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    • 专利摘要:
    Bimodal method and system to quantify interactions and long-range properties in force microscopy. The present invention refers to a bimodal method to quantify long-range interactions and properties in force microscopy, based on modulating in amplitude and, simultaneously, exciting at least two modes of vibration of the microscope's microlever, which uses the amplitude and phase shifts of the excited modes to quantify nanomechanical properties of samples under study. The invention also relates to a force microscopy system configured to carry out said method. (Machine-translation by Google Translate, not legally binding)
    公开号:ES2781793A1
    申请号:ES201930196
    申请日:2019-03-04
    公开日:2020-09-07
    发明作者:Garcia Ricardo Garcia；Amo Carlos Alvarez；Gisbert Victor Garcia
    申请人:Consejo Superior de Investigaciones Cientificas CSIC；
    IPC主号:
    专利说明:

    [0002] METHOD AND BIMODAL SYSTEM FOR QUANTIFYING INTERACTIONS AND LONG-RANGE PROPERTIES IN FORCE MICROSCOPY
    [0004] FIELD OF THE INVENTION
    [0006] The present invention is part of the field of force microscopy research techniques, said techniques being applied to samples based on all types of materials, organic and inorganic, whether in a liquid, gaseous or vacuum medium. The invention has application in fields such as the development of electromagnetic devices or in energy storage technologies.
    [0008] More specifically, the invention relates to a method of using a force microscope by modulating its amplitude, simultaneously exciting at least two modes of vibration of a microlever. The method allows the calculation of various quantitative properties related to long-range interactions, such as magnetic, electrostatic or Van der Waals-type interactions of the analyzed materials. Likewise, the method of the invention allows its application in real time, during the measurement itself.
    [0010] STATE OF THE ART
    [0012] Force microscopy is the most widely used technique for characterizing properties at the nanometer scale. As a result of their high resolution (lateral and vertical), force microscopes (AFMs) have been introduced both in research laboratories and in quality control departments in various industrial sectors (microelectronics, polymers, food, pharmacy, etc.).
    [0014] One of the singularities of the force microscope is its ability to provide maps of both topographic properties and short-range (contact) mechanical properties. Among the short-range properties are adhesion forces, Young's modulus or different mechanical parameters related to the flexibility of the material under study. Thus, a wide variety of methods have been developed in this area, such as, for example, the methods of force volume (or “force volume”, in English) (HJ Butt, B. Capella, M. Kappl, “Force Measurements with the Atomic Force Microscope: Technique, Interpretation and Applications " Surf. Sci. Rep. 59 1-152 (2005)), "Peak Force Tapping" methods (such as, for example, that described in patent application US 2012/0131702 A1), multifrequency methods (R. García and ET Herruzo, "The emergence of multifrequency AFM ”, Nature Nanotechnology 7, 217 226 (2012)) or parametric methods (A. Raman, S. Trigueros, A. Cartagena, APZ Stevenson, M. Susilo, E. Nauman and S. Antoranz Contera, “ Mapping nanomechanical properties of live cells using multi-harmonic atomic force microscopy ”, Nature Nanotechnology 6, 809-814 (2011)).
    [0016] These methods are widely used to characterize the nanomechanical properties of polymers, biomolecules, cells, hybrid materials or nanostructures. However, the above methods cannot characterize long-range interactions, for example magnetic forces, quantitatively and at the nano-scale with the same speed, generality, and precision as short-range properties.
    [0018] The present invention is based on the use of multi-frequency methods of bimodal force microscopy. In this line, some techniques previously proposed in the state of the art are described in patent documents US 7958563 B2 and US 7921466 B2. Bimodal force microscopy is a method of force microscopy that operates by simultaneously exciting two modes of vibration (resonances) of a microlever (or "cantilever", as it is commonly known in the state of the art) of a force microscope. The modes can be, in order of frequency from lowest to highest, the first and the second, the first and the third or, in general, any two. The modes can be both flexural and torsional. This simultaneous excitation allows the duplication of channels of The previous bimodal methods and those derived later have made it possible to determine nanomechanical properties of the sample such as Young's modulus (R. García, R. Proksch, “Nanomechanical mapping of soft matter by bimodal force microscopy”, Eur. Polym. J.2 49, 1897-1906 (2013); ET Herruzo, AP Perrino, R. García, Nature Communications 5, 3126 (2014); CA Amo, AP Perrino, AF Payam, R. García, “Mapping Elastic Properties of Heterogeneous Ma terials in Liquid with Angstrom-Scale Resolution ” ACS Nano 11, 8650 8659 (2017)). A condition for determining nanomechanical properties by the above methods requires that the tip of the force microscope and the sample remain in contact for a fraction of the oscillation.
