Method for measuring dynamic physical properties, method for controlling push-in amount of probe, and device for measuring dynamic physical properties

Abstract

To provide a method for measuring dynamic physical properties with which it is possible to prevent variations in the push-in amount of a probe without determining a contact point.SOLUTION: A method for measuring dynamic physical properties according to the present invention includes the steps of: moving a cantilever or a stage from a first starting point to a first end point at a first position of a sample to press a probe against the sample, and acquiring a force curve at the first position; determining the maximum push-in amount δmax at the first position on the basis of information included in the force curve at the first position; determining a second end point by using a set push-in amount δset and the maximum push-in amount δmax at the first position; and moving the cantilever or the stage from a second starting point to the second end point at a second position of the sample to press the probe against the sample and acquiring a force curve at the second position.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a method for measuring the mechanical properties of a sample, a method for controlling the amount of probe depression, and a measuring device. [Background technology]

[0002] Atomic force microscopes (AFMs) are widely used for nanoscale imaging of sample surface topography and as force mapping instruments to measure local mechanical properties of samples.

[0003] AFM force mapping methods are broadly divided into two: force volume (force volume mode) and pulse force (pulse force mode). The force volume method measures the indentation force-indentation curve (force curve) by pressing a cantilever probe against a sample at a constant speed. The pulse force method measures the indentation force-indentation curve (force curve) by intermittently contacting the cantilever probe with the sample by vibrating the cantilever at its non-resonant frequency (Non-Patent Documents 1 and 2). The pulse force method is also sometimes called the peak force tapping method (peak force tapping mode) (Non-Patent Documents 3 to 5). The force volume method can perform force mapping measurements by maintaining a constant maximum indentation force. On the other hand, the pulse force method can perform force mapping measurements at higher speeds than the force volume method. The force volume method and pulse force method share the common feature of controlling the cantilever probe using the indentation force as a trigger.

[0004] When measuring the distribution of mechanical properties of a sample using an AFM, a cantilever probe is pressed against the sample at multiple positions to obtain a force curve at each position. The force curve is then analyzed using elastic contact theory and other methods to evaluate the mechanical properties, such as the elastic modulus, at each position. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Rosa Zeiser, A., et al., "The simultaneous measurement of elastic, electrostatic and adhesive properties by scanning force microscopy: pulsed-force mode operation", Measurement Science and Technology, Vol. 8, pp. 1333-1338. [Non-patent document 2] Krotil, H.-U., et al., "Pulsed force mode: a new method for the investigation of surface properties", Surface and Interface Analysis, Vol. 27, pp. 336-340. [Non-patent document 3] Heu, C., et al., "Glyphosate-induced stiffening of HaCaT keratinocytes, a Peak Force Tapping study on living cells", Journal of Structural Biology, Vol. 178, pp. 1-7. [Non-patent document 4] Calzado-Martin, A., et al., "Effect of Actin Organization on the Stiffness of Living Breast Cancer Cells Revealed by Peak-Force Modulation Atomic Force Microscopy", ACS Nano, Vol. 10, pp. 3365-3374. [Non-patent document 5] Efremov, YM, et al., "Viscoelastic mapping of cells based on fast force volume and PeakForce Tapping", Soft Matter, Vol. 15, pp. 5455-5463. Summary of the Invention [Problem to be solved by the invention]

[0006] As described above, when measuring the distribution of mechanical properties of a sample using an AFM, the cantilever probe is controlled using the indentation force as a trigger. For example, force mapping measurements are performed by holding the maximum indentation force constant. Holding the maximum indentation force constant results in a large indentation volume for soft samples and a small indentation volume for hard samples. Therefore, when performing force mapping measurements on samples whose surface elastic modulus varies significantly from location to location (e.g., cells), the indentation volume can vary significantly from location to location, potentially increasing damage to the sample and reducing the accuracy of the mechanical property measurements due to the difference in indentation volume.

[0007] From these perspectives, there is a need for a method to control the cantilever probe by maintaining a constant indentation amount rather than a constant indentation force in force mapping measurements on samples whose mechanical properties vary greatly from location to location. Typically, to evaluate the indentation amount, information about the position where the probe first comes into contact with the sample surface (contact point) is required. However, when the sample is soft (e.g., a cell), the indentation force rises slowly, making it impossible to determine the contact point with high accuracy. This difficulty in determining the contact point makes it difficult to control the indentation amount.

[0008] An object of the present invention is to provide a method for measuring mechanical properties, a method for controlling the amount of probe depression, and an apparatus for measuring mechanical properties that can suppress fluctuations in the amount of probe depression without determining the contact point. [Means for solving the problem]

[0009] The present invention relates to a method and an apparatus for measuring mechanical properties as follows: [1] A method for measuring mechanical properties of a sample by pressing a probe fixed to a cantilever against the sample placed on a stage, the method comprising the steps of: pressing the probe against the sample at a first position on the sample by moving the cantilever or the stage from a first start point to a first end point, and acquiring a force curve for the first position; and calculating a maximum pressing amount δ at the first position based on information included in the force curve for the first position. max and a step of determining a predetermined set push-in amount δ set and the maximum pushing amount δ at the first position max and at a second position on the sample, pressing the probe against the sample by moving the cantilever or the stage from a second start point to the second end point, thereby obtaining a force curve at the second position. [2] Maximum pushing amount δ at the first position max is the contact point z on the force curve at the first position c The method for measuring mechanical properties according to [1], wherein the mechanical properties are determined without using information from the above. [3] The maximum pushing amount δ at the first position max is the arbitrary pushing force F1, the maximum pushing force F max , and the maximum pushing force F max Maximum pushing amount δ when max and the indentation amount δ1 at the arbitrary indentation force F1. [4] The maximum pushing amount δ at the first position max is calculated by the following formula 1, the method for measuring mechanical properties described in [3].

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[10] A method for controlling a probe depression amount when a probe fixed to a cantilever is pressed against a sample placed on a stage, the method comprising the steps of: pressing the probe against a first position of the sample by moving the cantilever or the stage from a first start point to a first end point while acquiring a force curve for the first position; and calculating a maximum depression amount δ at the first position based on information included in the force curve for the first position. max and a step of determining a predetermined set push-in amount δ set and the maximum pushing amount δ at the first position maxand at a second position on the sample, pressing the probe against the sample by moving the cantilever or the stage from a second start point to the second end point.

[11] Maximum pushing amount δ at the first position max is the contact point z on the force curve at the first position c The method for controlling the probe depression amount according to

[10] , wherein the depression amount is determined without using information on the above.

