半刚性链分子的统计热力学（Ⅰ）

用柔性连接点联系的刚棒模型代表半刚性链分子,对其进行统计热力学分析。半刚性链分子的混合自由能是克分子分数、溶质分子的长径比、链分子的有序度、刚柔性以及温度的函数。溶液体系具有极小浓度V_2~*。当V_2~*V_2~*是获得稳定的各向异性相的必要条件。V_2~*是链分子的长径比、刚柔性及温度的函数。V_2是溶液浓度。     

Prediction of thermodynamic properties of polymer solutions by a group-contribution method

The Flory–Huggins lattice-theory expression for solvent activity in a polymer-solution is commonly used to calculate the thermodynamic interaction parameter χ with the aid of experimental data from vapor pressure osmometry. This expression assumes that χ is independent of composition. However, experimental data for a variety of polymer-solvent mixtures indicate that χ exhibits an appreciable concentration dependence. A group contribution method, UNIFAC (UNIQUAC Functional-Group Activity Coefficients) incorporating the free-volume correction of Oishi and Prausnitz is used to predict the dependence of χ on solvent concentration. Agreement with previously reported experimental data is within 15%. Calculated values of χ obtained from the Flory–Huggins expression for solvent activity and from the corresponding Gibbs free energy of mixing (which does not assume that χ is independent of composition) are compared. Calculations based on the Gibbs free energy of mixing predict a somewhat larger value of χ relative to those based on solvent activity. The specific Gibbs free energy of mixing for polystyrene-solvent mixtures is calculated using the UNIFAC model, and is found to represent qualitatively the phase equilibrium behavior. Quantitative discrepancies are observed, however, for the polystyrene-acetone system in light of the actual experimental solubility reported by Suh and Clark (20). Most of the thermodynamic predictions for polymer-solvent systems investigated herein are correlated qualitatively with the relative mismatch between solubility parameters of both components.     

改进的聚合物溶液理论

在高分子溶液理论中引入Gibbs分布 ,用统计物理学方法重新推导出了聚合物溶液的热力学公式 .将高分子溶液的自由能和熵分三部分进行了计算 ,无热平动部分 ,无热构象部分和构象有热部分 .无热平动自由能和无热构象自由能分别等于Flory Huggins混合自由能公式的前两项 ,构象有热部分引入了Gibbs分布 ,考虑了链段 溶剂分子相互作用对高分子构象的影响 .在分子间的相互作用足够小时 ,又回到了FH公式     

Mixing Properties of Two-Dimensional Lattice Solutions of Amphiphiles

Lattice Monte Carlo simulations of two-dimensional amphiphile solutions are used to examine the accuracy of the mixing properties predicted by lattice theories such as the Flory-Huggins theory, random-solution approximation, and quasichemical approximation. The internal energy, Helmholtz free energy, and entropy of mixing have been calculated from the configurational energy data obtained from the simulations, and the effect of nonrandom mixing on these properties has been determined. The quasichemical approximation predicts the entropy and Helmholtz free energy of mixing accurately for the amphiphile solution, but fails to predict the energy of mixing, due to the presence of microphase (self-aggregation) separation, which is beyond the reach of the quasichemical approximation, a mean-field theory. Helmholtz free energy of mixing is predicted accurately, and the shielding of the solvophobic segments in the microphase leads to small energies of mixing compared to the entropy of mixing. Copyright 2000 Academic Press.     

Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations

A volume-translated Peng-Robinson (VTPR) equation of state (EOS) is developed in this study. Besides the two parameters in the original Peng-Robinson equation of state, a volume correction term is employed in the VTPR EOS. In this equation, the temperature dependence of the EOS energy parameter was regressed by an improved expression which yields better correlation of pure-fluid vapor pressures. The volume correction parameter is also correlated as a function of the reduced temperature. The VTPR EOS includes two optimally fitted parameters for each pure fluid. These parameters are reported for over 100 nonpolar and polar components. The VTPR EOS shows satisfactory results in calculating the vapor pressures and both the saturated vapor and liquid molar volumes. In comparison with other commonly used cubic EOS, the VTPR EOS presents better results, especially for the saturated liquid molar volumes of polar systems. VLE calculations on fluid mixtures were also studied in this work. Traditional van der Waals one-fluid mixing rules and other mixing models using excess free energy equations were employed in the new EOS. The VTPR EOS is comparable to other EOS in VLE calculations with various mixing rules, but yields better predictions on the molar volumes of liquid mixtures.     

