Volume: critical fraction, local

The previous expression returns the value of the droplet radius corresponding to the maximum of the monomer chemical potential curve (f ), and says that, for a given amount of costabilizer in the particle (Uj,)>the droplet radius must be smaller than in order to be locally stable. The same equation can be expressed in terms of the critical costabilizer volume fraction, (p, as follows ... 

X (z) t b c cD mean area per chain comprising brush layer 4.1 local volume fraction of blend component A at depth z 2.1 local composition with plateau in ( >(z) profile 3.2.1 critical volume fraction 2.1 critical volume fraction of very thin film between symmetric walls 3.2.2 ... 

The kinetics of spiropyran and azobenzene photoisomerization deviate from first order when these dyes are entrapped in a solid matrix below Tg.24-34 This behavior has been attributed to the presence of a distribution of free volume within the matrix, as shown in Table 3.11 .35 When the probe is located in sites of free volume Vf greater than the critical volume for isomerization Vfc, the reaction proceeds at the same rate as in solution. For sites of Vf < Vfc, the reaction is retarded, since it becomes controlled by the matrix molecular motions. At low temperature, the local molecular motions are frozen and fluctuations of local free volume become increasingly small as the temperature decreases. Consequently the fraction of sites where Vf < Vk increases. 

The dominant mechanism of deformation depends mainly on the type and properties of the matrix polymer, but can vary also with the test temperature, the strain rate, and the morphology, shape, and size of the modifier particles (Bucknall 1977, 1997, 2000 Michler 2005 Michler and Balta-Calleja 2012 Michler and Starke 1996). Properties of the matrix determine not only the type of the local yield zones but also the critical parameters for toughening. In amorphous polymers with the dominant formation of crazes, the particle diameter, D, is of primary importance, while in some other amorphous and in semicrystalline polymers with the dominant formation of dilatational shear bands or intense shear yielding, the interparticle distance ID, i.e., the thickness of the matrix ligaments between particles, seems to be also an important parameter influencing the efficiency of toughening. This parameter can be adjusted by various combinations of modifier particle volume fraction and particle size. 

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