Nature and Properties of Water in Montmorillonite-Water Systems1

PHILIP F. Low2

ABSTRACTData are presented on several properties of water in mont-

morillonite-water systems. The data indicate that these prop-erties differ from the same properties of bulk water becauseof differences in intermolecular bonding. Also, it is found thatthe value, J, of each property is described by the general equa-tion / = J° exp /3/(mw/mm) in which /" is the value of thegiven property in pure bulk water, m^/mm is the mass ratio ofwater to montmorillonite and /J is a constant. The proposalis made that, since all of the water properties obey a commonequation, their deviation from the corresponding properties ofbulk water must be caused by a common factor. By makingappropriate substitutions for mn/mm and analyzing the result-ing equations, the common factor is shown to be interaction ofthe water with the surfaces of the montmorillonite layers. Thenature of this interaction, and ways in which it might affectintermolecular bonding, are discussed.

Additional Index Words: clay, hydrogen bond, thermody-namics.

Low, P. F. 1979. Nature and properties of water in montmoril-lonite-water systems. Soil Sci. Soc. Am. J. 43:651-658.

FOR SEVERAL YEARS the author has entertained thehypothesis that long-range interaction between

water and the surfaces of clay minerals influences thestructure and properties of the water and, thereby,many of the chemical and physical processes that occurin soils and sediments (1, 16, 17, 24). In support ofthis hypothesis, he and his colleagues have found thatthe interlayer water in montmorillonite differs frombulk water, e.g., in specific volume (1), specific heatcapacity (22), heat of compression (13), specific ex-pansibility (3, 25) and viscosity (18, 19). Heretofore,however, most of these properties have not been de-scribed mathematically. Nor have they been interre-lated. The objectives of the present paper are toreanalyze existing data and contribute new data on theproperties of interlayer water, to describe these prop-erties mathematically and to show their interrelations.If these objectives are accomplished, our understand-ing of water in soils and sediments will be greatlyenhanced.

Before examining the results, consider any extensiveproperty, X, of a two-component system composed ofwater and montmorillonite. If we designate the massesof water and montmorillonite by mw and mm, respec-tively, then xw, the partial specific property of thewater in the system, is defined by

"tO ~~ l^ -A- I Qi**V)jP' T ttlm I J

where P is the pressure and T is the temperature. Fur-ther, <t>x, the apparent specific property of the water inthe system, is defined by

<t>x = (X - mm x°m)/mw [2]where x°m is the specific property (i.e., the value of theproperty per unit mass) of the pure montmorillonite.From these definitions, it is evident that xw is a dif-ferential quantity, whereas, 0X is an average quantity.

If we solve Eq. [2] for X and let X equal, successively,the heat capacity, C, the enthalpy, H, the entropy, S,and the volume, V', the resulting equations are:

[3][4][5][6]

C = mm c°m + mw <t>c

H = mm h°m + mw <f>H

S = mm s°m + mw 0S

V = mm v° mw <t>v

in which c°m, h°m, s°m, and v°m are the specific heat ca-pacity, specific enthalpy, specific entropy and specificvolume, respectively, of the pure montmorillonite andQC, ^H, Qs and <t>v are the apparent specific heat capac-ity, apparent specific enthalpy, apparent specific entro-py and apparent specific volume, respectively, of thewater in the system. We will now operate on Eq. [ 3 ] toEq. [6] to derive several equations that we shall uselater.

Differentiation of Eq. [4], [5], and [6] with re-spect to T holding P constant, and differentiation ofEq. [3] and [5] with respect to P holding T constant,yields:

(dH/BT)P = mm(3h°m/3T)P + mw(d4>H/8T)P [7]

(aS/ai> = mm(ds°m/dT)P + mw(3^s/3T)p [8]

(3V/ST)P = mm(dv°m/dT)P + mw(3f>v/3T)p [9]and

(3C/aP)T = mm(dc°m/dP)T + mw(d*c/dP)T [10]

(3S/aP)T = mm(3s°m/dP)T + mw(3ts/3F)T. [11]

Also, a second differentiation of Eq. [6] with respectto T, holding P constant, gives

