Star polymers intrinsic viscosity

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

Dendrimers have a star-like centre (functionality e.g. 4) in contrast to a star however, the ends of the polymer chains emerging from the centre again carry multifunctional centres that allow for a bifurcation into a new generation of chains. Multiple repetition of this sequence describes dendrimers of increasing generation number g. The dynamics of such objects has been addressed by Chen and Cai [305] using a semi-analytical treatment. They treat diffusion coefficients, intrinsic viscosities and the spectrum of internal modes. However, no expression for S(Q,t) was given, therefore, up to now the analysis of NSE data has stayed on a more elementary level. 

In 1959, Zimm and Kilb (34) made some calculations of the intrinsic viscosities of certain branched polymer molecules, taking into account the hydrodynamic interaction between portions of the polymer chain, using a modification of the Rouse procedure. They carried out these difficult calculations for a quite restricted range of models, obtaining numerical results for equalarmed stars with 3, 4, and 8 branches, and for one modified star with 2 long branches and 8 shorter branches. They found that their numerical results for this set of structures could be approximately represented by ... 

C. Assume that the GPC curve of Polymer A is that of a polydisperse, tetrafunctionally star-branched polychloroprene (i.e. apolydis-perse polymer made up of different molecular weight star-shaped polymers having four arms of equal length). Calculate the weight and number molecular weight averages, the polydispersity and the intrinsic viscosity of this star-branched polychloroprene. 

Another approach to incorporate a block structure was to use the multifunctional precursor shown in Fig. 35 and grow blocks from the core of the hyperbranched structure. Such star-like polymers with 80 pnBA blocks were obtained [ 130]. In a similar way, hyperbranched polymers from VBC were used to initiate the ATRP of nBA [130] and St [264]. Dendrigraft polystyrene was found to display a lower intrinsic viscosity and higher thermal stability than linear polystyrenes [264]. 

If the Flory-Fox equation could be assumed for both linear and branched chains, it would follow that gr, = In fact, such a relationship is not found experimentally. Zimm and Kilb [1959] carried out a theoretical analysis of the intrinsic viscosity of star polymers, in the absence of excluded volume, which led to a prediction... 

Equation (1.70) may be approximated by a simple relation between gr, and g of the form gr, = g. Analysis of experimental intrinsic viscosity data on star polymers in theta solvents indicates that while substantially better than the relation based on the Flory-Fox equation, Eq. (1.70) is still inaccurate, and that a better empirical description is given by [Douglas et al., 1990]... 

Compared to linear analogues of identical molecular weight and monomer composition, star-shaped polymers have smaller Ra, Rn, and lower intrinsic viscosity [i] [222, 226, 227] ... 

Low intrinsic viscosities and high ku values were determined by dilute solution viscosity measurements, indicative of large hydrodynamic interactions supporting the conclusions drawn from LS that intramolecular association does occur at low concentrations. Comparative examination of R and Rh values showed that Rvzwitterionic polymers, which was attributed to dissociation of the aggregates, to some extent, under the applied shear rate in the capillary. Because these forces are generally not very strong, it was concluded that the critical shear rate should be small. Compared to linear cB-fimctionalized polymers, the lower stability of the aggregates formed by the end-functionalized stars was attributed to the steric repulsion of the unfiinctionalized arms. 

The exploration of new polymer architectures has been the focus of significant recent research, motivated by the fundamental hypothesis that a polymer s properties are intimately related to its structure. This concept has led to the development and optimization of synthetic techniques for the preparation of graft, star, dendritic, ladder, and hyperbranched polymers as well as a variety of hybrid and more complex architectures. Cyclic polymers are of particular interest because their circular shape and lack of end groups has a profound effect on their physical properties such as intrinsic viscosity and hydrodynamic volumes (/). 

Figure 5 shows the dependence of the intrinsic viscosity of linear ([t]]l) and star ([t ]s) PLAs in chloroform solution on the polymer molecular weight, as determined by light scattering in HFIP. It is evident that branched PLAs have smaller intrinsic viscosity than linear ones at the equivalent molecular weight. This is a clear demonstration of the branched architecture of PLA polymerized with PET, since branched polymers are known to have smaller hydrodynamic volumes than their linear counterparts. 

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