Method and device for determining the particle size in a flowing sample
Patent Information
- Application Number
- EP2024715493
- Authority / Receiving Office
- EP · EP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2023-03-27
- Filing Date
- 2024-03-25
- Publication Date
- 2026-02-11
Smart Images
Figure EP2024057926_03102024_PF_FP_ABST
Abstract
Description
[0001]Fraunhofer Society for the Promotion of Applied Research Our reference: 230274WO - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Method and device for determining the particle size in a flowing sample - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - DESCRIPTION The invention relates to a method and a device for determining the average particle size of particles in a flowing liquid medium by means of dynamic light scattering (DLS). Dynamic light scattering (DLS) is a method for determining particle sizes in which a particle suspension to be examined is irradiated with coherent laser light. Using the light scattered by the particles, the speed of Brownian motion of the particle sample is measured, from which the size of the particles is derived using the Stokes-Einstein relation.When measuring particles suspended in a flowing medium, referred to herein as the sample, Brownian motion must be separated from the flow of the sample to obtain the most accurate results. This problem has already been addressed in document DE 102016212164 B3.Disclosed herein is a method in which a liquid medium is passed through an optically transparent channel in which a laminar flow propagates, the liquid medium is irradiated by means of laser light, scattered laser light is detected two-dimensionally in a spatially resolved manner by means of one or more optical detectors to produce an image, each image having a scattered light pattern, two images forming an image pair are produced successively with a specific delay time ^^ and at least two image pairs with different delay times ^^ are produced, the scattered light patterns of the images of each image pair are brought into alignment with one another under relative displacement and, if two optical detectors are used, optionally rotation, a maximum correlation value being determined in each case.This correlation value undergoes an exponential decay depending on the delay time. Based on this finding, a coefficient, the decay constant, of a correlation function ^^2( ^^), also called autocorrelation, dependent on the delay time ^^, is determined from the correlation values of at least two image pairs using a numerical fit. From this, the hydrodynamic radius ^^ is calculated. ^^of the particles. The separation of the movement of the flowing medium from the Brownian motion actually to be measured, also referred to herein as "flow compensation," is achieved by determining the maximum correlation values, on the one hand, with a linear shift of the scattered light patterns, on the other. The particle sizes derived from the thus compensated measurement are already significantly more accurate than those derived from a static, i.e., uncompensated measurement. However, the derived value of the particle size still shows deviations and therefore gives rise to an improvement of the known method. The invention is therefore based on the object of improving the known method with regard to the accuracy of determining the particle size. This object is achieved by a method according to claim 1 and a device according to claim 14. The method according to the invention provides,that the medium is guided through an optically transparent channel in a step a), the medium is irradiated by laser light in a step b), scattered laser light is detected in a step c) by means of one or more optical detectors in a two-dimensional spatially resolved manner to produce an image, each image having a scattered light pattern, two images forming an image pair being produced consecutively with a specific delay time τ and at least two image pairs being produced with different delay times τ, the scattered light patterns of the images of each image pair being brought to coincide with one another in a step d), at least with a relative shift, a maximum correlation value and a shift amount s being determined in each case,In a step e), a displacement velocity v is determined from at least one of the displacement amounts s of the at least two recording pairs and the associated delay time τ, and in a step f), at least one coefficient of a correlation function ^^2( ^^) dependent on the delay time τ is determined from the correlation values of the at least two recording pairs by means of a numerical fit, and a value for the average particle size is derived from the at least one coefficient, with a correction being made as a function of the determined displacement velocity ^^. The invention is based on the finding that the determined deviations of the hydrodynamic radii determined in a known manner from the actual particle size are due to an inhomogeneous velocity distribution of the flowing medium within the channel. The smaller the channel is at a constant flow rate,the more inhomogeneous the velocity profile becomes, even if the flow still remains laminar. This is due to increasing shear with decreasing distance from the channel wall. The correction according to the invention when determining the value for the particle size is therefore also referred to hereinafter as "shear compensation." When applying the method described in DE 102016212164 B3 for determining the particle size, the mean particle radius is therefore determined to be too small as soon as a significant variation in the flow profile occurs. To counteract this phenomenon, the laser beam can be focused as precisely as possible on the center of the channel, where the flow velocity exhibits the smallest variation in laminar flow and only particles with almost the same speed scatter the light of the