Topics Covered
Background
Dynamic Light Scattering
Polymers
Non-Invasive Backscatter Optics
Case Studies
Case Study 1: Measuring Polymer Molecular Size and Weight
Case Study 2 - Monitoring Polymer Phase Transitions
Case Study 3: Monitoring changes in polymer conformation
Conclusions
Zetasizer Nano System
Background
Light scattering techniques are widely used
for the characterization of solutions of polymers and macromolecules.
Dynamic Light
Scattering
Dynamic light scattering (also know as
photon correlation spectroscopy (PCS) and quasi-elastic light scattering (QELS))
measures the time-dependent fluctuations in the intensity of scattered light
that occurs because the particles are undergoing Brownian motion. The velocity
of this Brownian motion is measured and is called the translational diffusion
coefficient D. This diffusion coefficient can be converted into particle size
using the Stokes-Einstein equation.
Polymers
Polymers are used in a wide variety of
applications due to their diversity of properties. The molecular structure,
conformation and orientation of the polymer molecules can greatly affect the
macroscopic properties of the material.
Random coil polymer molecules have open
conformations. This results in low refractive index differences with the
continuous phase and as a result they scatter very little light. For such weakly
scattering samples, the intensity of scattering observed using conventional DLS
instruments (i.e. 90° detection) may not be sufficient for successful sizing
measurements to be performed.
Non-Invasive
Backscatter Optics
The Zetasizer Nano range of instruments incorporates non-invasive
back scatter (NIBS™) optics. The scattered light is detected at an angle of
173°. The novel optics arrangement maximises the detection of scattered light
while maintaining signal quality. This provides the exceptional sensitivity that
is required for measuring the size of molecules smaller than 1000
Daltons.
Case Studies
This application note summarises
measurements made on various polymers in solution using the Zetasizer Nano S. The Nano S contains a 4mW He-Ne laser
operating at a wavelength of 633nm and an avalanche photodiode (APD)
detector.
Case Study 1: Measuring Polymer
Molecular Size and Weight
Even thought absolute molecular weight
measurements are obtained using static light scattering, molecular weight can
sometimes be inferred from DLS measurements by exploiting the Mark-Houwinck
relationship that defines the intrinsic viscosity of a polymer solution in terms
of the molecular weight of the solute.
This turns out to be closely related to the
translational diffusion coefficient (D) of the molecules in the following
equation:
D = kM- α
Where k is a constant for a particular
polymer in a solvent, M is the molecular weight of the solute and á is a
conformational parameter describing the compactness of the molecule in solution.
A measured value for á of 1 suggests
that the solute molecules are rigid rods; a value of 0.5 to 0.67 is obtained
with random coils and a value of 0.3 occurs for spheres. Therefore, it is
possible to obtain information regarding the conformation of a solute molecule
in a particular solvent from DLS measurements.
Table 1 summarises DLS sizing measurements
performed on a number of polystyrene samples of various molecular weights
dissolved in toluene. The z-average diameter is the mean diameter based on the
intensity of scattered light.
Table 1. z-average diameters (in
nanometres) obtained for various known molecular weight polystyrene samples
dissolved in toluene
|
|
|
|
980 |
3.2 |
|
9860 |
7.0 |
|
9600 |
14.2 |
|
1214000 |
29.2 |
Taking logs of the equation D = kM , the
following expression is obtained;
Log
D = Log k - α Log
M
Therefore a graph of Log D versus Log M will
give a plot whose slope is á. The
translational diffusion coefficient, D, is related to particle size through the
Stoke-Einstein equation. Therefore, a plot of Log particle size versus Log M
also allows determination of the value of á. Figure 1 shows such a plot for the
data contained in table 1. The slope of the line is 0.31 indicating that the
polystyrene molecules have adopted a spherical conformation in
toluene.
Figure 1. Plot of the log z-average
diameter versus log molecular weight for polystyrene in toluene. The slope of
the line is 0.31 indicating that the molecules have a spherical conformation is
solution.
Case Study 2 - Monitoring Polymer
Phase Transitions
Poly(N-isopropylacrylamide) (PNIPAM) is one
of the most well known polymers that exhibits a reversible,
temperature-dependent phase transition. The temperature at which this occurs is
known as the cloud point or lower critical solution temperature (LCST). PNIPAM
is soluble at temperatures below the LCST and the polymer has a random coil
conformation. At temperatures above the LCST, the polymer chains collapse into a
globule. This sharp transition is attributed to alterations in the hydrogen
bonding of water molecules to the amide group of the side chain.
