A method for calculating the thermal response liquid phase water seepage velocity of PNIPAM hydrogel

Abstract

The application provides a kind of PNIPAM hydrogel thermal response liquid phase water seepage velocity calculation method, first, according to the ratio of NIPAM monomer and MBA crosslinking agent, the polymerization degree N is calculated, and the molecular chain structure parameters of hydrogel are quantified;Subsequently, according to the swelling-shrinkage behavior of hydrogel at different temperatures, the thermal response characteristic pressure function is constructed to represent the liquid phase seepage driving force;And combined with the seepage channel length, effective aperture and water dynamic characteristics, the seepage velocity calculation model is established, and the dynamic seepage velocity of liquid water in hydrogel is solved.The method of the application can accurately reflect the structural change of poly-N-isopropyl acrylamide hydrogel under temperature trigger and the internal liquid phase transmission rule, significantly improve the quantitative analysis ability of thermal responsive hydrogel seepage behavior, and provide reliable theoretical basis and calculation tool for mass transfer prediction, temperature control release design, thermal response performance optimization and related multi-field coupling simulation of hydrogel material.

Description

Technical Field

[0001] This invention relates to the field of polymer materials, and in particular to a method for preparing PNIAPM hydrogel and regulating its thermal response properties. Background Technology

[0002] Thermally responsive hydrogels based on PNIAPM (poly-N-isopropylacrylamide) have become a research focus in recent years for applications such as dehumidification, atmospheric water collection, and thermal management. Thermally responsive hydrogels possess a critical volumetric phase transition temperature, meaning that a volumetric phase transition occurs above this temperature, accompanied by direct desorption of liquid water. The migration rate of the internal liquid water after the volumetric phase transition directly affects the desorption rate and is a crucial basis for analyzing the dynamic distribution of internal moisture content during the dehumidification process.

[0003] Existing solutions disclose a Yeh-multiscale finite element method (patent application number CN201610556975.1) for simulating Darcy velocity in porous media. This method uses Yeh's Galerkin model to obtain the head pressure value and the Cholesky decomposition method to calculate the Darcy velocity in porous media. While this method can calculate the liquid phase seepage velocity in non-thermally responsive conventional porous media such as soil and rock, it cannot be used to calculate the head pressure and seepage velocity characteristics caused by the critical volume phase transition of thermally responsive hydrogels. Furthermore, existing research and inventions lack methods for calculating the liquid phase water seepage velocity inside thermally responsive hydrogels when the temperature rises above the critical temperature.

[0004] In existing technologies, no method has been disclosed for calculating the liquid-phase water permeation velocity within thermoresponsive polymer hydrogels. Traditional Darcy's law calculations for permeation velocities in porous media typically rely on the potential difference in pressure head, implying a pressure difference within the porous medium. However, liquid-phase water permeation in thermoresponsive polymers is primarily driven by temperature and lacks a mechanical pressure difference; therefore, the driving force for liquid-phase water permeation cannot be calculated using conventional porous media. Calculation methods based on Darcy's law for conventional porous media cannot effectively reflect the liquid-phase water permeation process driven by the material's thermoresponsive characteristics. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the liquid phase water permeation velocity of PNIPAM hydrogels, which solves the problem of difficulty in quantifying the desiccation rate and dynamic characteristics of temperature-sensitive hydrogels in the prior art. To achieve the above objective, this invention adopts the following technical solution:

[0006] A method for calculating the liquid phase water permeation velocity in a PNIPAM hydrogel with thermal response includes the following steps:

[0007] Step S1: Calculate the degree of polymerization N of the poly-N-isopropylacrylamide hydrogel.

[0008] The degree of polymerization N of a single molecular chain of poly(N-isopropylacrylamide) hydrogel is calculated based on the mass ratio of N-isopropylacrylamide monomer to N,N′-methylenebisacrylamide crosslinking agent, and is used to quantify the molecular chain structural parameters.

[0009] Step S2: Calculate the driving force of liquid phase water seepage

[0010] Based on the thermal response behavior of poly(N-isopropylacrylamide) hydrogel when the temperature rises above the critical temperature, the driving force of liquid phase water seepage is calculated using the thermal response characteristic pressure function.

[0011] Step S3: Characterize permeability and tortuosity

[0012] The porous structure of the freeze-dried hydrogel was obtained by mercury intrusion porosimetry and X-ray computed tomography, and the permeability κ and tortuosity τ were measured at the corresponding water content.

