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In this work, the static sorption technique has been extended to measure the diffusivity as well as the solubility of gases in polymers at elevated pressures. This has been accomplished by operating several static sorption capsules in parallel in order to measure the fractional mass uptake of a gas by a polymer with time. Equilibrium and diffusion data of propylene and ethylene in atactic polypropylene have been measured in the temperature range of 25−70 °C. The group-contribution, lattice-fluid equation of state (GCLF-EoS) was used to correlate the equilibria data with a single value of the binary interaction parameter for each of the systems. The Vrentas−Duda free-volume theory was employed to describe the propylene and ethylene diffusivity data. The chemical potential gradient used in the free-volume correlation of the diffusivity data was obtained from the GCLF-EoS.

A new model has been developed for inverse gas chromatography experiments for binary polymer−solvent systems. The model includes both bulk and surface effects and has been solved using the method of Laplace transforms. Retention data near the glass transition temperature were collected from the literature and correlated and predicted with the model. Frequently investigators estimate a polymer's glass transition temperature (Tg) from the Z-shaped retention data that often occur in this temperature range. The results presented here suggest that there is little or no correlation between the Z-shaped retention diagram and the glass transition temperature. New results are also presented on the origins of the Z-shaped retention diagram and on how a combination of bulk absorption, bulk diffusion, and surface adsorption contribute to it.

A general procedure has been developed to predict the vapor−liquid equilibria (VLE) of solvent/copolymer systems with the Panayiotou and Vera equation of state (PV-EOS), using binary interaction parameters deduced from homopolymer VLE data. Mixing rules are proposed for the PV-EOS pure-component parameters and homopolymer−solvent binary interaction parameters in order to predict solvent solubilities in copolymer systems. This methodology has been evaluated with VLE data acquired in this study for water, methanol, and methyl acetate in poly(vinyl acetate), poly(vinyl alcohol), and a copolymer comprised of these two homopolymers containing 88% (molar) poly(vinyl alcohol) repeat units. The predictions from the PV-EOS of the copolymer VLE are in excellent agreement with our experimental data.

Two new volumetric sorption techniques have been developed to measure thermodynamic and mass-transport properties in polymer−solvent systems at elevated pressures. They are both variations of the pressure-decay technique and differ in how the initial gas density is measured. In the first and simplest variation, the initial density is measured by extrapolation of the mass uptake curve from the region of usable data to the experiment starting time. In the second variation, the initial density is measured gravimetrically using a small titanium capsule. Concern has been voiced as to whether the extrapolation-type experiment is capable of measuring the initial gas density as accurately as a dual-chamber technique. To evaluate the accuracy of the extrapolation technique, solubility and diffusion data were collected for carbon dioxide, ethylene, and nitrogen in low-density polyethylene (LDPE) using both methods. The results indicate that the simpler extrapolation method produces the same diffusivity and solubility results as the more complicated dual-chamber method.

A new experimental technique has been developed to measure the solubility of gases and vapors in polymers and other sorbents at elevated pressures. The technique involves measuring the total weight of a vessel containing the sorbent material pressurized with a vapor, assessing the amount of vapor in the headspace of the vessel with an appropriate equation of state, and evaluating the total amount of vapor in (on) the sorbent material by the difference. Adsorption isotherms for carbon dioxide and nitrogen on an activated carbon were measured with the static sorption technique. These data were found to agree well with data taken with a standard volumetric technique. Sorption data obtained using this method for carbon dioxide in poly(vinyl acetate) and propylene in poly(propylene) compare well with data acquired by established techniques. The group-contribution lattice-fluid theory equation of state was used to predict solubility in these systems, and the Panayiotou−Vera equation of state was applied to correlate the solubility data.

Unsteady‐state sorption of a vapor or liquid by a polymer is modeled to include the influence of the moving phase boundary associated with the polymer swelling and diffusion‐induced convection. A formulation presented clearly elucidates the influence of these two effects on the overall sorption process. Numerical solutions of the model equations indicate the errors that can be induced when swelling or convection are neglected. For most polymer‐solvent systems, the influence of the diffusion‐induced convection associated with volume changes in mixing can be neglected in the analysis of sorption processes. In contrast, the correction for the moving boundary or swelling of the polymer phase can be quite significant, particularly when a large step change in solvent concentration is considered.

