Chain conformations in polymers

The alkane with additional two carbon atoms, -butane (CH3-CH2-CH2-CH3), has different stable conformational states, referred to as trans (T) and gauche (G and G ), as shown in Fig. 2.3. The 

The rotational isomeric state approximation, which is a convenient procedure for dealing with the conformational states of polymers, was introduced by Flory. Each molecule is treated as existing only in 

Let us now consider an alkane with n carbons. The question is how many different conformations this molecule can take. The molecule with n carbons has n — l(T main-chain bonds. The two end bonds do not contribute to different conformations, whereas each of the other carbon-carbon bonds is in one of the 

The first part of this chapter deals with the statistics of the Gaussian chain. Expressions for the characteristic dimension of the random chain (average end-to-end distance or radius of gyration) are derived as a function of molar mass, chain flexibility and temperature. 

The particularly simple relationships between the average end-to-end distance of the random coil and the chain length that are derived in section 2.4 are valid under the ideal solution conditions referred to as theta conditions. The dimension of the unperturbed polymer chain is only determined by the short-range effects and the chain behaves as a phantom chain that can intersect or cross itself freely. It is important to note that these conditions are also met in the pure polymer melt, as was first suggested by Flory (the so-called Flory theorem) and as was later experimentally confirmed by small-angle neutron scattering. 

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Single-Chain Conformation in Polymer Solutions The excess mixing enthalpy... 

The literature outlines the considerable efforts dedicated to the measurement of chain conformation in polymer nanocomposites, sometimes yielding contradicting results depending on the chemical system, size ratio between polymer and filler, and filler concentration (Jouault et al. 2010a, 2010b Crawford et al. 2013 Tung et al. 2013). 

Crawford M. K., Smalley R. J., Cohen G., et al. Chain conformation in polymer nanocomposites with uniformly dispersed nanoparticles. Phys. Rev. Lett. 110 no. 19 (2013) 196001-1-196001-5. 

Ozmusul M S, Picu C R, Sternstein S S and Kumar S K (2005) Lattice Monte Carlo simulations of chain conformations in polymer nanocomposites. Macromolecules 38 4495-4500. 

In usual rheological measurements, we apply a strain (or stress) to a material and measure the resulting stress (or strain). The applied strain may largely change the stmcture of the stress-sustaining units, for example, the polymer chain conformation in polymer solutions/melts, the spatial distribution of... 

Besides crystalline order and structure, the chain conformation and segment orientation of polymer molecules in the vicinity of the surface are also expected to be modified due to the specific interaction and boundary condition at the surface between polymers and air (Fig. 1 a). According to detailed computer simulations [127, 128], the chain conformation at the free polymer surface is disturbed over a distance corresponding approximately to the radius of gyration of one chain. The chain segments in the outermost layers are expected to be oriented parallel to the surface and chain ends will be enriched at the surface. Experiments on the chain conformation in this region are not available, but might be feasible with evanescent wave techniques described previously. Surface structure on a micrometer scale is observed with IR-ATR techniques [129],... 

Kraus, J., Muller-Buschbaum, P., Kuhlmann, T., Schubert, D. W. and Stamm, M. (2000) Confinement effects on the chain conformation in thin polymer films. Europhys. Lett., 49, 210-216. 

Jones, R. L Kumar, S. K., Ho, D. L., Briber, R. M. and Russell, T. P. (2001) Chain conformation in ultrathin polymer films using small-angle neutron scattering. Macromolecules, 34, 559-567. 

Before discussing details of their model and others, it is useful to review the two main techniques used to infer the characteristics of chain conformation in unordered polypeptides. One line of evidence came from hydrodynamic experiments—viscosity and sedimentation—from which a statistical end-to-end distance could be estimated and compared with values derived from calculations on polymer chain models (Flory, 1969). The second is based on spectroscopic experiments, in particular CD spectroscopy, from which information is obtained about the local chain conformation rather than global properties such as those derived from hydrodynamics. It is entirely possible for a polypeptide chain to adopt some particular local structure while retaining characteristics of random coils derived from hydrodynamic measurements this was pointed out by Krimm and Tiffany (1974). In support of their proposal, Tiffany and Krimm noted the following points ... 

In addition to quantitative crystallinity data, IR and Raman have been proven valuable tools to extract information on chain conformation in the three major phases [112-114], local order in amorphous polymers [115,116] high throughput characterization [117] and structural and polymorphic changes on heating and cooling semi-crystalline polymers [118-120]. 

The polymer we consider here is a semi-flexible chain which has some bending stiffness (Eq. 3). We first estimated the chain conformation in the melt. The calculated mean-square end-to-end distance R2n between atoms n-bond apart has shown that the chains have an ideal Gaussian conformation R2 is a linear function of n (see Fig. 35 given later). The value of R2 for n = 100... 

The conformation of the chains of isotactic polymers in the crystalline state is generally helical and corresponds to a succession of nearly trans and gauche torsion angles, the exact values depending on the bulkiness of the side groups. Molecular mechanics calculations have been extensively used for the prediction of the chain conformation of polymers in the crystal.29... 

Boulanger, P., Pireaux, J. J., Verbist, J. J. and Delhalle, J., XPS study of polymer chain conformation in amorphous and crystalline poly(ethylene terephthalate) samples, J. Electron Spectrosc. Rel. Phenom., 63, 53-73 (1993). 

Bueche,F., Kinzig,B.J., Coven,GJ. Polymer Chain Conformations in Bulk Polymers. Polymer Letters 3,399-402 (1965). 

After the Natta s discovery of highly stereospecific polymerization processes, the interest in the preparation and properties of optically active polymers has greatly increased. In fact, the use of asymmetric catalysts or monomers to obtain optically active polymers may supply interesting informations on the mechanism of steric control in stereo-specific polymerization furthermore optical activity is an useful tool to study the polymer stereoregularity and the chain conformations of polymers in the molten state or in solution. 

As pointed out above with relation to the data at 87 °C, the Tic of the crystalline-amorphous interphase is appreciably longer than that of the amorphous phase, suggesting the retention of the helical molecular chain conformation in the interphase. We also note that a Tic of 65-70 s for the crystalline phase is significantly shorter than that for other crystalline polymers such as polyethylene and poly-(tetramethylene oxide), whose crystalline structure is comprised of planar zig-zag molecular-chain sequences. In the crystalline region composed of helical molecular chains, there may be a minor molecular motion in the TiC frame, with no influence on the crystalline molecular alignment that is detected by X-ray diffraction analyses. Such a relatively short TiC of the crystalline phase may be a character of the crystalline structure that is formed by helical molecular chain sequences. 

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