DTS Nano Series Training Course Size Day

ZETASIZER NANO SERIES AND HPPS TRAINING COURSE

Dr Mike Kaszuba (Product Technical Specialist)E-mail:[email protected]

PART ONETHEORY OF SIZE BY DLS 1

DLS and BROWNIAN MOTION

Dynamic Light Scattering or

Photon Correlation Spectroscopy or

Quasi-Elastic Light Scattering

measures Brownian motion

and relates it to size

2

BROWNIAN MOTION

Random movement of particles due to the bombardment

by the solvent molecules that surround them

2

BROWNIAN MOTION

Temperature must be accurately known because we need to know the viscosity

The temperature needs to be stable otherwise convection currents in the sample will cause non-random movements which will ruin correct size interpretation

The larger the particle the more slowly the Brownian motion will be

Higher the temperature the more rapid the Brownian motion will be

Velocity of the Brownian motion is defined by the translational diffusion coefficient (D)

2

STOKES-EINSTEIN EQUATION

d(H) =3 D

kT

D = diffusion coefficient

d(H) = hydrodynamic diameterk = Boltzmann’s constantT = absolute temperature= viscosity

where

2

HYDRODYNAMIC DIAMETER

The diameter which is measured in DLS is a value

that refers to how a particle moves within a liquid

It is called the HYDRODYNAMIC DIAMETER

The diameter that is obtained is the diameter of a

sphere that has the same translational diffusion

coefficient as the particle

2

HYDRODYNAMIC DIAMETER:Effect of Ionic Strength

1/K

1/K (Debye Length) is the thickness of the electrical double layer

It is dependent upon the ionic strength of the medium

In low ionic strength media (eg DI water) the double layer is extended

A latex standard diluted in DI water will give the wrong result (too high)

Particle Diameter

Hydrodynamic Diameter

3

HYDRODYNAMIC DIAMETER:Effect of Ionic Strength

1/K

1/K (Debye Length) is the thickness of the electrical double layer

It is dependent upon the ionic strength of the medium

In high ionic strength media the double layer is suppressed

Latex standards should be diluted in 10mM NaCl to suppress the double layer and hence give the correct result (ISO13321)

Particle Diameter

Hydrodynamic Diameter

3

HYDRODYNAMIC DIAMETER:Effect of Surface Coatings

A layer of molecules on the particle surface will slow the diffusion speed down

The hydrodynamic diameter will therefore be influenced

Reported hydrodynamic diameter

3

NON SPHERICAL PARTICLES

RAPID

SLOW

EQUIVALENT SPHERE

The hydrodynamic diameter reported will be based upon the sphere which has the same average diffusion coefficient as that of the particles

3

INTERACTION OF LIGHT WITH MATTER: Rayleigh Approximation

For small particles (d /10 or around 60nm for He-Ne laser) scattering is isotropic i.e. equal in all directions

Rayleigh approximation tells us that I d6 and I 1/4

where I = intensity of scattered light, d = particle diameter and = laser wavelength

4

INTERACTION OF LIGHT WITH MATTER: Rayleigh-Gans-Debye (RGD) Theory

A modification of Rayleigh theory

Used for particles somewhat larger than those described

as Rayleigh scatterers but with a small relative refractive

index

Used in HPPS software version 1 to convert the

measured Intensity distribution data into Volume

4

INTERACTION OF LIGHT WITH MATTER: Mie Theory

When the size of the particles become equivalent to the wavelength of the laser, the scattering becomes a complex function with maxima and minima with respect to angle

Mie theory is the only theory that explains correctly the maxima and minima in the plot of intensity with angle

This theory is used in version 3 of the HPPS and Nano Series software

4

INTERACTION OF LIGHT WITH MATTER: Mie Theory

Polystyrene latex spheres at 174.65o: RIParticle= 1.59, AbsParticle= 0.001, RIMedium= 1.33, = 633nm

