Network chain — continued

Swelling data indicate that crosslink density in the continuous phase of the 70 30 and 60 A0 networks is high. Crosslink densities were estimated from the data in Table III by the method of Hill and Kozlowski ( ). Results were for 80 20, "Vg = 10" moles of elastically effective network chains/cm for 70 30, Vg = 2.5 x lO" chains/cm for 60 AO, Vg = A.3 x 10" chains/cm. These estimates suggest that the crosslink densities are within the range reported for conventional, highly crosslinked acrylic HMMM and polyester HMMM enamels (19,20). 

For an athermal case, the continuous deswelling of the network takes place (Fig. 9, curve 1) which in the result of compressing osmotic pressure created by linear chains in the external solution (the concentration of these chains inside the network is lower than in the outer solution, cf. Ref. [36]). If the quality of the solvent for network chains is poorer (Fig. 9, curves 2-4), this deswelling effect is much more pronounced deswelling to strongly compressed state occurs already at low polymer concentrations in the external solution. Since in this case linear chains are a better solvent than the low-molecular component, with an increase of the concentration of these chains in the outer solution, a decollapse transition takes place (Fig. 9, curves 2-5), which may occur in a jump-like fashion (Fig. 9, curves 3-4). It should be emphasized that for these cases the collapse of the polymer network occurs smoothly, while decollapse is a first order phase transition. 

With very few exceptions, polymers consist of macromolecules (or network chains) with a range of molar masses. Since the molar mass changes in intervals of M0, the distribution of molar mass is discontinuous. However, for most polymers these intervals are extremely small in comparison to the total range of molar mass and the distribution can be assumed to be continuous, as exemplified in the figure above. 

The number of elastically active chains, N, determining the equilibrium rubber elasticity, is derived from the following consideration. A chain in the gel is elastically active, if the branch points at each of its ends issue at least three paths to infinity. Such elastically active network chain (EANC) can have many long side branches but none of them may have an infinite continuation. The number of EANC s, N, is thus calculated from the number of EANC ends, i.e., branch points issuing three or more bonds with infinite continuation. The distribution of units according to the number of bonds with infinite continuation is described by a pgf T(z)... 

An elastically active network chain is active in the equilibrium elastic response of the network to deformation. From the topological point of view, an EANC is a chain between two active branch points. An active branch point is a imit from which at least three paths issue to infinity. In the case under consideration, only some of the chemically tetrafunctional diamine units can become active branch points. If the polyepoxide were more than bifunctional, it would also contribute to the number of EANC s. In analogy with Eq. (14), the pgf for the numbo- of bonds with infinite continuation issuing from a diamine unit T,(z) is given by... 

The number of elastically active network chains EANC, N, is contributed only by diepoxide units. According to the reasoning given in Section 4.2.3, the distribution of diepoxide units with respect to the number of bonds with infinite continuation is given by the pgf... 

Figure 2.30 Idealized network structure of a crosslinked polymer. indicates a crosslink (junction) and —> signifies continuation of the network structure. Wavy, lines between crosslinks are active network chain segments. (Note that for a tetrafunctional crosslink, as shown here, the number of crosslinks is one-half the number of active network chain segments.)...

Let us now introduce the concept of degree of continuity of a phase. In the beginning of the IPN synthesis, polymer network I obviously exhibits continuity of both the network structure and its phase. When monomer II is uniformly swollen in, before polymerization of II, one phase also exists. Polymer network I is continuous (the sample is usually a swollen elastomer), and the monomer II is also distributed everywhere. Upon polymerization of II, phase separation takes place. Polymer network I is still continuous, but is partially or wholly excluded from some regions of space. Assuming the previous even distribution of monomer II, we have reason to believe polymer network II will exhibit some degree of chain continuity. Sometimes, polymer network II also appears to exhibit a degree of phase continuity. Usually, polymer network II has less continuity than polymer network I. A simple example of greater and lesser phase continuity in everyday life is chicken-wire in air. 

If the linking of silicate chains continues in two dimensions, sheets of SiO tetrahedral units result (Table 18.4). Various clays and mica have this sheetUke structure. Clays, which are essential components of soils, are aluminosilicates— some Si + ions are replaced by Al ions plus other cations that take up the additional positive charge. Feldspar, a component of many rocks and a network silicate, is weathered in the following reaction to form clay. 

All the quantities so far defined relate to ideal networks, i.e., continuous branched structures without free chain ends. In reality, the number of such free chain ends increases with decreasing primary chain molecular weight. The molar concentration MX niol/g of effective network chains can, according to P. J. Flory, be calculated from the molar concentration [MJ of all the chains present for M )q > (M ) ,... 

Here k is a parameter which measures the strength of the constraints. For k = 0 we obtain the phantom network limit, and for infinitely strong constraints (k = oo) the affine limit is obtained. Erman and Monnerie [27] developed the constrained chain model, where constraints effect fluctuations of the centers of the mass of chains in the network. Kloczkowski, Mark, and Erman [28] proposed a diffused-constraint theory with continuous placement of constraints along the network chains. 

While X (temperature) continuously changes, conditions 94 give rise to a phase transition, which sharply changes the network chain conformation, which, in turn, leads to a significant decrea.se (or increase) in the gel volume — a so-called collapse (or overswelling, superswelling) of gels. 

The long decay time (j ) of the other component is t5q>ical of semidiluted polymer solutions. A T value continuously increases with an increasing solvent content. This component is apparently originated from the relaxation of network defects which are disentangled from network chains in a swollen state. At the equilibrium swelling degree, the relative fraction of the 7 relaxation component could be used as a measure of the fraction of highly mobile network defects. The... 

Later refinements of the constrained junction model place the effects of the constraints on the centres of mass of the network chains [13] or consider distributing the constraints continuously along the chains [14]. 

M. Gordon The basic topological idea by Case and by Scanlan is that a network chain is active if at least three links issuing from each of the two teiminal junction points lead to paths through the network which can be continued to the surface of the specimen. In the statistical theory, the surface is projected to infinity, and the extinction probability of a link is used in the calculation. The basic theory is reviewed in reference 25 of our paper, and extended in a forthcoming paper. Coll. Czech. Communications, Gordon, Kuch rik and Ward, late 1970. 

The equilibrium theory predicts for some cases an increase following a sharp decrease in the volume of the network phase (Fig.3). The volume increase forces the network chains already formed to become strained and the ratio /greater than unity. The volume fraction of the network phase is small after the onset of phase separation and monomers contained in the liquid phase are continuously transferred into... 

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