[12] A device for measuring a force curve at a second position of a sample placed on the stage, the device comprising: a stage for placing a sample thereon; a cantilever; a probe fixed to the cantilever; a detector for detecting a deflection of the cantilever; an XY moving unit for relatively moving the sample and the cantilever in the X-axis direction and the Y-axis direction; a Z moving unit for relatively moving the sample and the cantilever in the Z-axis direction; and a controller for controlling the detector, the XY moving unit, and the Z moving unit, wherein the controller controls the detector, the XY moving unit, and the Z moving unit to move the cantilever or the stage in the Z-axis direction from a start point to an end point at a plurality of positions of the sample placed on the stage, thereby pressing the probe against the sample and acquiring a force curve at each position, and the controller controls the detector, the XY moving unit, and the Z moving unit to move the cantilever or the stage in the Z-axis direction from a start point to an end point at a plurality of positions of the sample placed on the stage, the control unit controlling the detector, the XY moving unit, and the Z moving unit to move the cantilever or the stage in the Z-axis direction from a start point to an end point, set and a maximum depression amount δ at the first position determined based on information included in the force curve at the first position. max and controlling the Z movement unit so that the second end point is determined using the second end point.

[13] Maximum pushing amount δ at the first position max is the contact point z on the force curve at the first position c The mechanical property measuring device according to

[12] , wherein the mechanical property is determined without using information. [Effects of the Invention]

[0010] According to the present invention, it is possible to provide a method for measuring mechanical properties, a method for controlling the amount of probe depression, and an apparatus for measuring mechanical properties, which can suppress fluctuations in the amount of probe depression without determining the contact point. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a schematic diagram showing an example of a position where a probe is pressed on a sample. [Figure 2] FIG. 2 shows an example of a force curve for explaining the principle of the method for measuring mechanical properties according to the present invention. [Figure 3] Figure 3A is a schematic diagram showing the positional relationship between the sample and the cantilever probe when a force curve is acquired, and Figure 3B is a graph showing the relationship between each parameter when a force curve is acquired. [Figure 4] FIG. 4 shows another example of a force curve for explaining the principle of the method for measuring mechanical properties according to the present invention. [Figure 5] FIG. 5 shows the simulation results of the relationship between Δδd and α. [Figure 6] FIG. 6 shows the simulation results showing the relationship between n and α. [Figure 7] FIG. 7 shows the simulation results showing the relationship between Δδε and α. [Figure 8] FIG. 8 is a schematic diagram showing the configuration of a mechanical property measuring device according to one embodiment of the present invention. [Figure 9]FIG. 9A is a map image of the elastic modulus E of MDCK cells obtained by conventional force curve mapping. FIG. 9B is a map image of the elastic modulus E of MDCK cells obtained by force curve mapping according to the present invention. FIG. 9C is a map image of the maximum indentation amount δmax obtained by conventional force curve mapping. FIG. 9D is a map image of the maximum indentation amount δmax obtained by force curve mapping according to the present invention. FIG. 9E is an image showing the difference between the map image of the elastic modulus E shown in FIG. 9A and the map image of the elastic modulus E shown in FIG. 9B. [Figure 10] 10A and 10B are box plots of maximum depression amount δmax and Δδ in conventional force curve mapping measurements and force curve mapping measurements according to the present invention, respectively. [Figure 11] FIG. 11 is a graph showing the average value and variation of the maximum depression amount Δmax when the value of S is changed. DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings. However, the present invention is not limited to these. In this specification, a numerical range expressed using "to" means a range that includes the numerical values ​​written before and after "to" as the lower and upper limits.

[0013] (Method for measuring mechanical properties) The method for measuring mechanical properties according to the present invention measures the mechanical properties of a sample by repeatedly pressing a probe fixed to a cantilever against a sample placed on a stage to obtain a force curve (also referred to as a force-distance curve or force-distance curve). More specifically, in the method for measuring mechanical properties according to the present invention, the process of pressing the probe against the sample by moving the cantilever or the stage in the Z-axis direction to obtain a force curve is repeated while changing the position at which the probe is pressed in the X-axis and / or Y-axis directions, thereby measuring the distribution of the mechanical properties of the sample. In this case, in the process of obtaining force curves from the second time onwards, the movement of the cantilever or the stage is feedback-controlled based on information contained in the force curves obtained up to that point, thereby suppressing variations in the amount of probe pressing from one location to another.

[0014] In the method for measuring mechanical properties according to the present invention, during the feedback control, the contact point z in the force curve is calculated based on the information contained in the force curve obtained up to that point. c The maximum pressing amount δ when the force curve was obtained without using the information max Then, the determined maximum pushing amount δ max and a predetermined set depression amount δ set The end point of the cantilever or stage movement is determined using the above. In the process of acquiring force curves from the second time onwards, the cantilever or stage is moved to this end point so that the probe is pressed against the sample. In this way, feedback control of the cantilever or stage movement can suppress variations in the amount of probe pressing from location to location, even for samples whose mechanical properties vary greatly from location to location.

[0015] That is, the method for measuring mechanical properties according to the present invention includes the steps of: pressing a probe against a sample at a first position on the sample by moving a cantilever or a stage from a first start point to a first end point, thereby acquiring a force curve at the first position; and calculating a maximum pressing amount δ at the first position based on information included in the force curve at the first position. max and a step of determining a predetermined set push-in amount δ set and the maximum pushing amount δ at the first position max and determining a second end point using the force curve obtained at the second position of the sample by pressing the probe against the sample by moving the cantilever or stage from the second start point to the second end point. The step of obtaining the force curve at the second position is performed after the step of obtaining the force curve at the first position.

[0016] Of course, after the step of acquiring the force curve at the second position, a step of pressing the probe against the sample by moving the cantilever or the stage from a third start point to a third end point at a third position on the sample to acquire a force curve at the third position may be further performed. In this case, before the step of acquiring the force curve at the third position, the maximum depression amount δ at the first or second position (preferably the second position) is calculated based on information contained in the force curve at the first or second position. max and a step of determining a predetermined set push-in amount δ set and the maximum pushing amount δ at the first position or the second position. max A step of determining a third end point is also performed using the above method. In the step of obtaining a force curve at a third position, the cantilever or the stage is moved to the third end point determined in this step, thereby pressing the probe against the sample.

[0017] In this way, after the step of pressing the probe against the sample at the nth position (n is an integer) of the sample and acquiring a force curve for the nth position, a step of pressing the probe against the sample at the (n+1)th position of the sample and acquiring a force curve for the (n+1)th position may be further performed. In this case, too, before the step of acquiring the force curve for the (n+1)th position, the maximum depression amount δ at that position (any of the first to nth positions) is calculated based on information contained in the force curve for one of the first to nth positions (preferably the nth position). max and a step of determining a predetermined set push-in amount δ set and the maximum pushing amount δ of any one of the first position to the nth position. max A step of determining the (n+1)th end point is also performed using the above formula. In the step of acquiring a force curve at the (n+1)th position, the cantilever or the stage is moved to the (n+1)th end point determined in this step, thereby pressing the probe against the sample.

[0018] FIG. 1 is a schematic diagram showing an example of the position where the probe is pressed against the sample. This figure shows an example of acquiring force curves at 30 positions in a square area (dashed line) containing multiple cells, which is shown schematically as a hexagon. "1" indicates the first position of the sample, "2" indicates the second position of the sample, and "30" indicates the 30th position of the sample. Note that the order in which the force curves are acquired is not limited to the example shown in FIG. 1.

