Branched polymers structure

A successful theory, or simulation method, for branched polymer rheology should predict the frequency-dependent linear viscoelasticity of an arbitrary mixture of branched (and linear) spedes, whether those species are stars, H molecules, combs, or irregular branched structures. Such a theory, if it could be developed, would allow one to design polymer branching structures to produce the desired linear viscoelastic response. It could also potentially be used to infer from linear viscoelastic data information about the type of branching present in the melt [56, 57,5]. This latter use of linear viscoelastic data is referred to as analytical rheology. 

Structurally viscous grades are based on branched polymers (branching being effected by the use of tri- or higher functional phenols). These polymers exhibit a sharp decrease in viscosity with increasing shear rate which makes them particularly suitable for extrusion and blow moulding and also, it is claimed, in reducing drip in case of fire. 

Due to dieir compact, branched structure and to die resulting lack of chain entanglement, dendritic polymers exhibit much lower melt and solution viscosity dian their lineal" counterparts. Low a-values in die Mark-Houwink-Sakurada intrinsic viscosity-molar mass equation have been reported for hyperbranched polyesters.198 199 Dendrimers do not obey diis equation, a maximum being observed in die corresponding log-log viscosity-molar mass curves.200 The lack of chain entanglements, which are responsible for most of the polymer mechanical properties, also explains why hyperbranched polymers cannot be used as diermoplastics for structural applications. Aldiough some crystalline or liquid... 

Experimental data on the solution properties and melt rheology of highly branched structures are scarcely found in the literature. This might be because of the structural nonuniformity of hyperbranched polymers, which makes it difficult to obtain reliable data. Because of the purely statistical nature of the poly-... 

Dendrimers, a relatively new class of macromolecules, differ from traditional Hnear, cross-Hnked, and branched polymers. The conventional way of introducing an active moiety into polymers is to Hnk it chemically into the polymeric backbone or a polymer branch. This synthetic approach results in a topologically complex material. Therefore, a significant effort has to be devoted to improve the structural complexities and functions of the polymers. 

Alternatively, the structural units of the polymer may be connected together in such a manner as to form nonlinear, or branched, structures of one sort or another. Some, at least, of the structural units must then possess a valency greater than two. A typical nonlinear pol3oner structure in which the branching units represented by Y are trivalent may be indicated as follows ... 

For the purpose of deriving the weight fraction distribution, attention is directed to the fact that a molecule containing n /-functional branches is composed oi fn—n+1 chains. The average size of a chain being independent of the location of the chain in a branched structure, the quantity fn — n + 1 may be taken as a measure of the average weight of an n-chain polymer. It follows that... 

In order to determine the branching structure factor e, Foster ( ) studied a large qroup of high pressure low density polyethylene resins (HP-LDPE). Using the MWBD method, he calculated the whole polymer number average number of branch points per JOOO carbon atoms from SEC data as a function of e. Then the Xfj values were compared with those obtained by nMR. 

Several assumptions were made in using the broad MWD standard approach for calibration. With some justification a two parameter equation was used for calibration however the method did not correct or necessarily account for peak speading and viscosity effects. Also, a uniform chain structure was assumed whereas in reality the polymer may be a mixture of branched and linear chains. To accurately evaluate the MWD the polymer chain structure should be defined and hydrolysis effects must be totally eliminated. Work is currently underway in our laboratory to fractionate a low conversion polydlchlorophosphazene to obtain linear polymer standards. The standards will be used in polymer solution and structure studies and for SEC calibration. Finally, the universal calibration theory will be tested and then applied to estimate the extent of branching in other polydlchlorophosphazenes. 

An important polymer modification reaction is the grafting to or from a polymer backbone by some chemical method to produce a branched structure Q). The characterization of the products of these reactions is often somewhat less well defined than block copolymers (2) due to the complexity of the mixture of products formed. It is therefore useful to prepare and characterize more well defined branched systems as models for the less well defined copolymers. The macromonomer method (3 ) allows for the preparation of more well defined copolymers than previously available. 

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