Principal diffusivity

These selection rules lead to the sharp, principal, diffuse and fundamental series, shown in Figures 7.5 and 7.6, in which the promoted electron is in an x, p, d and / orbital, respectively. Indeed, these rather curious orbital symbols originate from the first letters of the corresponding series observed in the spectrum. 

These letters come from the adjectives used by spectroscopists to describe spectral lines sharp, principal, diffuse, and fundamental. 

The wave functions nlm) for the hydrogen-like atom are often called atomic orbitals. It is customary to indicate the values 0, 1, 2, 3, 4, 5, 6, 7,. .. of the azimuthal quantum number / by the letters s, p, d, f, g, h, i, k,. .., respectively. Thus, the ground-state wave function 100) is called the Is atomic orbital, 200) is called the 2s orbital, 210), 211), and 21 —1) are called 2p orbitals, and so forth. The first four letters, standing for sharp, principal, diffuse, and... 

State designation sharp principal diffuse fundamental... 

The words sharp, principal, diffuse, and fundamental were used to describe certain lines in atomic spectra, and it is the first letter of each word that is used to name s, p, d, and/states. 

Strictly speaking, an orbital is not a physical reality but refers to a particular solution of complicated wave equations associated with the theoretical description of atoms and they are referred to by the initial letter of the terms describing the spectral lines sharp, principal, diffuse and fundamental. 

In most cases, fluorescent molecules undergo anisotropic rotations because of their asymmetry. A totally asymmetric rotor has three different rotational diffusion coefficients, and in cases where the absorption and emission transition moments are not directed along one of the principal diffusion axes, the decay of r(t) is a sum of five exponentials (see Box 5.3). 

The subshells are labelled s, p, d and f. These letters originally came from old spectroscopic terms sharp , principal , diffuse and fundamental , but these terms are no longer important. 

The new axes q, are known as the principal axes of diffusion and Di, Dz, and D3 are principal diffusion coefficients (i.e., diffusivity along the directions of the principal axes). Diffusion along a principal axis direction is not affected by concentration gradient along other directions. That is. 

The index number refers to the principal quantum number and corresponds to the K shell designation often used for the electron of the normal hydrogen atom. The principal quantum number 2 corresponds to the L shell, 3 to the M shell, and so on. The notation s (also p, cl, f to come later) has been carried over from the early days of atomic spectroscopy and was derived from descriptions of spectroscopic lines as sharp, principal, diffuse, and fundamental, which once were used to identify transitions from particular atomic states. 

The outermost layer of the skin, the cornified layer or stratum corneum, has been identified as the principal diffusion barrier for substances, including water [2,3]. It is approximately 10 to 20 pm thick when dry but swells to several times this thickness when fully hydrated [17], It contains 10 to 25 layers lying parallel to the skin surface of nonviable cells, the corneocytes, which are surrounded by a cell envelope and imbedded in a lipid matrix. This architecture is often modeled as a wall-like structure, with the corneocytes as protein bricks embedded in a lipid mortar [18]. Similarly to the viable epidermis, desmosomes (corneodesmosomes) contribute to the cell cohesion. 

Usually, the values t = 0, 1, 2, 3 are termed s, p, d, f, respectively, the names coming from observations in the alkali spectra where sharp, principal, diffuse, and fundamental series have been distinguished [Ryd89] higher /-values are then named in alphabetical order.) The numbers within the brackets label the electrons from 1 to Z. Hence, the most compact form which will be used in discussions can be written as... 

Woessner47 has also treated the case of a methyl group attached to an axially symmetric ellipsoid, whereas Levy et al.66 derived equations for the methyl internal rotation superposed on a fully anisotropic motion. The effect of anisotropic reorientation can dramatically alter the relationship between rigidly held methine, methylene, and methyl C—H vectors. Deviation from the ratio T,(CH)/ T,(CH3) = 3 can be considerable, depending on the relative orientation of C—H vectors with respect to the principal diffusion axes. 

FIG. 12.—Orientation of the principal-axis system of inertia tensor (x. y. z1) and that of the rotational diffusion tensor (x,y,z) for compound 31. The principal diffusion axis x is perpendicular to the plane of the drawing. [Reproduced with permission from P. Dais, Carbohydrate Res., 263 (1994) 13-24, and Elsevier Science B.V.]... 

The selection of letters for this spectroscopic shorthand dates back to the early days of spectroscopy when certain lines were designated as sharp, principal, diffuse, and fundamental. These terms have no real meaning today, but the letters are still used.) An electron with n = 1 and l = 0 is a Ls electron whereas an electron with n = 4 and l = 3 is a 4/ electron. Thus, the shorthand for neon indicated that neon has two electrons in the U state, two electrons in the 2s state, and six electrons in the 2p state. 

The terms with L = 0,1,2,3 are called S, P, D, F these letters were adapted from the pre-1900 labeling of spectroscopic transitions as giving "sharp," "principal," "diffuse", and "fundamental" lines. 

Write the expression for the diffusivity in terms of the principal diffusion coefficients for ... 

It is conventional to label specific states by replacing the angular momentum quantum number with a letter we signify = 0 with s, = 1 with p, = 2 with d, = 3 with f, (.= 4 with g, and on through the alphabet. Thus, a state with n = and = 0 is called a Is state, one with n = 3 and F = 1 is a 3p state, one with n = 4 and = 3 is a 4/state, and so forth. The letters s, p, d, and / derive from early (pre-quantum mechanics) spectroscopy, in which certain spectral lines were referred to as sharp, principal, diffuse, and fundamental. These terms are not used in modern spectroscopy, but the historical labels for the values of the quantum number are still followed. Table 5.1 summarizes the allowed combinations of quantum numbers. 

The letters derive from the names of spectroscopic lines 5harp, principal, diffuse, and fundamental. Sublevels with I values greater than 3 are designated alphabetically g sublevel, h sublevel, etc.) Sublevels are named by joining the n value and the letter designation. For example, the sublevel (subshell) with n = 2 and / = 0 is called the 2s sublevel. 

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