Free Volume Theory Research Articles

Generalized viscosity model based on free-volume theory for amino acid salt solutions as green CO2 capture solvents

Green processes that use environmentally friendly materials have gained significant attention, in particular in the fuel processing section. Alkaline salts of natural amino acids (NAAs), known as NAA salt solutions (NAASs), have significant potential to replace conventional solvents for achieving greener CO2 capture. Thermophysical properties, including the viscosity of NAASs, are essential for developing processes and their optimization. This study aims to develop a generalized theoretical model derived from free-volume theory (FVT) for estimating the viscosity of NAASs. Four different cases for parameter regression were applied to the largest viscosity databank investigated thus far (19 NAAs, three alkaline compounds, 29 NAASs, and 2039 data points), and the performance of the model using the parameters from the cases was evaluated. The highest accuracy was achieved (average absolute relative deviation percentage (AARD) = 1.54 %, average relative deviation percentage (ARD) = 0.09 %, R-squared (R2) = 0.9969) in the concentration- and solution-specific cases, but many parameters were required for the whole databank. In contrast, the most general case using global parameters resulted in the least number of parameters (six adjustable parameters) and showed reasonable accuracy (AARD = 10.42 %). A specific case in which the model parameters were obtained from each NAAS with a simple modification of the barrier energy parameter (α) yielded a higher accuracy (AARD = 4.12 %, ARD = 0.53 %, R2 = 0.9606) with a smaller number of parameters for the entire databank. The results demonstrated that the FVT is capable of modeling the viscosities of NAASs and can thus be employed for the simulation and optimization of thermophysical properties.

Viscosity Modeling of Pure Alcohols Based on the Significant Structure Theory and a Cubic Equation of State

In this study, a previously developed model [Macías-Salinas, R.; Viscosity Modelling of Reservoir Fluids over Wide Temperature and Pressure Ranges. Chem. Eng. Trans. 2013, 32, 1573.] based on the significant structure theory (SST) in conjunction with the Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) cubic equations of state (CEoS) was modified for the accurate correlation of the viscosity of 25 pure alcohols from methanol to n-dodecanol, branched alcohols, diols, and triols at temperatures from 0 to 272 °C and pressures from 0.98 to 4860 bar, obtaining two final model versions (SST-SRK and SST-PR) valid for both gas and liquid phases in the case of methanol, ethanol, 2-propanol, and 2-methyl-1-propanol and only in liquid phase for the rest of alcohols considered here. In regard to n-decanol, n-undecanol, n-dodecanol, 1,3-propanediol, and 1,4-butanediol, they were studied at different temperatures but only at a pressure of 1 bar. The resulting model versions were correlated with 2418 dynamic viscosity experimental data, obtaining overall values of average absolute deviation (AAD), statistical bias, and absolute maximum deviation (AMD) of 1.4808, 0.0503, and 7.9217%, respectively, with the SST-SRK approach and 1.4799, 0.0476, and 7.4515%, respectively, with the SST-PR approach. The two modeling approaches were compared with the friction theory [Zéberg-Mikkelsen, C. K.; Viscosity Modeling of Associating Fluids Based on the Friction Theory: Pure Alcohols. Fluid Phase Equilib. 2002, 194–197, 1191.] (FT) and free volume theory [Allal, A.; A New Free Volume Model for Dynamic Viscosity and Density of Dense Fluids Versus Pressure and Temperature. Phys. Chem. Liq. 2001, 39, 1.] (FVT), using the same experimental viscosity database of this work under the same conditions of temperature and pressure, obtaining more accurate results with the SST approach for most of the modeled alcohols.

A thermodynamic study on relationship between gas separation properties and microstructure of polyurethane membranes

The lattice fluid (LF) thermodynamic model and extended Vrentas’ free-volume (E-VSD) theory were coupled to study the gas separation properties of the linear thermoplastic polyurethane (TPU) membranes with different chemical structures by analyzing their microstructures. A set of characteristic parameters were extracted using the repeating unit of the TPU samples and led to prediction of reliable polymer densities (AARD < 6%) and gas solubilities. The viscoelastic parameters, which were obtained from the DMTA analysis, were also estimated the gas diffusion vs. temperature, precisely. The degree of microphase mixing based on the DSC analysis was in order: TPU-1 (4.84 wt%) < TPU-2 (14.16 wt%) < TPU-3 (19.92 wt%). It was found that the TPU-1 membrane had the highest degree of crystallinity, but showed higher gas solubilities and permeabilities because this membrane has the least degree of microphase mixing. These values, in combination with the gas permeation results, showed that the content of the hard segment along with the degree of microphase mixing and other microstructural parameters like crystallinity were the determinative parameters.

