Net,excess and absolute adsorption and adsorption of helium

The definitions of absolute, excess and net adsorption in microporous materials are used to identify the correct limits at zero and infinite pressure. Absolute adsorption is shown to be the fundamental thermodynamic property and methods to determine the solid density that includes the micropore volume are discussed. A simple means to define when it is necessary to distinguish between the three definitions at low pressure is presented. To highlight the practical implications of the analysis the case of adsorption of helium is considered in detail and a combination of experiments and molecular simulations is used to clarify how to interpret adsorption measurements for weakly adsorbed components.     

Interpretation of adsorption excess quantities: the absolute surface excess concentration

The concept of absolute surface excess of adsorption accounts for the expansion of compression of the volume of a pure liquid under the influence of a solid surface. The absolute surface excess amount of substance can prove to be a powerful measure of the adsorption at a solid/binary liquid interface, too. The contributions of the composition and volumetric effects to the adsorption can be separated from each other in this concept, and both of them are experimentally accessible quantities.     

Net,excess and absolute adsorption in mixed gas adsorption

The formulation of a thermodynamic framework for mixtures based on absolute, excess or net adsorption is discussed and the qualitative dependence with pressure and fugacity is used to highlight a practical issue that arises when extending the formulations to mixtures and to the Ideal Adsorbed Solution Theory (IAST). Two important conclusions are derived: the correct fundamental thermodynamic variable is the absolute adsorbed amount; there is only one possible definition of the ideal adsorbed solution and whichever starting point is used the same final IAST equations are obtained, contrary to what has been reported in the literature.     

A quasi lattice-local composition model for the excess Gibbs free energy of liquid mixtures

Two new expressions for the excess Gibbs energy of liquid mixtures are derived from Guggenheim's quasi-lattice model and Wilson's local composition concept. These are called the Local Surface Guggenheim equation (LSG) and the Local Composition Guggenheim equation (LCG). The LSG equation is similar, but not identical to UNIQUAC. The new equations require only two adjustable parameters per binary, and no higher-order parameters for extension to multicomponent systems.A critical discussion is given of Guggenheim's quasi-lattice expression for the excess Gibbs energy of athermal mixtures. This expression gives the combinatorial contribution to the new equations.A new method is proposed in the evaluation of the pure component structural parameters, independent of particular assumptions about the lattice parameters.The application of the LSG and the LCG equations to practical problems of phase-equilibria is considered in detail.     

Crystal nucleation and the solid-liquid interfacial free energy

We present the results of molecular dynamics simulation of crystal nucleation in a supercooled Lennard-Jones liquid. Temperature and baric dependences of the nucleation rate, the Zeldovich factor, nucleus size diffusion coefficient, the radius, and the pressure in a critical crystal nucleus are defined in computer simulation. The data obtained have been used in the framework of classical nucleation theory to calculate the effective surface energy of crystal nuclei γ(e). It is shown that the value of γ(e) at T = const exceeds the value of the interfacial free energy at a flat crystal-liquid interface γ(∞) and γ(e) < γ(∞) at p = const.     

Inhomogeneous polymer solutions: Theory of the interfacial free energy and the composition profile near the consolute point

The Flory–Huggins formulation of the combinatorial entropy, supplemented with residual free energy, is applied locally to obtain the interfacial free energy and the concentration profile of polymer in the interface between two demixed polymer solution phases. Two choices were investigated for the residual free energy: a “regular solution” formulation and an empirical formulation of Koningsveld for polystyrene in cyclohexane. Asymptotic, analytical solutions of the equations near the critical solution point and solutions obtained by numerical calculations are given as a function of temperature for several molecular weights. At temperatures farther below the critical temperature the equations have no solutions. The reason for this is not entirely clear. The local formulation of the free energy used here is an improved version of a previous one, which gave wrong results for asymmetric systems (polymer in a low molecular weight solvent). This newer version is consistent with our theory of critical opalescence and gives a relation between the interface “thickness” and the correlation range of the concentration fluctuations. The calculated correlation ranges were in good accord with those found experimentally by Debye, Chu, and Woerman. That the newer version of our equations for an interface gives no acceptable solutions at lower temperatures could be caused by a “collapse” of a diffuse to a sharp interface as suggested by Nose.     

A model for the free energy of adsorption on low energy surfaces.

