air interface

Advances

in Colloid and Interface Science, 45 (1993) 215-241

215

Elsevier Science Publishers B.V., Amsterdam 00156 A

RECENT DEVELOPMENTS IN THE MODELING OF THE MONOLAYERS STRUCTURE AT THE WATER/AIR INTERFACE P. DYNAROWICZ Faculty Poland

of Chemistry,

Jagiellonian

University,

Ingardena

3, 30-060 Krakdw,

CONTENTS Abstract ........................................ 1. Introduction .................................... 2. Models of the Interface .............................. 2.1 Static Models ................................ 2.1.1 The Helmholtz Model (Parallel Plate Capacitor Model) ...... 2.1.2 The ‘Macroscopic’ Model (Multilayer Model) ............ 2.1.3 The Demchak and Fort Model (Three Layer Capacitor Model) . . 2.1.4 The Vogel and Mobius Model (Two Layer Capacitor Model) ... 2.2 Dynamic Model ............................... 2.3 Thermodynamic Models .......................... 2.3.1 Adsorbed Films ........................... 2.3.1.1 Two-Dimensional Solution Model ............. 2.3.2 Insoluble Films ............................ 3. Orientation of Molecules at the Interface .................... 3.1 Absolute Orientation of Surface Dipoles ................. 3.2 Average Orientation Angle of Molecules at the Surface ......... References .......................................

215 215 220 220 220 223 224 226 227 228 228 229 229 232 232 234 238

ABSTRACT Different models recently used to characterize adsorbed and Langmuir monolayers at the water/air interface are reviewed in this paper. Methods for the determination of the orientation of molecules at the surface are described and compared.

INTRODUCTION

Many phenomena of interest to chemists, physicists, biologists or engineers take place on interfaces and involve only surface regions while the bulk of each phase practically does not participate in the process. In contrast to the growing technolo&es used to study various types of solid OOOl-8686/93/$24.00 0 1993 -

Elsevier Science Publishers B.V. All rights reserved.

216

surfaces, relatively few advances have been made in studying the water/air interface in particular due to the inherent problem of its study. Nevertheless over the years many attempts have been made to examine the structure of the water/air interface. This is quite understandable since the water/air interface is of frequent natural occurrence and many different processes and phenomena take part at this boundary. All the properties of the water/air interface are connected with the characteristic feature of this interface, i.e. a considerable difference in the dielectric permittivity of two phases that are in contact: water shows 80 times greater permittivity than air does. This difference is due to the spontaneous orientation of water dipoles at the phase boundary. The consequence of such an orientation of water molecules is the presence of the potential jump of water (VWor xW) 111.The absolute value of this potential (or surface potential of any other phase) is not a measurable quantity because it involves solely the work required to bring the isolated charge across the interface [2] and there is no experimental way to distinguish between short range (chemical) and long range (electrostatic) interactions included in this work 131.Nevertheless, it is possible to estimate the value of surface potential of water based either on computer simulation methods (applying an appropriate molecular model) or by measuring the potential shift, Ax (using a model of the interface). Unfortunately, the surface potential jump of water, predicted by computer simulation studies, varies not only in value but also in sign. Three main simulation methods have been applied for studying the water/air interface, i.e., electrostatic (with point dipole/point quadrupole molecular model) [41, Monte Carlo (applying ST2 [5] or TIPS2 161potential model) and molecular dynamics (using CC 171,TIP4P [81 or SPC 191 model). The surface potential jump of water was calculated to be 0.029 V [4], 0.08 V 151,0.07 V 161,0.16 V [71, -0.13 V [81, and 0.24 V 191. The experimental methods for the determination of x, are based on the measurements of changes in surface potential of water due to variation of concentration and temperature with a so-called voltaic cell, using either static [lo] (ionization [ll] or condenser 1121)or dynamic [13-X] methods. The value of the surface potential jump of water suggested by several authors vary over a large range. For example, Kamieliski 1161 basing on extrapolation of experimental results of adsorption potential shift, Ax,suggested the value of 1 V for xW.This very high value of surface potential jump gave rise to immediate objections and the analysis of the ‘real’ free energy of hydration of ions carried out by Frumkin 1171proved the erroneousness of the value suggested by Kamiefiski. According to a number of authors, the absolute value of surface potential of water is of

217

the order of 0.1-0.2 V, as originally suggested by Frumkin [17]. For example, Randles and Schiffrin [19] considering the temperature dependence of the surface potential of dilute solutions of nonadsorbed electrolytes have reported xWto be 0.07-0.13 V. In another paper [20], the value of 0.08 + 0.06 V was evaluated. A similar value (0.13 V) was obtain by Battisti and Trasatti [21]. A smaller value for xW(0.025 V) was estimated by Farrell and co-workers [22,23] using a voltaic cell to measure the variation with concentration of the surface potential of several dilute aqueous solutions, and applying the model of Madden et al. of the interface [24]. In this model it is assumed that the potential near the liquid surface decays exponentially from the surface into the solution, reaching a constant value several molecular diameters from the surface. Here, the ions are not assumed to be hydrated and can penetrate the surface layer. The model presented by Duncan-Hewitt [251, in which the ions are hydrated and do not penetrate the interface, is more realistic. Based on experimental results from Borazio et al. [231, applying the Grahame equation for calculation of surface charge density and relating it to the Helmholtz model of oriented water dipoles (described in Section 3.1.1 of this paper), the value for x, = 0.025 V was calculated [25]. Recently, Koczorowski et al. [26] have applied a ‘macroscopic’ model of the surface potential (discussed in Section 2.1.2) in which a surface multilayer is treated as equivalent monolayer with bulk properties, and using experimental estimates presented in Refs. [201 and [22], have reported the value x, = O-09 V. Not only the value, but also the direction of the potential jump ofwater has long been controversial. Frumkin [WI gave the conclusion of preferential orientation of surface water dipoles with the oxygen atom pointing toward the gas phase, and hydrogen atoms toward the bulk water. Schiffrin [27] evaluated the temperature coefficient of xW and found dXw/dT equal to -0.39 f 0.04 mV/K which proves that the absolute value of x, is positive, i.e. a preferred orientation of water molecules is in accordance with Frumkin’s idea. Recent surface studies based on temperature dependence of the second harmonic signal [281 have also confirmed this orientation of surface water dipoles. In general, a thermodynamic approach to the study of the water/air interface, described as an equilibrated, closed system, has always been taken [29]. However, it is important to remember that the interface undergoes dynamic processes such as evaporation and condensation, as well as diffusion to and from the bulk liquid phase. It is possible to estimate that a surface molecule lifetime is about a microsecond [301. Therefore, the water/air interface, in contrast to solid surfaces, is continuously renewed.

