Surfactant Molecule

We model such a surfactant molecule by a “dumbbell” or a rigid rod of length ℓ which has two interaction centers located at the 2 ends, which is analogous to an electrical dipole.

From:

Strongly Coupled Plasma Physics
,
1990

Proceedings of the International Briefing on Colloid and Surface Science

Makoto
Harada
, …
Iwao
Watanabe
, in


Studies in Surface Science and Catalysis, 2001

i

Introduction


Surfactant molecules
are adsorbed, and regularly aligned on the aqueous solution surface (gas/liquid interface). On the solution site, the charged groups of surfactants concenter water molecules as well every bit ions to institute specific surface structures. DDABS is a zwitterionic surfactant with a cationic quaternary ammonium group and an anionic sulfoic grouping. The surface structures of attracted ions depend on the concentration and nature of an electrolyte added to the solution. In this work, the surface structures of bromide ions adsorbed on the surface movie of DDABS were analyzed by XAFS technique, which can be an effective tool to probe such local diminutive structures. The total-reflection total-electron-yield (TRTEY) XAFS method

[1]
allows united states of america to distinguish the data on the local construction of Br
at the solution surface from that in majority.

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Mesoporous Molecular Sieves 1998

Dominique
Langevin
, in


Studies in Surface Science and Catalysis, 1998

1.1

Surfactant Aggregation


Surfactant molecules
are dispersed as monomers in water when their concentration c is very low. At some point the solubility limit is reached, and either the excess surfactant precipitates or it forms aggregates in which the hydrophobic part of the molecule is subconscious in the interior, to minimize contact with water. These aggregates are in equilibrium with monomers, and the monomer concentration remains close to the solubility limit chosen “cac” (for critical aggregation concentration). When the hydrophobic part of the surfactant is made of CH

two
chains, ane tin can evaluate merely the difference in chemical potential
of the surfactant in the aggregates and in the bulk solution (as a monomer) from the free enthalpy gain ∆g when a CH2
group is removed from water and incorporated in an paraffin environs (∆g
 
~
 
kT per CHii
grouping). This leads to the well known relation[2]:

(1)

In

c
a
c

=

a



b
northward

where a and b are constants and n is the number of CH2
units (b
 
=
 
∆m/kT). Since b ~
 
one, an increase of due north past two units leads approximately to a decrease of the cac past a cistron x.

When n is too big, aggregates are not formed, and the excess surfactant precipitates : the solubilization limit is called the Krafft point. This is the case of CTAB (cetyl trimethyl ammonium bromide) at room temperature. CTAB micelles can however be obtained at college temperatures, to a higher place 25
 
°C. The limit temperature above which aggregation in majority is observed is called Krafft temperature. The Krafft temperature depends mainly on the number of CH2
units, but likewise on the nature of the polar part of the surfactant molecules: for case sulfates have smaller Krafft temperatures than sulfonates with the same chain.

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From Zeolites to Porous MOF Materials – The 40th Anniversary of International Zeolite Conference

Norikazu
Nishiyama
, …
Korekazu
Ueyama
, in


Studies in Surface Science and Catalysis, 2007

1.1.

Synthesis


Surfactant molecules
were deposited on a silicon substrate by a spin-coating method. The forerunner solution was prepared using Brij thirty (C

12EO4), HthreePO4, EtOH, and deionized water in the mole ratios of 1.5H3POiv: 0.75 Brij 30: 50EtOH: 100H2O. The surfactant-solvent mixture was dropped onto the silicon substrate while information technology was spinning at 500 rpm, then the substrate was spun upwards to 4000 rpm for lx south. The H3PO4/Brij 30 composite motion-picture show was arranged to lie vertically in a Teflon-lined stainless steel vessel (50 cmiii). The H3POfour/Brij thirty blended films were treated with a TEOS vapor (Fig. 1(a)) and with TEOS and HCl vapors (Fig. one(b)) as follows: a small amount of TEOS (and HCl (5N)) was placed in the bottom of the vessel autonomously from the substrate. The vessel was placed in an oven at 120°C for 1.five h. Calcination was performed at 300°C in air for five h with a heating rate of 1°C /min.


Fig. 1.
Vapor stage synthesis of silica-phosphate complex films. (a) Treated with a TEOS vapor, (b) treated with TEOS and HCl vapors.



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Mesoporous Molecular Sieves 1998

Thousand.S.
Attard
, …
J.M.
Elliott
, in


Studies in Surface Science and Catalysis, 1998

Abstruse

Mixtures of
surfactant molecules
and water form intricate iii-dimensional structures at high surfactant concentrations. These phases tin can be utilised as molds for the germination of highly ordered mesoporous materials such every bit inorganic oxides and metals. It has already been shown that not-ionic surfactant assemblies can exist employed in the synthesis of mesoporous silicas [1]. By applying the same principles to metals, we take produced a new family of mesoporous materials.

The hexagonal phases formed by a number of ternary non-ionic surfactant
 
+
 
h2o
 
+
 
metal precursor systems take enabled us to prepare mesoporous metals such every bit platinum. The hexagonal pore structure of mesoporous platinum, as observed by TEM, was a direct cast of the surfactant phase from which it was formed [2]. By changing the chain length of the surfactant, the pore size could be altered, and surface surface area measurements of the platinum materials were greater than those of commercially available platinum blackness. These novel, nanostructured, metals are of considerable involvement for applications in catalysis and electronic devices.

