Supporting information

Molecular understanding of sorption in mesoscale organizedzeolites with MFI structure

*Robin Kolvenbach, Luis Francisco Gonzalez-Peňa, Andreas Jentys, Johannes A. Lercher*

Department Chemie, Catalysis Research Center, Technische Universität München, Lichtenbergstr.4, 85748 Garching, Germany

**Corresponding Author**

*E-mail:

Content

(SI1) Materials

(SI2) Methods and Experimental procedures

(SI3) Supplementary figures

(SI4)References of Supplementary information

(SI1) Materials

Zeolite HZSM-5 with a Si/Al ratio of 45 (confirmed by AAS) was provided by Süd-Chemie AG. A concentration of 0.27 mmol g-1 for terminal (SiOH) and of 0.21 mmol/g for bridging (SiOHAl) hydroxyl-groups was determined using 1H-MAS NMR[1] n-pentane and n-hexane (Fluka, GC Standard, ≥ 99.8%) were used without further purification. n-butane was obtained from Air Liquide (purity ≥ 99.0%).

The modification of the zeolite surface by chemical liquid deposition (CLD) of tetraethyl orthosilicate (TEOS) was performed according to Zheng et al. [2, 3]. Following this procedure, 1.5 mL of TEOS and 10 g of zeolite were dispersed in 164.5 g of hexane and heated up to 353 K for 1 h under reflux. The hexane was evaporated in a rotary evaporator. The sample was dried at 343 K for 8 h and calcined at 823 K for 5 h. This procedure was repeated three times

**(SI2) Methods and experimental procedures**

**In-situ time-resolved infrared spectroscopy**

A Bruker IFS 66 v/s Fourier transform IR spectrometer was used to collect IR spectra during static sorption uptake and periodic pressure modulation experiments. For the sorption isotherms the spectrometer was run in standard mode, whereas it was operated in rapid scan mode for the uptake kinetic measurements. The spectrometer was combined with a high vacuum cell connected to a unit which allows generating a square wave pressure perturbation over the sample. This unit consists of two magnetically driven plates sealed with UHV bellows. The volume perturbation was kept as small as possible in order to avoid a temperature gradient over the sample, which would distort the transport significantly. On the other hand it was sufficiently large to obtain data with an appropriate signal to noise ratio. In our experiments a perturbation of ΔV=±5% was used as an optimum compromise between both effects.

The zeolite samples were inserted as self-supporting wafers into the vacuum IR cell and subsequently activated below 10-7 mbar at 823 K for 1 h (heating rate of 10 K min-1). Sorbate gas, i.e., n-butane, n-pentane or n-hexane, was added with partial pressure of 0.1 mbar at 343, 373 and 403 K. The sorbate partial pressure changes were followed by an in-line MKSBaratron (MKS 616A11) pressure transducer. A series of 100 IR spectra with time resolution of 600 ms was recorded during 400 modulation cycles.

All spectra were normalized to the lattice vibrations between 2105 and 1740 cm-1. The concentration of the sorbate molecules within the sample was obtained from integration of their characteristic CH stretching and bending vibrations, respectively, which were 3045-2745 cm-1 and 1406-1506 cm-1 for n-butane, 3020-2745 cm-1 and 1422-1517 cm-1 for n-pentane and 3020-2740 cm-1 and 1406-1506 cm-1 for n-hexane.

**Determination of concentration profiles**

The concentration on the external surface and inside the pores was calculated from the overall intensity profiles obtained by fast time resolved IR spectroscopy utilizing the differences in the molar extinction coefficients of the molecules present inside the zeolite channel system and at the outer surface of the zeolite particles. The intensity change in each spectrum collected in the series of time resolved spectra during the pressure modulation can be described for the CH-stretching or bending vibration by Eqs. (1) and (2):

(1)

(2)

With ΔICH-stretchand ΔICH-bendbeing the change in intensities of the IR-bands obtained from integration the IR-spectrum at the corresponding wavenumbers, ε is the respective extinction coefficient, w weight of the IR wafer, R is the radius of the IR wafer, ∆cint is the concentration change of the sorbate within the zeolite channel system and ∆cext is the concentration change of the molecules adsorbed at the external surface of the zeolite particle. The numerical solution of the two equations results ∆cint and ∆cext given by Eqs. (3) and (4):

(3)

(4)

The profiles of ∆cintand ∆cext can be obtained applying Eqs. (3) and (4) to each data point of the series of time resolved IR spectra collected during the periodic pressure modulations.

