Method for predicting fiber yield stress based on unimolecular mechanics

Abstract

The invention provides a method for predicting fiber yield stress based on monomolecular mechanics, and relates to the technical field of monomolecular level determination of interaction among chain tracks, lacing molecules and chains in fibers, the method comprises the steps of preparing a fiber sample, preparing a functionalized atomic force microscope probe, and testing atomic force microscope (AFM) imaging and monomolecular force spectrum (SMFS). The method comprises the following steps of: verifying a single molecule signal, reconstructing a fiber medium chain track by utilizing a force-distance curve of a single molecule, quantifying the interaction between fiber medium chains, establishing a quantitative relationship between the single molecule and macromechanics, carrying out a static tensile experiment of polymer fibers, and verifying the quantitative relationship by utilizing the dependency of the molecular density and the utilization rate of a lace on tensile orientation. According to the method, the chain track in the fiber can be reconstructed, the molecular density of the lace and the strength of interaction between the chains are quantified, then the ultimate yield stress (sigma SMFS) of the fiber is calculated, and the quantitative relation between single molecules and macromechanics is established.

Description

Technical Field

[0001] This invention relates to the field of single-molecule level determination of chain trajectories, tying molecules, and interchain interactions in fibers, and in particular to a method for predicting fiber yield stress based on single-molecule mechanics. Background Technology

[0002] Understanding the relationship between the mechanical response at the microscopic level of fibers (e.g., individual polymer chains) and their macroscopic mechanical properties is crucial for transitioning fiber materials from "empirical preparation" to "rational design." Due to the complexity of material systems and the lack of suitable methods to characterize the single-molecule structure and mechanical properties of real materials, achieving a quantitative correlation between single molecules and macroscopic mechanical properties remains challenging. Therefore, designing a method for predicting fiber yield stress based on single-molecule mechanics is essential. Summary of the Invention

[0003] To overcome the shortcomings of the prior art, the purpose of this invention is to provide a method for predicting fiber yield stress based on single-molecule mechanics.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] This invention provides a method for predicting fiber yield stress based on single-molecule mechanics, comprising:

[0006] Step 1: Prepare fiber samples;

[0007] Step 2: Fabrication of functionalized atomic force microscope probes;

[0008] Step 3: Test atomic force microscopy imaging and single-molecule force spectroscopy;

[0009] Step 4: Verify single-molecule signals;

[0010] Step 5: Reconstruct the chain trajectory in the fiber using the force-distance curve of a single molecule;

[0011] Step 6: Quantitative analysis of interchain interactions in fibers;

[0012] Step 7: Establish a quantitative relationship between single molecules and macroscopic mechanics;

[0013] Step 8: Conduct a static tensile test on the polymer fiber;

[0014] Step 9: Verify the quantitative relationship by using the dependence of tether molecular density and utilization on stretching orientation.

[0015] Preferably, in step 1, the preparation of the fiber sample specifically includes:

[0016] For radial imaging and single-molecule force spectroscopy experiments, polymer fibers were embedded and solidified, and then sliced ​​at -120°C using an Ultracut E microtome equipped with a glass scalpel, with the slicing direction perpendicular to the fiber axis, to obtain fiber samples.

[0017] Preferably, in step 2, the preparation of a functionalized atomic force microscope probe specifically involves:

[0018] A piranha solution was prepared in which the volume ratio of H2O2 / H2SO4 was 3:7. An atomic force microscope probe was treated with the prepared piranha solution. After treatment, the probe was placed in an oven to dry. After drying, the atomic force microscope probe was placed in a dry nitrogen-purged dryer filled with 3-aminopropyldimethylmethoxysilane vapor for functionalization modification.

[0019] Preferably, in step 3, the atomic force microscopy imaging and single-molecule force spectroscopy are tested, specifically as follows:

[0020] Atomic force microscopy imaging was performed on an atomic force microscope, and single-molecule force spectroscopy experiments were conducted in air. The atomic force microscope probe was a silicon nitride probe. Using the single-molecule force spectroscopy method based on atomic force microscopy, single molecules were pulled out of the polymer fiber in air, and typical force-distance curves were collected.

[0021] Preferably, in step 4, verifying the single-molecule signal specifically involves:

[0022] Whether the curve is stretched out of the crystal can be determined by whether it has peak signals with periodicity greater than 10 nm and long plateau signals with high force values.

[0023] Preferably, in step 6, the quantitative analysis of interchain interactions in the fibers specifically includes:

[0024] The peak force value of the periodic peak signal greater than 10 nm and the plateau force value of the high force value long plateau signal in the force-distance curve are used to quantify the inter-chain interactions in the fiber.

[0025] Preferably, in step 7, establishing a quantitative relationship between single molecules and macroscopic mechanics specifically involves:

[0026] Assuming all ligature molecules are the final load-bearing units, then the ultimate yield stress of the fiber, i.e., σ SMFS for:

[0027] σ SMFS =Fn t =Fn / S (1)

[0028] In the formula, F is the activation force for chain slip in the crystal region obtained through single-molecule force spectroscopy experiments, and n t The density of ligature molecules in the fiber is:

[0029] n t =n / S (2)

[0030] In the formula, n is the number of ligature molecules contained in a single polymer chain, and S is the area occupied by polymer molecules on the radial cross section of the fiber.

[0031] Preferably, in step 8, a static tensile test is performed on the polymer fiber, specifically as follows:

[0032] The modulus and fracture strain of each sample group were averaged from at least 15 samples. The actual yield stress of the fiber was obtained through stress-strain curves, which are:

[0033] σ y =ασ SMFS =αFn t (3)

[0034] In the formula, σ y σ represents the actual tensile yield stress of the fiber, α represents the utilization rate of the ligature molecules, and σ represents the actual tensile yield stress of the fiber. SMFS This is the theoretical ultimate yield stress;

[0035] By comparing the actual tensile yield stress with the ultimate yield stress, we can determine whether the quantitative relationship between the single molecule and macroscopic mechanics is correct.

