Simulation and model development for the equation of state of heteronuclear non‐additive copolymer chains

Molecular dynamics simulations of hard alternating copolymer chains composed of size asymmetric nonadditive segments were performed. Different degrees of polymerization, densities, size ratios and nonadditivities were used. The equation of state for these copolymers was investigated and models based on the first order thermodynamic perturbation theory (TPT1) and the polymeric analog of the Percus‐Yevick approximation (PPY) were developed to predict the compressibility factor of the copolymers. The models predicted the compressibilities of the mixtures accurately at small size ratios, low degrees of polymerization and higher densities. The TPT1 model was generally more accurate in predicting the compressibility factor than the PPY model.     

Equation of state of nonadditive d-dimensional hard-sphere mixtures

An equation of state for a multicomponent mixture of nonadditive hard spheres in d dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard spheres proposed by us [A. Santos, S. B. Yuste, and M. Lopez de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on the known exact second and third virial coefficients and requires as input the compressibility factor of the one-component system. A comparison is carried out both with another recent theoretical proposal based on a similar philosophy and with the available exact results and simulation data in d=1, 2, and 3. Good general agreement with the reported values of the virial coefficients and of the compressibility factor of binary mixtures is observed, especially for high asymmetries and/or positive nonadditivities.     

A corresponding states principle for the equation of state of hard body fluid mixtures

A theoretically based corresponding-states principle is developed for athermal mixtures consisting of hard molecules. The principle states that when scaled appropriately, the excess compressibility factor for such mixtures reduces to a universal function of the effective packing fraction of the mixture. The latter represents the number density reduced by means of the effective molecular volume, which is defined as the volume a molecule excludes to any point of another molecule and depends on the geometry of both molecules. The scaling factor is related to a sort of effective nonsphericity parameter for the mixture that depends on composition as well as the nonsphericity parameters of the molecules which form the mixture and their effective molecular volumes. The universal function represents the excess compressibility factor of a pure hard-sphere fluid. Results are in good agreement with available simulation data.     

Pressure and temperature dependence of hydrophobic hydration: volumetric, compressibility, and thermodynamic signatures

The combined effect of pressure and temperature on hydrophobic hydration of a nonpolar methanelike solute is investigated by extensive simulations in the TIP4P model of water. Using test-particle insertion techniques, free energies of hydration under a range of pressures from 1 to 3000 atm are computed at eight temperatures ranging from 278.15 to 368.15 K. Corresponding enthalpy, entropy, and heat capacity accompanying the hydration process are estimated from the temperature dependence of the free energies. Partial molar and excess volumes calculated using pressure derivatives of the simulated free energies are consistent with those determined by direct volume simulations; but direct volume determination offers more reliable estimates for compressibility. At 298.15 K, partial molar and excess isothermal compressibilities of methane are negative at 1 atm. Partial molar and excess adiabatic (isentropic) compressibilities are estimated to be also negative under the same conditions. But partial molar and excess isothermal compressibilities are positive at high pressures, with a crossover from negative to positive compressibility at approximately 100-1000 atm. This trend is consistent with experiments on aliphatic amino acids and pressure-unfolded states of proteins. For the range of pressures simulated, hydration heat capacity exhibits little pressure dependence, also in apparent agreement with experiment. When pressure is raised at constant room temperature, hydration free energy increases while its entropic component remains essentially constant. Thus, the increasing unfavorability of hydration under raised pressure is seen as largely an enthalpic effect. Ramifications of the findings of the authors for biopolymer conformational transitions are discussed.     

Structure factor for hard hyperspheres in higher dimensions

The structure factor for hard hyperspheres in two to eight dimensions is computed by Fourier transforming the pair correlation function obtained by computer simulation at a variety of densities. The resulting structure factors are compared to the known Percus-Yevick equations for odd dimensions and to the model proposed by Leutheusser [J. Chem. Phys. 84, 1050 (1986)] and Rosenfeld [J. Chem. Phys. 87, 4865 (1987)] in even dimensions. It is found that there is fine agreement among all these approaches at low to moderate densities but that the accuracy of the analytical models breaks down as the freezing transition is approached. The structure factor gives another insight into the decrease in the ordering of the hyperspheres as the dimension is increased.     

