MIXED GAS TRANSPORT STUDY THROUGH POLYMERIC MEMBRANES: A NOVEL TECHNIQUE

Transcription

1 MIXED GAS TRANSPORT STUDY THROUGH POLYMERIC MEMBRANES: A NOVEL TECHNIQUE Sukhtej Singh Dhingra Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Chemical Engineering E. Marand, Chair G. L. Wilkes R. M. Davis D. G. Baird H. Marand June 19, 1997 Blacksburg, Virginia. Keywords: Mixed gas, Permeability, Solubility, Diffusion, Polymer Copyright 1997, Sukhtej S. Dhingra

2 MIXED GAS TRANSPORT STUDY THROUGH POLYMERIC MEMBRANES: A NOVEL TECHNIQUE Sukhtej Singh Dhingra (ABSTRACT) The gas transport and separation properties of polymers have been successfully exploited in commercial ventures. Industrial applications employing membrane processes range from production of pure gases to barrier coatings for protection against environmental elements. Membrane separations are simple, energy efficient processes, which can be economically competitive with traditional separation technologies. Membrane separation and permeation characteristics for a particular mixed gas system is typically calculated from single-component transport parameters, namely, diffusion coefficients and solubility constants. In certain gas systems involving gaseous or vapor mixtures, where mass transport is affected by coupling effects or competition between penetrants for unrelaxed free volume, such calculations can lead to erroneous estimates of the membrane separation efficiency. Attempts to study the true transport phenomena effective during mixed gas permeation through membranes have been restricted due to experimental limitations. Also, the absence of rigorous theoretical models hinders the complete understanding of the transport phenomena. The current research involves design and development of an experimental set-up for observing mixed gas permeation through non-porous membranes with real time

3 resolution. The technique employs a gas chromatograph as the selective detector for monitoring the variation in gas concentration, as the gases permeate through the membrane. The same set-up can also be used for conducting single gas permeation experiments. The novelty in the experimental set-up is the In-line sampling interface, used for injection of permeate gases in the GC without introducing any leaks in the permeate volume. Also, a novel data cropping technique is used to elucidate the transport properties of gases through membranes under mixed gas permeation conditions. Mixed gas feed concentration studies performed on a rubbery polymer (PDMS: poly dimethyl siloxane) showed no coupling effects. However, with a glassy polymer (NEW TPI: thermoplastic polyimide), the synergistic effects of gases is observed to play a major role in altering the gas transport and separation properties of the membrane.

4 Acknowledgments I would like to express my sincere thanks to the many individuals who helped me through my stay in Blacksburg: First and foremost, my advisor, Dr. Eva Marand, for her guidance, support and the long hours she spent on the dissertation; to the other members of the committee, Dr. G. L. Wilkes, Dr. R. M. Davis, Dr. D. G. Baird and Dr. H. Marand, for their continued encouragement and suggestions; to Dr. B. D. Freeman and his research group at NCSU, Raleigh, for their advice in the design of the experiment; to the colleagues in my lab, for their patience and friendship; to the friends of mine, for their continued care and interest; to my brother and sister-in-law, for their inspiration; and to my parents for their blessings. iv

5 Table of Contents List of Illustrations List of Figures List of Tables...vii...ix Chapter 1: Introduction and Objectives...1 Chapter 2: Literature Review Introduction Membrane Separation Technology Membranes: Types and Applications Membrane Transport Models Theory of Gas Permeation through Polymer Membranes Fundamentals Gas Permeation in Rubbery Polymers Gas Permeation in Glassy Polymers Gas Permeation in Crystalline Polymers Effects of Operating Conditions on Polymer Permeability Temperature effects on Permeability Pressure and Concentration effects on permeability Experimental Methods Sorption Method Integral Permeation Method Differential Permeation Method Mixed Gas Permeation Applications Conclusions References...84 v

6 Chapter 3: Experimental Technique for Mixed Gas Transport Study through Polymeric Membranes Introduction Theory Experimental Materials Experimental Instrumentation Operational Procedure Results and Discussion Conclusions References..120 Chapter 4: Feed Concentration Effects on Mixed Gas Transport through Polymeric Membranes Introduction Theory Solubility Coupling Diffusion Coupling Experimental Materials Gas Permeation Measurements Results and Discussion Conclusions References..141 Chapter 5: Conclusions and Future Considerations..143 Appendix A: Curve Fitting Method (FORTRAN Program Codes)..146 Appendix B: Error Analysis..159 Appendix C: Sample Calculations..164 Vita..173 vi