Thermodynamics of mixing of polymers

A method of calculating free energy of mixing of two polymers has been proposed. From a study of the sorption of organic solvents vapour by different polymers and their mixtures, Gibbs free energy of mixing for polymer-solvent systems are calculated. The free energy of mixing of two polymers has been calculated by the method proposed. Heats of mixing of polymers have been measured with a Calvet type microcalorimeter. Entropy of mixing has been calculated. Stabilities of polymer-polymer systems have been discussed.     

Free energy of an inhomogeneous polymer–polymer–solvent system. II

A complete expression for the enthalpy of mixing of inhomogeneous polymer–polymer–solvent systems applicable for small as well as large concentration fluctuations has been developed. This is used to express the free energy of inhomogeneous polymer–polymer–solvent systems in an extended form of the Landau-Ginzburg functional. The gradient energy parameters obtained here are consistent with the published results. The free energy functional has been applied to develop a generalized continuity equation for spinodal decomposition in polymer–polymer systems. A linearized version of this continuity equation has been used to study the effect of the gradient terms on the dominant wavelength during spinodal decomposition.     

Thermodynamics of aqueous solutions containing poly (N-isopropylacrylamide)

Hydrogels undergo reversible and discontinuous volume changes in response to variation of solution conditions such as solvent composition, temperature, salt concentration, and pH. In this contribution we focus our attention on the experimental and theoretical investigation of these swelling equilibria of aqueous cross-linked poly (N-isopropylacrylamide) solutions as well as on the connected demixing behavior of the linear polymer dissolved in water. For the experimental study of the (liquid + liquid) equilibrium an alternative method based on refractive index measurements is suggested. In order to calculate the swelling behavior a model combining an expression for the Gibbs free energy of mixing with an expression for the elastic network is applied. As a model for the Gibbs free energy of mixing the UNIQUAC-approach and the Koningsveld–Kleintjens model are used. For the elastic network contribution again two different theories, namely the phantom network theory and the affine network theory, were applied. Whereas the type of network theory has only a small influence on the calculation results, the Gibbs free energy of mixing has a large impact. Using the UNIQUAC-approach the swelling equilibria can be correlated close to the experimental data, however, this model predicts a homogeneous mixture for linear polymer chains in water. In contrast to this situation the Koningsveld–Kleintjens model does a good job in calculating the swelling equilibria as well as the demixing curve, however, the adjustable parameter must be changed slightly.     

Modification of Particle Filled Polymers with High Energy Electrons Under In-Stationary Conditions of Melt Mixing

Summary: Polymer modification with high energy electrons is well-established in polymer industry and used for degradation, cross-linking, grafting, curing, and polymerization. These applications use local and temporal precise input of energy in order to generate excited atoms or molecules and ions for subsequent molecule changes via radical induced chemical reactions. In the present study, high energy electrons have been used to modify polyolefine (polyethylene and polypropylene) systems in presence of a grafting agent under stationary and in-stationary conditions. Polymer modification with high energy electrons under stationary conditions characterizes a process where required absorbed dose is applied to polymers in solid state and at room temperature. Polymer modification with high energy electrons under in-stationary conditions is a novel process where required absorbed dose is applied in molten state during melt mixing process. In this novel process, the penetration depth of electrons is limited to a part of mixing volume. The total mixing volume is modified due to the change of polymer mass within the penetration depth of electrons during mixing process. A 1.5 MeV electron accelerator has been directly coupled to a banbury mixing chamber in order to study this novel process. In comparison to the stationary process, the main differences are working at higher temperature, absence of any crystallinity, intensive macromolecular mobility as well as intensive mixing during dose application. The influence of both processes on mechanical properties and flame resistance of polymer composites is discussed.     

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.     

Excited state radiationless decay process with Duschinsky rotation effect: formalism and implementation

Duschinsky rotation effect is a simple and effective way to characterize the difference between the ground state and excited state potential energy surfaces. For complex molecules, harmonic oscillator model is still the practical way to describe the dynamics of excited states. Based on the first-order perturbation theory a la Fermi golden rule, the authors have applied the path integral of Gaussian type for the correlation function to derive an analytic formalism to calculate the internal conversion rate process with Duschinsky rotation effect being taken into account. The validity of their formalism is verified through comparison with previous work, both analytically for the case of neglecting Duschinsky rotation and numerically for the ethylene molecules with two-mode mixing. Their expression is derived for multimode mixing.     