Molecular interactions in poly(ethylene glycol)-water mixtures at various temperatures: density and isentropic compressibility study.

The densities and sound velocities of mixtures of water with poly(ethylene glycol), poly(ethylene glycol) monomethylether, and poly(ethylene glycol) dimethylether with mean molar weights between 250 and 500 have been measured as a function of mixture composition and temperature between 10 and 40 degrees C. Isentropic compressibilities are derived from the data and are compared to those for the ethylene glycol/water system and for other organic solvent/water mixtures. Relative minima in the mixture volume to ideal volume ratio and in the dependence of the compressibility upon mixture composition are discussed in terms of the conformational variability of the chainlike oligomers, of hydrogen-bonded networks, and of water clusters between the oligomer chains.     

Molecular dynamics study on homonuclear and heteronuclear chains of Lennard–Jones segments

We report molecular dynamics (MD) simulation data for three simulated fluids: a homopolymer with 16 tangent Lennard–Jones (LJ) segments at the reduced temperature of 1.25, an equimolar binary homopolymer fluid with eight tangent LJ segments at 15 state points, and three corresponding copolymers with equimolar segment fraction and varying segment distribution at 15 state points. We find that the compressibility factors and energies do not change as the segment distribution varies in the copolymer example. The simulation data are compared with thermodynamic perturbation theory (TPT1) calculations. The TPT1 compressibility factors compare favorably with the MD data at high reduced temperatures but differ significantly at lower temperatures.     

Volumes and compressibilities of pentanol in aqueous dodecyltrimethylammonium bromide solutions at 15, 25 and 35°C

Ultrasonic velocities and densities of the water-dodecyltrimethylammonium bromide (DTAB)-pentanol (PentOH) ternary system were measured at 15, 25 and 35°C as a function of the surfactant and alcohol concentrations. The apparent molar volumes and isentropic compressibilities of PentOH were calculated. The standard partial molar volumes increase with surfactant concentration continuously whereas the standard partial molar isentropic compressibilities show sharp changes in slope at about 0.25 mol-kg^–1 DTAB, which can be ascribed to a micellar structural transition. The volume data for alcohol in micellar solutions were treated by a model reported for the distribution of polar additives between aqueous and micellar phases. In the application of the model to compressibility, the contributions due to the pressure effect on the shift of both the micellization equilibrium and the alcohol distribution constant cannot be neglected. This is in contrast to what is found in the case of heat capacity. The distribution constant and the partial molar volumes and compressibilities of PentOH in the micellar phase have been derived by linear regression. Also, the apparent molar volumes and isentropic compressibilities of DTAB in water-pentanol mixed solvents at fixed composition have been calculated. These properties as a function of the surfactant concentration show maxima depending on the temperature and the mixed solvent composition. The decrease beyond the maximum can be attributed to the extraction of PentOH from the aqueous into the micellar phase, where its concentration tends to zero with the progressive increase of the surfactant concentration. As a consequence, by increasing the surfactant concentration, the apparent molar properties of the surfactant in the mixed solvent shifts towards the value in water.     

Modeling and simulation of equation of state for nonadditive hard disk mixtures

We present exact results for mixtures of nonadditive hard disks and use some of them to derive a consistent model for the equation of state. We also performed molecular dynamics simulation for hard disks over a wide range of size ratios. Comparison of the model to the data shows that the model is accurate for all densities in the case of additive and slightly nonadditive (nonadditivity parameter within ±0.1) mixtures. For large nonadditivity, the model is accurate for low to moderate densities only, and starts to deteriorate at high densities.     