    [0020] Within the techniques based on bimodal microscopy, different methods have also been proposed to calculate some quantitative properties related to long-range interactions and, more specifically, Van der Waals-type interactions. In this context, some bimodal methods have been proposed to measure the Hamaker constant associated with Van der Waals interactions of type 1 / d2 (that is, inversely proportional to the square of the distance d). In one of these methods, feedback loops act on the two excited modes at their frequencies (E T. Herruzo and R García, “Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus”, Beilstein J. of Nanotechnol . 3, 198-206 (2012)). This implementation is quite accurate, but it has several limitations. On the one hand, the use of a frequency feedback to control the topography presents many instabilities. On the other hand, frequency feedback requires more complex electronic circuits, which slows down the measurement process. In a different implementation, the Hamaker constant was deduced through an iterative process and graphical adjustment (CY Lai, S. Perri, S. Santos, R. García, M. Chiesa, “Rapid quantitative chemical mapping of surfaces with sub-2 nm resolution ”, Nanoscale 8, 9688 9694 (2016)). This method is, on the one hand, very slow since it only has one equation to determine two parameters (a curve needs to be adjusted for different values of the amplitude). On the other hand, you cannot generalize to other types of long-range interactions, such as the constants of magnetic or electrostatic interaction.
    [0022] In general, in the bimodal microscopy techniques described above, when there is a change in a physical property (manifested in a change in the observables) and, due to the feedback provided by the topography, this leads to a change in the distance between tip and sample. In this way, if the number of equations that relate the force and the observables is increased, it will also be possible to determine more properties of the sample as the parameter of the long-range interaction. By long-range interactions are understood those interactions that can be expressed in the form:
    [0024]
    [0027] where n is an integer or with an exponential dependency of the type:
    [0029]
    [0030] where a and p are positive quantities representing the parameters of the long-range interaction, and d is the distance between the tip of the microscope and the surface of the material. Fa is the maximum value of the interaction (Fa> 0). An interaction force that is a summation of the previous expressions is also considered a force of length scope. Figure 1 of this document shows the dependence of three types of long-range interactions characterized, respectively, by exponents n = 2, n = 4 and p = 5 nm-1.
    [0032] Under the operating conditions of the bimodal microscope, it is known that certain conditions are satisfied in the virial of the interaction force, V, and in the dissipated energy (JR Lozano and R. García, "Theory of multifrequency atomic force microscopy", Physical Review Letters 100 (7), 0761024 (2008)., JR Lozano and R. García, "Theory of phase spectroscopy in bimodal atomic force microscopy", Physical Review B 79, 0141104 (2009)). Furthermore, if the second mode vibration amplitude, A2, is much smaller than the first mode vibration amplitude, Ai (that is, A2 << Ai), the change in the second mode resonance frequency f Af2 is related directly with an integral of the first mode force gradient (S. Kawai, T. Glatzel, S. Koch, B. Such, A. Baratoff and E. Meyer, "Systematic achievement of improved atomic-scale contrast via bimodal dynamic force microscopy ”, Physical Review Letters 103 (22) (2009); (E T. Herruzo and R. García, “ Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus ”, Beilstein J. of Nanotechnol. 3, 198 -206 (2012)).
    [0034] When the excitation frequencies coincide or are very close to the resonance frequencies of the excited modes, the following equations are satisfied for the virials of the modes of interest Vi (i = 1,2):
    [0035] Vi - ( k 1 AiA 01 / 2Q 1) eos <p! (E.3)
    [0036] (E.4) where k¡, Q i , A i , A o¡ , Q i are, respectively, the force constants, quality factors, amplitudes, free amplitudes and phase shifts of the excitation force with respect to the oscillation of the i- mode micro lever. The subscript 1 indicates the lowest frequency mode (main) and the subscript 2 indicates the highest frequency mode (minor). A very common bimodal drive embodiment matches the frequency of the lower mode to the resonance frequency of the first mode of the microlever, while the frequency of the upper mode matches the value of the resonance frequency of the second mode.
