Facilitated transport of thiophenes through Ag 2 O-filled PDMS membranes

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Facilitated transport of thiophenes through PDMS membranes Rongbin Qi, Yujun Wang, Jiding Li *, Shenlin Zhu State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University. Beijing 100084, China Abstract Facilitated transport membranes of polydimethylsiloxane (PDMS) with silver oxide ( O) as the carrier were prepared and used for the separation of thiophenes/n-octane mixtures. The effect of the degree of O loading, feed temperature on the pervaporation properties of membranes was investigated experimentally. O-filling leads to an increase in selectivity to thiophenes but a decrease in total flux simultaneously. Feed temperature shows different impact on selectivity of thiophenes for and unfilled membranes because of the distinct transport mechanism within them. Selectivity-permeability trade-off was analyzed for and unfilled membranes. Keywords: Facilitated transport; Silver; Desulfurization of gasoline; Pervaporation 1. Introduction Organosulfur impurities present in gasoline produce SOx in automotive exhaust and consequently lead to severe environmental problems. Worldwide concerns over environment have inspired an increasing interest both in academia and industry for deep desulfurization of gasoline [1, 2]. As a membrane based separation technique, pervaporation possesses great predominance and potential for desulfurization of gasoline, in which the separation mechanism is based on the difference of sorption and diffusion properties of the feed compounds. In our previous work [3, 4, 5], PDMS was selected for pervaporative desulfurization of model gasoline. PDMS/PAN composite membranes were prepared and characterized for the purpose. With n-octane/thiophene as the primary components making up model gasoline, the fundamental problems in relation to the mechanism and contributing factors in the desulfurization process of gasoline by pervaporation were investigated. Experimental results showed that PDMS membrane is selective for thiophenes and considerable fluxes were gained. However, the separation of thiophene/hydrocarbon mixtures has not been much effective because the physico-chemical properties of thiophenes and various hydrocarbons are not efficiently distinguishable. According to the analysis of Robeson [6], greater permeability and higher selectivity couldn t be achieved simultaneously within solution-diffusion mechanism when using conventional polymeric membranes. But in heterogeneous membranes consisted of a polymeric phase and certain carrier particles, the reversible reactions between carrier and penetrant provide another transport mechanism through the membrane in addition to the solution-diffusion. Thanks to the complexation reaction between silver ion (Ag + ) and the double bonds of the solute, Ag + is mostly used as the carrier for the facilitated transport of unsaturated hydrocarbons [7, 8, 9]. Investigation *Corresponding author. Tel. +86 10 62782432; Fax: +86 10 62770304 E-mail: lijiding@mail.tsinghua.edu.cn 1

on desulfurization of transport fuels by adsorption also confirmed the existence of strong π-complexation bond between Ag + and thiophene or substituted thiophenes [10, 11]. Therefore, Ag + -containing salts or oxides could be reasonably employed to promote the transport of thiophenes within the membrane. In current work, O was taken as the filler for preparation of the fixed-site carrier PDMS membranes, in which the facilitated transport of thiophenes was expected. With the mixture of n-octane/thiophene/2-methyl-thiophene as the model gasoline, the pervaporative desulfurization performance of membranes was investigated. Contributing factors including O contents in the membranes, feed temperature were evaluated experimentally. 2. Experimental Ethyl orthosilicate, dibutyltin dilaurate, n-heptane (Beijing Chemical Company, China) were purchased for the preparation of PDMS membrane. Silver oxide ( O, Beijing Beihua Fine Chemical Co. Ltd., China) was ground with a muller before used as the membrane filler. Asymmetric microporous PAN membrane (provided by Beijing Megavision Membrane & Engineering Co. Ltd., China) was employed as supports. n-octane (China Medicine (Group) Shanghai Chemical Reagent Corporation), thiophene (Tianjin Chemical Company, China) and 2-methyl-thiophene (98% pure, Acros) were chosen as the representative components making up the model gasoline. PDMS, crosslinking-agent ethyl orthosilicate and catalyst dibutyltin dilaurate were dissolved in n-heptane at ambient temperature. Silver oxide was added into the solution under stirring. The resulting suspension was then sonicated for 30 minutes to promote the dispersion of silver oxide powder. After degassed under vacuum, the solution is cast onto the PAN membrane. The membrane was first vulcanized under room temperature to evaporate the solvent, and then introduced into a vacuum oven to complete crosslinking. Membranes with the following degree of O-filling were prepared and used in current work: 100 wt% PDMS-0 wt% O, 98 wt% PDMS-2 wt% O, 95 wt% PDMS-5 wt% O, 92 wt% PDMS-8 wt% O, 90 wt% PDMS-10 wt% O. Pervaporation experiments were carried out in a continually fed cell. Details of the apparatus and the measurement procedure are available elsewhere [3, 4]. Compositions of feed and permeate were analyzed by gas chromatography (HP6890, USA). Enrichment factor k i defined as follows is adopted to characterize the separation performance of the membrane: ω k i = (1) ω P i F i F P where k i is the enrichment factor for component i; ωi and ωi refer to the weight fraction of component i in the feed and permeate respectively. 3. Results and discussion 3.1 SEM analysis of membrane SEM characterization of the membrane was carried out to investigate the dispersion of O particles in the polymeric phase of the membrane. From the SEM photographs in Fig.1, it can be seen that the porous PAN substrate is covered by a flat faultless layer. In the dense top layer, O particles are uniformly dispersed and well adhesive with PDMS matrix. No 2