Modified Free Volume Theory for Self-Diffusion of Small Molecules in Amorphous Polymers

Diffusion of small molecules in amorphous polymers near the glass transition is a topic of interest for a variety of technological applications. Within this study, the free volume theory (FVT) of Vrentas and Duda as a predictive tool for estimating self-diffusion coefficients is extended by suggesting modifications to certain aspects of this model. These modifications encompass the description of the free volume of the mixture, the viscosity–diffusivity interplay, and the energetics of the diffusion. To support the derived modifications, they are exercised on the diffusion of three active ingredients in polyvinylpyrrolidone. The results are partly compared with experimental data based on dielectric spectroscopy as well as secondary ion mass spectrometry (adopted from the literature). Concerning the specific hole free volume, an approach for describing nonideal mixtures achieved by means of estimating the mixtures’ Vogel temperature at each composition is proposed. Moreover, a new fragility-dependent parameter, ξ1, is introduced into the main equation of the FVT model, which brings the model in harmony with the fractional Stokes–Einstein (F-SE) relation at the pure diffusant limit, hence improving its predictions at higher diffusant mass fractions. Furthermore, the F-SE equation is employed to describe the pre-exponential factor as well as the effective molar jump energy at the pure diffusant extreme. The resulting molar energy is subsequently combined with an empirically obtained effective energy at the pure polymer limit and weighted according to a quadratic expression analogous to the cohesive energy of a solution. In conclusion, the modified FVT model discussed in this study presents a fully predictive platform for describing diffusion in polymers and offers an extended temperature and compositional applicability range compared to the original version of FVT. This model is expected to be applicable to the diffusion of small molecules, which are commensurate in size with typical segments of the polymer.

Role of heating rate on the triple-shape memory effect of amorphous polymers: A cooperative thermodynamic model

The triple-shape memory effect (triple-SME) in amorphous polymers arises from the staged structural rearrangement of their macromolecular chains upon heating. However, the working mechanism behind the heating-rate dependence of the triple-SME in shape memory polymers (SMPs) is not well understood due to the complex compositions. Herein, we adopt the extended free volume theory to investigate the effect of local vibration and structural rearrangement of macromolecular chains on the shape memory behavior of SMPs. By introducing the phase transition theory, the dependences of the glass transition, thermomechanical behavior, and triple-shape recovery behavior of SMPs on thermal history are then discussed. The accumulation of the remote free volume upon heating is identified as the driving force for the SME in SMPs. The effectiveness of the proposed model is further evaluated by applying it to predict the shape memory behavior of epoxy SMPs with dual- and triple-SMEs at various heating rates. This study is expected to provide a practical methodology for understanding the working mechanism of triple-SME in amorphous polymers.

Computational Strategies for Entropy Modeling in Chemical Processes.

Computational simulations of entropy are important in understanding the thermodynamic forces that drive chemical reactions on a molecular scale. In recent years, various algorithms have been developed and applied in conjunction with molecular modeling techniques to evaluate the change of entropy in solvation, hydrophobic interactions, and chemical reactions. The aim of this review is to highlight four specific computational entropy calculation methods: normal mode analysis, free volume theory, two-phase thermodynamics, and configurational entropy modeling. The technical aspects, applications, and limitations of each method will be discussed in detail.

Analysis of diffusion of plant metabolites from polyethylene glycol hydrogels using free volume theory.

The present work aims to comprehensively analyze the diffusion of plant metabolites from the polyethylene glycol (PEG) hydrogels for controlled release applications. For this study, a mathematical model based on free volume theory has been utilized to simulate the diffusion of low molecular weight plant metabolites. The results demonstrate that the mesh size of the crosslinked network, thereby the diffusion coefficient of the natural compound can be computed using the current framework. The proposed model has also been validated using the experimental data. The diffusion period has been observed to vary within a wide range of 3.42 h for Cinnamaldehyde to 49.25 h for Grandinin. An empirical parametric relationship between the diffusion time and molecular weight of both the hydrogels and natural compounds is established. It appears that the reported modeling approach will be clinically useful for improving the design of the sustained drug delivery systems.

