Basic properties of pore structures

Pore size distribution of the polymer-cement composite joint sealants is closely associated with their macro-mechanical properties²¹, and with such durability indicators as anti-permeability and corrosion resistance. Based on the MIP results, this section analyzes the basic pore structure properties of the joint sealants by using the differential curves for pore size distribution, as well as the pore structure parameters. These parameters include the mean pore size (the ratio of total pore volume to the mean pore surface area), the most probable pore size (the pore size corresponding to the peak on the differential curve for pore size distribution), the median pore size (the pore size corresponding to a cumulative mercury intrusion volume of 50%), and the total pore volume.All the pore sizes mentioned in this section refer to the pore diameters.

In Table 3, the pore structure parameters of tested specimens in various groups are listed. Depending on the pore size, the pore structures measured by MIP in reference²² are classified into four types: Macropores (greater than 1000 nm), capillary pores (100–1000 nm), transition pores (10–100 nm), and gel pores (less than 10 nm). In accordance with such classification method, the respective pore volumes of aforementioned four pore types in the present specimens are depicted as shown in Fig. 11, and their percentages in total pore volumes are illustrated in Fig. 12.

Regarding the effects of powder-liquid ratio and cement ratio, the total pore volume and various characteristic pore sizes of the joint sealants decrease continuously with the increase in powder-liquid ratio (Y1 → DZ → Y2). In particular, the pore size area inhabiting the most probable pore size of specimens in group Y2 shrinks from the macropore area to the gel pore area. Besides, the percentage of macropores decreases, the proportion of pores with diameters below 1000 nm increases, and the pore structure is refined overall. The main reasons are that at high powder-liquid ratios, the solid content volume inside the joint sealants is relatively large, and the materials have high density and strong resistance to dry shrinkage deformation. As a result, the pores formed after water evaporation are small in terms of their number and size, and the originally closed small pores are not easily inter-connected. The effects of cement ratio on the pore structure of joint sealants basically exhibit identical trends. With increase in cement ratio (CR1 → DZ → CR2), the total pore volume of joint sealants and various characteristic pore sizes decrease continuously, and the gel and transition pores show marked increases in quantity, whose pore size distribution moves gradually towards the micropore end. This suggests that increasing the cement ratio leads to decrease of pore volume, diminishing of pore size and enhancement of density inside the joint sealants. This phenomenon is primarily attributable to the increasingly pronounced water absorption and hydration effects of cement with its increasing dosage. On the one hand, this reduces the evaporation of water and the number of dry shrinkage pores resulting thereby. On the other hand, this leads to a continuous increase in cement hydrates. Owing to the filling and blocking effects of these hydrates, the pores inside the joint sealants can be reduced and refined accordingly.

Regarding the effects of cement type and filler blending, the hydration effect becomes weaker after changing to the low-grade white cement (DZ → CT1) because of the lower cement grade, so that less hydrates are produced and more amount of water is evaporated. Consequently, the total pore volume of joint sealants and various characteristic pore sizes all increase, and the pore structure is coarsened overall. After blending with sulphoaluminate cement (DZ → CT2), the joint sealants exhibit drastically decreased total pore volume and characteristic pore sizes, with the percentage of macropores being only 51.59%. This suggests remarkable refinement in the pore structure of joint sealants. The main reason is that the sulphoaluminate cement sets and hardens quickly upon encounter of water to generate substantial hydrates, which greatly reduces the evaporation of water and hinders the formation, communication and expansion of internal pores. After blending with talc powder (DZ → T1) or mica powder (DZ → T2), the total pore volume is reduced and the density is improved for the joint sealants. This is primarily owing to the accumulating and filling actions of the two fillers. Nevertheless, the sizes of various characteristic pores decrease after blending with mica powder, while showing slight increases after blending with talc powder. This is attributed to differences in the fineness and crystal morphology between the two fillers, which thus produce varying effects on the pore size distribution of the sealants. For instance, after blending with mica powder, the percentage of macropores in the joint sealants decreases, whereas the percentages of capillary, transition and gel pores increase. Contrastively, after blending with talc powder, the percentages of gel and transition pores decrease, whereas the percentages of macropores and capillary pores increase.

Regarding the effects of emulsion blending and latex powder addition, the total pore volume, various characteristic pore sizes and macropore percentage all increase significantly for the joint sealants after blending with styrene-acrylic emulsion (DZ → H). The total pore volume and most probable pore size, in particular, increase by 45.4% and 41.8%, respectively. This is primarily attributed to the relatively thin styrene-acrylic emulsion, which results in a small solid content volume, as well as substantial water evaporation. After adding latex powder (DZ → J), the content of polymer fraction in the joint sealants increases, and the total pore volume and various characteristic pore sizes somewhat decrease by the dispersive, film forming and filling actions of the latex powder.