218

Fig. 1. Forces at the surface of water.

The overall equilibrium structure of the free water surface is maintained by two kinds of forces (Fig. 1): the cohesive forces between molecules, producing a net force down, and the opposing tangential force which acts parallel to the surface, called the surface tension, y, which is defined by

where o is the amount of work it takes to create a unit area A of the surface, i.e. to raise a number of molecules from the bulk liquid phase to the surface to fill an area A. Since the work is at constant pressure and temperature, it equals the free energy, GS. The measurements of surface tension have been the primary method for studying the water/air interface and are still in popular use. Many different techniques have been suggested for precise surface tension measurements (for a review see Refs. 1311and 1321).An excess of molecules of a given substance on the surface of a liquid causes the surface tension to decrease. The decrease resulting from the presence of the monomolecular film is termed the surface pressure, 7c,and is given by: rc = ‘y,,- ‘y, where yOand y are the surface tension of pure liquid, and its reduced value in the presence of a monolayer. The formation of a monolayer at the water/air interface can occur either by the spreading of the organic substance from a volatile organic solution over water, or by the adsorption of molecules dissolved in the bulk water into the interface. In the first case, practically water insoluble and non-volatile organic substance, dissolved in an appropriate organic solvent (e.g. chloroform), when placed on the surface of water, spreads and covers the entire

219

surface. The requirements for the spreading to occur is that the molecules of the organic substance must be attracted to the water more than they attract each other. A one-molecule thick film, termed Langmuir monolayer, is then formed, provided the area of the surface is sufficient to accommodate all the molecules spread. The main class of compounds that form stable monolayers on the water surface are those referred to as amphipathic. Molecules of these compounds possess a hydrophilic head group, which is attracted to the water, and a long hydrophobic tail (at least 12 carbons for the case of the hydrophobic part) which prevents the monolayer from dissolving into the water. However, a number of short-chain organic molecules have dipolar character and amphipathic structure. They dissolve in water and adsorb to the interface to form a monolayer. The question which then arises is, for a given bulk concentration of the solute, what is its concentration on the surface? A thermodynamic treatment of this problem by Gibbs yields an equation for the quantity called surface excess, r, namely, the number of molecules per unit volume in the surface beyond what is found in the same volume in the bulk phase: r=-RT-

a

a In a

wherein a is the activity and R is the gas constant. By fitting surface tension vs activity data to a polynomial and differentiating the fitted function, it is possible to calculate the surface excess (expressed in molecules/cm2). For binary solutions where solute molecules are adsorbed, the surface excess increases rapidly with solute added until it reaches a maximum called the Gibbs monolayer. Multiplying the value of r by the Avogadro number, the number of molecules adsorbed at 1 cm2 of the surface can be estimated. Adding the number of molecules already present at the surface (connected with bulk concentration of solute) to the number of molecules calculated from r, the total number of adsorbed molecules (N) can be obtained. Over the years there have been many attempts to verify the Gibbs equation. For the experimental verification several methods can be used. For example it is possible to cut off the surface with a razor blade and measure the concentration of the adsorbate. Actually this was done in 1930s [33]. More recently other techniques such as ellipsometry [34-361, radioactive tracing 1371,linear reflectivity of light f38-411, UV photoelectron spectroscopy [42,43] and IR spectroscopy 1441have been applied to determine the concentration of adsorbates at the surface. The adsorption at the free water surface always causes the decrease in surface tension.

220

However the electric surface potential of water may either increase or decrease depending on the chemical character and structure of the adsorbed compound. In the case of adsorption of a molecule with polar group and nonpolar part (for example phenol) the decrease of the surface potential is observed [45]. However, if the adsorbed molecule possesses two or more polar groups and if one of them is more hydrophilic than the others (e.g. halogenophenols), the increase of the negative surface potential of water can be observed [461. Since the early part of the century, surface potential measurements have proved to be a useful tool for characterizing monolayers at the water/air interface and have been used as often as surface pressure isotherms. Macroscopically measured voltage is the sum of different contributions connected with microscopic properties of the monolayer. A detailed model of surface potential has yet to be developed.