nonselective voids could be found on the carrier-solute interface. Fig.1. Cross-section and top surface morphologies of the membrane. 95 wt% PDMS-5 wt% O;(A) Cross-section and (B) top surface 3.2 Effect of O contents on pervaporation properties With n-octane as the main component of gasoline, along with thiophene and 2-methyl-thiophnene as the representative organosulfurs present in gasoline, the sulfur removal performance of the membranes were investigated experimentally. The corresponding sulfur content in the feed is about 1000μg/g, with the mole ratio of thiphene and 2-methyl-thiophene 1:1. Total flux (kg/m 2 h) 6 5 4 3 30 50 70 2 1 0 2 4 6 8 10 O content in membrane (wt%) Fig.2. Effect of O content on total flux Fig. 2 demonstrates the effect of O content on total flux of the model gasoline under different feed temperatures. It can be seen that, with the increase of O loading in PDMS membranes, total fluxes decrease and higher feed temperature makes this trend more evident. Owing to the ultra low concentrations of thiophene and 2-methyl-thiophene in the model gasoline, the majority of feed and permeate is n-octane. Within the fixed-site carrier PDMS membranes, the 3

primary transport mechanisms for permeating molecules include the diffusion through the polymeric phase, diffusion through pores of the carrier, sorption onto the carrier, surface diffusion in the carrier and desorption from the carrier. For n-octane, the filled O particles are inert and completely impermeable. The diffusivity of n-octane would decrease due to the tortuosity effect and the total flux decrease accordingly. Higher feed temperature would make the components more permeable through the membrane, which leads to a more prominent effect of the O filling on the permeating flux. On the other hand, a complexation reaction as Eq. (2) exists between Ag + ion and C=C double bonds in thiophenes: (2) According to RC circuit model [12, 13], the continuous reversible reaction between the carrier and solute would result in fluctuation of local concentration in the membrane, which leads to a higher free energy, a higher chemical potential and a higher flux for the desired component. Consequently, the above complexation would accelerate sorption onto and desorption from the carrier particles and facilitate transport of thiophenes. Selectivity to thiophenes would increase because of the facilitation effect in O filled membranes. This is verified by the experimental findings shown in Figs. 3 and 4. With the membranes having a normalized top layer of 15μm, when O loading increases from 0 to 5 wt%, the total fluxes decrease from 3.31 to 2.85 kg/m 2 h at 50, while the corresponding enrichment factors increase from 3.55 to 4.46 and from 2.24 to 2.61 for thiophene and 2-methyl-thiophene respectively. 6.0 5.5 30 50 70 Enrichment factor 5.0 4.5 4.0 3.5 2.5 0 2 4 6 8 10 O content in membrane (wt%) Fig.3. Profiles of thiophene enrichment factor with O loading 4