    [0038] Figure 2 shows an image of a microlever of those used in force microscopy (PPP-NCHAud model, Nanosensors). Figure 3 shows the frequency spectrum of the micro-lever shown in Figure 2. The spectrum shows the values of the frequencies of the first two flexural modes of the micro-lever. Figure 3b shows the thermal spectrum of the first mode and Figure 3c the thermal spectrum of the second mode. Figure 4 shows the vertical oscillation of a microlever when the first two resonance modes are simultaneously excited, the amplitude of the second mode being much smaller than the amplitude of the first mode.
    [0040] In the current state of the art, until now it has not been possible to obtain analytical relationships between microscope observables and long-range forces for long-range interaction force models with exponents n> 2. This limitation prevents them from being obtained. form maps of topography and long-range interactions. There is therefore, in the present technical field, the need to solve this limitation which would considerably increase the capabilities of the bimodal force microscopes implemented according to known techniques. Additionally, developing alternatives in this technology that make it possible to dispense with the use of multiple feedback loops would be equally desirable, for the reasons stated above.
    [0042] The present invention provides a solution to this need, by means of a novel bimodal method to quantify long-range interactions and properties in force microscopy, and of a system that implements said method.
    [0044] BRIEF DESCRIPTION OF THE INVENTION
    [0046] As described in the preceding section, a first object of the present invention refers to a method of using a bimodal force microscope by modulating its amplitude, simultaneously exciting at least two modes of vibration of the microscope's microlever, being one of them the main mode that allows to follow the topography and the other being the secondary mode, characterized by having a higher frequency than the main mode.
    [0048] The invention is based, preferably, on the application of the virial theorem independently of the excited modes, to obtain two integral equations of the interaction force and its gradient. These integrals can be solved analytically by, for example, residue theory. The previous process allows to relate the observables measured directly by the microscope, with the characteristic parameters of the long-range interactions (without contact) of the sample. In the method of the invention, the values of the amplitude and the phase of the main mode and the variations of the amplitude and the phase of the secondary mode are preferably used to quantify the parameters that characterize the interaction.
    [0049] Thus, the present method allows the calculation of various quantitative properties related to long-range interactions such as magnetic, electrostatic, and Van der Waals properties of materials. The method can be applied in real time during the measurement, or after the acquisition of the experimental data.
    [0051] Preferably, said first object of the invention is carried out by means of a bimodal method to quantify properties of long-range interactions in force microscopy, which comprises modulating the amplitude of the main mode and simultaneously exciting at least two modes of vibration of a micro-lever of a force microscope where, advantageously, the amplitude and phase shifts of the secondary mode are used, in addition to the amplitude and phase values of the main mode, to determine the virials of the excited modes and, from them , quantify the parameters of the long-range interaction.
    [0053] More specifically, the method of the invention comprises carrying out the following steps:
    [0054] a) having, on the head of a force microscope, a microlever with a tip, adapted to interact with a sample under study, and where said microlever has at least two modes of vibration, one of said modes being a main mode and, the other, a secondary mode;
    [0055] b) providing a first actuator to variably vibrate the microlever and a second adjustable actuator to provide a relative displacement of the microlever with respect to at least one region of the sample, at a distance thereon;
    [0056] c) generating one or more excitation signals through the first actuator, adding said excitation signals to vibrate the microlever;
    [0057] d) calibrate one or more of the following parameters associated with the operation of the microlever:
    [0058] - force constant of the main and secondary modes;
    [0059] - quality factor of the main and sub modes;
    [0060] - inverse of the optical sensitivity of the photodiode of the force microscope, for the main and secondary modes;
    [0061] - radius, R, of the tip of the microlever;
    [0062] f) setting a feedback loop of the amplitude of the main mode of vibration, which keeps said amplitude constant, modifying the deflection distance between the tip of the microscope and the surface of the sample;
    [0063] g) detecting, by means of a processing unit, the deflection signal of the microlever;
    [0064] h) registering, by means of the processing unit, the signals corresponding to the vibration modes, simultaneously or after the acquisition of an image of the sample topography;
    [0065] i) transform, through a processing unit, the processed data into one or more observables to obtain, from them, parametric maps of the long-range interactions of the sample.
    [0067] It is important to highlight, once again, the fact that the method of the invention, as stated in the previous lines, allows a complete obtaining of the parametric maps of the sample under study by means of a single feedback in amplitude of the first main mode of vibration. Therefore, in a preferred embodiment of the invention, the method of the invention excludes any additional steps in which two feedbacks are used in the entire method, such as a frequency feedback of the secondary mode. Thanks to the approach of the present invention, the described method can be carried out quickly and easily, without loss of precision.
