Semiflexible polymer

A. Yethiraj. Monte Carlo simulation of confined semiflexible polymer melts. J Chem Phys 707 2489-2497, 1994. 

As the temperature is decreased, the chains become increasingly rigid zc then approaches 1 if we assume that there is only one fully ordered crystalline structure and Zconf for the liquid becomes smaller than 1. This means that, at this level of approximation, the disordered state becomes less favorable than the crystalline ground state. A first-order disorder-order phase transition is expected to occur under these conditions. Flory interpreted this phase transition as the spontaneous crystallization of bulk semiflexible polymers [12], However, since the intermolecular anisotropic repulsion essential in the Onsager model is not considered in the calculation, only the short-range intramolecular interaction is responsible for this phase transition. 

Table 1 Thermal and geometrical data of selected semiflexible polymers giving rise to thermotropic hexagonal mesophases or main-chain disordered crystalline phases (adapted from [11])... 

S. Jun, J. Bechhoefer, andB.-Y. Ha, Diffusion-limited loop formation of semiflexible polymers Kramers theory and the intertwined time scales of chain relaxation and closing. Europhys. Lett. 64, 420-426 (2003). 

The computation of the density of states within the LCT is nontrivial since the LCT free energy F T) = —(31nZ(7 ) is derived as an expansion in the product of the van der Waals interaction energies e and (3 = l/k T. This free energy series for semiflexible polymer systems has been developed [50, 51] through second order in p,... 

The onset of glass formation in a polymer melt is associated with the development of orientational correlations that arise from chain stiffness. At the temperature Ta, there is a balance between the energetic cost of chain bending and the increased chain entropy, and below this temperature orientational correlations are appreciable while the melt still remains a fluid. Such a compensation temperature has been anticipated based on a field theoretic description of semiflexible polymers by Bascle et al. [120]. The temperature 7a is important for describing liquid dynamics since the orientational correlations (and dynamic fluid heterogeneities associated with these correlations) should alter the polymer dynamics for T < Ta from the behavior at higher... 

In the present article, we focus on the scaled particle theory as the theoretical basis for interpreting the static solution properties of liquid-crystalline polymers. It is a statistical mechanical theory originally proposed to formulate the equation of state of hard sphere fluids [11], and has been applied to obtain approximate analytical expressions for the thermodynamic quantities of solutions of hard (sphero)cylinders [12-16] or wormlike hard spherocylinders [17, 18]. Its superiority to the Onsager theory lies in that it takes higher virial terms into account, and it is distinctive from the Flory theory in that it uses no artificial lattice model. We survey this theory for wormlike hard spherocylinders in Sect. 2, and compare its predictions with typical data of various static solution properties of liquid-crystalline polymers in Sects. 3-5. As is well known, the wormlike chain (or wormlike cylinder) is a simple yet adequate model for describing dilute solution properties of stiff or semiflexible polymers. 

Figures 7 and 8 display such plots for various lyotropic liquid-crystalline polymer systems, which range in q from 5.3 to 200 nm. As expected, most data points come close to the theoretical curve. This finding suggests that liquid crystallinity of stiff-chain or semiflexible polymer solutions has its main origin in the hard-core repulsion of the polymers.

Phase diagrams of ternary systems containing two semiflexible polymer components 1 and 2 can be calculated from thermodynamic functions given by Eqs. 26-28. The thick solid curves and thin solid segments in Fig. 9 are calculated binodals and tie lines, respectively [17]3. In the calculation, the diameter... 

In contrast to the case of rodlike polymers, no adequate expression of Vscf (a) is available for semiflexible polymers. Thus, at present, we cannot directly calculate F for semiflexible polymer solutions by Eq. (62). However, as will be shown in Sect. 8.2, we need no direct calculation of F to obtain (E) in a steady-state flow. So, in the following sections, we will be concerned only with the case of steady-state flow. 

Since Chen used the second virial approximation in his phase boundary calculation, it is adequate to compare his results with the phase boundary concentrations calculated from Onsager s expression of S (cf. Sect. 2.5) and cj(N) of Eq. (18) together with the OTF. Chen expressed the phase boundary concentrations in terms of reduced quantities Cj = L2dc j and cA = L2dc A, which depend only on N. As shown in Fig. Al, the relative differences in both Q and cA between the two procedures are less than 13% over the whole range of N. This confirms the relevance of the OTF for semiflexible polymer systems. 

Investigations in the past years have proved that applying the concept of flexible spacer, polymers can be synthesized systematically, which exhibit the l.c. state. Owing to the flexible linkage of the mesogenic molecules to the polymer main chain, very similar relations can be expected with respect to 1-l.c., like chemical constitution and phase behavior, or dielectric properties and field effects for the l.c. side chain polymers. This will be in contrast to main chain polymers, where the entire macromolecule, or in case of semiflexible polymers parts of the macromolecules, form the l.c. structure. The introduction of a flexible spacer between backbone and mesogenic group can be performed in a broad variety of chemical reactions. Some arbitrarily... 

What about semiflexible polymers It is, in principle, possible to include the effect of the chain stiffness through the parameter y in (3.1). As shown... 

Fig. 3.8. Typical snapshots (top and side views) of folded semiflexible polymers with l/a 20 from Monte Carlo simulations. The chain lengths are (a) L/a = 500, (b) L/a = 1,000, and (c) L/a = 2,000. The dependence of the radius of gyration on the chain length obeys the scaling law Rg Lv with the exponent v = 0.197 0.019 (see [32] for more details)...

Fig. 3.9. Dynamical process of the folding of a semiflexible polymer with contour length L/a = 512 and Kuhn length l/a cs 20. (Top) Snapshots obtained through Brownian dynamics simulations, and (bottom) the fluorescence intensity profile of the T4 DNA during the folding and corresponding schematic pictures (see [26] and [34] for more details)...

A simple model calculation of the folding transition in line with the above analysis has demonstrated that the degree of the remanent charge inside the folded part is a crucial factor for the transition manner (Fig. 3.12). If the folded part is completely neutralized by oppositely charged low molecular solvents, then the scenario developed for neutral semiflexible polymers can be applied. 

In the second type of semiflexible polymer molecule, rigid units are interspersed with flexible ones. Some examples of molecules of this kind are given in Chapter 11. The freely jointed chain model might be a suitable model for such semiflexible polymers. If a persistently flexible molecule and a freely jointed molecule are characterized by the same values of L and Xp (or, equivalently, of bx and Nk), then the gross statistical measures of the coil dimensions of the two such isolated chains will be the same, despite the differences in the type of flexibility. 

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