[0036] Preferably, in step 9, the quantitative relationship is verified by utilizing the dependence of tether molecular density and utilization rate on stretching orientation, specifically as follows:

[0037] The quantitative relationship between single molecules and macroscopic mechanics is verified by utilizing the dependence of tether molecular density and utilization on stretching orientation. The quantitative relationship between single molecules and macroscopic mechanics is further verified by whether tether molecular density and utilization increase with the degree of stretching.

[0038] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0039] This invention provides a method for predicting fiber yield stress based on single-molecule mechanics. The method includes preparing fiber samples, fabricating functionalized atomic force microscopy probes, testing atomic force microscopy (AFM) imaging and single-molecule force spectroscopy (SMFS), verifying single-molecule signals, reconstructing chain trajectories in the fiber using the force-distance curves of single molecules, quantifying inter-chain interactions in the fiber, establishing a quantitative relationship between single molecules and macroscopic mechanics, conducting static tensile experiments on polymer fibers, and verifying the quantitative relationship using the dependence of tether molecular density and utilization rate on tensile orientation. This invention can reconstruct chain trajectories in fibers, quantify tether molecular density and the strength of inter-chain interactions, and then calculate the ultimate yield stress (σ) of the fiber. SMFS To establish a quantitative relationship between single molecules and macroscopic mechanics. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1A This is a schematic diagram of PCL fiber sample preparation and single-molecule force spectroscopy experiment.

[0042] Figure 1B This is a schematic diagram of typical force-distance (FE) curves obtained from PCL fibers; Type I and Type II curves are marked in blue and green, respectively, and the worm chain (WLC) model fitting (black line) can be used to determine the distance (ΔL) between the major peaks;

[0043] Figure 1C for Figure 1B The diagram shows an enlarged view of the force modes on the FE curve circled by the orange dashed line; the corresponding force-induced chain behavior diagrams include force-induced melting (Type I) and interlamellar slip (Type II); the worm chain (WLC) model fitting (gray line) can be used to determine the distance (ΔL) between small serrated peaks. S Melting force is defined as the maximum force observed in Type I mode;

[0044] Figure 1D This is a histogram of the melting force (blue line) (n=27) and interlamellar slip force (green line) (n=50) in PCL fibers; the dashed line is the corresponding Gaussian fitting curve.

[0045] Figure 1E The histogram of ΔLs in PCL fibers (n=100); the dashed line is the corresponding Gaussian fitting curve;

[0046] Figure 2A for Figure 1B A schematic diagram of the amplified force pattern in the force-distance (FE) curve circled within the purple box;

[0047] Figure 2B for Figure 1B A schematic diagram of the tightening of ligands between two crystal layers in the force-distance (FE) curve circled in the purple box;

[0048] Figure 2C A statistical histogram of the profile length (L) within a long period; the inset shows a schematic diagram of the polymer chain in the long period;

[0049] Figure 2DA statistical histogram of the tether molecular profile lengths in polycaprolactone (PCL) fibers; the inset shows a schematic diagram of the tether molecules between two crystal layers;

[0050] Figure 3A A schematic diagram of the heating curves of polycaprolactone (PCL) and polyethylene (PE) fibers using differential scanning calorimetry (DSC).

[0051] Figure 3B The density of tethered molecules in PCL and PE fibers (n t ) Schematic diagram;

[0052] Figure 3C This diagram shows the yield stress of PCL and PE fibers measured by tensile testing and the ultimate yield stress measured by single-molecule force spectroscopy (SMFS) experiments.

[0053] Figure 4A This is a schematic diagram of the stress-strain curve of polycaprolactone (PCL) fiber.

[0054] Figure 4B This is a schematic diagram of the stress-strain curve of polyethylene (PE) fiber.

[0055] Figure 4C This is a schematic diagram of the tensile yield stress and ultimate yield stress of polycaprolactone (PCL) fiber.

[0056] Figure 4D This is a schematic diagram showing the tensile yield stress and ultimate yield stress of polyethylene (PE) fibers.

[0057] Figure 4E The tying molecular density (n) of polycaprolactone (PCL) fibers t A diagram showing the utilization rate (α);

[0058] Figure 4F The tying molecular density (n) of polyethylene (PE) fibers t A diagram showing the utilization rate (α);

[0059] Figure 5 This is a schematic diagram of the radial cross-section of the polymer fiber and a corresponding schematic diagram of the height image obtained by atomic force microscopy (AFM) of the polymer fiber; due to the large diameter of polycaprolactone (PCL) fiber (approximately 100 μm), the circular cross-section of the PCL fiber was not observed in the 30 μm atomic force microscopy scanning image;

[0060] Figure 6A A schematic diagram of the superimposed force-distance (FE) curves obtained from polycaprolactone (PCL) fibers;

[0061] Figure 6BA schematic diagram of the superimposed force-distance (FE) curves obtained for polyethylene (PE) fibers;

[0062] Figure 7A The diagram shows the ΔL histogram and Gaussian fitting (black line) of polycaprolactone (PCL) fibers.

[0063] Figure 7B The diagram shows the ΔL histogram and Gaussian fitting (black line) of polyethylene (PE) fibers; the thickness (h) of a single crystalline layer is determined to be 9.8 nm and 12 nm, respectively.

