Unperturbed chain

The conformation of polymer chains in an ultra-thin film has been an attractive subject in the field of polymer physics. The chain conformation has been extensively discussed theoretically and experimentally [6-11] however, the experimental technique to study an ultra-thin film is limited because it is difficult to obtain a signal from a specimen due to the low sample volume. The conformation of polymer chains in an ultra-thin film has been examined by small angle neutron scattering (SANS), and contradictory results have been reported. With decreasing film thickness, the radius of gyration, Rg, parallel to the film plane increases when the thickness is less than the unperturbed chain dimension in the bulk state [12-14]. On the other hand, Jones et al. reported that a polystyrene chain in an ultra-thin film takes a Gaussian conformation with a similar in-plane Rg to that in the bulk state [15, 16]. 

In the RIS model for PE described by Abe et al. [143], the conformational partition function, Z, of the unperturbed chain with n bonds is formulated using a well-known statistical weight matrix for bond i, Uj, that is usually written in a 3 x 3 form. 

The probability for a conformation of an unperturbed chain of n C-C bonds on the underlying diamond lattice can be expressed in terms of the probability for state r) at the second bond and the conditional probability for state 7] at bond i (2 < i < n), given state at the preceding bond. These probabilities, which are usually denoted by p,/ 2 and q , respectively, are extracted from 2 of Eq. (4.1) using the conventional partial derivatives [35,36]. Then the probability, p, for a specified conformation of the entire chain is ... 

P2 mean square contraction of an otherwise unperturbed chain with bundles... 

Z° >, which signifies of the mean end-to-end distance of the unperturbed chain, equals Nb /3. 

Up to this point we have considered only unperturbed chain statistics. However, even under -conditions when A2=0 unperturbed statistics cannot be... 

In some specific cases, dissolved macromolecules take up the shape predicted by the above theories of isolated chain molecules. In general, however, the interaction between solvent molecules and macromolecules has significant effects on the chain dimensions. In poor solvents, the interactions between polymer segments and solvent molecules are not that much different from those between different chain segments. Hence, the coil dimensions tend towards those of an unperturbed chain if the dimension of the unperturbed coil is identical to that in solution, the solution conditions are called conditions (ff solvent, temper-... 

Various properties of hydrocarbon chains are calculated with the use of three different variants of the RIS model lattice chains, unperturbed chains, and off-lattice chains with excluded volume. The properties examined are , , and . It is found that lower and inverse moments of rare more sensitive to excluded volume effects than . 

The generator matrix treatment of simple chains with excluded volume described earlier S 010) properly reproduces the known chain length dependence of the mean-square dimensions in the limit of infinite chains. The purpose of this paper is to compare the behaviour of finite generator matrix chains with that of Monte-Carlo chains in which atoms participating in long-range interactions behave as hard spheres. The model for the unperturbed chain is that developed by Flory et at. for PE (S 027). 

Angular scattering functions, PIijI, are computed for subchains located in the middle and at the end of a PE chain. The RIS model developed by Flory et at, (S 004 - S 006) is used for the unperturbed chain. Chain expansion is introduced using a matrix treatment which satisfactorily reproduces several configuration-dependent properties of macromolecules perturbed by long-range interactions. 

Conformational characteristics of PTFE chains are studied in detail, based upon ab initio electronic structure calculations on perfluorobutane, perfluoropentane, and perfluorohexane. The found conformational characteristics are fully represented by a six-state RIS model. This six-state model, with no adjustment of the geometric or energy parameters as determined from the ab initio calculations, predicts the unperturbed chain dimensions, and the fraction of gauche bonds as a function of temperature, in good agreement with available experimental values. 

The influence of the chain expansion produced by excluded volume on the mean-square optical anisotropy is studied in six types of polymers (PE, PVC, PVB, PS, polylp-chlorostyrene), polylp-bromostyrenel. RIS models are used for the configuration statistics of the unperturbed chains. The mean-square optical anisotropy of PE is found to be insensitive to excluded volume. The mean-square optical anisotropy of the five other polymers, on the other hand, is sensitive to the imposition of the excluded volume if the stereochemical composition is exclusively racemic. Much smaller effects are seen in meso chains and in chains with Bernoullian statistics and an equal probability for meso and racemic diads. 

The unperturbed chain dimensions of near-monodisperse atactic PS are evaluated from intrinsic viscosity measurements. Negative values for the temperature coefficient of chain dimensions are found. Under conditions where specific solvent effects are eliminated or minimized, measurements yield results in excellent agreement with the theoretical predictions for atactic PS. 

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. 

Ab initio calculations with full geometry optimization on diphenyl carbonate and diphenylpropane are carried out to determine the bond geometries and the conformational energies and then to compute the unperturbed chsin dimensions of the bisphenol A polycarbonate. Application of these results to the RIS model of the PC chain leads to the prediction of the unperturbed chain dimension. 

Conformational Energy and Unperturbed Chain Dimensions of Polypeptide Homopolymers ... 

Rlo mean-square gyration radius of unperturbed chain... 

The two dimensionless parameters a and p appear to be especially helpful. a is the ratio of the radius of gyration of any intermediate along the approach to the phase boundary and the radius of gyration of the unperturbed chains, i.e., the 0-state (see Eq. (4). The latter were determined experimentally in 1.5 M NaCl. The second parameter is the shape sensitive ratio p of the radius of gyration and the hydrodynamic radius (see Eq. (17). 

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