Fragility of glass-forming polymer liquids

The fragility of polymeric glass-forming liquids is calculated as a function of molecular structural parameters from a generalized entropy theory of polymer glass-formation that combines the Adam-Gibbs (AG) model for the rate of structural relaxation with the lattice cluster theory (LCT) for polymer melt thermodynamics. Our generalized entropy theory predicts the existence of distinct high and low temperature regimes of glass-formation that are separated by a thermodynamically well-defined crossover temperature T(I) at which the product of the configurational entropy and the temperature has an inflection point. Since the predicted temperature dependence of the configurational entropy and structural relaxation time are quite different in these temperature regimes, we introduce separate definitions of fragility for each regime. Experimentally established trends in the fragility of polymer melts with respect to variations in polymer microstructure and pressure are interpreted within our theory in terms of the accompanying changes in the chain packing efficiency.     

The mesoscopic dynamics of thermodynamic systems

Concepts of everyday use such as energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and the general rules that the macroscopic properties of systems at equilibrium follow. Outside equilibrium and away from macroscopic regimes, most of those rules cannot be applied directly. Here we present recent developments that extend the applicability of thermodynamic concepts deep into mesoscopic and irreversible regimes. We show how the probabilistic interpretation of thermodynamics together with probability conservation laws can be used to obtain Fokker-Planck equations for the relevant degrees of freedom. This approach provides a systematic method to obtain the stochastic dynamics of a system directly from its equilibrium properties. A wide variety of situations can be studied in this way, including many that were thought to be out of reach of thermodynamic theories, such as nonlinear transport in the presence of potential barriers, activated processes, slow relaxation phenomena, and basic processes in biomolecules, such as translocation and stretching.     

Thermodynamics for single-molecule stretching experiments

We show how to construct nonequilibrium thermodynamics for systems too small to be considered thermodynamically in a traditional sense. Through the use of a nonequilibrium ensemble of many replicas of the system which can be viewed as a large thermodynamic system, we discuss the validity of nonequilibrium thermodynamics relations and analyze the nature of dissipation in small systems through the entropy production rate. We show in particular that the Gibbs equation, when formulated in terms of average values of the extensive quantities, is still valid, whereas the Gibbs-Duhem equation differs from the equation obtained for large systems due to the lack of the thermodynamic limit. Single-molecule stretching experiments are interpreted under the prism of this theory. The potentials of mean force and mean position, now introduced in these experiments in substitution of the thermodynamic potentials, correspond respectively to our Helmholtz and Gibbs energies. These results show that a thermodynamic formalism can indeed be applied at the single-molecule level.     

Gaussian excitations model for glass-former dynamics and thermodynamics

We describe a model for the thermodynamics and dynamics of glass-forming liquids in terms of excitations from an ideal glass state to a Gaussian manifold of configurationally excited states. The quantitative fit of this three parameter model to the experimental data on excess entropy and heat capacity shows that "fragile" behavior, indicated by a sharply rising excess heat capacity as the glass transition is approached from above, occurs in anticipation of a first-order transition--usually hidden below the glass transition--to a "strong" liquid state of low excess entropy. The distinction between fragile and strong behavior of glass formers is traced back to an order of magnitude difference in the Gaussian width of their excitation energies. Simple relations connect the excess heat capacity to the Gaussian width parameter, and the liquid-liquid transition temperature, and strong, testable, predictions concerning the distinct properties of energy landscape for fragile liquids are made. The dynamic model relates relaxation to a hierarchical sequence of excitation events each involving the probability of accumulating sufficient kinetic energy on a separate excitable unit. Super-Arrhenius behavior of the relaxation rates, and the known correlation of kinetic with thermodynamic fragility, both follow from the way the rugged landscape induces fluctuations in the partitioning of energy between vibrational and configurational manifolds. A relation is derived in which the configurational heat capacity, rather than the configurational entropy of the Adam-Gibbs equation, controls the temperature dependence of the relaxation times, and this gives a comparable account of the experimental observations without postulating a divergent length scale. The familiar coincidence of zero mobility and Kauzmann temperatures is obtained as an approximate extrapolation of the theoretical equations. The comparison of the fits to excess thermodynamic properties of laboratory glass formers, and to configurational thermodynamics from simulations, reveals that the major portion of the excitation entropy responsible for fragile behavior resides in the low-frequency vibrational density of states. The thermodynamic transition predicted for fragile liquids emerges from beneath the glass transition in case of laboratory water and the unusual heat capacity behavior observed for this much studied liquid can be closely reproduced by the model.     