[0019] In the method for measuring mechanical properties according to the present invention, before obtaining a force curve at a specific position (for example, the 14th position), the maximum indentation amount δ at the time when the force curve was obtained is calculated based on information contained in the force curves obtained up to that point (for example, the force curve at the 11th position, the force curve at the 13th position, etc.). max and then set the push amount δ set and the maximum pushing amount δ maxThe end point (for example, the 14th end point) of the movement of the cantilever or stage when acquiring a force curve at the specific position (for example, the 14th position) is determined using the above formula. When acquiring a force curve at the specific position (for example, the 14th position), the probe is pressed against the sample by moving the cantilever or stage to the determined end point. In other words, unlike conventional measurement methods, a constant maximum pressing force F is applied regardless of the location. max Instead of pressing the probe against the sample with a set pressing amount δ set The probe is pressed against the sample by moving the cantilever or stage to an end point that is individually determined to correspond to the maximum pushing amount δ of the probe, regardless of the variation in mechanical properties at each location. max can be kept substantially constant.

[0020] For example, in Figure 1, the part at position 2, which corresponds to the adhesion site of two cells, is harder than the part at position 14, which corresponds to the center of the cell. Therefore, for the same maximum pushing force F max When the probe is pressed at the 2nd position and the 14th position, the maximum pushing amount of the probe is δ max On the other hand, in the method for measuring mechanical properties according to the present invention, for example, before acquiring a force curve at the second position, the maximum indentation amount δ at the first position is calculated based on information included in the force curve at the first position. max is determined, and a predetermined set pushing amount δ set and the maximum pushing amount δ at the first position max The second end point is determined using the above formula. Then, when acquiring a force curve at the second position, the cantilever or stage is moved to this second end point to press the probe against the sample. Similarly, before acquiring a force curve at the 14th position, the maximum pressing amount δ at the 13th position (or 11th position) is determined based on the information contained in the force curve at the 13th position (or 11th position). max Determine the set push amount δ set and the maximum pushing amount δ at the 13th position (11th position) maxThe 14th end point is determined using the above formula. Then, when acquiring a force curve at the 14th position, the cantilever or stage is moved to this 14th end point to press the probe against the sample. In this way, when acquiring a force curve at the second position, the cantilever or stage is moved to the second end point determined based on the information contained in the force curve at the first position, which has a similar hardness, to press the probe against the sample. Therefore, the maximum pressing amount δ at the second position is max Set the pushing amount δ set Similarly, when acquiring a force curve at the 14th position, the cantilever or stage is moved to the 14th end point determined based on the information contained in the force curve at the 13th position (11th position) of similar hardness to press the probe against the sample. Therefore, the maximum pressing amount δ at the 14th position is max Set the pushing amount δ set In other words, regardless of the difference in hardness between the second position and the fourteenth position, the maximum probe push amount δ max Approximately constant (set pushing amount δ set (a value close to

[0021] When the end point (m-th end point) of the movement of the cantilever or stage when acquiring the force curve for the m-th position (m is an integer greater than n) is determined based on the information contained in the force curve for the n-th position, the positional relationship between the n-th position (e.g., the first position) and the m-th position (e.g., the second position) is not particularly limited, and they may be adjacent to each other, separated from each other, or the same. maxFrom the viewpoint of maintaining a constant value, it is preferable that the nth position (e.g., the first position) and the mth position (e.g., the second position) are adjacent to each other. Here, "the nth position and the mth position are adjacent to each other" means that when force curves are acquired l times (l is an integer equal to or greater than m), the position at which the force curve is acquired closest to the mth position is the nth position. For example, as shown in FIG. 1, when force curves are acquired at equal intervals in both the X-axis direction and the Y-axis direction for a sample placed on an XY plane, the force curve acquisition positions are arranged in a matrix (checkerboard pattern). In this case, if the nth position is adjacent to the mth position in the X-axis direction or the Y-axis direction (if there are no other force curve acquisition positions between them), it can be said that "the nth position and the mth position are adjacent to each other." Furthermore, from the viewpoint of improving measurement speed, it is more preferable that the nth position be the position measured immediately before the mth position. For example, it is preferable that the end point (second end point) of the movement of the cantilever or stage when obtaining a force curve for the second position is determined based on the information contained in the force curve for the first position, and it is preferable that the end point (fourteenth end point) of the movement of the cantilever or stage when obtaining a force curve for the fourteenth position is determined based on the information contained in the force curve for the thirteenth position.

[0022] As described above, in the method for measuring mechanical properties according to the present invention, in the step of acquiring a force curve at the m-th position (e.g., the second position), the cantilever or the stage is moved to the predetermined m-th end point to press the probe against the sample. This m-th end point is a predetermined set pressing amount δ set and the maximum pushing amount δ at the n-th position (for example, the first position) determined based on the information included in the force curve at the n-th position. max Here, the information included in the force curve at the nth position used to determine the mth end point is not particularly limited. For example, the information included in the force curve at the nth position used to determine the mth end point may be the arbitrary pushing force F1, the maximum pushing force F2, the maximum pushing force F3, the maximum pushing force F4, the maximum pushing force F5, the maximum pushing force F6, the maximum pushing force F7, the maximum pushing force F8, the maximum pushing force F9, the maximum pushing force F10, the maximum pushing force F11, the maximum pushing force F12, the maximum pushing force F13, the maximum pushing force F14, the maximum pushing force F15, the maximum pushing force F16, the maximum pushing force F17, the maximum pushing force F18, the maximum pushing force F19, the maximum pushing force F19, the maximum pushing force F19, the maximum pushing force F20, the maximum pushing force F21, the maximum pushing force F22, the maximum pushing force F23, the maximum pushing force F24, the maximum pushing force max, and maximum pushing force F max Maximum pushing amount δ when max and the push-in amount δ1 at an arbitrary push-in force F1. In this case, the maximum push-in amount δ at the nth position (for example, the first position) is max is the arbitrary pushing force F1, the maximum pushing force F in the force curve at the nth position. max , and maximum pushing force F max Maximum pushing amount δ when max and the push-in amount δ1 at an arbitrary push-in force F1. More specifically, the maximum push-in amount δ at the nth position max is the pushing force F1 at any time in the force curve at the nth position, and the maximum pushing force F max , and maximum pushing force F max Maximum pushing amount δ when max It may be calculated by the following formula 1 based on Δδ which is the difference between the push-in amount δ1 at time F1 and the push-in amount δ2 at time F2.

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[0023] In a particular force curve, any pushing force F1 is greater than 0 N and the maximum pushing force F max There is no particular limitation as long as it is less than the maximum pressing force F max The ratio S of any pressing force F1 to the force curve may be the same or different. For example, the ratio S may be the same within the range of 0.05 to 0.6 for multiple force curves.

