Virial Contributions Research Articles

Molecular Insights into the Mechanical Properties of Polymer–Fullerene Bulk Heterojunctions for Organic Photovoltaic Applications

We investigate the mechanical properties of $\pi$-conjugated polymeric materials composed of regioregular poly(3-hexylthiophene) (P3HT) and fullerene C$_{60}$ using coarse-grained molecular dynamics simulations. Specifically, we perform tensile simulations of P3HT:C$_{60}$ composites with varied degrees of polymerization and C$_{60}$ mass fractions to obtain their stress-strain responses. Decomposition of stress tensor into kinetic energy and virial contributions indicates that the tensile moduli of the pure P3HT samples are greatly dependent on non-bonded interactions and on bonded interactions associated with bond-stretching, while the addition of C$_{60}$ leads to an increase in the tensile modulus originating from enhanced non-bonded interactions associated with C$_{60}$. Additionally, the tensile strength of the P3HT:C$_{60}$ samples correlates well with molecular chain entanglements, which are characterized by the average number of kinks per chain obtained from primitive path analysis. We also find that the upper and lower yield points characterizing strain softening become more pronounced with increasing C$_{60}$ mass fraction. Persistent homology analysis indicates that the emergence of the yield points correlates well with the coalescence of microvoids in the course of tensile deformation, resulting in the generation of larger voids. These results provide a fundamental understanding of the molecular determinants of the mechanical properties of $\pi$-conjugated polymer-fullerene composites, which can also help to interpret and predict the mechanical properties of other polymer composites containing fullerene.

Statistical-thermodynamic model for light scattering from eye lens protein mixtures.

We model light-scattering cross sections of concentrated aqueous mixtures of the bovine eye lens proteins γB- and α-crystallin by adapting a statistical-thermodynamic model of mixtures of spheres with short-range attractions. The model reproduces measured static light scattering cross sections, or Rayleigh ratios, of γB-α mixtures from dilute concentrations where light scattering intensity depends on molecular weights and virial coefficients, to realistically high concentration protein mixtures like those of the lens. The model relates γB-γB and γB-α attraction strengths and the γB-α size ratio to the free energy curvatures that set light scattering efficiency in tandem with protein refractive index increments. The model includes (i) hard-sphere α-α interactions, which create short-range order and transparency at high protein concentrations, (ii) short-range attractive plus hard-core γ-γ interactions, which produce intense light scattering and liquid-liquid phase separation in aqueous γ-crystallin solutions, and (iii) short-range attractive plus hard-core γ-α interactions, which strongly influence highly non-additive light scattering and phase separation in concentrated γ-α mixtures. The model reveals a new lens transparency mechanism, that prominent equilibrium composition fluctuations can be perpendicular to the refractive index gradient. The model reproduces the concave-up dependence of the Rayleigh ratio on α/γ composition at high concentrations, its concave-down nature at intermediate concentrations, non-monotonic dependence of light scattering on γ-α attraction strength, and more intricate, temperature-dependent features. We analytically compute the mixed virial series for light scattering efficiency through third order for the sticky-sphere mixture, and find that the full model represents the available light scattering data at concentrations several times those where the second and third mixed virial contributions fail. The model indicates that increased γ-γ attraction can raise γ-α mixture light scattering far more than it does for solutions of γ-crystallin alone, and can produce marked turbidity tens of degrees celsius above liquid-liquid separation.

The initial magnetic susceptibility of polydisperse ferrofluids: A comparison between experiment and theory over a wide range of concentration.

Temperature dependencies of the static initial magnetic susceptibility for ferrofluids at various concentrations are studied using experiment and statistical-mechanical theories. Magnetic susceptibility measurements are carried out for twelve samples of magnetite-based fluids stabilized with oleic acid over a wide range of temperatures (210 K ≲T ≲ 390 K); all samples have the same granulometric composition but different volume ferroparticle concentrations (0.2 ≲ φ ≲ 0.5). Experimental results are analyzed using three theories: the second-order modified mean-field theory (MMF2) [A. O. Ivanov and O. B. Kuznetsova, Phys. Rev. E 64, 41405 (2001)]; its correction for polydisperse ferrofluids arising from Mayer-type cluster expansion and taking into account the first terms of the polydisperse second virial coefficient [A. O. Ivanov and E. A. Elfimova, J. Magn. Magn. Mater 374, 327 (2015)]; and a new theory based on MMF2 combined with the first terms of the polydisperse second and third virial contributions to susceptibility. It turns out that the applicability of each theory depends on the experimental sample density. If twelve ferrofluid samples are split into three groups of strong, moderate, and low concentrated fluids, the temperature dependences of the initial magnetic susceptibility in each group are very precisely described by one of the three theories mentioned above. The determination of a universal formula predicting a ferrofluid susceptibility over a broad range of concentrations and temperatures remains as a challenge.

