The Effect of Composition

On the other hand, the molecules of component 2 are surrounded mainly by molecules of 1, i.e. they find themselves in a strange environment. We would expect, therefore, that its activity coefficient would be very different from one and, using the same physical argument, that this difference would decrease with increasing values of X2. 

These qualitative arguments about deviations from ideality (Raoult s law) should remind us of the Lewis-Randall rule (Section 11.8.3). Indeed Raoult s law, even though it was proposed before the Lewis-Randall rule, represents a special case of the latter. 

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Liquid-liquid equilibria are much more sensitive than vapor-liquid equilibria to small changes in the effect of composition on activity coefficients. Therefore, calculations for liquid-liquid equilibria should be based, whenever possible, at least in part, on experimental liquid-liquid data. 

A trial-and-error procedure is required with any K-value correlation that takes into account the effect of composition. One cannot calculate K values until phase compositions are known, and those cannot be known until the K values are available to calculate them. For K as a function of T and P only, the DePriester charts provide good starting values for the iteration. These nomographs are shown in Fig. 13-14/7 andZ . SI versions of these charts have been developed by Dadyburjor [Chem. Eng. Prog., 74(4), 85 (1978)]. 

Mangipudi et al. [63,88] reported some initial measurements of adhesion strength between semicrystalline PE surfaces. These measurements were done using the SFA as a function of contact time. Interestingly, these data (see Fig. 22) show that the normalized pull-off energy, a measure of intrinsic adhesion strength is increased with time of contact. They suggested the amorphous domains in PE could interdiffuse across the interface and thereby increase the adhesion of the interface. Falsafi et al. [37] also used the JKR technique to study the effect of composition on the adhesion of elastomeric acrylic pressure-sensitive adhesives. The model PSA they used was a crosslinked network of random copolymers of acrylates and acrylic acid, with an acrylic acid content between 2 and 10%. 

Benkoski, J.J., Fredrickson, G.H. and Kramer, E.J., The effect of composition drift on the effectiveness of random copolymer reinforcement at polymer-polymer interfaces. Macromolecules (2001, in press). 

Eigelstein, H. C., and E. N. Skinner. The Effect of Composition on the Scaling of Iron-Chromium-Nickel Alloys Subjected to Cyclic Temperature Conditions, ASTM, STP No. 165 (1954). 

Graft copolymerization of methylmethacrylate onto paper wood pulp using ceric ammonium nitrate as the initiator has been studied. Different experimental conditions have been used, including both water and water-organic solvent systems. The effects of composition of the grafting medium and grafting temperature on the grafting process are examined. 

With regard to the effect of composition, ferrous metals fall into three broad categories ... 

In a previous section it has already been observed that high-strength 2000 and 7000 series alloys are sensitive to the presence of water vapour in corrosion fatigue tests. Stress-corrosion susceptibilities of these alloys in low temperature aqueous solutions and the effect of composition and heat treatment have been widely investigated . It is not surprising therefore that when subjected to corrosion fatigue in similar environments, substantial environmental effects can be observed particularly at low frequencies of less than 1 Hz and AA values above These environmental effects tend to be... 

The time to perforation may be influenced considerably by the random occurrence of pits that happen to meet after starting from opposite sides of a sheet. This chance meeting of pits may be determined only to a slight extent by the composition of the material and, therefore, will interfere with observations of the effects of composition. 

Fig. 8-3. Curves showing the effect of composition on the intensities of the analytical lines in the silica-alumina system. Marked absorption and enhancement effects "are showm. (Courtesy of K. K. Scott, Determination of Major Elements in Clays by X-ray. Spectroscopy, Fall, 1956 Meeting, Refractories Division, American Ceramic Society.)...

Fig. I. Effect of pressure on the melting temperature of argon, (a) Pure argon, (b) argon-helium, (c) argon-hydrogen.Qualitative difference between curves (b) and (c) is due to the effect of composition on the liquid-phase fugacity of argon (M6).

Equations (35) and (36) constitute what is called the unsymmetric convention of normalization, because yt and y g° t0 unity in different ways. The asterisk serves as a reminder that the activity coefficient so designated is normalized in a manner different from the customary one. Separate notation for activity coefficients normalized according to Eq. (36) is psychologically useful because the effect of composition on y is radically different from that on y. 

In addition to deciding on the method of normalization of activity coefficients, it is necessary to undertake two additional tasks first, a method is required for estimating partial molar volumes in the liquid phase, and second, a model must be chosen for the liquid mixture in order to relate y to x. Partial molar volumes were discussed in Section IV. This section gives brief attention to two models which give the effect of composition on liquid-phase thermodynamic properties. 

The difficulties encountered in the Chao-Seader correlation can, at least in part, be overcome by the somewhat different formulation recently developed by Chueh (C2, C3). In Chueh s equations, the partial molar volumes in the liquid phase are functions of composition and temperature, as indicated in Section IV further, the unsymmetric convention is used for the normalization of activity coefficients, thereby avoiding all arbitrary extrapolations to find the properties of hypothetical states finally, a flexible two-parameter model is used for describing the effect of composition and temperature on liquid-phase activity coefficients. The flexibility of the model necessarily requires some binary data over a range of composition and temperature to obtain the desired accuracy, especially in the critical region, more binary data are required for Chueh s method than for that of Chao and Seader (Cl). Fortunately, reliable data for high-pressure equilibria are now available for a variety of binary mixtures of nonpolar fluids, mostly hydrocarbons. Chueh s method, therefore, is primarily applicable to equilibrium problems encountered in the petroleum, natural-gas, and related industries. 

