Ionic Hydration and Water Sorption Isotherms of Ion Exchange Resins

that the D'Arcy and Watt equation is unable to distinguish between a secondary hydration shell and the bulk water in the case of monovalent cations bu...
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Langmuir 1993,9, 1786-1793

1786

Ionic Hydration and Water Sorption Isotherms of Ion Exchange Resins Deoki Nandan, B. Venkataramani,’ and A. R. Guptaf Chemistry Division, Bhabha Atomic Research Centre, Trombay, Bombay 400085, India Received October 8, 1992. In Final Form: April 12,1993 Water vapor sorption isotherms of AP+,Mg2+,and Cs+ forms of variously cross-linked Dowex 50W ion exchange resins have been determined at 298 f 2 K using the isopiestic technique. Swelling pressures (r)and swellingfree energies (AG,) for the respective ionic forms have been computed from the isotherms by conventional approach. These data as well as the water sorption data on the Li+,Na+, and K+forms of variously cross-linked Dowex SOW resins reported earlier from this laboratory have been analyzed wing the D’Arcy and Watt equation and ita modified forma to distinguish between the strong and weak water sorption sites and multilayer formation. The ionic hydration numbers obtained from cross-linkingeffects and vapor pressure isotope effecta of cationites are found to be comparable to those derived from the present analysis based on the DArcy and Watt equation. These in turn have been compared with the hydration numbers of cations as obtained by various techniques using electrolyte solutions. It is found that the D’Arcy and Watt equation is unable to distinguish between a secondary hydration shell and the bulk water in the case of monovalent cations but can identify the secondary shell water molecules in the case of the Al3+ form very clearly. Multilayer formation in the water sorption isotherm is found to be related to swelling pressures, and swelling free energies are essentially free energies of dilution of cations.

Introduction Water vapor sorption isotherms of monovalent cationic forms of variously cross-linked Dowex 50W resin1P2and Nafion 1173*6have been analyzed to give information regarding cation hydration numbers, swelling pressures, and swelling free energies in the resin phase.lb It has been shown that ion exchange resins of polystyrenedivinylbenzenesulfonate (PSS-DVB)type behave like single ion solution^,^^ because the ionogenic groups are osmotically inactive and unhydrated.lOJ1 Hydrogen isotope effects in the dehydration of resins in different ionic forms have been used as a probe to study the counterionwater interactions.H From these studies it has been concluded that in low and moderately cross-linked and fully swollen resins, water is present either as the hydration sphere around the counterion or in the form of free or bulk water. These studies have led to a molecular interpretation of selectivitygin the PSS-DVB type resins in alkali metal forms. Thismodelgexplainsthe selectivity sequence for a given set of cations as well as the effect of cross-linking on the selectivity in terms of counterionwater and water-water interactions in the resin phase. However, in general besidescounterion-water and waterwater interactions, various other interactions, such as ionogenic group-water and ionogenic group-counterion interactions, play an important role in ion exchange selectivity.

* To whom all correspondence should be addressed. +Present address: JN 4, 9/11, Blue Heaven, Sector 10, Vashi, New Bombay 400703, India. (1) Nandan, D.; Gupta, A. R. Indian J. Chem. 1974,12,808. (2) Nandan, D.; Gupta, A. R. J. Phys. Chem. 1977,81,1174. (3) Pushpa, K. K.; Nandan, D.; Iyer, R. M.J. Chem. SOC.,Faraday Trans. 1 1988,84,2047. (4) Kellomaeki, A. Acta Chem. Seand. 1978, A32, 747. (5) Iyer, S. T.;Nandan,D.; Iyer, R. M.Zndian J. Chem. 1992,31A,317. (6) Gupta, A. R.; Nandan, D.; Sarpal, 5. K. J. Phys. Chem. 1982,86, 3257. (7) Gupta, A. R.; Nandan, D. J. Phys. Chem. 1985,89,4329. (8)Inamdar, N. C.; Sarpal, S. K.; Gupta, A. R. Indian J. Chem. 1991, 30A, 313. (9) Gupta, A. R. Indian J. Chem. 1990,29A, 409. (10) Marinsky,J. A.; Hoegfeldt, E. Chem. Sci. 1976, 9, 233. (11) Zundel, G.Hydration and Intermoleculorlnteractio~;Academic Preas: New York, 1966.

