The surface area of hardened cement paste as measured by various techniques

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1 Concrete Science and Engineering, Vol. 1, March 1999, pp The surface area of hardened cement paste as measured by various techniques Jeffrey J. Thomas 1, Hamlin M. Jennings 1,2 and Andrew J. Allen 3 (1) Departments of Civil Engineering and (2) Materials Science and Engineering, Northwestern University, Evanston, IL, USA (3) Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA REVIEW PAPERS ABSTRACT Hydrated cement paste has a high specific surface area due almost entirely to the calcium-silicate-hydrate reaction product. The surface area of cement paste is closely related to many crucial properties, including strength and permeability, and it is therefore a useful predictive measurement. It is also a useful parameter for studying the nature of the calcium-silicate-hydrate gel itself. Unfortunately, the surface area of cement paste is difficult to measure accurately, and different techniques have given widely varying values. This review discusses these different techniques, summarizes the surface area results given by each, and attempts to rationalize the differences in these results by considering the different physical principles by which each technique generates a surface area value. I. INTRODUCTION The surface area of a porous material, as given by the total internal boundary between the solid phase and the pore system, is one of the most useful microstructural parameters for defining its properties. For example, given a known total porosity, the surface area gives a measure of the fine pores present, and indicates the potential for reactions between solid phases and intruded active species. In the case of disordered porous microstructures such as those that occur in cement paste and concrete, measurement of the total surface area can give an indication not only of the fineness of the microstructure, but also of the tortuosity of the pore phase, and hence of the permeability. Hardened cement paste, which is the ubiquitous product formed upon mixing cement and water, is the main ingredient of concrete the world s most widely-used manufactured material. Cement paste possesses a reactive porous microstructure that is known to contain a high internal surface area, and a reliable measure of the surface area, as a function of the hydration time and conditions, should provide important diagnostic information on the evolution of the properties as hydration proceeds. However, the microstructure of cement paste is quite complex, containing several reaction products as well as unreacted clinker grains and porosity, and measuring a definitive value of surface area for cement paste is beset with several difficulties. One major challenge to the measurement of surface area in hydrating cement paste arises from the heterogeneous microstructure involved, and the very wide lengthscale range applicable (from a few nanometers to tens of micrometers). Mindess and Young [1] have classified cement paste pores by size, and Table 1 lists the different size ranges and the properties influenced by each. It should be emphasized that there is considerable overlap in both the size range and role of the different pore types [2]. While this pore scheme has proved useful in cement paste and concrete microstructure characterization, much recent evidence suggests that the fine pore space in and around the C-S-H gel should not be considered simply as inert voids (of various shapes) within a monolithic solid phase. The interaction of the pore water with the C-S-H gel means that the nature of the pore water and the structure of the Table 1 Classification of the pores in cement according to size, after Mindess and Young [1] Designation Diameter Description Properties affected Capillary Pores > 50 nm Large capillaries Strength, permeability nm Medium capillaries Strength, permeability, shrinkage (high RH) Gel Pores nm Small (gel) Shrinkage capillaries (to 50% RH) nm Micropores Shrinkage, creep < 0.5 nm Interlayers Shrinkage, creep ISSN En cours/99 RILEM Publications S.A.R.L. 45

2 Concrete Science and Engineering, Vol. 1, March 1999 fine pore space (not just interlayer space) are intimately related to the structure and properties of the solid C-S-H. In this connection, several authors have pointed out the approximately fractal, or scale-invariant, nature of the microstructure of hydrated cement paste, both in the solid/pore mass distribution [3] and in the roughness of the surface at the pore/solid interface [4]. The measured surface area can be greatly influenced by the detectable roughness as well as by the pore sizes accessed. While fine features inevitably dominate the total surface area value, the amount and distribution of larger features is also of interest. For example, the strength and toughness of a set cement is determined primarily by the amount of coarse (capillary) porosity [1]. Therefore, methods such as mercury intrusion porosimetry, which do not measure surface in the finest pores, remain useful in engineering research. In any case, for a given technique it is important to consider which part of the microstructure is being assessed, and how this relates to the properties of interest. Another difficulty associated with determining the surface area of cement paste is the problem of defining the internal boundary between the solid phase and the pore system. The primary reaction product in cement paste is the C-S-H* gel, which is a mostly-amorphous calcium silicate hydrate phase, of variable composition, which forms from the hydration of alite (impure C 3 S) and belite (impure C 2 S), the two main constituents of unhydrated cement. The C-S-H gel contains a network of very fine pores called gel pores (see Table 1), giving it an extremely high specific surface area, and making the total surface area of a given cement paste essentially determined by its C-S-H gel content. The surface area of the C-S-H gel is quite variable, with a conservative value being 200 m 2 /g. To put this in perspective, the specific surface area of (unhydrated) portland cement powder is less than 1 m 2 /g, while the surface area of a fine silica fume with an average particle size of 100 nm has a surface area of around 20 m 2 /g [5]. In addition to the water in the gel pores, the solid C-S-H phase also contains chemically bound water as part of its internal structure. This creates a basic uncertainty in