7 List of Figures Figure 2.1: Schematic representation of gas transport through a membrane Figure 2.2: Typical forms of permeability dependence on gas concentration during gas transport through polymer membranes Figure 2.3: Typical forms of sorption isotherms observed during gas sorption in polymer membranes Figure 2.4: Typical forms of concentration dependent diffusion coefficients in gas transport through polymer membranes Figure 2.5: Schematic representation of general experimental methods used for measuring gas transport properties of polymer Figure 2.6: Schematic diagram of dual transducer barometric technique used for gas sorption measurements in polymers Figure 2.7: Typical permeation and time-lag curve Figure 2.8: Schematic diagram of mixed gas sorption apparatus used in mixed gas sorption measurements in polymers Figure 3.1: Schematic of the experimental set-up used for measuring single gas as well as mixed gas permeation properties of membranes Figure 3.2: Schematic of the membrane cell Figure 3.3: Procedure for injecting permeate gas samples into the gas chromatograph using the in-line sampling interface Figure 3.4: Comparison of the permeate flux profile between the experimental values and that calculated from estimated transport parameter values Figure 3.5: Calculated residual values plotted against S and D values for PDMS membrane Figure 3.6: Calculated residual values for S and D for PDMS polymers to check for global minima Figure 3.7: (a) Complete permeate pressure flux profile, (b) Cropped permeate pressure flux profile used for estimation of gas transport parameters for a membrane vii

8 Figure 3.8: Cropping technique applied to mixed gas permeation data for PDMS membrane, based on measured steady state concentration value for permeate gas mixture Figure 3.9: Confirmation for the estimated values of gas transport parameters for individual gases under mixed gas permeation conditions for PDMS membrane Figure 4.1: Change in the overall transport parameter values with mixed gas feed concentration for rubbery membrane (PDMS) Figure 4.2: Change in the overall transport parameters values with mixed gas feed concentration for glassy polymer membrane (NEW TPI) Figure A.1: Source code for BASECORR program Figure A.2: Source code for SPLITFILE program Figure A.3: Source code for PERMFIT program Figure A.4: Source code for PERMSIMUL program Figure A.5: Source code for MERGE program Figure B.1: Source code for UNCERTAINTY program..162 Figure C.1: Pressure-time response from PT1 and PT2 for single gas permeation experiment Figure C.2: Total permeate pressure response for mixed gas permeation experiment Figure C.3: Gas chromatogram at steady state permeation for three sample injections Figure C.4: Permeate-time response for individual gases, used during curvefitting, after employing the data cropping technique viii

9 List Of Tables Table 2.1: Membrane separation processes for non-porous membranes Table 2.2: Various transport models for membrane separations Table 2.3: Various experimental set-ups designed by researchers for gas transport study Table 3.1: Permeability results (in Barrer) for Standard Reference polyester membrane at 30 o C Table 3.2: Permeability results (in Barrer) for poly amide-imide at 35 o C Table 3.3: Comparison between estimated gas transport parameters estimated by using complete and cropped permeate pressure flux profile Table 4.1: Gas transport parameter values measured during mixed gas and pure gas permeation experiments for rubbery polymer (PDMS) Table 4.2: Gas transport parameter values measured during mixed gas and pure gas permeation experiments for glassy membrane (NEW TPI) Table 4.3: Quantitative identification of the dominating gas during binary gas permeation through glassy polymer Table 4.4: Comparison of selectivity values between mixed and pure gas permeation results, as well as between the rubbery (PDMS) and the glassy polymer (NEW TPI) Table C.1: Permeate mixed gas feed composition analysis results..170 Table C.2: Gas transport results for CO 2 /CH 4 with PDMS membrane ix

10 Chapter 1 Introduction and Objectives Membrane based gas separation processes, over the last three decades, have proved their potential as better alternatives to traditional separation processes. The conventional processes, for example absorption, cryogenic distillation, and pressure swing adsorption (PSA) are energy intensive, as well as responsible for some environmental pollution. An illustrative cost comparison of an ethyl cellulose membrane system with a standard PSA approach for 35% oxygen enrichment of air shows a reduction of 47% in capital costs, and 38% in operating costs for the membrane based process [1]. The membrane based separation processes are not only cost effective and environmentally friendly, but also, with many novel polymeric materials available, offer much more versatility and simplicity in customized system designs. Gas transport properties of polymer membranes are not only important to industrial production of high purity gases, but also plays a role in the application of membranes as barrier materials for food packaging and beverage industry. Because of many practical benefits, much effort is being exerted to understand the phenomena involved during gas transport through membranes as well as to synthesize

11 novel polymers with better separation properties. Although interest in polymers has been around for a century, major developments were made only in the last three decades [2]. The sudden advances were caused by the developments in the field of synthetic polymers. These polymers not only exhibited better thermal and mechanical properties than natural polymers, but also presented a wide range of gas transport and separation properties. While progress was being made in developing new polymer membranes, the study of the involved transport phenomena was limited by instrumentation. Simple experimental techniques are still being used to study the transport phenomena. The observed behavior is then described in terms of known transport models, which were based on liquid transport through materials. Also, experimental results from single gas transport studies through membranes are primarily used for estimating gas separation properties. It was only in the last decade that the first mixed gas permeation experiments were conducted to evaluate the true separation property of membranes [3]. Most of the models describing the mixed gas transport behavior are based on modifications to single gas transport models. Furthermore, these models only provide a description of the mixed gas transport phenomena under steady-state and simplified experimental conditions. The lack of experimental data, thus, hinders our understanding of the true mixed gas transport phenomena through membranes. Hence an effort is warranted that would be aimed at the design of an experimental technique, which would allow simultaneous observation of the gas transport behavior through a membrane under mixed gas conditions, thus better defining the membrane separation characteristics. Advancement in sensor technology due to improved electronics now offers a better chance of observing the true transport phenomena with more sensitivity and accuracy. The availability of high speed computing devices then permits better modeling of mixed gas permeation. The focus of this thesis is on the development of such an experimental technique, which would help in our understanding of the involved transport phenomena under real conditions. 2

