Lateral diffusion in an archipelago. Dependence on tracer size.

In a pure fluid-phase lipid, the dependence of the lateral diffusion coefficient on the size of the diffusing particle may be obtained from the Saffman-Delbrück equation or the free-volume model. When diffusion is obstructed by immobile proteins or domains of gel-phase lipids, the obstacles yield an additional contribution to the size dependence. Here this contribution is examined using Monte Carlo calculations. For random point and hexagonal obstacles, the diffusion coefficient depends strongly on the size of the diffusing particle, but for fractal obstacles--cluster-cluster aggregates and multicenter diffusion-limited aggregates--the diffusion coefficient is independent of the size of the diffusing particle. The reason is that fractals have no characteristic length scale, so a tracer sees on average the same obstructions, regardless of its size. The fractal geometry of the excluded area for tracers of various sizes is examined. Percolation thresholds are evaluated for a variety of obstacles to determine how the threshold depends on tracer size and to compare the thresholds for compact and extended obstacles.     

Membrane lateral mobility obstructed by polymer-tethered lipids studied at the single molecule level

Obstructed long-range lateral diffusion of phospholipids (TRITC-DHPE) and membrane proteins (bacteriorhodopsin) in a planar polymer-tethered 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer is studied using wide-field single molecule fluorescence microscopy. The obstacles are well-controlled concentrations of hydrophobic lipid-mimicking dioctadecylamine moieties in the polymer-exposed monolayer of the model membrane. Diffusion of both types of tracer molecules is well described by a percolating system with different percolation thresholds for lipids and proteins. Data analysis using a free area model of obstructed lipid diffusion indicates that phospholipids and tethered lipids interact via hard-core repulsion. A comparison to Monte Carlo lattice calculations reveals that tethered lipids act as immobile obstacles, are randomly distributed, and do not self-assemble into large-scale aggregates for low to moderate tethering concentrations. A procedure is presented to identify anomalous subdiffusion from tracking data at a single time lag. From the analysis of the cumulative distribution function of the square displacements, it was found that TRITC-DHPE and W80i show normal diffusion at lower concentrations of tethered lipids and anomalous diffusion at higher ones. This study may help improve our understanding of how lipids and proteins in biomembranes may be obstructed by very small obstacles comprising only one or very few molecules.     

Two-Dimensional Continuum Percolation Threshold for Diffusing Particles of Nonzero Radius

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing obstructed diffusion is the percolation threshold. The thresholds are well known for point tracers, but for tracers of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. Here thresholds are obtained for circular obstacles on the continuum. Random obstacle configurations are generated by Brownian dynamics or Monte Carlo methods, the obstacles are immobilized, and the percolation threshold is obtained by solving a bond percolation problem on the Voronoi diagram of the obstacles. The percolation threshold is expressed as the diameter of the largest tracer that can cross a set of immobile obstacles at a prescribed number density. For random overlapping obstacles, the results agree with the known analytical solution quantitatively. When the obstacles are soft disks with a 1/r¹² repulsion, the percolating diameter is ∼20% lower than for overlapping obstacles. A percolation model predicts that the threshold is highly sensitive to the tracer radius. To our knowledge, such a strong dependence has so far not been reported for the plasma membrane, suggesting that percolation is not the factor controlling lateral diffusion. A definitive experiment is proposed.     

Lateral diffusion in an archipelago. The effect of mobile obstacles.

Lateral diffusion of mobile proteins and lipids (tracers) in a membrane is hindered by the presence of proteins (obstacles) in the membrane. If the obstacles are immobile, their effect may be described by percolation theory, which states that the long-range diffusion constant of the tracers goes to zero when the area fraction of obstacles is greater than the percolation threshold. If the obstacles are themselves mobile, the diffusion constant of the tracers depends on the area fraction of obstacles and the relative jump rate of tracers and obstacles. This paper presents Monte Carlo calculations of diffusion constants on square and triangular lattices as a function of the concentration of obstacles and the relative jump rate. The diffusion constant for particles of various sizes is also obtained. Calculated values of the concentration-dependent diffusion constant are compared with observed values for gramicidin and bacteriorhodopsin. The effect of the proteins as inert obstacles is significant, but other factors, such as protein-protein interactions and perturbation of lipid viscosity by proteins, are of comparable importance. Potential applications include the diffusion of proteins at high concentrations (such as rhodopsin in rod outer segments), the modulation of diffusion by release of membrane proteins from cytoskeletal attachment, and the diffusion of mobile redox carriers in mitochondria, chloroplasts, and endoplasmic reticulum.     

