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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5907_Библиотеки_им_академика_М_И_Перельмана.pdf
54
Nano Physical Pharmaceutics of Micelle-Based Systems
polymerization of PEG is high at room temperature, because
water only exists in the thin layer among micelles, while the
high-concentration aqueous solution is extremely viscous. As the
temperature increases, the hydrogen bond between PEG and water
molecules is destroyed, causing water loss and spherical micelle
formation. Becher et al. studied the shape of micelles by measuring
the light scattering data and viscosity of polyethylene glycol
lauryl ether aqueous solution and found that when the number of
the surfactant molecules are longitudinally arranged into round
rod-shaped micelles.
2.1.3 Mixed Micelle
Mixed micelles are mixtures of amphiphile systems (including
surfactants, polymers, and copolymers) that aggregate into the
the individual amphiphile. Alcohol with six or more carbon atoms
can be added to the micelle solution, and embedded between
the surfactant molecules to form a mixed micelle. Since the total
surface charge of the micelle remains unchanged, while the surface
area expands due to the embedding of alcohol molecules, the
surface charge density of the micelle decreases, and hence the
decrease of ionic repulsion and CMC value. The mixed micelle
mentioned above.
2.2 Preparation of Micelles
Polymeric micelles (PMs) are formed from amphiphilic block
copolymers, which have hydrophobic polymer chains linked
to hydrophilic polymeric chains. Their good biocompatibility,
stability and drug-loading capability have led to the development
of nanomedicines, and some are already industrialized or
currently being tested in clinical trials. The preparation of PMs,
which are the focus of this chapter, can be summarized into
two methods.
Effects on Micelle Assembly
55
the segments to dissolve the bulk sample. Notably, this method
only works under the premise that the total MW of the copolymer
is small enough with a short-length insoluble block. Other ways
including prolongated stirring, thermal, or ultrasound treatments
are used to “anneal” the solution for better solubility. However,
research shows that these techniques have the disadvantage that
they easily lead to non-equilibrium micelles, especially when
the core-forming chains are below phase transition temperature
(Tg). The annealing treatment can only lead to the dispersion of
samples into the selective solvent, rather than forming micelles
based on a unimer–aggregate equilibrium. In other words, the
morphology of the starting bulk sample [8].
a non-selective solvent to achieve complete dissolution at the
molecular level. Then, a selective solvent for one segment is added
in order to trigger aggregation of the dissolved chains and hence
micelle formation. To remove the initial non-selective solvent, the
method of evaporation or dialysis against selective solvent was
common way to prepare micelle solution [9]. Other ways, such as
changing pH value or temperature to reach the unimer–micelle
equilibrium, can be used to prepare stimulus-responsive micelles
that undergo morphology change with applied stimulus, as will be
discussed in Section 2.5.
2.3 Effects on Micelle Assembly
2.3.1 Critical Micelle Concentration
The minimum concentration of surfactant molecules that associate
to form micelles in the solvent is the CMC. When the concentration
of the surfactant is below CMC, it has a strong adsorption tendency
such that the hydrophilic group is dissolved in water and the
hydrophobic group is exposed to the air to reduce the surface
tension of the air/water interface. As the concentration increases,
56
Nano Physical Pharmaceutics of Micelle-Based Systems
the adsorbed molecules at the interface increase until saturation.
Then the surfactant enters the solution, and when reaching CMC,
micelles are formed through intermolecular association. If so,
the properties of the solution, such as osmotic pressure, density,
interfacial tension, and molar conductivity, all show sudden
changes.
Therefore, when the concentration of many aqueous solutions
of amphiphilic substances increases, the properties of the
is usually much larger than that caused by the increase of strong
electrolytes in the aqueous solution. For example, by plotting the
surface tension, conductivity or light scattering intensity against
concentration, it is easy to see the non-ideal deviation through
the change of the slope of the curve, and the root cause is the
formation of micelles. As the concentration of surfactant molecules
increases, their structures can change from single molecules to
spherical, rod-shaped and layered micelles. It is generally believed
that the concentration when spherical micelles are formed is the
transformed into rod-shaped micelles is the second CMC.
2.3.2 Mechanism of Micellization
The micellization of surfactants can reduce the total free energy
of the solution. The aggregation of the hydrophobic moiety makes
it lose a certain degree of freedom, which means that the entropy
will decrease [4]. Compared with single molecules, the translational
entropy and rotational entropy of micelles are both reduced. On
the other hand, the interaction between the hydrophilic group in
the surfactant molecule and water reduces the free energy of the
system, while the free energy of the system increases by reducing
the contact between the hydrophobic moiety and water molecules
through micellization. In addition, the hydrophilic groups may
be ionized and charged, and the resulting electrostatic repulsion
will not be conducive to the generation of micelles. It can be seen
micelle assembly from block copolymer.