defining the boundary between solid and pores from which a surface area value should be derived, and it is important to differentiate between gel pores, which contribute to the true surface area, and features within the internal structure of the solid C-S-H, which do not. Thus, some experimental methods may miss some of the true surface area, while * Cement chemistry notation: C = CaO, S = SiO 2, H = H 2 0. other methods may measure what is effectively too much surface area. The nature of the C-S-H gel affects surface area measurements in other ways. The surface area of cement paste increases with hydration time, as more of the C 3 S and C 2 S react to form C-S-H gel. However, the surface area of a given cement paste is not necessarily proportional to the amount of C-S-H gel it contains. The surface area per gram of C-S-H in a cement paste can vary widely depending on many processing variables, including the cement composition, the reaction temperature, and the water-to-cement ratio (w/c). For example, the surface area of the C-S-H gel tends to be higher when the w/c is higher (although water sorption surface measurements are an exception, as discussed later). Such an increase strongly indicates that the C-S-H gel does not form with a fixed microstructure, but it adapts its morphology to the physical surroundings. Microscopists have long observed what appear to be two different types of C-S-H gel in cement paste, a dense form which forms near the clinker grains and a less-dense form which grows outward into the pore structure [e.g. 6]. These two morphologies are often called inner product and outer product, or, as has more recently been proposed, phenograins and groundmass [7]. It is tempting to assume that the lessdense form of C-S-H gel contains most or all of the gel pores not associated with the C-S-H internal structure, and that this phase is the primary contributor to the total surface area [8], although as of yet there is no direct evidence of this. Another important consideration for interpreting surface area is the condition of the sample during the measurement. Some techniques, notably gas sorption, require drying of the specimen prior to surface area measurement. Removal of the water from the microstructure is likely to cause significant structural changes, such as shrinkage or collapse of the gel pores, and it is of major concern to consider how a surface area determined using a method that requires a drying pre-treatment relates to the equivalent surface area for the undisturbed (saturated) microstructure. For values of surface area obtained from different techniques to have any comparative significance, details of the sample preparation must be carefully monitored and controlled, and the surface area values must be normalized to the same units. For comparison purposes and in common with general practice in cement research, we have normalized surface values in this paper to the surface area per unit mass of D-dried paste (ground paste equilibrated to a water vapor pressure of 0.5 µm of Hg). However, it may be that surface area values would make 46

3 Thomas, Jennings, Allen more physical sense if normalized to unit mass or volume of saturated cement paste. Despite the difficulties associated with measuring and interpreting the surface area of cement paste, it is clear that this material parameter provides a particularly valuable way of characterizing the C-S-H gel. Several different techniques have been used to measure the surface area of cement paste, including gas sorption typically with either water or nitrogen, mercury intrusion porosimetry (MIP), small-angle scattering using both x- rays (SAXS) and neutrons (SANS), and nuclear magnetic resonance (NMR). Each of these techniques measures the surface area of the C-S-H gel pores using different physical principles. Unfortunately, each technique also gives different surface area values, although the ranges of values for some techniques overlap. It should be mentioned that some of these methods have been used to evaluate the microstructure of cement paste for some time, but they have only recently been focused specifically on surface area measurement. In this paper, all of the above-mentioned techniques will be discussed in some detail with the exception of MIP, which is not sensitive to the smallest pores and therefore measures a much lower surface area than other techniques. For each technique, the physical principles used to measure surface area are explained, and the methods and assumptions used to obtain a surface area value from the raw experimental data are outlined, together with the uncertainties involved. The surface area results reported in the literature for the technique are summarized, including the overall range of values and the effects of parameters such as w/c and age, if known. The various techniques and results are discussed in relation to the issues addressed above, and some explanations are offered for the different surface area values obtained. By combining surface area measurement with other more comprehensive microstructural characterization, and with thermodynamic models for cement hydration, we illustrate how the different surface area methods might be used together to develop new insights into microstructural development during cement hydration. 2. SPECIFIC SURFACE AREA NORMALIZATION Each surface area technique normalizes the specific surface area differently. Gas sorption measures surface area per mass of dried paste, small-angle scattering results are per unit sample volume, and NMR results are generally reported per mass of starting cement powder. Occasionally results are reported per mass of ignited paste in order to normalize the values obtained after different drying methods; this is similar to the mass of starting cement powder. More recently, some surface area results have been reported per mass of dried C-S-H. Table 2 illustrates the effect of the normalization on the numerical value of the surface area by showing the change in the magnitude of a surface area value as it is converted into different units. Clearly, it is difficult to compare the results from different techniques unless the values are first converted to the same normalization. However, this is often not as simple as multiplying by a constant factor. For example, as a paste hydrates, the mass of original cement powder, the total volume, and the mass of ignited paste all remain relatively constant, but the mass of dried paste