3.2 2.8 30 50 70 Enrichment factor 2.6 2.4 2.2 2.0 1.8 0 2 4 6 8 10 O content in membrane (wt%) Fig.4. Profiles of 2-metyl-thiophene enrichment factor with O loading 3.3 Effect of feed temperature on pervaporation properties Effect of feed temperature on the pervaporative desulfurization efficiency using PDMS membranes was also evaluated experimentally. Fig. 5 illustrates the total flux variation versus feed temperature. Without exception, all the experimental evidence confirms an increase in permeability with increasing feed temperature for both and unfilled membranes. Two parallel impacts of temperature on the permeant and membrane should be responsible for this: one is the increase of the mobility of individual permeating molecules which promotes their movement both in the bulk feed solution and within the membrane, one is the enhanced mobility of the polymer segments which offers more free volume for permeating molecules to occupy. As a minor contributing factor, changes occurring on the carrier-polymer interface play a certain role in the results obtained. 5.5 Total flux (kg/m 2 h) 5.0 4.5 4.0 3.5 2.5 2% 5% 2.0 1.5 30 40 50 60 70 Feed temperature( ) Fig.5. Temperature dependence of total flux in and unfilled membranes 5

As shown in Figs. 6 and 7, the increase in the degree of swelling of the membrane with temperature results in a decrease in selectivity to thiophenes. Additionally, experimental results indicats that extent to which feed temperature affects the enrichment factors of thiophenes is different in filled and unfilled membranes. It is so mainly because the transport of thiophenes in and unfilled membranes are dominated by different mechanism. Theoretically, the total flux of the permeant through the carrier-filled membrane is the sum of two different parts: one is the solution-diffusion flux of uncomplexed species, one is the facilitated flux of solute due to the carrier-solute complexation. In PDMS membrane, the facilitated fluxes of thiophenes lie on the reversible reaction between Ag + and thiophenes, while the solution-diffusion fluxes of thiophenes in pure PDMS membrane are determined by the solution and diffusion properties theirof. 6.0 Enrichment factor 5.5 5.0 4.5 4.0 3.5 2% 5% 2.5 30 40 50 60 70 Feed temperature( ) Fig.6. Effect of temperature on selectivity to thiophene 2.8 2% 5% Enrichment factor 2.6 2.4 2.2 2.0 30 40 50 60 70 Feed temperature( ) Fig.7. Effect of temperature on selectivity to 2-methyl-thiophene 6

3.4 The upper bound curve for thiophenes/n-octane separation Using the data for a large number of membranes, Robeson qualitatively constructed an upper bound curve for gas separation process, in which the selectivity of the more permeable gas was plotted as a function of its permeability on a log-log scale [6]. Nearly all the data cluster below the upper bound implies that there is a trade-off for the polymeric membranes between the permeability and selectivity. However, it has been demonstrated that facilitated transport membranes would not comply with such a rule. 8 7 Thiophene/n-octane selectivity 6 5 4 3 Upper bound 8 9 10 20 30 40 50 60 70 80 Thiophene permeability (10-8 m 2 /h) Fig. 8. Selectivity-permeability trade-off curve of PDMS membranes for separation of thiophene/n-octane mixtures 2-Methyl-thiophene/n-octane selectivity 2.8 2.4 Upper bound 2 4 5 6 7 8 9 10 20 30 40 50 2-Methyl-thiophene permeability (10-8 m 2 /h) Fig.9. Selectivity-permeability trade-off curve of PDMS membranes for separation of 2-methyl-thiophene/n-octane mixtures 7

