Generalized Flory–Huggins model for heat‐of‐mixing and phase‐behavior calculations of polymer–polymer mixtures

An extended and generalized Flory–Huggins model for calculating the heats of mixing and predicting the phase stability and spinodal diagrams of binary polymer–polymer mixtures is presented. In this model, the interaction parameter is considered to be a function of both temperature and composition. It is qualitatively shown that the proposed model can calculate the heats‐of‐mixing curves containing exothermic, endothermic, and S‐shaped or sigmoidal types and predict the spinodals, including the upper and lower critical solution temperatures, and closed‐loop miscibility regions. Using experimental results of analog calorimetry for four polymer mixtures of polystyrene/poly(vinyl chloride) (PS/PVC), polycarbonate (PC)/poly(ethylene adipate) (PEA), polystyrene/poly(vinyl acetate) (PS/PVAc), and ethylene vinyl acetate copolymer (EVA Co)/chlorinated polyethylene (CPE), the capabilities of the proposed functionality for the interaction parameter was studied. It is shown that this function can be used satisfactorily for the heat‐of‐mixing calculations and phase‐behavior predictions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1328–1340, 2000     

关联二元体系超额焓的改进模型

在已提出的二元体系超额焓分子热力学模型基础上,用体积分数表征溶液宏观组成以校正由于分子尺寸不同引起的分子之间特殊交互效应,推导出关联二元溶液超额焓的三参数改进模型.用近10年发表的有代表性的上百个二元非对称体系实验数据,主要是含不同分子尺寸、形状、结构组分的复杂体系实验数据,对所提超额焓改进模型进行了检验.结果表明,对含不同分子尺寸、形状、结构组分的非对称体系,改进模型的关联精度明显优于原模型.同时,在φ→0 或φ→1的极限条件下,改进模型同样成立.     

Thermodynamic properties of polymer solutions: effect of free volume fraction of solvent molecules

Knowledge about the thermodynamic properties of a polymer solution is essential to its applications. These properties are derived on the basis of a statistical mechanics approach by modifying the classic Flory–Huggins theory in this study. The analytical result derived is fitted to the available experimental data such as toluene–polystyrene and benzene–silicone polymer solutions in the literature, and its performance is satisfactory. We show that the inconsistency between the Flory–Huggins theory and experimental observations for many polymer solutions might arise from the negligence of the effects of the free volume fractions of solvent and polymer and the change in the disorientation entropy of polymer molecules.     

State diagram of phase transition temperatures and solvent‐induced recovery behavior of shape‐memory polymer

In this study we analyzed the phase and state transitions of shape‐memory polymers (SMPs)/solvent mixtures using the Flory–Huggins (FH) theory by extension of Vrentas and the Couchman–Karasz theory for glass transition, as well as Clausius–Clapeyron relation for melting transition. Using scaling relations of model parameters, we have obtained a theoretical prediction of state diagrams of the phase transition temperature and solvent‐induced recovery in SMPs. The inductive decrease in transition temperature is identified as the driving force for the solvent‐induced shape‐memory effect in SMPs Consequently, the thermodynamics of the polymer solution and the relaxation theory were employed to characterize the dependencies of shape recovery time on the FH parameter and the ratio of the molar volume of solute to solvent. With the estimated model parameters, we constructed the state diagram for SMP, which provides a powerful tool for design and analysis of phase transition temperatures and solvent‐induced recovery. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

CO2–CH4 phase equilibria on modified multi‐walled carbon nanotubes using Gibbs excess energy models based on vacancy solution theory

CO₂ and CH₄ equilibrium adsorption are predicted by Excess Gibbs energy models based on vacancy solution theory, for single and binary mixture on Multi‐Walled Carbon Nanotubes (MWCNTs) functioned by –NH₂ group. The experimental data of single gas adsorption isotherms were obtained at moderate pressures and temperatures using the volumetric method in a static gaseous set up. Firstly, the equilibrium pressures related to the adsorbed amounts, for single gases, were correlated on Wilson and Flory–Huggins activity coefficient equations based on vacancy solution theory and the model parameters were determined by fitting the model on the experimental data. Secondly, the pure component parameters were implemented in extended Wilson and Flory–Huggins equations for CO₂ and CH₄ mixture to predict the gas–solid phase equilibria. The results showed fairly good agreement between the experiments and both Gibbs models. Finally, the studied models were compared with the popular model of Extended Langmuir. The results revealed more accurately and precisely prediction of Wilson and Flory–Huggins against Langmuir model for mixed gas of CO₂ and CH₄ on MWCNT–NH₂. © 2011 Canadian Society for Chemical Engineering     

