The effect of concentration,temperature, and molecular weight on the dynamics of rigid-rod molecules in semi-dilute solutions

The dynamics of rigid-rod-like molecules are studied using rheo-optical techniques. Measurements of flow birefringence as a function of shear rate are utilized to understand the scaling behavior of rotational diffusivity with respect to concentration and temperature. The concentration scaling exponent increases with increasing concentration and the scaling laws are valid in narrow concentration windows. The Doi-Edwards (DE) scaling law D_r ∼ c⁻², holds at very high concentrations (cL³ > 150). The concentration scaling exponent decreases dramatically with increasing temperature at concentrations, cL²d > 1. Scaling of rotational diffusivity, with respect to temperature and solvent viscosity in the semidilute regime, does not follow the predictions of DE theory (and related caging ideas). On the contrary, a model proposed by Fixman was found to explain both the temperature and concentration dependence of the rotational diffusivity. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 181–190, 1998     

Measuring diffusivity in supercooled liquid nanoscale films using inert gas permeation. I. Kinetic model and scaling methods

We describe in detail a diffusion model used to simulate inert gas transport through supercooled liquid overlayers. In recent work, the transport of the inert gas has been shown to be an effective probe of the diffusivity of supercooled liquid methanol in the experimentally challenging regime near the glass transition temperature. The model simulations accurately and quantitatively describe the inert gas permeation desorption spectra. The simulation results are used to validate universal scaling relationships between the diffusivity, overlayer thickness, and the temperature ramp rate for isothermal and temperature programmed desorption. From these scaling relationships we derive simple equations from which the diffusivity can be obtained using the peak desorption time or temperature for an isothermal or set of TPD experiments, respectively, without numerical simulation. The results presented here demonstrate that the permeation of gases through amorphous overlayers has the potential to be a powerful technique to obtain diffusivity data in deeply supercooled liquids.     

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.     

Structural correlations and cooperative dynamics in supercooled liquids

The relationships between diffusivity and the excess, pair and residual multiparticle contributions to the entropy are examined for Lennard-Jones liquids and binary glassformers, in the context of approximate inverse power law mappings of simple liquids. In the dense liquid where diffusivities are controlled by collisions and cage relaxations, Rosenfeld-type excess entropy scaling of diffusivities is found to hold for both crystallizing as well as vitrifying liquids. The crucial differences between the two categories of liquids emerge only when local cooperative effects in the dynamics result in significant caging effects in the time-dependent behaviour of the single-particle mean square displacement. In the case of glassformers, onset of such local cooperativity coincides with onset of deviations from Rosenfeld-type excess entropy scaling of diffusivities and increasing spatiotemporal heterogeneity. In contrast, for two- and three-dimensional liquids with a propensity to crystallise, the onset of local cooperative dynamics is sufficient to trigger crystallization provided that the liquid is sufficiently supercooled that the free energy barrier to nucleation of the solid phase is negligible. The state points corresponding to onset of transient caging effects can be associated with typical values, within reasonable bounds, of the excess, pair, and residual multiparticle entropy as a consequence of the isomorph-invariant character of the excess entropy, diffusivity and related static and dynamic correlation functions.     

A perturbed hard-sphere equation of state for liquid metals

A perturbed hard-sphere equation of state, developed previously for liquid alkali metals and liquid refractory metals, has been applied for PVT calculation of some pure liquid metals including alkaline earth metals, tin, lead, antimony, bismuth, and rubidium over a wide range of temperatures and pressures. Two temperature-dependent parameters appear in the equation of state, which are universal functions of the reduced temperature, i.e. two scale parameters are sufficient to calculate the temperature-dependent parameters. The scaling parameters can be easily obtained by employing a corresponding-states principle based on a Lennard-Jones potential energy function. Employing the present equation of state, the liquid densities of aforementioned metals at temperatures ranging from the melting point to 2000?K and at pressures ranging from vapour pressure up to 40,000?bar have been calculated and compared with experimental data. The average absolute deviation in predicted densities compared with experimental data is 1.54%.     