12 The objective of this research is twofold. The primary objective is to experimentally measure transport parameters namely, diffusion coefficient, solubility coefficient and permeability, for any given mixed gas-polymer system. This involves the development of an experimental technique that permits simultaneous detection of concentration changes and gas permeation rate under mixed gas condition. By studying single gas permeation through the same membrane, using the same set-up, a comparison is possible between the membrane performance under ideal and real conditions. The second objective is to study the synergistic effects of gases on the gas transport and separation properties of the membrane. These synergistic effects of gases are observed by comparing the membrane performance with respect to the mixed feed gas composition. Thus, with this research an experimental method is being presented which provides an insight as well as confirms the need for studying gas transport and separation properties of a membrane under more realistic conditions References 1. W. J. Koros, editor, Barrier Polymers and Structures, ACS Symposium Series 423, American Chemical Society, V. Stannett, The Transport of Gases in Synthetic Polymeric Membranes- an Historic Perspective, Journal of Membrane Science, 3, 97 (1978). 3. W. J. Koros and R. T. Chern, Separation of Gaseous Mixtures using Polymer Membranes, Handbook of Separation Process Technology, edit. R. W. Rousseau, (1987). 3

13 Chapter 2 Literature Review 2.1. Introduction The success of membrane separation processes can be confidently judged from the vast amount of literature presented in journal publications and books [1-15]. Before being applied to gas separation, membrane technology has been used in the industry for many years for separating liquids and liquid-solid mixtures. The knowledge gained during these years was then gradually transferred to gas separating membrane systems. The successful transformation was also due to developments in the field of synthetic polymeric materials. These materials exhibited a wide range of thermal and mechanical properties, along with practical gas separation capabilities. Thus, the availability of numerous polymer membranes and the simplicity of the process lead to the evolution of lab scale research to commercial applications. The resulting industrial applications now successfully compete against well established gas separation processes like cryogenic distillation and pressure swing adsorption. With the importance of membrane based gas separation as a chemical process unit operation established, the focus was directed towards customization of the technology to cater to specific applications. This then required an understanding of the

14 transport phenomena involved during gas permeation through a membrane. Also, studies on modification of polymer structure were conducted to enhance membrane gas transport and separation properties. Formulation of the gas transport phenomena through polymer membranes is directed towards two areas: (1) development of quantitative theories based on the thermodynamics and kinetic properties of the gas-polymer system. Regular polymer solution theory has been the basis for almost all the present approaches, and (2) experimental study of gas transport through various polymers. The observed behavior is then correlated to known phenomenological models. Thus, based on the focus of research, either microscopic (molecular) theories or macroscopic (continuum) theories are employed [14]. Both aspects of the transport phenomena have been covered in this review. With respect to describing mixed gas transport through polymer membranes, very limited data is available in literature. The theories presented in literature are based on either single gas transport or over-simplified theoretical considerations for mixed gas transport through membranes. As the present research is focused on the development of an experimental technique to study mixed gas transport process in real time, as well as to study the feed composition effects on the gas transport, the review is limited to the theoretical and experimental consideration deemed essential to the present research. Although the research presented in this thesis deals exclusively with gas separation through polymer membranes, this review begins by outlining the membrane separation technology based on the types and applications of the membrane. Next, general theoretical considerations are presented which form the basis for the transport models developed to describe the observed transport phenomena. The following two sections then summarize the studies conducted on gas permeation through polymers, and the effect of operating conditions on the performance of a given membrane with respect to its transport and separation properties. With a brief overview of the experimental and 5

15 parameter estimation techniques employed to characterize the gas transport phenomena, the review concludes with description of some practical industrial applications involving gas separations with polymer membranes Membrane Separation Technology Membranes: Types and Applications Membrane based separation processes are attractive for several reasons, namely (1) the process is simple; (2) there are diverse applications, which can be studied by the same basic formulations; (3) there is no phase change involved, which is measured in commercial applications as energy savings; (4) the process is generally carried out at atmospheric conditions which, besides being energy efficient, can be important for sensitive applications encountered in pharmaceutical and food industry, and finally (5) modules can be added and optimized in a process design to achieve the desired separation. The diversity of membrane based separation systems makes it difficult to categorize them clearly. The systems are typically labeled either on the basis of type of membrane employed, or on the driving force applied to assist penetrant transport through the membrane [7]. The type of membranes used for separation are classified as porous, non-porous (tight) and liquid membranes. With each type of membrane used, further classification is based on the type of applied driving force for the penetrant. Porous Membranes Porous membranes are studied in terms of their pore size. These are then classified as either microporous or ultraporous membranes. The microporous membranes have pore sizes in the range of 200 to 3000 nm, with the transport of penetrant molecules through these pores labeled as viscous (Poiseuille) type [7,17]. The pressure driven molecules then 6

