PVC/PBA random copolymers obtained by SET–DTLRP: Pressure effect on glass transition,rheology, and processing

A study of the effect of pressure on the glass transition and viscosity of poly(vinyl chloride) (PVC)–poly(butyl acrylate) random copolymers prepared by Single Electron Transfer–Degenerative Chain Transfer Living Radical Polymerization and able to act as self‐plasticized PVCs, is presented. The research has a dual purpose, as it focuses on polymer physics, as well as on applied polymer processing. Results of dynamic mechanical thermal analysis, pressure–volume–temperature (PVT), and extrusion capillary tests were combined, to analyze the additivity of the free volume and the effect of frequency and pressure on the glass transition of the copolymers, T_g. Free volume additivity, which is on the basis of self‐plasticization, was revealed by T_g and activation energy of flow, E_a, results. dT_g/dP results were linked to the number of segments involved in the glass transition temperature. Using an ad hoc model, which involves parameters obtained by PVT and the activation energy of flow, the pressure‐viscosity coefficient was determined. This allowed estimating the viscosity as a function of the shear rate, the temperature and the pressure, offering suitable data to be employed in virtual injection molding. J. VINYL ADDIT. TECHNOL., 25:76–84, 2019. © 2018 Society of Plastics Engineers     

Viscoelastic and pressure–volume–temperature properties of poly(vinylidene fluoride) and poly(vinylidene fluoride)–hexafluoropropylene copolymers

The relationship between the pressure, volume, and temperature (PVT) of poly(vinylidene fluoride) homopolymers (PVDF) and poly(vinylidene fluoride)–hexafluoropropylene (PVDF–HFP) copolymers was determined in the pressure range of 200–1200 bar and in the temperature range of 40°C–230°C. The specific volume was measured for two homopolymers having a molecular weight (M_w) of 160,000–400,000 Da and three copolymers containing between 3 and 11 wt % HFP with a molecular weight range of 320,000–480,000 Da. Differential scanning calorimetry (DSC) was used to simulate the cooling process of the PVT experiments and to determine the crystallization temperature at atmospheric pressure. The obtained results were compared to the transitions observed during the PVT measurements, which were found to be pressure dependent. The results showed that the specific volume of PVDF varies between 0.57 and 0.69 cm³/g at atmospheric pressure, while at high pressure (1200 bar) it varies between 0.55 and 0.64 cm³/g. For the copolymers, the addition of HFP lowered its melting point, while the specific volume did not show a significant change. The TAIT state equation describing the dependence of specific volume on the zero‐pressure volume (V₀,T), pressure, and temperature has been used to predict the specific volume of PVDF and PVDF–HFP copolymers. The experimental data was fitted with the state equation by varying the parameters in the equation. The use of the universal constant, C (0.0894), and as a variable did not affect the predictions significantly. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 230–241, 2001     

Rheology studies of polyethylene/chemical blowing agent solutions within an injection molding machine

An in‐line capillary rheometer nozzle equipped to a conventional reciprocating 55‐ton injection molding machine was used to study the viscosity of single phase low density polyethylene (LDPE)/chemical blowing agent (CBA) solutions under high shear rate in the concentration range of 0 to 5 wt%. The steady shear viscosity of LDPE with endothermic and exothermic chemical blowing agents was measured for shear rates ranging from 170 to 200,000 s^?1 and under pressure conditions up to 36 MPa. Pressure‐volume‐temperature (pvT) measurements were determined to account for the pressure effects and the changes of the free volume during processing. The viscosity reduction of the polymer‐CBA solution was found to be dependent on the concentration of the chemical blowing agent and melt pressure. A model based on a simplified Cross‐Carreau model, incorporating the pvT behavior of LDPE, and the free volume concept was proposed to estimate the viscosity reduction resulting from the addition of a chemical blowing agent. The model employs a scaling method based on concentration‐dependent and pressure‐dependent shift factors to collapse the viscosity measurement to a master curve at each temperature. POLYM. ENG. SCI., 45:1108–1118, 2005. © 2005 Society of Plastics Engineers     

