Probing the Depth-Dependence of Molecular Sieve Membrane Composition by Step-Scan Photoacoustic (SS-PAS) Spectroscopy

We report the quantitative, non-destructive determination of the concentration profile of an organic molecule in a nanoporous polycrystalline zeolite molecular sieve membrane, by step scan infra-red photoacoustic experiments and analysis. An important application of stepscan photoacoustic spectroscopy is the transport-model-independent experimental description of membrane transport, by simultaneous measurement of the concentration profile, membrane thickness and membrane flux. A heterogeneous zeolite membrane model system was constructed by growing a zeolite MFI layer on a macroporous α-alumina substrate. Step scan photoacoustic spectroscopy is then used with a large range (10-500 Hz) of incident signal modulation frequencies to obtain a series of depth-dependent infra-red spectra. Ordered nanoporous materials deposited in the form of 1-100 micron films or membranes are receiving a great deal of attention for a range of technological applications including molecular sieving membranes for separations, catalytic membrane reactors, and templates for guest materials such as nanowires, nanotubes and nanoclusters. The knowledge of spatially-resolved membrane composition, particularly the distribution of the guest species as a function of depth, is highly desirable in these applications. However, quantitative profiling methods such as energy-dispersive X-ray analysis and IR microscopy are destructive (i.e. they require cross-sectioning the sample). Moreover, the microscopic mass transport properties of guest species in molecular sieving membranes depend strongly on their local concentration. Since intra-membrane concentration profiles have thus far been inaccessible experimentally, theoretical models (e.g., Maxwell-Stefan, atomistic, or mesoscopic) are required to interpret available experimental information (viz. the trans-membrane flux measured at different feed pressures and temperatures). One important application of step-scan photoacoustic spectroscopy is the transport-model-independent characterization of membrane transport by simultaneous measurement of the permeant concentration profile, membrane thickness, and trans-membrane flux. In this work we experimentally demonstrate for the first time the quantitative, nondestructive measurement of concentration profile of TPA structure directing species in a nanoporous model zeolite MFI membrane system. We exploit the technique of step scan photoacoustic spectroscopy (SSPAS) for this purpose. In SSPAS, infra-red radiation modulated (chopped) at an acoustic frequency (in the 5-1000 Hz range) is absorbed by a sample and converted to heat, which propagates out of the sample as an acoustic wave to create modulated pressure in the gas surrounding the sample in the cell. This signal is detected by a sensitive microphone and transformed to an infra-red spectrum. The depth (μs) over which the thermal signal is generated, is directly related to the modulation frequency (f) as μs = (α/πf). Here α is the thermal diffusivity (m/s) of the material. Depth-dependent information can be obtained by varying the modulation frequency. The use of a step scan interferometer allows the chosen modulation frequency to provide the same sampling depth over the entire spectral range. We first derive a simple analytical expression describing the strength of the photoacoustic signal from a membrane of continuously varying composition, and discuss its application in conjunction with SSPAS measurements to concentration-profile a model zeolite MFI membrane system. The photoacoustic signal density arising from a depth x in the sample, taking into account incident light absorption as well as propagation of the resultant acoustic wave through the solid, is given by: s / x e e I μ β β − − = (1) where β is the optical absorption coefficient (or alternatively, the sum of absorption coefficients associated with each of the vibrational bands of the solid) . The optical absorption length μβ, is defined as β μβ / 1 = . For a thermally homogeneous (i.e. thermal diffusivity practically constant with depth) and optically heterogeneous (i.e. depth-dependent optical absorption) sample, the photoacoustic signal intensity (Q) for a particular sampling depth can be expressed as: ( ) ∫ − + − = s 1 s 0 dx e K Q μ μ β β (2) where K is a system-dependent constant. For the case of an organic-templated zeolite membrane, we now express the local absorption coefficient at depth x, as ) ( 1 0 x C β β β + = , where β0 is the optical absorption coefficient of the inorganic zeolite membrane, β1 is the absorption coefficient per unit concentration of the organic guest species, and C(x) the depthdependent concentration if the guest species. Equation (2) becomes: ( ) ∫ − + + − + = s 1 s 1 0 0 x ) x ( C 1 0 dx e )) x ( C ( K Q μ μ β β β β (3) Equation (3) can be conveniently used to depth-profile a membrane with an unknown concentration profile. This can be done by writing the integral as a discretized summation over a number of layers, each representing increments in the sampling depth. By carrying out SSPAS experiments at progressively decreasing modulation frequencies (i.e. progressively increasing sampling depths), the concentration within each incremental layer can be determined sequentially. Here we demonstrate a case where an analytical solution of (3) is used with a deliberately engineered concentration profile. A double-layered membrane (Figure 1a) is constructed, composed of an upper membrane layer with an evenly distributed guest species and a lower layer without guest species, supported on a substrate. For this system, C(x) is a step function with magnitude C0 (0L1). The host membrane concentration is constant upto a depth L2 and zero beyond. Figure 1b shows a schematic of the membrane.