Solvent Diffusion Coefficient Research Articles

Determination of CO2 diffusion coefficient in sodium carbonate solutions and implications for decarbonization kinetics

Sodium carbonate solution is a promising carbon capture absorber due to its low cost, rich content, environmental friendliness, and low heat requirement for regeneration, but its large-scale application is limited by its low diffusion coefficient and thus unsatisfied chemical absorption kinetics. Most importantly, the diffusion coefficient parameters of CO2 absorption into sodium carbonate solutions at different concentrations and temperatures are lacked in the existing literature, which leads to a certain bias in the understanding of its absorption kinetics. Based on this, in this paper, a molecular dynamics simulation method was used to calculate the diffusion behavior of CO2 in sodium carbonate solution at different parameters and compared with the existing fitting equations in the literature. The data calculated from literature presented a severe overestimation of diffusion coefficient in low temperature solvent, underestimation of diffusion coefficient in high temperature solvent. The maximum deviation between our simulated data and calculated data of fitted formula in literature exceeded 30%. Based on this, a new fitting formula was proposed in this paper using the temperature adjusted method. The results showed that the maximum error between simulated data and fitted new formula is 24.82%, AARD, SD, RMSD are only 9.21%, 11.13%, and 11.15% respectively. The maximum absolute error was 11.73%, AARD, SD, RMSD are only 4.55%, 5.53%, and 5.53% for CO2 mass transfer kinetics calculation, which significantly contributes to the accuracy of carbon capture process calculations.

Fiber spinning from polymer solutions

The thinning of a cylinder of a polymer solution in a volatile solvent is argued to be controlled by solvent diffusion through a dense polymer layer at the cylinder surface. This naturally leads to the exponential time dependence of cylinder radius that is observed in experiments using a fast camera, such as capillary breakup extensional rheometry (CaBER). The relaxation time is controlled by the thickness of the dense (and often glassy) polymer layer and the diffusion coefficient of solvent through that layer. If correct, this means that while CaBER is very useful for understanding fiber spinning, the relaxation time does not yield a measure of the extensional viscosity of polymer solutions in volatile solvents.

The Missing Relationship between the Miscibility of Chiral Dopants and the Microscopic Dynamics of Solvent Liquid Crystals: A Molecular Dynamics Study

Nematic liquid crystals (LCs) are known to undergo a phase transition to chiral nematic LCs possessing helices upon doping with enantiomeric molecules known as chiral dopants. The relationship between the helical pitch (p), the molar fraction (x), and the power of the chiral dopant to induce a helix in a nematic solvent (βM) is expressed as p=1/(x·βM). The helical pitch is easily controlled by the concentration of the chiral dopant when the dopant molecule is miscible with the host nematic LC. However, it has not yet been clarified what the miscibility of the chiral dopant molecules with the nematic LCs depends. Therefore, we performed all-atom molecular dynamics (MD) simulations for the system composed of both Δ and Λ isomers of a chiral dopant molecule dispersed in a nematic LC and investigated the relationship between the microdynamics of the chiral molecules and their miscibility with the nematic solvent. The miscibility of the chiral dopant molecules with the LC solvent was found to correlate with the diffusion coefficient of the LC solvent. In the system where the chiral dopant molecules with high miscibility were added, the diffusion coefficient of the LC solvents was comparable to that of the system in which the chiral molecule was not doped. Furthermore, it was confirmed that more elongated chiral dopants were more miscible with the nematic solvent consisting of calamitic molecules, and that these dopant molecules did not have a significant effect on the diffusion behavior of the LC molecules.

Nonequilibrium configurations of swelling polymer brush layers induced by spreading drops of weakly volatile oil.

Polymer brush layers are responsive materials that swell in contact with good solvents and their vapors. We deposit drops of an almost completely wetting volatile oil onto an oleophilic polymer brush layer and follow the response of the system upon simultaneous exposure to both liquid and vapor. Interferometric imaging shows that a halo of partly swollen polymer brush layer forms ahead of the moving contact line. The swelling dynamics of this halo is controlled by a subtle balance of direct imbibition from the drop into the brush layer and vapor phase transport and can lead to very long-lived transient swelling profiles as well as nonequilibrium configurations involving thickness gradients in a stationary state. A gradient dynamics model based on a free energy functional with three coupled fields is developed and numerically solved. It describes experimental observations and reveals how local evaporation and condensation conspire to stabilize the inhomogeneous nonequilibrium stationary swelling profiles. A quantitative comparison of experiments and calculations provides access to the solvent diffusion coefficient within the brush layer. Overall, the results highlight the-presumably generally applicable-crucial role of vapor phase transport in dynamic wetting phenomena involving volatile liquids on swelling functional surfaces.