**Modeling of the transport network**

A sketch of the proposed transport network is shown in Figure 1. The concentration profiles ∆cint and ∆cext are described by a set of equations describing the uptake onto the external surface (including a pre-adsorbed state), the pore entrance step and the diffusion inside the micropores. The uptake onto the external surface and the pore entrance step are described by first order kinetic process as given in Eq. (5) and (6):

(5)

(6)

Where kads is the rate constant of the adsorption at the external surface, kpore entrance is the rate constant of transport from the external surface into the micropore and a is an additional factor describing the amount of molecules being in the pre-adsorbed state. By merging Eqs. (5) and (6) the concentration change on the external surface can be obtained (Eq. (7)):

(7)

The concentration change within the zeolitic micropores is described by the uptake kinetics of a sorbate into a microporous solid at isothermal conditions as described by Crank[4] for small concentration changes (constant D):

(8)

Both concentration profiles as well as their sums for either the CH-stretching or bending vibration were fitted using Eqs. (7, 8). The Arrhenius law was used in order to keep the amount of parameters as low as possible. By this means the activation energy of diffusion and the corresponding pre-exponential factor according to Eq. (9) were used as variables:

(9)

The parameters EA,D,app, D0,app, k and a were obtained by nonlinear parameter fitting using a CMA evolutional strategy implemented in MATLAB[5].

**Gravimetric sorption experiments**

The gravimetric sorption isotherms of n-butane, n-pentane and n-hexane on either silicon dioxide or ZSM-5 were measured in a Seteram TG-DSC 111 thermoanalyzer connected to a high vacuum system. About 35mg of the silicon dioxide or 20mg of the ZSM-5 sample was placed in a quartz sample holder and activated at 723K for 1 h under vacuum (p<10-4mbar) with an incremental heating rate of 10K min-1. The equilibration with the sorbate was performed in small pressure steps from 3x10-2 to 13mbar in case of the zeolite and from 3x10-2 to 150mbar for the silicon dioxide. In both cases the mass increase and the thermal flux were measured. The heat of adsorption was directly obtained by integration of the observed heat flux signal.

The adsorption isotherms were analyzed in terms of a dual site Langmuir model for the ZSM-5 (Eq. (10)) and a standard Langmuir isotherm (Eq. (11)) for the silicon dioxide.

(10)

(11)

Where K denotes the equilibrium constant of adsorption, n is the amount of sorbate on the sample, nmax is the maximum surface coverage of the individual adsorption site and p is the pressure. All three temperatures were analyzed simultaneously using the van’t Hoff equation in order to reduce the number of parameters.

**(SI3) Supplementary figures**

Figure S1

Figure S1: Nitrogen physisorption isotherms of the parent (a) and the surface modified sample (b) adapted from Ref. 1

Figure S2

Figure S2: αscomparitive plot[6] of the parent (a) and the surface modified (b) material adapted from Ref. 1. Two separated linear regions at αs=0.5, which corresponds to the micropore volume and at αs=1.2 corresponding to the sum of the micro- and mesopore volume were identified.

Figure S3

Figure S3: Gravimetric adsorption isotherm of n-butane (left), n-pentane (middle) and n-hexane (right) on H-ZSM5 at 343, 373 and 403 K. The fitting was performed according to a dual Langmuir formalism.

Figure S4

Figure S4: Gravimetric adsorption isotherm of n-butane (right), n-pentane (middle) and n-hexane (right) on fumed silica at 343, 373 and 403 K. The fitting was performed according to the Langmuir formalism.

Figure S5

Figure S5: Intensity (left axis) for the CH-stretching (left) and bending (right) vibrations and the by deconvolution obtained internal (orange) and external (magenta) concentration profiles (right axis) of n-pentane in parent H-ZSM5 at 343, 373 and 403K during a periodic volume perturbation around 0.1mbar.

Figure S6

Figure S6: Intensity (left axis) for the CH-stretching (left) and bending (right) vibrations and the by deconvolution obtained internal (orange) and external (magenta) concentration profiles (right axis) of n-hexane in parent H-ZSM5 at 343, 373 and 403K during a periodic volume perturbation around 0.1mbar.

Figure S7

Figure S7: Intensity (left axis) for the CH-stretching (left) and bending (right) vibrations and the by deconvolution obtained internal (orange) and external (magenta) concentration profiles (right axis) of n-butane in surface modified H-ZSM5 at 343, 373 and 403K during a periodic volume perturbation around 0.1mbar.

Figure S8

Figure S8: Intensity (left axis) for the CH-stretching (left) and bending (right) vibrations and the by deconvolution obtained internal (orange) and external (magenta) concentration profiles (right axis) of n-pentane in surface modified H-ZSM5 at 343, 373 and 403K during a periodic volume perturbation around 0.1mbar.

Figure S9

Figure S9: Intensity (left axis) for the CH-stretching (left) and bending (right) vibrations and the by deconvolution obtained internal (orange) and external (magenta) concentration profiles (right axis) of n-hexane in surface modified H-ZSM5 at 343, 373 and 403K during a periodic volume perturbation around 0.1mbar.

**(SI4) References of supplementary information**

1.Reitmeier SJ, Gobin OC, Jentys A, Lercher JA (2009) Angew Chem Int Edit 533:538

2.Zheng S, Heydenrych HR, Roger HP, Jentys A, Lercher JA (2003) Top Catal 101:106

3.Zheng SR, Tanaka H, Jentys A, Lercher JA (2004) J Phys Chem B 1337:1343

4.Crank J (1975) The Mathematics of Diffusion, Oxford University Press, Oxford

5.Hansen N(2006)Towards a New Evolutionary Computation. Advances on Estimation of Distribution Algorithms, Springer, New York.

6.Sing KSW (1970) Surface Area Determination, Butterworths, London

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