Surface molar concentrations

Let d be the volumetric molar concentration of Mi in Q and C12 the surface molar concentration of M12 on TG. Assuming that both types of ions have the same diffusion coefficient D > 0 and since crystalline is immobile, mass conservation for M% gives... 

Figure 13 (a) Plot of surface ox) gen concentration against weight % PLA in miscible (2 kDa) blends with PSA. (b) Plot of surface oxygen concentration against weight % PLA in immiscible (50 kDa) blends with PSA. (c) Comparison of bulk and surface molar concentrations of PLA in miscible blends with PSA (Dacies et al, 1996). 

Pore dijfusion in fluid-filled pores. These pores are sufficiently large that the adsorbing moleciile escapes the force field of the adsorbent surface. Thus, this process is often referred to as macropore dijfusion. The driving force for such a diffusion process can be approximated by the gradient in mole fraction or, if the molar concentration is constant, by the gradient in concentration of the diffusing species within the pores. 

A similar argument can be applied to the mass transfer process when a concentration gradient exists. Thus, if the molar concentration of A remote from the surface is Ca, and at the surface it is Caw, the moles of A transferred to the surface will be (M/pHC — Cam ), if the density (p) can be assumed to be constant over the range of concentrations encountered, Thus the moles of A transferred to the surface per unit area and unit time (-/V Ov-o is given by ... 

Consider the movement of an element of fluid consisting of n molar units of a mixture of two constituents A and B from a region outside the boundary layer, where the molecular concentrations are CAs and CBs, to the surface where the corresponding concentrations are CAw and CBw. The total molar concentration is everywhere Cr- The transfer is effected in a time t and takes place at an area A of surface. 

A solute diffuses from a liquid surface at which its molar concentration is C, into a liquid with which it reads. The mass transfer rate is given by Fick s law and the reaction is first order with respect to the solute, fn a steady-state process the diffusion rate falls at a depth L to one half the value at the interface. Obtain an expression for the concentration C of solute at a depth z from the surface in terms of the molecular diffusivity D and the reaction rate constant k. What is the molar flux at the surface ... 

Dissolve bis-NHS-PEG5 into the solvent of choice at a concentration of lmg/ml also containing an equal molar concentration of triethylamine as base. Add the crosslinker solution to the surface or to the particles to coat them fully. When working with particles, centrifuge them to remove solvent prior to resuspending in the crosslinker solution. 

Let us say that this new surface equilibrium temperature of the water is 15.5 °C then the vapor pressure is 0.0174 atm. At the surface of the water, not only does water vapor exist, but so must the original gas mixture components of air, O2 and N2. By Dalton s law the molar concentration of the water vapor is... 

LDAO/SDS Interaction. Mixing of cationic and anionic surfactant solutions results In the formation of a mixed species that Is more surface active than the Individual species. The enhanced synergistic effect has been explained (2,3) by showing that a close-packed adsorption of electroneutral R R takes place (R" " and R represent the long chain cation and anion respectively). In the case of Ci2 and C14-DAO, a 1 1 LDAO/SDS molar ratio produces a minimum In surface tension and Is accompanied by an Increase In pH In the bulk solution the association seems to be of the type R R", and the absence of visible precipitate may be attributed to the solubilization of the R R" complex In the solution. In the region where LDAO Is In excess, the structure Is probably [cationic (LDAOH ) anionic (SDS)] nonlonlc (LDAO), while [cationic (LDAOH anionic (SDS)] anionic (SDS) Is formed when SDS Is In excess. Equal molar concentration results In cationic (LDAOH ) anionic (SDS) complex which should favor precipitation. However, at pH >9, there Is no Indication of precipitation (even when the total solute concentration Is 0.35 M). When the pH Is below 9, then precipitation will take place. 

The simplest case of compositional dependence is the zero-order reaction, in which the concentration gradient is not affected by concentration. Denoting the molar concentration of the ith element (or component) as c, (and neglecting surface area and volume of solution effects), we have... 

The equation of state can be furnished if the partial molar fraction xf can be described in terms of the real surface excess The molar fraction is defined as the molar concentration of the component in the surface layer divided by the total molar concentration of all components in the layer. Since the molar concentrations can also be expressed in terms of the surface area, the molar fraction is equivalent to the partial coverage 9i of the component. Now we have x f = 6i = Ficoi. In terms of the surface coverage 9i and the bulk concentration Ci of the zth component, Eqs. 6 and 7 can be transformed to give... 

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