The capillary-column inverse gas chromatography method was used to measure the diffusion and partition coefficients of ethylbenzene, styrene, and acrylonitrile in polybutadiene (PBD) at infinite dilution of the solvents. Experiments were performed over a temperature range of 50–125 °C. At temperatures well above the glass-transition temperature of PBD, the diffusivities were correlated using an Arrhenius expression. The Arrhenius parameters in turn were intercorrelated and shown to be a function of the occupied volume, thus providing a method for predicting the diffusion of other solvents in the same polymer. Further, the activation energy was predicted using the Duda-Vrentas free-volume approach. The activation energy thus obtained was compared with the activation energy of the Arrhenius approach. The weight-fraction activity coefficient data were compared to the predictions of the group contribution, lattice-fluid equation-of-state, and the UNIquac Functional-group Activity Coefficient (UNIFAC) free-volume models. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1046–1055, 2002

The Dow Chemical Company has recently introduced a new family of copolymers of ethylene and styrene identified as ethylene−styrene interpolymers (ESIs). The ability of the group-contribution lattice-fluid equation of state (GCLF EoS) to predict the volumetric properties of a series of ESIs of different compositions, the solubility parameter of a given copolymer, and the solubility of toluene was tested. The two latter experiments were conducted in the temperature range 50−150 °C. On average, the error in density was less than 1.1% in the temperature and pressure ranges of 100−250 °C and 6.9−690 bar, respectively. The solubility parameter of the polymer was measured using inverse gas chromatography. The solubility parameter was found to have a strong temperature dependency that the model could not reproduce accurately. At 25 °C, however, the model predictions were found to be in the range of the literature data. The GCLF EoS gave good predictions for the solubilities of the vapors at low styrene contents. Discrepancies at high styrene contents were attributed to a less accurate description of the sorption of solvents in pure polystyrene. The investigation shows that crystallinity has an influence on the solvent solubilities even if they are treated on a crystal-free basis.

The inverse gas chromatography method was used for the investigation of the partition and diffusion coefficients of polysulfone and polyetherimide with NMP, γ-butyrolactone, DMSO, acetic acid, propionic acid, THF, and water over a range of temperature from 200 to 270 °C. The weight-fraction infinite-dilution activity coefficients for the solvents, the Flory−Huggins interaction parameters, and the solubility parameters of the polymers are reported.

The ability to predict the drying behavior of thin films and coatings is of great importance to the coating industry and governs the economical production of various polymeric products. In conventional drying processes, a continuous layer of polymer solution is deposited onto a substrate, which is dried in an oven with forced air convection. Recently, a gap dryer was developed that eliminates the need for forced gas flow and provides direct solvent recovery. A model that incorporates simultaneous heat and mass transfer in the bulk polymer and gas phases and jump conditions across the interface is utilized to describe the drying of a binary polymer–solvent system in a gap dryer. Solvent self‐diffusion in the polymer phase is described by the free‐volume theory, and the Flory‐Huggins theory is used to describe polymer–solvent thermodynamics. Simulations indicate the possibility of condensation in the gas phase that can decrease both drying efficiency and coating quality. A method to resolve this problem is proposed, as well as a comparison between the performance of a gap dryer and a conventional convection‐oven dryer.

This study demonstrates that insight into the tribological reactions taking place in mixed and boundary lubrication can be provided by combining microsample four-ball wear tests with chemical analysis using gel permeation chromatography (GPC) as the principal analytical tool. At the end of the microsample four-ball wear test the lubricant turns into a grease-like mixture preventing the liquid lubricant from recirculating into the wear track and thus causing failure. Analyses of the various lubricant samples after their failure in the microsample test all show a relatively small amount of insoluble deposits and a large quantity of unreacted fresh lubricant. Virtually no intermediate reaction products were found. Combining this information with lubricant stability and the fact that a large quantity of lubricant flowed through the sliding junction while only a small portion was oxidized suggests that two very different thermal environments exist in the concentrated contact. The insoluble deposits are typical of thermal oxidative reactions that require temperatures of400°C or above. The unreacted lubricant found at failure indicates that this portion of the lubricant sample was maintained at temperatures of 150°C or below. The formation of grease-like mixture with as little as four percent reacted material indicates the remaining liquid lubricant and its insoluble reaction deposits were well mixed throughout the test. These findings suggest that the hot zones causing severe lubricant degradation are in the immediate vicinity of the asperity-asperity contacts while the low temperature zone - the valleys between asperities which are in the majority - are much cooler.