Thermodynamics and transport properties of valine and cysteine peptides in water

The study of thermodynamic and transport properties of amino acids gives access to knowledge about interactions between distinct molecules necessary to understand a variety of biological processes. In this work, we have performed molecular dynamics simulations of valine and cysteine peptides with lengths of (n) = 1, 2, 4, 8 & 16 monomers in an aqueous environment to estimate the solvation free energy and diffusion coefficients. We modeled our system using OPLS-AA parameter sets and TIP3P water at 310 K temperature. Solvation free energy of both the peptides have been reported using two thermodynamic integration (TI) based methods: TI and TI-CUBIC. The solvation free energy of both the peptides increases with the chain length. The estimated values using both methods are in good agreement with a statistical error of < 3%. The solvent accessible surface area (SASA) of solutes and hydrogen bonds between solute and solvent have also been presented to get more insights on solvation processes. The increase in solvation energy of both peptides with chain length is further corroborated by increase in the number of hydrogen bond (between peptide and water) and SASA with the chain length. In addition, the self diffusion coefficient of both solute and solvent along with their binary diffusion coefficient have been estimated for both the peptides. Furthermore, the effect of chain length on solvation free energy as well as diffusion coefficients have been studied.

Compression Relaxation of Multi-Structure Polymer Composites in Penetrating Liquid Medium.

Multi-structural polymer composites are widely used in the mechanical engineering, automotive, aviation and oil refining industries, as well as in the printing industry as a shock-absorbing deckle on the offset cylinders of printing machines. During offset printing, composites come into contact with inks and washing solutions, the components of which penetrate the material and cause the polymers to swell. This process degrades the print quality, and for this reason the study of its features is relevant. The prerequisites for this work are the study of the fundamental laws of diffusion and sorption of liquids by polymers with different micro- and macro-structures in different physical states and in different forms (e.g., films, sheets, fibers and fabrics). The combination of polymer materials in the composition of multi-structural fabric blankets makes it possible to obtain materials with unique mechanical properties and high resistance to liquid penetrating media and to use them in high-tech processes of multi-color printing with high resolution and color rendering. This article reports for the first time the kinetics and thermodynamics results obtained from the swelling of multi-structural polymeric blankets in solvents used in printing, and the effect of sorption of different polar liquids on the viscoelastic strain under compression during the operation of the damping systems of printing machines. Using mathematical models of activated liquid diffusion in polymers and deformation of a viscoelastic body, the swelling rate constants, solvent diffusion coefficients (the kinetic characteristics of the swelling process) and Flory−Huggins parameters (the thermodynamic characteristics of the interaction of the solvent with the composite) for composite−solvent systems with several chemical composition variants were determined. The elastic modulus and the viscosity coefficient of the composite under liquid saturation were calculated based on the experimental cyclic compression data. The range of change in the compression and restoration times of the polymeric blankets (0.09 s ÷ 0.78 s) was determined. It was shown that the composite swelled to a limited extent in all the studied liquids. All solvents used were thermodynamically poor (χ > 0.5). It has been established that rubber−fabric blankets coated with nitrile rubber are the least resistant to the action of dichloroethane, and that blankets with layers of polyolefins are not resistant to ethyl acetate. Water significantly affects the physicochemical properties of rubber−fabric blankets with a large proportion of cotton fabric layers. The data obtained can serve as a basis for optimizing the compositions of inks and cleaning solutions, as well as a theoretical basis for the thermodynamics of composite−solvent systems.