Very useful information on the ion-water interactions in the resin phase can be obtained by determining and analyzing simply the water sorption isotherms. For this purpose many approaches have been used. The BET equation has been fitted by KellomaekP to the water sorption isotherms of ion exchangers only in the low water activity region ( Na+ > K+ 2 Cs+. In the case of monovalent cationic forms of the resins, swelling pressures do not develop when the primary hydration of the cation is takingplace.2 Even in the highest cross-linked resin (12% DVB) primary hydration of the cations is complete, except possibly for Cs+. For Cs+, hydration number has been reported to be about 8 (see Table X), whereas 12% DVB resin in Cs+ form imbibes only 6.8 mol of water (Table I). In the case of Mg2+and A13+forms of the resin, apparently hydration of the cation is complete even in 12 % DVB resin. Mg2+and A13+forms imbibe 23.7 and 29.1 mol of water per mole of ion, reepectively, (Table I),much greater than their hydration numbers (see Table X). However in the multivalent cationic forms of the resin the trend of the higher the swellingthe higher the swelling pressure is not observed. Multiple bonding of R803- groups to di- and trivalent ions (that is, electrostatic effects), possibly restricts the hydration of cations in the resin and subeequently the expansion of the resin network. In this respect, these multivalent cationic forms of the resin resemble a Cs+ form of the resin with lower swelling pressures at higher cross-linking. This is consistentwith the greater selectivity of resins for these cations. Further, the choice of 1% crosslinking as reference non-cross-linked exchanger may not be strictly valid, where the hydration of the cation is not complete as in the case of Cs+ and multivalent cationic forms of the resins.

I

I

0.4

I

I

0.6

I

0.8

I

I 1.0

a,

I O

a,

(21) Boyd, G. E.; Soldano, B. A. 2.Elektrochem. 1953,57, 162.

I

0.2

Figure 3. Water vapor sorption isotherms of 1% ( 0 ) , 2 % (O), 4% (A),8% (e),and 12% (X) cross-linked Dowex 60W reem in the Cs+ form at 298 K.

SwellingFreeEnergies (AGsw). The integral swelling free energiesof various resinates were computed using the following equation (eq 2)2*3*4J6

For obtaining &/awat a, = 0, the following BET equation was used3v4(eq 3) a, 1 --=1-awn,

1 + (B-Ua, Bn, Bn,

(3)

where B and nmare constants. For the present system, [aw/(l- a,)] (1/&) was plotted against a, up to aw= 0.4, which gave straight lines with intercepta 0.03,0.006, and 0.004 for Cs+,Mg2+,and A13+ forms, respectively. The inverse of these intercepts is &/aw at aw = 0. AGsw computed for the three ionic forms are also given in Table I. The AGsw values for other alkali metal ionic forms available in literature? are also included in Table I, for comparison. As can be seen, apart from the usual sequence for cross-linking, i.e. 12 % > 8 % > 4 % > 2 % > 1 % ,the following ionic sequence is obtained for AG,, for each individual cross-linking: M+ > Mg2+> A13+ (M = alkali metal ion). The implicationsof these results on the hydration of ions and other interactions in the resin phase will be discussed in the following section dealing with D’Arcy and Watt analysis of water sorption isotherms. Analysis of the Water Sorption Isotherms by the D’Arcy and Watt Equation. The D’Arcy and Watt equation14J6used to analyze the water sorption isotherms is versatile in the sense that it not only can analyze Langmuir (monolayer) or multilayer-type isotherm but can also distinguish between different types of sorption

Water Sorption Isotherms of Ion Exchange Resins

Langmuir, Vol. 9, No.7, 1993 1789

sites that constitute the Langmuir isotherm. The general form of the DArcy and Watt equation islS 1 K{Kla, k'ka, W = C +Caw+1- ka, p o 1 + Kia,

(4)

where W is the amount of sorbate (g/g of dry resin) and the f i t term on the right-hand side refers to the Langmuir type sorption sites, the second term refers to the sorption sites which can be approximated to linear sorption isotherm, and the third term to the multilayer formation. In this equation, a, = p/po is the water activity, Ki = mni/N, where m is the molecular weight of water, ni the number of sites of the ith type, N is Avogadro's number, and i is the number of different types of primary sites. Ki is the interaction parameter related to the heat of sorption of sorbate (water)on the ithsite.16 Cis a constant assigned for the linear form of sorption isotherm. k' = mD/N where D is the number of sites for multilayer formation and k' is a parameter related to the heat of sorption of sorbate in the multilayer formation. In the earlier analysis14,eq 4 was used as such to analyze the water sorption data of Li+, Na+, and K+ forms of variously cross-linked Dowex 50W resins. A contribution from the second term obtained in that analysis led to a broad conclusion about the existence of weak sorption sitea, but no specific information regarding the number and strength of binding of the sites could be obtained. When i was set to 2, alongwith the secondterm, the number of strong sites was distributed between i = 1 and i = 2 (without significant change in the value for the second or third term). In the earlier analysis, the sum of the contribution from the first and second term was assigned as the primary hydration number of the cations. Thus, the primary hydration numbers were 3.2 for Li+, 2.8 for Na+, and 1.8 for K+. No specific attempt was made to obtain additional informationregarding strong (first term) and weak (second term) sites. In the present study, apart from the original D'Arcy and Watt equation (eq 4) two other modifications of the equation were used to analyze the water sorption data. 1. The second term of the D'Arcy and Watt equation was set to zero, and the data were analyzed using the first and the third term. This modification results in the following equation: W=