16 flow through the membrane independent of their size, shape or mass, thereby rendering the microfiltration process as nonselective on a molecular scale. The ultrafiltration membranes, with a pore size of less than 10 nm, are more useful for penetrant separation on a molecular level. The separation is mainly achieved by sieving of the molecules. Although, steric hindrance at the entrance of the pores and frictional resistance in the pores also play an important role during the separation process. The penetrant transport is labeled as Knudsen Flow, where the pore size of the membrane is smaller than the mean free path of the molecules. The diffusion rate of the molecule is then related to the inverse square root of its molar mass [6,17]. The separation achieved is very low, except for the case where molecules with significant molecular weight difference are being separated. The major drawback of the filtration process is fouling [7]. Besides plugging the pores of a membrane, the buildup of a residual layer at the membrane surface, as well as reduction in pore size due to surface adsorption, leads to membrane fouling. This phenomena then causes drastic reduction in efficiency of a membrane separation property, and in some cases, renders the membrane useless. Anti-fouling designs are based on the creation of turbulent flow of the feed mixture, thereby preventing any accumulation of the penetrants on the surface of the membrane. Some of the successful techniques used are pulsated flow, self cleaning spiral vortices, and spiral wound membranes [7]. These membranes are being extensively used in the pharmaceutical and food industry. Major applications involving microfiltration include sterile filtration, semiconductor and waste water treatment, whereas ultrafiltration processes are employed in electrocoat paint, juice extraction, pulp and paper, and protein purification. In membranes having a pore size less than 3 nm, the separation is influenced by the osmotic pressure of the solution. Application of sufficient upstream pressure is necessary in order to overcome the osmotic pressure of the feed solution and permit the solvent to 7

17 permeate through the membrane. This pressure driven separation process is referred to as reverse osmosis. An important feature of reverse osmotic membranes is the preferential separation of molecules due to their high adsorptivity in the membrane. The most important commercial application of these membranes is the desalination of salt water. Cellulose acetate blends, used as reverse osmotic membranes, now account for 50 % of the desalinated water produced in the world [18]. These membranes are also used in food, metal finishing, pulp and paper, and textile industry [6,18]. Besides using polymers for fabricating porous membranes, ceramic and polymerceramic composites are also being used as porous membranes. The inherent thermal and chemical stability observed with these materials are exploited during separation at high temperature and corrosive conditions. The hydrophilic nature of these membranes are sometime utilized in treating aqueous solutions and emulsions. Recently, molecular sieve membranes have been developed for filtration purposes. These membranes, known as molecular sieve carbon membrane (MSCM), are based on porous carbon product, with pore size of the order of molecular dimensions, obtained by pyrolysis of organic compounds [19]. Thermoset polymers are generally used for making these membranes, as they can withstand high temperature during all stages of the pyrolysis process. The only drawback observed with this system is the poor reproducibility in the synthesis of these membranes. Liquid Membranes A liquid membrane is a stable emulsion of an aqueous reagent solution and an immiscible hydrocarbon phase and is primarily used in the separation of liquids. The liquid membrane solution physically separates the feed solution from the permeate solution, as both solutions are immiscible in the liquid membrane [7]. With favorable thermodynamic conditions being maintained at the two interfaces, the solute is transferred from the feed to the permeate solution. A complexing agent is sometimes added to the liquid membrane to 8

18 expedite the solute transfer. This assisted process is then accordingly named as facilitated transport or mediated transport [20]. In some cases microporous polymer membranes are impregnated with the liquid membrane solution to provide support and stability. The shortcomings of these supported membranes are observed in loss of liquid to the contacting solutions, low permeate flux, and its high sensitivity to overpressure. The commercial potential for liquid membranes is still in its exploration stage. Non-Porous Membranes Non-porous membranes primarily consist of polymer membranes. The non-porous structure of the polymer is related to the non-continuous passages present in the polymer chain matrix. These passages are created and destroyed due to thermally induced motion of the chains. Therefore, the transport of a penetrant is based on its movement through these passages. The effects of penetrant activity (driving force) and operating conditions then play an important role in governing the gas transport rate and separation property of the membrane. The first non-porous membrane used for separation purposes was natural rubber [11]. With the capability of controlling the chemical structure and properties of synthetic polymers, new possibilities were opened to improve the transport and separation properties of membranes. As mentioned earlier, the classification of non porous membrane separation processes is based on the applied driving force. The classifications for non-porous membrane separation processes is summarized in table 2.1. Some of the processes are also applicable to porous and liquid membranes. Among the processes listed in table 2.1, only the pervaporation process involves a phase change during separation. The separation is based on vaporization of liquid feed as it permeates through the membrane. The vaporization is achieved by maintaining vacuum conditions on one side of the membrane. The success of the technique is attributed to high 9

