Molecular dimensions unperturbed

In earlier chapters an unperturbed coil referred to molecular dimensions as predicted by random flight statistics. We saw in the last chapter that this thermodynamic criterion is met under 0 conditions. 

The relation between [rf and molecular dimensions for branched polyethylenes has been investigated experimentally by several groups. The most extensive study is that of Hama and co-workers (42), who measured . by light-scattering in a-chloronaphthalene for fraction of two LDPE and two HDPE samples. They calculated the unperturbed values of [Pg.44]

If the interaction forces between polymer and solvent molecules can be neglected (the so-called -solution) the polymer molecule is in an unperturbed conformational state. In this situation, the molecular dimensions and the limiting viscosity number can be predicted rather accurately. For a normal dilute polymer solution, however, only approximate values of these quantities can be estimated. 

The hydrodynamic equivalent molecular dimensions can be related to the unperturbed dimensions by the introduction of a hydrodynamic expansion factor ah. Then Eq. (9.15) reads... 

Unperturbed molecular dimension, K, and conformational parameter, a, in different solvents -Sample Solvent JC x lO it... 

The modified titration curves of the fractionated (MA-St)n aqueous NaCl at various ionic strengths from 0.009 to 0.27 resembled the potentiometric behaviors of the maleic acid copolymer with n-butyl vinyl ether and poly(methacrylic acid) in aqueous salts. There was no precipitation or turbidity in the deionized polymer solution, except in aqueous NaCl of 0.27 M. The conformational transition from the compact to extended coil form was seen in diagp ams of the intrinsic viscosity vs. qp and the reduced viscosity in the range 0.1 < aj < 0.4 was independent of polymer concentration. Both the potentiometric and viscometric titration data showed that the pH-induced conformational transition of (MA-St)n in aqueous NaCl is due to intramolecular interaction. The unperturbed molecular dimensions were calculated from the viscosity data and the acid compact form of this copolymer was found to be not so compact as the conformations of globular proteins. Dilatometry did also indicate existence of the transition,and the transition was observed in aqueous solutions of various salts chlorides, bromides, perchlorates and thiocyanates of Na" ", K" ", Rb" ", Cs" " and... 

The morphology of methyl, ethyl, cetyl, decyl, and isobutyl copolymers hydrophilic-hydrophobic sequence has been studied and compared in THF and dimethylsulfoxide solvents, using viscosity and light-scattering techniques.The macromolecular chains have a segregated conformation, which allows the solvent to solvate compatible segments of the copolymer. The unperturbed molecular dimension of the isobutyl vinyl ether-MA copolymer are smaller than that for poly (isobutyl vinyl ether), as shown by the Stockmayer-Fixman equation. 

The first calculation on atomistic systems of chain molecules near solid surfaces was performed in Ref. 21 modeling the surfaces as two impenetrable walls placed at a distance much greater than the molecular dimensions. The overall chain density of the model has been chosen such that the local density far from the walls was equal to that of the bulk liquid at 300 K. Since all the properties of molecules far from the walls were found to match those of unperturbed chains, as described by the rotational isomeric state (RIS) model at this temperature, the chains in contact with the impenetrable walls can be considered to be in equilibrium with the unperturbed bulk liquid. 

Molecular Dimensions of Linear Poly(ethylene) (Unperturbed ... 

Kurata, M., Tsunashima, Y., Iwama, M., and Kamada, K., Viscosity-molecular weight relationships and unperturbed dimensions of linear chain molecules, in Polymer Handbook, 2nd ed., Brandrup, J. and Immergut, E. H., Eds, John Wiley Sons, New York, 1975, iv, 1-60. 

As explained earlier (Sect. 1.3.1), macromolecules in a low-molecular-weight solvent prefer a coiled chain conformation (random coil). Under special conditions (theta state) the macromolecule finds itself in a force-free state and its coil assumes the unpertubed dimensions. This is also exactly the case for polymers in an amorphous melt or in the glassy state their segments cannot decide whether neighboring chain segments (which replace all the solvent molecules in the bulk phase) belong to its own chain or to another macromolecule (having an identical constitution, of course). Therefore, here too, it assumes the unperturbed ) dimensions. 

This effect can be illustrated by Fig. 14.2. The effective range of local modification of the sample states is determined by the effective lateral dimension 4ff of the tip wavefunction, which also determines the lateral resolution. In analogy with the analytic result for the hydrogen molecular ion problem, the local modification makes the amplitude of the sample wavefunction increase by a factor exp( — Vi) 1.213, which is equivalent to inducing a localized state of radius r 4tf/2 superimposed on the unperturbed state of the solid surface. The local density of that state is about (4/e — 1) 0.47 times the local electron density of the original stale in the middle of the gap. This superimposed local state cannot be formed by Bloch states with the same energy eigenvalue. Because of dispersion (that is, the finite value of dEldk and... 

The mean-square dipole moments of POE and POMg are determined from dielectric constant measurements on dilute solutions in benzene. The values obtained are in good agreement with those predicted using the RIS models for these chains. In addition, the unperturbed dimensions of POMg are calculated as a function of molecular weight using the RIS theory. 

Molecular mechanics techniques are employed to calculate the molecular structure and conformational energies of model compounds for polyphenylmethylsllylene and polysilastyrene. In both isotactic and syndiotactic stereochemical forms. The structural and conformational energy data provided are used to calculate, by application of the RIS theory, the unperturbed chain dimensions, given as the characteristic ratio, and its temperature coefficient. 

The Flory-Williams RIS models describing the conformational characteristics of polyesters and polyamides are combined to calculate the dimensions of the alternating polyesteramide PEA. Excellent agreement is found with experimental values of the unperturbed dimensions. New determinations of molecular dipole moments are reported for dimethyl-frans-1,4-cyclohexanedicarboxylate and for trans-1,4-cyclohexanedlol diacetate. 

The reference state dimensions unperturbed dimensions, because of the unknown influence of the presence of crosslinks, possibly specific diluent effects, and perhaps at high swelling even an excluded volume effect. We have pointed out that (r2)0 may depend on the concentration of the diluent. Therefore the reference state is in general not a constant. We have also pointed out that, if (r2)0 contains a molecular expansion term due to an excluded volume effect, the use of the Flory-Huggins free enthalpy of dilution is no longer adequate. A difference between the % parameter in a network and the X parameter of the same polymer material but then in solution, may occur because the presence of crosslinks may modify %. 

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