypocotyl tissue by aqueous phase partitioning and assessed for homogeneity by the use of membrane-specific enzyme assays. The highly pure (ca. 95%) plasma membrane vesicles maintained a pH differential across the membrane and accumulated a tritiated azido analogue of 3-indoleacetic acid (IAA), 5-azido-[7-3H]IAA ([3H]N3IAA), in a manner similar to the accumulation of [3H]IAA. The association of the [3H]N3IAA with membrane vesicles was saturable and subject to competition by IAA and auxin analogues. Auxin-binding proteins were photoaffinity labeled by addition of [3H]N3IAA to plasma membrane vesicles prior to exposure to UV light (15 sec; 300 nm) and detected by subsequent NaDodSO4/PAGE and fluorography. When the reaction temperature was lowered to -196 degrees C, high-specific-activity labeling of a 40-kDa and a 42-kDa polypeptide was observed. Triton X-100 (0.1%) increased the specific activity of labeling and reduced the background, which suggests that the labeled polypeptides are intrinsic membrane proteins. The labeled polypeptides are of low abundance, as expected for auxin receptors. Further, the addition of IAA and auxin analogues to the photoaffinity reaction mixture resulted in reduced labeling that was qualitatively similar to their effects on the accumulation of radiolabeled IAA in membrane vesicles. Collectively, these results suggest that the radiolabeled polypeptides are auxin receptors. The covalent nature of the label should facilitate purification and further characterization of the receptors.

NASA Discipline Number 29-20↗

Fully Nonlinear Modeling and Analysis of Precision Membranes

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Pai, P. Frank↗

The Origin and Early Evolution of Membrane Proteins

Membrane proteins mediate functions that are essential to all cells. These functions include transport of ions, nutrients and waste products across cell walls, capture of energy and its transduction into the form usable in chemical reactions, transmission of environmental signals to the interior of the cell, cellular growth and cell volume regulation. In the absence of membrane proteins, ancestors of cell (protocells), would have had only very limited capabilities to communicate with their environment. Thus, it is not surprising that membrane proteins are quite common even in simplest prokaryotic cells. Considering that contemporary membrane channels are large and complex, both structurally and functionally, a question arises how their presumably much simpler ancestors could have emerged, perform functions and diversify in early protobiological evolution. Remarkably, despite their overall complexity, structural motifs in membrane proteins are quite simple, with a-helices being most common. This suggests that these proteins might have evolved from simple building blocks. To explain how these blocks could have organized into functional structures, we performed large-scale, accurate computer simulations of folding peptides at a water-membrane interface, their insertion into the membrane, self-assembly into higher-order structures and function. The results of these simulations, combined with analysis of structural and functional experimental data led to the first integrated view of the origin and early evolution of membrane proteins.

Pohorille, Andrew↗

Automated Solvent Seaming of Large Polyimide Membranes

A solvent-based welding process enables the joining of precise, cast polyimide membranes at their edges to form larger precise membranes. The process creates a homogeneous, optical-quality seam between abutting membranes, with no overlap and with only a very localized area of figure disturbance. The seam retains 90 percent of the strength of the parent material. The process was developed for original use in the fabrication of wide-aperture membrane optics, with areal densities of less than 1 kg/m2, for lightweight telescopes, solar concentrators, antennas, and the like to be deployed in outer space. The process is just as well applicable to the fabrication of large precise polyimide membranes for flat or inflatable solar concentrators and antenna reflectors for terrestrial applications. The process is applicable to cast membranes made of CP1 (or equivalent) polyimide. The process begins with the precise fitting together and fixturing of two membrane segments. The seam is formed by applying a metered amount of a doped solution of the same polyimide along the abutting edges of the membrane segments. After the solution has been applied, the fixtured films are allowed to dry and are then cured by convective heating. The weld material is the same as the parent material, so that what is formed is a homogeneous, strong joint that is almost indistinguishable from the parent material. The success of the process is highly dependent on formulation of the seaming solution from the correct proportion of the polyimide in a suitable solvent. In addition, the formation of reliable seams depends on the deposition of a precise amount of the seaming solution along the seam line. To ensure the required precision, deposition is performed by use of an automated apparatus comprising a modified commercially available, large-format, ink-jet print head on an automated positioning table. The printing head jets the seaming solution into the seam area at a rate controlled in coordination with the movement of the positioning table.