(a*pyaT»), = mm(3*v°m/3T*)P + m«,(3^v/arV [12]

From thermodynamics, we know that the followingequations apply:

(3H/3T)p = C(3C/3P)T = -

• (dh°m/ST)P = c°m [13]

(3c°m/3P)T = -T(3*v°m/3T*)p [14]

(3S/aP)T = -(3V/8T)P ;(3s°m/dP)T = -(3v°m/dT)P [15]

(dS/3T)P = C/T ; (3s°m/3T)P = c°m/T [16]

Hence, we find:

*c = (a#H/aT)p [17]by combining Eq. [3], [7], and [13];

(3<PC/3P)T = -T(a**r/9T*)P [18]1 Journal Paper no. 7381; contribution from the.Dept. of

Agronomy, Purdue Univ. Agric. Exp. Stn., West Lafayette, IN47907. Received 30 Oct. 1978. Approved 27 Feb. 1979.

"Professor of Soil Chemistry.

651

652

L02

LOI

U»

SOIL SCI. SOC. AM. J., VOL. 43, 1979

INTERLAYER DISTANCE (A)50 _______100 0 ____ 50 100 ISO

LI-MONTMORIUONITE No- MOMTMORILLONITE

ZO 4jO 2JO 40 6X3mw/mm (g/g)

Fig. 1—The dependence of ?„, the partial specific volume of the water, on mv>/mm, the mass ratio of water to montmorillonite,in Li- and Na-montmorillonite systems at 25°C.

by combining Eq. [10], [12], and [14];(df>s/eP)T = -(3*v/37>

by combining Eq. [9], [11], and [15];and

by combining Eq. [3], [8], and [16].Further, we can obtain:

by dividing Eq. [17] by Eq. [19];(3*s/3*v)p = -4>c/T(d<i>s/dF)T

by dividing Eq. [20] by Eq. [19] ;and

[19]

[20]

[21]

[22]

/3 7> [23]by dividing Eq. [18] by Eq. [19]. To the author'sknowledge, Eq. [17] to [23] have not been derivedheretofore. They show that the same kind of thermo-dynamic relations exist between the apparent specificproperties of the water in the system as between thecorresponding ihermodynamic -properties Jar the sys-tem as a whole.

Attention is directed to the physical significance ofxw and 0X. The former is the increase in the propertyX of a montmorillonite-water system resulting fromthe addition, at a constant temperature and pressure,of one gram of water to such a large quantity of the sys-tem that its composition remains virtually unchanged.The latter is the difference, per gram of water, betweenthe value of the property X for the system and thevalue of this property for the component montmorillo-nite in its pure state. Both xw and <t>x are structure-sensitive and will have a value characteristic of purebulk water unless the structure of either the water or

montmorillonite is perturbed by their interaction. OurX-ray data (20) show that the a and b dimensions ofthe unit cell of montmorillonite (a ssfr/V^) do notchange with mw/mm, the mass ratio of water to mont-morillonite, when mw/mm > 1.0 g/g. Most of our in-vestigations were conducted at values of mw/mm inexcess of 1.0 g/g. Consequently, we will assume thatthe observed changes in xw, $x, (d<f>x/dT)Pf (30x/3-P)r,etc., with mw/mm are the result of changes in the struc-ture of the water only. Additional credibility is givento this assumption if it is realized that the structure ofthe liquid water is more easily perturbed than thestructure of the solid montmorillonite.

Conceptually, it is possible to resolve the derivativeof <t>x with respect to P and T into two components,namely, that due to changes in the vibration, rotation,and translation of the molecules, which we shall callthe vibrational component, and that due to changes inthe configuration or arrangement of the molecules,which we shall call the configurational component.In interpreting the experimental results, we shall em-phasize the latter because it has special significancefor an open-structured liquid like water. In addition,it is easier to understand. Nevertheless, we shall givetacit recognition to the existence of the former.

