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A simple, inexpensive method is described for the measurement of specific volumes of thermoplastic melts during extrusion at low shear stresses. Data for several polyolefins agree closely with specific volumes obtained by dilatometry or compression measurements on static melts. Data can be obtained at a variety of temperatures more rapidly than by dilatometry. The method described yields specific volumes essentially at atmospheric pressure, but extension to higher pressures and the measurement of compressibilities is possible, with more complicated apparatus. Simultaneous measurements can be also made of apparent shear rates, and these can be converted to absolute shear rates, and viscosities, by application of standard techniques. The simple procedure described does not permit the concurrent measurement of useful apparent shear and volume viscosities because the initial state of the system reflects operational as well as polymer properties. It is suggested that an extension of the present method would provide such data.

The corresponding states correlation with the surface tension (γ) of polymers after Patterson et al. has been modified by considering the molecular weight (M) dependence of the equation-of-state parameters, which may be estimated by either the Flory-Orwoll-Vrij (FOV) theory or the cell model (CEM). It has been found that the corresponding states principle-cum-FOV predicts the γs of polystyrene melts over a wide range of M satisfactorily. However, its CEM counterpart is rather irrelevant to the present system of interest. Indeed, the three classical linear equations proposed for the variations of γ with M are intimately correlated with the foregoing models, and hence, facilitating the predictions of the γs of polymer end groups. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 697–703, 1998

A novel approach is developed to estimate the interaction energy density, B, of polymer solutions by the melting point depression method using a crystallizable molecule as the probe. It rests on the classical Flory-Huggins lattice model of polymer solutions, and considers the polymer-solvent interaction parameter to be concentration dependent. The ternary system dimethyl terephthalate (DMT)/bis(2-ethylhexyl)adipate (DOA)/poly(vinyl chloride) (PVC) is chosen for the present study. The data of B for the three possible binary interactions are reported as the functions of composition at elevated temperatures. For a plasticized PVC resin containing 20 vol % DOA, the B is estimated to be 6 MJ m -3 , which is approximately 2 MJ m -3 higher than the B value cited in the literature for the PVC mixed with almost 100% DOA. The thermodynamic stability of the ternary system is discussed.

Orthogonal array design (OAD) using two-level OA8(27) matrix was employed for the optimization of solid-phase microextraction (SPME) conditions for the determination of 4-nonylphenol (4-NP) in water. The parameters under consideration for the optimization of SPME conditions include: injector port temperature, initial oven temperature, desorption time, and pH. The effect of dissolved humic substances on the extraction efficiency of SPME for the determination of 4-NP was also investigated. The method is capable of parts per billion detection limit with a %RSD of 6.5%. Thus, the SPME approach is suitable for analytical determination of 4-NP in environmental water samples compared to conventional liquid-liquid extraction (LLE) technique. © 1996 John Wiley & Sons, Inc.

The swelling behavior of the networks of natural rubber, an epoxidized natural rubber, low-density polyethylene, polystyrene, and poly(methyl methacrylate) are studied in six classes of solvents at 60°C. The data of the swelling coefficient are successfully treated by a modified version of the empirical equation proposed by Gee, as to determine the solubility parameter of a polymer, δ2. It is found that increasing the temperature would decrease the δ2's of these polymers with a common rate of 0.02 (J/mL)1/2/K. A semiempirical model is proposed to rationalize the present finding satisfactorily. © 1995 John Wiley & Sons, Inc.

Allyl esters of palm olein, palmitic, and oleic acids were synthesized by transesterification and esterification methods using KOH and absolute H2SO4 as catalysts, respectively. Three allyl esters, namely, allyl palmitate, allyl epoxystearate, and epoxidized allyl ester of palm olein, were successfully polymerized in the presence of t-butyl perbenzoate at 120°C to obtain oligomers with the average number of backbone atoms approximately equal to the number of skeletal atoms of the long-dangling side chains. The kinetic data of polymerization were conformed to the rate equation proposed by other workers. No oxirane cleavage was detected during the chain reaction. The melting behavior of these comb-shaped polymers was compared with that of their respective allylic monomers. The polymer of epoxidized allyl ester of palm olein exhibits a glass transition temperature at 204.4 K. The critical molecular weights of the polymers of allyl esters investigated are predicted to be not lower than 104.

Based on the Saito's model for random chain scission, a novel procedure is developed to determine the activation energy of polymer degradation process. Basically, this is a simple viscometric technique which yields reliable results. In fact, it is superior to the existing viscometry which has been widely used to study the kinetics of random scission. The present method is successfully applied to the thermal degradation of natural rubber, polycarbonate, and poly(tetramethylene oxide) in bulk.