Modeling and simulation of solvent behavior and temperature distribution within long stick propellants with large web thickness undergoing drying

Drying is a complicated physical process which involves simultaneous heat and mass transfer in the removal of solvents inside propellants. Inappropriate drying techniques may result in the formation of a hard skin layer near the surface to block the free access of most solvent through for long stick propellants with large web thickness, which lead to lower drying efficiency and worse drying quality. This study aims to gain a comprehensive understanding of drying process and clarify the mechanism of the blocked layer near the propellant surface. A new three-dimensional coupled heat and mass transfer (3D-CHMT) model was successfully developed under transient conditions. The drying experiment results show that the 3D-CHMT model could be applied to describe the drying process well since the relative error of the content of solvent between simulation and experiment values is only 5.5%. The solvent behavior simulation demonstrates that the mass transfer process can be divided into super-fast (SF) and subsequent minor-fast (MF) stages, and the SF stage is vital to the prevention of the blocked layer against the free access for solvent molecules inside propellant grains. The effective solvent diffusion coefficient (Deff) of the propellant surface initially increases from 3.4 × 10−6 to 5.3 × 10−6 m2/s as the temperature increases, and then decreases to 4.1 × 10−8 m2/s at 60–100 min. The value of Deff of surface between 0–1.4 mm has a unique trend of change compared with other regions, and it is much lower than that of the internal at 100 min under simulation conditions. Meanwhile, the temperature of the propellant surface increases rapidly at the SF stage (0–100 min) and then very slowly thereafter. Both the evolution of Deff and temperature distribution demonstrate that the blocked layer near the propellant surface has been formed in the time period of approximately 0–100 min and its thickness is about 1.4 mm. To mitigate the formation of blocked layer and improve its drying quality of finial propellant products effectively, it should be initially dried at lower drying temperature (30–40 °C) in 0–100 min and then dried at higher drying temperature (50–60 °C) to reduce drying time for later drying process in double base gun propellants. The present results can provide theoretical guidance for drying process and optimization of drying parameters for long stick propellants with large web thickness.

Model-Based Evaluation of Drying Kinetics and Solvent Diffusion in Pharmaceutical Thin Film Coatings

Fluid-bed coating processes make it possible to manufacture pharmaceutical products with tuneable properties. The choice of polymer type and coating thickness provides control over the drug release characteristics, and multi-layer pellet coatings can combine several active ingredients or achieve tailored drug release profiles. However, the fluid-bed coating is a parametrically sensitive process due to the simultaneous occurrence of polymer solution spraying and solvent evaporation. Designing a robust fluid-bed coating process requires the knowledge of thin film drying kinetics, which in turn critically depends on an accurate description of concentration-dependent solvent diffusion in the polymer. This work presents a mathematical model of thin film drying as an enabling tool for fluid-bed process design. A custom-built benchtop drying cell able to record and evaluate the drying kinetics of a chosen polymeric excipient has been constructed, validated, and used for data collection. A semi-empirical mathematical model combining heat transfer, mass transfer, and film thickness evolution was formulated and used for estimating the solvent diffusion coefficient and solvent distribution in the polymer layer. The combined experimental and computational methodology was then used for analysing the drying kinetics of common polymeric excipients: poly(vinylpyrrolidone) and two grades of hydroxypropyl methylcellulose. The experimental setup together with the mathematical model represents a valuable tool for predictive modeling of pharmaceutical coating processes.

Quantitative Interpretation of Protein Diffusion Coefficients in Mixed Protiated-Deuteriated Aqueous Solvents.

Diffusion-ordered nuclear magnetic resonance (NMR) spectroscopy is widely used for the analysis of mixtures, dispersing the signals of different species in a two-dimensional spectrum according to their diffusion coefficients. However, interpretation of these diffusion coefficients is typically purely qualitative, for example, to deduce which species are bigger or smaller. In studies of proteins in solution, important questions concern the molecular weight of the proteins, the presence or absence of aggregation, and the degree of folding. The Stokes–Einstein Gierer–Wirtz estimation (SEGWE) method has been previously developed to simplify the complex relationship between diffusion coefficient and molecular mass, allowing the prediction of a species’ diffusion coefficient in a pure solvent based on its molecular weight. Here, we show that SEGWE can be extended to successfully predict both peptide and protein diffusion coefficients in mixed protiated–deuteriated water samples and, hence, distinguish effectively between globular and disordered proteins.