Lateral diffusion in a mixture of mobile and immobile particles. A Monte Carlo study.

The lateral diffusion coefficient for mixtures of mobile and immobile particles is obtained from Monte Carlo calculations of random walks by mobile tracers in the presence of immobile obstacles on a triangular lattice. The diffusion coefficient of the mobile species is obtained as a function of the area fractions of mobile and immobile species. The results are applied to diffusion of band 3 in the erythrocyte membrane, and indicate that obstruction of diffusion of mobile band 3 by band 3 and glycophorin attached to the membrane skeleton is not sufficient to explain the observed diffusion coefficient.     

Influence of obstacles on lipid lateral diffusion: computer simulation of FRAP experiments and application to proteoliposomes and biomembranes

Fluorescence Recovery After Photobleaching experiments were simulated using a computer approach in which a membrane lipid leaflet was mimicked using a triangular lattice obstructed with randomly distributed immobile and non-overlapping circular obstacles. Influence of the radius r and area fraction c of these obstacles and of the radius R of the observation area on the relative diffusion coefficient D ^* (Eq. (1)) and mobile fraction M was analyzed. A phenomenological equation relating D ^* to r and c was established. Fitting this equation to the FRAP data we obtained with the probe NBD-PC embedded in bacteriorhodopsin/egg-PC multilayers suggests that this transmembrane protein rigidifies the surrounding lipid phase over a distance of about 18 Å (two lipid layers) from the protein surface. In contrast, analysis of published diffusion constants obtained for lipids in the presence of gramicidin suggests that in terms of lateral diffusion, this relatively small polypeptide does not significantly affect the surrounding lipid phase. With respect to the mobile fraction M, and for point obstacles above the percolation threshold, an increase in R led to a decrease in M which can be associated with the existence of closed domains whose average size and diffusion properties can be determined. Adaptation of this model to the re-interpretation of the FRAP data obtained by Yechiel and Edidin (J Cell Biol (1987) 115:755–760) for the plasma membrane of human fibroblasts consistently leads to the suggestion that the lateral organization of this membrane would be of the confined type, with closed lipid domains of 0.5 µm² in area.Abbreviations and notations used BR bacteriorhodopsin - DMPC dimyristoylphosphatidylcholine - diOC18 dioctadecyloxatricarbocyanine - egf-PC egg-yolk phosphatidylcholine - NBD-PC 1-acyl2-[t2-[(7-nitro-2-1,3-benzoxadiazol-4-yl)amino]dodecanoyl]-sn-glycero-3-phosphocholine - MOPS 3-[N-morpholino]propane sulfonic acid - FRAP Fluoresence Recovery After photobleaching - D observed diffusion coefficient - D0 diffusion coefficient in the absence of obstacles - D ^* relative diffusion constant (Eq. 1) - M mobile fraction - c obstacle area fraction - r obstacle radius - R observation area radius - r _d diffusion area radius Correspondence to: A. Lopez     

Obstructed diffusion in phase-separated supported lipid bilayers: a combined atomic force microscopy and fluorescence recovery after photobleaching approach

Proteins and other macromolecules are believed to hinder molecular lateral diffusion in cellular membranes. We have constructed a well-characterized model system to better understand how obstacles in lipid bilayers obstruct diffusion. Fluorescence recovery after photobleaching was used to measure the lateral diffusion coefficient in single supported bilayers composed of mixtures of 1,2-dilauroylphosphotidylcholine (DLPC) and 1,2-distearoylphosphotidylcholine (DSPC). Because these lipids are immiscible and phase separate at room temperature, a novel quenching technique allowed us to construct fluid DLPC bilayers containing small disk-shaped gel-phase DSPC domains that acted as obstacles to lateral diffusion. Our experimental setup enabled us to analyze the same samples with atomic force microscopy and exactly characterize the size, shape, and number of gel-phase domains before measuring the obstacle-dependent diffusion coefficient. Lateral obstructed diffusion was found to be dependent on obstacle area fraction, size, and geometry. Analysis of our results using a free area diffusion model shows the possibility of unexpected long-range ordering of fluid-phase lipids around the gel-phase obstacles. This lipid ordering has implications for lipid-mediated protein interactions in cellular membranes.     

The membrane skeleton of erythrocytes. A percolation model.

