Statistical segment length definition

There have been recent efforts to predict, or at least rationalize, the x parameters of these and other polyolefin-polyolefin blends. Bates et al. (1992) and Fredrickson et al. (1994) suggest that the x parameter is correlated to a difference in statistical segment length of the polymer molecules, on a volume-normalized basis. The volume normalization is required because the definition of the statistical segment length depends on how the monomer unit... 

A—B diblock copolymers adsorb spontaneously at the interface between two immiscible A and B homopolymers. Our objective here is to make quantitative predictions of the nature of the adsorbed layer, fri this case, the phase behavior depends on (Mily one x parameter, that between the A and B homopolymers, and the statistical segment lengths of the A and B chains. The specific example that we will smdy is the adsorption of a SPB(89)-SPB(63) diblock copolymer at the interface between SPB(89) and SPB(63) homopolymers at room temperamre [A = SPB(89) and B = SPB(63)]. For this system, x = 0.0064 (system 33 in Table 19.1), I A = 0.49 nm, and /b = 0.75 nm. We consider the interface between SPB(89) and SPB(63) homopolymers with Na = 4,230 and Nr =3,600. It is straightforward to show that the two homopolymeis are highly immiscible because xAave =6.2 which is much greater than 2 (see Eq. (19.8) for definition of Nave)- We consider the adsorption of a SPB(89)-SPB(63) diblock copolymer with NAb = 790 and Nsb = 730 where the subscript b refers to the chains comprising the block copolymer. We consider two flat homopolymer-rich phases with the diblock copolymer adsorbed at the interface. The z-axis of our coordinate frame is perpendicular to the interface. The results of SCFT predictions for 0 e volume fraction of the A-B... 

Polymer Chain composition and definition of monomer Monomer volume V/(nm ) Statistical segment length /, (nm) Temperature (°C) Refs. 

The junctions of the cluster network have definite sizes (the length of the cluster segment is assumed to be equal to that of the polymer statistical segment [1]. 

To determine the fractality of an object, three aspects are usually considered [12]. First, as noted previously, a real physical object possesses fractal properties only in a definite scale range (see Figure 11.1). The boundary sizes for a macromolecular section can be determined using the data of several publications [22, 36, 105]. The lower boundary is related to the finite size of a structural element in terms of the cluster model, this is the length of the statistical segment... 

The definition of a segment stiffness depends on its nature. If a long stiff segment can be described as a worm-like chain, characterized by a particular smooth and uniform curvature, then the chain persistence length is a good initial descriptor. For a hypothetical worm-like chain of contour length L and statistical mechanical average square of the unperturbed end-to-end distance o, it was shown by Porod and Kratky [49,50], that in the limit of L -> oo,... 

The scattering curves cannot be described neither with broken segments nor with a distribution of broken segments (18), equation 2-12 gives an average misorientation between monomer unit equal to 14 for a statistical length equal to 300 A. The neutron scattering data provide a definite proof that the soluble PDA are much better described as a chain with a continuous curvature. 

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