2

MODELSOF INTERFACE

2.1 Static Models 2.1.1 The Helmholtz model (parallel plate condenser model) The water/air interface is polarized by spontaneous orientation of water dipoles near the interface which orient themselves with oxygen atoms toward the air. The formation of adsorbed monolayer, causing the removal of a number of oriented water dipoles when the new dipoles of the adsorbed compound are introduced into the surface, results in changes of both surface tension and electric surface potential of water. These changes are dependent on the density of adsorbed dipoles per unit area, the orientation of adsorbed molecules at the surface and on their chemical character and structure of the adsorbed compound. The monomolecular film formed at the free surface of water, consisting of N dipoles of adsorbed compound, has the structure of electrical double layer. It is impossible to determine the structure of such a double layer based on electrocapillary curve investigations in the way that it is possible at the liquid metal/solution interface. Therefore it was assumed that the electrical double layer at the water/air interface has the structure of a parallel plate condenser [47] (Fig. 2). The parallel plate condenser represents the monolayer as a dipole sheet with two layers of uniformly distributed charges, one containing positive (+q), the other negative (-9) charges, separated by a distance 1. Thus the surface charge density, o, equals &Nq. The potential difference

221 t6

L

-6 Fig. 2. The representationof a monolayeras a dipolesheet. between both condenser plates is o/C!, where C is the condenser capacity which could be calculated from the following dependence: C=&Ec/l

(3)

where E is the dielectric permittivity of the material filling the space between the capacitor plates, and ~~ is the dielectric permittivity of vacuum. From the above equations the Helmholtz formula can be established Ax = o/C = f NqI/EEO = N~EEE~ =

$AEE~

(4)

where E is the relative permittivity of the film, ~~ is the permittivity of free space, b is so-called effective dipole moment, which is the vertical component of the dipole moment of the molecule at the surface (this should not be mistaken for a molecular dipole moment of a free molecule), N is the total number of molecules at 1 cm2 of free surface and A is the average area occupied by the molecule at the surface (A= l/N>. In surface chemistry the assumption is often made that E = 1, either because molecules are treated as isolated entities [481 or because of the lack of a known value 130,491. This is true only for the relative permittivity in gaseous media. However there has been a lot of discussion regarding the value of the dielectric permittivity of the monolayer. For example, Adam et al. 1501 suggested that the value 5 c E c 10 should be used. However, Schuhmann 1511 proves that the dielectric permittivity of the monolayer can be taken as 2 which is the dielectric permittivity of short-chained hydrocarbons. In the case of adsorbed gaseous films the value of 1 is

222

usually accepted [52-541 which seems to be logical considering the fact that in the soluble monolayer the adsorbed molecules are separated and orient themselves with their hydrophobic chains toward the gaseous phase, whose permittivity is 1. As seen from the Helmholtz equation the effective dipole moment, b (actually b/e> can be determined from the dependence of Ax vs N. In the case of adsorbed film, assuming that the value of the dielectric permittivity of the monolayer is the same within the investigated concentration range, the linear dependence Ax = f(N) indicates that the effective dipole moment of the molecule in the film remains constant. It is possible to derive the Helmholtz formula in different way; first considering the fact that the uniform assembly of molecular dipoles at the interface gives rise to a polarization within the layer. Next, assuming the analogy with the parallel plate capacitor and keeping in mind that polarization is the dipole moment per unit volume, the component of polarization normal to the interface, P, can be given by P, = EE,,AV/l= $A1

(5)

The Helmholtz equation is thus found again. Also, the Helmholtz equation can be deduced directly from Coulomb’s law for point dipoles, assuming an infinite plane with a homogeneous distribution of identical dipoles [511. The Helmholtz formula has been used from the nineteen-twenties [15,55-571 to the present [30,52,54,58-661 for analyzing the data of surface potential obtained for insoluble and adsorbed films as well. Equation (4) is valid for interpreting the surface potential for monolayers formed by uncharged molecules. In the case of ionized films, the double-layer potential, Y,,, must be taken into consideration 1301: AV = ($Ass,,) + %, ‘I”, for 1: 1 electrolytes can be expressed by the following formula, valid at 25°C 1301: Y. = (2kT/e) sinh-l(137/Aq)

(7)

where k is the Boltzman constant, T is absolute temperature, e is electronic charge, Ciis the concentration of ions in moles/l, A is the area for one ionized group in the film, expressed in (A)2. At 25”C, 2kT/e has the numerical value 51.4 [30,671.

223

2.1.2

The Znacroscopic’ model (multilayer

model)

Recently, a ‘macroscopic’ model of the surface potential has been proposed by Koczorowski et al. [26,681. This model has been developed based originally on the Helmholtz formula (Eqn. 4). It has been assumed that the contribution to the surface potential of pure solvent, xs, is given not only by oriented surface dipoles in the first layer. This contribution is the strongest; however, it is also effective in the further few layers. Here, the surface layer expands to a macroscopic thickness, and xs is the resultant of a summation of few (monolayer) terms. The Helmholtz equation, modified in this way, has the form:

where E, is the dielectric permittivity of the solvent in the bulk phase, Ei,s is the hypothetical local permittivity of the subsequent ith layer, ec is the dielectric permittivity of vacuum, ps is the dipole moment of solvent molecule, Nt is the sum of all solvent molecules present in the several layers included in the summation, and 0 is the average angle made by the molecular dipole to the normal to the interface. Since lim (E$Ei,s)= 1, i-t

and lim (co&) = 0 [26], values of g do not differ very much from 1. This i-3

modified Helmholtz equation enables calculation of xs from macroscopic bulk properties of the solvent. For example the surface potential of water, x,, estimated from tabulated macroscopic quantities (Q, = 78.0, b = 1.84 D, Ni obtained from molecular volume) has the value of 90 mV [26] which is in good agreement with xWvalues estimated by other authors [18-211. In the case of adsorption of an organic molecule (B) at the water surface, the change in the water surface potential, Ax, can be obtained from the following formula [26]: f%f=Xw(~) -X,x