The extension of coordination number model by using the local composition theory: mixtures

The extension of a new coordination number model to mixture is presented in this work. Extended model agrees well with the Monte Carlo (MC) simulation results for square-well (SW) mixture fluids and shows better results compared with other models. To test our model, we compare the compressibility factors from various models for SW fluids at different λ values and for SW fluid mixtures at λ=1.5. Although our model is obtained by fitting simulation data at λ=1.5, it shows better results for the different λ values than other coordination number model. Compared with the compressibility factors of various binary mixtures of SW fluids calculated from other models, this model presents better results. Because our model considers the temperature dependency importantly by using the total site number, it predicts coordination number and compressibility factor well in the wide temperature range and enables one to derive an equation of state (EOS) through integration of the coordination number equation.     

Influence of the pressure on the properties of chromatographic columns. I. Measurement of the compressibility of methanol-water mixtures on a mesoporous silica adsorbent

The compressibilities of aqueous solutions of methanol or acetonitrile containing 0, 20, 40, 60, 80 and 100% (v/v) organic solvent were measured with a dynamic chromatographic method. The elution volumes of thiourea samples (2 microL) in these solutions were measured at different average column pressures, adjusted by placing suitable capillary restrictors on-line, after the detector. The reproducibility of the measurements was better than 0.2%. In the range of average pressures studied (10-350 bar), the maximum change in elution volume of thiourea is 1.3% (in pure water) and 4.0% (in pure methanol). This difference is due to the different compressibilities of these pure solvents. For mixtures, the plots of the elution volume of thiourea versus the pressure are convex downward, which is inconsistent with the opposite curvature predicted by the classical Tait model of liquid compressibility. This difference is explained by the variation of the amount of thiourea adsorbed with the pressure. The deconvolution of the two effects, adsorption of thiourea and solvent compressibility, allows a fair and consistent determination of the compressibilities of the methanol-water mixtures. A column packed with non-porous silica particles was also used to determine the compressibility of methanol-water and acetonitrile-water mixtures. A negative deviation by respect to ideal behavior was observed.     

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.     

Isotropic hard core dumbell fluid: Equation of state

A monte-Carlo calculation has been made for 108 hard core dumbbells of the compressibility factor in the isotropic density range. These compressibility factors are compared to several approximate theories, and comments are made on the utility of these approximate theories.     

Isentropic compressibilities of the mixture chlorobenzene + n-hexane + (n-heptane or n-octane) at 298.15 K

In this work, the applicability of the free length and the collision factor theories (FLT and CFT, respectively) to predict multicomponent changes of isentropic compressibilities is analysed and compared. To this end, appropiate expansions for ternary mixtures were derived from the original works, and then applied to a mixture containing unlike compounds in terms of functional molecular groups. Experimental data of excess molar volumes from open literature and new experimental isentropic compressibilities of the mixture chlorobenzene?+?n-hexane?+?(n-heptane or n-octane) were used to compute the parameters. A good accuracy was obtained when ternary prediction is attempted in this partially soluble mixture at different temperatures by the collision factor theory. These results show the versatility of this model for estimation in complex multicomponent mixtures with phases splitting.     

Densities,sound velocities,and refractive indexes of (tetralin + n-decane) and thermodynamic modeling by Prigogine–Flory–Patterson model

Mixtures of tetralin (1,2,3,4-tetrahydronaphthalene), an aromatic cyclic molecule, and n-decane present asymmetries in chemical nature, shape, and chain length, and are frequently found, e.g., in naphtha or kerosene fractions. Aiming at understanding the impact of these asymmetries on some thermophysical properties, this work presents densities, sound velocities, and refractive indexes for this binary system along with the properties of the pure components at T = (293.15, 303.15, 313.15, 323.15, 333.15, and 343.15) K over whole composition range and atmospheric pressure. From these data, the following derived properties were obtained: isentropic compressibility, molar refractivity, excess volume, excess isentropic compressibility, molar refractivity deviations, and thermal expansion coefficient. Several sound velocity mixing rules were tested, and the best result was for Nomoto mixing rule. Pure component densities and sound velocities were correlated with Prigogine–Flory–Patterson (PFP) model. The binary interaction parameter for this model was obtained from correlation of excess volumes and isentropic compressibilities. This model correlated experimental densities very well and correlated reasonably well sound velocities and thermal expansion coefficient.     