Small ionic radii limit time step in Martini 3 molecular dynamics simulations.

Among other improvements, the Martini 3 coarse-grained force field provides a more accurate description of the solvation of protein pockets and channels through the consistent use of various bead types and sizes. Here, we show that the representation of Na+ and Cl- ions as "tiny" (TQ5) beads limits the accessible time step to 25fs. By contrast, with Martini 2, time steps of 30-40fs were possible for lipid bilayer systems without proteins. This limitation is relevant for systems that require long equilibration times. We derive a quantitative kinetic model of time-integration instabilities in molecular dynamics (MD) as a function of the time step, ion concentration and mass, system size, and simulation time. We demonstrate that ion-water interactions are the main source of instability at physiological conditions, followed closely by ion-ion interactions. We show that increasing the ionic masses makes it possible to use time steps up to 40fs with minimal impact on static equilibrium properties and dynamical quantities, such as lipid and solvent diffusion coefficients. Increasing the size of the bead representing the ions (and thus changing their hydration) also permits longer time steps. For a soluble protein, we find that increasing the mass of tiny beads also on the protein permits simulations with 30-fs time steps. The use of larger time steps in Martini 3 results in a more efficient exploration of configuration space. The kinetic model of MD simulation crashes can be used to determine the maximum allowed time step upfront for an efficient use of resources and whenever sampling efficiency is critical.

Hydrodynamically driven self-assembly of lignin bowls and spheres by line-type micro-mixer

We report a strategy to continuously prepare lignin bowls and spheres using hydrodynamic flow in a simple line-type micro-mixer device. The kinetics of the non-equilibrium self-assembly of lignin was controlled by hydrodynamic shearing forces. It indicates that the convective-diffusive mixing and mass transfer of lignin macromolecules at the boundary of THF and water lamellar fluids are critical for the self-assembly of well-defined lignin nanoparticles. The shearing force of water on THF decreased with the decreasing of flow rate ratio (FRR) of water to THF from 30 to 7.5, resulting in an increase in lignin bowls yield from 20.9% to 54.7%. Furthermore, the diameter of lignin nanoparticles can be controlled from 100 to 550 nm by changing the flow rate. In addition, the diffusion coefficient of solvent also plays an imperative part in the self-assembly process. Under the same hydrodynamic conditions, solvents with higher diffusion coefficients generate more nanospheres.

Diffusion of glucose in water: A molecular dynamics study

A glucose molecule, simple structure of carbohydrate, has many functions in our body. It is transported to every cell and served as of energy source. The investigation of transport properties of glucose in aqueous medium would be useful to understand the body metabolism. In this research work, molecular dynamics (MD) simulations have been utilized to study the transport and structural properties of glucose in water at different temperature (298.15 K, 303.15 K, 308.15 K, and 312.15 K). The self diffusion coefficients of glucose and water have been estimated from mean square displacement plot (MSD) by using Einstein’s relation. Further, Darken’s relation has been used to find the binary diffusion coefficients of the mixture. The structural analysis of the system has been estimated with the help of radial distribution function (RDF) of its constituent atom/molecule pairs. The outcomes from the MD simualtions depicts that the temperature dependence of self diffusion coefficients of solute and solvent follow Arrhenius behavior, which further assist to calculate the activation energy of the system. The results from the present work agree well with the previously reported experimental values.

Protein hydration shell formation: Dynamics of water in biological systems exhibiting nanoscopic cavities

This work explores the singular scenarios emerging from nanoscopic cavities, located in aqueous solutions, that include biomolecules and, as a consequence, the process of biomolecule hydration shell formation. The research presents a nano-scale study, performed in various systems related with protein-water solutions, using all-atoms molecular dynamics simulations. This research shows that if a protein falls within an empty nanoscopic cavity located in an aqueous solution, it will take a time, with a magnitude significant for biological processes, to rebuild its whole network of hydrogen bonds with the solvent molecules. During that protein isolation time the dynamics of the biomolecule, and therefore the corresponding bioactivity, will be seriously compromised. In the case of the protein barstar (radius of gyration of 1.17 nm) located in the centre of cavities with radius r from 2.5 to 4.5 nm, and solvent diffusion coefficients for bulk and physiologic water (2.4 and 1.5 μm2/ms, respectively), that time is found to be of the order of tens-hundreds of picoseconds, a significant temporal range concerning the dynamics and bioactivity of proteins. On the other hand, the dynamics of formation of the inner protein hydration shell has been followed using an atomic view. The required time has been found to decrease with r, as the network of water molecules approaching the biomolecule resembles that of the biological water corresponding to that biomolecule. That resemblance increases as those water molecules have previously been in close contact with the protein. The dynamics of those systems has been modelled using a two states model. Isolated bulk water is taken as reference for the computer simulations. Comparison with experimental data is also provided.