KIK',a, k'ka, 1 Klaw 1- ka,

+-

+

This modification will enable us to find out the weak sorption sites which are Langmuir-type. 2. The second term was dropped (C= 0) and i was set to 2, that is, the f i t term will have two sets of parameters, Kl', K1 and Kz', K2. This modification results in the following equation, in the expanded form: W=

K,'Kla, K,'K-,a, 1 Klaw 1 K2a,

+

+ -

+

+-1kk'a, - ka,

(6)

This modification was done to split the total number of Langmuir sites obtainable from the Fist modification (eq 5) into weak and strong sorption sites. In the following discussion, use of eq 4 is referred to as method 1, eq 5 as method 2, and eq 6 as method 3. A computer program based on nonlinear least-squares analysiswas used for fitting the equation to water sorption data. The program calculates the water sorbed at various water activitiesusingthe optimized parameters. The error in fitting the experimental data to the computed values for a certain set of values for the different parameters is given by

Table 11. Water Sorption Data for Cs+ Form of 4% DVB Dowex 50W Resin amount of water sorbed difference water (g/g of dry resin) ( o b 4 - calcd) activity a, observed calculatedo (g/g of dry resin) 0.195 0.0710 0.0690 0.0020 0.305 0.0892 0.0898 O.ooo8 0.510 0.1256 0.1311 -0.0055 0.615 0.1619 0.1568 0.0051 0.680 0.1720 0.1761 -0.0041 0.730 0.1960 0.1940 0.0020 0.0021 0.894 0.3128 0.3107 0.970 0.5404 0.5417 -0,0013 0.0002 1.000 0.9447 0.9445 error sum squareb = 0.8756 X l(r standard deviationC= 0.0072 a

Using eq 4. Equation 7. Equation 8.

Table 111. Water Sorption Data for Ala+ Form of 4% DVB Dowex 50W Resin water activity

amount of water sorbed (g/g of dry resin) a, observed calculated" 0.170 0.2291 0.2170 0.270 0.2476 0.2570 0.450 0.3247 0.3330 0.3582 0.505 0.3502 0.631 0.3796 0.3706 0.5047 0.5047 0.755 0.880 0.6665 0.6483 0.910 0.7154 0.7102 0.8657 0.955 0.8558 1.2840 1.000 1.2850 error s u m squareb = 0.6426 X 10-9 standard deviationC= 0.03637

difference (obsd - calcd) (g/g of dry resin) 0.0121 -0.0094 -0,0083 -0.0080 O.Oo90 O.oo00

0.0082 0.0052 -0.0099 0.0010

Using eq 4. Equation 7. Equation 8.

error sum square = c(Wi(obsd)- Wi(calcd)I2 (7) 1

The program optimizes the parameters by minimizingthe above function (eq 7). As an example, in Tables I1 and I11the actual values of water sorbed at different water activities by Cs+and A13+ forms of the resins and the values calculated by fitting the data to D'Arcy and Watt equation (eq 4)are given. The error sum square (eq 7) and standard deviation defied by standard deviation = ( ( z r 2 ) / n-[(zr/n)21]1/2 (8) where r = I[ Wi(0bsd) - Wi(calcd)]l and n is the number of data points, are also listed at the end in Tables I1 and 111. The total amount of water actually associated with the differentcategoriesof sites at saturation (a, = 1)for various ionic forms of resins are included in Tables IV-IX. The amount of water associated with each type of site (Wj) is given in terms of the number of moles of water per mole of ion. In method 1,W1represents water associated with strong sites and W, that associated with weak sites. In method 2, WI represents total water associated with both strong and weak sites. In method 3, W1 represents water associated with strong sites and W2 that aesociated with weak sites. W3 in all the three methods give the amount of water in the multilayer. Thus we have method 1:

W = Wl+ W,+ W, ( a t a , = l )

(9)

method 2: W = W, + W, (at a, = 1) (10) method 3: W = W, + W2 + W , (at a, = 1) (11) Tables IV-IX also include values of the interaction parameters of different types of sorption sites (KI, K2, k )

1790 Langmuir, Vol. 9,No. 7, 1993

Nandan et al.