Osmotic compressibility of soft colloidal systems

A turbidimetric analysis of particle interaction of model pH-responsive microgel systems consisting of methacrylic acid-ethyl acrylate cross-linked with diallyl phthalate in colloidal suspensions is described. The structure factor at zero scattering angle, S(0), can be determined with good precision for wavelengths greater than 500 nm, and it measures the dispersion's resistance to particle compression. The structure factor of microgels at various cross-linked densities and ionic strengths falls onto a master curve when plotted against the effective volume fraction, phi(eff) = kc, which clearly suggests that particle interaction potential and osmotic compressibility is a function of effective volume fraction. In addition, the deviation of the structure factor, S(0), of our microgel systems with the structure factor of hard spheres, S(PY)(0), exhibits a maximum at phi(eff) approximately 0.2. Beyond this point the osmotic de-swelling force exceeds the osmotic pressure inside the soft particles resulting in particle shrinkage. Good agreement was obtained when the structural properties of our microgel systems obtained from turbidimetric analysis and rheology measurements were compared. Therefore, a simple turbidimetric analysis of these model pH-responsive microgel systems permits a quantitative evaluation of factors governing particle osmotic compressibility.     

Excess molar volumes and isentropic compressibility of binary systems {trioctylmethylammonium bis(trifluoromethysulfonyl)imide + methanol or ethanol or 1-propanol} at different temperatures

This paper reports measurements of densities for the binary systems of an ionic liquid and an alkanol at T = (298.15, 303.15, and 313.15) K. The IL is trioctylmethylammonium bis(trifluoromethylsulfonyl)imide [OMA]⁺[Tf₂N]^? and the alkanols are methanol, or ethanol, or 1-propanol. The speed of sound at T = 298.15 K for the same binary systems was also measured. The excess molar volumes and the isentropic compressibilities for the above systems were then calculated from the experimental densities and the speed of sound, respectively. Redlich–Kister smoothing polynomial equation was used to fit the excess molar volume and the deviation in isentropic compressibility data. The partial molar volumes were determined from the Redlich–Kister coefficients. For all the systems studied, the excess molar volumes have both negative and positive values, while the deviations in isentropic compressibility are negative over the entire composition range.     

Densities,speeds of sound,excess volumes and viscosities of binary mixtures of mtbe with tetralin and decalin at 303.15 k

Measurements of densities, speeds of sound, excess volumes and viscosities of binary mixture of methyl tert-butyl ether with tetralin and decalin are reported at 303.15?K over the entire range of composition. Excess volumes are measured using batch dilatometer technique. Sound speeds are obtained using ultrasonic interferometer. Densities are computed from excess volume data. Isentropic compressibilities are derived from density and sound speed data. Speeds of sound are evaluated on the basis of Jacobson's free length theory and Schaff's collision factor theory. The predicted values are in good agreement with the experimental results. The viscosity data are analysed on the basis of corresponding states approach. Excess volumes and deviation in isentropic compressibilities are negative and deviation in viscosities are positive over the entire composition range. The experimental results are discussed in terms of possible molecular interactions between unlike molecules.     

Integral equation theory for symmetric nonadditive hard sphere mixtures

An integral equation theory is presented for the pair correlation functions and phase behavior of symmetric nonadditive hard sphere mixtures with hard sphere diameters given by sigma(A)(A)() = sigma(BB) = lambdad and sigma(AB) = d. This mixture exhibits a fluid-fluid phase separation into an A-rich phase and a B-rich phase at high densities. The theory incorporates, into the closure approximation, all terms that can be calculated exactly in the density expansion of the direct correlation functions. We find that the closure approximation developed in this work is accurate for the structure and phase behavior over the entire range of lambda, when compared to computer simulations, and is significantly more accurate than the previous theories.     

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.