[0064] Figure 8A A schematic diagram of one-dimensional integrated small-angle X-ray scattering (SAXS) curves of polycaprolactone (PCL) with different yield moduli;

[0065] Figure 8B A schematic diagram of one-dimensional integrated small-angle X-ray scattering (SAXS) curves of polyethylene (PE) with different yield moduli;

[0066] Figure 9 This is a schematic diagram of a typical single-molecule force-distance (FE) curve obtained from polyethylene (PE) fibers; each force-distance curve in the figure is staggered along the y-axis.

[0067] Figure 10 A schematic diagram showing the profile length (L) and number of tethered molecules (n) of a single polymer chain in polycaprolactone (PCL) and polyethylene (PE) fibers;

[0068] Figure 11A This is a schematic diagram of the unit cell parameters of polycaprolactone (PCL); the left column is the view viewed from the XY plane, and the right column is the projection view viewed along the Y-axis. The polymer chain has a zigzag conformation. Color explanation: light green represents carbon atoms; red represents oxygen atoms.

[0069] Figure 11B This is a schematic diagram of the unit cell parameters of polyethylene (PE).

[0070] Figure 12 A schematic diagram of X-ray diffraction (XRD) data for polycaprolactone (PCL) and polyethylene (PE) fibers;

[0071] Figure 13 This is a schematic diagram comparing the crystallinity of fibers obtained by differential scanning calorimetry (DSC) and single-molecule force spectroscopy (SMFS).

[0072] Figure 14 This is a histogram of the melt force of polyethylene (PE) fibers. The black line is a schematic diagram of the corresponding Gaussian fitting curve.

[0073] Figure 15This is a schematic diagram of the stress-strain curves of polycaprolactone (PCL) and polyethylene (PE) fibers in a uniaxial tensile test.

[0074] Figure 16A A schematic diagram of a typical single-molecule force-distance (FE) curve obtained for PCL-C1 fiber; the force-distance curves in each figure are staggered along the y-axis.

[0075] Figure 16B A schematic diagram of a typical single-molecule force-distance (FE) curve obtained for PCL-C2 fibers;

[0076] Figure 16C A schematic diagram of a typical single-molecule force-distance (FE) curve obtained for PCL-C3 fibers;

[0077] Figure 17A A schematic diagram of a typical single-molecule force-distance (FE) curve obtained for PE-M2 fiber; the force-distance curves in each figure are staggered along the y-axis.

[0078] Figure 17B A schematic diagram of a typical single-molecule force-distance (FE) curve obtained for PE-M3 fiber;

[0079] Figure 18 This is a schematic diagram of the method flow of the present invention;

[0080] Figure 19A This is a schematic diagram showing the contour length (L) within the layered structure of polycaprolactone (PCL) fibers under different degrees of stretching.

[0081] Figure 19B This is a schematic diagram showing the contour length (L) within the layered structure of polyethylene (PE) fibers under different degrees of stretching.

[0082] Figure 19C This is a schematic diagram showing the number (n) of connecting chains in a single polymer chain of polycaprolactone (PCL) fiber under different degrees of stretching.

[0083] Figure 19D This is a schematic diagram showing the number (n) of connecting chains in a single polymer chain of polyethylene (PE) fiber under different degrees of stretching. Detailed Implementation

[0084] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0085] The purpose of this invention is to provide a method for predicting fiber yield stress based on single-molecule mechanics. Utilizing single-molecule force spectroscopy (SMFS) based on atomic force microscopy (AFM), the chain trajectories within the fiber are reconstructed, the density of tethered molecules and the strength of interchain interactions are quantified, and then the ultimate yield stress (σ) of the fiber is calculated. SMFS A quantitative relationship between single molecules and macroscopic mechanics was established. Furthermore, this quantitative relationship was verified by utilizing the dependence of tether molecular density and utilization on stretching orientation.

[0086] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0087] like Figure 18 As shown, this invention provides a method for predicting fiber yield stress based on single-molecule mechanics, comprising:

[0088] Step 1: Prepare fiber samples;

[0089] Step 2: Fabrication of functionalized atomic force microscope probes;

[0090] Step 3: Test atomic force microscopy (AFM) imaging and single-molecule force spectroscopy (SMFS);

[0091] Step 4: Verify single-molecule signals;

[0092] Step 5: Reconstruct the chain trajectory in the fiber using the force-distance curve of a single molecule;

[0093] Step 6: Quantitative analysis of interchain interactions in fibers;

[0094] Step 7: Establish a quantitative relationship between single molecules and macroscopic mechanics;

[0095] Step 8: Conduct a static tensile test on the polymer fiber;

[0096] Step 9: Verify the quantitative relationship by using the dependence of tether molecular density and utilization on stretching orientation.

[0097] In step 1, the fiber sample is prepared, specifically as follows:

[0098] For radial imaging and single-molecule force spectroscopy experiments, polymer fibers were embedded and solidified, and then sliced ​​at -120°C using an Ultracut E microtome equipped with a glass scalpel, with the slicing direction perpendicular to the fiber axis, to obtain fiber samples.

[0099] In step 2, the functionalized atomic force microscope probe is prepared, specifically as follows:

[0100] A piranha solution was prepared in which the volume ratio of H2O2 / H2SO4 was 3:7. An atomic force microscope probe was treated with the prepared piranha solution. After treatment, the probe was placed in an oven to dry. After drying, the atomic force microscope probe was placed in a dry nitrogen-purged dryer filled with 3-aminopropyldimethylmethoxysilane vapor for functionalization modification.

[0101] In step 3, atomic force microscopy imaging and single-molecule force spectroscopy are tested, specifically as follows:

[0102] Atomic force microscopy (AFM) imaging is performed on an atomic force microscope (CypherESAFM), and single-molecule force spectroscopy experiments are conducted in air. The atomic force microscope probe is a silicon nitride probe. Using the atomic force microscopy-based single-molecule force spectroscopy method, single molecules are pulled out of the polymer fiber in air, and typical force-distance (FE) curves are collected.

