Pore Volume Distribution in Ultrafiltration Membranes - ACS Publications

16 Pore Volume Distribution in Ultrafiltration Membranes Downloaded by GEORGE MASON UNIV on March 15, 2016 | http://pubs.acs.org Publication Date: December 12, 1985 | doi: 10.1021/bk-1985-0269.ch016

LEOS ΖΕΜΑΝ and GABRIEL TKACIK Millipore Corporation, Bedford, MA 01730 Three polysulfone asymmetric ultrafiltration membranes having distinctly different ultrafiltration properties were charac terized by high-resolution scanning electron microscopy (SEM), nitrogen sorption/desorption isotherms as well as by water permeability and polydisperse solute rejection measurements. Even for the most retentive membranes, the surface pores were visualized by SEM. Frequency distribution of pore radii was approximated adequately by a log-normal distribution function. Tentative prediction of solute rejections was made from these results and compared with measured rejection curves for poly disperse dextrans. The agreement obtained was satisfactory. Pore radii calculated from sorption/desorption isotherms by two different methods were substantially larger than those sug gested by SEM of the membrane surfaces. A hypothesis can be made that the isotherms reflect primarily pore volume d i s t r i butions in the subsurface (matrix) region of the asymmetric structures.

Pore structures of t y p i c a l polymeric u l t r a f i l t r a t i o n membranes, produced by so c a l l e d "phase inversion methods," consist of i n t e r connected, i r r e g u l a r , three-dimensional networks of pores, i n t e r s t i c e s and voids i n t h e i r skin layers. An investigator i n t h i s area t y p i c a l l y has precise information on composition of casting solutions and other physicochemical factors a f f e c t i n g membrane formation. Functional measurements of transport i n terms of convective permeability, s e l e c t i v i t y or d i f fusive permeability are usually also a v a i l a b l e . However, without proper techniques for quantitative description of membrane pore structures, and t h e i r shape and s i z e d i s t r i b u t i o n s , membrane de velopment e f f o r t s remain l a r g e l y empirical. Several attempts to characterize quantitatively pore struc tures i n u l t r a f i l t r a t i o n membranes have been described i n the l i t e r a t u r e . Preusser(l) analyzed surface p o r o s i t i e s of Amicon mem branes, using a carbon r e p l i c a technique and a high-resolution transmission electron microscopy (TEM). A s i m i l a r approach was

0097-6156/85/0269-0339$06.00/0 © 1985 American Chemical Society Lloyd; Materials Science of Synthetic Membranes ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

Downloaded by GEORGE MASON UNIV on March 15, 2016 | http://pubs.acs.org Publication Date: December 12, 1985 | doi: 10.1021/bk-1985-0269.ch016

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M A T E R I A L S SCIENCE O F SYNTHETIC

