DE2440376B2 - Particle size analysis of polydisperse systems with the help of laser light scattering - Google Patents

Description

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The invention relates to a method for the particle size analysis of polydisperse systems, in particular dye dispersions, with the aid of laser scattered light measurement, in which the frequency spectrum of the scattered light is first measured for each scattering angle Θ, then the calf width Av is determined for each frequency spectrum and from this the Function Av (k ² ) is calculated, where k is a known function of the scattering angle Θ. Furthermore, the invention relates to a device for carrying out this method. The device is based on a scattered light spectrometer with a laser light source, a measuring cuvette and a photodetector for the coherent demodulation of the scattered light, a frequency analyzer for the spectral decomposition of the demodulated signal and a computer for determining the particle parameters.

The optical methods have the particular advantage that the measuring probe practically does not light causes mechanical disturbances of the system and that optical measurements can be carried out very quickly in the In contrast to all processes that are linked to mechanical particle transport. Under the The scattered light method has hitherto mainly been the measurement of the scattering intensity as a function of the scattering angle have been applied, all of which are based on Mie's scattering theory. These methods are in theirs The range of application is limited because it is only relatively narrow distribution widths and, among these, only spherical ones Particles with known optical refractive indices and absorption indices can be analyzed. The following is described a diffuse light method, which is essentially different from this, with which dye suspensions in the Particle range below about 1 μπι good results were achieved.

The method uses the known fact that the random, statistical movement of monodisperse scattering particles due to the optical Doppler effect (FIG. 1) leads to a defined broadening of the spectrum of the scattered light (FIG. 2). It is known that the broadening of the scattered light of an incident light beam with an exactly monochromatic spectrum is Lorentz-shaped with half a half width Av & which is given in units of the reciprocal period of oscillation

η =

2π

(Dr translational diffusion coefficient;

(4 π 11 / X ₀ ) sin (0/2), scatter vector;

Scattering angle;

Vacuum wavelength of the incident

Light;

Refractive index of the medium.)

By measuring the frequency width of the scattered light, the diffusion coefficient of Determine translation. This in turn is based on the Sokes-Einstein equation, which is valid for spherical particles

K _n T

linked to the particle radius r (Kb = Boltzmann factor, T = absolute temperature, η = viscosity of the medium). The application of this relation to non-spherical particles yields a particle size which corresponds to the radius of a spherical particle which is equivalent in terms of the diffusion coefficient. For particles suspended in water (20.degree. C.) in the radius range from 25 nm to 500 nm, at a scattering angle of 90 "value widths Avs of about 500 to 24 Hz are obtained.

The extraordinarily high spectral resolution v / 4vs of about 3 χ 10 ^{13 is} necessary for such measurements

0.6μ) = 5χ 10 »Hz;

The outlay on equipment is nevertheless very low. A gas laser is used as the radiation source, e.g. B. a He-Ne laser with emission at A ₀ = 0.6328 µm.

The frequency analysis of the scattered light takes place after demodulation of the scattered light by electrical means, either according to the heterodyne or the homodyne method. The demodulation of the scattered light spectrum, i.e. its transformation into a low-frequency range, is achieved by differential frequency formation, in the heterodyne case between scattered light and direct laser light, in the homodyne case between the individual components of the scattered light spectrum itself Interference pattern, the spatial frequency of which also decreases with decreasing aperture angle. A light channel so narrow that the entire effective detector surface is covered by only one coherence surface is blocked by two diaphragms, ie is irradiated at all times by a uniform intensity level. This intensity now changes over time with the difference frequencies (beat frequencies) of all light components captured. The signal current of the detector changes accordingly. It is then the frequency analysis of the light passing through an electronic frequency analysis of the signal voltage, the square of which represents the heterodyne or homodyne performance spotting tower of the scattered light, when the half width of a Lorentzian-shaped scattered light spectrum - as above - with Avs and Ανι, α or Avhom corresponding to the half-value widths of the heterodyne or homodyne measured power spectrum are referred to, then applies

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and both the heterodyne and the homodyne spectrum are again Lorentz-shaped. Since it is generally easier to measure Homodynspektren that more representation is limited to the case of homodyne detection The aim is then in each case the half-width of Homodynspektrums are denoted by Av.

In the method for particle size analysis according to the preamble of this application, the frequency spectrum of the scattered light is first measured at discrete scattering angles Θ, then the half- width Av is determined for each frequency spectrum and the function Av (k ² ) is calculated from this

According to formula 1, a straight line with the slope Dt results for monodisperse systems for Av (k ² ) . The particle radius r is then obtained from the formula for the translational diffusion coefficient Dj-.