Prediction of the viscosity of natural gas at high temperature and high pressure using free-volume theory and entropy scaling

Eighteen models based on two equations of state (EoS), three viscosity models, and four mixing rules were constructed to predict the viscosities of natural gases at high temperature and high pressure (HTHP) conditions. For pure substances, the parameters of free volume (FV) and entropy scaling (ES) models were found to scale with molecular weight, which indicates that the ordered behavior of parameters of Peng-Robinson (PR) and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) propagates to the behavior of parameters of viscosity model. Predicting the viscosities of natural gases showed that the FV and ES models respectively combined with MIX4 and MIX2 mixing rules produced the best accuracy. Moreover, the FV models were more accurate for predicting the viscosities of natural gases than ES models at HTHP conditions, while the ES models were superior to PRFT models. The average absolute relative deviations of the best accurate three models, i.e., PC-SAFT-FV-MIX4, tPR-FV-MIX4, and PC-SAFT-ES-MIX2, were 5.66%, 6.27%, and 6.50%, respectively, which was available for industrial production. Compared with the existing industrial models (corresponding states theory and LBC), the proposed three models were more accurate for modeling the viscosity of natural gas, including gas condensate.

Interfacial Adsorption Kinetics of Methane in Microporous Kerogen.

Rapid declines in unconventional shale production arise from the poorly understood interplay between gas transport and adsorption processes in microporous organic rock. Here, we use high-fidelity molecular dynamics (MD) simulations to resolve the time-varying adsorption of methane gas in realistic organic rock samples, known as kerogen. The kerogen samples derive from various geological shale fields with porosities ranging between 20% and 50%. We propose a kinetics sorption model based on a generalized solution of diffusive transport inside a nanopore to describe the adsorption kinetics in kerogen, which gives excellent fits with all our MD results, and we demonstrate it scales with the square of the length of kerogen. The MD adsorption time constants for all samples are compared with a simplified theoretical model, which we derive from the Langmuir isotherm for adsorption capacitance and the free-volume theory for steady, highly confined bulk transport. While the agreement with the MD results is qualitatively very good, it reveals that, in the limit of low porosity, the diffusive transport term dominates the characteristic time scale of adsorption, while the adsorption capacitance becomes important for higher pressures. This work provides the first data set for adsorption kinetics of methane in kerogen, a validated model to accurately describe this process, and a qualitative model that links adsorption capacitance and transport with the adsorption kinetics. Furthermore, this work paves the way to upscale interfacial adsorption processes to the next scale of gas transport simulations in mesopores and macropores of shale reservoirs.

Water Sorption in Rubbery and Glassy Polymers, Nifedipine, and Their ASDs.

Polymers like poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA) or hydroxypropyl methylcellulose acetate succinate (HPMCAS) are commonly used as a matrix for amorphous solid dispersions (ASDs) to enhance the bioavailability of the active pharmaceutical ingredients (APIs). The stability of ASDs is strongly influenced by the water sorption in the ASD from the surrounding air. In this work, the water sorption in the neat polymers PVPVA and HPMCAS, in the neat API nifedipine (NIF), and in their ASDs of different drug loads was measured above and below the glass-transition temperature. The equilibrium water sorption was predicted using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) combined with the Non-Equilibrium Thermodynamics of Glassy Polymers (NET-GP).The water-sorption kinetics were modeled using the Maxwell-Stefan approach whereas the thermodynamic driving force was calculated using PC-SAFT and NET-GP. The water diffusion coefficients in the polymers, NIF, or ASDs were determined using the Free-Volume Theory. Using the water-sorption kinetics of the pure polymers and of NIF, the water-sorption kinetics of the ASDs were successfully predicted, thus providing the water diffusion coefficients in the ASD as a function of relative humidity and of the water concentration in polymers or ASDs.

A new group contribution model for prediction liquid hydrocarbon viscosity based on free-volume theory

In this paper a group contribution model for predicting the viscosity values of n-alkanes and iso-alkanes in the liquid phase based on Free-Volume Theory was developed. A database with 2129 experimental data with a temperature range up to 573.15 K and a pressure range up to 4000 bar was used to develop the model. The total weighted average percentage error is 4.894%. The model was tested on the next 472 experimental data with a temperature range up to 564.15 K and a pressure range up to 2019 bar and a mean percentage error that was obtained is 5.155%.