A new empirical diffusion model for solvents in sprayed seals based on evaporation measurements

ABSTRACT Prediction of solvent diffusion and evaporation rate in the initial days after construction of a sprayed seal is of special concern for pavement performance assessment. It is still a major challenge as solvent evaporation is a very complicated process. In this study, laboratory tests were conducted on bitumen-solvent binder films, under different experimental conditions and varying solvent properties. A solution of Fick’s diffusion equation was then used to calculate solvent diffusion coefficient (D) values for the initial 7 days. While a strong correlation was found between D and solvent viscosity as well as D and solvent distillation range, no relationship was found between D and solvent aniline point nor aromatic content. These findings were utilised in developing a multiple linear regression (MLR) diffusion model for the initial 7 days of evaporation. The evaluation of the model indicated close agreement between the predictions and experimental values (R 2 = 0.95). The model enables road agencies to predict solvent diffusion and residual solvent for the early life of a sprayed seal without needing to conduct extensive experiments thereby saving time and labour cost. Accurate prediction of residual solvent via the developed model will further ensure long-term performance of sprayed seals.

Synergistic enhancement of mechanical, viscoelastic, transport, thermal, and radiation aging characteristics through chemically bonded interface in nanosilica reinforced EPDM‐CIIR blends

AbstractThe study investigates the influence of bis(3‐triethoxysilylpropyl)tetrasulfide (TESPT) grafted nanosilica (NS) reinforcement on the mechanical, viscoelastic, thermal, and transport characteristics as well as behavior after exposure to different cumulative γ‐radiation doses of EPDM‐CIIR blends for application in nuclear and hydrocarbon environments. The tensile strength and modulus of the nanocomposites were enhanced upto 64% and 118%, respectively whereas solvent diffusion coefficient reduced by 22%. The degradation onset temperature improved from 485°C for unfilled blends to 503°C for the nanocomposites. γ‐radiation aging resistance of EPDM‐CIIR blends improved with incorporation of nanosilica, with blends containing 7.5phrNS showing optimum properties and radiation aging resistance. The property improvements are attributed to the dispersion of NS and chemically interfaced covalent linkages between SiO2‐EPDM/CIIR chains that provides large interfacial area for effective stress transfer and creates barrier to free radical and solvent permeation. The applicability of Korsmeyer‐Peppas, Peppas‐Sahlin, and Higuchi models to predict of sorption behavior are investigated. Coats‐Redfern and Horowitz‐Metzger models were employed to evaluate the activation energy for thermal degradation. Slight decline in properties at higher nanofiller contents was due to the formation of agglomerates. TEM, FTIR, and rheological curves were utilized to corroborate these observations. FTIR and ESR analysis provided insight on the chemical changes in the nanocomposites after irradiation.

Experimental study of diffusion of vaporized solvent in bitumen at elevated temperatures

The diffusion coefficient of gaseous solvent in bitumen is an essential parameter in numerical modeling of solvent-assisted thermal recovery processes. The reported measurements of solvent diffusion coefficient are relatively scarce, especially at the high temperature. In this study, a new constant-pressure experimental technique for one-dimensional diffusion tests, which accounts for the bitumen swelling and density change, was developed. A novel analytical model was used to interpret the experimental swelling data. The diffusion coefficients of propane, butane, pentane, hexane and heptane, were measured at temperatures varying from 90 °C to 195 °C. It was found that the diffusion coefficient, at similar solvent solubility, increases with the temperature for all solvents. For different solvents at the same temperature and solubility, the diffusion coefficient decreases with increasing molecular weight of the solvent. A modified power-law correlation of diffusion coefficient with bitumen viscosity and solvent-bitumen mixture viscosity was developed based on the experimental results from this study and other reported studies. The correlation can provide a quick estimation of the diffusion coefficient of gaseous solvent into bitumen.

