Molecular Thermodynamic Model Research Articles

A lattice molecular thermodynamic model for thermo-sensitive random copolymer hydrogels

Recent advances in polymer chemistry have enabled the design of a wide range of copolymer hydrogels consisting of stimulus-responsive blocks and other functional blocks used in many fields. In this work, a new molecular thermodynamic model is developed based on our previous work for the swelling behavior of temperature-sensitive random copolymer hydrogels. The influences of polymer species, the molar fraction f, and the cross-linking degree on the swelling behaviors of copolymer hydrogels are investigated. The calculated swelling curves of PNIPAm-ENAG copolymer hydrogels have been compared with the corresponding experimental results. It is shown that the results obtained by model are quite consistent with the experimental data, and this indicates the validity of our model.

Surface thermodynamic properties of ionic liquids from new molecular thermodynamic model and ion-contribution equation of state

We aim to develop a new molecular thermodynamic model for predicting the surface thermodynamic properties of pure ionic liquids (ILs) based on the statistical mechanical expression developed by Winterfeld et al. (1978. AIChE. J. 24, 1010). In this respect, contributions to surface tension from the hard-sphere repulsion, Lennard–Jones dispersion force, and electrostatic interactions were considered and assumed to be additive in the development of the model. According to Winterfeld et al. approach, the surface tension of ILs is closely related to their pair potential function, pair radial distribution function and liquid densities. The required densities were predicted from our previous ion-contribution equation of state. The reliability of the proposed model was checked by calculating 464 surface tension data points for 13 different ILs over temperature range within 268.6–393K. The overall average absolute deviation of the correlated surface tensions from the experimental ones was found to be 1.55%. This result demonstrates the good performance of the proposed model and the rationality of molecular parameters, i.e., the soft-sphere diameter, σ dispersive energy, ε and inverse shielding length parameter, Γ. The uncertainty of the predicted surface tension was of the order of ±8.14%. Finally, our method has also been employed to estimate the sound velocities in ILs. The uncertainty of the calculated sound velocities was equal to ±9.25%.

A Molecular Thermodynamic Model for Restricted Swelling Behaviors of Thermo-sensitive Hydrogel

A molecular thermodynamic model was developed for describing the restricted swelling behavior of a thermo-sensitive hydrogel confined in a limited space. The Gibbs free energy includes two contributions, the contribution of mixing of polymer and solvent calculated by using the lattice model of random polymer solution, and the contribution due to the elasticity of polymer network. This model can accurately describe the swelling behavior of restricted hydrogels under uniaxial and biaxial constraints by using two model parameters. One is the interaction energy parameter between polymer network and solvent, and the other is the size parameter depending on the degree of cross-linking. The calculated results show that the swelling ratio reduces significantly and the phase transition temperature decreases slightly as the restricted degree increases, which agree well with the experimental data.

Dynamic Interfacial Behavior of Poly(oxyethylene) Lauryl Ether Based Surfactant Mixtures

The adsorption behavior of binary mixtures comprising nonionic surfactants at the air–water interface has been studied by bubble pressure tensiometry at concentrations above and below their critical micelle concentrations. Surfactants with the same hydrocarbon chains but different degree of ethoxylations were chosen as the components to understand their mixing behavior at equilibrium and dynamic conditions. At short times, the adsorption is found to be diffusion limited for individual components as well as for the mixtures, as predicted by the Ward and Tordai model. The effective diffusion coefficient of the monomers in the mixed state displays a dynamic synergism, consistent with the molecular thermodynamic model for dynamic surface tension. However, the equilibrium surface tension and micellar diffusion coefficient of the mixtures exhibit ideal behavior.

The strong specific effect of coions on micellar growth from molecular-thermodynamic theory.

