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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5628_Библиотеки_им_академика_М_И_Перельмана.pdf
64
Nano Physical Pharmaceutics of Micelle-Based Systems
also the lower limit of the surfactant’s application temperature,
for satisfactory results.
Cloud Point. The solubility of non-ionic surfactants in aqueous
solution decreases with increasing temperature, and the solution
which is called the cloud point [12]. Cloud point is the eigenvalue
example, for Tween surfactants, the cloud point of Tween 20 is
for the occurrence of cloud point is that as the temperature rises,
the hydrogen bond between polyethylene glycol and water is
destroyed and the solubility decreases. The hydrogen bond can
be formed again after cooling, and the solution becomes clear.
When the chain length of polyethylene glycol is the same, the
longer the carbon chain length, the lower the cloud point of
the surfactant. When the carbon chain length is the same, the
cloud point increases with the growth of the polyethylene glycol
segment.
2.3.4.2 Electrolytes
The addition of a strong electrolyte to ionic surfactant solution
can reduce CMC because of the electrostatic interaction between
the electrolyte ions and the oppositely charged surfactant ions,
which reduces the electrostatic repulsion between the polar
groups and reduces the electrical work consumed during
the properties of the dodecyl trimethyl ammonium bromide
(DTAB) micelle, a cationic surfactant. The properties of non-ionic
electrolyte.
Structure and Stability of Polymeric Micelles
65
Table 2.7 Eect of the electrolyte on the properes of DTAB micelle
NaCl concentration/mol · L
–1
CMC/mol · L
–1
Aggregation Number
0.000 0.0146 61
0.100 0.00428
0.502 90
2.3.4.3 Organic substances
CMC value of surfactants. Organic compounds with strong polarity
particularly at lower concentrations; For other organic substances,
larger concentrations are required to reduce the CMC value.
dielectric constant or dissolution parameters, and improving the
interaction of water with surfactants or micelles, such as urea,
methylamine, guanidine salts, short-chain alcohols, ethylene
glycol, fructose, and xylitol, etc.; Urea, methylamine and guanidine
salts can destroy the structure of water, increase hydration of
the hydrophilic moiety, prevent gelation, and improve the CMC
value of the surfactant aqueous solution, especially for PEGbased non-ionic surfactants. They can increase the CMC value
at high concentrations by reducing the cohesive energy density
and increasing the concentration of monomeric surfactants. For
solutions containing ionic surfactants, the presence of these
compounds can reduce the dielectric constant, leading to stronger
mutual repulsive force of the ionic end of the micelle.
2.4 Structure and Stability of Polymeric
Micelles
PMs are generally prepared from amphiphilic block copolymers
philic and hydrophobic chain segments, where the hydrophobic
moiety of the copolymer joins to form a semisolid core and the
66
Nano Physical Pharmaceutics of Micelle-Based Systems
hydrophilic part forms a crown with hydrogen bonds between
the surrounding water molecules [13]. When the concentration
is lower than CMC, the copolymer exists as a single molecule in
the whole solution. When the concentration goes above CMC, the
polymer obtains micelles by self-assembly. Most polymers have
lower CMC (as low as 10
–10
M) compared to small molecule
surfactants, and are able to form systems with high stabilities [14].
Besides, micelles of some copolymers also have excellent kinetic
stability.
Various theories have been developed to predict the
structural parameters of micelle (CMC, aggregation number m,
nuclear radius Rc, shell thickness L, hydrodynamic radius Rh)
based on copolymer characteristics, including functions of
molecular weight and chemical composition [15]. In all these
theories, the total Gibbs free energy G
(m)
of micelles can be divided
and mathematical methods, including the Gibbs free energy G
(shell)
of the core, Gibbs free energy G
(shell)
of the shell and Gibbs free
energy G
(interface)
of the core/shell interface:
G(micelle) = G(core) + G(shell) + G(interface) (2.9)
2.4.1 Thermodynamical Stability
According to the early results of Price and Quintana, micelle
formation from block copolymers in organic media is enthalpydriven [16]. Gibbs free energy DG0:
DG0 = DH0 = TDS
0
(2.10)
The DS0 caused by the loss of the combined entropy is negative,
which is not conducive to micellization, because the copolymer
chain in micelles has small swelling in the non-associative state.
Moreover, the block connection is located at the core/shell
interface of micelle, which also leads to a decrease in the number
of possible conformations. The negative value of DH0 is due to the
exothermic energy exchange caused by the interaction between
polymer and solvent replacing the polymer/solvent interaction.
Structure and Stability of Polymeric Micelles
67
Thus, the formation of micelle nuclei contributes the most to the
exothermic process.