With respect to the effects of additive and fiber addition, the total pore volume and various characteristic pore sizes all increase markedly after incorporating plasticizer (DZ → Z). The heightened percentage of macropores to 77.72% and the mere10.50% occupation of gel and transition pores suggest that the density of joint sealants is reduced, and the pore size distribution moves towards the macropore end. According to preliminary analysis, the probable reason is the thickening of newly mixed joint sealants by the swelling effect of plasticizer on emulsion particles, which makes the air bubbles not easily escapable and breakable. Meanwhile, with the absorption and evaporation of the plasticizer, the intermolecular force between some polymer molecules increases again. The process in which this internal stress tends to an equilibrium state again (similar to drying shrinkage) may also trigger production of certain amounts of pores. Further research is needed to clarify the specific cause of such phenomenon. Despite an increase in the most probable pore size after incorporating coupling agent (DZ → L), the total pore volume, mean pore size and median pore size of the joint sealants are all somewhat reduced. The change in pore size distribution is manifested by the decreased volume and percentage of macropores, as well as the increased volume and percentage of capillary pores. The reason is that the coupling agent enhances the interaction between inorganic and organic fractions in the joint sealants, thereby improving the material density. Meanwhile, the dispersion uniformity of inorganic powder is improved after surface modification with the coupling agent,which also lowers the probability of pore formation to a certain extent. After incorporating carbon fiber (DZ → X), the total pore volume of joint sealants remains fundamentally unchanged, while the sizes of various characteristic pores all increase to some extents, suggesting coarsening of the pore structure. The main reason is that the distribution density of the fibers inside joint sealants is not entirely uniform after carbon fiber blending. Thus, at sites with dense fiber distribution, the material cohesion and density are improved by the bridging and anti-cracking functions of the fibers, and the number of pores exhibits an overall decline. Contrastively, at sites with thinner fiber distribution, the material cohesion is relatively small, thereby resulting in a greater shrinkage deformation following film formation and hardening, as well as an increased volume of macropores.

As for the effects of various processing conditions, the polymer fraction in the joint sealants undergoes certain cross-linking under temperature aging after cold drawing and hot pressing. Besides, the hot pressing process leads to closing of partial pores inside the materials. Thus, despite less change in the median pore size of joint sealants than without treatment at this time, the total pore volume and mean pore size decrease markedly, especially the most probable pore size. Besides, the gel and transition pores increase slightly in terms of percentage, and their structures undergo certain degrees of refinement. After wet–dry cycling, part of the cement hydrates and inorganic components of the sealants are lost by the hydrolytic actions to form pores, thereby resulting in increased total pore volume and most probable pore size. Nevertheless, the median and mean pore sizes change little as compared to without treatment, and the percentages of various pore types remain fundamentally unchanged. This suggests that there is no obvious change in the pore size distribution of the sealants following wet–dry cycling. After long-term ultraviolet irradiation, the total pore volume and various characteristic pore sizes all decrease, and more macropores and transition pores are refined separately into capillary and gel pores. The primary reason is cross-linking of partial polymer molecules under ultraviolet irradiation aging, which improves the sealant density.

On the whole, for the polymer-cement composite joint sealants prepared in this paper, the internal pore structure is dominated by macropores with sizes above 1000 nm (almost accounting for over 60% of the total pore volume), while the volume of gel pores sizing below 10 nm is relatively small (accounting for less than 10% of the total pore volume). In addition, the total pore volume of joint sealants reflects the magnitude of internal total pore volume, which characterizes the overall material density. The variation trends of various characteristic pore sizes are overall consistent with the variation trend of total pore volume. This is because the improvement of material density is often accompanied by refinement of pore structure, and vice versa. Nevertheless, given the correlation of the magnitudes of various characteristic pore sizes with the pore size distribution, the pore size distribution changes greatly in some cases or the variation trends of total pore volume and pore size distribution are inconsistent. Hence, there is also a case where the individual characteristic pore size increases, or the overall pore structure is coarsened despite a decrease in total pore volume (e.g. the specimens in groups T1 and L, and those cold-drawn and hot-pressed specimens in group K of this section). Clearly, it is not advisable to infer the pore structure properties of joint sealants by change of a certain index. Instead, they should be determined through a multi-index comprehensive approach based on changes of multiple pore structure parameters^23,24.

Fractal characteristics of pore structure

This section describes the fractal characteristics of pore structure inside the studied joint sealants based on the fractal model of thermodynamic relationship²⁵.With this model, the assumption on pore structure in the process of fractal dimension solving is closer to the actual situation. The essential basis for the model is that the increase in surface energy of mercury liquid during the MIP process is equal to the work done by the external force on the mercury. In other words, the following relationship is established between the pressure on mercury \(p_{{\text{h}}}\) and the mercury intrusion volume V_h^25,26:

where \({{\sigma _{\rm{h}}}}\) denotes the surface tension of mercury, \(\theta\) denotes the contact angle between mercury and specimen, and S denotes the pore surface area of specimen.