increases as more non-evaporable water is bound into the structure. Similarly, as the w/c increases, the specimen volume associated with a given mass of dried paste or starting cement powder increases. It has been suggested [9] that surface area results should be reported per mass of C-S-H, since this is the phase which contributes to the high surface area. This makes good physical sense, but it presents some additional problems. The mass of the C-S-H in a paste depends on the drying condition, so this would have to be standardized. A more serious problem is in accurately determining the amount of C-S-H in a cement paste. This is notoriously difficult because of the amorphous structure and lack of constant composition, as has been discussed by Taylor [10]. For the purposes of comparison, hydration models can be used to estimate the amount of C-S-H in a paste with reasonable accuracy. As was originally shown by Powers [11], it is possible to predict the volumes of different phases in a cement paste based on the cement composition, degree of hydration and w/c. Combining this model with the Avrami-type Table 2 Specific surface area of a 0.4 w/c Type I OPC paste in various units, normalized to the value for m 2 /g of dry paste Units Surface area relative to m 2 /g of dry paste Young paste (1) Mature paste (2) m 2 /g of D-dried paste m 2 /g of starting cement powder m 2 /g of ignited paste m 2 /cm 3 of paste m 2 /g of D-dried C-S-H (1) 35% Hydrated (approximately 1 day old) (2) 90% hydrated (approximately 1 year old). 47

4 Concrete Science and Engineering, Vol. 1, March 1999 Fig. 1 The predicted density of a typical OPC paste after D-drying as a function of age, for different w/c. Fig. 3 Percent weight loss on ignition of dry cement paste as a function of age. The w/c of the paste did not significantly affect the results. Each point is an average value from specimens with w/c ranging from 0.3 to 0.6. Data from [13] and [14]. Fig. 2 The predicted mass of D-dried C-S-H in a unit volume of typical OPC paste, as a function of age, for different w/c. model for the hydration kinetics developed by Taylor [12], it is possible to predict the amounts of the major phases in cement paste as a function of the starting composition of the cement, the w/c, and the age [9]. This approach can be used to estimate such parameters as the amount of C-S-H in a paste and the density of a paste after D-drying (see Figs. 1 and 2), allowing one type of specific surface area units to be converted to another. One obvious difficulty with this approach is that results reported in the literature often do not include the composition of the OPC or even the exact age of the specimens. However, using the models mentioned above, it is usually possible to make a first approximation conversion from one type of unit to another for the purposes of comparing the results of different techniques. In this paper, wherever needed, surface area results are converted to a basis of grams of D-dried paste using this approach. These units were chosen because they are the most familiar cement paste surface area units, not because they are the most physically useful or the easiest to use. In fact, the properties of a cement paste are probably controlled more by the surface area per mass or volume of saturated paste. While some gas sorption results are reported per gram of ignited paste, in many cases, the weight loss on ignition is also given, allowing the results to be converted to grams of dry paste. If not, the conversion can be estimated using reported weight loss on ignition found by other researchers. Reported results for percent weight loss on ignition as a function of age are shown in Fig. 3; the loss on ignition was not found to vary with w/c [13, 14]. 3. GAS SORPTION Gas sorption is the oldest and most widely-used technique for measuring the surface area of cement paste, and it is also by far the technique with the most published results. The physics of gas sorption and its application to surface area measurement are covered in books [15, 16], and a comprehensive review of the application of the gas sorption method to cement paste has been written by Rarick et al. [17]. 48

5 Thomas, Jennings, Allen The basic concept behind the gas sorption technique is to adsorb a monolayer of gas molecules onto the internal surface of a material. The surface area is then given by S N mσ = m (1) where S is the specific surface area, N m is the number of gas molecules in one monolayer, σ is the cross-sectional area of a gas molecule, and m is the mass of the specimen. An important characteristic of this technique is that the specimen must be pretreated to remove all adsorbed gas molecules and the subsequent measurement must be performed starting in a vacuum. For cement paste, this requires removing the water from the C-S-H gel pores a major disadvantage because of the resulting changes to the C-S-H gel structure. A gas sorption measurement is conducted by slowly introducing the sorptive gas into a chamber containing the specimen and measuring the change in either the pressure or the sample weight. From these data, a plot of gas adsorbed versus pressure, or sorption isotherm, is obtained. In some cases the corresponding desorption isotherm is also measured to look for possible hysteresis effects. There are two general methods of obtaining an isotherm. In both cases, the specimen is first treated to remove adsorbed gas molecules and then placed into an evacuated specimen chamber. The gravimetric method involves measuring the weight increase of the specimen with a microbalance as the pressure of the sorptive gas is incrementally increased, to determine how much gas is adsorbed. A more complex and powerful method is the volumetric method. With this method, the sorptive gas is introduced into a manifold of known volume. The manifold is then exposed to the specimen chamber and allowed to equilibrate, and then it is isolated and the amount of gas adsorbed by the specimen is calculated from the ideal gas law. This process is repeated many times to obtain the isotherm. The volumetric method is normally performed by automated instruments which can determine sorption and desorption isotherms with excellent resolution. Once the experimental isotherm is obtained, further analysis is needed to determine the amount of gas required to form one monolayer of adsorption, and thus the surface area. The shape of the isotherm depends on the nature of the sorptive gas and