Polymer notations Volume fraction

This result should be compared with Eq. (8.28) for the case of the ideal mixture. It is reassuring to note that for n = 1, Eq. (8.36) reduces to Eq. (8.28). Next let us consider whether a change of notation will clarify Eq. (8.36) still more. Recognizing that the solvent, the repeat unit, and the lattice site all have the same volume, we see that Ni/N is the volume fraction occupied by the solvent in the mixture and nN2/N is the volume fraction of the polymer. Letting be the volume fraction of component i, we see that Eq. (8.36) becomes... 

We consider a polymer system consisting of n kinds of stiff polymers, and use the matrix notation approach introduced by Akcasu [13-15], Some of these components could be copolymers. Component I has a degree of polymerizations N, volume fraction 4>, monomer volume V, and segment size b. For stiff polymers, the averaged fluctuating density is defined as ... 

Notes The values of A, B, and C and thus of y are based on a reference volume Vre/ = 0.1 nm Polymer notation A d- label preceding the polymer acronym indicates a per-deuterated polymer partially deuterated polymers are labeled as dy, df, etc., for selective deuteration of 3, 4, etc., hydrogens. Numbers in subscripted parentheses after the polymer name indicate the primary comonomer fraction, e.g., SPB(6s) is a saturated polybutadiene with 66 mol% butadiene Polymer acronyms P2VP poly(2-vinyl pyridine), P4MS poly(4-methylstyrene), PBMA poly(n-butyl methacrylate), PCHA poly(cyclohexyl acrylate), PEB poly(ethyl butylene), PIB polyisobutylene, PI polyisoprene, PMMA poly(methyl methacrylate), PPMA poly(n-pentyl methacrylate), PP polypropylene, HHPP head-to-head polypropylene, PS polystyrene, PVME poly(vinyl methyl ether), PXE poly(2,6-dimethyl-l,4-phenylene oxide), SPB saturated polybutadiene, SPI saturated polyisoprene... 

While passing on to polynary systems, we have, to change our notation. If the. subscript 1 remains to denote I,MWf,. the polymer honiologms should be denoted by 2 etc. which is inconvenient. On the other hand, the components of binary systems are most naturally denoted by the subscripts 1 and 2. I o emphasize the difference between the binary and the polynary systems, it is reasonable to change the notation of volume fractions (i, and (p,. respectively). 

Notation cp = volume fraction, = correlation length, p= C./6, v= excluded volume parameter, 1 - 2x, N= number of bonds per chain, x= Flory-Huggins polymer-solvent interaction parameter, Vc = cross-over from swollen to ideal. Subscripts cr = critical, / = ideal, d = dilute, s = semi-dilute, m = marginal regime, c = concentrated regime, ov= cross-over from dilute to semi-dilute, cp = cross-over from concentrated to phase separated, sm = cross-over from semi-dilute to marginal, me = cross-over from marginal to concentrated. 

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