Interfacial slip friction at a fluid-solid cylindrical boundary

Recently we proposed a method to calculate the interfacial friction coefficient between fluid and solid at a planar interface. In this work we extend the method to cylindrical systems where the friction coefficient is curvature dependent. We apply the method to methane flow in carbon nanotubes, and find good agreement with non-equilibrium molecular dynamics simulations. The proposed method is robust, general, and can be used to predict the slip for cylindrical nanofluidic systems.     

Interfacial friction between semiflexible polymers and crystalline surfaces

The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with adjustable intrinsic stiffness. The structure and relaxation dynamics of polymer chains near interfaces are quantified by the radius of gyration and decay of the time autocorrelation function of the first normal mode. We found that the friction coefficient at small slip velocities exhibits a distinct maximum which appears due to shear-induced alignment of semiflexible chain segments in contact with solid walls. At large slip velocities, the friction coefficient is independent of the chain stiffness. The data for the friction coefficient and shear viscosity are used to elucidate main trends in the nonlinear shear rate dependence of the slip length. The influence of chain stiffness on the relationship between the friction coefficient and the structure factor in the first fluid layer is discussed.     

Molecular dynamics study of the interface between water and 2-nitrophenyl octyl ether

We present results of molecular dynamics simulations of the interface between water and 2-nitrophenyl octyl ether (NPOE). This system is analyzed in detail using a procedure to calculate intrinsic profiles of several important properties (density, radial distribution functions, hydrogen bonds, molecular orientation, self-diffusion). The interface was found to be molecularly sharp but corrugated by thermal fluctuations. Using a method based on capillary wave theory, we have estimated the interfacial tension and obtained good agreement with values calculated from the virial route. The results were compared to simulations of the water/nitrobenzene interface. The presence of an alkyl chain in NPOE introduces an added degree of hydrophobicity, which causes an increase in the interfacial tension. Furthermore, interfacial NPOE molecules are less organized than nitrobenzene and show a distinct dynamic response. These results shed light on the observed differences between these two organic liquids in electrochemical studies.     

Molecular dynamics study of the n-hexane-water interface: towards a better understanding of the liquid-liquid interfacial broadening

By molecular dynamics simulations, we have studied the hydrophilic-hydrophobic interface between water and n-hexane liquid phases. For all temperatures studied our computed interfacial tension agrees very well with the experimental value. However, the interfacial width calculated from capillary wave theory systematically overestimates the width obtained from fitting either the total density or composition profile. We rationalize the applicability of capillary wave theory for our system by reconsidering the usual value taken for the correlation length. This is motivated by the presence of order at the interface. Possible implications for recent experimental studies on the structure of model alkane-water interfaces are discussed, including the significance of the intrinsic width parameter.     

Finite system size effects in the interfacial dynamics of binary liquid films

We study the relaxation dynamics of capillary waves in the interface between two confined liquid layers by means of molecular dynamics simulations. We measure the autocorrelations of the interfacial Fourier modes and find that the finite thickness of the liquid layers leads to a marked increase of the relaxation times as compared to the case of fluid layers of infinite depth. The simulation results are in good agreement with a theoretical first-order perturbation derivation, which starts from the overdamped Stokes' equation. The theory also takes into account an interfacial friction, but the difference with no-slip interfacial conditions is small. When the walls are sheared, it is found that the relaxation times of modes perpendicular to the flow are unaffected. Modes along the flow direction are relatively unaffected as long as the equilibrium relaxation time is sufficiently short compared to the rate of deformation. We discuss the consequences for experiments on thin layers and on ultralow surface tension fluids, as well as computer simulations.     

Formation and rheological properties of the supercritical CO2-water pure interface

From the interfacial tension (gamma) measurement, we have analyzed the interfacial organization that occurs between pure H2O and pure CO2 from a kinetical and rheological point of view. This article is the followup to a previous one, where we showed that this equilibrated interface is composed of small H2O-CO2 cluster blocks [Tewes, F.; Boury, F. J. Phys. Chem. B 2004, 108, 2405]. By analyzing the variation of gamma with the square root of time, we found that the organization of the H2O-CO2 interface is, in the initial times, controlled by the diffusion of the CO2 molecules into the water. We compared the frictional coefficient determined from the measured CO2 diffusion coefficient with the frictional coefficient calculated from the Stokes equation (frictional ratio). From that, we concluded that it is a hydrated form of CO2 that diffuses and that the degree of hydration decreases with pressure. Rheological properties of the equilibrated interface vary with CO2 pressure, in the range of 50-90 bar, from a viscoelastic comportment to a purely elastic behavior, showing a change in the interfacial organization. The high equilibrium part of the elasticity (110 mN/m) obtained at 90 bar suggests a highly structured interface. Two phenomena could explain the interfacial rheological behavior: (i) an increase and a growth of the blocks H2O-CO2 cluster with the CO2 pressure or (ii) an increase in the interfacial capacity to form stable clusters under interfacial area compression.     