MEMBRANES

used l a t e r by Fane, F e l l and Waters(2). The r e p l i c a approach pro vides only i n d i r e c t v i s u a l i z a t i o n s of membrane surfaces. Also, i t i s often very d i f f i c u l t to d i s t i n g u i s h between r e a l surface features and a r t i f a c t s . U n t i l several years ago, the r e s o l u t i o n of scanning electron microscopy (SEM) was not s u f f i c i e n t l y powerful to provide direct v i s u a l i z a t i o n of surface-contained pores. A new generation of SEM instruments with u l t r a high resolution (20-5θΧ) i s , however, becoming a v a i l a b l e . The analysis can now be assisted by powerful computer-linked image analyzers. Broens, Bargeman and Smolders (_3) reported on the use of n i t r o gen sorption/desorption method for studying pore volume d i s t r i b u t i o n s i n u l t r a f i l t r a t i o n membranes. The pore volume d i s t r i b u t i o n s were calculated for a c y l i n d r i c a l c a p i l l a r y model. More recent r e s u l t s from the same laboratory are published i n this volume (4) . In our view, a p p l i c a b i l i t y of c y l i n d r i c a l pore models for asymmetric mem branes should be v e r i f i e d , rather than assumed. This can be done, for example, by analysis of both branches of the sorption isotherm. For a reasonable model choice, the two pore volume d i s t r i b u t i o n s should be i n substantial agreement. The method of thermoporometry, developed by Brun, Lallemand, Quinson and Eyraud(5), represents another method applicable, at least i n p r i n c i p l e , to characterization of pore volume i n u l t r a f i l t r a t i o n membranes (4,6). However, for asymmetric membranes, pore volumes explored by thermoporometry may not be the volumes a s s o c i ated with membrane skins and " f u n c t i o n a l pores. Some authors (7,8) have used measured parameters of solute and solvent transport for c a l c u l a t i o n of membrane pore size d i s t r i b u tions. D i f f i c u l t i e s associated with t h i s approach are of both ex perimental and theoretical nature. The experiments need to be carried out under conditions that minimize or eliminate effects of boundary phenomena (polarization) and of solute adsorption (fouling) on the measured c o e f f i c i e n t s . This i s rarely done. An even more serious obstacle i n this approach i s the absence of quantitative and v a l i d r e l a t i o n s between measured transport parameters and the size parameters of a "representative pore." I t i s therefore highly desirable to develop more quantitative methods for characterization of pore structures. The results of recent investigations, including u l t r a f i l t r a t i o n (water flux and r e j e c t i o n of a polydisperse solute), high-resolution SEM and n i t r o gen sorption/desorption analysis, are described below. Materials Polysulfone membranes A, Β and C had been prepared by machinecasting polymer solutions on a spun-bonded polyethylene substrate with subsequent immersion i n a coagulation bath. Typical u l t r a f i l t r a t i o n membrane morphologies were v i s u a l i z e d by SEM: high degree of structure asymmetry, the presence of large voids ( f i n g e r - l i k e c a v i t i e s ) and a globular (nodular) substructure beneath the skin. Diameters of nodules i n the skin regions were t y p i c a l l y about IOOOX for a l l three membranes. The Dextran polymers used were Pharmacia Dextran Τ f r a c t i o n s T10 ( l o t No. 16026), T40 ( l o t No. 21945), T70 ( l o t No. 23155) and T500 ( l o t No. 19073). Size-exclusion chromatography columns were calibrated with these f r a c t i o n s . Molecular weight d i s t r i b u t i o n s of these l o t s were determined by Pharmacia. 11

Lloyd; Materials Science of Synthetic Membranes ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

16.

Z E M A N AND TKACIK

341

Pore Volume Distribution

Experimental U l t r a f i l t r a t i o n experiments were performed with an Amicon 8050 c e l l at 25°C using a s t i r r e r speed of approximately 700 rpm. Water fluxes (hydraulic conductivities) were measured at Δρ = 1 p s i ; dextran rejection was measured for feed solutions containing 0.2% T40, 0.2% T10 and 0.1% T500 (see Materials) under conditions of low concentration p o l a r i z a t i o n . Transmembrane fluxes of dextran s o l utions were of the order of 0.2 χ 10~ cm/s at Δρ = 1 p s i . Feeds and permeates were analyzed by size-exclusion chromatography as described i n Reference 9, and the chromatographs were used to c a l culate the r e j e c t i o n curves (Figure 1). Scanning electron microscopy of membrane samples was performed by International S c i e n t i f i c Instruments, Santa Clara, C a l i f o r n i a (courtesy of Dr. R. Buchanan). The micrographs were obtained with a DS130 scanning electron microscope, 5kV accelerating voltage, 0° t i l t angle and 90,100X magnification. Samples were thinly coated with gold and no other non-routine sample treatment was used. Nitrogen sorption/desorption isotherms of membrane samples ( c a r e f u l l y dried at room temperature) were obtained by Micrometrics Instrument Corp., Norcross, Georgia. About 1.5g of each membrane samples was used for measurements of BET surface areas, 21 point sorption and 22 point desorption isotherms. The instrument used was DigiSorb 2500 with f u l l y automated control. The most s i g n i f i cant experimental error introduced was from saturation pressure v a r i a t i o n of about + 1.5 mm Hg (that i s , about 0.2% error i n r e l a t i v e pressure). After careful removal of the polyethylene backing, membrane thickness was measured by an accurately calibrated micrometer. The o v e r a l l density of each membrane was determined by weighing on an a n a l y t i c a l balance accurate to + 0.1 mg. Results U l t r a f i l t r a t i o n , Thickness, Density Membranes were characterized by water flux measurements, u l t r a f i l t r a t i o n of a polydisperse dextran as well as thickness and o v e r a l l density measurements. Data are summarized i n Table I. Table I. Membrane Properties