[0024] In the method for measuring mechanical properties according to the present invention, in the force mapping measurement, the maximum indentation amount of the probe from the sample surface is set to a predetermined indentation amount δ set (e.g., 1 μm). Usually, to evaluate the indentation amount, the contact point between the probe and the sample surface (contact point z c) is required. Here, the contact point z c When the cantilever is moved relative to the stage, this refers to the position of the cantilever (the position of the Z piezo scanner supporting the cantilever) at the moment the probe contacts the sample surface. When the stage is moved relative to the cantilever, this refers to the position of the stage (the position of the Z piezo scanner supporting the stage) at the moment the probe contacts the sample surface. However, in actual force mapping measurements, if the sample is soft, the indentation force (contact force) rises slowly, so the contact point z c Therefore, the accuracy of measuring mechanical properties (such as elastic modulus, viscoelasticity, and adhesive force) also decreases. This problem is one of the unsolved issues in current AFM measurements. c Therefore, in the method for measuring mechanical properties according to the present invention, the contact point z c The amount of indentation is controlled to be approximately constant without using information on the mechanical properties of the specimen. The principle of the method for measuring mechanical properties according to the present invention will be described with reference to Figs. 2, 3A and 3B.

[0025] FIG. 2 shows an example of a force curve to explain the principle of the method for measuring mechanical properties according to the present invention. FIG. 3A is a schematic diagram showing the positional relationship between the sample 200 (stage 110) and the cantilever probe 120 when acquiring a force curve. The sample 200 is placed on the stage 110. The cantilever probe 120 has a cantilever 122 and a probe 124. FIG. 3B is a graph showing the relationship between various parameters when acquiring a force curve. FIGS. 3A and 3B show how the stage 110 carrying the sample 200 is brought closer to the cantilever probe 120. In FIGS. 3A and 3B, z indicates the position of the stage 110 in the Z-axis direction (the position of the Z piezo scanner supporting the stage 110), and d indicates the position of the tip of the cantilever 122 in the Z-axis direction. The left side of Figure 3A shows the state before the sample 200 and the probe 124 come into contact, the center side of Figure 3A shows the state at the moment when the sample 200 and the probe 124 come into contact, and the right side of Figure 3A shows the state when the probe 124 is pressed most firmly against the sample 200.

[0026] In the force curve of Figure 2, the pushing amount at the pushing force F1 is δ1, and the maximum pushing force F max The maximum pushing amount when max The pushing force F1 is the maximum pushing force F max The position of the stage 110 (the position of the Z piezo scanner) when the probe 124 and the sample 200 come into contact with each other is defined as z c The position of the stage 110 (position of the Z piezo scanner) when the indentation force is F1 is defined as z1, and the maximum indentation force F max The position of stage 110 (position of the Z piezo scanner) at this time is defined as z max In this case, the following formulas 2 and 3 hold true. k is the spring constant of the cantilever 122. F1 / k in formula 2 corresponds to d1 in FIGS. 3A and 3B, and F max / k is the d in Figures 3A and 3B max is equivalent to

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[0027] In conventional force mapping measurements, the maximum indentation force F max However, in the force mapping measurement according to the present invention, the maximum indentation amount δ max We want to measure it with δ as a constant. max To determine the contact point z c Here, the maximum pushing amount δ shown in FIG. max Consider the quantity Δδ, which is the difference between the contact point z and the push-in amount δ1 (Equation 4). Equation 4 can be converted to Equation 5 using Equation 2 and Equation 3. As can be seen from Equation 5 below, Δδ is c Without using the value of max ) values.

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[0028] The contact theory of elastic and viscoelastic bodies is a theory that expresses the relationship between external force F and indentation amount δ, and where the function form is g, the relationship is F = βg(δ). Here, β is a variable related to the size and Poisson's ratio of the contact body, and is constant on the same force curve. Regarding the function g, elastic models include the Hertz model, and viscoelastic models include the Ting model. Here, if S is defined as in Equation 6 below, δ1 can be expressed as in Equation 7 below.

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[0029] Therefore, the above formula 4 can be transformed into the following formula 8.

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[0030] The above formula 8 can be expressed as the following formula 9 using a specific function h.

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[0031] Therefore, δ max is the contact point z c Thus, in the method for measuring mechanical properties according to the present invention, it is possible to determine the mechanical properties by using Δδ and S (i.e., F1 and F2) which can be precisely measured by AFM without using information on the mechanical properties of the sample. max ) to find the maximum push amount δ max Then, the maximum pushing amount δ max is the set push amount δ set In the subsequent force curve measurement, the end point of the movement of the stage 110 or the cantilever 122 (in the example shown in FIG. 3A, the end point z max ) is determined.

[0032] Below, we will show an example of an analysis using the Hertz model when the sample is a (perfectly) elastic body. When the sample is an elastic body, it is known that the functional form of the force curve can be well fitted by the Hertz model of elastic contact theory. According to the Hertz model (spherical probe), when the probe is spherical, the indentation force F is proportional to the 3 / 2 power of the indentation amount δ, as shown in Equation 10 below (note that when the probe is conical, the indentation force F is proportional to the square of the indentation amount δ). Therefore, S can be expressed as shown in Equation 11 below.

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[0033] Here, S (i.e., F1 / F max ) is a value that can be precisely measured. The following equation 12 can be derived from the above equation 11, and Δδ can be expressed as the following equation 13 from the above equations 4 and 12.

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[0034] Therefore, the maximum pushing amount δ max is expressed as the following Equation 1. As mentioned above, Δδ and S are quantities that can be precisely measured (see Equations 5 and 6). Therefore, the maximum pushing amount δ max is the contact point z c It can be determined using Δδ and S, which can be precisely measured by AFM, without using information on

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[0035] Furthermore, as another example, we will also show an example of analysis using the Ting model when the sample is a viscoelastic body. When the sample is a viscoelastic body, it is known that the function form of the force curve can be well fitted by the Ting model of viscoelastic contact theory (the indentation process is also known as the Lee-Radok model) (Non-Patent Document 6). When the sample is a viscoelastic body, the sample softens due to the effect of viscosity while the probe is being pressed. For this reason, as shown in Figure 4, depending on the viscoelasticity variable, the indentation force also increases as the indentation amount increases until the indentation amount reaches a certain value. However, once the indentation amount exceeds a certain value, the indentation force may decrease as the indentation amount increases. [Non-Patent Document 6] Efremov, YM, et al., "Measuring viscoelasticity of soft biological samples using atomic force microscopy", Soft Matter, Vol. 16, pp. 64-81.

[0036] In the force curve of Figure 4, the pushing amount at the pushing force F1 is δ1, and the maximum pushing force F max The pushing amount at this time is δ2, and the maximum pushing amount is δ max The pushing force at this time is F2. The pushing force F1 is the maximum pushing force F max The position of the stage (the position of the Z piezo scanner) when the probe and the sample come into contact is defined as z c The position of the stage 110 (position of the Z piezo scanner) when the indentation force is F1 is defined as z1, and the maximum indentation force F max The position of the stage 110 (position of the Z piezo scanner) at the time of the pressing force F2 is defined as z2, and the position of the stage 110 (position of the Z piezo scanner) at the time of the pressing force F2 is defined as z max Let's say.

