Scaling of the viscosity of the Lennard-Jones chain fluid model, argon, and some normal alkanes

In this work, we have tested the efficiency of two scaling approaches aiming at relating shear viscosity to a single thermodynamic quantity in dense fluids, namely the excess entropy and the thermodynamic scaling methods. Using accurate databases, we have applied these approaches first to a model fluid, the flexible Lennard-Jones chain fluid (from the monomer to the hexadecamer), then to real fluids, such as argon and normal alkanes. To enlarge noticeably the range of thermodynamics conditions for which these scaling methods are applicable, we have shown that the use of the residual viscosity instead of the total viscosity is preferable in the scaling procedures. It has been found that both approaches, using the adequate scaling, are suitable for the Lennard-Jones chain fluid model for a wide range of thermodynamic conditions whatever the chain length when scaling law exponents and prefactors are adjusted for each chain length. Furthermore, these results were found to be well respected by the corresponding real fluids.     

Scaling law of shear viscosity in atomic liquid and liquid mixtures

A scaling law relating the shear viscosity of one and two component liquid mixtures to their excess thermodynamic entropies defined through pair correlation functions is derived by approximating the mode coupling theory expressions of frictions and then combining with the Stokes-Einstein relation. Molecular dynamics simulation has been performed to generate the data of shear viscosity for one and two component liquid mixtures to test the derived scaling law. The derived scaling laws yield numerical results of shear viscosity for one component and two component liquid mixtures, which are in excellent agreement with the molecular dynamics simulation results for a wide range of density and interaction potential.     

Accurate and local formulation for thermodynamic properties directly from integral equation method

A local formulation for determination of excess chemical potential is derived out by applying an assumption of linear dependence of correlation function and bridge function on the charging parameter to the Kirkwood charging formula and scaling the bridge function, the scaling parameter is specified by a Gibbs–Duhem relation. The local formulation for the excess chemical potential only requires the correlation function and bridge function of the investigated state as input and is therefore free of an unwieldy thermodynamic integration. A comprehensive comparison between the presently calculated thermodynamic quantities for a Lennard–Jones (LJ) fluid including two key quantities, i.e. the excess chemical potential and excess entropy, corresponding simulation data available in literature, and corresponding calculated results by several other global and local formulations, indicates that the present formulation is the only one capable of predicting locally and excellently all of the thermodynamic properties of the LJ fluid. The GCMC simulation is carried out for a core-softened potential fluid and the LJ fluid near critical state and at subcritical state near the gas–liquid coexistence line to obtain the excess chemical potential which is also in excellent agreement with the theoretical prediction from the present formalism; this indicates that the present formalism is of general interest in fluid statistical mechanics and applicable to parameter space covering over the entire phase diagram.     

Systematic coarse-graining of potential energy landscapes and dynamics in liquids

Recent efforts have shown that the dynamic properties of a wide class of liquids can be mapped onto semi-universal scaling laws and constitutive relations that are motivated by thermodynamic analyses of much simpler models. In particular, it has been found that many systems exhibit dynamics whose behavior in state space closely follows that of soft-sphere particles interacting through an inverse power repulsion. In the present work, we show that a recently developed coarse-graining theory provides a natural way to understand how arbitrary liquids can be mapped onto effective soft-sphere models and hence how one might potentially be able to extract underlying dynamical scaling laws. The theory is based on the relative entropy, an information metric that quantifies how well a soft-sphere approximation to a liquid's multidimensional potential energy landscape performs. We show that optimization of the relative entropy not only enables one to extract effective soft-sphere potentials that suggest an inherent scaling of thermodynamic and dynamic properties in temperature-density space, but that also has rather interesting connections to excess entropy based theories of liquid dynamics. We apply the approach to a binary mixture of Lennard-Jones particles, and show that it gives effective soft-sphere scaling laws that well-describe the behavior of the diffusion constants. Our results suggest that the relative entropy formalism may be useful for "perturbative" type theories of dynamics, offering a general strategy for systematically connecting complex energy landscapes to simpler reference ones with better understood dynamic behavior.     

