Network-constrained crystal

Starting with Eq. 2.31 instead of Eq. 2.3 and repeating the procedure that led to Eq. 2.15, the conjugate force for the diffusion of component i in a network-constrained crystal takes the new form... 

Another system obeying Fick s law is one involving the diffusion of small interstitial solute atoms (component 1) among the interstices of a host crystal in the presence of an interstitial-atom concentration gradient. The large solvent atoms (component 2) essentially remain in their substitutional sites and diffuse much more slowly than do the highly mobile solute atoms, which diffuse by the interstitial diffusion mechanism (described in Section 8.1.4). The solvent atoms may therefore be considered to be immobile. The system is isothermal, the diffusion is not network constrained, and a local C-frame coordinate system can be employed as in Section 3.1.3. Equation 2.21 then reduces to... 

The system contains two network-constrained components—host atoms and vacancies the crystal is used as the frame for measuring the diffusional flux, and the vacancies are taken as the Ncth component. Note that there is no mass flow within the crystal, so the crystal C-frame is also a E-frame. With constant temperature and no electric field, Eq. 2.21 then reduces to... 

Birefringence measurements have been shown to be very sensitive to bimodality, and have therefore also been used to characterize non-Gaussian effects resulting from it in PDMS bimodal elastomers [5,123]. The freezing points of solvents absorbed into bimodal networks are also of interest since solvent molecules constrained to small volumes form only relatively small crystallites upon crystallization, and therefore exhibit lower crystallization temperatures [124—126]. Some differential scanning calorimetry (DSC) measurements on... 

In many cases, changes in one extensive quantity are coupled to changes in others. This occurs in the important case of substitutional components in a crystal devoid of sources or sinks for atoms, such as dislocations, as explained in Section 11.1. Here the components are constrained to lie on a fixed network of sites (i.e., the crystal structure), where each site is always occupied by one of the components of the system. Whenever one component leaves a site, it must be replaced. This is called a network constraint [1]. For example, in the case of substitutional diffusion by a vacancy-atom exchange mechanism (discussed in Section 8.1.2), the vacancies are one of the components of the system every time a vacancy leaves a site, it is replaced by an atom. As a result of this replacement constraint, the fluxes of components are not independent of one another. 

Sharaf, M. A. Kloczkowski, A. Mark, J. E., Networks Undergoing Strain-Induced Crystallization. Analysis in Terms of the Constrained-Junction Model. Comput. Polym. Sci. 1992,2,84-89. 

Biodegradable shape-memory polymer networks with single POSS moieties located in the center of the network chains would promote POSS crystallization even within a constraining network structure. Successful synthesis of POSS initiated poly(e-caprolactone) (PCL) telechelic diols, utilizing a POSS diol as initiator, was reported by Lee et al. [116]. The POSS-PCL diols were terminated with acrylate groups and photocured in the presence of a tetrathiol crosslinker. Scheme 1 shows the chemical reaction for the synthesis of POSS-PCL network. 

M. Vilfan, G. Lahajnar, I. Zupancic, S. Zumer, R. Blinc, G.P. Crawford, and J.W. Doane, Dynamics of a nematic liquid crystal constrained by a polymer network a proton NMR study, J. Chem. Phys. 103 (1995). 

---