Influence of organic acid modification on enhancing the grinding efficiency and particle size distribution

Abstract

In this study, the widely used grinding aids (GAs) TIPA, DEIPA, and DEG were chemically modified via esterification with organic acids of varying hydrocarbon chain lengths to improve grinding efficiency and cement performance. A total of 25 Portland cement samples were produced using commercial and modified GAs at 0.05% and 0.1% dosages. The effects of GA modification on adsorption behavior, grinding efficiency, particle size distribution (PSD), zeta potential, and molecular polarization characteristics were systematically investigated. The results demonstrated a clear structure-performance relationship between the molecular structure of modified GAs and their grinding behavior. Hexanoic acid modification of TIPA and DEIPA increased molecular polarizability and adsorption capacity, resulting in a more uniform PSD and up to 7–10% higher grinding efficiency compared to the corresponding commercial GAs. In contrast, DEG modified with propanoic acid exhibited the best overall performance among DEG-based formulations, providing improved particle dispersion and enhanced grinding characteristics. The findings further revealed that the ester/hydroxyl group balance and hydrocarbon chain length strongly influenced molecular dipole moment and polar interactions with cement particles. Overall, the proposed polarization-based mechanism successfully explains the enhanced adsorption, dispersion, and grinding performance of the modified GAs.

Introduction

Approximately 60% of the total energy consumed in cement production is attributed to the clinker grinding stage¹. The high surface energy of fine particles generated during grinding promotes agglomeration, which decreases grinding efficiency and increases energy demand^2,3. One strategy to enhance energy efficiency and reduce carbon emissions is the incorporation of alternative materials and mineral additives^4–6. However, high replacement levels of these materials may result in reductions in early-age strength^7,8. Another approach involves improving the sustainability of cementitious systems and increasing the allowable mineral additive substitution ratio by using chemical admixtures^9–11. In this context, grinding aids (GAs) represent one of the most effective tools for enhancing energy efficiency and improving cement performance^12,13.

GAs are organic additives typically used at low dosages (0.01–0.1%). They reduce the attractive forces between fine particles by neutralizing the surface charges generated during grinding. This reduces agglomeration, promotes particle dispersion, and enables the target fineness to be achieved with lower energy consumption. Furthermore, the adsorption of GA molecules onto particle surfaces forms a lubricating layer that enhances powder fluidity, resulting in improved grinding performance and better transportability and storability^2,14. Among organic admixtures, the most commonly used GAs include amine- and glycol-based compounds such as triethanolamine (TEA), triisopropanolamine (TIPA), diethanolisopropanolamine (DEIPA), and diethylene glycol (DEG)^15,16. Each admixture contains distinct functional groups and interacts differently with cement particles. For instance, TIPA is known to enhance late-age strength by influencing the formation of hydration products, whereas DEIPA improves early strength by accelerating hydration kinetics^17,18. Although DEG provides high grinding efficiency, its standalone use is limited due to inadequate fluidity¹². Similarly, dosage-dependent variations in TEA setting time¹⁹, early strength reductions caused by air entrainment in TIPA²⁰, and rheological limitations associated with amine-based admixtures²¹ have motivated the chemical modification of these additives. Such modifications alter functional groups and enhance adsorption behavior, thereby improving both grinding efficiency and cement performance^1,22. The literature further reports that modified GAs improve particle size distribution and optimize powder flowability, thereby reducing energy consumption and improving product performance^2,14. Collectively, these studies demonstrate that GA modifications not only refine the grinding process but also enhance both the fresh and hardened-state properties of cement^1,18,23,24. In this context, the interactions between various additives and GAs in cement-based systems have been systematically investigated using atomistic modeling^25–28.

In this context, the particle size distribution (PSD) influenced by GA modification emerges as a key factor affecting both the rheological characteristics and hydration kinetics of cementitious systems. For instance, an increased proportion of particles within the 11–32 μm range helps to balance the high-water demand of the 0–10 μm fraction, leading to a more optimal overall distribution. Studies on the rheology of cement-based materials consistently indicate that mixtures enriched in the 10–30 μm particle range exhibit superior flow properties and improved rheological behavior²⁹. Additionally, while the 0–10 μm fraction hydrates rapidly at early ages, the 11–32 μm particles sustain hydration over 1–7 days, forming C-S-H and contributing significantly to early- and mid-age compressive strength³⁰. Neither the aforementioned studies nor the existing literature provides a comprehensive and systematic evaluation of how different chemical modifications of GA types influence grinding efficiency and particle size distribution (PSD). Previous studies have primarily focused either on the performance of conventional GAs or on limited chemical modifications without establishing a direct relationship between molecular structure, polarization characteristics, and grinding behavior. In particular, the effects of esterification-induced changes in functional groups, molecular polarity, and dipole moment on clinker surface interactions and particle dispersion mechanisms remain largely unexplored.

Within the scope of this study, TIPA, DEIPA, and DEG, which are widely used commercial GAs, were chemically modified via esterification using organic acids with three different carbon chain lengths. Unlike previous studies, the proposed approach enabled systematic tuning of ester/hydroxyl group balance and molecular polarizability, thereby allowing direct investigation of the structure–performance relationship governing GA efficiency. This approach enabled controlled alteration of molecular polarity, steric configuration, and functional group distribution, thereby providing a systematic framework for evaluating structure-performance relationships. Both the synthesized GAs and their unmodified commercial counterparts were applied at two widely preferred dosages in practice (0.05% and 0.1% by weight of clinker + gypsum) to assess their effects on grinding efficiency under comparable conditions. In addition to conventional performance metrics, a multi-scale characterization strategy was adopted. The zeta potential of the ground cement particles was measured to elucidate changes in surface charge and dispersion behavior, while the adsorption characteristics of the GAs were evaluated to better understand their affinity toward clinker phases. Furthermore, PSD analyses were conducted in detail to reveal how molecular modifications influence particle fragmentation, agglomeration tendencies, and the overall fineness distribution. A key novelty of this study is the development of a polarization-based mechanism linking esterification-induced molecular changes to adsorption behavior, interparticle electrostatic interactions, and grinding efficiency. By correlating molecular dipole moment and polarizability with PSD evolution and dispersion performance, the study establishes a direct connection between molecular-scale chemical structure and macroscopic comminution behavior. Consequently, this work provides a more comprehensive mechanistic understanding of GA action than currently available in past literature.

Materials and methods

Synthesis materials

Specific ester compounds were synthesized through the reaction of commercially applicable alkanolamines with selected carboxylic acids in the presence of appropriate catalysts. As carboxylic acids, acetic acid, hexanoic acid, and propanoic acid were chosen, each representing different hydrocarbon chain lengths. The alkanolamines used in the synthesis were triisopropanolamine (TIPA), diethylene glycol (DEG), and diethanol isopropanolamine (DEIPA). The selection of these alkanolamines and organic acids was based on findings from preliminary studies^3,31. The names of the organic amine compounds (GAs) utilized in the study are presented in Table 1. In the nomenclature of the modified grinding aids, the suffix numbers “1”, “2”, and “3” represent the type of organic acids used in the esterification process. Specifically, “1” corresponds to acetic acid modification, “2” corresponds to hexanoic acid modification, and “3” corresponds to propanoic acid modification. For example, M-TIPA-2 denotes the hexanoic acid–modified TIPA grinding aid.