3

Membrane Hydraulic Conductivity (cm s/g)

A 1.60x10"

Β 4.19x10"

03x10^

Water Flux (GFD/psi)

2.3

6.1

6.0

Rejection of dextran with r = 5θΧ

0.90

0.60

0.44

Thickness (cm)(without) support)

0.007

0.009

0.009

s

y

C

2

s

3

Density (g/cm )

0.370

0.215

0.238

Porosity % (calculated from density)

0.730

0.843

0.826

τ, .^ Membrane Density Porosity = 1 - zr-z τ—^ Polymer Density Polymer Density = 1.370 g/cm 3


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M A T E R I A L S SCIENCE O F SYNTHETIC M E M B R A N E S

Dextran r e j e c t i o n curves f o r membranes A, Β and C are plotted i n Figure 1. SEM of Surface Pores SEM photomicrographs were obtained as described above. Rough pore s i z e analysis was performed on 3X photographic magnifications of o r i g i n a l micrographs by i n s c r i b i n g c i r c l e s i n dark areas on the membrane surface (putative pores) and counting frequencies for each size c l a s s . For a l l three membranes, data points f i t t e d well on log-normal d i s t r i b u t i o n curves (Figure 2). Each curve can be de scribed by the values of mean radius ( r ) and standard deviation (σ) (Table I I ) . Table I I . Pore Size Analysis by SEM Downloaded by GEORGE MASON UNIV on March 15, 2016 | http://pubs.acs.org Publication Date: December 12, 1985 | doi: 10.1021/bk-1985-0269.ch016

m

Membrane Mean pore radius,

r (5() m

Standard deviation (log-normal), σ Number of pores/cm Area analyzed

2

21.3 0.62

2

(cm )

3.94X10

41.0

40.4 0.56 10

4.37xl0"

9

3.44X10

0.74 10

8

1.58x10"

10

1.49x1ο

θ

1.23χ10""

Nitrogen Sorption/Desorption Nitrogen sorption/desorption isotherms of membranes A, Β and C ex h i b i t narrow hysteresis loops i n regions close to saturation points (Figures 3a,b,c). The experimental points on both branches of the three isotherms were f i t t e d by an a n a l y t i c a l function. In each case, c o r r e l a t i o n c o e f f i c i e n t s were greater than 0.9995. This allowed not only averaging of experimental data, but also s i m p l i f i e d numerical procedures of isotherm analysis. Analysis was performed only i n the regions for which experimental points were available. Since the early work of Wheeler (10), there has been a con tinuous e f f o r t to extract information on adsorbent pore size d i s t r i b u t i o n from gas sorption isotherms. The most c r u c i a l step i s a s e l e c t i o n of a proper pore shape model. C y l i n d r i c a l (11) and p a r a l l e l plate (12) pore models have been used most often. For membrane samples i n the present study, pore volume d i s t r i b u t i o n analysis was carried out with a c y l i n d r i c a l model (11), and a model-independent approach of Brunauer et a l . (13). a) C y l i n d r i c a l pore model This model imposed several r e s t r i c t i o n s (14). Pore volume d i s t r i b u t i o n s (AV /Ar vs. r) were calculated using the pro cedure of Barett et a l . (11). The multilayer thickness of nitrogen adsorbate was calculated using Halsey's equation (15) with values for monolayer thickness (3.54&) and Halsey's exponent (1/3) recommended by Dollimore and Heal (16) . Pore volume d i s t r i b u t i o n s (Figures 4a and b) are plotted only for those regions i n which r a d i i are deter minable with errors of less than 10%. b) Model-independent approach Brunauer, Mikhail and Bodor (13) developed a method of pore structure analysis which employs a hydraulic radius, r ^ , as a measure of pore s i z e . This radius i s defined as r ^ = V/S where V i s the volume of a group of pore "cores" with the wall surface area S. The "core" refers to the empty