Experimental evidence of the role of viscosity in the molecular kinetic theory of dynamic wetting

We report an experimental study of the dynamics of spontaneous spreading of aqueous glycerol drops on glass. For a range of glycerol concentrations, we follow the evolution of the radius and contact angle over several decades of time and investigate the influence of solution viscosity. The application of the molecular kinetic theory to the resulting data allows us to extract the coefficient of contact-line friction ζ, the molecular jump frequency κ(0), and the jump length λ for each solution. Our results show that the modified theory, which explicitly accounts for the effect of viscosity, can successfully be applied to droplet spreading. The viscosity affects the jump frequency but not the jump length. In combining these data, we confirm that the contact-line friction of the solution/air interface against the glass is proportional to the viscosity and exponentially dependent on the work of adhesion.     

On the theory of dilute polyelectrolyte solutions: Extensions,refinements, and experimental tests

We synthesize a quantitative theory for the radius of gyration, second virial coefficient, intrinsic viscosity, and friction coefficient for polyelectroytes in dilute solution from existing treatments of electrostatic and hydrodynamic interactions within and among wormlike chains. Comparison with data for K-PSS demonstrates the importance of accounting for nonlinearities in the electrostatics and the finite diameter of the polymer backbone.     

Molecular dynamics investigation of the intrinsic structure of water-fluid interfaces via the intrinsic sampling method

Capillary wave fluctuations smooth out the structure of fluid interfaces, making difficult the detailed analysis of the interfacial structure. Most computer simulation investigations performed to date have focused on the computation of average density profiles, ignoring the characterization of the intrinsic structure of the interface. Recent theoretical developments have reversed this situation, making possible the detailed investigation of the interfacial intrinsic structure at an unprecedented level of detail. In this article we investigate via molecular dynamics simulations the intrinsic structure of water-alkane (hexane and dodecane) interfaces. The implementation of the recently introduced, intrinsic sampling method to compute the intrinsic surface of water-fluid interfaces is discussed. We provide quantitative molecular information on the structure, corrugation, and stiffness of the liquid surfaces. The intrinsic structure of water at alkane interfaces is shown to be insensitive to the alkane-chain length, and can be very accurately described by the intrinsic structure of the water free surface.     

Dendritic PtCo alloy nanoparticles as high performance oxygen reduction catalysts

We studied the physical properties and the concentration profile of benzene+water+caprolactam mixtures near the fluid-fluid interface using self-consistent field (SCF) theory. This yields the interfacial tension which plays an important role in describing the stability of transient liquid droplets of one phase in the other. The studies were performed at a fixed temperature of 313K. Flory-Huggins binary interaction parameters and the compound lattice segment numbers are input parameters for the applied SCF theory. These parameters were derived from activity coefficient relations, which are used to describe experimental liquid-liquid and vapor-liquid phase equilibrium measurements. Using first principles, the benzene-water interface was studied and the resulting interfacial tension was found to be in agreement with experimental values. This study illustrates that caprolactam accumulates at the benzene-water interface, acting as a weak surfactant. The interfacial tension is also demonstrated to be affected by the caprolactam concentration and the SCF results are in fair agreement with the experimental observations.     

Interfaces in polymer blends

We investigate the structure and thermodynamics of interfaces in dense polymer blends using Monte Carlo (MC) simulations and self‐consistent field (SCF) calculations. For structurally symmetric blends we find quantitative agreement between the MC simulations and the SCF calculations for excess quantities of the interface (e.g., interfacial tension or enrichment of copolymers at the interface). However, a quantitative comparison between profiles across the interface in the MC simulations and the SCF calculations has to take due account of capillary waves. While the profiles in the SCF calculations correspond to intrinsic profiles of a perfectly flat interface the local interfacial position fluctuates in the MC simulations. We test this concept by extensive Monte Carlo simulations and study the cross‐over between “intrinsic” fluctuations which build up the local profile and capillary waves on long (lateral) length scales. Properties of structurally asymmetric blends are exemplified by investigating polymers of different stiffness. At high incompatibilities the interfacial width is not much larger than the persistence length of the stiffer component. In this limit we find deviations from the predictions of the Gaussian chain model: while the Gaussian chain model yields an increase of the interfacial width upon increasing the persistence length, no such increase is found in the MC simulations. Using a partial enumeration technique, however, we can account for the details of the chain architecture on all length scales in the SCF calculations and achieve good agreement with the MC simulations. In blends containing diblock copolymers we investigate the enrichment of copolymers at the interface and the concomitant reduction of the interfacial tension. At weak segregation the addition of copolymers leads to compatibilization. At high incompatibilities, the homopolymer‐rich phase can accommodate only a small fraction of copolymer before the copolymer forms a lamellar phase. The analysis of interfacial fluctuations yields an estimate for the bending rigidity of the interface. The latter quantity is important for the formation of a polymeric microemulsion at intermediate segregation and the consequences for the phase diagram are discussed.     