Correlations for mixing energy in processes using Rushton turbine mixer

This study reports the research results on a mixing process using a stirred tank mixer under the action of a rotating magnetic field (RMF). Dimensionless correlations are proposed to predict the power consumption and mixing time for the mixing systems analysed. The results suggest that the mixing behaviour of the experimental set-ups tested may be assessed using the dimensionless mixing energy as the product of the power input and mixing time. In addition, an innovative strategy is proposed on the basis of the synergistic effect of the rotational Rushton turbine and the RMF generator. The values of the dimensionless energy thus obtained were used to compare the mixing process performed by the mixing devices tested. It is shown that the mixing process under the RMF action has significantly higher values of energy consumption than the conventional Rushton turbine. The total energy consumption for the mixing process performed by the RMF mixer may be reduced by concomitant use of a rotational agitator.     

Enhanced mixing of droplets during coalescence on a surface with a wettability gradient

We investigated the dynamics of head-on collisions between a moving droplet and a stationary droplet on a surface with a wettability gradient. The mixing of fluids is achieved passively through convective mass transfer caused by the release of surface energy during coalescence, and also through diffusive mass transfer. The coalescence dynamics were visualized with a high-speed camera; the internal flow patterns were resolved with measurement of micro-PIV (particle image velocimetry). The results show that the released surface energy creates a pair recirculation flow inside the merged droplet when the stationary droplet is placed near the gradient, whereas most released surface energy is converted into oscillation when the stationary droplet is far from the gradient. This distinction is attributed to the motion of the contact line during coalescence. The mixing of fluorescently labeled oligonucleotides in these two modes is revealed with confocal micro-laser induced fluorescence technique. The results of 3D scans demonstrate that the motion of the contact line during coalescence distributes the fluids in a complicated manner, thus beneficial for mixing. This mechanism of enhanced mixing is applicable also for platforms other than a surface with a wettability gradient; prospective applications include improving the mixing of biochemical fluids.     

Comparison of different mixing rules for prediction of density and residual internal energy of binary and ternary Lennard–Jones mixtures

Mixing rules are necessary when equations of state for pure fluids are used to calculate various thermodynamic properties of fluid mixtures. The well-known van der Waals one-fluid (vdW1) mixing rules are proved to be good ones and widely used in different equations of state. But vdW1 mixing rules are valid only when molecular size differences of components in a mixture are not very large. The vdW1 type density-dependent mixing rule proposed by Chen et al. [1] is superior for the prediction of pressure and vapor–liquid equilibria when components in the mixture have very different sizes. The extension of the mixing rule to chain-like molecules and heterosegment molecules was also made with good results. In this paper, the comparison of different mixing rules are carried out further for the prediction of the density and the residual internal energy for binary and ternary Lennard–Jones (LJ) mixtures with different molecular sizes and different molecular interaction energy parameters. The results show that the significant improvement for the prediction of densities is achieved with the new mixing rule [1], and that the modification of the mixing rule for the interaction energy parameter is also necessary for better prediction of the residual internal energy.     

Lattice treatment of thermodynamic properties of ring and linear polymer mixtures

Expressions for the entropy and free energy of mixing a solvent with a mixture of linear and cyclic polymer molecules are derived. The entropy of mixing is deduced from the number of ways of arranging on a honeycomb lattice a mixture of totally flexible molecules made up of N_R rings and N_C chains. An equation is obtained through the combination of two independent expressions for the number of ways of arranging rings and chains. The free energy of mixing is deduced from the entropy and the enthalpy of mixing, using two distinct interaction parameters for ring and for chain molecules. The chemical potentials for solvent, ring polymer, and linear polymer are derived from the free energy of mixing. These quantities are found to be functions of the mole fraction of rings in the polymer mixture. © 1993 John Wiley & Sons, Inc.     

Electrically conductive carbon nanofiber/polyethylene composite: effect of melt mixing conditions

The effect of melt mixing conditions on the morphological, rheological, electrical, electromagnetic interference (EMI) shielding effectiveness (SE), and tensile properties of 7.5 vol% vapor grown carbon nanofiber (VGCNF)/polyethylene composites were investigated. 7.5 vol% VGCNF was used because such loading is required to obtain a composite with satisfactory EMI SE. The composites were compounded by melt mixing and the parts were prepared by hot‐compression molding. The dispersion and distribution of nanofibers were enhanced by increasing the mixing energy, i.e. mixing time and/or rotation speed. The influence of mixing energy on the electrical and EMI SE properties was found to be a function of rotation speed, i.e. shear stress. For composites compounded at 20 rpm, increasing the mixing energy from 70 to 2300 J/ml decreased the EMI SE from 29.5 to 23.9 dB. However, for composites prepared at 100 rpm, increasing the mixing energy from 600 to 1700 J/ml decreased the EMI SE from 25.4 to 18.6 dB. No considerable influence on the yield stress, Young's modulus, and strain at break were found for different processing conditions. Copyright © 2009 John Wiley & Sons, Ltd.     

