As to the diffusivities of benzene in silicalite-1, most of the experimental data reported in the literature at specific temperatures are within one, or at most, two orders of magnitude.¹³

These experimental diffusivity values were mostly measured at low loadings.

At high concentrations, the diffusivities are, however, much less documented due to the very strong sorbate–sorbate interactions between the sorbed benzene molecules at high loadings which make the measurements difficult and with some techniques impossible.

The FR technique used in this study is a quasi-steady state relaxation technique in which a parameter influencing the equilibrium state of the system is perturbed periodically at a particular frequency.

An outstanding advantage of the frequency-response technique is its ability to characterise multi-kinetic processes which may be present in a FR spectrum over a broad range of time constants.

Over the past decade, the FR technique has been extensively studied both experimentally and theoretically and has proved to be a powerful method for determining intracrystalline mass transfer of molecules through zeolite crystals.^{16–18,46–52}

In our frequency response method an equilibrium state is perturbed by applying a square-wave modulation to the volume of the gas phase.

The theoretical solutions of the frequency-response technique have been comprehensively developed over the past decade.

The full FR parameters (phase lag and amplitude) are experimentally derived from a Fourier transformation of the volume and pressure square-waves.

The phase lag Φ_Z−B = Φ_Z − Φ_B is obtained, where Φ_Z and Φ_B are the phase lags determined in the presence and the absence of zeolites, respectively.

The amplitude is embodied in the ratio P_B/P_Z, where P_B and P_Z are the pressures response to the ±1% volume perturbations in the absence and presence of sorbents, respectively.

From the solution of Fick's second law for the diffusion of a single diffusant in a solid subjected to a periodic, sinusoidal surface concentration modulation, the following equations can be obtained⁴⁷in-phase: (P_B/P_Z) cos Φ_Z−B − 1 = Kδ_in + Sout-of-phase: (P_B/P_Z) sin Φ_Z−B = Kδ_outwhere K is a constant related to the gradient of the adsorption isotherm, S is a constant that represents a very rapid adsorption/desorption process, which may co-exist with the diffusion process being measured, δ_in and δ_out are the overall in-phase and out-of-phase characteristic functions, respectively, which depend on the theoretical models describing the overall kinetic processes of a system.

These theoretical models have been comprehensively developed over the past decade^{46,47,49,50,57}.

The principal features of the FR apparatus developed in our group have been previously described.⁵¹

The silicalite-1 zeolite samples used in this study are summarised in Table 1.

The formation of such strong sorbate–sorbate chains of molecules has been proposed by Sacerdote and Mentzen et al⁵. by comparing X-ray powder diffraction data and calorimetrically determined differential adsorption heats, with computer simulated atom–atom interactions for this system at a loading of 8 m. u.c.⁻¹

X-ray and FT-Raman investigations^4,5,32 presented a conformation of benzene molecules sorbed in silicalite-1 at loadings between 4 and 6 m. u.c.⁻¹ with four molecules located at the intersections and the other added molecules occupying the sinusoidal channel segments.

For loadings higher than 6 m. u.c.⁻¹, four molecules remain in the intersections and the rest of the benzene molecules move to the straight channel segments forming infinite chains in the straight channels.

Neutron diffraction studies³⁵ showed that up to a loading of 4 m. u.c.⁻¹, the sorbed benzene molecules fill the intersections.

At a loading of 6 m. u.c.⁻¹, the two additional molecules are located in the straight and sinusoidal channel segments, respectively, to form dimers with the molecules already in the intersections.

The sorbed benzene molecules at the higher loading of 8 m. u.c.⁻¹ occupy the three types of sites in a new arrangement of interconnected chains.

The results deduced by ¹³C CP NMR spectra clearly showed an increase in the molecular mobility of the sorbed benzene in MFI zeolites with a high concentration of structural defects.⁷¹

Obviously, structural defects handicap the formation of clusters.

The increase in diffusivity of benzene in silicalite-1 with increase in loading was detected by Shah et al. using a gravimetric technique and large crystals.²⁴

This technique is, however, not able to distinguish different kinetic processes occurring in the system and the explanation for this phenomenon offered by Shah et al. is not satisfying.