The Mechanism for Ionic and Water Transport in Nafion Membranes ...

THE MECHANISM FOR IONIC AND WATER TRANSPORT IN NAFION MEMBRANES FROM RESONANCE DATA VITALY l.VOLKOV·, EVGENY V.VOLKOV··, SERGE F.TIMASHEV· • Karpov Institute of Physical Chemistry) 0, Vorontsovo Pole, Moscow, 103064, Russia "Physics Department, Moscow State University, Moscow 1l7234, Russia

The mechanism of ionic and molecular transport in nanosystems can be understood on the basis of magnetic resonance studies of the transport interconnection channel structure. the ionic and molecular state and the translational mobility in different spatial scales. Ion-exchange polymer membranes were studied as model systems. The ion exchange membranes bear acid or basic charged groups; these groups along with mobile ions and water molecules constitute a transport channel network. Nafion, a perfluorinated ion-exchange membrane (from DuPont) is a well known regularstructured ion-exchange system. The membrane structure consists of perfluorinated polymer chains and an ethereal side-chain with sulfonic acid groups capable of exchanging positive counter ions (protons or alkali and other metal ions). Fig. 1 shows the structures of the polymer chains and transport channels.

Schematic representation of the amorphous fragment of a sulfonated cation exchange membrane. I - main polymer chain; 2 hydrated counterions and ionogenic groups at low water content; 3 - ion and water transfer "channels" at high water content; LI=4 nm from low-angle X-ray scattering data; L2=IO nm from Mossbauer spectra; II and 12 from ENDOR and NMR relaxation data; h rrom porosimetry and ENDORdata.

Figllre I .

267 1. Fraissard and O. Lapina (eds.i, Magnetic Resonance in Colloid and Interface Science, 267-275. © 2002 Kluwer Academic PubLishers.

268 The structure of transport channels was studied using porosimetry, X-ray scattering, Mossbauer spectroscopy, EPR, ENDOR, NMR-relaxation and PFG NMR techniques [I] . The transport channels were found to occupy almost a quarter of the polymer volume and to be very regularly structured. They are about 3-5 nm in width, sulfonic acid groups being ca. 7 nm from one another and the charged groups being rather evenly distributed. The diameter of ionogenic groups, including hydrated metal ions, is about 1.0 nm. These structural characteristics depend strongly on the concentration of water, sulfur groups and on the polymer pretreatment. Magnetic resonance.is a powerful tool for studies in the field.

EPR [2-4] If counter-ions are paramagnetic or are to be used as a paramagnetic probe, EPR is the preferred technique. Analysis of EPR spectra provides information on the charged group distributions, the probability of arranging these groups, coordination bonding between charged groups and metal ions. Application of the END OR technique makes it possible to study not only the nearest neighbours but also remote coordination spheres. Detailed information on the neighbourhood of the paramagnetic centre (I to 1.5 nm) can be obtained by combining EPR and ENDOR studies. High resolution NMR. [5-7] Subjects of NMR studies were internal water and Li', Na·, Cs+ cations sorbed by the Nafion membrane. The aim was to understand the behaviour of water and the ions. by simultaneous measurement of both the chemical shift and the line width. We have investigated the dependence of chemical shifts and line widths on humidity. The line width is reciprocally proportional to the spin-spin relaxation times, and thus it is proportional to the residence times of ions on the sulfonic acid group. High resolution W NMR studies allow the number of water molecules ho in the first hydration shell of ions to be determined [5]. The value of ho is smaller than that for aqueous solutions of acid and salts containing the same cations (Fig. 2, 3). For protons, ho is always equal to 2. Hence, the proton in aqueous solution usually exists in the form ofH 5 0 z·, not as H30+. The ho value is maximal for Na +, as can be seen from the dependence of ho on the crystallographic radii of cations (Fig. 3). It is also possible to determine the fraction of broken H -bonds against that in pure water. The probability of breaking the hydrogen bond decreases from Li· to Cs + for alkali metal ions and from Mg2+ to Ba2+ for alkaline earth metal ions (Fig. 4) . High resolution alkali metal NMR studies allow the mechanism of ionic interaction with the ionogenic sulfo group to be established and, consequently, the nature of membrane selectivity to be understood [6, 7]. The type of cation-sulfo group interaction depends on the water content. When · the number of water molecules per charged group (n) is less than ho, the cation and the charged group interact directly to form a contact ionic pair. lfn > ho, there are isolated ionic pairs. The number of contact ionic pairs and the diffusional ionic mobility, which is determined by the residence time 'd, depend on n. The 23Na and I33Cs NMR data allow us to calculate the fraction of contact ionic pairs and to estimate a value proportional to 'd [6].

