H-polymers and combs

The arm retraction mechanism of star dynamics can be applied to other 

The backbone of the polymer moves by reptation along the contour of its tube, with curvilinear diffusion dominated by the branch point friction (br- An H-polymer is the simplest comb polymer with q = 4 branches per molecule. For any trifunctional comb polymer g 4) the 

The length of the confining tube of the backbone is Lbb to the reptation time of the backbone  

The diffusion coefficient of entangled H-polymcrs and combs is the mean-square size of the backbone divided by its reptation time  

The stress relaxation modulus of combs and H-polymers consists of an arm-retraction part at shorter times t tarm) and a reptation part at longer times (Tarm frep)----------------------------------------- 

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However, the agreement between theory and experiment in these comparisons is the result of substantial data fitting, and one cannot definitely say that the theory gives better than qualitative agreement. Also, it now appears that the formula used in McLeish et al. to account for polydispersity effects is qualitatively inadequate to account for H polymers and combs. 

Figure 2.4 Sketches illustrating various branched structures star, H-polymer, dense comb, Cayley tree, and dendrimer.

Similar arguments can be used to derive expressions for the reptation times of the backbones of H or pom-pom polymers [50]. Comparisons between theory and experimental data have been carried out by McLeish et al. [24] for model H polymers and of Daniels et al. [25,54] for model comb polymers. Good agreement between theory and experiment requires use of a fitting parameter (the parameter p in Eq. 9.9), small adjustments of the parameters, M, ... 

Functionalized polymers with comb-like, rotaxanic-, and dendrimeric structures [H. Ritter, GITFachz. Lab. 1994, 38(6), 615-619]. 

Ju, H.K. Kim, S.Y. Lee, Y.M. pH/temperature-respon-sive behaviour of semi-lPN and comb-type graft hydrogels composed of alginate and poly(A-isopropylacrylamide). Polymer 2001, 42, 6851-6857. 

Another important feature controlling the properties of polymeric systems is polymer architecture. Types of polymer architectures include linear, ring, star-branched, H-branched, comb, ladder, dendrimer, or randomly branched as sketched in Fig. 1.5. Random branching that leads to structures like Fig. 1.5(h) has particular industrial importance, for example in bottles and film for packaging. A high degree of crosslinking can lead to a macroscopic molecule, called a polymer network, sketched in Fig. 1.6. Randomly branched polymers and th formation of network polymers will be discussed in Chapter 6. The properties of networks that make them useful as soft solids (erasers, tires) will be discussed in Chapter 7. 

T.H. Wines and P. Somasundaran2002, Effects of adsorbed block copolymer and comb-like amphiphilic polymers in solution on the electrical percolation and light scattering behavior of reverse microemulsions of heptane/water/AOT, J. Colloid Interf. Sci. 256, 183-189. 

The entire subject of the viscoelasticity of branched polymers is an active area of research at present. The linear viscoelastic properties of nonsymmetric stars, H-shaped polymers, polymeric combs, and randomly branched species are being investigated both theoretically and experimentally [78-82], and new ideas about their nonlinear responses both during shear and during extension are being considered [83]. With these and other initiatives, the molecular understanding of flow behavior in entangled-polymer liquids will surely expand rapidly in the next few years. 

Ishimoto K, Arimoto M, Okuda T, Yamaguchi S, Aso Y, Ohara H, Kobayashi S, Ishii M, Morita K, Yamashita H, Yabuuchi N (2012) Biobased polymers synthesis of graft copolymers and comb polymers using lactic acid macromonomer and properties of the product polymers. Biomacromolecules 13 3757-3768... 

J. W. M. Noordermeer, O. Kramer, F. H. M. Nestler, J. L. Schrag, and J. D. Ferry. Viscoelastic properties of polymer solutions in high-viscosity solvents and limiting high-frequency behavior. II. Branched polystyrenes with star and comb structures. Macromolecules, 8 (1975), 539-544. 

