Viscosity of liquid mixtures: the Vesovic-Wakeham method for chain molecules

New expressions for the viscosity of liquid mixtures, consisting of chain-like molecules, are derived by means of Enskog-type analysis. The molecules of the fluid are modelled as chains of equally sized, tangentially joined, and rigid spheres. It is assumed that the collision dynamics in such a fluid can be approximated by instantaneous collisions. We determine the molecular size parameters from the viscosity of each pure species and show how the different effective parameters can be evaluated by extending the Vesovic-Wakeham (VW) method. We propose and implement a number of thermodynamically consistent mixing rules, taking advantage of SAFT-type analysis, in order to develop the VW method for chain molecules. The predictions of the VW-chain model have been compared in the first instance with experimental viscosity data for octane-dodecane and methane-decane mixtures, thus, illustrating that the resulting VW-chain model is capable of accurately representing the viscosity of real liquid mixtures.     

Shape factors in equations of state. Part II. Repulsion phenomena in multicomponent chain fluids

An equation of state for the multicomponent fluid phase of nonattracting rigid particles of arbitrary shape is presented. The equation is a generalization of a previously presented equation of state for pure fluids of rigid particles; the approach describes the volumetric properties of a pure fluid in terms of a shape factor, zeta, which can be back calculated by scaling the volumetric properties of pure fluids to that of a hard sphere. The performance of the proposed equation is tested against mixtures of chain fluids immersed in a "monomeric" solvent of hard spheres of equal and different sizes. Extensive new Monte Carlo simulation data are presented for 19 binary mixtures of hard homonuclear tangent freely-jointed hard sphere chains (pearl-necklace) of various lengths (three to five segments), with spheres of several size ratios and at various compositions. The performance of the proposed equation is compared to the hard-sphere SAFT approach and found to be of comparable accuracy. The equation proposed is further tested for mixtures of spheres with spherocylinders. In all cases, the equation proved to be accurate and simple to use.     

Computer simulation study of the global phase behavior of linear rigid Lennard-Jones chain molecules: comparison with flexible models

The global phase behavior (i.e., vapor-liquid and fluid-solid equilibria) of rigid linear Lennard-Jones (LJ) chain molecules is studied. The phase diagrams for three-center and five-center rigid model molecules are obtained by computer simulation. The segment-segment bond lengths are L = sigma, so that models of tangent monomers are considered in this study. The vapor-liquid equilibrium conditions are obtained using the Gibbs ensemble Monte Carlo method and by performing isobaric-isothermal NPT calculations at zero pressure. The phase envelopes and critical conditions are compared with those of flexible LJ molecules of tangent segments. An increase in the critical temperature of linear rigid chains with respect to their flexible counterparts is observed. In the limit of infinitely long chains the critical temperature of linear rigid LJ chains of tangent segments seems to be higher than that of flexible LJ chains. The solid-fluid equilibrium is obtained by Gibbs-Duhem integration, and by performing NPT simulations at zero pressure. A stabilization of the solid phase, an increase in the triple-point temperature, and a widening of the transition region are observed for linear rigid chains when compared to flexible chains with the same number of segments. The triple-point temperature of linear rigid LJ chains increases dramatically with chain length. The results of this work suggest that the fluid-vapor transition could be metastable with respect to the fluid-solid transition for chains with more than six LJ monomer units.     

Hybrid method coupling fluctuating hydrodynamics and molecular dynamics for the simulation of macromolecules

We present a hybrid computational method for simulating the dynamics of macromolecules in solution which couples a mesoscale solver for the fluctuating hydrodynamics (FH) equations with molecular dynamics to describe the macromolecule. The two models interact through a dissipative Stokesian term first introduced by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We show that our method correctly captures the static and dynamical properties of polymer chains as predicted by the Zimm model. In particular, we show that the static conformations are best described when the ratio sigma/b=0.6, where sigma is the Lennard-Jones length parameter and b is the monomer bond length. We also find that the decay of the Rouse modes' autocorrelation function is better described with an analytical correction suggested by Ahlrichs and Dunweg. Our FH solver permits us to treat the fluid equation of state and transport parameters as direct simulation parameters. The expected independence of the chain dynamics on various choices of fluid equation of state and bulk viscosity is recovered, while excellent agreement is found for the temperature and shear viscosity dependence of center of mass diffusion between simulation results and predictions of the Zimm model. We find that Zimm model approximations start to fail when the Schmidt number Sc < or approximately 30. Finally, we investigate the importance of fluid fluctuations and show that using the preaveraged approximation for the hydrodynamic tensor leads to around 3% error in the diffusion coefficient for a polymer chain when the fluid discretization size is greater than 50 A.     