[0013] Step S4: Calculate the liquid phase water seepage velocity

[0014] The liquid water flow velocity in the regions where volumetric phase transition has occurred and those where volumetric phase transition has not occurred is calculated based on the permeability κ, tortuosity τ, thermal response characteristic pressure, and the length of the phase transition region in the hydrogel.

[0015] Step S5: Determine the calculation time interval Δt

[0016] Set the time step Δt for seepage simulation calculations to allow for dynamic updates of water content;

[0017] Step S6: Calculate the moisture content of poly-N-isopropylacrylamide at the target time.

[0018] The moisture content at each moment is calculated based on the state equation for the change of moisture content with time during the dehumidification process.

[0019] Preferably, the poly(N-isopropylacrylamide) hydrogel is prepared by polymerization of monomer N-isopropylacrylamide and crosslinking agent N,N′-methylenebisacrylamide in a preset ratio, wherein the ratio is used to calculate the degree of polymerization N to determine the number of NIPAM monomers in a single molecular chain.

[0020] Preferably, in step S1, the degree of polymerization N is calculated using the following formula:

[0021]

[0022] In the formula: —Degree of polymerization of poly(N-isopropylacrylamide);

[0023] —NIPAM monomer addition amount, g;

[0024] —MBA additions, g.

[0025] Preferably, in step S2, the driving force for liquid phase water permeation, i.e., the additional characteristic pressure caused by the thermal response, is calculated using the characteristic pressure function of the thermal response after the critical volume phase transition of the poly-N-isopropylacrylamide hydrogel, using the following formula:

[0026]

[0027] In the formula: —Additional characteristic pressure caused by thermal response, Pa;

[0028] —Water content of poly-N-isopropylacrylamide hydrogel in the calculated state, g / g;

[0029] — The conversion coefficient is set to 1.57 for the solid-liquid interaction in porous media.

[0030] Preferably, in step S3, the permeability of the freeze-dried poly(N-isopropylacrylamide) porous media at the specified moisture content is measured and calculated using a mercury porosimeter and X-ray computed tomography. and tortuosity .

[0031] Preferably, in step S4, the liquid water percolation velocity in the regions of the poly-N-isopropylacrylamide hydrogel that have undergone volume phase transition and those that have not is calculated using the following formula:

[0032]

[0033] In the formula: —Liquid phase water seepage velocity, m / s;

[0034] —Permeability of porous media, m 2 ;

[0035] —Degree of curvature;

[0036] — The distance between the heated and cold ends of the hydrogel, in meters (m).

[0037] Preferably, in step S6, the liquid phase water permeation velocity is corrected based on the updated moisture content to achieve dynamic calculation of the thermal response dehumidification process of poly-N-isopropylacrylamide.

[0038] Preferably, in step S6, the seepage velocity is corrected considering the dynamic changes in water content using the following formula:

[0039]

[0040] In the formula: — Moisture content at time t, g / g;

[0041] —Calculate the time interval, in seconds;

[0042] B, C – Width and thickness of poly-N-isopropylacrylamide hydrogel, in meters;

[0043] — Length of the region where a volumetric phase transition has occurred, in meters.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] This invention constructs a calculation model for the seepage driving force based on the thermal response characteristics of poly(N-isopropylacrylamide) hydrogel, which enables accurate quantitative calculation of the seepage velocity of liquid water under temperature change conditions, and significantly improves the accuracy of predicting the seepage behavior of thermally responsive hydrogels.

[0046] This invention calculates the degree of polymerization N by introducing the ratio of NIPAM monomer to MBA crosslinking agent, thereby achieving quantitative characterization of the molecular chain structure parameters of hydrogels and improving the controllability and repeatability of model input parameters.

[0047] This invention establishes a pressure function associated with the thermal expansion and phase transition characteristics of hydrogels, thereby enabling dynamic inversion of the seepage driving force under external temperature control conditions and improving the ability to fit the physical reality of the thermal response seepage process.

[0048] This invention proposes a structured seepage velocity calculation procedure, realizing a complete methodological chain from obtaining material composition and thermal response characteristic parameters to solving the final seepage velocity, thereby improving engineering feasibility and experimental verifiability.

[0049] This invention, by comprehensively considering multiple factors such as molecular chain structure, thermal response characteristic pressure, and liquid phase permeation physical mechanism in the model, expands the applicability of permeation velocity prediction under different temperature fields and material ratios, thereby enhancing the universality and reliability of the method.