[0103] In step 4, the single-molecule signal is verified, specifically as follows:

[0104] Whether the curve is stretched out of the crystal can be determined by whether it has peak signals with periodicity greater than 10 nm and long plateau signals with high force values.

[0105] In step 5, the chain trajectory in the fiber is reconstructed using the force-distance curve of a single molecule, specifically as follows:

[0106] By analyzing the chain behavior in the force curves, the trajectories of the chains in the fibers are constructed. This method, based on single-molecule force spectroscopy (SMFS), reveals the slip between crystal layers and between polycrystalline layers, and locates amorphous chains in the chain trajectory, thus breaking through the limitations of traditional methods in locating amorphous chains and resolving the complete picture of the chain trajectory.

[0107] In step 6, the quantitative analysis of interchain interactions in the fibers specifically involves:

[0108] Quantitative analysis of interchain interactions in fibers: The interchain interactions (F) in fibers are quantified by using the peak force (melting force) of periodic peak signals greater than 10 nm and the plateau force (intra-crystal chain slip force) of long plateau signals with high force values ​​(>200 pN) in simple curves.

[0109] In step 7, a quantitative relationship between single molecules and macroscopic mechanics is established, specifically as follows:

[0110] Assuming all ligature molecules are the final load-bearing units, then the ultimate yield stress of the fiber, i.e., σ SMFS for:

[0111] σ SMFS =Fn t =Fn / S (1)

[0112] In the formula, F is the activation force for chain slip in the crystal region obtained through single-molecule force spectroscopy experiments, and n t The density of ligature molecules in the fiber is:

[0113] n t =n / S (2)

[0114] In the formula, n is the number of ligature molecules contained in a single polymer chain, and S is the area occupied by polymer molecules on the radial cross section of the fiber.

[0115] In step 8, a static tensile test of the polymer fiber is performed, specifically as follows:

[0116] The modulus and fracture strain of each sample group were averaged from at least 15 samples. The actual yield stress of the fiber was obtained through stress-strain curves, which are:

[0117] σ y =ασ SMFS =αFn t (3)

[0118] In the formula, σ y σ represents the actual tensile yield stress of the fiber, α represents the utilization rate of the ligature molecules, and σ represents the actual tensile yield stress of the fiber. SMFS The theoretical ultimate yield stress is given by α, where the utilization rate of the ligature molecules can be expressed by the actual tensile yield stress σ. y Compared with the theoretical ultimate yield stress σ SMFS Ratio estimation;

[0119] By comparing the actual tensile yield stress with the ultimate yield stress, we can determine whether the quantitative relationship between the single molecule and macroscopic mechanics is correct.

[0120] In step 9, the quantitative relationship is verified by utilizing the dependence of tether molecular density and utilization on stretching orientation, specifically as follows:

[0121] The quantitative relationship between single molecules and macroscopic mechanics is verified by utilizing the dependence of tether molecular density and utilization on stretching orientation. The quantitative relationship between single molecules and macroscopic mechanics is further verified by whether tether molecular density and utilization increase with the degree of stretching.

[0122] This invention provides a specific embodiment to demonstrate the effectiveness of the above method, which includes:

[0123] Step 1: Use single-molecule force spectroscopy to achieve single-molecule stretching in the fiber.

[0124] In step 1, the fiber sample preparation for atomic force microscopy (AFM) and single-molecule force spectroscopy (SMFS) testing involves embedding polymer fibers in SPIPon 812 epoxy resin for radial imaging and SMFS experiments. The resin is cured at 60°C for 24 hours and then sliced ​​at -120°C using an Ultracut E microtome (Leica Reichert-Jung, Buffalo Grove, USA) equipped with a glass microtome blade. The slicing direction is perpendicular to the fiber axis. During the cutting process, care should be taken to minimize damage to the exposed surface.

[0125] The functionalized atomic force microscope (AFM) probe was prepared by treating the AFM probe with freshly prepared piranha solution (H2O2 / H2SO4 volume ratio of 3:7) for 2 minutes, drying the probe in an oven at 115°C for 10 minutes, and then placing the cleaned AFM probe in a dry nitrogen purge desiccator filled with 3-aminopropyldimethylmethoxysilane vapor at 25°C for 2 hours. After that, the probe was rinsed three times with methanol and then placed in an oven at 110°C for 10 minutes.

[0126] Atomic force microscopy imaging and single-molecule force spectroscopy testing: Atomic force microscopy (AFM) imaging of axial and radial sections of polymer fibers in CypherESAFM (Atomium The study was conducted at Research Center (Santa Barbara, USA). Split and sliced ​​fiber samples were located using an optical microscope. All images were acquired in air using a silicon cantilever beam (RTESPA-300, 300 kHz, 40 N / m) in tapping mode. Single-molecule force spectroscopy (SMFS) experiments were performed in air using a silicon nitride (Si3N4) AFM probe (MLCT, Bruker). First, the fiber cross-section was located using the instrument's optical microscope. Then, the probe was moved to the selected area for AFM imaging. The approximate circularity of the cross-section in the AFM image was used to determine if the cutting direction was perpendicular to the fiber axis. After positioning using AFM imaging, the AFM probe was moved above the fiber. Using AFM-based single-molecule force spectroscopy (SMFS), individual molecules were extracted from the polymer fiber in air, while typical force-distance (FE) curves were collected. The stretching rate was set to 500 nm / s, and the data acquisition rate was set to 10–16.7 kHz. The elastic modulus of the cantilever beam was determined using the thermal noise method.

[0127] Step 2: Verification of single-molecule signals.

