WO2015180864A1

WO2015180864A1 - A method for the characterization of particle-particle and particle-medium interactions

Info

Publication number: WO2015180864A1
Application number: PCT/EP2015/056591
Authority: WO
Inventors: Marco Alberto Carlo Potenza; Tiziano SANVITO; Paolo Milani
Original assignee: Eos S.R.L.
Priority date: 2014-05-30
Filing date: 2015-03-26
Publication date: 2015-12-03

Abstract

A method for characterizing particle-particle and particle-medium interactions from light scattering measurements of particles dispersed in a fluid medium, the method comprising the following steps: providing at least a first and a second collection of measurements of light scattered by said particles, each measurement pertaining to a set of independent quantities that define the complex field and/or the polarization state of the light scattered by a respective particle, identifying a set of parameters related to the independent quantities, the parameters being subject to change as a consequence of particle-particle or particle-medium interaction, c) comparing the second collection with the first collection of measurements, wherein the measurements are expressed in terms of the parameters, identifying any significant changes of the parameters between said collections of measurements, and optionally calculating the significant changes, qualitatively and/or quantitatively determining a particle-particle or particle-medium interaction as a function of the significant changes between the collections of measurements.

Description

A method for the characterization of particle -particle and particle-medium interactions

Field of the invention The present invention relates generally to optical techniques for measuring particles dispersed in a fluid medium.

Discussion of related art Recent developments in nanoscience, biomedical sciences, drug delivery, environmental sciences require the capability of quantitatively characterizing interactions between nanoparticles diluted in a medium and between the nanoparticles and the surrounding medium [1]. Moreover, methods capable to work in-line and following in real-time the kinetics of physico-chemical processes underlying particle interaction, clustering, dynamic aggregation, crystallization are strongly needed for many applications and the assessment of technological processes. Optical methods are almost unique in terms of flexibility, simplicity, robustness, non-invasivity, sampling speed, etc., so that many of them have been exploited to characterize particles and interactions. Nevertheless, in the nanometer size domain particles are endowed with sizes small enough to prevent for the effective exploitation of methods operating in the visible light range and based upon the determination of form/structure factors, as they are usually defined in traditional scattering descriptions. Moreover, some of the traditional methods need for proper calibrations and/or long measurements, which make them unsuitable for practical implementation. Traditional scattering methods are usually based upon the measurement of scattered intensity, so that the phase information is rigorously lost, as it is for example in small angle light scattering, laser diffraction, dynamic light scattering, optical particle counters. Within the visible range, methods giving simultaneously the amplitude and the phase of the scattered waves have been devised since long ago with early attempts on single particles as described in [2], [3]. Quite recently, methods simple enough to envisage the possibility of a widespread exploitation for industrial applications have been proven both for collections of particles and single particles illuminated by a laser light [4], [5], [6]. Depolarized light scattering methods like those suggested in [7], [8], [9] clearly show the feasibility of measurements based upon the polarization state of the emerging scattered wave.

In [2] and [3] two different methods have been devised to measure the complex amplitude of the field scattered by single particles. Irrespectively of the huge differences among them, both methods rely on the interference between the scattered wave and a reference one, thus determining the phase from the interference pattern in a way that is reminiscent of holography. Method described in [2] is difficult to be implemented. Method described in [3] has been demonstrated to be applicable for in line monitoring of fluids. In [4], [5], [6] the reference wave is the transmitted one, in a self -reference interference scheme that is very similar to in line holography. The method described in [4] operates through a statistical analysis of the interference pattern generated by a collection of a huge number of particles, relying on the properties of Fourier transforming two dimensional chirped functions; in [5] the amplitude and phase are simultaneously measured just from the visibility and position of the fringes within patterns formed by interference between a single spherical wave and the transmitted plane wave; in [6] a focused light beam is exploited in order to allow in line exploitation of these self-interference methods. [7], [8] and [9] are methods developed to study collections particles endowed with optical anisotropy, thus determining a scattered wave with a polarization in a direction perpendicular to that of the incoming beam. Due to the Brownian motions, particles rotate at random, and the depolarized scattered field fluctuates with time: the characteristic time needed to decorrelate the field is mainly related to the size of the particles. Nevertheless, rotations are affected by shape and, more importantly, by the internal structure as studied in great details for micron- sized fractal aggregates of colloids [10] .

