Static properties

The Evans method gives excellent results provided adequate care is taken. A most important requirement is that the solution temperature is measured reliably. One effective means of accomplishing this for H NMR is to insert into the NMR tube a capillary or additional coaxial sample of an NMR temperature calibrant solvent, usually methanol (158) or ethylene glycol (88). In this way the temperature measurement is made simultaneously with the susceptibility measurement. A second important factor is the variation of the solvent density with temperature (126). Because the density difference between the solvent and solution depends linearly on the concentration of the solute, it is only 

Observation of magnetic susceptibility relaxation after perturbation of a spin equilibrium would be the most direct way to measure the dynamics of the equilibrium. This does not appear to have been reported as measured in solution. In principle susceptibility relaxation as a function of frequency could be measured much as dielectric relaxation is examined. The requirement is for a sufficiently strong magnetic field with very sensitive detection. A nonequilibrium magnetic susceptibility has been generated by light at low temperatures in the solid state (39). 

A change in spin state among transition metal complexes in spin equilibrium invariably involves a change in the electron population of the a antibonding eg orbitals. This produces a substantial change in the properties of the metal-ligand bonds. This variability in the population of a antibonding orbitals is a conspicuous feature of the complexes of the 3d transition metals and accounts for many of their unique properties. 

Metal- Ligand Bond Length Differences between Spin States 

In both the Fe(II) and Fe(III) cases the spin state change involves a change in the population of the a antibonding eg orbitals of two d electrons. For the spin equilibrium of the d1 cobalt(II) complexes the population of the eg orbitals changes by only one electron. From examination of the structures of a series of [Co(terpy)2]2+ salts, a bond length difference between the two Co-N (central) distances of 21 pm was found between the spin states, with a difference of only 7 pm found between the four Co-N (distal) distances. This gives an average difference of 12 pm. 

Space-filling networks of particles normally display a frequency-independent modulus. Near the percolation threshold, theory predicts a relation (de Gennes, 1976 Feng and Sen, 1984) 

Storage modulus versus volume fraction relation for a flocculated silica-methyl lau-rate system. From Van der Aerschot and Mewis (1992). 

Relation between the power law indices of the concentration laws for modulus and yield stress comparison between experiment (rectangles) (van der Aerschot, 1989) and theory (lines). From Patel and Russel (1988). 

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Bishop M, Ceperley D, Frisch FI L and Kales M FI 1980 Investigation of static properties of model bulk polymer fluids J Chem. Phys. 72 3228... 

Static properties of some molecules ([193,277-280]). More recently, pairs of ci s have been studied [281,282] in greater detail. These studies arose originally in connection with a ci between the l A and 2 A states found earlier in computed potential energy surfaces for C2H in symmetry [278]. Similar ci s appear between the potential surfaces of the two lowest excited states A2 and B2 iit H2S or of 82 and A in Al—H2 within C2v symmetry [283]. A further, closely spaced pair of ci s has also been found between the 3 A and 4 A states of the molecule C2H. Here the separation between the twins varies with the assumed C—C separation, and they can be brought into coincidence at some separation [282]. 

In the next section we describe the basic models that have been used in simulations so far and summarize the Monte Carlo and molecular dynamics techniques that are used. Some principal results from the scaling analysis of EP are given in Sec. 3, and in Sec. 4 we focus on simulational results concerning various aspects of static properties the MWD of EP, the conformational properties of the chain molecules, and their behavior in constrained geometries. The fifth section concentrates on the specific properties of relaxation towards equilibrium in GM and LP as well as on the first numerical simulations of transport properties in such systems. The final section then concludes with summary and outlook on open problems. 

IV. SIMULATIONAL RESULTS—STATIC PROPERTIES A. Molecular Weight Distribution... 

In contrast to static properties, where LP and GM reveal generally the same behavior as that of conventional polymers, due to the self-assembling nature of the breakdown process the transport properties of GM are much more complex. Like conventional polymers, these materials are highly viscoelastic [73,74] and their novel rheology has been intensively studied recently, both experimentally [75,76] and theoretically [11,31,77-79]. A theoretical model... 

Y. Rouault. A Monte Carlo study of living polymers in 2D Effect of small chains on static properties. J Physique II 6 1301-1311, 1996. 

J. Wittmer, A. Milchev, M. Cates. Dynamical Monte Carlo study of equilibrium polymers Static properties. J Chem Phys 709 834-845, 1998. 