The water properties discussed in this paper weredetermined in systems containing different propor-tions of water and the <2 jam fraction of Li- or Na-saturated montmorillonite from Upton, Wyoming. Inthe different figures, these properties are plotted asfunctions of mw/mm. However, the interlayer distancescorresponding to the respective values of mw/mm arealso included. Interlayer distances were calculated byassuming that the water existed only in interlayer re-gions, that its density was 1.0 g/cm3 and that the speci-fic surface area of the montmorillonite was 800 m2/g.The plots in all the figures were exponential in na-ture and so the equations of the best fitting curveswere obtained by linear regression analysis using the

LOW. NATURE AND PROPERTIES OF WATER IN WATER-MONTMORILLONITE SYSTEMS 653

Table 1—Characteristic values of J°, the numerical coefficient preceding the exponential, and of 0, the numerical coefficient in theexponent, in each equation describing a property, J, of the interlayer water as a function of mjmm,

the mass ratio of water to Upton montmorillonite.J

vw(U)vw(Na)cw

<t>C(3</>V/37\p(d<t>£/dP)T

(d<t>s/dP)T(d<ti(T>d<l>s)T(d<i>tfdT)p(B<t>rfb<t>vlP(d^dbvlpi»Eq.[38]V

Units

cm'g-1

cm'g-1

cal g"1 deg-1

cal g-' deg-1

cm' g-' deg-1

cal g"1 deg"1 atm"1

cal g"1 deg"1 atm"1

cal g-1 deg-1

cal cm"3

cal deg"1 cm'3cpcm'1

Range of mu/mm

1.0 - 5.01.0 - 5.00.04- 2.10.35- 3.31.7 -28.01.7 -28.03.9 -27.01.7 -28.00.35- 3.30.35- 3.30.35- 3.30.12- 4.80.23- 1.0

J"

1.002 ± 0.0021.002 ± 0.0021.010 ± 0.0161.001 ± 0.004

(2.60 ± 0.03) x 10-1

(-8.55 ±0.12) x 10-'(-6.26 ±0.10) x 10"'

13.7 ± 0.15(3.36 ± 0.013) x 10-'(1.60 ± 0.03) x 10'(5.37 ± 0.09) x 10!

0.8937T2511 ± 3

00.027 ± 0.0040.036 ± 0.0060.005 ± 0.00180.020 ± 0.0030.49 ±0.05

-0.17 ± 0.050.53 ±0.13

-0.70 ± 0.150.020 ± 0.003

-0.51 ± 0.14-0.51 ±0.14

0.41T0.0042 ± 0.0005

t The method by which these constants were obtained precluded the calculation of the confidence interval.

natural logarithm of the water property and mw/mm asvariables.

Presented in Fig. 1 are data calculated from the re-sults of Anderson and Low (1) showing the depend-ence of vw, the partial specific volume of water, inthe montmorillonite-water system on mm/mw at 25°C.3The equations describing the best-fitting curves are:

vw = 1.002 exp [Q.Q27/(mw/mm)} [24]and

vw = 1.002 exp [0.036/(mu)/mm)] [25]for the Li-montmorillonite and Na-montmorillonite,respectively. Confidence intervals (confidence coeffi-cient = 95%) for the constants in these and subse-quent equations, and the range of mw/mm over whichthey apply, are presented in Table 1. It should benoted that the factor preceding the exponential inboth Eq. [24] and Eq. [25] is within experimentalerror of 1.0029 cm3 g~S which is the value of v°w, thespecific volume of pure-bulk water, at 25 °C. Thus,vw decreases exponentially with increasing mw/mmand does not become equal to v°u until substantialvalues of mw/mm are reached. The necessary conclu-sion is that the molecules in the interlayer water arenot as closely packed as those in bulk water.

Close packing can be regarded as the result of eitherbroken or bent hydrogen bonds, depending on themodel of water that is adopted (5, 8). According tothe "mixture" model, close packing is produced bythe breaking of hydrogen bonds that keep the watermolecules in an open, tetrahedral arrangement; where-as, according to the "continuum" model, it is producedby the bending of these bonds. It is reasonable topostulate, therefore, that the interlayer water has few-er broken or bent hydrogen bonds than bulk water.However, it is also reasonable to postulate that thehydrogen bonds are longer in the former than in thelatter or that there are more vacancies in its structure.A choice between these postulates will be made later.

