27Al and 29Si solid-state NMR characterization of calcium-aluminosilicate-hydrate

Calcium silicate hydrate (C-S-H) is the main constituent of hydrated cement paste and determines its cohesive properties. Because of the environmental impact of cement industry, it is more and more common to replace a part of the clinker in cement by secondary cementitious materials (SCMs). These SCMs are generally alumina-rich and as a consequence some aluminum is incorporated into the C-S-H. This may have consequences on the cohesion and durability of the material, and it is thus of importance to know the amount and the location of Al in C-S-H and what the parameters are that control these features. The present paper reports the (29)Si and (27)Al MAS NMR analyses of well-characterized C-A-S-H samples (C-S-H containing Al). These samples were synthesized using an original procedure that successfully leads to pure C-A-S-H of controlled compositions in equilibrium with well-characterized solutions. The (27)Al MAS NMR spectra were quantitatively interpreted assuming a tobermorite-like structure for C-A-S-H to determine the aluminum location in this structure. For this purpose, an in-house written software was used which allows decomposing several spectra simultaneously using the same constrained spectral parameters for each resonance but with variable intensities. The hypothesis on the aluminum location in the C-A-S-H structure determines the proportion of each silicon site. Therefore, from the (27)Al NMR quantitative results and the chemical composition of each sample, the intensity of each resonance line in the (29)Si spectra was set. The agreement between the experimental and calculated (29)Si MAS NMR spectra corroborates the assumed C-A-S-H structure and the proposed Al incorporation mechanism. The consistency between the results obtained for all compositions provides another means to assess the assumptions on the C-A-S-H structure. It is found that Al substitutes Si mainly in bridging positions and moderately in pairing positions in some conditions. Al in pairing site is observed only for Ca/(Si+Al) ratios greater than 0.95 (equivalent to 4 mmol.L(-1) of calcium hydroxide). Finally, the results suggest that penta and hexa-coordinated aluminum are adsorbed on the sides of the C-A-S-H particles.     

Characterization of framework and extra-framework aluminum species in non-hydrated zeolites Y by 27Al spin-echo, high-speed MAS, and MQMAS NMR spectroscopy at B0 = 9.4 to 17.6 T

27Al spin-echo, high-speed MAS (nu(rot) = 30 kHz), and MQMAS NMR spectroscopy in magnetic fields of B0 = 9.4, 14.1, and 17.6 T were applied for the study of aluminum species at framework and extra-framework positions in non-hydrated zeolites Y. Non-hydrated gamma-Al2O3 and non-hydrated aluminum-exchanged zeolite Y (Al,Na-Y) and zeolite H,Na-Y were utilized as reference materials. The solid-state 27Al NMR spectra of steamed zeolite deH,Na-Y/81.5 were found to consist of four signals. The broad low-field signal is caused by a superposition of the signals of framework aluminum atoms in the vicinity of bridging hydroxyl protons and framework aluminum atoms compensated in their negative charge by aluminum cations (delta(iso) = 70 +/- 10 ppm, C(QCC) = 15.0 +/- 1.0 MHz). The second signal is due to a superposition of the signals of framework aluminum atoms compensated by sodium cations and tetrahedrally coordinated aluminum atoms in neutral extra-framework aluminum oxide clusters (delta(iso) = 65 +/- 5 ppm, C(QCC) = 8.0 +/- 0.5 MHz). The residual two signals were attributed to aluminum cations (delta(iso) = 35 +/- 5 ppm, C(QCC) = 7.5 +/- 0.5 MHz) and octahedrally coordinated aluminum atoms in neutral extra-framework aluminum oxide clusters (delta(iso) = 10 +/- 5 ppm, C(QCC) = 5.0 +/- 0.5 MHz). By chemical analysis and evaluating the relative solid-state 27Al NMR intensities of the different signals of aluminum species occurring in zeolite deH,Na-Y/81.5 in the non-hydrated state, the aluminum distribution in this material was determined.     