Effects on Micelle Assembly
57
Micellization is mainly driven by the entropy change
between the hydrophobic moiety and water, water molecules
have a tendency to be driven from the hydrophobic region to the
bulk aqueous solution, for which the disorder increases, so the
entropy of the system increases. The micellization process can be
expressed by free energy and CMC through the following equation:
DG0 = RT ln(CMC) (2.1)
where DG0 is the standard free energy change of micellization, R
is the gas constant, T is the absolute temperature of the system,
and CMC can also be expressed by enthalpy:
ln(CMC) =
DH
0
+Constant
(2.2)
RT
It is assumed that the standard enthalpy change of micellization
is DH0, and is independent of the aggregation number and
temperature.
From the perspective of thermodynamics, there is a dynamic
equilibrium in the process of forming micelles with an aggregation
number of “m” from a single surfactant molecule (Z), where the
equilibrium constant K is:
mZ Zm (2.3)
Zm
[]
=
(2.4)
K
m
m
Z
[]
DGm0 refers to the free energy for transferring a single
surfactant molecule from water medium to a micelle.
mDGm0 = –RT ln K (2.5)
In the basic equation of micellization, RT lnK can be replaced
equivalently by mDGm0, where the concentration is expressed in
mole fraction.
58
Nano Physical Pharmaceutics of Micelle-Based Systems
0
mDGm
lnXm =− + mln X1 + lnm
(2.6)
RT
Xm refers to the number of moles of surfactant molecules in a
micelle with aggregation number of m, X1 is the mole fraction of
the monomer, and Xm is a function of m X1.
This equation can be regarded as a distribution function of
the micelle volume, and the collaboration of micelle formation is
X1 in the equation. Xm obtained by X1 in a narrow
range close to the CMC is more reasonable.
DGm0 = DUm0 + Wm
DUm0 represents the change of the free energy of hydrophobic
hydrocarbyl groups in the surfactant molecule in the transfer from
water to the micelle core. Wm represents the free energy resulting
from repulsion between polar head groups. For a given surfactant
system, the micellization and CMC depend on the relative balance
of forces that favor and delay molecular aggregation, and also
2.3.3 Influence of the Surfactant Structure on CMC
The micellization of surfactants in aqueous solution is controlled
by two opposite forces. The hydrophobic force, which drives
hydrophobic moiety out of the aqueous environment and
aggregate to form the nucleus, is the main driving force for
micellization. The polar head group extends into the water to form
a shell after being dissolved, and the electrostatic repulsion or
steric hindrance is not conducive to the formation of micelles.
There is a delicate balance between the driving force and the
counterforce. In addition, factors such as the volume of hydrophobic
groups, the structure of polar groups, co-solutes, pH and temperature
2.3.3.1 Volume of hydrophobic groups
The volume of the hydrophobic group in surfactant has the greatest
hydrophobic moiety, it is possible to enhance the hydrophobic
Effects on Micelle Assembly
59
Table 2.2 lists corresponding values to some surfactants.
Table 2.2 Value A & B of various surfactants
Surfactant Temperature/°C A B
C
m
25 1.92 0.290
C
mSO2
Na 40 1.59 0.294
C
mSO4
Na 45 1.42 0.265
C
mNH3
HCl 25 –
Note: Cm represents the carbon chain with m carbon atoms.
phobicity of surfactants can be estimated by Table 2.3 and can
the micelles increases.
Table 2.3 Properties of substituent groups
Substituent Group Classification
–CH
3
Hydrophobic
–CH
2
– Hydrophobic
–Cl, –Br, –F Hydrophobic
–N(CH
3)2
Hydrophobic
CMC
of surfactant
the molecule
decreases
increases.
as
For
compounds
the length of
with
the
carbon
the
same
chain
polar
in
group, the relationship is described as Equation 2.8:
where
m is the number
B are constants,
which are
of carbon
related
atoms
to the
in
the carbon
structure
chain,
of
surfactants,
A and
be used to speculate and compare
structures.
drugs
that as the
the CMC value
Table
and the
hydrophobicity
2.4 lists a
properties
variety
of
their micelles.
of the
of the drug drops
the micellization
of amphiphilic
The comparison shows
substituents
and
the aggregation
of similar
diphenylmethane
gradually
elevate,
number
of
Table 2.4 Eect of substuent on diphenylmethane drugs and properes of
micelles
Drug R R¢ R
CMC
(mol·kg–1)
Aggregation
Number
Diphenylamine H H H 0.132
3
O-methyl-diphenhydramine CH3 H H 0.096
Brominated diphenylamine Br H H 0.053
11
H H H 0.132
3
O-methyl-diphenhydramine CH3 H H 0.096
Brominated diphenylamine Br H H 0.053
11
3
60
Nano Physical Pharmaceutics of Micelle-Based Systems
Table 2.3 (Continued)
Substituent Group Classification
–SCH
3
–OCH
2CH3
–OCH
3
–NO
2
–CHO
–COOH
–COO
–NH
2
–NH
3
Hydrophobic
Hydrophobic
Slightly hydrophilic
Slightly hydrophilic
Hydrophilic
Slightly hydrophilic
Slightly hydrophilic
Hydrophilic
Slightly hydrophilic
–OH Slightly hydrophilic
Oxy Mephenhydramine Cl H CH 0.045
13
Regardless of ionic or non-ionic surfactants, the CMC decreases
with
longer
carbon
reduced
ionic
surfactants
for
of
the former is
hydrophilic group is the same
the
same
branched
carbon
atom
in the
to about
surfactant
value of
chains
chain.