Dependence on chain length of NMR relaxation times in mixtures of alkanes

Many naturally occurring fluids, such as crude oils, consist of a very large number of components. It is often of interest to determine the composition of the fluids in situ. Diffusion coefficients and nuclear magnetic resonance (NMR) relaxation times can be measured in situ and depend on the size of the molecules. It has been shown [D. E. Freed et al., Phys. Rev. Lett. 94, 067602 (2005)] that the diffusion coefficient of each component in a mixture of alkanes follows a scaling law in the chain length of that molecule and in the mean chain length of the mixture, and these relations were used to determine the chain length distribution of crude oils from NMR diffusion measurements. In this paper, the behavior of NMR relaxation times in mixtures of chain molecules is addressed. The author explains why one would expect scaling laws for the transverse and longitudinal relaxation times of mixtures of short chain molecules and mixtures of alkanes, in particular. It is shown how the power law dependence on the chain length can be calculated from the scaling laws for the translational diffusion coefficients. The author fits the literature data for NMR relaxation in binary mixtures of alkanes and finds that its dependence on chain length agrees with the theory. Lastly, it is shown how the scaling laws in the chain length and the mean chain length can be used to determine the chain length distribution in crude oils that are high in saturates. A good fit is obtained between the NMR-derived chain length distributions and the ones from gas chromatography.     

Dual Relativity and Lorentz Transformations for Liquid-Like Media and Statistics from Scaling Concepts for Geometry

A dual class of Lorentz transformations (dual LT) for linear and Brownian motions in liquid-like media, is presented and discussed. It descends from two LT groups, for self-diffusion in simple liquids (BLT) and its geometrical analogy (GLT), which turned out to represent promising basic tools to deal with statistics at different length scales. Time dilation and length contraction of BLT occur upon ordering the originally indistinguishable molecular disorder in the liquid medium (i.e., a diffusivity lowering), giving rise to universality and scaling laws in polymer solutions. Dual LT exhibit a rich phenomenology, leading to a scale-dependent motion concept, where Brownian and quantum movements somewhat correspond. Density correlations in simple liquids, for instance, are suggested on this basis to behave like radial wave functions at the atomic scale. We also report some remarks on statistics in general, and its connection towards geometry.     

Do directional primary and secondary crack patterns in thin films of maghemite nanocrystals follow a universal scaling law?

Cracks due to a shrinking film restricted by adhesion to a surface are observed in nature at various length scales ranging from tiny crack segments in nanoparticle films to enormous domains observed in the earth's crust. Here, we study the formation of cracks in magnetic films made of maghemite (gamma-Fe2O3) nanocrystals. The cracks are oriented by an external magnetic field applied during the drying process which presents a new method to produce directional crack patterns. It is shown that directional and isotropic crack patterns follow the same universal scaling law with the film height varying from micrometer to centimeter scales. Former experimental studies of scaling laws were limited to small variations in height (1 order of magnitude). The large variation in height in our experiments becomes possible due to the combined use of nanocrystals and electron microscopy. A simple two-dimensional computer model for elastic fracture leads to structural and scaling behaviors, which match those observed in the experiments.     

Revision of a multiparameter equation of state to improve the representation in the critical region: application to water

We have developed a crossover formalism for the thermodynamic surface of pure fluids, which can be applied to any multiparameter equation of state. This procedure has been used to incorporate scaling law behavior into a representation of the thermodynamic properties of water and steam developed by Pruss and Wagner (PW EOS) and adopted recently by the International Association for the Properties of Water and Steam. Our revision to this equation retains most of the functional form and coefficients of the PW EOS, but replaces two of the terms with a crossover representation of scaling law behavior. In order to develop this model, we first developed a new crossover formulation for steam in the critical region, and second, we have incorporated universal crossover functions into the original PW EOS. In the modified form, the PW equation of state reproduces the scaling laws down to dimensionless temperatures τ=10⁻⁷. Far from the critical point the equations practically coincide.     

Improving platinum group metal–free oxygen reduction reaction electrocatalyst activity: suggestions from density functional theory studies

In this opinion, the limitations of platinum group metal–free oxygen reduction reaction electrocatalyst activity based on scaling laws and resulting Balandin-Sabatier volcano plots are presented. Previous theoretical work aimed at overcoming this limitation is discussed. A theoretical study of a novel approach toward catalyst activity improvement, dynamic strain engineering, is proposed and tested for a possible platinum group metal–free oxygen reduction reaction active site. It is shown that not only can this approach produce thermodynamic limiting potentials well beyond scaling law relationship limits but also be capable of doing so in an energy-efficient manner.     