    [0069] In a preferred embodiment of the invention, the method also comprises a verification step e) according to the following sub-steps:
    [0070] e.1) check that the amplitude of vibration of the secondary mode of the microlever s is lower than the amplitude of vibration of the main mode;
    [0071] e.2) check that the static deflection of the microlever is less than the value of the amplitude Ai;
    [0072] e.3) check that the energy dissipated in the sample per period of vibration is less than the average kinetic energy per period.
    [0074] In another preferred embodiment of the invention, the assembly formed by the tip and the microlever is placed on a heterogeneous sample to measure the parameters of the long-range interactions between the tip and the sample.
    [0076] In another preferred embodiment of the invention, in step (c) the microlever is excited according to a main mode and a secondary mode of vibration. More preferably, the resulting signal reaching the microlever is expressed according to the following mathematical relationship dependent on time t:
    [0077] Pexc = Pexd Pexc two = Pqi e or s 2 n ft t + F 02 e or s 2nf2 t;
    [0078] where Oj and f F are respectively the excitation signal and the excitation frequency of mode i are transferred to the actuator that excites vibration microlever.
    [0080] In another preferred embodiment of the invention, in step (h) in which the data shown in the parametric property maps of the sample are transformed, the amplitude and phase shifts of the secondary mode are used, the amplitude values and the phase of the main mode to determine the virials of the main V i and secondary V 2 modes and, from them, quantify the parameters of the long-range interaction of the sample.
    [0082] In another preferred embodiment of the invention, the data on the amplitude and phase shifts of the secondary mode and the values of the amplitude and phase of the main mode are converted, by means of an analytical calculation, into the parametric maps and that of the interaction of long range of the sample.
    [0084] In another preferred embodiment of the invention, the long-range interaction comprises a Van der Waals interaction force, which is modeled according to an expression of the type -a / d2, and the interaction parameter a is calculated by the equation
    [0089] In another preferred embodiment of the invention, for an interface geometry of the sphere-plane type, the Hamaker constant is calculated using the equation:
    [0094] In another preferred embodiment of the invention, the long-range interaction is modeled according to an expression of the type a / d4, and the interaction parameter a is calculated using the following expression:
    [0098] where the mean distance zc between the tip and the sample is given by:
    [0101] In another preferred embodiment of the invention, in step (h) the interactions are modeled as a / d n type expressions in the parametric maps of the properties of the sample interaction, and the changes in the amplitude and phase of the mode are used. secondary and the amplitude and phase values of the main mode to determine the virials of the main and secondary modes and, from them, the values of the parameter a of the interaction.
    [0103] In another preferred embodiment of the invention, in step (h) the interactions are modeled as expressions of type F to exp ( -fid) in the parametric maps of the properties of the sample interaction, the changes in the amplitude and the phase of the secondary mode and the values of the amplitude and the phase of the main mode to determine the virials of the main and secondary modes and from them the values of the parameter fi of the interaction.
    [0105] In another preferred embodiment of the invention, for interaction forces of the type F a -exp ( -fid), the interaction parameter fi is calculated by the following expression:
    [0110] In another preferred embodiment of the invention, the measurement is carried out having the sample immersed in a liquid, in a gaseous medium or under vacuum.
    [0112] A second object of the present invention relates to a force microscopy system which, advantageously, comprises:
    [0113] - a force microscope equipped with a microlever in which a tip adapted to interact with a sample under study is arranged, where said microlever has at least two modes of vibration, one of said modes being a main mode and the other , a secondary mode;
    [0114] - a first actuator configured to make the microlever vibrate variably
    [0115] - a second actuator configured to provide a relative displacement of the microlever with respect to at least one region of the sample, at a distance thereon;
    [0116] - a means for generating one or more excitation signals through the first actuator;
    [0117] - a feedback loop of the amplitude Ai of the main mode of vibration, adapted to keep said amplitude Ai constant by modifying the deflection distance between the tip of the microscope and the surface of the sample;
    [0118] - a unit for processing the deflection signal of the microlever, equipped with hardware and / or software means configured to carry out a method according to any of the embodiments described in the present document.
    [0119] Throughout the description and claims the word "comprise" and its variants are not intended to exclude other technical characteristics, additives, components or steps. For those skilled in the art, other objects, advantages and characteristics of the invention will emerge partly from the description and partly from the practice of the invention.
    [0121] BRIEF DESCRIPTION OF THE FIGURES
    [0123] The following is a brief description of each of the figures used to complete the description of the invention that follows. Said figures are related to the state of the art or to preferred embodiments of the invention, which are presented as non-limiting examples thereof.