In some high-temperature applications, it is desirable to deliver the lubricant as a thin liquid film without recirculation. For these conditions, the buildup of the deposit on the hot surfaces outside the actual bearing contact area can be a problem. In this study, a mathematical model is developed which incorporates several chemical and physical processes which are taking place when a thin liquid film of lubricant is converted to a deposit at elevated temperatures. Specifically, the model utilizes kinetic studies of the degradation of tricresyl phosphate and the evaporation of this lubricant at modest temperatures, <280°C, and modest levels of TCP degradation to predict the final or terminal amount of deposit which will be produced over a broad range of temperature. The key to this model is incorporating the influence of the evaporation of the liquid lubricant on the diffusion of oxygen in the gas phase. The diffusion of the evaporated lubricant molecules away from the liquid phase inhibits the diffusion of the oxygen in the gas phase. Consequently, the oxidation of the liquid lubricant is significantly reduced by the unavailability of oxygen even when the liquid film is exposed to a moving stream of air.

Gel permeation chromatography is shown to be a valuable technique for analysis of the oxidation and thermal degradation products of various types of esters. Esters potentially useful as synthetic lubricant basestocks, such as tridecyl pelargonate (a mono-ester), di-2-ethylhexyl sebacate (a diester) and trimethylolpropane triheptanoate (a neopentyl polyolester) form products of up to 50 000 molecular weight when oxidized at high temperatures. The oxidation products have been separated by molecular weight using preparative gel permeation chromatography (GPC) and then have been analyzed spectrographically. The polymeric products of oxidation show similar chemical bond structure for the various types of esters studied. The importance of oxygen and metal catalysis on product formation is demonstrated. The influence of steel surfaces on the products of oxidation suggests a tribochemical reaction resulting in the ultimate formation of a "friction polymer."

The inverse gas chromatography (IGC) method has been evaluated as a method to determine diffusion coefficients in polymer—solvent systems near the glass transition temperature. The poly (vinyl acetate)—toluene system was used for this purpose. Diffusion and partition coefficients were measured over a wide range of temperature. At temperatures significantly above the glass transition of the polymer, the capillary column model developed by Pawlisch and co-workers^1,2 was used. At temperatures near the glass transition temperature, the modification of the capillary column model, proposed by Vrentas et al.³ was used. A sensitivity analysis of the capillary column model was made to delineate the range of applicability of the model. The diffusion coefficients obtained from IGC were compared with those extrapolated from the gravimetric sorption technique. The values agree within the expected range of error. Finally, free-volume theory was evaluated for its ability to predict the temperature and concentration dependencies of diffusion coefficients at temperatures near the glass transition from high temperature IGC data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1233–1240, 1997

Inverse gas chromatography (IGC) is a very fast, accurate, and reliable technique to measure diffusion coefficients. This technique however, has been limited to measurements in the infinite dilution region, i.e., in the region of negligible amount of solvent in the polymer. We have extended the scope of inverse gas chromatography to measure diffusion coefficients at finite concentrations of the solvent. This involves doping the carrier gas with a solvent of interest to achieve finite concentrations of solvent in the carrier gas and hence in the polymer. The carrier gas is passed through a saturator maintained at constant temperature to achieve this purpose. Diffusion coefficients for polyvinyl acetate—toluene, and polystyrene—toluene systems were determined at finite concentrations. The results were compared with the traditional gravimetric sorption and piezoelectric sorption measurements reported in the literature. The data are in excellent agreement with the values reported, correlate well with the Vrentas—Duda free volume theory, and can also be predicted from infinitely dilute data using the free volume theory. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1279–1290, 1997

