A typical granular interference pattern named “speckle” is observed [9] [10] when a coherent beam coming from a laser illuminates a rough object. Besides, a laser light scattered from diffuse objects produces a similar pattern.

If this surface presents some type of local movement, then the intensity pattern evolves in time. This phenomenon, known as “dynamic laser speckle” (DLS), can be observed in biological samples [9] and in non-biological industrial processes, including the drying of paint, corrosion and heat exchange [10] . This effect takes place when the sample changes its surface properties due to the movement of the scattering centers; changes in the optical path due to variations of refractive index; configuration changes or combination of these situations [10] . The temporary evolution of the speckle patterns is correlated with the “activity” of the sample and may provide an interesting tool to characterize the parameters involved in these processes. In this case, the speckle patterns showed a high activity for the initial hydro-adsorption process and it is minimal when this process is complete.

LOI: Loss on ignition.

We propose a DLS method to characterize the water adsorption of the zeolite. We employed a 10 mW He-Ne laser to illuminate the samples. Dynamic speckle pattern were recorded with a CCD camera connected to a frame grabber to digitize the images as shown in Figure 1. During this process, 30 mg of each zeolite sample were impregnate with 10μl distilled water. The total experiment was carried out at 19˚C and 60% of humidity.

We used Oulamara et al. method [9] to show the temporal evolution of speckle. In our case, 320 successive images (25 frames per second) of dynamic speckle were recorded for each state of the adsorption process and selecting a column of them. With these columns, a pseudo-image of 320 × 240 was constructed and so-called Temporary History Speckle Patterns (THSP).

The speckle activity of the sample changes their intensity in the horizontal direction. Therefore, when a phenomenon shows low activity, time variations of the speckle pattern are slow and the THSP shows elongated shape. When the phenomenon is very active, the THSP resembles an ordinary speckle pattern. See Figure 2.

The moment of inertia of the co-occurrence matrix method [10] was used for a quantitative estimate of THSP. The moment of inertia is defined by:

where represents the number of occurrences of the gray-level i followed in the time direction by gray-level in the THSP image, which forms an intermediate matrix called a co-occurrence matrix.

In our case, the initial value of I decreases as the water is adsorbed by the zeolite surface until reaching the steady state, thus it is directly related to the adsorbed water amount.

For modeling the amount of adsorbed water on solids vs. time, different models have been reported [13] - [23] .

Hawkes and Flink [13] studied the kinetics of water loss and solute uptake for solutions of differing composition and concentration. Several of the osmotically pre-concentrated freeze dried apple slices for organoleptic acceptability were evaluated using the following equation:

where is the normalized solids, is defined as the mass transfer coefficient and is the time.

Azuara et al. [14] [15] [16] developed a two-parameter equation from mass balance considerations. This equation was used to predict the kinetics of osmotic dehydration and the final equilibrium point in cereals and fruits [14] :

In Equation (3a), WFL is the water lost by the foodstuff at time t, is a constant related to water loss and is the water lost at equilibrium. In Equation (3b), is solids gained by the foodstuff at time, is a constant related to solids gain and is the amount of solids gained at equilibrium.

Finally, Peleg [17] developed an empirical model for sorption curves in the form of moisture vs time relationships of milk powder and rice, exposed to moist atmosphere or soaked in water. The model enabled prediction of moisture contents after long exposure from experimental data obtained in a relatively short time, i.e., before the moisture level appeared to reach a plateau. The model implied that the moisture equilibrium was somewhat higher than that determined on the assumption that the sample reached a constant weight, [17] - [23] :

where is the moisture after time, the initial moisture, and are constants.

In this paper, we try to use the expressions of the reported models applied to the data (moment of inertia) obtained by dynamic speckle technique.

Taking into account the above considerations, Equations (2)-(4) must be modified and turned into:

“” Hawkes and Flink variable is set as the remaining water instead of adsorbed water, then Equation (2) could be stated as:

where “”, represents the amount of initial water standardized.

So, in dynamic speckle technique we use the expression:

where is the moment of inertia as a function of time, is the initial moment of inertia and represents the water remaining on the surface of the zeolite,

Azuara’s et al. model equation became:

where is the steady state moment of inertia.