carbon
1/2
is
reduced
with
generally
carbon
in
the carbon
Generally
chain,
of the
to
the same
much
atoms,
speaking, for each additional
the
CMC
of ionic
original
about 1/3
number
one,
of carbon
smaller
and
the CMC
of the original
than the latter. If the
and the hydrophobic
the CMC of surfactant
chain
is higher than the CMC
surfactant
of nonone.
atoms, the
CMC
group contains
s with
is
As
of
Table 2.5 CMC and micelle volume of hexadecyl PEG
CMC × 10
4
n (mol·kg–1) Micelle Volume × 10
–1
Aggregation Number
6 12.3 2430
590
9 2.1 1.4 220
12 2.3 150
21 3.9 0.82 150
Effects on Micelle Assembly
61
surfactants without branched chains. The benzene ring is slightly
despite being composed of six carbon atoms.
2.3.3.2 Chemical structure and volume of hydrophilic groups
hydrophobic groups are the same, non-ionic surfactant generally
shows lower CMC value than ionic surfactant, and the micellar
aggregation number is higher. As for non-ionic surfactants with
the length of PEG chain segments. As shown in Table 2.5, with
the increase of the PEG chain length, the hydrophilicity and CMC
values both rise.
2.3.3.3 Synergy of hydrophilic groups and hydrophobic
groups
During micellization, due to the simultaneous existence of driving
force and counterforce in the system, the delicate balance between
Table 2.6 lists the corresponding micellar aggregation number of
various surfactants in water.
The following Fig. 2.1 shows the general principal and the
process of micelle assembly from the block copolymers. The detail
mechanism and structural tailoring of such micelle. Here, for
Surfactant Temperature/°C Aggregation Number
C
8HSO4
Na Room temperature 20
C
10H21SO4
Na Room temperature 50
C
12H25SO4
Na 23
C
12H25
N(CH3)3Br – 50
C
14H29
N(CH3)3Br –
C
12H25
O(C2H4O)8H 25 123
C
12H25
O(C2H4O)12H 25 81
C
12H25
O(C2H4O)18H 25 51
C
9H19(C6H4
)O(C2H4O)10H 25
C
9H19(C6H4
)O(C2H4O)15H 25 80
C
9H19(C6H4
)O(C2H4O)20H 25 62
62
Nano Physical Pharmaceutics of Micelle-Based Systems
Figure 2.1 The spherical micelle and its microstructure assembly from block
copolymer. The formula related to the table is shown in 1.10, 1.15.
Effects on Micelle Assembly
63
length of amphiphilic block copolymer should be tuned in the
polymerization for getting the Flory parameter c
hydrophobic
> 0.5
while c
hydrophilic
< 0.5 by the function 2.18. This is the thermodynamic condition for the self-assembly of amphiphilic block
copolymers in solutions. Then, the composition of the copolymer
should be further regulated for tuning the packing parameter
(b) in the range of 0~1/3 according to function 2.20, which results
in a spherical morphology.
2.3.3.4 Eects of counterions
process. For example, the micelle volume of cationic surfactants
changes with the order of the counterion I– > Br– > Cl–, while the
micelle size corresponding to anionic surfactants varies with the
order of counterion Cs+ + > Na+. In general, the weaker hydration
ability of the counterion, the larger the micelles formed by the
surfactant. This is due to the fact that ions with weak hydration
are more easily adsorbed on the surface of the micelles, thereby
reducing the electrostatic repulsion between polar groups.
The CMC of surfactants under organic counterion (e.g., maleic
2.3.4 Influence of External Conditions on CMC
2.3.4.1 Temperature
The solubility of ionic surfactant in water is limited, it rises up
slowly as the temperature increases, resulting in the slight increase
of CMC. In the meantime, the molecular thermal movement is
aggravated, which is not conducive to the formation of micelles,
leading to higher CMC as well. However, for non-ionic surfactants,
the CMC decreases with increasing temperature.
Krafft Point. For ionic surfactant, the solubility in water
varies with temperature. As the temperature rises, the solubility
increases sharply at a certain point, and the temperature
the corresponding solubility is called the ionic surfactant CMC [11].