[0037] First, consider the monotonically increasing portion of the force curve in Figure 4 (between the indentation amount of 0 and δ2; hereafter also referred to as the "increasing function portion"). As mentioned above, if the sample is an elastic body, when the probe is spherical, the indentation force F is proportional to the 3 / 2 power of the indentation amount δ, and when the probe is conical, the indentation force F is proportional to the square of the indentation amount δ. On the other hand, when the sample is a viscoelastic body, the relationship between the indentation force F and the indentation amount δ cannot be uniquely determined. Therefore, the functional form of the increasing function portion is approximately defined as an n-th power equation, as shown in Equation 14 below.

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[0038] Here, S is expressed as F1 / F as in Equation 6 above. max Then, δ2 is expressed as the following equation 15 (see equation 1). Here, Δδd is δ2-δ1 (see FIG. 4) and can be calculated by the following Equation 16 (see Equation 5). d is a value that can be determined from values ​​that can be precisely measured.

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[0039] Here, the relaxation modulus E(t) of a sample, which is a viscoelastic body, is a function of time t and is expressed as in the following equation 17. In equation 17, E1 is the relaxation modulus at time t=1, and α is a value representing the viscosity (fluidity) that relaxes with time t (0≦α≦1, when α=0 the sample is a perfectly elastic body).

number

[0040] From the results of the simulations performed by the inventors using the Ting model, Δδ d It was found that Δδ does not depend on E1, but only on α. ​​For example, Figure 5 shows the relationship between Δδ and S when S is 0.6. d An example of a simulation result showing the relationship between E1 and α (α, Δδ d ) plot). In this graph, E1(N / m 2 ) is 1×10 2 , 3×10 2 , 1×10 3 and 5 × 10 3 The four simulation results for the cases are shown, and the four curves are in good agreement. In other words, the power exponent α of the power rheological variable in the above formula 17 can be expressed as the following formula 18. As can be seen from this, the Δδ obtained from the measurement results d It has been confirmed that the curves also match well when S is different (for example, when S is 0.3, 0.5, 0.7, or 0.9).

number

[0041] Furthermore, from the results of another simulation conducted by the inventors using the Ting model, it was found that n also changes depending only on α, not on E1. For example, Figure 6 shows an example of a simulation result showing the relationship between n and α ((α, n) plot for each E1). In this graph, E1 (N / m 2 ) is 1×10 2 , 1×10 3 , 5×10 3 and 1 × 10 4 The four simulation results for the case are shown, and the four curves are in good agreement. In other words, the exponent n of the force curve in Equation 14 above can be expressed as in Equation 19 below. As can be seen from this, if α is found, n can also be found without fitting the force curve. Furthermore, if n can be found, δ2 can also be found using Equation 15.

number

[0042] Next, the monotonically decreasing part of the force curve in Figure 4 (where the pressing amount is δ2 to δ max Here, as in the increasing function section, the relaxation modulus E(t) of the sample is a function of time t and is expressed as in Equation 17 above.

[0043] From the results of another simulation performed by the inventors using the Ting model, Δδ ε It was found that Δδ does not depend on E1, but only on α. ​​For example, Figure 7 shows that Δδ ε An example of a simulation result showing the relationship between E1 and α (α, Δδ ε ) plot). In this graph, E1(N / m 2 ) is 1×10 2 , 1×10 3, 5×10 3 and 1 × 10 4 The four simulation results for Δδ are shown, and the four curves are in good agreement. ε can be expressed as the following equation 20. As can be seen from this, if α is found, Δδ ε can be obtained.

number

[0044] As shown in Figure 4, the maximum pushing amount δ max is expressed as the following Equation 21. As described above, δ2 and Δδ ε can be determined from quantities that can be precisely measured. max is the contact point z c It can be determined using quantities that can be precisely measured by AFM without using information from other sources.

number

[0045] By the above procedure, whether the sample is an elastic body or a viscoelastic body, the maximum indentation amount δ at the first position can be calculated based on the information contained in the force curve at the first position. max Then, a predetermined set depression amount δ can be determined. set and the maximum pushing amount δ at the first position max The end point (second end point) of the movement of the cantilever or stage in measuring the force curve at the second position is determined using the above equations.

[0046] In the step of determining the second end point, the set push-in amount δ set and the maximum pushing amount δ at the first position max There is no particular limitation on how to use the set push-in amount δ. set and the maximum pushing amount δ at the first position maxThe second end point may be determined based on the result of comparison with the maximum depression amount δ at the first position. max is the set push amount δ set If it is larger than the maximum pushing amount δ max is the maximum pushing amount δ at the first position max More preferably, the set depression amount δ set The second end point can be determined so that the distance between the probe and the stage when the cantilever or the stage is positioned at the second end point is longer than the distance between the probe and the stage when the cantilever or the stage is positioned at the first end point. On the other hand, the maximum depression amount δ at the first position max is the set push amount δ set If it is smaller than the maximum pushing amount δ max is the maximum pushing amount δ at the first position max More preferably, the set depression amount δ set In other words, the second endpoint can be determined so that the distance between the probe and the stage when the cantilever or the stage is positioned at the second endpoint is shorter than the distance between the probe and the stage when the cantilever or the stage is positioned at the first endpoint.

[0047] As will be described later, the method for measuring mechanical properties according to the present invention can be performed using an atomic force microscope (AFM). As mentioned above, AFM force mapping methods are broadly divided into two types: the force volume method (force volume mode) and the pulse force method (pulse force mode). In the pulse force method, the cantilever is vibrated at its non-resonant frequency, causing the probe to intermittently contact and press against the sample. Therefore, the distance between the start and end points of the cantilever movement when measuring a force curve is always constant. On the other hand, in the force volume method, the distance between the start and end points of the cantilever or stage movement does not need to be constant and may be different each time a force curve is measured. In the method for measuring mechanical properties according to the present invention, the distance between the start and end points of the cantilever or stage movement may also be constant or may be different each time a force curve is measured.

[0048] For example, in the method for measuring mechanical properties according to the present invention, when a probe is pressed against a sample as in the force volume method without vibrating the cantilever, the distance between the start point and end point of the movement of the cantilever or stage may be different each time a force curve is measured. max is the set push amount δ set If different from the first end point, the second end point will be at a different position in the Z-axis direction from the first end point. In this case, the distance between the second start point and the second end point may be different from (or the same as) the distance between the first start point and the first end point.

[0049] Furthermore, in the method for measuring mechanical properties according to the present invention, when the probe is pressed against the sample while vibrating the cantilever as in the pulse force method, the distance between the start point and end point of the cantilever movement is always constant. That is, the distance between the second start point and the second end point is the same as the distance between the first start point and the first end point. The maximum pushing amount δ at the first position max is the set push amount δ setIf the second end point is different from the first end point in the Z-axis direction, the second end point will be at a different position in the Z-axis direction from the first end point. And, because the distance between the second start point and the second end point is the same as the distance between the first start point and the first end point, the second start point will be at a different position in the Z-axis direction from the first start point. In other words, the distance between the probe and the stage when the cantilever is located at the second start point is different from the distance between the probe and the stage when the cantilever is located at the first start point.