In Fig. 2 are_ data showing both the partial specificheat capacity, "cw, and <t-c of the interlayer water in Na-

montmorillonite as a function of mw/mm. The data on(?w were tabulated in the paper of Oster and Low (22),whereas the data on <t>c were calculated by using in Eq.[3] other data that they provided. The best-fittingcurves in this figure are described by the equations:

cw = 1.01 exp [0.005/(m«,/mm)] [26]and

= 1.00 exp [0.02/(mu)/mm)]. [27]

INTERLAYER DISTANCE (A*)25 SO 75

• Provided that the components of their system were essentiallyincompressible, Anderson and Low actually measured ww but, tofacilitate understanding by using a more familiar term, reported(!/««,) instead and inaccurately called it the density.

mw/mm

Fig. 2—The dependence of ?„, the partial specific heat capacity,and of <t>c, the apparent specific heat capacity, of the wateron ma/mm, the mass ratio of water to montmorillonite, in Li-and Na-montmorillonite systems at temperatures near 25°C.

654 SOIL SCI. SOC. AM. J., VOL. 43, 1979

4,0

INTERLAYER DISTANCE (X)200 400 600 800

~Qx

•r

ao28

mw/mm (g/g)Fig. 3—The dependence of (d<f>vjST)P, the apparent specific ex-

pansibility of the water, on mu/mm, the mass ratio of water tomontmorillonite, in Na-montmorillonite systems at 25 °C.

Note that the factor preceding the exponential in eachequation is close to 1.0 cal g"1 deg-1, which is thevalue of c°w, the specific heat capacity of pure bulkwater. Note also that "cw and <t>c do not become equalto c°u, until the films of interlayer water have appre-ciable thickness. The relatively high values of cw and<t>c can be ascribed to the extra heat absorbed in ad-ditional lengthening, breaking or bending of hydrogenbonds or to the heat absorbed in exciting additionalmodes of vibration that are peculiar to the structureof the interlayer water.

Clementz and Low (3) used a sensitive dilatometerto measure (dV/BT)P and calculated (8v°m/dT)P fromthe dependence of the lattice parameters of layer sili-cates on temperature as reported by McKinstrey (21).The value of (dv°m/dT)P was found to be 1.4 X 10~5

cm3 g"1 deg"1. Hence, they were able to use Eq. [9]to determine (d<t>v/dT)P, the apparent specific expansi-bility, of the interlayer water. This determination wasmade over different intervals of temperature at eachof several values of mw/mm. Figure 3 presents their re-sults on the relation between (d<t>v/dT)P and mw/mmat 25°C.

The equation of the best-fitting curve in Fig. 3 is(d-t>v/dT)p = 2.60 X 10~4 exp [QA9/(mw/mm)]. [28]The factor preceding the exponential equals (3v°w/BT)P, the specific expansibility of pure bulk water, at25 °C. We see, therefore, that the interlayer water ismore expansible than pure bulk water.

Increasing the temperature of water has two struc-tural effects, namely: (i) a lengthening of intermole-cular hydrogen bonds, and (ii) a breaking or bendingof some of these bonds. The former effect tends to

increase the specific volume; whereas, the latter effecttends to decrease the specific volume (5). Hence, itis reasonable to conclude that the hydrogen bonds inthe interlayer water are more easily lengthened orless easily broken or bent than those in bulk water.

From the data provided by Clementz and Low (3),a plot of (s<f>v/dT)P vs. T was made for each value ofmw/mm* In every case, the resulting plot was a straightline. The slope of this line, which equals (d2-f>v/sTlt)P,was determined by linear regression analysis. Its valuewas substituted into Eq. [18] to obtain the correspond-ing value of (d</>c/SP)T. Thus, the data in Fig. 4 wereobtained.

