Crosslink density, polymer network

As in linear polymers, the relative influence of the molecular structure (scale of nanometers and monomers), and the macromolecular structure (crosslink density), on network properties, depends on temperature, as shown in Fig. 10.9. In the glassy state, the physical behavior is essentially controlled by cohesion and local molecular mobility, both properties being mainly under the dependence of the molecular scale structure. As expected, there are only second-order differences between linear and network polymers. Here, most of the results of polymer physics, established on linear polymers, can be used to predict the properties of thermosets. Open questions in this domain concern the local mobility (location and amplitude of the (3 transition). 

Pan, S.-J. Mark, J. E., Model Networks of End-Linked Polydimethylsiloxane Chains. XV. Spatially Heterogeneous Networks Containing Domains of Very High Crosslink Density. Polym. Bull. 1982, 7, 553-559. 

Siegfried, Manson, and Sperling s data (Figure 4.3) show the data to the left of the line, vertically stacked. (All of the polymer network I compositions have the same crosslink density.) Hence network I is assumed to dominate network II. 

In equations 6.36 and 6.36, represents the crosslink density of network I per unit volume of total IPN. J. Michel, S. C. Hargest, and L. H. Sperling, J. Appl. Polym. Sci. (to be published), proposed a form where represents the crosslink density of the dry network I, and 01 and 02 represent the volume fractions of networks I and II, respectively. 

B. N. Kolarz, Ion Exchangers XIX. Some Properties of the Carboxylic Cation Exchangers Obtained by Intermesh Polymerization of Methacrylic Acid into Styrene and Divinylbenzene Porous Copolymers, /. Polym. Sci. 47C, 197 (1974). PS/PMA IPNs. Both polymers crosslinked with DVB. Effect of porosity of network I. Effect of crosslink density of network I. Ion exchange properties. 

It is also clear that activity of a filler should be related to any definite property of material. It was proposed to introduce the concept of structural, kinetic, and thermod3uiamic activity of fillers. Structural activity of a filler is its abihty to change the polymer structure on molecular and submolecular level (crystallinity degree, size and shape of submolecular domains, and their distribution, crosslink density for network pol3rmers, etc.). Kinetic activity of a filler means the ability to change molecular mobility of macromolecides in contact with a solid surface and affect in such a way the relaxation and viscoelastic properties. Finally, thermodynamic activity is a filler s ability to influence the state of thermodynamic equilibrium, phase state, and thermodynamic parameters of filled polymers — especially important for filled poljmier blends (see Chapter 7). 

Fluorosilicones consist of PDMS backbones with some degree of fluoro-aliphatic side chains. The fluorinated group can be trifluoropropyl, nonafluorohexylmethyl, or fluorinated ether side group [78,28,79]. These polymers differ not only in substituent group, but also in the amount of fluoro-substitution relative to PDMS, the overall molecular weight and crosslink density, and the amount of branching. In most commercially available cases, these polymers are addition cure systems and the reactions are those discussed previously for silicone networks. 

Once P(F ° ) and P(Fg° ) have been calculated, it is possible to calculate a number of network structure parameters including the weight fraction of sol, wg, and the "effective" crosslink density. A given polymer or crosslinker will be part of the sol only if all of its groups are attached to finite chains. Thus, the weight of the sol is given by... 

It is possible to calculate a number of different kinds of "effective" crosslink densities. Bauer et al have used a quantity they termed the "elastically effective crosslink density " (Cel) correlate cure with solvent resistance and other physical properties of coatings (7-10). The correlation was basically empirical. Formally, the is a calculation of the number of functional groups attached to the infinite network for which there are at least two other paths out to the network on the given polymer or crosslinker. Thus, chains with only one or two paths to the infinite network are excluded. The following expression can be written for... 

Table II shows Tgs obtained from DSC traces. (Footnotes a and b in Table II show T s values of three reference polymers two PIBs, whose Mns are similar to the Mns of MA-PIB-MA used in the network synthesis, and a PDMAAm the difference in the Tg for the Mn=4,000 and 9,300 PIBs is due to the dependence of Tg on Mn(72)). The DSC traces of the networks exhibited two Tgs, one in the range of -63 to -52 °C (PIB domains) and another in the range of 90 to 115 °C (PDMAAm domains) indicating microphase separated structures. The Tgs associated with the PIB phase in the PDMAAm-1-PIB networks were higher than those of the reference homoPIBs which may be due to PIB chain-ends embedded in the glassy PDMAAm phase restricting segmental mobility. The Tg of the PIB phase in the PDMAAm-1-PIB increases by increasing the PIB content which may be due to an increase in crosslink density. In contrast, the Tg for the PDMAAm phase in the network decreases upon increasing the PIB content. Interaction of the (-CH2-CH-) moiety of the PDMAAm with the flexible PIB and thus the formation of a more flexible structure may explain this phenomenon.

Depending on the conditions of synthesis, copolymerization of divinyl/vinyl-monomers in the presence of an inert solvent leads to the formation of expanded (preswollen) or heterogeneous (porous) structures [54,99,100]. If the solvent remains in the network (gel) phase throughout the copolymerization, expanded networks are formed. If the solvent separates from the network phase the network becomes heterogeneous. According to Dusek et al., heterogeneities may appear in poor solvents due to the polymer-solvent incompatibility (x-induced syneresis), while in good solvents due to an increase in crosslink density (v-induced syneresis) [99]. 

The crosslink density of a polymer network determines the number of elastically effective chains. Some of the chains are tied to a network and... 

If we accept the model proposed for these mixed monofunctional/ difunctional systems, we can draw some conclusions about the network structure in polymers based on I alone. For example, Fig. 7 shows how the Tg varied with the relative crosslink density in the mixed systems. The abcissa represents the probability that a monomer chosen at random is linked to the network at both ends. At moderate degrees of crosslinking, the expected relationship between Tg and crosslink density is linear, so the data were approximated by a straight line (10). From the extrapolation in Fig. 7, one concludes that a typical bis-phthalonitrile cured to a Tg of 280 0 has a relative crosslink density of 0.5, or about 70% reaction of nitrile groups. 

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