The weight-average molecular weight is estimated by an extrapolation technique based on a linear relation between the viscosity-average molecular weight Mv and a Mark–Houwink–Sakurada constant. This method may also be used to assess the unperturbed dimensions of polymers. If the Mv data are known with high accuracy, then the straight line may be stretched to reach the number-average molecular weight confidently. The slope of the linear plot is associated with the molecular weight distribution and as such can be utilized to compute the polydispersity index.

A simple, inexpensive glass viscometer can be constructed to time the rate at which a rod falls into a liquid held in a concentric closed-end glass cylinder. This equipment can be used to measure absolute values of apparent viscosities of Newtonian and non-Newtonian fluids. Calibration is not required. The technique is an adaptation of a method used previously with polymer melts at elevated temperatures. The present article describes the modifications needed for lower-viscosity fluids, such as paints, and validates the flow analysis with results of study of a characterized Newtonian fluid.

Two novel procedures have been established to estimate the intrinsic viscosity and the Huggins constant accurately. It is shown that these numerical methods are superior to the existing models, namely the Huggins, Nagy–Kelven–Tudos, and Reilly–Van Der Hoff–Ziogas equations. This finding is attributed to the more even distribution of errors in the dependent variables of the present analyses. The viscometic data of a poly(vinyl chloride) sample in tetrahydrofuran are analyzed by the foregoing five approaches whose accuracies are compared in terms of their variances of estimates.

A linear expression is derived from Tobolsky's equation related to the dead-end polymerization method to determine the rate constant for the initiator dissociation. This novel graphical method applies remarkably well to the kinetic data collected by dilatometry from the polymerization of methyl methacrylate initiated by 2,2′-azobisisobutyronitrile and benzoyl peroxide in toluene at 60°C. Results obtained for these two initiators are consistent with those published in the literature. Applicability of the method is confined to at least 5% and at most 13% decomposition of initiator. However, these limiting values are sensitive to the experimental techniques employed. The effects of induced decomposition of benzoyl peroxide and thermal polymerization of methyl methacrylate are shown to be negligible in the present investigations.

The phase-separation process in segmented copolymers is treated by first-order kinetics which couples with the Fox equation to derive an expression for describing the change of soft segment Tg with the annealing time. Kinetic data of five commercial polyurethanes have been analyzed. The studies conclude that the phase-segregation mechanisms involve two elementary steps which can be characterized by two discrete relaxation times. It has been shown quantitatively that a polyether-based polyurethane (ET) recovers its original domain structure faster than a polyester soft-segment material. The average activation energy of the demixing process of an ET polyurethane is found to be about 23 kJ.mol−1 and is not influenced by hydrogen bonding.

A semiempirical equation is developed to compute the unperturbed parameter from the critical concentration of polymer solutions derived from the viscometric and kinetic data. This equation gives satisfactory results for various vinyl polymers including poly(vinyl chloride), polystyrene and poly(methyl methacrylate) among others that follow the Schulz molecular weight distribution function. It is found that the segments of a Gaussian polymer chain are associated with an equal number of foreign segments near its center of mass, when the polymer solution has attained a uniform segment density at the critical concentration. The effect of molecular weight distribution on the present studies is significantly large that it merits an empirical treatment. Defects of the model is also discussed.

A novel method developed to evaluate the unperturbed parameter Kθ from the viscometric data of dilute polymer solutions can be considerably simplified by making the reasonable assumption that the Huggins' constant under theta conditions, kHθ, is equal to ½ for a number-average degree of polymerization of over about 2000. Two linear equations are derived pertaining to the present analysis, one to deal with the experimental data, and the other specially to estimate the intrinsic viscosity [η]θ which corresponds to κHθ. All calculations were done by the linear least-squares method. The Kθ was computed by the Mark–Houwink–Sakurada equation. It is shown that reliable results on Kθ can be obtained for polystyrene and poly(vinyl acetate).

The classical expression for estimating the polymer-solvent interaction parameter χ from melting point data of the solvent is refined by considering χ to be concentration-dependent. Differential scanning calorimetry (DSC) measurements are performed on blends of cis-polyiso-prene-dimethyl terephthalate (DMT) and trans-polyisoprene–DMT. It is found that the presence of DMT would not affect the DSC events of the polyisoprenes appreciably. However, in both cases, the melting point of DMT decreases, and the rate of depression increases with increasing proportions of polymer. These DSC data are analyzed by the proposed procedure. The results on the interaction energy density parameter are presented as a function of the blend concentration, and rationalized by the specific interactions between different moieties on the component molecules. The limitations of the present technique are discussed.