Diffusion Behavior of VOC Molecules in Polyvinyl Chloride Investigated by Molecular Dynamics Simulation

Due to the threats posed by many volatile organic compounds (VOCs) to human health in indoor spaces via air, the mass transfer characteristics of VOCs are of critical importance to the study of their mechanism and control. As a significant part of the mass transfer process, diffusion widely exists in emissions from floors (e.g., PVC floors) and in sorption in porous materials. Molecular simulation studies by can provide unparalleled insights into the molecular mechanisms of VOCs. We construct the detailed atomistic structures of PVC blend membranes to investigate the diffusion behavior of VOC molecules (n-hexane) in PVC by molecular dynamics (MD). The variation in the diffusion coefficient of n-hexane in PVC with respect to temperature is in line with Arrhenius' law. The effect of temperature on the diffusion mechanism was investigated from the perspectives of free volume, cavity distribution and polymer chain mobility. It was found that the relationships between the diffusion coefficients of n-hexane in the polymer and the inverse fractional free volume are exponential and agree well with the free volume theory. Hopefully, this study will offer quantitative insights into the mass transport phenomena of VOCs within polymeric materials.

A predictive procedure to model gas transport and intrinsic properties of rubbery polymeric membranes using equilibrium thermodynamics and free volume theory

A predictive procedure to model gas transport and intrinsic properties of rubbery polymeric membranes using equilibrium thermodynamics and free volume theory

Modelling strategy for tailorable mechanics and thermochemically driven shape memory effect in amorphous polymers

Thermochemically responsive shape-memory polymers (SMPs) with biocompatibility and variable stiffness have shown great potential in biomedical applications. However, it is difficult to characterize the relaxation behavior and visco-elastoplastic deformation of this kind of SMPs due to the complex interactions between polymer segments and solvent molecules. Herein, a thermo-chemo-mechanical coupling model was proposed to predict the shape-memory behavior and thermomechanical properties of SMPs at different solvent volume fractions and temperatures. By combining the Vrentas–Duta free volume theory and the Flory-Huggins theory, the effect of free volume change on the Gibbs free energy, chemical potential, thermal expansion coefficient, and relaxation time of SMPs was investigated. Subsequently, these functions were substituted into the Maxwell and Boyce models to characterize the visco-elastoplastic mechanical behavior of thermochemically responsive SMPs under large deformation. Based on the phase transition model, the chemical plasticizing effect of solvent molecules on the glass transition temperature, shape-recovery strain, and yield strength of SMPs was further investigated. The numerical results are in good agreement with the experimental results. The proposed model is expected to provide theoretical guidance for designing SMPs with tailorable mechanics.

Lithium-Ion and Chloride-Ion Transfer in Chiral and Racemic 3-Hydroxyquinuclidinium Perchlorate: Influence of Defects and a Mixed Plastic Crystal Matrix

Organic ionic plastic crystals (OIPCs) are promising solid electrolytes. To observe the effect of defects and a mixed OIPC matrix on ionic conductivity, lithium-ion transfer and chloride-ion transfer in chiral and racemic (+/±)-3-hydroxyquinuclidinium perchlorate plastic crystals were studied. The pure chiral material and racemic mixture and their corresponding doped mixtures showed different thermal behaviors. Powder X-ray diffraction revealed that the cubic crystal structure appeared in both the high-temperature phase of the pure chiral material and the whole temperature range for the racemic system. Solid-state nuclear magnetic resonance spectra indicated the possible ion mobility of the two undoped matrices. The lithium-ion conductivity in the chiral material (above −10 °C) and racemic mixture (in the whole temperature region) increased 2.5–3 orders of magnitude, while the chloride-ion conductivity in the chiral material only increased obviously above 50 °C. Positron annihilation lifetime spectroscopy demonstrated the dependence of ionic conductivity on defect volumes of the pure chiral material and its doped mixtures, and the defects of the doped mixtures expanded largely. The ionic conductivity and defect volume of the doped mixtures containing lithium ions and chloride ions qualitatively obeyed the Cohen–Turnbull free volume theory.

A time-temperature-ageing shift model for bitumen and asphalt mixtures based on free volume theory

ABSTRACT This paper aims to develop a general form of the time-temperature-ageing shift model for bituminous materials based on free volume theory and validate its application in the Finite Element (FE) modelling for predicting aged asphalt mixtures’ mechanical responses. The frequency sweep, dynamic modulus, and Fourier Transform Infrared Spectroscopy (FTIR) tests were used to validate the proposed time-temperature-ageing shift model. A generalised Maxwell model incorporating the proposed shift model of asphalt mixtures was used to predict the mechanical responses of aged asphalt mixtures using FE modelling, verified via laboratory cyclic load tests. Results indicate that the time-temperature-ageing shift function can model the complex shear modulus and dynamic modulus master curves of bituminous materials, addressing the modulus dependency of temperature and ageing. Temperature dominates the modulus change of bituminous materials in the ageing process. The coefficients of the time-temperature-ageing shift model have clear physical meanings and can potentially quantify the effects of asphalt mixtures’ air voids on their temperature and ageing susceptibilities. The time-temperature-ageing shift model can be incorporated into the constitutive relations of the FE model to effectively couple and efficiently predict the effects of temperature and ageing on the mechanical responses of aged asphalt mixtures.