laser beam. This leads to minor measurement errors even for channel cross-sections up to 7 mm. For smaller channel cross-sections,Especially with a size below one millimeter, the shear forces are no longer negligible, even with stronger laser focusing, and flow compensation is no longer sufficient to achieve satisfactory results in particle size determination. For example, the relative measurement error caused by shear is already 50% for particles with a diameter of 200 nm for a channel cross-section of 0.5 mm and a flow rate of 500 µl / min. Therefore, the invention is of outstanding importance, particularly for the analysis of small liquid quantities in the range of ml or µl, so-called microfluidics. The invention is further based on the consideration that the shear occurring along the channel edge is proportional to the flow velocity or flow rate, from which the inventors concluded,that compensation for this effect through a velocity-dependent correction promises success. Finally, the invention is based on the finding that during flow compensation in step d), a parameter proportional to the flow velocity is already determined in the form of a displacement amount s. In step e), the flow velocity can therefore be determined without additional measurement from the displacement amount, which can be measured in pixels in a digital image recording, for example, and from the already determined displacement time. The flow velocity is thus recorded, for example, in the unit pixels / µs and is available for a velocity-dependent correction of the measurement result. In principle, it is sufficient if this determination of the velocity is carried out based on a pair of recordings from a measurement,since the flow rate is constant within a measurement. Preferably, however, the displacement velocity ^^ in step e) is determined from the displacement amounts ^^, ^^ and the corresponding delay times ^^ ^^ at least two pairs of images by ∑ ^^ Averaging, particularly preferably according to the following formula^^ = ^^ ^^ This reduces the statistical error in determining the speed, because Delay times are given greater weight. In the event that two optical detectors are used, in addition to the obligatory relative displacement of the scattered light patterns to compensate for the flow, it may be necessary to subject the scattered light patterns to a static calibration consisting of a relative displacement and a relative rotation to one another in order to compensate for any translational and rotational imaging errors due to misalignment of the detectors relative to one another. This static calibration is only an optional correction in that it can be omitted, for example, when only one detector is used to generate the two images of an image pair, or when two detectors are aligned with pixel precision. In this sense, step d) above refers to "at least under relative displacement".Preferably, the correlation function ^^2( ^^) is an exponential function, and the at least one determined coefficient is the decay rate ^^( ^^). This preferably behaves no differently in the method according to the invention than in the cited prior art. The correlation function is advantageously determined by means of least-squares fitting with the following exponential function according to BJ Frisken, Revisiting the method of cumulants for the analysis of dynamic light-scattering data, Applied optics 40 (24), pp. 4087-4091, 2001. DOI: 10.1364 / ao.40.004087, given ^^2= + ^^ ^^ ^^ ^^ ^^ ∙ +. ^^=2 ^^ ^ ^ ^^ ^^ 2 where ^^0 is the baseline of the correlation function, ^^ is a parameter to compensate for the measurement e- ^ ^ ^^ ^^=2 ^^ ^ ^ ^^ ^^ to the descriptionequal to zero 2 ! wird. Alternatively, the correlation function is advantageously specified by least squares fitting with the following exponential function = + ^^ ^^ ^^ ^^ ^−2 ^^ ^^ + 2 ⋅ ^^ ^ ^ ^^ ^^ ^ where ^^0 is the baseline of the correlation function, ^^ is a parameter to compensate for the measurement sensitivity and the coefficients^^^^ of the series ^^=2 ^^ ^ ^ ^^ ^^ Parameter for description equal to zero 2 ! becomes. ^^2 or ^^2 can be used to calculate the polydispersity index, which is a measure of the width of the particle size distribution. ^^2 = 0 or ^^2 = 0 corresponds to an assumed monomodal particle size distribution with a width of zero (delta function). This approximation is entirely sufficient in many practical cases. In this case, the series is truncated after the first summand (1), i.e., the expression in parentheses after the exponential term is omitted. The correction in step f) advantageously depends linearly on the determined displacement velocity ^^. This keeps the computational effort low and has proven to be a sufficient correction for reducing the error. Thus, the relative error of the determined particle diameter under the conditions assumed above (0.5 mm channel cross-section and 500 µl / min flow rate) and for particles with a diameter of 200 nm is only 3%.The correction in step f) can be made, for example, by inserting a speed-dependent correction term into the correlation function ^^2. ( ^^ ) for example according to (1) or (1') or by a speed-dependent correction of the at least one determined coefficient or by a speed-dependent correction of the derived hydrodynamic radius ^^ ^^ itself. In particular, all mathematically equivalent calculation operations for rate-dependent correction are encompassed by the invention. The decay rate ^^( ^^) in step f) is advantageously corrected according to the following formula ^^0= ^^( ^^) − ^^ ∙ ^^ (2) or alternatively the following correction term ^^( ^^) = ^^ ∙ ^^ + ^^0 (3)inserted into the correlation function ^^2( ^^), for example, according to (1) or (1'), where ^^0 is the corrected decay rate and ^^ is a parameter from a calibration of the decay rate determination under variation of the displacement velocity ^^. The