All these methods have been introduced to measure properties of either single or a plurality of particles.

Summary of the invention According to the invention, a method is proposed for characterizing particle -particle and particle-medium interactions from light scattering measurements of particles dispersed in a fluid medium, said method comprising the following steps: a) providing at least a first and a second collection of measurements of light scattered by said particles, each measurement pertaining to a set of independent quantities that define the complex field and/or the polarization state of the light scattered by a respective particle, b) identifying a set of parameters related to said independent quantities, said parameters being subject to change as a consequence of particle-particle or particle-medium interaction, c) comparing the second collection with the first collection of measurements, wherein said measurements are expressed in terms of said parameters, d) identifying any significant changes of the parameters between said collections of measurements, and optionally calculating said significant changes, e) qualitatively and/or quantitatively determining a particle -particle or particle-medium interaction as a function of the significant changes between said collections of measurements.

Such a method can be applied for the characterization in real-time and for quantitative measurement of the interactions occurring between unsupported small particles dispersed in a gaseous or a liquid medium with particular respect to particle assembling, aggregation and clustering, crystallization, as well as between particles and the surrounding gaseous or liquid medium leading to the formation of complex assemblages made by different materials and building blocks such as core-shell systems.

The complex field and/or the polarization state of the wave scattered by particles or clusters subject to interactions can be exploited to get quantitative information about the interactions themselves. Measuring the complex field corresponds to simultaneously determine two independent quantities of the scattered wave, either the real and the imaginary parts or the amplitude and phase, and/or the polarization state. Here the phase to be measured is different from that recovered by holographic methods, being the phase lag of the scattered wave measured with respect to the phase of the incoming wave.

The objects referred here to as "particles" can be any kind of assemblage of atoms/molecules, such as for example engineered objects, dust grains, crystals, powders, combustion products, macromolecules, proteins, viruses, and any material composed of a liquid or gas suspension of objects, like for example colloidal suspensions, emulsions, aerosols. Atoms and molecules themselves are considered here.

Within the present invention, the term "particles" encompasses also clusters of particles. Here, "clusters of particles" or even "clusters" can be any kind of assemblage of particles as said above, where the assemblage is substantially determined by the interactions between particles, or between particles and the surrounding medium. A cluster of particles here is understood to be a collection of particles which properties are not simply the sum of the properties of the particles, the interactions playing the main role. Examples are assemblages of atoms/molecules, a few or many particles, one particle interacting with the surrounding medium. Assemblages are generated and controlled by the interactions which are the object of the present invention. A cluster of particles can be formed for example during processes of aggregation, crystallization, flocculation, swelling, adsorption of molecules, hydration or dehydration processes, layering with a portion of the surrounding medium, etc., whatever the chemical, physical, biological or any other process determines the formation or the structure, or even a structure change.

The size of the objects refereed here as to "particles" and "clusters" extends from below a nanometer to microns, the focus here being the characterization of the interactions between the components irrespectively from the size of the object itself, as well as from the size of any structure formed by the objects. The phenomena referred here as to "interactions" can be the result of any kind of force, potential, exchange, influence of the surrounding medium, change of thermodynamic parameters of the system, acting at a microscopic level as one or more particles have an effect one upon another. Interactions can be the result of two-way, one-to-one effect among particles, as well as one-way, causal effect determined by the influence of one particle upon the surrounding region, which influences other particles or even the original particle itself. Examples of different kind of interactions can be electrostatic, depletion, Debye, London or Casimir effect for dielectric media. When one, or more than one, particle or cluster of particles is present within a region illuminated by light it acts as a scattering center and a fraction of the beam is removed due to either pure scattering or due to scattering and absorption. A new emerging wave is generated, called scattered wave, which features depend on the size, composition, internal structure, shape of the scattering center. Light scattering is traditionally adopted for the characterization of single or multiple particles illuminated by a light beam, typical examples being the dynamic light scattering methods, static light scattering methods, single particle scattering, as well as any other method based upon the scattering of light. Information about the interactions as defined above and the characterization of clusters can be obtained from measurements made with these and other methods known to any expert in the field.

