Entropy Drives Interpolymer Association in Water: Insights into Molecular Mechanisms

Interpolymer association in aqueous solutions is essential for many industrial processes, new materials design, and the biochemistry of life. However, our understanding of the association mechanism is limited. Classical theories do not provide molecular details, creating a need for detailed mechanistic insights. This work consolidates previous literature with complementary isothermal titration calorimetry (ITC) measurements and molecular dynamics (MD) simulations to investigate molecular mechanisms to provide such insights. The large body of ITC data shows that intermolecular bonds, such as ionic or hydrogen bonds, cannot drive association. Instead, polymer association is entropy-driven due to the reorganization of water and ions. We propose a unifying entropy-driven association mechanism by generalizing previously suggested polyion association principles to include nonionic polymers, here termed polydipoles. In this mechanism, complementary charge densities of the polymers are the common denominators of association, for both polyions and polydipoles. The association of the polymers results mainly from two processes: charge exchange and amphiphilic association. MD simulations indicate that the amphiphilic assembly alone is enough for the initial association. Our proposed mechanism is a step toward a molecular understanding of the formation of complexes between synthetic and biological polymers under ambient or biological conditions.

Acetylation of Nanocellulose: Miscibility and Reinforcement Mechanisms in Polymer Nanocomposites

The improvement of properties in nanocomposites obtained by topochemical surface modification, e.g., acetylation, of the nanoparticles is often ascribed to improved compatibility between the nanoparticle and the matrix. It is not always clear however what is intended: specific interactions at the interface leading to increased adhesion or the miscibility between the nanoparticle and the polymer. In this work, it is demonstrated that acetylation of cellulose nanocrystals greatly improves mechanical properties of their nanocomposites with polycaprolactone. In addition, molecular dynamics simulations with a combination of potential of mean force calculations and computational alchemy are employed to analyze the surface energies between the two components. The work of adhesion between the two phases decreases with acetylation. It is discussed how acetylation can still contribute to the miscibility, which leads to a stricter use of the concept of compatibility. The integrated experimental-modeling toolbox used has wide applicability for assessing changes in the miscibility of polymer nanocomposites.

Understanding Nanocellulose-Water Interactions: Turning a Detriment into an Asset

Modern technology has enabled the isolation of nanocellulose from plant-based fibers, and the current trend focuses on utilizing nanocellulose in a broad range of sustainable materials applications. Water is generally seen as a detrimental component when in contact with nanocellulose-based materials, just like it is harmful for traditional cellulosic materials such as paper or cardboard. However, water is an integral component in plants, and many applications of nanocellulose already accept the presence of water or make use of it. This review gives a comprehensive account of nanocellulose-water interactions and their repercussions in all key areas of contemporary research: fundamental physical chemistry, chemical modification of nanocellulose, materials applications, and analytical methods to map the water interactions and the effect of water on a nanocellulose matrix.

The thermodynamics of enhanced dope stability of cellulose solution in NaOH solution by urea

The addition of urea in pre-cooled alkali aqueous solution is known to improve the dope stability of cellulose solution. However, its thermodynamic mechanism at a molecular level is not fully understood yet. By using molecular dynamics simulation of an aqueous NaOH/urea/cellulose system using an empirical force field, we found that urea was concentrated in the first solvation shell of the cellulose chain stabilized mainly by dispersion interaction. When adding a glucan chain into the solution, the total solvent entropy reduction is smaller if urea is present. Each urea molecule expelled an average of 2.3 water molecules away from the cellulose surface, releasing water entropy that over-compensates the entropy loss of urea and thus maximizing the total entropy. Scaling the Lennard-Jones parameter and atomistic partial charge of urea revealed that direct urea/cellulose interaction was also driven by dispersion energy. The mixing of urea solution and cellulose solution in the presence or absence of NaOH are both exothermic even after correcting for the contribution from dilution.

