US 11,441,991 B2Granted

Multi-angle dynamic light scattering

AssigneeMalvern Panalytical Limited

InventorsDouglas Hamilton, Jason Corbett

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Abstract

A method of determining particle size distribution from multi-angle dynamic light scattering data, comprising: obtaining a series of measured correlation functions g(θi) at scattering angles θi; and solving an equation comprising [ g ⁡ ( θ 1 ) … g ⁡ ( θ n ) ] = [ α 1 ⁢ K ⁡ ( θ 1 ) … α n ⁢ K ⁡ ( θ n ) ] ⁢ x , wherein: K(θi) is the instrument scattering matrix computed for angle i, x is the particle size distribution, and αi is the scaling coefficient for angle i. The method comprises using the steps: a) providing initial estimates for scaling factors α2 to αn, and defining α1=1; b) iterating scaling factors α2 to αn using a non-linear solver; c) solving for x using a linear solver; d) calculate residual; e) repeat steps b) to d) while the residual is greater than a predefined exit tolerance.

Claims14

Dependent claims

A method of determining particle size distribution from multi-angle dynamic light scattering data, comprising:

a light source configured to illuminate a sample on or in a sample holder, wherein the sample comprises a fluid with suspended particles;
a detector configured to detect light scattered by the particles in the sample;
and
a processor, wherein the processor is configured to:
determine a series of measured correlation functions g(θi) at scattering angles θi from the scattered light detected by the detector;
solve an equation comprising:
[
g
⁡
(
θ
1
)
…
g
⁡
(
θ
n
)
]
=
[
α
1
⁢
K
⁡
(
θ
1
)
…
α
n
⁢
K
⁡
(
θ
n
)
]
⁢
x
wherein:
KW is the instrument scattering matrix computed for angle i, x is the particle size distribution, and α1 is the scaling coefficient for angle i;
a) provide initial estimates for scaling factors a2 to an, and defining a1=1;
b) iterate scaling factors a2 to an using a non-linear solver;
c) solve for x using a linear solver;
d) calculate residual;
e) repeat steps b) to d) while the residual is greater than a predefined exit tolerance;
determine a resulting particle size distribution when the residual is not greater than the predefined exit tolerance;
and
display the resulting particle size distribution.

52 more elements

A method of determining particle size distribution from dynamic light scattering data, comprising:

a light source configured to illuminate a sample on or in a sample holder, wherein the sample comprises a fluid with suspended particles;
a detector configured to detect light scattered by the particles in the sample and determine measurement data from the scattered light;
and
a processor, wherein the processor is configured to:
determine, from the scattered light detected by the detector, measured correlation functions g(θ1) to g(θn);
solve an equation of the form:
[
g
⁡
(
θ
1
)
…
g
⁡
(
θ
n
)
]
=
[
α
1
⁢
K
⁡
(
θ
1
)
…
α
n
⁢
K
⁡
(
θ
n
)
]
⁢
x
wherein:
g(θi) is the measured correlation function for measurement time i, corresponding with a scattering angle θi, K(θi) is the instrument scattering matrix computed for the angle θi, x is the particle size distribution and αi is the scaling coefficient for measurement time i (with a1=1);
the vector x takes the form:
[x1, xN, n1, . . . , nn], where x1 to xN are the scattering intensities corresponding with each size bin, and the terms n1 to nn are noise intensities corresponding with each of the measurement times or angles;
and
columns in K are computed as the expected instrument response according to each element in x, with columns in K at indexes according to elements x1 to xN calculated for each correlator lag-time,τ and angle, θ, and columns at indexes n1 to nn calculated as a computed noise contribution for each correlator lag-time,τ, at each angle, θ, based on an assumption about the characteristics of the noise;
determine a resulting particle size distribution based at least on the computed expected instrument response and the computed noise contribution;
and
display the resulting particle size distribution.

51 more elements

A method of determining a particle size distribution, x, from a dynamic light scattering measurement, comprising:

a light source configured to illuminate a sample on or in a sample holder, wherein the sample comprises a fluid with suspended particles;
a detector configured to detect light scattered by the particles in the sample and measure a time sequence of scattering intensity;
and
a processor, wherein the processor is configured to:
determine a measured correlation function, g, derived from the time sequence of scattering intensity;
solve a system of linear equations comprising:
[
g
0
]
=
[
K
γ
⁢
Γ
]
⁢
x
by minimising the sum of residuals:
∥Kx−g∥2+∥γΓx∥2
where K is an instrument scattering matrix, r is a regularisation matrix, and γ is a regularisation vector comprising regularisation coefficients for each particle size in the particle size distribution, x;
determine a resulting particle size distribution based at least on the regularisation vector;
and
display the resulting particle size distribution.

22 more elements

Dependencies are inferred from the claim text.

Facts

Application: 16/965,204Filed 6 Feb 2019
Priority: EP 181554286 Feb 2018
Published: US 2021/0063295 A14 Mar 2021
Granted: 13 Sep 2022
Term ends: Not estimatedThe source records don’t support an estimate.

Classification5 codes

G01N 15/0211
By optical means: investigating a scatter or diffraction pattern
G01N 2015/0222
Investigating a scatter or diffraction pattern: from dynamic light scattering, e.g. photon correlation spectroscopy
G01N 2015/025
By optical means: methods for single or grouped particles
G01N 2021/4711
Angular selective: multiangle measurement

Family

US 2021/0063295 A1Pre-grant publication · published 4 Mar 2021
US 11,441,991 B2This patent

From the US filing history. Foreign family members aren’t listed.

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