269

9

3 2

1

1I(2n +5)

0~__4 -_ _~_ _~0,_12___0~,1_6___

0,6

0,8 8

1/ n

-0,5 6

-1,0 2

-1,5

1

Figure 2. Proton chemical shifts of water as a function of moisture content in perfluorinated sulfocationite membranes. Points stand for experimental values, curves I through 8 for data calculated by equation (7); curve 9 for data calculated by equation (5); I - Lt, 2 - Na+, 3 - K+, 4 - Rb+, 5 - Cs+, 6 - Bal +, 7Cal., 8 - Mg l ., and 9 - W (5].

ho /

I

4

"

__ Na+(~.8) ....

I I I

Li+ (3.3)

3

I I

2

....

K+Q.5) Rb+(3.3) Cs. + . (3.0) "" "

I

H+(2.0)

,

0

0.57 0.76

l.01

1.34 1.49 l.68

Figure 3. Hydration number ho for H+ and alkali metal ions for Nation·type membranes [5).

r,A

270

a

0.6 0.4

'Li+ ,Mg2+ 2+ JVa , C , a, ,, ...

'i;r +

+,

2+

K ,Ba Rb+ ... ...

0.2

o

1.0 Figure 4. Proportion of broken H-bonds,

1.5

2.0

r,A

a, for alkaline earth metal ions in perfluorinated Nation type membranes[5]

It is seen from Fig. 5, that for CST the fraction of contact ionic pairs is greater than that for Na', but the residence time of Cs +ions on the SO) - group is smaller. This is because of different crystallographic radii, which make Na+ positively hydrated but Cs+ negatively hydrated . These data explain why Cs + ions penetrate the membrane easier than Na" ions: the Cs + ion interacts more strongly with SO) - groups than Na + and is more readily sorbed, but the residence time for Cs+ is shorter and Cs+ moves faster than Na+.

T I, T 2 relaxation measurements. Self-diffusion coefficient measurements. Spin-lattice and spin-spin relaxation processes were studied for protons of water molecules and for 7Li of Lt ions in Lt ionic form of the Nation membranes to obtain the correlation times for water and Lt mobilities. The correlation times and the motion activation energies were calculated from the temperature dependence of the relaxation rates r l, r2 using models based on the Bloembergen, Purcel, Pound theory. The method of calculation is given elsewhere [8]. The next step was to understand what kind of motion is characterized by these correlation times. From IH relaxation data [8], tH20 is the time of water molecule rotation by one radian, this being about the time for the elementary jump of a water molecule to the distance comparable to its size, 0.3 nm. From the 7Li relaxation data [9], th is the time of water motion oscillation about LiT ions; this is really the time for a hydrogen atom of a water molecule to move to the distance of the hydrogen bond between water molecules. td is the residence time of Lt ion on the SO) - group. These parameters characterize the elementary diffusion processes in the membrane completely. It is possible to calculate the macroscopic self-diffusion coefficients. The simplest way is to use the Einstein equation. For water, the self-diffusion coefficient will be

DC

H,O -

=~ 6 'f Hp

(1)

271

1,0

Pc

a)

b)

Ard

Cs+ Na+

0,5

°o

1

2

3

---ij-

o

n

4

1

Figure 5. The fraction of contact ionic pairs, Pc' (a) and the residence times

td

3

2

Cs+ Na+

4

n

ofNa+ or Cs· ions on the sulfo group

(b). (Obtained from 2JNa and IllCS NMR data [6]).