Equilibrium calculations of viscosity and thermal conductivity across a solid-liquid interface using boundary fluctuations

We calculate viscosity and thermal conductivity in systems of Lennard-Jones particles consisting of coexisting solid and liquid with different interface wetting properties using the recently developed equilibrium boundary fluctuation theory. We compare the slip length and equivalent liquid length obtained from these calculations with those obtained from nonequilibrium molecular dynamics. The equilibrium and nonequilibrium calculations of the slip length and the sum of the thermal equivalent lengths are in good agreement. We conclude that for both interfacial properties, the nonequilibrium simulations were probing the linear response. The significant dependence of the intrinsic equivalence length on the interfacial temperature difference used to generate the thermal gradient is explained as a consequence of the different thermodynamic states of the two interfaces.     

Hydrophilicity and the viscosity of interfacial water

We measure the viscosity of nanometer-thick water films at the interface with an amorphous silica surface. We obtain viscosity values from three different measurements: friction force in a water meniscus formed between an oxide-terminated W tip and the silica surface under ambient conditions; similar measurements for these interfaces under water; and the repulsive "drainage" force as the two surfaces approach at various speeds in water. In all three cases, we obtain effective viscosities that are approximately 10(6) times greater than that of bulk water for nanometer-scale interfacial separations. This enhanced viscosity is not observed when we degrade the hydrophilicity of the surface by terminating it with -H or -CH3. In view of recent results from other interfaces, we conclude that the criterion for the formation of a viscous interphase is the degree of hydrophilicity of the interfacial pair.     

On the curvature dependence of the interfacial tension in a symmetric three-component interface

We consider a symmetric interface between two polymers A(N) and B(N) in a common monomeric solvent S using the mean-field Scheutjens-Fleer self-consistent field theory and focus on the curvature dependence of the interfacial tension. In multi-component systems there is not one unique scenario to curve such an interface. We elaborate on this by keeping either the chemical potential of the solvent or the bulk concentration of the solvent fixed, that is we focus on the semi-grand canonical ensemble case. Following Helfrich, we expand the surface tension as a Taylor series in the curvature parameters and find that there is a non-zero linear dependence of the interfacial tension on the mean curvature in both cases. This implies a finite Tolman length. In a thermodynamic analysis we prove that the non-zero Tolman length is related to the adsorption of solvent at the interface. Similar, but not the same, correlations between the solvent adsorption and the Tolman length are found in the two scenarios. This result indicates that one should be careful with symmetry arguments in a Helfrich analysis, in particular for systems that have a finite interfacial tension: one not only should consider the structural symmetry of the interface, but also consider the constraints that are enforced upon imposing the curvature. The volume fraction of solvent, the chain length N as well as the interaction parameter chi(AB) in the system can be used to take the system in the direction of the critical point. The usual critical behavior is found. Both the width of the interface and the Tolman length diverge, whereas the density difference between the two phases, adsorbed amount of solvent at the interface, interfacial tension, spontaneous curvature, mean bending modulus as well as the Gaussian bending modulus vanish upon approach of the critical point.     

Effect of pendent chains on the interfacial properties of thin polydimethylsiloxane (PDMS) networks

The interfacial properties of end-linked polydimethylsiloxane (PDMS) films on silicon are examined. Thin cross-linked PDMS films (～10 μm thick) were synthesized over a self-assembled monolayer supported on a silicon wafer. By systematically varying the concentration of monofunctional PDMS in a mixture with telechelic precursor molecules, structures ranging from near-ideal elastic networks to poorly cross-linked networks composed of a preponderance of dangling/pendent chains were synthesized. Lateral force microscopy (LFM) employing bead probes was used to quantify the effect of network structure on the interfacial friction coefficient and residual force. Indentation measurements employing an AFM in force mode were used to characterize the elastic modulus and the pull-off force for the films as a function of pendent chain content. These measurements were complemented with conventional mechanical rheometry measurements on similar thick network films to determine their bulk rheological properties. All networks studied manifested interfacial friction coefficients substantially lower than that of bare silicon. PDMS networks with the lowest pendent chain content displayed friction coefficients close to 1 order of magnitude lower than that of bare silicon, whereas networks with the highest pendent chain content manifested friction coefficients about 3 times lower than that of bare silicon. At intermediate sliding velocities, a crossover in the interfacial friction coefficient was observed, wherein cross-linked PDMS films with the least amount of pendent chains exhibit the highest friction coefficient. These observations are discussed in terms of the structure of the films and relaxation dynamics of elastic strands and dangling chains in tethered network films.     