不同粒度八面体纳米钼酸镉的表面热力学性质

室温条件下,采用反相微乳液法制备了一系列不同粒度的八面体纳米CdMoO4,并对其组成、结构及形貌进行了表征.基于纳米CdMoO4与块体CdMoO4热力学性质的本质差异,结合化学热力学基本理论与热动力学原理,导出了获取纳米CdMoO4表面热力学性质的关系式;在此基础上,利用原位微量热技术成功获得了所制备的不同粒度八面体纳米CdMoO4的表面热力学函数,如比表面Gibbs自由能、比表面焓和比表面熵.本文为获取纳米材料表面热力学函数提供了一种有效而普适的新方法.     

Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems

A common assumption in the glass science community is that the entropy of a glass can be calculated by integration of measured heat capacity curves through the glass transition. Such integration assumes that glass is an equilibrium material and that the glass transition is a reversible process. However, as a nonequilibrium and nonergodic material, the equations from equilibrium thermodynamics are not directly applicable to the glassy state. Here we investigate the connection between heat capacity and configurational entropy in broken ergodic systems such as glass. We show that it is not possible, in general, to calculate the entropy of a glass from heat capacity curves alone, since additional information must be known related to the details of microscopic fluctuations. Our analysis demonstrates that a time-average formalism is essential to account correctly for the experimentally observed dependence of thermodynamic properties on observation time, e.g., in specific heat spectroscopy. This result serves as experimental and theoretical proof for the nonexistence of residual glass entropy at absolute zero temperature. Example measurements are shown for Corning code 7059 glass.     

Statistical-mechanical theory of rheology: Lennard-Jones fluids

The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a suitable flow configuration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones fluid. For that purpose we have used the density-fluctuation theory for the Newtonian viscosity, the modified free volume theory for the self-diffusion coefficient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modified free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we first have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate (gamma*) times reduced relaxation time (taue*) that is independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against taue*gamma* they are found clustered around the reduced (universal) non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones fluid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function.     

Global thermodynamics of hydrophobic cavitation, dewetting, and hydration

Pure water experimental and simulation results are combined to predict the thermodynamics of cavity formation, spanning atomic to macroscopic length scales, over the entire ambient liquid temperature range. The resulting cavity equation of state is used to quantify dewetting excess contributions to cavity formation thermodynamics and construct a thermodynamic perturbation theory of hydrophobic hydration. Predictions are compared with large cavity simulations and experimental rare-gas hydration thermodynamics data (for He, Ne, Ar, Kr, Xe, and Rn). Key findings include the strong temperature dependence of the critical length scale for hydrophobic dewetting and the evaluation of fundamental solute-solvent interaction contributions to rare-gas hydration chemical potentials.     

Ag3PO4微晶表面热力学函数的温度及形貌效应

在室温下采用离子交换法制备了四足状、 立方体状和十二面体状Ag₃PO₄微晶及Ag₃PO₄块体, 并进行了表征. 以Ag₃PO₄微/纳米和块体材料热力学性质的区别为基础, 结合化学热力学理论和热动力学基本原理, 导出摩尔表面热力学关系式. 在此基础上, 采用原位微量热技术获取Ag₃PO₄的化学反应动力学信息和表面热力学函数, 讨论了形貌和温度对表面热力学性质变化的影响. 结果表明, 四足状Ag₃PO₄的摩尔表面焓(\begin{array}{c}{H}_m^s\end{array})、 摩尔表面Gibbs自由能(\begin{array}{c}{G}_m^s\end{array})和摩尔表面熵(\begin{array}{c}{S}_m^s\end{array})最大, 立方体状次之, 十二面体状最小; \begin{array}{c}{H}_m^s\end{array}和\begin{array}{c}{S}_m^s\end{array}随温度的升高而增大, \begin{array}{c}{G}_m^s\end{array}则随温度的升高而减小.     

