Junction points point

The amount of branching introduced into a polymer is an additional variable that must be specified for the molecule to be fully characterized. When only a slight degree of branching is present, the concentration of junction points is sufficiently low that these may be simply related to the number of chain ends. For example, two separate linear molecules have a total of four ends. If the end of one of these linear molecules attaches itself to the middle of the other to form a T, the resulting molecule has three ends. It is easy to generalize this result. If a molecule has v branches, it has v 2 chain ends if the branching is relatively low. Branched molecules are sometimes described as either combs or... 

If the concentration of junction points is high enough, even branches will contain branches. Eventually a point is reached at which the amount of branching is so extensive that the polymer molecule becomes a giant three-dimensional network. When this condition is achieved, the molecule is said to be cross-linked. In this case, an entire macroscopic object may be considered to consist of essentially one molecule. The forces which give cohesiveness to such a body are covalent bonds, not intermolecular forces. Accordingly, the mechanical behavior of cross-linked bodies is much different from those without cross-linking. 

Traditional rubbers are shaped in a manner akin to that of common thermoplastics. Subsequent to the shaping operations chemical reactions are brought about that lead to the formation of a polymeric network structure. Whilst the polymer molecular segments between the network junction points are mobile and can thus deform considerably, on application of a stress irreversible flow is prevented by the network structure and on release of the stress the molecules return to a random coiled configuration with no net change in the mean position of the Junction points. The polymer is thus rubbery. With all the major rubbers the... 

The main experimental techniques used to study the failure processes at the scale of a chain have involved the use of deuterated polymers, particularly copolymers, at the interface and the measurement of the amounts of the deuterated copolymers at each of the fracture surfaces. The presence and quantity of the deuterated copolymer has typically been measured using forward recoil ion scattering (FRES) or secondary ion mass spectroscopy (SIMS). The technique was originally used in a study of the effects of placing polystyrene-polymethyl methacrylate (PS-PMMA) block copolymers of total molecular weight of 200,000 Da at an interface between polyphenylene ether (PPE or PPO) and PMMA copolymers [1]. The PS block is miscible in the PPE. The use of copolymers where just the PS block was deuterated and copolymers where just the PMMA block was deuterated showed that, when the interface was fractured, the copolymer molecules all broke close to their junction points The basic idea of this technique is shown in Fig, I. 

Fig. 2. This figure illustrates the Uansition from failure by simple ehain scission to failure by crazing with chain scission. In PS crazes the scission tends to occur not at the junction point but in the PS copolymer block.

A box or fitting must be installed at each conductor sphce connection point, receptacle, switch, junction point, or pull point for the connection of conduit system. In Division 1 areas only explosion-proof boxes or fittings are allowed. General purpose gasketed cover type fittings are allowed in Division 2 areas. 

In solutions saturated (i.e., excess solid present) at some pH, the plot of log Co versus pH for an ionizable molecule is extraordinarily simple in form it is a combination of straight segments, joined at points of discontinuity indicating the boundary between the saturated state and the state of complete dissolution. The pH of these junction points is dependent on the dose used in the calculation, and the maximum value of log Co is always equal to log. Sb in a saturated solution. [26] Figure 2.2 illustrates this idea using ketoprofen as an example of an acid, verapamil as a base, and piroxicam as an ampholyte. In the three cases, the assumed concentrations in the calculation were set to the respective doses [26], For an acid, log Co (dashed curve in Fig. 2.2a) is a horizontal line (log Co = log So) in the saturated solution (at low pH), and decreases with a slope of —1 in the pH domain where the solute is dissolved completely. For a base (Fig. 2.2b) the plot of log Co versus pH is also a horizontal line at high pH in a saturated solution and is a line with a slope of +1 for pH values less than the pH of the onset of precipitation. 

The mathematical abstraction of the topology of a pipeline network is called a graph which consists of a set of vertices (sometimes also referred to as nodes, junctions, or points)... 

One of the earlier assumptions regarding microscopic deformation in networks is that the junction points in the networks move affinely (linearly) with macroscopic deformation. It follows that chain end-to-end vectors deform affinely also, and... 

If restricted junction fluctuations are taken into account, the chain deformation is increased, and is more anisotropic. The effect of increasing k is much more evident in networks of low functionality, since fluctuations of junction points are of minor importance in networks of high functionality. 

C. C. Han, H. Yu and their colleagues (23) have presented some new SANS data on end-linked trifunctional isoprene networks. These are shown in Figure 10. Those materials of low molecular weight between crosslinks exhibit greater chain deformation consistent with the thesis that the junction points are fixed. This is the reverse of that found by Beltzung et al. for siloxane networks. 