In constructing a generalized thermodynamics for the fluid-vapor-solid equilibrium in poorly wetted systems the specific free energy of adsorption at saturation vapor pressure is a basic and elusive term. If the adsorbed phase is modeled as a two dimensional gas, systems for which a complete spectrum of data is available can serve as an empirical basis for constructing and testing adsorption-contact angle relationships. From the extension of such relationship other often inassessible terms can be estimated. Such a construct is reported here and extended to the estimation of the excess adsorption entropy at saturation vapor pressure in non-wetting systems     

Water coordination structures and the excess free energy of the liquid

We assess the contribution of each coordination state to the hydration free energy of a distinguished water molecule, the solute water. We define a coordination sphere, the inner-shell, and separate the hydration free energy into packing, outer-shell, and local, solute-specific (chemical) contributions. The coordination state is defined by the number of solvent water molecules within the coordination sphere. The packing term accounts for the free energy of creating a solute-free coordination sphere in the liquid. The outer-shell contribution accounts for the interaction of the solute with the fluid outside the coordination sphere and it is accurately described by a Gaussian model of hydration for coordination radii greater than the minimum of the oxygen-oxygen pair-correlation function: theory helps identify the length scale to parse chemical contributions from bulk, nonspecific contributions. The chemical contribution is recast as a sum over coordination states. The nth term in this sum is given by the probability p(n) of observing n water molecules inside the coordination sphere in the absence of the solute water times a factor accounting for the free energy, W(n), of forming an n-water cluster around the solute. The p(n) factors thus reflect the intrinsic properties of the solvent while W(n) accounts for the interaction between the solute and inner-shell solvent ligands. We monitor the chemical contribution to the hydration free energy by progressively adding solvent ligands to the inner-shell and find that four-water molecules are needed to fully account for the chemical term. For a chemically meaningful coordination radius, we find that W(4) ≈ W(1) and thus the interaction contribution is principally accounted for by the free energy for forming a one-water cluster, and intrinsic occupancy factors alone account for over half of the chemical contribution. Our study emphasizes the need to acknowledge the intrinsic solvent properties in interpreting the hydration structure of any solute, with particular care in cases where the solute-solvent interaction strength is similar to that between the solvent molecules.     

Thermodynamic parameters of excess and absolute adsorption of CH4 and SF6 on carbons

Isosteres, isosteric heats, and heat capacities of methane and sulfur hexafluoride on carbons with different porosities were calculated to characterize the excess adsorption and absolute adsorption. The nonlinear character of isosteres of excess adsorption and absolute adsorption of sulfur hexafluoride on FAS carbon with developed mesoporosity was shown.     

Influence of the solvation process on solute adsorption in reversed phase liquid chromatography

The adsorption isotherms of phenol were acquired by frontal analysis on six different reversed phase adsorbents from five different organic solvent solutions. The end-capped octadecyl columns only differed in the bonding density of the C(18) ligands. The inverse method was used to confirm the estimated isotherm parameters derived from the frontal experiments. The effect of the bonding density of the end-capped octadecyl bonded phase on the adsorption properties of phenol from different mobile phase compositions was investigated. The adsorption behavior of phenol has changed from Langmuir type to BET type with the change of the organic modifier and the bonding density of the adsorbent.     

An efficient method for computing excess free energy of liquid

We present a new theoretical method for efficient calculation of free energy of liquid. This interaction entropy method allows one to compute entropy and free energy of liquid from standard single step MD (molecular dynamics) simulation directly in liquid state without the need to perform MD simulations at many intermediate states as required in thermodynamic integration or free energy perturbation methods. In this new approach, one only needs to evaluate the interaction energy of a single (fixed) liquid molecule with the rest of liquid molecules as a function of time from a standard MD simulation of liquid and the fluctuation of distribution of this interaction energy is then used to calculate the interaction entropy of the liquid. Explicit theoretical derivation of this interaction entropy approach is provided and numerical calculations for the benchmark liquid water system were carried out using three different water models. Numerical analysis of the result was performed and comparison of the computational result with experimental data and other theoretical results were provided. Excellent agreement of calculated free energies with the experimental data using TIP4P model is obtained for liquid water.     

A note on excess Gibbs energy models,equations of state and the local composition concept

A density-dependent local composition expression for the residual energy is derived from a generalized NRTL expression for the excess energy and the van der Waals fluid theory. Integration of this expression yields a volume-dependent expression for the Helmholtz energy from which equations of state utilizing the local composition concept are derived and which in the high-density limit contain the well-known activity coefficient models.The local composition versions of the Carnahan—Starling—van der Waals, the Redlich—Kwong—Soave and the Peng—Robinson equations of state are derived. It is further shown that the group contribution versions of the NRTL, the Wilson and the UNIQUAC excess models may be derived from the generalized NRTL expression for the residual energy when applied to groups instead of molecules.It is thus demonstrated that all current local composition activity-coefficient models can be derived from a local composition version of the van der Waals equation of state using different sets of assumptions. In the same way the van Laar, the Scatchard—Hildebrand and the Flory—Huggins activity coefficient models are obtained from the van der Waals equation of state using the original mixing rules.     

