Branched polymer phases

Figure 15. Schematic representation of the different phases of a linear cliain with selfattraction on the Sierpinski gasket with at most two visits per site allowed (a) the swollen phase (b) branched polymer phase with branches made of the doubled-up chain (c) the collapsed phase...

As yet, models for fluid membranes have mostly been used to investigate the conformations and shapes of single, isolated membranes, or vesicles [237,239-244], In vesicles, a pressure increment p between the vesicle s interior and exterior is often introduced as an additional relevant variable. An impressive variety of different shapes has been found, including branched polymer-like conformations, inflated vesicles, dumbbell-shaped vesicles, and even stomatocytes. Fig. 15 shows some typical configuration snapshots, and Fig. 16 the phase diagram for vesicles of size N = 247, as calculated by Gompper and Kroll [243]. 

The effect of lateral methyl groups in the spacer on the phase behavior has been studied in several polybibenzoates [18,19] derived from poly(tetramethy]ene p,p bibenzoate), P4MB. The branched polymers display transition temperatures significantly lower than P4MB. Moreover, the substituents have a clear effect on the kind of mesophase formed. Thus, P4MB displays a smectic A mesophase, while the lateral methyl groups... 

Highly branched polymers, polymer adsorption and the mesophases of block copolymers may seem weakly connected subjects. However, in this review we bring out some important common features related to the tethering experienced by the polymer chains in all of these structures. Tethered polymer chains, in our parlance, are chains attached to a point, a line, a surface or an interface by their ends. In this view, one may think of the arms of a star polymer as chains tethered to a point [1], or of polymerized macromonomers as chains tethered to a line [2-4]. Adsorption or grafting of end-functionalized polymers to a surface exemplifies a tethered surface layer [5] (a polymer brush ), whereas block copolymers straddling phase boundaries give rise to chains tethered to an interface [6],... 

One of the possible alternative to micelles are spherical dendrimers of diameter generally ranging between 5 and 10 nm. These are highly structured three-dimensional globular macromolecules composed of branched polymers covalently bonded to a central core [214]. Therefore, dendrimers are topologically similar to micelles, with the difference that the strnctnre of micelles is dynamic whereas that of dendrimers is static. Thus, unlike micelles, dendrimers are stable nnder a variety of experimental conditions. In addition, dendrimers have a defined nnmber of fnnctional end gronps that can be functionalized to prodnce psendostationary phases with different properties. Other psendostationary phases employed to address the limitations associated with the micellar phases mentioned above and to modnlate selectivity include water-soluble linear polymers, polymeric surfactants, and gemini snrfactant polymers. 

To predict macrosyneresis in the case of dissolved polymer chains being crosslinked it is necessary to know the change in the number of elastically effective network chains as a result of changing the number of chemical crosslinks and the effect of v on (r2),. and possibly on y. Moreover, if the molecular weight of primary chains is finite and the sol fraction is important, a complete description of the phase separation requires treating the system as a multicomponent one, containing a network phase and a multicomponent diluent with branched polymer species. If additional crosslinking is carried on in an extracted network the latter complication can be eliminated. 

In a two-phase system similar to that used by Price, Stamatoff (29) obtained from 2,6-dichloro-4-bromophenol a branched polymer having approximately the statistical ratio of ortho and para ether linkages. When the reaction was carried out using the anhydrous salt of the phenol in the presence of highly polar aprotic solvents, such as dimethyl sulfoxide, the product was the linear poly(2,6-dichlorophenylene oxide) (Reaction 23). 

We emphasize at the outset that this article deals with flexible linear chains only, neither branched polymers [54,159] nor the packing of stiff chains near surfaces [52,53] will find much attention. However, we also shall not cover films formed by end-grafted chains ( polymer brushes [160-172]), although in brushes formed from two different types of chains A,B interesting phase separation behavior can occur [165,166] that is related to the phase separation in non-grafted films as treated here. Also films formed from strictly two-dimensional chains in a plane [173-175] are outside of our attention.,... 

At pressures above these limits, the solubility of CO2 in the polymer phase remains relatively constant as seen on the right hand branches of Figures 4 and 5. This condition affects the distribution of CO2 and polymer between the two phases. When the composition of the polymer phase is almost constant, a preferential partitioning of CO2 into the SCF phase drives a certain amount of polymer from the polymer phase into the SCF phase based on the criterion of phase equilibria. This effect together with the solvent density increase due to pressure cause the enhancement of the solubility of polymer in the SCF phase as observed on the left hand branches of Figures 4 and 5. 

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