16.

343



STOKES RADIUS CA>

Figure 1.

Rejection c o e f f i c i e n t s vs. Stokes r a d i i f o r a polydisperse dextran feed.

Membranes: Α ( - · - ) ,

Β(-^4τ),

C(-B-). t

1

1

ι

1

1

1

1

1

r

RADIUS OF CIRCLE INSCRIBED IN PORE CA>

Figure 2.

Normalized d i s t r i b u t i o n s of pore size from SEM f o r membranes A ( # ) , B ( A ) , C ( D ) d i s t r i b u t i o n curves ( s o l i d

and the f i t t e d log-normal

lines).


344


MEMBRANE A

150

S B E T 20.0 m /g 2

V d 0.278 cm3/g c

< P > 100 (cm3/g)


v

s t

50

0.6

0.8

1.0

MEMBRANE Β S BET 60 V (stp) (cm3/g)

4

V

c d

1

6

5

m 2 /

9

0.15cm3/g

0

20

0.2

MEMBRANE C S β E"T V(stp) (cmVg)

2

0

V

c d

8

0

m 2 /

9

0.053 cm3/g

0.2

Figure 3. Nitrogen adsorption ( O ) and desorption ( Δ ) isotherms of membranes A, Β and C. Solid l i n e s represent the best f i t of an a n a l y t i c a l function.


16.



(a) BJH-adsorp.


0.0014

(c) BMB-adsorp.

0.0014

0.0010

0.0010 AV /Ar

AV/Ar

(cc/g. Λ)

(cc/g.Â)

c

h

0.0006

0.0006

0.0002

0.0002

c 100

—-—

200

300

400

(b) BJH-desorp.

0.0014

0.0010

0.0014

0.0010

A

AV /Ar

AV/Ar

(cc/g. Â)

(cc/g.Â)

c

h

0.0006

0.0006

/

B

\ 0.0002

0.0002

100

200

300

P O R E R A D I U S (A)

400

c

100

200

300

400

100

200

300

400

A* ^ Λ H Y D R A U L I C C O R E RADIUS ( Â )

Figure 4. Pore volume d i s t r i b u t i o n s calculated f o r membranes A, Β and C according to a c y l i n d r i c a l model (11): 4a - adsorption, 4b - desorption, and according to the method of Brunauer et a l . (13), 4c - adsorption, 4d - desorption.