[0050] In the above description, the cantilever or stage is moved from the (n+1)th start point to the (n+1)th end point at the (n+1)th position of the sample to press the probe against the sample, and the force curve for the (n+1)th position is acquired by determining the (n+1)th end point based on information contained in one of the force curves from the first position to the nth position. However, the method for measuring mechanical properties according to the present invention is not limited to this. For example, when acquiring the force curve for the (n+1)th position, the (n+1)th end point may be determined based on information contained in multiple force curves from the first position to the nth position. For example, if the step of acquiring a force curve for a third position is performed after the steps of acquiring a force curve for a first position and a force curve for a second position, the third end point for acquiring the force curve for the third position may be determined based on information contained in the force curve for the first position and information contained in the force curve for the second position. Using information contained in multiple force curves in this way in combination is expected to prevent over-control of the cantilever or stage movement.

[0051] The type of sample is not particularly limited, and examples of samples include cells, biological tissues, biopolymers such as nucleic acids and collagen, proteins, resins, rubbers, gels, diamonds, graphene, nanoparticles, nanotubes, nanowires, nanobubbles, metals, and ceramics.

[0052] The mechanical properties measured by the method for measuring mechanical properties according to the present invention are not particularly limited. Examples of the mechanical properties include elastic modulus, viscoelasticity, and adhesive force. Those skilled in the art can calculate these mechanical properties from the force curve using known methods.

[0053] (Method for controlling the amount of probe pressure) The method for controlling the probe indentation amount according to the present invention is a method for controlling the probe indentation amount based on the same concept as the method for measuring mechanical properties according to the present invention. The method for controlling the probe indentation amount according to the present invention can be applied to other purposes besides measuring the mechanical properties of a sample. For example, the control of the probe indentation amount can also be applied to applying a quantitative mechanical stimulus to a sample.

[0054] A method for controlling the amount of probe depression according to the present invention is a method for controlling the amount of probe depression when a probe fixed to a cantilever is pressed against a sample placed on a stage. The method for controlling the amount of probe depression according to the present invention includes the steps of: pressing the probe against the sample at a first position on the sample by moving the cantilever or the stage from a first start point to a first end point while acquiring a force curve at the first position; and calculating a maximum depression amount δ at the first position based on information included in the force curve at the first position. max and a step of determining a predetermined set push-in amount δ set and the maximum pushing amount δ at the first position max and pressing the probe against the sample at a second position on the sample by moving the cantilever or stage from the second start point to the second end point (while acquiring a force curve at the second position). The step of pressing the probe against the sample at the second position is performed after the step of pressing the probe against the sample at the first position.

[0055] Of course, after the step of pressing the probe against the sample at the second position, a step of pressing the probe against the sample at a third position on the sample by moving the cantilever or stage from a third start point to a third end point (while acquiring a force curve at the third position) may be further performed. In this case, before the step of pressing the probe against the sample at the third position, the maximum pressing amount δ at the first or second position (preferably the second position) may be calculated based on information contained in the force curve at the first or second position. max and a step of determining a predetermined set push-in amount δ set and the maximum pushing amount δ at the first position or the second position. max The method further includes a step of determining a third endpoint using the above-mentioned method. In the step of pressing the probe against the sample at a third position, the cantilever or the stage is moved to the third endpoint determined in this step, thereby pressing the probe against the sample.

[0056] In this way, after the step of pressing the probe against the sample at the nth position (n is an integer) of the sample, a step of pressing the probe against the sample at the (n+1)th position of the sample may be further performed. In this case, too, before the step of pressing the probe against the sample at the (n+1)th position, the maximum pressing amount δ at that position (any of the first to nth positions) is calculated based on information contained in the force curve for that position (preferably the nth position). max and a step of determining a predetermined set push-in amount δ set and the maximum pushing amount δ of any one of the first position to the nth position. max In the step of pressing the probe against the sample at the (n+1)th position, the cantilever or the stage is moved to the (n+1)th end point determined in this step, thereby pressing the probe against the sample.

[0057] By doing this, the maximum probe pushing amount δ can be calculated regardless of the variation in mechanical properties at each location and without using information on the contact points.max can be kept substantially constant.

[0058] (Mechanical property measuring device) There are no particular limitations on the apparatus for implementing the method for measuring mechanical properties and the method for controlling the probe indentation amount according to the present invention. For example, the method for measuring mechanical properties and the method for controlling the probe indentation amount according to the present invention can be implemented using a scanning probe microscope, and are preferably implemented using an atomic force microscope (AFM). Below, an apparatus including an AFM will be described as an example of an apparatus for implementing the method for measuring mechanical properties (method for controlling the probe indentation amount) according to the present invention, i.e., an apparatus for measuring mechanical properties (apparatus for controlling the probe indentation amount) according to the present invention. This apparatus can not only measure the mechanical properties of a sample, but can also apply a quantitative mechanical stimulus to the sample.

[0059] Fig. 8 is a schematic diagram showing the configuration of a mechanical property measuring apparatus according to one embodiment of the present invention. As shown in Fig. 8, the mechanical property measuring apparatus according to one embodiment of the present invention includes a stage 110, a cantilever probe 120, a detection unit 130, an XY movement unit 140, a Z movement unit 150, and a control unit 160. Each of these components may be the same as those of a known AFM. Fig. 8 also shows an optical system, such as a half mirror and an objective lens.

[0060] The stage 110 is a platform on which the sample 200 is placed. The stage 110 supports the sample 200 so that the sample 200 and the cantilever probe 120 can come into contact with each other.

[0061] The cantilever probe 120 has a cantilever 122 and a probe 124 fixed to the tip of the cantilever 122. When the probe 124 is pressed against the sample 200, the cantilever 122 bends. As will be described later, the bending of the cantilever 122 is detected by a detection unit 130. The cantilever 122 and the probe 124 are not particularly limited and can be appropriately selected from known cantilevers and probes. The shape of the probe 124 is also not particularly limited and may be, for example, needle-like or spherical.

[0062] The detector 130 detects the amount of deflection of the cantilever 122. The detector 130 is not particularly limited and can be appropriately selected from known detectors. For example, the detector 130 may have a light source 132 (e.g., a semiconductor laser) and a photodiode 134 (e.g., a four-segment photodiode) and detect the deflection (displacement) of the cantilever 122 using an optical lever method.

[0063] The XY moving unit 140 moves at least one of the stage 110 and the cantilever 122 to move the sample 200 and the probe 124 relative to each other in the X-axis and Y-axis directions. The Z moving unit 150 moves at least one of the stage 110 and the cantilever 122 in the Z-axis direction to press the probe 124 against the sample 200. To perform force mapping with high precision, both the XY moving unit 140 and the Z moving unit 150 also have sensors that detect the amount of movement of the stage 110 or the cantilever 122 with high precision. The configurations of the XY moving unit 140 and the Z moving unit 150 are not particularly limited as long as they can perform the above functions. For example, the XY moving unit 140 is an XY piezo scanner and its controller, and the Z moving unit is a Z piezo scanner and its controller. In the example shown in FIG. 8, the XY moving section 140 and the Z moving section 150 are an XYZ piezo scanner and its controller that move the stage 110 in the X-axis, Y-axis, and Z-axis directions.

