Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.     

An improved renormalization group theory for real fluids

On the basis of White's theory, an improved renormalization group (RG) theory is developed for chain bonding fluids inside the critical region. Outside the critical region, the statistical associating fluid theory based on the first-order mean sphere approximation [Fluid Phase Equilibria 171, 27 (2000)] is adopted and all the microscopic parameters are taken directly from its earlier application of real fluids. Inside the critical region, the RG transformation for long-range density fluctuation is derived in the k space, which illustrates explicitly the contributions from the mean-field term, the local density fluctuation, and the nonlocal density fluctuation. The RG theory is applied to describe physical behavior of ten n alkanes (C1-C10) both near to and far from the critical point. With no additional parameters for chain bonding fluids, good results are obtained for critical specific heat and phase coexistence curves and the resulting critical exponents are in good agreement with the reported nonclassic values.     

Homogeneous nucleation in vapor-liquid phase transition of Lennard-Jones fluids: a density functional theory approach

Density functional theory (DFT) with square gradient approximation for the free energy functional and a model density profile are used to obtain an analytical expression for the size-dependent free energy of formation of a liquid drop from the vapor through the process of homogeneous nucleation, without invoking the approximations used in classical nucleation theory (CNT). The density of the liquid drop in this work is not the same as the bulk liquid density but it corresponds to minimum free energy of formation of the liquid drop. The theory is applied to study the nucleation phenomena from supersaturated vapor of Lennard-Jones fluid. The barrier height predicted by this theory is significantly lower than the same in CNT which is rather high. The density at the center of the small liquid drop as obtained through optimization is less than the bulk density which is in agreement with other earlier works. Also proposed is a sharp interface limit of the proposed DFT of nucleation, which is as simple as CNT but with a modified barrier height and this modified classical nucleation theory, as we call it, is shown to lead to improved results.     

Spin-adapted density matrix renormalization group algorithms for quantum chemistry

We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett. 57, 852 (2002)] to quantum chemical Hamiltonians. This involves using a quasi-density matrix, to ensure that the renormalized DMRG states are eigenfunctions of S?(2), and the Wigner-Eckart theorem, to reduce overall storage and computational costs. We argue that the spin-adapted DMRG algorithm is most advantageous for low spin states. Consequently, we also implement a singlet-embedding strategy due to Tatsuaki [Phys. Rev. E 61, 3199 (2000)] where we target high spin states as a component of a larger fictitious singlet system. Finally, we present an efficient algorithm to calculate one- and two-body reduced density matrices from the spin-adapted wavefunctions. We evaluate our developments with benchmark calculations on transition metal system active space models. These include the Fe(2)S(2), [Fe(2)S(2)(SCH(3))(4)](2-), and Cr(2) systems. In the case of Fe(2)S(2), the spin-ladder spacing is on the microHartree scale, and here we show that we can target such very closely spaced states. In [Fe(2)S(2)(SCH(3))(4)](2-), we calculate particle and spin correlation functions, to examine the role of sulfur bridging orbitals in the electronic structure. In Cr(2) we demonstrate that spin-adaptation with the Wigner-Eckart theorem and using singlet embedding can yield up to an order of magnitude increase in computational efficiency. Overall, these calculations demonstrate the potential of using spin-adaptation to extend the range of DMRG calculations in complex transition metal problems.     

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.     

State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve

We study the nitrogen binding curve with the density matrix renormalization group (DMRG) and single-reference and multireference coupled cluster (CC) theory. Our DMRG calculations use up to 4000 states and our single-reference CC calculations include up to full connected hextuple excitations. Using the DMRG, we compute an all-electron benchmark nitrogen binding curve, at the polarized, valence double-zeta level (28 basis functions), with an estimated accuracy of 0.03 mEh. We also assess the performance of more approximate DMRG and CC theories across the nitrogen curve. We provide an analysis of the relative strengths and merits of the DMRG and CC theory under different correlation conditions.     