Table 1.

Naming of GAs produced using organic acids in modification.

Type of organic acid	Commercial GA
	TIPA	DEIPA	DEG
	Modified GA
Acetic acid [CH3COOH]	M-TIPA-1	M-DEIPA-1	M-DEG-1
Hexanoic acid [CH3(CH2)4COOH]	M-TIPA-2	M-DEIPA-2	M-DEG-2
Propanoic acid [CH3(CH2) COOH]	M-TIPA-3	M-DEIPA-3	M-DEG-3

Cement production materials

The cements produced within the scope of this study were obtained by grinding 96% clinker and 4% gypsum (Bursa Cement Inc., Türkiye) in a laboratory ball mill (Micro Analysis Ltd., Türkiye) until a target Blaine fineness of 3900 ± 100 cm²/g was achieved. This target Blaine value was determined based on previous research^21,23. The cements obtained are Portland-type cements in accordance with the TS EN 197-1 Standard. In this context, some physical and chemical properties of the clinker and gypsum used are shown in Table 2.

Table 2.

Properties of cement production materials.

Compound/Item (%)
	SiO2	Al2O3	Fe2O3	CaO	MgO	SO3	Na2Oeq	Cl	Combined Water (T < 230 °C)	Other	C3S	C2S	C3A	C4AF	Loss of ignition
Clinker	21.52	5.43	3.31	65.38	1.04	0.38	0.83	0.01	-	1.58	56.51	19.06	8.79	10.07	0.52
Gypsum	4.98	1.21	0.83	28.94	0.83	39.67	0.37	-	18.93	4.24	-	-	-	-	-

Methods

Synthesis of Modified Grinding Aids via Esterification

Esterification is a reversible equilibrium reaction in which the water formed can shift the equilibrium back toward the reactants. To drive the reaction toward product formation, a system enabling continuous water removal was employed. All syntheses were conducted in a 250 mL two-necked glass reactor equipped with a reflux condenser and a distillation unit. A vacuum line connected to the distillation outlet facilitated continuous water removal during the reaction.

In a typical procedure, 0.8 mol of carboxylic acid and 0.7 mol of an alkanolamine were mixed, and 0.05 mol of sulfuric acid (H₂SO₄) was added as a catalyst. The reaction was carried out at 110 °C for 3 h under reflux with continuous stirring at 600 rpm, and vacuum-assisted water removal promoted the forward reaction. In addition to this synthesis method, Kaya et al.³¹ reported detailed FT-IR, ¹³C NMR, and GC-MS analyses of monoester and diester products, which comprehensively support the reproducibility and reliability of product characterization.

The theoretical computation method

The grinding performance of TIPA, DEG, and DEIPA alkanolamine compounds (AY KİM-Bursa Ltd., Turkey), as well as their modified esters formed with organic acids of varying chain lengths, such as acetic, propanoic, and hexanoic acids, was investigated using the Gaussian 09 software package to gain a better understanding of their behavior³². The structures of all targeted molecules were modeled using GaussView 5.0, and semi-empirical methods, including optimization and frequency calculations in the PM6 basis set, were used to determine their most probable geometric structures. The absence of negative frequencies in the molecular frequency calculations indicates that the molecules were optimized at their minimum-energy geometry. To reveal the electronic structures of the molecules, the structures of modified esters formed by alkanolamine compounds with different organic acids were examined before and after formation. In this context, the physicochemical properties of the molecules, such as the Mulliken charges of heteroatoms, dipole moments, and polarization, were calculated using the same method and basis set. In addition to molecular electronic structure calculations, adsorption energy values reported in Table 4 were estimated using a molecular interaction approach based on isolated-molecule energy differences in the GAs phase. Specifically, the relative stabilization energy of the modified derivatives was calculated from the total energy difference between the pre- and post-esterification states. It should be noted that these values do not represent adsorption energies obtained from explicit cement surface models (e.g., C₃S or C₃A slab calculations) but rather provide a comparative indicator of molecular interaction potential.

Table 4.

Grinding Efficiency, Adsorption Behavior, and Zeta Potential Responses of Cements with GAs.

Type of cement	Blaine (cm2/g)	Requirements for Target Blaine		Energy Consumed (kWh/ton)	Relative Energy Efficiency (%)	Adsorption Energy (-eV)	Zeta Potential (-mv)
		Number of Rotations	Grinding time (min)
Control	3950	8830	126.1	52.73	-	-	10.6
TIPA-0.05	3915	7870	112.4	47.00	10.87	8.09	6.10
TIPA-0.1	4010	8070	115.3	48.19	8.61
M-TIPA-1-0.05	3850	7510	107.3	44.85	14.95	8.43	4.05
M-TIPA-1-0.1	3851	7900	112.9	47.17	10.53
M-TIPA-2-0.05	3871	7240	103.4	43.23	18.01	8.74	2.86
M-TIPA-2-0.1	3851	7470	106.7	44.61	15.40
M-TIPA-3-0.05	3722	7810	111.6	46.64	11.55	8.63	5.67
M-TIPA-3-0.1	3917	8050	115.0	48.07	8.83
DEIPA-0.05	3915	8050	115.0	48.07	8.83	7.49	7.50
DEIPA-0.1	3988	8200	117.1	48.97	7.13
M-DEIPA-1-0.05	3808	7760	110.9	46.34	12.12	7.86	6.33
M-DEIPA-1-0.1	3780	8100	115.7	48.37	8.27
M-DEIPA-2-0.05	3860	7500	107.1	44.79	15.06	8.72	5.78
M-DEIPA-2-0.1	3820	7410	105.9	44.25	16.08
M-DEIPA-3-0.05	3815	7680	109.7	45.86	13.02	8.40	5.91
M-DEIPA-3-0.1	3920	7520	107.4	44.91	14.84
DEG-0.05	3910	8110	115.9	48.43	8.15	5.80	8.70
DEG-0.1	3824	8060	115.1	48.13	8.72
M-DEG-1-0.05	4051	7800	111.4	46.58	11.66	8.05	5.53
M-DEG-1-0.1	3872	7730	110.4	46.16	12.46
M-DEG-2-0.05	3865	7600	108.6	45.38	13.93	8.21	5.20
M-DEG-2-0.1	3820	7800	111.4	46.58	11.66
M-DEG-3-0.05	3834	7550	107.9	45.08	14.50	8.10	4.94
M-DEG-3-0.1	3807	7400	105.7	44.19	16.19

The PM6 semi-empirical method was selected due to its relatively low computational cost, the inability of the total organic carbon (TOC) method to account for adsorption occurring under grinding conditions, and its ability to effectively capture general electronic trends, changes in molecular polarity, and relative stabilization behavior among structurally similar grinding aids. However, several limitations should be considered when interpreting the results for cement-related adsorption phenomena. First, PM6 does not explicitly model clinker mineral surfaces or interfacial atomic structures; therefore, surface-specific effects, such as localized charge distributions, surface hydration states, and coordination environments, cannot be fully represented. Second, the method has limited accuracy in describing weak intermolecular interactions, particularly hydrogen bonding, van der Waals forces, and long-range dispersion interactions, which are significant in GA adsorption and particle dispersion mechanisms. In addition, the calculations were performed in the gas phase, without explicit solvent or pore-solution effects, whereas real cement grinding systems involve highly heterogeneous solid–liquid interfaces. Consequently, quantitative adsorption energies obtained from PM6 calculations may deviate from experimentally observed values.