Viscoelastic solutions of ionic surfactants with an added salt exhibit a surprisingly strong dependence of their behavior on the nature of the added coion. We apply a recently proposed molecular-thermodynamic model to elucidate the effect of a coion's specificity on the aggregation of cationic and anionic surfactants. We show that micellar growth and branching are opposed by penetration of coions inside a micelle's corona leading to an increase of the aggregate's preferential curvature. These effects result from hydration/dehydration and dispersion attraction of coions and are only important at high salinity where electrostatic repulsion of coions from the micelle is screened and where branching of micelles and viscosity maxima are observed. At low and medium salinity, the coion plays a minor role; its effect on critical micelle concentration and sphere-to-rod transitions is insignificant. Our molecular-thermodynamic approach describes the specific effects of both counterions and coions and their different roles at different salinity levels based on a unified physical picture.

Modeling of Micelle-Solution Equilibria for Mixed Nonionic Micelles with Strong Specific Interactions in Coronae: Group-Contribution Approach

A molecular thermodynamic model of micellization is proposed that takes into account strong specific interactions in the mixed micelle and hydration in micellar corona. To describe local interactions between molecular segments in the micelle we employ a quasichemical group contribution model of the bulk phase. “Segments-and-bonds” formalism is applied and correction for the connectivity of molecular chains is derived for the chemical potential in quasichemical approximation. The proposed general method may be used in combination with other bulk phase models, particularly with SAFT. The new method is applied to describe (1) the equilibrium distribution of alkanols between the N-dodecanoyl-methyl-glucamine micelle and dilute aqueous solution, and (2) the free energies of transfer of m-ethylene glycol mono-n-alkyl ether surfactants from aqueous solution to the micelles. Comparison with experiment shows the robustness of our approach.

A molecular thermodynamic model for the stability of hepatitis B capsids.

Self-assembly of capsid proteins and genome encapsidation are two critical steps in the life cycle of most plant and animal viruses. A theoretical description of such processes from a physiochemical perspective may help better understand viral replication and morphogenesis thus provide fresh insights into the experimental studies of antiviral strategies. In this work, we propose a molecular thermodynamic model for predicting the stability of Hepatitis B virus (HBV) capsids either with or without loading nucleic materials. With the key components represented by coarse-grained thermodynamic models, the theoretical predictions are in excellent agreement with experimental data for the formation free energies of empty T4 capsids over a broad range of temperature and ion concentrations. The theoretical model predicts T3/T4 dimorphism also in good agreement with the capsid formation at in vivo and in vitro conditions. In addition, we have studied the stability of the viral particles in response to physiological cellular conditions with the explicit consideration of the hydrophobic association of capsid subunits, electrostatic interactions, molecular excluded volume effects, entropy of mixing, and conformational changes of the biomolecular species. The course-grained model captures the essential features of the HBV nucleocapsid stability revealed by recent experiments.

Specific ion effects on the self-assembly of ionic surfactants: a molecular thermodynamic theory of micellization with dispersion forces.

The self-assembly of amphiphilic molecules is a key process in numerous biological and chemical systems. When salts are present, the formation and properties of molecular aggregates can be altered dramatically by the specific types of ions in the electrolyte solution. We present a molecular thermodynamic model for the micellization of ionic surfactants that incorporates quantum dispersion forces to account for specific ion effects explicitly through ionic polarizabilities and sizes. We assume that counterions are distributed in the diffuse region according to a modified Poisson-Boltzmann equation and can reach all the way to the micelle surface of charge. Stern layers of steric exclusion or distances of closest approach are not imposed externally; these are accounted for through the counterion radial distribution profiles due to the incorporation of dispersion potentials, resulting in a simple and straightforward treatment. There are no adjustable or fitted parameters in the model, which allows for a priori quantitative prediction of surfactant aggregation behavior based only on the initial composition of the system and the surfactant molecular structure. The theory is validated by accurately predicting the critical micelle concentration (CMC) for the well-studied sodium dodecyl sulfate (SDS) surfactant and its alkaline-counterion derivatives in mono- and divalent salts, as well as the molecular structure parameters of SDS micelles such as aggregation numbers and micelle surface potential.

