A method for determining c-s-h pore structure in the irreversibly shrinkage range

Abstract

The application discloses a kind of calculation methods for determining C-S-H pore structure in irreversible shrinkage range, comprising the following steps: establishing C-S-H pore structure model;Using Helmholtz free energy to describe the energy of C-S-H pore structure model;Establish the relationship between the energy part related to physical entropy and pore structure;Establish the relationship between the energy part related to total volume and pore structure;Establish the relationship between the energy part related to surface energy and pore structure;Determine the calculation parameter, and carry out energy calculation to C-S-H pore structure model in given calculation range;Determine the effective C-S-H pore structure energy calculation range;Based on the principle of energy minimization, determine the structure information and structure parameters corresponding to stable C-S-H pore structure model.The application solves the problem that various experimental measurement methods and structure models in the prior art are qualitatively described in the structure characterization of C-S-H pore structure under different humidity, without quantitatively describing C-S-H pore structure information.

Description

Technical Field

[0001] This invention relates to the field of cement materials technology, and in particular to a calculation method for determining the pore structure of CSH within the irreversible shrinkage range. Background Technology

[0002] CSH (Cementitious Drying Shrinkage) is the main hydration product of silicate cement, accounting for 60%–70% of the total volume. It is considered an important component affecting the durability and other properties of cement-based materials, and is also the main source of irreversible drying shrinkage. Generally, after the cement paste has completely dried for the first time, the irreversible portion of drying shrinkage is almost fully developed, accounting for about 50% of the total primary drying shrinkage. Therefore, irreversible drying shrinkage is extremely important. However, current research on cement paste drying shrinkage mainly focuses on reversible shrinkage. Macroscopic experiments have established the relationship between humidity and deformation, and some relatively mature theories have been formed, such as capillary pressure theory, disintegration pressure theory, surface energy theory, and interlayer water movement theory. Regarding the mechanism of irreversible shrinkage, there are currently only some explanatory hypotheses and conjectures, such as changes in interparticle bonding, changes in pore size distribution and moisture distribution in the system, and a complete theory has not yet been formed. Most studies show that the shrinkage deformation of hardened cement paste in the humidity range of 11%RH–40RH% or 50%RH is reversible, while the range of irreversible shrinkage is between 80%RH and 40%RH.

[0003] Changes in the microstructure of cement paste (CSH) are a significant manifestation of irreversible shrinkage. Currently, adsorption experiments, scanning electron microscopy (SEM), small-angle X-ray scattering (SAX), neutron small-angle scattering (SAX), and nuclear magnetic resonance (NMR) can all observe structural changes in CSH within the irreversible shrinkage range. However, sample pretreatment methods and the inherent irreversible nature of CSH structure hinder the accurate capture of pore structure information under different humidity conditions in adsorption experiments. While SAX and NMR effectively address the limitations of adsorption experiments, they lack a comprehensive theoretical framework for quantitatively describing the pore structure of CSH and do not provide quantitative descriptions of CSH structure under varying humidity conditions. In summary, existing experimental measurement methods and structural models for characterizing CSH structure under different humidity levels largely remain at the qualitative descriptive level. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a calculation method that can quantitatively describe the CSH pore structure within the irreversible shrinkage range under given humidity conditions.

[0005] Technical Solution: To achieve the above objectives, the present invention provides a calculation method for determining the CSH pore structure within the irreversible shrinkage range, comprising the following steps:

[0006] Step S1: Establish the CSH pore structure model;

[0007] Step S2: Use Helmholtz free energy to describe the energy of the CSH pore structure model;

[0008] Step S3: Replace the physical entropy in the Helmholtz free energy with information entropy, and introduce coefficients to establish the relationship between the energy component related to physical entropy and the pore structure;

[0009] Step S4: Calculate the adsorption stress based on the thermodynamic model of the mesoporous material, and replace the environmental pressure in the Helmholtz free energy with the adsorption stress to establish the relationship between the energy component related to the total volume and the pore structure.