Test measurements were carried out on spherical polystyrene latices which were satisfactory in every respect. The latex radii specified by the manufacturer could be confirmed with great accuracy from the scattered light measurement. In addition, plotting the frequency width Av over the square of the scattering vector k ² resulted in the theoretically required linear relationship (FIG. 3). The evaluation of the spectral measurement at an angle θ to determine the half- width Av is done in such a way that a Lorentz distribution is optimal on the measurement curve!

is adjusted, the half-width of which then represents the result (FIG. 4).

After these tested on monodisperse particles measurement and evaluation polydisperse, suspended in water and other liquids, organic dye particles have been investigated The result of these measurements was a non-linear course of the Av (J ²⁾ curve such that in the angular range below about 130 ° uniform positive curvature occurs Above about 130 ° the curve then rises a little less and can change depending on the sample, amount and sign of the curvature (see Fig. 7 and 8). The common characteristic of the investigated polydisperse systems was a positive curvature of the Av (k ² ) curve in the angular range up to about 130 °.

The method described above can therefore no longer be used.

The invention is now based on the object of making a statement about, even in the case of polydisperse systems to obtain the characteristic particle data with the help of laser light scattering.

According to the invention, this object is described in the characterizing part of the claim Way solved further developments of the invention as well as one for carrying out the invention Apparatus suitable for the method are described in the subclaims.

The method according to the invention allows it to be carried out in conjunction with the new measuring apparatus a complete particle size analysis in a few minutes. This made use as a routine analysis device The characteristic particle data obtained in this way agree very well with the Values that you can e.g. B. using the disc centrifuge measuring method receives

In the following, the invention will be described in greater detail on the basis of an exemplary embodiment shown in the drawing described. It shows

F i g. 1 the principle of frequency change in laser light scattering,

F i g. 2 the frequency broadening as a result of the scattering process,

Fig. 3 Av (k ² ) for monodisperse latices,

4 shows the evaluation by adapting a Lorentz function,

F i g. 5 the structure of the scattered light cuvette,

F i g. 6 the construction of the measuring apparatus,

Fig. 7 Av (k ¹ ) diagram of a polydisperse dye dispersion,

Fig. 8 Av (k ² ) diagram of a polydisperse dye dispersion.

FIGS. 1-4 have already been explained in the introduction. FIG. 5 shows schematically the structure of FIG Stray light cuvette. The cuvette consists of the cylindrical glass vessel 1 with the two sides Tube sockets 2 and 3. The two tubes 2 and 3 are angled upwards in the direction of the cuvette axis. The tube 2 is placed approximately in the middle of the cuvette and consists of black glass. The cuvette is in the Apparatus adjusted so that the primary light beam 4 is incident on the axis of the lateral tube extension 2 PriirSrstrahl is then outside the cylindrical measuring space 1 by multiple reflection and absorption practically completely extinguished in the pipe wall. The tube 2 thus acts as a light trap for the primary beam 4th

The bottom of the cylindrical measuring vessel 1 is conical. At its lowest point this is

Tube 3 attached. It is used to suck off the measuring liquid 5 and to fill in rinsing liquids. This arrangement allows an automated cyclic loading of the cuvette alternately Rinsing and measuring liquid so that a large number of samples can be measured automatically.

In Fig. 6 the optical and electronic part of the measuring apparatus is shown schematically. The solid lines represent the signal and data flow, the dashed lines indicate the control functions. ι ο The laser beam of a He-Ne laser 6 (A ₀ = 0.6328 μπι) radiating in the TEMoo oscillation is focused by means of a long focal length lens 7 (f = 60 cm) in a cuvette 8 in which the to be examined Substance is located The diameter of the beam in the cuvette 8 is approximately 100 μιπ. Between the cuvette 8 and the laser 6 there is a shutter 9 which can be completely closed.

The light emerging from the measuring cell 8 scattered light passes through a double pinhole diaphragm assembly 10 onto the photocathode of a photomultiplier 11, and is demodulated there and about 10 ⁷ fold amplified with double hole aperture array 10, the aperture can be reduced, so that the entire active detector area of one coherence area is covered. The intensity level detected with the detector is then spatially constant. In this way, the scattering angle Θ can be set in the range from 10 ° to 170 ° in steps of, for example, 10 ° with an accuracy of ± 1/150 °.