The solid line in Fig. 4 represents the best-fittingcurve. Its equation is(d<f>c/8P)T = -8.55 X 10-5exp [-O.l7/(mw/mm)] [29]in which —8.55 X 10~5 is the experimental value of(dc°w/dP)T, the change in the specific heat capacityof pure bulk water with P at constant T. The truevalue of this quantity is —8.74 X 10~5 cal g"1 deg"1

atm"1. Again an exponential relation is observed.An increase in pressure should shorten hydrogen

bonds and break or bend some of them. Bond break-ing or bending should be more effective in reducingthe specific heat capacity of the water than bond short-ening because it alters the arrangement of the watermolecules and, thereby, the contributions due to struc-tural relaxation and/or specific modes of vibration.Consequently, it appears from the data on (d<t>c/dP)rthat the interlayer water undergoes less bond breakingor bending under pressure than bulk water. This con-clusion will be reinforced later.

Kay and Low (13) measured the electromotive forcegenerated instantaneously by the thermopiles of aCalvet differential microcalorimeter when heat was re-leased by the application of pressure to a montmorillo-nite-water mixture in the reaction cell of the micro-calorimeter. The pressure was applied in successive,small increments and between increments the tem-perature was allowed to return to its initial value of25°C. Therefore, the process was essentially isother-mal. Since tests showed that it was also reversible,the following equation is applicable by virtue of theSecond Law of thermodynamics:

(dS/dP)T = [30]

in which (dQ/3P)T, the isothermal heat of compression,is positive if heat is gained by the system and negativeif it is lost. By using their data and the appropriatecalorimetric constant determined by Clementz andLow (3), the value of (dQ/dP)r was found for eachvalue of mw/mm. From the result, the correspondingvalue of (dS/dP)T was calculated by means of Eq.[30].5 Then the value of (ds°m/3P)T was calculatedby using Eq. [15] and the value of (dv°m/dT)P givenearlier. It was found to be -3.39 X 10~7 cal g"1 deg"1

4 The values of T used in these plots were the mid-tempera-tures of the temperature intervals, AT, over which volumechanges were measured.

6 Any reorientation of the flat montmorillonite particles ac-companying increases of P or T makes an insignificant contribu-tion to the change in configurational entropy of the system be-cause the number of particles is infinitesimal compared to thenumber of water molecules.

LOW: NATURE AND PROPERTIES OF WATER IN WATER-MONTMORILLONITE SYSTEMS 655

atm"1. Finally, the calculated values of (8S/8F)T and(ds°m/dF)T were substituted into Eq. [11] to deter-mine the value of (Ws/3P)r. The latter quantity isshown as a function of mw/mm in Fig. 5.

The equation representing the best-fitting curve inFig. 5 is(9-t>s/dF)T = -6.26 X 10-« exp[0.53/(mw/mm)]. [31]The prefactor in this equation differs only slightlyfrom (ds°w/dP)T, the change in the specific entropyof pure bulk water with pressure at constant tempera-ture, which equals —6.34 X 10~6 cal g"1 deg"1

atm"1. Obviously, (3*s/3-P)T becomes more negativeas mw/mm decreases. Since entropy is a measure ofrandomness or disorderliness, this means that the lossin randomness or disorderliness of the interlayer waterper unit of applied pressure increases as the films ofinterlayer water get thinner. Now, as mentioned ear-lier, an increase in the pressure on the water shouldshorten hydrogen bonds and break or bend some ofthem. The shortening of bonds would decrease the en-tropy, whereas, the breaking or bending of bondswould tend to increase it. A reasonable conclusionis, therefore, that the hydrogen bonds in the interlayerwater are either more compressible or less breakable orbendable than those in bulk water. Of course, if va-cancies or defects exist in the structure of the inter-layer water, their elimination under pressure wouldalso decrease the entropy significantly.

We can test the internal consistency or our data bymeans of Eq. [19], viz., (a^s/3P)T = -(d<f>v/dT)P.By substituting the righthand side of Eq. [28] for

-76

INTERLAYER DISTANCE200 400 600 800

QX

T_

i -80

<T> -

-8620 24 28 32

mw/mm

Fig. 4—The dependence of (d<t>c/dP)i, the rate of change ofthe apparent specific heat capacity of the water with pressureat constant temperature, on mn/mm, the mass ratio of water tomontmorillonite, in Na-montmorillonite systems at 25°C.