[0128] In step 2, the presence of periodic peak signals on the 20-50 nm scale and long plateau signals with high force values ​​(>200 pN) is used to determine whether the curve is stretched out of the crystal. A simple force curve originates from the unfolding of a single chain from a single crystalline and amorphous region, while a complex step-like signal represents the unfolding of a single chain from multiple crystalline and amorphous regions. Through comparative experiments, the force value of the plateau force curve obtained by desorption at the polymer-crystal interface is less than 100 pN, proving that the periodic peak signals and long plateau signals with high force values ​​(>200 pN) correspond to the process of polymer chains unfolding from fibers.

[0129] Step 3: Reconstruct the mid-chain trajectory of the fiber using single-molecule force-distance curves;

[0130] In step 3, in simple force curves, periodic peak signals correspond to force-induced melting of folded chains in crystalline regions; high force values ​​(>200 pN) and long plateau signals correspond to amorphous chains sliding across crystalline layers under external force. In complex step-like force curves, periodic peak signals correspond to the superposition of force-induced melting and crystalline layer crossing of polymer chains, and high force values ​​and long plateau signals correspond to the superposition of polymer chains crossing multiple crystalline layers. The number of steps is consistent with the number of crystalline layers. Based on the above analysis of chain behavior, the trajectory of chains in fibers can be constructed. This method based on single-molecule force spectroscopy (SMFS) can locate amorphous chains in chain trajectories by revealing inter-crystalline and inter-polycrystalline slip, thereby breaking through the limitations of traditional methods in locating amorphous chains and resolving the complete picture of chain trajectories.

[0131] Step 4: Quantify the molecular density of ties in the fiber, such as... Figure 2C As shown, the profile length (L) of the molecular chain within the long period (containing one crystalline region and one amorphous region) is equal to the profile length of each stage of the force curve plus the long period value (L) measured by small-angle X-ray scattering (SAXS). p , Figure 8A and Figure 8B The length of the ligamentous molecule is equal to the length of the interlamellar chain. Figure 2A From phase 1 to phase 2, or Figure 2B From stage 1 to stage 3) plus the length of the amorphous region (L) p -h, where h is the thickness of a single crystal layer), the density of ligature molecules in the fiber (n t ) can be calculated using the following formula: n t =n / S, where n is the number of ligature molecules contained in a single polymer chain, and S is the area occupied by polymer molecules on the radial cross section of the fiber. Dividing the total length of the polymer chain (L0) by L gives the number of lamellae (m) traversed by a single polymer chain. L0 is estimated based on the molecular weight of the polymer, while the value of n is equal to m-1.

[0132] S can be calculated using the following formula: S = (L0X)c ab) / (2h). Where X c The fiber crystallinity is measured by differential scanning calorimetry (DSC), where a and b are the unit cell parameters of the polymer (Figure 11), and h is the layer thickness obtained by single-molecule force spectroscopy (SMFS) (Figure 7).

[0133] Step 5: Quantify the inter-chain interactions in the fiber. Quantify the inter-chain interactions (F) in the fiber by using the peak force value (melting force) of the periodic peak signal in the simple curve and the plateau force value (>200pN) of the long plateau signal (intra-crystal chain slip force). Both force-induced melting and intra-crystal chain slip correspond to the coordinated fracture of the inter-chain segments in the single crystal, so they exhibit similar force values.

[0134] Step 6: Establish a quantitative relationship between single molecules and macroscopic mechanics. Assuming all ligature molecules are the final load-bearing units, the ultimate yield stress of the fiber (i.e., σ) is... SMFS σ can be calculated using the following formula: SMFS =Fn t =Fn / S, where both force melting and intracrystalline chain slip correspond to the synergistic fracture of inter-chain segments in a single crystal wafer, thus exhibiting similar force values ​​( Figure 1D );

[0135] Static tensile tests on polymer fibers were conducted on an Instron 68TM-5 universal testing machine at a tensile rate of 10 mm / min at room temperature. The modulus and fracture strain of each sample group were averaged from at least 15 samples. The actual yield stress (σ) of the fiber was obtained through stress-strain curves. y The utilization rate (α) of the ligament molecules can be measured by the actual tensile yield stress (σ). y ) and ultimate yield stress (σ SMFS The ratio of σ to σ is estimated using the following formula: y =ασ SMFS =αFn t By comparing the actual tensile yield stress (σ) y ) and ultimate yield stress (σ SMFS To determine whether the quantitative relationship between a single molecule and macroscopic mechanics is correct.

[0136] Step 7: Verify the quantitative relationship between single molecules and macroscopic mechanics by utilizing the dependence of tylosing molecular density and utilization rate on stretching orientation. Theoretically, stretching orientation during spinning will increase tylosing molecular density (n t ) and utilization rate (α), select samples with different degrees of stretching and repeat steps 1-7, and measure the tether molecular density (n t Whether the single molecule and utilization rate (α) increase with the increase of stretching degree, to verify the quantitative relationship between the single molecule and macroscopic mechanics;

[0137] The following uses polyester lactone (PCL) fiber and polyethylene (PE) fiber as examples to introduce the methods provided in this application for determining chain trajectories, tying molecules, and interchain interactions in fibers, as well as establishing a quantitative relationship between single molecules and macroscopic mechanics:

[0138] like Figure 1A As shown, polymer fibers were fixed using resin embedding and cryosectioned below the polymer's glass transition temperature to prepare fiber cross-sections. Atomic force microscopy (AFM) height images show that the cross-sections are approximately circular, indicating that the cutting direction is perpendicular to the fiber axis. Figure 5 Therefore, by stretching a functionalized atomic force microscope (AFM) probe perpendicular to the cross-section using the method described in the example, polymer chains can be pulled out of the fiber along the axial direction.

