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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5628_Библиотеки_им_академика_М_И_Перельмана.pdf
14
The Fundamentals and Powerful Tool for Nano Physical Pharmaceutics
are typical representatives of the self-assembly phenomenon in
organisms. Lipid molecules are bonded noncovalently, so they can
undergo rapid rearrangement, for instance, changing positions
other biological constituents whose molecules bond covalently,
such as polynucleotides, proteins, and polysaccharides.
1.2.2.2 Phase behaviors of lipid bilayers
For a one-component lipid bilayer, as the temperature is lower
than the melting temperature (Tm) of phospholipids, the bilayers
are in the solid-gel state (Lb), and their tail acyl chains are arranged
in order. With the temperature increasing, the lipids would
undergo phase transition from Lb La). At ambient
temperatures, the phase of lipid with the high melting point is
usually Lb (such as sphingomyelins) or L
b
(chain-inclined solid
phase) (such as DPPC or DSPC). For low-melting lipids, such as
DOPC, POPC, or SOPC, their phase is La. In order to increase the
higher than the melting temperature of phospholipids.
The phase behaviors of binary lipid bilayers have been depicted
as a function of compositions and temperatures. In two-component
membranes, containing high and low-melting-temperature lipids,
Lb and La phases could coexist. The two lipids are miscible in
conversely, as the chains are dissimilar adequately, they are
Membranes containing three or more lipids are closer to
biological membranes than binary mixtures. Since the content of
cholesterol in animal cell membranes is about 35–45 mole% of
total lipids, the phase behaviors of mixtures containing cholesterol
are more attractive [28]. Ternary mixtures of lipids, i.e., highmelting lipid + low-melting lipid + cholesterol, are the combination
with least components that can produce rich phase behaviors
[29]. At present, the phase diagrams of three-component lipid
mixtures: DPPC/DOPC/cholesterol at temperatures from 15° to
45° [30, 31], DPPC/diphytanoyl-PC/cholesterol at temperatures
from 10° to 60° [32] and DSPC/DOPC/cholesterol at ambient
temperature [33], have been determined. Results show that a high
Stability of Nanosystems in Solutions
15
of bilayers and transforms the Lb phase into a new phase, i.e., the
liquid ordered phase (Lo). The coexistence of two macroscopic
liquid phases (L
o
+ liquid disordered phase Ld) emerges over a
wide range of compositions and temperatures. Here, the Lo phase
is rich in cholesterol, while Ld is poor in cholesterol. In addition,
it seems to be that cholesterol could increase the ordering of the
Ld phase, but decrease that of the Lo phase. That is, compared
in properties of coexisting domains in the ternary mixture.
1.3 Stability of Nanosystems in Solutions
Due to the high surface area and surface energy, the self-assembled
nanoparticles are thermodynamically unstable in the waterdispersed system. The particles tend to aggregate together to
reduce their surface energy, that is, they are prone to coagulating
and become instable. So, stabilizers are needed necessarily. On
the other hand, the intense Brown motion of nanoparticles makes
have kinetic stability. Scholars believe that the former is more
important, because once the thermodynamic stability is lost, the
particles will aggregate together and grow up, resulting in the
system losing the kinetic stability. The stability of nanosystems in
solutions has always been an important issue in colloidal science.
In this section, the stability theory of colloids, i.e., DLVO theory
will be introduced.
1.3.1 DLVO Theory
In the 1940s, Soviet scholars Derjaguin and Landau, as well as
Dutch scholars Verwey and Overbeek, proposed the calculation
methods of mutual attraction energy and repulsion energy
respectively. They are used to describe the interaction between
colloidal particles quantitatively. This theory has been called the
DLVO theory simply.
16
The Fundamentals and Powerful Tool for Nano Physical Pharmaceutics
1.3.1.1 Interaction energy between nanoparticles
The attractive energy-making nanoparticles aggregate together
and the repulsive energy preventing them from aggregating exists
simultaneously. These two energies, both of which are related to
the distance between particles, determine the stability of the
system.
