Polydisperse rods

Numerical calculations have been carried out for (i) ternary systems consisting of rods of two lengths x and x and a diluent with x = 1 (ii) solutions of polydisperse rods having a most probable distribution (iii) a Poisson distribution of rods in solution and (iv) various Gaussian distributions of rods in a diluent In all cases longer rods are preferentially partitioned into the nematic phase. For Xa = 2xb in case (i) the ratio of the concentration of either of the species in one of 

Fractionation is less pronounced for the much narrower Poisson distribution For a Gaussian distribution it varies with the breadth assigned to that distribution, as expected. 

Concomitantly with the partitioning of solute species between the coexisting phases, broadening of the biphasic gap (measured by the concentration difference between the two phases) is predicted the more so the greater the disparity 

Experiments confirm these predictions qualitatively but not quantitatively. We have mentioned above that the ratios, Vp/Vp, of the volume fractions in the coexisting phases for unfractionated polypeptides polyaramidesand polyisocyanates 15,26,27) greater than the ratios calculated for monodisperse 

The predicted fractionation of species between the isotropic and nematic phases is universally confirmed 15.22,23,25,27.36) selectivity is generally somewhat 

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Rod-Coil Diblock Copolymers Based on Polydisperse Rods. 71... 

In contrast to the rod-coil diblock copolymer consisting of perfectly monodisperse rods, the liquid crystalline morphologies of rod-coil diblock copolymer containing polydisperse rods seem to be studied in less detail. In certain cases, the polydisperse nature of the rod-segments could hinder self-assembly into regularly ordered supramolecular structures. However, due to relatively simple synthetic procedures, liquid crystalline polymer can be of benefit for new materials with controlled internal dimensions ranging from the nanometer to macroscopic scale. 

Later, Burning and Lekkerkerker [37] observed isotropic—nematic phase separation in a dispersion of sterically stabilized boehmite rods, which approximate hard rods, in cyclohexane. Buitenhuis et al. [43] studied the effect of added 35 kDa polystyrene (/ g = 5.9nm) on the hquid crystal phase behaviour of sterically stabilized boehmite rods with average length L = 1.1 nm and average diameter D = ll.lnm in ortho-dichlorobenzene. Different phase equihbria were observed. Two biphasic equilibria dilute isotropic phase Ij + nematic N, concentrated isotropic phase I2 + nematic N and a triphasic equilibrium 1 -F I2 + N (see photo. Fig. 6.20). In this system the boehmite rods are quite polydisperse. Therefore comparison with theory should be done with an approach including polydisperse rods. We further note no li +12 coexistence was observed experimentally but... 

The general predictions of Eq. (5.14) are in agreement with experiment for a variety of lyotropic LCPs [88]. One consequence of this theory for a system of polydisperse rods (a distribution of x values) is the possibility of fractionation [89] longer rods would distribute themselves into the anisotropic LC phase while short ones would be relegated to the isotropic phase in the two-phase regime. The theory can also be extended [90] to make predictions about ternary mixtures - rods, random coUs, and solvent - and is in agreement with experimental observations [91] that indicate the strong incompatibility of the two kinds of polymers. It has been adapted to treat semiflexible polymers also. 

History. Starting from the ID point statistics of Zernike and Prins [116] J. J. Hermans [128] designs various ID statistics of black and white rods. He applies these models to the SAXS curves of cellulose. Polydispersity of rod lengths is introduced by distribution functions, / , (,r)108. Hermans describes the loss of correlation along the series of rods by a convolution polynomial . One of Hermans lattice statistics is namedparacrystalby Hosemann [5,117]. Hosemann shows that the field of distorted structure is concisely treated by the methods of complex analysis. A controversial subject is Hosemann s extension of ID statistics to 3D [63,131,227,228],... 

As shown by Strobl [230], the integral breadths B in a series of reflections is increasing quadratically if (1) the structure evolution mechanism leads to a convolution polynomial, (2) the polydispersity remains moderate, (3) the rod-length distributions can be modeled by Gaussians (cf. Fig. 8.44). For the integral breadth it follows... 

In a very recent investigation, hydrophobic PFS (Sect. 7.1) was attached to a hydrophilic PEO block to form an amphiphilic PFSi2-[Ru]-PE07o block copolymer [331]. Rodlike micelles were observed in water for this copolymer (Fig. 24). These micelles have a constant diameter but are rather polydisperse in length, and DLS measurements indicate that they are flexible. Crystallization of the PFS in these micelles was observed and is thought to be the key behind the formation of rodlike structures. The cylindrical micelles can be cleaved into smaller rods whenever the temperature of the solution is increased or whenever they are exposed to ultrasound. 

At the end of the polymerization reaction, octadecyl 3-(3,5-di-ferf-butyl-4-hydroxyl)propionate, and in addition 2,5-di-ferf-but-yl-p-cresol are added as antioxidants in order to protect the product during solvent elimination, drying and storage. Morphologies, such as rods, points or capsules can be obtained by tailoring the polydispersity of the poly(styrene) block (10). 

In a hard-rod system, at sufficiently high volume fraction a transition is usually expected from the nematic to the smectic A phase [37], a lamellar phase with layers perpendicular to the nematic director. However, as elegantly demonstrated by Livolant [29], in DNA the smectic phase is replaced by columnar ordering this behavior can easily be explained on the basis of strand flexibility [38] or length polydispersity [39], both favoring the COL phase over smectic. 

A.W. Chow, and G.G. Fuller, The rheo-optical response of rod-like chains subject to transient shear flow. Part I Model calculations on the effects of polydispersity, Macromolecules 18, 786 (1985) A.W. Chow, G.G. Fuller, D.G. Wallace and J.A. Madri, The rheo-optical response of rod-like chains subject to transient shear flow. Part II. Two-color flow birefringence measurements, Macromolecules 18,793 (1985) A.W. Chow, G.G. Fuller, D.G. Wallace and J.A. Madri, The rheo-optical response of rod-like shortened collagen protein to transient shear flow, Macromolecules, 18, 805 (1985). 

These results show that the supramolecular structures of thin films of block copolymers can be manipulated by varying the rod-to-coil ratios. Variables such as the polydispersity, the nature of the structures, and their crystallinity can be controlled in this manner. The factors that govern the formation of ordered structures from these copolymers are, however, complex. Important factors include entropy effects associated with the flexible coil segments, crystallization of the rods, and steric considerations. Upon crystallization of the rods, the entropies of the coil blocks may be increasingly compromised as a result of increasing steric repulsion. This may effect the sizes of the aggregates that are formed. The organization of ordered structures can furthermore be controlled by non-specific interactions such... 

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