5

OPTICAL CONFIGURATION OF THE NANO ZS

6

UNIQUE FEATURES OF THE HPPS, NANO S AND NANO ZS (1): NIBS

The HPPS, Nano S and Nano ZS measures the

scattered light at an angle of 173o

This is known as backscatter detection

The optics are not in contact with the sample

The detection optics are therefore said to be non-

invasive

7

Several reasons for using NIBS detection: The laser does not have to travel through the entire

sample This reduces multiple scattering effects This means that higher concentrations of sample can

be measured Contaminants such as dust particles within the

dispersant scatter light mainly in the forward direction Therefore backscatter detection reduces the effects

of dust

7

UNIQUE FEATURES OF THE HPPS, NANO S AND NANO ZS (1): NIBS

The measurement position within the cuvette of the HPPS, Nano S and Nano ZS can be changed

This allows a much larger range of sample concentrations to be measured

In the HPPS, the measurement position is changed by moving the cuvette

In the Nano S and Nano ZS, the measurement position is changed by moving the focussing lens.

The cuvette position is automatically determined by the software

7

UNIQUE FEATURES OF THE HPPS, NANO S AND NANO ZS (2): VARIABLE MEASUREMENT POSITION

Small particles or dilute samples Measure close to cell centre to maximise measurement volume and minimise flare

7


Concentrated samplesMeasure close to the cell wall to reduce the light path through

the sample and hence minimise multiple scattering

7


HOW DOES A DLS EXPERIMENT WORK?

We need a way of measuring the Brownian motion

of particles and relating this to size

In DLS, the intensity fluctuations of scattered light

arising from Brownian motion are measured.

How do these fluctuations in the intensity of

scattered light arise?

8

THE SPECKLE PATTERN

LaserIncident Beam

Axis

SampleCell

ScreenSpecklePattern

8

BROWNIAN MOTION AND SCATTERED LIGHT

Screen

Two beams interfere and‘cancel each other out’

resulting in a decreased intensity in the scattered light

Consider 2 stationary particles

9


Screen

Two beams interfere and‘enhance each other’

resulting in an increased intensity in the scattered light

9


Many scattered beams interfere with one anotherresulting in a very complex

intensity pattern of ‘speckles’

Screen

Consider many

particles

9

INTENSITY FLUCTUATIONS

For a system of particles undergoing Brownian motion, a

speckle pattern is observed where the position of each

speckle is seen to be in constant motion

This is because the phase addition from the moving

particles is constantly evolving and forming new patterns

The rate at which these intensity fluctuations occur will

depend on the size of the particles

9

INTENSITY FLUCTUATIONS

Large Particles

Small Particles

Time

Time

Inte

nsity

Inte

nsity

10

HOW A CORRELATOR WORKS

Inte

nsity

Time

0 t tt t t

11

HOW A CORRELATOR WORKS

If the particles are large, the signal will be changing

slowly and the correlation will persist for a long time

If the particles are small and moving rapidly then the

correlation will disappear more rapidly

11

TYPICAL CORRELOGRAM FROM SAMPLE CONTAINING LARGE PARTICLES

12

0

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0.8000

0.9000

0.1000 10. 1000. 1.e+5 1.e+7 1.e+9

Cor

rela

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ent

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Raw Correlation Data

TYPICAL CORRELOGRAM FROM SAMPLE CONTAINING SMALL PARTICLES

12

0

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0.1000 10. 1000. 1.e+5 1.e+7 1.e+9

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Raw Correlation Data

THE CORRELATION FUNCTION

The correlation function G()

= <I(t).I(t+)>

where is the time difference (the sample time) of the correlator

13


G() = A[1 + B exp(-2)]where:- A = the baseline of the correlation functionB = intercept of the correlation function = Dq2where:-D = transational diffusion coefficientq = (4n / o) sin (/2)where:-n = refractive index of solutiono = wavelength of the laser=scattering angle