Lubrication properties of bottle-brush polyelectrolytes: an AFM study on the effect of side chain and charge density

The effect of side chain to charge ratio on the frictional properties of adsorbed layers formed by bottle-brush polyelectrolytes with poly(ethylene oxide) side chains has been investigated. The brush polyelectrolytes were preadsorbed from 0.1 mM NaNO(3) solutions onto mica and silica surfaces; the interfacial friction was then measured in polyelectrolyte-free solutions via AFM (with the silica surface acting as the colloidal probe). It was concluded that the decisive factor for achieving favorable lubrication properties is the concentration of nonadsorbing poly(ethylene oxide) side chains in the interfacial region. However, contrary to what may be expected, the results showed that an ideal brush layer structure with the adsorbed polymers adopting comb-like conformation is not necessary for achieving a low coefficient of friction in the asymmetric mica-silica system. In fact, the lowest coefficient of friction (<0.01) under applied pressures as high as 30 MPa was observed for a system with a side chain to charge ratio of 9:1, incapable of forming brush-like layers.     

Ab initio calculation of the adhesion and ideal shear strength of planar diamond interfaces with different atomic structure and hydrogen coverage

We propose a method to calculate the ideal shear strength τ of two surfaces in contact by ab initio calculations. This quantity and the work of adhesion γ are the interfacial parameters usually derived from tip-based friction force measurements. We consider diamond interfaces and quantitatively evaluate the effects of surface orientation and passivation. We find that in the case of fully passivated interfaces, γ is not affected by the orientation and the alignment of the surfaces in contact. On the contrary, τ does show a dependence on the atomic-scale roughness of the interface. The surface termination has a major impact on the tribological properties of diamond. The presence of dangling bonds, even at concentrations low enough to prevent the formation of interfacial C-C bonds, causes an increase in the resistance to sliding by 2 orders of magnitude with respect to the fully hydrogenated case. We discuss our findings in relation to experimental observations.     

Slip flow in graphene nanochannels

We investigate the hydrodynamic boundary condition for simple nanofluidic systems such as argon and methane flowing in graphene nanochannels using equilibrium molecular dynamics simulations (EMD) in conjunction with our recently proposed method [J. S. Hansen, B. D. Todd, and P. J. Daivis, Phys. Rev. E 84, 016313 (2011)]. We first calculate the fluid-graphene interfacial friction coefficient, from which we can predict the slip length and the average velocity of the first fluid layer close to the wall (referred to as the slip velocity). Using direct nonequilibrium molecular dynamics simulations (NEMD) we then calculate the slip length and slip velocity from the streaming velocity profiles in Poiseuille and Couette flows. The slip lengths and slip velocities from the NEMD simulations are found to be in excellent agreement with our EMD predictions. Our EMD method therefore enables one to directly calculate this intrinsic friction coefficient between fluid and solid and the slip length for a given fluid and solid, which is otherwise tedious to calculate using direct NEMD simulations at low pressure gradients or shear rates. The advantages of the EMD method over the NEMD method to calculate the slip lengths/flow rates for nanofluidic systems are discussed, and we finally examine the dynamic behaviour of slip due to an externally applied field and shear rate.     

Nanotribology of octadecyltrichlorosilane monolayers and silicon: self-mated versus unmated interfaces and local packing density effects

We use atomic force microscopy (AFM) to determine the frictional properties of nanoscale single-asperity contacts involving octadecyltrichlorosilane (OTS) monolayers and silicon. Quantitative AFM measurements in the wearless regime are performed using both uncoated and OTS-coated silicon AFM tips in contact with both uncoated and OTS-coated silicon surfaces, providing four pairs of either self-mated or unmated interfaces. Striking differences in the frictional responses of the four pairs of interfaces are found. First, lower friction occurs with OTS present on either the tip or substrate, and friction is yet lower when OTS is present on both. Second, the shape of the friction versus load plot strongly depends on whether the substrate is coated with OTS, regardless of whether the tip is coated. Uncoated substrates exhibit the common sublinear dependence, consistent with friction being directly proportional to the area of contact. However, coated substrates exhibit an unusual superlinear dependence. These results can be explained qualitatively by invoking molecular plowing as a significant contribution to the frictional behavior of OTS. Direct in situ comparison of two intrinsic OTS structural phases on the substrate is also performed. We observe frictional contrast for different local molecular packing densities of the otherwise identical molecules. The phase with lower packing density exhibits higher friction, in agreement with related previous work, but decisively observed here in single, continuous images involving the same molecules. Lateral stiffness measurements show no distinction between the two OTS structural phases, demonstrating that the difference in friction is not due to divergent stiffnesses of the two phases. Therefore, the packing density directly affects the interface's intrinsic resistance to friction, that is, the interfacial shear strength.