Table IV. Parameten of D’Arcy and Watt Equation Obtained by Three Methods for Li+ Form of Variously Cross-Linked Dowex SOW Resins. %cross-linking 1

2 4 12

method 1 2 3 1 2 3 1 2 3 1 2 3

W1 0.72 2.36 1.04 0.64 2.35 1.87 0.66 2.24 0.41 0.65 1.68 0.43

K1 17.16 2.24 2.19 25.04 2.27 2.31 25.6 2.22 104.0 28.2 4.39 149.9

Kz

WZ 1.37

Wc 2.37

1.95 2.58

0.71

0.47 2.33

2.19

0.59 2.52

2.14

0.57

WS 49.26 49.99 49.93 31.22 32.09 31.87 18.68 19.43 19.07 6.04 7.51 6.64

kx10-9 980.1 978.4 978.6 967.0 963.7 964.8 939.2 934.1 936.7 836.9 790.0 822.0

W1+ Wzor WI+ Wc 3.09 2.36 2.41 3.22 2.35 2.58 2.99 2.24 2.60 3.17 1.68 2.57

errorsumsquare* 0.009

0.0003 0.0003 0.009

0.0003 0.0002 0.008

0.0002

o.oooo1 0.008 o.Ooo1

o.oooo1

a W1, Wz, W,, and W3 are the amounta of water associated with different types of sorption sites at aw = 1 and are expressed as moles per mole of the ion. Data from ref 14. Error sum Square E,”(Wj(0bil) - Wi(Cal))’.

*

Table V. Parameters of D’Arcy and Watt Equation Obtained by Three Methods for Na+ Form of Variously Cross-Linked Dowex SOW Resins. %cross-linking 1 2 4

8

method 1

2 3 1 2 3 1 2 3 1

2 3 12

1

2 3 a Data

W1 1.54 2.10 2.10 1.48 2.09 2.09 1.56 2.04 0.44 1.63 1.66 0.84 1.32 1.94 0.97

K1 3.21 2.33 2.33 3.53 2.32 2.32 3.86 2.65 3.44 3.90 3.81 6.82 4.28 2.60 4.66

WZ

Kz

0.02

0.02

W, 0.81 0.84

0

0

0.65 1.57

1.26 0.07

0.95

1.47 0.99

1.03

1.12

WS 48.59 48.81 48.83 30.32 30.56 30.56 17.09 17.26 17.28 8.17 8.20 8.08 6.13 6.40 6.34

kX10-3 982.9 982.3 982.3 973.2 972.3 972.3 951.7 950.6 950.2 855.1 854.3 857.6 859.1 849.4 860.6

WI+ Wzor WI+ Wc 2.35 2.10 2.12 2.32 2.09 2.09 2.21 2.04 2.01 1.70 1.66 1.79 2.31 1.94 2.00

errorsumaquare 0.006 O.ooOo3 O.ooOo3 0.009

o.oooo1 o.oooo1 0.002 o.oooo1 0.m1 0.002

0.00000 0.00000 0.002 0.m1 0.00000

from ref 14. Other details as in Table N.

Table VI. Parameters of D’Arcy and Watt Equation Obtained by Three Methods for K+ Form of Various Cross-Linked Dowex SOW Resins* %cross-linking 1

2 4 8 12

method 1 2 3 1 2 3 1 2 3 1 2 3 1

2 3 0

WI 1.03 0 0 0.97 1.33 0.92 0.92 1.48 0.67 0.92 1.30 0.69 0.88 1.27 0.74

KI 12.02 0 0 12.46 6.55 10.37 12.95 5.32 17.36 13.60 7.01 18.24 14.38 6.99 16.33

WZ 0

KZ

Wc 0.36

0

0.61 0.46

1.69 0.82

0.92

1.25 0.74

0.74

1.62 0.82

0.70

1.22

WS 48.15 49.53 49.53 27.04 27.28 27.23 15.22 15.56 15.42 6.86 7.23 7.10 5.81 6.24 6.07

kx10-9 986.0 980.4 980.0 977.2 976.1 976.4 964.2 961.4 962.7 910.3 901.3 905.1 898.3 885.5 891.3

WI+ Wzor WI+ W, 1.40 0 0 1.58 1.33 1.38 1.74 1.48 1.59 1.66 1.30 1.43 1.70 1.27 1.44

errorsumsquare 0.006

0.029 0.029 0.007

O.ooOo3

o.oooo1

0.005 O.ooOo4

o.oooo1 0.004

o.ooo02 0.00000 0.003 0.m2

0.00000

Data from ref 14. Other details as in Table N.

and also the error in fitting the experimental values to computed values (eq 7).