Pressure‐volume‐temperature properties and thermophysical analyses of AO‐60/NBR composites

AO‐60/nitrile‐butadiene rubber (AO‐60/NBR) composites with different AO‐60 contents were prepared and characterized by pressure‐volume‐temperature (PVT) dilatometry in the pressure and temperature ranges of 0–80 MPa and 25–80°C, respectively. The PVT data were analyzed in terms of the empirical Tait equation of state. The thermal expansion coefficient (α) and isothermal compressibility (β) were calculated from the best fit of the Tait equation to the PVT data. The results showed that α and β increased with AO‐60 content, and these results were related to the activity of the molecular chains and the free volume of the composite. The relations were demonstrated by the positron annihilation spectroscopy (PALS) studies. The present study hopes to provide theoretical guidance to the quantitative study of the PVT relationships and thermophysical properties of rubber materials. POLYM. ENG. SCI., 59:949–955, 2019. © 2018 Society of Plastics Engineers     

Influence of temperature,molecular weight,and molecular weight dispersity on the surface tension of polystyrene,polypropylene, and polyethylene. II. Theoretical

Experimental data for the surface tension of polystyrenes of different molecular weights (3400–200,000) and different molecular weight dispersities (1–3) and of different polyolefins are compared with the predictions of the Patterson–Rastogi and Dee–Sauer cell theories, which infer the surface tension from pressure–volume–temperature (PVT) data. PVT data for these polymers were obtained from the literature and experimentally and are fitted to the Flory–Orwoll–Vrij equation of state. Both theories predict that the surface tension will decrease linearly with increasing temperature and increase with molecular weight, thereby corroborating the experimental data. However, both theories underestimate the entropy change in the surface formation per unit area at a constant volume for low molecular weight and polydisperse systems and underestimate the effect of molecular weight dispersity on surface tension. Both theories feature two parameters, m and b, that quantify the enthalpic and entropic contributions to surface tension. The theoretical predictions are fitted to the experimental data for monodisperse polystyrene (with a molecular weight above the molecular weight of entanglement), polypropylene, and linear low‐density polyethylene to quantify the enthalpic contribution to surface tension. b is then evaluated as a function of molecular weight and molecular weight dispersity and is found to decrease with increasing molecular weight and to increase with increasing molecular weight dispersity, showing that end‐group excess at the surface has some effect on surface tension. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 2201–2212, 2002     

Pressure–temperature–viscosity relationship for heavy petroleum fractions

This paper deals with the influence that both pressure and temperature exert on the viscosity of heavy petroleum fractions, such as bitumen of different penetration grades, in temperature and pressure ranges comprised between 60 °C and 160 °C and 0–400 bars, respectively. From the viscous flow tests carried out, it is apparent that bitumen behaves as a Newtonian liquid in the above-mentioned range of temperature and pressure. The temperature–pressure–viscosity relationship for bitumen of different penetration grades, mainly used for paving applications, can be modelled using a modified WLF model, the FMT model. This model includes different physical parameters, such as material compressibility and expansivity, which have been obtained from pressure–volume–temperature (PVT) measurements.     

Thermodynamic study of surfaces of liquid polybutadienes and their interfaces with poly(dimethylsiloxane)

Surface tension of liquid polybutadienes (PBD) as well as interfacial tension between them and poly(dimethylsiloxane) (PDMS) were measured in the temperature range from 25 to 150°C. The measured pressure–volume–temperature (PVT) data were used for the determination of reduction parameters of pressure, volume, and temperature in several equations of state for polymers. The reduction parameters were used for the estimates of surface tension and compared with experimental data. Interfacial tensions were used to determine Flory‐Huggins interaction parameters using the Roe and Helfand theories for the system PBD‐PDMS. The results obtained using both the theories were somewhat different; the difference being the least with the segment chosen as a part of molecule containing 4–5 nonhydrogen atoms. Modifications of PBD that were investigated increase the density. Maleic ester end groups increase both surface tension and interfacial tension and bring a positive contribution to the Flory‐Huggins interaction parameter (to its enthalpic component), whereas the pending maleic anhydride groups have shown the opposite effect; their negative contribution to Flory‐Huggins parameters concerns mainly its entropic component. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Estimates for material shrinkage in molded parts caused by time‐varying cavity pressures

