1. Characterization of the phenomenon 1. Characterization of the phenomenon

1. Characterization of the phenomenon 1. Characterization of the phenomenon

Adsorption from solution at solid/liquid interfacesolution at solid/liquid interface differs from that at solid/gas (vapour, or pure liquid) interface, where individual substance adsorbs.

In the case of solutions at least two components are presenttwo components are present that can form a compact layer at the adsorbent surface.

When the solution concentration is changed, mutual displacement of the components in the surface layer has to occur because neither on the surface nor in the bulk

solution there are free spaces.

Therefore only substitution of the molecules of one component by those of another is possible.

This is the most characteristic feature of adsorption from solution that distinguishes that from gaseous phase.

2. Thermodynamic description of the adsorption process 2. Thermodynamic description of the adsorption process

In this system the adsorbed surface layer can be also well described by

Guggenheim-Adam equation, as it was in the liquid/gas and solid/gas systems:

0 P

i

i

Γ =

∑

The definitions of surface excess described earlier are also valid here.

Reduced adsorption n_i^σ(n) is the excess number of moles of component i in the systems compared with the number of moles of that component in the reference system (without adsorption) containing the same total number of moles of all components in the liquid phase and the same concentration of component i in that phase„

(J. Ościk, Adsorption, PWN 1982, p.109).

From the above definition it results that:

i i

) n (

i

n nx

n

= −

Where n_i is the total number of moles of component i in the system, n is the total number of moles of all components, and x_i is the mol fraction of component i in equilibrium with the adsorbent.

(2)

2. Thermodynamic description of the adsorption process 2. Thermodynamic description of the adsorption process

Often n, n_i, n_i^σ(n) are defined relative to1 g of the adsorbent and the reduced surface excess of component i is expressed:

:

(3)

Then total reduced surface excess of all components equals zero and it is expresses:

Reduced adsorption n_i^σ(v) can be defined in very similar way as that of n_i^σ(n) and it refers to the same volume of the solution V^l at the same concentration c_i:

S n

) n ( i

σ

= Γ

0

i

) n (

i

=

∑ Γ

l i i

) v (

i

n c V

n

= −

(5)

where V^l is the volume of liquid phase, V^l = V – V^a (V is total volume of the system and V^a is volume of the solid phase (adsorbent)), c_i is the concentration of

component i in the equilibrium solution.

If V^l and n_i^σ(v) are referred to 1 g of adsorbent, then:

S n

) v ( i

σ

=

Γ

Assuming that partial molar volumes V_i of the components of the solution are independent of concentration and of adsorption one can write:

0 V _i^(v)

i

i ,

m Γ =

∑

The total number of moles of component i in the surface layer n_i^s(n) or n_i^s(v) are described by equations:

∑

+

= +

= ^{σ σ}

i s i i

) n ( i s

i )

n ( i ) n ( s

i n x n n x n

n ₍₈₎

s i , m i

s i i

) v ( i s

i )

v ( i )

v ( s

i n c V n c n V

n ^{= σ + = σ +}

∑

and

Where is the total number of moles in the surface layer, V^s is the volume of the surface layer.

∑

=

i s i

s n

n

The magnitudes n_i^s can be evaluated only if the thickness of the surface layer l^s is known and its position in the system. In the case of ideal adsorbed surface layer and ideal equilibrium solution:

n_i^s(n) = n_i^s(v) = n_i^s.

3. General adsorption equation from binary solution 3. General adsorption equation from binary solution

Consider homogenous surface of adsobent and adsorption occurring from a binary solution consisting of component 1 and 2 completely miscible. Then it can be

assumed that at adsorption equilibrium there are two binary solutions, i.e. the surface solution (surface layer or surface phase) and the bulk solution.

The thermodynamic equilibrium implies that:

(10)

where µ₁^s and µ₂^s are the chemical potentials of the component 1 and 2 respectively, and µ₁ and µ₂ are the corresponding chemical potentials in the bulk.

(11)

Based on this condition a general equation of adsorption isotherm from binary solutions can be derived

(for details see J. Ościk, Adsorption, PWN 1982, p.111-113).