Discussion

Li+Form of the Resin. The amount of water associated with strong (Wd and weak (W,or WZ) primary sorption sites (that is, the first and second terms in the D’Arcy and Watt equation, analyzed by different methods) at a, = 1 for the Li+ form of the resin is given in Table IV. Nearly 0.65 mol of water per mole of the ion is associated with and about 2.Ck2.6 mol per mole is strong sites (WI) associated with the weak site ( W,or Wd. Thus, the total amount of water associated with the sorption sites (weak and strong) is 3.0 to 3.2 mol per mole. The D’Arcy and Watt equation looks upon the rest of the water associated

with Li+ as multilayer formation or bulk water. Crosslinking effects2give a value of 4 for the primary hydration number. Hydration of ion in the resin as well as electrolyte solutions have been studied by a number of techniques and the hydration numbers obtained for the ions relevant to the present study have been compiled and are given in Table X. It is seen from Table X,that about 13 mol of (22)Dzidic, I.; Kebarle, P. J. Phys. Chem. 1970, 74, 1468. (23) Schustar, P.; Jakubetz, W.; Mariw, W . In Topics in Current Chemistry; Springer-Verlng: Berlin-Heidelberg, 1975; Vol. 60,p 119. (24) Burgess, J. Metal Ions in Solution; E h Harwood Sons: Chichester, 1978. (25) Jqcso,G.; Bopp,P.;.Heinziier, K. ReportKFKI-l977-101,1977. (26) Hemzinger, K.; Pahkas, G. In Interactions of Water in Ionic and Non-ionic Hydrates; Kleeberg, H., Ed.; Springer-Verlag: BerlinHeidelberg, 1987;p 1.

Water Sorption Isotherms of Zon Exchange Resins

Langmuir, Vol. 9, No. 7, 1993 1791

Table VII. Parameters of D’Arcy and Watt Equation Obtained by Three Methods for Cs+ Form of Variously Cross-Linked Dowex SOW Resins. %cross-linking method W1 K1 W Z K2 W, W3 kxl0-8 W1+ WzorWl+ W, errorsumsquare 1 1 0.74 21.83 2.71 37.75 992.0 3.45 0.0002 2 2.91 1.79 2.91 38.3 992.0 O.OOO6 3 1.63 2.78 1.29 0.86 2.92 38.29 992.0 O.OOO6 1.11 22.10 2 1 1.77 2.20 983.0 2.88 0.0002 2 2.69 1.47 22.20 983.0 2.69 0.0003 3 2.07 1.66 0.70 2.77 22.13 983.0 0.39 0.0002 13.13 972.0 4 1 0.73 30.25 2.24 2.97 0.00009 2 2.50 1.86 2.50 13.59 969.0 0.0002 3 1.64 2.67 0.96 0.42 2.60 13.49 969.0 0.0002 3.77 969.0 8 1 0.59 26.25 3.18 4.05 O.ooOo7 961.0 2 3.16 1.17 4.16 3.16 0.0002 3 1.91 1.30 1.38 0.56 3.29 963.0 0.0002 4.56 3.85 974.0 3.01 12 1 0.53 39.00 3.32 0.0002 2 3.19 1.16 3.19 963.0 0.0003 3.64 3 1.93 1.15 1.42 3.35 966.0 3.47 0.55 0.0003 Data from present study. Other details as in Table IV. Table VIII. Parameters of D’Arcy and Watt Equation Obtained by Three Methods for M d + Form of Vadously Cross-Linked Dowex SOW Renins. %cross-linking method WI K1 Wz Kz Wc W3 k x 10-8 W I +W2or W1+ W, errorsumquare 1 1 3.14 >250 9.78 48.48 993.7 12.92 O.OOO54 2 11.1 2.7 50.1 992.6 11.1 0.0083 3 11.08 2.7 0 0 11.08 50.1 992.6 0.0083 980.5 2 1 3.34 >250 13.2 9.78 29.9 0.00047 2 11.16 3.3 11.16 31.8 987.3 0.0063 988.7 3 3.01 117.4 7.28 0.39 0.0002 30.6 10.29 962.2 4 1 3.70 125.1 6.42 23.28 10.12 o.oO071 2 6.86 11.4 943.9 26.52 0.0015 6.86 953.1 3 4.06 41.0 4.30 0.67 25.02 8.36 0.0002 891.9 8 1 4.48 50.5 4.22 12.52 8.70 0.00074 2 6.18 17.4 6.18 859.5 14.98 0.00053 868.2 14.36 3 5.18 26.4 1.62 0.76 0.0002 6.80 12 1 3.80 125.6 925.3 13.50 9.70 6.0 0.00021 848.1 9.38 2 6.16 16.5 0.00093 6.16 3 3.64 92.2 4.38 0.86 7.62 895.7 8.02 0.0003 a Data from present study. Other details as in Table IV. Table IX. Parameters of D’Arcy and Watt Equation Obtained by Three Methods for Al*+Form of Variously Cross-Linked Dowex SOW Resins. % cross-linking method Wl Ki w3 kx10-9 W l +Wzor W I +W e error sum q u a r e 1 1 6.66 149.4 7.74 55.8 967.7 14.40 o.Ooo19 9.84 20.4 955.9 9.84 2 60.33 0.0016 6.33 208.5 3 6.42 0.56 57.42 12.75 964.0 0.00034 4.83 472.3 18.72 2 1 13.89 43.38 982.1 0.00020 10.71 51.24 969.5 2 489.4 0.0011 10.71 521.9 13.74 0.73 3.06 16.80 45.3 979.7 3 0.00043 5.43 17.07 954.0 4 1 395.7 11.64 27.87 O.OOO64 12.54 12.54 32.25 937.5 4.8 2 0.0026 4.80 29.64 948.0 249.7 3 10.47 0.48 15.27 0.001 907.1 647.9 8 1 10.02 15.69 5.79 15.81 0.00017 943.3 18.0 9.45 21.75 2 9.45 0.0013 13.38 887.3 5.43 >3750 18.06 3 7.95 0.58 0.00031 984.7 13.14 10.41 18.63 5.49 12 1 68.4 0.00053 959.3 2 14.85 2.9 14.04 14.85 0.0029 12.06 974.0 3 4.11 >3750 12.81 0.58 16.92 0.0011 a