Low-temperature magnetic susceptibility of concentrated ferrofluids: The influence of polydispersity

In this paper we address the question of theoretical explanation of extremely high low-temperature initial magnetic susceptibility of concentrated ferrofluids . These laboratory synthesized samples [A.F. Pshenichnikov, A.V. Lebedev, J. Chem. Phys. 121(11) (2004) 5455; Colloid J. 67(2) (2005) 189] demonstrated the record-breaking values χ ~ 120 – 150 at temperatures ~ 230–240 K. The existing models predict such high susceptibility only under the assumption of unreasonably large dipolar coupling constant, which is out of the range of applicability. Here we calculate the second virial contribution to susceptibility for polydisperse ferrofluid, modeled by the dipolar hard sphere fluid. In the resulting expression there exists the parameter, which plays a part of dipolar coupling constant and which is defined in a form of double averaging of high powers of particle sizes over the granulometric distribution. For real particle size distribution this effective parameter at least twice exceeds the commonly defined polydisperse dipolar coupling constant. We show that the low-temperature magnetic susceptibility of the record-breaking ferrofluids could be explained theoretically on the basis of the first terms of the polydisperse second virial contribution in combination with the second-order modified mean field model. • Record-breaking magnetic susceptibility of ferrofluids at low temperatures. • Second virial contribution to magnetic susceptibility of polydisperse ferrofluids. • Interparticle dipole correlations are more pronounced in dense ferrofluids. • Presented model describes the ferrofluid susceptibility χ ~ 120 at temperature 240 K.

Atomic-scale simulation of the thermodiffusion of hydrogen in palladium

We report molecular-dynamics simulations of Pd:H to elucidate transport properties, with special focus placed on determining the temperature dependence of the heat of transport Q*. Simulation results are analyzed using the Green-Kubo approach. It is found that Q* describing the thermodiffusion of hydrogen increases linearly with temperature. By contrast, the reduced heat of transport Q*′=Q*−h2, with h2 the partial enthalpy of hydrogen, is approximately temperature independent. By computing separately the potential, kinetic, and virial contributions to Q*, it is possible to understand key features of the thermodiffusion process. In particular, the sum of the kinetic and potential energy of hydrogen atoms is increased above that of an average hydrogen atom by an amount comparable to the migration energy during a successful hop. However, the virial term in the energy flux is less than what would be expected based on the average local stress contribution due to the hydrogen atoms. Detailed calculations show that the relevant component of the stress tensor due to a hopping hydrogen atom exhibits a minimum at the transition state. Hence, while Q* has significant positive contributions due to the excited nature of the hopping hydrogen atom, the reduced heat of transport Q*′ can still be negative. The results here present important insight into the failure of simple kinetic theories of thermodiffusion, and provide a new perspective that can be tested on other systems.

Communications: Self-energy and corresponding virial contribution of electrostatic interactions in dissipative particle dynamics: Simulations of cationic lipid bilayers

General expressions of self-energy and corresponding virial terms for electrostatic interactions in dissipative particle dynamics simulations are derived in this article. In the lattice-sum electrostatics, we found the essential process is to solve the electric field equation of each individual point charge. Strong inward pressure caused by the self-energy is eliminated by subtracting the corresponding virial from the total virial. The resulting method is tested by simulating cationic lipid bilayers in constant pressure ensemble.

General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions

Three distinct forms are derived for the force virial contribution to the pressure and stress tensor of a collection of atoms interacting under periodic boundary conditions. All three forms are written in terms of forces acting on atoms, and so are valid for arbitrary many-body interatomic potentials. All three forms are mathematically equivalent. In the special case of atoms interacting with pair potentials, they reduce to previously published forms. (i) The atom-cell form is similar to the standard expression for the virial for a finite nonperiodic system, but with an explicit correction for interactions with periodic images. (ii) The atom form is particularly suited to implementation in modern molecular dynamics simulation codes using spatial decomposition parallel algorithms. (iii) The group form of the virial allows the contributions to the virial to be assigned to individual atoms.

