High Specific Interaction of Polymers with the Pores of Hydrophobic

Tibor Macko , Martina Adler , Harald Pasch , Joeri F. Denayer , Achim Raphael. Journal of Liquid Chromatography & Related Technologies 2004 27 (11), 1...
1 downloads 0 Views 165KB Size
© Copyright 1996 American Chemical Society

JUNE 26, 1996 VOLUME 12, NUMBER 13

Letters High Specific Interaction of Polymers with the Pores of Hydrophobic Zeolites Christoph Buttersack,* Holger Rudolph, Jens Mahrholz, and Klaus Buchholz Sugar Institute, Technical University, P.O. Box 4636, D-38036 Braunschweig, Germany Received August 31, 1995. In Final Form: March 14, 1996X Poly(ethylene oxide) (PEO), poly(acrylic acid) (PA), dextran, and some oligomeric saccharides were found to be adsorbed from the aqueous phase on a dealuminated FAU-type zeolite (Si/Al ) 110). PEO was also adsorbed on a MFI-type zeolite (Si/Al > 1000), but dextran was not. Inulin and levan were excluded from the FAU-type zeolite. Addition of ethanol (dextran) or increase of pH (PA) caused a strong decrease of the adsorption equilibrium. The Fickian diffusity D of the trimer of dextran (isomaltotriose, Mw ) 504) related to that in the aqueous bulk phase D0 was D/D0 ) 10-3 and decreased to D/D0 ) 10-8 at Mw ) 40 000. D/D0 values for PEO (Mw ) 9000, 20 000, and 40 000) in the FAU zeolite were situated between 2 and 5 × 10-7. The high specific interaction indicates that the polymer not only is deposited on the surface of the zeolite crystal but must penetrate to some extent into the pores. The FAU zeolite can selectively adsorb oligomers and polymers containing R(1-6) glycosidic linkages (raffinose, stachyose, isomaltotriose, dextran) while those built up by β(1-6) or R,β(1-4) bonds are sterically excluded.

Introduction Polymers can penetrate small pores of different materials ranging from porous rocks (tertiary oil recovery) to pillard clays and track-etched membranes which justifies that considerable research concentrates on the theory of adsorption equilibrium and dynamics of macromolecules in confined spaces.1-8 In the simplest case the polymers are conceived as hard spheres so that the penetration of the pores is mainly dependent on the ratio Λ ) rH/rp between hydrodynamic radius of the polymer coil and the pore radius of the adsorbent.1 Λ determines both the diffusion coefficent and the equilibrium distribution; the X

Abstract published in Advance ACS Abstracts, May 15, 1996.

(1) Hejtmanek, V.; Schneider, P. Chem. Eng. Sci. 1994, 49, 2575. Sahimi, M. J. Chem. Phys. 1992, 96, 4718. (2) Thompson, A. P.; Glandt, E. D. J. Chem. Phys. 1993, 99, 8325. (3) Guo, Y.; Langley, K. H.; Karasz, F. E. Phys. Rev. B 1994, 50, 3400. Zimm, B.; Lumpkin, O. Macromolecules 1993, 26, 226. (4) Teraoka, I.; Langley, K. H.; Karasz, E. F. Macromolecules 1993, 26, 287. (5) Brochard-Wyart, F.; Raphael, E. Macromolecules 1990, 23, 2276. (6) Guillot, G.; Le´ger, L.; Rondelez, F. Macromolecules 1985, 18, 2531. (7) Brochard, F.; de Gennes, P. G. J. Chem. Phys. 1977, 67, 52. (8) Muthukumar, M.; Baumga¨rtner, A. Macromolecules 1989, 22, 1937 and 1941.

