Diffusion state

The quantity of solute B crossing a plane of area A in unit time defines the flux. It is symbolized by J, and is a vector with units of molecules per second. Fick s first law of diffusion states that the flux is directly proportional to the distance gradient of the concentration. The flux is negative because the flow occurs in a direction so as to offset the gradient ... 

Diffusion is the movement of mass due to a spatial gradient in chemical potential and as a result of the random thermal motion of molecules. While the thermodynamic basis for diffusion is best apprehended in terms of chemical potential, the theories describing the rate of diffusion are based instead on a simpler and more experimentally accessible variable, concentration. The most fundamental of these theories of diffusion are Fick s laws. Fick s first law of diffusion states that in the presence of a concentration gradient, the observed rate of mass transfer is proportional to the spatial gradient in concentration. In one dimension (x), the mathematical form of Fick s first law is... 

Also for other systems, V a values for hole transfer depend only weakly on the basis set [14, 41, 46]. This is at variance with results for the coupling of excess electron transfer where energies of more diffuse states are involved in the ground strategy this would correspond to employing energies of unoccupied molecular orbitals. 

Table 1.1 shows the proportion of the several constituents found in the dissolved, diffusible state. Actually, phosphate is present in five classes of compounds inorganic dissolved, inorganic colloidal, water-soluble esters, ester-bound in caseins, and lipid. These can be determined by making the following analyses ... 

It has to be noted that the detection of the various diffusive states as well as active transport depends on the time scale of observation. For short time scales, the short-range motion of tracked particles may seem similar and indicates the same local microenvironment for the particles as it is dominated by Brownian motion [37,41], Confined diffusion as well as active transport require a minimal duration for detection and appear at longer time scales (see MSD plot). To display confined diffusion, the particle has to experience the boundaries of confinement in its local microenvironment which restrict the free diffusion on longer time scales. Similarly, for active transport, the second part of (3) 4DAf is predominant on short time scales. The active transport component v2At2 becomes dominant at longer observation periods. 

Fick s law of molecular diffusion states that, for a binary mixture of components A and B, the molar flux of component A by ordinary molecular diffusion relative to the molar average velocity of the mixture in the positive z direction, is proportional to the concentration gradient dcA/dz, which is negative in the direction of ordinary molecular diffusion ... 

The delocalized state can be considered to be a transition state, and transition state theory [105], a well-known methodology for the calculation of the kinetics of events, [12,88,106-108] can be applied. In the present model description of diffusion in a zeolite, the transition state methodology for the calculation of the self-diffusion coefficient of molecules in zeolites with linear channels and different dimensionalities of the channel system is applied [88], The transition state, defined by the delocalized state of movement of molecules adsorbed in zeolites, is established during the solution of the equation of motion of molecules whose adsorption is described by a model Hamiltonian, which describes the zeolite as a three-dimensional array of N identical cells, each containing N0 identical sites [104], This result is very interesting, since adsorption and diffusion states in zeolites have been noticed [88],... 

Considering the dynamic equilibrium between the adsorbed state and the diffusion state [12], T, the jump frequency of molecules between sites is [12]... 

State Shape Particle arrangement Relative distance between particles Diagrammatic representation Movement of particles Diffusion State... 

When dealing with currents in ionic solutes, one must take into account the finite diffusion of ions within the electrolyte. As mentioned in Section 6.21, Fick s83 second law of diffusion states that the time-dependence of the concentration profile in a one-dimensional planar system Co(x,t) depends linearly on the derivative of the concentration gradient ... 

Gas Phase Electron Affinities of DNA Bases and Base pairs (Valence and Diffuse States)... 

Solvation of DNA bases/base pairs is of fundamental importance to biological processes as they take place in aqueous media. The effect of hydration on neutral bases or base pairs has been addressed using quantum chemical methods [106-112] as well as molecular dynamics (MD) simulations [113, 114], It is known that unlike the gas phase, dipole bound anions do not exist in condensed environments because such diffuse states are destabilized in the aqueous phase [115]. The drastic change in the nature of excess electron binding in the presence of water molecules with uracil has been observed experimentally by Bowen and co-workers [95b] using negative electron photoelectron spectroscopy (PES). They observed that even with a single water molecule the dipole bound state of uracil anion in gas phase... 

Fick s first law of diffusion states that the concentration of particles crossing unit area in unit time J is proportional to the concentration gradient normal to the unit area dc/dx. The constant of proportionality D is known as the diffusion coefficient. Symbolically, for the current through a plane set at right angles to the x direction,... 

The product cv represents a diffusion current, i.e., the number of particles crossing a unit area in unit time. But Fick s first law of diffusion states that the diffusion current is proportional to the concentration gradient, the constant of proportionality being the diffusion coefficient D. Thus the diffusion coefficient for an aerosol particle is, from Eq. 9.11,... 

Effusion is the passage of a gas through a tiny hole usually into a chamber of lower pressure. Thomas Graham experimentally determined that the rate of effusion is inversely proportional to the square root of the molecular mass. Graham s law of diffusion states ... 

In the equilibrium state, this is, of course, zero. When the potential is increased, then the concentration (O) is depleted near the surface, while (R) is increased. Eventually a quasi-stationary state will be established, one in which the depletion of O at the electrode is balanced by a diffusion of O from the solution, while the excess of R will similarly be balanced by a diffusion of R away from the electrode to the solution. We can write for such a stationary diffusion state ... 

Write down in dimensionless form the material balance equation for a laminar flow tubular reactor accomplishing a first-order reaction and having both axial and radial diffusion. State the necessary conditions for solution. 

During the diffusion stage of evaporation the amount of solvent remaining in the film can be plotted against time divided by the square of the film thickness this plot eliminates the effect of varying thickness in experimental results and illustrates the fact that doubling the film thickness will quadruple the time to a given state of dry in the diffusion state of evaporation (57). 

Nitrobenzene, j zra-dinitrobenzene (/zDNB) and me/a-dinitrobenzene (mDNB) anions have both diffuse multipole-bound and valence-anion states. For nitrobenzene and m-dinitrobenzene, the diffuse states are believed to correspond to dipole-bound anions whereas />DNB anions are considered to be primarily described as quadrupole-bound states. Nitrobenzene anions (NB ) in both valence and dipole-bound states were examined using RET spectroscopy. R<3ra-dinitrobenzene (zero dipole moment and a large quadrupole moment) and me <3-dinitrobenzene (large dipole moment and a small quadrupole moment) were also studied using R T 106 20 shows the /-dependence of the reaction rates for... 

Meta-dinitrobenzene has a large dipole moment (p = 4.29 D), very close to that of nitrobenzene, and a quadrupole moment of Q = - -18 a.u. Its parallel and perpendicular polarizabilities are estimated to be 21.2 and 17 A, respectively. From the electrostatic model, the predicted electron affinity of mDNB is 105 25 meV, corresponding to a peak in the RET curve at around n = 7. The curve for mDNB (not shown) is very different from the RET curve corresponding to pDNB. The broad peak at = 11-12 is not present and is replaced by a very small peak at = 8, close to the predicted value for the dipole-bound mDNB anion. The anions reported here are not observed to undergo field detachment. Again, this observation is attributed to the coupling of these diffuse states with the ground valence anion state. 

At this point let us restrict our considerations to a binary system in which there is a spatial concentration gradient. Pick s first law of diffusion states that there is a linear relation between the species flux and the concentration gradient ... 

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