If concentrated polymer solutions confined in thin film geometry are considered, it turns out that the static properties readily match the theoretic expectations (Fig. 17) whereas the problem with dynamics is more complex [16,17] writing Zgff = -f-1, one expects a corresponding decrease in the... 

A. Milchev, K. Binder. Polymer solutions confined in slit-hke pores with attractive walls An off-lattice Monte Carlo study of static properties and chain dynamics. J Computer-Aided Mater Des 2 167-181, 1995. 

Thermal conductivity is not a static property of a material. It can vary according to the density, operating temperature and type of gas entrapped within the voids. 

Lyapunov Dimension An interesting attempt to link a purely static property of an attractor, - as embodied by its fractal dimension, Dy - to a dynamic property, as expressed by its set of Lyapunov characteristic exponents, Xi, was, first made by Kaplan and Yorke in 1979 [kaplan79]. Defining the Lyapunov dimension, Dp, to be... 

The mechanical properties of plastics enable them to perform in a wide variety of end uses and environments, often at lower cost than other design materials such as metal or wood. This section reviews the static property tests. Chapter 5 provides more information on the meaning of these type data. 

The data included provides examples of what are available. As an example static properties (tensile, flexural, etc.) and dynamic properties (creep, fatigue, impact, etc.) can range from near zero too extremely high values. They can be applied in different environments from below the surface of the earth, to over the earth, and into space. 

Thermodynamic, statistical This discipline tries to compute macroscopic properties of materials from more basic structures of matter. These properties are not necessarily static properties as in conventional mechanics. The problems in statistical thermodynamics fall into two categories. First it involves the study of the structure of phenomenological frameworks and the interrelations among observable macroscopic quantities. The secondary category involves the calculations of the actual values of phenomenology parameters such as viscosity or phase transition temperatures from more microscopic parameters. With this technique, understanding general relations requires only a model specified by fairly broad and abstract conditions. Realistically detailed models are not needed to un-... 

The static properties of an isolated chain constitute a good starting point to study polymer dynamics many of the features of the chain in a quiescent fluid could be extrapolated to the kinetics theories of molecular coil deformation. As a matter of fact, it has been pointed out that the equations of chain statistics and chain dynamics are intimately related through the simplest notions of graph theory [16]. 

A three-dimensional meshwork of proteinaceous filaments of various sizes fills the space between the organelles of all eukaryotic cell types. This material is known collectively as the cytoskeleton, but despite the static property implied by this name, the cytoskeleton is plastic and dynamic. Not only must the cytoplasm move and modify its shape when a cell changes its position or shape, but the cytoskeleton itself causes these movements. In addition to motility, the cytoskeleton plays a role in metabolism. Several glycolytic enzymes are known to be associated with actin filaments, possibly to concentrate substrate and enzymes locally. Many mRNA species appear to be bound by filaments, especially in egg cells where they may be immobilized in distinct regions thereby becoming concentrated in defined tissues upon subsequent cell divisions. 

Note that the accuracy with which the MD calculation can estinate the gyration radius is only about 10%, and thus it is not clear whether the slight disagreement between the MC and MD results for (Rg) in Fig. 5.2 is significant. We empharize a comparison of dynamic properties here because the usefulness of MC to estinate any dynamic properties of polymers is doubled often in the literature. Comparisons her static properties on smaller length scales -... 

On the other hand, one strength of the approach is the availability of algorithms (such as the slithering snake algorithm) by which undercooled polymer melts can be equilibrated at relatively low temperatures. This allows the static properties of the model to be established over a particularly wide parameter range. Furthermore, the lattice structure allows many questions to be answered in a well-defined, unique way, and conceptional problems of the approach can be identified and eliminated. Last but not least, the lattice structure allows the formulation of very efficient algorithms for many properties. 

We would like to point out that an order parameter indicates the static property of the lipid bilayer, whereas the rotational motion, the oxygen transport parameter (Section 4.1), and the chain bending (Section 4.4) characterize membrane dynamics (membrane fluidity) that report on rotational diffusion of alkyl chains, translational diffusion of oxygen molecules, and frequency of alkyl chain bending, respectively. The EPR spin-labeling approach also makes it possible to monitor another bulk property of lipid bilayer membranes, namely local membrane hydrophobicity. 

Besides the static scaling relations, scaling of dynamic properties such as viscosity rj and equilibrium modulus Ge [16,34], see Eqs. 1-7 and 1-8, is also predicted. The equilibrium modulus can be extrapolated from dynamic experiments, but it actually is a static property [38]. 

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