Method for viscosity measurements at high pressure

The technique of quasielastic light scattering is utilized to determine the viscosity of fluids subjected to large hydrostatic pressures. In this method, a small concentration of insoluble polystyrene spheres of known diameter, 0.109 μm, is added to the fluid. The high-pressure cell in which the fluid is contained has three optical windows. The laser light scattered from the suspended spheres is analyzed to determine the diffusion coefficient of the spheres. Since, by the Stokes law, the viscosity of the fluid is determined from the measured diffusion coefficient and known particle radius r. A small correction is required for the contraction of the spheres and for refractive-index change of the water under pressure. Results on the viscosity of water at 25°C up to pressures of 2.5 kbar are reported and compared with published results. This method is applicable to lubricants and polymer solutions where the viscosity is many orders of magnitude greater than that of water.     

Transport coefficients for hard-chain fluid

Diffusion coefficient and shear viscosity are calculated for fluids containing molecules modelled as chains of tangent hard spheres. A formula for the Stokes–Einstein relation is proposed for hard chain fluids to calculate the shear viscosity from the diffusion coefficient. The numerical results show a good agreement between theoretical values and molecular dynamics results     

Extended conformations of isolated molecular bottle-brushes: Influence of side-chain topology

A Monte Carlo study is presented to discuss the influence of the side-chain topology on the enhancement of the persistence length of a molecular bottle-brush in a dilute athermal solution due to the excluded volume interactions between the side chains. The structures investigated consisted of freely jointed backbones of 100 hard spheres (beads) of diameter 1 to which 50 equally flexible side chains were grafted. The diameter of the side-chain beads was varied from 1 to 3 in the same units. For every given size of the side-chain bead, the length of the side chains was varied from 4 to 20 beads. The ratio between the persistence length and the bottle-brush diameter, which is the determining factor for lyotropic behavior of conventional semi-flexible chains, was found to be almost independent of the side-chain length. At the same time, it was found to increase considerably with increasing size of the side-chain beads, suggesting that by a proper choice of the chemistry lyotropic behavior of molecular bottle-brushes due to excluded-volume interactions between the side chains might be achieved. Moreover, relatively short side chains can be used since the side chain length has only a minor influence on the ratio between the persistence length and the diameter. These findings are in a good agreement with recent experimental observations.     

Vapor-liquid phase coexistence and transport properties of two-dimensional oligomers

Grand-canonical transition-matrix Monte Carlo and histogram reweighting techniques are used herein to study the vapor-liquid coexistence properties of two-dimensional (2D) flexible oligomers with varying chain lengths (m = 1-8). The phase diagrams of the various 2D oligomers follow the correspondence state (CS) principle, akin to the behavior observed for bulk oligomers. The 2D critical density is not influenced by the oligomer chain length, which contrasts with the observation for the bulk oligomers. Line tension, calculated using Binder's formalism, in the reduced plot is found to be independent of chain length in contrast to the 3D behavior. The dynamical properties of 2D fluids are evaluated using molecular dynamics simulations, and the velocity and pressure autocorrelation functions are investigated using Green-Kubo (GK) relations to yield the diffusion and viscosity. The viscosity determined from 2D non-equilibrium molecular dynamics simulation is compared with the viscosity estimated from the GK relations. The GK relations prove to be reliable and efficient for the calculation of 2D transport properties. Normal diffusive regions are identified in dense oligomeric fluid systems. The influence of molecular size on the diffusivity and viscosity is found to be diminished at specific CS points for the 2D oligomers considered herein. In contrast, the viscosity and diffusion of the 3D bulk fluid, at a reduced temperature and density, are strongly dependent on the molecular size at the same CS points. Furthermore, the viscosity increases and the diffusion decreases multifold in the 2D system relative to those in the 3D system, at the CS points.     

Coordination numbers for rigid spheres of different size—estimating the number of next-neighbour interactions in a mixture

The maximum number of rigid spheres which can be attached to a central sphere of different diameter is calculated numerically. It is shown that this coordination number is not proportional to the surface ratio of the spheres, but roughly to power 1.2 of the diameter ratio. This has consequences for the methods by which averages of molecular properties are calculated; for several binary liquid mixtures it is shown that replacing molar fractions by contact fractions makes plots of excess properties versus concentration appear more symmetrical, thereby reducing the number of terms required in Redlich-Kister correlations.     

