Solvation effects for polymers at an interface: a hybrid self-consistent field-density functional theory approach

Using polyatomic density functional theory of Kierlik and Rosinberg, we show that Wertheim's thermodynamic perturbation theory (TPT) incorporates solvation effects in a systematic, although simplified form. We derive two approximate solvation potentials, which require the knowledge of the correlation function in the reference unbonded fluid only. The theoretical predictions are tested against many-chain Monte Carlo simulations for moderate chain lengths. The predictions of the end-to-end distance in the bulk are in a reasonable agreement with simulations for the TPT(M-1) approximation, while the simpler TPT2_e approximation leads to the solvation potential that is shorter ranged and considerably less accurate. The resulting conformations are used in the subsequent self-consistent field theory calculations of hard-sphere polymers at a hard wall. While the incorporation of the solvation effects has little impact on the density profiles, the predictions of the components of the end-to-end distance vector as a function of the distance to the wall are much improved.     

Equation of state and liquid-vapor equilibria of one- and two-Yukawa hard-sphere chain fluids: theory and simulation

The accuracy of several theories for the thermodynamic properties of the Yukawa hard-sphere chain fluid are studied. In particular, we consider the polymer mean spherical approximation (PMSA), the dimer version of thermodynamic perturbation theory (TPTD), and the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR). Since the original version of SAFT-VR for Yukawa fluids is restricted to the case of one-Yukawa tail, we have extended SAFT-VR to treat chain fluids with two-Yukawa tails. The predictions of these theories are compared with Monte Carlo (MC) simulation data for the pressure and phase behavior of the chain fluid of different length with one- and two-Yukawa tails. We find that overall the PMSA and TPTD give more accurate predictions than SAFT-VR, and that the PMSA is slightly more accurate than TPTD.     

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.     

An improved thermodynamic perturbation theory for Mercedes-Benz water

We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient.     

链状分子状态方程的推导及热容的推算

在Barker Henderson, Zhang以及Wertheim 等微扰理论的基础上,以方阱势硬球流体为参考体系,将Zhang的解析表达方法与Wertheim 的链成键自由能的处理方法结合起来,推导出自由链接的链状分子流体的Helmholtz自由能的解析表达式,并得到了压缩因子、内能、恒容热容等热力学性质的计算式.计算结果与MC(Monte Carlo)模拟结果吻合良好.对Zhang的解析表达式与“TPT D”(二阶Wertheim微扰理论)的结合也作了推导和计算.     

Performance evaluation of third-order thermodynamic perturbation theory and comparison with existing liquid state theories

To evaluate the performance of a recently proposed third-order thermodynamic perturbation theory (TPT), we employ the third TPT for calculation of thermodynamic properties such as compressibility factor, internal energy, excess chemical potential, gas-liquid coexistence curve, and critical properties of several fluids. By comparing the third-order TPT results with corresponding simulation data available in literature and supplied in the present report and theoretical results from several other theoretical approaches, one concludes that the third-order TPT is, in general, more accurate than other approaches such as Barker-Henderson second-order TPT using a macroscopic compressibility approximation (MCA-TPT), self-consistent Ornstein-Zernike approach, Monte Carlo perturbation theory, and a specially devised equation of state. Specifically, the third-order TPT can predict quantitatively a double critical phenomena of gas-liquid transition and a low-density liquid (LDL)-high-density liquid (HDL) transition associated with a soft core (SC) potential fluid very satisfactorily, but the predictions for the LDL-HDL transition based on the second-order MCA-TPT are quantitatively very bad or qualitatively incorrect. The failure of the second-order MCA-TPT for the SC fluid can be ascribed to the facts that for the SC potential the second-order and third-order terms of the perturbation expansion are not small quantities and that the second-order term is underestimated by the MCA. It is concluded that the present third-order version of the TPT is reliable for varying model fluids.     