An investigation of the roles of surface aluminum and acid sites in the zeolite MCM-22

Ammonia adsorption studies reveal that the observed Lewis acidity in the zeolite MCM-22 is derived from at least two types of framework aluminum sites (AlF), that is, octahedral AlF and three-coordinate AlF. Comparative ammonia or trimethylphosphine (TMP) adsorption experiments with MCM-22 confirm that octahedral Al species gives rise to the signal at delta(iso) approximately 0 in the 27Al NMR spectrum; this is a superposition of two NMR signals from the different Al species on the water-reconstructed zeolite surface. A sharp resonance assigned to framework Al reversibly transforms on ammonia adsorption to delta(iso)27Al approximately 55 from tetrahedral AlF, while the broad peak is assigned to nonframework aluminum which results from hydrothermal treatment. This study also demonstrates the effectiveness of 27Al magic angle spinning (MAS) and multiple quantum (MQ) MAS NMR spectroscopy as a technique for the study of zeolite reactions.     

Spectroscopic characterization of natural calcite minerals

The FT-IR, FT-Raman, NMR spectral data of ten different limestone samples have been compared. FT-IR and FT-Raman spectral data show that calcium carbonate in limestone, principally in the form of calcite, as identified by its main absorption bands at 1426, 1092, 876 and 712 cm(-1). The sharp diffractions at the d-spacings, 3.0348, 1.9166 and 1.8796 confirm the presence of calcite structure and the calculated lattice parameters are: a=4.9781 A, c=17.1188 A. The range of 13C chemical shifts for different limestone samples is very small, varying from 198.38 to 198.42 ppm. The observed chemical shifts are consistent with the identical C-O bonding in different limestone samples. 27Al MAS NMR spectra of the samples exhibit a central line at 1 ppm and another line at 60 ppm corresponding to octahedral and tetrahedral Al ions, respectively. The five component resonances were observed in 29Si MAS NMR spectrum of limestone and these resonances were assigned to Si (4 Al), Si (3 Al), Si (2 Al), Si (1 Al) and Si (0 Al) from low field to high field.     

29Si and 27Al MAS NMR spectra of mullites from different kaolinites

Mullites synthesized from four kaolinites with different random defect densities have been studied by 27Al and 29Si magic angle spinning nuclear magnetic resonance spectroscopy (MAS NMR) and X-ray diffraction (XRD). All these mullites show the same XRD pattern. However, 29Si and 27Al MAS NMR spectra reveal that the mullites derived from kaolinites with high defect densities, have a sillimanite-type Al/Si ordering scheme and are low in silica, whereas those mullites derived from kaolinites with low defect densities, consist of both sillimanite- and mullite-type Al/Si ordering schemes and are rich in silica.     

Solid-state NMR spectra of paramagnetic silica-based materials: observation of 29Si and 27Al nuclei in the first coordination spheres of manganese ions

Some silica-based solids, prepared by the sol/gel method in the presence of high Mn2+ concentrations, have been characterized by the 29Si, 27Al MAS NMR spectra and 29Si T1 measurements. The single-pulse 29Si and 27Al MAS NMR spectra have shown broad spinning sideband patterns that are interpreted in terms of anisotropic bulky magnetic susceptibility (BMS) and dipole-field effects. In the absence of paramagnetic isotropic shifts, the 29Si and 27Al nuclei observed in the single-pulse NMR spectra have been assigned to nuclei remote from paramagnetic centers. It has been demonstrated that the 29Si and 27Al nuclei, which are in the vicinity of the manganese ions, can be detected by the Hahn-echo MAS NMR experiments at different carrier frequencies.     

丝光沸石水蒸气/酸浸渍脱铝的多核固体核磁共振研究

采用¹H,²⁹Si,²⁷Al魔角旋转固体核磁共振(MASNMR)及¹H-²⁹Si交叉极化(CP)技术研究丝光沸石水蒸气/酸浸渍脱铝过程中各种铝物质的结构与性质.结果表明,丝光沸石上骨架铝原子在水分子作用下,生成非骨架四配位铝物质[Al(OH)₃(H₂O)],分别在²⁷Al谱δ45和¹H谱δ3.0处出现共振信号,这种铝物质不同于扭曲四配位铝,在高温下进一步水合生成Al(OH)₃(H₂O)₂和Al(OH)₃(H₂O)₃,即非骨架五配位和六配位铝物质.¹H-²⁹SiCP和¹H谱证实,水蒸气脱铝使丝光沸石产生了大量的硅羟基和铝羟基.     