Viscoelastic properties of an isolated polymer chain with arbitrary flexibility,chain length and hydrodynamic interactions from 4‐dimensional Dirac propagator

Kholodenko's theory of semiflexible polymer chains, the conformation and properties of which are obtained from the Dirac propagator, shows applicability to dilute solutions of semiflexible polymers of arbitrary persistence and contour lengths by calculating the static scattering function and the squared end‐to‐end distance of the polymer chain. In the present work, the theory is extended and applied to obtain the intrinsic viscosity with consideration of hydrodynamic interactions. The intrinsic viscosity formula is derived as function of chain length and persistence length. The hydrodynamic interactions are also taken into account following the Kirkwood and Riseman scheme. From this calculation, we obtain the general expression for the intrinsic viscosity and diffusion coefficients covering the whole range of chain flexibilities without confusion with the excluded volume effects. Calculated limiting values of hydrodynamical observables are in complete agreement with those known for random coils and rigid rods.     

水基自形成CoFe2O4 磁性液体的零磁场粘滞特性

The plot of viscosity versus particle volume fraction for the water carrier of self-formed CoFe2O4 magnetic fluid is abnormal in zero magnetic field. However,the viscosity theory of the suspension with the global rigid particle filling cannot explain the experiment well. That is because the nanoparticles have aggregated before preparation of magnetic fluid. The fact is found that the sedimentation without magnetic field and the becoming chains in magnetic field of this type of magnetic fluid need the big particles which core are pre-aggregates by researching the interaction of particles of magnetic fluid. Around the big particles,nanoparticles are absorbed with the type of dynamic state. It is on that idea that the model of fluctuant aggregation is made. So,the average diameter,Einstein ratio and particles size distributive deviation of free suspended bodies in zero magnetic fluid are the functions of the particles volume fraction. And then,Popplewell’s formula of the viscosity is modified with this model. As a result,a well-fitted curve is obtained.     

Heat conduction in chain polymer liquids: molecular dynamics study on the contributions of inter- and intramolecular energy transfer

In this paper, the molecular mechanisms which determine the thermal conductivity of long chain polymer liquids are discussed, based on the results observed in molecular dynamics simulations. Linear n-alkanes, which are typical polymer molecules, were chosen as the target of our studies. Non-equilibrium molecular dynamics simulations of bulk liquid n-alkanes under a constant temperature gradient were performed. Saturated liquids of n-alkanes with six different chain lengths were examined at the same reduced temperature (0.7T(c)), and the contributions of inter- and intramolecular energy transfer to heat conduction flux, which were identified as components of heat flux by the authors' previous study [J. Chem. Phys. 128, 044504 (2008)], were observed. The present study compared n-alkane liquids with various molecular lengths at the same reduced temperature and corresponding saturated densities, and found that the contribution of intramolecular energy transfer to the total heat flux, relative to that of intermolecular energy transfer, increased with the molecular length. The study revealed that in long chain polymer liquids, thermal energy is mainly transferred in the space along the stiff intramolecular bonds. This finding implies a connection between anisotropic thermal conductivity and the orientation of molecules in various organized structures with long polymer molecules aligned in a certain direction, which includes confined polymer liquids and self-organized structures such as membranes of amphiphilic molecules in water.     

Transient ordering in a quasi-two-dimensional liquid near freezing

We report the results of a theoretical study of locally ordered fluctuations in a quasi-two-dimensional colloid fluid. The fluctuations in the equilibrium state are monitored by the aperture cross-correlation function of radiation scattered by the fluid, as calculated from molecular dynamics simulations of near hard spheres with diameter sigma confined between smooth hard walls. These locally ordered fluctuations are transient; their decay can be monitored as a function of the time between the cross-correlated scattered radiation signals, but only the single-time cross-correlated signals are discussed in this paper. Systems with thicknesses less than two hard sphere diameters were studied. For wall separation H in the range 1 sigma/=1.57 sigma, hexagonal fluctuations persist in the dense liquid up to H=1.75 sigma, and fluctuations with square ordered symmetry, that of the solid to which the liquid freezes, only emerge at densities approximately 2% below freezing. For H=1.8 sigma and 1.85 sigma, hexagonal ordered flucuations are no longer found, and the square ordered fluctuations dominate the dense liquid region as the system freezes into a two layer square solid. For H=1.9 sigma and 1.95 sigma, where the liquid freezes into a two layer hexagonal solid, both square and hexagonal ordered fluctuations are observed. At lower densities, the ordered fluctuations only exhibit square symmetry. Hexagonal ordered fluctuations appear at densities approximately 7% below freezing and become more dominant as the density is increased, but the square ordered fluctuations persist until the system is converted into the solid.     