A Thermodynamic Model for Square-well Chain Fluid: Theory and Monte Carlo Simulation

A thermodynamic model for the freely jointed square-well chain fluids was developed based on the thermodynamic perturbation theory of Barker-Henderson, Zhang and Wertheim. In this derivation Zhang's expressions for square-well monomers improved from Barker-Henderson compressibility approximation were adopted as the reference fluid, and Wertheim's polymerization method was used to obtain the free energy term due to the bond connectivity. An analytic expression for the Helmholtz free energy of the square-well chain fluids was obtained. The expression without adjustable parameters leads to the thermodynamic consistent predictions of the compressibility factors, residual internal energy and constant-volume heat capacity for dimer, 4-mer, 8-mer and 16-mer square-well fluids. The results are in good agreement with the Monte Carlo simulation. To obtain the MC data of residual internal energy and the constant-volume heat capacity needed, NVT MC simulations were performed for these square-well chain fluids.     

A perturbation density functional theory for the competition between inter and intramolecular association

Using the framework of Wertheim's thermodynamic perturbation theory we develop the first density functional theory which accounts for intramolecular association in chain molecules. To test the theory new Monte Carlo simulations are performed at a fluid solid interface for a 4 segment chain which can both intra and intermolecularly associate. The theory and simulation results are found to be in excellent agreement. It is shown that the inclusion of intramolecular association can have profound effects on interfacial properties such as interfacial tension and the partition coefficient.     

Coarse-grained molecular dynamics modeling of strongly associating fluids: thermodynamics, liquid structure, and dynamics of symmetric binary mixture fluids

Symmetric binary mixtures capable of strong association via a highly directional and saturable specific interaction between unlike molecules are investigated by canonical molecular dynamics simulations. The specific interaction of the molecules is defined in a new coarse-grained pair potential that can be applied in continuous molecular dynamics as well as in Monte Carlo simulations. The thermodynamic, structural, and dynamic properties of the associating mixture fluids are investigated as a function of density, temperature, and association strength of the specific interaction. Detailed analysis of the simulation data confirms a two-stage mechanism in the formation of specific bonds with increasing interaction strength, including a fast dimerization process and a subsequent stage of perfecting the bonds. A large heat capacity peak is found during the formation or breaking of the bonds, reflecting the large energy fluctuation introduced by the strong association. The fractions of nonbonded molecules obtained from the simulations as a function of density, temperature, and interaction strength are in excellent agreement with the predictions of Wertheim's thermodynamic perturbation theory. The translational and rotational dynamics of the Tmer mixture are effectively retarded with increasing association strength and are analyzed in terms of autocorrelation functions and a non-Gaussian parameter for the translational dynamics. The lifetimes of molecules in bonded and nonbonded states provide detailed information about the transformation of molecules between the bonded state and the nonbonded state. Finally, simulation sampling problems inherent to strongly interacting systems are easily overcome using the parallel tempering simulation technique. This latter result confirms that with the new continuous coarse-grained simulation potential we have a versatile and flexible interaction potential that can be used with many available molecular dynamics and Monte Carlo algorithms under various ensembles.     

Non-hard sphere thermodynamic perturbation theory

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.     

Calculating thermodynamic properties from perturbation theory: II. An analytic representation for the square-well chain fluid

An analytic representation of thermodynamic properties of the freely jointed square-well chain fluid is developed based on the thermodynamic perturbation theory of Barker–Henderson, Zhang and Weitheim. By using a real function expression for the radial distribution function and incorporating structural information for square-well monomer of TPT1 model, an analytic expression for the Helmholtz energy of square-well chain fluid is expanded from Zhang’s analytic expressions for thermodynamic properties of square-well monomer. The expression leads to good predictions of the compressibility factor, residual internal energy and constant-volume heat capacity for 4-mer, 8-mer and 16-mer square-well fluids when compared with the Monte Carlo (MC) simulation results. The incorporating structural information for square-well dimer of TPT-D model is also calculated. To obtain the constant-volume heat capacity needed, NVT MC simulations were performed.     

Monte Carlo study of interfacial properties of associating fluids

Canonical Monte Carlo Simulations have been performed to calculate liquid-vapor properties of the associating square well and Lennard-Jones fluids with one and two sites. Simulations were carried out by using several values of reduced temperatures and association energies. The orthobaric densities, as well as the surface tension of associating square well fluids, were calculated and compared with those reported previously in literature; a good agreement was found among them. Results of surface tension of two-sites associating Lennard-Jones fluids are presented here for the first time.     