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Mesoporous Materials, Synthesis and Properties

Robert
Mokaya
, in


Encyclopedia of Physical Scientific discipline and Applied science (Third Edition), 2003

Ii.A.1

Behavior of Surfactants in Solutions

In aqueous solution,
surfactant molecules
exist as very active components with variable structures in accordance with increasing concentrations. At low concentrations, surfactant molecules exist as monomolecules, but with increasing concentration the surfactant molecules aggregate together to grade micelles, which has the consequence of decreasing the entropy of the solution. The driving force for the aggregation of surfactant molecules to micelles is to minimize repulsive interactions between their hydrophobic tails and water. The resulting micelles are either spherical or rod-shaped. The initial concentration at which the surfactant molecules begin to aggregate into micelles is called the critical micelle concentration, CMC. As the surfactant concentration increases farther, hexagonal close packed arrays of micelle rods appear, producing hexagonal phases (such as those that pb to the formation of MCM-41). The side by side step, as the surfactant concentration increases, is the formation of a lamellar phase, which is sometimes but not always preceded, by the germination of a cubic stage. The changes are illustrated in

Fig. 2. The particular stage of the surfactant does non only depend on its concentration, only also on the nature of the surfactant molecules and their environment. Important environmental factors include variables such as the length of the surfactant hydrophobic (alkyl) carbon chain, the nature of the surfactants’ hydrophilic head grouping, the properties of the counterion, pH, temperature, ionic strength, and the presence of other additives/dopants. It has been found that in nigh cases the CMC decreases with increase of chain length of the surfactant, and the valency of the counterions. Conversely the CMC increases with increasing counterion radius, pH, and temperature.


FIGURE 2.
Stage sequence of a surfactant/h2o system. The scheme shows the formation of micelles after the disquisitional micelle concentration (CMC) and the sequence of phases as the concentration of surfactant increases beyond the CMC.



Every bit stated above, the extent of micellization, the shape of the micelles, and the aggregation of micelles into liquid crystals depends on the surfactant concentration and other factors such as temperature. A more detailed analogy of the micellization process is shown in
Fig. iii. At very low concentration, the surfactant is present every bit gratuitous molecules dissolved in solution. At the critical micelle concentration (CMC1 in
Fig. 3), the private surfactant molecules form small, spherical aggregates (micelles). At higher concentrations (CMC2 in
Fig. iii), the amount of solvent nowadays between the micelles decreases and as a result the spherical micelles can coalesce to form elongated cylindrical micelles. These cylindrical micelles can so pack together into various liquid crystal (LC) phases. Initially, rod-like micelle amass to form hexagonal close-packed LC arrays. As the concentration increases, cubic bicontinuous LC phases form followed by LC lamellar phases.


Figure 3.
A phase diagram showing the relationship between temperature, concentration, and liquid-crystal structure for a surfactant/water system.



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SURFACE AND INTERFACE PHENOMENA

Reinhard
Miller
,
Valentin B.
Fainerman
, in


Handbook of Surfaces and Interfaces of Materials, 2001

1.6

Surface Tension of Micellar Solutions

The assemblage of
surfactant molecules
within the solution majority (eastward.chiliad., micelle germination) significantly affects the shape of the surface tension isotherm. In

Figure 7, diverse possible shapes of the curves are shown schematically, representing the concentration dependence of surface tension of a surfactant solution in the region above the disquisitional micelle concentration (CMC). Such dependencies have been reported in a number of experimental studies.


Fig. 7.
Schematic of the shape of interfacial tension isotherms for surfactants adsorbed at a liquid-fluid interface.



The surface tension
γ
tin can be either almost constant, increase, or decrease, or the curve tin exhibit an extremum behavior. The theoretical assay of surface tension isotherms for
c
> CMC was first performed for solutions of single nonionic or ionic surfactants [95]. Subsequently, Rusanov generalized the theory to surfactant mixtures [96].

For the solution of a single ionic surfactant, the Gibbs adsorption equation in the postcritical concentration region (c
> CMC) reads

where the subscript 1 refers to the surfactant monomers in the solution.
Equation (92)
as well can exist represented in the class

(93)




d
γ


d
c


=

Γ


d

μ
i



d

ln
c


=

R
T
Γ

(

1
+


d

ln

f
1



d

ln

c
1




)



d

ln

c
1



d

ln
c



where
c
is the full concentration of surfactant and
f
is the action coefficient. The derivative
d
ln
c
1
/dln
c
can exist calculated from the equation that describes the surfactant balance in the solution based on the mass activeness law. It was shown in [95] that

(94)




d

ln

c
1



d

ln
c


=

c


c
ane






(



d
c


d

c
ane




)




1


=

one

1

α
+
n
α



where
a
= (c – c
1)/c
is the degree of micellar aggregation of the surfactant and due north is the assemblage number. Bold that the approximation
f
1
= const is valid, Eqs.
(93)
and
(94)
yield

For surfactant concentrations beneath the CMC and
α
≅ 0,
Eq. (95)
transforms into the usual Gibbs equation for solutions of a single surfactant,
dγ/d
In
c

–RTΓ, whereas for the limiting case of large micellar concentrations (a
= ane),
Eq. (95)
yields that
dγ/d
ln
c

–RTΓ/n. The adsorption close to the CMC is about equal to that at high micellar concentrations (the adsorption layer is saturated by the surfactant). The last 2 expressions allow us to compare the slopes of the surface tension isotherms immediately below and to a higher place the CMC:

(96)


north



(

d
γ
/
d

ln
c

)


α
=
0


/



(

d
γ
/
d

ln
c

)



α
=
i



Whereas
n
is usually in the range betwixt l and 100,
Eq. (96)
indicates that at
c
> CMC, the surface tension isotherm is nearly parallel to the abscissa axis.

For some systems, a discontinuous shape of the surface pressure level isotherm (a decrease of the slope) is observed in the surfactant concentration range far below CMC. This behavior was ascribed in [97] to the formation of dimers in the solution bulk. This explanation is consistent with Eqs.
(95)
and
(96). On the other hand, assemblage in the surface layer is accompanied by a similar behavior of the surface tension isotherm [encounter, e.1000.,
Eq. (64)
and
Figs. five
and
6]. Therefore, it seems well-nigh impossible by an analysis of the surface tension isotherm only to discriminate between the premicellar aggregation of a surfactant in the majority and the formation of two-dimensional aggregates in the surface layer. In this regard, other experimental bear witness would be instructive, for case, studies of the electric electrical conductivity (for ionic surfactants) or the dynamic surface tensions. Whereas the aggregation in the bulk takes place simultaneously with preparation of the solution, the beingness of characteristic kinks in the dynamic surface tension curves tin unambiguously indicate that the aggregation in the adsorption layer takes identify [98,
99].