For monodisperse particles the correlation function is

13


G() = A[1 + B g1()2]For polydisperse particles the correlation function is

where:- g1() is the sum of all exponential decayscontained in the correlation function

13

OBTAINING SIZE FROM THE CORRELATION FUNCTION

Size is obtained from the correlation function by using various algorithms

In the DTS software, the mean diameter (z-average) and the width of the distribution (polydispersity) are obtained by using the cumulants analysis as described in ISO13321

13

OBTAINING SIZE FROM THE CORRELATION FUNCTION

The size distribution displayed is obtained from a non-negative least squares (NNLS) analysis

The size distribution is a plot of the relative intensity of light scattered by particles in various size classes

There are 70 size classes logarithmically spaced It is an INTENSITY distribution

13

EVALUATING THE CORRELATION FUNCTION

If the INTENSITY distribution is a fairly smooth peak, there is little point in conversion to a VOLUME distribution using Mie theory

However, if the INTENSITY plot shows a substantial tail, or more than one peak, then a VOLUME distribution will give a more realistic view of the importance of the tail or second peak

NUMBER distributions are of little use because small errors in data acquisition can lead to huge errors in the distribution by number and are not displayed

13

INTENSITY, VOLUME AND NUMBER DISTRIBUTIONS

NUMBER43

VOLUME= r3

INTENSITY= d 6

Diameter (nm)

Rel

ativ

e %

in c

lass

5 10 10050

1 1

Diameter (nm)

Rel

ativ

e %

in c

lass

5 10 10050

1

1000

Diameter (nm)R

elat

ive

% in

cla

ss5 10 10050

1

1,000,000

Mixture containing equal numbers of 5 and 50nm spherical particles

THE CUMULANTS ANALYSIS

The decay in the correlation function [G] is exponential

The simplest way of obtaining a size from this curve is to use the cumulants analysis as described in ISO13321

A 3rd order fit of a polynomial to a semi-log plot of the correlation function is performed

If the distribution is polydisperse, the semi-log plot will be curved

14


ISO13321 states that a 3rd order fit of a polynomial should be used

Ln[G1] = a + b + c2

The value of b = z-average diffusion coefficient 2c/b2 = polydispersity index (the width of the

distribution) This method only gives a mean and a width and is

only a good description for reasonably narrow monomodal samples

It is an INTENSITY mean size15


0.2

0.3

0.5

0.4

0.7

0.6

0.8

0 1 20.5 1.5

Ln G1

Time (ms) (x 103)

b = z-average diffusion coefficient

2c/b2 = polydispersity

index

15

POLYDISPERSITY INDEX

0 to 0.05 - Only normally encountered with latex standards or particles made to be monodisperse

0.05 to 0.08 - Nearly monodisperse sample. PCS cannot normally extract a distribution within this range

0.08 to 0.7 - This is a mid-range polydispersity, it is the range over which the distribution algorithm based on NNLS best operates over

Greater than 0.7 - Very polydisperse. Care should be taken in interpreting results as the sample may not be suitable for the technique, e.g. a sedimenting high size tail may be present

16

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DETERMINATION OF THE INTENSITY SIZE DISTRIBUTION

The intensity distribution shown in the DTS software is obtained by analysis of the correlation function by a non-negative least squares (NNLS) analysis

The analysis of light scattering data can produce a number of possible solutions for the same set of data (smooth distributions/multiple peaks)

In order to cater for different applications, two analysis models are available in the software

Both of these algorithms are NNLS with the only difference being the level of smoothing applied to the data prior to analysis


17


A general purpose algorithm is available that is suitable for most samples

However this will not maximize the resolution available by the technique where some information is known about the sample

A second analysis model is provided so that knowledge about the sample can be used to improve the measurement resolution

17


For a sample where no information is available, then

the general purpose model should be used

For a sample known to be multimodal, such as a

synthetic mixture of materials, or a single molecular

species containing aggregates, then multiple narrow

modes should be selected

17

PART TWODLS EXPERIMENTAL 18

UPPER SIZE LIMIT OF DLS

DLS will have an upper limit with respect to size When particle motion is not random (e.g.

