Static Properties of Macromolecules

The function/is sometimes referred to as the probability density (i.e., the probability per unit volume). 

2 The Equilibrium Configuration (or Distribution) Function for Polymer Molecules 

In the most general form, the equilibrium (or probability) distribution function /(r) for a chain at the position r can be written as (Bird et al. 1987 Huang 1987  

For an ideal spring (Hookean behavior), the potential U is given by (see Appendix 4A) 

Substituting Eq. (4.6) into (4.4) and determining the normalized factor such that the total probability of any value of r is unity (i.e., //(r) dr = 1) we have 

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In this chapter, we present currently held molecular theories for the viscoelasticity of linear, flexible macromolecular chains. We begin with a presentation of the static properties of macromolecules and the stochastic processes in the motion of macromolecular chains, as much as they will be necessary to present the molecular aspects of viscoelasticity in this and later chapters. We first present the molecular theories of Rouse (1953) and Zimm (1956), which are basically applicable to dilute polymer solutions and unentangled polymer melts, and then present the molecular theory of Doi and Edwards (1978a, 1978b, 1978c, 1979), which is applicable to concentrated polymer solutions and entangled polymer melts. 

Static Properties of Macromolecules and Stochastic Processes in the Motion of Macromolecular Chains... 

The results of this consideration may be summarized as follows. The study of global properties of macromolecules in dilute solutions by means of static and dynamic LS and by viscometry allows the determination of the molar mass and four differently defined equivalent sphere radii, R, and (see... 

A detailed description of statically or dynamically local properties must be based on the stereochemical composition of the monomers and their potential energy landscape [1, 37-44]. On the other hand, the global, i.e., large-scale, properties of macromolecules tend to be insensitive to the stereochemical details of the monomers. Therefore, a coarse-grained description becomes adequate by considering model chains. All chemical specificity can then be represented by a few characteristic parameters to be specified in the following. 

A. Milchev, K. Binder. Static and dynamic properties of adsorbed chains at surfaces Monte Carlo simulations of a bead-spring model. Macromolecules 29 343-354, 1996. 

He, G. L., Merlitz, H., Sommer, J. U. and Wu, C. X. (2007) Static and dynamic properties of polymer brushes at moderate and high grafting densities A molecular dynamics study. Macromolecules, 40, 6721-6730. 

Whereas polymer transport in dilute solution has been widely studied, investigations of polymer transport in concentrated solutions have been reported only infrequently. When solutions of high molecular weight polymers are concentrated in a way that intermolecular interactions between individual molecules occur, it becomes increasingly evident that both the static and dynamic properties of the macromolecules may be markedly altered compared to their behaviour in dilute solution l). 

The year 2003 is the tenth anniversary of the first Femtochemistry Conference and the fiftieth anniversary of Watson and Crick s celebrated discovery of the DNA double helix [1], Remarkable progress has been made in both fields femtosecond spectroscopy has made decisive contributions to Chemistry and Biology, and advances in the elucidation of static nucleic acid structures have profoundly transformed the biosciences. However, much less is known about the dynamical properties of these complex macromolecules. This is especially true of the dynamics of the excited electronic states, including their evolution toward the photoproducts that are the end result of DNA photodamage [2],... 

Characteristic frequencies may be found from dielectric permittivity data or, even better, from conductivity data. The earlier data by Herrick et al. (6) suggest that there is no apparent difference between the relaxation frequency of tissue water and that of the pure liquid (7). However, these data extend only to 8.5 GHz, one-third the relaxation frequency of pure water at 37°C (25 GHz), so small discrepancies might not have been uncovered. We have recently completed measurements on muscle at 37°C and 1°C (where the pure water relaxation frequency is 9 GHz), up to 17 GHz. The dielectric properties of the tissue above 1 GHz show a Debye relaxation at the expected frequency of 9 GHz (8 ) (Figure 3). The static dielectric constant of tissue water as determined at 100 MHz compares with that of free water if allowance is made for the fraction occupied by biological macromolecules and their small amount of bound water (1, 9). 

Tissues are composites of macromolecules, water, ions, and minerals, and therefore their mechanical properties fall somewhere between those of random coil polymers and those of ceramics. Table 6.1 lists the static physical properties of cells, soft and hard tissues, metals, polymers, ceramics, and composite materials. The properties listed in Table 6.1 for biological materials are wide ranging and suggest that differences in the structure of the constituent macromolecules, which are primarily proteins, found in tissues give rise to the large variations in strength (how much stress is required to break a tissue) and modulus (how much stress is required to stretch a tissue). Because most proteins are composed of random chain structures, a... 

Intercalated compounds offer a unique avenue for studying the static and dynamic properties of small molecules and macromolecules in a confined environment. More specifically, layered nanocomposites are ideal model systems to study small molecule and polymer dynamics in restrictive environments with conventional analytical techniques, such as thermal analysis, NMR, dielectric spectroscopy and inelastic neutron scattering. Understanding the changes in the dynamics due to this extreme confinement (layer spacing < Rg and comparable to the statistical segment length of the polymer) would provide complementary information to those obtained from traditional Surface-Force Apparatus (SFA) measurements on confined polymers (confinement distances comparable to Rp [36]. 

Amirzadeh J, McDonell ME (1982) Scaling analysis of static properties for semidilute solutions Macromolecules 15 927-933... 

Amirzadeh, J. McDonnell, M. E., "Scaling Analysis of Static Properties for Semidilute Solutions," Macromolecules, 15, 927 (1982). 

Kubota, K. Abbey, K. M. Chu, B., "Static and Dynamical Properties of a Polymer Solution with Upper and Lower Critical Solution Points. NBS 705 Polystyrene in Methyl Acetate," Macromolecules, 16, 137 (1983). 

Models of this kind are employed in molecular dynamics simulations, to determine static and dynamic properties of a given system this permits to verify the consistency and reliability of the model, to explain the molecular origin of physical characteristics of a system or to calculate properties for which no experimental data are available. Great interest has been devoted, for example, to the study of the structure and dynamics of liquid water, ice and solutions. Liquid water simulations are used to represent the hydrogen bond network in the liquid phase and to explain some unusual and not yet understood properties of water, such as its high thermal capacity, in terms of its structure. Still more important is the elucidation of the molecular origin of dynamic phenomenons such as the solvations of ions in water and the interaction of macromolecules with the solvent. 

Molecules are dynamic, undergoing vibrations and rotations continually. Therefore the static picture of molecular structure provided by MM is not realistic. Flexibility and motion are clearly important to the biological functioning of biomacromolecules. These molecules are not static structures, but exhibit a variety of complex motions both in solution and in the crystalline state. Energy minimization concerns only the potential energy term of the total energy and so it treats the biomacromolecule as a static entity. The dynamic properties of the atoms in a macromolecule or the momentum of the atoms in space requires the description of the kinetic term. The momentum (p) is related to the force exerted on the atom (Ft) and the potential energy (V) by... 

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