Free-volume method

In considering fluids, a variety of approaches have been used to compute entropy and free energy a free-volume method,111-112 thermodynamic perturbation theory,113-116 thermodynamic integration,117-121 umbrella sampling,122-124 and a Monte Carlo recursion method.125-126 The entropy of association of two protein molecules in water has also been computed.127... 

The procedure is based on the UNIFAC-Free Volume method developed by T. Oishi and J. M. Prausnitz, "Estimation of Solvent Activities in Polymer Solutions Using a Group-Contribution Method," Ind. Eng. Chem. Process Des. Dev., 17, 333 (1978). The UNIFAC-FV method is presented by Aa. Fredenslund, J. Gmehling, and P. Rasmussen, Vapor-Liquid Equilibria Using UNIFAC, Elsevier Scientific Publishing, New York (1977). The group... 

The permachor method is an empirical method for predicting the permeabiUties of oxygen, nitrogen, and carbon dioxide in polymers (29). In this method a numerical value is assigned to each constituent part of the polymer. An average number is derived for the polymer, and a simple equation converts the value into a permeabiUty. This method has been shown to be related to the cohesive energy density and the free volume of the polymer (2). The model has been modified to liquid permeation with some success. 

Viscosity of Resin Solutions. The viscosity of coatings must be adjusted to the appHcation method to be used. It is usually between 50 and 1000 mPa-s(=cP), at the shear rate involved in the appHcation method used. The viscosity of the coating is controUed by the viscosity of the resin solution, which is in turn controUed mainly by the free volume (4). The factors controlling free volume are temperature, resin stmcture, solvent stmcture, concentration, and solvent-resin interactions. 

Volume of vessel (free volume V) Shape of vessel (area and aspect ratio) Type of dust cloud distribution (ISO method/pneumatic-loading method) Dust explosihility characteristics Maximum explosion overpressure P ax Maximum explosion constant K ax Minimum ignition temperature MIT Type of explosion suppressant and its suppression efficiency Type of HRD suppressors number and free volume of HRD suppressors and the outlet diameter and valve opening time Suppressant charge and propelling agent pressure Fittings elbow and/or stub pipe and type of nozzle Type of explosion detector(s) dynamic or threshold pressure, UV or IR radiation, effective system activation overpressure Hardware deployment location of HRD suppressor(s) on vessel... 

Density. Most fillers added in rubber base formulation have a density between 2 and 2.7 g/cm-, except barium sulphate (4-4.9 g/cm- ) and zinc oxide (5.6 g/cm ). Addition of filler increases the free volume of the polymer and, in general, there is a critical concentration of filler at which the density of the formulation increases. The method of incorporation of filler in the adhesive formulation is important because air voids may appear when a poor dispersion is produced. 

It is a good idea to run the laboratory reactor without catalyst to check for homogeneous reactions. However, this method does not work when the homogeneous reaction involves reactants that do not occur in the feed but are created by a heterogeneous reaction. It then becomes important to maintain the same ratio of free volume to catalyst volume in the laboratory reactor used for intrinsic kinetic studies as in the pilot or production reactors. 

G. D., Prediction of incompressible free Surface flows with an element-based finite volume method, Comput. Fluid Dyn. J. 4 (1995) 353-371. 

Mechanical and chemical methods for qualitative and quantitative measurement of polymer structure, properties, and their respective processes during interrelation with their environment on a microscopic scale exist. Bosch et al. [83] briefly discuss these techniques and point out that most conventional techniques are destructive because they require sampling, may lack accuracy, and are generally not suited for in situ testing. However, the process of polymerization, that is, the creation of a rigid structure from the initial viscous fluid, is associated with changes in the microenvironment on a molecular scale and can be observed with free-volume probes [83, 84]. 

A review of the application of ESR to the study of free radical polymerisation is given by Yamada and co-workers [146]. A survey of the application ESR spectroscopy spin label/probe methods in heterogeneous polymer systems is provided by Veksli and co-workers [147]. Spin probe methods allow the study of the MD of the polymer, its free volume, phase separation and phase morphology. 

If R is known, it is possible to fit the parameters k, ktCC0, A, At, fcp and fct using kinetic data from a single experiment. Thus, if the reaction diffusion parameter is known from the unsteady state after-effect experiments, the kinetic constant evolution can be determined as a function of free volume, and thus conversion. More details about this method will be published elsewhere (18). 

Several material properties exhibit a distinct change over the range of Tg. These properties can be classified into three major categories—thermodynamic quantities (i.e., enthalpy, heat capacity, volume, and thermal expansion coefficient), molecular dynamics quantities (i.e., rotational and translational mobility), and physicochemical properties (i.e., viscosity, viscoelastic proprieties, dielectric constant). Figure 34 schematically illustrates changes in selected material properties (free volume, thermal expansion coefficient, enthalpy, heat capacity, viscosity, and dielectric constant) as functions of temperature over the range of Tg. A number of analytical methods can be used to monitor these and other property changes and... 

Because efficient methods for computing free volumes from molecular simulations were introduced only recently, their connections to the dynamical properties of liquids have yet to be explored systematically. Nonetheless, initial investigations have already allowed scrutiny of some historical notions about these properties. Here, we briefly discuss two of these initial studies. Their results illustrate that some early free-volume based ideas about the origins of dynamics are consistent with simulation data, but those ideas will need significant revision if they are to be applied in a general way. 

Further development of the Flory-Huggins method in direction of taking into account the effects of far interaction, swelling of polymeric ball in good solvents [4, 5], difference of free volumes of polymer and solvent [6, 7] leaded to complication of expression for virial coefficient A and to growth of number of parameters needed for its numerical estimation, but weakly reflected on the possibility of equation (1) to describe the osmotic pressure of polymeric solutions in a wide range of concentrations. 

The method is based on the fact that the rate of conformational change required for excimer formation depends on the free volume induced by the segmental motions of the polymer occurring above the glass transition. DIPHANT (compound 3 in Figure 8.3) was used as an excimer-forming probe of three polymer samples consisting of polybutadiene, polyisoprene and poly(dimethylsiloxane).a)... 

In many applications, such as chromatography, equilibrium titrations or kinetics, where series of absorption spectra are recorded, the individual rows in Y, C and R correspond to a solution at a particular elution time, added volume or reaction time. Due to the evolutionary character of these experiments, the rows are ordered and this particular property will be exploited by important model-free analysis methods described in Chapter 5, Model-Free Analyses. 

Detonation, Free Volume Theory of Multi-component Fluid Mixtures. The free volume theory of the liq state is extended to multi-component fluid mixts by using the method of moments in the treatment of the order-disorder problem. The results of this extension are given in the article by Z.W. 

This is shown semiquantitatively for a series of polyimides, where hydrogen/ fluorine, and symmetric/asyirunetric analogues were synthesized and measured. The free-volume contribution is estimated by a free-volume normalization method developed for this purpose.In these materials, the contribution of changes in free volume to the observed change in dielectric constant ranged from 25 to 95% in moisture-free materials. ... 

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