Thermodynamic scaling of polymer dynamics versus T-T(g) scaling

A thermodynamic scaling law for the relaxation times of complex liquids as a function of temperature and volume has been proposed in the literature: τ(T,V) = f(TV(γ)), where γ is a material-dependent constant. We test this scaling for six materials, linear polystyrene, star polystyrene, two polycyanurate networks, poly(vinyl acetate), and poly(vinyl chloride), and compare the thermodynamic scaling to T-T(g) scaling, where τ = f(T-T(g)). The thermodynamic scaling law successfully reduces the data for all of the samples; however, polymers with similar structures but different glass transition (T(g)) and pressure-volume-temperature (PVT) behavior, i.e., the two polycyanurates, cannot be superposed unless the scaling law is normalized by T(g)V(g) (γ). On the other hand, the T-T(g) scaling successfully reduced data for all polymers, including those having similar microstructures. In addition, the T-T(g) scaling is easier to implement since it does not require knowledge of the PVT behavior of the material. The relationship between T(g)V(g) (γ)∕TV(γ) and T-T(g) scaling is clarified and is found to be weakly dependent on pressure.     

Adsorption-Desorption Flow of Condensable Vapors through Mesoporous Media: Network Modeling and Percolation Theory

Flow of condensable vapors in mesoporous media is investigated theoretically and experimentally during adsorption and desorption processes. A typical permeability curve of a condensable vapor is strongly enhanced in the capillary condensation region. This is because additional capillary pressure gradients are imposed on the capillary-condensed pores, which act as "good" conductors compared to the noncondensed pores, which are considered "poor" conductors. The percolation scaling properties that hold for a system of "good" and "poor" conductors are confirmed for the cases examined. As the ratio of gas flow/capillary-enhanced flow decreases, the rise of permeability with pressure becomes sharper. The network connectivity has a strong impact on the maximum permeability value and on the width of the scaling law regions. The contribution of surface flow does not affect the permeability in the peak region, but results in a shrinkage of the scaling law regions. During desorption, a marked hysteresis in the permeability curves is found and it is attributed only to thermodynamic hysteresis. The maximum permeability values in this case are higher and shifted to lower relative pressures. Copyright 2000 Academic Press.     

Irreversible adsorption of tethered chains at substrates: Monte Carlo study

The irreversible adsorption of single chains grafted with one end to the surface is studied using scaling arguments and computer simulations. We introduce a two-phase model, in which the chain is described by an adsorbate portion and a corona portion formed by nonadsorbed monomers. The adsorption process can be viewed as consisting of a main stage, during which monomers join by "zipping" (along their order in the chain) the surface, and a late stage, in which the remaining corona collapses on the surface. Based on our model we derive a scaling relation for the time of adsorption t(M) as a function of the number M of adsorbed monomers; t(M) follows a power law, M(alpha), with alpha > 1. We find that alpha is related to the Flory exponent nu by alpha = 1 + nu. Using further scaling arguments we derive relations between the overall time of adsorption, the characteristic time of adsorption (given by the crossover time between the main and the last stage of adsorption), and the chain length. To support our analysis we perform Monte Carlo simulations using the bond fluctuation model. In particular, the sequence of adsorption events is very well reproduced by the simulations, and an analysis of the various density profiles supports our theoretical model. Especially the loop formation during adsorption clearly shows that the growth of the adsorbate is dominated by zipping. The simulations are also in almost quantitative agreement with our theoretical scaling analysis, showing that here the assumption of a linear relation between Monte Carlo steps and time is well obeyed. We conclude by also discussing the geometrical shape of the adsorbate.     

Thermodynamic scaling of α-relaxation time and viscosity stems from the Johari-Goldstein β-relaxation or the primitive relaxation of the coupling model

By now it is well established that the structural α-relaxation time, τ(α), of non-associated small molecular and polymeric glass-formers obey thermodynamic scaling. In other words, τ(α) is a function Φ of the product variable, ρ(γ)/T, where ρ is the density and T the temperature. The constant γ as well as the function, τ(α) = Φ(ρ(γ)/T), is material dependent. Actually this dependence of τ(α) on ρ(γ)/T originates from the dependence on the same product variable of the Johari-Goldstein β-relaxation time, τ(β), or the primitive relaxation time, τ(0), of the coupling model. To support this assertion, we give evidences from various sources itemized as follows. (1) The invariance of the relation between τ(α) and τ(β) or τ(0) to widely different combinations of pressure and temperature. (2) Experimental dielectric and viscosity data of glass-forming van der Waals liquids and polymer. (3) Molecular dynamics simulations of binary Lennard-Jones (LJ) models, the Lewis-Wahnstr?m model of ortho-terphenyl, 1,4 polybutadiene, a room temperature ionic liquid, 1-ethyl-3-methylimidazolium nitrate, and a molten salt 2Ca(NO(3))(2)·3KNO(3) (CKN). (4) Both diffusivity and structural relaxation time, as well as the breakdown of Stokes-Einstein relation in CKN obey thermodynamic scaling by ρ(γ)/T with the same γ. (5) In polymers, the chain normal mode relaxation time, τ(N), is another function of ρ(γ)/T with the same γ as segmental relaxation time τ(α). (6) While the data of τ(α) from simulations for the full LJ binary mixture obey very well the thermodynamic scaling, it is strongly violated when the LJ interaction potential is truncated beyond typical inter-particle distance, although in both cases the repulsive pair potentials coincide for some distances.     