Capillary forces exerted by a water bridge on cellulose nanocrystals: the effect of an external electric field

Capillary forces play an important role during the dewatering and drying of nanocellulosic materials. Traditional moisture removal techniques, such as heating, have been proved to be deterimental to the properties of these materials and hence, there is a need to develop novel dewatering techniques without affecting the desired properties of materials. It is, therefore, important to explore novel methods for dewatering these high-added-value materials without negatively influencing their properties. In this context, we explore the effect of electric field on the capillary forces developed by a liquid-water bridge between two cellulosic surfaces, which may be formed during the water removal process following its displacement from the interfibrillar spaces. All-atom molecular dynamics (MD) simulations have been used to study the influence of an externally applied electric field on the capillary force exerted by a water bridge. Our results suggest that the equilibrium contact angle of water and the capillary force exerted by the water bridge between two nanocellulosic surfaces depend on the magnitude and direction of the externally applied electric fields. Hence, an external electric field can be applied to manipulate the capillary forces between two particles. The close agreement between the capillary forces measured through MD simulations and those calculated through classical equations indicates that, within the range of the electric field applied in this study, Young-Laplace equations can be safely employed to predict the capillary forces between two particles. The present study provides insights into the use of electric fields for drying of nanocellulosic materials.

“Like Recycles Like”: Selective Ring‐Closing Depolymerization of Poly(L‐Lactic Acid) to L‐Lactide

Chemical recycling of poly(L‐lactic acid) to the cyclic monomer L‐lactide is hampered by low selectivity and by epimerization and elimination reactions, impeding its use on a large scale. The high number of side reactions originates from the high ceiling temperature (T_c) of L‐lactide, which necessitates high temperatures or multistep reactions to achieve recycling to L‐lactide. To circumvent this issue, we utilized the impact of solvent interactions on the monomer–polymer equilibrium to decrease the T_c of L‐lactide. Analyzing the observed T_c in different solvents in relation to their Hildebrand solubility parameter revealed a “like recycles like” relationship. The decreased T_c, obtained by selecting solvents that interact strongly with the monomer (dimethyl formamide or the green solvent γ‐valerolactone), allowed chemical recycling of high‐molecular‐weight poly(L‐lactic acid) directly to L‐lactide, within 1–4 h at 140 °C, with >95 % conversion and 98–99 % selectivity. Recycled L‐lactide was isolated and repolymerized with high control over molecular weight and dispersity, closing the polymer loop.

Water as an Intrinsic Structural Element in Cellulose Fibril Aggregates

While strong water association with cellulose in plant cell walls and man-made materials is well-established, its molecular scale aspects are not fully understood. The thermodynamic consequences of having water molecules located at the microfibril-microfibril interfaces in cellulose fibril aggregates are therefore analyzed by molecular dynamics simulations. We find that a thin layer of water molecules at those interfaces can be in a state of thermal equilibrium with water surrounding the fibril aggregates because such an arrangement lowers the free energy of the total system. The main reason is enthalpic: water at the microfibril-microfibril interfaces enables the cellulose surface hydroxyls to experience a more favorable electrostatic environment. This enthalpic gain overcomes the entropic penalty from strong immobilization of water molecules. Hence, those particular water molecules stabilize the cellulose fibril aggregates, akin to the role of water in some proteins. Structural and functional hypotheses related to this finding are presented.

Quantifying the Contribution of the Dispersion Interaction and Hydrogen Bonding to the Anisotropic Elastic Properties of Chitin and Chitosan

The elastic tensors of chitin and chitosan allomorphs were calculated using density functional theory (DFT) with and without the dispersion correction and compared with experimental values. The longitudinal Young's moduli were 114.9 or 126.9 GPa for α-chitin depending on the hydrogen bond pattern: 129.0 GPa for β-chitin and 191.5 GPa for chitosan. Furthermore, the moduli were found to vary between 17.0 and 52.8 GPa in the transverse directions and between 2.2 and 15.2 GPa in shear. Switching off the dispersion correction led to a decrease in modulus by up to 63%, depending on the direction. The transverse Young's moduli of α-chitin strongly depended on the hydroxylmethyl group conformation coupled with the dispersion correction, suggesting a synergy between hydrogen bonding and dispersion interactions. The calculated longitudinal Young's moduli were, in general, higher than experimental values obtained in static conditions, and the Poisson's ratios were lower than experimental values obtained in static conditions.