The phenomenology of shrinkage is established through injection molding experiments in which shrinkage was measured at 25‐mm intervals along the length and width of rectangular plaques, molded in an instrumented mold. A simple solidification model, which assumes the solidified material to be elastic, is developed for the effect of time‐varying temperature and pressure histories on part shrinkage. This model predicts a linear dependence of shrinkage on an “effective pressure,” which combines the thermal diffusivity of the material, the wall thickness, and the time‐varying cavity pressure into a single parameter that is uniquely related to the shrinkage. The effective pressure is shown to effectively correlate in‐plane shrinkage data. The solidification model characterizes two material parameters, which can be estimated from the pressure‐volume‐temperature (PVT) diagram for the material, that describe the sensitivity of the shrinkage to the local cavity pressure history. The residual stresses predicted by this model are rather crude. POLYM. ENG. SCI., 59:1648–1656 2019. © 2019 Society of Plastics Engineers     

Modeling/simulating the injection molding of isotactic polypropylene

A unified formulation is presented for modeling the injection molding of isotactic polypropylene (i‐PP). The crystallization kinetics are based upon the differential Nakamura equation in which the characteristic time is dependent upon temperature, pressure and flow‐induced shear stress, without any explicit need for an induction time. A Cross/WLF model is used to represent the shear viscosity in which η_O is dependent upon temperature, pressure and crystallinity. Use is made of a recent correlation for the PVT behavior of i‐PP with an explicit dependence upon crystallinity. A finite‐difference implementation of the modeling is applied to two independent molding experiments available from the literature, with notable results concerning the late‐time cavity pressure traces and time‐dependent gapwise shrinkage prior to ejection.     

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

A 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(?-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.     

Geometrical dependence of viscosity of polymethylmethacrylate melt in capillary flow

The shear viscosity of polymethylmethacrylate (PMMA) melt is particularly investigated by using a twin‐bore capillary rheometer at four temperatures of 210, 225, 240, and 255°C with different capillary dies. Experimental results show that the geometrical dependence of shear viscosity is significantly dependent on melt pressure as well as melt temperature. The measured shear viscosity increases with the decrease of die diameter at lower temperatures (210 and 225°C) but decreases with the decrease of die diameter at higher temperatures (240 and 255°C). Based on the deviation of shear viscosity curves and Mooney method, negative slip velocity is obtained at low temperatures and positive slip velocity is obtained at high temperatures, respectively. Geometrical dependence and pressure sensitivity of shear viscosity as well as temperature effect are emphasized for this viscosity deviation. Moreover, shear viscosity curve at 210°C deviates from the power law model above a critical pressure and then becomes less thinning. Mechanisms of the negative slip velocity at low temperatures are explored through Doolittle viscosity model and Barus equation, in which the pressure drop is used to obtain the pressure coefficient by curve fitting. Dependence of pressure coefficient on melt temperature suggests that the pressure sensitivity of shear viscosity is significantly affected by temperature. Geometrical dependence of shear viscosity can be somewhat weakened by increasing melt temperature. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3384–3394, 2013     

Toward a viscoelastic modeling of anisotropic shrinkage in injection molding of amorphous polymers