on the type of material being measured. The heat of adsorption of the sorptive gas determines the type of adsorption that occurs. If the heat of adsorption is high, the molecules will adsorb nearly a complete monolayer before starting the next layer, while if the heat of adsorption is low there will be a piling effect as some of the molecules are adsorbed on top of partially formed layers. Pores which have entrances that are smaller than the pore diameter (so-called ink bottle pores), have a tendency to fill completely because of the concave shape of the adsorbed gas layer. This phenomenon, known as capillary condensation, creates a hysteresis in the adsorption/desorption cycle because a pore which has been completely filled by capillary condensation is more difficult to empty on desorption. Analyzing the sorption isotherm to determine the surface area requires making some assumptions about the system. By far the most common method was derived by Brunauer, Emmet, and Teller [18] and is called the BET method. In fact, a surface area measurement performed by gas sorption is commonly called a BET measurement. By assuming that the heat of adsorption is constant throughout the formation of the first monolayer and that the heat of adsorption for subsequent monolayers is equal to the heat of condensation of the bulk liquid, they were able to derive a relationship between the relative pressure of the gas and the volume adsorbed per unit specimen mass which allows the surface area to be calculated from the multilayer adsorption region of the isotherm. The standard BET equation can be written as ( ) P 1 P C 1 rel rel BET (2) V( 1 Prel) = V C + m BET VmC BET where P rel (= P/P 0 ) is the pressure of the gas in equilibrium with the specimen, P, relative to the saturation vapor pressure, P 0, V is the amount of gas adsorbed at pressure P, C BET is a constant, and V m is the amount of gas required for a monolayer of coverage. The surface area, S, of the specimen can then be calculated from V m by substituting N m = V m /v in equation (1), where v is one molecular volume. An important aspect of gas sorption measurements is selection of the sorptive gas. In addition to the heat of adsorption mentioned above, important factors to consider are the size of the gas molecule, the polarity of the gas molecule, and the chemical reactivity between the sample and the gas. In general, the smaller the gas molecule the higher the surface area measured, because smaller molecules are better able to align themselves to cover a rough surface. In addition, if there are pores which have openings in the size range of the gas molecules, then smaller molecules can measure a considerably higher surface area. Polar molecules can cause difficulties in measuring surface area because they can align themselves in more than one way on a surface, making the effective cross-sectional area difficult to deter- 49

6 Concrete Science and Engineering, Vol. 1, March 1999 mine. Finally, if the molecule reacts with the specimen, or is absorbed by the specimen, the validity of the measurement will be compromised. 3.1 Application of gas sorption to cement paste As mentioned in the above section, one of the drawbacks of the gas sorption technique for measuring the surface area of cement paste is the requirement that the specimen be dried. There are two general problems associated with the drying pretreatment. First, any gel pores which remain filled with water will not be accessed by the adsorbate molecules and will not be included in the surface area measurement. The smallest pores are the most difficult to empty of water, but they also have the highest relative surface area. In addition, it has often been suggested that the drying process destroys or alters the C-S- H gel structure, causing gas sorption measurements to measure too low of a surface area even after adequate drying. In general, colloidal materials collapse and are damaged on drying, and various techniques have been developed to preserve their structure. For cement paste, the simplest techniques for removing the water in preparation for a gas sorption measurement are oven drying at 105 C or vacuum drying using a rotary pump. Although this technique effectively removes all of the pore water, it is often felt to be too damaging to the specimen, and gentler drying techniques have been developed. The most common drying method, D-drying [19], involves equilibrating the specimen to the pressure of water vapor at the temperature of dry ice (-78 C), which is close to 0.5 µm of Hg. A similar technique, called P-drying [20], involves equilibrating to the water vapor pressure of a mixture of the hydrates of Mg(ClO 4 ) 2, which is 8 µm of Hg. In both cases the drying is done using a rotary pump. Another technique used to prepare cement paste specimens for gas sorption is solvent exchange. Before drying, the specimen is placed into a bath of high-vapor-pressure solvent such as methane or pentane, thus allowing the pore water to exchange with the solvent. The solvent is then removed using a standard method such as D-drying or by simply outgassing the specimen in the instrument before the measurement. Solvent exchange results in significantly higher gas sorption surface area values. Gas sorption surface area measurements of cement paste are normally conducted using either water vapor or nitrogen as the sorptive gas. Because equilibrium is approached very slowly, measurements of cement paste surface area using water vapor are conducted using a variation of the gravimetric method. This involves exposing the specimen to a series of desiccators containing salt solutions with different water vapor pressures. Table 3 Effect of w/c on the nitrogen and water BET surface areas of mature OPC paste, after Mikhail and Selim [24] Surface Area (m 2 /g of dry paste) w/c H 2 O N Table 4 Effect of the molecular size of the sorptive gas on the BET surface area of a mature OPC paste with w/c = 0.4, after Mikhail and Selim [24] Sorptive Gas Cross-sectional area Surface area (nm 2 ) (m 2 /g of dry paste) H 2 O N CH 3 OH C 3 H 7 OH C 6 H Nitrogen surface area results are obtained using the volumetric method described in the previous section. Unfortunately, the surface area values of cement paste measured by nitrogen and water vapor sorption are usually quite different. This is discussed further below. 