Experimental Specific Volumes Research Articles

Modeling the thermodynamic behavior of copolymers using equation of state

A simplified procedure with minimum input information for calculating an analytical equation of state for copolymer melts from density and surface tension at the room temperature, as scaling constants, is presented. The second virial coefficients are calculated from a two-parameter corresponding states correlation, which is constructed with two constants as scaling parameters, i.e., the molar density (ρ r) and surface tension at room temperature (γ r). This new correlation has been applied to the Tao–Mason equation of state to calculate the volumetric behavior of copolymer melts including poly(ethylene-co-propylene), poly(ethylene-co-vinyl acetate), poly(ethylene-co-metacrylic acid), poly(ethylene-co-acrylic acid), poly(ethylene-co-vinyl alcohol), poly(styrene-co-acrylonitrile), and poly(acrylonitrile-co-butadiene). The experimental specific volumes were correlated satisfactorily with our procedure and average absolute deviation percent for 7,431 data point is within 0.93 %.

Modification of Tao-Mason equation of state: application to polymer melts

The present work addresses a simplified procedure for the calculation of certain parameters in the Tao-Mason (TM) equation of state (EOS) needed to calculate the volumetric properties of polymer melts using surface tension γf and liquid density at freezing temperature ρf, with scaling parameters at compressed state and in the temperature range of 298.15 to 423.15 K and pressures up to 200 MPa. The polymers in question are polyethylene glycol (PEG), polypropylene glycol (PPG), polypropylene (PP) and polyvinyl choloride (PVC). The calculated densities were in good agreement with the ones obtained from the experimental specific volumes as well as polymer chain-of-rotator (PCOR) EOS. The accuracies were found to be of the order of 1.5%. Finally, the modified TM EOS was further assessed through comparing with the Ihm-Song-Mason (ISM) EOS.

Determination of the effect of pressure on viscosity of an isotactic polypropylene

Despite the importance of the effect of pressure on the flow properties of a polymeric material, it is often overlooked also because of the difficulties involved in the experimental measurements. In this study, the effect of pressure on viscosity for an isotactic polypropylene was characterized in both a direct and an indirect method. In particular, a homemade device was adopted to obtain data of viscosity under high pressure and high shear rates. In addition, an indirect method based on the Simha–Somcynsky equation of state was adopted to obtain the dependence of free volume on temperature and pressure on the basis of experimental specific volume measurements; the Doolittle equation was then applied to verify the dependence of viscosity on free volume. The two methods provided similar results, confirming that, at least for polypropylene, the indirect method based on specific volume measurements can be used instead of the more complex direct measurement of the viscosity under pressure.

(Pressure + volume + temperature) properties for binary oligomeric solutions of poly(ethylene glycol mono-4-octylphenyl ether) with 1-octanol or acetophenone at pressures up to 50 MPa

Densities were measured with a high-pressure densitometer for two binary oligomeric systems of poly(ethylene glycol mono-4-octylphenyl ether) (PEGOPE) with 1-octanol or acetophenone at temperatures from 298.15 K to 348.15 K and pressures up to 50 MPa. While the excess volumes are negative in (acetophenone + PEGOPE) over the entire composition range, those are found to change from positive to negative with increasing mole fraction of the solvent in (1-octanol + PEGOPE). The pressure-effect on the liquid densities can be represented accurately by the Tait equation. Moreover, an empirical equation with two characteristic parameters correlates well the PVT data over the entire experimental conditions for each binary system. The experimental specific volumes were also correlated with the Flory–Orwoll–Vrij (FOV) and the Schotte equations of state to within the experimental uncertainty.

Pressure−Volume−Temperature Properties for Binary Oligomeric Solutions of Poly(ethylene glycol) and Poly(ethylene glycol methyl ether) with Acetophenone up to 50 MPa

Pressure−volume−temperature (PVT) properties were measured with a high-pressure densitometer for the oligomeric solutions of acetophenone + poly(ethylene glycol)-200 (PEG-200) and acetophenone + poly(ethylene glycol methyl ether)-350 (PEGME-350) at temperatures from 298.15 K to 348.15 K and pressures up to 50 MPa. While the excess volumes are positive in acetophenone + PEG-200 over the entire composition range, those are found to change from positive to negative with increasing the mole fraction of the solvent in acetophenone + PEGME-350. The pressure effect on the liquid densities can be represented accurately by the Tait equation. Moreover, an empirical equation with two characteristic parameters correlates well the PVT data over the entire experimental conditions for each binary system. The experimental specific volumes were also correlated with the Flory−Orwoll−Vrij (FOV) and the Schotte equations of state to within the experimental uncertainty.

Application of the ISM EoS for polymer melts

A method for predicting an analytical equation of state for polymer melts from surface tension and liquid state density at the freezing temperature ( γ f, ρ f), as scaling constants, is presented. B 2( T) follows a promising corresponding-states principle. Calculation of α( T) and b( T), the two other temperature-dependent constants of the equation of state, are made possible by scaling. As a result, γ f and ρ f are sufficient for the calculation of thermophysical properties of polymer melts. We applied the procedure to predict specific volumes of polyethylene glycol (PEG), polypropylene glycol (PPG), polypropylene (PP) and polyvinylchloride (PVC) at compressed state with temperature range from 298.15 to 423.15 K and pressures up to 200 MPa. The experimental specific volumes were correlated satisfactorily with our procedure and the results are within 3%.

