24,577 research outputs found
Size Information Obtained by Using Static Light Scattering Technique
Detailed investigation of static light scattering has been attempted
in this work using dilute water dispersions of homogenous spherical particles,
poly(-isopropylacrylamide) microgels and simulated data. When
Rayleigh-Gan-Debye approximation is valid, for large particles, the simple size
information, the static radius and distribution , can be
accurately obtained from SLS. For small particles, the root mean-square radius
of gyration and the molar mass of particles
measured using the Zimm plot are discussed. The results show that the molar
mass measured using the Zimm plot over the average molar mass of particles is a
function of the size distribution. With the assistance of simulated data, the
effects of the reflected light and noises have been investigated in detail.
Measuring the static radius from the SLS data provides one method to avoid the
stringent requirements for the sample quantity and the instrument capability at
small scattering angles
Investigating Diffusion Coefficient Using Dynamic Light Scattering Technique
In this work, the Z-average, effective, apparent diffusion coefficients and
their poly-dispersity indexes were investigated for dilute poly-disperse
homogeneous spherical particles in dispersion where the Rayleigh-Gans-Debye
approximation is valid. The results reveal that the values of the apparent and
effective diffusion coefficients at a scattering angle investigated are
consistent and the difference between the effective and Z-average diffusion
coefficients is a function of the mean particle size, size distribution and
scattering angle. For the small particles with narrow size distributions, the
Z-average diffusion coefficient can be got directly at any scattering angle.
For the small particles with wide size distributions, the Z-average diffusion
coefficient should be measured at a small scattering angle. For large
particles, in order to obtain a good approximate value of Z-average diffusion
coefficient, the wider the particle size distribution, the smaller the
scattering angle that the DLS data are measured. The poly-dispersity index of
the effective diffusion coefficient at a scattering angle investigated is
consistent with that of the Z-average diffusion coefficient and without
considering the influences of noises, the difference between the
poly-dispersity indexes of the Z-average and apparent diffusion coefficients is
determined by the mean particle size, size distribution and scattering angle
together.Comment: 6 figures 6 table
New Interpretation for Laser Light Scattering Technique
The new method proposed in this work not only measures the particle size
distribution and the average molar mass accurately using the static light
scattering (SLS) technique when the Rayleigh-Gans-Debye approximation is valid
for dilute poly-disperse homogenous spherical particles in dispersion, but also
enables us to have insight into the theoretical analysis of the dimensionless
shape parameter . With the method, a new size, static radii , can
be measured. Based on the new static particle size information, detailed
investigation of the normalized time auto-correlation function of the scattered
light intensity reveals that there exist three different
particle sizes: the static radius, hydrodynamic radius and apparent
hydrodynamic radius that is the hydrodynamic radius obtained using the
cumulants method. With a simple assumption that the hydrodynamic radius
is in proportion to the static radius , the expected values of
calculated based on the static and commercial particle size
information are consistent with the experimental data. With the assistance of
simulated data, the apparent hydrodynamic radius is discussed. The results show
that the apparent hydrodynamic radius is different from the mean hydrodynamic
radius and is determined by the optical, hydrodynamic characteristics and size
distribution of particles and scattering vector. The analysis also reveals that
is determined by not only the structure of particles but also the
relationship between the optical and hydrodynamic characteristics of particles
even for mono-disperse model.Comment: 9 figures, 9 table
Discussing the Relationship between the Static and Dynamic Light Scattering
Both the static and dynamic light scattering techniques are
used to obtain the size information from the scattered intensity, but the
static radius and the apparent hydrodynamic radius are
different. In this paper, the relationship between SLS and DLS is discussed
using dilute water dispersions of two different homogenous spherical particles,
polystyrene latexes and poly(-isopropylacrylamide) microgels, with a simple
assumption that the hydrodynamic radius is in proportion to the static
radius , when Rayleigh-Gans-Debye approximation is valid. With the
assistance of the simulated data, the apparent hydrodynamic radius
has been discussed. The results show that the apparent hydrodynamic radius is
different with the mean hydrodynamic radius of particles and is a composite
size obtained from averaging the term in the static size
distribution with the weight
Different Particle Sizes Obtained from Static and Dynamic Laser Light Scattering
Detailed investigation of static and dynamic laser light scattering has been
attempted in this work both theoretically and experimentally based on dilute
water dispersions of two different homogenous spherical particles, polystyrene
latexes and poly(-isopropylacrylamide) microgels. When Rayleigh-Gans-Debye
approximation is valid, a new radius , referred to as a static radius,
can be obtained from the static light scattering . If the absolute
magnitude of the scattered intensity and some constants that are related to the
instrument and samples are known, the average molar mass for large particles
can be measured. The size information obtained from SLS is purely related to
the optical properties of particles, i.e., to and its distribution
. The size information obtained from dynamic light scattering is more complicated, the size distribution of which is a composite
distribution that is not only related to the optical properties of particles,
but also related to the hydrodynamic properties and the scattering vector.