3.2 Surface area results from gas sorption The surface area of well-hydrated cement paste as measured using water vapor, denoted as S H2O, is remarkably consistent at about 200 m 2 /g of dry paste [21-23]. The surface area obtained using nitrogen, S N2, is normally much lower and is much more variable [17]. More results have been reported from nitrogen BET than any other technique, and the range in values for S N2 is disturbingly large. In the book by Taylor [10], the typical range of S N2 for mature OPC paste is given as m 2 /g of dry paste, but even higher results have been obtained after solvent exchange. As shown in Table 3, when S H2O and S N2 are measured for mature, D-dried pastes of different w/c, the results are quite contradictory [24]. While S H2O is nearly constant, S N2 increases dramatically with w/c. It should be noted that if these results are converted to a basis of hydrated paste volume, the increase in S N2 with w/c would be less dramatic and S H2O would decrease with increasing w/c. The effect of the specific surface area normalization on how the w/c affects results will be discussed further later. The results shown in Table 3 clearly illustrate both of the 50

7 Thomas, Jennings, Allen major issues associated with the interpretation of gas sorption surface area measurements of cement paste: the higher values were obtained when measuring S H2O and the larger variation was obtained when measuring S N2. After D-drying, gas sorption using water vapor invariably measures a higher surface area than does nitrogen, and the magnitude of the discrepancy between S H2O and S N2 suggests that the difference is due to more than just the modest difference in their molecular sizes. Table 4 shows the effect of sorptive gas size on the measured surface area of the same cement paste [24]. The surface area increases modestly with decreasing cross-sectional area except for the large increase in surface area associated with water. The difference between S H2O and S N2 was the subject of a vigorous debate in the literature in the 1960s and early 1970s, and various conceptual models of the C-S-H gel structure were developed to explain the discrepancy. The Powers-Brunauer model [25, 26] states that C-S-H gel consists of randomly-arranged colloidal particles, each containing a few closely-bonded structural layers. On drying, these layers collapse and do not permit reentry of water. Proponents of this model claim that dried cement paste contains many ink-bottle gel pores which water molecules could enter but that larger nitrogen molecules could not [25, 26], so that water sorption measured the full surface area of cement paste. The Feldman-Sereda model [27] also describes the basic structural unit of C-S-H gel as a layer, but instead of forming particles, the layers are distributed randomly so that occasional interlayer spacings form throughout the C-S-H gel. According to this model, water vapor can move reversibly in and out of these interlayer spacings, which distorts the surface area measurements made with water, and thus it is nitrogen which provides the more accurate measure of surface area. The Munich model [28] is a physical model in which C-S-H gel is made up of discrete particles bonded together by van der Waals forces, with a bonding strength strongly affected by moisture content. As with the Feldman-Sereda model, this model predicts that water vapor interacts with the C-S-H gel structure, making it unsuitable for a surface area measurement. Although the debate over the relative merits of S N2 and S H2O was never conclusively resolved, the weight of the evidence suggested that water vapor interacts with the dried microstructure in a way that invalidates the resulting surface area measurement [29]. Recent evidence also supports this conclusion: small-angle scattering measurements of cement paste using both x-rays [14] and neutrons [30] have shown that the surface area and Table 5 Effect of drying treatment on the nitrogen BET surface area of mature OPC paste, after Litvan [31] Drying Method Surface Area (m 2 /g) P-drying 58 D-drying 88 Oven drying 102 Methanol-pentane exchange / D-drying 208 the C-S-H gel structure are fully recovered upon rewetting a D-dried specimen, indicating that water can indeed reenter the interlayer space. Today, nitrogen BET is the standard measurement technique for measuring the surface area of cement paste, at least in part because of the availability of automated equipment that require tanks of the compressed sorptive gas. Given the large and often unexplained variability in reported values of S N2, it is not surprising that many researchers preferred to deal with the more consistent values obtained from water vapor. Very different values of S N2 were reported in the literature for cement paste specimens hydrated under similar conditions. It quickly became apparent that the largest source of variation in S N2 is the drying technique. Table 5 shows the value of S N2 obtained after various drying treatments; the values have been converted to a basis of D-dried paste [31]. The first three entries in Table 5 illustrate the increase in S N2 as stronger drying treatments remove more water from the paste. The extremely high surface area after solvent exchange suggests a more complex relationship between drying and S N2, however, as discussed below. When specimens are carefully prepared using identical drying procedures, the values obtained from nitrogen BET are generally repeatable, and show consistent and sensible trends. Increasing the w/c of the paste causes an increase in S N2, as discussed above, as does increasing the age of the paste. Figure 4 shows the variation in S N2 with age for cement pastes with w/c = 0.5 and w/c = 0.33 [13]. The lower w/c specimen reaches a maximum and final surface area value by 28 days, while the higher w/c specimen continues to increase in surface area out to 180 days. This behavior has been reported by others [32], and has been interpreted as indicating that once the available space has been filled with product, the surface area has reached its maximum value even though hydration may continue [13, 33]. The development of S H2O with age was explored for C 2 S and C 3 S pastes, and the surface area was found to increase continuously with the degree of hydration [34]. Given the high intrinsic surface area of the C-S-H gel, with its nanometer-sized gel pores, it seems reasonable 51