An algorithm for large scale density matrix renormalization group calculations

We describe in detail our high-performance density matrix renormalization group (DMRG) algorithm for solving the electronic Schrodinger equation. We illustrate the linear scalability of our algorithm with calculations on up to 64 processors. The use of massively parallel machines in conjunction with our algorithm considerably extends the range of applicability of the DMRG in quantum chemistry.     

Predicting interfacial tension between water and nonpolar fluids from a Cahn-type theory

We propose an accurate method to predict interfacial tension between water and nonpolar fluids by using Cahn gradient theory. The only necessary elements are (i) a water contact energy function and (ii) an equation of state (EoS) for the nonpolar fluid, chosen here as the Peng-Robinson EoS. The contact energy, a function of the fluid (adsorbate) surface density, is related to interfacial tension (IFT) by means of the Gibbs adsorption equation. Examining a large number of IFT data, we observe that the water contact energy is a universal function of adsorbate's surface density when proper scaling variables are used: it depends neither on adsorbate nor on temperature. A corresponding-states principle appears to govern the interfacial behavior between water and any nonpolar compound that is sparingly soluble in water. A predictive method (without any adjustable parameter) is therefore available for estimating IFT between water and any nonpolar fluid, whether the fluid is in supercritical or in subcritical states. The method performs well when the adsorbate is sparingly soluble in water, but slightly overestimates IFTs when the adsorbate's solubility in water is significant (e.g., CO2 and H2S). A similar behavior should also hold for interfaces involving a solid substrate.     

Phase equilibria and surface tension of pure fluids using a molecular layer structure theory (MLST) model

This paper presents a new model based on thermodynamic and molecular interaction between molecules to describe the vapour–liquid phase equilibria and surface tension of pure component. The model assumes that the bulk fluid can be characterised as set of parallel layers. Because of this molecular structure, we coin the model as the molecular layer structure theory (MLST). Each layer has two energetic components. One is the interaction energy of one molecule of that layer with all surrounding layers. The other component is the intra-layer Helmholtz free energy, which accounts for the internal energy and the entropy of that layer. The equilibrium between two separating phases is derived from the minimum of the grand potential, and the surface tension is calculated as the excess of the Helmholtz energy of the system. We test this model with a number of components, argon, krypton, ethane, n-butane, iso-butane, ethylene and sulphur hexafluoride, and the results are very satisfactory.     

气液色谱法研究聚合物/溶剂体系气液平衡

 用气液色谱法测定了聚二甲基硅氧烷（PDMS）／溶剂、聚甲基丙烯酸甲酯（PMMA）／溶剂体系在不同温度下以质量分数表示的无限稀溶剂活度系数和Flory－Huggins相互作用参数。应用UNIFAC和UNIFAC－FV模型对PDMS／溶剂、PMMA／溶剂体系中以质量分数表示的无限稀溶剂活度系数进行了估算。结果表明,用这两个模型预测PDMS／溶剂、PMMA／溶剂体系中的无限稀溶剂活度系数有待修正或采用其它模型进行估算。     

Calculation of surface tension of metals using density gradient theory and PC-SAFT equation of state

The Cahn-Hilliard theory was combined with PC-SAFT equation of state (EOS), in order to describe both the phase behaviors and the surface tension of different types of metals (Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Fe, Zn, Cd, In, Sn, Pb, and Bi). The only two inputs of the theory are the Helmholtz free-energy density and the influence parameter. The PC-SAFT equation of state was applied to determine Helmholtz free-energy density and bulk properties. The influence parameter is obtained by fitting to the experimental data of surface tension. The results show a useful possibility to calculate surface tensions which are in satisfactory agreement with experimental data.     

Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations

We present projected gradient algorithms designed for optimizing various functionals defined on the set of N-representable one-electron reduced density matrices. We show that projected gradient algorithms are efficient in minimizing the Hartree-Fock or the Muller-Buijse-Baerends functional. On the other hand, they converge very slowly when applied to the recently proposed BBk (k=1,2,3) functionals [O. Gritsenko et al., J. Chem. Phys. 122, 204102 (2005)]. This is due to the fact that the BBk functionals are not proper functionals of the density matrix.     