O-Methylation in Carbohydrates: An NMR and MD Simulation Study with Application to Methylcellulose

Methylated carbohydrates are important from both biological and technical perspectives. Specifically, methylcellulose is an interesting cellulose derivative that has applications in foods, materials, cosmetics, and many other fields. While the molecular dynamics simulation technique has the potential for both advancing the fundamental understanding of this polymer and aiding in the development of specific applications, a general drawback is the lack of experimentally validated interaction potentials for the methylated moieties. In the present study, simulations using the GROMOS 56 carbohydrate force field are compared to NMR spin–spin coupling constants related to the conformation of the exocyclic torsion angle ω in d-glucopyranose and derivatives containing a 6-O-methyl substituent and a ¹³C-isotopologue thereof. A ³J_CC Karplus-type relationship is proposed for the C5–C6–O6–C_Me torsion angle. Moreover, solvation free energies are compared to experimental data for small model compounds. Alkylation in the form of 6-O-methylation affects exocyclic torsion only marginally. Computed solvation free energies between nonmethylated and methylated molecules were internally consistent, which validates the application of these interaction potentials for more specialized purposes.

Entropy drives the adsorption of xyloglucan to cellulose surfaces - A molecular dynamics study

The adsorption of nonionic polymers to cellulose is of large importance both in the plant cell wall during synthesis and for the development of sustainable materials from wood. Here, the thermodynamics of adsorption of the polysaccharide xyloglucan (XG) to both native and chemically modified cellulose with carboxyl groups was investigated using molecular dynamics simulations. The free energy of adsorption was calculated as the potential of mean force between an XG oligomer and model cellulose surfaces in a range of temperatures from 298 K to 360 K. It was found that the adsorption near room temperature is an endothermic process dominated by the entropy of released interfacial water molecules. This was corroborated by quantitative assessment of the absolute entropy per water molecule both at the interface and in the bulk. In the case of native cellulose, the adsorption became exothermic at higher temperatures, while the relatively strong interactions between water and the charged groups of the oxidized cellulose impede such a transition. The results also indicate that the extraction of strongly associated hemicelluloses would be facilitated by low temperature.

Wettability of cellulose surfaces under the influence of an external electric field

HYPOTHESIS

Interfacial tensions play an important role in dewatering of hydrophilic materials like nanofibrillated cellulose, and are affected by the molecular organization of water at the interface. Application of an electric field influences the orientation of water molecules along the field direction. Hence, it should be possible to alter the interfacial free energies to tune the wettability of cellulose surface through application of an external electric field thus, aiding the dewatering process.

SIMULATIONS

Molecular dynamics simulations of cellulose surface in contact with water under the influence of an external electric field have been conducted with GLYCAM-06 forcefield. The effect of variation in electric field intensity and directions on the spreading coefficient has been addressed via orientational preference of water molecules and interfacial free energy analyses.

FINDINGS

The application of electric field influences the interfacial free energy difference at the cellulose-water interface. The spreading coefficient increases with the electric field directed parallel to the cellulose-water interface while it decreases in the perpendicular electric field. Variation in interfacial free energies seems to explain the change in contact angle adequately in presence of an electric field. The wettability of cellulose surface can be tuned by the application of an external electric field.

Functionalization and patterning of nanocellulose films by surface-bound nanoparticles of hydrolyzable tannins and multivalent metal ions

Inspired by the Bogolanfini dyeing technique, we report how flexible nanofibrillated cellulose (CNF) films can be functionalized and patterned by surface-bound nanoparticles of hydrolyzable tannins and multivalent metal ions with tunable colors. Molecular dynamics simulations show that gallic acid (GA) and ellagic acid (EA) rapidly adsorb and assemble on the CNF surface, and atomic force microscopy confirms that nanosized GA assemblies cover the surface of the CNF. CNF films were patterned with tannin-metal ion nanoparticles by an in-fibre reaction between the pre-impregnated tannin and the metal ions in the printing ink. Spectroscopic studies show that the Fe^III/II ions interact with GA and form surface-bound, stable GA-Fe^III/II nanoparticles. The functionalization and patterning of CNF films with metal ion-hydrolyzable tannin nanoparticles is a versatile route to functionalize films based on renewable materials and of interest for biomedical and environmental applications.

Toward Improved Understanding of the Interactions between Poorly Soluble Drugs and Cellulose Nanofibers