A sequential four-ball wear test has been developed to study the chemical changes that take place in boundary or mixed film lubrication. In the first sequence, the 52100 steel balls are mated by a 60-minute run-in at 40 Kg load under fully flooded conditions using a 78 centistoke at 40°C white oil. The second segment of the test is run with up to five microliters of the desired lubricant. Lubricant failure in this sequence is defined as a sharp rise in friction, indicating a lack of lubricant supply to the conjunction. Lubricant changes resulting in the failure are determined by a gel permeation chromatography (GPC) analysis of the lubricant at the time of failure compared with the GPC analysis of the new lubricant used, in the lest. Failure appears to occur where the degraded lubricant becomes too thick to flow into the conjunction. In most cases, a relatively small amount of severely oxidized lubricant forms a grease-like mixture containing a relatively large amount of un-reacted. lubricant. The life of lubricants in these tests appears to be dependant, on the reactions driven by frictional heating that take place between the lubricant, dissolved oxygen, and the bearing surface.

The structure of films formed on iron foil and silicon carbide wafers during high temperature (700 degrees C) deposition of two lubricants, tricresol phosphate (TCP) and poly phenyl ether (PPE), were studied using scanning and transmission electron microscopy, energy dispersive x-ray analysis, x-ray diffraction, and rate measurements. It was found that on iron foils, TCP decomposes and some of the molecular fragments which remain interact chemically with the iron. A two-layer structure forms. The bottom layer apparently consists of fairly large oriented cementite (Fe3C) crystals. The top layer contains particles of iron phosphide structures. In thicker films, other iron carbides, iron phosphides, and iron-phosphate crystals are also present. The size, chemical content, and degree of crystallinity of the particle structures was found to change with depth of deposit. The rate of deposition declined with time, and this correlated with a decline in the iron concentration near the surface, suggesting that iron plays a catalytic role in film formation. In contrast, the deposition of PPE resulted in the formation of cone-shaped structures, which were primarily carbonaceous but had some iron-containing crystals on their outer surfaces along with evidence of Fe5C2. The rate of deposition remained constant. Finally, on silicon carbide it was found that the rate of deposition was slow (non-catalytic), and that only amorphous particles, rich in phosphorus, formed.

This study involves the development of correlating equations for the prediction of the bulk moduli of mineral oil-based lubricants, polymer containing lubricants, and several classes of synthetic fluids including methyl silicones, perfluoropolyether, polybutenes, poly α-olefin, polyphenyl ethers, and esters. This technique only requires the viscosity, the density, and deviation factor which is related to structural effects and free volumes of the fluids. Although prediction techniques are available in the literature for mineral oils, this is the first study to consider the predictions of the bulk moduli of polymer solutions and nonmineral oil based fluids.

Recent studies have shown that solid films formed from vapor-delivered lubricants can provide effective lubrication for load-bearing systems at elevated temperatures. A model is developed to describe the processes occurring in the conjunction between two load-bearing surfaces which are being lubricated by a film deposited from a vapor phase. This analysis combines models of the chemical kinetics of the deposition process and the wear process under ideal conditions in which all the wear is due to the reaction of the lubricant vapor with this surface material. The analysis is applied to the case of 1/2 in. M50 steel ball bearings being lubricated in a four-ball wear tester by a vapor at 370°C containing 0.5 mole percent tricresyl phosphate in a nitrogen carrier gas. Under conditions of 600 rpm and a 10 kg load, the analysis indicates that the temperature in the conjunction is 540°C. This analysis elucidates the coupled processes which take place during vapor-deposited lubrication at elevated temperatures.

The ability to predict the drying behavior of coating is of great importance to the coating industry. For this purpose, the model developed by Vrentas and Vrentas has been used to predict the concentration profile as well as the thickness and the temperature change of the polymer film as a function of time. The model incorporates the coupling between heat and mass transfer and diffusion induced convection which occurs when a single layer of a binary polymer solution is dried in a convection heated oven.The model was solved numerically by using the finite difference approximation and it was applied to the well characterized polyvinylacetate(PVAC)-toluene system. The effects of operating conditions on

In this study, diffusion behavior is investigated for polyethylene-polystyrene semi-interpenetrating polymer networks (PES-IPN) with toluene and chloroform and for a polyethylene/toluene system. The results show that diffusion in the semi-IPN material consists of a continuous polyethylene phase containing disperse polystyrene and that the transport in this material closely parallels transport in the homogeneous polyethylene. Consequently, the measured diffusion coefficients can be correlated, using the free-volume theory and parameters which characterize the free volume of the continuous phase, as a function of temperature and concentration. In addition, from the diffusivities of toluene in the polyethylene and the solubilities in the polyethylene and polystyrene, the diffusion coefficients of the PES-IPN/toluene system are predicted with an unsteady-state diffusion model developed in this study. Predictions with the new unsteady-state model are comparable with the experimental data. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 51–57, 1997