19 separation obtained during liquid separation, even though the mass transport rate is very low [21]. The process is normally used in the separation of azeotropic mixtures. Table 2.1: Membrane separation processes for non-porous membranes. Process Name Pervaporation Vapor permeation Gas permeation Reverse osmosis Thermoosmosis Dialysis (osmosis) Electrodialysis Applied Driving Force Vapor pressure Vapor pressure Pressure Pressure Temperature Concentration Electric Potential The vapor permeation process is similar to the pervaporation process. The only difference is that the feed phase is vapor instead of a liquid. The strong dependence of the separation process on the feed vapor pressure requires special considerations in order to avoid vapor condensation within the membrane [22]. The technique has been successfully used in removal of trace amounts of organic vapors from gases. Gas permeation process has been the most successful process because of its diverse applications. Simplicity and versatility of the process have been the major contributing factors for its success. The gas transport is based on gas dissolution in a membrane, followed by diffusion of the gas through the thickness of the membrane, under the influence of the applied driving force. The relative sorption and diffusion rates of gases then lead to separation of the gas mixture. Production of high purity industrial gases like oxygen, nitrogen, etc. are few of the many applications of this process. As this 10

20 process is the focus of the present study, some industrial applications are discussed in detail later in this chapter. The electrodialysis process is based on application of an electrical potential difference for separation of ionic species from aqueous solution, and uncharged particles [7]. The applications for such electrically charged membranes, on a small scale, include production of table salt, as a preconcentration step, and in waste water treatment. Thus, with wide range of possible applications, the research in the membrane separations area is directed towards exploring new membrane materials, as well as understanding gas transport and separation phenomena. As the present research is focused on the study of the transport phenomena involved during gas separation by membranes, a general review on the transport models used for describing the gas transport through membranes is presented in the following section Membrane Transport Models Various transport models are presented in literature explaining the observed transport phenomena through non-porous membranes. Some models are based on thermodynamic and statistical mechanical principles, whereas others are based on correlations between the observed transport phenomena and the physical properties of the membrane material. These transport models are classified according to the phase of the feed. For the case of liquid separation through membranes, a number of models are presented, depending on the type of membrane-solution system being considered [23]. However, gas separation through membranes is primarily described by a single model. The important models [24] are summarized in table 2.2. All the seven models are valid for liquid separation through membranes, whereas gas separation through membranes is best described by the solution diffusion model and the solution-diffusion-imperfection model. The solution-diffusion imperfection model 11

21 includes various modifications applied to the solution-diffusion model. Two other models, namely irreversible thermodynamics and preferential sorption capillary flow model have been also used on a limited basis to describe gas transport through membranes [25]. As the present study is focused on gas transport through membranes, liquid theories are not reviewed here. An excellent review on the transport models for liquid separation through membranes is presented by Soltanieh and Gill [24]. Table 2.2: Various transport models for membrane separations. 1. From irreversible thermodynamics (IT) 2. Frictional model 3. Solution-diffusion model 4. Solution-diffusion-imperfection model 5. Diffusion viscous flow model 6. Finely porous model 7. Preferential sorption-capillary flow model. The solution diffusion model describes the transport of gases through a membrane as a three step process [11]: (1) sorption of gas in the membrane, (2) diffusion through the membrane due to an applied concentration gradient, and (3) desorption of the gas. Both the sorption/desorption and diffusion steps are dependent on the characteristics of the membrane material and the gases, and are studied separately with various sorption and diffusion models. While sorption models are based on the thermodynamics of the penetrant-membrane interaction, the diffusion is primarily modeled with Fick s laws of diffusion, presented in different forms [26]. In general, convective mass transfer through membrane is assumed to be absent for single component mass transfer. However, for multicomponent mass transfer, the convective terms have been theoretically shown to contribute to the penetrant mass transfer of the penetrant [27]. The diffusion of a gas in a gas mixture is expressed in terms of an active diffusion (same as single gas diffusion) as 12

22 well as a passive diffusion (due to the presence of the other penetrants). This is mathematically represented as J A = I A + x AN AB (2.1) where, J A is the total diffusional flux of component A, I A is the active diffusional flux of component A, x A is the mole fraction of A in the polymer, and N AB is the molar flux of passive displacement of the binary mixture of A and B (assuming no net displacement of polymer chains during gas transport) Thus, based on the relative interaction among the gases and between gases and membrane, the penetrant mass transfer is altered in the presence of other components. The use of classical thermodynamics to explain the involved transport phenomena is less appropriate, as the involved mass transfer occurs under non-equilibrated conditions. Hence, irreversible thermodynamic approach is used to model the transport phenomena [28]. The proposed models are based on network thermodynamics and bond graph notation. With respect to network thermodynamics each cell (known as Lumps in network thermodynamic terminology) of a reticulated real membrane system is assumed to follow classical thermodynamics. Whereas, the bond graph notation applies the electrical circuits analogy to describe the solution diffusion behavior for each cell [29]. The analogy of gas transport through membrane with electrical circuits is expressed in terms of resistance (diffusion) and capacitance (sorption capacity) of the circuit (membrane) for a given applied potential difference (penetrant concentration gradient). The preferential sorption capillary flow model is based on gas transport through micropores present in a dense membrane. The transport phenomenon is then described in terms of surface diffusion of gas molecules along the pore walls. The separation of gases is then achieved due to preferential adsorption of penetrant at the surface and its surface 13