Characterization of silica-pillared derivatives from aluminum-containing kanemite

A series of aluminum-containing kanemite (Al-kanemite) samples with several Si/Al molar ratios were synthesized. The Al-kanemite samples were pillared with silica. X-ray diffractograms showed that the layered structure of the Al-kanemite samples was maintained at Si/Al= infinity approximately 10 but was broken at Si/Al = 5, 2.5, and 1. 29Si MAS NMR spectra of the Al-kanemite samples, except for that of Si/Al = 1, mainly showed peaks of Q(3) sites, which were attributed to Si(OSi)(3)(OH) groups, although peaks assigned to Si(OAl)(OSi)(2)(OH) were also seen. The 27Al MAS NMR spectra indicated that the Al-kanemite samples had only four-coordinate aluminum atoms. The FTIR spectra of pyridine adsorbed on the pillared Al-kanemite derivatives revealed Lewis acid sites on the surface. The nitrogen adsorption isotherms of the derivatives were classified as type I (Langmuir) absorption isotherms. Using the alpha(s) method, the specific surface areas of the derivatives were 572-756 m(2)g(-1), and the pore sizes were calculated as 1.25-1.83 nm. The pillared Al-kanemite derivatives had slit-shaped micropore structures.     

29Si chemical shift anisotropies in calcium silicates from high-field 29Si MAS NMR spectroscopy

29Si chemical shift anisotropy (CSA) data have been determined from (29)Si MAS NMR spectra recorded at 14.1 T for a number of synthetic calcium silicates and calcium silicate hydrates. These are beta- and gamma-Ca(2)SiO(4), Ca(3)SiO(4)Cl(2), alpha-dicalcium silicate hydrate (alpha-Ca(2)(SiO(3)OH)OH), rankinite (Ca(3)Si(2)O(7)), cuspidine (Ca(4)Si(2)O(7)F(2)), wollastonite (beta-Ca(3)Si(3)O(9)), pseudowollastonite (alpha-Ca(3)Si(3)O(9)), scawtite (Ca(7)(Si(6)O(18))CO(3).2H(2)O), hillebrandite (Ca(2)SiO(3)(OH)(2)), and xonotlite (Ca(6)Si(6)O(17)(OH)(2)). The (29)Si MAS NMR spectra of rankinite and wollastonite clearly resolve manifolds of spinning sidebands from two and three Si sites, respectively, allowing the CSA parameters to be obtained with high precision for each site. For the (29)Si Q(1) sites in rankinite and cuspidine, the CSA asymmetry parameters (eta(sigma) approximately 0.6) contrast the general expectation that sorosilicates should possess small eta(sigma) values as a result of the nearly axially symmetric environments of the SiO(4) tetrahedra. The (29)Si CSA parameters provide an improved insight into the electronic and geometric environments for the SiO(4) tetrahedra as compared to the values solely for the isotropic chemical shift. It is shown that the shift anisotropy (delta(sigma)) and the CSA asymmetry parameter (eta(sigma)) allow a clear distinction of the different types of condensation of SiO(4) tetrahedra in calcium silicates. This relationship may in general be valid for neso-, soro-, and inosilicates. The CSA data determined in this work may form a valuable basis for (29)Si MAS NMR studies of the structures for tobermorites and calcium silicate hydrate phases resulting from hydration of Portland cements.     

Direct solid-state NMR spectroscopic evidence for the NH4AlF4 crystalline phase derived from zeolite HY dealuminated with ammonium hexafluorosilicate

