The conformational states of polymers

Nevertheless, some progress has been made. This section shows how useful conformational calculations have been performed even without the aid of computers, especially on polymers with obvious steric constraints. The next section describes how proton and carbon NMR provide substantial experimental checks on such calculations. 

Rotational isomeric state (RIS) theory, developed by Flory [19], makes the approximation of describing each of these minima as a single conformational state of the molecule. It is a very general theory, able to cope with any proposed potential and any number of minima, and to translate these into bulk data such as radius of gyration. 

For larger molecules, the theory retains the central notion of each bond having a finite and usually small number of isomeric states, but adds factors to account for steric and related longer-range interactions. 

The probabilities of occurrence of each of the above states are now expressed as two by two matrices C/ and (7, (where g = gauche, t = trans) 

Here the probabilities in each matrix are normalised to make the highest probability unity in each. In the more general theory, the factor x is re-expressed in terms of the rotational constraints on individual bonds, and one typically needs five such variables for an acceptable description of an un-symmetrical vinyl polymer in which each bond has three rotational states. In the above case it may simply be defined as the relative probability of the gg state in the racemic dyad. 

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The synthesis of optically active polymers was tackled with the purpose not only of clarifying the mechanism of polymerization and the conformational state of polymers in solution, but also to explore the potential of these products in many fields as chiral catalysts, as stationary phases for chromatographic resolution of optical antipodes, for the preparation of liquid crystals, and so on. 

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... 

As revealed by IR-spectroscopy, the attachment of the polymer proceeds via acylation of aminopropyls absorbances of both amides (1650 cm-1) and esters (1740 cm-1) contribute to the spectrum of polyacrylate-coated aminopropyl-Aerosil (specific surface area 175 m2/g) [55], During the reaction, the accumulation of p-nitrophenyl ester groups in the support is accompanied by the liberation of p-nitrophenol into the contacting solution. Thus, the evaluation of the conformational state of adsorbing macromolecules can be performed by the simultaneous study of both processes by UV-spectroscopy as shown in Fig. 7. Apparently, at... 

The chemical structure of any heteropolymer macromolecule is defined by its configuration o / where ol = 1,2 denotes the type of monomeric unit. A special feature of this structure in the system in hand is that its formation is largely conditioned by the conformational state of macromolecules involved. Hence, under the statistical consideration of these macromolecules it was suggested [22] to differentiate polymer chains apart from configuration oq also... 

The problem is further complicated for vinyl polymers with their problems of stereoisomerism. The first descriptions of the conformational state of isotactic polypropylene in solution go back 25 years (178, 179, 192, 193). Corradini, Allegra, and Ganis proposed a model, still essentially valid today, according to which macromolecules possess a local helical structure analogous to that observed in the crystalline state. The helix segments are rather short, only a few monomer units, after which an inversion of the helix sense occurs, with simultaneous alteration of its direction (Figure 15). As a whole this disordered con-... 

In an effort to correlate the conformational features of polysilane derivatives with their properties, calculations are performed to determine the relative stabilities of the conformational states of the meso and racemic diads of polysilapropylene. Energy maps are constructed in terms of internal rotation angles to calculate the average properties of the chain. The calculations show that the difference In energy between the various states of the meso and racemic dlad Is small. Hence, PSP can be considered to be more flexible than the analogous carbon polymer, PP. The characteristic ratios of the unperturbed end-to-end distances for the /so- and syndiotaclic PSP are less than those for the PP of corresponding tacticity. 

As RNA molecules are highly negatively charged due to their sugar-phosphate backbone, the conformational state of these molecules is strongly dependent on the concentration of positively charged counterions. In the absence of Mg2+ or other polyvalent counterions, and in low monovalent salt concentrations, RNA becomes denatured as a result of ineffective Debye screening of the repulsive forces between different parts of the polymer. 

The effect of the side chain structure on the solution behavior as well as in the solid state of vinyl polymers has been studied in the past for a number of poly(methacrylate)s [72,73,76], The conformational study of polymers containing... 

The transition of the polymer from the rubbery to the glassy state principally changes the deformation behaviour and mechanical response of the material. The dominant role of intermolecular forces in the glassy state of polymer fully suppresses the effect of the conformational elasticity of network chains, at least at low strains. 

The properties of very dilute polymer solutions are determined by the conformational states of the separate polymer molecules. 

Intramolecular excimer emission, the polarization of fluorescence, nonradiative energy transfer and the use of medium-sensitive fluoropliores has been used to study the conformational mobility of polymers in dilute solution, the interpenetration of drain molecules, the association of polymers with each other or with small species and the cooperative transition of certain poly-carboxylic acids from a compact to an expanded state. 