23 diffusivity. The basic equations are similar to the solution diffusion model, except that film theory is used to model the boundary layer for penetrant concentration at the pore surface [24,25]. All three models described above are used to model single gas transport though dense membranes. Based on the limited amount of work conducted with mixed gas transport through membranes, the transport phenomenon is modeled using various aspects of these models. Simulation studies, based on these models, then provides a theoretical basis for predicting true mixed gas transport phenomena. Experimental verification is still restricted to ideal operating conditions Theory of Gas Permeation Through Polymer Membranes Fundamentals The first study on gas permeation through polymer dates back to 1829, when Thomas Graham observed the inflation of a wet pig bladder with CO 2 [11,30]. It was in 1866, when Graham formulated the Solution diffusion process, where he postulated that the permeation process involved the dissolution of penetrant, followed by transmission of the dissolved species through the membrane. The other important observations made at that time were: 1. Permeation was independent of pressure. 2. Increase in temperature lead to decrease in penetrant solubility, but made the membrane more permeable. 3. Prolonged exposure to elevated temperature affected the retention capacity of the membrane. 4. Differences in the permeability could be exploited for application in gas separations. 14

24 5. Variation in membrane thickness altered the permeation rate but not the separation characteristics of the polymer. Fick in 1855, by analogy to Fourier s law of heat conduction, proposed the law of mass diffusion where the penetrant flux J, for one dimensional diffusion, is represented as. J = D C x (2.2) Here D is the gas diffusion coefficient, C/ x is the concentration gradient applied across the membrane, and C is concentration of the dissolved gas given as the amount of gas per cubic centimeter of the membrane. In late 1870 s, Stefan and Exner showed that gas permeation through soap membrane was proportional to the product of solubility coefficient (S) and Fick s diffusion coefficient (D). These results were extended by von Wroblewski to present a quantitative solution to the Graham s solution-diffusion model [11]. The dissolution of gas was based on Henry s law of solubility, where the concentration of the gas in the membrane was directly proportional to the applied gas pressure as shown in equation 2.3. C = S p (2.3) Wroblewski further showed that under steady state conditions, and assuming diffusion and solubility coefficients to be independent of concentration, the gas permeation flux, illustrated in figure 2.1, can be expressed as p J = D S f p h p p = P h (2.4) 15

25 Where ( p/h) is the applied pressure gradient across the membrane thickness (h), P is defined as the gas permeability of the membrane. The conventional unit for expressing P is Barrers, where 1 Barrer = (cm 3 (STP) / cm. sec. cmhg). Upstream (High) Pressure (p f ) Polymer Membrane x = 0 x = h Downstream (Low) Pressure (p p ) Figure 2.1: Schematic representation of gas transport through membrane. In 1920, Daynes showed that it was impossible to evaluate both diffusion and solubility coefficients by steady-state permeation experiments. He presented a mathematical solution using Fick s second law of diffusion (equation 2.5), for calculating the diffusion coefficient, which was assumed to be independent of concentration. This time lag method is still used in estimating the gas diffusion coefficient. A detailed description of this method is presented in this review later on. 2 C = D C (2.5) 2 t x The gas separation property of a membrane is estimated in terms of a separation factor a AB [12] defined for a binary gas system as y x A B α AB = A y x B (2.6) 16

26 here, y i is the mole fraction of component i in the gas mixture at the downstream pressure side and x i is the mole fraction of component i at the upstream side of the membrane. The mole fraction y i is related to the permeate flux, at steady state, as y A = J A JA + J B (2.7) Using equations 2.4 and 2.7, equation 2.4 can be written as JA JB PA α AB = = x A x B P B p p A B x x A B (2.8) where, p i is the applied partial pressure difference for i th component. Assuming negligible downstream pressure, as compared to the feed pressure and no interactions due to binary gas mixture, the separation factor is simplified to give an ideal separation factor * α AB [12]. The ideal selectivity of the membrane is thus defined as the ratio of permeability values for two gases measured under similar conditions, as defined by equation 2.9. Factorization of the permeability leads to the ideal selectivity to be expressed in terms of ideal diffusional and solubility selectivities, which represent the separation properties of the polymer based on the kinetic and thermodynamic behavior of the permeating gases and polymer, respectively [12]. α AB PA DA = = P B D B S S A B (2.9) Based on single gas permeation experiments, the ideal selectivity is commonly used to gauge the membrane s separation performance for any pair of gases. Even though this gives a good approximation, experimental results are required to estimate the true selectivity. 17