S0743-7463(95)00727-X CCC: $12.00

latter is mainly exploited in size exclusion chromatography.9 However, when Λ is near to unity, the diffusion can be higher than that predicted by the hard sphere model.2-8 It is assumed that the entropic barriers generated by the small apertures of the pores cause the dissolved polymer to lose its random coil structure so that the polymer chain reptates like a snake through the pores.7 Also in concentrated solutions and melts reptation has been discussed to represent the molecular basis of diffusion,10 and the phenomenon has been recently observed by different techniques.11 Obviously, inside the pore space the extent of reptation is slowed down with decreasing pore radius. Considering a typical macromolecule having a hydrodynamic radius of rH ) 10 nm, Λ would be 27 when this molecule is thought to exist inside a zeolite pore with rp ) 0.37 nm. The experiments reported for polymers in confined spaces do not exceed Λ ) 2, and no example considering the penetration of zeolite pores (9) Tijssen, R.; Bos, J. NATO ASI Ser. C 1992, 383, 397. (10) Lodge, T. P.; Rotstein, N. A.; Prager, S. Adv. Chem. Phys. 1990, 79, 1. (11) Russell, T. P.; Delaine, V. R.; Dozier, W. D.; Felcher, G. P.; Agrawal, G.; Wool, R. P.; Mays, J. W. Nature 1993, 365, 235. Ka¨s, J.; Strey, H.; Sackmann, E. Nature 1994, 368, 226.

© 1996 American Chemical Society

3102 Langmuir, Vol. 12, No. 13, 1996

Letters

by macromolecules has been investigated up to now. Polymers may be synthesized within the zeolite pores, but this occurs after entering of the monomers, and the polymer is then fixed as an integral part of the zeolite lattice.12 The longest molecules which have been adsorbed by zeolite pores are n-paraffins up to 26 C atoms from the liquid phase13 and up to 20 C atoms from the gas phase.14,15 The results reported in this article are joined to earlier investigations concerning the aqueous phase adsorption of saccharides on apolar FAU-type zeolites produced by dealumination with SiCl4.16,17 The fact that disaccharides can enter the pores of FAU-type zeolites although their molecular diameter is somewhat greater in solution than in the adsorbed state encouraged us to extend our investigations to larger molecules. Experimental Section FAU zeolite (Si/Al ) 110, Na+ form) with an average crystal diameter of 6 µm produced by treatment with SiCl4,18 and MFI zeolite (Si/Al > 1000, “silicalite-1”) with an average crystal diameter of 9 µm were made available by Degussa Company, Hanau, Germany. Particle size analysis was performed by laser diffraction spectrometry after ultrasonic treatment (Sympatec Helos, System-Partikel-Technik, Clausthal-Zellerfeld, Germany). Silicalite was preconditioned by washing first at pH ) 2 (15 h, 60 °C). Both the MFI- and the FAU-type zeolite were treated several times with 0.1 M NaCl (finally for 15 h at 60 °C (MFI) and 2 h at 100 °C (FAU)), washed with water, and then dried as previously described.16 For liquid phase adsorption a 1 or 1.5 g portion of dry zeolite was placed in 5 or 10 mL of an aqueous solution of the adsorbate (e10 mL/g). The time of equilibration was stopped (3-50 days) when no change of the adsorbate concentration (no change within an error of (1% within 1 week) was observed. The supernatant liquid, obtained after centrifugation, was analyzed by refractometry after HPLC on a Ca2+-exchanged ion-exchange column (HPX-78C, Biorad; eluent, water). Polyacrylate solution was acidified to pH ) 2.5 prior to injection, and the peak was detected by UV at 190 nm. In order to resolve the lower molecular weight fractions of dextran, an Ag+-loaded ion-exchange column (HPX42A, Biorad; eluent, water) was used. The change of concentration in the aqueous phase was used to calculate the excess adsorption. The measurement of diffusion was carried out in several glass vessels filled with 5 mL of an aqueous solution containing 2 g/L of dextran (Mw ) 1000, 6000, 40 000 from Fluka) or with 10 mL of 10 g/L poly(ethylene oxide) (Mw ) 9000, 20 000, 40 000 from Serva). After addition of 1 g of preconditioned zeolite the mixture was shaken up to an appropriate time, immediately centrifuged or microfiltrated, and analyzed by HPLC as described above. The uptake curve (adsorbed amount relative to the equilibrium value) was assumed to be determined only by constant Fickian diffusity19 and analyzed by fitting to the theoretical function20 up to an adsorbed amount of 60% of the equilibrium value. Such a limitation minimizes the failure produced by the polydispersity of both the zeolite particles and the polymers. The geometry of the molecules to be adsorbed was estimated (12) Millar, G. J.; Lewis, A. R.; Bowmaker, G. A.; Cooney, R. P. J. Mater. Chem. 1993, 3, 867. Enzel, P.; Zoller, J. J.; Bein, T. J. Chem. Soc. Chem. Commun. 1992, 633. Pereira, C.; Kokotailo, G. T.; Gorte, R. J. J. Phys. Chem. 1991, 95, 705. (13) Alkandary, J. A. M.; Al-Ammeri, R.; Salem, A. B. S. H. Sep. Sci. Technol. 1995, 30, 3195, and references cited therein. (14) Heink, W.; Ka¨rger, J.; Pfeifer, H.; Datema, K. P.; Nowak, A. K. J. Chem. Soc., Faraday Trans. 1992, 88, 3505, and references cited therein. (15) Eic, M.; Ruthven, D. M. Stud. Surf. Sci. Catal. 1989, 49, 879. (16) Buttersack, C.; Wach, W.; Buchholz, K. J. Phys. Chem. 1993, 97, 11861. (17) Buttersack, C.; Laketic, D. J. Mol. Catal. 1994, 94, L 283. (18) Beyer, H. K.; Belenkykaya, I. M. Stud. Surf. Sci. Catal. 1980, 5, 203. (19) Bu¨low, M.; Micke, A. Adsorption 1995, 1, 29. (20) Ka¨rger, J.; Ruthven, D. M. Diffusion in Zeolites; Wiley: New York, 1992; p 236.

