Size- and shape-dependent phase transformations in wurtzite ZnS nanostructures

This paper describes the equilibrium morphologies of zinc sulfide nanoparticles in the wurtzite phase as a function of size, determined using ab initio Density Functional Theory (DFT) simulations and a shape-dependent thermodynamic model predicting the Gibbs free energy of a nanoparticle. We investigate the relative stabilities of a variety of nanoparticle shapes based on the wurtzite structure and show how the aspect ratio of wurtzite nanorods moderates the size-dependent phase transformation to the zinc blende phase. We find that while wurtzite nanoparticles are thermodynamically unstable with respect to the low energy rhombic dodecahedron morphology in the zinc blende phase at all sizes, shape- and size-dependent phase transformations occur when other zinc blende morphologies are present. Despite popular synthesis of zinc sulphide nanoparticles in the wurtzite phase, an in-depth thermodynamic study relating to the relative stability of wurtzite shapes and comparison with the zinc blende phase does not exist. Therefore this is the first thermodynamic study describing how shape can determine the solid phase of zinc sulfide nanostructures, which will be of critical importance to experimental applications of nanostructured zinc sulfide, where phase and shape determines properties.     

Universal relation for size dependent thermodynamic properties of metallic nanoparticles

The previous model on surface free energy has been extended to calculate size dependent thermodynamic properties (i.e., melting temperature, melting enthalpy, melting entropy, evaporation temperature, Curie temperature, Debye temperature and specific heat capacity) of nanoparticles. According to the quantitative calculation of size effects on the calculated thermodynamic properties, it is found that most thermodynamic properties of nanoparticles vary linearly with 1/D as a first approximation. In other words, the size dependent thermodynamic properties P(n) have the form of P(n) = P(b)(1 -K/D), in which P(b) is the corresponding bulk value and K is the material constant. This may be regarded as a scaling law for most of the size dependent thermodynamic properties for different materials. The present predictions are consistent literature values.     

Size-dependent growth of polymorphs in nanopores and Ostwald's step rule of stages

More than 100 years after Ostwald postulated his step rule of stages, predictive understanding as to early crystallization stages of polymorphic materials is still premature. We studied crystallization of the polymorphic pharmaceutical acetaminophen in nanoporous glasses as a model for early stages of bulk crystallization since the surface energy significantly contributes to the total Gibbs free energy of nanosized crystals in both cases. Systematic studies of transitions between different polymorphs inside nanoporous glasses show that the thermodynamic stability of the polymorphs depends on the crystal size. Accordingly, the transient occurrence of different polymorphs during crystal growth in bulk systems can be related to surface energy contributions to the total Gibbs free energy of the developing crystals. In nanosized early-stage crystals with high surface-to-volume ratios other polymorphs may be stable than in large crystals with low surface-to-volume ratios. Improved control of the crystallization of polymorphic materials by imposing well-defined confinement is a promising strategy to tailor release of polymorphic drugs and to optimize optical, electronic, magnetic and ferroelectric properties of polymorphic materials.     

Size effect on thermodynamic properties of CaMoO4 micro/nano materials and reaction systems

CaMoO₄ micro/nano hollow spheres with three different sizes were prepared via a reverse-microemulsion route at room temperature. Through designing a novel thermochemical cycle, the relationship between thermodynamic properties of nano CaMoO₄ and bulk CaMoO₄ was built. Combined with in situ microcalorimetry, change regularities for the thermodynamic properties of the prepared CaMoO₄ micro/nano materials and reaction systems were obtained. The results reveal that size effect has significant influence on thermodynamic properties of micro/nano materials and reaction systems. Along with the size decreasing, the standard molar enthalpy, standard molar Gibbs free energy and standard molar entropy of reaction of micro/nano reaction systems decreased, but the standard molar enthalpy of formation, standard molar Gibbs free energy of formation and standard molar entropy of micro/nano materials increased.     