Rood, Robert↗

The Earliest Ion Channels in Protocellular Membranes

Cellular membranes with their hydrophobic interior are virtually impermeable to ions. Bulk of ion transport through them is enabled through ion channels. Ion channels of contemporary cells are complex protein molecules which span the membrane creating a cylindrical pore filled with water. Protocells, which are widely regarded as precursors to modern cells, had similarly impermeable membranes, but the set of proteins in their disposal was much simpler and more limited. We have been, therefore, exploring an idea that the first ion channels in protocellular membranes were formed by much smaller peptide molecules that could spontaneously selfassemble into short-lived cylindrical bundles in a membrane. Earlier studies have shown that a group of peptides known as peptaibols is capable of forming ion channels in lipid bilayers when they are exposed to an electric field. Peptaibols are small, non-genetically encoded peptides produced by some fungi as a part of their system of defense against bacteria. They are usually only 14-20 residues long, which is just enough to span the membrane. Their sequence is characterized by the presence of non-standard amino acids which, interestingly, are also expected to have existed on the early earth. In particular, the presence of 2-aminoisobutyric acid (AIB) gives peptaibols strong helix forming propensities. Association of the helices inside membranes leads to the formation of cylindrical bundles, typically containing 4 to 10 monomers. Although peptaibols are excellent candidates for models of the earliest ion channels their structures, which are stabilized only by van der Waals forces and occasional hydrogen bonds between neighboring helices, are not very stable. Although it might properly reflect protobiological reality, it is also a major obstacle in studying channel behavior. For this reason we focused on two members of the peptaibol family, trichotoxin and antiamoebin, which are characterized by a single conductance level. This indicates that their structures are unique and stable. In addition, it is also believed that the trichotoxin channel displays some selectivity between potassium and chloride ions. This makes trichotoxin and antiamoebin ideal models of the earliest ion channels that could provide insight into the origins of ion conductance and selectivity. In the absence of crystal structure of the trichotoxin and antiamoebin channels, we propose their molecular models based on experimentally determined number of monomers forming the bundles. We use molecular dynamics simulations to validate the models in terms of their conductance and selectivity. On the basis of our simulations we show that the emergence of channels built of small, alpha-helical peptides was protobiologically plausible and did not require highly specific amino acid sequences, which is a convenient evolutionary trait. Despite their simple structure, such channels could possess properties that, at the first sight, appear to require markedly larger complexity. To this end, we will discuss how the amino acid sequence and structure of primitive channels give rise to the phenomena of ionic conductance and selectivity across the earliest cell walls, which were essential functions for the emergence and early evolution of protocells. Furthermore, we will argue that even though architectures of membrane proteins are not nearly as diverse as those of water-soluble proteins, they are sufficiently flexible to adapt readily to the functional demands arising during evolution.

Mijajlovic, Milan↗

Curved-Focal-Plane Arrays Using Deformed-Membrane Photodetectors

A versatile and simple approach to the design and fabrication of curved-focal-plane arrays of silicon-based photodetectors is being developed. This approach is an alternative to the one described in "Curved Focal-Plane Arrays Using Back- Illuminated High-Purity Photodetectors" (NPO-30566), NASA Tech Briefs, Vol. 27, No. 10 (October 2003), page 10a. As in the cited prior article, the basic idea is to improve the performance of an imaging instrument and simplify the optics needed to obtain a given level of performance by making an image sensor (in this case, an array of photodetectors) conform to a curved focal surface, instead of designing the optics to project an image onto a flat focal surface. There is biological precedent for curved-focal-surface designs: retinas - the image sensors in eyes - conform to the naturally curved focal surfaces of eye lenses. The present approach is applicable to both front-side- and back-side-illuminated, membrane photodetector arrays and is being demonstrated on charge-coupled devices (CCDs). The very-large scale integrated (VLSI) circuitry of such a CCD or other array is fabricated on the front side of a silicon substrate, then the CCD substrate is attached temporarily to a second substrate for mechanical support, then material is removed from the back to obtain the CCD membrane, which typically has a thickness between 10 and 20 m. In the case of a CCD designed to operate in back-surface illumination, delta doping can be performed after thinning to enhance the sensitivity. This approach is independent of the design and method of fabrication of the front-side VLSI circuitry and does not involve any processing of a curved silicon substrate. In this approach, a third substrate would be prepared by polishing one of its surfaces to a required focal-surface curvature. A CCD membrane fabricated as described above would be pressed against, deformed into conformity with, and bonded to, the curved surface. The technique used to press and bond the CCD membrane would depend on the nature of the supporting material (see figure). For example, if the third substrate were made of quartz frit, the substrate would be prepared by suffusing it with epoxy. Then one would take advantage of the porosity of the frit by applying a partial vacuum to the opposite surface of the frit, causing atmospheric pressure to push the CCD membrane against the curved surface. The curing of the epoxy would bond the CCD membrane to the curved surface. Alternatively, if the third substrate were made of a nonporous material, the curved substrate surface would be prepared by coating it with a wax or an uncured epoxy. The CCD membrane would be pressed against the coated, curved surface by use of a suitably pressurized balloon. The CCD membrane would then become bonded to the curved surface by curing of the epoxy or freezing of the wax.