A three-parameter equation is put forward to evaluate the [η] of polymer solution from a wide range of concentrations, up to a relative viscosity of 100. The equation is tested by viscometric data of polystyrene, poly(vinyl chloride), poly(1-vinylnaphthalene), poly(2-vinylnaphthalene), and poly(4-vinylbiphenyl) at different temperatures and in a variety of solvents including mixed solvents. A statistical method is employed to analyze the experimental data. It is found that the values of [η] obtained by the new equation are consistently lower than those derived from the Huggins equation. However, the discrepancy is not more than 3% on average, and it does not affect the values of Mark-Houwink constants significantly. Other parameters of the equation are also computed.

Both the rate constant of initiator dissociation, kd, and the chain transfer constant, Cx, are determined by monitoring the rates of monomer and transfer agent conversions in a chain polymerization. Statistical analysis that takes into account the errors of experimental variables has been used to treat the kinetic data for the polymerization of styrene initiated by benzoyl peroxide (Bz2O2) in carbon tetrachloride at 60°C. Values of kd and Cx produced by this error-in-variable method (EVM) are in accordance with those reported in literature. More important, the EVM algorithm always results in the smallest standard deviations of estimates, and hence, it is superior to the usual least-squares calculations. Other distinct features of the method are outlined. The initiator efficiency for Bz2O2 is estimated to be 0.72 under the present conditions.

The general validity of four single-point methods for intrinsic viscosity ([η]) determination is verified to be unacceptable even for dilute polymer solutions. Also, a direct method based on a truncated version of Huggins equation is shown to be less practical in that it involves advanced experimentation and is valid only at sufficiently low concentrations. In view of the shortcoming and sophistication of the above procedures, an effective approach is introduced to resolve these problems. This novel computation expresses the Huggins coefficient in terms of [η], and the associated equations are calibrated against the polymer system of interest. This procedure is tested using various polymer solutions with results compatible with those acquired by other means. The advantage of the proposed technique is discussed.

A linear equation is proposed to quantify the glass transition behavior of miscible polymer blends in terms of the polymer-polymer interaction density parameter whose values are obtainable from the melting point depression method. This practical model is successfully applied to four series of binary polyblends containing poly(hydroxy ether) of biphenol A, poly(vinyl chloride), poly(vinylidene fluoride), and poly(2,4-dimethyl-1,4-phenylene oxide) as the common components. Each of these groups of polymer systems exhibits a distinct type of intermolecular interaction that can be characterized by the two coefficients of the model equation. In connection with the present analysis, three novel expressions are introduced for describing the glass transition temperature—composition relations of the polymer systems of interest.

A polystyrene melt has been extruded through successive capillaries arranged to produce converging and diverging flow patterns through the twin orifices. Applied pressure at fixed mass flow rate through the combined dies is equal to the sum of the pressure drops in the single capillaries in both flow modes. The Bagley end correction was found to apply to each die in the sequence. Bagley plots were linear with a particular upper capillary at given apparent shear rate in the lower die. No effect of shear history could be detected on the viscous behavior of the polymer, but preshearing in converging flow produced a slight reduction in die swell.

The assumptions involved in the analysis of flow of polymer melts in a closed end falling coaxial cylinder viscometer(1–3) are examined and it is shown that true values of shear rate and shear stress at the wall of the moving cylinder can be obtained by assuming classical Poiseuille flow. Flow curves obtained with a variety of apparatus geometries, driving loads and polymers are consistent with those of other measurement techniques. This apparatus, which is a simple modification of a capillary extrusion rheometer, provides measurements of apparent viscosity at much lower shear rates than can be obtained with the former viscometers. A quantitative measurement of end correction effects is provided by the present analysis. End effects, which are formally similar to those in capillary extrusion, were measured for several polystyrenes and polyethylenes. On a examine les hypotheses qu'implique l'analyse de l'ecoulement de polymeres en fusion dans un viscosimetre comprenant un cylindre coaxial a extremites fermees et tombant; on a constate qu'on peut obtenir les vraies valeurs du taux de cisaillement et de l'effort de cisaillement sur la paroi du cylindre en mouvement en supposant qu'il s'agit de l'ecoulement classique de Poiseuille. Les courbes d'ecoulement qu'on a obtenues, en employant differentes formes geometriques de l'appareil et charges de poussee ainsi que divers polymeres, ont bien concorde avec celles qui resultent de l'utilisation d'autres methodes de mesure. Ledit appareil, qui est un simple modification d'un rheometre a extrusion capillaire, permet d'obtenir des mesures de la viscosite apparente a des taux de cisaillement bien plus faibles que dans le cas des viscosimetres prealablement employes. L'analyse actuelle fournit une mesure quantitative des effets finals de correction; on a mesure, dans le cas de plusieurs polystyrenes et polyethylenes, les effets finals qui sont formellement semblables a ceux qu'on rencontre dans le cas de l'extrusion capillaire.