    [0125] Figure 1 shows the dependence of three types of long-range interactions characterized, respectively, by exponents n = 2, n = 4 and p = 5 nm-1. The curves are normalized to their maximum value that is established for a distance do = 0.168 nm.
    [0127] Figure 2 shows an image of one of the microlevers used in force microscopy in bimodal configurations. In this case it corresponds to the PPP-NCHAu model (Nanosensors, Germany). In the image, the reflection of light from the optical device used to measure the signal deflection is visible.
    [0129] Figure 3 shows a part of the frequency spectrum in air of the microlever shown in Figure 2. The peaks that appear in the image indicate the frequencies of the first two flexural modes (a). Details of the thermal spectrum are shown for the first mode (b) and for the second mode (c). The spectrum has been obtained from thermal noise.
    [0131] Figure 4 shows an example of the excitation signal of the first mode (a), of the second mode (b) and the deflection of the microlever before the simultaneous excitation of the first two modes, and where the amplitude of vibration of the second mode is much less than the amplitude of vibration of the first mode.
    [0132] Figure 5 shows a diagram of the most relevant elements of the method object of this invention.
    [0134] Figure 6 shows a diagram of the operation of a force microscope under the excitation of two vibration modes for the measurement of long-range interactions where the main mode is amplitude modulated and the second mode does not have any feedback.
    [0136] Figure 7 shows a diagram of the method object of the present invention, according to an embodiment of the invention.
    [0138] Figure 8 shows four graphs that represent the results of this method, applied to the analysis of a MoS2 sample deposited on a silicon oxide (SiO2) surface, simultaneously determining: the topography (a), the main virial (b), the secondary virial (c) and the Hamaker constant map of each material (d).
    [0140] Figure 9 shows a comparative graph of the histograms of the Hamaker constant obtained on SiO2 and on MoS2. The data has been extracted from Fig. 8d.
    [0142] Figure 10 shows a diagram of the method object of the present invention, according to a preferred embodiment of the invention.
    [0144] Figure 11 shows a diagram of the method object of the present invention, according to a preferred embodiment of the invention.
    [0146] Figure 12 shows a diagram of the method object of the present invention, according to a preferred embodiment of the invention.
    [0148] Description of the numerical references of the Figures:
    [0150]
    [0151]
    [0154] DETAILED DESCRIPTION OF THE INVENTION
    [0156] As described in the preceding paragraphs, the present invention refers to a bimodal method to quantify properties of long-range interactions in force microscopy, said method being based on the modulation of the amplitude of a first excitation mode and on the determination , independently, of the virials of the interaction associated with the main and secondary modes. In said method, therefore, the amplitude of the main mode, the frequency and phase shifts of the secondary mode, and the virials of both modes are used to quantify the parameters of long-range interactions.
    [0158] Figure 5 shows a diagram of the main elements of the present invention to characterize long-range interactions. Figure 6 describes the operation of a force microscope (1) under the excitation of two modes of vibration, while a microlever arranged on the head of the microscope (1) moves over the surface of the sample to study, and where they are established a series of conditions for each of the modes. The lower frequency mode is preferably controlled by a feedback loop that maintains its amplitude at a fixed value, while the higher frequency mode (secondary) evolves freely, according to the intensity of the long-range interaction .
    [0160] More specifically, the bimodal method for quantifying properties of long-range interactions in force microscopy of the invention preferably comprises the following steps:
    [0161] a) Provide, on the head of a force microscope (1), a microlever (2) with a tip (3) at its end, adapted to interact with a sample (4) under study, and where said microlever (2) has at least two modes of vibration, one of said modes being a main mode and the other a secondary mode.
    [0162] b) Provide a first actuator (not shown in the figures) to make the microlever (2) vibrate in a variable manner and a second adjustable actuator (not shown in the figures) to provide a relative displacement of the microlever (2) with respect to, at least one region of the sample (4), at a distance (5) above it.
    [0163] c) Generate excitation signals (6) through the first actuator to vibrate the main and secondary modes of the microlever (2), by means of an excitation force Fexc of the type:
    [0165]
    [0166] where Fo, and f are, respectively, the excitation force and the excitation frequency of mode i that excite the vibration of the microlever (2).
    [0167] d) Calibrate the following parameters associated with the operation of the microlever (2):
    [0168] - force constant (ki, k2), of the main and secondary modes;
    [0169] - quality factor ( Qi, Q2) of the main and sub modes;
    [0170] - inverse of the optical sensitivity of the photodiode (7) of the force microscope (1), for the main and secondary modes;
    [0171] - radius, R, of the tip (3) of the microlever (2).