Cellulose nanofibers (CNFs) have interesting physicochemical and colloidal properties that have been recently exploited in novel drug-delivery systems for tailored release of poorly soluble drugs. The morphology and release kinetics of such drug-delivery systems heavily relied on the drug-CNF interactions; however, in-depth understanding of the interactions was lacking. Herein, the interactions between a poorly soluble model drug molecule, furosemide, and cationic cellulose nanofibers with two different degrees of substitution are studied by sorption experiments, Fourier transform infrared spectroscopy, and molecular dynamics (MD) simulation. Both MD simulations and experimental results confirmed the spontaneous sorption of drug onto CNF. Simulations further showed that adsorption occurred by the flat aryl ring of furosemide. The spontaneous sorption was commensurate with large entropy gains as a result of release of surface-bound water. Association between furosemide molecules furthermore enabled surface precipitation as indicated by both simulations and experiments. Finally, sorption was also found not to be driven by charge neutralization, between positive CNF surface charges and the furosemide negative charge, so that surface area is the single most important parameter determining the amount of sorbed drug. An optimized CNF-furosemide drug-delivery vehicle thus needs to have a maximized specific surface area irrespective of the surface charge with which it is achieved. The findings also provide important insights into the design principles of CNF-based filters suitable for removal of poorly soluble drugs from wastewater.

Regular Motifs in Xylan Modulate Molecular Flexibility and Interactions with Cellulose Surfaces

Xylan is tightly associated with cellulose and lignin in secondary plant cell walls, contributing to its rigidity and structural integrity in vascular plants. However, the molecular features and the nanoscale forces that control the interactions among cellulose microfibrils, hemicelluloses, and lignin are still not well understood. Here, we combine comprehensive mass spectrometric glycan sequencing and molecular dynamics simulations to elucidate the substitution pattern in softwood xylans and to investigate the effect of distinct intramolecular motifs on xylan conformation and on the interaction with cellulose surfaces in Norway spruce (Picea abies). We confirm the presence of motifs with evenly spaced glycosyl decorations on the xylan backbone, together with minor motifs with consecutive glucuronation. These domains are differently enriched in xylan fractions extracted by alkali and subcritical water, which indicates their preferential positioning in the secondary plant cell wall ultrastructure. The flexibility of the 3-fold screw conformation of xylan in solution is enhanced by the presence of arabinofuranosyl decorations. Additionally, molecular dynamic simulations suggest that the glycosyl substitutions in xylan are not only sterically tolerated by the cellulose surfaces but that they increase the affinity for cellulose and favor the stabilization of the 2-fold screw conformation. This effect is more significant for the hydrophobic surface compared with the hydrophilic ones, which demonstrates the importance of nonpolar driving forces on the structural integrity of secondary plant cell walls. These novel molecular insights contribute to an improved understanding of the supramolecular architecture of plant secondary cell walls and have fundamental implications for overcoming lignocellulose recalcitrance and for the design of advanced wood-based materials.

Solid nanofoams based on cellulose nanofibers and indomethacin-the effect of processing parameters and drug content on material structure

The unique colloidal properties of cellulose nanofibers (CNF), makes CNF a very interesting new excipient in pharmaceutical formulations, as CNF in combination with some poorly-soluble drugs can create nanofoams with closed cells. Previous nanofoams, created with the model drug indomethacin, demonstrated a prolonged release compared to films, owing to the tortuous diffusion path that the drug needs to take around the intact air-bubbles. However, the nanofoam was only obtained at a relatively low drug content of 21wt% using fixed processing parameters. Herein, the effect of indomethacin content and processing parameters on the foaming properties was analysed. Results demonstrate that a certain amount of dissolved drug is needed to stabilize air-bubbles. At the same time, larger fractions of dissolved drug promote coarsening/collapse of the wet foam. The pendant drop/bubble profile tensiometry was used to verify the wet-foam stability at different pHs. The pH influenced the amount of solubilized drug and the processing-window was very narrow at high drug loadings. The results were compared to real foaming-experiments and solid state analysis of the final cellular solids. The parameters were assembled into a processing chart, highlighting the importance of the right combination of processing parameters (pH and time-point of pH adjustment) in order to successfully prepare cellular solid materials with up to 46 wt% drug loading.

A molecular dynamics study of the effect of glycosidic linkage type in the hemicellulose backbone on the molecular chain flexibility