Study on segmental interaction parameter between ethylene and vinyl acetate monomer units of EVA by inverse gas chromatography

A method of analysis of inverse gas chromatography (IGC) measurements on copolymers to calculate segmental interaction parameters was proposed. Poly(ethylene‐co‐vinyl acetate) (EVA), poly(vinyl acetate) (PVAc), and dotriacontane (C32) were studied at 120°C with eight different probes of varying polarities by IGC. The value of the segmental interaction parameter between ethylene units and vinyl acetate units in EVA was found to be 1.18, which is consistent with the literature values. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 693–698, 1999     

Development of a predictive model for polymer/solvent diffusion coefficient calculations

A new calculation procedure for free‐volume parameters is considered in this work by using viscosity prediction methods and the Levenberg‐Marquardt calculation scheme. All parameters used in the Vrentas–Duda free‐volume theory can be estimated from pure component properties. The prediction results are compared with experimental data for some polymer/solvent systems. The diffusion coefficient calculated by Vrentas–Duda theory can be used in the modeling of membrane separation processes. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

基于COSMO-RS模型的分离油酚混合物的离子液体萃取剂筛选

低温煤焦油中酚类化合物的分离对其充分利用具有重要意义。基于COSMO-RS模型,以间甲酚和异丙苯作为模型化合物,研究了离子液体在分离油酚体系中的应用;利用Turbomole软件建立了包含27种离子液体阴离子和48种离子液体阳离子的s-图谱数据库,结合COSMOtherm软件对组成的1296种离子液体进行筛选,探讨了阴阳离子对间甲酚分离效果的影响,并对筛选得到适宜的离子液体进行液液相平衡实验验证。结果表明,离子液体阴离子对间甲酚分离效果影响较大,以Cl^-和CH₃COO^-为阴离子的离子液体与间甲酚之间具有较强的氢键相互作用,因此具有较好的分离效果;阳离子对间甲酚分离效果影响较小,碳链或支链的增加能适当提高离子液体对间甲酚的分离效果。实验得到的bmimOAc、bmimCl、emimOAc、TPAC四种离子液体-间甲酚-异丙苯的液液相平衡数据表明,四种离子液体对间甲酚均具有较大的分配系数和选择性,且萃取分离效果的顺序为：emimOAc > bmimOAc > TPAC > bmimCl,与COSMO-RS模拟筛选得到的结果一致,表明筛选具有较高的准确性。     

Critical micelle concentration of an ammonium salt through DPD simulations using COSMO‐RS–based interaction parameters

In order to determine the critical micelle concentration (CMC) of aqueous dodecyltrimethylammonium chloride (DTAC), a screening of the DTAC gathering process at different molalities by performing dissipative particle dynamics (DPD) simulations over mesomolecules whose beads interact via repulsive conservative forces was performed. Conductor‐like screening model for real solvent quantum methodology, applied to molecular segments that describe the DTAC chemistry and were mapped onto the DPD beads, allows us the computing of activity coefficients at infinite dilution to obtain thermodynamic Flory–Huggins interaction parameters, from which we calculated the maxima repulsive conservative forces, that is, the DPD interaction parameters. Results indicate that at room temperature the CMC is 0.0217 mol/kg, the aggregation number ranges from 46 to 54 molecules, and the aggregate radius varies from 19.58 to 22.02 Å; all values are in excellent agreement with literature reported experimental ones of 0.0213 mol/kg, 47 5 molecules, and 20.1 Å. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4413–4423, 2013     

Glass‐transition and melting behavior of poly(ethylene terephthalate)/poly(ethylene 2,6‐naphthalate) blends

The glass‐transition temperatures and melting behaviors of poly(ethylene terephthalate)/poly(ethylene 2,6‐naphthalate) (PET/PEN) blends were studied. Two blend systems were used for this work, with PET and PEN of different grades. It was found that T_g increases almost linearly with blend composition. Both the Gibbs–DiMarzio equation and the Fox equation fit experimental data very well, indicating copolymer‐like behavior of the blend systems. Multiple melting peaks were observed for all blend samples as well as for PET and PEN. The equilibrium melting point was obtained using the Hoffman–Weeks method. The melting points of PET and PEN were depressed as a result of the formation of miscible blends and copolymers. The Flory–Huggins theory was used to study the melting‐point depression for the blend system, and the Nishi–Wang equation was used to calculate the interaction parameter (χ₁₂). The calculated χ₁₂ is a small negative number, indicating the formation of thermodynamically stable, miscible blends. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 11–22, 2001     