The spectrin network on the cytoplasmic surface of the erythrocyte membrane is modeled as a triangular lattice of spectrin tetramers. This network obstructs lateral diffusion of proteins and provides mechanical reinforcement to the membrane. These effects are treated in a systematic and unified manner in terms of a percolation model. The diffusion coefficient is obtained as a function of the fraction of normal spectrin tetramers for both static and fluctuating barriers. The elasticity of the network is calculated as a function of the fraction of normal spectrin and the ratio of bending to stretching energies. For static barriers, elasticity and lateral diffusion are incompatible: if a network is connected enough to be elastic, it is connected enough to block long-range lateral diffusion. The elasticity and the force required for mechanical breakdown go to zero at the percolation threshold; experimental evidence suggests the existence of a stability threshold at or near the percolation threshold. The model is qualitatively applicable to other cells with membrane skeletons, such as epithelial cells, in which localization of membrane proteins is essential to differentiation.     

Lateral diffusion in an archipelago. Distance dependence of the diffusion coefficient.

An understanding of the distance dependence of the lateral diffusion coefficient is useful in comparing the results of diffusion measurements made over different length scales, and in analyzing the kinetics of mobile redox carriers in organelles. A distance-dependent, concentration-dependent diffusion coefficient is defined, and it is evaluated by Monte Carlo calculations of a random walk by mobile point tracers in the presence of immobile obstacles on a triangular lattice, representing the diffusion of a lipid or a small protein in the presence of immobile membrane proteins. This work confirms and extends the milling crowd model of Eisinger, J., J. Flores, and W. P. Petersen (1986. Biophys J. 49:987-1001). Similar calculations for diffusion of mobile particles interacting by a hard-core repulsion yield the distance dependence of the self-diffusion coefficient. An expression for the range of short-range diffusion is obtained, and the distance scales for various diffusion measurements are summarized.     

Lateral Diffusion in an Archipelago: Effects of Impermeable Patches on Diffusion in a Cell Membrane

Lateral diffusion of molecules in lipid bilayer membranes can be hindered by the presence of impermeable domains of gel-phase lipid or of proteins. Effective-medium theory and percolation theory are used to evaluate the effective lateral diffusion constant as a function of the area fraction of fluid-phase lipid and the permeability of the obstructions to the diffusing species. Applications include the estimation of the minimum fraction of fluid lipid needed for bacterial growth, and the enhancement of diffusion-controlled reactions by the channeling effect of solid patches of lipid.     

Effect of hydrodynamic interactions on the diffusion of integral membrane proteins: tracer diffusion in organelle and reconstituted membranes.

A persistent discrepancy exists between theoretical predictions and experimental observations for the diffusion coefficients of integral membrane proteins in lipid bilayers free of immobilized proteins. Current thermodynamic theories overestimate tracer diffusion coefficients at high area fractions. We explore the hypothesis that the combined effect of hydrodynamic and thermodynamic interactions reconciles theory with experiment. We have determined previously the short- and long-time tracer diffusivities, Ds and Dl, respectively, of integral membrane proteins in lipid bilayers as a function of their area fraction, phi. The results are based on two-particle hydrodynamic and thermodynamic interactions and are precise to O(phi). Here we extend the results for Dl to high phi by combining the hydrodynamic results for Ds into theories for Dl based on many-particle thermodynamic interactions. The results compare favorably with the experimental measurements of Dl as a function of protein area fraction for bacteriorhodopsin in reconstituted membranes and for complex III of the mitochondrial inner membrane. The agreement suggests that both hydrodynamic and thermodynamic interactions are important determinants of diffusion coefficients of proteins in lipid bilayers. Additional experiments are required to verify the role of hydrodynamic interactions in protein diffusion in reconstituted systems.     

Effect of hydrodynamic interactions on the diffusion of integral membrane proteins: diffusion in plasma membranes.