A novel approach to predict anisotropic shrinkage of amorphous polymers in injection moldings was proposed using the PVT equation of state, frozen‐in molecular orientation, and elastic recovery that was not frozen during the process. The anisotropic thermal expansion and compressibility affected by frozen‐in molecular orientation were introduced to determine the anisotropy of the length and width shrinkages. Molecular orientation calculations were based on the frozen‐in birefringence determined from frozen‐in stresses by using the stress‐optical rule. To model frozen‐in stresses during the molding process, a nonlinear viscoelastic constitutive equation was used with the temperature‐ and pressure‐dependent relaxation time and viscosity. Contribution of elastic recovery that was not frozen during the molding process and calculated from the constitutive equation was used to determine anisotropic shrinkage. Anisotropic shrinkages in moldings were measured at various packing pressures, packing times, melt temperatures, and injection speeds. The experimental results of frozen‐in birefringence and anisotropic shrinkage were compared with the simulated data. Experimental and calculated results indicate that shrinkage is highest in the thickness direction, lowest in the width direction, and intermediate in the flow direction. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 2300–2313, 2005     

Capillary flow of low‐density polyethylene

The capillary flow of a commercial low‐density polyethylene (LDPE) melt was studied both experimentally and numerically. The excess pressure drop due to entry (Bagley correction), the compressibility, the effect of pressure on viscosity, and the possible slip effects on the capillary data analysis have been examined. Using a series of capillary dies having different diameters, D, and length‐to‐diameter L/D ratios, a full rheological characterization has been carried out, and the experimental data have been fitted both with a viscous model (Carreau‐Yasuda) and a viscoelastic one (the Kaye—Bernstein, Kearsley, Zapas/Papanastasiou, Scriven, Macosko, or K‐BKZ/PSM model). Particular emphasis has been given on the pressure‐dependence of viscosity, with a pressure‐dependent coefficient β_p. For the viscous model, the viscosity is a function of both temperature and pressure. For the viscoelastic K‐BKZ model, the time‐temperature shifting concept has been used for the non‐isothermal calculations, while the time–pressure shifting concept has been used to shift the relaxation moduli for the pressure‐dependence effect. It was found that only the viscoelastic simulations were capable of reproducing the experimental data well, while any viscous modeling always underestimates the pressures, especially at the higher apparent shear rates and L/D ratios. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

On the effect of pressure on the shear and elongational viscosities of polymer melts

The effect of pressure and temperature on the shear and elongational deformation rate–dependent viscosities has been experimentally investigated for several polymers (HDPE, LDPE, LLDPE, PP, PC, PMMA, and PS) on a capillary rheometer with a back‐pressure device. Pressure, β, and temperature, α, coefficients have been determined through simultaneous fitting of the shear and extensional viscosity data by the modified White‐Metzner model. The dependence of β and α on temperature and pressure, respectively, was investigated and it has been found that simple relationships exist between pressure and temperature sensitivity coefficients for individual polymers. Polym. Eng. Sci. 44:1328–1337, 2004. © 2004 Society of Plastics Engineers.     

Precise measurement of the PVT of polypropylene and polycarbonate up to 330°C and 200 MPa

An apparatus for measuring the pressure—volume—temperature (PVT) properties of polymers using a metal bellows has been developed at temperatures from 313 to 623 K and pressures up to 200 MPa. A calibration of the device was performed by measuring PVT of mercury and water. The experimental uncertainty of specific volumes was estimated to be within ±0.2%, while that of temperatures was within ±0.1 K below 300°C and ±0.3 K above 300°C. The estimated uncertainty of pressures was ±0.1 MPa below 100 MPa and ±0.25 MPa above 100 MPa. The PVT properties of polypropylene and polycarbonate were measured by the apparatus in the temperature ranges from 40 to 300°C and from 40 to 330°C, respectively, and pressures from 10 to 200 MPa. The effects of a sample cup and sample forms were investigated. The use of the sample cup showed a little effect on the measurments of PVT properties for both samples. The shape (pellet and pillar) of the samples caused a small difference in the specific volumes only under high temperatures and low pressures. The PVT properties in a melt state were correlated by the Simha-Somcynsky equation of state, showing a good agreement with measurements. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 141–150, 1997     

Theoretical and experimental studies of anisotropic shrinkage in injection moldings of various polyesters