The method of the present invention is based upon the quantitative analysis of the complex amplitude and/or the polarization state of the scattered electric field, which are influenced from particle-particle and particle-medium interactions forming clusters of particles. These parameters can be characterized upon time to investigate the interactions. The effect of external parameters like pH, temperature, composition of the surrounding medium, just to cite a few examples, can be exploited to induce, increase, or reduce the interactions as it is usually done by exploiting other methods. The method is based upon any way to measure a quantity or, simultaneously, more independent quantities such as the real part of a component of the complex field, imaginary part of a component of the complex field, scalar quantities related to the real part and/or imaginary part of the complex field, and scalar quantities related to the polarization state.

Brief description of the drawings

A preferred but non-limiting embodiment of the invention will now be described with reference to the appended drawings in which:

Fig. 1 is a flowchart representing a method according to the invention;

Fig. 2 is a diagram reporting results obtained with a numerical simulation for the effect of coating Ag nanospheres with a layer of dielectric material with refractive index 1.45 (black circles) and 1.6 (black squares). The naked Ag sphere is indicated by an arrow. Dielectric material forming spheres without the Ag inclusion will produce signals indicated by the corresponding open symbols;

Fig. 3a is a diagram reporting results obtained with numerical simulations for fields scattered by clusters with a temporal evolution. The size of the clusters increases by a factor 1.5, 2, 3, 4;

Fig. 3b is a diagram reporting the intensity of the signal expected for dynamic Light Scattering measurements at 90 deg as a function of size increase. Description of the invention

With reference to Fig. 1, a method is disclosed for characterizing particle-particle and particle-medium interactions from light scattering measurements of particles dispersed in a fluid medium.

The method comprises a step of providing at least a first and a second collection of measurements of light scattered by the particles (steps 110 and 120 in Fig. 1). Each measurement pertains to a set of independent quantities that define the complex field and/or the polarization state of the light scattered by a respective particle. This set of independent quantities consists of at least one scalar quantity selected from the group consisting of: real part of a component of the complex field, imaginary part of a component of the complex field, scalar quantities related to the real part and/or imaginary part of the complex field, scalar quantities related to the polarization state. The collections of measurements may be obtained with any light scattering technique which is known in the art, provided that this technique is suitable for providing measurements of the above mentioned independent quantities. An example of a suitable light scattering technique is disclosed by the Italian patent application N° TO2004000100. According to an embodiment of the invention the measurements of the second collection may be taken at a later time than the measurements of the first collection. According to another embodiment, the measurements may be taken in parallel; this could be the case, for example, of a collection of measurements taken from a first sample of particles, and another collection of measurements taken from a second sample of the same kind of particles, but with different conditions of the medium. In general, the measurements may be directly provided by a measuring apparatus, or may be retrieved from a database of measurements.

The method further comprises a step of identifying a set of parameters related to the above mentioned independent quantities (step 130 in Fig. 1); these representative parameters are chosen between those parameters that are subject to change as a consequence of the particle-particle or particle-medium interaction to be investigated. Therefore, the set of parameters consists of at least one scalar quantity selected from the group consisting of: real part of a component of the complex field, imaginary part of a component of the complex field, scalar quantities related to the real part and/or imaginary part of the complex field, scalar quantities related to the polarization state. According to an embodiment of the invention, the representative parameters coincide with the measured independent quantities provided by steps 110 and 120. The method further comprises a step of comparing the second collection with the first collection of measurements (step 140 in Fig. 1). In this step the measurements are expressed in terms of said parameters. If the parameters do not coincide with the independent quantities defining the complex field and/or the polarization state of the scattered light scattered, this step may require the conversion of the values of the measurements expressed in terms of the independent quantities into values of the measurements expressed in terms of the parameters. According to an embodiment of the invention, the step of comparing the second collection with the first collection of measurements comprises:

representing said first and second collection of measurements by, respectively, a first and a second statistical distribution of said parameters, and

- comparing the second statistical distribution with the first statistical distribution.

The method further comprises a step of identifying any significant changes of the parameters between said collections of measurements, and optionally calculating said significant changes (step 150).

According to an embodiment of the invention, the step of identifying changes of the parameters comprises:

identifying any significant changes between said statistical distributions, and optionally calculating said significant changes as changes of characteristic quantities of said statistical distributions.

The method further comprises a step of qualitatively and/or quantitatively determining the particle-particle or particle-medium interaction as a function of the significant changes between said collections of measurements (step 160).