High-density polyethylene (HDPE) hollow fiber membrane via thermally induced phase separation. I. Phase separation behaviors of HDPE–liquid paraffin (LP) blends and its influence on the morphology of the membrane

Phase separation behaviors of the blends that consist of high-density polyethylene (HDPE) and LP was investigated by means of thermal analysis. The miscibility of the two components was evaluated in terms of the Flory–Huggins interaction parameter, determined from the Hoffman–Weeks plot, gave a value of 0.36. This leads us to a conclusion that this blend system is applicable to the preparation of microporous hollow fiber membrane by melt spinning of the blend. The homogeneous blends in the molten state become heterogeneous systems to yield microporous HDPE membranes in the course of cooling due to thermally induced phase separation. The influence of the phase separation on the membrane morphology was also discussed. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 2135–2142, 1999     

随机共聚高分子凝胶溶胀和体积相变行为的分子热力学模型

基于随机共聚高分子溶液的格子模型,建立了一个可以描述温度和pH双重响应的随机共聚高分子凝胶溶胀行为的分子热力学模型。该模型考虑了溶剂与不同高分子的混合、高分子网络的弹性以及包含小分子离子在凝胶内外分布的Donnan平衡和聚合物网络上的大分子离子及其反离子之间的静电相互作用的离子影响对化学势的贡献。与其他模型不同的是,该模型还考虑了高分子的组成f。该模型有两类可调的模型参数,一类是溶剂与不同高分子网络之间的相互作用能参数ε槇ij,另一类是高分子网络自身的尺寸参数Mc。研究结果表明,该分子热力学模型只需较少的模型参数就可较好地描述温度和pH双重敏感的随机共聚高分子凝胶的溶胀行为。     

基于COSMO-SAC模型的离子液体萃取剂的选择

COSMO-SAC模型是计算无限稀释活度因子的一种有效方法,只需知道分子结构,即可进行有机物或离子液体的无限稀释活度因子计算。COSMO-SAC模型中最耗时的计算步骤是产生σ-图谱(σ-profile)的量子化学计算。利用Materials Studio软件中的DMol3模块,建立了包含32种离子液体阴离子和191种离子液体阳离子的σ-图谱数据库。利用σ-图谱数据库和COSMO-SAC模型,针对离子液体液液萃取过程,提出了离子液体萃取剂的计算机辅助分子设计方法。以乙醇-乙酸乙酯体系为研究对象,选择了适宜的离子液体萃取剂,采用乙醇-乙酸乙酯-离子液体三元体系的液液平衡文献数据进行了验证。     

Development of activity coefficient model based on COSMO method for prediction of solubilities of solid solutes in supercritical carbon dioxide

A COSMO base activity coefficient model was newly developed to predict the solubilities of solid solutes in supercritical carbon dioxide. This activity coefficient model describes that the system is composed of the surface segments on the solvent molecule and vacancy unlike the conventional model based on COSMO method. The density change of supercritical fluid can be represented by the change of the surface area of the vacancy. This prediction model is referred to “COSMO-vac (vacancy)” model. The solubilities of 16 pharmaceuticals in supercritical carbon dioxide were predicted by COSMO-vac model. The averaged deviations between the logarithmic experimental and predicted results are smaller than unity. Furthermore, the predicted results for the solutes composed of only C, H and O atoms are better than those for the solutes including the other atoms. The percentage of the predicted results within the order of the experimental data at the pressure over 15 MPa is higher than that at the pressures below 15 MPa.     

Effect of solvent on electrical conductivity and gas sensitivity of PEDOT: PSS polymer composite films

Poly(3,4‐ethylenedioxythiophene)/poly(styrene sulfonate) (PEDOT:PSS) was blended with polyethylene oxide (PEO) and polyvinyl alcohol (PVA) and composite film was cast. Additional solvents of dimethyl sulfoxide (DMSO) and ethylene glycol (EG) were mixed and their effects on electrical conductivity and structural changes were investigated. The electrical conductivity increased in response to the additional solvent, leading to an increase in the PEDOT ratio relative to the control. PEDOT:PSS/PEO composite film had a much higher electrical conductivity than PEDOT:PSS/PVA. When blended with PEO, the quinoid structure revealed by Raman spectroscopy increased relative to the PVA‐blended case, indicating higher electrical conductivity. The current–voltage response and gas sensitivity showed much better performance in PEDOT:PSS/PEO/DMSO composite film. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42628.     