[0139] After localization using atomic force microscopy (AFM) imaging, the AFM probe is moved above the fiber, and single-molecule force spectroscopy (SMFS) based on AFM is used to extract individual molecules from the polycaprolactone (PCL) fiber in air. Figure 1B It shows a typical force-distance (FE) curve;

[0140] Inside the fiber, a polymer chain typically passes through multiple crystalline and amorphous regions. During the single-molecule stretching process, the AFM probe pulls the polymer upward from one end, causing the molecular chain to gradually unfold from the crystalline region or move between the crystalline and amorphous regions until the connection between the molecule and the probe breaks or the molecular chain completely detaches from the fiber.

[0141] Complex step-like patterns were observed in over 85% of the force curves. Figure 1B The three curves in the upper middle section are due to the unfolding of the single chain from multiple crystalline and amorphous regions. When these curves are superimposed, they show multiple dense force regions (Figure 6). Only about 10% of the curves show a simple force pattern. Figure 1B The bottommost curve (at the bottom) originates from the unfolding of a single chain from a single crystalline region and an amorphous region. Upon closer observation, two distinct force modes can be observed in the force-distance (FE) curve: a main sawtooth peak (Type I mode, blue) and a sawtooth plateau (Type II mode, green). Figure 1B The orange circle highlights the Type I and Type II patterns. Figure 1C The middle part was further magnified;

[0142] For the Type I mode, small sawtooth peaks are superimposed on the main peak. Figure 1C(Left figure) As the distance increases, the force value of the small peaks gradually decreases. This is because the molecular chain segments (stem) are gradually shortened before catastrophic fracture occurs. This mode corresponds to the force-induced melting of a folded structure containing two chain segments, similar to the force-induced melting phenomenon observed in single crystals. The spacing between the main peaks in the Type I mode ( Figure 1B ΔL in the figure is equivalent to twice the thickness of the crystal region, and therefore can be used to calculate the thickness h of a single crystal layer (Figure 7). Statistically, the maximum force observed in the type I mode (defined as the melting force) is 442 ± 39 pN. Figure 1D (blue line in the middle);

[0143] For the Type II mode, the peak force on the sawtooth platform remains almost constant. Figure 1C The right figure shows that chain segments of similar size broke continuously due to the peak force ( Figure 1D The green line in the diagram is comparable to the melting force, therefore the serrated plateau is considered to be caused by the tightening of the tie chain or the shortening of the tail through chain slippage within the crystal layers. Combining these results, amorphous polycaprolactone (PCL) chains (including ring chains, tie chains, and tail chains) may slip between crystal layers under mechanical loading. This phenomenon is defined as cross-lamella slipping. Therefore, these two force modes reflect different behaviors, where the profile length increment (ΔLS) of the small serrated peak is approximately 0.89 nm. Figure 1E The length of the force curve is consistent with that of a single repeating unit in PCL, and these results confirm that the force curve originates from the stretching of individual molecules in the PCL fiber.

[0144] Recognition of chordate molecules:

[0145] Analyzing the force-induced molecular chain behavior helps to reconstruct the arrangement of individual molecular chains in polymer fibers, thus providing a direct method for identifying and characterizing these tethered molecules. Figure 2A and 2B Showing Figure 1B A magnified view of the curve within the purple box;

[0146] exist Figure 2A In the process, a brief zigzag plateau appears after elastic stretching, indicating that intralayer chain slippage tightens the telomeres (from stage 1 to stage 2). Subsequently, further elastic stretching of the individual PCL chain leads to a sudden drop in force, indicating that the PCL folded structure in the inner layers melts, followed by intralayer chain slippage in the upper layers. Figure 2A (From phase 2 to phase 3);

[0147] exist Figure 2BIn the process, after elastic stretching, a long serrated plateau appears, indicating that the long ligament molecules between the two crystal layers gradually tighten (from stage 1 to stage 3). Once tightened, the stress is further transferred to the polymer chains in the subsequent crystal layers through the ligament molecules (stage 3).

[0148] Based on the above analysis, the behavior of polymer chains (especially ligated molecules) under force-induced conditions has been effectively characterized.

[0149] like Figure 2C As shown, the profile length (L) of the molecular chain within the long period (containing one crystalline region and one amorphous region) is equal to the profile length of each stage of the force curve plus the long period value (L) measured by small-angle X-ray scattering (SAXS). p , Figure 8A and Figure 8B The L value is mainly distributed in the range of 20-100 nm, which is much smaller than the outline length of the entire molecular chain (585 nm). These results indicate that the molecular chain tends to traverse multiple crystal layers rather than fold within a single crystal layer.

[0150] The length of the ligand molecule is equal to the length of the interlayer chain ( Figure 2A From phase 1 to phase 2, or Figure 2B From stage 1 to stage 3) plus the length of the amorphous region (L) p -h, where h is the thickness of a single crystal layer), Figure 2D The length distribution of tylosing molecules is shown, mainly concentrated between 10-60 nm, but some tylosing molecules are longer than 100 nm. During fiber stretching, longer tylosing molecules are more difficult to straighten, and their effective utilization rate directly affects the mechanical properties of the fiber.

[0151] σ is calculated based on ligament molecular density and stress. SMFS :

[0152] The identification of chalaza molecules at the single-molecule level lays the foundation for further research on chalaza molecular density. The density of chalaza molecules in a fiber (n...) t ) can be calculated using the following formula: n t =n / S;

[0153] Where n is the number of connecting segments / chains contained in a single polymer chain, S is the area occupied by the polymer molecule on the radial cross section of the fiber, and the total length of the polymer chain (L0) divided by L can be used to obtain the number of crystal layers (m) traversed by a single polymer chain. L0 is estimated based on the molecular weight of the polymer, and the value of n is equal to m-1.