8 Concrete Science and Engineering, Vol. 1, March 1999 Fig. 4 Nitrogen BET surface area as a function of age, at two different w/c, after Hunt [13]. Estimated uncertainties of plotted values are less than 10%. to state that the S N2 of a mature cement paste with a moderate w/c should not be lower than about 30 m 2 /g. It is now clear that most of the values on the lower end of the S N2 range are probably in error. It was recently observed [35] that relatively minor levels of carbonation of cement paste cause a dramatic decrease in S N2, and that cement paste that is ground and dried in preparation for a BET surface area measurement is susceptible to carbonation over time even if stored in a sealed plastic container [36]. It is therefore quite tempting to ascribe some of the apparently random variation in S N2 to carbonation, particularly the lowest values. The degree to which S H2O is affected by carbonation is not known. Another important variable that was discovered to affect the surface area is the drying rate. Hunt et al. [37] found that S N2 was lower when the paste was dried more slowly. Paste that was crushed before vacuum drying had an S N2 value 30 m 2 /g higher than paste dried in the form of a half-inch diameter cylinder, which dried more slowly due to restriction by the paste itself. For this reason, crushing cement paste before drying has become standard practice for gas sorption. However, crushed cement paste will still exhibit a decreased S N2 if the drying rate is restricted by other means [37]. The highest values of S N2 are obtained after solvent exchange (see Table 5). Litvan [31] measured S N2 after various solvent exchange procedures involving methanol and n-pentane, and obtained values ranging from m 2 /g, as compared to 57 m 2 /g after straight D-drying. The large difference was attributed to the more rapid rate of drying obtained with volatile solvents. Litvan [31] noticed that solvent exchange caused the difference in magnitude between S N2 and S H2O to nearly disappear for his own samples, and he suggested that both measurements were valid. However, as mentioned earlier S N2 varies significantly with w/c while S H2O does not, so the techniques cannot be considered equivalent. The effect of solvent exchange on S N2 was clarified by Parrott et al. [38, 39], who performed a two-step drying procedure on hydrated C 3 S paste: the paste was first dried by equilibrating it to a salt solution of known RH, and then it was subjected to a solvent exchange procedure to remove the rest of the water. When the initial drying step was omitted, the S N2 value was about 160 m 2 /g for 0.6 w/c paste and 100 m 2 /g for 0.4 w/c paste. However, S N2 decreased significantly with decreasing RH of the salt solution, reaching a minimum value of around 30 m 2 /g. Interestingly, the decrease occurred primarily between RH values of 70% and 40%. In this humidity range water is removed from the capillary porosity but not from the smaller gel pores which contribute most to the surface area. After resaturating dried specimens, Parrott et al. [38, 39] found that the surface area loss caused by the initial drying step was reversible, but that the pore structure nonetheless underwent some irreversible changes. They concluded that the effects of solvent exchange and drying rate on S N2 are both related to the presence of capillary tension stresses which develop when water is removed directly from the pore system. These stresses cause a rearrangement of the pore structure that prevents some of the smallest pores from being accessed by the nitrogen. The Jennings-Tennis model [9] was devised as an attempt to reconcile that variation in S N2 which was not associated with the drying technique used (only D-drying was considered). Given the age, w/c, and OPC composition, the model accurately predicted the resulting S N2 after D-drying [9]. The model proposed that the pore space of a given cement paste microstructure can be divided into two regions with fixed volumes, one that nitrogen can penetrate and one that it cannot. The C-S-H gel is modeled as being made up of particles of a fixed size which can exist in either region. As the w/c increases, more of the C-S-H particles are assigned to the nitrogen-accessible box, and S N2 increases. This model, although somewhat unphysical, does explain one surprising trend in the literature which had not been previously discussed: the observation that, after the capillary pore volume is subtracted, the apparent gel pore volume measured by nitrogen decreases as the surface area increases. Whatever the cause or causes of the variation in S N2 with drying technique, interpretation of the results has 52

9 Thomas, Jennings, Allen been made more difficult by the lack of details describing specimen preparation in much of the early literature [17]. Eventually the importance of the specimen preparation method on the S N2 values obtained was recognized, and straight D-drying of coarsely-ground paste has become the standard preparation technique for BET surface area measurements of cement. This is somewhat surprising given that solvent exchange yields much higher values of S N2, and thus presumably allows more of the fine gel structure to be accessed. Solvent exchange is time consuming and increases the complexity of specimen preparation, and it can be argued that the magnitude of the surface area value is unimportant as long as the results from different specimens can be compared directly. On the other hand, solvent exchange reduces potential variation caused by the rate of drying during D-drying. The higher values obtained with solvent exchange are also in better agreement with the values obtained from small angle scattering and NMR. 4. SMALL-ANGLE SCATTERING (SANS AND SAXS) Small-angle scattering is a powerful tool for characterizing complex microstructures. An intense beam of either neutrons (SANS) or x-rays (SAXS) is passed through the specimen, and a small component is scattered out of the incident beam direction by interactions with microstructural features within the bulk of the material. A schematic of a conventional pinhole-geometry SANS experiment is shown in Fig. 5. For cement paste and similar porous materials, the resulting scattering profile, which is the intensity of scattered neutrons or x-rays as a function of the scattering angle, is effectively a form of a Fourier transform of the solid/pore microstructure. It can be used to determine, for example, size distributions and volume fractions of microstructural features, fractal components within the microstructure, and the total surface area. Because SANS and