[0064] The control unit 160 controls the detection unit 130, the XY movement unit 140, and the Z movement unit 150. The control unit 160 presses the cantilever probe 120 against the sample 200 placed on the stage 110 at a plurality of positions on the sample 200 to acquire a force curve at each position. When acquiring a force curve at a second position after acquiring a force curve at a first position, the control unit 160 controls the end point of the movement of the cantilever 122 or the stage 110 to be equal to or greater than a predetermined set pressing amount δ set and a maximum pushing amount δ at the first position determined based on information contained in the force curve at the first position. max The control unit 160 controls the Z movement unit 150 so that the second end point is determined using the maximum push-in amount δ at the first position. max is determined without using the contact point in the force curve for the first position.

[0065] (effect) As described above, according to the method for measuring mechanical properties, the method for controlling the probe indentation amount, and the device for measuring mechanical properties according to the present embodiment, the maximum indentation amount δ is determined without using a contact point based on information contained in the force curve acquired up to that point. max The end point of the movement of the cantilever or stage is determined using the above equation, and the cantilever or stage is moved to this end point to press the probe against the sample. Therefore, the method for measuring mechanical properties, the method for controlling the probe depression amount, and the device for measuring mechanical properties according to this embodiment can suppress fluctuations in the probe depression amount from location to location, even for samples whose mechanical properties vary greatly from location to location.

[0066] The present invention will be described in more detail by the following examples, but the present invention is not limited to these examples. [Example]

[0067] In this example, force mapping measurements were performed on confluent canine kidney tubular epithelial cells (MDCK cells) to measure the distribution of elastic modulus, and the results are shown.

[0068] 1. Cell Preparation A 60 mm culture dish containing MDCK cells was removed from the CO2 incubator and confirmed to be subconfluent under a microscope. The medium in the dish was aspirated and then washed three times with 1 mL of phosphate-buffered saline (PBS) to remove the medium and dead cells. 1 mL of trypsin-EDTA solution (Trypsin-5 mM EDTA 0.25%; Sigma) was added to the dish and left in a CO2 incubator for 10 minutes to detach the cells from the bottom of the dish. 3 mL of MEM medium (Sigma-Aldrich) supplemented with 10% fetal bovine serum (FBS), 1% penicillin / streptomycin, and 1% non-essential amino acid solution was added to the cell suspension in the dish. After pipetting several times, the cell suspension in the dish was transferred to a 15 mL centrifuge tube. The tube was centrifuged at 1000 rpm for 2 minutes, then rotated 180° and centrifuged again for 2 minutes to precipitate the cells to the bottom of the tube. The supernatant was then aspirated using an aspirator, and 1 mL of MEM medium was added to the tube and pipetted to prepare a cell suspension.

[0069] After adding 2 mL of MEM medium to a new 35 mm culture dish, the cell count reached 1.0 × 10 4 cells / cm 2 The dish containing the cell suspension was transferred into a CO2 incubator, and the cells were cultured until they became confluent.

[0070] 2. Force Mapping Measurements We prepared a homemade AFM (see Figure 8) by combining an upright optical microscope (Eclipse FN1; Nikon) with a cantilever, a photodetector, a water-immersion objective, a laser light source, a piezo stage (P-563.3CD; Physik Instruments), and a digital piezo controller (E-761; Physik Instruments). Laser light from the laser light source was focused onto the cantilever using the objective, and the reflected light was detected by the photodetector. The cantilever deflection was calculated based on the change in the position of the reflected light. This AFM uses a water-immersion objective, enabling measurements of cells in culture. The piezo stage can move within a range of 300 μm in each of the X, Y, and Z axes. This AFM can be controlled and operated as desired using a program written in LabVIEW (a development environment for instrumentation and control; National Instruments).

[0071] The cantilever used was a liquid-use silicon nitride cantilever (BioLever mini, BL-AC40TSC2; Olympus) with a nominal spring constant of 0.1 N / m or less. The probe used was a spherical silica bead (Funakoshi) with a radius of 2.5 μm. The silica bead (probe) was attached to the tip of the cantilever using an epoxy resin adhesive. The indentation force was calculated from the cantilever deflection and spring constant using Hooke's law. The cantilever spring constant was determined using the thermal vibration method.

[0072] Force curves were obtained by pressing the probe against the cell in the Z-axis direction at a pitch of 3 μm in the X-axis and Y-axis directions in a 60 μm × 60 μm area (see Figure 1). For force mapping measurements, the medium was replaced with CO2-independent medium (Invitrogen) and the temperature was maintained at 30°C.

[0073] For force mapping measurements, the maximum pushing force F max is constant (F max= 2nN) to the MDCK cell, and max The probe is pressed against the MDCK cell so that the pressure is constant (1 μm) (i.e., the set pressure δ set The force mapping measurement according to the present invention was carried out.

[0074] In the force mapping measurement according to the present invention, in measuring the force curve at the (n+1)th position, the end point of the stage's movement in the Z-axis direction (the (n+1)th end point) was set as follows, based on the information contained in the force curve at the nth position acquired immediately before. That is, at the nth position of the sample, the stage was moved in the Z-axis direction from the nth start point to the nth end point to press the probe against the sample, and the force curve at the nth position was acquired. Based on the information contained in the force curve at the nth position, the maximum indentation amount δ at the nth position was calculated using the above formula 1. max The set push-in amount δ was determined. set (1 μm) and the maximum push-in amount δ at the nth position max The position (value) of the nth end point is corrected so that it is the same as the (n+1)th end point. max It was decided.

[0075] The elastic modulus (Young's modulus) E was calculated from the force curve using the Hertz contact model expressed by the following equation 22:

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[0076] 3.Measurement results 9A is a map image of the elastic modulus E of MDCK cells obtained by conventional force mapping. FIG. 9B is a map image of the elastic modulus E of MDCK cells obtained by force mapping according to the present invention. FIG. 9C is a map image of the maximum indentation amount δ when conventional force mapping is performed. max 9D is a map image of the maximum indentation amount δ when the force mapping measurement according to the present invention is performed. max 9E is an image showing the difference between the map image of the elastic modulus E shown in FIG. 9A and the map image of the elastic modulus E shown in FIG. 9B.

[0077] 9C and 9D show that the conventional measurement method shows that the cantilever probe indentation varies greatly from location to location (FIG. 9C), whereas the measurement method according to the present invention shows that the indentation is approximately constant (FIG. 9D). Furthermore, FIGS. 9A, 9B, and 9E show that the measurement method according to the present invention can acquire information on mechanical properties different from that of conventional measurement methods. For example, the conventional measurement method calculates the elastic modulus from data that includes information on a portion 2.0 to 3.0 μm deep from the surface at some locations, whereas the measurement method according to the present invention appears to calculate the elastic modulus from data that includes information only on a portion shallower than 1.5 μm deep from the surface at all locations.