The formation of difunctional alkyllithium initiator from the adduct of 5-BuLi and PEB in nonpolar solvent enabled the synthesis of H-shaped polymers, regular combs, centipedes, and barbwires. ° Quirk and Tsai ° prepared a trifimc-tional alkyllithium initiator based on l,3,5- ri5(l-phenylethenyl) benzene and used it for the synthesis of three-arm star polymers in benzene. Three-arm star polymers exhibiting multimodal distributions were obtained due to the intermolecular aggregation of initiator rendering initiation incomplete or slow. The addition of a polar solvent such as THF (THF/Ii = 20) to the initiator solution in benzene produced three-arm star polymer with narrow MWD. ° ... 

Polymer LC systems of more complex structure which are int mediate between comb-shaped LC polymers and LC polymers with mesogenic groups in the main chains have recently been synthesized using polycondensation meAods [29-31]. A schematic illustration of their macromolecules is shown in Fig. 6.3g, h, and some examples of the synthesis of such polymers are given below ... 

Tobita, H., Saito, S. Size exclusion chromatography of branched polymers Star and comb polymers. Macromol. Theory Simul (1999) 8, pp. 513-519... 

By means of anionic polymerization, it is possible to produce in the laboratory linear polymers that are nearly monodisperse and have many types of branching such as multi-armed stars and combs and H-shaped molecules. For example, there have been reports of studies of anionically polymerized polystyrene, polybutadiene, and polyisoprene. An example of the anionic polymerization of a branched polymer is the technique of Roovers and Toporowski [22] for making comb polystyrenes. The varieties of model branched polymer that can be produced today by means of block polymerization and coupling chemistries include stars, H-shaped molecules, super-H molecules (multi-armed stars at both ends of a backbone segment), and combs of various types [23]. So-called pom-pom polymers are of special interest, because their rheological behavior has been modeled by McLeish and Larson [24]. These molecules have several arms at each end of a central crossbar, and polybutadienes having this structure have been synthesized [25,26]. 

By use of chlorosilane chemistry, various branched structures can be prepared. For example, star-branched PBd can be prepared [27] and hydrogenated to produce analogs of star-branched polyethylene [46]. Hadjichristidis etal. [47] have reported the latest developments in the preparation of polyethylene analogs based on butadiene. Using the methods they describe, a remarkable array of structures can be produced, including stars, H-shaped molecules, super-H molecules (three-armed stars at both ends of a backbone segment), pom-poms (multiarmed stars at the ends of a backbone) and combs of various types. Rheological data have been published for the polymers they described [48]. 

Figure 9.4 Illustration of branched polymers H, pom-pom, and comb molecular architectures.

Finally, we remark that the idea of self-consistent dynamic dilution was applied first by Marrucci [20] to the case of monodisperse linear polymers, and was then adapted by BaU and McLeish [11] to monodisperse stars. We also note that theories combining reptation, primitive path fluctuations, and constraint release by dynamic dilution have been applied successfully by Milner and McLeish and coworkers to monodisperse linear polymers [21], monodisperse stars [13], bimodal star/star blends [22], and star/linear blends [23], as well as H-branched polymers [24], and combs [25]. The approach taken for all these cases is similar at early times after a small step strain, the star arms and the tips of linear molecules relax by primitive path fluctuations and dynamic dilution. At some later time, if there are linear chains that reach their reptation time, there is a rapid relaxation of these linear chains. This produces a dilation of the effective tubes that surround any remaining unrelaxed star arms by constraint-release Rouse motion (see Section 7.3). Finally, after dilation has finished, the primitive path fluctuations of remaining portions of star arms begin again, in the dilated tube. We refer to this set of theories for stars, linears, and mixtures thereof as the Milner-McLeish theory . The details of the Milner-McLeish theory are beyond the scope of this work, but the interested reader can learn more from the original articles as well as from McLeish and Milner [26], McLeish [14], Park and Larson [27], and by Watanabe [19]. 

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