corrected decay rate corresponds to the measured decay rate at a displacement velocity of 0: ^^0 = ^^( ^^ = 0). In the former case, the decay rate would first be determined by fitting the correlation function and then the result would be corrected; in the latter case, the correction would be incorporated into the correlation function. These are two equivalent and therefore interchangeable calculation steps. In both cases, the correction depends linearly on the displacement velocity. To calibrate the decay rate determination, according to an advantageous embodiment of the method, at least two different displacement velocities ^^ ^^the decay rate ^^( ^^ ^^ ) after steps a) to f) but without correction and from the value pairs [ ^^ ^^ , ^^( ^^ ^^ )] a straight line is derived whose slope forms the parameter ^^ for the functions (2) or (3). This can be done, for example, by calculating from two pairs of values n [ ^^ ^^ , ^^( ^^ ^^ )] the difference quotient ^^^^( ^^2)− ^^( ^^1) or by fitting a straight line equation to at least two pairs of values [ ^^ ^^ , ^^( ^^ ^^ )] is determined, the slope of which forms the parameter ^^. Alternatively, the decay rate ^^( ^^) is corrected in step f) according to the following formula =^^( ^ − ^ ∙ ^^ or alternatively the following correction term ^^ ( ^^ ) = ^^0∙ ( ^^ ∙ ^^ + 1 ) + ^^ ∙ ^^ (5), into the correlation function ^^2 ( ^^ )for example, according to (1) or (1'), where ^^0 is the corrected decay rate, A and B are coefficients from a calibration of the decay rate determination under variation of the displacement velocity ^^. Here too, in the former case, the decay rate would first be determined from the correlation function by means of a fit and then the result would be corrected, and in the latter case the correction would be incorporated into the correlation function. And here too, these are two equivalent and therefore interchangeable calculation steps in which the correction depends linearly on the displacement velocity. In contrast to the simpler correction variant of formulas (2) and (3), this correction contains an additional coefficient A, which takes the following consideration into account.The inventors have discovered that the shear effect mentioned above is not only proportional to the flow velocity, but also has a different impact on particles of different sizes, which leads to a size-dependent error in addition to the velocity-dependent error. The correction variants of formulas (4) and (5) also take this effect into account and, in a sense, lead to a second approximation to an even better measurement result. For this purpose, at least two calibration measurements of the disintegration rate ^^ are performed for at least one first and one second particle size. ^^ ( ^^) at different displacement speeds ^^ and each from the Relationship ^^ ^^ ( ^^ ) = ^^ ^^ ∙ ^^ + ^^ 0, ^^ the gradient ^^ ^^ and the intercept ^^ 0, ^^ = ^^ ^^ ( ^^ = 0) can be determined, Index j refers to the particle size. From the value pairs [ ^^ 0, ^^ , ^^ ^^ ] and the straight line equation ^^( ^^0) = ^^ ∙ ^^0+ ^^, the coefficients A and B are then determined. In other words, different speeds are tuned for different particle sizes and the decay rate ^^ ^^ ( ^^ ) determined, whereby the various particles are used individually (i.e., monomodally). The accuracy of the subsequent measurement is enhanced if particle sizes are used for calibration that are within the range of the expected particle size to be measured. The hydrodynamic radius ^^ is determined as the value of the mean particle size in a conventional manner. ^^ of the particles from the corrected or uncorrected decay rate ^^ according to the following formula ^ ^2 ^^ ^^ ^ ^ ^ or by inserting the following conversion term ^ 2^^ =^ ∙ ^^ ^^∙ ^^6∙ ^^∙ ^^ ∙ ^^ ^^ (7) into the correlation function ^^2( ^^) for example according to (1) or (1'), where in each case^^ = 4 ^^ ^^0∙ si ^^ the scattering vector with the refractive index ^^ of the liquid medium, the wavelength ^^ n( 2)0 of the laser light and the scattering angle ^^, ^^ ^^is the Boltzmann constant, ^^ is the ambient temperature, and ^^ is the dynamic viscosity of the liquid medium. The decay rate^^ here refers generically to the corrected decay rate ^^0 as well as the uncorrected decay rate ^^( ^^). The ambient temperature is usually measured, and the viscosity and refractive index of the medium (e.g. ^^0 = 1.33 – solvents such as water or ethanol are used as a medium), the wavelength of the laser (e.g. ^^ = 450 ^^ ^^), and the mean scattering angle (e.g. ^^ = 90°) are known. The correction in step f) can, as already explained, also be performed by a velocity-dependent correction of the derived hydrodynamic radius ^^ ^^ According to one embodiment of the method, the hydrodynamic radius ^^ ^^ ( ^^) is derived from the uncorrected decay rate ^^( ^^) according to formula (6) and corrected according to the following formula ^^ = ^ ^ ( ^ . Alternatively, the following correction term ^^ ^^ = ^ ^ be inserted into the conversion term (7). In each case, ^^ ^^0 the corrected hydrodynamic radius and ^^ a coefficient from a calibration of the radius determination under variation of the displacement velocity ^^. The nomenclature for the hydrodynamic radius is based on that of the decay rate: ^^ ^^ refers to both the corrected hydrodynamic radius ^^ ^^0 as well as the uncorrected hydrodynamic radius ^^ ^^ ( ^^). To calibrate the radius determination, at least two different displacement speeds ^^ ^^ the hydrodynamic radius ^^ ^^ ( ^^ ^^ ) is determined according to steps a) to f) in conjunction with the conversion according to (6) or (7) but without correction. The pairs of values thus obtained [ ^^ ^^ , ^^ ^^ ( ^^^^ )] a function ^^ ^^ ( ^^) = 1 ^ ^∙ ^^+ ^^(10) from which the coefficient m is taken. The device according to the invention comprises an optically transparent channel, a laser aligned