WBPB/&~&B(~$ + (N~-U&O&~BJ)-

N~-~J~o%)

(10)

where &(B) is the surface potential of aqueous solution containing B at a given concentration, Ni is the mean number of water molecules per unit area of the surface of pure water while NW and Nn are the number of water molecules and substance B per unit area of the surface at a given bulk concentration of B in the solution. In the above equation, G(B) and &n(w)are the permittivities of the patches of solution surface occupied by

224

water and B, respectively, and CI, and j_$,are molecular dipole moments of water and substance B. Considering the conditions of a ‘Gibbs monolayer’ (at surface saturation) the above equation reduces to [26]:

The model has been verified and a good correlation between calculated and experimental data has been found 1261. 2.1.3 The Demchak and Fort model (three-layer capacitor model) Improvements to the Helmholtz model were made by Davies and Rideal [l] who suggested that the effective dipole moment of a molecule (CL)should be treated as the sum of the three main components: CL1 represents the polarization of the water molecules induced by the presence of the monolayer, j& and & represent the effective dipole moment of hydrophilic headgroup and hydrophobic tail, respectively. Since all these components of the total effective dipole moment of the molecule are vectorially additive, it is possible to write the following:

cL=&+cl2+cL3

(12)

Demchak and Fort [491have completed the above equation with the local dielectric permittivities in the vicinity of water dipoles (Ed), hydrophilic (Q) and hydrophobic (EJ groups and considered the monolayer at the water/air interface as a three-layer capacitor (Fig. 3) each layer corresponding to the three main contributions to Ax:

WATER

Fig. 3. The Demchak and Fort three-layer capacitor model.

225

Demchak and Fort attempted to estimate Ed,E3 and iI /Ed by systematic substitution of the hydrophilic and hydrophobic group of the investigated compound. The value of the total effective dipole moment, CL,can be estimated directly from experiments (from the dependence Ax = f(N), using the Helmholtz equation), assuming that E = 1. Knowing the bond dipole moments [69] and angles between them [70] it is possible to calculate the group dipole moments, L2 and Lg. Then solving in pairs equations of type (14): i

= (j&/El)

+ @2/&2)

(14)

+ @3/E3)

for compounds with different hydrophilic groups and the same hydrophobic parts (and vice versa) and assuming that the contribution from the aqueous subphase is the same, one can estimate local dielectric permittivities. Demchak and Fort [49] considered dimethyl ester of 4,4’-dicarboxy-p-terphenyl (DMT) and 4-carboxy-p-terphenyl (MT) to estimate Ed, and MT together with 4-amino-p-terphenyl (AT) to obtain Ed: DM’JJ

h/E1

+ i&xm1,/E2

+ ii+m~~,lE3

= ii

(15)

(17)

Substituting the obtained values to the particular equations (15)-(18), the value of L1/~l can be calculated. Demchak and Fort showed that for the above-mentioned terphenyl compounds, ~~ = 7.2, ~~ = 5.3, P~/E~ = 40 mD [49]. Assuming that these calculated quantities were similar for other insoluble monolayer films, Demchak and Fort were led to predict the value of the total effective dipole moments of aliphatic molecules and a good agreement was found for one particular conformation. The Demchak and Fort model is based on a number of assumptions: (1) the contribution &/E~ does not depend on the kind of monolayer forming molecules,

226

(2)the value of local dielectric permittivity in the vicinity of a hydrophilic group is independent on the chemical character of hydrophobic group. In other words, &2is the same for compounds with different hydrophobic groups. Similarly, the value of s3 does not depend on the nature of hydrophilic groups. (3) the average orientation of monolayer forming molecules is the same. For simplicity, in Ref. [491experimental values of 1 were taken for the condensed monolayer where the vertical orientation of molecules can be assumed. Applying the Demchak and Fort model, Oliveira and co-workers [71], using previously published data of effective dipole moments for halocarboxylic acids (chloro-, bromo-, and iodo- derivatives of hexadecanoic and octadecanoic acid) [1,72-751, have shown that the average value of &3= 2.8 (2.13-3.88). Considering the latter and applying the experimental results of F obtained for octadecyl methyl sulphoxide and octadecyl p-tolyl sulphoxide, they have found bl/sl = -65 mD, and &2= 6.4 [71]. The Demchak and Fort approach has also been used for soluble films. Measurements of surface potential and surface tension of aqueous solutions of acetic acid , chloro-, dichloro-, trichloroacetic acid, propionic acid and short-chain alcohols (methanol, ethanol, 2,2,2-trifluoroethanol) were carried out [76]. Values of s2 = 4.2, s3 = 2.4 (1.7 for alcohols) and &I&r of the order of -100 to -200 mD have been reported. Further investigations with acetic and pivalic acid, pivaldehyde, trifluoro-, trichloro-, and tribromoacetic acid proved that the value of% (3.1) is higher than s3 (1.26-1.42) and &/~r is small (-55 to -100 mD) 1771.Similar results (s2 = 4.3; &3= 1.4; &/si of the order of -100 to -200 mD) have been obtained for butyl alcohol isomers [78] and for propionic acid derivatives (Ed= 3.0; &3= 1.5; Lr/sr up to -126 mD> [79]. In the case of aromatic compounds (benzoic, p-toluic, p-fluorobenzoic acid, benzaldehyde, tolualdehyde) the calculations gave s2 = 1.4 or 1.8, and e3 = 1.0 [80].

