Equation of state of copolymer melts: The poly(vinyl acetate)–polyethylene pair

The pressure—volume—temperature properties of a series of copolymers ranging in content from 18 to 40 wt % of vinyl acetate, and up to a maximum pressure of 1800 kg/cm² are studied. The results for the melt state can be satisfactorily fitted by the scaled equation of state, developed previously and applied to single-component systems and to mixtures. The dependence of the scaling parameters for the copolymers on composition deviates from that expected for a mixture, where volumes at elevated pressures can be predicted without further recourse to experiment. These differences are discussed in terms of the sequential structure of the copolymer chain and its series of interfaces between the two species.     

Thermal behavior of selected Czech marble samples

The definition as well as prediction of rock thermal behavior seems to be a quite difficult problem significantly effected by rock composition and structure. Temperature increase causes various changes of rock material (such as decomposition, oxidation, phase and polymorphic transformation, etc.). These changes are connected to thermal expansion with following appearance of tensions and cracks in minerals and rock structure. After consequential temperature decrease, developed tensions and cracks still influence the process. This study presents the application of thermogravimetric analysis, differential thermal analysis and thermomechanical analysis in characterization of selected marble thermal behavior. The texture and morphological orientation of calcite grains for marble samples was determined by optical microscopy. FTIR spectroscopy application along with X-ray diffraction (XRD) extended data about mineralogical composition. According to optical microscopy, the calcite grains show marked morphological anisotropy in one direction for some samples. Therefore, the thermal expansion had to be measured in three different (perpendicular to each other) directions. It is evident, that the effect of temperature on the final marble properties depends not only on mineralogical composition, but also on structure, texture and morphological orientation of grains. All these facts significantly influence the interpretation of differences in various marble thermal behavior.     

Graphical Representations of Speed: Obstacles Preservice K‐8 Teachers Experience

This study examines the difficulties college students experience when creating and interpreting graphs in which speed is one of the variables. Nineteen students, all preservice elementary or middle school teachers, completed an upper‐level course exploring algebraic concepts. Although all of these preservice teachers had previously completed several mathematics courses, including calculus, they demonstrated widespread misconceptions about the variable speed. This study identifies four cognitive obstacles held by the students, provides excerpts of their graphical constructions and verbal interpretations, and discusses potential causes for the confusion. In particular, misconceptions arose when students interpreted the behavior and nature of speed within a graphical context, as well as in situations where they were required to construct a graph involving speed as a variable. The study concludes by offering implications for the teaching and learning of speed and its interpretation within a graphical setting.     

Inhomogeneity effects on the crack driving force in elastic and elastic-plastic materials

This article evaluates the effect of material inhomogeneities on the crack-tip driving force in general inhomogeneous bodies and reports results for bimaterial composites. The theoretical model, based on Eshelby material forces, makes no assumptions about the distribution of the inhomogeneities or the constitutive properties of the materials. Inhomogeneities are modeled by making the stored energy have an explicit dependence on the reference coordinates. Then the material inhomogeneity effect on the crack-tip driving force is quantified by the term C_inh, which is the integral of the gradient of the stored energy in the direction of crack growth. The model is demonstrated by two model problems: (i) bimaterial elastic composite using asymptotic solutions and (ii) graded elastic and elastic-plastic compact tension specimen using numerical methods for stress analysis.     

Thermal expansivity of particulate composites: Interlayer versus molecular model

We continue the comparison of the results of an interlayer model, based on the theory of elastic continua, and a molecular model, derived from a theory of mixtures, previously presented in terms of bulk moduli K. We now derive expressions for the dependence of the thermal expansivity _c on the volume fraction _f of the filler, at low and elevated values of _f . Correspondencies between the characteristic parameters, viz. adhesion and repulsion ratios on the one hand, and interlayer content and thermal properties of matrix, filler, and layer, on the other, are examined. Since in the molecular theory both andK are derived from an equation of state, the identical set of parameters determines both functions and suggests correlations between them.     