    [0172] e) Optionally, carry out one or more of the following verification stages:
    [0173] e.1) Check that the amplitude of vibration of the secondary mode of the microlever (2) is less than the amplitude of vibration of the main mode (preferably, A2 s 0.1 Ai).
    [0174] e.2) Check that the static deflection of the microlever (2) is negligible compared to the value of the amplitude Ai (being, at least, preferably an order of magnitude lower).
    [0175] e.3) Check that the energy dissipated in the sample (4) per period of vibration is less than the average kinetic energy per period (being, at least, preferably an order of magnitude lower).
    [0176] f) Set a feedback loop (9) of the amplitude, Ai, of the main vibration mode, which keeps said amplitude Ai constant , modifying (8) the distance (5) (deflection) between the tip (3) of the microscope ( 1) and the sample surface (4).
    [0177] g) Detecting, by means of a processing unit (10), the deflection signal of the microlever (2);
    [0178] h) recording (10), by means of the processing unit, the signals corresponding to the modes of vibration, simultaneously or after the acquisition of an image of the topography of the sample (4);
    [0179] i) transform (11), using a processing unit, the processed data into one or more observables (12) and obtain, from them, parametric maps (13) of the long-range interactions of the sample (4) .
    [0181] In the present bimodal method for quantifying properties of long-range interactions in force microscopy, the amplitude, Ai, and the phase of the first mode, 0i, and the variations of the amplitude and phase of the second mode are converted, by a calculation analytical, simultaneous or subsequent to the acquisition of a topographic image, in parametric maps (13) that express the properties of the long-range interaction of the sample (4).
    [0183] According to the bimodal method to quantify properties of long-range interactions in force microscopy object of the present invention, the tip system (3) -microlever (2) is placed on a heterogeneous sample (4) to measure various long-range properties such as the parameters of magnetic and electrostatic interactions or the Hamaker constant, H, of its interface.
    [0185] According to a possible preferred embodiment of the invention, in step (h) of the method in which the data shown in the parametric maps (13) of properties of the sample (4) are transformed, the amplitude Ai and the phase of the first mode, 0i, the changes of the amplitude and the phase shift of the secondary mode, to calculate the virials Vi and V2 associated with the main and secondary modes of a long-range interaction of the type:
    [0187]
    [0188] and, from the previous parameters, the interaction constant a and the mean tip-sample distance z c is determined.
    [0190] If the amplitude of the secondary mode is much smaller than that of the main mode (A1 >> A2) and static deflection is neglected, the tip distance (3) -sample (4) depends exclusively on the deflection of the main mode:
    [0191] d (t) «zc zt (t) (E.7)
    [0193] The virial expressions for the main and secondary modes of a force that follows equation (E.6) are given by:
    [0195]
    [0196] V, -na to Ai 2ttí
    [0197] "i ni (E.9)
    [0198] where intermediate expressions have been used:
    [0200]
    [0202] The superscripts (n) indicate derivative of order n and "i" is the imaginary unit.
    [0204] According to another possible embodiment of the invention, in step (h) of the method in
    [0205] which transform the data shown in the parametric maps of properties of the
    [0206] sample, the amplitude Ai is used and the phase of the first mode, 0i, the changes of the amplitude
    [0207] and the secondary mode offset to calculate the virials Vi and V2 of an interaction of
    [0208] long-range exponential type:
    [0210]
    [0212] The virial expressions are:
    [0214]
    [0216] DETAILED DESCRIPTION OF AN EXAMPLE OF EMBODIMENT OF THE INVENTION
    [0218] In a preferred embodiment of the invention, the first two modes are excited
    [0219] flexural of the microlever (2) (although, in other embodiments, it is possible to
    [0220] excite any combination of flexural and torsional modes). Also, at the stage
    [0221] (a) of the method, the system formed by the tip (3) and the microlever (2) is located on
    [0222] a heterogeneous sample (4), which may show changes in the long-term interactions
    [0223] scope.