2.1.4 The Vogel and Mijbius model (two-layer capacitor model) In 1988 Vogel and Mobius [811suggested a model of the interface in which the local dielectric permittivities are not considered explicitly but they are included in effective dipole moments cl, and Lo. The effective dipole moment of the head group region, &, includes the dipole moment of the polar group, the polarization of the water subphase, and any contribution from the double layer while cw represents the hydrophobic group dipole moment. Thus the total effective dipole moment of the molecule in the film, CL,can be expressed by the following equation:

227

ji=jia+s;o

(19)

This model of the monolayer structure can easily be compared to the Demchak and Fort model since:

(21) The Vogel and Mobius model is shown schematically in Fig. 4. This approach has been recently used by Yazdanian et al. [83] to study the influence of different ions on fatty acid monolayers.

FW

Fa

AIR WATER

Fig. 4. The Vogel and MGbius two-layer capacitor model.

2.2 Dynamic Model Based on the Demchak and Fort model, Oliveira et al. [84] have recently proposed a dynamic model that explains quantitatively the shift of the surface potential which occurs during the compression of the monolayer. Thus this model can be applied for insoluble films only. It is suggested that the Ax = f(N) isotherm reflects changes in the headgroup layer. The hydrophilic part of monolayer forming molecule is believed to remain always in the water phase and its reorientation can be neglected during the compression. In other words, j& remains constant while the monolayer is compressed. However, significant changes are expected in the local dielectric permittivity in the vicinity of a hydrophilic group, s2. In the gaseous phase where the molecules are well separated, &2is supposed to have the value close to those for bulk water (78.5). A relatively small value of &2calculated for a fully condensed monolayer [71] suggests that under compression &2decreases from 78.5 at large areas to about 6.4 1711at critical area, A, = 20 (Aj2 per molecule. In

228

contrast to the hydrophilic groups, the hydrophobic part of the molecule undergoes reorientation - at large areas the molecules are tilted at some angle 6 relative to the interface. The orientation of molecules becomes more vertical under compression and for a fully compressed monolayer molecules are expected to take an orientation vertical to the surface. The term j&/~ is supposed to vanish at large areas per molecule and decreases during the compression to reach the value of about -65 mD at 20 (A)” [71]. In consequence, two contributions for unionized monolayer, i.e. ii1/sl and &/E~ cancel out and the isotherm reflects changes in the headgroup layer. The significant decrease in E, is believed to result from reorganization and structuring of water molecules in the vicinity of hydrophilic groups. The consequence of this process is the formation of domains [841. 2.3 Thermodynamic

Models

2.3.1 Adsorbed films Adsorbed (or Gibbs) monolayers are formed at the water/air interface by the adsorption of solute molecules from the bulk phase to the surface. The subject of adsorbed monolayers developed rapidly at the end of the nineteenth century when Traube [851, found that - based on surface tension measurements of homologous carboxylic acids and aliphatic alcohols - with dilute aqueous solutions, the difference between surface tension of pure solvent (yO)and that of the solution (yi), called surface pressure, n, is proportional to the concentration (ci) of solute: 7~= ‘~0- ‘yj= kcj

(22)

In the above equation, k is an empirical constant which is positive when a solute is not ionized, and negative when it is an electrolyte. Further investigations carried out by Szyszkowski [861 led to the semiempirical formula: x = ~0- yi = b In (1+ aci)

(23)

wherein b is a constant characteristic of the homologous series of organic compound, and a is a constant characteristic of each compound. Differentiating Eqn. (23) with respect to ci and using the Gibbs adsorption equation, the following equation can be obtained:

r=b

ac

RT (1+ ac)

229

Based on Eqns. (23) and (24) it is possible to show that for dilute solutions (ac << 1 >,(l/I)bac = RT. Under these conditions, b ln(1 + ac) z bat, and it follows that: x(1/I> = RT (for 1 mole) or nA = kT (for one molecule)

(25)

Equation (25) is analogous to the ideal gas law. This leads to the conclusion that, in dilute solutions, film forming molecules obey the equation of state of a two-dimensional ideal gas. Adsorbed molecules form at the water/air interface, the so-called gaseous monolayer. By analogy to the ideal gas law, it can be assumed that adsorbed molecules do not attract each other but move continuously with complete independence on the free water surface. The ideal gas law can be applied for diluted solutions only where the molecules are widely separated, intermolecular forces can be neglected in comparison to the thermal energy of translational motions and the dimension of molecules is so small as to be negligible in relation to the area of the surface in which the molecules are confined. As the concentration of solute increases, the intermolecular forces limit the freedom of molecules motions and the isotherms 7tA= f(n) - by analogy with pV = f(p) isotherms for gases - show the deviation from ideality. Deviation from ideal behaviour can be taken into consideration by introducing appropriate corrections into the surface equation of state [87,88]; a two-dimensional modification of the van der Waals equation (n + a/A2>(A - b) = kT, being one of the best known. It has been found out that deviations from ideal behaviour become larger as the hydrophobic chain of the adsorbed molecule increases. 2.3.1.1 Two-dimensional solution model In the other approach, the adsorbed monolayer can be modeled as a two-dimensional (2D) solution 1891.The interface is treated as a phase consisting of the same components as in the bulk but in different concentration due to the surface force field. This model can be combined with either ideal [90] or regular [91,921 solution theory and has been used to derive the parameters of interaction between adsorbed molecules in mixed films 193-961. The two-dimensional solution approach is much closer to the surface region picture than the 2D gas approach since the 2D solution model accounts for the solvent molecules which are present, together with adsorbed molecules, in the film. 2.3.2 Insoluble films

By analogy to gaseous adsorbed monolayers, insoluble monolayers in the most expanded state (region G on the X/A isotherm, Fig. 5) can be

230

Fig. ,5. Pressure-area

isotherm for insoluble monolayer.