[0078] Figure 10A shows a conventional force mapping measurement (F max constant) and the force mapping measurements according to the present invention (δ max Maximum pushing amount δ max Figure 10B shows the box plot of the force mapping measurement (F max constant) and the force mapping measurements according to the present invention (δ max constant) in Δδ(F max The amount of pressure δ when max and the difference between the push-in amount δ1 at F1 (F1=0.1F max ) From these graphs, it can be seen that the measurement method according to the present invention has a shorter maximum push-in amount δ than the conventional measurement method. maxIt can be seen that the variation is small.

[0079] Figure 11 shows the relationship between S(=F1 / F max ) when the value of the maximum push-in amount δ max 1 is a graph showing the average value and the variation (standard deviation) of the maximum push-in amount δ max Since it is more suitable for control if the average value and variation of S do not fluctuate, it is suggested that it is preferable to set F1 so that S is in the range of 0.05 to 0.6. [Industrial Applicability]

[0080] The method for measuring mechanical properties, the method for controlling the probe depression amount, and the device for measuring mechanical properties according to the present invention are useful, for example, for measuring the mechanical properties of soft samples such as cells whose mechanical properties vary greatly from location to location, and for applying quantitative mechanical stimuli to the samples. [Explanation of symbols]

[0081] 100 Mechanical property measuring device 110 Stages 120 Cantilever Probe 122 Cantilever 124 probes 130 Detector 140 XY moving part 150 Z moving part 160 control section 200 samples

Claims

1. A method for measuring mechanical properties of a sample by pressing a probe fixed to a cantilever against the sample placed on a stage, comprising: a step of pressing the probe against the sample by moving the cantilever or the stage from a first start point to a first end point at a first position on the sample, and acquiring a force curve at the first position; A maximum pushing amount δ at the first position is calculated based on information included in the force curve at the first position. ｍａｘ determining Predetermined set push amount δ ｓｅｔ and the maximum pushing amount δ at the first position ｍａｘ determining a second endpoint using At a second position on the sample, the cantilever or the stage is moved from a second start point to a second end point to press the probe against the sample, thereby acquiring a force curve at the second position; A method for measuring mechanical properties, including:

2. The maximum pushing amount δ at the first position ｍａｘ is the contact point z on the force curve at the first position ｃ The method for measuring mechanical properties according to claim 1, wherein the mechanical properties are determined without using information on the above.

3. the maximum pushing amount δ at the first position ｍａｘ is an arbitrary pushing force F in the force curve at the first position １ , maximum pushing force F ｍａｘ , and the maximum pushing force F ｍａｘ Maximum pushing amount δ when ｍａｘ and the arbitrary pushing force F １ The amount of pressure δ when １ The method for measuring mechanical properties according to claim 1, wherein the mechanical properties are determined based on Δδ, which is the difference between

4. the maximum pushing amount δ at the first position ｍａｘ The method for measuring mechanical properties according to claim 3, wherein is calculated by the following formula 1: [Equation 1] (In the above formula 1, S is F １ / F ｍａｘ It is.)

5. In the step of determining the second end point, the maximum pushing amount δ at the first position ｍａｘ is the set pushing amount δ ｓｅｔ if greater than 1, determine the second end point so that the distance between the probe and the stage when the cantilever or the stage is positioned at the second end point is longer than the distance between the probe and the stage when the cantilever or the stage is positioned at the first end point; the maximum pushing amount δ at the first position ｍａｘ is the set pushing amount δ ｓｅｔ If the distance between the probe and the stage when the cantilever or the stage is positioned at the second end point is smaller than the distance between the probe and the stage when the cantilever or the stage is positioned at the first end point, the second end point is determined. The method for measuring mechanical properties according to claim 1.

6. the maximum pushing amount δ at the first position ｍａｘ is the set pushing amount δ ｓｅｔ 2. The method for measuring mechanical properties according to claim 1, wherein, when the distance between the second start point and the second end point is different from the distance between the first start point and the first end point, the distance between the second start point and the second end point is different from the distance between the first start point and the first end point.

7. the distance between the second starting point and the second ending point is the same as the distance between the first starting point and the first ending point; the maximum pushing amount δ at the first position ｍａｘ is the set pushing amount δ ｓｅｔ when the cantilever or the stage is positioned at the second starting point, the distance between the probe and the stage is different from the distance between the probe and the stage when the cantilever or the stage is positioned at the first starting point. The method for measuring mechanical properties according to claim 1.

8. a step, which is performed before the step of determining the second end point, of pressing the probe against the sample at a third position of the sample by moving the cantilever or the stage from a third start point to a third end point, and acquiring a force curve at the third position; A maximum push-in amount δ at the third position is determined based on information included in the force curve at the third position, which is performed before the step of determining the second end point. ｍａｘ determining further comprising In the step of determining the second end point, the set push-down amount δ ｓｅｔ , the maximum pushing amount δ at the first position ｍａｘ and the maximum pushing amount δ at the third position ｍａｘ determining the second end point using The method for measuring mechanical properties according to claim 1.

9. The method for measuring mechanical properties according to claim 1 , wherein the first position and the second position are adjacent to each other.

10. A method for controlling the amount of probe pressing when a probe fixed to a cantilever is pressed against a sample placed on a stage, comprising: At a first position on the sample, pressing the probe against the sample by moving the cantilever or the stage from a first start point to a first end point while acquiring a force curve at the first position; A maximum pushing amount δ at the first position is calculated based on information included in the force curve at the first position. ｍａｘ determining Predetermined set push amount δ ｓｅｔ and the maximum pushing amount δ at the first position ｍａｘ determining a second endpoint using At a second position on the sample, pressing the probe against the sample by moving the cantilever or the stage from a second starting point to a second ending point; A method for controlling the amount of probe depression, including:

11. The maximum pushing amount δ at the first position ｍａｘ is the contact point z on the force curve at the first position ｃ The method for controlling the probe depression amount according to claim 10, wherein the depression amount is determined without using information on the above.

12. A stage for placing the sample, A cantilever and a probe fixed to the cantilever; a detector for detecting the amount of deflection of the cantilever; an XY moving unit for moving the sample and the cantilever relatively in the X-axis direction and the Y-axis direction; a Z-movement unit for relatively moving the sample and the cantilever in the Z-axis direction; a control unit that controls the detection unit, the XY movement unit, and the Z movement unit; and the control unit controls the detection unit, the XY movement unit, and the Z movement unit to press the probe against the sample by moving the cantilever or the stage in the Z-axis direction from a start point to an end point at a plurality of positions of the sample placed on the stage, and to acquire a force curve at each position; When acquiring a force curve for a second position after acquiring a force curve for a first position, the control unit determines whether the end point of the movement of the cantilever or the stage is equal to or smaller than a predetermined set depression amount δ ｓｅｔ and the maximum depression amount δ at the first position determined based on information included in the force curve at the first position. ｍａｘ and controlling the Z movement unit so that the second end point is determined using A device for measuring mechanical properties.

13. The maximum pushing amount δ at the first position ｍａｘ is the contact point z on the force curve at the first position ｃ The apparatus for measuring mechanical properties according to claim 12, wherein the mechanical properties are determined without using information on the above.

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