to the channel for generating a laser beam, at least one detector aligned to the channel at a scattering angle to the laser beam, which detector is configured to successively generate two two-dimensional spatially resolved images of a scattered light pattern with a specific delay time ^^ and output them as digital image data, wherein the two images form an image pair and wherein the at least one detector is further configured to generate at least two image pairs with different delay times ^^, an evaluation electronics for the digital image data, which is configured to bring the scattered light patterns of the images of each image pair into coincidence at least with relative displacement to one another and in doing so each determine a maximum correlation value and aTo determine the displacement amount s, to determine a displacement velocity ^^ from at least one of the displacement amounts s of the at least two image pairs and the associated delay time ^^, to determine at least one coefficient of a correlation function ^^2( ^^) dependent on the delay time ^^ from the correlation values of the at least two image pairs by means of a numerical fit, to derive a value for the average particle size from the at least one coefficient and, in doing so, to carry out a correction depending on the determined displacement velocity ^^. The at least one detector can be formed, for example, by a CMOS sensor or a CCD sensor including the respective readout electronics. The sensor and readout electronics are also referred to hereinafter as a camera. When designing the detector, it must be taken into account that the delay time ^^ is preferably in a range from one orseveral microseconds up to one or more milliseconds. The at least one detector must therefore be able to generate images with the required resolution and the required frequency. This can be implemented with a detector with a very fast readout sensor or alternatively with two detectors each aligned to the same channel section, whereby the detectors can then be read out simultaneously or with temporal overlap and therefore more slowly. The second and further pairs of images can be generated by the same detector or detectors at time intervals that are long enough for the subsequent readout and any data storage and / or processing. The evaluation electronics preferably has a data memory that is configured to store the image data output by the detector or detectors. It further has a processor that, for example, by means of aProgram code is configured to process the image data, in particular to filter, compress, crop, and above all to evaluate it as described above. Preferably, the same or optionally a different processor is used to control the laser and the detector(s) and thus trigger the recordings. The arrangement of the channel, the laser, and the detector relative to one another is preferably such that, firstly, an angle of approximately 90° is enclosed between the laser beam and the viewing axis(es) of the detector (hereinafter camera axis), and secondly, an angle of approximately 90° is enclosed between the laser beam and the flow direction in the channel, and secondly, an angle of approximately 90° is enclosed between the camera axis(es) and the flow direction in the channel. In this case, the three axes ideally form a rectangular coordinate system. Alternatively, it has proven advantageous if, between theAn angle of approximately 90° is enclosed between the laser beam and the camera axis(es), and an angle of approximately 0° is enclosed between the laser beam and the flow direction in the channel, and an angle of approximately 90° is enclosed between the camera axis(es) and the flow direction in the channel. It is important that an angle of approximately 90° is maintained between the flow direction in the channel and the camera axes so that flow compensation can be carried out reliably. Further advantages and details of the invention are explained below with reference to the figures. They show: Figure 1 shows a recording of a scattered light pattern of nanoparticles using a CMOS detector camera; Figure 2 shows a diagram with the measured data of the maximum correlation values with and without displacement (flow compensation) and the displacement amounts, each plotted against the delay time; Figure 3 shows a diagram of the derived diameters as a function of the flow rate for three differentParticle diameters, Figure 4 shows a diagram of the determined displacement velocity as a function of the applied flow rate; Figure 5 shows a diagram of the determined disintegration rate as a function of the determined displacement velocity for the three different particle diameters; Figure 6 shows a diagram of the gradients of the linear relationships between disintegration rate and displacement velocity from the diagram in Figure 5 as a function of the disintegration rate for the three different particle diameters without flow; Figure 7 shows a diagram of the determined particle diameters as a function of the flow rate after correction; Figure 8 shows a diagram of the determined particle diameters as a function of the determined displacement velocity for determining a radius correction and Figure 9 shows a diagram of the corrected particle diameters as a function of the flow rate. Figure 1 shows a typical image produced with the device according to the inventionof a scattered light pattern. A CMOS camera was used for this purpose. A similar image is generated with a time delay of ^^ by a similar second camera. By splitting the images of such an image pair between two CMOS cameras, measurements with correlation or delay times ^^ are possible that are much smaller than the maximum frame rate of the individual cameras. However, the use of two cameras or detectors that image the same sample volume, for example through a beam splitter, requires an additional, initial, static