This is completely inconsistent with the reported micellization,
low molecular weight surfactant and hydrophilic-hydrophobic
segmented copolymer in aqueous solutions. A typical example
is PEO-b-PPO-b-PEO block copolymer, whose micellization is an
entropy-driven process due to the hydrophobic interaction near
For block polymer to associate in selective organic solvents, the
standard enthalpy and the Gibbs free energy can be approximated
DG0 = RT ln (CMC) (2.11)
dln CMC
(
1
T
CMC is the critical micelle concentration expressed in mole
fraction, DH0 has nothing to do with temperature, and the integral
is:
0
)
(2.12)
0
DH R=
d
DH
lnCMC = + constant
(2.13)
RT
2.4.2 Structural Stability
The scaling theory is developed to describe the relationship
between the structural characteristics and properties of a certain
segmented copolymer (mainly two segmented copolymer AB) on
the basis of a simple model, such as the nuclear radius RC, corona
thickness L and aggregation number Z of a segment in selective
copolymers with B being the insoluble block; it forms either
crew-cut micelles with Rc » L or the so-called hairy micelles. For
the crew-cut micelles, assuming uniformly stretched nuclear
segments and short shell segments, the radius RC of the core is
shown in Equation 2.14:
68
Nano Physical Pharmaceutics of Micelle-Based Systems
RC ~ aγ
1/3
N
B
2/5
(2.14)
where NB is the number of monomer units of the insoluble
segment, and g is the interfacial tension between two chain
segments, a is the length of the fragment. The scale P of the
aggregation number is shown in Equation 2.15:
P ~ NBγ (2.15)
In 1982, Daoud and Cotton derived the star copolymer model
for describing star-shaped micelles [19]. This model predicts the
total radius R of the micelle and the number and aggregation of
soluble block monomer units as shown in Equation 2.16:
R ~ N
A
3/5
f
1/5
(2.16)
with f being the number of arms. For block copolymer micelle,
the number of arms corresponds to the aggregation number P,
4/5
.it follows that L ~ P
1/5
N
A
3/5
with P ~ N
B
The scaling concept describing polymer concentration
distributions and free energies is mainly applied to micellular
solution containing long polymer chains. In fact, the above scale
interactions. Furthermore, numerical values for micellar properties
cannot be obtained directly because scaling laws can only predict
trends, such as how a given micellar parameter scales with a
given copolymer parameter. Therefore, the scaling model must
2.4.3 Micelle Structural Tailoring
In 1982, Noolandi and Hong proposed a self-consistent mean-
model of segmented copolymers and homopolymers [20]. It is the
tool for the study of copolymers and their co-mingled systems.
They derived the micellar characteristics by minimizing the Gibbs
Structure and Stability of Polymeric Micelles
69
energy of an isolated micelle using numerical values of the
Flory–Huggins interaction parameters c, molecular weight and
composition of the copolymer. The theoretical values were in fair
agreement with those obtained experimentally. Leibler et al. then
improved the theory by minimizing the total Gibbs energy not
only for one micelle but for the whole micellar system [21].
The Flory–Huggins solution theory derived the relations
between the mixing entropy, the heat of mixing, and the free energy
of mixing for polymer solutions from the lattice-like model of
liquids using statistical thermodynamics in the form of Equation
DFm = DUm – TDSm = RT [n1lnΦ1 + n2lnΦ2 + n1Φ2 c12
where n
1
and Φ1 refer to the mole number and volume fraction
of the solvent, n
2
and Φ2, respectively, refer to the mole number
and volume fraction of the polymer, c is called Flory–Huggins
interaction energy between the polymer and the solvent. The value
of the polymer solvent action parameter c can be used as a semiquantitative criterion for the merits of the solvent. If c is greater
than 0.5, the polymer generally cannot be dissolved; If c is lower
than 0.5, the polymer can be dissolved, and the smaller it is,
the better the solvency ability of the solvent is.
solubility of their hydrophilic and hydrophobic moieties in aqueous
solution (the determining factor is the solubility parameter of the
hydrophilic and hydrophobic moieties in aqueous solution) [22].
The solubility of amphiphilic block copolymers can be described
by the Flory–Huggins parameter as shown in Equation 2.18:
c
p-s
= (dp – ds)2Vs/KT + 0.34 (2.18)
where dp and ds refer to the solubility parameters of the polymer
and the solvent, Vs is the molar volume of the solvent, and 0.34
is the contribution value of entropy. The solubility parameter can
be calculated from the Hildebrand–Scatchard equation, DE
vap
is
d = DE V
vap
/
70
Nano Physical Pharmaceutics of Micelle-Based Systems
the evaporation energy of the solvent, and V is the molar volume
of the solvent used:
(2.19)
In a polymer solution, the formation of nanoparticles of
polymer) requires the driving force of an external solvent, and
two thermodynamic conditions need to be met simultaneously
to complete the self-assembly [23]. Firstly, the c
p-s
of the high
hydrophilic chain segment of the solubility should be below 0.5.
Secondly, c
p-s
of the low hydrophobic chain segment of solubility
should be above 0.5. The morphology of the aggregates can
be realized by adjusting the chemical composition of polymer.