Data from present study. Other details as in Table IV.

water per mole of Li+ is present together in primary and secondary hydration shells. In 12% DVB resin, only 9 mol of water per mole of Li+ is present (Table IV). Thus, in the latter, the secondary hydration shell of Li+ is not complete. Analysis of the water sorption data by the D’Arcy and Watt equation (Table IV) indicates that in ~~~

~

(27) Narten, A. H.; Vaelow, F.;Levy, H.A. J. Chem. Phys. 1973,58, 5017.

(28)Maeda, M.; Ohtaki, H.Bull. Chem. SOC.Jpn. 1976,48,3755. (29) Terekhova, D. S., Ryss, A. 1.;Radchenko,I. V. Zh.Strukt. Khim. 1969, IO, 923. (30)Lawrence, R. M.;Kruh, R. F.J. Chem. Phys. 1967,47, 4758. (31) Ohtamo, N.;Arakawa, K. Bull. Chem. SOC.Jpn. 1979,52,2755; 1980,53, 1789.

(32) Glueckauf, E. Trans. Faraday SOC.1966,61, 1241. (33) Gieae, K.;Kaatze, U.; Pottel, R. J. Phys. Chem. 1970, 74,3718.

12% DVB cross-linked resins, 6 mol of water is present in the multilayer and 3 mol is associated with the primary sorption sites (both weak and strong). Thus,the DArcy and Watt equation fails to distinguish between secondary hydration shell water molecules and bulk water. As the water content of the Li+ form increases (with decrease in the cross-linking) the amount of water 8880ciated with the f i t two terms of the D’Arcy and Watt equation (“1 + WZ) or (W I+ WJ, remainnearlythe same, but that present as multilayer increases. So, at lower crowlinkings, the secondary hydration and bulk water (multilayer formation)become indistinguishable. Accordingly, as the cross-linking decreases, the D’hcy and Watt equation only shows an increase in the multilayer for-

1792 Langmuir, Vol. 9,No. 7, 1993 technique 1. VPIE studies Primary

Li+

Nandan et al. Table X. Hydration Numbera of Cation3 Na+ K+ CS+

4.9** 8.7**

3.0' 6.0

2.mobilities 3.conductivities (Gusev) 4. diffusion 5. compreesibilitiea 6.NMR peak area

3.5-7 2-3 5 2.7

2-4 2.5-3.5 3 3.9

1 3.2

7.dielectric constants 8.MD simulations 9.entropies 10.X-ray diffraction X-ray diffraction

3.4-5.0 6 6.1 5 4 4*1

3.0-4.6 4 6.5 4

1.0-4.6 4 7.8 3

4

11. neutron diffraction 12.dielectric studies 13.cross-linkingeffects 14.DArcy & Watt analysis

4 3.2-5.5 4 3.0-3.2

8 2.1-4.5 3.5 2.0

NMR

a

* 1.5

2.3' 6.7

Mga+

Ala+

2.81 5.2 5.5 1

5.3

10.5-13 8 9 7-16 6

11

10-13 6

1.0-3.9 7.9

15.5 6.0 13 6-8

21

8.0 6-8 (PI 12-13

12.0 5-6 (P) 13-18

(total)

(total)

2-4

8 1.1-3.2 3.3 1.2-1.8

8 1.1-1.5 2.8 3.0-3.5

ref 8 '353 K **303K 24 24 24 24 24 24 24 25,26 24 24 27,28 29,30 27,31 32,33 2 (PW) (PW)

PW, present work. P = primary.

