Semi-flexible chain polymer

The polymer we consider here is a semi-flexible chain which has some bending stiffness (Eq. 3). We first estimated the chain conformation in the melt. The calculated mean-square end-to-end distance R2n between atoms n-bond apart has shown that the chains have an ideal Gaussian conformation R2 is a linear function of n (see Fig. 35 given later). The value of R2 for n = 100... 

The rearrangement of more than one inner site in a flexible or semi-flexible chain molecule can be conveniently performed if the geometric constraints that guarantee chain closure are taken into account every time a site is repositioned [50] (see Fig. 1). Performance can be enhanced by favoring low-energy trial positions for each growing site (extended continuum configurational bias, or ECCB method). Since this method can be applied to inner sites of arbitrary functionality, it has been used to study linear, branched, and crosslinked polymers [50-52]. 

In this section, we review three representative cases of flow-induced mesophases. PET serves as an example of a semi-rigid polymer with intrinsic rigid building blocks. The shear-induced smectic ordering in the flexible-chain polymer iPP provides a special case of induced rigidity, which is still far from fully understood. PDES has been chosen as an example of a stretch-induced condis crystal. Various experimental techniques have been employed to characterize flow-induced mesophases. While scattering methods probe the ordering, a direct technique to measure the molecular mobility is nuclear... 

Thermotropic PLC s evolved in academic research laboratories by incorporating known monomeric liquid crystals into polymer chains. From such studies two types of PLC s have been developed 1) side-chain polymers with variable flexibility in the main chain, and 2) semi-flexible linear polymers. In the former the monomeric mesogen appears as a pendant sidechain attached to the main chain by a flex-... 

The semi-flexibility of polymer chains due to the hindered internal rotation is revealed by the correction from the contribution of the internal rotation in the mean-square end-to-end distance, as... 

However, the conformation statistics in Flory s treatment gives the conformational free energy, rather than the conformational entropy adapted in the Gibbs-DiMarzio theory. In addition, W was calculated with respect to the fully ordered state therefore. In W = 0 simply implies the return to the fully ordered state, rather than frozen in a disordered state. Furthermore, reflects the static semi-flexibility, while the glass transition should be related with the d3mamic semi-flexibility of polymer chains. Therefore, fundamental assumptions of the Gibbs-DiMarzio thermodynamic theory are misleading. 

Fetters LJ, Lohse DJ, Graessley WW (1999) Chain dimension and entanglement spacings in dense macromolecnlar systems. J Polym Sci, Polym Phys Ed 37 1023-1033 Fischer EW, Bakai A, Patkowski AW, Steffen W, Reinhardt L (2002) Hettaophase fluctuations in supercooled liquids and polymers. J Non-Cryst Solids 307-310 584-601 Flory PJ (1956) Statistical thcamodynamics of semi-flexible chain molecules. Proc R Soc London A234 60-73... 

Fig. 3.10. Schematic representation of a flexible-chain polymer in semi-dilute solution in a good solvent. The chains constitute a 3-dimensional lattice whose unit size corresponds to the mean separation between two tangling points. Between such points (shown magnified), the section of chain behaves as if it were free in solution...

Linear polymers in the semi-crystalline state are metastable nanostructured systems with the complicated morphology, which are divided into nano-, submicro-, or microphases with crystalline, amorphous, and intermediate (mesophase and other) molecular packing. These different phases are connected in the flexible-chain polymers, such as PE, POM, poly(ethylene terephthalate) (PET), and many others, via strong covalent coupling between crystallites and disordered regions since the typical polymer molecules of l-lOOpm in contour length participate in several nanophases. Due to the multilevel structure, polymers with rather high levels of crystallinity may show up unique dynamics and properties which vary with the thermal and mechanical histories of materials. This has been confirmed by different techniques (DMA, DSC, NMR, DRS, and others) in numerous studies. 

Flory PJ (1941) Thermodynamics of high polymer solutions. J Chem Phys 9(8) 660 Flory PJ (1942) Thermodynamics of high polymer solutions. J Chem Phys 10(1) 51-61 Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, Ithaca Flory PJ (1955) Theory of crystallization in copolymers. Trans Faraday Soc 51 848-857 Flory PJ (1956) Statistical thermodynamics of semi-flexible chain molecules. Proc R Soc Lond A Math Phys Sci 234(1196) 60-73... 

Finally, some rather recent devdopments must be noted. Several years ago, Yamakawa and co-workers [25-27] developed the wormlike continuous cylinder model. This approach models the polymer as a continuous cylinder of hydrodynamic diameter d, contour length L, and persistence length q (or Kuhn length / ). The axis of the cylinder conforms to wormlike chain statistics. More recently, Yamakawa and co-workers [28] have developed the helical wormlike chain model. This is a more complicated and detailed model, which requires a total of five chain parameters to be evaluated as compared to only two, q and L, for the wormlike chain model and three for a wormlike cylinder. Conversely, the helical wormlike chain model allows a more rigorous description of properties, and especially of local dynamics of semi-flexible chains. In large part due to the complexity of this model, it has not yet gained widespread use among experimentalists. Yamakawa and co-workers [29-31] have interpreted experimental data for several polymers in terms of this model. 

Angstroms by the optical properties of the materials used, it will be necessary in the future to use much longer polymer chains. Semi-flexible chains with long persistence lengths, such as some of the water-soluble polysaccharides, are good potential candidates. 

The viscosity of PES decreases with an increase in shear rate. PES as a polymer consists of semi-rigid molecular chains which have a strong affect on rheological behavior. Hence, a decrease in the degree of apparent viscosity of PES is less than that of a flexible-chain polymer, but higher than a rigid-chain polymer, with increase in shear rate. 

A number of polyphosphazenes of repeat unit [-PRR N-] also exhibit liquid-crystalline phases [166-168]. It is certainly intriguing that apparently the only classes of flexible chains that extensively exhibit liquid-crystalline phases are the polysiloxane and polyphosphazene semi-inorganic polymers. 

It is noted that the UV absorbance of the 10(g)-32(sc) sample decreased after the annealing treatment, as shown in Fig. 28a. Presumably, most polysilane chains lie down before annealing in the quartz substrate plane, as the film was prepared by the spin-coating technique. However, the thermal annealing treatment of semi-flexible 32 tends to orient some of the polymer chain segments perpendicularly and/or tilt them to the substrate plane, leading to the decrease in the apparent UV absorbance at 321 nm, as illustrated in Fig. 27. 

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