New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures

Huron, M.-J. and Vidal, J., 1979. New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures. Fluid Phase Equilibria, 3: 255-271.Good correlations of vapour-liquid equilibria can be achieved by applying the same two-parameter cubic equation of state to both phases. The results primarily depend on the method used for calculating parameters and, for mixtures, on the mixing rule. True parameters are the covolume b and the energy parameter a/b. For this latter one, deviations from a linear weighting rule are closely connected to the excess free energy at infinite pressure. Thus any mixing rule gives a model for the excess free energy, or any accepted models for this property can be used as mixing rules.From the above, an empirical polynomial mixing rule is used for data smoothing and evaluation, while for practical work a local composition model is used. The mixing rule thus obtained can be reduced to the classical quadratic rule for some easily predicted values of the interaction energies. For highly polar systems, it includes three adjustable parameters. Using literature data, the new mixing rule is applied, in the low and high pressure range, to binary mixtures with one or two polar compounds, giving good data correlation and sometimes avoiding false liquid-liquid immiscibility.     

A new molecular thermodynamic model for multicomponent Ising lattice

A new molecular thermodynamic model is developed for multicomponent Ising lattice based on a generalized nonrandom factor from binary system. Predictions of the nonrandom factor and the internal energy of mixing for ternary and quaternary systems match accurately with simulation results. Predictions of liquid-liquid phase equilibrium for ternary systems are in nearly perfect agreement with simulation results, and substantially improved from Flory-Huggins theory and the lattice-cluster theory. The model also satisfactorily correlates the experimental data of real ternary systems. The concise expression and the accuracy of the new model make it well suited for practical engineering applications.     

New parametrization method for dissipative particle dynamics

We introduce an improved method of parametrizing the Groot-Warren version of dissipative particle dynamics (DPD) by exploiting a correspondence between DPD and Scatchard-Hildebrand regular solution theory. The new parametrization scheme widens the realm of applicability of DPD by first removing the restriction of equal repulsive interactions between like beads, and second, by relating all conservative interactions between beads directly to cohesive energy densities. We establish the correspondence by deriving an expression for the Helmoltz free energy of mixing, obtaining a heat of mixing which is exactly the same form as that for a regular mixture (quadratic in the volume fraction) and an entropy of mixing which reduces to the ideal entropy of mixing for equal molar volumes. We equate the conservative interaction parameters in the DPD force law to the cohesive energy densities of the pure fluids, providing an alternative method of calculating the self-interaction parameters as well as a route to the cross interaction parameter. We validate the new parametrization by modeling the binary system SnI(4)SiCl(4), which displays liquid-liquid coexistence below an upper critical solution temperature around 140 degrees C. A series of DPD simulations were conducted at a set of temperatures ranging from 0 degrees C to above the experimental upper critical solution temperature using conservative parameters based on extrapolated experimental data. These simulations can be regarded as being equivalent to a quench from a high temperature to a lower one at constant volume. Our simulations recover the expected phase behavior ranging from solid-liquid coexistence to liquid-liquid coexistence and eventually leading to a homogeneous single phase system. The results yield a binodal curve in close agreement with the one predicted using regular solution theory, but, significantly, in closer agreement with actual solubility measurements.     

Water Solubilization in Mixed Nonionic Surfactants Microemulsions

The systems investigated were water/sucrose laurate/ethoxylated mono-di-glyceride/oleic phase. The oleic phase used first was the pure oils R (+)-limonene, isopropylmyristate, and caprylic-capric triglyceride; these oils were then mixed with ethanol at different mixing ratios (w/w). The total area of the one phase microemulsion region is dependent on the mixing ratios (w/w) of the mixed surfactants and that of the ethanol/oil. The largest microemulsion phase area formed with a surfactants mixing ratio (w/w) equals unity. For the systems where the oleic phase was a mixture of oil and ethanol, the total area of the monophasic microemulsion increases with the increase in the ethanol/oil mixing ratio (w/w). The Gibbs free energy of solubilization was estimated. It increases as the mixing ratio (w/w) of ethoxylated mono-di-glyceride/sucrose laurate increases and with the increase in the ethanol/oil mixing ratio (w/w). The Gibbs free energy of solubilization decreases with the increase in the water content in the water-in-oil microemulsions. The values of the Gibbs free energy of solubilization are higher for oil-in-water microemulsions compared to those of the water-in-oil microemulsions.