Random Coil

4 Key excerpts on "Random Coil"

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  The Physics of Amorphous Solids

  • Richard Zallen(Author)
  • 2008(Publication Date)
  • Wiley-VCH

    (Publisher)

  Perhaps the chief motive for the appearance of rivals of the Random Coil model is a perceptual one, namely the human difficulty in visualizing a three-dirnen- sional intermeshed-coil arrangement (like that of Fig. 3.12, but with fmite- thickness fleshed-out chains) that succeeds in densely filling space. But it turns out that this packing problem presents no real difficulty in three (or more) dimensions, because of the protean diversity of polymer form. The situation is portrayed by Flory (1975), in characteristic insightful fashion: Whereas dense packing of polymer chains may appear to be a distressing task, a thorough examination of the problem leads to the firm conclusion that macro- molecular chains whose structures offer sufficient flexibility are capable of meet- ing the challenge without departure or deviation from their intrinsic proclivities. In brief, the number of configurations that the chains may assume is sufficiently great to guarantee numerous combinations of arrangements in which the condi- tion of mutual exclusion of space is met throughout the system as a whole. More- over, the task of packing chain molecules is not made easier by partial ordering of 122 CHALCOGENIDE GLASSES AND ORGANIC POLYMERS Figure 3.16 A two-dimensional square-lattice self-avoiding walk of about 250 steps. The circles mark three places where the walk is deflected when it encounters itself. the chains or by segregating them. Any state of organization short of complete abandonment of disorder in favor of creation of a crystalline phase offers no ad- vantage, in a statistical-thermodynamic sense. The last two sentences of the quoted paragraph have a wider generality than amorphous polymers; they correctly imply the inappropriateness of heteroge- neous (e.g., microcrystalline) models for amorphous solids. The proper mod- els for the structure of amorphous solids are the homogeneous ones: random close packing, continuous random network, and the Random Coil model.

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  Mass Spectrometry in Structural Biology and Biophysics

  Architecture, Dynamics, and Interaction of Biomolecules

  • Igor A. Kaltashov, Stephen J. Eyles, Dominic M. Desiderio, Nico M. Nibbering, Dominic M. Desiderio, Nico M. Nibbering(Authors)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  According to this view, a protein conformation is a continuous subset of the conformational space (i.e., a continuum of well-defined configurations) that is accessible to a protein confined to a certain local minimum. The utility of this definition becomes obvious when we consider non-native protein conformations, although unfortunately it is not without its own problems. 2 1.3.4 What Are Non-Native Protein Conformations? Random Coils, Molten Globules, and Folding Intermediates In the case of unfolded proteins, which are assumed to be completely nonrigid polypeptide chains, the Random Coil (55), we must consider the ensemble of molecules displaying an impressive variety of configurations (Fig. 1.6). In a truly Random Coil, as might be the case for a synthetic polymer with identical monomer units in a good solvent, there may well be no conformational preferences for the chain. However, proteins are decorated with side chains of a different chemical nature along their length, such that in water or even in a chemical denaturant one might expect there to be local preferences due to hydrophilic or hydrophobic interactions, and indeed steric effects. Thus for a number of proteins studied in solution, some persistent local and nonlocal conformational effects have been detected, indicating that an unfolded protein generally is not in fact a truly Random Coil. On the other hand, the enthalpy of these interactions is very small in comparison to the entropy of the flexible chain so the overall free energy of each of these conformers will be very similar. On a free energy surface, these would be represented as shallow wells in the generally flat surface of unfolded state free energy. Figure 1.6 Representative configurations of a Random Coil (a freely joined chain of 100 hard spheres) and the distribution of its radius of gyration R g. The R g values of a model protein phosphoglycerate kinase are indicated for comparison

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  Physical Chemistry of Polymers

  A Conceptual Introduction

  • Sebastian Seiffert(Author)
  • 2020(Publication Date)
  • De Gruyter

    (Publisher)

  2.1 Coil conformation 2.1.1 Micro-and macroconformations of a polymer chain Let us begin by considering how a polymer chain might look like. The shape of a polymer is determined by three factors, as illustrated in Figure 13(A). The first factor is the monomer segmental length, that is, the length of the elementary structural unit plus the bond that connects it to the next. In many simple vinyl polymers, such as polyethylene (PE), polypropylene (PP), polyvinylchloride, or polystyrene (PS), this is a covalent carbon – carbon bond with a length of 1.54 Å. The second fac-tor is the monomer bonding angle, φ . It has a value of 109.6° for an sp 3 -hybridized carbon – carbon bond. Both of these parameters are determined by the specific chemistry of the monomer, which means that they are fixed for a given polymer. The third factor is the monomer bond torsion angle, θ . This factor is not fixed, be-cause the bonds can rotate quite easily. As a consequence, the macroconformation of a chain will result from the sequence of its monomer bond torsional microconfor-mations. A polymer chain may therefore adopt many different shapes, two of which are depicted in Figure 13(B) and (C). In Figure 13(B), you see a structure in which all the bonds are trans -conformed. This all-trans conformation leads to an ordered, rod-like macroconformation. Entropy, however, does not favor such ordered states. More favorable, by contrast, is the structure depicted in Figure 13(C). Here, the mi-croconformation is a random cis – trans mix that leads to a macroconformation of a Random Coil, which does not show a high degree of order.

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  Fundamentals of Polymer Science

  An Introductory Text, Second Edition

  • Michael M. Coleman, Paul C. Painter(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  Nuovo Cimento. Suppl. to Vol. 15. 1. 40 (1960).

  D.  RANDOM WALKS, RANDOM FLIGHTS AND DISORDERED POLYMER CHAINS

  In the preceding section we have seen that we can construct an ordered conformation for a polymer chain by allowing the bonds to sit in their minimum energy positions. We will defer a discussion of the extent to which such ordered arrangements are found until we consider polymer crystals, but clearly we can proceed in a logical fashion from describing ordered conformations, to describing the packing of such chains in crystals, to the overall shape and appearance of these crystals (which we will call morphology) and ultimately to attempts to relate these various facets of structure to properties.

  To accomplish the same thing for polymers that for whatever reason have a disordered or random chain conformation might at first sight seem a much more formidable and perhaps even impossible task, because of the enormous range of conformations or configurations available to such a chain. Even if each bond were to be restricted to three possible positions (say trans and the two gauche positions), and if for simplicity we assume that each of these is of equal energy, there would be 310,000 conformations (equal to 104,771 ) available to a chain consisting of 10,000 bonds!* It is this huge number of possibilities that saves us, however, because it allows a statistical approach, which results in extraordinary insight into the nature of these materials and their properties, because such properties must ultimately depend upon an average of contributions from all the different chains, together with effects due to their interactions.

  In his classic book on rubber elasticity, Treloar** presented a picture of the general form of a disordered or Random Coil or, if we state it even more precisely, a statistical conformation of a polymer chain, which is reproduced in figure 7.11 . It was obtained by using polyethylene as a model polymer and allowing the valency angles to have their normal values. The C-C-C bond angle is thus fixed at a value close to 109°, but rotations around

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