Junction Functionality. Some results bearing on the possible effect of cross-link functionality on the upturn in modulus are shown in Figure 5(20). The magnitude of the increase in [f ] does not show any obvious correlation with , which again suggests the predominant importance of the intramolecular characteristics of the short chains. At least from the evidence at hand (20), the functionality of the junction points seems relatively unimportant in this regard. 

Figure 8 illustrates(29) the close relationship between the chain defining the molar mass between junction points of the perfect network (M ) and the chain of v bonds of the preceding sections. The illustrations in (b) and (c) are for the RA2 +... 

The networks studied were prepared from reactions carried out at different initial dilutions. Aliquots of reaction mixtures were transferred to moulds, which were maintained at the reaction temperature under anhydrous conditions, and were allowed to proceed to complete reaction(32). Sol fractions were removed and shear moduli were determined in the dry and equilibrium-swollen states at known temperatures using uniaxial compression or a torsion pendulum at 1Hz. The procedures used have been described in detail elsewhere(26,32). The shear moduli(G) obtained were interpreted according to Gaussian theory(33 34 35) to give values of Mc, the effective molar mass between junction points, consistent with the affine behaviour expected at the small strains used(34,35). 

Figure 8. Part of a tetrafunctional network formed from an RA t and RBi polymerization corresponding to Mc°, the molar mass between junction points of the perfect network (a). Detail of the chain structure defining Mc° for HDl reacting with an OPPE, n is the number-average degree of polymerization of each arm with respect to oxypropylene units, (b). Part of the chain structure defining v, the number of bonds in the chain forming the smallest ring structure (C), for the reaction system in (b) (29). Reproduced, with permission, from Ref. 21. Copyright 1980, Stein-...

Figure 9. Molar mass between elastically effective junction points (Mc) relative to that for the perfect network (Mc°) versus extent of intramolecular reaction at gelatin (pr,c) for polyurethane networks (29).

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. 

The two-network theory for a composite network of Gaussian chains was originally developed by Berry, Scanlan, and Watson (18) and then further developed by Flory ( 9). The composite network is made by introducing chemical cross-links in the isotropic and subsequently in a strained state. The Helmholtz elastic free energy of a composite network of Gaussian chains with affine motion of the junction points is given by the following expression ... 

In order to probe the effect of junction point functionality on chain conformation and morphology of miktoarm star block copolymer architectures, a series of PI PS (n = 2, 4, 16) was synthesized [166]. A single batch of both living PS and PI arms have been used, in order to ensure that all chemically identical arms (either A or B) have the same molecular weights. The living A and B chains were reacted with the appropriate chlorosilane, under appropriate experimental conditions, to produce the corresponding //-stars, as shown in Scheme 88. 

In miktoarm-star copolymers (or heteroarm star copolymers ), the unlike blocks are connected at one junction point, as shown in Fig. 34. As in linear-block copolymers, exactly two blocks are linked. Hence, it seems tempting to approximate those copolymers as a set of diblocks with the free ends of one block component joined together in a cluster [111]. 

The dependence of the lamellar thickness and the number of arms (n = 1, 2, 4 and 16) for symmetric PSn-arm-PIn miktoarm stars shows an increase in the spacing with n (Fig. 43). This indicates an additional chain stretching induced by the spatial confinements close to the junction point. However, the exactness of the results may be influenced by non-separable impurities. As these contamination species are resistant to detection via standard SEC and other separation techniques, it can be reasoned that previous results reported in the literature might suffer from the same shortcomings [121]. 

Fig. 46 Schematic diagram of elemental process during transition from Hex cylinder to bcc sphere (i) undulation of interface (a, b), (ii) break-up of cylinders into ellipsoids (b, c), (iii) relaxation of domains from ellipsoids into spheres (c, d), and (iv) relaxation in junction distribution to attain uniform distribution (d, e). Pole where concentration of junction points is low may work as memory of grain conservation upon reverse transition from bcc sphere to Hex cylinder. Small arrows in part (b) indicate diffusion of chemical junctions along interface in process (ii). From [136], Copyright 2000 American Chemical Society...

A product used in upholstery and as a resilient packaging material. It is made by spraying a loose mat of curled animal hair with latex and applying heat to vulcanise the rubber. The resilience of the product comes from the fibres, the junction points of which are anchored by the rubber. 

Calculations of displacements and rotations at specific locations may be required where clearance problems are involved. In cases where small-size branch pipes attached to stiffer run pipes are to be calculated separately, the linear and angular movements of the junction point must be calculated or estimated for proper analysis of the branch. 

Microsample holders are made from four-hole alumina capillaries. Small receptacles for the crucibles containing reference and sample are welded to the two thermocouples of the DTA holder at the hot junction points (Fig. 13 a). 

Thermal electric noise thermometry 1. Josephson junction point contact 2 Conventional amplifier 0.001-1 4-1400 Mean square voltage fluctuation Nyquist s law oc fegT Other sources of noise serious problem for T > 4 K... 

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