Figure 2 shows the results obtained from a
temperature scan of a sample of PNIPAM prepared in deionised water at a 0.01%
w/v concentration. Measurements were made at 0.5°C intervals using a temperature
range of 10 to 40°C. A delay time of 5 minutes was used at each temperature to
ensure that the sample viscosity was equilibrated before the measurements were
taken. Both the mean count rate (in kilo counts per second (kcps)) and z-average
diameter (nm) are plotted as a function of temperature (°C).
Figure 2. The mean count rate (kcps) and
z-average diameter (nm) of PNIPAM plotted as a function of
temperature.
The large increase in the mean count rate at
a temperature of 32°C is consistent with previously published LCST values for
PNIPAM. This increase in the scattered light results from a change in the
refractive index of the PNIPAM molecules as they undergo a transition from
random coil to condensed globule. The refractive index of the condensed globule
structure is higher than that of the random coil polymer.
Figure 3 shows the intensity size
distributions obtained at (a) 10°C and (b) 40°C. When the PNIPAM molecules are
in a random coil configuration, the size distribution is broader compared to
when the polymer is in a condensed globule. The polydispersity index values
obtained at these two temperatures are 0.491 and 0.087 respectively. The lower
value of 0.087 confirms the narrower size distribution seen at 40°C.
Figure 3. Intensity size distributions of
0.01%w/v PNIPAM measured at (a) 10°C and (b) 40°C.
Case Study 3: Monitoring changes
in polymer conformation
Dynamic light scattering can easily monitor
temperature dependent changes in the conformation of polymer particles. Figure 4
shows the effect on the mean count rate and z-average diameter of a polymer
particle dispersion as the temperature was increased. The measurements were made
at 1°C intervals with an equilibration time of 5 minutes at each
temperature.
Figure 4. The effect of increasing
temperature on the mean count rate and z-average diameter of a polymer particle
dispersion.
The z-average diameter increases with
increasing temperature. Normally, an increase in the z-average diameter is an
indication of particle aggregation. This would also result in an increase in the
mean count rate. However, in the results obtained in this study, the mean count
rates decrease upon heating. Therefore, the increase in the mean diameter
indicates that the polymer particles are swelling with increasing temperature.
As the conformation of these swollen particles becomes more open with increasing
temperature, the refractive index of particles decreases with a resultant
decrease in the mean count rate.
Conclusions
The Zetasizer Nano series with NIBS™ optics allows for study of
very small, weakly scattering particles such as polymers at low concentrations.
The Nano software allows for the easy setup of temperature versus size and
intensity measurements with full control over equilibration times. Monitoring
both mean count rate and particle size as a function of temperature elicits
information on changes in polymer conformation and helps to understand what
processes are occurring.
Zetasizer Nano
System
The Zetasizer Nano system from Malvern Instruments is the first
commercial instrument to include the hardware and software for combined dynamic,
static, and electrophoretic light scattering measurements. The wide range of
sample properties available for measurement with the Zetasizer Nano system
include, particle size, molecular weight, and zeta potential.
The Zetasizer Nano system was specifically designed to meet the
low concentration and sample volume requirements typically associated with
pharmaceutical and biomolecular applications, along with the high concentration
requirements for colloidal applications. Satisfying this unique mix of
requirements was accomplished via the integration of a backscatter optical
system and the design of a novel cell chamber. As a consequence of these
features, the Zetasizer Nano specifications for sample size and
concentration exceed those for any other commercially available dynamic light
scattering instrument, with a size range of 0.6nm to 6µm, and a concentration
range of 0.1mg/mL lysozyme to 40% w/v.
Complementary to the patented hardware
design, is the DTS software, providing instrument control and data analysis for
the Zetasizer Nano System. The DTS software utilizes self
analyzing algorithms to insure that the optical setup is optimized for each set
of experimental conditions, and includes a unique "one click" measure, analyze,
and report feature designed to minimize the new user learning
curve.
Source: "Characterisation of Polymers Using Light
Scattering Techniques", Application Note by Malvern
Instruments.
For more information on this source please
visit Malvern
Instruments Ltd (UK) or Malvern Instruments
(USA).