醋酸离子液体[C2mim][OAc]水溶液的摩尔表面Gibbs自由能

在288.15-318.15 K温度范围内测定了不同浓度离子液体1-乙基-3-甲基咪唑醋酸盐([C₂mim][OAc])水溶液的表面张力和密度;在改进李以圭等人的溶液表面张力模型基础上,提出摩尔表面Gibbs自由能新概念,建立了摩尔表面Gibbs自由能随溶液浓度变化的线性经验方程,利用这个经验方程估算了[C₂mim][OAc]水溶液的摩尔表面Gibbs自由能,并进一步预测了该溶液的表面张力,其预测值与相应的表面张力实验值高度相关并非常相似。由此可见,摩尔表面Gibbs自由能与等张比容极其类似,可能成为预测离子液体及其溶液性质的一种新的半经验方法。在指定溶液浓度下,根据溶液的摩尔表面Gibbs自由能随温度呈线性变化的规律,得到了新的Eötvös方程,与传统的Eötvös方程相比,新Eötvös方程的每一个参数都有明确的物理意义:斜率的负值是摩尔表面熵,截距是摩尔表面焓,在指定浓度的溶液中摩尔表面焓几乎不随温度变化。     

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.     

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.     

Substrate effect on the melting temperature of gold nanoparticles

Previous experimental, molecular dynamics, and thermodynamic researches on the melting temperature of Au nanoparticles on tungsten substrate provide entirely different results. To account for the substrate effect upon the melting point of nanoparticles, three different substrates were tested by using a thermodynamic model: tungsten, amorphous carbon, and graphite. The results reveal that the melting point suppression of a substrate-supported Au nanoparticle is principally ruled by the free surface-to-volume ratio of the particle or the contact angle between the particle and the substrate. When the contact angle θ is less than 90°, a stronger size-dependent melting point depression compared with those for free nanoparticles is predicted; when the contact angle θ is greater than 90°, the melting temperature of the supported Au nanoparticles are somewhat higher than those for free nanoparticles.     

Viscosity,refractive index,and surface tension of multicomponent systems: Mathematical representation and estimation from data for binary systems

An equation previously developed for estimation of the excess thermodynamic properties of multicomponent systems from binary mixing data has been applied to other physical properties through extrathermodynamic properties such as the excess Gibbs free energy of activation for viscous flow, molar refractivity, and exess surface free energy. This equation provides reasonably accurate predictions for viscosity, refractive index and surface tension of ternary and quaternary systems, given the properties of the various binary combinations of the components. The equation also serves quite well as a point-of-departure for mathematical representation of experimental data, in that all of the data considered could be represented within experimental uncertainty with the aid of no more than one adjustable parameter for each multicomponent system.     

Temperature dependence of the surface free energy of a crystal-liquid interface

A dimensionless complex containing the surface free energy of a crystal-liquid interface γ, and the entropy jump, temperature, and density of a crystal phase is described using the phenomenology of thermodynamic similarity; this complex remains constant at the melting line. It is demonstrated that the complex refines the result obtained by Skripov and Faizullin in [6] and enables us to estimate the temperature dependence of γ. Our calculations show that the surface free energy of the crystal-liquid interface of normally melting compounds is a monotonically increasing function of temperature.     

Role of size-dependent effects and interfaces in physicochemical properties of consolidated nanomaterials

The major distinctive features of size-dependent effects in nanomaterials were specified. The surface energy, melting temperature, phase equilibria, phonon spectrum, electronic structure, and conductivity type were analyzed in relation to the crystallite size for consolidated nanomaterials based on metals, alloys, intermetallics, carbides, borides, nitrides, oxides, and semiconductors. The interface effects in physicochemical properties of nanomaterials were highlighted. Special attention was given to little studied issues.     