According to an embodiment of the invention, the step of determining the particle-particle or particle-medium interaction comprises:

qualitatively and/or quantitatively determining a particle -particle or particle-medium interaction as a function of the significant changes between said statistical distributions.

The determination of a couple of independent quantities, the real and imaginary part of the field scattered by aggregates of particles, enable the determination a set of parameters that allows to measure the interactions. Notice that this corresponds to measure both the amplitude and the phase of the scattered wavefronts, or any other combination of parameters which is substantially equivalent to the real and imaginary parts of the complex scattered field, as it can be clear to whom is expert in the field. Many processes determined by particle -particle and/or particle-medium interactions are included here, such as for example the cases of two or more particles sticking together, the formation of a layer of molecules around a given particle or a cluster of particles, housing of atoms/molecules within a structure, the formation of ramified and branched structures resulting from the aggregation of several particles or clusters of particles, swelling, as well any change in dimensions, shape and structure of a particle or cluster due to chemical and/or physical interactions with the medium. All the inverse phenomena, as well as aging effects and any other phenomena where interactions play a role in changing the optical properties of the particles or clusters of particles. Moreover, the method takes advantage from monitoring over time the kinetics of any process in which particles are interacting together and/or with the surrounding medium to form or dissolve clusters of particles, for example by changing external conditions. The possibility that the interactions among particles are mediated by the surrounding medium is also included, as a particular case of the previous one.

The light scattered from clusters of particles having dimensions comparable to the optical wavelength is determined by the cluster size. Size roughly imposes the overall amount of power removed from the incoming field. The method of the invention is based on the fact that we consider the light scattered by a generic cluster of particles, where one or more than one among these features 1) composition, 2) structure, 3) shape, change with one or more than one external parameters, or even only with time. Together with the size, said features determine the optical properties of the cluster of particles, and therefore the scattered wave properties. The role played by each feature depends upon the size or more specific properties of the cluster of particles and/or of its building blocks and interactions themselves. Their combination determines both the real and the imaginary parts of the scattered field, or any other combination of equivalent parameters. Notice that the opposite is simply not true. Even by knowing exactly the scattered wave complex amplitude, recovering the features of the cluster of particles remains almost impossible in general. Therefore, the method of the invention does not rely on determining the features of the clusters of particles or a collection of them, which is often impossible. By contrast, comparing the parameters recovered from the scattered wave measured before and after the interactions occurred is enough to characterize the interactions themselves. Also, following the kinetic of a process occurring to clusters of particles in terms of said parameters provides the information about the interactions. Changes of the real and imaginary parts of the field can be assessed as a function of external conditions, such as pH, gas concentration, temperature, chemical potential, for example, or just as a function of time in case of kinetic or aging processes. The breakthrough here is to determine how the interactions change one or more independent quantities simultaneously.

The proposed method is particularly suitable for the characterization of interactions in those cases where the composition of the particles constituting the cluster is unknown. Changes in the parameters recovered from the scattered wave can be measured even if the size distribution, shape, internal structure of aggregate is not known. The starting conditions are characterized in terms of the two parameters, and their change is monitored by measuring differences determined by the interactions. As an example, following the kinetics of a reaction gives insight into properties like the activation energy, as simply described by the Arrhenius' law. Furthermore, the presence of phase transitions, the transition from a surface-driven to bulk-driven reaction, etc. can be evidenced.

Quantitatively speaking, the advantage of measuring of quantities such as the real and imaginary parts of the scattered field with respect to the usual cross section measurement can be explained as follows. For the sake of simplicity, here we assume that the scattered field is uniformly distributed into space, a property that is really true just for extremely small particles. Nevertheless, the same argument can be extended to any size by introducing the actual expansion of the scattered field (for example by using the Mie theory for sphere-like clusters, or with more complex approaches for non-spherical or non- uniform objects), as it can be easily understood by any expert in the field. Measuring the imaginary part of the scattered field ultimately corresponds to measure the amplitude, which once squared gives the scattered intensity measured with traditional techniques to measure the particle size, a. Accessing the real part is important as well, since this quantity is directly related to the total extinction cross section (through the so called Optical Theorem). This includes both scattering and absorption. The complex scattered field is ultimately related to the so-called optical thickness of the scatterer, s = 2a(m - 1) where m is the relative refractive index. Roughly speaking, the refractive index does provide the information about the amount of material contained within the scatterer. Notice that ultimately this distinction cannot be maintained for the actual cases due to the effect of size, composition, shape and internal structure, so that just assessing the actual size is a very difficult issue.