Despite these limitations, the PM6 approach remains suitable for the comparative evaluation conducted in this study, as the investigated molecules share similar backbone structures and functional groups. Therefore, the calculated dipole moments, polarizability values, and relative stabilization energies were primarily used to identify qualitative trends and establish structure–performance relationships rather than to provide absolute thermodynamic adsorption parameters.

Clinker grinding method

The clinker grinding process was conducted in a laboratory mill equipped with a 1.5 kW motor and a 5 kg capacity, in accordance with the dimensions specified by Bond³³. The grinding performance of the GAs was compared based on the target Blaine fineness value. The ball distribution used in grinding was optimized based on a preliminary study, and, accordingly, the ball distribution recommended in the Bond standard test was used²³. In the grinding process, GAs were used at 0.05% and 0.1% by weight of the clinker and gypsum, respectively. The cement samples obtained were named according to the GA type and dosage. For example, the cement obtained using 0.05% TIPA was named TIPA-0.05. The energy consumed in the clinker grinding process was calculated using Eq. 1. Each grinding experiment was conducted in triplicate to ensure reproducibility. The reported values of Blaine fineness, energy consumption, and PSD parameters represent the average of three independent tests. The relative standard deviation (RSD) for energy consumption measurements was below 3%, whereas the RSD for Blaine fineness measurements was below 2%. These low deviations confirm the reliability of the experimental procedure.

1

Where E_g is the grinding energy (kWh/tonne), T_g is the grinding time (hours), A is the amperage, m is the feed rate (kg), and T_d is the mill factor (a fixed value taken as four from the manufacturer).

Determination of particle size distribution and zeta potential

The particle size distribution (PSD) of the ground powder samples was determined using a Malvern Mastersizer 2000 laser diffraction instrument equipped with a Hydro 2000 S wet dispersion unit. To minimise the potential errors caused by cement particles forming agglomerates and affecting the results, the samples were subjected to 10 min of ultrasonic mixing before measurement. Zeta potential (ZP) measurements of the produced cements were performed using a Zetasizer ZS90. During all ZP measurements, the temperature and voltage were maintained at 23 °C and within the range of 50–100 V, respectively³⁴.

Calculation of the n value according to the Rosin–Rammler distribution

The Rosin–Rammler distribution is a commonly used method for expressing particle size distribution as a continuous function, defining the fineness of powder materials and the homogeneity of their distribution. Within the scope of this study, the n values for the size distributions were determined using Eq. 2.

2

Where R denotes the mass fraction remaining above a specific particle size; X denotes the particle size (µm); X^l denotes the characteristic size (the particle size through which 63.2% passes); n denotes the slope parameter of the distribution.

Although numerous studies have investigated the influence of commercial grinding aids on cement performance, no previous study has systematically correlated molecular electronic properties—such as dipole moment and polarizability—of esterified alkanolamine derivatives with experimentally measured grinding energy reduction and detailed Rosin–Rammler PSD slope parameters under controlled laboratory conditions. Furthermore, the effect of organic acid chain length on the electrostatic interaction potential of grinding aids has not been quantitatively examined. Therefore, this study aims to bridge molecular-scale electronic structure analysis with macroscopic grinding performance and particle size distribution behavior.

Results and Discussion

The effects of the modified GAs on grinding efficiency, zeta potential, and PSD are presented under separate subsections. Since the modification process directly influenced all measured properties, the related findings are first detailed in Sect. 3.1 under chemical effects. This approach was adopted to avoid repetition in subsequent sections and to provide a more comprehensive interpretation of the study results.

Polarization-based interaction mechanism between cement particles and grinding aids

Following the grinding process, cement particles acquire highly active surfaces characterized by elevated surface energy and heterogeneous charge distribution. The coexistence of cationic and anionic sites on these surfaces leads to ionic imbalance and the formation of an electric double layer, which governs interparticle interactions^35,36. The electrostatic field generated on the cement surface effectively induces polarization (electron displacement) in surrounding molecules³⁷.

Grinding aids possess functional groups such as hydroxyl, amine, and carboxyl, which create electron-rich or proton-attracting regions, thereby imparting high molecular polarizability^38,39. The electric field arising from surface ions perturbs the electron distribution of GA molecules, inducing dipole formation. Consequently, these molecules become physically adsorbed onto the cement surface through electrostatic attraction^40,41.

In this context, the interaction between the additive molecule and the particle surface occurs primarily through dipole–induced dipole-type Van der Waals forces. The associated polarization energy can be expressed as a function of the molecule’s polarizability (α) and the strength of the electric field generated by the surface (E), as shown in Eq. (3):

µ_induced = α × E (3).

In this mechanism, µ_induced represents the induced dipole moment generated within the additive molecule. As the molecular polarizability increases, the electrostatic attraction between the additive and the cement surface becomes stronger. Consequently, the molecules tend to orient themselves in a specific direction relative to the surface. This alignment enables functional groups—such as hydroxyl or amine groups—to position themselves toward oppositely charged sites on the cement surface, thereby forming an ordered adsorption layer^41,42.

This polarization-driven adsorption mechanism directly enhances grinding efficiency. During mechanical grinding, the high surface energy of cement particles promotes agglomeration. The adsorption of polar GA molecules onto these surfaces increases electrostatic repulsion and diminishes Van der Waals forces, thereby improving particle dispersion. As a result, less mechanical energy is required to achieve the desired fineness³⁸. Furthermore, the oriented layer formed by polarized additive molecules improves the flowability of the cement powder. The directional arrangement of functional groups reduces interparticle cohesion, which enhances powder rheology. Therefore, polarization acts as a multifaceted phenomenon influencing both molecular-level adsorption and macroscopic powder flow behavior. In this context, simulations were performed to evaluate the performance of the modified GAs by determining the dipole moment, polarizability, and electronegativity values of atoms exhibiting partial negative charge. These results are presented in Table 3, while the molecular simulations of the commercial GAs are shown in Fig. 1. In the DEG modification series, both monoester and diester derivatives were obtained during synthesis. Based on GC–MS characterization²⁶, the dominant derivative in each modification system was selected for grinding experiments. Computational data for both mono- and diester forms are provided to illustrate electronic trends; however, experimental grinding results correspond to the predominant synthesized structures.

Table 3.

Dipole moment, polarization, and Mulliken charges of heteroatoms in modified esters with TIPA, DEIPA, and DEG molecules*.