[0010] Step S5: Establish the relationship between the energy component related to surface energy and pore structure;

[0011] Step S6: Determine the calculation parameters and perform energy calculations on the CSH pore structure model within the given calculation range;

[0012] Step S7: Determine the effective range for calculating CSH pore structure energy;

[0013] Step S8: Based on the principle of minimum energy, determine the structural information and structural parameters corresponding to the stable CSH pore structure model.

[0014] Specifically, step S1, establishing the CSH pore structure model, involves: based on the quantitative description of the Jennings model, the CSH pore structure model consists of CSH basic units and pores, where the pores are cylindrical and follow a single log-normal distribution. The pore distribution f(x) is:

[0015]

[0016] In the formula, φ is the position parameter, δ is the shape parameter, and x is the diameter of a single pore;

[0017] Establish the relationship between the total surface area, total pore volume, and total volume of the CSH basic unit in the CSH pore structure model:

[0018]

[0019] In the formula, S sur V represents the total surface area of ​​the CSH pore structure model. p V is the total pore volume. s ρ is the total volume of the CSH basic unit. s S represents the density of the basic unit of CSH. mis the specific surface area of ​​the basic unit.

[0020] Specifically, step S2, which describes the energy of the CSH pore structure using Helmholtz free energy, is as follows:

[0021] F=μN-TS-PV+γA (3),

[0022] In the formula, F is the Helmholtz free energy, μ is the chemical potential, N is the number of solid phases, T is the temperature, S is the physical entropy, P is the ambient pressure, and V is the total pore volume. p The total volume V of the CSH basic unit s The sum, where γ is the surface energy and A is the total surface area S of the CSH pore structure model. sur .

[0023] In step S3, the information entropy H is used to replace the physical entropy S in equation (3), and the information entropy is:

[0024] H=-∫f(x)ln(f(x))dx (4).

[0025] Specifically, step S3, which introduces a coefficient to establish the relationship between the energy component related to physical entropy and the pore structure, refers to introducing a coefficient k representing the numerical relationship between physical entropy and information entropy into the energy component TS related to physical entropy in the CSH pore structure.

[0026] TS=kVH (5).

[0027] In step S4, calculating the adsorption stress based on the thermodynamic model of the mesoporous material and replacing the ambient pressure in the Helmholtz free energy with the adsorption stress to establish the relationship between the energy component related to the total volume and the pore structure refers to calculating the adsorption stress σ based on the thermodynamic model of the mesoporous material and replacing the ambient pressure P in the Helmholtz free energy with the adsorption stress σ to establish the relationship between the energy component PV related to the total volume of the CSH pore structure and the pore structure, where the adsorption stress σ is:

[0028]

[0029] In the formula, h is the thickness of the adsorption film, and γ sl R is the solid-liquid interface energy. g V is the ideal gas constant. L Let p be the molar volume of the adsorbed phase, p / p0 be the relative humidity, Π(h) be the expression for the dissociation pressure, and d be the molar volume of the adsorbed phase. max To find the maximum aperture, take an infinite value, d min To determine the minimum aperture, take 1 nm, d c denoted as the critical diameter, f(x) represents the pore distribution, x is the diameter of a single pore, and h′ is the thickness h of the adsorption film.

[0030] Specifically, establishing the relationship between the energy component related to surface energy and the pore structure in step S5 refers to calculating the relationship between the energy component γA related to surface energy γ in the CSH pore structure model in step S2 and the pore structure.

[0031]

[0032] In the formula, γ l This represents the surface energy of the adsorbed phase.

[0033] Specifically, step S6 involves determining the calculation parameters and performing energy calculations on the CSH pore structure model within a given calculation range. Under given humidity conditions, all components in the expression (3) for the energy of the CSH pore structure can be associated with the pore distribution f(x). Therefore, the energy of the CSH pore structure is regarded as a function expression of the shape parameter φ and the position parameter δ of the pore distribution, i.e., F(φ, δ). A point-by-point calculation method is used to take values ​​for the shape parameter φ and the position parameter δ one by one within the given calculation range to perform energy calculations on the CSH pore structure model.