A high-shear capillary viscometer was used to determine the viscosity of mineral oil lubricants containing an olefin copolymer up to shear rates of a million reciprocal seconds. Comprehensive measurements were conducted for a range of polymer concentrations from 1–3 wt percent polymer and a temperature range of 38–120° C. The experimental technique utilizes a theoretical analysis procedure to handle the complications associated with viscous heating, the influence of pressure on the viscosity, and the excess pressure drop which occur at the entrance and exit of the capillary. The viscosity of the polymer solutions is determined over the complete range of shear rate starting from the lower Newtonian limit, through the shear-thinning region, and finally, the Newtonian behavior at high shear rates. It is shown that the standard ASTM plot for viscosity-temperature behavior can be used to correlate the viscous behavior for a given polymer concentration over this broad range of shear rates and shear stresses.

The wear characteristics of aluminum-silicon alloys were studied using a pin-on-disk-type wear tester with different types of lubricants under fully flooded condition. Aluminum-silicon alloy pin specimens were run against the same aluminum-silicon disc surfaces. Wear tests showed that wear resistance of aluminum-silicon alloy was largely influenced by the type of lubricant. Test results showed that hydrocarbon-based fluids such as mineral oils or poly-a-olefins exhibit better wear-protecting property and higher load-carrying capacity than polar base fluids such as polyol esters or polyalkylene glycols. This is contrary to the results of iron-iron systems. The effect of water on the wear and scuffing resistance of aluminum-silicon alloy was also investigated. Water was found to promote the formation of aluminum oxide and silicon oxide layers on the surface which reduced the wear rate and increased scuffing load for aluminum-silicon alloy.

While numerous scattering and rheological studies have investigated the disordering mechanism of low-molecular-weight poly(styrene-b-isoprene) (SI) diblock copolymers, relatively few efforts have addressed the real-space morphologies and transport properties of such copolymers at conditions near the order−disorder transition (ODT). In this work, the morphological features of seven compositionally symmetric (50/50 w/w S/I) copolymers ranging in molecular weight from 5000 to 20000, as well as several of their blends, are examined by transmission electron microscopy and small-angle neutron scattering. These results are used to interpret toluene gravimetric sorption data collected at various temperatures. At temperatures above the styrenic glass transition temperature, microphase-ordered copolymer melts are found to exhibit Fickian diffusion. In the case of a copolymer with an experimentally accessible ODT, anomalous sorption (as evidenced by equilibrium overshoot in gravimetric mass-uptake curves) is observed at temperatures near, but below, the ODT. Within the disordered state, Fickian diffusion is regained, indicating that the onset of anomalous diffusion is related to a solvent-induced ODT under isothermal conditions.

Diffusion and equilibrium coefficients in ternary polymer−solvent−solvent systems were measured using inverse gas chromatography (IGC). The technique provides a new approach to probe diffusion in ternary polymer−solvent−solvent systems. The self-diffusion coefficients of a solvent in a mixture of a polymer and a second solvent were measured. Experiments were performed for the diffusion of toluene and methanol in the poly(vinyl acetate) (PVAC)−toluene−methanol system and for diffusion of toluene and heptane in the polybutadiene (PDB)−toluene−heptane system. Predictions of diffusivities in ternary systems based on the free-volume theory are also critically analyzed and compared with the experimental data.

A high-shear capillary viscometer was used to determine the viscosity of mineral oil lubricants containing an olefin copolymer up to shear rates of a million reciprocal seconds. Comprehensive measurements were conducted for a range of polymer concentrations from 1–3 wt percent polymer and a temperature range of 38–120° C. The experimental technique utilizes a theoretical analysis procedure to handle the complications associated with viscous heating, the influence of pressure on the viscosity, and the excess pressure drop which occur at the entrance and exit of the capillary. The viscosity of the polymer solutions is determined over the complete range of shear rate starting from the lower Newtonian limit, through the shear-thinning region, and finally, the Newtonian behavior at high shear rates. It is shown that the standard ASTM plot for viscosity-temperature behavior can be used to correlate the viscous behavior for a given polymer concentration over this broad range of shear rates and shear stresses.