sedimentation, creaming) DLS is not the correct technique to use

Upper limit is set by the onset of sedimentation Upper size limit is therefore sample dependent No advantage in suspending particles in a more

viscous medium to prevent sedimentation because Brownian motion will be slowed down by the same extent

19


Another factor that needs to be considered is the number of particles that will be present in the detection volume

The amount of scattered light produced by large particles would be sufficient to make successful measurements

However, the number of particles in the scattering volume may be so few that severe fluctuations of the momentary number of particles in the scattering volume will occur

This results in a phenomenon called number fluctuations which leads to problems in the definition of the baseline of the correlation function

19


In order to overcome number fluctuations, the concentration of the sample needs to be increased

This may lead to multiple scattering effects which can be minimised by using backscatter detection (such as the Nano S)

This is the reason why the upper size limit of a backscatter system is higher than an instrument which has 90o detection

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DETECTION VOLUME: Nano S90/Nano S

19


Detector

Laser

Detectionvolume

19


Detector Laser

Detectionvolume

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LOWER SIZE LIMIT OF DLS

Lower size limit depends on

the sample concentration

refractive index of sample compared to diluent

laser power and/or wavelength

detector sensitivity

optical configuration of the instrument

The lower size limit is typically 2nm

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SAMPLE PREPARATION:Sample Concentration

Measurements can be made on any sample in which the particles are mobile

However, each type of sample material has its own ideal range of concentration where measurements should be made

If the concentration is too low, there may not be enough light scattered to make a measurement

This is unlikely in the Nano S/Nano ZS and HPPS except in extreme circumstances

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If the sample is too concentrated, an effect called multiple scattering may occur

This will reduce the apparent size and the intercept value (signal to noise ratio)

When multiple scattering is insignificant, the size and intercept will be independent upon concentration

Instruments which have backscatter detection extend the concentration over which samples can be measured before seeing the effect of multiple scattering

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Sample Concentration For DLS Measurements

CORRECT CONCENTRATION

z-A

VE

RA

GE

DIA

ME

TER

(nm

)

SAMPLE CONCENTRATIONLOW HIGH

MULTIPLESCATTERING CONVENTIONAL

DLS INSTRUMENT

BACKSCATTERDLS INSTRUMENT

CORRECT CONCENTRATION

MULTIPLE SCATTERING

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The upper limit of concentration is also governed by the onset of particle/particle interactions

This phenomenon will influence the diffusion speed of particles and hence influence the apparent size

20


The contribution of multiple scattering and

particle/particle interactions at different concentrations

for a particular sample on the apparent size is not

known

During method development, determining the correct

sample concentration may involve several size

measurements at different concentrations

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An important factor in determining the maximum concentration a sample can be measured at is the size of the particles

Particle Size Minimum Recommended Concentration

<10nm 0.5g/l Only limited by thesample materialinteraction, aggregation, gelation etc.

10nm to 100nm 0.1mg/l 5% mass (assuming a density of 1gcm-3)

Maximum Recommended Concentration

100nm to 1m 0.01mg/ml 1% mass (assuming a density of 1gcm-3)

>1m 0.1g/l1% mass (assuming a density of 1gcm-3)

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SAMPLE CONCENTRATION:Minimum Concentration For Small Particles

For particle sizes smaller than 10nm, the major factor in determining the minimum concentration is the amount of scattered light the sample generates

The concentration should generate a minimum count rate of 10kcps in excess of the scattering from the dispersant

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The maximum concentration will be set by the properties of the sample itself

Examples: Gelation or similar: A gel is unsuitable for

measurement by DLS Particle/particle interactions: These will affect the

diffusion rate of the particles leading to an incorrect result

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SAMPLE CONCENTRATION:Maximum Concentration For Small Particles

