Network formation functionality

With appropriate choice of reaction conditions, hyperbranched polymers can be formed by sclf-condcnsing vinyl polymerization of monomers that additionally contain the appropriate initiator (NMP, ATRP), when the compounds are called inimers, or RAFT agent functionality. Monomers used in this process include 340,716 341717 and 34204 (for NMP), 108714,714 and 344 and related monomers720 723 (for ATRP) and 343408 (for RAFT). Careful control of reaction conditions is required to avoid network formation. 

As mentioned previously, the use of multifunctional monomers results in branching. The introduction of branching and the formation of networks are typically accomplished using trifunctional monomers, and the average functionality of the polymerization process will exceed 2.0. As the average functionality increases, the extent of conversion for network formation decreases. In... 

Striking support of this contention is found in recent data of Castro (16) shown in Figure 14. In this experiment, the polymerization (60-156) has been carried out in a cone-and-plate viscometer (Rheometrics Mechanical Spectrometer) and viscosity of the reaction medium monitored continuously as a function of reaction time. As can be seen, the viscosity appears to become infinite at a reaction time corresponding to about 60% conversion. This suggests network formation, but the chemistry precludes non-linear polymerization. Also observed in the same conversion range is very striking transition of the reaction medium from clear to opaque. 

In this study computational results are presented for a six-component, three-stage process of copolymerization and network formation, based on the stochastic theory of branching processes using probability generating functions and cascade substitutions (11,12). 

Generalization of Flory s Theory for Vinyl/Divinyl Copolvmerization Using the Crosslinkinq Density Distribution. Flory s theory of network formation (1,11) consists of the consideration of the most probable combination of the chains, namely, it assumes an equilibrium system. For kinetically controlled systems such as free radical polymerization, modifications to Flory s theory are necessary in order for it to apply to a real system. Using the crosslinking density distribution as a function of the birth conversion of the primary molecule, it is possible to generalize Flory s theory for free radical polymerization. 

The two conditions stated above do not assure the occurrence of gelation. The final and sufficient condition may be expressed in several ways not unrelated to one another. First, let structural elements be defined in an appropriate manner. These elements may consist of primary molecules or of chains as defined above or they may consist of the structural units themselves. The necessary and sufficient condition for infinite network formation may then be stated as follows The expected number of elements united to a given element selected at random must exceed two. Stated alternatively in a manner which recalls the method used in deriving the critical conditions expressed by Eqs. (7) and (11), the expected number of additional connections for an element known to be joined to a previously established sequence of elements must exceed unity. However the condition is stated, the issue is decided by the frequency of occurrence and functionality of branching units (i.e., units which are joined to more than two other units) in the system, on the one hand, as against terminal chain units (joined to only one unit), on the other. 

Chain-growth polymerizations are diffusion controlled in bulk polymerizations. This is expected to occur rapidly, even prior to network development in step-growth mechanisms. Traditionally, rate constants are expressed in terms of viscosity. In dilute solutions, viscosity is proportional to molecular weight to a power that lies between 0.6 and 0.8 (22). Melt viscosity is more complex (23) Below a critical value for the number of atoms per chain, viscosity correlates to the 1.75 power. Above this critical value, the power is nearly 3 4 for a number of thermoplastics at low shear rates. In thermosets, as the extent of conversion reaches gellation, the viscosity asymptotically increases. However, if network formation is restricted to tightly crosslinked, localized regions, viscosity may not be appreciably affected. In the current study, an exponential function of degree of polymerization was selected as a first estimate of the rate dependency on viscosity. 

The parameters of neutron scattering theory of polymer networks are A, the macroscopic stretching of the sample, or linear degree of swelling, f, the network functionality, K. which accounts for restricted junction fluctuations and a, a measure of the degree to which chain extension parallels the macroscopic sample deformation. The functionality is known from knowledge of the chemistry of network formation, and A is measured. Both K and a must be extracted from experiments. 

Introduction of new precursor architectures brings about new challenges in description and modeling of network formation because the apparent reactivities of functional groups become dependent on the size and shape of the precursors... 

For the application of hyperbranched polymers as precursors in network formation, the functionality averages are important. The number-average functionality is given by the equation... 

Higher-order averages are also important for network formation the number average value of functional groups per weight-average degree of polymerization is defined by... 

For a theoretical description of crosslinking and network structure, network formation theories can be applied. The results of simulation of the functionality and molecular weight distribution obtained by TBP, or by off-space or in-space simulations are taken as input information. Formulation of the basic pgf characteristic of TBP for crosslinking of a distribution of a hyperbranched polymer is shown as an illustration. The simplest case of a BAf monomer corresponding to equation (4) is considered ... 

Kumar, K., and Verma, M. (2007). Functionalization of psyllium with methacrylic acid through grafting and network formation for use of polymers in water treatment. /. Appl. Polym. Sci. 103,1025-1034. 

We realized, however, that if the polyesteramides merely acted as multi 2-hy-droxypropyl-amide functional polymers, they could never provide good flow and optical appearance of the coatings. From the mathematical theory of network formation [24] it is known that a binder formulation with a 2-functional resin and a crosslinker bearing many (> 5) functional groups reaches its gel-point at low chemical conversion, as shown in Fig. 21. 

Differences in Network Structure. Network formation depends on the kinetics of the various crosslinking reactions and on the number of functional groups on the polymer and crosslinker (32). Polymers and crosslinkers with low functionality are less efficient at building network structure than those with high functionality. Miller and Macosko (32) have derived a network structure theory which has been adapted to calculate "elastically effective" crosslink densities (4-6.8.9). This parameter has been found to correlate well with physical measures of cure < 6.8). There is a range of crosslink densities for which acceptable physical properties are obtained. The range of bake conditions which yield crosslink densities within this range define a cure window (8. 9). 

Having discussed self-assembly strategies toward noncovalently functionalized side chain supramolecular polymers as well as studies toward the orthogonahty of using multiple noncovalent interactions in the same system, this section presents some of the potential applications of these systems as reported in the literature. The apphcations based on these systems can be broadly classified into two areas 1) self-assembled functional materials and 2) functionalized reversible network formation. 

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