2 s

2 1

s

l

= µ , µ = µ

µ

1 s 2 2

s 1

2 s s l

1

x x x x

x x x

= +

s s i

l

n

x = n

and

(12)

The αααα value is dependent on the composition of bulk solution and therefore Eq. (12) does not describe adsorption equilibrium.

The general equation (12) correlates changes of the surface solution composition x₁^s and changes of the bulk solution composition x₁.

This equation is also called 'equation of true (individual) adsorption 'equation of true (individual) adsorption isotherm of component 1 from solution

isotherm of component 1 from solution'.

( )

1 2

1 s 1

l

1 1 x

x x

x x x

− α +

= α +

α

= α

where α is distribution coefficient (function), and it is defined:

s 2 1

2 s l

x x

x

= x

α

(14) Experimentally always excess adsorptionexcess adsorption is determined.

The measurements can be conducted by a static or dynamic method.

In static method concentration of the adsorbing component is measured before and after adsorption process.

Depending on the system, the adsorption equilibrium can set a long time, within minutes or even hours.

The adsorbed amount can be calculated from Eq. (14).

4. Surface excess and true adsorption 4. Surface excess and true adsorption

( )

m x x

n n

o 1 o )

n ( 1

= −

σ

where n^o is the total number of moles of the solution used in the experiment;

n^o = n₁^o + n₂^o, m is the adsorbent mass, x₁^o, x₁ are the molar fractions of the component 1 in the initial and final (adsorption equilibrium) solutions.

(15) If the specific surface of the adsorbent is known the surface excess Γ

1(n) can be calculated.

( )

S m

x x

n

) n

( 1 1

1

= − Γ

Analogically n₁^σ(v) can be determined experimentally:

( )

m c c

n V

o ) 1

v ( 1

= −

σ (16)

( )

S m

c c

V

) V

( 1 1

1

= −

Γ

Where V is the volume of the solution used.

The dynamic methods are in fact chromatographic ones.

Most often the mobile front analysis is applied.

In the method the solution flows along the column filled with an adsorbent.

If the component 1 adsorbs stronger than the component 2 then at the beginning of adsorption process only component 2 will appear in the solution leaking from the column.

When a given volume of the liquid is leaked out the component 1 appears in the leakage.

This moment is termed retention volume (front volume). Usually this front is not sharp and the concentration of component 1 increases smoothly up to its bulk concentration. This is shown in Fig. 4.1.

Fig. 4.1. Determination of the retention volume V_R in the dynamic method of adsorption

measurement.

The filled with the lines field corresponds to the adsorbed amount which can be calculated from Eq. (18) or (19).

where V_R – the retention volume, V_m,2 – Molar volume of the component 2.

If the specific surface of the adsorbent sample is known then the surface excess Γ can be calculated.

1 ) R

v (

1

c

m n

= V

1 2

, m ) R

n (

1

x

m V

n

= V

(18)

(19)

5. Types of the adsorption isotherms 5. Types of the adsorption isotherms

Like for solid/gas systems also for solid/liquid systems the adsorption isotherms have been classified.

The first classification was given by Ostwald and Izaquerre in 1922.

They distinguished three types of the isotherms, which are shown in Fig. 5.1.

Fig. 5.1. Excess adsorption isotherms from binary solutions after Ostwalda i Izaguirre;

a) UU shape isotherm – positive adsorption only, b) S shape isotherm – positive and S negative adsorption, c) linear isotherm.

The linear isotherm is obtained for molecular sieves which can adsorb one component only.

The maximum on the isotherm depends on the adsorption energy.

The higher the energy the lower equilibrium concentration at which the maximum appears.

Later on Schy and Nagy in 1960 developed the isotherms classification and distinguished 5 types of the excess adsorption isotherms from binary solutions

5 types of the excess adsorption isotherms from binary solutions.

Fig. 5.2. Nagy and Schay's classification of adsorption isotherms from binary solutions.

In order to determine individual adsorption of a given component the knowledge of total number of the moles present in the surface layer n^s and its volume V^s are needed.

The relationship between excess adsorption of component 1 and individual adsorption of the components n₁^s and n₂^s from binary solution can be expressed by Eq. (20).

where n^o is the total number of moles used for experiment.

