Network structure, dependence

It has been shown in Chapter XI that the force of retraction in a stretched network structure depends also on the degree of cross-linking. It is possible therefore to eliminate the structure parameter ve/Vo) by combining the elasticity and the swelling equations, and thus to arrive at a relationship between the equilibrium swelling ratio and the force of retraction at an extension a (not to be confused with the swelling factor as). In this manner we obtain from Eq. (XI-44) and Eq. (39)... 

These studies show that the H-bonding network structures depend strongly on the nature of the chiral solute. The solvent induced chirality signatures provide significantly more detailed information about the explicit interactions between water and... 

FIGURE 40.2 Arrangement of polymer chains into linear, branched, and network structure depending on the functionality of the repeating units. 

The gel formation can be linked to the functionality, f, and a branching coefficient, a. The branching coefficient a gives the probability that a specific functional group (of functionality > 2) is connected to another branch point. One can deduce from statistical reasoning that a gel appears at a critical branching coefficient, a. For f=3, a gel appears when is 0.5, i.e., there is a 50% chance that each branch is connected to another branch point. The network structure depends on the concentration of branch points and the degree of polymerization. 

Polymer networks or crosslinked networks are molecular-based networks whose network structures depend entirely on covalent bonding or on physical interactions between the macromolecules. Just like in diamond, each pair of adjacent junction points in the network are separated by only one covalent bond. In a polymer network, two junction points are separated by linear sub-chains of several bonds or many covalent bonds. When the connectivity from the junction point is through chemical bonds, they are called chemical crosslinks , as found in thermosets. The crosslinks generated due to the entanglement of long polymer chains are known as physical crosslinks . In case of thermoset polymers, the crosslinks are chemical crosslinks. 

The densely packed organic thin films of alkanes tend to exhibit alterations of the network structures, depending on the parity of the number of the methylene units—a result called the odd-even effectP Binary mixtures of primary linear alcohols that differ by one methylene group show ideal mixing if the shorter alcohol possesses an odd number of carbon atoms. In contrast, if the shorter component is even numbered, co-crystals are formed. The appearance of mixing (random or ordered) on the surface rather than phase separation is ascribed to the similar symmetries of the unit cells of the pure components. ... 

As it is seen from Eq. (23), the thermodynamic opportunity of the reaction initiation (AG = 0) is defined by network properties (Ccon, fix, Tiim), as well as by the conditions of production, storage, and exploitation (/iph, a), and by external influence (T, A). As mentioned previously, the Ccon value is the function of chemical structure of the network and the solvent (in a number of cases the solvent amount disposed in the network may depend on ph and intermolecular bonds distribution). 

Typically IPNs exhibit some degree of phase separation in their structure depending on how miscible the component polymers are. However, because the networks are interconnected such phase separation can occur only to a limited extent, particularly by comparison with conventional polymer blends. Polymer blends necessarily have to be prepared from thermoplastics IPNs may include thermosets in their formulation. 

The final physical properties of thermoset polymers depend primarily on the network structure that is developed during cure. Development of improved thermosets has been hampered by the lack of quantitative relationships between polymer variables and final physical properties. The development of a mathematical relationship between formulation and final cure properties is a formidable task requiring detailed characterization of the polymer components, an understanding of the cure chemistry and a model of the cure kinetics, determination of cure process variables (air temperature, heat transfer etc.), a relationship between cure chemistry and network structure, and the existence of a network structure parameter that correlates with physical properties. The lack of availability of easy-to-use network structure models which are applicable to the complex crosslinking systems typical of "real-world" thermosets makes it difficult to develop such correlations. 

Recently the polymeric network (gel) has become a very attractive research area combining at the same time fundamental and applied topics of great interest. Since the physical properties of polymeric networks strongly depend on the polymerization kinetics, an understanding of the kinetics of network formation is indispensable for designing network structure. Various models have been proposed for the kinetics of network formation since the pioneering work of Flory (1 ) and Stockmayer (2), but their predictions are, quite often unsatisfactory, especially for a free radical polymerization system. These systems are of significant conmercial interest. In order to account for the specific reaction scheme of free radical polymerization, it will be necessary to consider all of the important elementary reactions. 

In pseudoplastic substances shear thinning depends mainly on the particle or molecular orientation or alignement in the direction of flow, this orientation is lost or regained at the same speed. Additionally many dispersions show this potential for particle or molecule interactions, this leads to bonds creating a three-dimensional network structure. They are often build-up from relatively weak hydrogen or ionic bonds. When the network is disturbed. 

When the monomer concentration exceeds c [see Eq. (112) and Fig. 38], the different polymer molecules are no longer separated but interpenetrate each other forming a transient network of lifetime xg. At constant temperature this network structure is characterized by a concentration-dependent correlation length (c), which may be considered as the mean mesh size of the pseudo gel. 

From a practical point of view, it is advantageous that critical gel properties depend on molecular parameters. It allows us to prepare materials near the gel point with a wide range of properties for applications such as adhesives, absorbents, vibration dampers, sealants, membranes, and others. By proper molecular design, it will be possible to tailor network structures, relaxation character, and the stiffness of gels to one s requirements. 

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