Nikzad, Shouleh↗

Electrodeionization Using Microseparated Bipolar Membranes

An electrochemical technique for deionizing water, now under development, is intended to overcome a major limitation of prior electrically-based water-purification techniques. The limitation in question is caused by the desired decrease in the concentration of ions during purification: As the concentration of ions decreases, the electrical resistivity of the water increases, posing an electrical barrier to the removal of the remaining ions. In the present technique, this limitation is overcome by use of electrodes, a flowfield structure, and solid electrolytes configured to provide conductive paths for the removal of ions from the water to be deionized, even when the water has already been purified to a high degree. The technique involves the use of a bipolar membrane unit (BMU), which includes a cation-exchange membrane and an anion-exchange membrane separated by a nonconductive mesh that has been coated by an ionically conductive material (see figure). The mesh ensures the desired microseparation between the ion-exchange membranes: The interstices bounded by the inner surfaces of the membranes and the outer surfaces of the coated mesh constitute a flow-field structure that allows the water that one seeks to deionize (hereafter called "process water" for short) to flow through the BMU with a low pressure drop. The flow-field structure is such that the distance between any point in the flow field and an ionically conductive material is small; thus, the flow-field structure facilitates the diffusion of molecules and ions to and from the ion-exchange membranes. The BMU is placed between an anode and a cathode, but not in direct contact with these electrodes. Instead, the space between the anion-exchange membrane and the anode is denoted the anode compartment and is filled with an ionic solution. Similarly, the space between the cation-exchange membrane and the cathode is denoted the cathode compartment and is filled with a different ionic solution. The electrodes are made of titanium coated with platinum.

Lyons, Donald↗

Search for selective ion diffusion through membranes

The diffusion rates of several ions through some membranes developed as battery separators were measured. The ions investigated were Li(+), Rb(+), Cl(-), and So4. The members were crosslinked polyvinyl alcohol, crosslinked polyacrylic acid, a copolymer of the two, crosslinked calcium polyacrylate, cellulose, and several microporous polyphenylene oxide based films. No true specificity for diffusion of any of these ions was found for any of the membranes. But the calcium polyacrylate membrane was found to exhibit ion exchange with the diffusing ions giving rise to the leaching of the calcium ion and low reproducibility. These findings contrast earlier work where the calcium polyacrylate membrane did show specificity to the diffusion of the copper ion. In general, Fick's law appeared to be obeyed. Except for the microporous membranes, the coefficients for ion diffusion through the membranes were comparable with their values in water. For the microporous membranes, the values found for the coefficients were much less, due to the tortuosity of the micropores.

