Tracer diffusion constant

Fig. 10.12 The molecular-weight dependence of the tracer diffusion constant obtained for the nearly monodisperse polystyrene samples in a polystyrene matrix of molecular weight P = 2 X 10 at 174°C. The solid line represents Dq = 0.008M . Reproduced, by permission, from Ref. 28.

This diffusion constant describing the diffusion of a labeled chain is called the tracer diffusion constant. It decreases with N and the monomer concentration c. The sharpness of the concentration dependence of Dt depends on the size exponent. For example, in good solutions (v = 3/5), Dt and in theta solutions (v = 1/2), Dj The longest relaxation time t is... 

A rapid increase in diffusivity in the saturation region is therefore to be expected, as illustrated in Figure 7 (17). Although the corrected diffusivity (Dq) is, in principle, concentration dependent, the concentration dependence of this quantity is generally much weaker than that of the thermodynamic correction factor d ap d a q). The assumption of a constant corrected diffusivity is therefore an acceptable approximation for many systems. More detailed analysis shows that the corrected diffusivity is closely related to the self-diffusivity or tracer diffusivity, and at low sorbate concentrations these quantities become identical. 

A simple case is the diffusion of a single type of ion in a solution containing a sufficient excess of an indifferent electrolyte (see page 116), which then occurs in the same way as in the case of a non-electrolyte. Isotope (tracer) diffusion has the same character, where a concentration gradient of the radioactive isotope of an ion, present in a much lower concentration, is formed in a solution with a much larger, constant salt concentration. 

The above sections have focused upon homogeneous systems with a constant composition in which tracer diffusion coefficients give a close approximation to selfdiffusion coefficients. However, a diffusion coefficient can be defined for any transport of material across a solid, whether or not such limitations hold. For example, the diffusion processes taking place when a metal A is in contact with a metal B is usually characterized by the interdiffusion coefficient, which provides a measure of the total mixing that has taken place. The mixing that occurs when two chemical compounds, say oxide AO is in contact with oxide BO, is characterized by the chemical diffusion coefficient (see the Further Reading section for more information). 

When the concentration levels are higher, such as Ni diffusion between two olivine crystals with the same compositions except for Ni content (e.g., one contains 100 ppm and the other contains 2000 ppm), it may be referred to as either tracer diffusion or chemical diffusion. Tracer diffusivity is constant across the whole profile because the only variation along the profile is the concentration of a trace element that is not expected to affect the diffusion coefficient. 

Thermal or low-energy neutron scattering experiments have been most valuable in throwing light on molecular motion in plastic crystals. These experiments measure changes in the centre of mass of a molecule. Diffusion constants obtained from neutron experiments differ widely from those obtained from tracer experiments since neutron scattering is mainly determined by rotational diffusion. The scattering function has the form... 

Fig. 8.2 Oxygen tracer diffusivities and oxygen permeabilities through liquid boron oxide, fused silica, and a polycrystalline alumina with a grain size of 5 nm. Tracer diffusivity values for B203 and Si02 were obtained from Refs. 9 and 19, respectively. Tracer diffusivity values for A1203 were obtained from data reported in Ref. 18 using a grain size of 5 /im (Ref. 13). Oxygen permeability constants were obtained using the procedure outlined in the text.2...

Fig. 2.18. Arrhenius plots of various relevant diffusion constants for Ni/Hf and Co/Zr diffusion couples. The upper dashed and solid line are based on tracer diffusion data for Ni and Co in crystalline a-Zr [2.38,28]. The lower curve is for self diffusion of a-Zr [2.103], The open squares are Co tracer diffusion data in amorphous Co89Zru [2.28], Solid circles are the interdiffusion constant D obtained by SSAR on Ni/Hf diffusion couples [2.79], Open circles, upward triangles, downward triangles, and diamonds are interdiffusion constants obtained from studies of SSAR in Co/Zr diffusion couples [2.28]. The latter data were determined from RBS studies and direct cross-sectional TEM observation of the thickness of the amorphous layer. The downward arrows indicate an upper bound for the intrinsic diffusion constant of Zr in the amorphous layer during SSAR...

The diffusion constant and activation energy can be measured directly by radioactive tracer techniques in which the initial distribution of radioactive ions is followed as a function of time and distance. Values of the diffusion constant and activation energies thus determined are then compared with values from ionic conductivities. 

It was discussed in Sect. 4.2 that there is a very slow change in the a-dynamics in stacked thin films of P2CS. There may be several possibilities for this slow change. If heterogeneous diffusion in thin polymer layers is an essential process, then direct measurement of diffusion constant of a tracer polymer chain in a thin layer of the... 

Fig. 9 Arrhenius-plot of the parabolic rate constant measured for the growth of CoO on Co in air [91] compared with that calculated from Wagners theory and the tracer diffusion coefficient for Co in CoO [89, 90].

Fig. 21.5. Characteristic values related to proton conduction (a) , self-diffusion (b) and reorientation (c) in sulphuric acid aqueous solutions at 290 K as a function of H2SQ, concentration expressed in weight % (top scale) or molarity (bottom scale). For pure HjO, the QNS study yields the same D value as measured by NMR spin-echo or tracer methods . In the same graph (b) is reported the residence time xp measured by QNS and defined in Eqn (21.5). The rotational diffusion constant >, defined in Eqn (21.8) is reported in graph (c) together with the characteristic rotational time x, = fi/6 >,.

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