Hard-core Volume Research Articles

Predictive Approach to the Phase Behavior of Polymer–Water–Surfactant–Electrolyte Systems Using a Pseudosolvent Concept

A predictive approach to the phase behavior of four-component polymer–water–surfactant–electrolyte systems is formulated by viewing the four-component system as a binary polymer–pseudosolvent system, with the pseudosolvent representing water, surfactant, and the electrolyte. The phase stability of this binary system is examined using the framework of the lattice fluid model of Sanchez and Lacombe. In the lattice fluid model, a pure component is represented by three equation-of-state parameters: the hard-core volume of a lattice site (v*), the number of lattice sites occupied by the component (r), and its characteristic energy (ε*). We introduce the extra-thermodynamic postulate that r and v* for the pseudosolvent are the same as for water and all surfactant–electrolyte composition-dependent characteristics of the pseudosolvent can be represented solely through its characteristic energy parameter. The key implication of the postulate is that the phase behavior of polymer–pseudosolvent systems will be identical for all pseudosolvents with equal values of characteristic energy, despite their varying real compositions. Based on the pseudosolvent model, illustrative phase diagrams have been computed for several four-component systems containing alkyl sulfonate/sulfate surfactants, electrolytes, and anionic or nonionic polymers. The pseudosolvent model is shown to describe all important trends in experimentally observed phase behavior pertaining to polymer and surfactant molecular characteristics. Most importantly, the pseudosolvent model allows one to construct a priori phase diagrams for any polymer–surfactant–electrolyte system, knowing just one experimental composition data for a system at the phase boundary, using available thermodynamic data on surfactants and electrolytes and without requiring any information on the polymer.

Supercooled melt structure and dynamics of single-chain nanoparticles: A computer simulation study.

By using coarse-grained molecular dynamics simulations, we have investigated the structure and dynamics of supercooled single-chain cross-linked nanoparticle (SCNP) melts having a range of cross-linking degrees ϕ. We find a nearly linear increase in glass-transition temperature (Tg) with increasing ϕ. Correspondingly, we have also experimentally synthesized a series of polystyrene-based SCNPs and have found that the measured Tg estimated from differential scanning calorimetry is qualitatively consistent with the trend predicted by our simulation estimates. Experimentally, an increase in Tg as large as ΔTg = 61K for ϕ = 0.36 is found compared with their linear chain counterparts, indicating that the changes in dynamics with cross-links are quite appreciable. We attribute the increase in Tg to the enlarged effective hard-core volume and the corresponding reduction in the free volume of the polymer segments. Topological constraints evidently frustrate the local packing. In addition, the introduction of intra-molecular cross-linking bonds slows down the structural relaxation and simultaneously enhances the local coupling motion on the length scales within SCNPs. Consequently, a more pronounced dynamical heterogeneity (DH) is observed for larger ϕ, as quantified by measuring the dynamical correlation length through the four-point susceptibility parameter, χ4. The increase in DH is directly related to the enhanced local cooperative motion derived from intra-molecular cross-linking bonds and structural heterogeneity derived from the cross-linking process. These results shed new light on the influence of intra-molecular topological constraints on the segmental dynamics of polymer melts.

Studies on ion dynamics of polymerized ionic liquids through the free volume theory

Over the last decade, the volume has been envisioned as a critical variable controlling the dynamics of glass-forming systems in general, and charge transport of ionic conductors in particular. Herein, we use theoretical and experimental approaches to investigate the volume effects in a specific 1,2,3-triazolium-based poly(ionic liquid) (PIL) at both the macro and nano scales. The size of the local free volume cavity in the studied system was determined by positron annihilation lifetime spectroscopy (PALS). On the other hand, the theoretical approach enabled us to estimate the hard-core volume (Vhc) and thus free volume (Vf) in the studied PIL. Since the experimental value determined for Vf is relatively large it can be considered as the main factor controlling the superionic properties of this material. Furthermore, the analysis of specific volume and relaxation dynamics in T-P plane in terms of the locally correlated lattice (LCL) and cooperative free volume (CFV) models shows that none of them works for the studied system.

Directing Liquid Crystalline Self-Organization of Rodlike Particles through Tunable Attractive Single Tips.