Correlation for prediction of vapor pressures of pure fluids incorporating renormalization group formulations with corresponding-states principle

A simple correlation for predicting the vapor pressures of coal liquids between the freezing and critical points, and extending to normal fluids, has been developed on the basis of renormalization group theory and phenomenological scaling theory. The Clapeyron equation has been reduced to the integral form

to represent vapor pressure using a generalized correlation developed by Sivaraman et al. (1983) for the prediction of latent heats of vaporization of normal fluids and coal-liquid model compounds. L*, the dimensionless latent heat of vaporization, andΔz, the difference between the compressibility factors of the saturated vapor and liquid, are given by the corresponding-states correlations

and

based on the formulations of Pitzer et al. (1955). A simple expression for the latent heat of vaporization developed by Torquato and Stell (1982) is incorporated into this correlation. The vapor-pressure correlation has been tested successfully for 23 pure-component systems including aromatic and heterocyclic compounds often found in coal liquids and shale oil in the region 0 〈 ε = (T_c-T)/T_c 〈 0.69. The deviations in the predicted vapor pressures are in the range 0.11–5.45%.     

Interfacial properties of Lennard-Jones chains by direct simulation and density gradient theory

We perform a series of molecular dynamics simulations of Lennard-Jones chains systems, up to tetramers, in order to investigate the influence of temperature and chain length on their phase separation and interfacial properties. Simulation results serve as a test to check the accuracy of a statistical associated fluid theory (soft-SAFT) coupled with the density gradient theory. We focus on surface tension and density profiles. The simulations allow us to discuss the success and limitations of the theory and how to estimate the only adjustable parameter, the influence parameter. This parameter is obtained by fitting the surface tension, and then used to obtain the density profiles in a predictive manner. A good agreement is found if the temperature dependence of this parameter is neglected.(c) 2004 American Institute of Physics.     

On the spin and symmetry adaptation of the density matrix renormalization group method

We present a spin-adapted density matrix renormalization group (DMRG) algorithm designed to target spin and spatial symmetry states that can be difficult to obtain while using a non-spin-adapted algorithm. The algorithmic modifications that have to be introduced into the usual density matrix renormalization group scheme in order to spin adapt it are discussed, and it is demonstrated that the introduced modifications do not change the overall scaling of the method. The new approach is tested on HNCO, a model system, that has a singlet-triplet curve crossing between states of the same symmetry. The advantages of the spin-adapted DMRG scheme are discussed, and it is concluded that the spin-adapted DMRG method converges better in almost all cases and gives more parallel curves to the full configuration interaction result than the non-spin-adapted method. It is shown that the spin-adapted DMRG energies can be lower than the ones obtained from the non-spin-adapted scheme. Such a counterintuitive result is explained by noting that the spin-adapted method is not a special case of the non-spin-adapted one; consequently, the spin-adapted result is not an upper bound for the non-spin-adapted energy.     

Isothermal vapor-liquid equilibria for binary and ternary mixtures formed by 1-butanol,acetonitrile and benzene

Isothermal vapor-liquid equilibrium data are presented for the binary acetonitrile-1-butanol and ternary 1-butanol-acetonitrile-benzene systems at 60 °C. The experimental results are well correlated with the UNIQUAC associated-solution model.     

Isothermal vapor-liquid equilibria of bromochloroalkanes with heptane or cyclohexane: Measurement and analysis in terms of group contributions

Isothermal vapor-liquid equilibria (VLE) have been measured for liquid bromochloromethane + heptane or cyclohexane at 25‡C and 40‡C, and for 1-bromo-chloroethane + heptane or cyclohexane at 40‡C. These experimental results, along with our previous ones on excess enthalpies, as well as literature data on activity coefficients at infinite dilution, are interpreted in terms of the DISQUAC group contribution model, and are compared with UNIFAC predictions.