For micellar solutions of one:1-charged ionic surfactants, assuming the electrical neutrality of the surface layer and
neglecting the concentration dependencies of the activity coefficients for ions, we tin transform the Gibbs adsorption
equation (20)
into the class

(97)




d
Γ


d

ln
c


=

R
T

Γ
1


(



d

ln

c
1



d

ln
c


+


d

ln

c
2



d

ln
c



)


where the subscripts 1 and two refer to the surface-agile ion and the counterion in the monomeric form, respectively. The derivatives on the right hand side of
Eq. (97)
can be calculated from the ion remainder and the mass activity law [95]:

(98)




d

ln

c
one



d

ln
c


=


i


n
1

α

β

(

1

β

)

/

(

1

α
β

)



ane

α
+

northward
1

α

[

1
+

(

one

α

)


β
2

/

(

one

α
β

)


]




(99)




d

ln

c
two



d

ln
c


=

1

ane

α
β



[

1

β
+
β

(

1

α

)



d

ln

c
i



d

ln
c



]


a =
(c – c
1)/c
is the degree of micellar aggregation of a surface-agile ion, and
β
=
n
2/north
1
is the degree of counterion binding by micelles;
n
one
and
northward
two
are the micellar aggregation numbers for surface-active ions and counterions, respectively. Therefore,
Eq. (97)
transforms into

(100)




d
γ


d

ln
c


=

R
T

Γ
1


[



i

β


i

α
β


+

(

ane
+
β


1

α


1

α
β



)



d

ln

c
1



d

ln
c



]


For
α
= 0, the derivative
d
In
c
1
/d
Inc
= 1 and
Eq. (100)
transforms into the ordinary Gibbs equation for ionic surfactants in the absence of inorganic electrolyte,

(101)





(

d
Γ
/
d

ln
c

)



α
=
0


=

2
R
T

Γ
one


whereas in the limiting case of loftier concentrations of micelles (α
= 1),
Eq. (100)
yields

(102)





(

d
γ
/
d

ln
c

)



α
=
one


=

2
R
T

Γ
1


(

1

β

)


Using Eqs.
(101)
and
(102), nosotros can compare the slopes of surface tension isotherms immediately below and higher up CMC:

(103)





(

d
γ
/
d

ln
c

)



α
=
ane


/



(

d
γ
/
d

ln
c

)



α
=
0


=
1

β

Thus, in the postcritical region, the slope of the surface tension isotherm becomes significantly lower (commonly
β
is in the range between 0.8 and 0.nine). Still, in dissimilarity to nonionic surfactants [cf.
Eq. (96)], this slope is pregnant; therefore,
Eq. (103)
can exist used to estimate the degree of counterions binding by micelles [95]. The comparison shows that the values of
β
calculated from
Eq. (103)
concord well with information obtained using other independent methods.

Much more than complicated expressions for
dγ/d
ln
c
were derived in [96] for mixtures of nonionic surfactants and for ionics in the presence of nonionic surface-active admixtures. For this case, an additional organization parameter was introduced, the micellization caste of the second surfactant (admixture). From assay of the respective equations, it was shown that if the admixture is able to penetrate into the micelles, then, with increasing micellar concentration, the concentration of monomers of the admixture (denoted past the subscript 3) attains some maximum value. Similar variations in the concentration of the monomers of surface-agile ions and counterions besides take place when a single ionic surfactant is dissolved: with increasing micellar concentration, the concentration of monomeric surface-active ions attains its maximum value, whereas the monomeric concentration of counterions exhibits a monotonous increment [100]. As the derivative
d
In
c
3/d
ln
c
changes sign, the sign of the derivative
dΓ/d
ln
c
changes too; that is, the surface tension tin can achieve a minimum value for sure relative values of Γ1
and Γthree. It was estimated in [96] that the minimum is attained if Γiii
≫ Γ1.

Some other (and, mayhap, more than authentic) prediction of an extremum behavior of the surface tension isotherm for a mixture of a chief surfactant and any admixed surfactant (subscript 3 for its monomers) tin can be made if the constant
k, which describes the distribution of the admixture between micelles and solution, is considered. The derivatives
d
ln
c
three
/d
ln
c
and
dγ/d
ln
c
are different from those obtained in [96], and enable united states to perform a detailed assay of the dependence of the surface tension isotherm on the solubilization ability and surface activity of the admixture. In the limit at
α
= i, the derivative
dγ/d
ln
c
tin be approximated by

(104)





(

d
γ
/
d

ln
c

)



α
=
1


=

ii
R
T

Γ
1


(

1

β

)

+
R
T

Γ
3

k
/

(

1
+
thou

)


For ionic surfactant solutions with a nonionic admixture at
c> CMC, the minimum in
y
can appear if the adsorption activity of the admixture is high, and at the same fourth dimension, the admixture is strongly solubilized in the micelles (k
> one):

For
k≫ 1,
Eq. (105)
becomes simpler and does not involve the admixture distribution constant

indicating that a minimum appears if the adsorption of the strongly solubilized admixture is several times lower than the adsorption of the main surfactant. Nosotros believe that expression (105) is in better correspondence with experimental results than the condition Γ3
≫ Γ1. For example, solutions of sodium dodecyl sulfate (SDS) oft comprise a contamination (dodecanol), the surface activity of which is much higher. The fact that a surface tension bend does not showroom any minimum, that is, the status (105) is satisfied, unambiguously indicates the purity of the main surfactant. Whereas the ratio of adsorption activities for dodecanol and SDS is virtually one thousand, the absenteeism of a minimum in the surface tension isotherm of SDS solutions indicates, according to condition (106), that the concentration of dodecanol in SDS does not exceed 0.04%. However, this concentration is sufficient to ensure the influence of the dodecanol nowadays in the solution on the dynamical and equilibrium behavior of SDS.