calibration step, since the orientations of the cameras with respect to the sample are regularly slightly different. This requires a transformation ^^′2 = ^^^^, ^^, ^^( ^^2) of one of the two images ^^1 and ^^2, where the components ^^ and t of the transformation represent a shift of the image in pixels in the ^^ direction and in the ^^ direction, respectively, and the component ^^ of the transformation representsa rotation of the image. These components are determined by taking a picture of the scattered light with both cameras at the same time ^^ and numerically determining those components ^^, ^^ and ^^ for which the normalized cross-correlation ^^ of the two pictures is maximized: ^^^ ^^1, ^^^^, ^^, ^^( ^^2)^= ^^( ^^1, ^^ ′ 2)= Here,∑ ^^, ^^ The summation over an image section that is chosen small enough to ensure complete overlap of the two images even after moving and rotating the image ^^2. This is advantageously followed by a second calibration step. This serves, regardless of whether one or two detectors were used, to determine the flow direction. For this purpose, two images separated by a delay time ^^ > 0 ^^1 ( ^^ = 0) and ^^2( ^^ = ^^) of the scattered light is required. The delay time is, for example, 100 µs. The ensemble of light-scattering particles moves collectively by a certain distance in one direction during the delay time ^^. This results in a similar shift in the scattered light pattern, which must be compensated (flux compensation) by bringing the scattered light patterns of the images ^^1( ^^ = 0) and ^^2( ^^ = ^^) into alignment with each other under relative displacement. The shift occurs in the unit of pixels by the components ^^^^ ^^ ^^ ^^ in the ^^-direction or and ^^^^ ^^ ^^ ^^ in the ^^-direction, which components in turn are maximized by maximizing the cross-correlation ^^( ^^1 ( ^^ = 0 ) , ^^ ′ 2 ( ^^ = ^^ ) ) between the two images. As a result of the calibration, the flow direction can be determined. ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^ ^ ^ as a vector of unit length. During the measurement to determine the particle size, the laser and / or the cameras are used to generate the image pairs with different delays ^^ ^^ triggered. The images from the cameras are transferred to the evaluation electronics. The static transformation ^^^^, ^^, ^^from the first calibration is applied to the second image ^^2 when using two detectors, for example. ( ^^ ^^ ) each pair of images. For flux compensation, the shift amount ^^( ^^ ^^ ) for each image pair ^^1( ^^ = 0) and ^^′2( ^^ = ^^ ^^ ) by changing the value of ^^ ( ^^ ^^ ) is found where the cross-correlation between ^^1( ^^ = and ^^′′2( ^^ = ^^ ^^ ) is maximized. Here ^^′′2( ^^ = ^^ ^^ ) which around ^^( ^^ ^^ ) ∙ ^^^^^ ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ shifted in the direction of flow ^^′2( ^^ = ^^ ^^ ). For this optimization problem, a Nelder-Mead algorithm is used, in which the computational effort is reduced by using the flow direction determined in the second calibration step described ^^^^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ is reduced to a one-dimensional problem. The maximum correlation value ^^2( ^^ ^^ ) is as the cross-correlation between the image ^^1( ^^ = 0) and ^^′′2( ^^ = ^^ ^^). In principle, the exposures of a pair of exposures at ^^ > 0 can be triggered either by triggering only the laser or only the camera, or by synchronously triggering both components. The following trigger scheme is preferred: - Exposure of camera 1 starts, - Laser pulse 1 on, - Laser pulse 1 off, - Exposure of camera 1 ends, - Exposure of camera 2 starts, - Laser pulse 2 on with a distance ^^ > 0 to laser pulse 1, - Laser pulse 2 off, - Exposure of camera 2 ends. Alternatively, the laser can remain permanently switched on between the two exposures if the exposure time of the cameras can be set short enough. However, for many cameras, this cannot be set to less than, for example, 100 µs, which is why correlation times < 100 µs can only be measured with a pulsed laser. Figure 2 shows the result diagram of a measurement of the maximum correlation values ^^2 ( τ i )without flux compensation (not part of the invention) as circles and compared len correlation values g2(τ i ) using the flux compensation as squares and the corresponding displacement amounts s ( τ i ) in pixels as triangles, each plotted against the corresponding delay times τ i in µs. The correlation values are standardized and range between 0 and 1, with a value of 0 representing no correlation and a value of 1 representing complete agreement between the two images. Furthermore, the diagram in Figure 2 shows a fitted curve for each of the correlation measurement series in the form of the following exponential function (correlation function): ^^2= + ^^ ^^ ^^ ^^ ^^ ∙ + ^ 2 where ^^0 is the baseline of the correlation function, ^^ is a parameter to compensate for the measurement sensitivity, and ^^2 is a parameter to describe the decay rate distribution. In this case, the series from the exponential function (1) was terminated after the first summand. As can be seen in Figure 2, the correlation values begin ^^2 ( τ i ) without compensation for the shift, the coefficients decay earlier than the compensated values, because the contribution of the flow motion to the decorrelation is initially larger than that of Brownian motion. This leads to a flatter exponential decay of the correlation function ^^2 ( ^^ )or in other words, mathematically to a larger decay rate ^^, whereby the derived particle size is much smaller than the actual one. For example, the determined radius with flux compensation is 80.6 nm compared to an uncompensated value of 37.1 nm. In addition, the shape of the uncompensated correlation function deviates from a simple exponential decay, which leads to a too high µ2 and thus to a greatly overestimated width of the particle size