Figure 1. Adsorption isotherms of glucose (‚) , sucrose (b), stachyose (9), isomaltotriose (O), and dextran with an average degree of polymerization of 6.5 (0) and 36 (3) on a dealuminated FAU zeolite (Si/Al ) 110) at 25 °C. by molecular modeling by in vacuo force field calculation with MM+ using the HyperChem-Autorelease 3 package from Autodesk.

Results and Discussion Adsorption Equilibrium. Figure 1 shows the adsorption isotherms of some representatives of the homologous series of 1-6 linked glucose units ((glc R(1-6))n glc) on a strong apolar (dealuminated) FAU-type zeolite. For comparision this figure also includes the isotherm of glucose. Glucose is only poorly adsorbed while isomaltotriose shows a greater affinity and a considerable adsorption capacity of about 120 mg/g. This amount corresponds to the existence of one monosaccharide unit per supercage. Thus the total three-dimensional pore system of the zeolite would be filled with saccharide molecules. The higher affinity of the disaccharide compared with the monosaccharide has already been discussed.16 Although carbohydrate molecules are usually considered as prototypes of hydrophilic substances they are characterized by a specific pattern of hydrophobic regions provided by the CH moieties.21 Strong adsorption was explained by the ability of the guest molecule to maximize its apolar interaction with the inner surface of the zeolite by reducing the extent of hydration and changing its conformation (induced fit).16,17 Disaccharides dissolved in water have a molecular volume of about 0.35 nm3.22 Related to a spherical geometry this volume corresponds to an equivalent diameter of 0.88 nm. As the pore diameter of the FAU zeolite is 0.74 nm, the conformation of the molecule inside the pores must be fitted to its nonpolar environment. Obviously this hypothesis can also be applied on the adsorption of an R(1-6) linked dextran oligomer composed of 6.5 units on the average (Figure 1). Analysis of the remaining polydispersive mixture has shown that tetra-, penta-, and hexasaccharides have a higher affinity to the zeolite than the lower weight fraction. Also a single tetrasaccharide such as stachyose (gal R(1-6) gal R(1-6) glc R(1-2)β fru-f) was proven to be very strongly adsorbed (Figure 1). Stachyose as well as dextran shows a (21) Lichtenthaler, F. W.; Immel, S. Int. Sugar J. 1995, 97, 13. (22) Galema, S.; Hoiland, H. J. Phys. Chem. 1991, 95, 5321.

Letters

Langmuir, Vol. 12, No. 13, 1996 3103 Table 1. Excess Adsorption Equilibrium Constant K (in mL/g) for the Interaction of Saccharides with a FAU Zeolite (Si/Al ) 110) at 25 °C glc gal fru glc r(1-2)β fru glc R(1-3) fru gal R(1-6) glc r(1-2)β fru glc r(1-2)β fru (3-1)R glc gal R(1-6) gal R(1-6) glc r(1-2)β fru glc β(1-6) glc glc β(1-4) glc glc R(1-4) glc glc R(1-6) glc glc β(1-4) glc β(1-4) glc glc R(1-4) glc R(1-4) glc glc R(1-6) glc R(1-6) glc glc R(1-4) glc R(1-4) glc R(1-4) glc (glc R(1-6))34 glc R(1-6) glc

a

glucose galactose fructose sucrosea turanosea raffinose melezitose stachyose gentiobiose cellobiose maltose isomaltose cellotriose maltotriosea isomaltotriose maltotetraosea dextran