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Colloid and Surface Chemistry

Eugene D.
Shchukin
, …
Andrei S.
Zelenev
, in


Studies in Interface Scientific discipline, 2001

II.2.2

Langmuir and Szyszkowski Equations. Accounting for the Adsorbed Molecules Own Size (Mutual Repulsion)


The effect of the size of
surfactant molecules
can in the starting time approximation be accounted for, if 1 assumes the existence of some limiting value of the adsorption, Γ

max, such that the adsorption no longer changes once it has been reached. Such an supposition allows 1 to integrate the Gibbs equation in the concentration range where adsorption does not alter, i.due east:

R
T

Γ

max


=



d
σ


d

ln
c


=
const
.

The integration of this expression yields

(Two.17)

π
=

Δ
σ
=
R
T

Γ

max


ln
c
+
B

where
B
is the integration abiding. An equation like to the one above, describing the concentration dependence of the surface tension in the region of relatively loftier surfactant concentrations
three

was offered by Milner (1907). This equation suggests that the surface tension is a linear role of the logarithm of the solution concentration.

Szyszkowski (1908-1909) carried out precise measurements of the surface tension of solutions containing various carboxylic acids ranging from butyric to caproic, as well as their isomers. He managed to find an empirical relationship that described with high precision all of his results:

(II.18)

π
=

σ
0


σ
=
b
ln

(

A
c
+
1

)

,

where the constant
b
is the aforementioned for the entire homologous serial, and constant
A
increases 3 – 3.5
 
times with increasing the hydrocarbon chain by one CH2
segment, which agrees with the Ducleaux-Traube dominion (Fig. II-12).


Fig. II-12.
The validity of the Ducleaux- Traube rule for the iii surfactants, the neighboring members of the same homologous series



The Szyszkowski
equation (II.18)
satisfies both limiting weather: it is consistent with the linear dependence of the surface tension on concentration within the Henry region, and agrees with
eq. (II.17)
at sufficiently high concentrations. At the same time, the criteria which define “low” and “sufficiently high” concentrations are set. Indeed, at low (as compared to α
 
=
 
1/A) concentrations the logarithm can be expanded in series, yielding

π
=

σ
0


σ

A
b
c
.

Within this range the derivative -dσ/dc
is constant and equals

(II.19)








d
c


=
G
=
A
b
=
δR
T

exp

(



μ


μ
0


(
s
)





R
T



)

.

Inside the Henry region the dependence of the adsorption on concentration is given by

Γ
=


A
b


R
T



c
.

If
c
» α,
eq. (II.18)
readily yields
eq. (II.17), since nether these atmospheric condition In (Ac 
+1) ≈ ln (Ac). The integration constant
B
equals RT
Γmax
ln
A, and the empirical constant
b
in the Szyszkowski equation is interpreted as

(2.20)

b
=
R
T

Γ

max


.

Therefore, we take established once again that the linear dependence of the adsorption on concentration corresponds to the initial linear region in the surface tension – concentration dependence (see
Fig. (Two-7)). Since
b
is constant within the homologous serial, it is the value of abiding
A
that determines the steepness of the adsorption increment with increasing concentration. For this reason constant
A
is referred to as the
adsorption activity. By comparing
eqs. (Ii. 19)
and
(Ii.20)
i establishes that
A
is related to the work of adsorption,


μ
0



μ
0


(
south
)



, as

(Two.21)

A
=

G
b

=

G

R
T

Γ

max




=

δ


Γ

max




exp

(




μ
0



μ
0


(
s
)





R
T



)

.

The highest limiting value of the adsorption corresponds to the logarithmic region in the surface tension – concentration dependence. This
ascertainment can be explained past the germination of a dense monomolecular layer. At high concentrations the surface tension isotherms plotted in σ – ln
c
coordinates are parallel to each other with slopes of -RT
Γmax
(Fig. II-13)


Fig. Ii-13.
The surface tension isotherms plotted in σ – ln (c) for the three surfactants, the neighboring members of a homologous serial



The decrease in the surface tension at constant adsorption, occurring in agreement with the Gibbs equation, is solely due to the increase in chemical potential of the adsorbed substance acquired past the increased concentration of the latter in solution. As is ordinarily known, the increase in the chemical potential in a stable two-component organization always corresponds to the concentration increase. For the present example it translates into the increase of surface concentration, and consequently, of the adsorption. Therefore, in the concentration region where the surface tension linearly depends on the log of concentration, a slow but finite, increase in adsorption not detected experimentally should occur. At the same fourth dimension a sharp increase in the chemical potential of the surfactant molecules in the adsorption layer
corresponds to a small increment in adsorption. This allows one to draw an analogy between the properties of adsorption layers at maximum adsorption and those of condensed phases at elevated pressure. In the case of condensed phases a negligibly minor increment in density corresponds to a rise in chemical potential. Information technology will be shown further that this analogy has an important physical pregnant for the description of properties of adsorption layers formed by insoluble surfactants.

The independence of the maximum adsorption (or the lowest possible expanse per molecule in the dense adsorption layer
s
min 
=
south
ane) of the surfactant chain length tin can only be explained if we assume that as the adsorption values reach Γmax, the surfactant molecules are closely packed and oriented normal to the surface. Estimates of the limiting values of adsorption, Γmax 
=
b
/ RT, from the experimental σ(c) dependencies, with the successive evaluation of minimum area per molecule,
s
1 
=
 
i/NA
Γmax, for carboxylic acids, are ≈0.21
 
nm2, which agrees with the values established by other methods, e.g. by X-ray diffraction on surfactant crystals.

Allow us now clarify the general relationship between Γ and
c
values over the entire range of concentrations. The derivative of the Szyszkowski
equation (2. 18)
with respect to concentration reads:






d
c


=



A
b


A
c
+
ane


=

R
T

Γ

max



A

A
c
+
i


Comparison of the to a higher place expression with the Gibbs
equation (II. 5)
yields the relationship between the adsorption and the concentration:

(II.22)

Γ
=

Γ

max




A
c


A
c
+
1


=

Γ

max



c

α
+
c


.