mation. This is substantiated by the increase in the value of the interaction parameter for the multilayer formation, k, as the cross-linking decreases. Na+ Form of the Resin. Nearly a constant value of 2 mol of water per mole is associated with Na+ in the resin phase (Table V), for all the cross-linkings. Both the water molecules have comparable values for the interaction unlike for Li+where the value for parameter (K1 and Kz), K1 was larger than K2. Hence, when the second term is set to zero (method 2 and 31,even at lower cross-linkings, both the water molecules are associated either as W1 or ( W1 WZ). To some extent, the weaker of the two water molecules could be distinguished at higher cross-linking (12% DVB resin). Cross-linking effects2give a value of 3.5 for the primary hydration number of Na+. Various techniques give values between 2 and 5 for the hydration number of Na+ (Table X). Thus, the D'Arcy and Watt equation could identify only the primary hydration shell around Na+;the secondaryhydration shell water molecules become indistinguishable from bulk water. K+Form of the Resin. Results of the analysis of water sorption data by the D'Arcy and Watt equation indicate that a totalof 1.2-1.8 mol of water per mole are associated with K+in the resin phases (Table VI). Out of this, nearly 1 mol interacts more strongly than the rest of the water molecules, as distinctly seen in higher cross-linked resin. Cross-linking effects2give a value of 3.3 for the primary hydration number of K+. Various techniques give values between 1 and 7 for the hydration number of K+ (Table X). Thus, the D'Arcy and Watt equation distinguishes only the primary hydration shell water molecules. In 1% DVB resin, when the second term is set to zero (methods 2 and 31, it appears as though all the water molecules are present as bulk water and there is no hydration shell around K+ (Table VI). This means that in presence of a largeamount of water, there is no hydration shell structure around K+.Vapor pressure isotope effects (VPIE)studies8indicate that in the case of K+,even before the primary hydration shell gets completed, water molecules start forming H-bonds among themselves. Thus, the distinction between the primary and secondary hydration shellsis lost. Especially,when the water content is more (as in 1%DVB resin), the bulk water structure is formed at the expenseof hydration shellstructure around K+ (at room temperature). VPIE studies also indicate that the primary hydration number of 2.3 reallyrepresents

+

water molecules present as nearest neighbors around K+ in fully swollen form, which do not form H bonds among themselves. Cs+Form of the Resin. Analysis of water sorption data indicates that 3.0-3.5 mol of water per mole are associated with Cs+ in the resin phase (Table VII). All the water molecules interact very weakly with the cation. Hence, when the second term in the DArcy and Watt equation is set to zero (method 2), the total number of sorption sites is nearly the same as those obtained by method 1 (WI + Wc) or method 3 (WI + WZ). Crosslinking effects give a value of 2.8 for the primary hydration number for Cs+ (present work, vide infra). Various techniques give values between 1 and 8,for the hydration number of Cs+ (Table X). VPIE studies*give a value of 2.8 for the primary hydration number (Table X). VPIE studies also indicate that Cs+behaves like K+,in the sense that the bulk water structure is stronger than the hydration shell around the cation (at room temperature). However, unlike K+, at higher water content (asin 1 % DVB resin), specific values for the sorption site are obtained in the case of Cs+for all three methods (Table VII). This could be due to the presence of solvent-shared structure3in the resin phase-SOs-(HzO)Cs+ which has been invoked to explain the selectivity of Cs+by the ion-exchange resins. Me+Form of the Resin. In the Me2+ form of low crow-linked (1% and 2% DVB)resin, the analysis of the water sorption data by all three methods showsthat about 12-13 water molecules are associated strongly with the cation (Table VIII) and can be distinguished from the bulk water. Aa the cross-linking increases, only method 1 seems to give the same result. When the second term is put to zero (method 2 and 3) the number of water molecules per Mg2+ distinguishable from the bulk water are between 6 and 8. Thia could be attributed to the primary hydration number of Mg2+in the resin phase. The crow-linkingeffect gave a value of 8 for the hydration number (videinfra). Other techniqueshave shown (Table X) that the primary hydration shell has 6-13 water molecules. Thus,the analysis of the water sorption data by the DArcy and Watt equation is able to distinguish to some extent between primary and secondary hydration and is unable to differentiatebetween secondmyhydration shell water and bulk water molecules. These conclusions are consistent with the analysis of swelling pressure data,