    [0225] In step (d) of the method, the radius, R, of the tip (3) is calibrated using a sample
    [0226] (4) nanoparticles of known radius where, from the apparent size measure
    [0227] From the nanoparticles given by the microscope (1) and, knowing the radius of the nanoparticles, the radius, R, of the tip (3) is obtained. The radius of the tip can also be obtained from other methods, such as the Sergio Santos method (Sergio Santos, Li Guang, Tewfik Souier, Karim Gadelrab, Matteo Chiesa, and Neil H. Thomson '' A method to provide rapid in situ determination of tip radius in dynamic atomic force microscopy ” Review Science Instruments, 83, 043707 (2012)). Alternatively, the radius can be calibrated if a sample is available whose Hamaker constant is known.
    [0229] The method of the invention makes it possible to measure certain properties that will depend on the interaction force model (parameters a, p, Hamaker's constant of the interface). To do this, at least two observables are determined, that is, quantities directly measured by the microscope (1), simultaneously and independently. Numerical values are obtained using analytical formulas. All this maximizes the operating speed of the force microscope (1).
    [0231] The method of the invention makes use of at least two independent equations that analytically relate the physical parameters of the interaction and the observables of the microscope (1). The mentioned equations will allow the determination of the parameters of the long-range interaction. This allows the characterization of the long-range interactions of a sample (4), in a reproducible way, in real time and with high lateral resolution. The formulas are analytical and do not have convergence problems associated with iterative numerical methods.
    [0233] In a preferred embodiment of the method of the invention that is illustrated in Figure 7, in step (h) of the method, the changes in amplitude Ai and the phase of the secondary mode 02 are used, and the virials of the main mode V1 and of the secondary V2 to determine the parameter a of one of the most common long-range interactions in force microscopy,
    [0235]
    [0236] The equations for a and for the mean distance zc between the tip (3) and the sample (4) turn out to be:
    [0238]
    [0239] For the specific case of a Van der Waals interaction between a hemispherical tip (3) of radius R and a flat sample (4), the relationship between the interaction parameter a and the Hamaker constant of the interface H is given by
    [0240] 6th
    [0242] R (E.21)
    [0244] Additionally, in stage (h) of the method in which the data obtained are transformed into the parametric maps of the Hamaker constant of the sample (4). A demonstration of the method to determine the Hamaker constant for different materials is presented in Figures 8 and 9, as a non-limiting example of a preferred embodiment of the invention.
    [0246] In another embodiment of the method of the invention that is illustrated in Figure 10, in step (h) of the method, the changes in amplitude A2 and the phase of the secondary mode 02 are used, and the virials of the main mode Vi and the secondary V2 to determine the parameter a of magnetic dipole forces:
    [0248]
    [0249] Starting from equation (E.22) it is also possible to solve equations (E.8) and (E.9) in an analytical way. First, the variable that will be used to simplify the equations is introduced:
    [0251]
    [0252] from where the following results can be obtained:
    [0254]
    [0257] In another embodiment of the method of the invention that is illustrated in Figures 11 and 12, in step (h) of the method, the changes in amplitude A2 and the phase of the secondary mode 0i are used, and the virials of the main mode Vi and of the secondary V2 to determine the parameter p of forces of the type described by equation (E.14). To do this, equations (E.15) and (E.16) can be approximated as
    [0259]
    [0260] ^ 2 = -F ae ~ í] Zc § ( 8 p 2 ( A2 2AD)
    [0261] (E.27)
    [0263] From the previous equations it follows:
    [0265]
    [0266] where the Taylor expansions have been used for the modified Bessel functions of the first kind:
    [0268]
    [0269] with x = fiA j , and under the conditions Ai >> Ai and f iA j <3, with j = 1,2 and 0 < f iA j <3.
    [0271] The mean distance (5) between the tip (3) and the sample (4) is controlled by keeping the amplitude of the main mode, A i , constant while the microlever (3) moves along the length and width of the sample (4) .