( )

s 2 s

1 s

1 )

n (

1

n n n x

n

= − +

If n₁ and n₂denote number of moles of the components of the bulk solution at equilibrium, and n₁^s and n₂^s number of moles in the surface solution per 1 g of adsorbent, then:

n = n₁ + n₂ and _s

s s 1

1 n

x = n ₍₂₁₎

s 2 s

1

s

n n

n = +

(

)

s 1 o

s

o

n n n n

n

n = − = − +

where x₁^o is mol fraction of component 1 in the initial solution (prior to the adsorption) for m = 1 g and in accordance with Eq. (14).

(25)

From mass balance in the surface and bulk phases it results:

One obtains:

(15)

(26) (24) s

o

n n

n = +

s 1 s 1

o 1

o

x nx n x

n = +

( )

m x x

n n ¹

o 1 o )

n ( 1

= −

σ

( ) (

)

s 1 s 1

o 1 o )

n (

1 n x x n x x

n^σ = − = −

( ) ( )

s s

1 1 s 2 s

1 s

1 )

n ( 1 1

s 1 s )

n (

1 n x x n n n n x n n x

n^σ = − ⇒ ^σ = − − = − ⁽²⁷⁾

This equation can be rearranged to obtain Eq. (28) and then Eq. (29).

( ) ^{( )}

s 2 1

s 1 1

s 2 s

1 s

1 )

n (

1 n n n x n 1 x n x

n^σ = − + = − −

1 s 2 2

s 1 )

n (

1

n x n x

n

= −

(28) (29)

This equation is called 'composite adsorption isotherm', therefore that it relates the 'composite adsorption isotherm' surface excess of component 1 (n₁^σσσσ(n)) with surface solution composition (n₁^s and n₂^s) and with that of bulk x₁ and x₂.

(12)

Let us consider adsorption process that takes place from non-ideal binary solution on an adsorbent. The process can be described with the help of the general equation.

where αααα was defined :

Now, by analysis of extremal cases important conclusions can be drawn. Namely:

⇒ If xx_{1 1} →→ 00(origin of the adsorption isotherm of component 1), then in Eq. (12) 11++ ((αααααααα––1) x1) x₁₁→→ 11

and hence: xx₁₁^ss = = ααααxααααx₁₁ →→→→→→→→ xx₁₁^ss = 0, no adsorption of component 1=

⇒ If xx₁₁ = 1= 1 (end of the adsorption isotherm of component 1), then 11 ++ ((αααααααα–– 1) x1) x₁₁ == αααααααα

and hence xx₁₁^ss = x= x₁₁ = 1, the adsorption layer consists of pure component 1= 1

⇒ If the component 1 adsorbs strongly then magnitude αααααααα>>>> 1, at all its concentrations1 x₁ in the bulk solution.

Then (αααα – 1) ≈ αααα

( )

1

1

1 x

x^s_l x

− α +

= α

s s

x x

x x

2 1

2

= 1

α (13)

If the component 1 adsorbs strongly then magnitude αααα >> 1, at all its concentrations x₁ in the bulk solution.

Then (αααα – 1) ≈ αααα

1 (20)

1

1 1 x

x^S x

α +

≈ α and

This equation is similar to Langmuir equation for gas adsorption on a solid adsorbent.

Moreover:

for αααα ^{>> 1 also} αααα^x₁ ^{>> 1 and x}₁^{s~ 1} in a broad range of the concentration.

It means that the adsorption isotherm will have an convex; shape, what is shown in Fig. 5.3.

If the adsorption of component 1 is small, then for most its concentrations x₁, αααα ^{<< 1 , and} hence: αααα ^{– 1 ≈ –}1, and for small x₁ one obtains:

1 s 1

1 1 x

x x

−

= α (21)

x₁^s ~ x₁ small, therefore x₁^s is also small in a broad range of x₁ (curve 2).

Fig. 5.3. Isotherms of individual (true) adsorption from binary solution expressed in molar

fractions;

11 – positive adsorption of component 1 in whole range of its concentration in bulk solution, 2 – negative adsorption of this component in the 2

whole range of the concentration,

33 – small adsorption of both components (1 and 2) of the solution,

α αα αα αα

α – azeotropic point.

When the adsorption activity of both components of binary solution are similar then αααα ^{> 1} at small x₁, and αααα ^{< 1} at larger x₁.