27 Although, the study of gas permeation is 150 years old, significant advances have been made only in the last three decades. The interest in the field was generated from the developments of new synthetic polymeric materials. The study of gas transport and separation through polymer membranes is based on the morphology of the polymer. The gas transport through amorphous polymers is further divided into gas transport study through rubbery and glassy polymers. Even though the gas transport behavior is similar for each classification, each category is being dealt separately in the following subsections in order to bring out their salient features Gas Permeation in Rubbery Polymers Sorption Gas solubility in rubbery polymers is well defined in terms of Henry s law of solubility shown in equation 2.3 [1]. The model is valid for low molecular weight gases and at low gas pressures. Positive deviations to this model have been observed due to the swelling of polymer matrix in the presence of penetrants. The strong synergistic interactions primarily occur with vapors and water sorption. Non-ideal gas phase effects are sometimes corrected by replacing the gas pressure terms with corresponding fugacities [3]. Diffusion The gas transport through rubbery materials is described in terms of Fick s law for diffusion. The diffusion coefficient is shown to be concentration independent whenever Henry s law of solubility is applicable. Since rubbery polymers do not exhibit good selectivity, not much effort has been exerted to study concentration effects on gas transport through rubbery polymer. The high concentration dependence generally observed in vapor sorption was studied with respect to experimental conditions and is 18

28 presented in the appropriate section of this chapter. Gas fugacity values are again used to correct for non-ideality of the gas phase. Mixed gas Sorption The solubility of a gas mixture into a rubbery polymer is also evaluated in terms of Henry s law. The partial pressure, and Henry s law solubility coefficient value of the gases are used to calculate the partial solubility of the gas [31]. The effects from the second gas are assumed negligible. Mixed gas Diffusion The permeate flux measured during mixed gas permeation is shown to be sum of the permeate flux of individual gases, based on the partial pressure of gases. Therefore, the diffusion coefficient value remained the same as that for single gas transport through rubbery membrane [31]. Thus, gas-gas interactions, as well as, gas-polymer interactions does not affect the diffusion coefficient of the gases in rubbery polymer. In conclusion, the gas transport phenomena for rubbery polymers are well defined in terms of Henry s Law of solubility and Fick s laws of diffusion. The relative solubility of the gases is the controlling factor in the selectivity of the rubbery membrane. Since the mechanical and thermal stabilities of these membranes are not favorable, the industrial applications are limited to simple adsorption of trace amounts of organic vapors from process stream. 19

29 Gas Permeation in Glassy Polymers Non-equilibrium Behavior Gas transport through glassy polymers has been the focus of intense research because of favorable separation properties observed with these polymers. However, full characterization of the gas transport and separation properties of a glassy polymer is limited by the time dependent changes of the polymer s physical properties. These changes are important in evaluating the performance of the polymer during its anticipated service life. Attempts have been made to explain the observed time-dependent transport behavior at a molecular level. Models have been proposed to describe the observed transport behavior based upon statistical, mechanical-structural, and thermodynamic considerations [14]. These explanations fall into three basic theories, namely 1) The hole vacancy theory, where certain work is assumed to be done on the polymer matrix to create or expand a hole for the gas molecule. The successful creation and expansion leads to the diffusion of gas molecule through the membrane. 2) The activated complex theory, which describes the movement of gas molecules with sufficient energy through the matrix by overcoming a potential energy barrier. 3) The fluctuation theory, which is based on thermal fluctuations in the matrix leading to an emergence of excess space which then permits the passage of gas molecules. All three explanations presented above are originally derived from the free volume molecular theory. This theory postulates that the movement of gas molecules is dependent upon the available free volume in the polymer matrix, as well as, sufficient energy of the gas molecules to overcome attractive forces between chains. The presence of free volume within the polymer was first proposed by Fujita in 1960 [8]. The concept is based on the presence of three components for the specific volume of any polymer. The three components consists of: (1) the occupied volume of 20

30 the macromolecules, (2) the interstitial free volume, which is small and is distributed uniformly throughout the material, and, (3) the hole free volume, which is large enough to allow gas transport. The hole free volume is commonly referred to as excess free volume, and for the case of glassy polymers gains importance as the polymer chains are under thermal non-equilibrium. These intersegmental frozen defects then provide extra gas sorption sites in the polymer. Mathematically, the free volume is expressed as n f = n - n o (T) (2.10) where, n f is the free volume in the polymer matrix, n is the total macroscopic volume and n o (T) is the volume occupied by the polymer. The interstitial volume dependence on temperature is crucial in defining the difference between the rubbery and the glassy state of an amorphous polymer. The glass transition temperature is often defined as the point where the expansion coefficient of the polymer changes. The polymer below its glass transition temperature is treated as a solid and is termed a glassy polymer, whereas the polymer above its glass transition temperature is a rubbery polymer and exhibits viscous liquid like properties. Thus a glass transition temperature of a polymer is highly dependent on the annealing process. The concept of free volume has been used to qualitatively describe the non-equilibrated nature of the polymer. However, the model is limited by its quantitative description of the nature of polymer chain mobility and free volume size distribution. The simplicity of the free volume theory, as being a single parameter model, has been the important reason for its wide application in gas transport studies through polymer membranes [32]. With respect to the involved gas transport phenomena, the effects of gas-polymer interactions are considered more important than the non-equilibrium behavior of a polymer. An application of free volume theory to study gas transport through polymers was presented by Stern, Fang and Frisch in 1972 [33]. Beginning with the Doolittle form for thermodynamic diffusion coefficient D T, defined by equation 2.11, the fractional free 21