Dispersions of rodlike colloidal particles exhibit a plethora of liquid crystalline states, including nematic, smectic A, smectic B, and columnar phases. This phase behavior can be explained by presuming the predominance of hard-core volume exclusion between the particles. We show here how the self-organization of rodlike colloids can be controlled by introducing a weak and highly localized directional attractive interaction between one of the ends of the particles. This has been performed by functionalizing the tips of filamentous viruses by means of regioselectively grafting fluorescent dyes onto them, resulting in a hydrophobic patch whose attraction can be tuned by varying the number of bound dye molecules. We show, in agreement with our computer simulations, that increasing the single tip attraction stabilizes the smectic phase at the expense of the nematic phase, leaving all other liquid crystalline phases invariant. For a sufficiently strong tip attraction, the nematic state may be suppressed completely to get a direct isotropic liquid-to-smectic phase transition. Our findings provide insights into the rational design of building blocks for functional structures formed at low densities.

Connecting Pressure-Dependent Dynamics to Dynamics under Confinement: The Cooperative Free Volume Model Applied to Poly(4-chlorostyrene) Bulk and Thin Films

We apply our cooperative free volume (CFV) rate model for pressure-dependent dynamics to describe the relaxation times for poly(4-chlorostyrene) (P4ClS) bulk and thin films. The CFV model expresses segmental relaxation times, τ, as a function of temperature, T, and thermodynamic free volume, Vfree = V – Vhc, where the limiting hard core volume, Vhc, is obtained via analysis of a polymer’s experimental PVT data using the locally correlated lattice (LCL) model equation of state. In adapting CFV to describe thin films, we assume that the main effect of confinement is that the interface serves to change the average free volume (average density) compared to bulk. We formulate a simple weighted average expression (involving just a single interface related parameter) to describe the free volume of a film as a function of thickness, h, and use this h-dependent Vfree within the CFV model expression. Using just ambient pressure relaxation time data on bulk P4ClS, along with PVT data, we parametrize the CFV model, w...

Pressure-Dependent Dynamics of Polymer Melts from Arrhenius to Non-Arrhenius: The Cooperative Free Volume Rate Equation Tested against Simulation Data

We apply the cooperative free volume (CFV) model to analyze the segmental relaxation times, τ(T,V), of a model 20-mer polymer melt simulated via molecular dynamics over a broad pressure range. Thermodynamic characterization of the 20-mer allows determination of the constant contribution from the hard-core volume (Vhc), which then yields predictions for the free volume, Vfree = V – Vhc. The CFV rate model is based on an activation free energy that increases with the number of cooperating segments, n*, wherein the system’s free volume, Vfree, is what determines n*. The model predicts that on isotherms ln τ vs 1/Vfree is linear with T-dependent slopes. The 20-mer melt data follow this linear behavior at all temperatures. Assuming a fixed activation energy per cooperating segment leads to a very simple analytic form that describes all of the 20-mer melt’s high T behavior, including the Arrhenius to non-Arrhenius transition regime. This form reflects the importance of a gas kinetic contribution as well as both...

Explaining the T,V-dependent dynamics of glass forming liquids: The cooperative free volume model tested against new simulation results.

In this article, we derive a rate model, the "cooperative free volume" (CFV) model, to explain relaxation dynamics in terms of a system's free volume, Vfree, and its temperature, T, over widely varied pressure dependent conditions. In the CFV model, the rate a molecule moves a distance on the order of its own size is dependent on the cooperation of surrounding molecules to open up enough free space. To test CFV, we have generated extensive T,V dependent simulation data for structural relaxation times, τ, on a Kob and Andersen type Lennard-Jones (KA-LJ) fluid. The Vfree = V - Vhc values are obtained by estimating the limiting hard core volume, Vhc, through analysis of the KA-LJ PVT data. We provide the first simulation evidence that shows ln τ to be linearly proportional to 1/Vfree on isotherms, with T-dependent slopes, thus confirming our recent analysis of experimental systems. The linear relationship exhibited by the simulation data is further shown to occur at temperatures both above and below the transition to Arrhenius behavior. We also show that the gas kinetic T-dependent contribution is important in simulation results and that there can be a significant entropic contribution from lingering molecular hard-cores at high T. A key result is that non-Arrhenius relaxation behavior is always exhibited on isobars of the KA-LJ fluid, even at high T. The CFV model predicts all of this behavior over a surprisingly wide range of the KA-LJ T,V space, fitting it with just a single set of three parameters. The CFV approach leads to a framework wherein the number of cooperating particles, and thus, the process free energy of activation, is inversely proportional to Vfree, and this is the foundation for the form of the model's volume contribution, a form that we find to hold for all systems and at all temperatures.