This study involves the development of correlating equations for the prediction of the bulk moduli of mineral oil-based lubricants, polymer containing lubricants, and several classes of synthetic fluids including methyl silicones, perfluoropolyether, polybutenes, poly α-olefin, polyphenyl ethers, and esters. This technique only requires the viscosity, the density, and deviation factor which is related to structural effects and free volumes of the fluids. Although prediction techniques are available in the literature for mineral oils, this is the first study to consider the predictions of the bulk moduli of polymer solutions and nonmineral oil based fluids.

Recent studies have shown that solid films formed from vapor-delivered lubricants can provide effective lubrication for load-bearing systems at elevated temperatures. A model is developed to describe the processes occurring in the conjunction between two load-bearing surfaces which are being lubricated by a film deposited from a vapor phase. This analysis combines models of the chemical kinetics of the deposition process and the wear process under ideal conditions in which all the wear is due to the reaction of the lubricant vapor with this surface material. The analysis is applied to the case of 1/2 in. M50 steel ball bearings being lubricated in a four-ball wear tester by a vapor at 370°C containing 0.5 mole percent tricresyl phosphate in a nitrogen carrier gas. Under conditions of 600 rpm and a 10 kg load, the analysis indicates that the temperature in the conjunction is 540°C. This analysis elucidates the coupled processes which take place during vapor-deposited lubrication at elevated temperatures.

The dispersion of a solute slug in laminar tube flow has been simulated by a numerical method (the Flux Corrected Transport Algorithm) for a set of tube lengths embracing the pure convection through Taylor dispersion regimes. The results reveal unexpected double peak breakthrough curves for tubes of intermediate length. Experimental evidence of double peaks which qualitatively confirms the simulations is discussed.

A simple method based on free-volume theory to predict the pressure-viscosity coefficients of liquid lubricants has been developed. The method only requires the viscosity-temperature relationship and the viscosity at the temperature of interest. The method provides good accuracy when it was tested for 162 data points for various fluid types over wide ranges of temperature and viscosity.

The effects of high pressure, high temperature and high shear rate on the viscosity of VI improved oils are simulated in a series of high-shear experiments by either lowering the experimental temperature or increasing the molecular weight of the base oil. This study clearly demonstrates that there is no significant difference between the two methods for simulating the high temperature and high pressure conditions.

Oil-soluble copper salts such as copper naphthenate have been evaluated as additives to mineral oil, synthetic hydrocarbon, and polyol ester base stocks in the Penn State microoxidation test. These tests were carried out at 225°C under test conditions which show good agreement with the behavior of automotive crankcase oils in the Hi-series hot engine test. At concentrations of 200ppm of copper in a mineral oil, the primary oxidation rate of the mineral oil is increased with the conversion of these primary oxidation products, but further reaction to condensation polymers is substantially decreased. These effects can be seen in both low-carbon steel systems and glass systems. At concentration levels of 2000 ppm copper in the mineral oil, copper is a very effective oxidation inhibitor, and also inhibits condensation polymerization reactions of the primary oxidation products. At these high concentrations, copper also is an effective metal deactivator. Iron corrosion products from a low-carbon steel catalyst surface are essentially stopped by the action of the copper additive.Soluble copper salts are equally effective in the synthetic hydrocarbon and polyol ester studied. The use of 2000 ppm soluble copper in these base stocks produces a lubricant that compares favorably in oxidative stability with the best commercial SAE-grade automotive crankcase oils. In the prevention or delay of deposit formation, 2000 ppm of soluble copper in a mineral oil appears to be superior to typical state-of-the-art SAE crankcase oils.

The removal of impurities, such as residual solvents, unreacted monomers, catalysts, and side‐reaction products from polymers represents an important step in polymer processing. Conventional devolatilization techniques for the purification of polymers have limited effectiveness. Devolatilization with supercritical fluids, however, can enhance impurity removal by increasing the thermodynamic driving force and molecular diffusivity.