Polymer notations Volume

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... 

In order to introduce the notation and some of the necessary concepts, as well as to motivate the introduction of the functional integral techniques, first some exact results from the configurational statistics of individual polymer chains are introduced. Functional integral techniques are then applied to these simpler problems before discussing the more difficult problems of polymer excluded volume and the description of polymers in bulk. 

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... 

Universal SEC calibration reflects differences in the excluded volume of polymer molecules with identical molecular weight caused by varying coil conformation, coil geometry, and interactive propenies. Intrinsic viscosity, in the notation of Staudinger/ Mark/Houwink power law ([77]=fC.M ), summarizes these phenom-... 

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 ... 

For a given polymer-diluent combination the quantity / generally should be a function of both temperature and diluent concentration, and hence it is more appropriately denoted by the notation Fujita and Kishimoto (1961) have shown that if the increase in free volume by the addition of a diluent is proportional to the volume of added diluent (the proportionality factor, being in general a function of temperature, is denoted by y(T)), f(yltT) turns out to be a linear function of v1 given by the expression ... 

The specific heat capacity is the heat that must be added per kg of a substance to raise the temperature by one Kelvin or one degree Celsius. The molar heat capacity is the specific heat multiplied by the molar mass (the molar mass of a structural unit in the case of polymers). Specific and molar heat capacity may be defined at constant volume or at constant pressure. The heat added causes a change in the internal energy (It) and in the enthalpy (heat content, H) of the substance. The following notations can be formulated ... 

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. 

The microscopic mass balance of polymer functional groups and volatile components given in Eqs. (27) has to be modified in order to take into account the variable reaction volume due to polymer crystallization. Here we do not follow the notation in Ref. 74 rather, we use concentrations and rates of reaction per unit volume of amorphous phase instead of concentrations per unit volume of particle [A ]p = [A ]/(l — and so on, in order to use the same kinetic rate laws [Eqs. (49)] as in the melt. 

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