[0034] Specifically, in step S7, determining the effective CSH pore structure energy calculation range involves: based on the principle that the greater the compressive stress of a compressed object, the greater the corresponding deformation and the smaller the pore volume, in step S6, for a given shape parameter φ and position parameter δ, the adsorption stress σ and the total pore volume V are calculated according to formulas (3) and (6). p ;

[0035] If the adsorption stress σ and the total pore volume V are calculated p If the relationship between the given shape parameters φ and position parameters δ does not conform to the principle that the greater the stress, the smaller the pore volume, then the CSH pore structure energy calculated by the given shape parameters φ and position parameters δ is invalid, and the given point is excluded.

[0036] The effective CSH pore structure energy calculation range is defined as the combination of points where the remaining points within the calculation range are valid.

[0037] Specifically, step S8, which involves determining the structural information and structural parameters corresponding to a stable CSH pore structure model based on the principle of minimum energy, involves: based on the principle that the smaller the energy of the CSH pore structure under given conditions, the more stable the structure, finding the value points of the shape parameter φ and the position parameter δ when the energy of the CSH pore structure is minimized within the effective calculation range, thereby determining the structural information and structural parameters corresponding to a stable CSH pore structure model. The structural information includes the pore distribution, pore volume, and porosity of the CSH pore structure, and the structural parameters include the position and shape parameters of the pore distribution.

[0038] Beneficial effects: The present invention has the following advantages: 1. Under given humidity conditions, the present invention can establish a CSH pore structure model and calculate the energy of the CSH pore structure, and obtain quantitative information of the CSH pore structure within the irreversible range based on the shape parameter φ and position parameter δ corresponding to the point with the minimum energy in the model in the calculation results.

[0039] 2. The method of this invention considers the stable state of CSH pore structure from the perspective of energy. The calculation results are not affected by the actual deformation process, which fills the research gap caused by the complexity of the actual deformation process and the difficulty in experimental measurement. It provides a quantitative data description of the reorganization behavior of CSH structure within the irreversible drying shrinkage range, thus laying the foundation for the study of the mechanism of irreversible shrinkage of cement paste. Attached Figure Description

[0040] Figure 1 This is a flowchart of the method of the present invention;

[0041] Figure 2 The results for the CSH pore structure energy under 80% RH in Example 1 are within the calculated range;

[0042] Figure 3 (a)-(f) are graphs showing the relationship between the shape parameters, position parameters and pore volume and adsorption stress of the CSH pore structure in Example 1.

[0043] Figure 4 This represents the invalid CSH pore structure calculation region within the calculation range at 80% RH in Example 1.

[0044] Figure 5 This is a pore volume distribution curve of the CSH pore structure at 80% RH in Example 1;

[0045] Figure 6 The results for the CSH pore structure energy at 60% RH in Example 2 are within the calculated range;

[0046] Figure 7This refers to the invalid CSH pore structure calculation region within the calculation range at 60% RH in Example 2.

[0047] Figure 8 This is a pore volume distribution curve of the CSH pore structure at 60% RH in Example 2. Detailed Implementation

[0048] The technical solution of the present invention will be described in detail below with reference to the embodiments and accompanying drawings.

[0049] like Figure 1 The diagram shown is a flowchart of the method of the present invention. Example 1 describes the energy calculation of the CSH pore structure and the determination of the final stable CSH pore structure under 80% RH humidity conditions, including the following steps.

[0050] Step S1: Establish the CSH pore structure model, specifically: based on the quantitative description of the Jennings model, the CSH pore structure model consists of CSH basic units and pores, where the pores are cylindrical and follow a single log-normal distribution. The pore distribution f(x) is:

[0051]

[0052] In the formula, φ is the position parameter, δ is the shape parameter, and x is the diameter of a single pore;

[0053] Establish the relationship between the total surface area, total pore volume, and total volume of the CSH basic unit in the CSH pore structure model:

[0054]

[0055] In the formula, S sur V represents the total surface area of ​​the CSH pore structure model. p V is the total pore volume. s ρ is the total volume of the CSH basic unit. s S represents the density of the basic unit of CSH. m is the specific surface area of ​​the basic unit.

[0056] Step S2: The energy of the CSH pore structure model is described using Helmholtz free energy, specifically as follows:

[0057] F=μN-TS-PV+γA (3),

[0058] In the formula, F is the Helmholtz free energy, μ is the chemical potential, N is the number of solid phases, T is the temperature, S is the physical entropy, P is the ambient pressure, and V is the total pore volume. p The total volume V of the CSH basic unit sThe sum, where γ is the surface energy and A is the total surface area S of the CSH pore structure model. sur .

