Relaxation bulk properties

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

The time constant, Td, for relaxation of the diffuse part of the double layer is determined by bulk properties of the medium ... 

As has long been known, every derivation of the bulk properties of matter from its atomic properties by statistical methods encounters essential difficulties of principle. Their effect is that in all but the simplest cases (i.e., equilibrium) the development does not take the form of a deductive science. This contrasts with the usual situation in physics e.g., Newtonian or relativistic mechanics, electromagnetism, quantum theory, etc. The present paper, after focusing on this difficulty, seeks a way out by exploring the properties of a special class of statistical kinetics to be called relaxed motion and to be defined by methods of generalized information theory. 

Two more difficulties require comment. The first is that in most of the early literature, authors did not recognize the importance of electrode polarization, and, hence, failed to make quantitative allowance for the presence of blocking and/or release layers. Thus, in most cases, it is not possible to reconstruct quantitative bulk properties from the data presented. (The present authors were not immune. They reported a correlation between a dielectric relaxation time and viscosity54), failing at that time to realize that the relaxation time being studied was actually the characteristic time for electrode polarization, and, hence was dominated by conductivity.)... 

Our result for RbaCeo differs from a recent determination by scanning tunneling microscopy [26] (A—77 K), possibly because NMR relaxation probes the minimum quasiparticle excitation energy, while tunneling probes the maximum in the quasiparticle density of states, or because of differences between surface and bulk properties. Our NMR relaxation data for Rb3C5o clearly deviate from an Arrhenius law below 8 K. At these tem-... 

The BFS method has been applied to a variety of problems, ranging from the determination of bulk properties of solid solution fee and bee alloys and the defeet strueture in ordered bee alloys [28] to more speeifie applieations ineluding detailed studies of the strueture and eomposition of alloy surfaees [29], ternary [30] and quaternary alloy surfaees and bulk alloys [31,32], and even the determination of the phase strueture of a 5-element alloy [33]. Previous appheations have foeused on fundamental features in monatomie [26] and alloy surfaces [29] surface energies, reconstructions, surface structure and surface segregation in binary and higher order alloys [34,35] and multilayer relaxations [36,37]. While most of the work deals with metallic systems, the lack of restrictions on the type of system that can be studied translated into the extension of BFS to the study of semiconductors [38]. 

Despite the limitations of empirical potentials, for the last three decades computer simulations have improved the knowledge on physical properties of metals and alloys. In particular, due to the development of empirical interatomic potentials [18,19], it has become possible to describe by the MD technique a great number of solid properties such as recrystallization, structural relaxation, energetic barriers and mixing [23]. The EAM developed by Foiles et al. [18] has successfully described bulk properties of metal and alloys and some surface relaxation and reconstruction features [17,18,24,25], and the empirical potential developed by Ackland and Vitek has been applied successfully to investigate the structure of the noble metal alloys [19] and the deposition of Cu clusters on Au (111) [26] and of Cu and Au clusters on Cu (001) surfaces [27]. 

While all relaxation times depend on temperature and pressure, only the global motions (viscosity, terminal relaxation time, steady-state recoverable compliance) are functions of Af , (and to a lesser extent MWD). The glass transition temperature of rubbers is independent of molecular weight because chain ends for high polymers are too sparse to affect this bulk property (Figure 3.14 Bogoslovov et al., 2010). The behavior can be described by the empirical Fox-Hory equation (Fox and Flory, 1954) ... 

The dielectric spectroscopy (DS) method occupies a special place among the numerous modem methods used for physical and chemical analysis of material, because it allows investigation of dielectric relaxation processes in an extremely wide range of characteristic times (l(f -10 s). Although the method does not possess the selectivity of NMR or ESR it offers impor tant and sometimes unique information on the dynamic and stractural properties of substances. DS is especially sensitive to intermolecular interactions, and cooperative processes may be monitored. It pro vides a link between the properties of the individual constituents of a complex material and the character ization of its bulk properties (see Fig. 1). 

The limit of accuracy of H-NMR experiments carried out in dilute solution is around 1-5%, depending on the resolution of the spectrum, and of approximately 10% for C NMR. If the polymer to be investigated proved to be insoluble, solid-state NMR techniques are available for further investigation. Solid-state NMR methods are also very useful for determining bulk properties of polymers such as relaxation behavior of local motions and mutual arrangements of chains and chain segments. 

Molecular dynamics has proved to be a powerful method for simulating and/or predicting several features of polymer systems. Properties on either side of the glass transition temperature (see Section 1.5) have been successfully simulated, as has the solid-to-liquid transition, and provided descriptions of the dynamics (segmental motions, chain diffusion, conformational transitions, etc.) that are in accord with relaxation measurements and such bulk properties as shear viscosities and elastic moduli. The method may also provide a good description of the variation in heat capacity and other thermodynamic fimctions across a phase transition. Several collections of these investigations have recently been published. ... 

C NMR. If the polymer to be investigated proved to be insoluble, solid-state NMR techniques are available for further investigation. Solid-state NMR methods are also very useful for determining bulk properties of polymers such as relaxation... 

The application of nuclear magnetic resonance spectroscopy within the food sector has, imtil recently, focussed primarily on the use of time domain (TD) techniques. These enable the quantitative measurement of bulk properties such as water and fat content in whole foods. The measurement relies on the intrinsic relaxation properties of the proton nucleus when a radio frequency pulse is applied to a sample placed in a magnetic field. The differential between the relaxation properties of major food components allows the proportion of these components to be estimated by reference to a calibration safes. This form of NMR spectroscopy is routinely applied for quality and composition checks and is often undertaken in situ as the instrumentation is both inexpensive and robust... 

Physical aging of a PP material can only be monitored indirectly via the changes in its bulk properties, such as density, crystallinity as assessed via DSC or relaxation processes as seen in DMTA. If better organization in amorphous phase is accepted as the dominant effect, this can well explain the increasing stress transfer between crystalline regions (sometimes called pseudonetwork effecL) having a positive effect on stiffness. 

Because NMR is so closely related to molecular motion, there has been much effort to tie spectroscopic parameters, such as relaxation times, to the known rheological and mechanical properties of materials. While there has been some success, as will be seen in Sec. III.D, a general correlation has yet to be established. One difficulty is that NMR is most sensitive to relatively rapid, local motions, while it is primarily slower, longer-range motions that are responsible for a polymer s bulk properties. Rheo-NMR experiments have attempted to provide the connection between micro- and macroscopic observations, and they will likely become a very useful tool in the NMR of polymers if the equipment becomes widely available [36]. 

Molecular mobility in amorphous materials is related to the macromolecular properties like viscosity it is generally quantified in terms of mean relaxation time and it determines physical stability and reactivity. The relaxation time is defined as the time necessary for a molecule or chain segment to diffuse across the distance of one molecule or chain segment. The relaxation time varies with temperature and the typical relaxation times at Tg are estimated to be 100-200 s (Ediger et al. 1996). Molecular relaxation times can be characterized by the change of several bulk properties like enthalpy or volume or spectroscopic properties. The extent of relaxation is described empirically by the Kohlrausch-Williams-Watts equation (Hodge 1994) ... 

---