Tracer diffusion coefficients of integral membrane proteins (IMPs) in intact plasma membranes are often much lower than those found in blebbed, organelle, and reconstituted membranes. We calculate the contribution of hydrodynamic interactions to the tracer, gradient, and rotational diffusion of IMPs in plasma membranes. Because of the presence of immobile IMPs, Brinkman's equation governs the hydrodynamics in plasma membranes. Solutions of Brinkman's equation enable the calculation of short-time diffusion coefficients of IMPs. There is a large reduction in particle mobilities when a fraction of them is immobile, and as the fraction increases, the mobilities of the mobile particles continue to decrease. Combination of the hydrodynamic mobilities with Monte Carlo simulation results, which incorporate excluded area effects, enable the calculation of long-time diffusion coefficients. We use our calculations to analyze results for tracer diffusivities in several different systems. In erythrocytes, we find that the hydrodynamic theory, when combined with excluded area effects, closes the gap between existing theory and experiment for the mobility of band 3, with the remaining discrepancy likely due to direct obstruction of band 3 lateral mobility by the spectrin network. In lymphocytes, the combined hydrodynamic-excluded area theory provides a plausible explanation for the reduced mobility of sIg molecules induced by binding concanavalin A-coated platelets. However, the theory does not explain all reported cases of "anchorage modulation" in all cell types in which receptor mobilities are reduced after binding by concanavalin A-coated platelets. The hydrodynamic theory provides an explanation of why protein lateral mobilities are restricted in plasma membranes and why, in many systems, deletion of the cytoplasmic tail of a receptor has little effect on diffusion rates. However, much more data are needed to test the theory definitively. We also predict that gradient and tracer diffusivities are the same to leading order. Finally, we have calculated rotational diffusion coefficients in plasma membranes. They decrease less rapidly than translational diffusion coefficients with increasing protein immobilization, and the results agree qualitatively with the limited experimental data available.     

A milling crowd model for local and long-range obstructed lateral diffusion. Mobility of excimeric probes in the membrane of intact erythrocytes.

A new model for lateral diffusion, the milling crowd model (MC), is proposed and is used to derive the dependence of the monomeric and excimeric fluorescence yields of excimeric membrane probes on their concentration. According to the MC model, probes migrate by performing spatial exchanges with a randomly chosen nearest neighbor (lipid or probe). Only nearest neighbor probes, one of which is in the excited state, may form an excimer. The exchange frequency, and hence the local lateral diffusion coefficient, may then be determined from experiment with the aid of computer simulation of the excimer formation kinetics. The same model is also used to study the long-range lateral diffusion coefficient of probes in the presence of obstacles (e.g., membrane proteins). The dependence of the monomeric and excimeric fluorescence yields of 1-pyrene-dodecanoic acid probes on their concentration in the membranes of intact erythrocytes was measured and compared with the prediction of the MC model. The analysis yields an excimer formation rate for nearest neighbor molecules of approximately 1 X 10(7) s-1 and an exchange frequency of approximately greater than 2 X 10(7) s-1, corresponding to a local diffusion coefficient of greater than 3 X 10(-8) cm2 s-1. This value is several times larger than the long-range diffusion coefficient for a similar system measured in fluorescence photobleaching recovery experiments. The difference is explained by the fact that long-range diffusion is obstructed by dispersed membrane proteins and is therefore greatly reduced when compared to free diffusion. The dependence of the diffusion coefficient on the fractional area covered by obstacles and on their size is derived from MC simulations and is compared to those of other theories lateral diffusibility.     

The spectrin network as a barrier to lateral diffusion in erythrocytes. A percolation analysis.

The spectrin network on the cytoplasmic surface of an erythrocyte can be modeled as a triangular lattice of spectrin tetramers (Tsuji, A., and S. Ohnishi, 1986. Biochemistry. 25:6133-6139). The tetramers act as barriers to protein diffusion, while dissociated dimer pairs, single dimers, and missing tetramers do not. Diffusion in the presence of these barriers is shown to be equivalent to bond percolation on the honeycomb lattice. Monte Carlo calculations for this system then yield the relative diffusion constant of a mobile integral protein as a function of the fraction of spectrin tetramers. At high concentrations of spectrin tetramer, long-range diffusion is blocked, but short-range diffusion is still possible. Monte Carlo calculations yield the average distance over which short-range diffusion can occur, as a function of the fraction of spectrin tetramers. Applications to erythrocyte development and hereditary hemolytic anemia are discussed.     

Self-association of class I major histocompatibility complex molecules in liposome and cell surface membranes.