SAXS operate on the same physical principle (diffraction), they are discussed together in this section, but some important differences between the two techniques do exist. Principally, almost all SANS measurements to date have been made using the configuration shown in Fig. 5 with a pinhole geometry, while a large proportion of SAXS studies have been carried out using a slit geometry, in which the scattered intensity is measured as a function of the scattering angle perpendicular to the source slit, and the data are line-smeared over a large angular range parallel to the source slit. Traditionally, the major challenge in applying small-angle Fig. 5 Schematic of a small-angle scattering experiment. scattering methods has been interpreting the scattering data in terms of the sometimes complex underlying microstructures that give rise to it. Until about 15 years ago it was not possible to interpret fully the scattering profiles obtained from complex materials with highly disordered microstructures, such as cement paste. The relatively recent discovery that the microstructure of cement paste contains fractal (scale invariant) properties over large parts of the size range has greatly increased the amount of useful microstructural information obtainable from small-angle scattering. The interpretation of SANS scattering data from highly disordered materials such as cement paste has been reviewed by Allen [40]. In this, and other papers, it was concluded that the primary source of the scattering in cement paste is the C-S-H gel structure. Furthermore, much of the C-S-H gel, for which a high surface area can be measured, is in the form of a disordered fractal structure, of which the open spaces actually comprise the so-called gel porosity and, perhaps, part of the capillary porosity as well. Small-angle scattering is an ideal technique for characterizing cement paste because specimens can be studied in their saturated state, thus avoiding possible problems associated with drying the C-S-H gel (discussed in the previous section). If the neutron flux is sufficiently high, experiments can be repeated continuously on the same specimen as it hydrates; such real time investigations of early cement hydration have provided valuable information about the kinetics and the microstructure development during early hydration [41, 42]. Neutrons are scattered by interactions with atomic nuclei, while x-rays are scattered by interactions with outer shell electrons. However, in both cases the scattering occurs at interfaces between two phases, and the data analysis for the two techniques is similar. In cement paste systems, the scattering of both x-rays and neutrons is dominated by the interface between C-S-H and the pore medium (water or air). Another difference between SANS and SAXS is that the wavelength of the x-rays used is typically up to one 53

10 Concrete Science and Engineering, Vol. 1, March 1999 order of magnitude smaller than neutron wavelengths. SAXS experiments generally use either Cu Kα or Mo radiation (wavelengths nm and nm, respectively), or radiation of a similar wavelength at a synchrotron facility. SANS experiments on cement paste typically use cold neutron wavelengths of nm. In this connection, the shorter the wavelength, the smaller the microstructural features that can cause scattering at a given scattering angle. However, in either SANS or SAXS studies, the effective maximum scattering angles, and associated minimum dimensions studied, are determined by the signal-to-noise ratio as the small-angle scattering signal decays away with increasing scattering angle. Reported SAXS surface areas are significantly higher than SANS surface areas, and it has been suggested that this difference is due to the x-rays seeing more of the fine C-S-H structure. However, before SANS and SAXS results can be compared directly, it is important that the methods of data analysis used to obtain the surface area values be understood. The methods of determining the surface area of a specimen from its small-angle scattering profile are discussed in detail in the next section. 4.1 Determining surface areas by small-angle scattering The raw experimental data from a conventional smallangle scattering experiment consist of the two-dimensional (2-D) scattered intensity distribution of neutrons or x-rays after passing through the specimen, as registered on the instrument s position-sensitive detector (see Fig. 5). For a specimen with no preferred orientations (such as cement paste), the 2-D data can be circularlyaveraged to give the scattered intensity as a function of the scattering angle, Φ. For slit-geometry SAXS experiments, the line-smeared raw data can be desmeared using algorithms that generally assume a microstructure with no preferred orientation. After subtraction of the empty-beam background, the scattering intensity is absolutely-calibrated with respect to a scattering standard sample, or, sometimes, by an absolute geometric calibration with respect to the incident beam. Note, however, that in many SAXS measurements of the surface area of cement paste, the absolute calibration step has been by-passed by using an alternative method to extract the surface area, as is discussed below. Finally, the sample flat-background incoherent scattering can be subtracted out to give the absolute macroscopic differential small-angle scattering cross-section, dσ/dω, versus Q, where Q is the scattering vector given by: Q = 4π ( ) λ sin Φ 2 (3) and λ is the neutron or x-ray wavelength. The macroscopic differential scattering cross-section, dσ/dω, is defined as the probability, per unit time and per unit incident flux (also a rate), that a neutron or x-ray photon will be scattered into a unit solid angle element, dω, by a unit sample volume (Units: m -1 sterad -1 ). Since, for cement systems, dσ/dω depends only on the magnitude of Q, the variation of dσ/dω with Q contains all the obtainable information on the microstructure associated with the scattering, provided certain conditions are met. The Q range and Q resolution must be large enough and good enough for the microstructural scale of interest, and the sample must be thick enough to provide a sufficient small-angle scattering signal without being so thick that significant multiple scattering occurs. Depending on the Q-range being considered, the relationship between dσ/dω and Q takes different forms. The range we are concerned with primarily is the so-called Porod regime, where