viewed as 2D gas phase of single component, or as 2D binary solution. The former model can be developed by analogy with kinetic molecular theory for three-dimensional gases [671.Let us consider a single molecule, of a mass m, which moves back and forth across a surface between two restricting barriers in the x direction. Its average velocity is vf Since the molecules exhibit perfect elasticity, the change in momentum is equal to the difference of the molecule’s momentum after (-rn$ and before the collision (m v$. Therefore the absolute value of A(momentum) is 2 mvfThe total time At between collisions with the same wall is 2mas the molecule has to cross the distance twice before returnin to the same spot), where 1 is the distance between barriers. The force, F, exerted by a molecule on impact equals: $= mV?l.The pressure, 7c,exerted on the wall (of an area 12) is 7c= 812. Converting this equation for a two-dimensional system, and assuming that the molecule moves in the x direction, it is possible to write the following:

Since pressure is isotropic it is possible to assume that the pressure exerted on both opposite walls is the same. If there are N molecules at the surface, half of them (N/2) exerts the pressure on one wall, and half (N/2) on the other. Therefore at the surface containing N molecules the following equation can be applied: N

(27)

For one degree of freedom, the mean kinetic energy of a molecule is 1/2kT. Molecules which are moving on the free surface have two degrees of

231

freedom of translational motion. Thus, xl’/N=xA=kT

(28)

The above equation is identical to Eqn. (25) which has been derived for adsorbed monolayers. It is also a straightforward two-dimensional analog of the three-dimensional ideal gas model. The applicability of Eqn. (28) to an insoluble monolayer is restricted to very low values of 7c.The deviations from Eqn. (28) with increases of 71: are very similar to what is observed for nonideal gases. An alternative way of looking at the floating monolayer is to consider it as a two-dimensional binary solution rather than 2D gas. Here, it is possible to apply the two-dimensional analog of the van ‘t Hoff equation derived for the dilute solution approximation 1671: xA,=NzkT

(29)

In the above formula, subscript 1 corresponds to solvent molecules, and subscript 2 to a solute. The floating monolayer exists in the gaseous state at very low 7c(co.1 mN/m) and is completely isotropic. It has been argued 159,611that the molecules in gaseous monolayers lie nearly flat on the surface. However, recent studies [97] have shown that the hydrophobic tails of monolayer forming molecules are out of the water surface even for infinitely diluted monolayers. Under compression, the L,G region appears, which is characteristic of a pressure x - 10 mN/m. It can be considered as a two-phase region of liquid-gas equilibrium, analogous to the equilibrium in three dimensions between a liquid and its vapor. The next phase (L,) is usually called a liquid expanded state which obeys the equation of state 1981: (n--,,)(A-b)=kT

(30

where x0 and b are empirical constants. Jura and Harkins [991 proposed different equation of state for the L, region: x=C+aA-blnA

(31)

The formation of expanded monolayers is dependent upon factors such as side chains (which interfere with the tendency of the chains to pack closely), the presence of double bonds, or the presence of additional polar groups in the molecule [ 1001.Upon further compression, the intermediate region (I) may appear which is liquid in nature, but has however much higher compressibility than the L, state. The empirical equation describing the I state of a film has the form 1991:

232

a=C+$A-b)

(32)

Further compression leads to a liquid-condensed (L,) type film which can be characterized by the following equation of state: A=p-cm

(33)

According to Adam [591and Langmuir [981,monolayer forming molecules in this state are closely packed but there is a certain amount of water molecules between them which can be squeezed out upon further compression to form a solid-like (S) film, characterized by the equation: x=b-aA

(34)

Here, the monolayer becomes highly ordered, with the molecules closely packed and steeply oriented to the surface. Eventually it is impossible to increase the pressure further since the collapse occurs and molecules are forced out of the monolayer forming lenses. 3. ORIENTATIONOF MOLECULESAT THE INTERFACE 3.1 Absolute Orientation of Surface Dipoles When molecules are introduced at the water/air interface, either by adsorption or by spreading, it might be expected that the polar group would cohere more strongly to the water molecule than would the nonpolar group. It is highly accepted that large amphipathic molecules adopt a preferred orientation at the interface. However, the behaviour of small dipolar molecules at the phase boundary has been disputed and it has been argued that the orientational effect can be averaged out by thermal agitation. Hardy [loll and Harkins [102,103] were the first to suggest that all amphipathic molecules orient themselves at the surface. Based on the idea of ‘force fields’ around molecules, more or less intense depending on the polarity and chemical structure, they postulated the principle of “least abrupt change in force field”. According to this principle, molecules should orient themselves so as to provide the most gradual possible transition from one phase to another. With this in mind it is possible to predict that alcohol molecules at the water/air interface should be oriented with the hydroxyl group towards the water phase and the hydrophobic tail towards the air. This can explain the principle “like dissolves like” (Ref. [103], p. 19). This law can also be applied to the case of pure liquid to predict the orientation of molecules in the surface layer 11031.