SAMPLE CONCENTRATION:Minimum Concentration For Large Particles

Even for larger particles, the minimum concentration is effectively still a function of the amount of scattered light, though the additional effect of “number fluctuations” must be taken into account

Such fluctuations must be avoided and this determines the lower limit for the required concentration and for a lower limit in the number of particles

The number of particles in the scattering volume should be at least 1000 (any number in the range 500 to 1000 is acceptable)

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SAMPLE CONCENTRATION:Maximum Concentration For Large Particles

Determined by multiple scattering

The Nano S/Nano ZS and HPPS is not sensitive to multiple scattering due to NIBS

However, with increasing concentration, the effect of multiple scattering becomes more and more dominant, until the results will be distorted

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SAMPLE CONCENTRATION:The Dilution Medium The diluent should be the same as the continuous

phase of the original sample

The equilibrium of absorbed species between the surface and bulk solution will be perfectly preserved if the diluting liquid is obtained form the original sample

This could be done by filtering or centrifuging

If this is not possible, the continuous phase should be made up to be as close as possible to that of the sample

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SAMPLE PREPARATION:Filtration

The dilution medium should be carefully filtered

before use to avoid contaminating the dilute sample

Aqueous dispersants are normally filtered at 0.2

microns, non polar dispersants can be filtered down

to 10 or 20nm

22

SAMPLE PREPARATION:Ultrasonication

Very useful preparation technique if used properly.

Minerals (e.g. TiO2) are ideal candidates for

dispersion by ultrasound

The particle size of some materials (e.g. carbon black) may depend purely on the power and length of sonication

Emulsions should not be ultrasonicated, this is a good technique for preparing them in the first place

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CHECKING CORRECT INSTRUMENT OPERATION

DLS instruments cannot be calibrated because they

use first principles in their measurement protocol

They can be verified that they are working correctly

by measuring sizing standards

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CHECKING CORRECT INSTRUMENT OPERATION:Latex Standards

Polymer latex spheres are very commonly used to verify

the operation of DLS instruments.

Standards suitable for DLS range from 20nm to 900nm

The result quoted on Duke Scientific latex standards is

the certified transmission electron microscopy result

The DLS result is quoted in the specification sheet and is

not a certified value

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SAMPLE PREPARATION OF LATEX STANDARDS

All latex standards are supplied at a concentration that is too high for DLS measurements

Latex standards should be diluted in filtered 10mM NaCl to suppress the electrical double layer (ISO 13321)

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DATA INTERPRETATION

The quality of the data obtained from the measurement is essential in determining how well the distribution algorithm is going to perform

The better the quality of the data, the more repeatable the answers obtained will be

In order to aid the interpretation of data, it is advised that various report pages and record view parameters are added to the default selection in the DTS software

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DATA INTERPRETATION

REPORTS

Correlogram Report Cumulants Fit Report Fit Report

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DATA INTERPRETATION

REPORTS

Correlogram Report Cumulants Fit Report Fit Report

PARAMETERS

Mean Count Rate Measured Intercept Measurement position Cumulants fit error Multimodal fit error Attenuator

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DATA INTERPRETATION:CORRELOGRAMS

The correlogram shows the correlation data displayed as the correlation coefficients displayed in each channel and provides information about the sample

The shape of the curve will show some obvious problems that may be present

The correlogram ought to be checked for noise contained within the data

Noisy data can result for various reasons; count rate too low, instability of the sample or external effects such as vibration or interference from another source

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rela

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Raw Correlation Data Large particles

Medium range polydispersity

Presence of very large particles/ aggregates (baseline not flat)

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0

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Raw Correlation Data Very small particles

Medium range polydispersity

No large particles/ aggregates present (flat baseline)

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0

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rela

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Raw Correlation Data Very large particles

High polydispersity

Presence of very large particles/ aggregates present (noisy baseline)

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CUMULANTS/DISTRIBUTION ALGORITHM FITS

The cumulants fit report shows the quality of the cumulants fit to the measured data indicating whether the z-average diameter and polydispersity obtained for a particular measurement are reliable

A fit error of less than 0.005 is considered good

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0.1000

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0.8000

0.9000

1. 10. 100. 1000.