Peleg’s model equation became:

where is the steady state moment of inertia and is the initial variation of moment of inertia.

Clinoptilolite used in this work is a heulandite-type, with chemical composition (Na,K)₆(Al₆Si₃₀O₇₂)∙20H₂O previously reported [8] [24] [25] . Data are included in Table 1.

The framework topology of this mineral consists of a two dimensional pore system formed by 8-ring channels linking together [2] . This channels disposition allowed to zeolite has good adsorption properties for CO₂, SO₂, NH₃ and NO_x gases [27] [28] [29] [30] .

The cation exchange capacity (CEC) of this material has been previously determined and a value of 330 meq/100 g was found [28] .

Chemical and physical properties of the zeolite can be modified with either inorganic basic or acid solutions. This fact mainly depends on the Si/Al ratio.

The acid treatment conduces to the alumination process from the alumino-silicate structure removing Al³⁺-ions progressively. On the other hand, an increase of the temperature or alkalinity reduces the silica content, due to dehydration processes and SiO₂ dissolution. This treatment also promotes the process of ion exchange cation (Na⁺ or K⁺)-H⁺. In basic treatment using, amoniacal solution, the silanol groups surface (hydroxyl) SiO₂∙OH, acquires a great concentration of -OH groups. Therefore, under this condition, the NH₄⁺ cations can be easily exchanged by other ions like Na⁺ or K⁺. All these reactions produce chemical surface modifications that are evidenced by changes in the composition, in textural and structural properties, which could be analyzed by different physical-chemical analysis techniques.

Textural properties, surface area, volume and pores size, have been analyzed with nitrogen physic-sorption isotherms by BET model. The measure was carried out for pure and modified samples with acid, basic treatment included the two calcinated samples. The results found together with some SEM-EDS chemical data are reported in Table 2.

The values obtained are typical for natural zeolites, however a noticeable change for zeolite calcinated at 500˚C was observed. In this case the S_BET value was almost double and the pore size was lower than those the other samples.

Table 2 shows the composition of the minerals. It should be noted that the composition of the exchangeable cations, especially Na⁺ for Z-H⁺ and Z-NH₄⁺ is lower than that of the unmodified mineral.

Figure 3 shows the comparative X-Ray diffraction patterns. The Z-N pattern is in agreement with the PDF 79-1461 previously reported [8] . All samples show the similar patterns, indicating that the structure does not change with the different treatments. However, X-ray diffraction lines of the calcinated samples are slightly shifted to lower 2θ probably due to the increase of the cell volume. On the other hand, the X-ray diffraction lines of the Z-H⁺ and Z-NH₄⁺ samples are slightly shifted to the higher 2θ suggesting a decrease of the volume cell in agreement with the low percentage of the Na⁺ (see Table 2).

Figure 4 shows the infrared spectra of the samples. The bands observed around 3600 cm⁻¹ and 1600 cm⁻¹ are assigned to stretching and bending modes of the water molecules. The bands located at 3424 cm⁻¹ are associated with the stretching of -OH groups from water molecules coordinated to cationic species, which are interacting with the covalent network that leads to hydrogen bonds of different sizes. The bands between 1200 and 400 cm^-1 are assigned to the stretching and bending modes of the T-O units (T = Si or Al) due to the [29] TO₄ tetrahedral groups (SiO₄ and AlO₄). The bands observed at 1206 and 607 cm⁻¹ are assigned to the asymmetric and symmetric stretching

modes of internal tetrahedral. The bands at 1053 and 794 cm⁻¹ are associated with the asymmetric and symmetric stretching modes of external linkages [30] , respectively.

The spectra of the acid form of the zeolite show that the external asymmetric mode ν_a T-O-T is lightly shifted to higher wave numbers respect to the natural zeolite. In this spectrum two new bands appear. One of them, located at 1384 cm⁻¹ is attributed to asymmetric stretching modes of the NO₃ bonds from the surface nitrate group which was generated by the HNO₃ treating. The other one, observed at 955 cm⁻¹ is assigned to Si-OH stretching mode of typical Brønsted acid site.