Water Sorption Isotherms of Ion Exchange Resins where it was inferred that the hydration of Mgz+was not complete in the resin phase at higher cross-linkings. AI8+Form of the Resin. For the A13+form of the resin, the analysisof the water sorption data indicates that about 13-18 water molecules are associated with the cation in low cross-linkedresins (Table 1x1. These water molecules can be clearly distinguished from bulk water. When the second term is set to zero and the first term split into two (method 31, the contribution from the parameter W Zis nearly the same as that of W,(method 1) for all crosslinkings. This means that the weak sorption sites can be clearly identified in the case of A13+ for all cross-linkinga as compared to other ionic forms. Thus, in the case of the A13+ form of the resin, the existence of primary and secondary hydration shells can be distinguished by the D’Arcy and Watt equation. As the charge of the cation increases, the D’Arcy and Watt equation is able to distinguish between secondary hydration shell water molecules and bulk water. Cross-linking effects give a value of 12 for the hydration number of A13+ (vide infra) and other techniques give 6 to 31 as the value for the hydration number of A13+ (Table X). These observations support the conclusions drawn from the swelling pressure data of the variously cross-linked A13+ form of the resin, that the hydration of A13+is not complete in higher crosslinked resins. The very high value for the interaction parameter K1 (method 3) compared to KZ (method 3) (Table IX) indicates that the first few water molecules interact with the cation very strongly compared to other water molecules (asobserved in the case of Li+ (Table IV) and Mgz+(Table VIII)). When method 2 is used for the analysis of the data, we get an averaged out value for all the water moleculespresent in the hydration shell (primary + secondary). Thus, for A13+and to some extent for Mgz+,W Z(method 3) refers to the secondary hydration shell,but for univalent cations, the secondary hydration shell cannot be distinguished from bulk water. Comparison of results for various parameters obtained from methods 1, 2, and 3 lead to the following: When the C term is set to zero, most of the water accounted for by this term goes into the Langmuir term (methods 1 and 21, when the C term is zero and the Langmuir term is split into two terms (method 3), the totalamount of water accounted for by the Langmuirterms remains the same (methods 2 and 3). However, in resins of high cross-likings (8%or 12%DVB), method 3 seems to give higher values, that is, WI(method 2) < (WI + WZ) (method3). This apparently arises because, in the absence of free water (multilayer term) hydration shells of cations become increasingly more predominant. From these analyses, it is obvious that (W1+ Wc) (method 1) or W1 (method 2) or (W1+ “2) (method 3) gives the water molecules associated with the hydration shells of cations. From the VPIE results on the monovalent ionic forms of the resins,8it was concluded that the primary hydration number of Li+ in resin is nearly 5 and the total hydration number (that is, primary + secondary hydration shells) about 13 (Table X). Thus, the analysis of water sorption isotherms of resins by the D’Arcy and Watt equation gives information only about the primary hydration shell and the secondary hydration shell cannot be separated or distinguished from multilayer formation for monovalent ions. The fact that VPIE (resin) gives a higher hydration number than the D’Arcy and Watt equation arises because the former is looking at the hydrogen bonding among the water molecules,whereas the latter looks at the totalenergy or interaction. As this interaction energy is mainly

Langmuir, Vol. 9, No. 7, 1993 1793 composed of electrostatic interaction between cations and water molecules, the hydrogen bonding energy between hydration shell water molecues (which is comparable to hydrogen bonding in liquid water) is only a small component of the total interaction energy and cannot be distinctly separated from the multilayer formation. It is for this reason that K1 (method 1) or K I(method 3) is much higher than K1 (method 2) or KZ(method 3). This means that the first water molecule is very strongly attached to the cation by electrostatic forces. The same feature was observed by Kebarle et al.2233in their studies on ionic hydration in gas phase using a mass spectrometric technique. The interaction energy between water molecules and the cation decrease sharply as the number of water moleculesincreases. The D’Arcy and Watt equation is unable to distinguish between hydration shell water molecule (above 3) and the multilayer water molecules. Gas phase studies of ionic hydration are usually confined to about 8 to 10 water molecules. On the other hand, VPIE studies of ionic hydration in resin phase can distinguish between primary, secondary, and bulk water molecules at room temperature, and this distinction sharpens as the temperature increases. N

Conclusions The analysis of water sorption isotherms in terms of cross-linkingeffects, swelling pressures, and swellingfree energies give a qualitative picture of the state of water in the resin phase. A 1 % cross-linked resin does not appear to be a valid referencefor calculatingthe swellingpressures of Cs+ and multivalent forms of resins. These features can now be easily explained on the basis of information obtained by the analysis of water sorption isotherms by the D’Arcy and Watt equation. The hydration numbers obtained from cross-linking effects are in qualitative agreement with those obtained from the fiit two terms of theD’Arcyand Wattequation (eq4). Swellingpregeurea are closely related to the multilayer formation, that is, the third term in the equation (eq 41, and as such do not give much information about the hydration of the cations in the resin. Swelling free energies are essentially free energies of hydration and are consistent with the greater hydration of the ions in the resin as the cross-linking decreases from 12 to 8 to 4% DVB. Below that crosslinking, the contribution to the free energies of swelling comes from the free energies of dilution which is usually stable (multilayer formation or osmotic swelling). That is the reason that free energies of swelling reach a limiting value at low cross-linkings. In conclusion, the present study shows that the water sorption isotherms of the ion exchange resins of various cross-linkingscan give valuable informationabout the state of water in the resin phase, provided they are analyzed from various angles, like cross-linking effecta, swelling pressures, free energies of swelling, and statistical mechanicalapproach to sorptionphenomena (asin the D’Arcy and Watt equation). Acknowledgment. The authors wish to thank Dr. J. P. Mittal, Associate Director, Chemistry Group, for his keen interest and encouragementduring the course of thii investigation.