The Flory mixing free energy: the effects of solute topology and monomer size

This note presents a lattice‐based derivation of the Flory free energy that does not invoke assumptions on the chain character of the solute. This derivation highlights two crucial features of the Flory free energy: (i) The mixing entropy S_mix is insensitive to the solute structural details. It depends only on the number of lattice sites occupied by the solute. (ii) In marked distinction, the mixing energy does vary with the topology of the solute, the monomer size and the dimensionality. Our discussion suggests re‐examination of the applicability of the Flory free energy to non‐polymeric solutions.     

Calculation of the crystal-melt interfacial free energy of succinonitrile from molecular simulation

The crystal-metal interfacial free energy for a six-site model of succinonitrile [N triple bond C-(CH(2))(2)-C triple bond N] has been calculated using molecular-dynamics simulation from the power spectrum of capillary fluctuations in interface position. The orientationally averaged magnitude of the interfacial free energy is determined to be (7.0+/-0.4)x10(-3) J m(-2). This value is in agreement (within the error bars) with the experimental value [(7.9+/-0.8)x10(-3) J m(-2)] of Marasli et al. [J. Cryst. Growth 247, 613 (2003)], but is about 20% lower than the earlier experimental value [(8.9+/-0.5)x10(-3) J m(-2)] obtained by Schaefer et al. [Philos. Mag. 32, 725 (1975)]. In agreement with the experiment, the calculated anisotropy of the interfacial free energy of this body-centered-cubic material is small. In addition, the Turnbull coefficient from our simulation is also in agreement with the experiment. This work demonstrates that the capillary fluctuation method of Hoyt et al. [Phys. Rev. Lett. 86, 5530 (2001)] can be successfully applied to determine the crystal-melt interfacial free energy of molecular materials.     

Adsorption volume and absolute adsorption: 2. Adsorption from liquid phase

A critical analysis of the isotherms of excess and absolute adsorption, as well as the adsorption space performed in the first part [1] is continued; however, as applied to the equilibrium physical adsorption from the liquid phase. The correct method is proposed for evaluating the adsorption volume of solid adsorbents with an arbitrary structure by the isotherm of excess adsorption of binary mixture of liquids. This method is successfully tested for nine different adsorption systems.     

Symmetrization of excess Gibbs free energy: A simple model for binary liquid mixtures

A symmetric expression for the excess Gibbs free energy of liquid binary mixtures is obtained using an appropriate definition for the effective contact fraction. We have identified a mechanism of local segregation as the main cause of the contact fraction variation with the concentration. Starting from this mechanism we develop a simple model for describing binary liquid mixtures. In this model two parameters appear: one adjustable, and the other parameter depending on the first one. Following this procedure we reproduce the experimental data of (liquid + vapor) equilibrium with a degree of accuracy comparable to well-known more elaborated models. The way in which we take into account the effective contacts between molecules allows identifying the compound which may be considered to induce one of the following processes: segregation, anti-segregation and dispersion of the components in the liquid mixture. Finally, the simplicity of the model allows one to obtain only one resulting interaction energy parameter, which makes easier the physical interpretation of the results.     

Hard spheres revisited: accurate calculation of the solid-liquid interfacial free energy

We revise the earlier [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)] direct calculation of the hard sphere solid-liquid interfacial free energy by the cleaving walls method. The revisions of the method include modified interactions with the cleaving walls and the use of a nonequilibrium work measurements approach, which allows for a more robust control of the accuracy of the obtained results. We find that the new values are lower compared to the original ones, which is consistent with the more recent indirect estimates based on extrapolation from the soft-sphere results [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)], as well as those obtained using the capillary fluctuations method [R. L. Davidchack, J. R. Morris, and B. B. Laird, J. Chem. Phys. 125, 094710 (2006)].     

Parallelized-over-parts computation of absolute binding free energy with docking and molecular dynamics

We present a technique for biomolecular free energy calculations that exploits highly parallelized sampling to significantly reduce the time to results. The technique combines free energies for multiple, nonoverlapping configurational macrostates and is naturally suited to distributed computing. We describe a methodology that uses this technique with docking, molecular dynamics, and free energy perturbation to compute absolute free energies of binding quickly compared to previous methods. The method does not require a priori knowledge of the binding pose as long as the docking technique used can generate reasonable binding modes. We demonstrate the method on the protein FKBP12 and eight of its inhibitors.     

乙腈-水的液液、固液相平衡和过量Gibbs自由能

测制了xCH~3CN+(1-x)H~2O的液液、固液平衡相图, 此系液液分层的简单低共熔混合物类相图。低共熔点温度为227.44K, 组成x=0.955。最高临界溶解温度为271.0K, 临界组成x=0.35, 临界指数n=2.64。两液相与冰的平衡温度为263.07K。计算出体系在263.07K的过量Gibbs自由能G~m^E, 液液分层时G~m^E的最大值为1174J·mol^-^1。