Surface tension of polystyrene blends: Theory and experiment

Surface tension of linear–linear and star/linear polystyrene blends were measured using a modified Wilhelmy method. Our results show that for both polystyrene blend systems, the surface tension‐composition profile is convex, indicating a strong surface excess of the component with lower surface energy. Star/linear blends display more convex surface tension profiles than their linear–linear counterparts, indicative of stronger surface segregation of the branched‐component relative to linear chains. As a first step toward understanding the physical origin of enhanced‐surface segregation of star polymers, self‐consistent field (SCF) lattice simulations (both incompressible and compressible models) and Cahn‐Hilliard theory were used to predict surface tension‐composition profiles. Results from the lattice simulations indicate that the highly convex surface tension profiles observed in the star/linear blend systems are only possible if an architecture‐dependent, Flory interaction parameter (χ = 0.004) is assumed. This conclusion is inconsistent with results from bulk differential scanning calorimetry (DSC) measurements, which indicate sharp glass transitions in both the star/linear and linear/linear homopolymer blends and a simple linear relationship between the bulk glass transition temperature and blend composition. To implement the Cahn‐Hilliard theory, pressure‐volume‐temperature (PVT) data for each of the pure components in the blends were first measured and the data used as input for the theory. Consistent with the experimental data, Cahn‐Hilliard theory predicts a larger surface excess of star molecules in linear hosts over a wide composition range. Significantly, this result is obtained assuming a nearly neutral interaction parameter between the linear and star components, indicating that the surface enrichment of the stars is not a consequence of complex phase behavior in the bulk. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1666–1685, 2009     

Surface segregation and surface tension of polydisperse polymer melts

The effect of polydispersity on surface segregation of a lower molecular weight polymer component in a higher molecular weight linear polymer melt host is investigated theoretically. We show that the integrated surface excess zM of a polymer component of molecular weight M satisfies a simple relation zM=2Ue(M/Mw-1)phiM, where Mw is the weight averaged molecular weight, phiM is the polymer volume fraction, and Ue is the attraction of polymer chain ends to the surface. Ue is principally of entropic origin, but also reflects any energetic preference of chain ends to the surface. We further show that the surface tension gammaM of a polydisperse melt of high molar mass components depends on the number average degree of polymerization Mn as, gammaM=gammainfinity+2UerhobRT/Mn. The parameter gammainfinity is the asymptotic surface tension of an infinitely long polymer of the same chemistry, rhob is the bulk density of the polymer, R is the universal gas constant, and T is the temperature. The predicted gammaM compare favorably with surface tension values obtained from self-consistent field theory simulations that include equation of state effects, which account for changes in polymer density with molecular weight. We also compare the predicted surface tension with available experimental data.     

基于密度泛函理论研究二元排斥Yukawa流体的表面结构性质

基于自由能密度泛函理论(DFT)考察了二元排斥Yukawa (HCRY)流体在不同外场下的密度分布. 基于微扰理论, 体系的Helmholtz自由能泛函采用硬球排斥部分和长程色散部分贡献之和, 其中Kierlik和Rosinberg的加权密度近似(WDA)被用来计算硬球排斥部分, 而色散部分采用平均场理论(MFT)进行描述. 为了验证DFT计算结果的合理性, 研究中采用巨正则Monte Carlo(GCMC)模拟计算了在不同主体相密度、硬核直径和位能参数比的条件下二元HCRY混合流体的密度分布. 结果表明, 该DFT计算结果与GCMC模拟值吻合良好.     

Surface tension of quantum fluids from molecular simulations

We present the first molecular simulations of the vapor-liquid surface tension of quantum liquids. The path integral formalism of Feynman was used to account for the quantum mechanical behavior of both the liquid and the vapor. A replica-data parallel algorithm was implemented to achieve good parallel performance of the simulation code on at least 32 processors. We have computed the surface tension and the vapor-liquid phase diagram of pure hydrogen over the temperature range 18-30 K and pure deuterium from 19 to 34 K. The simulation results for surface tension and vapor-liquid orthobaric densities are in very good agreement with experimental data. We have computed the interfacial properties of hydrogen-deuterium mixtures over the entire concentration range at 20.4 and 24 K. The calculated equilibrium compositions of the mixtures are in excellent agreement with experimental data. The computed mixture surface tension shows negative deviations from ideal solution behavior, in agreement with experimental data and predictions from Prigogine's theory. The magnitude of the deviations at 20.4 K are substantially larger from simulations and from theory than from experiments. We conclude that the experimentally measured mixture surface tension values are systematically too high. Analysis of the concentration profiles in the interfacial region shows that the nonideal behavior can be described entirely by segregation of H(2) to the interface, indicating that H(2) acts as a surfactant in H(2)-D(2) mixtures.     