Molecule	Dipole Moment (Debye)	Polarizability [α, atomic unit (a.u.)]	Atomic Charge Value
			Nitrogen	1. Oxygen	2. Oxygen	3. Oxygen	4. Oxygen	5. Oxygen
TIPA	0.857232	79.984333	−0.301	−0.592	−0.581	−0.574	-	-
M-TIPA-1	3.141252	102.180000	−0.318	−0.590	−0.576	−0.505	−0.475	-
M-TIPA-2	5.560966	129.653333	−0.319	−0.590	−0.586	−0.504	−0.472	-
M-TIPA-3	5.431978	108.574333	−0.319	−0.590	−0.586	−0.506	−0.467	-
DEIPA	3.357707	66.262333	−0.334	−0.604	−0.575	−0.567	-	-
M-DEIPA-1	3.917670	88.863000	−0.334	−0.603	−0.573	−0.475	−0.462	-
M-DEIPA-2	4.542433	112.245676	−0.316	−0.578	−0.557	−0.471	−0.469	-
M-DEIPA-3	4.800846	93.963667	−0.317	−0.589	−0.578	−0.472	−0.469	-
DEG	2.054800	39.577000	-	−0.553	−0.553	−0.479		-
M-DEG-1**	3.940915	41.839667	-	−0.552	−0.478	−0.466	−0.455	-
M-DEG-1–2***	4.562600	54.595667	-	−0.470	−0.466	−0.452	−0.466	−0.452
M-DEG-2	3.924901	60.173333	-	−0.552	−0.479	−0.472	−0.451	-
M-DEG-2-2	4.957200	71.512333	-	−0.479	−0.472	−0.448	−0.472	−0.448
M-DEG-3	4.784097	69.128667	-	−0.552	−0.479	−0.474	−0.446	-
M-DEG-3-2	5.583600	89.296333	-	−0.480	−0.475	−0.443	−0.475	−0.443

*Mulliken charges describe the distribution of electrons within a molecule, indicating which atoms possess a partial positive charge (electron deficiency) and which carry a partial negative charge (electron gain).

** Monoester: Formed when one hydroxyl group in the molecule reacts with a carboxyl group (i.e., a molecule containing a single carboxyl functional group).

*** Diester: Formed when two hydroxyl groups within the molecule react with carboxyl groups (i.e., in the presence of two carboxyl functional groups).

Fig. 1.

(a) TIPA, (b) DEIPA, and (c) DEG molecule representation and atomic charges in the Gaussian program.

In this study, differences in the dipole moment, polarizability, and electronegativity distributions of the investigated grinding aid additives (TIPA, DEIPA, and DEG derivatives) were assessed as key parameters governing their molecular interactions with the cement surface. The findings reveal that the modification processes substantially alter the electronic characteristics of the molecules. In particular, increases in dipole moment (µ) and polarizability (α) in the modified derivatives indicate enhanced interaction potential with the ionic fields present on the cement surface, thereby promoting stronger adsorption tendencies⁴².

The low dipole moment of unmodified TIPA (0.857 D) reflects a high degree of electronic symmetry and a weak permanent dipole. In contrast, the pronounced increases observed in its modified counterparts—M-TIPA-1 (3.14 D), M-TIPA-2 (5.56 D), and M-TIPA-3 (5.43 D)—demonstrate the emergence of a strong permanent dipole resulting from the presence of ester and hydroxyl functionalities. Likewise, the rise in polarizability from 79.98 a.u. (TIPA) to 129.65 a.u. (M-TIPA-2) indicates a marked increase in the molecule’s susceptibility to external electrostatic fields, such as those generated by Ca²⁺ centers on the cement surface. This enhanced response suggests that polarized molecules engage more strongly in induced dipole–dipole interactions, facilitating higher adsorption⁴³.

A similar trend is evident for DEIPA. The native dipole moment of 3.36 D increases to 4.54–4.80 D in M-DEIPA-2 and M-DEIPA-3 following modification, reflecting heightened electronic asymmetry and augmented interaction potential with cement surfaces. Concurrently, the increase in polarizability (from 66.26 a.u. to 112.25 a.u.) and the change in oxygen electronegativity (from − 0.604 to approximately 0.471) indicate a more deformable and polarizable electron cloud. Consequently, modified DEIPA molecules are expected to form stronger induced dipole interactions with Ca²⁺ sites.

This effect is even more pronounced in DEG-based derivatives. The dipole moment of DEG increases from 2.05 D in the unmodified molecule to 3.94–5.58 D after modification, while the polarizability rises substantially from 39.57 a.u. to 89.29 a.u. These changes confirm that external fields more easily perturb the electron clouds of the modified structures. The reduction in electron density on oxygen atoms (from ≈ − 0.55 to ≈ − 0.45) further suggests that electrons are weaker bound and more responsive to external forces, thereby strengthening physical adsorption via induced dipole resonance on the cement surface.

The hydrocarbon chain length of the organic acids used in GA modification introduces additional systematic effects. As the chain length increases (acetic < propanoic < hexanoic acid), the hydrocarbon segment of the molecule expands, producing two major outcomes. First, longer carbon chains enhance molecular polarizability due to the increased number of electrons and larger electron cloud volume, making the molecule more easily deformable under external electrostatic fields. Second, ester groups derived from long-chain acids impart partial hydrophobic character³⁹. This dual effect strengthens electrostatic adsorption on the cement surface while reducing intermolecular cohesion, thereby improving particle dispersion. As a result, the molecule not only establishes stronger polar interactions with the surface but also contributes to the separation of particles.

The chain length of the organic acid also influences surface wettability and powder rheology. Short-chain esters (e.g., acetic acid derivatives) exhibit strong hydrophilicity, promoting robust adsorption onto the cement surface. In contrast, long-chain esters (e.g., hexanoic acid derivatives) are less hydrophilic and create a partially oriented hydrophobic layer. This hydrophobic tail diminishes interparticle cohesion and enhances powder flowability. Thus, with increasing chain length, a dual-function behavior emerges: the polar functional groups bind effectively to charged surface sites, while the apolar hydrocarbon tail reduces particle–particle interactions^18,39.

Consequently, modified alkanolamine derivatives can form stronger electrostatic interactions with cement particles due to their increased dipole moment and polarizability. This reduces surface energy, thereby increasing grinding efficiency, improving powder dispersion, and facilitating ion transport at the onset of hydration. Therefore, dipole moment (µ), polarizability (α), and electronegativity distribution are fundamental parameters that directly determine the performance of a GA³⁷. Furthermore, the hydrocarbon chain length (3–5 carbons) in organic acids reduces interparticle cohesion, further enhancing performance. In particular, molecules with a dipole moment above 5 D, a polarizability of ~ 90 a.u., and a long hydrocarbon chain (M-TIPA2, M-DEIPA-2, and M-DEG3-2) stand out as the most effective grinding aids due to their high adsorption energy and strong polar interactions.

Grinding efficiency

To further evaluate the relationship between molecular properties and grinding performance, correlation analyses were conducted between dipole moment (µ), polarizability (α), and relative energy efficiency. A strong positive trend was observed, indicating that higher molecular polarizability and dipole moment are associated with improved grinding efficiency. While this correlation supports the proposed adsorption–polarization mechanism, it does not exclude the contribution of other factors such as steric effects, viscosity modification, or surface lubrication phenomena. The grinding efficiencies achieved using the synthesized GAs, the adsorption energies calculated at a dosage level of 0.05% through Gaussian simulations, and the zeta potential values of the cement samples are summarized in Table 4. Statistical comparisons between control and modified GA systems were performed using one-way ANOVA at a 95% confidence level. The reductions in energy consumption achieved with modified GAs were statistically significant (p < 0.05) compared with both the control and unmodified commercial additives. This confirms that the observed improvements exceed experimental variability.

