Molecular weight per crosslinked unit

The crosslinking index is usually expressed as moles of crosslinking agent per mole of repeating unit, X, or moles of crosslinked units per g of polymer, 1/MC (Mc = molecular weight per crosslinked unit), whereas the crosslink density px corresponds to p = l/vMc (v = specific volume of the polymer). 

It can seen from Figure 5.4 that the equilibrium compliance Je decreases uniformly from the 1007/DDS to the 828/DDS and is expected on the basis of the kinetic theory of rubberlike elasticity, since the concentration of network chains increases and the molecular weight per crosslinked unit, Mx, decreases in the same order. The Mx values calculated as /o/JT/g are remarkably close to the molecular weight values of the starting epoxy resins. 

Average molecular weight per crosslinked unit calculated from Jg-. Mx = pRTJg. 

The molecular weight per repeat unit (M) is useful in calculating many properties. For example, it can be used to obtain densities and specific volumes from the molar volumes listed in Chapter 3, specific heat capacities from the molar heat capacities listed in Chapter 4, the numbers of repeat units between crosslinks from Mc values, and the number of repeat units between entanglements from Me values. Table A. 1 lists the values of M for many polymers, in units of g/mole, and in alphabetical order by the polymer name. 

Crosslink density may be defined as the number of effective crosslinks per unit volume. The crosslink density is a key parameter in determining the properties of an epoxy resin after cure. It is dependent on the number of reactive sites (functionality), the molecular distance and chain mobility between functional sites, and the percentage of these sites that enter into reaction. Crosslink density is inversely related to the molecular weight between crosslinks Mc. 

The number of chains per unit volume can be related to the density p and the average molecular weight between crosslinks M ... 

Crosslinked polymers can be characterised conveniently by defining their crosslink density as branch points per unit volume or average molecular weight between crosslinks. This parameter in conjunction with the molecular nature of the polymer defines whether the material will behave as an elastomer or as a rigid material, which shows either ductile or brittle failure behaviour. Fillers can be used to modify properties further across the whole range of polymer behaviour. Because inorganic fillers are, compared to most polymers, much stiffer and less extensible materials, their incorporation into a polymer will usually produce a composite material of reduced strain to failure and increased stiffness relative to the polymer, i.e., the composite will be less elastomeric or less ductile. Nevertheless, large quantities of fillers are used in polymers that already have low strains to failure and show brittle failure behaviour. This chapter will confine itself to a discussion of the use of fillers in ductile and brittle crosslinked polymers. 

Equations have been derived which relate G(scission) and G(crosslinking) to changes in Mn, Mw and Mz. Crosslinking produces branched molecules and the relative hydrodynamic volume (per mass unit) decreases compared with linear molecules. Therefore, molecular weights derived from viscometry and gel permeation chromatography will be subject to error. 

The understanding of the macromolecular properties of lignins requires information on number- and weight-average molecular weights (Mn, Mw) and their distributions (MWD). These physico-chemical parameters are very useful in the study of the hydrodynamic behavior of macromolecules in solution, as well as of their conformation and size (1). They also help in the determination of some important structural properties such as functionality, average number of multifunctional monomer units per molecule (2, 3), branching coefficients and crosslink density (4,5). 

The absorbed energy density. Eg, required to destroy the gel completely in pre-crosslinked resists can be predicted as follows. Assume that the density of the material is pkg/m, the monomer molecular weight is Mo and that Avogadro s number is Na/(kg.mole). The number of monomer units per m i Na-p/Mo- If the crosslink density (i.e. the fraction of monomer units which are crosslinked) is do, then the number of crosslinks per unit volume is... 

For an ideal network the quantity pNAy In (where p is the elastomer density, gram per unit volume) is defined as. the average molecular weight of chain lengths between crosslinks, denoted by Me- So,... 

Suppose that the material consisted originally of N individual molecules of average molecular weight M per unit volume. The minimum number of links per unit volume which would be required to create a continuous system forming a giant molecule is A - 1. It would be incorrect to call it a network, inasmuch as it contains no net-like structure, i.e., it possesses no circuitous connections within its structure. As additional crosslinks are added, the structure acquires the character... 

Figure 6.1 FTIR spectra of (a) linear atactic polystyrene with molecular weight of 400 kDa, (b) poly(p-methylstyrene), and hypercrosslinked polystyrenes prepared by crosslinking styrene-0.5% DVB copolymer with (c) 0.3, (d) 0.5, (e) 1.0, and (0 1.5 mol of monochlorodimethyl ether per styrene repeating unit.

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