尺寸效应对氧化锌微/纳体系热力学性质的影响

采用微乳液水热辅助法合成了三种不同尺寸的手榴弹状ZnO 微/纳结构. 通过设计热化学循环, 建立了纳米ZnO与块体ZnO体系热力学性质之间的关系. 并结合微量热技术对不同尺寸ZnO微/纳体系的热力学性质进行了计算. 结果表明, 尺寸效应对微/纳体系热力学性质有显著的影响: 随着反应物尺度的减小, 体系的标准摩尔反应焓、标准摩尔反应Gibbs 自由能、标准摩尔反应熵均降低, 而材料自身的标准摩尔生成焓、标准摩尔生成Gibbs 自由能、标准摩尔熵均增加.     

Size-dependent thermodynamic properties of metallic nanowires

Analytical models for size-dependent melting temperature Tm(D), melting enthalpy DeltaHm(D), and surface energy gammasv(D) of metallic nanowires have been proposed in terms of the unified nanothermodynamical model where D denotes the diameter of nanowire. As D decreases, Tm(D), DeltaHm(D), and gammasv(D) functions are found to decrease almost with the same size-dependent trend. Due to the inclusion of the effect of dimensionality, the developed model can be applied to other low-dimensional systems. It is found that the ratio of depression of these thermodynamic parameters for spherical nanoparticle, nanowire, and thin film is 3:2:1 when D is large enough (>20h with h being the atomic diameter). The validity of the model is verified by the data of experiments, molecular dynamics simulations, and other theoretical models.     

Equilibrium morphology of face-centered cubic gold nanoparticles >3 nm and the shape changes induced by temperature

Many of the unique properties of metallic nanoparticles are determined not only by their finite size but also by their shape, defined by the crystallographic orientation of the surface facets. These surfaces (and therefore the nanoparticles themselves) may differ in a number of ways, including surface atom densities, electronic structure, bonding, chemical reactivities, and thermodynamic properties. In the case of gold, it is known that the melting temperature of nanoparticles strongly depends on the crystal size and that the shape may alter considerably (and yet somewhat unpredictably) during annealing. In this work we use first principle calculations and a thermodynamic model to investigate the morphology of gold nanoparticles in the range 3-100 nm. The results predict that the equilibrium shape of gold nanoparticles is a modified truncated octahedron and that the (size-dependent) melting of such particles is preceded by a significant change in the nanoparticle's morphology.     

A formulation of statistical mechanics of ordered systems

Expressions are derived for the thermodynamic functions (Gibbs free energy, Helmholtz free energy, etc.) of an ordered system in terms of the single-particle distribution function,p(x), and correlation functions. The thermodynamic functions are treated as functionals of the single-particle distribution function. By minimizing the Helmholtz free energy with respect top(x) under constraints of constantT, V andN, an integral equation is obtained from whichp(x) can be determined. The correlation function of the ordered state in the region near the coexistence surface between ordered and disordered state is expanded about the correlation function of the disordered state, and the series is truncated. Methods for calculating the thermodynamic functions and the single-particle distribution function are presented, and our result is discussed in relation to other treatments of phase coexistence in the literature.     

溶胶-凝胶法设计与制备金属及合金纳米材料的研究进展

溶胶-凝胶法是常见的制备金属氧化物的方法之一。在溶胶-凝胶法中,各种反应物能达到分子级的均匀混合,因此能制备成份复杂的氧化物材料。目前,溶胶-凝胶法也应用于设计与制备金属纳米材料,特别是合金纳米颗粒。例如,溶胶-凝胶法能应用于制备CoPt、FePt等磁性纳米合金材料以及CoCrCuNiAl高熵合金纳米材料,以及物相结构为有序相的Cu3Pt合金纳米材料。本文综述溶胶-凝胶法设计制备金属纳米材料的研究进展,包括溶胶-凝胶法实施的基本步骤、该方法在制备金属纳米材料方面的具体应用,并着重论述采用热力学计算设计金属及化合物的基本原理。该基本原理包括计算金属氧化物与还原性气体如氢气的还原反应的吉布斯自由能的变化量、金属氧化物的标准电极电位(不同于金属离子的标准电极电位)。最后探讨溶胶-凝胶法设计制备金属纳米材料存在的问题以及后续可能的发展方向。     