[0050] In summary, this invention constructs a method for calculating the liquid-phase water percolation velocity of poly(N-isopropylacrylamide) hydrogels based on thermal response characteristics, achieving accurate characterization of the internal liquid-phase water migration behavior of hydrogels under conditions exceeding the critical temperature. This invention utilizes the pressure function obtained from the research on thermal response characteristics to calculate the percolation driving force, and combines this with structural parameters and porosity characteristics obtained from material composition to achieve dynamic solution of the percolation velocity at various moments during the dehumidification process. This method effectively reveals the dehumidification mechanism of poly(N-isopropylacrylamide) hydrogels under thermal response conditions, providing a quantitative and repeatable calculation tool for the analysis of mass transfer characteristics, temperature-controlled release design, and prediction of thermal response behavior of hydrogel materials. It possesses technical advantages such as clear structure, controllable parameters, and strong applicability. Attached Figure Description

[0051] Figure 1 A flowchart illustrating a method for calculating the liquid phase water permeation velocity in a PNIPAM hydrogel thermal response, provided as an embodiment of the present invention;

[0052] Figure 2 A schematic diagram of a PNIPAM hydrogel for calculating the thermal response liquid phase water permeation velocity of a PNIPAM hydrogel, provided as an embodiment of the present invention;

[0053] Figure 3 A schematic diagram of pressure fitting curves of PNIPAM hydrogels with different degrees of polymerization perpendicular to the direction of liquid water flow, provided for an embodiment of the present invention, in a method for calculating the liquid water permeation velocity of thermally responsive PNIPAM hydrogels.

[0054] Figure 4 This invention provides a method for calculating the seepage velocity of liquid phase water in a PNIPAM hydrogel based on its thermal response, which relates the coefficient of the formula for the additional characteristic pressure caused by the thermal response of PNIPAM to the degree of polymerization. Detailed Implementation

[0055] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0056] like Figure 1 As shown in this embodiment, a method for calculating the liquid phase water permeation velocity of a PNIPAM hydrogel in thermal response is provided, including the following steps:

[0057] Step S1: Calculate the degree of polymerization N of the poly-N-isopropylacrylamide hydrogel.

[0058] The degree of polymerization N of a single molecular chain of poly(N-isopropylacrylamide) hydrogel is calculated based on the mass ratio of N-isopropylacrylamide monomer to N,N′-methylenebisacrylamide crosslinking agent, and is used to quantify the molecular chain structural parameters.

[0059] The poly(N-isopropylacrylamide) hydrogel is prepared by polymerization of monomer N-isopropylacrylamide (NIPAM) and crosslinking agent N,N′-methylenebisacrylamide (MBA) in a preset ratio, wherein the ratio is used to calculate the degree of polymerization N to determine the number of NIPAM monomers in a single molecular chain.

[0060] The degree of polymerization N is calculated using the following formula:

[0061]

[0062] In the formula: —Degree of polymerization of poly(N-isopropylacrylamide);

[0063] —NIPAM monomer addition amount, g;

[0064] —MBA additions, g.

[0065] like Figure 2 The image shows a schematic diagram of the PNIPAM hydrogel.

[0066] Step S2: Calculate the driving force of liquid phase water seepage

[0067] Based on the thermal response behavior of poly(N-isopropylacrylamide) hydrogel when the temperature rises above the critical temperature, the driving force of liquid phase water permeation is calculated using the thermal response characteristic pressure function.

[0068] The driving force for liquid phase water permeation, i.e., the additional characteristic pressure caused by the thermal response, is calculated using the characteristic pressure function of the thermal response after the critical volume phase transition of poly(N-isopropylacrylamide) hydrogel, as shown in the following formula:

[0069] ,

[0070] In the formula: —Additional characteristic pressure caused by thermal response, Pa;

[0071] —Water content of poly-N-isopropylacrylamide hydrogel in the calculated state, g / g;

[0072] —The conversion coefficient is set to 1.57 for the solid-liquid interaction in porous media;

[0073] a, b — fitting coefficients, which are related to the degree of aggregation N.

[0074] like Figure 4 The figure shows the relationship between the additional characteristic pressure coefficient caused by the thermal response and the degree of polymerization in this embodiment. .

[0075]

[0076] In the formula: —Additional characteristic pressure caused by thermal response, Pa;

[0077] —Water content of poly-N-isopropylacrylamide hydrogel in the calculated state, g / g;

[0078] — The conversion coefficient is set to 1.57 for the solid-liquid interaction in porous media.