Application of material forces to fracture of inhomogeneous materials: illustrative examples

The material forces concept has become an elegant tool in continuum mechanics for the calculation of the thermodynamic driving force of a defect. Based on this concept, we have recently shown that inhomogeneities essentially shield or anti-shield crack tips from applied far-field stresses. The goal of this paper is to illustrate this by considering the model example of a crack in a CT-type specimen that contains a bimaterial interface. The crack driving force is calculated as the sum of the far-field driving force and the crack-tip shielding or anti-shielding. Several cases of inhomogeneity in either thermal or elastic properties are considered. Rather simple hand calculations are provided in addition to numerical results to illustrate the advantages of using the material forces concept.     

Molecular weight-dependence of free volume in polystyrene studied by positron annihilation measurements

Positron annihilation lifetime measurements are reported for four monodisperse polystyrenes with molar mass M = 4,000, 9,200, 25,000, and 400,000. The temperature dependences of orthopositronium (o-Ps) lifetime (τ₃) and intensity (I₃) were measured from 5°C to T_g + 30°C for each sample. From these data, the free volume hole size, 〈v_f(τ₃)〉, and fractional free volume h_ps=CI₃〈v_f(τ₃)〉 were calculated. The temperature dependences of τ₃, 〈v_f(τ₃)〉 and h_ps show a discrete change in slope at an effective glass transition temperature, T_g,ps, which is measurably below the conventional bulk T_g. This suggests that τ₃ is sensitive to large holes which retain their liquid-like mobility in the glassy state. Good agreement was found for T > h_g,ps between h_ps and the theoretical free volume fraction h_th deduced from experimental P-V-T data for polystyrene using the statistical mechanical theory of Simha and Somcynsky. Below T_g,ps, deviations between h_ps and h_th are observed, h_ps falling increasingly below h_th as temperature decreases. Whereas h_ps and h_th depend strongly on M in the melt, each essentially independent of M in the glass. A free volume quantity, computed from the bulk volume, which is in good numerical agreement with the Simha-Somcynsky h-function in the melt, gives improved agreement with h_ps in the glassy state. © 1994 John Wiley & Sons, Inc.     

Theoretical equation of state of polymer blends: The poly(2,6-dimethyl-1,4-phenylene ether)–polystyrene pair

A recent theory of multicomponent fluids is applied for the first time to a compatible binary polymer blend. Good accord between the experimental pressure-volume-temperature measurements over the whole range of compositions by Zoller and theoretical predictions obtains. In particular, satisfactory predictions of high pressure from low-pressure information result. From the interplay between experiment and theory, the scaling quantities and thus the characteristic self- and cross interaction parameters are derived. The excess volumes are discussed and estimates of excess enthalpies presented. The theory predicts the actual enthalpy of the components or mixtures once the scaling parameters have been determined by means of volume-temperature data at atmospheric pressure. Enthalpy measurements to test these predictions are highly desirable.     

Concerning free volume quantities and the glass temperature

Free volume quantities proposed earlier by Boyer and Simha in connection with the glass transition are reformulated by taking into account the temperature dependence of the thermal expansivities α _l and α_g for the liquid and the glass, respectively. This necessitates an extrapolation of the liquid to temperatures below Tg which is performed by means of the reduced volume-temperature function established and given a theoretical foundation previously. For the glass, low temperature experimental data, encompassing all relaxations occuring below T_g, are required.

Two polymer series are examined in detail, namely, poly(methacrylates) and poly(vinyl) alkyl ethers, where α_g has been measured between at least 30°K and T_g. Results for poly(methylacrylate) and poly(styrene) are also given. The systematic decrease in the product (αl - αg) · T|_T=Tg with increasing length of the side chain noted previously is considerably reduced but not eliminated when the appropriately corrected expression is substituted instead. However, the free volume fraction related to the quantity αlT|_T=Tg remains more nearly invariant in the polymers analyzed.

An alternative treatment is discussed which considers an occupied volume expanding below T_g by a mechanism of thermal vibrations solely. Experimental and theoretical means of obtaining this quantity arc suggested.