Calculation of surface tension of metals using density gradient theory and PC-SAFT equation of state

The Cahn-Hilliard theory was combined with PC-SAFT equation of state (EOS), in order to describe both the phase behaviors and the surface tension of different types of metals (Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Fe, Zn, Cd, In, Sn, Pb, and Bi). The only two inputs of the theory are the Helmholtz free-energy density and the influence parameter. The PC-SAFT equation of state was applied to determine Helmholtz free-energy density and bulk properties. The influence parameter is obtained by fitting to the experimental data of surface tension. The results show a useful possibility to calculate surface tensions which are in satisfactory agreement with experimental data.     

Determination of the interfacial characteristics of a series of bolaamphiphilic poly(fluorooxetane) surfactants through molecular dynamics simulation

Constant surface tension (NgammaT) and constant volume (NVT) molecular dynamics simulations have been conducted on a series of bolaamphiphilic alpha,varpi-(diammonium disulfato)poly(fluorooxetane)s and on a typical "long-chain" anionic fluorosurfactant used to improve the flow-and-leveling characteristics of aqueous coatings, to compare their behavior at a water/air interface. Recent research has shown that the poly(fluorooxetane) surfactants considered in this paper could serve as an effective substitute for traditional fluorosurfactants used in flow-and-leveling applications.(1) From molecular dynamics simulation, we have determined the saturated interfacial area per surfactant, interfacial area per surfactant as a function of surface tension, density profiles, the degree of hydration for various atoms in each surfactant, the degree of counterion binding, and order parameters. Our results for saturated interfacial area per surfactant molecule are greater than what has been obtained by other researchers through parametric fitting of interfacial area from experimental surface tension data using the Davies isotherm. Possible explanations for this difference are discussed. The low interfacial areas occupied by each poly(fluorooxetane) at the water/air interface are the result of their ability to adopt a "looped" conformation, in which the carbon and oxygen backbone of each surfactant and the attached perfluoroalkyl chains are forced into the air phase. A geometrically defined penetration parameter was calculated from the density profiles, which reveals that each poly(fluorooxetane) surfactant is more effective at separating the air and water phases than the "long-chain" anionic fluorosurfactant. The degree of hydration measured for different atoms in poly(fluorooxetane) during simulation confirms that a "looped" conformation is adopted in which the surfactant backbone and the perfluoroalkyl chains are lifted away from the water surface. Calculation of order parameters revealed a much lower degree of ordering for the perfluoroalkyl side chains in each bolaamphiphile than in the "long chain" anionic fluorosurfactant. When viewed in the context of the penetration parameter analysis, the density profiles and hydration data suggest why each poly(fluorooxetane) is capable of significantly reducing surface tension when other fluorosurfactants with similarly short perfluoroalkyl moieties provide inadequate surface tension reduction for practical flow-and-leveling applications.     

Monte Carlo versus molecular dynamics simulations in heterogeneous systems: an application to the n-pentane liquid-vapor interface

The Monte Carlo (MC) and molecular dynamics (MD) methodologies are now well established for computing equilibrium properties in homogeneous fluids. This is not yet the case for the direct simulation of two-phase systems, which exhibit nonuniformity of the density distribution across the interface. We have performed direct MC and MD simulations of the liquid-gas interface of n-pentane using a standard force-field model. We obtained density and pressure components profiles along the direction normal to the interface that can be very different, depending on the truncation and long range correction strategies. We discuss the influence on predicted properties of different potential truncation schemes implemented in both MC and MD simulations. We show that the MD and MC profiles can be made in agreement by using a Lennard-Jones potential truncated via a polynomial function that makes the first and second derivatives of the potential continuous at the cutoff distance. In this case however, the predicted thermodynamic properties (phase envelope, surface tension) deviate from experiments, because of the changes made in the potential. A further readjustment of the potential parameters is needed if one wants to use this method. We conclude that a straightforward use of bulk phase force fields in MD simulations may lead to some physical inconsistencies when computing interfacial properties.     