The macromolecular conformation of the constituent polysaccharides in lignocellulosic biomass influences their supramolecular interactions, and therefore their function in plants and their performance in technical products. The flexibility of glycosidic linkages from the backbone of hemicelluloses was studied by evaluating the conformational freedom of the φ and ψ dihedral angles using molecular dynamic simulations, additionally selected molecules were correlated with experimental data by nuclear magnetic resonance spectroscopy. Three types of β-(1→4) glycosidic linkages involving the monosaccharides (Glcp, Xylp and Manp) present in the backbone of hemicelluloses were defined. Different di- and tetrasaccharides with combinations of such sugar monomers from hemicelluloses were simulated, and free energy maps of the φ - ψ space and hydrogen-bonding patterns were obtained. The glycosidic linkage between Glc-Glc or Glc-Man (C-type) was the stiffest with mainly one probable conformation; the linkage from Man-Man or Man-Glc (M-type) was similar but with an increased probability for an alternative conformation making it more flexible, and the linkage between two Xyl-units (X-type) was the most flexible with two almost equally populated conformations. Glycosidic linkages of the same type showed essentially the same conformational space in both disaccharides and in the central region of tetrasaccharides. Different probabilities of glycosidic linkage conformations in the backbone of hemicelluloses can be directly estimated from the free energy maps, which to a large degree affect the overall macromolecular conformations of these polymers. The information gained contributes to an increased understanding of the function of hemicelluloses both in the cell wall and in technical products.

Molecular dynamics simulations and NMR spectroscopy studies of trehalose-lipid bilayer systems

The disaccharide trehalose (TRH) strongly affects the physical properties of lipid bilayers. We investigate interactions between lipid membranes formed by 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and TRH using NMR spectroscopy and molecular dynamics (MD) computer simulations. We compare dipolar couplings derived from DMPC/TRH trajectories with those determined (i) experimentally in TRH using conventional high-resolution NMR in a weakly ordered solvent (bicelles), and (ii) by solid-state NMR in multilamellar vesicles (MLV) formed by DMPC. Analysis of the experimental and MD-derived couplings in DMPC indicated that the force field used in the simulations reasonably well describes the experimental results with the exception for the glycerol fragment that exhibits significant deviations. The signs of dipolar couplings, not available from the experiments on highly ordered systems, were determined from the trajectory analysis. The crucial step in the analysis of residual dipolar couplings (RDCs) in TRH determined in a bicelle-environment was access to the conformational distributions derived from the MD trajectory. Furthermore, the conformational behavior of TRH, investigated by J-couplings, in the ordered and isotropic phases is essentially identical, indicating that the general assumptions in the analyses of RDCs are well founded.

Molecular mechanisms for the adhesion of chitin and chitosan to montmorillonite clay

Molecular dynamics simulations were used to study the wet adhesion of chitin and chitosan oligomers to montmorillonite clay.

Molecular dynamics simulations of membrane-sugar interactions

It is well documented that disaccharides in general and trehalose (TRH) in particular strongly affect physical properties and functionality of lipid bilayers. We investigate interactions between lipid membranes formed by 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and TRH by means of molecular dynamics (MD) computer simulations. Ten different TRH concentrations were studied in the range wTRH = 0-0.20 (w/w). The potential of mean force (PMF) for DMPC bilayer-TRH interactions was determined using two different force fields, and was subsequently used in a simple analytical model for description of sugar binding at the membrane interface. The MD results were in good agreement with the predictions of the model. The net affinities of TRH for the DMPC bilayer derived from the model and MD simulations were compared with experimental results. The area per lipid increases and the membrane becomes thinner with increased TRH concentration, which is interpreted as an intercalation effect of the TRH molecules into the polar part of the lipids, resulting in conformational changes in the chains. These results are consistent with recent experimental observations. The compressibility modulus related to the fluctuations of the membrane increases dramatically with increased TRH concentration, which indicates higher order and rigidity of the bilayer. This is also reflected in a decrease (by a factor of 15) of the lateral diffusion of the lipids. We interpret these observations as a formation of a glassy state at the interface of the membrane, which has been suggested in the literature as a hypothesis for the membrane-sugar interactions.

The O-glycosylated linker from the Trichoderma reesei Family 7 cellulase is a flexible, disordered protein

Fungi and bacteria secrete glycoprotein cocktails to deconstruct cellulose. Cellulose-degrading enzymes (cellulases) are often modular, with catalytic domains for cellulose hydrolysis and carbohydrate-binding modules connected by linkers rich in serine and threonine with O-glycosylation. Few studies have probed the role that the linker and O-glycans play in catalysis. Since different expression and growth conditions produce different glycosylation patterns that affect enzyme activity, the structure-function relationships that glycosylation imparts to linkers are relevant for understanding cellulase mechanisms. Here, the linker of the Trichoderma reesei Family 7 cellobiohydrolase (Cel7A) is examined by simulation. Our results suggest that the Cel7A linker is an intrinsically disordered protein with and without glycosylation. Contrary to the predominant view, the O-glycosylation does not change the stiffness of the linker, as measured by the relative fluctuations in the end-to-end distance; rather, it provides a 16 Å extension, thus expanding the operating range of Cel7A. We explain observations from previous biochemical experiments in the light of results obtained here, and compare the Cel7A linker with linkers from other cellulases with sequence-based tools to predict disorder. This preliminary screen indicates that linkers from Family 7 enzymes from other genera and other cellulases within T. reesei may not be as disordered, warranting further study.

