Download 6 Chapter 1: Theoretical background 1.1 Barium sulfate Barium

Chapter 1: Theoretical background
1.1 Barium sulfate
Barium sulfate is the inorganic compound with the chemical formula BaSO4. It is a
white crystalline solid that is odorless and insoluble in water. It occurs as the mineral
barite, which is the main commercial source of barium and materials prepared from it.
The white opaque appearance and its high density are exploited in its main applications.
Almost all of the barium consumed commercially is obtained from the mineral barite,
which is often highly impure. Barite is processed by carbothermal reduction (heating
with coke) to give barium sulfide:
BaSO4 + 4C → BaS + 4 CO
Eq. 1.1
In contrast to barium sulfate, barium sulfide is soluble in water and readily converted to
the oxide, carbonate, and halides. To produce highly pure barium sulfate, the sulfide or
chloride is treated with sulfuric acid or sulfate salts:
BaS + H2SO4 → BaSO4 + H2S
Eq. 1.2
Barium sulfate produced in this way is often called blanc fixe, which is French for
"permanent white." Blanc fixe is the form of barium encountered in consumer products,
such as paints.
In the laboratory barium sulfate is generated by combining solutions of barium ions and
sulfate salts (chapter 3 materials&methods). Because barium sulfate is the least toxic
salt of barium due to its insolubility, wastes containing barium salts are sometimes
treated with sodium sulfate to immobilize (detoxify) the barium. Barium sulfate is one
of the most insoluble salts of sulfate. Its low solubility is exploited in qualitative
inorganic analysis as a test for Ba2+ ions as well as for sulfate.
6
(a)
(b)
Figure 1.1: Powder (a) and chemical structure (b) of barium sulfate.
1.2
Organophosphonic compounds
The organophosphonic compounds are complexes consisting of one or more groups CPO(OH)2. They are used as chelators and scaling inhibitors in several laboratory and
industrial studies. The organophosphonic compounds interact strongly with surfaces;
this property has resulted in a significant application of them. The reason they are
widely used (both in industry and in medicine), is the presence of phosphonates ions.
The phosphonate ions find application in industry and in particular in cooling water,
desalination processes and in oil-related suspension agglomeration. Even the
complexing ability and their metabolization by calcium ions contribute to the effort of
treatment of skeletal diseases.
Phosphonates are very soluble in water and slightly soluble in organic solvents. The
toxicity to aquatic ecosystems is very low, while for the human body is minimally
absorbed (through the gastrointestinal system), and is considered toxic, although is used
for scientific-medical reasons. The global consumption is around 56.000 tons
worldwide and is commonly used as HEDP (1-Hydroxyethylen 1diphosphonic-acid)
and DTPMP (Di-ethylene-triaminepentamethylene-phosphonic acid).
The phosphonates are adsorbed strongly in almost all surfaces of mineral rocks. This
behavior distinguishes them of amino carboxylic acids. Amino carboxylic acids are
much less reactive to mineral surfaces, especially at neutral pH. Some of the adsorbers
which are studied in relation to their interaction with phosphonates are calcium and
7
aluminum oxides, oxides of iron and zinc, the calcium phosphate mineral and barite.
The sewage sludge is also a very good adsorber (Nowack, 2003).
Finally, the phosphonate ions exhibit additional advantages over other substances
because they are extremely stable over a wide range, such as temperature and pH. For
this reason are widely used in petroleum industry, where changes of circumstances
within the processes exhibit large deviations (Browning, 1996).
The mechanism of action of the inhibitors is not fully known. In recent years, however,
it has become the subject of wide study and laboratory studies aimed at identifying and
understanding the process of action. The possible adsorption of inhibitor molecules is
crucial for the inhibition process. A possible way is the process of chemisorption,
forming chemical bonds between the inhibitor and substrate. Another possible scenario
is that organophosphonic inhibitors are adsorbed in the active centers of barite substrate,
developing electrostatic interactions between the phosphonates -PO(O22-) group with
some positively charged active centers, possibly with metal ions.
1.3
Adsorption
The kinetics of adsorption of inorganic and organic compounds on a solid phase,
usually has two stages: an initial stage of rapid removal of the adsorbed substance from
the solution which is followed by a stage of much slower adsorption until equilibrium is
reached. Because the concentration of the adsorbent remains practically constant during
the sorption kinetics can be considered pseudo-first order. [Kovaios et al., 2006]. The
rate of adsorption is given by:
d t
 k1    t 
dt
Eq. 1.3
where Γ and Γt (g m-2) are the equilibrium concentration and the concentration at time t
(s) of the adsorbed substance in solid phase, respectively and k1 (s-1) is the first order
rate constant.
Eq.1.3 gives:
8
 
ln 1  t



  k1t

Eq. 1.4


The value of k1 can be calculated from the slope of the line in the graph  ln 1 
t 
 in

function of t.
The pseudo-first order kinetics may be deemed inappropriate for describing the sorption
usually for two reasons: (a) the quantity is not proportional to the free adsorption sites,
and (b) the straight line given by the Eq. 1.4 does not pass through the origin. In this
case it may be adopted kinetic pseudo-second order:
d t
2
 k2     t 
dt
Eq. 1.5
where k2 (s-1 m2 g-1) is the apparent second-order kinetic constant.
Eq. 1.5 leads to:
t