Density scaling of the transport properties of molecular and ionic liquids

Casalini and Roland [Phys. Rev. E 69, 062501 (2004); J. Non-Cryst. Solids 353, 3936 (2007)] and other authors have found that both the dielectric relaxation times and the viscosity, η, of liquids can be expressed solely as functions of the group (TV?(γ)), where T is the temperature, V is the molar volume, and γ a state-independent scaling exponent. Here we report scaling exponents γ, for the viscosities of 46 compounds, including 11 ionic liquids. A generalization of this thermodynamic scaling to other transport properties, namely, the self-diffusion coefficients for ionic and molecular liquids and the electrical conductivity for ionic liquids is examined. Scaling exponents, γ, for the electrical conductivities of six ionic liquids for which viscosity data are available, are found to be quite close to those obtained from viscosities. Using the scaling exponents obtained from viscosities it was possible to correlate molar conductivity over broad ranges of temperature and pressure. However, application of the same procedures to the self-diffusion coefficients, D, of six ionic and 13 molecular liquids leads to superpositioning of poorer quality, as the scaling yields different exponents from those obtained with viscosities and, in the case of the ionic liquids, slightly different values for the anion and the cation. This situation can be improved by using the ratio (D∕T), consistent with the Stokes-Einstein relation, yielding γ values closer to those of viscosity.     

Electronic processes induced by high energy H+, H 2 + and H 3 + -ions: A scaling relation

A scaling relation is proposed which interrelates measurable quantities in the field of atomic collision physics performed with high velocity H⁺, H ₂ ⁺ and H ₃ ⁺ -ions. The relation may be written as $$Q(H^ + ) - 2*Q(H_2^ + ) + Q(H_3^ + ) = 0,$$ whereQ denotes an excitation or ionization cross section or a total or differential secondary particle yield evaluated at the same projectile velocity. The scaling relation will be tested by comparison with experimental data of yields and spectra from ion-induced secondary electron emission measurements and with cross section data for excitation and ionization of atoms and molecules. In general very good agreement is observed for high projectile velocities (v>2 a.u.).     

Relationship between viscosity coefficients and volumetric properties using a scaling concept for molecular and ionic liquids

In this work, a scaling concept based on relaxation theories of the liquid state was combined with a relation previously proposed by the authors to provide a general framework describing the dependency of viscosity on pressure and temperature. Namely, the viscosity-pressure coefficient (partial differentialeta/partial differentialp)T was expressed in terms of a state-independent scaling exponent, gamma. This scaling factor was determined empirically from viscosity versus Tvgamma curves. New equations for the pressure- and temperature-viscosity coefficients were derived, which are of considerable technological interest when searching for appropriate lubricants for elastohydrodynamic lubrication. These relations can be applied over a broad range of thermodynamic conditions. The fluids considered in the present study are linear alkanes, pentaerythritol ester lubricants, polar liquids, associated fluids, and several ionic liquids, compounds selected to represent molecules of different sizes and with diverse intermolecular interactions. The values of the gamma exponent determined for the fluids analyzed in this work range from 1.45 for ethanol to 13 for n-hexane. In general, the pressure-viscosity derivative is well-reproduced with the values obtained for the scaling coefficient. Furthermore, the effects of volume and temperature on viscosity can be quantified from the ratio of the isochoric activation energy to the isobaric activation energy, Ev/Ep. The values of gamma and of the ratio Ev/Ep allow a classification of the compounds according to the effects of density and temperature on the behavior of the viscosity.     