The spectrum of Z-NH₄⁺ shows in 3900 to 3200 cm⁻¹ range, bands assigned to the N-H stretching due to the presence of NH₄⁺ bonded to the surface. The band at 1632 cm^-1 results from the superposition of the ammonium component and the mode corresponding to the bending vibrations of adsorbed H₂O. The presence of ammonium FTIR bands suggest the adduct formation between the ion and Brønsted acid sites of the zeolite [31] [32] .

FTIR spectra of the samples do not show significant changes with the temperature in agreement with the X-ray diagrams. This fact is probably due to the high thermal stability of the structure [33] [34] .

Table 3 shows the relevant bands and their tentatively assignment of the samples.

Figure 5 shows the experimental data for original zeolite (Z-N) obtained with DLS technique (vs. time) (gray dots). Initial speckle activity decays monotonically to achieve stability in about 100 seconds.

Then, the experimental data were fitted using moment of inertia in Equations 6-8, and revealed the following values: a) Hawkes and Flink model [13] : [k = −12.9375, , [Equation (6)], (short blue dashes), b) Azuara et al. model [14] [, , ,) [Equation (7)] and c) Peleg [17] [, , ,) [Equation (8)] were applied (long red dashes).

From Figure 5, it can be observed that the best fit is obtained with the Peleg’s and Azuara’s et al. models which fit the data with the same curve.

Ref.: (a) External modes; (b) Internal modes.

These mathematical approaches are equivalent and produced the same results with the experimental trend but with a high error data. This effect is probably due to the zeolite containing micro and small mesopores, which produce greater water adsorption rate, so the first-order equation did not fit the experimental results. Then, we propose a new approach modifying the equation of Peleg, extending to the second order:

where, , , and.

Figure 5 shows that the fitting of the data is substantially improved with this approach. Also coefficient is close to one, showing that our approach is the best fit for the experimental data.

Taking into account the good fit for Z-N, the method was also applied for Z-H⁺, Z-NH₄⁺, Z-250 and Z-500 samples, in order to obtain the DLS activity (Figures 6 (a)-(d)). Data fitted to the experimental values are shown in Table 4.

Derivation of the Equation (9), the I rate of change vs time was obtained. Figure 7 shows the curves for all samples.

The I rate of change for the Z-N is the highest comparing with the other samples. (see Figure 7 black line). It reaches a faster saturation adsorption at small times.

However, the behavior is different for the other samples, especially for those thermally treated where the rate of change at small times is slow and saturation occurs at larger times for high temperature (Z-500). This effect is probably due to the decrease in the average pore size (see Table 2) because external (adsorbed water) and internal (coordinated water) dehydration were produced by the calcination processes.

Therefore, the reversible process will require the formation of new hydrogen-bridges to achieve rehydration of the pores. This process will be slower than for unheated samples. In previous report [34] , thermo-gravimetric analysis (TG) of clinoptilolites showed significant mass loss up to 500˚C, due to the loss of water coordinated to the intra-network ions (Na⁺ and K⁺). The complementary differential analysis (DT)

revealed two endothermic peaks at 167 and 500˚C [35] . This effect is in agreement with the existence of two different kinds of water molecules, adsorbed and coordinated molecules, respectively. For that reason it is expected that the rehydration process for the sample heated at 250˚C will be faster than that at 500˚C.

Regarding acid and base modified samples, the I rate of change behavior for Z-H⁺ resulted similar to Z-N. However, this value is slightly higher for Z-NH₄⁺ (Figure 7). This fact could be explained by the different sodium and potassium percentage (See Table 2), which resulted higher in the Z-H⁺ sample than in the Z-NH₄⁺ one. Na⁺ and K⁺ cations are the normal sites for the intra-network water adsorption and acidic zeolite resulted from the exchange of these cations by protonated ion species (H⁺), giving rise to the formation of new hydrogen-bridges. This effect facilitates rehydration of Z-H⁺ intra-network pores and a good hydro-adsorption capacity.

For Z-NH₄⁺, ammonium is also easily exchanged with Na⁺ and K⁺ ions, replacing the intra-network cations by “NH₄OH” groups. This fact produces a steric effect in the pores and a slower rate of water molecules adsorption than the acid sites provided by Z-H⁺. This behavior is consistent with an intermediate speckle activity for Z-NH₄⁺ (See Figure 7).