A novel approach to predict anisotropic shrinkage of slow crystallizing polymers in injection moldings was proposed, using the flow‐induced crystallization, frozen‐in molecular orientation, elastic recovery, and PVT equation of state. In the present study, three different polyesters, polyethylene terephthalate, polybutylene terephthalate, and polyethylene‐2,6‐naphthalate (PEN), are used. The anisotropic thermal expansion and compressibility affected by the frozen‐in orientation function and the elastic recovery that was not frozen during moldings were introduced to obtain the in‐plane anisotropic shrinkages. The frozen‐in orientation function was calculated from the amorphous contribution based on the frozen‐in and intrinsic amorphous birefringence and crystalline contribution based on the crystalline orientation function determined from the elastic recovery and intrinsic crystalline birefringence. To model the elastic recovery and frozen‐in stresses related to birefringence during molding process, a nonlinear viscoelastic constitutive equation was used with the temperature‐dependent viscosity and relaxation time. Occurrence of the flow‐induced crystallization was introduced through the elevation of melting temperature affected by entropy production during flow of the viscoelastic melt. Kinetics of the crystallization was modeled using Nakamura and Hoffman‐Lauritzen equations with the rate constant affected by the elevated melting temperature. Numerous injection molding runs were carried out by varying the packing time, packing pressure, flow rate, melt and mold temperature, and anisotropic shrinkage of moldings were measured. The experimental results were compared with the simulated data and found in a fair agreement. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 3526–3544, 2006     

A method for measuring PVT relationships of thermoplastics using an injection molding machine

The objective of this study is to establish a feasible method for generating pressure-specific volume-temperature (PVT) data for thermoplastics on a microcomputer-controlled injectionmolding machine (IMM). This method utilizes the injection barreel of the IMM as a pressure chamber for determining the specific volume of thermopla;stics at various pressure and temperature conditoins. An empirical equation of state based on the Tait equation s used to fit the PVT data of three resins — low-density polythelene (LDPE), polystyrene (PS), and acrylonitrile-butadiene-styrene copolymer (ABS). The comparsion between LPDE's PVT data generating from the IMM and from the classical bellows method indicated that the present method can be reasonably applied for determining the specific volume of thermoplastics as a function of presure and temperature.     

Linear thermoelastic characterization of anisotropic poly(ethylene terephthalate) films

All nine independent elastic constants have been determined for a biaxially stretched poly(ethylene terephthalate) (PET) film using novel mechanical methods. The orthotropic directions and the in‐plane Poisson's ratios were first characterized using vibrational holographic interferometry of tensioned membrane samples. The out‐of‐plane Poisson's ratio was obtained by measuring the change in tension with the change in pressure for constant strain conditions. Pressure–volume–temperature (PVT) equipment was used to measure the bulk compressibility as well as the volumetric thermal expansion coefficient (TEC). The in‐plane Young's moduli were obtained by tensile tests, while the out‐of‐plane modulus was calculated from the compressibility and other elastic constants that describe the in‐plane behavior. The in‐plane TECs in the machine and transverse directions were determined using a thermal mechanical analyzer (TMA). The out‐of‐plane TEC was determined using these values and the volumetric TEC determined via PVT. The resulting compliance matrix satisfies all of the requirements of a positive‐definite energy criterion. The procedure of characterization utilized in this article can be applied to any orthotropic film. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2937–2947, 2002     

Pressure–volume–temperature relationships of solid and molten polypropylene and poly(butene-1)

Experimental data on the dependence of the specific volume on temperature and pressure (PVT data) to 2000 kg/cm² of isotactic polypropylene and isotactic poly(butene-1) are reported and discussed. The temperature range covered is 30–297°C for polypropylene and 30–246°C for poly(butene-1), thus encompassing the solid and molten states of both materials. An empirical equation of state based on the Tait equation can be fitted to the melt data of both materials. The coefficients reported reproduce the measured specific volumes with a standard deviation of less than 0.001 cm³/g.