Fluorescent derivatives of a human MHC class I glycoprotein, HLA-A2, were reconstituted into dimyristoylphosphatidylcholine (DMPC) liposomes. Measurements of lateral diffusion of fluorescein-(Fl-) labeled HLA-A2 by fluorescence photobleaching recovery (FPR), of rotational diffusion of erythrosin-(Er-) labeled HLA-A2 by time-resolved phosphorescence anisotropy (TPA), and of molecular proximity by flow cytometric fluorescence resonance energy transfer (FCET) showed that these class I MHC molecules self-associate in liposome membranes, forming small aggregates even at low surface concentrations. The lateral diffusion coefficient (Dlat) of Fl-HLA-A2 decreases with increasing surface protein concentration over a range of lipid:protein molar ratios (L/P) between 8000:1 and 2000:1. The reduction in Dlat of HLA molecules in DMPC liposomes is found to be sensitive to time and temperature. The rotational correlation time for Er-HLA-A2 in DMPC liposomes at 30 degrees C is 87 +/- 0.8 microseconds, at least 10 times larger than that expected for an HLA monomer. There is also significant quenching of donor (Fl-HLA) fluorescence at 37 degrees C in the presence of acceptor-labeled (sulforhodamine-labeled HLA) protein indicating proximity between HLA molecules even at L/P = 4000:1. FPR and FCET measurements with another membrane glycoprotein, glycophorin, give no evidence for its self-association. HLA aggregation measured by FPR, FCET, and TPA was blocked by beta 2-microglobulin, b2m, added to the liposomes. The aggregation of HLA-A2 molecules is not an artifact of their reconstitution into liposomes. HLA aggregates, defined by FCET, were readily detected on the surface of human lymphoblastoid (JY) cells.(ABSTRACT TRUNCATED AT 250 WORDS)     

Ras diffusion is sensitive to plasma membrane viscosity

The cell surface contains a variety of barriers and obstacles that slow the lateral diffusion of glycosylphosphatidylinositol (GPI)-anchored and transmembrane proteins below the theoretical limit imposed by membrane viscosity. How the diffusion of proteins residing exclusively on the inner leaflet of the plasma membrane is regulated has been largely unexplored. We show here that the diffusion of the small GTPase Ras is sensitive to the viscosity of the plasma membrane. Using confocal fluorescence recovery after photobleaching, we examined the diffusion of green fluorescent protein (GFP)-tagged HRas, NRas, and KRas in COS-7 cells loaded with or depleted of cholesterol, a well-known modulator of membrane bilayer viscosity. In cells loaded with excess cholesterol, the diffusional mobilities of GFP-HRas, GFP-NRas, and GFP-KRas were significantly reduced, paralleling the behavior of the viscosity-sensitive lipid probes DiIC(16) and DiIC(18). However, the effects of cholesterol depletion on protein and lipid diffusion in cell membranes were highly dependent on the depletion method used. Cholesterol depletion with methyl-beta-cyclodextrin slowed Ras diffusion by a viscosity-independent mechanism, whereas overnight cholesterol depletion slightly increased both protein and lipid diffusion. The ability of Ras to sense membrane viscosity may represent a general feature of proteins residing on the cytoplasmic face of the plasma membrane.     

Topology of gel-phase domains and lipid mixing properties in phase-separated two-component phosphatidylcholine bilayers.

The influence of the lipid mixing properties on the lateral organization in a two-component, two-phase phosphatidylcholine bilayer was investigated using both an experimental (fluorescence recovery after photobleaching (FRAP)) and a simulated (Monte Carlo) approach. With the FRAP technique, we have examined binary mixtures of 1-stearoyl-2-capryl-phosphatidylcholine/1,2-distearoyl-phosphat idylcholine (C18C10PC/DSPC), and 1-stearoyl-2-capryl-phosphatidylcholine/1,2-dipalmitoyl-phospha tid ylcholine (C18C10PC/DPPC). Comparison with the 1,2-dimyristoyl-phosphatidylcholine/1,2-distearoyl-phosphatidylcholine (DMPC/DSPC) previously investigated by FRAP by Vaz and co-workers (Biophys. J., 1989, 56:869-876) shows that the gel phase domains become more effective in restricting the diffusion coefficient when the ideality of the mixture increases (i.e., in the order C18C10PC/DSPC-->C18C10PC/DPPC-->DMPC/DSPC). However, an increased lipid miscibility is accompanied by an increasing compositional dependence: the higher the proportion of the high-temperature melting component, the less efficient the gel phase is in compartmentalizing the diffusion plane, a trend that is best accounted for by a variation of the gel phase domain shape rather than size. Computer-simulated fluorescence recoveries obtained in a matrix obstructed with obstacle aggregates of various fractal dimension demonstrate that: 1) for a given obstacle size and area fraction, the relative diffusion coefficient increases linearly with the obstacle fractal dimension and 2) aggregates with a lower fractal dimension are more efficient in compartmentalizing the diffusion plane. Comparison of the simulated with the experimental mobile fractions strongly suggests that the fractal dimension of the gel phase domains increases with the proportion of high-temperature melting component in DMPC/DSPC and (slightly) in C18C10PC/DPPC.     