The attraction between particles is essentially the same as the
van der Waals attraction between molecules, but it is the mutual
attraction between particles made up of many molecules and is the
sum of each molecule’s contributions. The mutual attractive force
between particles is a long-range force, inversely proportional
to the third power of the distance. The repulsive force between
particles comes from the electrical double-layer structures
around the particles. The nanoparticles in contact with the liquid
will adsorb certain ions from the liquid selectively. So, the solid
electrical double-layer structure on the interface as shown in
Fig. 1.6. When the distance between particles is large, the electrical
double layers have not overlapped, so the repulsive force does
not act. However, once the particles are so close that the
electrical double layers overlap, the concentration of ions in the
overlapping part increases, and the osmotic pressure of the excess
ions will hinder the proximity of the particles, resulting in repulsive
interaction.
Figure 1.6 Schemac diagram of the electrical double layer of negavely
charged nanoparcles in aqueous solution.
Stability of Nanosystems in Solutions
17
The relationship between the total interactive energy and the
distance between particles is shown in Fig. 1.7. When the particles
are far apart from each other, the electrical double layers do not
overlap. Under the circumstances, only the attractive interaction
works, and the total potential energy is negative. As the distance
between particles is so close that the electrical double layers
overlap, the repulsive force plays a major role and the total
the distance decreasing, the attractive force between the particles
also increases. For the distance short to a certain extent, the
attractive force starts to dominate again and the potential
energy decreases. As can be seen from Fig. 1.7(c), the particles must
overcome an energy barrier to aggregate together, which is the
reason why the nanoparticles do not coagulate in solutions.
Therefore, although the particles might collide due to the Brown
motion, so long as the distance between the particles gets shorter
enough for the overlap of the electrical double layers, they are
then separated by repulsive interaction and do not aggregate
together.
External factors, such as the electrolyte concentration in a
For the highly charged surface in a dilute electrolyte solution, the
parcles in an electrolyte soluon as described by DLVO theory. Reproduced
from [34] under the terms of Creave Commons Aribuon 4.0 Internaonal
License.
18
The Fundamentals and Powerful Tool for Nano Physical Pharmaceutics
strong long-range repulsive force results in a high energy barrier
to be overcome for particle aggregation. So, the nanosystem is
stable. For higher concentrated electrolyte solution, a secondary
minimum emerges along the curve like the cure shown in Fig. 1.7,
and the energy barrier decreases somewhat. However, it is still
case, the particles are either at the weak secondary potential
energy corresponding to reversible aggregation (thermodynamic
equilibrium at the primary minimum corresponding to the
irreversible aggregation), or completely dispersed in the solution.
The latter case has been known as the kinetic stable state. As the
surface charge density or potential decreases, or the electrolyte
concentration increases), the energy barrier continues to drop.
When the energy barrier drops below the axis of U = 0, the
particles will rapidly coagulate and the nanosystem is unstable.
When the surface charge or potential approaches zero, the
two surfaces attract each other at any distance, and the system
concentration, surface charge density or potential on the stability
to prevent them from coagulating and improves the stability of
the system.
1.3.1.2 Effects of DLVO theory
When discussing the stability of nanoparticles, DLVO theory
between particles (U
vdW
) which promotes the coagulation and the
repulsive energy (UEL) which hinders it. The theory provides the
calculation methods of the repulsive energy and attractive energy
between colloid particles, based on which the stability of colloids
is quantitatively treated. The relationship between the critical
coagulation concentration (also known as the condensation value)
and the valence number of ions with opposite charges to the
colloidal particle is obtained. And the Schulze-Hardy rule (i.e., the
coagulation value is inversely proportional to the sixth power of
the valence number of counterions) is formulated theoretically.