A new model for correlation and prediction of equilibrium CO2 solubility in N‐methyl‐4‐piperidinol solvent

In this work, the equilibrium CO₂ solubility in the aqueous tertiary amine, N‐methyl‐4‐piperidinol (MPDL) was measured over a range of temperatures, CO₂ partial pressures and amine concentrations. The dissociation constant of the MPDL solution was determined as well. A new thermodynamic model was developed to predict the equilibrium CO₂ solubility in the MPDL‐H₂O‐CO₂ system. This model, equipped with the correction factor (C_f), can give reasonable prediction with an average absolute deviation of 2.0%, and performs better than other models (i.e., KE model, Li‐Shen model, and Hu‐Chakma). The second‐order reaction rate constant (k₂) of MPDL and the heat of CO₂ absorption (–ΔH_abs) into aqueous MPDL solutions were evaluated as well. Based on the comparison with some conventional amines, MPDL revealed a high‐equilibrium CO₂ loading, reasonably fast absorption rate when compared with other tertiary amines, and a low energy requirement for regeneration. It may, therefore, be considered to be an alternative solvent for CO₂ capture. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3395–3403, 2017     

Prediction of vapor–liquid equilibrium for polymer solutions based on the COSMO‐SAC model

To extend the application of the COSMO‐SAC model to phase‐equilibrium calculations of polymer solutions, a new strategy for estimating the charge‐density profile, the cavity volume and the cavity surface area of polymer molecules is proposed by finding reasonable parameters for the corresponding repeating structure units. The molecular parameters for polymers are obtained by summing up the corresponding COSMO calculated values of the repeating units calculated by the algorithms of DMol3 (a density functional theory) or MOPAC (a semi‐empirical method). Combining with the COSMO‐SAC model, the activities and equilibrium pressures for several typical polymer solutions are satisfactorily predicted indicating that the proposed method can be used for the prediction of vapor–liquid equilibrium of polymer solutions. It was also found that both DMol3 and MOPAC can be used though the results obtained from them are slightly different. The results in this paper show that the method proposed has the potential to predict other phase‐equilibrium properties of polymer systems. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Development of a mathematical model for studying bioethanol–water separation using hydrophilic polyetherimide membrane

An essentially predictive mathematical model was developed to simulate pervaporation process. The group contribution method UNIFAC was used for calculating the upstream activity coefficients. The diffusion coefficient in the membrane was predicted using free‐volume theory. Free‐volume parameters were determined with viscosity and temperature data, and the binary interaction solvent–polymer parameter was calculated by a group‐contribution lattice‐fluid equation of state (GCLF‐EOS). A simulator named PERVAP was developed applying the mathematical model. Pervaporation process was simulated for separating bioethanol–water through polyetherimide membrane. The simulated results were validated using experimental data of bioethanol/water separation through polyetherimide membrane. The model presented a satisfactory performance compared to experimental data. Related to the simulation of the studied separation, a 99% molar enriched bioethanol stream was obtained with a recovery of 94%. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Coiling/uncoiling behaviour of sodium polystyrenesulfonate in 2‐ethoxyethanol–water mixed solvent media as probed using viscometry

Precise measurements of the viscosities of solutions of sodium polystyrenesulfonate in water and in 2‐ethoxyethanol–water mixtures containing varying amounts of 2‐ethoxyethanol have been performed at 308.15, 313.15, 318.15 and 323.15 K. The intramolecular contributions to the reduced viscosities of the polyelectrolyte solutions were obtained through isoionic dilution maintaining the total ionic strengths of the solutions at polyelectrolyte concentrations of 0.0033, 0.0054 and 0.0080 eq L^?1 with sodium chloride. The Huggins constants were also obtained from the experimental data. The influences of the medium and the temperature on the intramolecular contributions to the reduced viscosities as well as on the Huggins constants have been interpreted from the points of view of the conformational characteristics and polyelectrolyte–solvent and polyelectrolyte–polyelectrolyte interactions prevailing in the polyelectrolyte solutions under investigation. Polyion chains were found to coil upon addition of 2‐ethoxyethanol to water or upon an increase of temperature. Thermodynamic affinities for polyelectrolyte–solvent and polyelectrolyte–polyelectrolyte interactions were found to depend greatly on the medium. © 2014 Society of Chemical Industry