Binary Diffusion Coefficients for Short Chain Alcohols in Supercritical Carbon Dioxide—Experimental and Predictive Correlations

Experimental binary diffusion coefficients for short-chain alcohols in supercritical carbon dioxide were measured using the Taylor dispersion technique in a temperature range of 306.15 K to 331.15 K and along the 10.5 MPa isobar. The obtained diffusion coefficients were in the order of 10-8 m2 s-1. The dependence of D on temperature and solvent density was examined together with the influence of molecular size. Some classic correlation models based on the hydrodynamic and free volume theory were used to estimate the diffusion coefficients in supercritical carbon dioxide. Predicted values were generally overestimated in comparison with experimental ones and correlations were shown to be valid only in high-density regions.

CO2 solubility and diffusivity in poly(vinyl acetate) studied using the PC-SAFT and free volume theory

Poly (vinyl acetate) (PVAc) is a polymer used in various industrial applications, and the quantitative determination of CO2 solubility and diffusion coefficient is important for designing foaming processes involving supercritical CO2. In this study, these two physical properties were obtained experimentally and theoretically using the perturbed chain–statistical associating fluid theory (PC–SAFT) and free volume theory at temperatures between 353 K and 473 K and pressures up to 20 MPa. CO2 solubility increased almost linearly with pressure and could be correlated with the PC–SAFT equation of state and binary interaction parameter kij within the average relative deviation of 2.1%. Furthermore, the fitted plot of kij versus temperature can be used to predict CO2 solubility at lower temperatures. The diffusion coefficient of CO2 in PVAc was experimentally determined from CO2 sorption curves. Its value increased with increasing CO2 solubility and temperature, which was consistent with the free volume theory.

The change of glass transition temperature under general stress state in amorphous materials

The phenomenon of the change in glass transition temperature (Tg) upon externally applied stresses in amorphous materials has been known for a long time. However, most of the existing works focus on the effects of hydrostatic stress state, while the effect of a general stress state on glass transition behaviors remains largely unknown. In this work, molecular dynamics (MD) simulations are first performed on typical amorphous polymers and alloys to probe the change of Tg under different stress states. It is found that Tg changes linearly with pure hydrostatic stress, while under shear stress, Tg changes nonlinearly with the stress magnitude. This further leads to an asymmetric change in Tg under uniaxial tension and compression loading conditions. Based on the above observations, a theoretical model based on the free volume theory and Eyring model is proposed to quantify the change of Tg under general stress states. Comparison with simulation results and existing experimental data reported in the literature demonstrate that the theoretical model can capture the stress dependence of Tg in amorphous materials. Potential applications in tuning Tg through external stress and the sensitivity of Tg to hydrostatic and shear stresses for different amorphous materials are subsequently discussed. The current work reveals the dependence of Tg on general stress states, pointing out potential routes to tune the mechanical properties of amorphous materials.

Temperature dependence of volatile organic compound emissions from surface coatings: Inter-species difference observed in real indoor environments and mechanistic understanding

Coatings often cover two-thirds of the surfaces in indoor environments and represent important sources of indoor volatile organic compounds (VOCs). Temperature is known to affect VOC emission rates from coatings, yet inter-species difference in the temperature dependence still needs to be understood. Based on time-resolved VOC measurements in an indoor air campaign conducted in residences in Beijing, China, we identified dibasic ester (DBE), a solvent mixture often used in coatings, and found that the concentration ratios of DBE components exhibited strong temperature dependence in an apartment when the indoor temperature declined stepwise over a multiweek period. To interpret the observational results, we developed a simplified mechanistic model relating the temperature dependence of VOC emission rates from coated surfaces to the temperature dependence of the diffusion coefficient of the emitted VOCs in the coating layer and further to a predicable molecular property of the emitted VOCs, molar volumes at 0 K, based on the free-volume theory. This correlation was quantitatively verified using the DBE data as well as using the data of alkanes, another set of VOCs that might be emitted from coatings, observed in two apartments in the same campaign. Given that indoor temperature varies considerably over seasons and across regions, the correlation proposed herein may help better predict indoor VOC emissions from coatings.