(d<t>v/dT)p in this equation and using the appropriateconversion factors for the necessary change of units,we obtain(d*s/dP)T = -6.29 X ID-6 exp [0.49/(m«/»«m)] • [32]Likewise, by substituting the right-hand side of Eq.[31] for (d*s/3P)T, we find(d*v/dT)p = 2.58 X 10-* exp [0.53/(mw/mm)]. [33]Comparisons of these equations with Eq. [31] and Eq.[28], respectively, shows that the results obtained bytwo independent methods, namely, the dilatometricand calorimetric methods, are in good agreement.

Division of Eq. [29] by Eq. [31] gives(30c/a*s)T = 13-7 exp [-Q.W/(mw/mm)]. [34]

We have found that the application of pressure causesthe interlayer water to undergo a smaller loss of </>cand a greater loss of *s than bulk water. Hence, asindicated by Eq. [34], the interlayer water has a rela-tively small value of (d<t>c/d<t>s)T- For example, whenmw/mm is as high as 4.0 g/g (interlayer distance s*100 A), the value of this quantity for the interlayerwater is only 84% of that for pure bulk water.

Substitution of T - 298° K in Eq. [20] and com-bination of the result with Eq. [27] gives(d<f>s/dT)P = 3.36 X 10-3 exp [0.02/(mu)/mm)]. [35]Evidently, the interlayer water undergoes more ran-domization per degree of temperature rise than pure,bulk water. However, by combining Eq. [21], [27],and [31] we see that(a*H/Wv)p = 1.6 X 105 exp [-0.51/(m»/mm)] [36]

INTERLAYER DISTANCE (I)•60 200 400 600 800

1 "70

-ao12 16 20

nr̂ /m,,, (q/g)24 32

Fig. 5—The dependence of (d0g/dP)r> the rate of change ofthe apparent specific entropy of the water with pressure atconstant temperature, on m,/mm, the mass ratio of water tomontmorillonite in Na-montmorillonite systems at 25 °C.

656 SOIL sci. soc. AM. j., VOL. 43, 1979

and, by combining Eq. [22], [27], and [31] with T= 298° K we find(tos/d*v)p = 5.37 X 102 exp [-Q.51/(mw/mm)]. [37]Consequently, less heat is absorbed, and the increasein randomness or disorderliness is smaller, per unitof volume expansion in the interlayer water than inbulk water. This can be true only if fewer bonds arebroken or bent in the process. We conclude, therefore,that the relatively large increase of randomness inthe interlayer water per degree of temperature rise isdue to enhanced bond extension instead of enhancedbond breaking or bending.

Shown in Fig. 6 are two curves of the average viscos-ity, r), of the interlayer water versus mw/mm. Curve 1was obtained by four different methods involving theviscous flow, self-diffusion and neutron scattering ofthe interlayer water. Curve 2 was obtained from meas-ured activation energies for Na+ conductance by as-suming the applicability of Walden's rule and rateprocess theory. These curves, and details of the meth-ods by which they were obtained, have been presentedelsewhere by the author (18, 19). Their respectiveequations are:

T? = 0.8937 exp [OAl/(mw/mm)] [38]and

r, = 0.8937 exp [0.62/(mto/mnt)] [39]in which 0.8937 equals the viscosity of pure bulk waterat 25°C. Equation [38] is presumed to be the morereliable.

For viscous flow to occur, the hydrogen bonds be-tween water molecules in adjacent layers must be brok-en, probably by molecular rotation (9, 29). The energyrequired to break these bonds is the activation energyfor the process (6) and so the viscosity increases as thestrength of the bonds and/or the number of bondsper unit volume, increase. In view of the fact thatthe molecules in the interlayer water are not as closelypacked as those in bulk water (Fig. 1), it is unlikelythat the interlayer water has more bonds per unitvolume. Therefore, in keeping with earlier evidence,it appears that the bonds in the interlayer water arenot as easily broken as those in bulk water. It shouldbe noted also that vacancies in the structure of thewater would tend to reduce its viscosity (26, 30) andso the foregoing data indicate that such vacancies arenot the cause of the relatively large values of vw and

v = 2511 exp [0.0042/(mu,/"Jm)] [40]