233

According to Kamienski [104], the orientation of water molecules at the boundary between water and air is due to the considerable difference in the dielectric permittivity of water and air. As a result, surface water dipoles orient themselves so that their stronger electric field (hydrogen atoms) is directed into the phase of higher dielectric permittivity (water) and oxygen atom is directed towards the air. Further evidence that surface dipoles of low molecular weight polar liquids do indeed adopt a preferred orientation, has been given by Good [105]. He proposed that the surface entropy of a liquid may be taken as a criterion of surface orientation. Orientational ordering at the interface of a liquid leads to a lower surface entropy than that in the conditions where the surface molecules are disordered. Lower values of the surface entropy for hydrogen bonding polar liquids in comparison to those for non-polar and polar non-hydrogen bonding compounds, have been interpreted as resulting from surface orientation. Further development regarding the orientation was given by Langmuir [106] in his principle of ‘independent surface action’. According to Langmuir, it is possible to suppose that each part of a molecule possesses a local surface tension. Let us take the ethanol/air interface for consideration to decide if alcohol molecules should be oriented with -OH groups towards the air or bulk liquid phase. In the first case, the free surface would be formed by hydroxyl groups, the surface energy of which is 190 ergs/cm2 (for comparison, the surface energy of water is 120 erg/cm2). In the second case, surface energy would be close to the value for short-chain hydrocarbons, i.e. 50 ergs/cm2. The principle of the minimum of energy favours the orientation with the hydrophobic part towards the air. This can be also confirmed by experimental results of surface tension measurements. If the hydroxyl group was directed towards the air, the surface tension of alcohol should be higher than 71.78 dynes/cm2 (the value of the surface tension for water at 25°C). If the orientation was opposite, the measured value of surface tension would be of the order of 20-22 dynes/cm2 (surface tension of liquid hydrocarbons). The measured value of the surface tension of ethyl alcohol (22 dynes/cm2) proves the orientation of surface alcohol molecules with the hydrophilic groups anchored in the bulk liquid phase. Harkins [103,107] gives one more piece of evidence for a particular orientation of molecules at the interface. In the process of surface formation, a molecule is first raised from the bulk into the surface (the energy Es being supplied), and next moved to the gas phase (with the ‘jumpingout’ energy, I$, required). The ratio ES/@ is thus a measure of the extent to which a surface molecule is symmetrically located with respect to the

234

liquid and gas phase. For symmetrical molecules, the value of the ratio is close to 1. For unsymmetrical molecules it is clear that surface molecules must be oriented so as to minimize ES. For film-forming molecules, their orientation at the interface can also be deduced considering the value and the sign of measured changes in surface potential, Ax. The adsorption of solute molecules at the interface, causing either the increase or the decrease of the surface potential jump of water, indicates the direction of the oriented dipoles of solute, in comparison with the orientation of surface water dipoles 11041. All these methods mentioned above make it possible to predict the so-called absolute orientation of surface molecules, i.e. the absolute direction of the surface dipole. Thus one can deduce whether the dipole on the interface is on average pointed ‘up’ or ‘down’. 3.2 Average Orientation Angle of Molecules at the Surface Another approach is the determination of the average orientation angle of surface dipoles. Considering small, highly polar molecules which form adsorbed films at the interface, the evidence of their orientation may be found as the results of experimental measurements of effective dipole moments [77791 and second harmonic light generated from the surface [108,109]. First, let us consider adsorbed films only. For some Gibbs monolayers it is possible to deduce the orientation of molecules by comparing the values of the area available at the surface for one adsorbed molecule (A = l/N) with its cross-sectional (geometrical) area. If the area available at the surface for one molecule at maximum surface coverage is several times larger than the molecule’s dimension, it is evident that the molecule has enough room to orientate itself between the vertical and horizontal (relative to the surface) position. In such a gaseous film the average orientation angle cannot be predicted in this way. However, when the molecular area at the surface is almost the same as its geometrical dimension, the vertical orientation of the molecule can be expected. More precise information concerning the orientation angle of surface dipoles can be obtained from the values of effective dipole moments of adsorbed molecules, $, and dipole moments of free molecules, l.~.The effective dipole moment (CL), which is the vertical component of the dipole moment of the molecule, can be determined from the dependence Ax = f(N), applying the Helmholtz equation and assuming that E= 1. Knowing CL, it is possible to determine the angle (6) between the dipole moment and the normal to the interface (Fig. 6). For molecules with the main axis

235

Fig. 6. Angle between dipole moments (01, between dipole moment and the main axis of the molecule (Q) and surface orientation angle (a); see text for explanation.

along the dipole moment direction, this angle (6) can be considered as the surface orientation angle. In the case of molecules for which the dipole moment can be treated as acting at a particular angle to the direction of C-C bond (Cp), this angle has to be taken into consideration when calculating the orientation angle. It was shown [llO,lll] that in alcohols, aldehydes, carboxylic acids, amines and amides, the dipole moment of the molecule makes an angle of about 62”, 55”, 74”, 68” and 48”, respectively. The use of this angle (@> and the angle between dipole moments (6) gives the value of the surface orientation angle (a) (Fig. 6). Applying this approach, surface orientation angles for a number of small amphipathic molecules have been determined. For example, the average orientation angle for acetic acid, trifluorotrichloro-, trimethyl acetic acid was reported to be 87.5”, 82.1”, 68.3”, and 76.3” to the water surface, respectively [77]. Similar values were obtained for propionaldehyde (63.7”), propionamide (71.4”), propionic acid (75.4”), 3-bromopropionic acid (67.8”), 2-chloroethanol(67.7”) [781,n-butanol(69.8”), iso-butanol(69.1”), set-butanol(70.6”), tert-butanol(72.4”) [791.As seen, all the investigated compounds take an almost perpendicular to the interface orientation at the interface (ca. 20” from the surface normal). This can be expected considering the presence of hydrophobic chains which have a tendency to avoid contact with the water phase. In this approach, the orientation angle of molecules is an average quantity and is dependent on the orientation of the dipole in the electric field originating from water molecules in the interfacial region. Thus it is possible to assume a simple model of orientation of adsorbed molecules,