Time evolution of the pulsed HF chemical laser system. II. Irreversible thermodynamic analysis

The time rates of change of level populations and radiation densities derived from a detailed kinetic model of the F + H₂ → HF + H laser are employed as input data for a time dependent thermodynamic analysis of this system. The laser is regarded as an irreversible heat engine generating thermodynamic work in the form of laser light. The development in time of the thermodynamic functions, efficiency and irreversible entropy production is determined by computing the contributions of pumping, radiation and relaxation to the entropy and energy of the lasing molecules. Effects of specific rate processes are evaluated by considering different kinetic schemes, i.e. different combinations of kinetic processes and initial conditions. It is shown, among others, that a laser without relaxation processes (“frictionless”) has poor efficiency despite the absence of energy losses and the low irreversible entropy production. On the other hand, the efficiency is high in lasers governed by fast rotational relaxation. This is because rotational relaxation, though leading to some energy losses and irreversible entropy production, compensates for the entropy decrease of the system (while lasing under partially inverted populations) by increasing the bath entropy. The major general conclusion of the analysis is that the thermodynamic constraints related to the kinetic scheme and not the extent of irreversibility of the lasing process is the crucial factor in determining the laser efficiency.     

局域平衡假设和反应-扩散过程

局域平衡假设作为不可逆过程热力学理论的基础通常被认为适用于一般条件下的物理化学过程。本文从玻耳兹曼方程和涨落的随机理论出发重新研究了局域平衡假设对反应—扩散过程的适用性。表明对于涉及非线性化学动力学的反应—扩散过程, 从随机理论得到的结果和局域平衡假设是不一致的。     

Hydrodynamic correlation functions for molten salts

Abstract

The linearized hydrodynamic equations for a binary ionic fluid, with specific reference to a dissociated molten salt, are used to evaluate correlation functions of local fluctuation variables and the corresponding response functions. Previous results for the instantaneous correlation functions are extended and connected with thermodynamic fluctuation theory. Different dynamical behaviours, depending on the relative magnitude of the relaxation frequency for charge fluctuations and the sound wave frequency, are demonstrated. When 4πσ/? > ck, charge fluctuations are uncoupled from mass fluctuations, the latter being isomorphous to those of a one-component neutral fluid. Kubo relations for the transport coefficients are derived in this regime. When 4πσ/? < ck, the behaviour of the ionic fluid becomes isomorphous to that of a neutral mixture, with electrical conduction playing a role analogous to interdiffusion and contributing, in particular, to the damping of sound waves. An interpolation formula between these two limiting behaviours of the relaxation frequencies is also derived. The consequences of these results for the light scattering spectrum of an ionic fluid are briefly discussed     

Molecular theory of irreversibility

A generalization of the Gibbs entropy postulate is proposed based on the Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy of equations as the nonequilibrium entropy for a system of N interacting particles. This entropy satisfies the basic principles of thermodynamics in the sense that it reaches its maximum at equilibrium and is coherent with the second law. By using a generalization of the Liouville equation describing the evolution of the distribution vector, it is demonstrated that the entropy production is a non-negative quantity. Moreover, following the procedure of nonequilibrium thermodynamics a transport matrix is introduced and a microscopic expression for this is derived. This framework allows one to perform the thermodynamic analysis of nonequilibrium steady states with smooth phase-space distribution functions which, as proven here, constitute the states of minimum entropy production when one considers small departures from stationarity.