where d is the water molecule size equal to ca. OJ nm. For Lt ions 2

DC =~ u+ 6-rd

(2)

where r is the distance between the sulfo groups. The self-diffusion coefficients De H20, De Lt can also be measured directly using the PFG NMR technique. The values of 'tH20, 'th, 'td, DC H2O, D\t, D\120, D\t are shown in Table 1 for different n, where n is the number of water molecules per SO)- group. TABLE 1. Values Of'tH20, 'tho 'to, DeH2o , D\t, DeH20 , D\t for Nafion membrane. n 4 20

'th, S 8'10,\0 7'10,11

'td, S

'tH20,S

10,8

10'9 10,10

10,9

D CH20,

D\j+,

De H20,

D\t,

m 2 /s

m 2/s

5·10,12

2·10,12

m 2 /s 10,12

3·10,10

4·10'\0

8·10,11

m 2/s 10,12 10,11

As can be seen from Table 1, the self-diffusion coefficients calculated from the microscopic data are in a good agreement with the experimental macroscopic self-diffusion coefficients measured independently by PFG NMR. This is a very important result: ion and molecule transfer in the Nafion membrane is controlled by the times of ions or molecules jumps. These jump times are controlled by the interaction of ions or molecules with the charged groups as well as by the membrane channel structure. The contribution of the interaction to self-diffusion increases if the water content in the membrane decreases, because cations of metals interact directly with the charged groups at low n < ho to produce cation-anion contact pairs. Thus, there is a relationship between the water proton chemical shift and water molecule

272

self-diffusion coefficients for the Nafion type membranes in alkali metal ionic species (Fig. 6) [5].

(42+

11

0,1

0,5

1,0

Figure 6. Self-diffusion coefficient of hydration water VS. its proton chemical shift for Lt, K+, Rb+, Cs+, Sa 2" Ca 2+ and Mg2+ ions in perfluorinated sulfocationite membranes for n = 2.5 . For W species (Oc -tSmol = 4 ppm and D = 10- 10 m2/s for n = 2.5.

10-10

10-11 0,5

1,0

mg-eq Ion - exchange capacity - - ml Figure 7. Dependence of water self-diffusion coefficient on the ion-exchange capacity for Nation-type ion-exchange membrane.

The relationship between Ds and 0 was investigated at h=2.5 < ho; 0 characterizes the bond of water molecules with the ionogenic groups including the (S03-Me+)(H20)n system. As shown by high resolution NMR, an increase in the chemical shift corresponds to an increase in the water molecule-charged group bonds. Apparently, the possibility of jumps of ions or water molecules should depend on the distance between the charged groups and on the size of

273 hydrated charged species [1,2). For example, the self-diffusion coefficient is strongly dependent on the ionogenic group concentration (see Fig. 7). At high water content and high charged group concentration, the hydrated shelJs of charged groups overlap and an infinite network of hydrogen bonds appears (Fig. 8).

TT Figure 8. Situation corresponding to high sulfo group concentration and high water content.

Under these conditions the influence of the interaction of water molecules and mobile ions with sulfo groups not very specific and therefore, the selectivity of ion-exchange membranes is not very high.

R - SO;-------. H 0

TT H20~OH2 OH 2

Figure 9 Model corresponding to low concentration of su lfo groups and low water content.

At low water content and low charged group concentration, the hydration shells of charged groups do not overlap and the main reason for ion and molecule transfer is the entropy factor. Under these conditions transfer becomes very sensitive to the nature of the ion and water content n. This is the region of selective transfer where high membrane selectivity can be observed (Fig. 9). The self-diffusion coefficient can be obtained from percolation theory. For the entropy contribution to the self-diffusion coefficient [I] (Fig. 10):

D = DO exp[

p(a - n1/ 3 )'1 ]

(3)

274 where p and Il characterize the probability of molecules or ions migrating between neighbouring functional groups, a is determined by the density of water packing within the counter-ion hydration shells. These are exactly the parameters determining the membrane selectivity.