Based on the experimental data gained in our earlier work, the upper bound curves for separation of n-octane/thiophene and n-octane/2-methyl-thiophene mixtures using unfilled PDMS membranes are constructed. Just as shown in Figs. 8 and 9, PDMS membranes can surpass the limit of the upper bound owing to the facilitated transport mechanism within the process. The above experimental results suggest that facilitated transport brings improvement in selectivity to thiophenes, but the total flux decrease slightly because of the tortuosity effect. In order to get more effective performance of facilitated transport for the solute, more active sites should be provided for the reversible complexation reaction between C=C bond and Ag + ion. But increasing the carrier loading would make the tortuosity effect sharpen. Accordingly, more fine O powder with more specific area should be used. And more, relatively regular shape and unity of O powder would reduce the sharpness of the powder surface and avoid the formation of dead end, which to some degree reduce the tortuosity effect and eliminate the formation of voids on the carrier-solute interface. 4. Conclusions O powder was taken as the active filler to prepare PDMS/PAN composite membranes for the purpose of gasoline desulfurization. SEM characterization indicates that O particles can uniformly disperse into the polymeric phase and are well adhesive with the PDMS matrix. With n-octane and thiophenes making up model gasoline, the effect of the degree of O loading, feed temperature on the pervaporation properties of membranes was investigated experimentally. O-filling leads to an increase in selectivity to thiophenes because of the facilitated transport of thiophenes induced by the complexation between Ag + and double bonds in thiophenes, as well as a decrease in total flux owing to the tortuosity effect of the impermeable O particles. With the rise of feed temperature, the total flux increases but the selectivity to thiophenes decreases simultaneously. Because the transport of thiophenes in and unfilled membranes were dominated by different mechanism, the extent to which feed temperature affects the selectivity to thiophenes is different. For the membranes with a normalized top layer of 15μm, when O loading increases from 0 to 5 wt%, the total fluxes decrease from 3.31 to 2.85 kg/m 2 h at 50, while the corresponding enrichment factors increase from 3.55 to 4.46 and from 2.24 to 2.61 for thiophene and 2-methyl-thiophene respectively. Selectivity-permeability trade-off curves of PDMS membranes using both the earlier and current data were constructed for separation of thiophene/n-octane and 2-methyl- thiophene/ n-octane mixtures. Nearly all the data for membranes locate above the upper bounds for pure PDMS membranes, which implies that O-filling results in improvements in both selectivity and permeability for thiophenes. Acknowledgement The authors would like to express their gratitude to Ministry of Science and Technology of China for the financial support (National 973 Project, No. 2003CB615701). References [1] S. Brunet, D. Mey, G. Pérot, C. Bouchyb, F. Diehl, On the hydrodesulfurization of FCC gasoline: a review, Applied Catalysis A, General 278(2005) 143. 8

[2] X. Ma, C. Song, A new approach to deep desulfurization of gasoline, diesel fuel and jet fuel by selective adsorption for ultra-clean fuels and for fuel cell applications, Catal. Today, 77 (2002) 107 [3] R. Qi, C. Zhao, J. Li, Y. Wang, S. Zhu, Removal of thiophenes from n-octane/thiophene mixtures by pervaporation, J. Membr. Sci. 269(2006) 94 [4] R. Qi, Y. Wang, J. Li, C. Zhao, S. Zhu, Pervaporation separation of alkane/thiophene mixtures with PDMS membrane, J. Membr. Sci. 280(2006) 545 [5] R. Qi, Y. Wang, J. Li, C. Zhao, S. Zhu, Sulfur removal from gasoline by pervaporation: the effect of hydrocarbon species. Sep. Purif. Technol., in press [6] L. Robeson. Correlation of separation factor versus permeability for polymeric membranes. J. Membr. Sci., 62 (1991) 165 [7] J. Kim, J. Won, Y. Kong. Silver polymer electrolytes by π-complexation of silver ions with polymer containing C=C bond and their application to facilitate olefin transport membranes. J. Membr. Sci., 237 (2004) 199 [8] Y. Park, J. Won, Y. Kang. Facilitated transport of olefin through solid PAAm and PAAm-graft composite membranes with silver ions. J. Membr. Sci., 183(2001) 163 [9] I. Pinnau, L. Toy. Solid polymer electrolyte composite membranes for olefin/paraffin separation. J. Membr. Sci., 184 (2001) 39 [10] A. Morisato, Z. He, I. Pinnau, et al. Transport properties of PA12-PTMo/AgBF4 solid polymer electrolyte membranes for olefin/paraffin separation. Desalination, 145 (2002) 347 [11] D. Bryant, R. Noble, C. Koval. Facilitated transport separation of benzene and cyclohexane with poly(vinyl alcohol)-agno 3 membranes. J. Membr. Sci., 127 (1997) 149 [12] Y. Kang, J-M Hong, J. Jang, et al. Analysis of facilitated transport in solid membranes with fixed site carriers-i. Single RC circuit model. J. Membr. Sci., 109 (1996) 149 [13] J-M Hong, Y. Kang, J. Jang, et al. Analysis of facilitated transport in solid membranes with fixed site carriers-ii. Series RC circuit model. J. Membr. Sci., 109 (1996) 159 9