Polymer translocation in solid-state nanopores: dependence of scaling behavior on pore dimensions and applied voltage

We investigate unforced and forced translocation of a Rouse polymer (in the absence of hydrodynamic interactions) through a silicon nitride nanopore by three-dimensional Langevin dynamics simulations, as a function of pore dimensions and applied voltage. Our nanopore model consists of an atomistically detailed nanopore constructed using the crystal structure of β-Si(3)N(4). We also use realistic parameters in our simulation models rather than traditional dimensionless quantities. When the polymer length is much larger than the pore length, we find the translocation time versus chain length scales as τ ～ N(2+ν) for the unforced case and as τ ～ N((1+2ν)/(1+ν)) for the forced case. Our results agree with theoretical predictions which indicate that memory effects and tension on the polymer chain play an important role during the translocation process. We also find that the scaling exponents are highly dependent on the applied voltage (force). When the length of the polymer is on the order of the length of the pore, we do not find a continuous scaling law, but rather scaling exponents that increase as the length of the polymer increases. Finally, we investigate the scaling behavior of translocation time versus applied voltage for different polymer and pore lengths. For long pores, we obtain the theoretical scaling law of τ ～ 1/V(α), where α ? 1 for all voltages and polymer lengths. For short pores, we find that α decreases for very large voltages and/or small polymer lengths, indicating that the value of α = 1 is not universal. The results of our simulations are discussed in the context of experimental measurements made under different conditions and with differing pore geometries.     

Long-range correlations, geometrical structure, and transport properties of macromolecular solutions. The equivalence of configurational statistics and geometrodynamics of large molecules

A special theory of Brownian relativity was previously proposed to describe the universal picture arising in ideal polymer solutions. In brief, it redefines a Gaussian macromolecule in a 4-dimensional diffusive spacetime, establishing a (weak) Lorentz-Poincaré invariance between liquid and polymer Einstein's laws for Brownian movement. Here, aimed at inquiring into the effect of correlations, we deepen the extension of the special theory to a general formulation. The previous statistical equivalence, for dynamic trajectories of liquid molecules and static configurations of macromolecules, and rather obvious in uncorrelated systems, is enlarged by a more general principle of equivalence, for configurational statistics and geometrodynamics. Accordingly, the three geodesic motion, continuity, and field equations could be rewritten, and a number of scaling behaviors were recovered in a spacetime endowed with general static isotropic metric (i.e., for equilibrium polymer solutions). We also dealt with universality in the volume fraction and, unexpectedly, found that a hyperscaling relation of the form, (average size) x (diffusivity) x (viscosity)1/2 ~f(N0, phi0) is fulfilled in several regimes, both in the chain monomer number (N) and polymer volume fraction (phi). Entangled macromolecular dynamics was treated as a geodesic light deflection, entaglements acting in close analogy to the field generated by a spherically symmetric mass source, where length fluctuations of the chain primitive path behave as azimuth fluctuations of its shape. Finally, the general transformation rule for translational and diffusive frames gives a coordinate gauge invariance, suggesting a widened Lorentz-Poincaré symmetry for Brownian statistics. We expect this approach to find effective applications to solutions of arbitrarily large molecules displaying a variety of structures, where the effect of geometry is more explicit and significant in itself (e.g., surfactants, lipids, proteins).     

基于分形动力学过程的腐蚀预测模型

腐蚀是一种复杂随机现象,可以用分形理论更好地描述。本文根据分形动力学过程,以一组基于不同表面条件下的腐蚀发生概率为参数,建立计算机模型来预测大气、土壤环境的金属腐蚀过程。计算结果和实际腐蚀特征吻合一致。此外,本文还讨论了幂函数腐蚀模型中指数n和各种腐蚀概率之间的定量关系,揭示了腐蚀发展规律。     

Competitive spreading versus imbibition of polymer liquid drops in nanoporous membranes: scaling behavior with viscosity

The way a liquid drop that is in contact with a nanoporous substrate evolves essentially depends on the competition between imbibition and spreading. Although the scaling behavior of this competitive process with liquid viscosity is important for various applications requiring the filling of nanoporous substrates (template-assisted fabrication, storage, and controlled release of liquids), they appear to be poorly investigated and insufficiently understood. We developed a model study to investigate the wetting and spontaneous imbibition of silicon oil drops of viscosities ranging from 1 to 100 Pa s on nanoporous alumina membranes (pore size of 200 nm). Our results show that the drop radius essentially follows the power law t1/10 time dependence as expected by Tanner's law. However, the scaling of the spreading velocity with the viscosity (approximately eta-n) was found to display an exponent that is comparable on both the reference (impermeable) and nanoporous substrates (n = 0.55) but notably higher than theoretically expected (0.1). More surprisingly, we show that despite the confinement, the rate of imbibition into the nanopores displays a weaker dependence on the viscosity, as compared to the spreading velocity on both the reference and nanoporous substrates. On the basis of Darcy's law for capillary-driven imbibition, this result was discussed in the context of the scaling behavior of the contact angle with the viscosity.     