The higher up adsorption isotherm equation is known every bit the Langmuir equation. Originally it was derived by other means and for some other system, namely for the adsorption from the gas phase onto a solid adsorbent. The surface of the latter independent fixed sites onto which the attachment of molecules of adsorbing substance occurred (i.east., the localized adsorption took place).

In the theoretical derivation of the Langmuir
equation (II.22)
which is usually presented in some item in physical chemistry textbooks, the solid surface is modeled equally a chessboard (Fig. Two-14), each site of which is able with equal probability to host the adsorbed molecules (no more than 1 molecule per site is allowed). The treatment is restricted to the case of localized adsorption, i.e. when the exchange between molecules of the gas stage and those adsorbed on the surface is considered, while the possibility of migration of molecules from i site to some other is non taken into account. The rates of adsorption and desorption are functions of the fraction of sites occupied, θa 
=
 
Γ / Γmax. If the molecules in the adsorption layer are not interacting with each other, the rate of adsorption,
υ
a, is proportional to the fraction of unoccupied sites, (one – θa), and the vapor pressure level
p:


Fig. Two-xiv.
A schematic diagram of localized adsorption according to Langmuir




υ
a

=

k
a


(

i


θ
a


)

p
;

the rate of desorption,
υ
d, depends only on a fraction of occupied sites, i.e:


υ
d

=

k
d



θ
a

,

where
k
a
and
chiliad
d
are the adsorption and desorption charge per unit constants, respectively.

At the initial moment of contact between the adsorbing gas molecules and the bare
solid surface, the adsorption charge per unit is the highest, while the desorption charge per unit is equal to zero (Fig. Two-fifteen). As the surface is covered with the adsorbed molecules, the rates of adsorption and desorption go equal to each other, and dynamic equilibrium,
υ
a 
=
υ
d, is established, i.e.


Fig. II-15.
Alter in the rates of adsorption,
υ
a, and desorption,
υ
d, as the dynamic equilibrium is established



(2.23)


θ
a

=

Γ


Γ

max




=



(


k
a

/

k
d


)


p


1
+

(


k
a

/

k
d


)


p


=



A


p



A


p
+
1


.

The adsorption action,
A′, thus has the pregnant of the ratio betwixt adsorption and desorption rate constants.

The experimental data for the adsorption on solid adsorbents from the gaseous stage in the range of moderate vapor pressure values of the adsorbing component often correlate well with the empirical Freundlich isotherm:

Γ
=
β

p

1
/
northward


,

where β and
n
are constants;
northward
is usually of the order of several units. Information technology is, nevertheless, necessary to emphasize that Freundlich isotherm neither has a elementary theoretical meaning, nor does it yield the initial linear dependence of the adsorption on concentration, or any finite constant value of limiting adsorption.

The Langmuir equation constituted an era in the theory of adsorption
and chemisorption and in the theory of heterogeneous catalysis based on it. The Langmuir equation can simply exist used to describe reversible processes and is non applicable to the description of chemisorption involving chemical bond formation. The transition from the example of a gas with pressure
p
to that of a solution of concentration
c
in contact with the solid stage (the adsorbent) does non significantly influence the logic of the described derivation. Therefore, the Langmuir equation can also be used to describe the localized adsorption from solution taking place at the solid interface.

The comparison of the empirical Szyszkowski
equation (II. 18)
with the Gibbs
equation (2.five)
indicates that Langmuir adsorption isotherm
(II.22)
is well suited also for the description of adsorption at the air – surfactant solution interface. It is interesting to point out that at the gas – solid interface, for which
eq. (2.22)
was originally derived diverse deviations from Langmuirian behavior are often observed.

The applicability of
eq. (Ii.22)
to a successful description of adsorption from a solution was established past Langmuir himself, when he compared his adsorption isotherm to the Gibbs equation and ended up with the Szyszkowski equation as a outcome. The transition from localized to non-localized adsorption (which tin can exist viewed as the transition from fixed adsorption sites to moving ones) does not, therefore, change full general trends in the adsorption in the cases described. Ane should also keep in mind that the liquid interface is more uniform in terms of energy than the solid interface, which contains active sites with different interaction potentials.
iv

The latter is probably the reason why
the Langmuir equation is well suited for the liquid surface.

The Langmuir adsorption isotherm (eq. (2.22)) satisfies the limiting atmospheric condition described earlier. At low concentrations
c
« α
 
=
 
1/A
it yields the asymptote

Γ
=

Γ

max



A
c
,

which corresponds to the linear dependence of adsorption on concentration. The slope of the Γ(c) line is defined by the value of
A. Comparison with the Ducleaux-Traube rule indicates that this slope increases by a factor of three
 
to 3.5 with the transition to each subsequent member in the homologous series. When
c 
=
 
α, the adsorption equals half the maximum value, i.eastward. Γ
 
=
 
Γmax
/ 2. In the case when
c
» α,
Ac 
+
 
1 ≈
Ac, which yields the second asymptote Γ
 
=
 
Γmax
(come across
eq. Ii.22). The value of α can besides exist determined from the intersection point of these two asymptotes (Fig. II-16). The adsorption isotherms plotted in



Γ
/

Γ

max




1


(

Γ
/

Γ

max



)




A
c


coordinates are identical for all substances that obey the Langmuir equation, and yield a single straight line with a unit of measurement slope. The surface tension isotherms can exist combined into i line
in a like way past using σ –
Ac
coordinates. For higher members of the homologous series that accept express solubility such combined isotherms tin be obtained up to the concentrations respective to saturated solutions.


Fig. II-16.
The conclusion of the adsorption activeness,
A



In the case of complete mutual solubility of components, the value of adsorption included in the Gibbs equation, defined by
eq. (Ii.2)
as the backlog of a component in the surface layer over the bulk volume, should laissez passer through a maximum and then reach cipher, corresponding to a pure surface active component. It is important to remember that in the range of high surfactant concentrations, the replacement of the adsorption as the excess quantity with the total amount of surfactant in the adsorption layer is not acceptable. Moreover, it is necessary to account for the bulk action coefficients of dissolved substances in the solution majority.

