Pentane-effect

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

The columns are indexed by the three states of bond i, the rows are indexed by the three states of bond i—1, and the order of indexing is t, g+, g. The statistical weight denoted by cr, which is approximately exp (-250/T), is the first-order weight of a gauche state relative to a trans state. The second-order interaction, which arises from the pentane effect where a bond pair is g gT, is weighted by to, which is approximately exp (-1000/T). 

Interdependent bond rotational potentials The origins of the interdependence of the bond rotational potentials in poly(methylene) can be understood in terms of the conformations of n-pentane (hence the phenomenon is termed the pentane effect). 

To estimate Lc more accurately Yamakawa and Shimada [52] computed (5 ) of polymethylene-like rotational isomeric state models with excluded volume by a Monte Carlo method. They considered that bead-bead interactions higher than ones leading to the pentane effect contribute to excluded-volume effects. They found that the simulated polymer in the unperturbed state can be modeled by a wormlike chain and that (5 )/(4 rtK) of perturbed chains begins to deviate from those of unperturbed ones at uk of 3—5. Thus, the Lc by Yamakawa and... 

State in the potential wells. Short range excluded volume resulting from rotational correlations between a4jacent bonds (pentane effect) is routindy incorporated into the calculations. Lower order moments of the end-to-end distance can be computed for this model but the complete distribution function necessary for determining (k) cannot be explicitly obtained. An expansion of o>(r) in terms of the moments of the distribution is possible, but unfortunately the convergence is very slow [16]. 

The first term for a — P < 5 is evaluated by direct enumeration of rotational isomeric states, thereby induding the pentane effect (longer range enumerations... 

It should be emphasized that Figure 10 was calculated for an idealized freely jointed chain melt in which the site diameter and bond length are the same. In order to make quantitative contact with experiments, it is necessary to more faithfully represent the monomer architecture through the intramolecular functions Cl y(k). A model that captures more of the local chemical structure of real polymer chains is the well-known rotational isomeric state model. In order to mimic a chain in a theta solvent or a melt, intramolecular repulsions are included between sites separated by less than or equal to four bonds (the pentane effect ). ... 

RIS parameters (Table 3.3) show that H-bonding, even in water, is sufficient to overcome some of the steric repulsions, including those associated with the 1,5 pentane effect, between syn-axial chain segments. 

In Sect. 2.1 we carried out a first estimate of the fraction of trans- and gauche-states in polyethylene. In this estimate, independence of the rotational isomeric states of different bonds was implicitly assumed. We now may check for the modification introduced by the pentane effect, as the Ising-model also provides us with equations for the fractions of the different pairs of conformational states. We rewrite the partition function... 

The pentane effect shows up quite clearly, as the fraction of pairs with sequences gauche -gauche and gauche -gauche is rather low. 

Here, tg is the energy difference between a trans and a gauche link and the number of gauche links in the spacer is g. The term g g=F g g=F is the additional energy resulting from the so-called pentane effect produced by a g g=F sequence in the spacer. Within the nematic phase the more anisotropic conformers are favored, as we have seen, and the conformational distribution becomes [66]... 

Application of this equation 5nelds Z = 1 - - 2a for ra-butane and Z = 1 -I- 4a -H 2a (l -H (o) for n-pentane, as expected. It correctly incorporates the first-order interaction and the pentane effect for longer chains. Interactions of higher order (depending on three or more successive bonds) are not included. This reliance on short-range (first- and second-order) interactions means that the expression cannot be expected to apply when longer range interactions play an important role, as they do imder circumstances where excluded volume is important. The... 

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