G1

Cor

rela

tion

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tion

Time (us)

Cumulants Fit

GOOD FIT ERROR 0.00037

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0.11

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0.13

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0.1700

0.18

10. 100. 1000. 10000.

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Cumulants Fit

GOOD FIT ERROR 0.008

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COUNT RATE REPEATABILITY

Perform at least 3 repeat measurements on the same sample

The count rates should be all within a few percent of one another

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Count ratedecreases withsuccessive measurements

Particle sedimentation is occurring

Remove sedimenting particles and measure only particles suitable for technique

COUNT RATESYMPTOM

POSSIBLE EXLANATION

ACTION

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Particle creaming is occurring

Prepare a better stabilised dispersion to prevent creaming

COUNT RATESYMPTOM

POSSIBLE EXLANATION

ACTION

Try and disperse sample in a more suitable dispersant to prevent particles dissolving

Particles are dissolving or breaking up

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COUNT RATESYMPTOM


Formation of bubbles during the duration of the measurement

Remove bubbles, de-gas dispersant

POSSIBLE EXLANATION

ACTION


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Count rateincreases withsuccessive measurements

Dispersion instability present. Aggregation, flocculation etc. occurring

Prepare a better stabilised dispersion

COUNT RATESYMPTOM

POSSIBLE EXLANATION

ACTION

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Measurements taken too soon after instrument was switched on - laser still warming up

Allow instrument 30 minutes to warm up after switching on before beginning measurements

COUNT RATESYMPTOM

POSSIBLE EXLANATION

ACTION

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COUNT RATESYMPTOM




POSSIBLE EXLANATION

ACTION


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COUNT RATESYMPTOM

POSSIBLE EXLANATION

ACTION

Count rate is random between successive measurements

Dispersion instability present. Sample is changing with time – aggregating, breaking up etc.

Prepare a better stabilised dispersion

Sample not suitable for PCS

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Sample contains large particles

Remove by filtration or centrifugation or allow to settle before commencing measurement

POSSIBLE EXLANATION

ACTIONCOUNT RATESYMPTOM

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COUNT RATESYMPTOM





POSSIBLE EXLANATION

ACTION

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COUNT RATESYMPTOM



Sample not properly mixed

Ensure thorough mixing

POSSIBLE EXLANATION

ACTION

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z-AVERAGE DIAMETER REPEATABILITY

The z-average diameter is calculated from the cumulants (monomodal) analysis

Repeat measurements should be within 1 or 2 percent of one another

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SIZE SYMPTOM POSSIBLE EXLANATION

ACTION

Size decreaseswith time

Temperature notstable

Allow plenty of time for temperatureequilibration (1 min per degreeplus 5 mins)

Sample not stable - solubilisation of break up ofparticles

Prepare a betterstabiliseddispersion

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SIZE SYMPTOM POSSIBLE EXLANATION

ACTION

Size increaseswith time

Temperature notstable

Allow plenty of time for temperatureequilibration (1 min per degreeplus 5 mins)

Sample not stable - aggregation ofparticles

Prepare a betterstabiliseddispersion

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REPEATABILITY OF SIZE DISTRIBUTIONS

The size distributions displayed are derived from a NNLS analysis and these should be checked for repeatability in terms of the peak positions and % areas obtained

If the distributions are not repeatable then it is suggested that the measurements are re-taken using longer measurement duration

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EXTRACTING THE MEASUREMENT SOP

The ability to highlight any measurement record and to extract the SOP is a very powerful tool in looking at data quality

The exact setup which was used to take that measurement can be accessed and any obvious errors in the measurement procedure can be highlighted (for example, incorrect measurement position for sample type, manual override of the measurement duration etc)

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DTS Nano Series Training Course Size Day

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