Under the Derjaguin integration approximation, the interaction
energy between two spherical particles with radii R1 and R2 can be
expressed as [35, 36]:
Stability of Nanosystems in Solutions
19
U = U
vdW
+ U
EL
(1.19)
A
H
8R
R
2
8R
R
2
DR(8 R + D)
U
vdW
=
+
2
+ ln
2
(1.20)
DRR + D) (4RR + D) (4RR + D)
6 (8
1
2 2
U = 4pee R jj exp( −kD)− (j + j )exp( −2kD)
(1.21)
EL 0 R 1 2 1 2
4
ee kT
−1
0 B
(1.22)
k =
2NIe
2
A
12
R =
RR
(1.23)
R
R + R
1 2
where AH is the Hamaker constant. D is the distance between the
surfaces of the two spheres. e is the dielectric constant of water.
e0 is the dielectric constant of vacuum, and j1, j2 are the surface
potentials of the two interacting particles, approximately equal
to their z potentials. k
–1
is Debye length, representing the
ionic strength, as well as electrolyte. kB is Boltzmann’s constant,
T is absolute temperature, NA is Avogadro’s number, I is ionic
strength and e is unit charge.
The variation of the total interaction energy U with the
distance D between particles has been shown in Fig. 1.7. The height
of the barrier is a sign of the stability of the system. When the
height of the barrier is zero, the system becomes unstable. The
curve, for which the barrier drops to zero due to the addition
dU
=0, U = 0
(1.23)
dD
Correspondingly, the added electrolyte concentration c is
the critical coagulation concentration, which is usually called the
coagulation value. By several steps of treatment, one can get a
20
The Fundamentals and Powerful Tool for Nano Physical Pharmaceutics
(1.25)
surfaces in dilute electrolyte solutions demonstrated that DLVO
theory is completely correct. According to the literature [34, 38],
reporting the relationship of the measured DLVO force and the
solutions, the maximum force is reached when the surface spacing
is 20–50 Å and the two micas could attract together eventually
below this interval. These results show that the DLVO theory
is basically correct. However, when the distance is very small,
the theory seems not to hold.
In addition, numerous studies have been conducted on the
electrical double layers or DLVO forces in various monovalent,
divalent and multivalent electrolyte solutions by means of SFA,
AFM or osmotic pressure. Related works include the force between
surfactant and lipid bilayer, the internal and external tension of
or metal oxide, and so on. Overall, the results are very consistent
with the DLVO theory.
1.3.3 Limitations of Classical DLVO
The success of the DLVO theory in describing the stability of colloids
is unquestionable. However, some experimental results have shown
mainly include: the DLVO theory can only describe short distance
(0.1–10 nm) interaction, when the distance is less than 0.1 nm,
the experimental results are inconsistent with the theory; the
4
g
cK=
26
Az
H
where
surface
Obviously,
sixth
power of the valence number
K is a
potent
the
constant,
ial.
and
For a
condensation
g is a
physical
certain
sol,
K g
value is inversely
z of the antisign
quantity
proportional
related
to the
to the
ions, which
theoretically illustrates the Schulze-Hardy rule.
1.3.2 Experimental Verif
ication of DLVO
The Powerful Tool for Study of Nano Physical Pharmaceutics
21
DLVO theory is best used for monovalent salts with concentrations
below 5 × 10
–2
M, and above 0.1 or 0.2 M (range of biological
interest or physiological concentrations), the DLVO theory loses
the predictability. These deviations are often attributed to the
presence of non-DLVO forces, such as hydration force, hydrophobic,
Considering the above limitations of the classical DLVO theory,
the DLVO model has been improved. Extended DLVO (or EDLVO)
theory is known as a model that considers Lewis acid-base
interactions or other non-DLVO forces. In most cases where
the EDLVO model is applied, the Lewis acid-base interaction is
considered to be an important supplement to the DLVO theory,
and the predicted results are in agreement with the coagulation
experiment.