May, C. E.↗

The casting of semi-permeable membranes in a microgravity environment

The National Electric Company of Venezuela, C.A.D.A.F.E., is sponsoring the development of this experiment which represents Venezuela's first scientific experiment in space. The experience can be classified as an educational one which could add knowledge to the fundamental study of polymeric membranes. Presently, semi-permeable membranes are being manufactured from several different kind of polymers all over the world and specific applications have been identified in fluid separation processes such as reverse osmosis, ultrafiltration and electrodyalisis. Although, the ultrastructure of asymetric and composite membranes have been under intensive study, still there are many questions about the factors affecting this structure and their degree of correlation. Nevertheless, there is indication that the entire morphological structure of polymeric membranes could be affected by the differences in specific gravity between the cast solution and the coagulation liquid, normally used in the membranes preparation process. The casting of semi-permeable membranes in space might help to identify the effect of gravity upon the structure of these membranes. It is important to recognize that the casting process involves changes of states (liquid-gas, liquid-solid) and that in a micro gravity environment, there will be a reduction on buoyancy-driven natural convection and density gradients

Ivan Vera↗

Electrochemical performance and transport properties of a Nafion membrane in a hydrogen-bromine cell environment

The overall energy conversion efficiency of a hydrogen-bromine energy storage system is highly dependent upon the characteristics and performance of the ion-exchange membrane utilized as a half-cell separator. The electrochemical performance and transport properties of a duPont Nafion membrane in an aqueous HBr-Br2 environment were investigated. Membrane conductivity data are presented as a function of HBr concentration and temperature for the determination of ohmic voltage losses across the membrane in an operational cell. Diffusion-controlled bromine permeation rates and permeabilities are presented as functions of solution composition and temperature. Relationships between the degree of membrane hydration and the membrane transport characteristics are discussed. The solution chemistry of an operational hydrogen-bromine cell undergoing charge from 45% HBr to 5% HBr is discussed, and, based upon the experimentally observed bromine permeation behavior, predicted cell coulombic losses due to bromine diffusion through the membrane are presented as a function of the cell state-of-charge.

Baldwin, Richard S.↗

Qualification of the RSRM case membrane case-to-insulation bondline inspection using the Thiokol Corporation ultrasonic RSRM bondline inspection system

Qualification testing of Combustion Engineering's AMDATA Intraspect/98 Data Acquisition and Imaging System that applies to the redesigned solid rocket motor (RSRM) case membrane case-to-insulation bondline inspection was performed. Testing was performed at M-67, the Thiokol Corp. RSRM Assembly Facility. The purpose of the inspection was to verify the integrity of the case membrane case-to-insulation bondline. The case membrane scanner was calibrated on the redesigned solid rocket motor case segment calibration standard, which had an intentional 1.0 by 1.0 in. case-to-insulation unbond. The case membrane scanner was then used to scan a 20 by 20 in. membrane area of the case segment. Calibration of the scanner was then rechecked on the calibration standard to ensure that the calibration settings did not change during the case membrane scan. This procedure was successfully performed five times to qualify the unbond detection capability of the case membrane scanner.

Cook, M.↗

Modeling of membrane processes for air revitalization and water recovery

Gas-separation and reverse-osmosis membrane models are being developed in conjunction with membrane testing at NASA JSC. The completed gas-separation membrane model extracts effective component permeabilities from multicomponent test data, and predicts the effects of flow configuration, operating conditions, and membrane dimensions on module performance. Variable feed- and permeate-side pressures are considered. The model has been applied to test data for hollow-fiber membrane modules with simulated cabin-air feeds. Results are presented for a membrane designed for air drying applications. Extracted permeabilities are used to predict the effect of operating conditions on water enrichment in the permeate. A first-order reverse-osmosis model has been applied to test data for spiral wound membrane modules with a simulated hygiene water feed. The model estimates an effective local component rejection coefficient under pseudosteady-state conditions. Results are used to define requirements for a detailed reverse-osmosis model.

Lange, Kevin E.↗

Permeable membrane experiment

The purpose of the Permeable Membrane Experiment is to gather flight data on three areas of membrane performance that are influenced by the presence of gravity. These areas are: (1) Liquid/gas phase separation, (2) gas bubble interference with diffusion through porous membranes and (3) wetting characteristics of hydrophilic membrane surfaces. These data are important in understaning the behavior of membrane/liquid/gas interfaces where surface tension forces predominate. The data will be compared with 1-g data already obtained and with predicted micrograviity behavior. The data will be used to develop designs for phase separation and plant nutrient delivery systems and will be available to the life support community for use in developing technologies which employ membranes. A conceptual design has been developed to conduct three membrane experiments, in sequence, aboard a single Complex Autonomous Payload (CAP) carrier to be carried in the Shuttle Orbiter payload bay. One experiment is conducted for each of the three membrane performance areas under study. These experiments are discussed in this paper.