236

analogous to that of permanent dipoles in the homogeneous external field, given by a simple interaction: a cos(8+,), where a = w/kT, 2w is the energy of orientation of molecule ‘up’ versus ‘down’, 8 is the angle between the adsorbed dipole and the normal to the interface, and 8c is the angle between the direction of the local field and the surface normal. The angle 0 can vary within the range 0 < 8 c 7~.Therefore, the minimum of the energy of dipoles occurs for 8 = 8,, and the maximum for 8 = 0 or JE, depending on the value of 0,. Remembering that the molecules in the adsorbed films behave as a two-dimensional ideal gas, it is possible to neglect the interactions between adsorbed molecules at the surface. First, let us assume that the minimum of the energy of dipoles corresponds to its vertical to the interface orientation, along the field direction. In this case, 8, = 0 or x, depending on the kind of adsorbed molecule, i.e., on the direction of dipole moment of adsorbed molecule in comparison to the water dipoles. In this case, the interaction is given by a cos 8, or a cos(8 - x), and the unnormalized form of the probability density function can be expressed by the formula : f(e) = exp(-a cos e), or f(e) = exp[-a cos((8 - x)1. Since the orientation is considered in the system of spherical polar coordinates, the experimental function from which one can estimate 8, g(B), can be expressed by the following formula: n

I g(8) f(e) sin 8 de (g(e))= O n

(35)

I f(e) sin 8 de 0

wherein g(8) = cos (0). Calculated from this expression, parameter a, for a number of small aliphatic and aromatic compounds, has the mean value of 0.4 [_112].This indicates that the distribution of orientation angles is very broad which could be expected for adsorbed gaseous films. From the parameter a, the energy of orientation was determined. The average value of w (0.4 kT) for one adsorbed molecule proves that the energy barrier of molecules ‘up’ versus ‘down’ is small and therefore the adsorbed molecule could theoretically take any orientation at the interface. Since these calculations have been performed assuming that the minimum of the energy of dipoles (maximum probability) corresponds to their orientation along the field direction, it is possible to verify the obtained results and calculate 8, from the temperature dependence 11131.Calculated in

237

this way the value of 6, (0 or n) [113] confirms the validity of the assumption previously made [112]. The other method, which also makes the determination of the average orientation angles possible, is the second harmonic generation (SHG) technique. SHG is the coupling of two photons of energy hv to produce a 2hv energy photon [114]. Non-linear optical phenomena occur in media exposed to very high li ht fluxes, as those associated with lasers. The A+ induced polarization, P, of the medium occurs through its linear (al)) and non-linear @s)

susceptibilities:

(36) The application of the SHG techniques for surface studies is possible because the non-linear process of generation of SH light is dipole-forbidden in the centrosymmetric media (in the bulk phase), but is allowed at interfaces where the symmetry is broken [115,116]. This very property gives SHG a high degree of sensitivity only to interfaces [lo81 and therefore this technique has recently been applied to study adsorbates at solid interfaces [109,117] as well as at the water/air interface [53,1181241. The orientation of adsorbed molecules can be deduced from the evaluation of the non-linear susceptibility, &$s [53,117-119,125,126]. The non-linear susceptibility is related to non-linear molecular polarizability, pt2), by the following relationship [ 1091: (37) wherein NS is the surface density of molecules adsorbed at the surface, T$$’ describes the coordinate transformation between molecular (&n,c) and the laboratory (x,y,z) systems, and the angular brackets denote an average over molecular orientations. The above equation is simplified when the molecular polarizability is dominated by a single component, qfk along the molecular axis, 5. The elements of $$$ which do not vanish at the interface are then directly proportional to &$?i. Because the water/air interface is symmetric about the xz and yz planes, only two independent components of 27 elements of E? do not vanish: z,Z,Z and ~,i,i where i = x or y [109,117-1191. Following the method developed by Tom et al. [125]. for uniaxial molecules, SH polarization can be expressed

238

as a function of (cos3 @/(sin2 6 cos 6), where 6 is the angle between molecular axis and the normal to the interface. When a delta distribution of 6 is assumed, the above expression reduces to (cot2 0). This method has been applied to determine the orientation of some substituted benzene paraderivatives [53,126] which form adsorbed films at the water/air interface. The average orientation angle was found to be almost the same for all the compounds investigated. For example the orientation angle for phenol, p-cresol, p-tert-butyl phenol, p-n-pentylphenol, p-bromophenol, p-nitrophenol and p-nitrobenzoic acid was reported to be 43”, 43”, 43”, 48”, 39”, 40” and 47” from the surface normal 1531.This approach has also been applied to estimate the orientation angle of long-chain molecules which can be spread at the free water surface to form insoluble monolayers [118,119]. During the compression, changes in the surface orientation are observed. For a full monolayer of pentadecanoic acid, (6) = 60” [118] while for a saturated film of sodium dodecylnaphthalene-sulphonate the average orientation angle is 30” [1191. Using the SHG technique, the influence of penta- and hexadecanoic acid on the orientation of p-nitrophenol has also been studied [1271. Both methods for the determination of the orientation angles of adsorbed molecules have been discussed and compared in Ref. 11131. As seen, either from the measurements of surface electric potential or from the polarization of the second harmonic light from the surface layer, one can gain information about the orientation of surface molecules. Considering the first method, however, we have to be aware of possible errors in the measurements of the dipole moment which is sensitive to both the dielectric permittivity of the surface layer and any orientational changes of surface water dipoles. In the case of the laser method, the orientation model assumes uniaxial molecules, which limits the applicability of the SHG technique for study monolayers formed by molecules of different chemical structure. Current investigations into the structure of monolayers are focused mainly on insoluble films. New experimental approaches including simulation of Langmuir monolayers are reviewed in the paper by Knobler 11281. REFERENCES 1 2 3 4

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