Vapor-liquid interfacial properties of rigid-linear Lennard-Jones chains

We have obtained the interfacial properties of short rigid-linear chains formed from tangentially bonded Lennard-Jones monomeric units from direct simulation of the vapour-liquid interface. The full long-range tails of the potential are accounted for by means of an improved version of the inhomogeneous long-range corrections of Janec?ek [J. Phys. Chem. B 110, 6264-6269 (2006)] proposed recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] valid for spherical as well as for rigid and flexible molecular systems. Three different model systems comprising of 3, 4, and 5 monomers per molecule are considered. The simulations are performed in the canonical ensemble, and the vapor-liquid interfacial tension is evaluated using the test-area method. In addition to the surface tension, we also obtain density profiles, coexistence densities, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the chain length and rigidity on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapor-liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. The surface tension has been scaled by critical properties and represented as a function of the difference between coexistence densities relative to the critical density.     

Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: the case of carbon dioxide

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter q=Q(*4)T*, where Q* is the reduced quadrupole moment of the molecule and T* the reduced temperature. The model can be applied to a variety of small quadrupolar molecules. We focus on carbon dioxide as a test case, but consider nitrogen and benzene, too. Experimental critical temperature, density, and quadrupolar moment are sufficient to fix the parameters of the model. The resulting agreement with experiments is excellent and marks a significant improvement over approaches which neglect quadrupolar effects. The same coarse-grained model was also applied in the framework of perturbation theory in the mean spherical approximation. As expected, the latter deviates from the Monte Carlo results in the critical region, but is reasonably accurate at lower temperatures.     

Modifying gradient theory to predict the surface properties of halogenated hydrocarbons

A new method is proposed for predicting the surface tension, density profile, and thickness of the surface layer of a liquid near an interface using gradient theory. The objects of study are halogenated hydrocarbons. The algorithm for calculating surface properties includes a new modification of the Peng-Robinson cubic equation of state (EoS) that does not require information on the critical parameters, and a new procedure for calculating the influence parameter. Validation of the procedure for predicting the surface properties of liquids shows that the agreement between the calculated surface tension of halogenated hydrocarbons and the existing literature data is sufficient for practical use.     

Extended version of the van der Waals capillarity theory

An extended version of the van der Waals capillarity theory describing the liquid-vapor interface in the temperature range from the triple to the critical point is suggested. A model functional of thermodynamic potential for a two-phase Lennard-Jones system taking into account the effect of the highest degree terms of gradient expansion has been constructed. The identity of the thermodynamic and the mechanical definition of Tolman's length has been proved in the framework of the adopted form of functional. The properties of nuclei of the liquid and the vapor phase are described. The paper determines: the work of formation of a nucleus, density profiles, size dependences of the surface tension, and the parameter delta in the Gibbs-Tolman-Koenig-Buff equation.     

Internal pressure and surface tension of bare and hydrogen coated silicon nanoparticles

We present a study of internal pressure and surface tension of bare and hydrogen coated silicon nanoparticles of 2-10 nm diameter as a function of temperature, using molecular dynamics simulations employing a reparametrized Kohen-Tully-Stillinger interatomic potential. The internal pressure was found to increase with decreasing particle size but the density was found to be independent of the particle size. We showed that for covalent bond structures, changes in surface curvature and the associated surface forces were not sufficient to significantly change bond lengths and angles. Thus, the surface tension was also found to be independent of the particle size. Surface tension was found to decrease with increasing particle temperature while the internal pressure did not vary with temperature. The presence of hydrogen on the surface of a particle significantly reduces surface tension (e.g., drops from 0.83 J/m(2) to 0.42 J/m(2) at 1500 K). The computed pressure of bare and coated particles was found to follow the classical Laplace-Young equation.     

On interfacial tension calculation from the test-area methodology in the grand canonical ensemble

We propose the extension of the test-area methodology, originally proposed to evaluate the surface tension of planar fluid-fluid interfaces along a computer simulation in the canonical ensemble, to deal with the solid-fluid interfacial tension of systems adsorbed on slitlike pores using the grand canonical ensemble. In order to check the adequacy of the proposed extension, we apply the method for determining the density profiles and interfacial tension of spherical molecules adsorbed in slitlike pore with different pore sizes and solid-fluid dispersive energy parameters along the same simulation. We also calculate the solid-fluid interfacial tension using the original test-area method in the canonical ensemble. Agreement between the results obtained from both methods indicate that both methods are fully equivalent. The advantage of the new methodology is that allows to calculate simultaneously the density profiles and the amount of molecules adsorbed onto a slitlike pore, as well as the solid-fluid interfacial tension. This ensures that the chemical potential at which all properties are evaluated during the simulation is exactly the same since simulations can be performed in the grand canonical ensemble, mimicking the conditions at which the adsorption experiments are most usually carried out in the laboratory.     