Slavin, Thomas J.↗

Solutocapillary Convection Effects on Polymeric Membrane Morphology

Macro voids are undesirable large pores in membranes used for purification. They form when membranes are cast as thin films on a smooth surface by evaporating solvent (acetone) from a polymer solution. There are two un-tested hypotheses explaining the growth of macro voids. One states that diffusion of the non-solvent (water) is solely responsible, while the other states that solutocapillary convection is the primary cause of macro void growth. Solutocapillary convection is flow-caused by a concentration induced surface-tension gradient. Macrovoid growth in the former hypothesis is gravity independent, while in the latter it is opposed by gravity. To distinguish between these two hypotheses, experiments were designed to cast membranes in zero-gravity. A semi-automated apparatus was designed and built for casting membranes during the 20 secs of zero-g time available in parabolic aircraft flight such as NASA's KC-135. The phase changes were monitored optically, and membrane morphology was evaluated by scanning electron microscopy (SEM). These studies appear to be the first quantitative studies of membrane casting in micro-gravity which incorporate real-time data acquisition. Morphological studies of membranes cast at 0, 1, and 1.8 g revealed the presence of numerous, sparse and no macrovoids respectively. These results are consistent with the predictions of the solutocapillary hypothesis of macrovoid growth.

Krantz, William B.↗

Low Crossover Polymer Electrolyte Membranes for Direct Methanol Fuel Cells

Direct Methanol Fuel Cells (DMFC's) using polymer electrolyte membranes are promising power sources for portable and vehicular applications. State of the art technology using Nafion(R) 117 membranes (Dupont) are limited by high methanol permeability and cost, resulting in reduced fuel cell efficiencies and impractical commercialization. Therefore, much research in the fuel cell field is focused on the preparation and testing of low crossover and cost efficient polymer electrolyte membranes. The University of Southern California in cooperation with the Jet Propulsion Laboratory is focused on development of such materials. Interpenetrating polymer networks are an effective method used to blend polymer systems without forming chemical links. They provide the ability to modify physical and chemical properties of polymers by optimizing blend compositions. We have developed a novel interpenetrating polymer network based on poly (vinyl - difluoride)/cross-linked polystyrenesulfonic acid polymer composites (PVDF PSSA). Sulfonation of polystyrene accounts for protonic conductivity while the non-polar, PVDF backbone provides structural integrity in addition to methanol rejection. Precursor materials were prepared and analyzed to characterize membrane crystallinity, stability and degree of interpenetration. USC JPL PVDF-PSSA membranes were also characterized to determine methanol permeability, protonic conductivity and sulfur distribution. Membranes were fabricated into membrane electrode assemblies (MEA) and tested for single cell performance. Tests include cell performance over a wide range of temperatures (20 C - 90 C) and cathode conditions (ambient Air/O2). Methanol crossover values are measured in situ using an in-line CO2 analyzer.

Prakash, G. K. Surya↗

Computer Simulations of Small Molecules in Membranes: Insights from Computer Simulations into the Interactions of Small Molecules with Lipid Bilayers

Two of Ernest Overton's lasting contributions to biology are the Meyer-Overton relationship between the potency of an anesthetic and its solubility in oil, and the Overton rule which relates the permeability of a membrane to the oil-water partition coefficient of the permeating molecule. A growing body of experimental evidence, however, cannot be reconciled with these theories. In particular, the molecular nature of membranes, unknown to Overton, needs to be included in any description of these phenomena. Computer simulations are ideally suited for providing atomic-level information about the behavior of small molecules in membranes. The authors discuss simulation studies relevant to Overton's ideas. Through simulations it was found that anesthetics tend to concentrate at interfaces and their anesthetic potency correlates better with solubility at the water-membrane interface than with solubility in oil. Simulation studies of membrane permeation revealed the anisotropic nature of the membranes, as evidenced, for example, by the highly nonuniform distribution of free volume in the bilayer. This, in turn, influences the diffusion rates of solutes, which increase with the depth in the membrane. Small solutes tend to move by hopping between voids in the bilayer, and this hopping motion may be responsible for the deviation from the Overton rule of the permeation rates of these molecules.

Pohorille, Andrew↗