distribution. From the displacement amounts s(τ i ) in Figure 2, the speed ^^ of the particles is further determined as follows ^^∑ ^^ ^^( ^^ ^^) where the summation is only done over those values where ^^2( ^^ ^^ ) > 0.3, because at higher ^^ ^^ the scattered light patterns are already decorrelated due to the Brownian motion of the particles that artifacts are increasingly being registered here. As the inventors discovered, however, flow compensation alone is not sufficient in microfluidic channels. To demonstrate this, the described compensation was tested in a rectangular microchannel measuring 500 µm x 500 µm and at different flow rates of up to 500 µl / min, which corresponds to an average velocity of 33 mm / s, using model particles of different particle diameters, each with very narrow size distributions. Figure 3 shows a diagram comparing flow-compensated measurements (solid lines) and uncompensated measurements (dashed lines, not part of the invention) of the particle diameter in nm plotted against the flow rate in µl / min.It can be seen that for larger particle diameters of 143 nm (circles) and 245 nm (triangles) at flow rates of 200 µl / min and more, the uncompensated diameters are very close together, making it difficult to distinguish between the particles. At a flow rate of 500 µl / min, the uncompensated system measures diameters of 37.1 and 37.6 nm, respectively. Although this problem no longer exists when flow compensation is applied, a further influence of the flow becomes apparent, particularly in small channels, which ensures that the derived particle diameter appears to decrease with increasing flow rate. Thus, there is clearly a dependence of the measurement result on the flow rate. The shear forces along the channel walls are thought to be responsible for this, resulting in an inhomogeneous velocity distribution across the channel cross-section.The inhomogeneous velocity distribution influences the measurement result in two ways: First, the flow compensation described above results in a homogeneous shift of the scattered light patterns in both images, causing the slower particles near the channel walls to be shifted too far and those in the center of the channel to be shifted too little. Second, the inhomogeneous velocity distribution also directly influences the decorrelation of the scattered light patterns, which apparently leads to an underestimation of the resulting particle sizes. See M. Hoppenbrouwers, W. van de Water, Dynamic Light Scattering in Shear Flows, Physics of Fluids 10 (9), pp. 2128-2136, 1998. DOI: 10.1063 / 1.869734; and D. Genoe, P. van Puyvelde, E. Peuvrel-Disdier, P. Navard, G. Fuller, Dynamic light scattering in shear: measurements of diffusion coefficients, Polymer 40 (6), pp. 1353-1357, 1999. DOI: 10.1016 / S0032-3861(98)00366-8.1,2.Since this is obviously an effect dependent on the flow rate, the relationship between the selected flow rate and the determined displacement velocity ^^ was first investigated. This is shown in Figure 4, with the determined displacement velocity in pixels / ms on the y-axis plotted against the flow rate in µl / min on the x-axis. As can be seen, there is a very good linear relationship between them. The conclusion from this is that the displacement velocity ^^, which is essentially included in the measurement, can be used to compensate for the shear effect. The diagram in Figure 5 shows the same result of the flow-compensated measurements as that in Figure 3 with a different parameterization. This time, instead of the derived particle diameter, the determined, inversely proportional disintegration rate ^^( ^^) in ms is shown. -1plotted against the displacement velocity ^^ in pixels / µs for all three particle sizes. A first approximation shows a linear relationship, which can be determined from the following straight line equation for each of the particle radii ^^: ^^ ^^ ( ^^ ) = ^^ ^^ ∙ ^^ + ^^ 0, ^^ (3') This linear relationship can either be used directly for a fast shear compensation by using a single particle radius for calibration. For example, if the gradient m is determined from the decay rate ^^( ^^) of such a calibration measurement using a linear fit, the function ^^( ^^) = ^^ ∙ ^^ + ^^0 (3)The shear-compensated decay rate ^^0 can be determined by inserting it into the correlation function ^^2( ^^) (equation (1) or (1')). This fast compensation is already quite accurate, but does not yet take into account the influence of particle size on the shear effect. By choosing an arbitrary particle radius for this shear compensation, a maximum relative error of less than 9% could be determined. On the other hand, the fast shear compensation in this first approximation only requires calibration with one particle size, which simplifies calibration. Figure 6 shows a diagram in which the previously determined slopes ^^ ^^ different particle diameters in ms -1 · µs / pixel depending on the decay rate of a static sample ^^ 0, ^^ = ^^ ^^ ( ^^ = 0), i.e. a measurement without flow, in ms -1 For this purpose, no measurement needs to be carried out without, because the decay rate ^^ 0, ^^of the static sample is also obtained as a coefficient (y-intercept) from the straight line equation (3'). It can be seen in the diagram that the gradients ^^ ^^ in turn, in a first approximation, exhibit a linear dependence on the particle size. Therefore, in the next step, the gradients ^^ ^^ again fitted with a linear function: ^^ ( ^^0 ) = ^^ ∙ ^^0+ ^^ This straight line equation inserted into the linear relationship between the decay constant and the displacement velocity ^^ ( ^^ ) = ^^ ∙ ^^ + ^^0results in ^^( ^^) = ( ^^ ∙ ^^0+ ^^ ) ∙ ^^ + ^^0= ^^0∙ ( ^^ ∙ ^^ + 1 ) + ^^ ∙ ^^ (5). By inserting this function into the correlation function ^^2( ^^) (equation (1) or (1')), an improved shear compensation of the decay rate ^^0 can be achieved, which also