0.2 0.3 1.0 23 1.3 20 -0.3 500 -0.3 0.2 0.45 1.8 -0.3 0.3 31 -0.1 >200

Taken from ref 16.

considerable adsorption capacity exceeding the value of one monosaccharide unit per supercage (113 mg/g). Both molecules contain R(1-6) glycosidic linkages. Their capacity is comparable with that of sucrose (glc R(1-2)β fru-f) which is a subunit of stachyose. Sucrose has already been shown to have a very high affinity to a dealuminated FAU zeolite.16 Usually a more or less spherical conformation of the oligosaccharides is favored in aqueous solution by entropic reason, and the corresponding contribution to the free energy must be overcompensated by hydrophobic interactions when the molecule exists inside the confined geometry of the zeolite lattice. Consequently, even the adsorption of an actual polymer such as dextran (degree of polymerization ) 36) may be explained by this hypothesis. As shown in Figure 1, its affinity is rather high, unless the adsorption capacity is low, which can easily be explained by steric hindrance between polymer chains inside the pores. However, severe objections against the existence of longer chains inside the zeolite pores have to be stated: 1. Observation of the zeolite crystals by scanning electron microscopy suggests that the particle is an aggregate of several primary crystals leading to a mesoporous system. In principle, such mesopores may be generated by the dealumination process although the method applied (treatment with SiO418) should prevent the formation of such a secondary structure.23 2. Dextrans are not complete linear macromolecules. By usual microbial synthesis (Leuconostoc mesenteroides B512) about 5% of the glucose units are branched by linkage of glucose at the 3-position.24 Both objections suggest that in the case of polymers surface adsorption is involved. If at all, the penetration is restricted on approximatly 20 monomer units (5% branching). The polymer only enters the mouth of the pores to a certain extent (docking). Because of this ambiguous interpretation, additional experiments were performed with a high silica FAU-type zeolite (silicalite-1). The smooth single crystals observed in the scanning electron microscope were produced without a dealumination step. The polymer used was the quite linear poly(ethylene oxide). The adsorption isotherms (Figure 2) in principle show a phenomenon comparable with those of dextrans on FAU-type zeolites (Figure 1). While the monomer unit (ethylene glycol) is only poorly adsorbed, the affinity of the respective polymer increases (23) Anderson, M. W.; Klinowski, J. J. Chem. Soc., Faraday Trans. 1 1986, 82, 3569. (24) Taylor, C.; Cheetham, N. W. H.; Walker, G. J. Carbohydr. Res. 1985, 137, 1.

Figure 2. Adsorption isotherms of ethylene glycol (b) and poly(ethylene oxide) with different degrees of polymerization (6.8, 13.6, 200, and 900) on a MFI-type zeolite (Si/Al > 1000) at 25 °C.

with the molecular weight and the adsorption capacity reaches a maximum at medium degrees of polymerization. The loading of 160 mg/g is somewhat higher than the value of 120 mg/g published for the adsorption of ethanol or 1-propanol on silicalite-1.25 With respect to the length of 3.6 or 5.2 nm for ethylene oxide and 1-6 linked glucose units, respectively, the length of each extended polymer chain at maximum capacity (dp ) 14 and 16.5) is of the same order of magnitude, namely, 50 or 34 nm. The proposed interaction of a polymer with the zeolite pores should depend on the nature of the monomer units or sequences of these units. This may be exemplified by comparing monosaccharides with oligo- and polysaccharides. Looking at Table 1, glucose has the lowest affinity toward the FAU zeolite. The affinity of the disaccharides can be higher or lower and depends on the nature of the glycosidic bond. The affinity increases in the following order: glc β(1-6) glc < glc β(1-4) glc < glc R(1-4) glc < glc R(1-6) glc. The negative value of -0.3 for gentiobiose (glc β(1-6) glc) means that this compound is excluded from zeolite pore volume. One can therefore assume the same behavior for gentiotriose. Cellotriose was found to be also excluded, and according to Table 1 the row of (25) Lin, Y. S.; Ma, Y. H. Stud. Surf. Sci. Catal. 1989, 49, 877.

