Arm number of the star

Based on the findings of the arm-first strategy, it is possible to obtain stars with well-defined arm length. The main problem of this strategy is the arm number distribution. Moreover, purification may cause many difficulties in the synthesis. In contrast, the core-first strategy requires multifunctional initiators and further polymerization initiated from the core. This is shown in Scheme 3. The maximum arm numbers of the stars are determined by the number of functionalities in the core. In the ideal case, the initiating efficiency of the core is close to unity, which will produce well-defined stars with precise numbers of arms. However, due to the steric hindrance and the limit of the polymerization techniques, it can be difficult to obtain full initiating efficiency. 

On the other hand, as soon as many stars are in the matrix, the entanglement points of the matrix are increased due to additional permanent crosslink points (i.e., centers of star polymers). Thus the average mesh size of the matrix decreases. In consequence, the cooperative diffusion becomes faster. But in the case of 12-arm star polystyrene as the test chain, the effect of star centers was not so obvious. According to the model of star shaped polymers by Daoud and Cotton,there is a region with size around the center of a star, inside which the chains of other polymers do not penetrate. The distance x is a function of the number of arms, i.e., / where f is the arm number of the star. So the unpenetrable distance of 12-arm star is larger than that of a 4-arm star, leading to an effective decrease in the number of entangled points. 

For well-controlled arm number of the star polymers, an efficient approach is the use of multifunctional initiators [157,158]. For instance, the four-armed initiator, NLI-1, which was prepared by the condensation reaction of the hydroxy groups in C(CH20CH2CH2CH20H)4 with a-bromoisobutyric acid, was used in the ATRP of (2,2-dimethyl-l,3-dioxoIane-4-yl)methyl acrylate (DMDMA) with CuBr/bpy as catalyst. After isolation from the polymerization system, four-armed poly(DMDMA)s, such as NLI-2 with Mw/Mn = 1.28—1.41 were obtained, and used in the successive ATRP of MMA, giving star-block copolymers NLB-3. It is known that the cycloacetal ring is unstable in acidic conditions, so the hydrolysis of the block copolymer NLB-3 was accomplished in a 1N HCl aqueous solution to give the amphiphilic star-block copolymer structure NLB-4 as shown in Scheme 3.37 [159]. 

Figure 12 Schematic representation of star block copolymers, (PEOx)y(HBFP), with variation in the lengths and numbers of the star arms, and TEM analysis of their corresponding micelles in aqueous solution. Modified with permission from Du, W. J. Li, Y. L. Nystrom, A. M. etal. J. Poiym. Sci., Part A Poiym. Chem. 2010, 48 (15), 3487-3496. ...

Feijen et al. have reported the thermogelling system using SC formation of star-shaped diblock copolymers, PEG- -(PLLA)8 and PEG- -(PDLA)8 [89,90]. They have investigated the effects of arm number of the branched architecture on their temperature-responsive gelation by comparing the PEG- -(PLLA)8/PEG-h-(PDLA)8 system with the... 

Generally, the number of the shell chains in a microsphere ranges from a few hundred to a few thousand. The range of the diameter of the core is from 10-100 nm. Such a core-shell structure is very similar to the (AB)n type star block copolymers, which have many arms and spherical polymer micelles of the block or graft copolymers formed in selective solvents that are good for the corona sequence and bad for the core sequence. In fact, many theoretical investigations of the chain con-... 

Star shaped macromolecules are polymers, where the one end of f > 2 (f functionality of the star) linear chains is chemically attached by covalent bonds to a small central linker unit, are the simplest form of branched polymers. Modern anionic polymerization techniques allow us to synthesize star systems with a large number of nearly monodisperse arms [133, 134],... 

The core first method has been applied to prepare four-arm star PMMA. In this case selective degradation of the core allowed unambiguous proof of the star structure. However, the MWD is a little too large to claim that only four-arm star polymers are present [81], Comb PMMAs with randomly placed branches have been prepared by anionic copolymerization of MMA and monodisperse PMMA macromonomers [82], A thorough dilute solution characterization revealed monodisperse samples with 2 to 13 branches. A certain polydispersity of the number of branches has to be expected. This was not detected because the branch length was very short relative to the length of the backbone [83]. Recently, PMMA stars (with 6 and 12 arms) have been prepared from dendritic... 

Nj,=N/f is the number of beads per branch or arm). For larger chains, however, the solvent can penetrate in outer regions of the star and the situation within these regions is more Hke a concentrated solution or a semi-dilute solution. These portions of the arms constitute a series of blobs, whose sizes increase in the direction of the arm end. The surface of a sphere of radius r from the star center is occupied by f blobs. Then the blob size is proportional to rf. Most internal blobs are placed in conditions similar to concentrated solutions and, consequently, their squared size is proportional to the number of polymer units inside them as in an ideal chain. This permits one to obtain the density of units inside the blob, as a function of r ... 

Equation (29) was previously derived by Zimm and Stockmayer [49] who used another technique. Figure 12 shows a plot of the theoretical increase of the radii of the stars as a function of the number of arms. 

Asymmetric PS stars of the type (PSA)n(PSB)n were also prepared by the divinyl-benzene (DVB) method [9]. Living PS chains, prepared by sec-BuLi initiation, were reacted with a small amount of DVB producing star homopolymers. The DVB core of the stars contains active anions which, if no accidental deactivation occurs, are equal to the number of the arms that have been linked to this core. These active sites are available for the polymerization of an additional quantity of monomer. Consequently further addition of styrene produced asymmetric star polymers... 

It was found that the reactivity ratios of the copolymerization system greatly influences the number of the arms of the star polymer. 

Fig. 6. Variation of (%N0)S with composition and arm number for AnBn star copolymers. N0 is the number of monomers in the diblock (reproduced with permission from [76])...

ABA tribiock, or all three can be different, as in an ABC triblock copolymer. Obviously, the number of possible block sequences increases rapidly with the number of blocks and the number of different types of block in the chain. One can also synthesize block copolymers with branched architecture, such as star-branched block copolymers, in which each of the arms of the star contains either the same or different block sequences (see Fig. 13-1). One or more of the blocks could also be stiff or liquid crystalline (Chiellini et al. 1994 Chen et al. 1996 Radzilowski et al. 1997 Jenekhe and Chen 1998). For a given type of block copolymer, the degree of polymerization N of the whole molecule, or the degree of polymerization Ni of one or more of the blocks, can be varied. Thus, the number of different types of block copolymers is practically endless. 

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