Additionally, Fig. 2 presents the average grinding efficiency values for each GA across all tested dosages, trying a comprehensive evaluation of their overall grinding performance. The results demonstrate that the use of GAs improves energy efficiency irrespective of the GA type. Moreover, all modified additives exhibit superior grinding performance compared to the commercial GAs. This enhancement may be attributed to the increased dipole moment and polarizability of the molecules resulting from the modification process, as previously discussed.

Fig. 2.

Average grinding efficiency of GAs.

Among the commercial GAs, the grinding performance follows the order TIPA > DEIPA > DEG. This trend is consistent with the molecular polarizability values, adsorption energies, and the corresponding zeta potential measurements of the cements (Tables 3 and 4). In the modification studies, hexanoic acid produced the most significant improvement for both TIPA and DEIPA, whereas propanoic acid yielded the highest performance for DEG. This outcome is likely related to the higher diester content observed in the DEG–propanoic acid modification, as reported in earlier GC-MS analyses³¹. The presence of two carboxyl groups in the diester structure of DEG appears to counterbalance the polarity reduction associated with the hydrocarbon chain. The dipole moment and polarizability values presented in Table 3 further support this interpretation.

Particle size distribution

The physical characteristics and particle size distribution (PSD) curves of the produced cements are presented in Table 5; Fig. 3. In the subsequent stage of the study, evaluations were conducted based on specific particle size ranges. The particle size distributions of the cements within ranges considered critical for hydration reactions were examined individually under separate subheadings. Accordingly, the size fractions of 0–10 μm, 11–32 μm, 33–45 μm, 46–60 μm, 61–90 μm, and particles larger than 90 μm were each evaluated separately. The following discussion is structured into subsections based on different PSDs. The significance of each range is highlighted in relation to literature-informed key properties of cementitious systems, including rheology, hydration, and strength. This approach aims to clarify the potential implications of the PSD improvements achieved in this study.

Table 5.

PSD data of the cement produced.

	0–10	11–32	33–45	46–60	61–90	91<	D10 1	D50 2	D90 3	d3.2 4	d4.3 5	n 6	Slope (%/log µm)
Control	36.15	31.15	11.08	6.21	6.06	9.35	2.28	19.0	78.0	4.46	47.1	0.804	50.116
TIPA-0.05	40.51	33.11	12.07	6.36	5.22	2.69	1.99	15.90	59.0	3.95	29.80	0.931	54.348
TIPA-0.1	41.8	31.33	11.79	6.67	5.92	2.48	1.80	15.40	60.70	3.66	25.20	0.900	52.359
M-TIPA-1-0.05	41.28	33.35	12.23	6.32	4.88	1.94	1.96	15.40	56.30	3.88	23.80	0.949	54.860
M-TIPA-1-0.1	41.81	36.21	11.90	5.52	3.50	1.07	2.02	14.80	50.20	3.91	25.80	1.010	57.333
M-TIPA-2-0.05	44.22	34.06	10.66	5.03	3.66	2.37	1.73	13.60	52.40	3.52	22.70	0.929	54.007
M-TIPA-2-0.1	45.49	36.06	9.86	4.58	3.34	0.65	1.65	12.80	46.80	3.36	19.30	0.982	55.068
M-TIPA-3-0.05	41.37	36.97	12.07	5.67	3.54	0.34	2.12	14.90	49.20	4.00	20.90	1.038	58.581
M-TIPA-3-0.1	42.96	35.43	11.60	5.70	3.83	0.47	2.00	14.10	50.00	3.78	20.80	0.998	57.227
DEIPA-0.05	39.42	32.41	11.33	5.95	4.96	5.93	2.01	16.50	68.20	4.01	38.90	0.863	52.267
DEIPA-0.1	40.15	31.19	11.75	6.73	6.04	4.12	1.93	16.30	65.50	3.86	29.3	0.878	52.264
M-DEIPA-1-0.05	41.21	32.52	12.14	6.42	5.16	2.56	1.87	15.5	58.5	3.79	25	0.925	53.500
M-DEIPA-1-0.1	41.16	32.06	11.23	5.79	4.41	5.35	2.05	15.3	64.1	3.92	43.1	0.864	53.508
M-DEIPA-2-0.05	41.52	34.28	12.21	5.99	3.69	2.31	1.69	15.1	53.9	3.54	31.3	0.964	53.202
M-DEIPA-2-0.1	43.98	35.53	10.85	5.23	3.7	0.70	1.76	13.6	49.3	3.53	20.4	0.984	55.274
M-DEIPA-3-0.05	39.52	33.29	11.38	5.93	4.97	4.90	2.24	16.3	64.6	4.21	44.9	0.891	54.795
M-DEIPA-3-0.1	40.93	31.4	11.31	6.19	5.41	4.78	2.02	15.8	65.6	3.9	30.8	0.862	52.926
DEG-0.05	36.04	32.48	13.51	8.16	7.22	2.56	2.2	18.8	64.6	4.13	27.7	0.966	54.503
DEG-0.1	37.70	34.11	14.51	7.32	5.38	0.98	2.19	18.5	56.4	4.48	24.5	1.025	56.704
M-DEG-1-0.05	40.51	33.11	12.07	6.36	5.22	2.69	1.99	15.9	59.0	3.95	29.8	0.931	54.348
M-DEG-1-0.1	40.79	32.96	12.58	6.44	5.21	1.97	2.10	15.8	57.3	4	24	0.947	55.713
M-DEG-2-0.05	40.93	31.4	11.31	6.19	5.41	4.78	2.02	15.8	65.6	3.9	30.8	0.862	55.066
M-DEG-2-0.1	41.42	33.76	12.37	6.37	4.56	1.50	1.99	15.2	54.7	3.85	29.9	0.966	55.589
M-DEG-3-0.05	41.38	35.37	11.81	6.31	4.71	0.42	1.89	15.1	52.8	3.84	21.6	0.998	55.318
M-DEG-3-0.1	40.75	35.74	11.57	6.37	4.51	1.05	2.11	14.4	53.7	3.92	22.2	0.994	56.911

^1,2,3 Particle size (µm) through which 10%, 50%, and 90% of cement particles pass ^4,5 Sauter Mean Diameter, Surface-Weighted Mean, and De Brouckere Mean Diameter, Volume-Weighted Mean ⁶ Slope parameter.

Fig. 3.

Particle size distribution curves of cements: (a) Cements produced with commercial GAs, (b) Cements produced with TIPA and M-TIPA series.

0–10 μm (the finest fraction)

Figure 4 presents the relative proportions of the 0–10 μm particle size fraction of the cements produced in the presence of GAs, compared with the control cement. The proportion of particles in the 0–10 μm range increases markedly in the presence of GAs compared with the control cement. Among commercial GAs, the fine fraction follows the order TIPA > DEIPA > DEG, indicating that TIPA inherently produces a higher amount of fine material. The modification process further enhances this effect for all commercial GAs. Notably, M-TIPA-2 exhibits the highest efficiency in increasing the fine fraction. Although DEIPA and DEG derivatives also increase the 0–10 μm content, their unmodified forms remain less effective than TIPA. Increasing the GA dosage from 0.05% to 0.10% generally results in a higher proportion of fine particles (Fig. 4).

Fig. 4.