Metallurgy of soft spheres with hard core: From BCC to Frank-Kasper phases.

Understanding how soft particles can fill the space is still an open question. Structures far from classical FCC or BCC phases are now commonly experimentally observed in many different systems. Models based on pair interaction between soft particles are at present much studied in 2D. Pair interactions with two different lengths have been shown to lead to quasicrystalline architectures. It is also the case for a hard core with a square repulsive shoulder potential. In 3D, global approaches have been proposed for instance by minimizing the interface area between the deformed objects in the case of foams or micellar systems or using a self-consistent mean-field theory in copolymer melts. In this paper we propose to compare a strong van der Waals attraction between spherical hard cores and an elastic energy associated to the deformation of the soft corona. This deformation is measured as the shift between the deformed shell compared to a corona with a perfect spherical symmetry. The two main parameters in this model are: the hard-core volume fraction and the weight of the elastic energy compared to the van der Waals one. The elastic energy clearly favours the BCC structure but large van der Waals forces favor Frank and Kasper phases. This result opens a route towards controlling the building of nanoparticle superlattices with complex structures and thus original physical properties.

Test of athermal terms of activity coefficients by large scale molecular dynamics simulation for vapor–liquid equilibria

The vapor–liquid equilibria for Ar (1) + Ar_dimer (2) system were calculated by molecular dynamics simulation to test the athermal terms of activity coefficient models. The calculations were carried out at 141 K. The interatomic distance between two atoms in Ar_dimer molecule was fixed to the distance of the first peak of the radial distribution function of pure Ar at 141 K. Lennard-Jones potential was adopted for the interatomic potentials between Ar–Ar, Ar–atom in Ar_dimer, and atom in Ar_dimer–atom in Ar_dimer. The number of atoms used for the calculations were from 3000 to 4200. The calculated results of activity coefficients for Ar (1) + Ar_dimer (2) system at 141 K are smaller than unity, and are between the calculated results by Flory–Huggins equation based on hard-core volume and that based on volume.

Stochastic dynamics of penetrable rods in one dimension: Occupied volume and spatial order

The occupied volume of a penetrable hard rod (HR) system in one dimension is probed through the use of molecular dynamics simulations. In these dynamical simulations, collisions between penetrable rods are governed by a stochastic penetration algorithm (SPA), which allows for rods to either interpenetrate with a probability δ, or collide elastically otherwise. The limiting values of this parameter, δ = 0 and δ = 1, correspond to the HR and the ideal limits, respectively. At intermediate values, 0 < δ < 1, mixing of mutually exclusive and independent events is observed, making prediction of the occupied volume nontrivial. At high hard core volume fractions φ0, the occupied volume expression derived by Rikvold and Stell [J. Chem. Phys. 82, 1014 (1985)] for permeable systems does not accurately predict the occupied volume measured from the SPA simulations. Multi-body effects contribute significantly to the pair correlation function g2(r) and the simplification by Rikvold and Stell that g2(r) = δ in the penetrative region is observed to be inaccurate for the SPA model. We find that an integral over the penetrative region of g2(r) is the principal quantity that describes the particle overlap ratios corresponding to the observed penetration probabilities. Analytic formulas are developed to predict the occupied volume of mixed systems and agreement is observed between these theoretical predictions and the results measured from simulation.