So far, we have described the effect of pressure and temperature on the phase equilibria of a pure substance. We now want to describe phase equilibrium for mixtures. Composition, usually expressed as mole fraction x or j, now becomes a variable, and the effect of composition on phase equilibrium in mixtures becomes of interest and importance. 

Prosser, H. J., Groffman, D. M. Wilson, A. D. (1982). The effect of composition on the erosion properties of calcium hydroxide cements. Journal of Dental Research, 61, 1431-5. 

The design of this fish study centered on sample collection, preservation, preparation, analysis, and QA/QC. There was no discussion of the effect of compositing on the sample population. No description was given of statistical techniques to be applied to the data for reporting results and for comparison with action levels and future data. Unfortunately, the omission of a statistical framework during planning of the field study is the rule rather than the exception in hazardous waste investigations. 

An important aspect is that of studying the effects of composition of the efectrolyte solution on the electrocapillary and capacitance curves. Identical curves are obtained for solutions of fluorides, sulfates, and certain other alkali metal salts having identical... 

Figure 2. Contour sensitivity analysis illustrating the effect of compositional changes on the response around the optimal formulation.

The effects of composition distribution on the morphology of PS-fc-P2VP diblock copolymers were investigated by Matsushita et al. [160]. They produced PS- -P2VP samples with various composition distributions but with constant average composition by blending. If the polydispersity indices of each block were lower than 1.7, the expected lamellar domains were detected (Fig. 49). 

Once the standard Gibbs free energy is known for a reaction, then the effect of composition can also be considered by adding in the concentration-dependent... 

An associated technique which links thermal properties with mechanical ones is dynamic mechanical analysis (DMA). In this, a bar of the sample is typically fixed into a frame by clamping at both ends. It is then oscillated by means of a ceramic shaft applied at the centre. The resonant frequency and the mechanical damping exhibited by the sample are sensitive measurements of the mechanical properties of a polymer which can be made over a wide range of temperatures. The effects of compositional changes and methods of preparation can be directly assessed. DMA is assuming a position of major importance in the study of the physico-chemical properties of polymers and composites. 

Phases may also become unstable with regard to compositional fluctuations, and the effect of compositional fluctuations on the stability of a solution is considered in Section 5.2. This is a theme of considerable practical interest that is closely connected to spinodal decomposition, a diffusion-free decomposition not hindered by activation energy. 

An early study of the influence of composition heterogeneity on the physical properties of copolymers was undertaken by Nielson (4), but to the knowledge of the authors, there have been no similar Investigations involving tin-based polymers. In this work a range of different acrylic co- and terpolymers has been prepared and the effects of composition and composition distribution on the physical and performance-related properties of the polymers in their native state and In paints have been examined. 

To investigate the effect of composition at high pressures, two-parameter bifurcation diagrams are constructed. An example is shown in Fig. 26.2. Cuts at fixed compositions are shown in Fig. 26.1. A nonextinction regime is found on each side of the stoichiometric point, within which the flame cannot be... 

With respect to micromechanisms of failure, at low values of Ak, discontinuous growth bands whose spacings correspond to many cycles of loading were observed (26,32). Figure 10 shows the effect of composition on r, the spacing of the bands, the yield stress o (estimated from the Dugdale relationship, r ifK /80 ), and tlJe... 

Figure 3 shows the effects of composition on the Tg s for both ionomer and nonionomer pseudo-IPN. They exhibit good linearity for both pseudo-IPNs. Nonionomer pseudo-IPN reveals two lines due to the phase separation. The bottom most one is PU and the top most one is VMCC, but they shifted inward due to the formation of pseudo-IPN. 

In terms of practical use, one of the most important features of phase equilibria can often be the effect of composition on some critical temperature. This can be a liquidus or solidus or a solid-state transformation temperature, such as the /3-transus temperature, (T ), in a Ti alloy. The solidus value can be critical, as solution heat-treatment windows may be limited by incipient melting. In some materials a solid-state transformation temperature may be of prime importance. For example, in Ti alloys it may be specified that thermomechanical processing is performed at some well-defined temperature below the / -transus temperature. The CALPHAD route provides a method where such temperatures can be quickly and reliably calculated. 

The effects of composition of heavy oils derived from petroleum and biomass, on their response to cracking over catalysts of various composition were investigated. The contribution to the conversion from different types of cracking was estimated and the effect of temperature on the product distribution was studied. 

To study the effects of composition on the photopolymerization behavior of acrylates, the group of Bowman et al. prepared gradient libraries where acrylate composition was varied in one dimension and light exposure was varied using a moveable shutter in the orthogonal direction [17-21]. An FTIR microscope was used to characterize the conversion across the samples and the data from multiple libraries was then used to derive kinetic models for the photopolymerization. 

The characteristics of particulate filled polymers are determined by the properties of their components, composition, structure and interactions [2]. These four factors are equally important and their effects are interconnected. The specific surface area of the filler, for example, determines the size of the contact surface between the filler and the polymer, thus the amount of the interphase formed. Surface energetics influence structure, and also the effect of composition on properties, as well as the mode of deformation. A relevant discussion of adhesion and interaction in particulate filled polymers cannot be carried out without defining the role of all factors which influence the properties of the composite and the interrelation among them. 

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