Relative particle quantities in the 0–10 μm size range of GA-containing cements compared with the control sample.

A comparative evaluation of Tables 4 and 5, and Fig. 4 reveals that TIPA is the most effective commercial GA in reducing the coarse fraction and increasing the 0–10 μm fraction. Among all modifications, the second, hexanoic acid, provides the greatest improvement in fine particle generation. These findings are consistent with the dipole moment, polarizability, and Mulliken charge values presented in Table 3, confirming the polarization-based mechanism described in Sect. 3.1 and supporting the enhanced performance achieved through molecular modification. Furthermore, the results support the hypothesis that increased molecular dipole moment and polarizability enhanced surface interaction potential. However, it should be emphasized that the present results demonstrate a strong correlation rather than direct mechanistic proof.

The use of GAs enhances the fine fraction by increasing impact and shear efficiency during grinding^21,44. Particles below 10 μm have a dominant influence on the Sauter mean diameter (d₃,₂) due to their very high specific surface area. A reduction in d₃,₂ accelerates early hydration by increasing nucleation density and enhancing the dissolution of C₃S and C₂S, thereby raising Ca²⁺ and [OH⁻] concentrations and promoting C–S–H formation⁴⁵. Alkanolamine-based GAs (e.g., TIPA, DEIPA) also influence C₃A–sulfate–aluminate reactions, regulating the ettringite–monosulfate balance and further improving early-age reactivity⁴⁶.

However, an excessive increase in the fine fraction may lead to elevated water demand and viscosity due to increased surface-mediated adsorption. Therefore, the PCE–GA–water ratio must be carefully optimized to avoid undesirable rheological effects⁴⁶.

From a microstructural standpoint, an increased 0–10 μm fraction enhances early C–S–H formation, refines capillary pores, and can improve durability properties such as carbonation resistance and permeability. Nevertheless, an overly high fine fraction may promote rapid early hydration via diffusion and increase drying shrinkage. Thus, the optimal 0–10 μm fraction must be balanced not only with PSD but also with admixture design⁴⁷. Overall, the increase in the fine fraction resulting from GA modification is expected to affect several properties of cementitious systems, including the permissible level of pozzolanic substitution.

11–32 μm (medium-fine transition)

Figure 5 presents the relative proportions of the 11–32 μm particle size fraction of the cements produced in the presence of GAs, compared with the control cement. The results show that the 11–32 μm fraction, which is relatively low in the control cement without GA, increases markedly with the use of grinding aids. Among the commercial GAs, the particle content in this range follows the order DEG > TIPA > DEIPA. The results also indicate that all commercial additives further increase the 11–32 μm fraction after modification. In the case of TIPA, the M-TIPA-3 derivative is the most effective in enhancing the particle content within this size interval. Although the DEIPA and DEG series exhibit similar trends, their performance remains inferior to that of TIPA in its unmodified state. Increasing the dosage from 0.05% to 0.10% generally results in a further increase in fine particle content (Fig. 5). Among the amine-based GAs, the second modification type was found to be the most effective for DEIPA. In contrast, for glycol-based DEG, the third modification yielded the greatest increase in the 11–32 μm fraction.

Fig. 5.

Relative particle quantities in the 11–32 μm size range of GA-containing cements compared with the control sample.

Amine-based GAs, such as TIPA and DEIPA, primarily accelerate early hydration by increasing the 0–10 μm fraction; however, sufficient enrichment in the 11–32 μm band also significantly contributes to the development of 7–28-day strength³⁰. The use of GAs reduces the proportion of coarse particles (≥ 45–60–90 μm). It shifts mass toward this medium-size range, thereby helping to balance the transition from hydration to the diffusion-controlled regime and promoting a more homogeneous microstructure⁴⁸. Thus, a well-regulated increase in the 11–32 μm fraction results in a more favorable particle packing structure, controlled water demand, and a continuous hydration profile, rather than a distribution dominated by ultrafine particles alone. For these reasons, maintaining a balanced enhancement of the 11–32 μm fraction is essential for achieving consistent early- and mid-age strength, as well as stable rheological and microstructural development³⁰. In this context, the modification strategies implemented in this study are expected to produce grinding aids that improve packing density, mechanical performance, and rheological behavior of cement systems.

Zhao et al.⁴⁹ reported that triethanolamine (TEA) modified with organic acids (M-TEA) exhibited superior performance compared to its unmodified commercial counterpart in optimizing the particle size distribution (PSD) of cement. Specifically, at the optimum M-TEA dosage, the fraction of particles within the 3–32 μm size range—widely recognized as the most critical interval governing cement hydration kinetics and strength development—reached 68.70%, corresponding to an increase of 12.42% relative to the control (blank) sample. This improvement was attributed to enhanced dispersion efficiency and reduced particle agglomeration resulting from the modified molecular structure.

In the present study, a comparable enhancement in the favorable PSD range was observed with the M-TIPA-2 modification. In particular, the proportion of particles within the 1–32 μm range increased by approximately 16% compared to the control mixture.

This improvement can be associated with the structural modification of TIPA via esterification, which likely alters the balance between hydroxyl and ester functional groups, thereby influencing adsorption behavior and interparticle forces. As a result, the modified GA enhances particle dispersion and stabilizes finer particles, leading to a more favorable PSD. The consistency between the findings of Zhao et al.⁴⁹, and the results of this study further support the hypothesis that targeted chemical modification of alkanolamine-based GAs is an effective strategy for tailoring PSD and, consequently, improving grinding efficiency and cement performance.

In another study, Zhao et al.⁵⁰ reported that the use of unmodified TEA increased the 3–32 μm fraction by approximately 6% compared to the control. This relatively limited improvement highlights the restricted effectiveness of conventional GAs. In contrast, the more pronounced increase observed in this study, particularly with M-TIPA-2, demonstrates that chemical modification significantly enhances PSD optimization and grinding efficiency.

33–45 μm (transition/medium-sized fraction) and 46–60 μm (large particle fraction start)

Figure 6 presents the relative proportions of the 33–45 μm particle size fraction of the cements produced in the presence of GAs, compared with the control cement. The results indicate that, while the 32–45 μm fraction remains essentially unchanged between the control cement and the cements produced with TIPA and DEIPA, it is notably higher in the DEG cement. However, once commercial GAs are modified, a substantial reduction in particle content within this size interval is observed. In particular, the second modification type produces the most pronounced reduction in the 33–45 μm range compared with the unmodified GAs. Although decreasing the proportion of particles in this interval offers advantages in terms of grinding energy efficiency and early-age performance, eliminating this fraction would be detrimental to mid-age strength development and microstructural uniformity in cementitious systems⁸.

Fig. 6.

Relative particle quantities in the 33–45 μm size range of GA-containing cements compared with the control sample.

The 32–45 μm interval is often defined as the “transition fraction” within the PSD, positioned between fine (< 30 μm) and coarse (> 45–60 μm) particles. This size range plays a crucial role in determining the grinding process’s energy efficiency. In control cement, it typically corresponds to 11–13% of the PSD. With the application of gas, especially modified amine-based additives, this proportion decreases to approximately 9–11%, indicating that coarse fractions are effectively fragmented and redistributed into finer size classes^51,52.

