Recent Progress in Constraining the Equation of State of Dense Neutron-Rich Nuclear Matter with Heavy-Ion Reactions

The nuclear symmetry energy E-sym(rho) is the most uncertain part of the Equation of State (EOS) of dense neutron-rich nuclear matter. In this talk, we discuss the underlying physics responsible for the uncertain E-sym(rho) especially at supra-saturation densities, the circumstantial evidence for a super-soft E-sym(rho) from analyzing pi(-)/pi(+) ratio in relativistic heavy-ion collisions and its impacts on astrophysics and cosmology.

Isospin dependence of the nuclear equation of state near the critical point

We discuss experimental evidence for a nuclear phase transition driven by the different concentrations of neutrons to protons. Different ratios of the neutron to proton concentrations lead to different critical points for the phase transition. This is analogous to the phase transitions occurring in He-4-He-3 liquid mixtures. We present experimental results that reveal the N/A (or Z/A) dependence of the phase transition and discuss possible implications of these observations in terms of the Landau free energy description of critical phenomena.

Calculating the equation of state parameters and predicting the spinodal curve of isotactic polypropylene/poly(ethylene-co-octene) blend by molecular dynamics simulations combined with Sanchez-Lacombe lattice fluid theory

Molecular dynamics simulations are adopted to calculate the equation of state characteristic parameters P*, rho*, and T* of isotactic polypropylene (iPP) and poly(ethylene-co-octene) (PEOC), which can be further used in the Sanchez-Lacombe lattice fluid theory (SLLFT) to describe the respective physical properties. The calculated T* is a function of the temperature, which was also found in the literature. To solve this problem, we propose a Boltzmann fitting of the data and obtain T* at the high-temperature limit. With these characteristic parameters, the pressure-volume-temperature (PVT) data of iPP and PEOC are predicted by the SLLFT equation of state. To justify the correctness of our results, we also obtain the PVT data for iPP and PEOC by experiments. Good agreement is found between the two sets of data. By integrating the Euler-Lagrange equation and the Cahn-Hilliard relation, we predict the density profiles and the surface tensions for iPP and PEOC, respectively. Furthermore, a recursive method is proposed to obtain the characteristic interaction energy parameter between iPP and PEOC. This method, which does not require fitting to the experimental phase equilibrium data, suggests an alternative way to predict the phase diagrams that are not easily obtained in experiments.

The glass transition temperatures of PS/PPO blends: Couchman volume-based equation and its verification

The glass transition temperatures (T-g) of PS/PPO blends with different compositions were studied under various pressures by means of a PVT-100 analyzer. A general relation of T-g and pressure of the PS/PPO system was deduced by fitting the experimental T-g's. Couchman volume-based equation was testified with the aid of those data. It was found that the experimental T-g's do not obey the Couchman equation of glass transition temperature based on thermodynamic theory. According to our studies, the major reason of the deviation is caused by the neglect of DeltaV(mix). (C) 2001 Published by Elsevier Science Ltd.

EQUATION OF STATE FOR POLYMER SOLIDS

A new equation of state for polymer solids is given by P = B0/4 98[(V0/V)7.14 - (V0/V)2.16 + T/T0] comparison of the equation of state with experimental data is made for six kinds of polymers at different temperatures and pressures. The results obtained shown that the equation is suitable to describe the compression behavior of solid polymers in the region without transition.

A NEW ISOTHERMAL EQUATION OF STATE FOR POLYMERS

A new isothermal equation of state for polymers in the solid and the liquid is given by P = B(T, 0)/(n - m){[V(T, 0)/V(T, P)]n + 1 - [V(T, 0)/V(T, P)]m + 1} where n = 6.14 and m = 1.16 are general constant's for polymer systems. Comparison of the equation with experimental data is made for six polymers at different temperatures and pressures. The results predict that the equation of state describes the isothermal compression behaviour of polymers in the glass and the melt states, except at the transition temperature.

DETERMINATION OF THE MARK-HOUWINK EQUATION FOR CHITOSANS WITH DIFFERENT DEGREES OF DEACETYLATION

The values of k and alpha in the Mark-Houwink equation have been determined for chitosans with different degrees of deacetylation (DD) (69, 84, 91 and 100% respectively), in 0.2 M CH3COOH/0.1 M CH3COONa aqueous solution at 30-degrees-C by the light scattering method. It was shown that the values of alpha-decreased from 1.12 to 0.81 and the values of k increased from 0.104 x 10(-3) to 16.80 x 10(-3) ml/g, when the DD varied from 69 to 100%. This is due to a reduction of rigidity of the molecular chain and an increase of the electrostatic repulsion force of the ionic groups along the polyelectrolyte chain in chitosan solution, when the DD of chitosan increases gradually.

EQUATION OF STATE FOR POLYMERS

In the theoretical study on equation of state for polymers, much attention has been paid to the polymer in liquid state, but less to that in solid state. Therefore, some empirical and semi-empirical equations of state have been used to describe its pressure-volume-temperature (P-V-T) relations.

Modification to the Hardisty equation, regarding the relationship between sediment transport rate and particle size

Bagnold-type bed-load equations are widely used for the determination of sediment transport rate in marine environments. The accuracy of these equations depends upon the definition of the coefficient k(1) in the equations, which is a function of particle size. Hardisty (1983) has attempted to establish the relationship between k(1) and particle size, but there is an error in his analytical result. Our reanalysis of the original flume data results in new formulae for the coefficient. Furthermore, we found that the k(1) values should be derived using u(1) and u(1cr) data; the use of the vertical mean velocity in flumes to replace u(1) will lead to considerably higher k(1) values and overestimation of sediment transport rates.