Heats of mixing, measurement

There are several different ways of obtaining an estimate of the interaction between two polymers. These include heat of mixing measurements, inverse gas chromatography, solvent vapour absorption, various scattering techniques and viscosity... 

Fig. 16. Heat of mixing measurements for mixtures of secondary octyl acetate with a chlorinated paraffin (used as analogues for an ethylene-vinyl acetate copolymer and chlorinated polyethylene) at 64.5 °C (x), 73.1 °C(0) and 83.5 °C ( ) as a function of composition. The heat of mixing is very temperature dependent and the composition dependence is not as would be expected from the Equa-tion-of-state theory. This will result in a temperature and composition dependence of the interactional parameter...

All these solutions exhibit essentially the same characteristics, the activity coefficients are less than unity and the heat of mixing, measured... 

This introduction is divided into five main parts. 1.1 The fundamental principles and basic relations which establish the notion of the heat of mixing as a thermodynamic function 1.2 The correlation of experimental data 1.3 The principles of heat of mixing measurements 1.4 An appraisal of modem techrriques to measure heats of mixing and a discussion of the different quantities obtained from experiments which yield pertinent information 1.5 A review of selected binary mixtures used as standard reference systems. 

Main types of calorimeter for heat of mixing measurement... 

The strength of the interaction between two polymers can be considered as a criterion for miscibility since for high polymers the interaction parameter needs to be negative. Several reviews of the techniques can be found in the literature. Most experimental methods for measuring the interaction parameter give the total interaction including both enthalpic and entropic parts or, in terms of the equation of state theory, X 2 TvQ 2- One noted exception to this is heat of mixing measurement, which by definition includes only enthalpic contributions. 

For the volume change of mixing and the enthalpy change (heat) of mixing, which are direcdy measurable, AV = and AH =. ... 

The heat of mixing (excess enthalpy) and the excess Gibbs energy are also experimentally accessible, the heat of mixing by direcl measurement and G (or In Yi) indirectly as a prodiicl of the reduction of vapor/hqiiid eqiiihbriiim data. Knowledge of H and G allows calculation of by Eq. (4-13) written for excess properties. 

The extremely low rates of solution of polymers and the high viscosities of their solutions present serious problems in the application of the delicate calorimetric methods required to measure the small heats of mixing or dilution. This method has been applied successfully only to polymers of lower molecular weight where the rate of solution is rapid and the viscosity of the concentrated solution not intolerably great.22 The second method requires very high precision in the measurement of the activity in order that the usually small temperature coefficient can be determined with sufficient accuracy. 

The integral heat of mixing is, of course, the quantity directly measured in the calorimetric method However, the heat change on diluting a solution of the polymer with an additional amount of solvent may sometimes be measured in preference to the mixing of pure polymer with solvent In either case, the desired partial molar quantity AHi must be derived by a process of differentiation, either graphical or analytical. 

Figure 6.3 Ag-Au solid solution. Comparison of measured hardnesses and values calculated from heats of mixing. Data from Sachs and Weerts (1930).

In those cases where concentrations are not measured directly, the problem of calibration of the in-situ technique becomes apparent. An assurance must be made that no additional effects are registered as systematic errors. Thus, for an isothermal reaction, calorimetry as a tool for kinetic analysis, heat of mixing and/or heat of phase transfer can systematically falsify the measurement. A detailed discussion of the method and possible error sources can be found in [34]. 

Reactive Interactions. Likewise, your material supplier may not be much help for reactive interactions on your compatibility chart. For these combinations, the first thing you need to know is how much heat or gas can be generated. In some cases, this can be as simple as using the heat of mixing published in a technical reference book. In others, it may involve use of special equipment to accurately measure the amount of heat and pressure generated during a complex chemical reaction. 

We have been actively developing two types of calorimeters which will operate at elevated temperatures and pressures. One type is a heat of mixing calorimeter to measure enthalpies of dilution in order to obtain differences in partial molal enthalpy... 

Calorimetric measurements can be used to obtain heats of mixing between different surfactant components in nonideal mixed micelles and assess the effects of surfactant structure on the thermodynamics of mixed micellization. Calorimetry can also be successfully applied in measuring the erne s of nonideal mixed surfactant systems. The results of such measurements show that alkyl ethoxylate sulfate surfactants exhibit smaller deviations from ideality and interact significantly less strongly with alkyl ethoxylate nonionics than alkyl sulfates. 

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