the small-angle scattered component follows a Q -4 power law whose intensity is proportional to the surface area of the interface between the scattering microstructural phases of interest. In the Porod regime, scattering from the porous material follows the Porod equation [43]: dσ Sv = 2 2 π ρ (4) dω 4 Q where S v is the surface area per unit sample volume and ρ is the difference in the scattering length density of the two materials forming the interface associated with the scattering. The term ρ 2 is called the scattering contrast. For cement paste, the contrast is between C-S-H and H 2 O, or between C-S-H and air. In practice, the sample flat-background parasitic scattering cannot be ignored when compared with the Porod scattering. For SANS this is because of a significant incoherent inelastic scattering contribution from water in the sample. For SAXS, other parasitic scattering contributions can occur, such as those that arise from fluorescence of some of the atomic species present, particularly when higher x-ray energies (i.e., lower wavelengths) are used. It is usually best to consider the actual data in the Porod regime to have the form: 2 2π ρ Sv I = + C (5) 4 Q where I is the experimentally determined absolute-calibrated scattering intensity and C is the flat background intensity. From equation (5) it can be seen that a plot of 54

11 Thomas, Jennings, Allen IQ 4 vs. Q 4 will be linear for Q values in the Porod regime, with a slope of C and an intercept, the Porod constant, given by 2π ρ 2 S v. Thus, if the data are absolutely-calibrated and the scattering contrast is known, S v is obtained from equation (5) as: S v CP = 2 2 π ρ (6) where the experimental Porod constant, C P, is the intercept of a straight-line fit to the data in the Porod regime. For uncalibrated data, or when the scattering contrast is unknown, it is also possible to calculate the surface area by utilizing the scattering invariant, I inv : 2 I Q d inv = Σ d dq 2 2 = 2π ρ φ Ω 0 (7) where φ v is the volume fraction of the scattering phase, and the flat background has been accurately subtracted out (note the π 2 factor compared to π in the earlier equations). By using equations (4) and (7) together, the ratio, S v /φ v, the surface per unit volume of scattering phase, can be calculated without using the contrast, hence giving S v if the value of φ v is known. The integral in equation (7) must be taken over the entire Q-range, and any uncertainties in the small-angle scattering profile or in the background subtraction are amplified by the Q 2 factor at high Q. Provided that the scattering contrast is known with a reasonable degree of accuracy, and the data can be absolutely calibrated, the contrast method (equation (6)) for calculating the surface area is preferable. Unfortunately, calculation of the scattering contrast for cement paste has proved to be difficult because of uncertainties about the density and composition of the C-S-H gel. In the case of SANS, the contrast can be calculated experimentally by taking advantage of the difference in contrast when specimens are exchanged with D 2 O (heavy water). For this reason most reported SANS surface area values have been calculated using the contrast method, while many SAXS studies have used the scattering invariant method. This difference in analysis procedure may be an important factor to consider when comparing the surface area values of cement paste obtained from the two techniques. Another challenge associated with calculating surface areas using scattering is determining the appropriate Q- range to use as the Porod region. Because the scattering features within the C-S-H gel are very small (on the order of 5 nm across), the minimum Q-value for the Porod range is quite high. In order to get an accurate straightline fit to the data, it is desirable to use as wide a Q-range as possible. In some early SANS experiments on cement v paste (not primarily focused on surface area measurement), this led to the use of a lower limit for the assumed Porod Q-range which was later shown to be not truly in the Porod region, resulting in an undercalculation of the Porod constant. A recent SANS study on 28 day old cement paste determined a Q-value of 1.4 nm -1 for the lower limit of the Porod regime [33] and this has been used in later studies. 4.2 Determination of the neutron scattering contrast of cement paste Determination of the correct scattering contrast is an important issue for calculations of cement paste surface area from small-angle scattering. For saturated cement paste, almost all of the surface area is in the interface between C-S-H and water, and the contrast can be written as: ( ) 2 ρ 2 = ρcsh ρh O (8) where ρ CSH and ρ H2O are the neutron (x-ray) scattering length (form-factor) densities in the solid C-S-H and pore water. When the average composition and density of a phase are known, as with H 2 O, ρ H2O can be calculated directly with the help of international tables of atomic neutron-scattering-lengths [44], or x-ray form-factors. The situation is more difficult for C-S-H, because the exact formula and density value which should be used in the calculations to determine ρ CSH is not clear. Because the C-S-H gel is an amorphous phase with a variable composition, some of the water in C-S-H is chemically bound into the structure, while there is additional water which is loosely bound in the interlayer spaces. The amount of water which should be associated with C-S-H for the purposes of calculating ρ CSH depends on how much of this water interacts with the neutrons as if it is part of the solid C-S-H phase, and this is not known a priori. In principle, the neutron scattering contrast of saturated cement paste can be determined experimentally by using H 2 O/D 2 O exchange. When a specimen is placed into D 2 O, the D 2 O exchanges fully with both the pore water and the water in the C-S-H gel [45], and this greatly alters the scattering contrast. By measuring the apparent surface area of a specimen as the amount of D 2 O is increased, a plot of the relative contrast versus D 2 O content is obtained, and this experimental plot can be compared to predicted curves based on various assumed values for the composition and density of the C-S-H gel. Earlier studies [41, 45] used a C-S-H formula of C 3 S 2 H 2.5 and a density of 2.15 g/cm 3, which were average values taken from the literature, and found acceptable agreement between the experimental contrast data and 55