Description of hot and dense hadron-gas properties in a new excluded-volume model

A new equation of state for a hot and dense hadron gas (HG) is obtained where the finite hard-core size of baryons has been incorporated in a thermodynamically consistent formulation of excluded volume correction. Our model differs from other existing approaches on the following points. We assign a hard-core volume only to each baryon and mesons though possess a small volume but they can fuse and interpenetrate into one another. Use of the full quantum statistics is made in obtaining the grand canonical partition function where excluded-volume correction has been incorporated by explicitly integrating over volume. We thus find that the new model works even for the cases of extreme temperatures and/or densities where most of other approaches fail. The model does not violate causality even at extreme densities. The temperature and density dependence of various thermodynamical quantities, e.g. pressure, baryon density, entropy and energy density compare well with the results of other microscopic HG models. After suitable parametrization of the centre-of-mass energy in terms of temperature and baryon chemical potential, we explore some new freeze-out criteria which exhibit full independence of the collision energy and of the structures of the colliding nuclei. We further demonstrate the suitability of our model in explaining various experimental results of the multiplicity-ratios of various particles and their antiparticles. Finally, we use our excluded-volume model to obtain the transport behaviour of the hot and/or dense HG such as shear viscosity to entropy ratio, speed of sound etc. and compare the results with earlier calculations.

Feshbach resonances and the unitary limit in a model of strongly correlated nucleons

A model of strongly interacting and correlated hadrons is developed. The interaction used contains a long range attraction and short range repulsive hard core. Using this interaction and various limiting situations of it, a study of the effect of bound states and Feshbach resonances is given. The limiting situations are a pure square well interaction, a delta-shell potential and a pure hard core potential. The limit of a pure hard core potential are compared with results for a spinless Bose and Fermi gas. The limit of many partial waves for a pure hard core interaction is also considered and result in expressions involving the hard core volume. This feature arises from a scaling relation similar to that for hard sphere scattering with diffractive corrections. The role of underlying isospin symmetries associated with the strong interaction of protons and neutrons in this two component model is investigated. Properties are studied with varying proton fraction. An analytic expression for the Beth Uhlenbeck continuum integral is developed which closely approximates exact results based on the potential model considered. An analysis of features associated with a unitary limit is given. In the unitary limit of very large scattering length, the ratio of effective range to thermal wavelength appears as a limiting scale. Thermodynamic quantities such as the entropy and compressibility are also developed. The effective range corrections to the entropy vary as the cube of this ratio for low temperatures and are therefore considerably reduced compared to the corrections to the interaction energy which varies linearly with this ratio. Effective range corrections to the compressibility are also linear in the ratio.

Test of athermal terms of activity coefficient models by Monte Carlo simulation with hard-core models

The infinite dilution activity coefficients of exactly athermal fluids were calculated by Monte Carlo simulation with hard-core models. The hard-core models used in this work were hard-sphere and hard-spherocylinder models. The Widom test particle method was adopted to calculate the residual chemical potentials of solutes in pure solvent and in pure solute solutions. The infinite dilution activity coefficients of solutes were obtained from the residual chemical potentials of solutes. The infinite dilution activity coefficients calculated by Monte Carlo simulation were compared with those of athermal terms in activity coefficient equations. Staverman–Guggenheim equation overestimates the activity coefficients. The deviations of activity coefficients increase with increasing the hard-core volume of solute. Flory–Huggins equation based on molar volume gives good results for the hard-spherocylinder systems. Elbro-FV equation gives good results for both the hard-sphere and hard-spherocylinder systems.

Pressure–volume–temperature (PVT) measurements of ionic liquids ([bmim +][PF 6−], [bmim +][BF 4−], [bmim +][OcSO 4−]) and analysis with the Sanchez–Lacombe equation of state

Pressure–volume–temperature measurements of the pure ionic liquids 1-butyl-3-methyl-imidazolium hexafluorophosphate ([bmim +][PF 6 −]), 1-butyl-3-methyl-imidazolium tetrafluoroborate ([bmim +][BF 4 −]), 1-butyl-3-methyl-imidazolium octylsulfate ([bmim +][OcSO 4 −]) were performed with a metal bellows apparatus at temperatures from 313 to 473 K and at pressures up to 200 MPa. The pressure–volume–temperature data were used to determine parameters of the Sanchez–Lacombe equation of state, which was used to calculate the hard core volume and free volume of ionic liquids. It was found that the hard core volume of the ionic liquid was related with anion size and was slightly smaller than the van der Waals volume estimated with Bondi methods. The free volumes of [bmim +][PF 6 −] and [bmim +][BF 4 −] calculated with the Sanchez–Lacombe equation of state showed a similar pressure dependence and were close to each other (ca. 10–14 cm 3/mol) whereas the values for [bmim +][OcSO 4 −] were much higher (ca. 18–25 cm 3/mol) over the range of pressure.

