Model volume

Here,. Ai(X) is the partial SASA of atom i (which depends on the solute configuration X), and Yi is an atomic free energy per unit area associated with atom i. We refer to those models as full SASA. Because it is so simple, this approach is widely used in computations on biomolecules [96-98]. Variations of the solvent-exposed area models are the shell model of Scheraga [99,100], the excluded-volume model of Colonna-Cesari and Sander [101,102], and the Gaussian model of Lazaridis and Karplus [103]. Full SASA models have been used for investigating the thermal denaturation of proteins [103] and to examine protein-protein association [104]. 

The free volume model seems to be more adequate to describe the plasticization behaviour of the systems of lower amine content. According to Eq. (5), the higher is the change of the expansion coefficient the lower is the influence of the diluent volume fraction. The three TGDDM-DDS mixtures cured with 20, 30 and 50 PHR of hardener were characterized l2) by changes of the expansion coefficient at the glass transition, respectively, of 0.63, 1.08 and 2.94x 10 3 °C l. The more dense and stiffer resin crosslinked with 50 PHR of DDS should be, in principle, the less... 

The action of a muscle is a consequence of electrochemically stimulated conformational relaxation processes that occur along every electroactive chain inside a polymeric film. A free-volume model dependent on the... 

Generally, the values of the scaling exponent are smaller for polymers than for molecular liquids, for which 3.2 < y < 8.5. A larger y, or steeper repulsive potential, implies greater influence of jamming on the dynamics. The smaller exponent found for polymers in comparison with small-molecule liquids means that volume effects are weaker for polymers, which is ironic given their central role in the historical development of free-volume models. The reason why y is smaller... 

If it slow, then nucleation is likely to be due solely to proximity. Model D is an example of volame nucleation idiere decomposition of a solid is involved whereas Model E is that involving gas or liquid nucleation of the solid. Note that if nucleation does not occur, the solid reacts uniformly throughout its whole volume (Model F). However, this mode is rare and the nucleation stages are more likely to occur. We wUl not dwell upon how these nucleation models were derived and will only present the results here. One is referred to Appendix I wherein one can study the mathematics used to obtain the net-result. 

CHROMATOGRAM (F(v)) F(v) conventional raw chromatogram heights as a function of retention volume " MODEL MODEL r CUm(S)TJ where - (j W dX)/X PROPORTIONAL TO WEIGHT OF POLYMER INJECTED INTO THE GPC... 

Studies of the effect of permeant s size on the translational diffusion in membranes suggest that a free-volume model is appropriate for the description of diffusion processes in the bilayers [93]. The dynamic motion of the chains of the membrane lipids and proteins may result in the formation of transient pockets of free volume or cavities into which a permeant molecule can enter. Diffusion occurs when a permeant jumps from a donor to an acceptor cavity. Results from recent molecular dynamics simulations suggest that the free volume transport mechanism is more likely to be operative in the core of the bilayer [84]. In the more ordered region of the bilayer, a kink shift diffusion mechanism is more likely to occur [84,94]. Kinks may be pictured as dynamic structural defects representing small, mobile free volumes in the hydrocarbon phase of the membrane, i.e., conformational kink g tg ) isomers of the hydrocarbon chains resulting from thermal motion [52] (Fig. 8). Small molecules can enter the small free volumes of the kinks and migrate across the membrane together with the kinks. 

Amira - Advanced 3 D Visualization and Volume Modeling (http //amira.zib.de/). 

Yavuzturk, C., J.D. Spitler, and S.J. Rees, 1999. A transient two-dimensional finite volume model for the simulation of vertical U-tube ground heat exchangers, ASHRAE Trans., 10592, 465-474. 

In polymer electrolytes (even prevailingly crystalline), most of ions are transported via the mobile amorphous regions. The ion conduction should therefore be related to viscoelastic properties of the polymeric host and described by models analogous to that for ion transport in liquids. These include either the free volume model or the configurational entropy model . The former is based on the assumption that thermal fluctuations of the polymer skeleton open occasionally free volumes into which the ionic (or other) species can migrate. For classical liquid electrolytes, the free volume per molecule, vf, is defined as ... 

Figure 2 The temperature dependence of the self-diffusion coefficient of 2,3-dimethyl-butane predicted by Cohen and Turnbull s free volume model. (From Ref. 25.)...

D Turnbull, MH Cohen. Free-volume model of the amorphous phase Glass transition. J Chem Phys 34 120-125, 1961. 

Due to their high aspect ratio, nanocarbons dispersed in a polymer matrix can form a percolating conductive network at very low volume fractions (< 0.1 %). The conductivity of a composite above the transition from an insulator can be described by the statistical percolation using an excluded volume model [22,23] to yield the following expression ... 

The configurational entropy model describes transport properties which are in agreement with VTF and WLF equations. It can, however, predict correctly the pressure dependences, for example, where the free volume models cannot. The advantages of this model over free volume interpretations of the VTF equation are numerous but it lacks the simplicity of the latter, and, bearing in mind that neither takes account of microscopic motion mechanisms, there are many arguments for using the simpler approach. 

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