Through dimensional analysis and discretization of Eq. (1), the measured pressure and mercury intrusion volume can be correlated with the surface fractal dimension of the material pore structure. Accordingly, the fractal model expression is derived as follows:

where n denotes the number of pressure application intervals during mercury intrusio, \({\bar p_{h,i}}\) and \(\Delta {V_{h,i}}\) represent the mean pressure and intrusion volume during the i-th mercury intrusion, \(C’\) is a constant obtained from fitting, which has no specific physical meaning, \({d_n}\) and \(\Delta {V_{h,n}}\) represent the pore size and cumulative intrusion volume corresponding to the nth mercury intrusion, and \({{D_{\text{p}}}}\) is the fractal dimension of pore surface area that is calculated based on the thermodynamic relationship (hereinafter referred to as the fractal dimension). Let \({W_n} = \sum\limits_{i = 1}^n {{{\bar p}_{h,i}}\Delta {V_{h,i}}}\) and \({Q_n} = V_{{\text{h}},{\text{n}}}^{1/3}/{d_{{\text{h}},{\text{n}}}}\), then the Eq. (2) can be further rewritten as:

According to Eq. (3), \(\ln \left( {{W_n}/d_n^2} \right)\) and \(\ln {Q_n}\) can be directly solved by utilizing the MIP measurement data. The slope of the linearly fit line between the two is denoted by \({{D_{\text{p}}}}\).

In Fig. 13, the \(\ln \left( {{W_n}/d_n^2} \right)-ln {Q_n}\) scatter plots of tested specimens in various groups are presented, as well as their fitted lines. Figure 14 displays the corresponding computational results for fractal dimension. As is clear, the correlation coefficients (R²) of the fitted lines for specimens in various groups are all greater than 0.99, suggesting distinct fractal characteristics of the pore structure for the studied joint sealants. Within the range of raw material ratios involved in this section, the fractal dimension values for the pore surface area of the sealants are between 2.6 and 2.8.

Since the fractal dimension characterizes the overall disorderliness and complexity of sealant pore structure, larger fractal dimension signifies more irregular and more complex pattern of the sealant pore size distribution. With respect to the MIP results, such complexity enhancement is often manifested as the refinement of pore structure. In other words, the percentage of small-sized pores increases, while the percentage of large-sized pores decreases. Conversely, when the pore size distribution of the joint sealants moves towards the macropore end, the fractal dimension value shows a corresponding decrease. For instance, as suggested in the foregoing analysis of basic pore structure parameters, when the powder-liquid ratio of the sealants increases from 0.30 to 0.55 (Y1 → Y2), various pore structure parameters all decrease, the percentage of macropores drops from 71.81 to 61.34%, and the corresponding fractal dimension value increases from 2.7280 to 2.7821. After changing to low-grade white cement (DZ → CT1), or blending with styrene-acrylic emulsion (DZ → H), the pore structure parameters of joint sealants all increase to varying degrees. The percentage of macropores increases by 13.40% and 6.13%, the percentage sums of gel and transition pores decrease by 9.19% and 1.91%, and the corresponding fraction dimension values​are reduced to 2.6352 and 2.7302, respectively. The pore structure inside the joint sealants is refined overall after long-term ultraviolet irradiation treatment,and the fractal dimension value increases from 2.7229 (without treatment) to 2.7369. After the wet–dry cycling treatment, little changes are observed regarding the percentages of pores within various size ranges, despite the increase of total pore volume inside the sealants. This indicates that the pattern of pore size distribution remains basically unchanged, so the corresponding change in fractal dimension value is also small (2.7223).

To further verify the above assumption, Fig. 15 lists the relationships between the pore fractal dimension value of each specimen and the percentage of 0–100 nm pores (namely gel pores and transition pores). Meanwhile, the weighted logarithmic average pore size δ is defined as:

where the subscript grepresents the four types of pore size ranges mentioned above, including macropores, capillary pores, transition pores and gel pores, \(\lambda_{g}\) stands for the percentage of each type of pores in the total pore volume, i.e. weight, \(d_{g}\) is the representative pore size of each type of pores, i.e. the average of upper and lower limits of corresponding pore size ranges.The upper limit of macropores is the maximum pore size measured during the test. Figure 16 presents the correlations of pore fractal dimension value of each specimen with the weighted logarithmic average pore size.

It is clearly observed from Figs. 15 and 16 that, on the whole, the proportion of small-size (0–100 nm) pores in the joint sealants increases with the increasing pore fractal dimension, whereas the weighted logarithmic average pore size decreases in a gradual manner. Besides, a good linearity is observed between the pore fractal dimension of joint sealants and the percentage of 0–100 nm pores. Thus, clearly, the fractal dimension of pore surface area obtained in this study is an ideal characterization of the complex pore structure of polymer-cement composite joint sealants for pavements. In addition, changes in the relative contents of pores with different sizes in the joint sealants may be effectively described by the fractal dimension value.