Strain variation during bimetallic PM preform tube extrusion

It is usually assumed that during plastic deformation of bimetals, the components must undergo an identical deformation for a sound metal forming operation. However, differences in microstructures and properties between simultaneously deformed metals make the flow heterogeneous. The present paper examines the variation in strain of each metal during extrusion of bimetallic tubes and transition joining between dissimilar PM preforms. It is shown that consolidation and metal matrix hardening mechanisms associated with PM preform deformation strongly affect the deformation behaviour of each metal and the onset of steady state deformation during extrusion.The results indicate that, during extrusion of PM bimetallic tubes, the difference in strain between core and sleeve is relatively small. The strain difference (between two metals) increases with increasing total strain, hard-core or low volume ratio during extrusion. In the case of transition joining of dissimilar PM preforms, softer metal experiences lower strain owing to triaxial constraints imposed by the tools and bottom hard metal.

Pressure–volume–temperature ( P– V– T) properties of Ge xSe 1− x inorganic polymeric glasses

We have studied the vitreous Ge x Se 1− x chalcogenide alloys, varying x from 0.0 to 0.12. P– V– T results have been obtained for pressures up to 200 J cm −3 and temperatures up to 240°C or so. The P*, V* and T* parameters of the Hartmann equation of state (EOS) were evaluated. With increasing Ge concentration the specific volume increases, passes through a maximum and then decreases. By contrast, the characteristic (hard-core) volume V* passes through a minimum and so does the characteristic temperature T*. On the basis of these results in conjunction with earlier ones we provide an expanded model of atomic packing and phase structures of the alloys.

The effect of stereoisomerism on dynamic viscosity: A study of cis-decalin and trans-decalin versus pressure and temperatureElectronic supplementary information (ESI) available: Dynamic viscosity η and density ρ of cis-decalin and trans-decalin versus temperature T and pressure P. See http://www.rsc.org/suppdata/cp/b3/b301202f/

Decahydronaphthalene (decalin) exists in two stereoisomeric molecular configurations, a cis and a trans configuration. The cis and trans isomers have different physical properties. In this work, a study of the stereoisomeric effect on the dynamic viscosity (and density) versus pressure and temperature has been carried out up to 100 MPa in the temperature range 293.15 K to 353.15 K. The viscosity of cis-decalin is higher than the one of trans-decalin in the considered temperature and pressure ranges due to the twisted structure of cis-decalin compared to the relative more symmetric and rigid structure of trans-decalin. Further, the density of cis-decalin is around 3% higher than for trans-decalin. The measured data have been used in order to perform an analysis of the stereoisomeric effects using recently developed viscosity approaches with a physical and theoretical background. For the hard-sphere scheme it has been found that the roughness factor is related to the specific structure of the stereoisomeric molecules, whereas the same hard-core volume is obtained for cis-decalin and trans-decalin. In the case of the free-volume model, the term arising from the energy barrier, which the molecules have to cross in order to diffuse, is approximately the same for cis-decalin and trans-decalin, but the characteristic molecular length and the molecular overlap of the free volume are different, and strongly related to the structural configuration of the stereoisomeric decalin molecules.

An improved entropic expression for polymer solutions

Elbro et al. [Macromolecules 23 (21) (1990) 4707] proposed a simple but successful entropic expression for polymer and other size-asymmetric solutions. The expression is similar to the Flory–Huggins model, but free-volume (FV) fractions are used instead of segment or volume fractions and much better results are obtained. The FV is simply defined as V f= V− V w, where V w is the van der Waals (vdW) volume, essentially a measure of molecule’s hard-core volume. In this work, we adopt the statement by Bondi that due to the packing of molecules, a higher than V w inaccessible volume represents more adequately the hard-core volume. Using experimental phase equilibrium data for athermal polymer (and other asymmetric) solutions, we show that the optimum V ∗/ V w ratio is equal to 1.2, which is very close to the value expected based on the packing density at 0 K for organic systems. Using the entropic expression by Elbro et al. [Macromolecules 23 (21) (1990) 4707] and V ∗=1.2V w yields improved results of activities for athermal polymer solutions and alkane–alkane systems over an extensive database. The results are better compared to other existing entropic expressions, e.g. those of Oishi–Prausnitz (Unifac-FV) and of Zhong–Masuoka.