Experimental study of diffusivity of hexane in bitumen‐saturated porous media under high temperature/pressure conditions

AbstractSolvent mass transfer plays a key role in a thermal gravity drainage process involving solvent. The diffusion coefficients of solvent in such a process are not well studied. This article presents the effective diffusion coefficients of solvent in bitumen‐saturated sands under high temperature/pressure conditions measured using a CT scanning technique. Experimental results show that the effective diffusion coefficient of n‐hexane in bitumen‐saturated sands varied with the solvent concentration or with the viscosity of solvent–bitumen mixture (i.e., De ∝ c0.4 or De ∝ μm−0.46). The solvent concentration weighted diffusion coefficient of n‐hexane in the bitumen under the condition 160–170°C/1,900 kPa had an order of magnitude of about 10−5 cm2/s for solvent volume concentration less than 0.2. The penetration distance of n‐hexane in bitumen‐saturated sands depended on the nonlinearity of diffusion and had a value of −2 cm after 1‐day diffusion. The stronger the nonlinearity of diffusion, the shorter the penetration distance.

Drying kinetic measurements of polymer nanolayers – Experimental results with a model-based validation and interpretation of solvent diffusion

This contribution presents a method to examine the drying process of thin films of polymer gravimetrically, ranging from a few micrometers to below 20nm using a quartz crystal microbalance (QCM). Polyvinyl acetate (PVAc) and toluene (tol) serve as the model system to validate the method by drying experiments, simulations and the determination of the concentration dependent solvent diffusion coefficient. The results show that even on the nanometer scale, the diffusion coefficient is not a function of film thickness, which is contrary to the observations that can be found in literature. A thin polymer film, still loaded with residual solvent, is placed into a flow channel with controlled drying conditions. The QCM gravimetrically measures the drying curve and precisely detects changes of mass fractions on the scale of a hundredth of a percent over the course of hours, which translates to changes in layer thickness as small as to 0.1nm per hour. The presented method is a general-purpose tool for measuring concentration-dependent diffusion coefficients, which is relevant to all sorts of thicknesses and coatings. Since nanolayers are employed, in a reasonable amount of time diffusion coefficients in the order of 10−18m2s−1 are accessible.

Fundamental origin of flux non-linearity in organic solvent nanofiltration: Formulation of a thermodynamic/diffusion framework

In this paper we critically discuss the hypothesis of membrane compaction under pressure, which has been invoked to explain solvent flux vs. Δp non-linearity in organic solvent nanofiltration (OSN) experiments with dense polymer membranes. Although physically sound, this hypothesis does not have experimental support. To demonstrate that the molecular origin of flux non-linearity is purely thermodynamic, we propose a thermodynamic-diffusion framework which describes solvent transport in OSN membranes in terms of the concentration gradient produced by the applied pressure across the membrane. Solvent diffusion coefficient in the membrane increases with increasing Δp, which further confirms that flux decline is not related to membrane compaction. The developed framework allows to quantify both frame of reference and non-ideal thermodynamic effects on solvent diffusion coefficients in OSN membranes. This study demonstrates that the solution-diffusion model, if properly corrected for frame of reference (i.e., convection) and non-ideal effects, provides a satisfactory description of small molecule transport in OSN membranes, without the need to resort to more complicated transport models.

Rapid determination of diffusivity in massive anisotropic porous materials

A method for rapid determination of diffusion coefficients of polar solvents in anisotropic porous materials, making it possible to control the state of products prepared from such materials without destruction, is reported. For implementation of the proposed method, no preliminary calibration of the local solvent concentration in solid phase for the used converter and each new “porous material-solvent” system is required; that circumstance largely increases the research productivity of the method. The method possesses flexibility in terms of the possibility for measuring the values involved in the calculation expression on curve sections with a high sensitivity to parameter changes and in the range with a stable and noise-protected output signal of the concentration converter, which fact ensures an in-creased control accuracy.