Cluster formation in fluids with competing short-range and long-range interactions

We investigate the low density behaviour of fluids that interact through a short-ranged attraction together with a long-ranged repulsion (SALR potential) by developing a molecular thermodynamic model. The SALR potential is a model of effective solute interactions where the solvent degrees of freedom are integrated-out. For this system, we find that clusters form for a range of interaction parameters where attractive and repulsive interactions nearly balance, similar to micelle formation in aqueous surfactant solutions. We focus on systems for which equilibrium behaviour and liquid-like clusters (i.e., droplets) are expected, and find in addition a novel coexistence between a low density cluster phase and a high density cluster phase within a very narrow range of parameters. Moreover, a simple formula for the average cluster size is developed. Based on this formula, we propose a non-classical crystal nucleation pathway whereby macroscopic crystals are formed via crystal nucleation within microscopic precursor droplets. We also perform large-scale Monte Carlo simulations, which demonstrate that the cluster fluid phase is thermodynamically stable for this system.

Modeling of the Effects of Ion Specificity on the Onset and Growth of Ionic Micelles in a Solution of Simple Salts

A new version of the molecular thermodynamic model has been developed that takes into account the effect of ion specificity on the free energy of aggregation. The specificity of salt is reflected by differences in the bare ionic sizes and polarizabilities leading to the difference in the dispersion interaction of ions with the aggregate. The model also contains parameters that characterize the compactness of ionic pairs formed between a mobile ion and surfactant's headgroup. The values of these parameters show that more chaotropic heads form tighter pairs with chaotropic ions whereas more cosmotropic heads form more compact pairs with cosmotropic ions. The formation of compact pairs in the micelle corona diminishes the preferable curvature of the aggregates and promotes their growth. The model has been applied to aqueous solutions of cationic (alkyltrimethylammonium, alkyldimethylammonium, and alkylpyridinium) and anionic (alkylsulfate and alkylcarboxylate) surfactants in the presence of simple 1:1 salts. With a single set of parameter values, the model reproduces the critical micelle concentration-salinity curves and the sphere-to-rod transitions or the absence of thereof and describes the aggregate growth for different simple salts, in good agreement with experiment.

Swelling Behaviors of Poly(N‐isopropylacrylamide) Nanosized Hydrogel Particles/Poly(vinyl alcohol)/Water Systems: Effect of the Degree of Hydrolysis of PVA

Using poly(vinyl alcohol) as a drug model, the swelling behaviors of thermosensitive poly(N‐isopropylacrylamide) gel with various concentrations of PVA are investigated. The swelling ratio in PVA9000 is larger than that of PVA89000 at the same composition because the fully hydrolyzed PVA acts as a steric hindrance. A lattice‐based molecular thermodynamic model is used to obtain interaction parameters and then directly applied to describe the swelling behaviors of the gel. Using only one adjustable parameter, the PVA selectivity can be theoretically predicted and the ternary phase diagrams of PNIPA/water/PVA system can be generated. Lastly, the calculated results are compared with the swelling data for PNIPA/PVA copolymer gel, and are found to be in good agreement with the proposed model. image

A lattice model for thermally-sensitive core–shell hydrogels

A lattice molecular thermodynamic model for describing the swelling behavior of thermally-sensitive core–shell hydrogels was developed by integrating a close-packed lattice model for mixing free energy and a Flory Gaussian chain model for the elastic free energy. The thermodynamic model is characterized with two parameters: the temperature-dependent exchange energy parameter ε and the Topology-dependent size parameter V*. The input values of both parameters can be obtained by experimental results of pure polymer hydrogels. With the help of proposed model, swelling behaviors of two kinds of hydrogel systems were analyzed: one is a doubly thermally-sensitive core–shell hydrogels (with two LCSTs) and the other comprises a thermally-sensitive hydrogel shell with a hard internal core. We show that the calculated results are in good agreement with the experimental data.

Molecular Thermodynamic Modeling of Gelation and Demixing in Solution of Cross-Associating Chains

A molecular thermodynamic model has been proposed that extends the previously known mean field theory of self-association to systems of cross-associating polymers. The extended theory has been applied to model gelation and phase behavior for mixtures of two associating polymers in a good solvent. The gelation threshold is described analytically. Relation between the new theory and SAFT (Macromolecules 2012, 45, 6686−6696 has been established. For ternary systems containing two associating polymers in athermal solvent, simple analytical formula has been obtained for the location of the upper critical consolute point in the long chain limit. Possible types of phase behavior (sol–sol, sol–gel, gel–gel) have been discussed.

