Otros hallazgos relacionados con el DHL que aportan a los proyectos de Generación

Principles and theory of FTIR-ATR spectroscopy have been described in chapter 1. In this section, the use of this technique for obtaining information about diffusion of small

molecules in polymers is presented.

As was explained earlier, Fick's second law for diffusion of 1-D diffusion in a layer with a constant diffusion coefficient is as follows;

^ = (5.2) St

dZ2

The boundary conditions for a region of -L < x < L with an initial uniform concentration, C0 and a constant concentration at the surface, CL are:

C = 0 at t < 0 ; 0 < z < L

C = CL at t > 0; z = L

C -C 0 _{— =} , 4 ^ ( - l ) n 1 — > - —— exp CL- C 0

n£l2n + l

The mass of sorbed penetrant in sorption kinetic experiments, is measured as a function of time. The equation 5.13 can be integrated over the thickness of the film to give the sorbed mass. The result of the integration is (equation 5.9):

M, , ^

8

+ l)V 0

— L= l - > ---^ re x p — --- ^ --- (5.9)

M , S ( 2 n + l ) V I 4L

)

Where Mt is the mass sorbed at time t, and is the mass sorbed at equilibrium. In FTIR transmission spectroscopy at low absorbances, the relationship between the absorption of electromagnetic waves and the quantity of the absorbing material is expressed by the Beer-Lambert law given by:

dl = oddz = -eCIdz (5.14)

Where a is the absorption coefficient, 8 is the molar extinction coefficient, / is the light intensity at position z, and C is the concentration of absorbing group. The above equation can be integrated to give:

A = -\n<

1 k

I I 0

Where / 0 is the intensity of the incident light, I is the intensity of the transmitted light, A is the measured absorption, and 2L is the thickness over which the absorbing group is present. The absorbances given in equation 5.15 is analogous to the mass uptake in equation 5.9

since it involves an integration of the concentration profile over the film thickness.

However, the major disadvantage of using transmission spectroscopy to measure sorption kinetics in polymer samples with equation 5.15 is that it involves removing the polymer film from the penetrant bath and blotting prior to spectroscopic analysis.

In contrast to the transmission method, FTIR-ATR spectroscopy can provide information about the diffusion kinetics in situ. The details of this technique have been described in section 1.3. In ATR spectroscopy, the rarer medium absorbs specific frequencies of light in the evanescent wave, the reflection is frustrated and the reflected wave has a reduced intensity at these wavelenghts, resulting in an absorption spectrum. In order to combine

the evanescent field strength equation with the Beer-Lambert law, it is necessary to assume that only weak absorption occurs. With this assumption:

i = e-A* ( l - A ) (5.16)

•*■0 or

dl = - I 0dA (5.17)

Integration is from 0 to L. This is because in the ATR configuration, the diffusing

molecule only enters the film from one side. The decay of the evanescent field is given by:

E = E0 exp

2no7rjsin2 0 - —

(5.19)

where E is the electric field strength at the interface, nj is the refractive index of the rarer medium and ri2 is the refractive index of the propagating medium. Since I = E2, the field strength of the evanescent wave (E) can be substituted. Thus rewriting the expression for multiple reflection, N, as:

A = fNe'C Ej; exp

2n27ijsin 9 - |

dz (5.20)

Where e* = e/I0. Substituting equation 5.13, into equation 5.20 and integrating gives:

A « ~ A 0