Things can be cast in a quantitative way by considering the expression for the field in a plane very close to the scatterer. By assuming that the light impinges along the z direction, the object will introduce amplitude and phase modulations in the transverse plane x - y. See [11] for reference and for a complete description of the assumptions. In the case of a purely dielectric structure, for example, the phase modulations are simply due to the optical thickness s(x, y) encountered by the impinging beam along the straight line at position (x, y) through the particle. The local phase change of the optical electric field is then given by:

(k² 1 2π) (1 - exp[- k s(x, y)])

Here k = 2π/λ, where λ is the light wavelength, and is the imaginary unit. By integrating the phase shifts over the cross section of the particle, the amplitude of the forward scattered field S(0) is obtained. Under the hypothesis of small optical thickness, namely k s(x, y) « 1, it is possible to expand in power series the exponential. At the second order of the expansion, the forward scattered amplitude S(0) turns out to be given by the sum of two terms, one describing the imaginary part and the latter the real one. The imaginary part, 7, is proportional to the optical thickness of the whole particle. The real part, R, is proportional to the integral of the squared value of the optical thickness. By interpreting these contributions in terms of global parameters of the particle, it is easy to find that the imaginary part is proportional to the polarizability of the whole particle, while the real one is proportional to the extinction cross section, as obtained by the Optical Theorem (see [11]). A further inspection can be done by assuming that the optical thickness of a particle with a given composition, structure, shape and orientation is described by an average value which we indicate here as SQ, and a zero average part fluctuating with (x, y), namely s(x, y) = SQ + ds(x, y). It is easy to obtain that the imaginary part is proportional to SQ, while the real part will be proportional to SO² + <Ss²> (< > indicate the average over the cross section of the particle). The pref actors which give the proportionality are such that the ratio RII = k so + k <Ss²> I so. This interpretation is particularly meaningful here, since it exhibits how the change or even only the spread of optical thicknesses introduced for a fixed SO, can be attributable to irregularly shaped, structured and/or inhomogeneous clusters with random orientations, as well as for any assemblage of matter with peculiar structures. Measuring a number of clusters undergoing interactions allows to determine a distribution of R and / values for each cluster at a given stage of the process. A distribution of parameters like RII can then be extracted. The following information is then available: 1) changes in SQ, which is directly related to changes in the average polarizability of the clusters, that is to the average density; 2) broadening/sharpening of the RII distribution, which is related to the optical thickness distribution around the average value SQ, delivering information about changes in shape, internal structures, etc.; 3) change of symmetry properties of the RII distribution, such as for example skewness, kurtosys, etc.; 4) changes in R for a fixed RII, indicating a change in the overall size distribution of the cluster population with a constant composition; 5) more in general, changes in both RII and / which are attributable to interactions among particles within a cluster, as it will be understood on the basis of any knowledge of the processes occurring in the system. Generally speaking, all these changes are ultimately related to the interactions among the particles constituting clusters. From this example it is evident how the analysis of the complex field is of paramount importance for extracting the information about the interactions determining the properties of a cluster, at variance with the traditional approaches.

In addition to the real and imaginary parts of the scattered field, further information can be obtained by illuminating clusters with a linearly polarized field and by measuring the field scattered with orthogonal polarization, as it is usually done in depolarized light scattering methods. In many cases this can be an important piece of information, related to the asymmetries and/or crystal like internal structure of clusters, or just the shape of the clusters. This information can be extracted just from the real and imaginary parts of the depolarized scattered fields, or also by measuring the rotational time constants as it is traditionally done in depolarized light scattering. For example, in the case of crystallization, it is well known that isometric shapes are typical for stable structures, while elongated shapes are mainly related to metastable states which slowly evolve with time in dependence of the external conditions. Similarly, different stacking modes are possible in materials formed by layers of the same composition, which form different polytypes. Density is uniform, but smectic structures have layers stacked with random orientations, and the degree of order indicates the energy needed to reorganize the structure, which is again related to interactions. The degree of order of the layers inside the structure determines the depolarization effects, so that it is measurable for clusters with the methods described in [7, 8, 9].