Co-nonsolvency effect of thermosensitive N-isopropylacrylamide nanometer-sized gel particles in water–PEG systems

Nanometer-sized N-isopropylacrylamide (NIPA) gel particles were prepared by precipitation polymerization, and their thermosensitive swelling behaviors in water–poly(ethylene glycol) (PEG) (MW = 200, 400) systems were investigated using photon correlation spectroscopy (PCS). The volume transition temperature decreased with increasing PEG concentration, and a completely unexpected swelling behavior was observed at high PEG concentrations. The cloud points of poly(N-isopropylacrylamide) (PNIPA) in water–PEG systems were also determined by thermo-optical analysis (TOA) in order to compare the volume transition temperatures of gel particles with the phase transition temperatures of linear PNIPA in given solvent mixtures. A lattice-based molecular thermodynamic framework was employed to calculate interaction parameters from binary liquid–liquid equilibria (LLE), and those parameters were then applied directly to describe the co-nonsolvency effects of the ternary solutions. By combining the molecular thermodynamic model for the mixing contribution with the Flory–Rehner (FR) model for the elasticity contribution, the reentrant swelling equilibria at various temperatures were calculated. Using only one adjustable parameter, we were able to describe the swelling behaviors at high temperature regions (above the LCST). Lastly, the predicted results were compared to PEG (MW = 200, 1000) selectivity data inside NIPA gel, and were found to be in good agreement with the proposed model without further adjustable parameters.

The Prediction of Asphaltene Precipitation from Crude-Oils

Asphaltene precipitation is undesirable deposition that causes difficult problems in oil production and transportation. A molecular thermodynamic model is proposed for predicting the asphaltene precipitation under live oil conditions and at a wide range of pressures and different solvent ratios. In this model, it is assumed that the precipitation phenomenon is a reversible process, and an equation of state is employed for phase behavior prediction. The vapor and liquid equilibrium calculations are performed separately and sequentially. The characterization of unknown-heavy fraction of petroleum (C7+) is obtained by the generalized molar mass distribution model, in which C7+ is represented by four pseudocomponents. The two heaviest pseudocomponents of C7+ are identified as asphaltenic components, are also considered as precipitating components. The model is verified by its ability to prediction of asphaltene precipitation in different thermodynamic conditions. It has been shown that the calculated results are in good agreement with the experimental data.

Micellization of dodecyltrimethylammonium bromide in water–dimethylsulfoxide mixtures: A multi-length scale approach in a model system

The micellization in mixed solvent was studied using conductimetry, density measurements (molar volumes), and small angle neutron scattering (SANS) to explore dodecyltrimethylammonium bromide (DTABr) micelle formation throughout the entire composition range of water–dimethylsulfoxide (DMSO) mixtures. As the concentration of DMSO was increased in the mixture, the critical micelle concentration (CMC) increased, the aggregation number decreased and the ionization degree increased, until no aggregates could be detected any more for DMSO molar fraction higher than 0.51. The results were consistent with the presence of globular micelles interacting via a coulombic potential. The experimental CMC values and aggregation numbers were successfully reconciled with a molecular thermodynamic model describing the micellization process in solvent mixtures (R. Nagarajan and C.-C. Wang, Langmuir 16 (2000) 5242). The structural and thermodynamic characterization of the micelles agreed with the prediction of a dissymmetric solvation of the surfactant entity: the hydrocarbon chain was surrounded only by DMSO while the polar head was surrounded only by water. The decrease in the ionization degree was due to the condensation of the counterions and was definitely linked to the geometrical characteristics of the aggregates and by no means to the CMC or salinity. This multi-technique study provides new insight into the role of solvation in micellization and the reason for the decrease in ionization degree, emphasizing the dissymmetric solvation of the chain by DMSO and the head by water. This is the first time that, for a given surfactant in solvent mixtures, micellization is described using combined analysis from molecular to macroscopic scale.