3104 Langmuir, Vol. 12, No. 13, 1996

Letters

Table 2. Excess Adsorption Equilibrium Constant K for the Interaction of Polymers with Apolar Zeolites polymer

zeolite

solvent

T (°C)

K (mL/g)

sodium polyacrylate Mw ) 2100

MFI

H2O pH ) 2.5 H2O pH ) 8.5 H2O pH ) 2.5 H2O pH ) 8.5 adsorption H2O pH ) 8.5 desorption

20 20 20 20 20

1.8 -0.2 >50 -0.2 -0.1

H2O H 2O H 2O H 2O

20 60 20 60

>400 >400 >400 >400

H 2O H 2O H 2O H 2O H2O/EtOH adsorption H2O/EtOH desorption

20 60 20 60 20 20

0.1 0.2 >200 >200 -0.2 7.8

FAU

poly(ethylene oxide) Mw ) 9000

MFI FAU

dextran Mw ) 6000

MFI FAU

levan Mw ) 5000

FAU

H2O H 2O

20 60

-0.1 -0.1

inulin Mw ) 5000

FAU

H2O H 2O

20 60

-0.3 -0.2

Table 3. Diffusion Coefficients of Dextran at 25 °C with Different Degree of Polymerization (dp) in Water (D0) and in FAU-Type Zeolite (Si/Al ) 110) (D) Related to the Hydrodynamic Radius rH or Λ ) rH/(0.37 nm) and Compared with Equation 2 (D/(D0B)) Mw 504 1000 6000 40000

dp 3 6.5 36 240

rH (nm)a 0.62 0.85 2.0 4.9

Λ

D0 (m2 s-1)b

D (m2 s-1)

D/D0

D/(D0B)

1.7 2.3 5.4 13

4.75 × 3.34 × 10-10 1.33 × 10-10 0.51 × 10-10

4 × 10-13 c 3.3 × 10-15 2.2 × 10-18 3.3 × 10-19

8 × 10-4 1.0 × 10-5 1.6 × 10-8 6.4 × 10-9

7 × 10-2 1 × 10-3 2 × 10-8 1 × 10-32

10-10

a Calculated from literature data.29 b Calculated via log D ) 7.9 - 0.51 log M . This equation fits the data of dextrans (M > 104)30 w w and disaccharides (sucrose, maltose, lactose).31 c Estimated from a measurement at 5 °C.

increasing affinity of trisaccharides is (glc β(1-6))2 glc ) (glc β(1-4))2 glc < (glc R(1-4))2 glc < (glc R(1-6))2 glc. As maltotetraose is excluded from the pores16 but oligomeric R(1-6) linked glucans are found to be strongly adsorbed, the row of increasing affinity of tetrasaccharides is as follows: (glc β(1-6))3 glc ≈ (glc β(1-4))3 glc ≈ (glc R(14))3 glc < (glc R(1-6))3 glc. Thus, regarding the chain elongation of these compounds, only the adsorption energy of the dextrans ((glc R(1-6))n glc) exceeds the increased gain of entropy of the solution state. It is a remarkable result that the ability of pore penetration cannot be correlated with the flexibilty of the adsorbed molecule. Both the glycosidic bonds of gentiobiose β(1-6) and isomaltose R(1-6) are very flexible26 because they consist of three angles of rotation compared with the usual two. Therefore the possibility of maximal hydrophobic interaction within the pores seems to be the only way of understanding. A detailed analysis of this phenomenon is currently tried by molecular mechanics. Also for the adsorption of oligomeric carbohydrate molecules consisting of different monomer units, no simple rule can be provided. An example is provided by the sucrose subunit which is present in both raffinose and melezitose. The strong affinity of the sucrose unit is retained in the case of raffinose but completely lost in the case of melezitose (Table 1). Because of the general increase of the affinity with the molecular weight, specific effects could only be measured for lower molecular compounds. The comparision of the adsorption of real polymers yields mostly either very high affinities or low values for the equilibrium constant indicating exclusion or probably some surface interaction (Table 2). As expected, exclusion depends on the pore diameter compared with the thickness a of a wormlike (26) Dowd, M. K.; Reilly, P. J.; French, A. D. Biopolymers 1994, 34, 625.