The O-H stretching frequency in H2O has beenfound to increase with the length and decrease withthe strength of the hydrogen bonds (2, 12, 23). TheO-D stretching frequency is lower than the O-Hstretching frequency by a constant factor of 1.36 andcannot be confused with the stretching frequency ofthe lattice hydroxyls. Therefore, J. Salle' de Chouand the author used infrared spectroscopy to study thedependence of v, the O-D stretching frequency in in-terlayer D2O, on mw/mm. A few of the results of theirstudy, which will be reported in greater detail else-where, are given in Fig. 7. These results are consistantwith the results of Jorgensen (11).

The equation that describes the best-fitting curvein Fig. 7 is

in which 2511 is the experimental value of v°, theO-D stretching frequency in pure D2O. Since, as notedearlier, v shifts to higher values as the hydrogen bondsbecome longer and weaker, it is reasonable to ascribethe observed shift in v to a lengthening and weakeningof the hydrogen bonds in the interlayer water. Never-theless, the interpretation of infrared spectra is diffi-cult (5, 7) and it may be that, under the conditionsexisting in the interlayer region, v shifted with mw/mmfor another reason. Anything that increases the forceconstant of the O-H bond will increase v.

If the spectroscopic evidence is interpreted as beingindicative of long, weak hydrogen bonds that areeasily extended and bent, it is only in partial agree-ment with the thermodynamic evidence and seems tocontradict the hydrodynamic evidence. In the latterregard, attention is called to the fact that v and i)are positively correlated in interlayer water but arenegatively correlated in bulk water; v increases with in-creasing temperature in bulk water (7) but 57 decreases(15). In an attempt to reconcile the various kinds ofevidence, the following tentative explanation is of-fered.

To minimize the interfacial energy, hydrogen bondsare formed between the oxygen atoms in the layer sur-faces of the montmorillonite and the neighboring wa-ter molecules and, in the process, the structure of thewater is strained to match that of the surface (24).Calculations show that the necessary extension of the

INTERLAYER DISTANCE (X)0 Z5 50 75 100

I2O

100

80

s.fc-

4,0

2O

———— CURVE I

———— CURVE Z

\

UO 20 10

Fig. 6—The dependence of 17, the average viscosity of the water,on m«,/mm, the ratio of water to montmorillonite, in Na-montmorillonite systems at 25°C.

LOW.' NATURE AND PROPERTIES OF WATER IN WATER-MONTMORILLONITE SYSTEMS 657

intermolecular hydrogen bonds would be as great as5% (20). In keeping with the observed correlationbetween v and bond length, v increases accordingly.This increase in length weakens the bond along itsaxis and makes it more extensible. However, the in-crease in length also increases the energy required tobend the bond, provided that the force constant forbending remains unchanged. This is shown by anequation presented by Eisenberg and Kauzmann (5),

= /° exp [p/(mw/mm)} [42]

viz.,A£7 = 1/2 k, (R - r)r (A0)2 [41]

in which At/ is the change in potential energy cor-responding to a change, A0, in the O-H • • • O bondangle, ke is the force constant, R is the oxygen-oxygendistance (i.e., the length of the hydrogen bond) and ris the O-H distance. Thus, relative to bulk water, thehydrogen bonds in the interlayer water are longer andmore extensible but less bendable.

The foregoing explanation is not the only one thatcan be offered. Hydrogen-bond formation involves aredistribution of charge in the molecules involved (14).Moreover, the surface oxygens have excess electronsand a strong electric field emanates from them in adirection perpendicular to the surface. Therefore, itis possible that the charge redistribution on hydrogenbond formation is altered by electric interaction ofthe water with the surface in such a way that the forceconstants for both O-H stretching and O-H • • • O bend-ing are increased. The result would be hydrogen bondsthat are more extensible but less breakable or bendablethan those in bulk water.