[0059] Step S3: Replace the physical entropy in the Helmholtz free energy with information entropy, and introduce a coefficient to establish the relationship between the energy component related to the physical entropy and the pore structure, where the information entropy is:

[0060] H=-∫f(x)ln(f(x))dx (4);

[0061] The introduction of a coefficient to establish the relationship between the energy component related to physical entropy and the pore structure refers to introducing a coefficient k in the energy component TS related to physical entropy in the CSH pore structure to represent the numerical relationship between physical entropy and information entropy. Specifically:

[0062] TS=kVH (5).

[0063] Step S4: Calculate the adsorption stress based on the thermodynamic model of the mesoporous material, and replace the ambient pressure in the Helmholtz free energy with the adsorption stress to establish the relationship between the energy component related to the total volume and the pore structure. This means calculating the adsorption stress σ based on the thermodynamic model of the mesoporous material, replacing the ambient pressure P in the Helmholtz free energy with the adsorption stress σ, and establishing the relationship between the energy component PV related to the total volume of the CSH pore structure and the pore structure. The adsorption stress σ is:

[0064]

[0065] In the formula, h is the thickness of the adsorption film, and γ sl R is the solid-liquid interface energy. g V is the ideal gas constant. L Let p be the molar volume of the adsorbed phase, p / p0 be the relative humidity, П(h) be the expression for the dissociation pressure, and d be the molar volume of the adsorbed phase. max To find the maximum aperture, take an infinite value, d min To determine the minimum aperture, take 1 nm, d c denoted as the critical diameter, f(x) represents the pore distribution, x is the diameter of a single pore, and h′ is the thickness h of the adsorption film.

[0066] Step S5: Establishing the relationship between the energy component related to surface energy and the pore structure refers to calculating the relationship between the energy component γA related to surface energy γ in the CSH pore structure model in step S2 and the pore structure.

[0067]

[0068] In the formula, γ l This represents the surface energy of the adsorbed phase.

[0069] Step S6: Determine the calculation parameters and perform energy calculation on the CSH pore structure model within the given calculation range. Specifically, under the given humidity conditions, all components in the expression (3) of the CSH pore structure energy can be associated with the pore distribution f(x). Therefore, the CSH pore structure energy is regarded as a function expression of the shape parameter φ and the position parameter δ of the pore distribution, i.e., F(φ, δ). The point-by-point calculation method is adopted to take the values ​​of the shape parameter φ and the position parameter δ one by one within the given calculation range and perform energy calculation on the CSH pore structure model.

[0070] The actual calculation range for the position parameter φ and shape parameter δ is between 0.1 and 3, with a calculation step size of 0.1. The temperature is room temperature (298.15 K), the humidity is 80% RH, and the correlation coefficient k is 1. Other relevant input parameters are shown in Table 1. Under these conditions, the energy distribution of the CSH pore structure model within the calculation range is as follows: Figure 2 As shown.

[0071] Table 1 shows the relevant parameters for energy calculation of the CSH pore structure model in Example 1.

[0072]

[0073] The determination of the effective CSH pore structure energy calculation range in step S7 is as follows: Based on the principle that the greater the compressive stress of a compressed object, the greater the corresponding deformation and the smaller the pore volume, in the calculation process of step S6, for a given shape parameter φ and position parameter δ, the adsorption stress σ and the total pore volume V are calculated according to formulas (3) and (6). p If the adsorption stress σ and the total pore volume V are calculated... p If the relationship between the given shape parameters φ and position parameters δ does not conform to the principle that the greater the stress, the smaller the pore volume, then the CSH pore structure energy calculated by the given shape parameters φ and position parameters δ is invalid, and the given point is excluded; until the CSH pore structure energy calculated by the remaining points within the calculation range is valid, the combination of these points is the valid CSH pore structure energy calculation range.