Calculating thermodynamic properties from perturbation theory: I. An analytic representation of square-well potential hard-sphere perturbation theory

The Barker–Henderson macroscopic compressibility approximation of the second-order perturbation term is improved by assuming that the numbers of molecules in every two neighbour shells are correlated, based upon the original assumptions. The results are better than those for the original macroscopic compressibility and local compressibility approximation, especially at high densities. A simple analytic representation of square-well potential hard-sphere perturbation theory is derived based upon this improvement. The method is tested by calculating thermodynamic properties with the four-term truncated form, and the results are in good agreement with those of Monte Carlo and Molecular Dynamics simulation.     

Heat capacities of Stockmayer fluids from Monte Carlo simulations and perturbation theory

The heat capacities of dipolar fluids are investigated using a thermodynamic perturbation theory approach and the NVT and NpT Monte Carlo simulation methods. The theoretical results are compared to corresponding simulation data. The comparison shows that the applied perturbation theory is appropriate for the heat capacity calculations. As an application, the isobaric heat capacity of ammonia is also studied by the Stockmayer fluid model.     

Thermodynamic properties of model solids with short-ranged potentials from Monte Carlo simulations and perturbation theory

Monte Carlo simulations have been performed to determine the excess energy and the equation of state of fcc solids with Sutherland potentials for wide ranges of temperatures, densities, and effective potential ranges. The same quantities have been determined within a perturbative scheme by means of two procedures: (i) Monte Carlo simulations performed on the reference hard-sphere system and (ii) second-order Barker-Henderson perturbation theory. The aim was twofold: on the one hand, to test the capability of the "exact" MC-perturbation theory of reproducing the direct MC simulations and, on the other hand, the reliability of the Barker-Henderson perturbation theory, as compared with direct MC simulations and MC-perturbation theory, to determine the thermodynamic properties of these solids depending on temperature, density, and potential range. We have found that the simulation data for the excess energy obtained from the two procedures are in close agreement with each other. For the equation of state, the results from the MC-perturbation procedure also agree well with the direct MC simulations except for very low temperatures and extremely short-ranged potentials. Regarding the Barker-Henderson perturbation theory, we have found that in general the second-order approximation does not provide significant improvement over the first-order one.     

Thermodynamic properties and aggregate formation of surfactant-like molecules from theory and simulation

The goal of this work is twofold: to predict the phase equilibria behavior of simplified surfactant models and to predict the population of aggregates as a function of pressure. We compare Monte Carlo simulation results of these systems with predictions from a modified version of the statistical associating fluid theory (soft-SAFT). Surfactant-like molecules are modeled as Lennard-Jones chains of tangent segments with one or two association sites. We study the influence of the number and location of the association sites on the thermodynamic properties and fraction of nonbonded molecules in all cases. The influence of the chain length is also investigated for a particular location of the sites. Results are compared with NPT Monte Carlo simulations to test the accuracy of the theory, and to study the molecular configurations of the system. Soft-SAFT is able to quantitatively predict the MC PVT results, independently of the location of the association sites. The theory is also able to capture the qualitative trend of the population of aggregates with pressure. Quantitative agreement is only obtained for specific locations of the sites.     

Test of athermal terms of activity coefficient models by Monte Carlo simulation with hard-core models

The infinite dilution activity coefficients of exactly athermal fluids were calculated by Monte Carlo simulation with hard-core models. The hard-core models used in this work were hard-sphere and hard-spherocylinder models. The Widom test particle method was adopted to calculate the residual chemical potentials of solutes in pure solvent and in pure solute solutions. The infinite dilution activity coefficients of solutes were obtained from the residual chemical potentials of solutes. The infinite dilution activity coefficients calculated by Monte Carlo simulation were compared with those of athermal terms in activity coefficient equations. Staverman–Guggenheim equation overestimates the activity coefficients. The deviations of activity coefficients increase with increasing the hard-core volume of solute. Flory–Huggins equation based on molar volume gives good results for the hard-spherocylinder systems. Elbro-FV equation gives good results for both the hard-sphere and hard-spherocylinder systems.     

Hard-sphere perturbation theories applied to concentrated colloidal dispersions

The application of hard-sphere perturbation theory to monodisperse colloidal dispersions is examined in detail. Osmotic pressures and radial distribution functions are calculated by these theories and compared with exact Monte Carlo results to allow a critical assessment of the accuracy of the theories. For most conditions encountered in practical colloidal dispersions the predictions of zero- and firstorder perturbation theories are very accurate.