The Z average is the intensity weighted mean hydrodynamic size of the ensemble collection of particles measured bydynamic light scattering (DLS). The Z average is derived from a Cumulants analysis of the measured correlation curve,wherein a single particle size is assumed and a single exponential fit is applied to the autocorrelation function.
The DLS autocorrelation function, along with the exponential fitting expression, is shown below, where I is the scatteringintensity, t is the initial time, τis the delay time, A is the amplitude or intercept of the correlation function, B is the baseline, Dis the diffusion coefficient, q is the scattering vector, λois the vacuum laser wavelength, ñ is the medium refractive index, θ isthe scattering angle, k is the Boltzmann constant, T is the absolute temperature, η is the viscosity of the medium, and RHisthe hydrodynamic radius.
In the Cumulants approach, the exponential fitting expression is expanded to account for polydispersity or peak broadeningeffects, as shown below.
The expression is then linearized and the data fit to the form shown below, where the D subscript notation is used to indicatediameter. The 1st Cumulant or moment (a1) is used to calculate the intensity weighted Z average mean size and the 2ndmoment (a2) is used to calculate a parameter defined as the polydispersity index (PdI).
It is important to note here, that the Cumulants analysis algorithm does not yield a distribution – it gives only the intensityweighted Z average and the polydispersity index.
The figure below shows a graphical representation of the procedures employed within the Cumulants analysis to calculatethe Z average and polydispersity index.
The initial slope (blue) of the correlation function is related to the z-average size, the curvature (red) indicates the nonlinearitydue to the width of the polydispersity.
FAQs
The Z average is the intensity weighted mean hydrodynamic size of the ensemble collection of particles measured by dynamic light scattering (DLS).
What is the Z average in DLS? ›
The Z-average arises when DLS data is analyzed by the use of the technique of cumulants (1). Since the calculation of the Z-average is mathematically stable, the Z-average result is insensitive to noise, and that makes it a preferred DLS size parameter.
What is z average and pdi? ›
For dynamic light scattering, the Z-average is used to present the average particle size, which is the intensity-weighted average size. PDI (Polydispersity Index), defined by PDI=µ2/Γ , which indicates the width of the distribution. As a rule of thumb, the following PDIs are shown for different samples. Sample Type. ...
What is the PDI value in DLS? ›
The value of Polydispersity Index may vary from 0.01 (mono dispersed particles) to 0.5-0.7, whereas, PDI Index value > 0.7 indicated broad particle size distribution of the formulation. The particle size and particle size distribution are very critical factors for performance evaluation of nanoparticles.
What is a normal z-score? ›
If the number of elements in the set is large, about 68% of the elements have a z-score between -1 and 1; about 95% have a z-score between -2 and 2 and about 99% have a z-score between -3 and 3.
What is a good Z value? ›
What Is a Good Z-Score? 0 is used as the mean and indicates average Z-scores. Any positive Z-score is a good, standard score. However, a larger Z-score of around 3 shows strong financial stability and would be considered above the standard score.
What is the difference between Z average and peak? ›
The way z-avg and peak1 is calculated is different. Z- average assumes you have a monodisperse sample with a gaussian distribution and the peak1 is calculated assuming you have multimodal distribution. Therefore, your z-avg is highly sensitive to high intensity scatterers( big particles).
What is a good PDI value? ›
PDI value that is range from 0.1 to 0.25 suggests that the size distribution is narrow, but if this value bigger than 0.5 it shows a very broad distribution. If a scientist wanted to achieve long-term stability, it is important to arrange the PDI parameter to be as low as possible (Yeo, 2013).
What does zeta potential tell you? ›
The magnitude of the zeta potential gives an indication of the potential stability of the colloidal system. If all the particles in suspension have a large negative or positive zeta potential then they will tend to repel each other and there will be no tendency for the particles to come together.
What is a good PDI for DLS? ›
The Polydispersity Index is dimensionless and scaled such that values smaller than 0.05 are rarely seen other than with highly monodisperse standards. Values greater than 0.7 indicate that the sample has a very broad size distribution and is probably not suitable for the dynamic light scattering (DLS) technique.
Which PDI values are considered good? A PDI value of ≤ 0.1 is considered a highly monodisperse sample; PDIs up to 0.3 are considered mostly monodisperse; a PDI from 0.3 to 0.7 is somewhat polydisperse; and a PDI > 0.7 is considered highly polydisperse and unsuitable for DLS.
How do you calculate PDI? ›
The pdi for that peak is the square of the standard deviation divided by the square of the mean. As an example consider the peak was at a mean size of 9.3nm and the st dev was 4.4nm. As a result then the pdi for this peak would be: 4.4*4.4/(9.3*9.3) = 0.22.
What does Z mean in standard deviation? ›
The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.
How to calculate z value? ›
The formula for calculating a z-score is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation.
What is Z-average molecular weight? ›
The Z-average molecular weight emphasizes large molecules even more than Mw. It is useful for some calculations involving mechanical properties. The method uses a centrifuge to separate the polymer. The molecular weight distribution represents the frequency of the polymer lengths.
What is the range of average z-score? ›
Z-scores generally range from -3 standard deviations (which would fall to the far left of the normal distribution curve) up to +3 standard deviations (which would fall to the far right of the normal distribution curve).