In the following, some examples of application of the method of the invention are discussed.

EXAMPLES

Example 1: Measure of the particle -particle interaction strength in fluid suspension. As it is well known from colloidal physics, the strength of particle -particle interactions can have a profound influence on particle aggregation. Generally speaking, aggregation can be described depending on one of the two limiting phenomena: either the diffusion of particles towards the aggregates or the sticking probability. The latter process, known as reaction-limited aggregation, is determined by the interaction strength, including effects of the activation barrier in the sticking of the particles. As a matter of fact, even for strong interactions, aggregates grow with characteristics typical of the reaction-limited processes due to external effects affecting the whole aggregate. The information contained in the aggregates is then changed, making very difficult, if not impossible, to measure the interaction strength from the features of aggregates. In principle, a solution could be to monitor the growth of clusters composed by just two particles (dimers), which are not so much affected by external effects. Nevertheless, this would require very detailed knowledge of the particles, in such a way that the presence of a few dimers is measurable. The method of the invention can be exploited to monitor the early stages of an aggregation process to characterize the interactions governing the formation of the simplest clusters that are formed. Irrespectively from the knowledge of the starting monomers, the power of this method relies on the fact that the maximum change in the scattering field occurs just when dimers are formed. Real and imaginary parts are changed accordingly. Moreover, despite the limitation said above, in some cases external conditions can be cast in such a way to leave the interaction acting without substantial external influence. In such a case, during the aggregation process when aggregates of a number of monomers are formed, also the dependence of the RII parameter upon R changes accordingly to the fractal dimension of the aggregates, which is a measure of the interaction strength. Measuring a collection of aggregates at one given stage of the process allows to extract the information about the fractal dimension from the plot of RII versus /. Finally, also properties of symmetry are changed, so that the random orientations will determine a spread in the fields that can be exploited as a signature of the presence of dimers. Here the depolarized light can be particularly useful, just for measuring the shape changes upon time, for example. Interactions can then be measured by following the process upon time, or by imposing external conditions changing the strength of the interactions.

Example 2: Characterization of the interactions determining the growth of an aggregate of proteins around given particles (protein corona) and forming a substantially concentric structure.

The approach constituting this invention gives insight into the structure of the core and the external layer of substantially concentric structures when composed of materials endowed with different optical properties. Irrespectively of the knowledge of the particles in terms of size, size distribution, composition and shape, following the process determined by the interactions in terms of the quantities R and / permits to distinguish coated particles from uncoated, thus assessing the probability of forming the corona and therefore the interactions between the particle and the proteins in the surrounding medium. Moreover, the same analysis can be exploited to say apart the coated particles and, for example, aggregates of just proteins or clusters of particles. This permits to quantitatively characterize the differential behavior of particle-protein interactions, protein-protein interactions and particle-particle interactions. A case of large interest is represented by Ag core nanospheres suspended in water and coated by a protein corona. Here we consider a monodisperse core size of 100 nm in diameter, to be coated by a protein corona 50 nm thick. Accurate numerical simulations brought evidence that during the growth process these clusters determine a real part of the scattered field increasing with the thickness of the protein layer. By contrast, the imaginary part is almost constant. This makes the difference with traditional methods, which are based upon the measurement of the scattered intensity, which is ultimately proportional to the imaginary part of the scattered field. Moreover, the imaginary part is much smaller than that of spheres composed by pure proteins, which can be easily quantified in terms of number and size. This allows to extract the effect of the interaction of proteins sticking onto the Ag cores. Both real and imaginary parts are much smaller than those expected for aggregates formed by two or several Ag cores.

More quantitatively, we report numerical results obtained in order to assess the effect of coating on Ag nanospheres 100 nm in diameter. We have considered the effect of proteins by introducing two different dielectric materials with refractive indexes n = 1.45 and n = 1.6. The thickness of the layer has been imposed to be such that the diameter of the whole objects is 105, 110, 120, 150, 200 nm, with a concentric Ag sphere. Results are plotted in Fig. 1 (black symbols). The position of the Ag core particles is indicated by an arrow. As soon as the coating thickness grows beyond 10-20 nm it becomes visible, provided that a direct comparison is possible with the Ag spherical cores.

Example 3: Characterization of the stability and/or sensitivity to external conditions of systems composed by interacting particles.