takes into account the influence of particle size on the shear effect. This shows that the difference to the rapid shear calibration according to (3) lies in the fact that the parameter ^^ becomes zero and ^^ becomes the slope ^^. The parameter A thus represents the missing influence of particle size, which makes the correction somewhat more accurate overall. The maximum relative error across all particle sizes is now less than 5%. As an alternative to the method described above of inserting the correction term from (3) or (5) into the correlation function ^^2( ^^), the uncorrected decay rate ^^( ^^) can be determined in an equivalent manner and the terms can be solved for ^^0, whereby in the former case a subsequent correction according to the formula ^^0= ^^( ^^) − ^^ ∙ ^^ (2) and in the second case a subsequent correction according to the formula =^^( ^^ − ^ ∙ ^^ The derived parameters ^^ and ^^ also serve to correct any decay rate measured at non-zero velocities. As already explained above, the corrected hydrodynamic radius ^^ can be calculated from the decay rate ^^0, corrected in either way, as the value of the mean particle size. ^^,0 of the particles according to the following formula ^^^^2 ^ ^^ ^ The result is shown as particle diameter in nm as a function of the flow rate in µl / min in Figure 7. As can be seen, the measurement result is almost constant for particle diameters up to approximately 150 nm and flow rates up to 500 µl / min, and even for particle diameters of approximately 250 nm, it is significantly less influenced by the flow rate compared to the result without shear compensation in Figure 3. The maximum relative error is, as already mentioned, less than 5% across all particle sizes. At this point, it should be mentioned again that, in an equivalent manner, the uncorrected hydrodynamic radius ^^ ^^ ( ^^) and then by the following correction term ^^ = ^ ^ ( ^ . can be corrected or alternatively the one after ^^ ^^ ( ^^) resolved correction term ^^ ^^ = ^ ^ into equation (7) and then into the correlation function ^^2 ( ^^ )can be used. Another alternative shear compensation method is explained using the diagrams in Figures 8 and 9. Figure 8 shows the determined, uncorrected particle radii ^^ ^^ ^^ ( ^^ ) in nm as a function of the determined displacement velocity ^^ in pixels / µs as shown in Figure 3 for three different particle diameters. This time the measured values ^^ ^^ and ^^ ^^ ( ^^ ^^ ) with the function ^^ ^^ ^^ = 1 (10) fitted, from which the coefficient ^^ ^^ is taken. From the mean ^^ = ^ഥ^ ^^ for all three particle radii inserted into the inverse function ^^ = 1 One also obtains diameter in nm plotted against the flow rate in µl / min as shown in the diagram in Figure 9. As expected, a comparison with the result from Figure 7 shows that this compensation again produces a greater inaccuracy, particularly for larger particle diameters, because here again the particle size was not taken into account in the correction. However, for diameters up to approximately 150 nm, reliable values can be determined within an acceptable error range of less than 5%. Using three example fit functions (3), (5) or (10), it was shown that the teaching of the invention is fundamentally not limited to a specific fit function for compensating the speed-dependent correction of the disintegration rate or the particle size. In view of simple calibration, it is advantageous to start from a function that preferably has no more than two fit parameters.
Claims
Patent Claims 1. Method for determining the average particle size of particles in a flowing liquid medium by means of dynamic light scattering (DLS), in which a) the medium is passed through an optically transparent channel (step a)), b) the medium is irradiated with laser light during this process (step b)), c) scattered laser light is detected two-dimensionally with spatial resolution by means of one or more optical detectors to generate an image, each image having a scattered light pattern, two images forming an image pair being generated consecutively with a specific delay time ^^ and at least two image pairs being generated with different delay times ^^ (step c)), d) the scattered light patterns of the images of each image pair are brought into alignment with each other by relative displacement,wherein a maximum correlation value and a displacement amount s are determined in each case (step d)), e) a displacement speed ^^ is determined from at least one of the displacement amounts s of the at least two recording pairs and the associated delay time ^^ (step e)), f) at least one coefficient of a correlation function ^^2 dependent on the delay time ^^ is determined from the correlation values of the at least two recording pairs by means of a numerical fit, ( ^^ )and from the at least one coefficient, a value for the mean particle size is derived, wherein a correction is made as a function of the determined displacement speed ^^ (step f)).
2. Method according to claim 1, characterized in that the correlation function ^^2( ^^) is an exponential function and the at least one determined coefficient is the decay rate ^^( ^^).
3. Method according to claim 2, characterized in that the correlation function ^^2= + ^^ ^^ ^^ ^^ ^^ ∙ + ^ ^^ 2 + ⋯ 2 is, where ^^0 is the baseline of the correlation function, ^^ a parameter for compensation ^ ^ ^^ ∑ ∞ ^^=2 ^^ ^ ^ ^^ ^^ ∑ ∞ ^^=2 ^^ ^ ^ ^^ ^^ 2 either set to zero or after the first summand 2 !is, or alternatively = + ^^ ^^ ^^ ^^ ^−2 ^^ ^^ + 2 ⋅ ^^ ^ ^ ^^ ^^ ^ is, where ^^0 is the baseline of the correlation function, ^^ a parameter for compensation ^ ^ ^^ ^^=2 ^^ ^ ^ ^^ ^^ ∑ ∞ ^^=2 ^^ ^ ^ ^^ ^^ optionally set to zero or after the first summand ^^2 2 2 ! ^^ is..
4. Method according to one of the preceding claims, characterized in that the correction in step f) depends linearly on the determined displacement speed ^^.