[0074] During the energy calculation process, the corresponding adsorption stress and pore volume can be obtained at each calculation point, such as... Figure 3As shown, Figures (a) and (b) show the curves of pore volume and adsorption stress as a function of position parameters when the shape parameter is fixed; Figure (c) shows the relationship between pore volume and adsorption stress when the shape parameter is fixed; Figures (d) and (e) show the curves of pore volume and adsorption stress as a function of shape parameters when the position parameter is fixed; and Figure (f) shows the relationship between pore volume and adsorption stress when the position parameter is fixed. In summary, when the position parameter is fixed, the relationship between adsorption stress and pore volume does not satisfy the general stress-strain relationship within a certain range. This range with an abnormal stress-strain relationship should be excluded and can be considered an invalid calculation range. Combining the constraints under different position parameter conditions, an invalid calculation region within the actual calculation range can be obtained, such as... Figure 4 As shown.

[0075] Step S8, based on the principle of minimum energy, determines the structural information and structural parameters corresponding to a stable CSH pore structure model. Specifically, based on the principle that the smaller the energy of the CSH pore structure under given conditions, the more stable the structure, the point where the shape parameter φ and position parameter δ are at minimum energy of the CSH pore structure is found within the effective calculation range. Thus, the structural information and structural parameters corresponding to a stable CSH pore structure model are determined. The structural information includes the pore distribution, pore volume, and porosity of the CSH pore structure, and the structural parameters include the position and shape parameters of the pore distribution.

[0076] After considering the invalid computation region, based on the principle of minimum energy, the actual deformation process of the CSH structure is roughly as follows: First, according to the direction of energy reduction, the CSH pore structure can deform along the direction of decreasing φ, decreasing δ, or simultaneously decreasing φ and δ. When the CSH pore structure deforms to the boundary of the invalid computation region, it can no longer deform along the direction of decreasing φ. However, if the structure's energy can continue to decrease along the direction of shape parameter change, then the CSH pore structure will continue to deform along the corresponding direction of shape parameter change. Subsequently, the CSH structure continues to deform along the direction of energy reduction. Finally, the CSH pore structure reaches its minimum energy value at a certain point on the boundary of the invalid computation region; this location also corresponds to the parameters of the CSH structure that is finally stable under this humidity condition. The parameters of the CSH pore structure that is finally stable under 80% RH humidity and the corresponding pore structure information are shown in Table 2, and the corresponding pore volume distribution curves are shown in... Figure 5 As shown.

[0077] Table 2 shows the parameters and corresponding pore structure information of the CSH pore structure that finally stabilizes at 80% RH humidity.

[0078]

[0079] Example 2 illustrates the energy calculation of the CSH pore structure and the determination of the final stable CSH structure under 60% RH conditions.

[0080] Steps S1-S5 are the same as in Example 1. Step S6 is identical to step S6 in Example 1 except that the relative humidity is 60% RH. Under this condition, the energy distribution of the CSH pore structure within the calculation range is as follows: Figure 6 As shown.

[0081] Step S7 is the same as step S7 in Example 1. Under this condition, the invalid calculation region of the CSH pore structure within the calculation range is as follows: Figure 7 As shown.

[0082] Step S8 is the same as step S8 in Example 1. The parameters of the finally stable CSH pore structure under this condition and the corresponding pore structure information are shown in Table 3, and the corresponding pore volume distribution curve is shown in Table 3. Figure 8 As shown.

[0083] Table 3 shows the parameters and corresponding pore structure information of the CSH pore structure that finally stabilizes at 60% RH humidity.

[0084]