[0079] like Figure 3 As shown, the pressure fitting curves perpendicular to the liquid phase water flow direction under different degrees of polymerization in this embodiment are used to calculate the additional characteristic pressure caused by the thermal response. . The pressure was calculated by combining the pressure perpendicular to the flow direction with the pressure perpendicular to the flow direction, obtained from the interaction force between poly(N-isopropylacrylamide) and water based on molecular dynamics simulations. The figure shows the pressure perpendicular to the flow direction for different water contents and different degrees of polymerization N (N=10~150, as shown by different legend curves in the figure).

[0080] Step S3: Characterize permeability and tortuosity

[0081] The permeability of freeze-dried poly(N-isopropylacrylamide) porous media at moisture content was calculated using mercury porosimetry and X-ray computed tomography. and tortuosity .

[0082] Step S4: Calculate the liquid phase water seepage velocity

[0083] Based on the permeability κ, tortuosity τ, thermal response characteristic pressure, and the length of the phase transition region in the hydrogel, the liquid phase water permeation velocity in the regions where volumetric phase transition has occurred and those where volumetric phase transition has not occurred is calculated.

[0084] The liquid water percolation velocity in the regions of poly(N-isopropylacrylamide) hydrogel that have undergone volume phase transition and those that have not is calculated using the following formula:

[0085]

[0086] In the formula: —Liquid phase water seepage velocity, m / s;

[0087] —Permeability of porous media, m 2 ;

[0088] —Degree of curvature;

[0089] — The distance between the heated and cold ends of the hydrogel, in meters (m).

[0090] Step S5: Determine the calculation time interval Δt

[0091] Set the time step Δt for seepage simulation calculations to allow for dynamic updates of water content;

[0092] Step S6: Calculate the moisture content of poly-N-isopropylacrylamide at the specified time and correct for the seepage velocity.

[0093] Based on the equation of state governing the change of moisture content over time during the dehumidification process, the moisture content at each moment is calculated. The liquid water permeation velocity is then corrected based on the updated moisture content to achieve dynamic calculation of the thermal response dehumidification process of poly(N-isopropylacrylamide).

[0094] The seepage velocity is corrected to account for dynamic changes in moisture content using the following formula:

[0095]

[0096] In the formula: — Moisture content at time t, g / g;

[0097] —Calculate the time interval, in seconds;

[0098] B, C – Width and thickness of poly-N-isopropylacrylamide hydrogel, in meters;

[0099] — Length of the region where a volumetric phase transition has occurred, in meters.

[0100] The following is a detailed explanation using specific data:

[0101] This example uses a poly(N-isopropylacrylamide) thermoresponsive polymer hydrogel with a NIPAM and MBA mass addition ratio of 1g:6mg, a length (distance between the heating section and the cold end of the hydrogel) width and height of 0.1m, 0.05m and 0.01m respectively, and an initial water content of 0.3g / g as an example. The internal liquid phase water permeation velocity was calculated and the water content change trend at each time point was analyzed.

[0102] Step S1: Based on the preparation ratio of poly(N-isopropylacrylamide) hydrogel monomer and crosslinking agent, the degree of polymerization N of a single molecular chain is calculated to be approximately 152.

[0103] Step S2: Using the thermal response characteristic pressure function of poly(N-isopropylacrylamide) hydrogel after the critical volume phase transition, the driving force for liquid phase water seepage at the initial water content at the initial moment was calculated to be 144.6 Pa.

[0104] Step S3: The permeability of the freeze-dried poly(N-isopropylacrylamide) porous media at the specified moisture content was measured and calculated using a mercury porosimeter and X-ray computed tomography. The tortuosity is 690.7 mD. It is 1.26;

[0105] Step S4: Initially, the distance between the heated and cold ends of the poly(N-isopropylacrylamide) hydrogel is 0.1 m. The calculated liquid water permeation velocity in the regions of the poly(N-isopropylacrylamide) hydrogel that have undergone volume phase transition and those that have not is 8.7 × 10⁻⁶ m. -7 m / s;

[0106] Step S5: Taking a calculation time interval of 60 seconds as an example, experimental observation shows that the distance between the regions where volumetric phase transformation has occurred and those where it has not occurred after 60 seconds is approximately 0.03 m. The water content after desorption for 60 seconds is 0.297 g / g. Since the water content is still greater than 0.25 g / g, the seepage velocity after desorption for 60 seconds remains unchanged at 8.7 × 10⁻⁶ m / s. -7 m / s;

[0107] Step S6: When the desorption time interval is 10000s, poly-N-isopropylacrylamide has completely undergone a volume phase transition. The water content after desorption for 6000 s is 0.26 g / g. Since the water content is still greater than 0.25 g / g, the seepage velocity after desorption for 60 s remains unchanged at 8.7 × 10⁻⁶ g / g. -7 m / s. After desorption continued for 10000 s, the water content was 0.21 g / g, which was lower than 0.25 g / g. The calculated seepage velocity after 10000 s of desorption was 8.3 × 10 m / s. -7 m / s.