Diffusivity, excess entropy, and the potential-energy landscape of monatomic liquids

The connection between thermodynamic, transport, and potential-energy landscape features is studied for liquids with Lennard-Jones-type pair interactions using both microcanonical molecular-dynamics and isothermal-isobaric ensemble Monte Carlo simulations. Instantaneous normal-mode and saddle-point analyses of two variants of the monatomic Lennard-Jones liquid have been performed. The diffusivity is shown to depend linearly on several key properties of instantaneous and saddle configurations-the energy, the fraction of negative curvature directions, and the mean, maximum, and minimum eigenvalues of the Hessian. Since the Dzugutov scaling relationship also holds for such systems [Nature (London) 381, 137 (1996)], the exponential of the excess entropy, within the two-particle approximation, displays the same linear dependence on energy landscape properties as the diffusivity.     

Correlations among residual multiparticle entropy, local atomic-level pressure, free volume and the phase-ordering rule in several liquids

A modified Wang-Landau density-of-states sampling approach has been performed to calculate the excess entropy of liquid metals, Lennard-Jones (LJ) system and liquid Si under NVT conditions; and it is then the residual multiparticle entropy (S(RMPE)) is obtained by subtraction of the pair correlation entropy. The temperature dependence of S(RMPE) has been investigated along with the temperature dependence of the local atomic-level pressure and the pair correlation functions. Our results suggest that the temperature dependence of the pair correlation entropy is well described by T(-1) scaling while T(-0.4) scaling well describes the relationship between the excess entropy and temperature. For liquid metals and LJ system, the -S(RMPE) versus temperature curves show positive correlations and the -S(RMPE) of liquid Si is shown to have a negative correlation with temperature, the phase-ordering criterion (based on the S(RMPE)) for predicting freezing transition works in liquid metals and LJ but fails in liquid Si. The local atomic-level pressure scaled with the virial pressure (σ(al)/σ(av)) exhibits the much similar temperature dependence as -S(RMPE) for all studied systems, even though simple liquid metals and liquid Si exhibit opposite temperature dependence in both σ(al)/σ(av) and -S(RMPE). The further analysis shows that the competing properties of the two effects due to localization and free volume on the S(RMPE) exist in simple liquid metals and LJ system but disappear in liquid Si, which may be the critical reason of the failure of the phase-ordering criterion in liquid Si.     

A Monte Carlo algorithm to study polymer translocation through nanopores. I. Theory and numerical approach

The process during which a polymer translocates through a nanopore depends on many physical parameters and fundamental mechanisms. We propose a new one-dimensional lattice Monte Carlo algorithm that integrates various effects such as the entropic forces acting on the subchains that are outside the channel, the external forces that are pulling the polymer through the pore, and the frictional effects that involve the chain and its environment. Our novel approach allows us to study the polymer as a single Brownian particle diffusing while subjected to a position-dependent force that includes both the external driving forces and the internal entropic bias. Frictional effects outside and inside the pore are also considered. This Monte Carlo method is much more efficient than other simulation methods, and it can be used to obtain scaling laws for various polymer translocation regimes. In this first part, we derive the model and describe a subtle numerical approach that gives exact results for both the escape probability and the mean translocation time (and higher moments of its distribution). The scaling laws obtained from this model will be presented and discussed in the second part of this series.     

Liquid Phase Behavior in Systems of 1-Butyl-3-alkylimidazolium bis{(trifluoromethyl)sulfonyl}imide Ionic Liquids with Water: Influence of the Structure of the C5 Alkyl Substituent

In the present paper a study of the liquid phase behavior in aqueous systems of imidazolium-based ionic liquids (ILs) with the bis{(trifluoromethyl)sulfonyl}imide anion is addressed. To highlight the influence of the C5 alkyl side group structure on their properties, a series of ILs with linear, branched, and cyclic substituents was studied. As was already shown in our previous work, very subtle changes in the cation structure at the molecular scale can have a significant and unexpected impact on the bulk properties. Therefore, in this work, the mutual solubilities of 1-butyl-3-alkylimidazolium bis{(trifluoromethyl)sulfonyl}imide ionic liquids and water were studied, both experimentally and by modeling, at atmospheric pressure as a function of temperature from 293.15 to 328.15 K. The solubilities of the ionic liquids in water are very low, typically around 10^?5 mole fraction units and were measured by a direct analytical method, making use of UV–Vis spectrophotometry. The solubilities of water in the ionic liquids were found to be around 0.20 mole fraction units and were measured using the cloud-point method. In addition to the experimental data, the liquid–liquid equilibria in the systems were modeled using the COSMO-RS methodology. Phase diagrams and the critical solution points were also estimated by applying the universal scaling laws based on the 3D Ising model, taking into account the non-linearity of the diameter and crossover to mean-field behavior.