1.4 The Powerful Tool for Study of Nano
Physical Pharmaceutics (NPP) [39]
When a beam of monochromatic, coherent light hits a dilute
macromolecule solution or suspension of colloidal particles and
(macromolecules or colloidal particles), the incident light is
scattered by each illuminated macromolecule or colloidal particle
macromolecules or particles mutually interfere, or combine, at a
distant from the fast photomultiplier tube (PMT) or avalanchephotodiode (APD) detector and produce a net scattered intensity
I(t) or photon counts n(t) which is not uniform on the detection
plane. If all the macromolecules or particles are stationary, the
scattered light intensity in each direction would be a constant i.e.,
independent of time. However, in reality, all the scatters in the
solution are undergoing constant Brownian motions, and this fact
I(t) with time if the
22
The Fundamentals and Powerful Tool for Nano Physical Pharmaceutics
macromolecules. The faster the relaxation process, the faster the
scence) and elastic (no absorption) light scattering. However,
in polymer and colloid science, light scattering is normally
referred to in terms of static (elastic) or dynamic (quasi-elastic)
measurements, or both, of the scattered light [40]. Static LLS as a
classical and absolute analytical method measures the angular
distribution of time-average scattered intensity. On the other
of the average light intensity (this is where the word dynamic
comes from), and its essence may be explained as follows. When
the incident light is scattered by one moving macromolecule
or particle, the detected frequency of the scattered light will be
slightly higher or lower than that of the original incident light
moves towards or away from the detector. Thus, the frequency
distribution of the scattered light is slightly broader than that
of the incident light. This is why dynamic LLS is also called
quasi-elastic light scattering (QELS). The frequency broadening
5–107 Hz) is so small in comparison with the incident light
15
recorded in the time domain through a time correlation function.
For this reason, dynamic light scattering is sometimes known as
spectroscopy (PCS) is then used to refer to the technique described
here.
The recorded observation of the light scattering can be traced
back to 1802 when Richard, J. B noticed the light path of the gold
on light scattering was Tyndall. He observed the scattering of the
natural light when it passed through a colloid amphiphilic. In
derived that the intensity of the scattered light by the nonabsorption, non-interaction and optically isotropic small particles
is reversely proportional to the fourth power of the incident
The Powerful Tool for Study of Nano Physical Pharmaceutics
23
wavelength. In 1944, Debye measured the molecular weight of
macromolecules from a dilute solution using light scattering
method. Later, Zimm [42] proposed the famous Zimm plot by
extrapolating both concentration and angular angle to zero value
at a single coordinate. Since then, light scattering, strictly, static
light scattering as a classical and absolute analytical method
has been widely used to characterize both synthetic and natural
macromolecules. However, light scattering at that time was
concentrations, from which three parameters of macromolecules,
namely the weight-average molecular weight (M
1/2
root-mean-square radius of gyration (〈R
2
〉
, simply 〈Rg〉) and the
z
), z-average
w
A2) can be obtained. This situation
was changed in the 1960s with the invention of the laser. In 1964,
radiation for the study of macromolecular solutions, poly(styrene),
and during the last two decades, thanks to the advance of stable
laser, ultrafast electronics and personal computers, LLS, especially
dynamic LLS has evolved from a very special instrument for
physicists and physical chemists to a routine analytical tool in
polymer laboratories or even to a daily quality-control device
in production lines [44, 45]. Commercially available researchgrade LLS instruments are normally capable of making static and
dynamic measurements simultaneously for studies of colloidal
particles in suspension or macromolecules in solution as well
as in gels and viscous media. Note: Sections 1.1 and 1.2 are
quoted from the doctoral thesis of the author Wei Li [39].
1.4.1 Static Laser Light Scattering (SLLS)
1.4.1.1 Scattering by a small particle
it a dipole that oscillates with the same frequency as the
incident light (Fig. 1.8). An oscillating dipole produces a secondary
words, the particle scatters the incident light. Consider a single,
optical isotropic particle (a macromolecule or a colloid particle)
with a polarizability a at origin o (Fig. 1.8) in vacuum. When