The best-known physically robust method for calculating the conformational properties of polymer chains is Rory s rotational isomeric state (RIS) theory. RIS has been applied to many polymers over several decades. See Honeycutt [12] for a concise recent review. However, there are technical difficulties preventing the routine and easy application of RIS in a reliable manner to polymers with complex repeat unit structures, and especially to polymers containing rings along the chain backbone. As techniques for the atomistic simulation of polymers have evolved, the calculation of conformational properties by atomistic simulations has become an attractive and increasingly feasible alternative. The RIS Metropolis Monte Carlo method of Honeycutt [13] (see Bicerano et al [14,15] for some applications) enables the direct estimation of Coo, lp and Rg via atomistic simulations. It also calculates a value for [r ] indirectly, as a "derived" property, in terms of the properties which it estimates directly. These calculated values are useful as semi-quantitative predictors of the actual [rj] of a polymer, subject to the limitation that they only take the effects of intrinsic chain stiffness into account but neglect the possible (and often relatively secondary) effects of the polymer-solvent interactions. 

Section 2.2.1.1 highlighted how the vibrational fine structure of pyrene, when dispersed under relatively dilute conditions, in the absence of excimer formation, can be used to reveal the pH-dependent response of PMAA. An alternative approach has used the occurrence of intermolecular excimer formation between dispersed pyrenyl probes under relatively concentrated conditions to monitor the conformational switch of the polymer [6,71]. When dispersed in PMAA, at concentrations higher than its solubility limit in water, partitioning of the probe between the hydrophobic polymer coil and the aqueous phase results [6,71]. Dependent on the pH of the solution and consequently the conformational state of the polyelectrolyte, the balance between these two distinct populations can be affected. For example, Fig. 2.7 shows the fluorescence emission spectra for the probe l,3-bis(l-pyrenyl)propane (1,3PP) when dispersed in aqueous solutions of PMAA [71]. At low pH, an emission spectrum consistent with that of monomeric unassociated pyrene is observed centered around... 

Our aim was to investigate the binding of counterions in dilute salt-free solutions of pectins with different levels and patterns of esterification. We used methods such as potentiometry and circuleu dichroism in order to obtain both general and local informations on the conformational states of the polymer depending on its ionic form. 

Molecules in the dissolved, molten, amorphous, and glassy states of macromolecules exist as random coils. This is a result of the relative freedom of rotation associated with the chain bonds of most polymers and the myriad number of conformations that a polymer molecule can adopt. As a consequence of the random coil conformation, the volume of a polymer molecule in solution is many times that of its segments alone. The size of the dissolved polymer molecule depends quite strongly on the d ee of polymer-solvent contact. In a thermodynamically good solvent, a high degree of interaction exists between the polymer molecule and the solvent. Consequently, the molecular coils are relatively extended. On the other hand, in a poor solvent the coils are more contracted. Many properties of macromolecules are dictated by the random coil nature of the molecules. We now discuss briefly the conformational properties of polymer chains. 

Study of the conformation of a statistical fractal in a system occurring below the critical point and in the isolated state at W2<0 showed that the fractal is very compact and has a globular conformation in both cases. This state of a fractal was called collapsed, by analogy with the collapsed state of polymers. 

Some miscible polymer blends show evidence of interactions between the two polymers by more subtle changes in the spectra. Such changes are also often seen in the spectra of H-bonded blends and they are due to changes in the conformational states of the polymers due to the interactions between them. 

The static flexibility of a semi-flexible polymer chain is related not only to the potential energy difference Ae, but also to the temperature T. The following quantities are often used to characterize the conformational states of semi-flexible polymer chains. 

Viscoelastic flow behaviour of dilute polymer solutions in porous media is described as a method for characterization of polymer-solvent-temperature systems. Porous media flow tests provide information on the solution state of polymer solutions and the molecular weight of the polymers used. Furthermore, flow-induced and thermally induced degradation effects - frequently observed in polymer solutions - can be characterized by the measurement of viscoelastic effects in flow through porous media. Decrease of molecular weight and changes of the conformation of macromolecules in solution are important parameters in these processes. 

In connection with studies concerning the conformational state of hydrophobic polyelectrolytes, the mode of interaction of dyes (and related compounds) with such polymers has been investigated. This matter appears to be quite complex but some aspects are to be pointed out. First, the extent of dye binding is generally related to the actual conformation of polymers chains as compared to more extended conformational states, tightly coiled polyanions can bind much more dye.15-19 This is not only observed for charged dyea-polyelectrolytes... 

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