5. Method according to one of the preceding claims, characterized in that the correction in step f) is optionally carried out by inserting a speed-dependent correction term into the correlation function ^^2 ( ^^ )or by a speed-dependent correction of at least one determined coefficient or by a speed-dependent correction of the derived hydrodynamic radius ^^ ^^ 6. Method according to claim 2 and 5, characterized in that the decay rate ^^( ^^) in step f) is corrected according to the following formula ^^0= ^^( ^^) − ^^ ∙ ^^ (2), or that the following correction term ^^( ^^) = ^^ ∙ ^^ + ^^0 (3), is inserted into the correlation function ^^2( ^^), where ^^0 is the corrected decay rate and ^^ is a parameter from a calibration of the decay rate determination under variation of the displacement velocity ^^.
7. Method according to claim 6, characterized in that for the calibration of the decay rate determination at at least two different displacement velocities ^^ ^^ the decay rate ^^( ^^ ^^) after steps a) to f) but without correction and from the value pairs [ ^^ ^^ , ^^( ^^ ^^ )] a straight line is derived, the slope of which forms the parameter ^^.
8. Method according to claims 2 and 5, characterized in that the decay rate ^^( ^^) is corrected in step f) according to the following formula =^^( ^^ − ^ ∙ ^^ or that the following correction term ^^ ( ^^ ) = ^^0∙ ( ^^ ∙ ^^ + 1 ) + ^^ ∙ ^^ (5), into the correlation function ^^2 ( ^^ ) is used, where ^^0 is the corrected disintegration rate, A and B are coefficients from a calibration of the disintegration rate determination under variation of the displacement speed ^^.
9. Method according to claim 8, characterized in that for the calibration of the disintegration rate determination for at least a first and a second particle size, at least two measurements of the disintegration rate ^^ ^^ (^^ ) at different displacement speeds ^^ and each linear relationship ^^ ^^ ( ^^ ) = ^^ ^^ ∙ ^^ + ^^ 0, ^^ the gradient ^^ ^^ and the intercept ^^ 0, ^^ = ^^ ^^ ( ^^ = 0) determined the index j refers to the particle size, and that from the value pairs [ ^^ 0, ^^ , ^^ ^^ ] and the straight line equation ^^( ^^0) = ^^ ∙ ^^0+ ^^ the coefficients A and B are determined.
10. Method according to one of claims 2 to 9, characterized in that the value of the mean particle size is the hydrodynamic radius ^^ ^^ of the particles from the corrected or uncorrected decay rate ^^ according to the following formula ^^ ^^ =^^2∙ ^^ ^^∙ ^^6∙ ^^∙ ^^ ∙ ^^ (6) or by inserting the following conversion term ^^ =^^2∙ ^^ ^^∙ ^^6∙ ^^∙ ^^ ∙ ^^ ^^ (7)is derived into the correlation function ^^2( ^^), 4where ^^ = ^^ ^^0 ^^ ∙ sin( ^^ 2) the scattering vector with the refractive index ^^0 of the liquid medium, the wavelength ^^ of the laser light and the scattering angle ^^, ^^ ^^ is the Boltzmann constant, ^^ is the ambient temperature, and ^^ is the dynamic viscosity of the liquid medium.
11. Method according to claims 5 and 10, characterized in that the hydrodynamic radius ^^ ^^ ( ^^) is derived from the uncorrected decay rate ^^( ^^) according to the formula (#) and corrected according to the following formula ^^ =^^ ^^( ^^) or that the following correction term ^^ ^^ = ^^ ^^0 is inserted into the conversion term (#), where ^^ ^^0 is the corrected hydrodynamic radius and ^^ is a coefficient from a calibration of the radius determination under variation of the displacement velocity ^^.
12. Method according to claim 11, characterized in that for the calibration of the radius determination at at least two different displacement speeds ^^ ^^ the hydrodynamic radius ^^ ^^ ( ^^ ^^ ) according to steps a) to f) in conjunction with claim 9 but without correction and is applied to the value pairs [ ^^ ^^ , ^^ ^^ ( ^^ ^^ )] a function ^^ ^^ ( ^^) = 1 ^ ^∙ ^^+ ^^ (10)is fitted, from which the coefficient m is taken.
13. Method according to one of the preceding claims, characterized in that the displacement velocity ^^ in step e) is formed from the displacement amounts s and the associated delay times ^^ of at least two pairs of images by averaging.
14. Device for carrying out the method according to one of claims 1 to 13, with an optically transparent channel, a laser aligned to the channel, at least one detector aligned to the channel at a scattering angle to the laser beam, which detector is configured to successively generate two two-dimensional spatially resolved images of a scattered light pattern with a specific delay time ^^ and to output them as digital image data, wherein the two images form an image pair, and wherein the at least one detector is further configuredto generate at least two image pairs with different delay times ^^, an evaluation electronics system for the digital image data, which is configured to - align the scattered light patterns of the images of each image pair with relative displacement to one another and thereby determine a maximum correlation value and a displacement amount s, - determine a displacement speed ^^ from at least one of the displacement amounts s of the at least two image pairs and the associated delay time ^^, - determine at least one coefficient of a correlation function ^^2 dependent on the delay time ^^ from the correlation values of the at least two image pairs by means of a numerical fit, ( ^^ ) to determine, to derive a value for the mean particle size from at least one coefficient and to carry out a correction depending on the determined displacement speed ^^.