Heat transport in epoxy networks: A molecular dynamics study

In this article, thermal behavior of an epoxy based thermoset polymer has been discussed using atomistic molecular dynamics simulations. The simulations were performed on crosslinked network of EPON-862 and curing agent-W (DETDA) using consistent valence force field (CVFF). Thermal conductivity was calculated using both equilibrium as well as non-equilibrium molecular dynamics approaches and the results were found to be in good agreement with experimental findings. Different contributions of heat flux vector towards thermal conductivity and their possible coupling are discussed in terms of various convective and virial contributions. In addition, discussion of power spectra analysis of velocity autocorrelation function for crosslinked network shows a broad distribution of low frequency vibrational modes suggesting distribution of relaxation times.

Macroion virial contribution to the osmotic pressure in charge-stabilized colloidal suspensions

Our interest goes to the different virial contributions to the equation of state of charged colloidal suspensions. Neglect of surface effects in the computation of the colloidal virial term leads to spurious and paradoxical results. This pitfall is one of the several facets of the danger of a naive implementation of the so called one component model, where the microionic degrees of freedom are integrated out to only keep in the description the mesoscopic (colloidal) degrees of freedom. On the other hand, due incorporation of wall induced forces dissolves the paradox brought forth in the naive approach, provides a consistent description, and confirms that for salt-free systems, the colloidal contribution to the pressure is dominated by the microionic one. Much emphasis is put on the no salt case but the situation with added electrolyte is also discussed.

Molecular theory of thermal conductivity of the Lennard-Jones fluid

In this paper the thermal conductivity of the Lennard-Jones fluid is calculated by applying the combination of the density-fluctuation theory, the modified free volume theory of diffusion, and the generic van der Waals equation of state. A Monte Carlo simulation method is used to compute the equilibrium pair-correlation function necessary for computing the mean free volume and the coefficient in the potential-energy and virial contributions to the thermal conductivity. The theoretical results are compared with our own molecular dynamics simulation results and with those reported in the literature. They agree in good accuracy over wide ranges of density and temperature examined in molecular dynamics simulations. Thus the combined theory represents a molecular theory of thermal conductivity of the Lennard-Jones fluid and by extension simple fluids, which enables us to compute the nonequilibrium quantity by means of the Monte Carlo simulations for the equilibrium pair-correlation function.

Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensation-charge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.

Computation of pressure components due to Class II force fields

It has been shown that purely angle dependent terms in a force field do not contribute to the total pressure in a molecular simulation. However, this is not the case for the individual components of the pressure tensor, and is also untrue for crossterms in the force field including bond stretch. In this article, we show that virial contributions to the pressure tensor are easily computed in terms of bond distance vectors and atom forces for the bond topologies present in a Class II force field. Results from a simulation of a phospholipid biomembrane using the cff97 force field show that angle and torsional crossterms make a significant contribution to the pressure tensor.

Quasi-particle picture for monatomic gases

A quasi-particle theory for monatomic gases in equilibrium is formulated and evaluated to yield the exact virial contributions to the thermodynamic state functions in lowest order of the density. Van der Waals blocking has necessarily to be accounted for in occupation number statistics. The quasi-particle distribution function differs from the Wigner function by a bilinear functional thereof. The progress made so far is promising with respect to a corresponding version of kinetic theory.

Correlation of Thermodynamic Data for Aqueous Electrolyte Solutions to Very High Ionic Strength Using INSIGHT: Vapor Saturated Water Activity in the System CaCl2-H2O to 250°C and Solid Saturation

Osmotic coefficients for the CaCl2-H2O system between 25 and 250°C and from the dilute region to solid saturation or beyond (i.e., to ≈ 12 mCaCl2 at the lowest temperature and ≈32 mCaCl2 at the highest) have been correlated using the following permutations and modifications of the basic Pitzer ion-interaction equation: (1) the basic Pitzer equation, (2) the Pitzer equation augmented by an ionic strength-dependent third virial contribution, (3) the Pitzer equation together with equilibria involving the formation of CaCl+ and CaCl20, and (4) the simultaneous combination of all of the above. The effectiveness, accuracy, and practicality of each approach are reviewed.

Measurement of the temperature variation of virial coefficients. III. The second virial coefficient of Carbon Disulphide, Methyl Chloride, Acetone, and Methanol, and certain of their binary mixtures

Second virial coefficients have been determined for carbon disulphide, methyl chloride, acetone, and methanol over the temperature range of 50-150� with some additional results at lower temperatures. Similar work has been conducted on the selected mixtures methyl chloride-carbon disulphide, methyl chloride-acetone, acetone-carbon disulphide, and methyl chloride-argon. Methanol, exceptionally, shows very significant third virial contributions in the sub-atmospheric pressure range. A comparison is made with recent models pertaining to molecular interactions between unlike molecules possessing dipolar and quadrupolar contributions to the intermolecular forces.