1

t
t k2
Eq. 1.6
k2Γ is known as the initial rate of sorption. To obey the sorption kinetics in pseudosecond order, graph of t

in function of t results the straight line whose slope is
t
equal to 1. From the ordinate in the origin of the line the constant k2 and the initial rate
of sorption are calculated.
To describe the kinetics of adsorption energy on heterogeneous solid surfaces often the
Elovich empirical equation (Low, 1960) is also used:
d t
  e   t
dt
Eq. 1.7
where α (mg∙ m-2∙s) is the initial rate of sorption, and β (m2∙g-1) is a constant.
Integrated form of Elovich equation is written:
9
t 
1
1 
1 
ln    ln  t 

   

The graph of Γt versus ln  t 

Eq.1.8
1 
results in a straight line, from the slope and
 
intercept on the origin parameters α and β are calculated.
The adsorption takes place in several stages including the transfer of solute from the
aqueous phase to the solid surface and diffusion inside it, which is usually slow. The
rate diffusion constant ki (μg m-2 s-0.5) is given by the equation:
t  ki t
Eq.1.9
when the kinetics of sorption is controlled by intra-particle diffusion, the graph of Γt
versus
gives a straight line from the slope of which the diffusion coefficient is
measured.
However if the transfer of solute from the aqueous phase to the liquid / solid interface
plays a more important role in the adsorption, then the model applied corresponds to
fluid film diffusion:
 
ln 1  t



  k fd t

Eq. 1.10


where, kfd is the rate constant of sorption. If the graph of  ln 1 
t 
 versus t gives a

straight line, then the sorption is controlled by diffusion through the liquid film
surrounding the particles of the solid sorbent. The kfd is calculated from the slope of the
line.
1.3.1 Isotherms theory
The adsorption models are necessary for the interpretation of experimental data of
adsorption of molecules in crystalline solids. Originally they were developed for the
10
ideal gas adsorption on solids and then expanded to include the case of aqueous
solutions. The profile of the isotherm depends on the mechanism by which the
adsorption takes place and therefore can be used for the investigation and its
interpretation. The most common isotherms are the Langmuir and Freundlich isotherms.
1.3.1.1 Langmuir Isotherm
The Langmuir isotherm equation is (Langmuir, 1918):

 mbCeq
1  bCeq
Eq. 1.11
where Γm (g m-2) is the monolayer capacity (surface concentration required to generate
monolayer) and b (mL g2) is the affinity constant between adsorbed substance and
sorbent.
Langmuir isotherm equation (Eq. 1.11) is derived from both kinetics and equilibrium
thermodynamics equations. In order for the equation to be effective it will require
reversible sorption. The Langmuir isotherm is subjected to the following assumptions:

Adsorption is produced in a fixed, energy-equivalent, position of the solid
surface

There is no interaction between the adsorbed molecules

The heat of adsorption is constant and independent of the surface area covered

The extent of adsorption increases with the concentration of adsorbed molecules
until a monomolecular layer corresponding to full surface covered is formed.
For values Ceq for which kaff Ceq << 1 Eq. 1.11 becomes:
 
i
 k aff Ceq
m
Eq. 1.12
11
The above equation shows that at low concentrations the covered surface is proportional
to the concentration of the molecule in solution adsorbed. In contrast, for values Ceq for
which kaff·Ceq >> 1 Eq. 1.11 becomes:
 
i
 1
m
Eq. 1.13
and therefore the covered surface is complete and independent of concentration.
The constants b and Γm are calculated from the slope and intercept on the origin of the
graph of a linear form (
:
1
1
1


  m  mbCeq
Eq. 1.14
1.3.1.2 Freundlich isotherm
Freundlich isotherm equation is (Freundlich, 1906):
  K f Ceqn
Eq. 1.15
where Kf (μg(1-n) ∙m-2 ∙ mLn) is the Freundlich sorption coefficient, a measure of affinity
between the substance and sorbent, n (dimensionless) is the Freundlich exponent, a
measure of the energy heterogeneity of adsorption sites and Ceq (μg mL-1) is the
equilibrium concentration of adsorbed substance in aqueous phase.
This equation is often used to describe adsorption on heterogeneous surfaces of
substances such as soils. Its use requires reversible sorption. The Freundlich
coefficients, Kf and n are obtained from the graph of a linear form:
log   log K f  n log Ceq
Eq. 1.16
The main weakness of the Freundlich isotherm is that it provides a continuous increase
in adsorption with increasing concentration. It does not provide the appearance of the
adsorption maximum corresponding to the formation of monolayers. It is also believed
12
that there is no linear region in the graph of concentration versus Ceq, as in the Langmuir
isotherm, for small values (kaff Ceq << 1) of covered surface. Thus, the application gives
satisfactory results only for intermediate values of surface coverage.
13