Chain flexibility stiffness

Fig. 20 a-d. Four types of cylindrical brushes with different flexibility of the side chain and the main chain a stiff backbone - stiff side chains b stiff backbone - flexible side chains c flexible backbone - stiff side chains d flexible backbone - flexible side chains... 

The diffusion of larger organic vapor molecules is related to absorption. The rate of diffusion is dependent on the size and shape of the diffusate molecules, their interaction with the polymer molecules, and the size, shape, and stiffness of the polymer chains. The rate of diffusion is directly related to the polymer chain flexibility and inversely related to the size of the diffusate molecules. 

The Tg is related to chain stiffness and the geometry of the polymer chain. Flexible polymers with methylene and oxygen atoms in the chain, such as polyethylene, polyoxymethylene, and polysiloxane (silicone), have relatively low Tg values. The Tg of polyoxymethylene is somewhat higher than would be anticipated because of the dipole character of the C—O—C group, which increases the intermolecular forces and restricts segmental motion. 

Then there are flexible linear polymers which curl up in solution to give a random cell. If the chain is stiff, such as in cellulose or in DNA, the coil becomes highly expanded. 

By building - in combinations of aromatic rings into the polymer chains, chemists are able to produce polymer chains with very low chain flexibility. In the limit they reach rigid-rod-type op polymers. Such polymers show substantial temperature - pressure -concentration regions in which the stiff polymer chains arrange in some form of orientation. This phase behaviour gave them the name Liquid Crystalline Polymers (LCP) and LCP have unique properties. 

As compared to the interphases detected in the case of the Cu/epoxy systems, the interphase measured in the case of the C-fibre/PPS system exhibits a negative stiffness gradient, i.e. decreasing local stiffness of the thermoplastic PPS with increasing distance from the C-fibre surface. The mean width 3/c 107 nm of the stiffness profile is 2.6 times smaller than that of the stiffness profile measured on the Cu/epoxy replica sample. Taking into consideration the spatial constraints imposed on polymer chains due to the presence of the nearby hard wall represented by the surface of the C-fibres, the observed increase in local stiffness can be ascribed to the respective loss in chain flexibility and mobility. 

Chain Flexibility. If two polymers have the same M, the stiff chain one will produce a coil of lesser density and greater [iq], compared with its flexible coil counterpart. 

As noted above, the first study of the problem of partial chain flexibility has been done by Flory (1) - one more problem in polymer science which he was the first to tackle. Flory has assumed the existence of a favorable arrangement of a number of consecutive base units. The configurational free energy of this arrangement differs by an amount e from other possible sequences. Apparently, these other arrangements do not have to be all identical thus e represents an average value. Flory points out that the stiffness of the chain is involved. He places the chains and solvent molecules on a lattice, a convenient although not a necessary step. 

Polymers 19-32 [27, 33, 296, 381-394] represent some examples used in nonlinear absorption studies. Investigations show that large 8 can be obtained if the unsaturated chain is stiff. This keeps distortion of the re-system as small as possible, and becomes more clear by comparing the data of the stiff ladder-type polymer 20 with the more flexible PPV 22. In other words, the more planar the entire re-system, the larger the amplitude of the TPA (Table 3.4). 

The chain conformation is determined by the interaction between neighboring segments and the interaction between distant segments along a polymer which, via chain flexibility, are located in each other s vicinity. The former effect determines the local chain stiffness. The latter is referred to as the excluded volume effect and influences the overall conformation. Both types of interaction can be of electrostatic and nonelectrostatic origin. In the absence of excluded volume effects (flexible polyions in a theta state or... 

For strongly asymmetric mixtures (e.g., mixtures where the A-chains are stiff while the B-chains are flexible) the semi-grandcanonical approach is clearly not feasible, and one must work in a canonical ensemble where both the number of A-chains nA and the number of B-chains nB are fixed. However, the finite size scaling ideas for PL(M) as exposed above still can be exploited if one considers the order parameter M in L x L subsystems of a much larger system [267]. The usefulness of this concept was demonstrated earlier for Ising models and Len-nard-Jones fluids [268-271]. Gauger and Pakula [267] find an entropy-driven phase separation without any intermolecular interactions. 

Apparently, the configuration of the parent polymer does influence the structure of the derived polysulfonate, chain flexibility of the former leading to an easier accommodation of the ionic groups into clusters, while chain stiffness decreases this probability. 

Figure 6. Phase diagram for athermal semiflexible chains of 8 (diamonds) and 16 (squares) segments generated by pseudo-Gibbs ensemble simulations (Fig. 5). The axis shows the reciprocal persistence length (q), which provides a measure of chain flexibility data shown at 1/q = 0.001 actually correspond to the infinitely stiff limit (l/q - 0). Chain flexibility increases as l/q increases. (Adapted from Escobedo and de Pablo [79].)...

Chain flexibility is determined by the ease with which rotation occurs about primary valence bonds. Polymers with low hindrance to internal rotation have low Tg values. Long-chain aliphatic groups — ether and ester linkages — enhance chain flexibility, while rigid groups like cyclic structures stiffen the backbone. These effects are illustrated in Table 4.1. Bulky side groups that are stiff and close to the backbone cause steric hindrance, decrease chain mobility, and hence raise Tg (Table 4.2). 

Chain flexibility — In the process of aggregation to form a crystalline solid, polymer molecules are opposed by thermal agitation, which induces segmental rotational and vibrational motion. Polymers with flexible chains are more susceptible to this agitation than those with stiff backbones. Consequently, chain flexibility reduces the tendency for crystallization. 

Indeed, Teramoto and co-workers [Sato et al., 1991, 2003 Ohshima et al. 1995] have pointed out that the viscosity of stiff-chain polymers is affected dramatically by chain flexibility. To illustrate this, in Figure 1.15, Sato et al. [2003] compare... 

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