In gild to decide the values of Γmax
and
A 
=
 
1/α from experimental Γ(c) dependence, 1 may write
eq. (II.22), allows ane to write as


c
Γ

=

α


Γ

max




+

c


Γ

max




.

The experimental data plotted in
c/Γ –
c
coordinates should then yield a directly line, the changed gradient and the intercept of which correspond to the values of Γmax
and α/Γmax, respectively.

Expressing the value of
A
in
eq. (II.18)
via the work of adsorption using eq (II.22), allows one to write:

(Two.24)

Γ
=

Γ

max




(

1
+
1
/
A
c

)



1


=

Γ

max





(

1
+



Γ

max




δ
c


exp


[





(


μ
0



μ
0


(
due south
)




)



R
T



]



)



1


.

Replacing in
eq. (II.18)
concentrations with adsorption using the
eq. (II.22), one may obtain the relationship between the two-dimensional pressure and the adsorption, namely

(II.25)

π
=

σ
0


σ
=
R
T

Γ

max



ln



Γ

max





Γ

max



Γ


.

In agreement with the in a higher place expression, the two-dimensional force per unit area should increment infinitely, as the adsorption tends to reach its limiting value Γmax. The measurements carried out with insoluble surfactants using Langmuir’s residuum showed that the abrupt increase in 2-dimensional pressure may indeed take place when the area per molecule
s
Yard
decreases to its minimum value
south
1, (Fig. 2-17).


Fig. Two-17.
The isotherms of two-dimensional pressure
π(south
Chiliad) in the region of high compression of adsorption layer



Such an increment in two-dimensional pressure is, nevertheless, non limitless. It is limited by some value
π
max, at which the adsorption layers lose their stability, folds like to hummocks on ice fields appear (Fig. Two-18), and polymolecular adsorption layers grade.


Fig. II-18.
Schematic representation of the loss of stability of the adsorption layers at
π 
=
π
max



The limiting value of the area per molecule,
s
ane, tin be viewed as the molecule’s own cantankerous-sectional area; for certain types of surfactants this value is approximately the same and is independent of the hydrocarbon concatenation length, which confirms our previous statement regarding the alignment of molecules normal to the surface in the compact adsorption layer. The independence of the limiting area per molecule from the surfactant hydrocarbon concatenation length in fact indicates that the former is determined by the cross-sectional area of the hydrocarbon chain.

Let us at present render to the surfactant concentration range where the adsorption has not yet reached its limiting value, simply the area per molecule,
south
1000, is no longer large plenty for the similarity betwixt the adsorption layer and the ideal two-dimensional gas to be valid. Nosotros can presume that in such a situation the arrangement of hydrocarbon chain segments at the surface takes (on boilerplate) the intermediate position between being vertically aligned and horizontally spread. In this case the size of private molecules, i.e. the intermolecular repulsion and (equally will be shown afterward) the attraction, will take an issue on adsorption.

If the attraction between molecules is weak, the dependence of the ii-dimensional force per unit area on the area per molecule (encounter
Fig. 2-17) can exist
described by the expression proposed past Volmer
5

(2.26)

π

(


s
G



due south
one


)

=
k
T

which is analogous to the platonic gas police corrected for the volume of private molecules.

In club to obtain the value of
s
1
from the experimentally adamant two-dimensional pressure – area per molecule dependence, it is convenient to plot data in the
πs
M

π
coordinates. In the absence of whatever noticeable attraction between molecules, the experimental information plotted in these coordinates fall onto a straight line (Fig II-19), the slope of which yields the surface area per molecule in the dense adsorption layer, while the intercept corresponds to kT=
 
four
 
mN m-ane
nmii.


Fig. II-19.
The
πs
M(π) isotherm with intermolecular repulsion taken into consideration



If the molecular weight,
G, of the studied substance is unknown, it is not possible to estimate adsorption in moles/mtwo, nor tin therefore, the area per molecule,
south
M, exist established from a known sample weight
chiliad. In this case, instead of
πs
G, the product of the two-dimensional pressure level and the macroscopic surface area
S
betwixt the barriers in the Langmuir balance (meet
Fig Two-ten) is plotted against
π, and
eq. (II.23)
tin can be rewritten as

π
Southward
=

s
1


yard
M


N
A

π
+

thousand
M

R
T
,

i.east. the experimental data fall onto a straight line in
πS

π
coordinates (see
Fig. II-20).
The extrapolation of this line to
π 
=
 
0 yields the molecular weight,
K; the expanse per molecule in the dense adsorption layer,
s
1, tin and so exist evaluated from the slope.


Fig. 2-20.
The conclusion of the molecular weight
Gi

and expanse per molecule
southward
1
from the
πS(π) isotherm



The described method was used to decide molecular weights of proteins and nucleic acids and to written report their structure in the adsorption layers. The method allows 1 to obtain valuable information regarding the conformation of molecules within the surface layer. The latter determines the expanse these molecules occupy in a two-dimensional picture show. During the measurements the pH of the medium was adjusted to values at which molecules are charged due to ionization, so that one did not take to introduce a correction for intermolecular attraction. The poly peptide conformation depends on the pH of the medium, which is crucial for the ionization and hydration of ionogenic groups
[10]. With changes in the pH, the slopes of the
πS
M(π) lines, i.e. the values of
due south
1, also change (Fig. Ii-20).

Upon the compression of films formed past globular proteins (such as albumine, globuline, hemoglobin, trypsine, and others) up to a force per unit area of ~20
 
mN m-1
the two-dimensional pressure isotherms are quite reversible. At somewhat higher compression, such that the area per amino-group reaches
~0.17
 
nm
2, the two-dimensional pressure increases abruptly, causing irreversible changes in the film construction. The films may learn some specific insolubility, as well as some peculiar structural and mechanical (rheological) properties, which are, to a great extent, related to changes in the conformation and structure of the protein molecules
[five]. A stronger compression of films to virtually 0.05 – 0.1
 
nmtwo
per group causes their collapse, resulting in the germination of folds (and, perhaps, fifty-fifty polymolecular layers) and final disengagement from the surface.