Pressure−Volume−Temperature Properties for Binary Polymer Solutions of Poly(propylene glycol) with 1-Octanol and Acetophenone

The pressure−volume−temperature (P−V−T) properties were measured for polymer solutions of poly(propylene glycol) + 1-octanol and poly(propylene glycol) + acetophenone at temperatures from 298 to 348 K and pressures up to 50 MPa. The experimental density data were used to calculate the excess volumes, which show a change from negative to positive as the mole fraction of the polymer component is increased for both systems. The Tait equation accurately represents the pressure effect on the liquid densities over the entire pressure range. A generalized equation with two characteristic parameters correlates well all of the P−V−T data for each binary system. The experimental specific volumes were also correlated satisfactorily with the Flory−Orwoll−Vrij and the Schotte equations of state.

ANALYSIS OF THE PRESSURE EFFECT ON THE CRYSTALLIZATION KINETICS OF POLYPROPYLENE: DILATOMETRIC MEASUREMENTS AND THERMAL GRADIENT MODELING

Dilatometric measurements in isobaric cooling mode were performed to study the pressure effects on the crystallization kinetics of polypropylene (PP) up to 100 MPa. The experimental specific volume curves were analyzed by taking into account the thermal gradient that appears in the sample even for relatively low cooling rates. The Tait equation was used to describe the specific volume of the purely amorphous phase, and linear variations of the purely crystalline phase specific volume are considered. The relative crystal linity was modeled using the Nakamura equation, which is relevant for non-constant cooling rates. Considering an Avrami exponent of 3, the Nakamura rate constant was obtained first at atmospheric pressure and then generalized for higher pressures considering the equilibrium melting temperature variation. The obtained intrinsic specific volume was validated by computing the thermal gradient in the sample and comparing the calculated average specific volume to the experimental one.

Pressure, Volume, and Temperature for Mixtures of Poly(ethylene glycol methyl ether)-350 + Anisole and Poly(ethylene glycol)-200 + Anisole from 298 K to 338 K and Pressures up to 50 MPa

PVT properties were measured for mixtures of poly(ethylene glycol methyl ether)-350 + anisole and poly(ethylene glycol)-200 + anisole at temperatures from 298 K to 338 K and pressures up to 50 MPa. Excess volumes are positive for these two polymer solution systems. The isothermal compressibilities were calculated with the aid of the Tait equation, which represented accurately the pressure effect on the liquid densities over the entire pressure range. The experimental specific volumes were correlated with the Flory−Orwoll−Vrij and the Schotte equations of state.

PVT Measurements for Mixtures of 1-Octanol with Oligomeric Poly(ethylene glycol) from 298 K to 338 K and Pressures up to 30 MPa

PVT properties were measured for mixtures of 1-octanol with fractionation cuts of poly(ethylene glycol)-200 or poly(ethylene glycol)-600 at temperatures from 298 K to 338 K and pressures up to 30 MPa. Excess volumes are positive for these two polymer solution systems. The pressure effect on the liquid densities was represented accurately by the Tait equation, with which the isothermal compressibilities were calculated. Both the Flory−Orwoll−Vrij and the Schotte equations of state were employed to correlate the experimental specific volumes. Accurate results were obtained from these two equations.

PVT Measurements for Mixtures of Poly(ethylene glycol methyl ether) with Poly(ethylene glycol) from 298 K to 338 K and Pressures up to 30 MPa

PVT properties were measured for fractionation cuts of poly(ethylene glycol methyl ether)-350, poly(ethylene glycol)-200, poly(ethylene glycol)-600, and their blends at temperatures from 298 K to 338 K and pressures up to 30 MPa. Excess volumes were found to be negative in blending poly(ethylene glycol)s with poly(ethylene glycol methyl ether). The pressure effect on the liquid densities was represented accurately by the Tait equation, which was used to calculate isothermal compressibilities for the oligomers and the oligomeric blends. Both the Flory−Orwoll−Vrij and the Schotte equations of state were employed to correlate the experimental specific volumes. Accurate results were obtained from these two equations.

An empirical equation of state for liquids

An empirical four-parameter equation is presented. It has been applied to 104 compounds in the liquid state, and it allows experimental specific volumes of liquids up to 300 MPa to be interpolated quite well at least in the temperature domain approximately ranging from melting to boiling at atmospheric pressure. In particular, results for saturated hydrocarbons, alcohol, esters, glycol, and alkyl halides have been considered. In each family of compounds, the four parameters were found not to vary much. It was then possible to characterize each family by mean values of two parameters. Using these two parameters together with two volume data determined at atmospheric pressure, it was possible to predict specific volumes of liquids up to 300 MPa with a 1% accuracy for the last four families quoted above

Pressure–volume–temperature relationships for polymeric liquids: A review of equations of state and their characteristic parameters for 56 polymers

AbstractA review of theoretical equations of state for polymer liquids is presented. Characteristic parameters for six equations of state, as well as parameters for the empirical Tait equation, are given for 56 polymers where pressure–volume–temperature (PVT) data over a wide range of conditions could be found in the literature. New PVT data are presented for four polymers: poly(epichlorohydrin), poly(ϵ‐caprolactone), poly(vinyl chloride), and atactic polypropylene. All six equations of state provide adequate fits of the experimental specific volume data for the 56 polymers in the low pressure range (up to 500 bar). The modified cell model of Dee and Walsh, the Simha–Somcynsky hole theory, the Prigogine cell model, and the semiempirical model of Hartmann and Haque, were all found to provide good fits of polymer liquid PVT data over the full range of experimental pressures. The Flory–Orwoll–Vrij and the Sanchez–Lacombe lattice–fluid equations of state were both significantly less accurate over the wider pressure range. © 1993 John Wiley & Sons, Inc.