Claims

1. A calculation method for determining the pore structure of CSH within the irreversible shrinkage range, characterized in that, Includes the following steps: Step S1: Establish the CSH pore structure model, specifically as follows: The CSH pore structure model consists of CSH basic units and pores, where the pores are cylindrical and follow a single log-normal distribution. for: （1）， In the formula, φ is the position parameter and δ is the shape parameter. The diameter of a single pore; Establish the relationship between the total surface area, total pore volume, and total volume of the CSH basic unit in the CSH pore structure model: （2）， In the formula, S sur V represents the total surface area of ​​the CSH pore structure model. p V is the total pore volume. s The total volume of the CSH basic unit. S represents the density of the basic unit of CSH. m Specific surface area of ​​the basic unit; Step S2: The energy of the CSH pore structure model is described using Helmholtz free energy, specifically as follows: （3）， In the formula, F is the Helmholtz free energy, μ is the chemical potential, N is the number of solid phases, T is the temperature, S is the physical entropy, P is the ambient pressure, and V is the total pore volume. p The total volume V of the CSH basic unit s The sum, where γ is the surface energy and A is the total surface area S of the CSH pore structure model. sur ; Step S3: Replace the physical entropy S in the Helmholtz free energy with information entropy H, and introduce coefficients to establish the relationship between the energy component related to physical entropy and the pore structure. Specifically, introduce coefficients representing the numerical relationship between physical entropy and information entropy into the energy component TS related to physical entropy. , （5）； Step S4: Calculate the adsorption stress based on the thermodynamic model of the mesoporous material, and replace the ambient pressure in the Helmholtz free energy with the adsorption stress to establish the relationship between the energy component related to the total volume and the pore structure. Specifically, establish the energy component related to the total volume of the CSH pore structure. The relationship between the pore structure and the adsorption stress is given by the formula. for: （6）， In the formula, h is the thickness of the adsorption film. For solid-liquid interface energy, V is the ideal gas constant. L Let p be the molar volume of the adsorbed phase, p / p0 be the relative humidity, П(h) be the expression for the dissociation pressure, and d be the molar volume of the adsorbed phase. max To find the maximum aperture, take an infinite value, d min To determine the minimum aperture, take 1 nm, d c This is the critical diameter. Pore ​​distribution, The diameter of a single pore; Step S5: Establish the relationship between the energy component related to surface energy and pore structure, specifically: calculate the relationship between the CSH pore structure model and surface energy. Related energy components : （7）， In the formula, It is the surface energy of the adsorbed phase; Step S6: Determine the calculation parameters and perform energy calculations on the CSH pore structure model within the given calculation range; Step S7: Determine the effective range for calculating CSH pore structure energy; Step S8: Based on the principle that the smaller the energy of the CSH pore structure, the more stable the structure, determine the structural information and structural parameters corresponding to the stable CSH pore structure model. The structural information includes the pore distribution, pore volume and porosity of the CSH pore structure, and the structural parameters include the location parameters and shape parameters of the pore distribution.

2. The calculation method for determining the CSH pore structure within the irreversible shrinkage range according to claim 1, characterized in that, Information entropy is: （4）。 3. A calculation method for determining the CSH pore structure within the irreversible shrinkage range according to any one of claims 1-2, characterized in that, The determination of calculation parameters in step S6, and the energy calculation of the CSH pore structure model within a given calculation range, specifically involves: treating the energy of the CSH pore structure as a functional expression of the position parameter φ and shape parameter δ of the pore distribution, i.e., F(φ,δ), and using a point-by-point calculation method to take values ​​for the position parameter φ and shape parameter δ one by one within the given calculation range to calculate the energy of the CSH pore structure model.

4. The calculation method for determining the CSH pore structure within the irreversible shrinkage range according to claim 1, characterized in that, Step S7, which involves determining the effective range for calculating the energy of the CSH pore structure, specifically involves: for a given position parameter φ and shape parameter δ, calculating the adsorption stress σ and the total pore volume V. p ; If the adsorption stress σ and the total pore volume V are calculated p If the relationship between the given location parameters φ and shape parameters δ does not conform to the principle that the greater the stress, the smaller the pore volume, then the CSH pore structure energy calculated by the given location parameters φ and shape parameters δ is invalid, and the given point is excluded. The effective CSH pore structure energy calculation range is defined as the combination of points where the remaining points within the calculation range are valid.

5. The calculation method for determining the CSH pore structure within the irreversible shrinkage range according to claim 1, characterized in that, Step S8, based on the principle that the smaller the energy of the CSH pore structure, the more stable the structure, determines the structural information and structural parameters corresponding to the stable CSH pore structure model. Specifically, within the effective calculation range, the point where the position parameter φ and shape parameter δ are at their minimum energy of the CSH pore structure is found, thereby determining the structural information and structural parameters corresponding to the stable CSH pore structure model.

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