[0154] To further verify the effectiveness of the method, single-molecule experiments were conducted on polyethylene (PE) fibers with the same serrated conformation. Figure 9The force curve of PE shows a similar overall trend to that of PCL. Calculations show that the n-value for PCL fibers is 7.3, while the n-value for PE fibers is 1.5. Figure 10 S can be calculated using the following formula: S = (L0X) c ab) / (2h);

[0155] Among them, X c The fiber crystallinity is measured by differential scanning calorimetry (DSC), a and b are the unit cell parameters of the polymer (Fig. 11), and h is the layer thickness obtained by single-molecule force spectroscopy (SMFS) experiment (Fig. 7).

[0156] Differential scanning calorimetry (DSC) and wide-angle X-ray diffraction (XRD) were used. Figure 3A and Figure 12 The crystalline-amorphous network of the polymer fibers was characterized. Differential scanning calorimetry (DSC) was performed on a TA Instruments Q200 DSC instrument with a nitrogen flow rate of 50 mL / min and a heating / cooling rate of 10 °C / min. Each sample (approximately 5 mg) was heated from 25 °C to a high temperature (100 °C for PCL; 200 °C for PE) at a rate of 10 °C / min. Wide-angle X-ray diffraction data were acquired on an X-ray diffractometer (SmartLab(3), Rigaku, Japan) using CuKα radiation at a scan rate of 3 ° / min and an X-ray wavelength of 10 °C / min. The melting temperatures of PCL fiber and PE fiber are 62.8℃ and 135.1℃, respectively, and their crystallinity is 56% and 54%, respectively.

[0157] Furthermore, single-molecule force spectroscopy (SMFS) provides a novel approach for quantifying the crystallinity of polymer fibers because it can distinguish the behavior of crystalline and amorphous chains. By analyzing a large dataset and based on the ratio of the length of the type I curve to the total length of both type I and type II curves, the crystallinity of PCL fibers was calculated to be 45%, and that of PE fibers to be 57%. The crystallinity values ​​obtained by the SMFS method are very close to those measured by DSC. Figure 13 This also confirms that our identification of chain states (crystalline or amorphous) at the single-molecule level is reliable. In short, this SMFS method is applicable to a variety of semi-crystalline polymer systems and provides a new approach to crystallinity characterization beyond traditional thermodynamic methods.

[0158] Calculations show that the area (S) occupied by a single polymer molecule in PCL and PE fibers is 6.36 nm. 2 and 2.53nm 2 ;

[0159] like Figure 3B As shown, the tying molecular density (n) of PCL fiber and PE fibert The corresponding wavelengths are 1.15nm. -2 and 0.58nm -2 Clearly, the typothesis density of PCL fibers is higher than that of PE fibers. Previous studies have shown that typothesis density has a significant impact on the yield stress of polymer materials. Assuming that all typothesis molecules are the final load-bearing units, the ultimate yield stress of the fiber (i.e., σ) is... SMFS σ can be calculated using the following formula: SMFS =Fn t =Fn / S;

[0160] Wherein, F is the activation force for chain slip in the crystal region (i.e., the force of mechanomelting or the force of interlamellar slip) obtained by single-molecule force spectroscopy (SMFS). Both mechanomelting and intralamellar chain slip correspond to the synergistic fracture of inter-segment interactions in a single crystal wafer, and therefore exhibit similar force values. Figure 1D In this invention, melt force is selected as the slip activation force for the crystalline chain. The slip activation forces for PCL fibers and PE fibers are 442 pN and 483 pN, respectively. Figure 1D and Figure 14 ), and the σ of PCL fiber and PE fiber were calculated. SMFS 509 MPa and 280 MPa respectively Figure 3C );

[0161] Subsequently, a tensile test was conducted on the fiber, and the results were as follows: Figure 15 As shown, the stress-strain curves indicate that the actual yield stress (σ) of PCL fibers and PE fibers is... y The pressures were 346 MPa and 227 MPa, respectively, both close to but lower than σ. SMFS ( Figure 3C This result is consistent with the prediction that "only a portion of chalaza molecules are effectively utilized due to the limitation of chalaza molecular orientation".

[0162] Validation of quantitative association:

[0163] The utilization rate (α) of the ligature molecules can be measured by the actual tensile yield stress (σ). y ) and ultimate yield stress (σ SMFS The ratio of σ to σ is estimated using the following formula: y =ασ SMFS =αFn t ;

[0164] Theoretically, the stretching and orientation during the spinning process increases the density of ligature molecules (n). tThe utilization rate (α) ultimately enhances the yield stress of polymer fibers. To verify the quantitative correlation between single molecules and macroscopic mechanical properties, single-molecule force spectroscopy (SMFS) experiments and tensile tests were conducted on PCL and PE fiber samples with different yield moduli using atomic force microscopy (AFM). Figure 16A -C and Figure 4A -B);

[0165] PCL-C1, PCL-C2, and PCL-C3 fibers were prepared by cold stretching at 45°C (below the melting temperature of 62.8°C), with the stretch ratio increasing from 5 to 10 and 14, respectively. PCL-C1 fiber exhibited high elongation at break and low stress. With increasing stretching, the elongation at break of PCL-C2 and PCL-C3 stabilized at around 25%, while the yield stress continued to rise. Figure 4A and C);

[0166] Commercial PE fibers prepared by melt spinning were named PE-M1, PE-M2, and PE-M3 according to their draw ratio from low to high. Similar trends in elongation and yield stress were observed in PE-M1, PE-M2, and PE-M3. Figure 4B and D);

[0167] Using the above single-molecule method, the L and n ( ) of PCL and PE fibers were analyzed. Figure 19A -D (as shown), σ SMFS ( Figure 4C and D), n t and α( Figure 4E Statistical analysis and calculations were performed on F. As the yield stress of PCL fibers increased from 84 MPa (PCL-C1) to 159 MPa (PCL-C2) and 254 MPa (PCL-C3), their tethering molecular density (n) also increased. t Ultimate yield stress (σ) SMFS Both the tensile yield stress (n) and utilization rate (α) gradually increased. Similarly, when the tensile yield stress of PE fiber increased from 227 MPa (PE-M1) to 318 MPa (PE-M2) and 411 MPa (PE-M3), its n... t σ SMFS As α increases, all parameters involved in the calculation are summarized in Table 1. These results are in high agreement with theoretical predictions, verifying the established quantitative correlation between single molecules and macroscopic mechanical properties.