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M A T E R I A L S SCIENCE OF SYNTHETIC M E M B R A N E S

part of a pore that contains an adsorbed f i l m on i t s walls. Quantities V and S are thermodynamically defined i n terms of the "core ' of the pore and do not include contributions from r e v e r s i b l e multilayer adsorption. This leads to a need for minor corrections i n the calculated core volume d i s t r i b u t i o n s . The curves calculated for the membrane sam ples (Figures 4b and c) were a l l corrected for the multi layer adsorption e f f e c t s . Theoretical analysis of gas sorption/desorption on a bed of packed spheres Scanning electron micrographs of the membrane samples suggested that the active layers of these membranes were comprised of spher i c a l agglomerates (nodules) with diameters around 1000A(0.1 micron). Aristov et a l . (17) developed a method for c a l c u l a t i n g sorption/ desorption isotherms for beds of regularly-packed uniform spheres. In these beds, pore s i z e i s determined by the number of nearest neighbors (coordination number) n, the sphere radius r, and the type of packing geometry. Two r a d i i characterize the pore s i z e : one for the "throat" and one for the " c a v i t y " of the pore (18) . Isotherms have been calculated s i m i l a r to those of Reference (9), for poly sulfone (density 1.370 g/cm ) spheres for values of η = 4,6,8,10 (tetrahedral, primitive c u b i c a l , body-centered c u b i c a l , bodycentered tetragonal geometries, r e s p e c t i v e l y ) . Nitrogen vapor at -195.6°C was assumed and the adsorbed layer thickness was calculated with Halsey's equation (15) as i n the c y l i n d r i c a l pore model. Cal culated isotherms are plotted i n Figure 5. Discussion Curves i n Figure 1 show substantial differences i n dextran r e j e c t i o n by the three membranes. An increase i n a r e j e c t i o n - c o n t r o l l i n g mean pore s i z e i n the order AC (Figures 3a,b,c).


1

3



16.

Z E M A N A N D TKACIK

347


n=8

r*-=§

V =222

V =429

T

T

V (etp) (cc/g)

0.85

0.95 P/Po

0.85

0.95 P/Po

Figure 5. Hysteresis regions of nitrogen adsorption and desorption isotherms calculated for regular packings of spheres with uniform r a d i i of 500 X.

Total pore volume, V ,

given f o r each packing.

American Chemical Society Library 1155 16th St., N.W.

Lloyd; Materials Science of Synthetic Membranes Washington, D . C . Society: 2 0 0 3Washington, 6 ACS Symposium Series; American Chemical DC, 1985.

T

348


dR/dr

s


(1/A) 0.01

Λ À fi

a)

120

160

200

/A Β dR/dr

240

b)

Λ

s

ifc γ γ

0.00

80

120

160

200

S T O K E S R A D I U S (A)

Figure 6. a) Derivatives of experimental r e j e c t i o n curves. Values of dR/dr were calculated

from smoothed r e

j e c t i o n data i n Figure 1 for membranes A, Β and C. b) Derivatives of theoretical r e j e c t i o n curves. Log-normal pore s i z e d i s t r i b u t i o n s from SEM (Figure 2) and equations of the s t e r i c r e j e c t i o n theory (19) were used.


16.


349


For a l l three membranes, narrow hysteresis was observed i n regions close to p/p = 1. The c y l i n d r i c a l pore model (11) analysis yielded d i f f e r e n t pore volume d i s t r i b u t i o n curves from adsorption and de sorption (Figures 4a,b). Curve maxima for desorption are located at higher r values than for adsorption. This i s a p h y s i c a l l y un r e a l i s t i c r e s u l t , suggesting lack of a p p l i c a b i l i t y of the c y l i n d r i c a l pore model. Analysis with the model-independent method of Brunauer et a l . (13) yielded desorption curve maxima at lower r ^ values than for the corresponding adsorption curves. There i s no reason to expect i d e n t i c a l curves i n this case - the difference i s a d i r e c t consequence of sorption hysteresis. Desorption-controlling pores are s t i l l considerably larger than surface pores v i s u a l i z e d by SEM, e s p e c i a l l y i f we consider the fact that hydraulic r a d i i are smaller than geometric r a d i i (r = 2r +t for a cylinder; r = 3r^+t for a sphere). It i s l i k e l y , therefore, that pores analyzed by the nitrogen sorption/desorption method are i n t e r s t i c e s i n the subsurface s t r a t a . In the membranes presented here, these strata consisted of agglom erated spherical nodules. I t i s worth noting that curve maxima i n Figures 4b,d are i n the unexpected order A>B>C. Theoretical isotherms calculated for regularly packed spheres look encouraging. In spite of simplifying assumptions, we obtained a q u a l i t a t i v e agreement with experimental isotherms, mainly narrow sorption hysteresis i n the regions close to p/p = 1. Total pore volumes depend strongly on the choice of η (coordination number). More detailed analysis, allowing for polydispersity of both r and n, i s required for quantitative interpretation of isotherms. Methods of quantitative characterization of porous membrane structures have been explored. It i s believed that knowledge ob tained through these and s i m i l a r methods w i l l lead to a better understanding of both membrane formation and membrane function processes. Legend of Symbols η coordination number of packed spheres ρ pressure (mm Hg) p saturation pressure (mm Hg) r radius of a sphere or a cylinder (X) r ^ hydraulic radius of a pore core (A) r mean pore s i z e (X) r Stokes radius of a solute R rejection coefficient S wall surface area of cores (cm /g) t thickness of adsorbed layer (X) V volume of pore cores (cm /g) V volume of c y l i n d r i c a l pores (cm /g) V i cumulative desorption volume (as volume of l i q u i d n2 at 77.4K, cm /g) . t o t a l pore volume of regular packing spheres (as volume of n2 at STP, cm /g). σ standard deviation of log-normal d i s t r i b u t i o n