It is noteworthy that many proteins in the monolayer state retain their enzymatic activity and are capable of taking part in specific chemical reactions. For this reason the colloid-chemic methods used to investigate the backdrop of poly peptide films, combined with other techniques, represent valuable tools for the study of the backdrop of proteins. These methods allow one to examine more closely mechanisms of transport phenomena that take place at cellar interfaces in biological systems. The latter are the interfaces at which the aggregating of surface agile substances with biological and physiological activity occur. These substances, when nowadays at such interfaces, reveal their of import unique backdrop (e.q. enzymatic activity).

The low rate at which equilibrium between the adsorption layer and the bulk is established is typical for high molecular weight surface active substances for which the surface tension gradually decreases with time. The measurement of the surface tension by static and semi-static methods (see
Chapter I, four) as a function of time during the germination of adsorption layers allows one to think information on the kinetics of adsorption phenomena
[11,12].

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Mesoporous Molecular Sieves 1998

A.
Galameau
, …
F.
Fajuia
, in


Studies in Surface Science and Catalysis, 1998

2

EXPERIMENTAL Section

The probes selected for the EPR study are
surfactant molecules, in which the paramagnetic eye is a nitroxide group. These radical-surfactants were dissolved in the cetyltrimethylammonium bromide (CTAB) micelles solution used for MTS synthesis. In order to monitor the behavior of dissimilar regions of the CTAB micelles, the probes had a nitroxide group positioned at two different sites within the surfactant molecule. The nitroxide group was in the cationic caput of the surfactant in iv-cetyldimethylammonium-ii,ii,6,6- tetramethyl-piperidine-fifty-oxyl (CAT 16), and near the cease of the hydrophobic alkyl concatenation in 12-doxylstearic acid (12DXSA). The fluorescent probe was pyrene. CAT16 was dissolved in water at 313
 
Chiliad, whereas 12DXSA and pyrene were dissolved in chloroform. CTAB solution in water was prepared at the initial concentration of 0.eleven
 
M and mixed with the proper amount of CAT16 solution to go a molar ratio CTAB/CAT16=200. The same CTAB/12DXSA ratio was obtained by evaporating chloroform from the proper portion of 12DXSA solution and so by adding the proper amount of CTAB solution. Similarly, CTAB/pyrene=2200 (monomer probe) and CTAB/pyrene=40 (excimer probe) were prepared.

A sodium silicate solution was prepared by mixing 1.32
 
1000 SiOii
Aerosil 200
 
5 in 20
 
ml NaOH 0.28
 
M. The solution was stirred overnight at 298
 
G. A portion of this solution was mixed with an equal volume of 0.xi
 
M CTAB/probe solution. The add-on time was taken as
fourth dimension zero. Samples prepared at time zero were inserted in the EPR crenel or in the fluorescence spectrometer, at the chosen temperature, and signal modifications were followed for at least 24
 
h. The synthesis process was repeated at different temperatures: 298, 323 and 333
 
K. For XRD analysis, the synthesis at each temperature was stopped at different times after CTAB-silica mixing. The resulting solid products were recovered past filtration, washed with water, dried at 353
 
K and analyzed by XRD.

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SURFACE AND INTERFACE PHENOMENA

Vincenzo
Vitagliano
, …
Luigi
Paduano
, in


Handbook of Surfaces and Interfaces of Materials, 2001

3.6.3.three

Micellar Composition Range: Surfactant Intradiffusion Coefficient

At surfactant compositions above the cmc a fraction of
surfactant molecules
aggregates, thereby causing a subtract of

D

s
. The measured surfactant intradiffusion coefficient is a mean value betwixt the intradiffusion coefficient of monomeric and micellized surfactant molecules

(3.53)


D
s

=

p
1
due south


D
i
south

+

p
G
due south


D
Grand
s

Ambrosone et al. [119], used the stage-transition model to calculate


p
one
s


=
X
cmc/Ten
from the cmc values. These authors considered only dilute micellar solution, bold


D
M
s


to be constant and


D
one
due south


to coincide with the surfactant intradiffusion coefficient measured at the cmc,


D
1

s
,
cmc


. With these assumptions
Eq. (3.53)
can be rewritten every bit:

(3.73)



D
s

X
=

10

c
k
c



D
1

due south
.
cmc


+

(

X


X

cmc



)


D
Thou
s


and then that the slope of the
D

s

X
trend plotted equally a function of (X – X
cmc) provides the


D
M
south


value. It is possible to chronicle


D
M
s


to the micelle hydrodynamic size past calculating the micelle apparent radius with the Stokes-Einstein equation [24]:

(three.74)



R

hy


=



k
B

T


6
π

η

cmc



D
Yard
s




where ηcmc
is the viscosity of the medium taken to be that of the solution at the cmc. The calculated
R
hy
values can be used to compute the aggregation number of the micelles
due north

(iii.75)


n
=


4
/
3
π

R

hy

3






Five
¯


G
southward

+
m



(


h
E


)


M


5

*
w





where (hEastward
)Yard
is the number of solvent molecules in the hydration shell of each ethoxylic unit of measurement of a micellized surfactant molecule and




Five
¯


One thousand
s


is the volume of each micellized surfactant molecule.

The


D
1000
s


also tin can exist adamant by solubilizing an apolar substance, such as tetramethylsilane or hexamethylsiloxane, into the micelles. Its intradiffusion coefficient is the same every bit that of the aggregates. Faucompré and Lindman [120] used this technique to measure the CeightE4
micellar intradiffusion coefficient. The direct knowledge of


D
M
s


joined with the estimation of


D
1
s


from premicellar data immune the ciphering of


p
ane
due south

, from which the free monomer concentration
c
1
could be derived. It was institute that
c
1
increases in the micellar composition range from 0.007 mol kg−ane
at the cmc to 0.009 mol kg−1
at
C
= 10 × cmc.

However, at very high surfactant concentration (>fifty cmc) the solubilized molecules diffuse faster than the surfactant, probably because micelles are and so close and interacting that
solubilized molecules tin pass from one amass to another [120].