[0108] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for calculating the liquid phase water permeation velocity of a PNIPAM hydrogel with thermal response, characterized in that, Includes the following steps: Step S1: Calculate the degree of polymerization N of the poly-N-isopropylacrylamide hydrogel. The degree of polymerization N of a single molecular chain of poly(N-isopropylacrylamide) hydrogel is calculated based on the mass ratio of N-isopropylacrylamide monomer to N,N′-methylenebisacrylamide crosslinking agent, and is used to quantify the molecular chain structural parameters. In step S1, the degree of polymerization N is calculated using the following formula: ； In the formula: N —Degree of polymerization of poly(N-isopropylacrylamide); —NIPAM monomer addition amount, g; —MBA additions, g; Step S2: Calculate the driving force of liquid phase water seepage Based on the thermal response behavior of poly(N-isopropylacrylamide) hydrogel when the temperature rises above the critical temperature, the driving force of liquid phase water seepage is calculated using the thermal response characteristic pressure function. In step S2, the driving force for liquid phase water permeation, i.e., the additional characteristic pressure caused by the thermal response, is calculated using the characteristic pressure function of the thermal response after the critical volume phase transition of the poly-N-isopropylacrylamide hydrogel, as shown in the following formula: ； In the formula: —Additional characteristic pressure caused by thermal response, Pa; w —Water content of poly-N-isopropylacrylamide hydrogel in the calculated state, g / g; —The conversion coefficient is set to 1.57 for the solid-liquid interaction in porous media; Step S3: Characterize permeability and tortuosity The porous structure of the freeze-dried hydrogel was obtained by mercury intrusion porosimetry and X-ray computed tomography, and the permeability κ and tortuosity τ were measured at the corresponding water content. Step S4: Calculate the liquid phase water seepage velocity The liquid water flow velocity in the regions where volumetric phase transition has occurred and those where volumetric phase transition has not occurred is calculated based on the permeability κ, tortuosity τ, thermal response characteristic pressure, and the length of the phase transition region in the hydrogel. Step S5: Determine the calculation time interval Δt Set the time step Δt for seepage simulation calculations to allow for dynamic updates of water content; Step S6: Calculate the moisture content of poly-N-isopropylacrylamide at the target time. The moisture content at each moment is calculated based on the state equation of moisture content change with time during the dehumidification process. In step S6, the seepage velocity is corrected to account for dynamic changes in moisture content using the following formula: ； In the formula: — Moisture content at time t, g / g; —Calculate the time interval, in seconds; B, C – Width and thickness of poly-N-isopropylacrylamide hydrogel, in meters; d — Length of the region where a volumetric phase transition has occurred, in meters.

2. The method for calculating the liquid phase water permeation velocity of a PNIPAM hydrogel according to claim 1, characterized in that, The poly(N-isopropylacrylamide) hydrogel comprises monomer N-isopropylacrylamide and crosslinking agent N,N′-methylenebisacrylamide, prepared by polymerization according to a preset ratio. The ratio is used to calculate the degree of polymerization N to determine the amount of monomer N-isopropylacrylamide in a single molecular chain.

3. The method for calculating the liquid phase water permeation velocity of a PNIPAM hydrogel according to claim 1, characterized in that, In step S3, the permeability of the freeze-dried poly(N-isopropylacrylamide) porous media at the specified moisture content is calculated using a mercury porosimeter and X-ray computed tomography. and tortuosity .

4. The method for calculating the liquid phase water permeation velocity of a PNIPAM hydrogel according to claim 1, characterized in that, In step S4, the liquid water percolation velocity in the regions of the poly-N-isopropylacrylamide hydrogel that have undergone volume phase transition and those that have not is calculated using the following formula: ； In the formula: —Liquid phase water seepage velocity, m / s; —Permeability of porous media, m 2 ; —Degree of curvature; — The distance between the heated and cold ends of the hydrogel, in meters (m).

5. The method for calculating the liquid phase water permeation velocity of a PNIPAM hydrogel according to claim 1, characterized in that, In step S6, the liquid phase water permeation velocity is corrected based on the updated moisture content to achieve dynamic calculation of the thermal response dehumidification process of poly(N-isopropylacrylamide).

Images