Free energy surfaces for the interaction of D-glucose with planar aromatic groups in aqueous solution

Multidimensional potentials of mean force for the interactions in aqueous solution of both anomers of D-glucopyranose with two planar aromatic molecules, indole and para-methyl-phenol, have been calculated using molecular dynamics simulations with umbrella sampling and were subsequently used to estimate binding free energies. Indole and para-methyl-phenol serve as models for the side chains of the amino acids tryptophan and tyrosine, respectively. In all cases, a weak affinity between the glucose molecules and the flat aromatic surfaces was found. The global minimum for these interactions was found to be for the case when the pseudoplanar face of β-D-glucopyranose is stacked against the planar surfaces of the aromatic residues. The calculated binding free energies are in good agreement with both experiment and previous simulations. The multidimensional free energy maps suggest a mechanism that could lend kinetic stability to the complexes formed by sugars bound to sugar-binding proteins.

Dynamics in atomistic simulations of phospholipid membranes: Nuclear magnetic resonance relaxation rates and lateral diffusion

It is shown that a long, near microsecond, atomistic simulation can shed some light upon the dynamical processes occurring in a lipid bilayer. The analysis focuses on reorientational dynamics of the chains and lateral diffusion of lipids. It is shown that the reorientational correlation functions exhibits an algebraic decay (rather than exponential) for several orders of magnitude in time. The calculated nuclear magnetic resonance relaxation rates agree with experiments for carbons at the C7 position while there are some differences for C3. Lateral diffusion can be divided into two stages. In a first stage occurring at short times, t<5 ns, the center of mass of the lipid moves due to conformational changes of the chains while the headgroup position remains relatively fixed. In this stage, the center of mass can move up to approximately 0.8 nm. The fitted short-time diffusion coefficient is D(1)=13 x 10(-7) cm(2) s(-1) On a longer time scale, the diffusion coefficient becomes D(2)=0.79 x 10(-7) cm(2) s(-1).

Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations

Atomistic molecular dynamics simulations of a lipid bilayer were performed to calculate the free energy of a trans-membrane pore as a function of its radius. The free energy was calculated as a function of a reaction coordinate using a potential of mean constraint force. The pore radius was then calculated from the reaction coordinate using Monte Carlo particle insertions. The main characteristics of the free energy that comes out of the simulations are a quadratic shape for a radius less than about 0.3 nm, a linear shape for larger radii than this, and a rather abrupt change without local minima or maxima between the two regions. In the outer region, a line tension can be calculated, which is consistent with the experimentally measured values. Further, this line tension can be rationalized and understood in terms of the energetic cost for deforming a part of the lipid bilayer into a hydrophilic pore. The region with small radii can be described and understood in terms of statistical mechanics of density fluctuations. In the region of crossover between a quadratic and linear free energy there was some hysteresis associated with filling and evacuation of the pore with water. The metastable prepore state hypothesized to interpret the experiments was not observed in this region.

The range and shielding of dipole-dipole interactions in phospholipid bilayers

In molecular dynamics simulations of lipid bilayers, the structure is sensitive to the precise treatment of electrostatics. The dipole-dipole interactions between headgroup dipoles are not long-ranged, but the area per lipid and, through it, other properties of the bilayer are very sensitive to the detailed balance between the perpendicular and in-plane components of the headgroup dipoles. This is affected by the detailed properties of the cutoff scheme or if long-range interactions are included by Ewald or particle-mesh Ewald techniques. Interaction between the in-plane components of the headgroup dipoles is attractive and decays as the inverse sixth power of distance. The interaction is screened by the square of a dielectric permittivity close to the value for water. Interaction between the components perpendicular to the membrane plane is repulsive and decays as the inverse third power of distance. These interactions are screened by a dielectric permittivity of the order 10. Thus, despite the perpendicular components being much smaller in magnitude than the in-plane components, they will dominate the interaction energies at large distances.