Lateral diffusion of membrane proteins in protein-rich membranes. A simple hard particle model for concentration dependence of the two-dimensional diffusion coefficient.

A model for the effect of protein concentration on the rate of lateral diffusion of integral membrane proteins is presented, in which the proteins are represented by equivalent hard circular particles on a surface. As the density of particles increases, the probability of finding a vacancy immediately adjacent to a tracer particle into which it may diffuse decreases, resulting in a concomitant reduction of the tracer diffusion coefficient. Using scaled particle theory to calculate the concentration-dependent probabilities, a simple approximate result is obtained in closed form, that is compared with the results of previously published Monte Carlo lattice simulations and experimental observations.     

Lateral diffusion and percolation in two-phase, two-component lipid bilayers. Topology of the solid-phase domains in-plane and across the lipid bilayer.

Fluorescence recovery after photobleaching (FRAP) has recently been used to examine the percolation properties of coexisting phases in two-component, two-phase phosphatidylcholine bilayers [Vaz, W. L. C., Melo, E. C. C., & Thompson, T. E. (1989) Biophys. J. 56, 869-876]. We now report the use of FRAP to study two additional problems in similar systems. The first is the effect of solid-phase obstacles on the lateral diffusion in the fluid phase. The second is the question of whether or not, in a single bilayer, solid-phase domains in one monolayer are exactly superimposed on solid domains in the apposing monolayer. To address the first problem, the lateral diffusion of N-(7-nitrobenzoxa-2,3-diazol-4-yl)-1-palmitoyl-2-oleoylphosp hatidylethanolamine (NBD-POPE), a probe soluble only in the fluid phase when solid and fluid phases coexist, has been studied in the mixture N-lignoceroyldihydrogalactosylceramide (LigGalCer)/dipalmitoylphosphatidylcholine (DPPC). Percolation of the fluid phase occurs at a high mass fraction of solid phase. This indicates that the solid domains have a centrosymmetric shape, a characteristic which makes this a good experimental system to test theoretical simulations of diffusion in an archipelago. It is shown that agreement between theory and experiment is poor, a result that had already been observed when the obstacles were integral membrane proteins. We develop an effective-medium model for diffusion in two-phase systems which explains both our results and those obtained with integral proteins. The distinctive feature of the model is the consideration of an annular region around the obstacles where the lipids are more ordered than in the bulk fluid phase. The diffusion coefficient is then calculated by extending the free area model to two-phase systems, taking these annuli into account. The second question, the organization of the solid-phase domains across the lipid bilayer, is examined in the systems LigGalCer/DPPC and dimyristoylphosphatidylcholine (DMPC)/distearoylphosphatidylcholine (DSPC) by comparing the diffusion of a fluid-phase-soluble, gel-phase-insoluble lipid derivative which spans the two monolayers of a bilayer (NBD-membrane-spanning-phosphatidylethanolamine, NBD-msPE) with that of a probe which is restricted to a single monolayer. In LigGalCer/DPPC, 20:80, the distribution of solid domains in one of the monolayers is independent of the distribution in the apposing monolayer. In contrast, in DMPC/DSPC, 50:50, the solid domains in one monolayer are exactly superimposed upon the solid domains existing in the apposing monolayer.     

Molecular Weight Dependence of Exciton Diffusion in Poly(3‐hexylthiophene)

A joint experimental and theoretical study of singlet exciton diffusion in spin‐coated poly(3‐hexylthiophene) (P3HT) films and its dependence on molecular weight is presented. The results show that exciton diffusion is fast along the co‐facial π–π aggregates of polymer chromophores and about 100 times slower in the lateral direction between aggregates. Exciton hopping between aggregates is found to show a subtle dependence on interchain coupling, aggregate size, and Boltzmann statistics. Additionally, a clear correlation is observed between the effective exciton diffusion coefficient, the degree of aggregation of chromophores, and exciton delocalization along the polymer chain, which suggests that exciton diffusion length can be enhanced by tailored synthesis and processing conditions.