A molecular dynamics simulation study of nanoscale liquid threads

The properties of liquid threads in angular direction are studied. On the basis of Gibbs theory, a thermodynamic model is constructed and a formula of surface of tension is derived. For the determination of surface tension, different methods are presented. We investigate seven different systems (the numbers of molecules N are 1600, 2240, 2880, 3360, 4000, 4800, and 5280) by molecular dynamics simulations. We analyze the surface tension obtained by various routes, then whether the classical Laplace equation is applicable in nanoscale can be determined. The results obtained by molecular dynamics simulations support that surface tension is dependent on the dividing surface curvature.     

Molecular dynamics simulations of vapor/liquid coexistence using the nonpolarizable water models

The surface tension, vapor-liquid equilibrium densities, and equilibrium pressure for common water models were calculated using molecular dynamics simulations over temperatures ranging from the melting to the critical points. The TIP4P/2005 and TIP4P-i models produced better values for the surface tension than the other water models. We also examined the correlation of the data to scaling temperatures based on the critical and melting temperatures. The reduced temperature (T/T(c)) gives consistent equilibrium densities and pressure, and the shifted temperature T + (T(c, exp) - T(c, sim)) gives consistent surface tension among all models considered in this study. The modified fixed charge model which has the same Lennard-Jones parameters as the TIP4P-FQ model but uses an adjustable molecular dipole moment is also simulated to find the differences in the vapor-liquid coexistence properties between fixed and fluctuating charge models. The TIP4P-FQ model (2.72 Debye) gives the best estimate of the experimental surface tension. The equilibrium vapor density and pressure are unaffected by changes in the dipole moment as well as the surface tension and liquid density.     

Some estimates of the surface tension of curved surfaces using density functional theory

Density functional theory is used to calculate the surface tension of planar and slightly curved surfaces, which can be written as gamma(R)=gamma(infinity)(1-2delta(infinity)R), where R is the radius of curvature of the surface. Calculations are performed for a Lennard-Jones fluid, split into a hard-sphere repulsive potential and an attractive part. The repulsive part is treated using the local density approximation. The attractive part is treated using a high temperature approximation (HTA) in which the pair correlation function is approximated by the Percus-Yevick pair correlation function of a uniform hard-sphere fluid evaluated at a position-dependent average density. An expression relating the Tolman length delta(infinity) to the density profile of the planar surface is derived. Numerical results are presented for the planar surface tension gamma(infinity) and for delta(infinity) and are compared with those using mean field theory (MFT) and with those using the square-gradient approximation. Values for gamma(infinity) using the HTA are 30%-40% higher than those using MFT. Values for delta(infinity) using the HTA are around -0.1 (in units of the Lennard-Jones parameter sigma) and only weakly dependent on temperature. These values are less negative than the values from MFT. The square-gradient approximation gives reasonable estimates of the more accurate nonlocal results for both the MFT and the HTA.     

Influence of non-universal effects on dynamical scaling in driven polymer translocation

We study the dynamics of driven polymer translocation using both molecular dynamics (MD) simulations and a theoretical model based on the non-equilibrium tension propagation on the cis side subchain. We present theoretical and numerical evidence that the non-universal behavior observed in experiments and simulations are due to finite chain length effects that persist well beyond the relevant experimental and simulation regimes. In particular, we consider the influence of the pore-polymer interactions and show that they give a major contribution to the non-universal effects. In addition, we present comparisons between the theory and MD simulations for several quantities, showing extremely good agreement in the relevant parameter regimes. Finally, we discuss the potential limitations of the present theories.     

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.     

Molecular dynamics investigation into the effect of temperature on the structure and properties of methyl methacrylate thin films on a Au(111) surface

An atomistic modeling approach is performed to investigate the effect of temperature on the structural properties of the MMA (methyl methacrylate) thin film and a Au(111) surface. The density profile and orientation of the MMA molecule in the thin film have been analyzed. We found that there is a significant effect on the density profile and orientation of the MMA molecule in the region near the interface between the thin film and the Au substrate. As the temperature increases, the density clearly decreases in this region; in addition, the orientation of the MMA molecule also changes. Next, we calculated and examined the relationships between the stress, surface tension, and free energy and the density profile. Finally, we analyzed the influence of temperature on the interaction strength between the MMA molecules and between the MMA molecules and the Au(111) surface. We found that the influence of the interaction strength is more significant between MMA molecules than between MMA molecules and the Au(111) surface.