One macroscopic dimensions

Components with One Macroscopic Dimension Wires, Rods, Tubes, and Fibers, 386... 

We will discuss several strategies to tether the properties of LCE actuators to certain specifications, and then present examples of actuator systems of different shapes and different domain sizes. We shall differentiate between macroscopic and microscopic LCE actuators. Films (Sect. 2.2.1) and fibers (Sect. 2.2.2) typically have at least one macroscopic dimension. Microscopic actuation systems from LCEs have received much interest lately and have recently been the subject of a specialized review [88]. In Sect. 2.2.3, we will discuss micrometer-sized actuators that are fixed on a solid substrate to yield stunuU-responsive surfaces. In Sect. 2.2.4, we will review several methods for preparation of coUoid-like actuators that are freely suspended in air or in a surrounding Uquid. 

Early theories of Guth, Kuhn, Wall and others proceeded on the assumption that the microscopic distribution of end-to-end vectors of the chains should reflect the macroscopic dimensions of the specimen, i.e., that the chain vectors should be affine in the strain. The pivotal theory of James and Guth (1947), put forward subsequently, addressed a network of Gaussian chains free of all interactions with one another, the integrity of the chains which precludes one from the space occupied by another being deliberately left out of account. Hypothetical networks of this kind came to be known later as phantom networks (Flory, 1964,... 

Electrochemistry at electrodes with microscopic dimensions (e.g., a disk of 10 j,m diameter) and nanoscopic dimensions (e.g., a disk of <100 nm diameter) constitutes one of the most important frontiers in modern electrochemical science [25]. Such micro- and nanoscopic electrodes allow for electrochemical experiments that are impossible at electrodes of macroscopic dimensions (e.g., disks of mm diameter we call such electrodes macroelectrodes ). Examples of unique opportunities afforded by micro- and nanoscopic electrodes include the possibility of doing electrochemistry in highly resistive media and the possibility of investigating the kinetics of redox processes that are too fast to study at electrodes of conventional dimensions (both are discussed in detail below). In addition, microscopic electrodes have proven extremely useful for in vivo electrochemistry [62]. 

Abstract In this work, we explain how small surfactant molecules with dimensions of one to two nanometers, when dissolved in water with a concentration of a few weight percent, organize themselves spontaneously into various structures with a long-range order over macroscopic dimensions of several centimeters, even though the molecules are all in the liquid state. It follows that two molecules that are more than a million times their main length apart stUl point, on average, in the same direction in three dimensional space. 

From Eq. 3.24 we see that X. 1/P, i.e., the mean free path of a gas molecule is inversely proportional to pressure. This fact is of tremendous importance in vacuum systems. It should be borne in mind that at 1 atm pressure, X is very small compared with the macroscopic dimensions (such as 1 cm) which implies that the molecules collide with one another far more frequently than they collide with the walls of the container and that a molecule moves a distance of several molecular diameters before colliding with another molecule. 

A thermodynamic system is a part of the physical universe with a specified boundary for observation. A system contains a substance with a large amount of molecules or atoms, and is formed by a geometrical volume of macroscopic dimensions subjected to controlled experimental conditions. An ideal thermodynamic system is a model system with simplifications to represent a real system that can be described by the theoretical thermodynamics approach. A simple system is a single state system with no internal boundaries, and is not subject to external force fields or inertial forces. A composite system, however, has at least two simple systems separated by a barrier restrictive to one form of energy or matter. The boundary of the volume separates the system from its surroundings. A system may be taken through a complete cycle of states, in which its final state is the same as its original state. 

The favored structure for most phospholipids and glycolipids in aqueous media is a bimolecular sheet rather than a micelle. The reason is that the two fatty acyl chains of a phospholipid or a glycolipid are too bulky to fit into the interior of a micelle. In contrast, salts of fatty acids (such as sodium palmitate, a constituent of soap), which contain only one chain, readily form micelles. The formation of bilayers instead of micelles by phospholipids is of critical biological importance. A micelle is a limited structure, usually less than 20 nm (200 A) in diameter. In contrast, a bimolecular sheet can have macroscopic dimensions, such as a millimeter (10 nm, or 10 A). Phospholipids and related molecules are important membrane constituents because they readily form extensive bimolecular sheets (Figure 1211). 

The next slightly more complicated situation concerns a fluid confined to a nanoscopic slit-pore by structured rather than unstructured solid surfaces. For the time being, we shall restrict the discussion to cases in which the symmetry of the external field (represented by the substrates) i)reserves translational invarianee of fluid properties in one spatial dimension. An example of such a situation is depicted in Fig. 5.7 (see Section 5.4.1) showing substrates endowed with a chemical structm e that is periodic in one direction (x) but quasi-infinite (i.e., macroscopically large) in the other one (y). 

With the dipole moments, it is necessary to consider what is actually being measured when one applies the Debye equation to the dielectric constant of a solution. One does not measure the dipole moments of single molecules, but rather the mean moment of a spherical aggregate of macroscopic dimensions embracing the single molecule carrying the dipole. 

A novel system has been found, which is ideally suited to explore this frontier clusters containing small or large numbers of atoms can now be made. These are new objects whose properties evolve from the free atom limit to that of the solid as a function of size, or of the number of atoms they contain. Such objects are of quantum scale when they are small, but achieve macroscopic dimensions as their size increases. Thus, one can study the evolution of properties which persist from quantum to macroscopic sizes, or else search for the earliest appearance of solid state properties, for example plasmon oscillations in solids, as a function of the number of atoms in the cluster. 

---