Semi-flexible rod

One model for rod-like colloids is tire tobacco mosaic vims (TM V), which consists of rods of diameter D about 18 nm and lengtli L of 300 nm [17,18]. These colloids have tire advantage of being quite monodisperse, but are hard to obtain in large amounts. The fd vims gives longer, semi-flexible rods (L = 880 nm, D = 9 nm) [18,19]. Inorganic boehmite rods have also been prepared successfully [20]. 

The rheological behaviour of polymeric solutions is strongly influenced by the conformation of the polymer. In principle one has to deal with three different conformations, namely (1) random coil polymers (2) semi-flexible rod-like macromolecules and (2) rigid rods. It is easily understood that the hydrody-namically effective volume increases in the sequence mentioned, i.e. molecules with an equal degree of polymerisation exhibit drastically larger viscosities in a rod-like conformation than as statistical coil molecules. An experimental parameter, easily determined, for the conformation of a polymer is the exponent a of the Mark-Houwink relationship [25,26]. In the case of coiled polymers a is between 0.5 and 0.9,semi-flexible rods exhibit values between 1 and 1.3, whereas for an ideal rod the intrinsic viscosity is found to be proportional to M2. 

Consider a semi-flexible rod with Young s modulus E— 10 Pa and cross-section Ly — L-— nm. Estimate the Kuhn length of this rod at room temperature. How does the Kuhn length change if the cross-section changes to Ly = L, = 5 nm ... 

The transition from slopes a<0.8 for semi-flexible rods at low molar masses to a=0.8 for flexible coils at high molar masses is often not detected because of the narrow range of molar masses available for the determination of a [/]]-M-rela-tionship. This is another reason that many different [q]-M-relationships are pub-... 

Scheme 9 Chemical structures of rigid rod-like dialkylpolysilanes (10 and 31) and semi-flexible dialkylpolysilane (32) used for the sergeants and soldiers-helix command surface experiments...

Another viable method to compare experiments and theories are simulations of either the cell model with one or more infinite rods present or to take a solution of finite semi-flexible polyelectrolytes. These will of course capture all correlations and ionic finite size effects on the basis of the RPM, and are therefore a good method to check how far simple potentials will suffice to reproduce experimental results. In Sect. 4.2, we shall in particular compare simulations and results obtained with the DHHC local density functional theory to osmotic pressure data. This comparison will demonstrate to what extent the PB cell model, and furthermore the whole coarse grained RPM approach can be expected to hold, and on which level one starts to see solvation effects and other molecular details present under experimental conditions. 

Fig. 6. Phase diagram for the solution of semi-flexible macromolecules. I isotropic phase, II anisotropic phase. III phase separation region. Dotted curves - phase diagram for the solution of rigid rods with the same p (see Fig. 2). T3 triple point temperature, 6 the theta temperature...

Unfortunately, there are very few discussions about the viscosity behavior for semi-flexible liquid crystalline polymers. Semenov (1988) calculated the viscosities of worm-like chains and found that 0 3/02 of this liquid crystalline polymers is always positive and decreases as the order parameter increases. The conclusion is different from that of rod systems. 

Rod-like macromolecules or semi-flexible chains such as cellulosics with a certain rigidity may form thermotropic and, in highly concentrated solution with suitable interactions, lyotropic liquid-crystalline phases. 

The hydrodynamic theories of Yamakawa et al. [2-4] contain the cylinder diameter d as well as q and Ml as parameters. These parameters can be determined from M dependent data of / or [rj, provided that the data exhibit behavior characteristic of rigid rods at low M and that of semi-flexible chains at high M. A simple procedure is then as follows. First, we plot l[rj (or Iff) for low values of M against InM. According to eq 2.38 (or eq 2.33),... 

Unquestionably, Yamakawa and collaborators have made a substantial contribution to the understanding of transport behavior of semi-flexible polymers in dilute solution. However, their theories still leave something to be desired, as revealed by the recent careful experiments mentioned above. Their formulation is essentially the combination of the the Kirkwood-Riseman hydrodynamics and the statistics of wormlike chains. As mentioned in Chapter 2, this hydrodynamics fails to be good for flexible chains, but we have seen that it seems to work well for stiff chains. The reason is that the Kirkwood-Riseman formalism gives the exact solution in the limit of rigid rods. 

The large micelles can differ strongly in flexibility and may be referred to as rigid rods, semi-flexible or highly flexible. As for polymers, they can be characterized by a persistence length. 

The problem is more difficult when polymers are considered. If they are supposed to be rigid rods, without "soft" interactions,the Flory lattice theory provides a model in agreement with experiments. If the macromolecular chain is semi-flexible, the situation is less clear. Several theories are currently developed their main features are described in this volume. They also describe the transition as first order, but with a strong second order component. 

Doi and Edwards developed the most extensive theory of dynamics of rod-like macromolecules in concentrated solutions [2,12], As discussed in the previous section, the majority of commercial TLCPs are not perfect rigid rods but are semi-rigid rods having some degree of flexibility. Although several experimental results support the validity of the rigid rod approximation for both lyotropic [13-15] and thermotropic liquid crystalline polymers [16-18], there is no complete theory on the dynamics of TLCPs. To better understand the dynamics of TLCPs in the melt, the Doi-Edwards theory on the dynamics of rod-like polymers in solution is summarized here. Readers may find further details of the theory in the original reference [2,12]. 

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