|
|
|
|
|
|
"The service provided by Viscotek representatives is unmatched by any other in the industry... A wonderful addition to the polymer community."
- E.F, Ph.D., Academic Institution
|
Tetra Detector Array
A revolutionary, integrated multiple-detector device designed for the characterization of natural and synthetic polymers and copolymers, proteins, protein conjugates, excipients and other macromolecules. Comprised of modular Refractive Index, Ultra-Violet, Low Angle Light Scattering and Viscometer detectors.
|
HTGPC
The Viscotek High Temperature GPC (HT-GPC) System is a revolutionary advanced detector system specifically designed for the characterization of polyolefins, natural and synthetic polymers, nanoparticles and other large molecules.
|
Nanoparticle and Protein Sizing
Viscotek is proud to introduce its range of Dynamic Light Scattering Detectors featuring rapid, accurate and sensitive sizing for proteins, biomolecules, nanoparticles & polymers and a pair of outstanding technologies unique to Viscotek. |
|
|
|
|
|
|
|
|
GPC Theory: Light Scattering Detector |
Design
Theory
The fundamental equation for the scattering of
light from polymer solutions is the Zimm equation.
M is the molecular weight of the polymer sample
and C is the sample concentration. A2 is the second
virial coefficient of the solution, which corrects for the
interaction of polymer molecules with each other. A2
may be calculated from the concentration dependence
of the light scattering signal.
Rθ is the excess Rayleigh scattering ratio of the solution
above that of the pure solvent, measured at angle
θ with respect to the incident beam.
I0 is the irradiance of the incident laser. Iθ is the
excess intensity of the scattered light above that of the
pure solvent at angle θ; in the present case it is the
baseline-corrected LALS signal. k is an instrument
constant related to the scattered light collection efficiency.
A schematic of the optical arrangement of the
LALS is shown in Figure 1.
Pθ is the particle scattering factor. It is a measure of
the angular dissymmetry of the scattered light and is
related to the size and the angle at which the scattering
is determined. Much of light scattering science
is devoted to the determination of Pθ but the beauty of
LALS is that it can be ignored.
- Pθ is exactly equal to unity for all molecules when
θ is zero.
- Pθ is 0.98 for molecules with radius of gyration
(RG) of 150 nm when θ is 7 degrees.
- RG of 150 nm constitutes the upper limit of separation
of GPC.
Therefore, with LALS, multiple angle measurements
are unnecessary because extrapolation or correction
for angular dissymmetry is unnecessary. This
reduction to a single angle greatly simplifies the processing
of data from multiple detectors.
K is a composite of optical and fundamental
constants.
-
n0 is the refractive index of the solvent.
- ν is the refractive index increment of the polymer
solution.
- NA is Avogadro’s number.
- λ0 is the wavelength of the incident light in
vacuum.
- p is an integer equal to 2 for vertically polarised
incident light, 1 for un-polarised.
The latter three parameters (NA, λ0 and p) are instrument
constants and can be merged with the detector
constants k and I0 in equation 2 to form a new constant
which we will call Lals.Cal. Equation 1 can now be
rearranged to separate the variables of molecular weight
and concentration from the other parameters.
At normal GPC/SEC concentrations the second
virial coefficient A2 is typically insignificant compared
to the first term in the denominator, so equation 4 can
be simplified by neglecting the A2 term.
Equation 4 is the general equation but equation 5
will be used in the present discussion for purposes of
simplification.
Elution Profiles
The elution profile consists of successive fractions
of the eluent sampled at equally spaced time intervals,
i. Each fraction will be characterised by its molecular
weight Mi and concentration Ci. The term Ci is determined
from the following equation, derived in The Deflection Refractometer.
RIi is the signal from the RI detector at interval i
and RI.Cal is the detector calibration constant.
Substituting equation 6 into equation 5 yields the elution
profile of molecular weight.
Note that the array index for the LALS signal is
offset from that of the RI detector by an amount δ.
This detector offset reflects the fact that the two detectors
do not measure each fraction simultaneously. They
have a time (volume) separation between them corresponding
to the volumes of the two detectors plus the
volume of the interconnecting tubing. Equation 7
reveals that molecular weight elution profile is proportional
to the ratio of the LALS detector signal to the
RI detector signal.
An elution profile for molecular weight on a broad
distribution polystyrene sample is shown in Figure 2,
overlaid with the RI and LALS signals. Notice that the
Mi profile has more noise at each end than in the
middle. This is due to the RI and LALS signals being
lower in magnitude near the ends of the peaks, so the
noise is relatively higher. In fact, the calculation of Mi
becomes so unreliable on the ends that the calculation
must be truncated at some point and Mi is obtained for
the rest of the distribution by extrapolation. The
extrapolation is shown in Figure 2 as the dashed line
and is much more extensive on the low molecular
weight end.
Determination of instrument constants (calibration)
The instrument constants RI.Cal, Lals.Cal and δ are
determined from the chromatograms of a narrow distribution
polymer standard — for example, polystyrene
standard 90K, shown in Figure 3. The offset δis easily
determined as the difference in the peak positions.
Figure 4 shows the same chromatograms after the offset
is applied. The RI calibration constant is determined
from the RI peak area and dn/dc as shown previously in
Part 1. The LALS calibration constant is determined
from the LALS peak area, which is directly proportional
to the weight-average molecular weight as shown
in the next section.
Molecular Weight Distribution
The molecular weight distribution can be represented
in several ways — the most important being the
number-average molecular weight MN and the weightaverage
molecular weight MW. MN is defined as the
average molecular weight (molar mass) over the successive
fractions of the sample, with the statistical
weight of each fraction being the number of molecules,
or molar concentration Ni. The molar concentration
is simply the ratio of the weight concentration
Ci and molar mass Mi, which are determined by equations
6 and 7, respectively.
The number-average molecular weight is therefore
defined as follows:
The weight-average molecular weight is defined as
the average molecular weight (molar mass) over the
successive fractions of the sample, with the statistical
weight of each fraction being the mass of molecules, or
weight concentration, Ci.
The summations in equations 9 and 10 are directly
related to peak areas in the GPC chromatogram.
The sum of Ci is proportional to the area of the RI
detector peak, per equation 6.
The sum of CiMi is proportional to the area of the
LALS detector peak, per equation 5.
Combining equations 10–12 reveals a very simple
relationship between MW and the chromatographic
peak areas.
The sum of Ci/Mi is proportional to the area of the
molar concentration peak, per equation 8. So MN can
also be considered a ratio of peak areas as follows:
However, molar concentration is a derived function,
not a detector signal, so MN does not have the
same type of simple relationship to detector peak areas
as does MW. The derivation of molar concentration
often results in greater error for determination of MN
than for MW. The reason for this is illustrated in Figure
5 where the relevant peaks are overlaid for a broad distribution
sample, polystyrene in THF. MW can be
determined very precisely because it is simply proportional
to the ratio of the LALS and RI peak areas, both
of which have excellent signal/noise. MN is determined
by the peak area of molar concentration, which
has considerable noise on the long elution side of the
peak. This noise is inherent in a broad distribution
sample and arises from the fact that molar concentrations
are higher where the molar mass (and therefore
the light scattering signal) is lower. MN will therefore
be determined by light scattering with less precision
than MW where the distribution is broad. Narrow distribution
samples will not exhibit this problem.
In summary, the LALS detector provides sensitive,
simple and accurate molecular weight measurement
for GPC/SEC. By measuring directly at very low angle
it avoids the complexity, assumptions and errors
inherent in angular correction.
|
|