Are Ellipsoids Feasible Micelle Shapes? An Answer Based on a Molecular-Thermodynamic Model of Nonionic Surfactant Micelles

The existence of ellipsoidal micelles in aqueous solution has been debated in the literature. Although a number of experimental studies suggest that certain surfactants form ellipsoidal micelles, many theoretical studies have claimed that micelles with an ellipsoidal shape cannot exist. To shed light on this topic, in this paper, we develop a curvature-corrected, molecular-thermodynamic model for the free energy of micellization of nonionic surfactant biaxial ellipsoidal micelles. We subsequently use this model to evaluate the feasibility of forming ellipsoidal micelles, compared to forming spherical, spherocylindrical, and discoidal micelles, and conclude that ellipsoidal micelles can exist in solution. Utilizing the model developed here, we also establish theoretical limits on the size of the ellipsoidal micelles. These limits depend solely on the chemical structure of the surfactant molecule.

Understanding phase behaviors of multicomponent polymer mixtures based on a molecular thermodynamic framework combined with molecular simulation

A new molecular thermodynamic model based on a closed-packed lattice model is developed for multicomponent systems. Based on Monte-Carlo (MC) simulation results, we introduce new universal functions to consider the chain length dependence of polymers, and are able to obtain more accurate critical volume fraction results in liquid–liquid equilibrium (LLE) calculations. In associated blend systems, specific interactions are used to characterize strongly interacting polymer mixtures with a secondary lattice. To minimize the number of adjustable model parameters, chain length parameters are calculated in a conventional way using molecular weight and specific volume. Our proposed model successfully describes binary LLE for polymer-solvent systems. Furthermore, the model parameters obtained from these binary systems are directly used to predict corresponding LLE ternary systems, and the results were in good agreement with experimental data.

Crowding effect on DNA melting: a molecular thermodynamic model with explicit solvent

A molecular thermodynamic model is developed to examine crowding effect on DNA melting. Each pair of nucleotides in double-stranded DNA and each nucleotide in single-stranded DNA are represented by two types of charged Lennard-Jones segments, respectively. Water molecules are mimicked explicitly as spherical particles, embedded in a dielectric continuum. Crowders with varying concentration, size, interaction strength, and chain length are considered. For DNA with a sequence of A(20), the melting temperature is predicted to increase by 1 K in the presence of Ficoll70 and by 7.5 K in the presence of Ficoll70-polyvinyl pyrrolidone360 mixture. The predictions agree well with experimental data. Furthermore, the melting temperature is found to increase with increasing crowder size, but reduce with increasing interaction strength and crowder length. The predicted changes of Gibbs energy, entropy and enthalpy are consistent with experimentally measured values. The study reveals that DNA melting in a crowded environment is influenced by both entropic and enthalpic effects.

Molecular thermodynamic model for swelling behavior and volume phase transition of multi-responsive hydrogels

A new molecular thermodynamic model for swelling behavior and volume phase transition of multi-responsive hydrogels was developed. The swelling behavior of hydrogels results from three contributions, the mixing of polymer network and solvent, the elasticity of polymer network and the ionic effect containing Donnan equilibrium of ions distributed inside and outside hydrogels and electrostatic interactions between the charges carried by the polymer network and the counter ions. Two kinds of model parameters are included; they are the interaction energy parameters between polymer network and solvent or between the two solvents, and a size parameter which is the molecular mass of the network between two cross-linking points. They should be determined from the experimental swelling curves of hydrogels. It is shown that this model can describe the swelling behavior and volume phase transitions of pH-sensitive and ion-sensitive hydrogels by using fewer model parameters comparing with other models. The different swelling behaviors such as shrinking at low pH and swelling at high pH, swelling at low pH and shrinking at high pH, shrinking at middle pH and swelling at both low pH and high pH, the swelling behaviors of pH- and temperature-sensitive hydrogels or temperature- and solvent-sensitive hydrogels, can be satisfactorily described.