关于等温循环方法推导开尔文公式的讨论

等温循环方法是物理化学教材中推导开尔文公式的一个经典方法。本文从热力学基本原理出发,明确指出其中小液滴可逆相变为气体的吉布斯自由能变化值应由吉布斯自由能判据求解,并对温度恒定、两相压强分别恒定时的判据进行了重新推导。同时,本文还提出了一种对推导开尔文公式的等温循环法的新理解方式,该方式在建立的"箱管模型"辅助下,意义明确,便于理解,更适宜教学使用。     

First-principles study of lattice dynamics and thermodynamics of TiO2 polymorphs

The structural, phonon, and thermodynamic properties of six TiO(2) polymorphs, i.e., rutile, anatase, columbite, baddeleyite, orthorhombic I, and cotunnite, have been systematically investigated by density functional theory. The predicted volumes, bulk modulus, and Debye temperature are in good agreement with experiments. The phonon dispersions of the TiO(2) polymorphs were studied by the supercell approach, whereas the long-range dipole-dipole interactions were calculated by linear response theory to reproduce the LO-TO splitting, making accurate prediction of phonon frequencies for the polar material TiO(2). The calculated phonon dispersions show that all TiO(2) polymorphs are dynamically stable at ambient pressure, indicating the high-pressure phases might be quenched to ambient conditions as ultrahard materials. Furthermore, the finite temperature thermodynamic properties of TiO(2) polymorphs were predicted accurately from the obtained phonon density of states, which is critical in the future study of the pressure-temperature phase diagram of TiO(2). The calculated Gibbs energies reveal that rutile is more stable than anatase at ambient pressure. We derived the Gibbs energy and heat capacity functions for all TiO(2) polymorphs for use in thermodynamic modeling of phase equilibria.     

A Free Energy Model for Curved Surfaces and Curved Thin Films in Emulsions

The formulation of surface thermodynamics for flat surfaces has been done so as to be free of the Gibbs surface construction. The advantage of these formulations is that it allows the choice of thermodynamic field variables that is more general than the traditional construction. However, a generalization to curved surfaces including thin films that exist in emulsion structures has not been published. The Hansen-Cahn construction is developed in a setting that allows curvature terms to be added to the free energy expression. The Laplace equation extended to include bending elasticity and spontaneous bending elasticity is derived by computing functional derivatives of the free energy. Results for both single interfaces and double interfaces are reported. Stability conditions for profile fluctuations are developed to include these additional properties.     

立方体纳米Cu2O表面热力学函数的粒度及温度效应

液相还原法合成了4种粒度在40-120 nm的立方体纳米氧化亚铜（Cu₂O）。利用X射线衍射仪（XRD）、显微拉曼光谱仪和场发射扫描电子显微镜（FE-SEM）对纳米Cu₂O的物相组成及形貌结构进行了表征。采用原位微热量技术实时获取纳米/块体Cu₂O与HNO₃反应过程的热动力学信息,结合热化学循环及动力学过渡态理论计算得到纳米Cu₂O的表面热力学函数。在薛永强等建立的无内孔球形纳米颗粒的热力学模型基础上,发展了立方体纳米颗粒的热力学模型。最后由理论结合实验结果分析了粒度和温度对表面热力学函数的影响规律及原因。结果表明,摩尔表面Gibbs自由能、摩尔表面焓和摩尔表面熵均随粒度减小而增大,且与粒度的倒数呈线性关系,这与立方体热力学模型规律一致;随着温度的升高,摩尔表面焓和摩尔表面熵均增大,摩尔表面Gibbs自由能则减小。本文不仅丰富和发展了纳米热力学基本理论,还为纳米材料表面热力学研究及应用提供了方法和思路。