From a hydration standpoint, particles within the 32–45 μm range can be considered “mid-late reactive grains,” contributing to strength development between 7 and 28 days by sustaining C–S–H formation. Previous work⁵³ highlights that grains of this size maintain meaningful reactivity during the mid-age period. Transferring part of this fraction into the < 30 μm range enhances early hydration while still supporting mid-age strength.

Figure 7 presents the relative proportions of the 45–60 μm particle size fraction of the cements produced in the presence of GAs, compared with the control cement. Commercial GAs cause only a slight increase in the 46–60 μm fraction, whereas the modification process leads to a pronounced reduction in this particle size range. This clearly indicates that coarse particles are effectively fragmented into finer sizes, thereby enhancing grinding efficiency, as noted in past work^51,54. Among the modifications, the second modification type shows the highest effectiveness in reducing the 45–60 μm content. The 45–60 μm interval represents the “onset of the coarse fraction,” and breaking down particles of this size typically requires substantial mechanical energy.

Fig. 7.

Relative particle quantities in the 46–60 μm size range of GA-containing cements compared with the control sample.

Although particles larger than 45 μm contribute minimally to early-age strength, they play a significant role in sustaining hydration at mid- and late ages. Grains within the 45–60 μm range are not entirely inert; rather, they participate in hydration after approximately 28 days and help regulate the transition from hydration to the diffusion-controlled phase^53,55 These particles serve as a long-term hydration reserve. Consequently, an excessive reduction of this fraction through GA use may suppress late-age strength development. A controlled, moderate decrease in the 45–60 μm fraction, therefore, represents an optimal approach, improving early-age performance while maintaining the capacity for long-term strength gain.

 61–90 μm (coarse fraction)

Figure 8 presents the relative proportions of the 61–90 μm particle size fraction of the cements produced in the presence of GAs, compared with the control cement. As illustrated in Fig. 8, all GAs, except DEG at 0.05%, substantially reduce the proportion of particles in the 61–90 μm range. Notably, the second type of modification applied to amine-based additives achieves reductions of up to 40%. Particles within the 61–90 μm interval exhibit limited solubility at early ages but serve as a sustainable reserve of reactivity under diffusion-controlled hydration between 1 and 28 days. Controlled reduction of this fraction enhances early-age strength by increasing the proportion of finer particles (0–32 μm); however, excessive reduction can compromise mid- to late-age hydration. Optimal performance is observed when the 10–30 μm fraction is maintained at a sufficient level, and the 61–90 μm fraction is reduced to a low, yet non-zero, level. Additionally, reducing the amount of coarse particles improves durability by refining the capillary pore structure⁵⁶. Nevertheless, over-refinement may increase the risks of hydration heat and shrinkage, underscoring the importance of a balanced particle size distribution. In this context, the 61–90 μm fractions achieved through GA modifications in this study are consistent with the recommended optimal range.

Fig. 8.

Relative particle quantities in the 61–90 μm size range of GA-containing cements compared with the control sample.

91 μm and above (very coarse fraction)

Figure 9 presents the relative proportions of the > 90 μm particle size fraction of the cements produced in the presence of GAs, compared with the control cement. Analysis of the results shows that the application of GAs markedly reduces the proportion of particles larger than 90 μm. These coarse particles are essentially inert during early hydration (1–7 days) and contribute minimally to the hydration process. Although they may exhibit limited diffusion-controlled reactivity at later ages (> 28 days), their impact on mechanical performance is negligible. Past work similarly notes that coarse fractions essentially act as a “dead reserve” and can restrict the overall degree of hydration^53,55.

Fig. 9.

Relative particle quantities in the > 90 μm size range of GA-containing cements compared with the control sample.

Regarding early-age strength, the inability of particles larger than 90 μm to participate in hydration results in a porous microstructure that limits strength development. Moreover, the limited hydration of these coarse particles maintains capillary continuity, increasing susceptibility to water permeability, chloride penetration, and carbonation⁵⁷. For optimal performance, it is recommended to maintain the > 90 μm fraction at a level below 2%⁸. In this study, while the control cement contained 9.35% of particles above 90 μm, most modified GAs—including the TIPA series, M-DEIPA-2, and M-DEG-3—achieved levels within the recommended range, except M-TIPA-2 at 0.05%.

Values of d10, d50, and d90

The d₁₀ value represents the fine-end fraction of cement particles. It plays a key role in promoting C–S–H nucleation by enhancing early hydration rates through its high specific surface area. However, an excessively high proportion of fine particles can increase water demand and adversely affect rheological properties. As shown in Table 5, the application of GAs reduces the d₁₀ value, reflecting an increase in the fraction of fine particles. The GA modification process further enhances this effect.

The d₅₀ value, which corresponds to the median particle size, indicates that 50% of the particles are smaller than this size. It serves as a critical parameter for evaluating grinding efficiency and the overall fineness of the system. Lower d₅₀ values generally enhance early-age strength, but excessively low values can increase water demand and compromise workability. The use of GAs was found to decrease the d₅₀ value significantly, and the relationship between d₅₀ and the proportion of particles below 32 μm is illustrated in Fig. 10.

Fig. 10.

Relationship between d50 and − 32 microns.

As illustrated in Fig. 10, a strong correlation exists between d₅₀ and the fraction of particles smaller than 32 μm. The application of GAs leads to an increase in the − 32 μm fraction and a corresponding decrease in d₅₀, a trend that is further enhanced by the GA modification process. This reduction in d₅₀ is particularly significant, as it promotes a higher degree of hydration and enables greater pozzolanic replacement.

The d₉₀ value represents the coarse end of the particle size distribution, indicating that 90% of the particles are smaller than this size. This parameter is critical because it reflects the presence of coarse fractions in the system. Higher d₉₀ values correspond to a predominance of coarse particles and lower early-age reactivity, whereas a reduction in d₉₀ indicates improved grinding selectivity, enhanced microstructural homogeneity, and reduced paste permeability⁵⁶. In the control cement without GA, d₉₀ is 78 μm; however, the application of GAs reduces this value to a range of 50–68 μm.

Values of d₃,₂ (Sauter Mean Diameter, Surface-Weighted Mean) and d₄,₃ (De Brouckere Mean Diameter, Volume-Weighted Mean)

In cement powder, d₃,₂ represents the surface-area-weighted mean particle diameter, while d₄,₃ represents the volume-weighted mean diameter. Since d₃,₂ emphasizes surface area, it is directly related to the cement’s specific surface and early-age hydration. Lower d₃,₂ values correspond to a higher fine fraction and larger specific surface, which accelerates early hydration and promotes dense C–S–H formation. In contrast, d₄,₃ is sensitive to coarse particles; higher d₄,₃ values slow early hydration and may negatively affect long-term strength⁵⁶.

In the control cement, d₃,₂ and d₄,₃ were 4.46 μm and 47.1 μm, respectively. The use of GAs reduced these values to 3.36 μm and 19.3 μm. Among commercial GAs, the lowest values were observed in the order TIPA > DEIPA > DEG, and all modification processes further decreased these diameters. The most pronounced reductions for TIPA and DEIPA were achieved with hexanoic acid modification, while for DEG, propanoic acid modification yielded the lowest values. This enhanced performance is attributed to the long hydrocarbon chain in the modifying organic acid, which provides both strong adsorption (Table 1) and a lubricating effect through its hydrophobic portion. Additionally, the high diester content in DEG-propanoic acid derivatives contributes to their superior performance compared to hexanoic acid.