An inexpensive, accurate falling coaxial cylinder viscometer is described. Viscosities can be measured at shear stresses at least as low as 103 dynes per cm2 and flow curves can be obtained with shear thinning fluids. Data for a polystyrene and a polyethylene polymer coincide with those from other techniques and with corresponding literature values. The lower Newtonian viscosities pf both polymers were experimentally accessible, and it is shown that estimation of ηo by extrapolation from viscosities in the non-Newtonian region may be subject to errors of uncertain magnitude. Shear history of the sample affects the Newtonian and low shear viscosities of high molecular weight polymer melts. On decrit un viscosimetre non-coǔteux dans lequel on peut determiner avec exactitude le temps de chute d'un cylindre coaxial dans un fluide. On peut mesurer des viscosites correspondent a des efforts de cisaillement aussi faibles que 103 dynes au centimetre carre et peut obtenir des courbes d'ecoulement pour des fluides dont la viscosite est reduite par le cisaillement. Les resultats obtenus dans le cas de deux polymeres (polystyrene et polyethylene) concordent avec ceux qui proviennent d'autres methodes et avec les valeurs correspondantes qui ont ete publiees. On a pu determiner experimentalement les viscosites newtoniennes plus faibles des deux polymeres et demontre que l'estimation de ηo par extrapolation des viscosites dang le secteur non-newtonien peut ětre sujette a des erreurs dont l'importance est aleatoire. Le degre de cisaillement auquel ont ete soumis les echantillons affecte les viscosites newtoniennes et a cisaillement faible des polymeres fondus qui possedent un poids molceulaire eleve.

This article considers possible erxors in experiment or analysis and alternative methods of data treatment for a falling coaxial cylinder viscometer. The viscometer uses a weighted rod falling into a polymer melt contained in a closed end concentric cylinder. Flow relations can be solved for non-Newtonian fluid response in steady, simple shearing flow. Although the rod fall is found not to be steady, as assumed, this produces negligible error in the computed flow curves. Consistent flow curves which were independent of apparatus geometry were obtained by a method in which instantaneous rod velocities were estimated graphically from raw data and an end correction was taken into account. On considere, dans le present travail, les erreurs qui peuvent se glisser dans les experiences ou analyses et la methodes alternatives du traitement des donnees dans le cas d'un viscosimetre base sur la chute d'un cylindre coaxial. Dam le dit viscosimetre, on laisse tomber une tige alourdie par un poids dans un polymere en fusion qui se trouve dans un cylindre ferme et concentrique. On peut resoudre les equations d'ecoulement relatives a la reaction d'un fluide non-newtonien engage dans un ecoulement stable et a cisaillement simple. Bien qu'on constate que la chute de la tige n'est pas aussi reguliere qu'on le supposait, l'erreur resultante dans les courbes d'ecoulement calculees est negligeable. On a obtenu des courbes consistantes d'ecoulement, qui ne dependaient pas de la geometrie de l'appareillage, en utilisant une methode dans laquelle on a evalue graphiquement les velocites instantanees de la tige, a partir de donnees brutes, et tenu compte d'une correction finale.

Viscoelastic properties of polymer fluids are single-valued functions of shear stress or shear rate only at high total applied shear. These parameters may vary with applied shear under milder shear histories. The mean total shear in capillary extrusion is shown to be a function of orifice geometry. Apparent flow curves can be measured at various total shear values by changing the length/radius ratio of the capillary. The true shear stress and true shear rate at the orifice wall correspond to infinite total shear conditions. The true flow curve and elastic parameters like die swell are not measured at equivalent total shear unless the capillary is extremely long.

A falling coaxial cylinder viscometer was used to measure the melt flow behaviour of a commercial polystyrene with Mw 260,000. The shear stress region extended down to 0.6 × 104 dynes/cm2 and shear rates were as low as 3 × 10−2 sec−1 at 186°C. The shear rate-shear stress plots were linear at low shear stresses with slopes (differential viscosities) of 3.3 × 105 poises at total shear less than 120 units and decreasing differential viscosity with higher total shear. The flow curves at relatively low total shear were initially dilatant and became pseudoplastic with increasing shear stress. The inflection point represents a Newtonian apparent viscosity, which agrees fairly well with literature values for polystyrenes of the same Mw. Newtonian apparent viscosity is characteristic of a point value of shear stress and shear rate and is not necessarily a plateau region. Observation of a Newtonian region with decreasing shear stress or shear rate does not prove that this flow regime persists unchanged to zero values of the experimental parameter. The existence and magnitude of the Newtonian apparent viscosity reflects shear history of the polymer as well as its constitution and molecular weight distribution.