Short-range intramolecular interaction

As the temperature is decreased, the chains become increasingly rigid zc then approaches 1 if we assume that there is only one fully ordered crystalline structure and Zconf for the liquid becomes smaller than 1. This means that, at this level of approximation, the disordered state becomes less favorable than the crystalline ground state. A first-order disorder-order phase transition is expected to occur under these conditions. Flory interpreted this phase transition as the spontaneous crystallization of bulk semiflexible polymers [12], However, since the intermolecular anisotropic repulsion essential in the Onsager model is not considered in the calculation, only the short-range intramolecular interaction is responsible for this phase transition. 

Equation (5.15b) is the fundamental assumption underlying London s theory, which is essential both for numerical evaluation and for physical interpretation of the perturbative expressions. Whereas short-range intramolecular interactions in (5.16a) and (5.16b) must be described with properly antisymmetric eigenfunctions satisfying... 

The numerical self-consistent (SC) MC/RISM procedure [51,52] employed to solve the matrix polymer RISM equation (4) with the RMMSA closure relation (6)-(7) was used in Ref. [53] to study water-containing Nafion systems. The single-chain MC simulation was based on the realistic rotational-isomeric-state (RIS) model [54], in which the short-range intramolecular interactions depending on the details of chemical structure were taken into account via appropriate matrices of statistical weights [54]. 

This equation describes the conformation partition function, Z, as a serial product of statistical weight matrices, U that incorporate the energies of all of the important short-range intramolecular interactions. 

The short range intramolecular interaction of a zeolite lattice can be represented by several potentials. The expressions that model the system most accurately are considered below. 

The collapse produced in both of these simulations arises from the intramolecular short-range attractive two-body interactions experienced by a polymer in a poor solvent. Another interesting type of collapse was recently proposed/45 then identified in a simulation on a diamond lattice/46 and subsequently verified by experiment with copolymers of acrylamide and V-isopropylacrylamide. 47 This collapse mechanism operates in grafted layers of chains when the short-range binary interactions are repulsive, but higher order interactions in W-clusters are attractive. The value of N is found experimentally to be three for copolymers of acrylamide and /V-isopropylacrylamide, 46 as was assumed in the simulation. 47 ... 

The near-infrared reflectance provides the response to plasmon oscillations of the electron gas (which are uniform excitations). This region of the spectrum is, however, not sensitive to the strength of the short-range coulombic interactions, which prevent conductivity in a Mott-Hubbard insulating state. This is illustrated by the frequency-dependent conductivity cx((o) measured in various salts exhibiting very different values of the conductivity at room temperature (Fig. 27). The peak of the conductivity at the frequency w0 correlates with the metallic character namely, a low frequency of the peak position corresponds to a high dc conductivity and vice versa. The structures below 0)o are attributed to the coupling with intramolecular modes. 

The local conformational preferences of a PE chain are described by more complicated torsion potential energy functions than those in a random walk. The simulation must not only establish the coordinates on the 2nnd lattice of every second carbon atom in the initial configurations of the PE chains, but must also describe the intramolecular short range interactions of these carbon atoms, as well as the contributions to the short-range interactions from that... 

Intramolecular interaction is a powerful factor that controls molecular architecture, particularly in the case of geometrically flexible molecular systems. The existence and energies of intramolecular classical hydrogen bonds and their role in chemistry and biochemistry are well known. They stabilize molecular conformations, promote short- and long-range proton transfers, participate in the creation of three-dimensional structures of large molecules and play a fundamental role in the phenomenon of molecular recognition. 

In the case of the unfolded (either a or / ) freely diffusing polypeptide, C(t) is seen to decay on time scales of 10-100, which are significantly slower and correspond to a wider dynamical range in comparison to the folded state. This is consistent with the fact that the underlying interactions are of the excluded volume type, which are short-ranged so that the dynamics is mostly diffusive and relatively slow. Immobilization on a repulsive surface does not alter C(t), since the surface-polypeptide interactions are very similar to the intramolecular interactions in this case. However, C(t) is observed to decay... 

In other words, it is assumed here that the particles are surrounded by a isotropic viscous (not viscoelastic) liquid, and is a friction coefficient of the particle in viscous liquid. The second term represents the elastic force due to the nearest Brownian particles along the chain, and the third term is the direct short-ranged interaction (excluded volume effects, see Section 1.5) between all the Brownian particles. The last term represents the random thermal force defined through multiple interparticle interactions. The hydrodynamic interaction and intramolecular friction forces (internal viscosity or kinetic stiffness), which arise when the macromolecular coil is deformed (see Sections 2.2 and 2.4), are omitted here. 

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