The frequency spectrum of the scattered light is shown in FIG. 2 shown The spectral decomposition takes place according to the homodyne method. The frequency components present in the scattered light are mixed with one another due to the non-linear characteristic curve of the photomultiplier 11. The mixing results in sums and difference frequencies. While the sum frequencies are in the optical area and are not displayed, the difference frequencies (beat frequencies) are in the low frequency range. The frequency analysis of the scattered light can then be carried out by an electronic frequency analysis of the signal voltage tapped at the working resistor of the photomultiplier. Under the condition of the homodyne frequency analysis, it applies to Lorentz-shaped power spectra of the scattered light (half-width Avs) that the homodyne electrical power spectra are also Lorentz-shaped (half- width Avhon) and that the condition Avhom = 2 · Av s is also fulfilled

The low-frequency signal is amplified at the preamplifier 12 and then fed to the frequency analyzer 13. The frequency analyzer 13 is a so-called real-time analyzer and consists of a large number of fixed-frequency filters connected in parallel to which the signal is available at the same time Frequency analyzers are used, e.g. B. also a Fourier analyzer. The output signal at the filters in the frequency analyzer 13 is scanned by the scanner 14 under computer control and stored in the computer 15. From the stored data, the computer determines the half- width Av of the frequency distribution while smoothing the signal with statistical fluctuations. The computer 15 then determines the mean particle diameter d and the half width α of the particle size distribution by adapting a logarithmic normal distribution to the set of values per /,} according to the method of the least square error. The evaluation proceeds in such a way that each value pair (Avi, k ² j) is assigned an equivalent diameter ^ / according to the following formulas:

Λ r,

= 1 · D ₁ , Ιή

D ₁ =

K _B T

3 π »ι d;

As explained above, Av 7 is half the width at half maximum of the measured homodyne frequency spectrum of the scattered light, ki is the scattering vector, which is essentially a function of the scattering angle Θ.

^ki -

(ΊΓ)

^sin

/ ΘΛ

This gives a set of values for particle diameters di, which is interpreted as the frequency density. The logarithmic normal distribution, which is characterized by the two parameters d and σ, is then optimally adapted to this frequency density under the condition of the smallest error square

The computer output is carried out by a writer or printer 16, the operating dialog with the Computer through the control unit 17.

The control of the measuring apparatus takes place fully automatically by the computer 15, which operates in real time works In addition to the arithmetic and storage functions already mentioned, the following control functions executed by the computer:

1. Close the aperture 9 in the primary laser beam to determine the noise level.

2. Setting the angle Θ / for measuring the scattered light according to a preselected angle program.

3. Determination and adaptation of the optimal gain of the preamplifier 12 to the intensity of the scattered light to be measured.

4. Setting the integration time of the filters in the frequency analyzer 13.

5. Setting the number, frequency and sequence of the signal polling at the output of the filter by the Scanner.

6. Monitoring for overloading of the frequency filter 8 and the photomultiplier 11.

The automatic control of the measuring function allows a significant reduction in the analysis time Der The computer controls the integration time of the filters in the frequency analyzer 13, the sequence and the number of the scans in such a way that the measurement time at a specified measurement accuracy is minimal. This control of the measuring process enables a complete Particle analysis in a few minutes with minimal operator effort. In contrast, the Analysis times for other comparable measuring methods between a few hours and a few days. the Operation is limited to filling the sample into the measuring cell 8 and some analysis-specific items Entries on the operating unit 17 in dialogue with the computer 15. The entire measuring process up to The finished protocol and the return of the device to a defined initial state is therefore handled by the Measuring apparatus carried out automatically

In addition 8 sheets of drawings

Claims (4)

Patent claims: 1. A method for the particle size analysis of polydisperse systems, in particular dye dispersions, with the aid of laser scattered light measurement, in which initially for each scattering angle Θ; the frequency spectrum of the scattered light is measured, then the half-width Av is determined for each frequency spectrum and the function Av ίο (k ² ) is calculated from this, where k is a known function of the scattering angle Θ, -, characterized in that zur_ determination of the mean particle diameter d and a variable characterizing the width σ of the particle size distribution, the characteristic curvatures of the function Av (&) in the range 10 ° <Θ, - £ 170 ° can be determined. 2. The method according to claim 1, characterized in that the positive curvature of the function Av (k ² ) is determined in the angular range 10 "<Θ, <130 °. 3. Apparatus for performing the method according to claim 1 and 2, consisting of a scattered light spectrometer with a laser light source, a measuring cuvette and a photodetector for coherent demodulation of the scattered light, a frequency analyzer for the spectral decomposition of the demodulated signal and a computer for determining the particle parameters d and σ, characterized in that a) that the frequency analyzer (13) has a plurality of fixed frequency filters connected in parallel has, at which the demodulated and amplified by a preamplifier (12) signal is pending at the same time, b) and that a scanner (14) is provided which interrogates and digitizes the output signal of the filter and is connected to the computer (15) for the transmission of the digitized values 4. Apparatus according to claim 3, characterized in that the following operations by the Computer (15) can be controlled: a) Setting the photodetector (11) to the scattering angle Θ » b) Adjustment of the gain level on the preamplifier (12), c) setting the integration time of the filters, d) Setting the number, frequency and sequence of the signal polling at the output of the filter through the scanner (14), e) actuation of a diaphragm (9) in the beam path and separate measurement of signal and Noise spectrum. 40