Motion of Monomers

1 General Formula In the preceding subsections, we considered the center-of-mass motion and also obtained a general formula for the statistical average of the Fourier transform of = r (t) r (0). In this subsection, we look at 

In the long time scale, the first term dominates, and becomes 

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Kinetic gelation simulations seek to follow the reaction kinetics of monomers and growing chains in space and time using lattice models [43]. In one example, Bowen and Peppas [155] considered homopolymerization of tetrafunctional monomers, decay of initiator molecules, and motion of monomers in the lattice network. Extensive kinetic simulations such as this can provide information on how the structure of the gel and the conversion of monomer change during the course of gelation. Application of this type of model to polyacrylamide gels and comparison to experimental data has not been reported. 

Whereas the motion of the particle obeys Eq. (8.1) at all times, we shall see that the motion of monomers in a polymer is not always described by Eq. (8.1) [or Eq. (8.2)]. When the motion of a molecule obeys Eq. (8.1), it is called a simple diffusive motion. The random motion of small particles in a liquid was observed long ago using a microscope by a biologist named Brown and is often referred to as Brownian motion. 

Such a smaller scaling exponent (1/2) compared with the simple fluids (1) can be attributed to the fact that the motions of monomers are slowed down due to their chain connection. Below or above this time window, the monomers or the whole chain exhibit the characteristics of simple fluids, following the scaling law... 

The Brownian motion of a polymer chain for self-diffusion is carried out by the integration of Brownian motions of monomers. Therefore, the entropic elasticity of chain conformation in a random coil allows a large-scale deformation, with its extent subject to the external stress for polymer deformatiOTi and flow, and hence exposes the characteristic feature of a mbber state in a temperature window between the glass state and the fluid state. 

Again, we impose that f be independent of N when p/p 1. The condition is given as V + m(3v - 1) = 0, i.e., u = -v/(3v - 1) or = -3/4. Thus, we find the correlation length decreases with an increasing concentration in a power law with an exponent of -3/4. The dependence is exactly the same as the one given by Eq. 4.6 for the blob size. Thus, the blob is essentially a sphere with a diameter equal to the correlation length. It indicates that the monomers within a blob move cooperatively and motions of monomers in different blobs are not correlated with each other. 

Tube and Primitive Chain In the preceding subsection, we paid attention to the short-time motion of monomers within a blob. The motion does not involve translation of the polymer chain as a whole. Here we look at the overall motion of the chain over a distance longer than the blob size. 

R.P. Wool (University of Illinois) Yes. The anisotropic motion of monomers in a melt permits the chain to relax its configuration first at... 

The simulations also revealed that flapping motions of one of the loops of the avidin monomer play a crucial role in the mechanism of the unbinding of biotin. The fluctuation time for this loop as well as the relaxation time for many of the processes in proteins can be on the order of microseconds and longer (Eaton et al., 1997). The loop has enough time to fluctuate into an open state on experimental time scales (1 ms), but the fluctuation time is too long for this event to take place on the nanosecond time scale of simulations. To facilitate the exit of biotin from its binding pocket, the conformation of this loop was altered (Izrailev et al., 1997) using the interactive molecular dynamics features of MDScope (Nelson et al., 1995 Nelson et al., 1996 Humphrey et al., 1996). 

HDH/DHD interface. If the motion of the polymer was the same for each portion of the molecule, i.e., isotropic, the concentration of deuterium across the interface would remain constant. However, if the monomer motion is anisotropic, such as with reptation, where the chain ends lead the centers, a high amplitude ripple in the concentration profile, as described below will be displayed. For a reptating chain, lateral motion of the central segment of the chain is permitted up to depths approximating the tube diameter, after which the central segments must follow the chain ends in a snake-like fashion. 

The structure of these globular aggregates is characterized by a micellar core formed by the hydrophilic heads of the surfactant molecules and a surrounding hydrophobic layer constituted by their opportunely arranged alkyl chains whereas their dynamics are characterized by conformational motions of heads and alkyl chains, frequent exchange of surfactant monomers between bulk solvent and micelle, and structural collapse of the aggregate leading to its dissolution, and vice versa [2-7]. 

The formation of a polymer from monomers is not entropically favorable. This is because we convert many monomer molecules into a few polymer molecules. This greatly reduces the disorder and motion of the system. The ordering effect observed in polymerization is mitigated somewhat in condensation polymerization processes, by the evolution of low molecular weight species, which contribute to the entropy of the system. 

In fact, the diffusion constant in solutions has the form of an Einstein diffusion of hard spheres with radius Re. For a diffusing chain the solvent within the coil is apparently also set in motion and does not contribute to the friction. Thus, the long-range hydrodynamic interactions lead, in comparison to the Rouse model, to qualitatively different results for both the center-of-mass diffusion—which is not proportional to the number of monomers exerting friction - as well as for the segment diffusion - which is considerably accelerated and follows a modified time law t2/3 instead of t1/2. 

The 140-residue protein AS is able to form amyloid fibrils and as such is the main component of protein inclusions involved in Parkinson s disease. Full-length 13C/15N-labelled AS fibrils and AS reverse-labelled for two of the most abundant amino acids, K and V, were examined by homonuclear and heteronuclear 2D and 3D NMR.147 Two different types of fibrils display chemical shift differences of up to 13 ppm in the l5N dimension and up to 5 ppm for the backbone and side-chain 13C chemical shifts. Selection of regions with different mobility indicates the existence of monomers in the sample and allows the identification of mobile segments of the protein within the fibril in the presence of monomeric protein. At least 35 C-terminal residues are mobile and lack a defined secondary structure, whereas the N terminus is rigid starting from residue 22. In addition, temperature-dependent sensitivity enhancement is also noted for the AS fibrils due to both the CP efficiency and motional interference with proton decoupling.148... 

The 13C NMR sensitivity can sometimes be a problem, but for the kind of samples studied here the effective concentration of monomer units is several molar which does not place excessive demands on present Fourier transform NMR spectrometers. In addition to the sensitivity of the chemical shift to structure (9), the relaxation of protonated carbons is dominated by dipole-dipole interaction with the attached proton (9). The dependence of the relaxation parameters T, or spin-lattice, and Tor spin-spin, on isotropic motional correlation time for a C-H unit is shown schematically in Figure 1. The T1 can be determined by standard pulse techniques (9), while the linewidth at half-height is often related to the T2. Another parameter which is related to the correlation time is the nuclear Overhauser enhancement factor, q. The value of this factor for 13C coupled to protons, varies from about 2 at short correlation times to 0.1 at long correlation... 

Intermediates corresponding to the coordination step are considered as sufficiently close to transition states of the insertion reaction, and hence as suitable preinsertion intermediates, only if the insertion can occur through a motion of the nuclei that is near to the least—principle of least nuclear motion.13,30,31 For instance, for alkene polymerizations preinsertion intermediates correspond to geometries with (a) a double bond of the olefin nearly parallel to the metal growing chain bond and (b) the first C-C bond of the chain nearly perpendicular to the plane defined by the double bond of the monomer and by the metal atom (50° < Gi < 130°, rather than 0i 180° see below). 

The association forces between juxtaposed surfactant monomers is physical, not chemical, so the motion of the hydrocarbon tails within a micelle is similar to the local motion in a sample of pure hydrocarbon. 

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