Engineered aggregates of particles, such as for example aggregates, particles forming a layer around a given core, hollow structures can be characterized as a function of external conditions. This gives insight into their capability to modify the structure under certain external conditions (such as pH, temperature, gas exposure, composition of the surrounding medium, etc.). Characterizing the behavior of these complex objects needs for an accurate assessment of a range of conditions where the interactions are fully under control. The present method is capable to generate numbers for the parameters where the interactions change, thus producing the wanted/unwanted effects.

An example is represented by the so-called aging of nanoparticle aggregates immersed in a liquid. The amount of material composing the cluster is constant with time, while the suspending liquid penetrates into the structure, which enlarges with time. This case can be easily studied by numerical simulations, showing the actual advantage of the present method with respect to the traditional optical methods. In Figs. 3a and 3b we report the fields scattered by single clusters from a collection with a distribution of sizes ranging from 0.1 up to 1 um in diameter, equally distributed. The material has been assumed to be endowed with a refractive index of 1.5 (in vacuum). Clusters are simulated to grow in size by factors 1.5, 2, 3, 4, and the corresponding scattered fields are represented in Fig. 3a. Fields are placed along lines approximately parallel to the diagonal. The size increase determines a leftward shift of the line. The starting conditions bring to fields located along the first alignment on the right side. Notice that here the change is mainly in the real part of the scattered field, and this change is as large as an order of magnitude or larger for a small change like the one studied here. This shows one of the advantages of the present method, which is sensible to changes of clusters such that a precise determination of single cluster properties becomes impossible. Nonetheless, by following the evolution of an ensemble of clusters and its evolution under given conditions allows to extract information about the interactions governing the process.

Example 4: Measure of the specific surface of particles Specific surface of a particle is defined as the sum of the surfaces of all the exchangeable sites accessible to a given ion or molecule. The specific surface depends on the method adopted to determine it, and on the ions to be adsorbed. For a suspension of particles of a given material with polydisperse size distribution and unknown optical properties, the process of ion exchange at the surface determines a change of the surface negative charge, which in turns determines a change in the surrounding cation concentration. This is the typical case for clays. As a first approximation, namely by neglecting the Stern layer, the number of cations is exponentially decreasing with distance from the particle surface, while the number of ions is exponentially increasing. The characteristic distance is simply determined by the valence of ions, the electric potential at the given distance and the temperature. As a result, the properties of stability of the suspension change due to the change in the double layer around each particle. By describing the repulsion-attraction effects due to Brownian motions through the Dejarguin-Landau-Vervey-Overbeek model, it is well known that Van der Waals attractive interactions between particles can be compensated by repulsive interactions due to the electrolyte concentration in solution. This implies that the effective potential of the interaction between particles is genuinely determined by the surface charges, which modify the cations and anions concentrations around them. By studying the optical properties of such a suspension, it will be possible to characterize the presence of clusters due to flocculation effects induced by the surface charges imposed processes such as for example dialysis. This example shows how it is possible to assess the behavior of particles as small as ions thanks to the characterization of the optical properties of much larger clusters formed after the effect of the ions on the surface of small particles like clays.

This example can be widely extended to the study of different properties of the surfaces. In fact, surface properties include the ability of the surface to exchange water and ions at all levels through physical and chemical processes, the energy of which depends on the particle size and the surface itself.

Example 5: Measure of the interactions between interlayer cations and the surface of layers in crystals Here we consider a material constituted by layers of atoms, such as the case of minerals.

Cations are contained within the coordination polyhedral. Depending on the hydration energy of the ion, namely the energy necessary to release the water molecules of the complexes, they can either readily lose them and form complexes with the structure, entering into the cavities (hydration energy is low); or they can enter the cavity with the water molecule (large hydration energy), thus causing swelling of the structure, with a consequent change of the optical properties. For clays for example, the size distribution and the average refractive index of the grains can widely change during a process like this, and therefore be accurately characterized by the present method.