0

h

Q

0

m

s

2

3

3

c

cc

3

3



350

MATERIALS SCIENCE OF SYNTHETIC MEMBRANES

Literature Cited 1. Preusser, H . J . Kolloid Z. u. Z. Polymere 1972, 250, 133-141. 2. Fane, A.G.; F e l l , C.J.D.; Waters, A.G. J. Membrane Sci. 1981, 9, 245-262. 3. Broens, L.; Bargeman, D.; Smolders, C.A. Proc. 6th Int. Symp. Fresh Water from the Sea, 1978, 3, 165-171. 4. Smolders, C.A.; Vugteveen, E. In "Materials Science of Synthetic Membranes"; Lloyd, D.R., Ed.; American Chemical Society: Washington, D . C . , 1985. 5. Brun, M . ; Lallemand, Α . ; Quinson, J . F . ; Eyraud, C. Thermochimica Acta 1977, 21, 59-88. 6. Desbrieres, J.; Rinaudo, M.; Brun, M.; Quinson, J . F . J. Chem. Phys. 1981, 78, 2, 187-191. 7. Schwarz, H.H.; Bossin, E . ; Fanter, D. J. Membrane Sci. 1982, 12, 101. 8. Chan, K . ; Matsuura, T . ; Sourirajan, S. Ind. Eng. Chem. Prod. Res. Dev. 1982, 21, 605. 9. Zeman, L.; Wales, M. Sep. Sci. and Technol. 1981, 16, 275-290. 10. Wheeler, A. Advan. Catalysis 1951, 3, 250. 11. Barrett, E.R.; Joyner, L . G . ; Halenda, P.P. J. Am. Chem. Soc. 1951, 73, 373. 12. Innes, W.B. Anal. Chem. 1957, 29, 1069. 13. Brunauer, S.; Mikhail, R.Sh.; Bodor, E . E . J. Colloid Interface Sci. 1967, 24, 451-563. 14. Faas, G.S., Master's Thesis, Georgia Institute of Technology, Atlanta, 1981. 15. Halsey, G. J. Chem. Phys. 1948, 16, 931-937. 16. Dollimore, D.; Heal, G.R. J. Colloid Interface Sci. 1970, 33, 508-519. 17. Aristov, B.G.; Karnaukhov, A.P.; Kiselev, A.V. Russ. J . Phys. Chem. 1962, 36, 1159-1164. 18. Kruyer, S. Trans. Faraday Soc. 1958, 54, 1758. 19. Zeman, L.; Wales, M. In "Synthetic Membranes, Vol. II"; Turbak, A . F . , Ed.; ACS SYMPOSIUM SERIES No. 154, American Chemical Society: Washington, D . C . , 1981; p. 411. RECEIVED August 30, 1984


Pore Volume Distribution in Ultrafiltration Membranes - ACS Publications

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