    权利要求:
    Claims (14)
    [1]
    1 Bimodal method to quantify properties of long-range interactions on a sample (4) with a force microscope (1),
    characterized in that it comprises carrying out the following stages:
    a) have, in the head of the force microscope (1), a microlever (2) with a tip (3), adapted to interact with a sample (4) under study, and where said microlever (2) has, at least two modes of vibration, one of said modes being a main mode and the other a secondary mode;
    b) providing a first actuator to make the microlever (2) vibrate variably and a second adjustable actuator to provide a relative displacement of the microlever (2) with respect to at least one region of the sample (4), to a distance (5) thereon;
    c) generating one or more excitation signals (6) through the first actuator, adding said excitation signals (6) to vibrate the microlever (2);
    d) calibrate one or more of the following parameters associated with the operation of the microlever (2):
    - force constant (ki, k2), of the main and secondary modes;
    - quality factor ( Qi, Q2) of the main and sub modes;
    - inverse of the optical sensitivity of the photodiode (7) of the force microscope (1), for the main and secondary modes;
    - radius, R, of the tip (3) of the microlever (2);
    f) setting a feedback loop (9) of the amplitude Ai of the main mode of vibration, which keeps said amplitude Ai constant , modifying (8) the deflection distance (5) between the tip (3) of the microscope (1) and the surface of the sample (4);
    g) detecting, by means of a processing unit (10), the deflection signal of the microlever (2);
    h) register (10), by means of the processing unit, the signals corresponding to the vibration modes, simultaneously or after the acquisition of an image of the sample topography (4), and use the displacements of the amplitude and the phase of the secondary mode, the amplitude values and the phase of the main mode to determine the virials of the main Vi and secondary V2 modes and, from these virials, quantify the parameters of the long-range interaction of the sample (4 );
    i) transform (11), by means of a processing unit, the data recorded in the previous step into one or more observables (12) and obtain, from them, parametric maps (13) of the long-range interactions of the sample (4).
    [2]
    2. - Method according to the preceding claim, which also comprises a verification stage e) according to the following sub-stages:
    e.1) check that the amplitude of vibration of the secondary mode of the microlever (2) is less than the amplitude of vibration, of the main mode;
    e.2) check that the static deflection of the microlever (2) is less than the value of the amplitude Ai;
    and.
    [3]
    3) check that the energy dissipated in the sample (4) per period of vibration is less than the average kinetic energy per period.

    [4]
    (4) heterogeneous, to measure the parameters of long-range interactions between the tip and the sample.

    [5]
    5.
    [6]
    6. - Method according to any of the preceding claims, where the data on the displacements of the amplitude and phase of the secondary mode and the values of the amplitude and phase of the main mode are converted, by means of an analytical calculation, into the parametric maps (13 ) of the long-range interaction of the sample (4).
    [7]
    7.
    [8]
    8.- Method according to claims 6-7 where, for an interface geometry of the sphere-plane type, the Hamaker constant is calculated using the equation:

    [9]
    9.- Method according to claim 6, where the long-range interaction is modeled according to an expression of the type a / d4, where the interaction parameter a is calculated by the following expression:

    [10]
    10.
    [11]
    eleven.
    [12]
    12.
    [13]
    13. Method according to any of the preceding claims, wherein the measurement is carried out having the sample (4) immersed in a liquid, in a gaseous medium or in a vacuum.
    [14]
    14.- Force microscopy system characterized by comprising:
    - A force microscope (1) equipped with a microlever (2), in which a tip (3) adapted to interact with a sample (4) under study is located, where said microlever (2) has at least two vibration modes, one of said modes being a primary mode and the other a secondary mode;
    - a first actuator configured to make the microlever (2) vibrate variably;
    - a second actuator configured to provide a relative movement of the microlever (2) with respect to at least one region of the sample (4), at a distance (5) thereon;
    - a means for generating one or more excitation signals (6) through the first actuator;
    - a feedback loop (9) of the amplitude Ai of the main vibration mode, adapted to keep said amplitude Ai constant by modifying (8) the deflection distance (5) between the tip (3) of the microscope (1) and the surface of the sample (4);
    - a processing unit (10) of the deflection signal of the microlever (2), equipped with hardware and / or software means configured to carry out a method according to any of the preceding claims.
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    同族专利:
    公开号 | 公开日
    WO2020178468A1|2020-09-10|
    ES2781793B2|2021-08-12|
    引用文献:
    公开号 | 申请日 | 公开日 | 申请人 | 专利标题
    EP1912055A1|2005-06-24|2008-04-16|Consejo Superior de Investigaciones Cientificas|Method of using an atomic force microscope and microscope|
    WO2014131925A1|2013-02-28|2014-09-04|Consejo Superior De Investigaciones Científicas |Bimodal method for quantifying non-topographical properties in force field microscopy|
    US20150309071A1|2014-04-23|2015-10-29|Oxford Instruments Asylum Research, Inc.|AM/FM Measurements Using Multiple Frequency of Atomic Force Microscopy|
    WO2008003796A1|2006-07-04|2008-01-10|Consejo Superior De Investigaciones Científicas|Method for using an atomic force microscope|
    US8650660B2|2008-11-13|2014-02-11|Bruker Nano, Inc.|Method and apparatus of using peak force tapping mode to measure physical properties of a sample|
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