Effective chain length

The double bond functions in a very analogous manner. It too interrupts effective chain length and determines the principal point of oxidative attack. In a manner quite analogous to the methyl group, through changes in the combustion velocity, the double bond also alters the octane number and critical compression ratio. 

Theory. Molecules are assumed to "sit" on a lattice of coordination number z and of cell size vjj. Each molecule (species 1) is assumed to occupy r sites (where r can be fractional), and the lattice has empty sites called holes. There are Nq holes and molecules. To account for the connectivity of the segments of a molecule, an effective chain length is defined as,... 

Peralkylated (I and II) derivatives have been synthesized that act as bridging ligands in analogous dicationic dinuclear complexes (Fig. 4) The effective chain lengths (population of rotamers) and flexibility (rotational barriers, nature of thiourea bridging unit) in these species depend on the degree of alkylation and the nature of the substituents on nitrogen. Reactions... 

The predicted values for substituted acetic (RCH2CO2H, z = 2) and formic acids (RCO2H, z= 1) are 0.8 and 1.6 respectively, agreeing with the observed values of 0.67 and 1.62. The intervention of a double or triple bond decreases the effective chain length, increasing p, and a double bond can be regarded effectively as having an z value of 1. An equation similar to Equation (4) can be advanced for a, values. 

Cevec, G. 1991. How membrane chain-melting phase-transition temperature is affected by the lipid chain asymmetry and degree of unsaturation an effective chain length model. Biochemistry, 30, 7186. 

In our computer studies of the conformational behavior of the shell-forming chains, we used MC simulations [91, 95] on a simple cubic lattice and studied the shell behavior of a single micelle only. Because we modeled the behavior of shells of kinetically frozen micelles, we simulated a spherical polymer brush tethered to the surface of a hydrophobic spherical core. The association number was taken from the experiment. The size of the core, lattice constant (i.e., the size of the lattice Kuhn segment ) and the effective chain length were recalculated from experimental values on the basis of the coarse graining parameterization [95]. 

Since hydrocarbon chains in the Uquid state are never fully extended, an effective chain length, /etf, can be defined that gives the statistically most likely extension as calculated by the same procedure used for the calculation of polymer chain dimensions. For a chain with n c = 11, the ratio of /max to /ett will be approximately 0.75. In the micellar core, because of restrictions imposed by the attachment of the hydrocarbon tail to the head group bound at the surface, the mobility of the chains may be significantly limited relative to that of bulk hydrocarbon chains. The presence of kinks or gauche chain conformations, which may be imposed by packing considerations, will result in a calculated Imax amounting to only about 80% of the theoretical maximum. 

Fig. 1. Adhesive Bonding Capabilities of Radiation Curable Coating Systems Containing Polymer Additives as a Function of Effective Chain Length and Specific Placement of Unsaturation Sites...

EFFECTIVE CHAIN LENGTH PER MOLECULAR WEIGHT FOR ACHIEVING ADHESIVE BONDING... 

The critical packing parameter, CPP, is described by eq 2, where v is the average volume of the amphiphile, a is the effective head group area, and / is the effective chain length of the surfactant in the molten state. The CPP can be used to predict the aggregate structures and to correlate stmctural clmges of the surfactant (or PIL) with changes to the self-assembly phases. 

Fig. 3.1 Log-log plot of the time dependence of the mean square displacement of the single monomer in an MD simulation of a polymer chain in good solvent. Only the four inner monomers are taken into account in order to suppress end effects. Chain-lengths are Nch = 30 (points), 40 (triangles) and 60 (diamonds) (from Ref. 61).

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