polymer chain. Such values were estimated by molecular modeling. With respect to the value of a ) 0.6 nm for isomaltose it is reasonable that dextran was adsorbed by the dealuminated FAU-type zeolite (dp ) 0.74 nm) but not by the MFI-type zeolite (dp ) 0.55 nm). The same was found for poly(acrylic acid) (a ) 0.7 nm). Poly(ethylene oxide) (a ) 0.4 nm) was strongly adsorbed on both MFIand FAU-type zeolite. When the dextran was dissolved in aqueous ethanol, the polymer was excluded from the zeolite pores, which is an argument in favor of the hydrophobic nature of the interaction already found to cause the analogous adsorption of disaccharides.16 The reverse process (release of dextran from the zeolite by addition of ethanol) was found to be incomplete. It might be assumed that a strong hysteresis occurs, thus requiring more desorption time. The adsorption properties of poly(acrylic acid) are expected to depend on the degree of dissociation. When the pH was increased from pH ) 2 (nondissociated) to pH ) 8 (dissociated), the affinity to the zeolite was significantly lower, which again confirms the hydophobic nature of the interaction. Complete reversibility (release of poly(acrylic acid) from the zeolite by shift of pH) was proven (Table 2). Table 2 contains also data of two type of fructans. Inulin contains three-bond β(2-1) linkages leading to a linear chain of -CR2-CH2-O- units with CR2 ) fructofuranoside as side group.27 Obviously because of its size, this molecule is completely excluded from the zeolite pores. Another fructan is levan which is built up by fivemembered furanose units linearly connected by flexible three-bond β(2-6) linkages.28 Although the monomer unit (fructose) was proven to have a high affinity compared (27) Liu, J.; Waterhouse, A. L.; Chatterton, N. C. J. Carbohydr. Chem. 1994, 13, 859. French, A. D. Carbohydr. Res. 1988, 176, 17. (28) Liu, J.; Waterhouse, A. L. Carbohydr. Res. 1992, 232, 1.

Letters

Langmuir, Vol. 12, No. 13, 1996 3105

Table 4. Diffusion Coefficients of Alcohols and Poly(ethylene oxide) at 25 °C in Water (D0) and in MFI-Type Zeolite (Si/Al > 1000) (D) Related to the Hydrodynamic Radius rH or Λ ) rH/(0.37 nm) and Compared with Equation 2 (D/(D0B)) dp ethanol 1-propanol 1-butanol 2-butanol PEO 9000 PEO 20000 PEO 40000

rH (nm) 0.20a

200 450 900

0.23a 0.24a 0.26a 3.7d 5.9a 9.0a

Λ

D0 (10-10 m2 s-1)

0.71 0.82 0.86 0.93 13 20 32

D (10-15 m2 s-1)

12.4b

16c

10.5b 9.3b 8.7b 0.89e 0.54e 0.35e

77c 55c 4.1c 0.043 0.013 0.0055

(29) Lebrun, L.; Junter, G. A. J. Membr. Sci. 1994, 88, 253. (30) Callaghan, P. T.; Pinder, D. N. Macromolecules 1983, 16, 968. (31) Schneider, F.; Emmerich, A.; Finke, D.; Panitz, N. Zucker 1976, 29, 222. Sano, Y.; Yamamoto, S. J. Chem. Eng. Jpn. 1993, 26, 633. (32) Ching, C. B.; Ruthven, D. M. Zeolites 1988, 8, 68. (33) Tominaga, T.; Matsumoto, S. Chem. Eng. Data 1990, 35, 45. (34) Bortel, E.; Kochanowski, A. Makromol. Chem. Rapid Commun. 1980, 1, 205. (35) Rossi, C.; Bianchi, U. B.; Magnasco, V. J. Polym. Sci. 1958, 30, 175. (36) Brown, W.; Stilbs, P.; Johnson, R. M. J. Polym. Sci., Polym. Phys. Ed. 1983, 21, 1029. Tanner, J. E.; Liu, K. J.; Anderson, J. E. Macromolecules 1974, 4, 586. Elias, H. G. Z. Phys. Chem. (Frankfurt) 1961, 28, 303. Kambe, Y.; Honda, C. Polym. Commun. 1983, 24, 208. (37) Calculated from Figure 4 in ref 14.

D/(D0B)

1.3 × 7.3 × 10-5 1.7 × 10-4 4.7 × 10-6 4.8 × 10-7 2.4 × 10-7 1.6 × 10-7

0.71 0.56 0.51 0.43 10-32 10-65