Solutions dilute, properties

PCEMA nanofiber, a PS-PCEMA-PtBA nanofiber, and a PS-PCEMA nanotube with a PAA-lined core. 

In a PHIC chain, the backbone, covered by a corona of hexyl groups, consists of a Unear sequence of imide units. Their counterparts in the PS-PCEMA nanofiber are the cross-linked PCEMA cylindrical core and the PS chains as the corona. Other than the size difference, the PHIC molecule and the PS-PCEMA nanofiber bear a remarkable structural resemblance. If the PCEMA crosslinking density is high, the PtBA chains in a PS-PCEMA-PtBA nanofiber and the PAA chains in a PS-PCEMA-PAA nanotube become trapped inside the cores even if the solvent is good for both PtBA and PAA. Thus, the triblock copolymer nanofibers and nanotubes can be viewed as giant polymer chains as well [18]. 

We have so far developed techniques for the fractionation and characterization of diblock copolymer nanofibers and compared the viscosity properties of dilute solutions of diblock copolymer nanofibers and worm-like polymer chains. Based on our structural analysis above, we beUeve that these techniques and conclusions should apply equally well to triblock nanofibers and nanotubes, and these topics are thus briefly reviewed below. 

While we have prepared nanofibers from several families of block copolymers [18,61-63], the discussion here will be restricted to PS-PI nanofibers. These fibers were prepared by first dispersing PS130-PI370 in AT,N-dimethyl acetamide, a selective solvent for PS, to effect cylindrical micelle formation. The PI cores were then cross-linked by adding sulfur monochloride S2CI2 [64]. This reagent cross-linked the PI via the following reaction  

It is difficult to study the dilute solution properties of very long nanofibers. They tend to sediment, and this makes quantitative measurements difficult. While ultracentrifugation [18] or density gradient centrifugation could have 

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P. W. AHen, Technique of Polymers Characterisation, Butterworths, London, 1959 Dilute Solution Properties of Acrylic andMethacylic Polymers, SP-160, Rohm and Haas Co., Philadelphia, Pa. 

The dilute solution properties of copolymers are similar to those of the homopolymer. The intrinsic viscosity—molecular weight relationship for a VDC—AN copolymer (9 wt % AN) is [77] = 1.06 x 10 (83). The characteristic ratio is 8.8 for this copolymer. 

An extensive investigation of the dilute solution properties of several acrylate copolymers has been reported (80). The behavior is typical of flexible-backbone vinyl polymers. The length of the acrylate ester side chain has Httle effect on properties. 

Tuzar, Z., Kratochvil, P., and Bohdanecky, M. Dilute Solution Properties of Aliphatic Polyamides. Vol, 30, pp. 117-159. 

The statistical distribution of r values for long polymer chains and the influence of chain structure and hindrance to rotation about chain bonds on its root-mean-square value will be the topics of primary concern in the present chapter. We thus enter upon the second major application of statistical methods to polymer problems, the first of these having been discussed in the two chapters preceding. Quite apart from whatever intrinsic interest may be attached to the polymer chain configuration problem, its analysis is essential for the interpretation of rubberlike elasticity and of dilute solution properties, both hydrodynamic and thermodynamic, of polymers. These problems will be dealt with in following chapters. The content of the present... 

Sylvester, N.D. and Tyler, J.S. "Dilute Solution Properties of Drag-Reducing Polymers," Ind.Eng.Chem.Prod.Res.Develop.. 1970, 9(4), 548 553. 

Other dilute solution properties depend also on LCB. For example, the second virial coefficient (A2) is reduced due to LCB. However, near the Flory 0 temperature, where A2 = 0 for linear polymers, branched polymers are observed to have apparent positive values of A2 [35]. This is now understood to be due to a more important contribution of the third virial coefficient near the 0 point in branched than in linear polymers. As a consequence, the experimental 0 temperature, defined as the temperature where A2 = 0 is lower in branched than in linear polymers [36, 37]. Branched polymers have also been found to have a wider miscibility range than linear polymers [38], As a consequence, high MW highly branched polymers will tend to coprecipitate with lower MW more lightly branched or linear polymers in solvent/non-solvent fractionation experiments. This makes fractionation according to the extent of branching less effective. 

Most important, however, was the discovery by Simha et al. [152, 153], de Gennes [4] and des Cloizeaux [154] that the overlap concentration is a suitable parameter for the formulation of universal laws by which semi-dilute solutions can be described. Semi-dilute solutions have already many similarities to polymers in the melt. Their understanding has to be considered as the first essential step for an interpretation of materials properties in terms of molecular parameters. Here now the necessity of the dilute solution properties becomes evident. These molecular solution parameters are not universal, but they allow a definition of the overlap concentration, and with this a universal picture of behavior can be designed. This approach was very successful in the field of linear macromolecules. The following outline will demonstrate the utility of this approach also for branched polymers in the semi-dilute regime. 

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. 

In this article, we have surveyed typical properties of isotropic and liquid crystal solutions of liquid-crystalline stiff-chain polymers. It had already been shown that dilute solution properties of these polymers can be successfully described by the wormlike chain (or wormlike cylinder) model. We have here concerned ourselves with the properties of their concentrated solutions, with the main interest in the applicability of two molecular theories to them. They are the scaled particle theory for static properties and the fuzzy cylinder model theory for dynamical properties, both formulated on the wormlike cylinder model. In most cases, the calculated results were shown to describe representative experimental data successfully in terms of the parameters equal or close to those derived from dilute solution data. 

Stockmayer and Fixman (2) summarised the state of knowledge of the dilute solution properties of branched polymers in 1953. Dexheimer and co-workers (10) have given a comprehesive survey of the literature up to 1968, including the effects of branching (both short and long) on properties. Nagasawa and Fujimoto (11) have reviewed the results of work on rationally synthesised branched polymers (mostly polystyrenes) up to 1973, with particular reference to their viscoelastic properties. 

Dilute Solution Properties of Model Branched Polymers... 

Orofino,T.A. Dilution-solution properties of polystyrene in 0-solvent media. II. An analysis of environmental effects. J. Chem Phys. 45,4310-4315 (1966). 

All the flexible polyquinolines are readily soluble in chlorinated hydrocarbons such as methylene chloride and chloroform. Semirigid polyquinolines are soluble in tetrachloroethane or / /-cresol, but rigid polyquinolines are soluble only in strong acids like sulfuric and trifluoromethane sulfonic acid. Dilute solution properties of polyquinolines have been investigated by techniques such as membrane osmometry, light scattering, viscometry, and gel-permeation chromatography (96,97). 

The synthesis and the properties, both in bulk and in solution, of asymmetric star polymers are reviewed. Asymmetry is introduced when arms of different molecular weight, chemical nature or topology are incorporated into the same molecule. The phase separation, aggregation phenomena, dilute solution properties etc. are examined from a theoretical and experimental point of view. Recent applications of these materials show their importance in modern technologies. 

The dilute solution properties of asymmetric three-arm polystyrene stars were studied by Fetters and coworkers [67] under different solvent conditions. These materials comprised two series of samples, the first having a short third arm with half the molecular weight of the two identical arms (SAS) and the second a long arm having twice the molecular weight of the other two arms (LAS). In toluene, a good solvent for PS, the two types of asymmetric stars exhibited identical values of g, defined as... 

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