The effect of density on the properties of short chain fluids

We incorporate density dependence into continuum Born-Green-Yvon (BGY) theory through calculation of the end-to-end intramolecular correlation function. Whereas in previous studies we had only performed this calculation for the case of an isolated (zero-density) square-well chain of m segments (3相似文献   

Friction coefficients of spheres having sticky or hairy surfaces

The theoretical equations for friction coefficients of spheres having sticky or hairy surfaces are presented. In the present treatment, the sticky surface is represented by a higher viscosity of fluid in the surface layer and the hairy surface is assumed to have a porous structure. The friction coefficients are given as functions of the thickness of the surface layer, the fluid viscosity in the surface layer and the segmental density of hairy chains.     

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.     

Dynamics of shear-thinning suspensions of core-shell structured latex particles

The rheological behavior and microstructure of shear-thinning suspensions of core-shell structured carboxylated latex particles were examined. The steady shear viscosity of the suspension increased with increasing dissociation of the carboxyl groups or increasing particle concentration, however the critical shear stress sigma(c) and inter-particle distance xi of the microstructure did not change. With increasing particle diameter, sigma(c) increased and xi decreased. These results were consistent with a Brownian hard sphere model, in which competition exists between the bulk mass transfer due to the applied field and diffusion of the particles. We confirmed that sigma(c) depends on xi, as expressed by sigma(c) = 3kT/4pi xi3. This relationship is consistent with the dynamics of a Brownian hard sphere model with particle diameter xi. Thus the dynamics of shear-thinning suspensions of core-shell particles can be explained by a Brownian thermodynamic model.     

Understanding the growth rates of polymer cocrystallization in the binary mixtures of different chain lengths

Polymer materials often contain a polydispersity of molecular lengths. We studied the linear growth rates of polymer lamellar crystals in the binary mixtures of different chain lengths by means of dynamic Monte Carlo simulations. Both chain lengths were chosen large enough to perform chain folding upon crystal growth but not very large to avoid the effect of chain entanglement in the bulk phase. We found that the crystal growth rates exhibit a linear dependence upon the compositions of mixtures. This linear relation implies that the overall crystal growth rates are integrated by the separate contributions of variable-length single polymers, supporting the model of intramolecular crystal nucleation. In each event of crystal growth of single polymers, long chains yield more crystallinity than short chains. This high efficiency explains higher crystal growth rates of long chains than that of short chains, and the explanation is quite different from the traditional view on the basis of their different melting points. In addition, with a partial release of sliding diffusion for crystal thickening, a new dependence of crystal growth rates occurs near the dilute end of long-chain compositions at high temperatures, which can be attributed to the preference of integer-number chain folding at the crystal growth front. The preferred fold lengths may vary with chain lengths and thus influence the crystal growth rates.     

Shape-persistent linear, kinked, and cyclic oligo(phenylene-ethynylene-butadiynylene)s: self-assembled monolayers

Shape-persistent rigid phenylene-ethynylene-butadiynylenes form lamellar self-assembled monolayers (SAMs) at the HOPG/TCB interface, which were studied by scanning tunneling microscopy (STM) with submolecular resolution. Substitution of the terminating acetylene functions with polar cyanopropyldimethylsilyl groups leads to 2D phase separation and defined rod-rod interactions, which determine the packing distances between the rigid rods. The results stimulated the connection of rigid rods via septiarylene clamp units. They covalently link two rigid rod units and define the intramolecular rod-rod distance that matches the alkoxy substituent chain lengths. The systems can be described as half-ring structures of two rigid rods connected via a rotatable joint unit. These acetylene-terminated half-ring structures were also oligomerized under Cu and Pd catalysis to yield defined acyclic and cyclic oligomers. Detailed STM studies decoded the molecular origin of the surface patterning of such systems. The dodecyloxy side chains are adsorbed along the HOPG main axes and, together with the alkoxy backbone angle, determine the adsorption direction of the adlayers.