Junction point density

The variation of Tg with ac (or Mc) is a reflection of the influence of junction-point density on the freedom of segmental motion. The maximum range of Tg values shown, 301 to 312K, possibly reflects the maximum influence for these MDI/POP triol systems. 

Number of junction points per unit volume in a polymer network. See also crosslink density. 

CTBN oligomers leads to a higher molecular weight of chains between network junction points and consequently, a lower crosslink density. 

H and 2H NMR have been used in styrene-butadiene rubber (SBR) with and without carbon-black fillers to estimate the values of some network parameters, namely the average network chain length N. The values obtained from both approaches were checked to make sure that they were consistent with each other and with the results of other methods [71, 72, 73]. To this purpose, a series of samples with various filler contents and/or crosslink densities were swollen with deuterated benzene. The slopes P=A/ X2-X 1) obtained on deuterated benzene in uniaxially stretched samples were measured. The slopes increase significantly with the filler content, which suggests that filler particles act as effective junction points [72, 73]. 

The basic driving force for microdomain formation in block copolymers is the reduction in the positive surface free energy of the system resulting from the increase of the domain size. This domain size increase gives rise to a decrease in the volume fraction of interfacial region in which junction points of the copolymers must be distributed. In addition, configurations of the block chains must also change in order to even-up the density deficiency in the interior of the domains. 

Branched polymers have side chains, or branches, of significant length which are bonded to the main chain at branch points (also known as jimction points), and are characterised in terms of the number and size of the branches. Network polymers have three-dimensional structures in which each chain is connected to all others by a sequence of junction points and other chains. Such polymers are said to be crosslinked and are characterised by their crosslink density, or degree of crosslinking, which is related directly to the number of junction points per unit volume. 

An important network property is the cross-link density or concentration of effective junction points in the infinite network. An A/ unit chosen at random will act as an effective junction point if three or more of its arms lead out to the infinite network, or to the container walls. (If only one arm is infinite, this A/ unit will be just hanging firom the network if, on the other hand, two arms are infinite. A/ forms part of a chain connecting two effective junction points, but it itself is not an effective junction point Consider tetrafunctional At as an example of Ay. TTie probability that A4 is an effective crosslink of degree 4 is just... 

Formation of hydrophobic clusters in a comb-grafted polymer gel leads to additional junction points and to an abrupt increase in the cross-Unking density (Yoshida et al. 1995). 

The behavior of a real network is determined by the totality of topological parameters not less than by the density of crosslinking. Neglecting the network topology will result in misleading conclusions. As an example. Table 1.3 demonstrates glass transition temperatures of abstract styrene-DVB copolymers calculated in accordance with the approach developed by Askadskyi [100, 101]. The author depicts the DVB junction point as denoted below (one junction includes four carbon atoms) ... 

Rubber networks will imbibe solvent liquids until the elastic retractive force of the network crosslinks counterbalances the swelling force exerted by the liquid. If no crosslinks are present, the rubber dissolves completely on immersion in an excess of solvent. The degree of swelling is thus a function of crosslink density. As crosslink density increases, the degree of swelling decreases and vice versa. The average crosslink between junction points can be related to swelling measurements from potential considerations, as shown below. 

Let us consider a system of n comb-shaped copolymers in volume V. Under the mean field approximation, each copolymer can be divided into a set of linear subchains which are jointed at the corresponding junction points and which are statistically independent. To specify the subchains having segments, an index k is introduced. Each subchain contains faNk monomer species of type a. In this case, the contribution from the -th subchain to the monomer density field at point r is given by... 

For AB-type polymers, the A-B junction point is taken at the micelle interface (Inoue et al., 910a,b), as before. The ends of the molecules are, admittedly, unrealistically placed for example, for spheres, the free end of the A block is at the center of the micelle and the bound end of the B block is constrained to a position on a sharply defined micelle spherical surface. Corresponding restrictions are placed on cylinder and lamellae formation. These assumptions, of course, lead to anomalous values for calculated densities, being high in the middle and low near the surface of the micelle. 

Microdomain stmctures of 3-miktoarm star terpolymers in a three-dimensional space were investigated using the dynamic density functional theory (DDFT). Analysis of DDFT demonstrates that the junction points are restricted to lie on... 

With the advancement of a curing reaction, the of the resin will increase, but the goal is to quantitatively predict the of a resin as a function of cure conversion. Several models have been proposed to correlate the with the conversion or extent of curing (a). With the increase in conversion, the concentration of reactive functionalities decreases, and crosslinks or junction points are formed, leading to the departure from Gaussian behaviour. Steric hindrance affects chain conformation at high crosslink densities. The models are based on the statistical description of network formation and calculation of the concentration of jrmction points of different functionalities as a function of conversion. However, one issue that complicates the calculation and which is not fully resolved is whether to consider all the junction points or only those which are elastically effective. 

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