UNIFAC-FV Applied to Dendritic Macromolecules in Solution: Comment on “Vapor−Liquid Equilibria for Dendritic-Polymer Solutions” (Lieu, J. G.; Liu, M.; Fréchet, J. M. J.; Prausnitz, J. M. J. Chem. Eng. Data 1999, 44, 613−620)

Dendrimers have been proposed as rheology modifiers for use as processing aids,1 as well as for other more specialized applications where predicting solubility in both small molecule solvents and polymer melts will be essential for tailoring the dendritic molecules for specific uses. The large number of end groups, core-shell structure, and constrained molecular conformations due to the high degree of branching make thermodynamic modeling of these macromolecules challenging. In a recent article, Lieu et al.2 report solvent activity coefficients measured in vapor-liquid equilibria experiments on dendritic polymer solutions. They further demonstrate that some but not all of their data can be correlated by a modified version of the Flory-Huggins lattice theory. The use of a model derived for linear polymer chains in semidilute solution to describe the more globular structure of dendrimers in solution is questionable, however, given the wealth of recent X-ray and small angle neutron scattering measurements as well as simulations3 of dendrimer structures in solution.4-10 Similarly, solution rheological properties strongly suggest a globular, unentangled structure for most dendrimers in solution and in the melt.9-13 Given this recent wealth of structural data, we propose that the solvent activity of dendrimer solutions may be predicted by group-contribution methods that have been modified to account for the free volume contributions of the molecular architecture. The free-volume modification14 of the UNIFAC15 model (UNIFAC-FV) is a predictive group-contribution method that accounts for the free volume of mixing of a structured macromolecule with a small molecule solvent. Flory’s polymer equation of state16 provides a correction for the effects of polymer architecture (as characterized by the molecular free volume) on raising the free energy of the solution. This correction involves a “reduced volume” (ratio of specific volume to the hard-core specific volume) for the solvent and the mixture (which is presumed to be additive). In calculating this reduced volume, an empirical dimensionless parameter (b) is introduced as an adjustable fit parameter. Oishi and Prausnitz14 successfully correlated VLE data for solutions of linear chains with the UNIFACFV theory with a single parameter value of b ) 1.28. As this parameter reflects the determination of the hard-core specific volume of the molecules, we might anticipate that it will be affected by a high degree of branching in the macromolecule, as this would be expected to affect the ability of the solvent to penetrate into the dendrimers. Further, this would be expected to manifest itself as an increasing value of the excluded hard-core volume as the solvent’s molecular size is increased for a fixed macro* Corresponding author. Figure 1. (a) Acetone activity in solution with the A4 dendrimer at 50 °C.2 (b) Chloroform activity in solution with the B4 dendrimer at 70 °C.2 376 J. Chem. Eng. Data 2002, 47, 376-377

Shear thickening and order–disorder effects in concentrated colloids at high shear rates

The rheology and microstructure of concentrated colloidal suspensions, within the shear thickening regime, are investigated using Stokesian dynamics. We consider systems stabilized by charge and/or polymer layers, at hard core volume fractions above 40%. At φv=0.44, charge stabilized systems show transitions from ordered to disordered flow, with only a small increase in suspension viscosity. At higher φv, we observe larger jumps in viscosity with changes between order and disorder and vice versa. At high shear rates, interparticle gaps can become very small. This work investigates two ways in which these gaps may be controlled: by modifying the charge interaction potential [Dratler et al. (1997)], or by including a model for the presence of a polymer brush [Potanin and Russel (1995)]. The thickening observed is dependent on the gaps of closest approach of particles, but only weakly for hard sphere lubrication forces. Strong thickening is only observed with the presence of an enhanced lubricating force, in this article that due to a polymer coat. Models with polymer coats give examples of strong thickening within the disordered branch of flow. The effects of the number of particles used within these systems, the geometry of the computational box, and whether the simulation is two or three dimensional, can have a profound effect on the microstructure.