31 volume of the polymer (ν f ) at a given temperature, pressure and gas concentration (ν) is represented by equation The subscript s denotes a reference state D T B = RTA d exp ν d f (2.11) ( T ) ( ) ( ) ν = ν, π, ν = 0 + α T - T - β π - π + γν (2.12) f f s s s s Here, the constants A d and B d are characteristic of the given penetrant -polymer system, and α is the thermal expansion coefficient = ν f T, s β is the compressibility = ν f p, s π and π s are hydrostatic pressures, which are related to gas pressures and, and γ is the concentration coefficient = ν f ν. s The diffusion coefficient is related to the thermodynamic diffusion coefficient by equation 2.13, where a is the activity of the gas. Thus, the fractional free volume is a measure of gas solubility in the polymer and is linearly related to the operating conditions, i.e. temperature, pressure and concentration. D = D T ln a 1 ln ν 1 ν T, p (2.13) 22

32 The free volume theory was also applied to study binary gas transport through polymers by Fang, Stern and Frisch in 1975 [34]. Using the same Doolittle equation for diffusion, the fractional free volume equation, shown in equation 2.14, was modified to include the concentration effects of the second component on the free volume of the polymer. ( T,,, ) ( ) ( ) ν = ν π ν = 0 ν = 0 + α T - T - β π - π + γ ν + γ ν (2.14) f f s s a b a a b b s s The effect of the second component on the free volume is assumed to be additive, which then restricts the applicability of the model to dilute systems, where the penetrant concentration is less than 0.2 volume fraction (i.e. ν a + ν b < 0.20). The resulting expressions for permeability and diffusion coefficient were then analytically solved with idealized assumptions. The validity of the model was questioned by the same authors due to its limited success in describing the experimental data [34]. To explain the mechanism behind the transport of gas molecules through the free volume present in the polymer matrix, the gas polymer system is defined in terms of liquid molecules traversing through a liquid membrane. The Cohen and Turnbull theory, and Brandt theory, both proposed in 1959, considered transport through liquid molecules denoted as hard spheres [1]. The Cohen and Turnbull model defined the diffusion as a redistribution of free volume within the liquid, whereas the model by Brandt described the process in terms of an activation energy barrier. Another theory proposed by Dibenedetto and Paul in 1963 [35-37] used the same concept as that of Cohen and Turnbull regarding free volume distribution, but with a different chain packing at the molecular level. All these theories assumed semicrystalline chain packing for the polymer chains at the molecular level [38]. The presence of small bundles of chains, which are parallel to each other, was experimentally shown using X-ray diffraction technique [8 and therein]. This parallel alignment of small polymer chain segments should not be confused with the regular chain packing observed, generally, in any crystalline or solid material. The 23

33 molecular scale packing in these bundles of chain segments was further assumed to have a coordination number of four. The model by Cohen and Turnbull assumes that four neighboring chains form a cage with large enough free volume, within the cage, to accommodate many penetrant gas molecules [1,4]. The gas transport is then explained in terms of density fluctuations causing an opening in the cage, leading to the displacement of the molecules into another cage. The repetition of this procedure then leads to transport of the gas through the membrane. The model proposed by DiBenedetto and Paul [36] describes the transport of gas molecules to be parallel to the polymer chains. Here the gas molecule is assumed to be trapped in the bundle under equilibrium. During a thermal fluctuation the expansion of the chains near the molecule leads to a creation of cylindrical passage, thereby allowing the gas molecule to make a diffusional jump to the other end of this passage. With the closing of the passage, the gas molecule is at a new position under thermal equilibrium. On the macroscopic scale, this movement coincides with a small displacement of the gas molecule along the chain length. These random displacements then result in the diffusion of the gas molecule through the membrane. Utilizing the two variations of gas transport through the bundle of polymer chains, Pace and Datyner [39] combined both the parallel and perpendicular motion of the gas molecules, to present an elaborate theory in They considered the case of a molecule moving along the polymer chain bundles and being stopped only by chain entanglements or a crystallite. In order to explain further motion of the gas molecule, it was proposed that the molecule then jumps into the adjacent bundles, similar to what Cohen and Turnbull had proposed. This jumping of the molecules in between bundles was considered to be the rate controlling step, with the diffusion along the bundle being three times faster than the perpendicular jump of the molecule. This transport behavior was then mathematically expressed in terms of polymer density, cohesive energy density, Lennard 24