Chain free end

The next step in the development of a model is to postulate a perfect network. By definition, a perfect network has no free chain ends. An actual network will contain dangling ends, but it is easier to begin with the perfect case and subsequently correct it to a more realistic picture. We define v as the number of subchains contained in this perfect network, a subchain being the portion of chain between the crosslink points. The molecular weight and degree of polymerization of the chain between crosslinks are defined to be Mj, and n, respectively. Note that these same symbols were used in the last chapter with different definitions. 

For density values g > 0.92 g/cm3 the deformation modes of the crystals predominate. The hard elements are the lamellae. The mechanical properties are primarily determined by the large anisotropy of molecular forces. The mosaic structure of blocks introduces a specific weakness element which permits chain slip to proceed faster at the block boundaries than inside the blocks. The weakest element of the solid is the surface layer between adjacent lamellae, containing chain folds, free chain ends, tie molecules, etc. 

The distribution of the thi monomer in molecular chains or in the whole polymer should affect the perfection of the vulcanizate network, free chain ends or the uncross-linked parts in the polymer making no contribution to the tensile strength but acting as a plasticizer of like structure as the polymer. 

The second theory is the Keele theory proposed by Plesch and Westermann [2, 4, 5] in which the propagation reaction is seen as a ring-expansion during which no free chain-end is formed ... 

It is believed that the surface structure of the porous packing material plays an important role. The presence of the free chain ends of styrene-divinylbenzene copolymer may prevent the movement of the macromolecules in the pore. 

It is possible that either Me has increased by degradation of the network structure or the resin is internally plasticized by free chain ends. If Me has increased, then the modulus in the rubbery plateau region for irradiated specimens should be less than that of a control. As discussed above, E (Tg+40) decreases up to a dose of 5000 Mrads. Between 5000 and 10,000 Mrads, E (Tg+40) increases but remains 6% below the control. For the 73/27 and 80/20 samples (10,000 Mrads) which have been sorbed/desorbed, E (Tg+40) is 18.5% greater than the control. 

The most noticeable property change is a decrease in the glass transition temperature of the epoxy resin as a function of absorbed dose. The decrease in Tg is due to plasticization by degradation products and free chain ends from chain scission. 

The morphologies of the large ionic clusters observed in these simulations rather suggest free chain end folding to produce rudimentary lattice structure as a possible pre transitional mechanism. 

The above models describe a simplified situation of stationary fixed chain ends. On the other hand, the characteristic rearrangement times of the chain carrying functional groups are smaller than the duration of the chemical reaction. Actually, in the rubbery state the network sites are characterized by a low but finite molecular mobility, i.e. R in Eq. (20) and, hence, the effective bimolecular rate constant is a function of the relaxation time of the network sites. On the other hand, the movement of the free chain end is limited and depends on the crosslinking density 82 84). An approach to the solution of this problem has been outlined elsewhere by use of computer-assisted modelling 851 Analytical estimation of the diffusion factor contribution to the reaction rate constant of the functional groups indicates that K 1/x, where t is the characteristic diffusion time of the terminal functional groups 86. ... 

Average configuration-dependent physical properties are evaluated for tri- tetra-, and hexafunctional polyethylene stars perturbed by electrostatic repulsion of charges placed at the free chain ends. Configuration-dependent properties evaluated are the probability for a trarts placement, expansion of , the mean-square radius of gyration, asymmetry of the distribution of the chain atoms, and asymmetry of the distribution described by the atoms considered to bear the charges. 

Free chain ends (unreacted functionalities) reduce the number of active network chains in a network compared with the same network without free ends. Disregarding possible presence of loops and entanglements, C — 1 C crosslinks are necessary according to Flory (55) to connect C chains into one giant macromolecule. Additional crosslinks will be elastically effective. Their number is given by... 

Mil. —, and A. G. Thomas Determination of degree of crosslinking in natural rubber vulcanizates. V. Effect of network flaws due to free chain ends. J. Polymer Sci. 43, 13 (1960). 

The decrease in homopolymer Tg with decreasing molecular weight has generally been attributed to an increase of free volume in low-molecular-weight bulk polymers caused by the increased concentration of chain ends. However, end blocks in block copolymer molecules have only a single-chain end while center blocks have no free-chain ends. One would therefore expect that the Tg of a microphase comprised of end blocks would be lower than that of a microphase comprised of center blocks of comparable molecular weight. 

Figme 4.5 Local view of the hydrophilic-hydrophobic interfaces (parallel surfaces) and surfactant pacidng for a bilayer interface. If bodt monolayers are identically constituted, the mid-surface of the bilayer (at the free chain-ends) is a minimal surface. (For an interface consisting of a reversed bilayer the surfactant molecules are inverted so that the head groups lie closest to the mid-surface, and the volume between the minimal surface and the two parallel surfaces contains the polar matter, i.e. water and surfactant head-groups.)... 

Problem 3.20 The structure of a three-dimensional random network may be described quantitatively by two quantities the density of crosslinking designated by the fraction e of the total structural units engaged in crosslinkages and the fraction 6f of the total units which occurs as terminal units or free chain ends (i.e., which are connected to the structure by only one bond). Alternative quantities, such as the number (mole) N of primary molecules and the number (mole) v of crosslinked units, in addition to M and Me, defined above, are also used to characterize a random network stmeture. Relate N and v to these other quantities. 

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