Strictly speaking, an apparent hydrodynamic radius is a composite
size obtained from averaging the term in the static size
distribution , with the weight that is also a
function of both and the scattering vector .Comment: 7 pages, 3 figure
Investigating Auto-correlation of Scattered Light of Mixed Particles
In this work, the normalized time auto-correlation function of the electric
field of the light that is scattered by the two kinds of
particles in dispersion is investigated. The results show that the logarithm of
can be consistent with a line and many reasons can cause the
deviations between an exponentiality and plots of as a function
of delay time . The nonexponentiality of is not only
determined by the particle size distribution and scattering angle but also
greatly influenced by the relationship between the concentrations, mass
densities and the values that the refractive index of the material expands as a
function of the concentration of the two kinds of particles.Comment: 8 figure
Investigation of Volume Phase Transition from the Different Properties of Particles
In this work, three different particle sizes: the static radius ,
hydrodynamic radius and apparent hydrodynamic radius
obtained using the light scattering technique, are investigated for dilute
poly-disperse homogenous spherical particles with a simple assumption that the
hydrodynamic radius is in proportion to the static radius, when the
Rayleigh-Gans-Debye approximation is valid. The results show that the expected
values of the normalized time auto-correlation function of the scattered light
intensity calculated based on the static particle size
information are consistent with the experimental data. The volume phase
transition is thus investigated using the equilibrium swelling ratios of static
radii and apparent hydrodynamic radii respectively. The changes of the static
particle size information and apparent hydrodynamic radius as a function of
temperature show the effects of the volume phase transition on optical
properties and the total influences of the volume phase transition on the
optical, hydrodynamic characteristics and size distribution of particles,
respectively. The effects of cross-linker on the volume phase transition are
also discussed.Comment: 6 figure
Auto-correlation Function Study of Scattered Light Intensity
In this work, the particle size distribution measured using the dynamic light
scattering (DLS) technique is compared with that obtained from the static light
scattering (SLS) technique or provided by the supplier measured using the
Transmission Electron Microscopy (TEM) technique for dilute
Poly(-isopropylacrylamide) microgel and standard polystyrene latex samples
in dispersion respectively. The results show that the narrow particle size
distribution that can be measured accurately using the SLS technique is not
suited to the determination by the DLS technique and the particle size
distribution obtained from the DLS technique is different from the value
provided by the supplier. With the assistance of the simulated data of the
normalized time auto-correlation function of the scattered light intensity
, the effects of the particle size distribution on the
nonexponentiality of measured at a scattering angle of
30 are investigated. The analysis reveals that the influences of
the particle size distribution are small on the nonexponentiality of
and very large on the initial slope of the logarithm of
. The values of the apparent hydrodynamic radius are also
largely influenced by the particle size distribution and the difference between
the distributions of the apparent hydrodynamic radius and hydrodynamic radius
of particles is determined by the method of cumulants.Comment: 6 figures, 7 table
A remark on a Bernstein type theorem for entire Willmore graphs in R^3
In this note we prove that every two-dimensional entire Willmore graph in
with square integrable mean curvature is a plane.Comment: In this note we answer a question proposed by Jingyi Chen and Tobias
Lam
RKKY interaction of magnetic impurities in multi-Weyl semimetals
We have systematically investigated the Ruderman-Kittel-Kasuya-Yosida (RKKY)
interaction between two magnetic impurities in Weyl semimetals with arbitrary
monopole charge . We find that the RKKY interaction becomes intrinsically
anisotropic for , and its dependence on Fermi energy and impurity
separation is directly controlled by the monopole charge. With the increase of
, the RKKY interaction becomes more long-ranged and more anisotropic, which
makes interesting magnetic orders easier to form and thus may have important
applications in spintronics.Comment: 6 pages, 2 figure
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