Stubenrauch et al. [121] extended the investigation on CeightEastwardiv
to more than full-bodied micellar solutions and found a
D

due south

decreasing tendency. They interpreted this evidence in terms of increasing intermicellar interactions.

For surfactants with a longer hydrophobic tail, intradiffusion measurement can exist done only at surfactant concentration much to a higher place the cmc, where the free monomer contribution in
Eq. (3.53)
can be neglected and the surfactant intradiffusion coefficient direct gives the micelles mobility. Nilsson et al. [122] and Brown et al. [82,
124], studied some C12Eastward
m

surfactants and found that
D

due south

shows an initial decreasing tendency with increasing surfactant concentration, which tin be imputed to either intermicellar interactions or micellar growth. The prevailing machinery was institute to vary with surfactant molecule structure. For C12Eastward5, proton relaxation measurements [122] showed that the
D

s

decrease was due mainly to the increasing aggregates size. Considering C12Efive, has a smaller hydrophilic head, it has no tendency to form picayune spherical micellar aggregates; in this instance the formation of extended continuous domains is favored. In the presence of these continuous domains the measured intradiffusion coefficient is dominated past the move of monomer units inside these domains. Such a process is usually indicated as
molecular diffusion.

Surfactants with more than bulky hydrophilic heads, such equally C12E7
and C12E8, form spherical aggregates. In these cases no experimental evidence of micellar size growth was found so information technology must be inferred that for these surfactants the decrease of
D

southward

with concentration is due to intermicellar interactions.

At college surfactant concentration
D

south

increases, approaching the self-diffusion value of pure liquid surfactant. Under these conditions micellar aggregates are so shut that substitution of monomers between unlike aggregates occurs.

In their works, Nilsson et al. [122], Chocolate-brown et al. [82,
124], Lindman and Wennerström [128], and Kato and Seimiya [88] besides studied the effect of temperature on
D
s. In order to normalize the intra-improvidence coefficient so as to account for the upshot of temperature on molecular movement, the authors used the ratio
D
due southη/T. They found that at constant surfactant concentration, this ratio goes through a maximum as a function of temperature. The temperature at which this maximum is reached diminishes by decreasing the length of the oxyethylene chain (encounter
Fig. 26). The initial increase may betoken desolvation and/or progressive wrinkle of the oxyethylene chains. The subsequent decrease can exist due to micellar size growth and/or increasing intermicellar interactions.


Fig. 26.
Reduced intradiffusion coefficients,
Ddue southη/T, of
C
12
Eastwardchiliad

at surfactant concentration of 2%, equally a office of temperature;
Tc

is the critical temperature.


Reprinted with permission from W. Brown, Z. Pu, and R. Rymdén,
J. Phys. Chem. 92, 6086 (1988). Copyright 1988, American Chemic Order.

Copyright ©
1988


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Surfactants, Industrial Applications

Tharwat F.
Tadros
, in


Encyclopedia of Physical Scientific discipline and Engineering science (Third Edition), 2003

Iii.A

Thermodynamics of Micellization

Micellization is a dynamic phenomenon in which
n

monomeric
surfactant molecules
Southward associate to course a micelle S


n
,

(3)




northward
Due south



South
n


.

Hartley envisaged a dynamic equilibrium whereby surface-active agent molecules are constantly leaving the micelles while other molecules enter the micelle. Experimental techniques using fast kinetic methods such as terminate flow, temperature and pressure jumps, and ultrasonic relaxation have shown that in that location are ii relaxation processes for micellar equilibrium. The first relaxation time τone
is of the order of x−vii
sec (ten−8–10−3
sec) and represents the lifetime of a surface agile molecule in the micelle, i.due east., it represents the clan and dissociation rate for a single molecule inbound and leaving the micelle. The 2d relaxation time τ2
corresponds to a relatively tiresome process, namely, the micellization–dissolution process represented past
Eq. (3). The value of τ2
is of the order of milliseconds (10−3–1
 
sec).

The equilibrium aspect of micelle formation can exist considered past application of the 2nd law of thermodynamics. The equilibrium constant for the procedure represented by
Eq. (iii)
is given by

(4)


K
=


[

South
n

]



S
north



=



C
m




C
due south
northward



,

where
C
s
and
C
chiliad
represent the concentration of monomer and micelle respectively.

The standard free energy of micellization, Δ
G
0, is and then given by

(5)



Δ

Thou
chiliad
0

=
R
T

In

Grand
=
R
T

In


C
thou


n
R
T

In


C
southward

,

and the gratuitous energy per monomer, Δ
1000
0
(=Δ
G
m
0/n), is given by

(half-dozen)



Δ

K
0

=

(



R
T

n


)


In


C
m


R
T

In


C
s

.

For many micellar systems,
n
is a large number (>fifty), and therefore, the commencement term on the right-hand side of
Eq. (six)
may be neglected:

(7)




Δ

G
0


=

R
T

ln


C
s


=

R
T

ln


cmc



.

Δ
Grand
0
is always negative and this shows that micelle germination is a spontaneous procedure. For case, for C12Esix, the cmc is eight.70
 
×
 
ten−5
mol dm−3
and Δ
M
0 
=
 
−33.1
 
KJ mol−1
(expressing the cmc as the mole fraction).

The enthalpy of micellization Δ
H
0
tin can be measured either from the variation of cmc with temperature or directly by microcalorimetry. From Δ
Thousand
0
and Δ
H
0, ane tin can obtain the entropy of micellization Δ
Due south
0,

(8)




Δ

1000
0


=


Δ

H
0




T
Δ

Southward
0




.

Measurement of Δ
H
0
and Δ
South
0
showed that the former is small and positive and the second is large and positive. This implies that micelle germination is entropy driven and is described in terms of the hydrophobic issue (fourteen). So hydrophobic chains of the surfactant monomers tend to reduce their contact with h2o, whereby the latter form “icebergs” by hydrogen bonding. This results in reduction of the entropy of the whole system. Withal, when the monomers associate to from micelles, these “icebergs” tend to cook (hydrogen bonds are broken), and this results in an increase in the entropy of the whole system.

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