Our evidence shows that every property of the in-terlayer water obeys the following general equation:

2560

INTERLAYER DISTANCE5 tO 15 20 25

2550

2540

2530

252002 04 06 08 10

n>w/rnm

Fig. 7—The dependence of v, the O-D stretching frequency, onmv/mm, the mass ratio of D,O to montmorillonite, in Na-montmorillonite systems at 25 °C.

in which J represents any given property of the inter-layer water, 7° represents the value of this propertyfor pure bulk water and /3 is a constant. Further, Eq.[42] can be written for two different water proper-ties, designated by the subscripts 1 and 2, and therespective equations can be combined to give

[43]

Thus, every water property is related to every otherwater property. Since a common equation describes allthe properties of the interlayer water, and since theseproperties are interrelated, it is reasonable to believethat they depend on a common factor, namely, thestructure of the water as influenced by its interactionwith the montmorillonite. Now let us turn our atten-tion to the nature of this interaction.

The structure of the interlayer water (which isgoverned by bond lengths and bond angles) can be af-fected by surface forces and by interlayer cations.Arguments presented previously (3, 4, 18) lead tothe conclusion that the influence of the cations is sec-ondary, unless the films of interlayer water are verythin. This conclusion can be substantiated in thefollowing way. First, write the expressions

andmw/mm =

mw/mm s* pXA/Z

[44]

[45]in which e is the cation exchange capacity of the mont-morillonite; Zi and "i are the valence and average mo-lality, respectively, of any exchangeable cation, i, dis-solved in the interlayer water; p is the density of thewater; A. is the interlayer distance (water film thick-ness) and A is the specific surface area of the mont-morillonite. Equation [45] is approximate becauseit is based on the assumption that all of the water inthe system is between superimposed layers within par-ticles and, since a small fraction of the water is in theinterstices between particles, this assumption is notstrictly valid. Combine Eq. [44] and [45] with Eq.[42] to obtain

and7 = 7° exp [p,

7 = 7° exp

[46]

[47]

respectively. For any given water property, the valuesof {}, e and A were constant in our systems and, al-though p was variable, its variation was small com-pared to that of A. Hence, 7 is an exponential func-tion of both 2Zi«i and X. Only one of these functionalrelations is direct. The other is indirect. If Eq. [46]is the direct one, any property of the water in bulkaqueous solutions should be an exponential functionof the total electrolyte concentration. However, thisis not the case. For example, the O-H (or O-D) stretch-ing frequency is not affected significantly by cations insolution (27, 28). Also the viscosity of aqueous solu-tions is essentially a linear function of the electrolyteconcentration and the contributions of the cations andanions are additive (10). The additivity of the ionic

658 SOIL SCI. SOC. AM. J., VOL. 43, 1979

contributions suggests that the viscosity depends onthe concentration of each ion separately and, there-fore, that the viscosity of a solution of a single ca-tionic species (e.g., the interlayer solution) wouldbe essentially a linear function of the concentrationof that species. We conclude, therefore, that Eq. [47]is the direct one and that / depends primarily on theproximity of the water to the layer surfaces as de-termined by A.. It necessarily follows that surface forcesinduce structural perturbations in the vicinal water.

Presented in Table 1 are the experimental values of7° and /? for the different properties of the interlayerwater. Note that /? has a specific value for each prop-erty and varies for the different properties withinrather wide limits. This means that all the propertiesof the interlayer water are not equally sensitive toperturbations in its structure. From their /? values, itappears that such properties as (d<f>v/dT)P and tj arerelatively sensitive to these perturbations, whereas,such properties as v, <t>c and vw are relatively insensi-tive. It should be mentioned here that, for any givenwater property, /? depends on factors associated withthe montmorillonite, e.g., its b dimension and cationexchange capacity (18, 25). The nature of thesefactors and their relative significance will be the sub-ject of future investigations.

In summary, we have shown that the nature andproperties of interlayer water differ from those of bulkwater, that the differences are significant and that theypersist to appreciable water contents. Moreover, wehave shown that these differences are related to dif-ferences in intermolecular bonding as influenced bythe surfaces of the montmorillonite layers. The bondsin the interlayer water appear to be more extensibleand compressible but less breakable or bendable thanthose in bulk water. However, the detailed nature ofthese bonds, and the molecular arrangement that theyproduce, remain to be resolved.