Particle size distribution slope (n)

The slope parameter (n) of the Rosin–Rammler distribution is a key indicator that defines the sharpness of the cement’s particle size distribution (PSD) curve and reflects particle homogeneity in the system. Higher n values correspond to a narrower particle size range and a more uniform distribution, whereas lower n values indicate a broader, more heterogeneous distribution^54,58. Changes in the n parameter are therefore directly related to grinding efficiency and critically influence cement particle surface area, flowability, and hydration behavior. In this study, the slope parameter was examined to assess the effect of GAs on the properties of cement powder. The obtained n values are presented in Table 5, while the relative n values of GA-modified cements compared to the control cement are illustrated in Fig. 10.

As shown in Fig. 11, the n value increases with the use of GA. This is attributed to GA’s ability to reduce interparticle cohesive forces, enhancing fracture efficiency during grinding, narrowing the PSD, and producing a more homogeneous particle distribution¹⁹. For cements produced with TIPA and its modified derivatives, the slope increased by 14% with TIPA, 21% with M-TIPA-1, 18% with M-TIPA-2, and 27% with M-TIPA-3 compared to the control cement. The previously discussed increase in molecular polarity, dipole moment, and polarizability (Table 3) facilitates the formation of finer particles through enhanced adsorption (Table 5). Additionally, the hydrophobic hydrocarbon chains of modified GAs act as a shield, reducing particle agglomeration. However, excessively high GA dosages may cause over-dispersion and subsequent re-agglomeration, known as the “secondary agglomeration threshold”⁵⁹, which could explain the slightly lower performance of M-TIPA-2 compared to other modifications.

Fig. 11.

Relative PSD slopes compared to the control mixture: (a) TIPA and modifications, (b) DEIPA and modifications, (c) DEG and modifications.

For DEIPA and its derivatives, the n value increased by 8% for DEIPA, 11% for M-DEIPA-1, 21% for M-DEIPA-2, and 9% for M-DEIPA-3 relative to the control cement. Among these, M-DEIPA-2 exhibited the most pronounced effect due to the combined influence of increased polarity and hydrocarbon chain length from the hexanoic acid modification. Unlike TIPA, secondary adsorption phenomena in DEIPA are more limited, resulting in more consistent improvements in PSD.

In the case of DEG and its modified derivatives, the n value increased by 24% for DEG, 16% for M-DEG-1, 14% for M-DEG-2, and 24% for M-DEG-3 compared to the control. The superior performance of M-DEG-3 is attributed to its higher diester content, which enhances adsorption, improves grinding efficiency, and yields a narrower particle size distribution than monoester derivatives. Overall, the PSD n value varies with GA type and dosage, making it a critical parameter for balancing grinding efficiency and cement reactivity. The relationship between the PSD n value and the − 32 μm fraction (percentage passing through the 32 μm sieve) is illustrated in Fig. 12.

Fig. 12.

Relationship between the PSD n value of cements and − 32 microns (a) TIPA and modified (b) DEIPA and modified (c) DEG and modified.

Figure 12 illustrates a strong linear relationship between the Rosin–Rammler slope parameter (n) and the − 32 μm fraction. The use of GA increases the n value while reducing coarse particles. For amine-based additives, modifications enhanced both the − 32 μm fraction and the n value, indicating improved grinding efficiency and a more homogeneous particle size distribution. In contrast, for DEG, the n value decreased despite an increase in the − 32 μm fraction, suggesting a preferential concentration of particles in the 32–60 μm range rather than in the finest fractions. This distinct behavior underscores that GAs’ effects on cementitious systems are multifaceted and that a comprehensive evaluation of all relevant parameters is essential to optimize performance.

Conclusions

In this study, the effects of modifying commonly used GAs, i.e., TIPA, DEIPA, and DEG, via organic acid esterification on grinding efficiency, zeta potential, polarization-based interaction mechanisms, and particle size distribution were investigated in detail. The main findings are summarized as follows:

• The increased dipole moment and polarizability of the modified GAs indicate stronger electrostatic interactions with cement particles. The enhanced interaction potential is consistent with reduced surface energy effects, improved grinding efficiency, and optimized PSD. These findings suggest that molecular-level polarization control can be used as a design parameter for next-generation grinding aids.

• Among all modifications, the second modification using hexanoic acid was the most effective in increasing the fine fraction, supporting the polarization-based GA mechanism proposed in this study. In this context, hexanoic acid modification, which improves fineness and grinding performance, can be considered a viable alternative for industrial optimization.

• The applied modification process increased the 11–32 μm particle fraction for all commercial GAs, contributing to a better-packed particle structure. Such particle packing improvement is expected to positively influence cement hydration kinetics and mechanical performance at later ages.

• No significant differences were observed among commercial GAs in the 32–45 μm fraction, although this fraction was higher in DEG-added cement. After modification, this range decreased significantly, indicating effective refinement of mid-sized particles. Since this reduction is a factor that improves energy efficiency, it suggests that such modifications could be considered for industrial grinding applications.

• The use of GA has increased the PSD slope parameter (n), demonstrating that this could provide an advantage in terms of improving the consistency of cement performance in large-scale production.

• In terms of mean particle diameters, the lowest d₃,₂ and d₄,₃ values for TIPA and DEIPA were achieved with hexanoic acid modifications, while for DEG, the lowest values corresponded to the propanoic acid modification. These results indicate that the optimal modification scheme depends on the base GA structure, underscoring the need for formulation-specific optimization in industrial applications.

This study evaluated the impact of chemically modifying TIPA, DEIPA, and DEG via esterification with organic acids of three different hydrocarbon chain lengths, aiming to enhance their influence on grinding performance and cement properties. In this context, future work is needed to investigate the microstructure and morphological changes, as well as granular imaging of particles, resulting from the organic acid modification procedure.

Author contributions

Y.K.: Formal analysis, Investigation, Writing- Reviewing and Editing; V.K.: Conceptualization, Methodology, Data Curation, Investigation, Writing- Original draft preparation; O.A.: Methodology, Investigation, Writing- Reviewing and Editing; Y.K.: Data Curation, Writing- Reviewing and Editing; A.M.: Conceptualization, Writing- Original draft preparation, Supervision, Project administration, Funding acquisition; K.R.: Data Curation, Writing- Reviewing and Editing; H.E.: Formal analysis, Data Curation, Writing- Reviewing and Editing.

Funding

The authors gratefully acknowledge the support of the Scientific and Technological Research Council of Turkey (TÜBİTAK) under Grant No. 222M245. They also extend their sincere appreciation to the Bursa Uludağ University Science and Technology Centre (BAP) for its support through Grant numbers FBG-2025-2550 and FGA-2025-2048. In addition, the second author wishes to express gratitude to TÜBİTAK for the 2211 A scholarship provided during his doctoral studies.The corresponding author acknowledges the financial support provided by the United Arab Emirates University for covering the Open-Access Article Processing Charge.

Data availability

All data used to generate the results and findings are presently available in the manuscript.

Declarations

Competing interests

The authors declare no competing interests.