[0168] Table 1 shows a schematic diagram of all parameters involved.

[0169]

[0170]

[0171] Furthermore, the α value provides a comprehensive assessment of the quantitative correlation between single molecules and macroscopic mechanical properties. Since the calculation of the ultimate yield stress is based on 100% utilization of the ultimately bearing ligature molecules, the theoretical maximum value of α is 100%. In reality, the α value is within a reasonable range—less than and close to 100%. Moreover, the α value gradually approaches 100% as the degree of tensile orientation increases. These results further validate the quantitative correlation.

[0172] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0173] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for predicting fiber yield stress based on single-molecule mechanics, characterized in that, include: Step 1: Prepare fiber samples; Step 2: Fabrication of functionalized atomic force microscope probes; Step 3: Test atomic force microscopy imaging and single-molecule force spectroscopy; Step 4: Verify single-molecule signals; Step 5: Reconstruct the chain trajectory in the fiber using the force-distance curve of a single molecule; Step 6: Quantitative analysis of interchain interactions in fibers; Step 7: Establish a quantitative relationship between single molecules and macroscopic mechanics; Step 8: Conduct a static tensile test on the polymer fiber; Step 9: Verify the quantitative relationship by using the dependence of tether molecular density and utilization on stretching orientation.

2. The method according to claim 1, characterized in that, In step 1, the fiber sample is prepared, specifically as follows: For radial imaging and single-molecule force spectroscopy experiments, polymer fibers were embedded and solidified, and then sliced ​​at -120°C using an Ultracut E microtome equipped with a glass scalpel, with the slicing direction perpendicular to the fiber axis, to obtain fiber samples.

3. The method according to claim 2, characterized in that, In step 2, the functionalized atomic force microscope probe is prepared, specifically as follows: A piranha solution was prepared in which the volume ratio of H2O2 / H2SO4 was 3:

7. An atomic force microscope probe was treated with the prepared piranha solution. After treatment, the probe was placed in an oven to dry. After drying, the atomic force microscope probe was placed in a dry nitrogen-purged dryer filled with 3-aminopropyldimethylmethoxysilane vapor for functionalization modification.

4. The method according to claim 3, characterized in that, In step 3, atomic force microscopy imaging and single-molecule force spectroscopy are tested, specifically as follows: Atomic force microscopy imaging was performed on an atomic force microscope, and single-molecule force spectroscopy experiments were conducted in air. The atomic force microscope probe was a silicon nitride probe. Using the single-molecule force spectroscopy method based on atomic force microscopy, single molecules were pulled out of the polymer fiber in air, and typical force-distance curves were collected.

5. The method according to claim 4, characterized in that, In step 4, the single-molecule signal is verified, specifically as follows: Whether the curve is stretched out of the crystal can be determined by whether it has peak signals with periodicity greater than 10 nm and long plateau signals with high force values.

6. The method according to claim 5, characterized in that, In step 6, the quantitative analysis of interchain interactions in the fibers specifically involves: The peak force value of the periodic peak signal greater than 10 nm and the plateau force value of the high force value long plateau signal in the force-distance curve are used to quantify the inter-chain interactions in the fiber.

7. The method according to claim 6, characterized in that, In step 7, a quantitative relationship between single molecules and macroscopic mechanics is established, specifically as follows: Assuming all ligature molecules are the final load-bearing units, then the ultimate yield stress of the fiber, i.e., σ SMFS for: σ SMFS =Fn t =Fn / S (1) In the formula, F is the activation force for chain slip in the crystal region obtained through single-molecule force spectroscopy experiments, and n t The density of ligature molecules in the fiber is: n t =n / S (2) In the formula, n is the number of ligature molecules contained in a single polymer chain, and S is the area occupied by polymer molecules on the radial cross section of the fiber.

8. The method according to claim 7, characterized in that, In step 8, a static tensile test of the polymer fiber is performed, specifically as follows: The modulus and fracture strain of each sample group were averaged from at least 15 samples. The actual yield stress of the fiber was obtained through stress-strain curves, which are: s y =as SMFS =αFn t (3) In the formula, σ y σ represents the actual tensile yield stress of the fiber, α represents the utilization rate of the ligature molecules, and σ represents the actual tensile yield stress of the fiber. SMFS This is the theoretical ultimate yield stress; By comparing the actual tensile yield stress with the ultimate yield stress, we can determine whether the quantitative relationship between the single molecule and macroscopic mechanics is correct.

9. The method according to claim 8, characterized in that, In step 9, the quantitative relationship is verified by utilizing the dependence of tether molecular density and utilization on stretching orientation, specifically as follows: The quantitative relationship between single molecules and macroscopic mechanics is verified by utilizing the dependence of tether molecular density and utilization on stretching orientation. The quantitative relationship between single molecules and macroscopic mechanics is further verified by whether tether molecular density and utilization increase with the degree of stretching.

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