Example 6: Measure of the interactions in complex fluids The presence of a solid content made of objects (hereinafter also referred to as "background particles") surrounding the particles (hereinafter also referred to as "significant particles") is one of the main issues when characterizing interactions in complex fluids. Heterogeneous suspensions can be composed by particles of different size/shape/structure/composition, which prevents the characterization of the particles of interest due to the scattering signal from the solid content. For example, this is the case of suspensions containing proteins, colloids, nanoparticles, cells or cell fragments, or any other biological structure which is present in biological media within which the characterization has to be performed. This is the typical case of the characterization of drug delivery systems, operating in real environment, such as blood, serum, plasma, which determine the interactions of the particles with the media itself. Accessing the polarization state of the radiation emerging in the forward direction, allows to discriminate the significant particles from the surrounding solid content. This makes it possible to access the information about the interactions in many systems where the significant particles are not otherwise distinguishable from the background particles.

In addition, in those cases when the solid content is very concentrated, multiple scattering determined from the solid content itself, can affect the polarization state of the emerging radiation. The possibility evidenced in [9] to get rid of the multiply scattered light can be of huge advantage, the signal of just the particles inducing effects on the polarization state can be made much larger than the signal coming from the solid content. The interactions of these particles can then be studied in a way that is impossible otherwise.

According to an embodiment of the method, the significant particles to be studied with respect to interaction can be discriminated from the background particles by identifying the significant particles as those associated to changes of the polarization state, while the background particles do not produce any change of the polarization state between successive measurements. According to another embodiment, the significant particles to be studied with respect to interaction can be discriminated from the background particles by identifying the significant particles as those associated to a predetermined polarization state of the light scattered by these particles, while the background particles do not produce such a polarization state. One of the techniques for identifying changes caused by interactions could be that of evaluating the rate of change of the time correlations of the intensity of the scattered light which has a particular polarization state (different from that of the incident light, but present in both first and second collections of measurements). In other words, the polarization of the forward scattered light can, for example, rapidly change with time, and in a random manner; in such a case, it is the rapidity with which the polarization state changes that is the indicator of interest for measuring the interaction.

References

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Claims

1. A method for characterizing particle -particle and particle-medium interactions from light scattering measurements of particles dispersed in a fluid medium, said method comprising the following steps:

a) providing at least a first and a second collection of measurements, each measurement pertaining to a set of independent quantities that define the complex field and/or the polarization state of the light scattered by a respective particle,

b) identifying a set of parameters related to said independent quantities, said parameters being subject to change as a consequence of particle-particle or particle-medium interaction,

c) comparing the second collection with the first collection of measurements, wherein said measurements are expressed in terms of said parameters,

d) identifying any significant changes of the parameters between said collections of measurements, and optionally calculating said significant changes,

e) qualitatively and/or quantitatively determining a particle -particle or particle-medium interaction as a function of the significant changes between said collections of measurements.

2. A method according to claim 1, wherein said step c) comprises

comparing the second statistical distribution with the first statistical distribution, wherein said step d) comprises

- identifying any significant changes between said statistical distributions, and optionally calculating said significant changes as changes of characteristic quantities of said statistical distributions, and

wherein said step e) comprises

3. A method according to any of the preceding claims, wherein said set of independent quantities consists of at least one scalar quantity selected from the group consisting of: real part of a component of the complex field, imaginary part of a component of the complex field, scalar quantities related to the real part and/or imaginary part of the complex field, scalar quantities related to the polarization state.

4. A method according to any of the preceding claims, wherein said set of parameters consists of at least one scalar quantity selected from the group consisting of: real part of a component of the complex field, imaginary part of a component of the complex field, scalar quantities related to the real part and/or imaginary part of the complex field, scalar quantities related to the polarization state.

5. A method according to any of the preceding claims, wherein said particles comprise significant particles to be studied with respect to interaction, and background particles, said method comprising the following steps: i) providing at least a first and a second collection of measurements of light scattered by said significant and background particles, each measurement pertaining to the polarization state of the light scattered by a respective particle,

ii) comparing the second collection with the first collection of measurements, iii) identifying any significant changes of the polarization state between said collections of measurements,

iv) discriminating between significant and background particles by identifying the significant particles as those associated to changes of the polarization state.

6. A method according to any of claims 1 to 4, wherein said particles comprise significant particles to be studied with respect to interaction, and background particles, said method comprising the following steps:

I) providing at least a first and a second collection of measurements of light scattered by said significant and background particles,

II) discriminating between significant and background particles by identifying the significant particles as those associated to a predetermined polarization state of light scattered by said particles, III) with respect to said polarization state, comparing the second collection with the first collection of measurements, and identifying any significant changes of said parameters between said collections of measurements.