Therefore (αααα – 1) changes its sign and the azeotropic pint appears on curve 3 (Fig. 5.3).

At a given concentration the curve crosses the straight line x₁^s = x₁, what means that no adsorption occurs at this point.

In other words, the composition of bulk solution is the same as that at the surface.

This is called adsorption azeotropy.

Fig. 5.3. Excess adsorption isotherm from binary solution:

1 – positive adsorption of component 1 in whole concentration range,

2 – negative adsorption of this component in whole concentration range,

3 – small adsorption of both components (1 and 2) of the solution,

α – azeotropic point.

The three curves in Fig. 5.3 represent all possible types of adsorption isotherms from binary solutions.

Obviously, they are isotherms of individual (true) adsorption.

The same isotherms plotted as excess isotherms are shown in Fig. 5.4.

Fig. 5.5. Excess (1) and individual (2) adsorption isotherm of benzene on wide- porous silica-gel. Thickness of the adsorbed layer is l^s = 0.375 nm.

Fig. 5.5. Excess (1) and individual (2) adsorption isotherm of benzene on wide-porous silica-gel.

Classification of adsorbents and adsorbats

Adsorbents and adsorbats – are classified with respect of the nature of interactions.

Interactions adsorbent – adsorbat are of the nature of interaction in condensed phases.

Chemical nature of adsorbent surface determines kind and energy of interactions adsorbent – adsorbat. Often the interactions are considered as being independent: dispersion electrostatic, dipole – dipole, dipole – induced dipole, donor – acceptor, hydrogen bonding, interaction of π electrons, chemical.

The interactions are: specific and nonspecific.

Intermolecular interactions In the process of adsorption from solution

In the case of adsorption from solution despite the interactions

adsorbent – adsorbat (S), the interactions between molecules of adsorbat (solute) (S) and solvent (R) are also important:

Interaction adsorbent - gas Interactions: adsorbent - solution

Adsorbent – adsorbat (gas) (S) Adsorbent - adsorbat (solute) (S), Adsorbent - solvent (R)

R – S.

Scheme of interactions In the adsorption process:

a) from a gasous phase, b) from binary solution

Nonspecific interactions (universal) – first of all, these are London dispersion (generally termed as van der Waalsa).

Specific interactions – most common are the electron-donor and electron- acceptor.

Hydrogen bond – are special case of specific electron-donor and electron- acceptor interactions.

Classification of molecules

Evell, Harrison, Berg – they have classified the molecules in respect of their ability to form hydrogen bonds in the liquids (solvents)

Pimentel and McCllean – introduced classification ta king into account Lewis’ theory of acids and bases: A – acidic, B – basic, AB – amphoteric, N – neutral..

Class General characterization Compounds AB* Ability to form three-dimensional

net of strong hydrogen bonds

water, gicol, gliceryne, aminoal- cohols, hydroxyloamins, hydrox- sacids, nitrophenoles, amides AB Presence of active hydrogen

atoms as well as oxygen, nitro- gen and fluorine atoms having the electron-donor properties; weaker hydrogen bondings,

alcohols, acids, phenols, primary and secondary amines, oximes, ammonium, HF, HCN

B Presence of electron-donor

atoms(oxygen, nitro gen, fluorine);

absence of active hydrogen atoms.

ethers, ketones, aldehydes, estrs, tertiary-amines (including deriva- tives of pirydyne), nitro-

compouns, nitryles, alkens.

A Active hydrogen atoms present;

no the electron-donor atoms. CHCl₃, CH₂Cl₂, CH₃CHCl₂ itp.

N No ability to form hydrogen bonds.

Aliphatic hydrocarbons, mercap- tans, halogenated compound do not belonging to A

Classification of adsorbents

According to Kiseliev:

Type I – nonspecific adsorbents – no functional gropups on their surface, do not Exchange ions– graphite soot, polymers, saturated hydrocarbons.

Type II – specific positive adsorbents – acidic –OH gropups on the sur- face, e.g.. SiO2·nH2O. Free orbitals d of Si atoms – cause shift of electrons in the surface ─OH and therefore some protons appears on the surface.

Type III – specific adsorbents negative – possess bonds or groups of atoms having excess negative charge. They can be obtained by covering the original nonspecific surface by a monolayer of molecules or macromo- lecules from group B.