Packing parameter b of the system in solution is used to describe
this kinetic parameter, and can be obtained by calculating
Equation 2.20:
b = VH/LCA
0
(2.20)
where VH refers to the volume occupied by the hydrophobic
chain, LC refers to the length of the aggregation region of the
hydrophobic chain segments, and A0 refers to the surface
area occupied by the hydrophilic chains. Generally speaking,
spherical nanomicelles are formed when 0 < b < 1/3, rod-shaped
nanomicelles are formed when 1/3 < b < 1/2; vesicles are formed
when 1/2 < b < 1; and planar bilayers are formed when b > 1 (Fig.
of spherical micelles, the range of the parameter b needs to be
structures can be regulated by modulating the ratio between
hydrophilic and hydrophobic chains according to the packing
parameter b
et al. synthesized amphiphilic segmented copolymers phenylPID
118
-b-PLA, which can self-assemble into spherical structure
of nanomicelles in water because its b value is lower than 0.1
[25, 26]. The hydrophilic temperature-sensitive PID shell can
stabilize micelles and enhance cell endocytosis, the hydrophobic
PLA core can improve the drug loading of hydrophobic drugs.
NPP of Polymeric Micelles in Drug Delivery
71
Figure 2.2 Nanostructures formed by amphiphilic block copolymers with
dierent packing parameters. The formula related to the table is shown in 2.18,
2.20.
2.5 NPP of Polymeric Micelles in Drug Delivery
PMs are widely used as nanocarriers for drug delivery and tumor
therapy due to their easy preparation and unique physiochemical
properties, excellent drug delivery and release, biocompatibility,
After that, PMs gradually became a common carrier for the delivery
of anticancer drugs and other bioactive molecules used in cancer
diagnosis and treatment.
A large number of studies have shown that the physiochemical
properties of nanocarriers vary with their forms, and determine
their functions and applications. For example, the in vivo stability
of micelles is related to the carrier surface charge density
( r
charge
), surface chain density (r
surface chain
by particle size (D), core volume (V
core
) or number of surface
chains (N
chain
), while the drug release behavior is related to
parameters such as D, N
chain
, and r
chain
. D and r
charge
controlled release of drugs in vivo can be achieved by precise
72
Nano Physical Pharmaceutics of Micelle-Based Systems
regulation on the physiochemical properties of micelles according
to the needs of environmental conditions and related
in vivo
thermodynamic and kinetic theories.
2.5.1 Physiochemical Properties of Micelles
2.5.1.1
The
and
changed
and
particle
instruments which
microstructure
can be further
Partsiicle size and distribut
micelle
particle
hydrophilic
ze is mainly characterized
size distribution [29, 30].
by adjusting the length of hydrophobic D chain (
chain
D
N
hydrophobic
size
can
be
usually
of
micelles, such
obtained
simulations. We have
with various
(PBMA)
micelles
core
diameter
established,
chain
and poly(
[23]. The
(R
which
lengths of poly(
N
-acryloylmorpholine)
relationships between the
) as
core
can be
following equations:
0.16
NN
3
agg 4BMA
pr
R
core
hydrophobic
3
=
(N
hydrophilic
0.16
measured
falls
through
synthesized
well
estimated
hydrophilic
M
W(BMA)
N
A
ion
by two
The
) with the correlation
N
hydrophilic
by
into
as the
as corona
0.6
0.6
dynamic/static
the
range
of 10~100
core
and
calculations
amphiphilic
n-butyl
block copolymers
methacrylate)
blocks
(PAM) to prepare
N N
BMA/AM
thickness
from
M
w
parameters
can , be
N
hydrophobic
2.21. The
light scattering
nm.
shell
dimensions
and
theoretical
blocks
(T
)
were
corona
N
in
agg
(2.21)
D
)
The
the
= (D
corona
r
surface chainSsurface chain
N
where
of
block
, M
agg
copolymers
– 2
h
=
W(BMA)
R
)/2 (2.23)
core
, /Nr, and N
for each micelle,
are the
A
polymer
the
molecular
aggregation
weight
(2.24)
number
of BMA,
the density of PBMA at the bulk state (approximately 1 mg/mL),
and the Avogadro constant, respectively, and micellar diameters
NPP of Polymeric Micelles in Drug Delivery
73
0.16 0.6
(Dh)
N
BMA NAM
. T
corona
was found to increase from 4 to
9 nm with increasing N
BMA/NAM
values in the range from 0.104
Dh and increased R
core
as increases
in N
BMA/NAM
values consequently led to the decreases in
T
corona
microstructure tailoring of core, corona, surface properties of
micelles.
Nottelet et al. synthesized a series of polyethylene glycolg-poly(ε-caprolactone) (PEG-g-PCL) graft copolymers by click
chemistry, and prepared micellar solutions with sizes ranging
from 30 nm to 80 nm [31]. The size of the micelles decreases
with longer hydrophobic PCL chain segments, which is mainly
due to decreased hydration from the less hydrophilic outer shell.
Moreover, the reduced proportion of PEG trapped in the
hydrophobic core leads to less swollen core, hence the smaller
size. The size distributions of the micelles are all between
0.21 and 0.40, which are higher than those prepared with
conventional linear copolymers. This is possibly due to the higher
energy required for the side-arm PEG to phase separation.
Figure 2.3 The denion and microstructural parameter of micelles by ne
tailoring. Reproduced with permission from [23]. The key parameters in the
gure are originally dened by us and illustrated in Equaons 2.21, 2.22,