Segment weighting factors

Interfaclal (excess) Gibbs energy per unit area (J m ) segment weighting factor in poljrmer adsorption theory (-) endpoint distribution in a segment of s segments (polymer adsorption (-)... 

From the field U [z] the segment weighting factors are obtained as... 

To the extent that the segmental friction factor f is independent of M, then Eq. (2.56) predicts a first-power dependence of viscosity on the molecular weight of the polymer in agreement with experiment. A more detailed analysis of f shows that segmental motion is easier in the neighborhood of a chain end because the wagging chain end tends to open up the structure of the melt and... 

For each methylene segment to be appended to the chain, the bond directions corresponding to the three possible rotamers are calculated from the transformation matrices in the usual way. The angular weighting factors are then determined and are multiplied with the statistical weights. These weights are normalized to probabilities, and a random number is used to select one rotamer. 

Small oscillatory torsions of molecular units within the segment produce a de-localization of the electronic density according to the Debye-Waller effect . In a very distorted structure as in the melt its smooth intensity distribution is not affected to a measurable extent. Rotational isomers, on the other hand, induce remarkable changes of the ru involved. Moreover, it is easily shown that the Boltzmann weighting factor of the molecular conformation ensemble also has a substantia] influence on the ru. It is strictly not possible to calculate the... 

In the preceding equations, rjs, p, and are weight factors which account for the difference between the interactions of the segments and of the solvent molecules with the surface, for the intermolecular interactions between the segments and the solvent molecules and for the nearest-neighbor bond correlations, respectively. 

It is worth noting that the surface parameter r/s cxp(yj which appears in the corresponding equation of the preceding paper42 does not appear in Eq. (1) because in the present derivation, the effect of Xs was included in the expression for the weight factor of a segment located in either layer 1 or 2 m. 

When the effect of bond correlations is neglected, only Eq. (13) is required to calculate the distribution of segment density from layer 1 to z/i the p s, which are present in the elements r, q , and p,- to represent the weight factors due to the bond correlations, become in that case equal to unity. 

Here the exponential weighting factors represent gaussian statistics (gyration radii = bf N / 6, where we allow different effective segment lengths bA, bB for... 

Consequently, a third segment (two steps from the first) may occasionally take the same position as the first segment. For Isolated molecules near a surface, steps towards or within the surface layer are biased with a weighting factor exp( ), all other steps are random, l.e., their weighting factor is unity. Since the DlMarzlo-Rubin single-chain model forms the basis of more sophisticated theories, we return to it in sec. 5.5a. 

The second relation is a special case of [5.5.71 if, for the layers z > 2/. a free walk of s segments is extended by one segment that segment contributes a weighting factor C z). 

When the system in which a curve model is created and any other systems with which that model is exchanged support a multiplicity factor, this can be set at a control vertex to a factor up to a limit defined by the degree of the curve. The shape of a segment of a rational B-spline curve can be controlled by increasing or decreasing the weight factor at the actual control vertex. When all control vertices have a weight factor of 1, the rational curve behaves as a non-rational one. 

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