热力学数据对1, 3-丁二烯燃烧特性的影响

基于G4方法, 计算了1,^{3-丁二烯框架燃烧反应机理中102个物种的热力学数据, 并考察了振动非谐性、 频率校正因子以及受阻内转动对结果的影响. 结果表明, 考虑振动非谐性或采用不同的频率校正因子, 对热力学数据的影响不大; 考虑内转动后, 对热力学数据有较大影响. 而且考虑内转动后, 得到的热力学数据与实验热力学数据吻合得更好. 用所得热力学数据模拟了1,3-丁二烯的绝热燃烧温度以及点火延迟时间, 结果显示, 要得到可靠的绝热火焰温度, 对小分子(如CO和CO₂等)的热力学数据需要采用实验结果. 将用所得热力学数据模拟得到的点火延迟时间, 与机理本身的热力学数据所得点火延迟时间进行对比, 二者差别显著, 表明所得热力学数据主要通过改变一些反应的逆反应速率常数来影响点火延迟时间. 进一步确定了用所得热力学数据对点火延迟时间有显著影响的一些物种.}     

Scaling of excitons in graphene nanoribbons with armchair shaped edges

The scaling behavior of band gaps and fundamental quantities of exciton, i.e., reduced mass, size, and binding strength, in three families of quasi one-dimensional graphene nanoribbons with hydrogen passivated armchair shaped edge (AGNRs) are comprehensively investigated by density functional theory with quasi-particle corrections and many body, i.e., electron-hole, interactions. Compared with single-walled carbon nanotubes (SWCNTs) where the scaling character features a single exponent, each family of AGNRs has its own single exponent, due to its intrinsic zero curvature, which also accounts for the absent "family spreading" of optical transition energies in the smaller width region in the Kataura plots of AGNRs as compared to those of SWCNTs. Moreover, the scaling relation between exciton binding strength and the geometric parameter is established.     

方阱链状分子临界性质的Monte Carlo模拟

在巨正则系综下对阱宽为λ=1.5,链长分别为4、8、16的方阱链状流体实施Monte Carlo模拟,采用建立在完整标度基础上的无偏的Q-参数方法,通过histogram reweighting技术以及有限尺寸标度理论得到了热力学极限下该系列流体的临界温度和临界密度.模拟结果表明,方阱链流体的临界温度随着链长的增加而升高.并且不同链长方阱流体的临界温度均低于已报道的结果.由于本文所采用的完整标度的无偏性,我们估计的临界点更加准确.并且流体的临界温度与链长之间的关系与Flory-Huggins理论相一致.我们还预测了无限链长方阱流体的临界温度,比已有结果略高.     

Relationships between self-diffusivity, packing fraction, and excess entropy in simple bulk and confined fluids

Static measures such as density and entropy, which are intimately connected to structure, have featured prominently in modern thinking about the dynamics of the liquid state. Here, we explore the connections between self-diffusivity, density, and excess entropy for two of the most widely used model "simple" liquids, the equilibrium Lennard-Jones and square-well fluids, in both bulk and confined environments. We find that the self-diffusivity data of the Lennard-Jones fluid can be approximately collapsed onto a single curve (i) versus effective packing fraction and (ii) in appropriately reduced form versus excess entropy, as suggested by two well-known scaling laws. Similar data collapse does not occur for the square-well fluid, a fact that can be understood on the basis of the nontrivial effects that temperature has on its static structure. Nonetheless, we show that the implications of confinement for the self-diffusivity of both of these model fluids, over a broad range of equilibrium conditions, can be predicted on the basis of knowledge of the bulk fluid behavior and either the effective packing fraction or the excess entropy of the confined fluid. Excess entropy is perhaps the most preferable route due to its superior predictive ability and because it is a standard, unambiguous thermodynamic quantity that can be readily predicted via classical density functional theories of inhomogeneous fluids.     

Zeta potential measurement of calcium carbonate

The problem of scaling, which one finds in industrial heat exchangers, particularly in atmospheric coolers in nuclear power stations, depends on calcium carbonate deposits from fresh water. To better understand this phenomenon, we have examined the eventual implication of superficial electric charge of precipitated crystal nuclei. After a bibliographical review showing a fundamental divergence from already published results, this paper describes an experimental plant to measure the zeta potential in controlled conditions of thermodynamic equilibrium, oversaturation, or undersaturation of a CaCO(3)-H(2)O-CO(2) system taking into account simultaneously the three phases: gas, liquid, and solid. The zeta potential is measured by a crystalline-plug method with calcite or aragonite crystals. The potential cancels at thermodynamic equilibrium and is always negative for other conditions, in particular for oversaturation where the possibility of scaling exists. The analysis of these results suggests that the potential determining ions of the system are Ca(2+) and HCO(-)(3).     

Thermodynamic length in a two-dimensional thermodynamic state space

The main goal of this paper is to reach an explicit formulation and possible interpretation of thermodynamic length in a thermodynamic state space with two degrees of freedom. Using the energy and entropy metric in a general form, we get explicit results about thermodynamic length along isotherms, its relation with work and with speed of sound. We also look at the relation between the determinants of the energy and entropy metrics and find that they differ by a factor of T4.