The Chain Conformation

Polymer molecules mostly exist as random coils in solutions and melts. Their largest dimension is much smaller than the fully extended chains, but several times 

The factor a is 1 for the unperturbed coil defined in this way, and is larger (or smaller) when a polymer molecule is expanded (or compressed) due to polymer-solvent interactions. Thus, for an idealized freely jointed chain in theta solvent, we have = nl, and the corresponding mean square radius of gyration = nf-/G. When one accounts for the steric effects that prevent distant chain segments from overlapping (excluded volume effect), the dependence of (r ) is predicted to be (closer to experimental observation), rather than [Eq. (5)]. This polymer coil size is much larger than that based on polymer density, and hence markedly influences the viscosity behavior of polymers. 

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Equation (23) predicts a dependence of xR on M2. Experimentally, it was found that the relaxation time for flexible polymer chains in dilute solutions obeys a different scaling law, i.e. t M3/2. The Rouse model does not consider excluded volume effects or polymer-solvent interactions, it assumes a Gaussian behavior for the chain conformation even when distorted by the flow. Its domain of validity is therefore limited to modest deformations under 0-conditions. The weakest point, however, was neglecting hydrodynamic interaction which will now be discussed. 

Much fewer experiments are available in solution where the few reported data are generally more concerned about the effect of molecular structure than about bond dissociation energy. In simple shear, it is generally agreed that chain flexibility dominantly influences the rate of bond scission, with the most rigid polymers being the easiest to fracture [157]. The results are interpreted in terms of the presence of good and poor sequences in the chain conformation. 

Although significant insight into the process of bond rupture has been gathered from the studies on the scission kinetics, it remains desirable at this stage to carry out further experimentation at a molecular level to get information on the chain conformation at the moment of fracture. As a first step in this direction, birefringence measurements have been attempted recently in the single jet cell... 

In other cases, polymorphic forms are characterized by slightly different conformations. In other words, while the chain conformations packed in the different polymorphs are different, they correspond, however, to small variations in the sequences of the dihedral angles along the main chain. 

In other cases the conformational changes are small, but in the sense of lengthening of the unit height in the chain conformation. This has been for instance, recently observed for s-PB. The transition from form I (s(2/l)2 helices) toward form II (s(5/3)2 helices (see Sect. 2.2) occurs under tensile stress and involves only... 

Although the diffraction techniques are unique in providing detailed information on the structural organization at the molecular level in the different crystalline forms, there are other characterization techniques which are sensitive to the chain conformation and in some cases to the chain packing, which can be used advantageously (and in some case more efficiently than diffraction techniques) in the recognition and quantification of the different polymorphs in polymeric materials. 

It is also well known that different polymorphic forms can present largely different crystallite moduli along the chain axis (both observed and calculated). These differences can be large if large variations in the chain conformations are involved, and can have a significant influence on the bulk properties... 

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],... 

While thin polymer films may be very smooth and homogeneous, the chain conformation may be largely distorted due to the influence of the interfaces. Since the size of the polymer molecules is comparable to the film thickness those effects may play a significant role with ultra-thin polymer films. Several recent theoretical treatments are available [136-144,127,128] based on Monte Carlo [137-141,127, 128], molecular dynamics [142], variable density [143], cooperative motion [144], and bond fluctuation [136] model calculations. The distortion of the chain conformation near the interface, the segment orientation distribution, end distribution etc. are calculated as a function of film thickness and distance from the surface. In the limit of two-dimensional systems chains segregate and specific power laws are predicted [136, 137]. In 2D-blends of polymers a particular microdomain morphology may be expected [139]. Experiments on polymers in this area are presently, however, not available on a molecular level. Indications of order on an... 

If we are sufficiently below however, the situation will be markedly different. During the deformation the chain conformational motion will be partially suppressed by neighboring chains, and those motions necessary to relax the chain will be blocked. 

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]. 

Figure 4.5 Schematic drawing of the chain conformations in the buik(a) and uitra-thin fiim (b).To darify the contourofthe singie chain, one chain is indicated as the soiid curve. Reproduced with permission from The Society of Poiymer Science, Japan.

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. 

Some forms of rings and chains of vertex-sharing tetrahedra in silicates. How the chain conformations adapt to the size of the cation octahedra is shown for two chains (the octahedron chain is a section of a layer)... 

In contrast to normal diffusion, Ar2n does not grow linearly but with the square root of time. This may be considered the result of superimposing two random walks. The segment executes a random walk on the random walk given by the chain conformation. For the translational diffusion coefficient DR = kBT/ is obtained DR is inversely proportional to the number of friction-performing segments. 

This expression accounts for the configurational entropy of an ideal binary mixture with identical molecular sizes, but not for that of a polymer solution, since polymer chains are large and flexible. For that case, more contributions arise from the chain conformational entropy, first considered by Meyer [19] and then derived by Huggins [20] and Flory [21]. In analogy with a nonreversing random walk on a lattice, the conformational contribution of polymer chains to the partition function is given by... 

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... 

During crystallization, the molecules change their conformation from the random coil to chain folded. The chain conformation in the crystalline state has been the subject of great discussion, since it reflects the path that molecules have followed during crystallization. In the case of sufficiently long... 

The chain conformation, or extension, can be described well by the squared separation R2n between atoms n-bonds apart within the chain,... 

When the fold type nucleus is formed from the melt, the chain conformation within the melt should be a random coiled one. Therefore, the chain conformation within the melt of ECSCs should be a random coiled one. The crucial difference between the melts of ECSCs and FCCs at small At is only that of ve. 

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