In(Dsxl013)

8 6 4

4

3

2

1

Figure 10. Dependence of water self-diffusion coefficients on moisture content in perfluorinated sulfocationite

membranes in the K+ form for p=-I.S9±O.OS and ,u=2.9±O.1 and in the Lt form for p=-I.5S±0.45 and ,u=2.3±O.S.

D,

m2/s

••

10-10 0

0

10- 11

10-12

10 -13

'---_-'--_.........._-'-_--'-_---'

o

Figure II . Dependences of water and Lt self-diffusion coefficients on water content for Li- form of Nafion-type

membranes. Lines are for the percolation equation (3). Points are for the experiment.

The dependence of the self-diffusion coefficients on the water molecule content is reproduced in Fig. II for water and Lt ions in Nafion membranes. It is clear that the self-diffusion process is described by percolation theory at low water content and that the parameters p, ).l and a are the same as those for water and Lt ions. This

275 means that at low water content the translational motions correlate for water molecules and for Lt ions. (The lines are parallel, see Fig. 11.) In conclusion, the elementary stages of water molecule and hydrated ion diffusion transfer can be assumed to be as follows . For example, T=300 K, n=20 I) "Oscillation" of H20 in the first hydrated Lt shell. 'th= 1O.los ; E = IS kJ/mol eLi spinlattice relaxation data [9]). 2) Jumps of water molecules at a distance equal to the water molecule diameter (OJ nm) 'tH20=0.9·10·los ; E=20.5 kJ/mol(IH relaxation data[8]). 3) Multistage diffusion of Lt ion from one sulfonic acid group to another DLt =r(n)/6'td(n), 'td=6.6·10-9 s, E=40 kJ/mol, r is the distance between S03' 'groups eLi spinspin relaxation data [9]). For low water content the situation is very similar but stages 2) and 3) are correlated. .

References

0/ Membrane Processes (phys. Chem. Series), Ellis Horwood, New York,246. Volkov V.1. and Timashev S.F.(1989) Magnetic resonance methods in the investigation of a perfluorinated ion exchange membrane, RussJ Phys. Chem., 63, I08. Volkov V.I., Gladkinh S.N ., Timashev S.F. etc.(1983) The investigation of pertluorinated sulfocation exchange membrane structure by NMR relaxation and paramagnetic probe methods, RussJChem.Phys., 2, 49. Volkov V.I., Muromtsev V.I., Pukhov K.K. etc. (1984) The investigation of pefluorinate sulfocation-exchange membrane structure by matrix ENDOR technique, Doki. Akad. Nouk. S.S.S.R, 276, 395. Volkov V.I., Sidorenkova E.A., Timashev S.F. etc. (1993) State and diffusion mobility of water in perfluorinated sulfocationate membranes according to proton magnetic resonance data, Russ J.Phys. Chem., 67, 914. Volkov V.I., Sidorenkova E.A., Korotchkova etc. (1994) The nature of the selectivity perfluorinated sulfocation exchange membranes to the alkali metals on high resolution NMR data for 7 Li , Na+, Cs' data, RussJPhys.Chem., 68, N2 2,275-281. Volkov V.I., Sidorenkova E.A., Korotchkova S.A. etc. (1994) The influence of non exchange sorbed electrolyte on the state and diffusion mobility of water and Na+, CST ions in perfluorinated sulfocation exchange membranes on high NMR 'H, Na+, CST date, RussJPhys.Chem., 68, N23, 500-505. Volkov V.I., Nesterov LA., Sundukov V.1. etc. (1989) The diffusion transfer of water in perfluorinated sulfocation exchange membranes as studied by pulse NMR, Russ-J.Chem.Phys., 8, 209. Nesterov LA., Volkov V.I., Pukhov K.K. etc. (1990) The magnetic relaxation of nuclei Li+ and litheum counterions and water molecules motions in perfluorinated su Ifocation exchange membranes. Russ.J.Chem,Phys., 9, 1155.

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