Multinuclear (1)H, (19)F, and (27)Al MAS (magic angle spinning) and corresponding 2D HETCOR (heteronuclear correlation) NMR spectroscopy, in combination with powder XRD measurements, provide the direct evidence for the NH(4)AlF(4) crystalline phase, which was formed from zeolite HY dealuminated with an aqueous (NH(4))(2)SiF(6) solution at 80 degrees C. The NH(4)AlF(4) crystalline phase exhibits a characteristic second-order quadrupolar-induced (27)Al NMR line shape spreading from 0 to -90 ppm (in a magnetic field of 11.7 T) and two (19)F resonances at -151 and -166 ppm in the (19)F NMR spectrum. An( 27)Al quadrupolar coupling constant (C(Q)) of 9.5 MHz and an asymmetry parameter (eta) of 0.1 were identified, for the first time, for the NH(4)AlF(4) crystalline phase observed. On the basis of the (19)F{(27)Al} TRAPDOR (transfer population in double resonance) NMR results, the (19)F resonances at -151 and -166 ppm are therefore assigned to (19)F spins associated with the fluorines in the terminal Al-F and the bridging Al-F-Al groups, respectively.     

Solid-state NMR identification and quantification of newly formed aluminosilicate phases in weathered kaolinite systems

The weathering of a specimen kaolinite clay was studied over the course of 369 d via solid-state 29Si magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy and high-field 27Al MAS NMR. The chosen baseline solution conditions (0.05 mol kg-1 of Al, 2 mol kg-1 of Na+, 1 mol kg-1 of NO3-, 1 mol kg-1 of OH-, and pH approximately 13.8) approximate those of solutions leaking from waste tanks at the Hanford Site in Richland, WA. Nonradioactive Cs and Sr cations were added to this synthetic tank waste leachate (STWL) solution at concentrations of 10(-3), 10(-4), and 10(-5) molal (m) to represent their radionuclide counterparts. The transformations of silicon- and aluminum-containing solid phase species were monitored quantitatively by using NMR spectroscopy, with the resulting spectra directly reporting the influence of the initial Cs and Sr on formation and transformation of the neo-formed solids. At the lowest concentration of Cs and Sr employed (10(-5) m in each cation) peaks consistent with the formation of zeolite-like minerals were detected via 29Si and 27Al MAS NMR as early as 33 d. At concentrations of 10(-3) m in each cation, new silicon species are not detected until 93 d, although neophases containing four-coordinate aluminum were detectable at earlier reaction times via 27Al MAS NMR. At the highest magnetic field strengths employed in this NMR study, deconvolutions of resonances detected in the tetrahedral region of the 27Al MAS spectra yielded multiple components, indicating the existence of at least four new aluminum-containing phases. Two of these phases are identified as sodalite and cancrinite through comparison with diffuse-reflectance infrared (DRIFT) spectra and powder X-ray diffraction (XRD) results, while a third phase may correlate with a previously detected aluminum-rich chabazite phase. All measurable solid reaction products have been quantified via their 27Al MAS resonances acquired at high magnetic field strengths (17.6 T), and the quantitative nature of the 27Al NMR data shows that cancrinite growth increases while sodalite reaches a steady state with respect to total aluminum in the solid phases. The data also relate the coupling of Cs sorption to the ripening of feldspathoid phases in this heterogeneous system as a function of time, and illustrate the important influence of co-contaminants on the environmental reaction kinetics studied here.     

Structural characterization of moganite-type AlPO4 by NMR and powder X-ray diffraction

Structural characterization of a new high-pressure AlPO(4) phase synthesized at 5 GPa and 1500 °C is reported. The phase is monoclinic (P2/a) with a = 8.7437(1) ?, b = 4.8584(1) ?, c = 10.8600(2) ?, β = 90.124(1)° (Z = 6). (31)P MAS NMR and two-dimensional (2D) (27)Al triple-quantum (3Q) MAS NMR revealed that it contains two tetrahedral P sites of 1:2 abundance ratio, and two tetrahedral Al sites with 1:2 ratio. 2D (31)P dipolar-recoupled double-quantum (DQ) MAS NMR and (27)Al → (31)P dipolar-based (through-space) and J coupling-based (through-bond) 3Q-heteronuclear correlation (HETCOR) experiments provided direct information on the linkages of these sites. The crystal structure was solved and refined from synchrotron powder X-ray diffraction data utilizing the information from NMR. The phase is isostructural to moganite, a rare SiO(2) polymorph, and its structure can be derived from the latter via an ordered replacement of tetrahedral Si sites by Al and P. The NMR parameters of the phase were also calculated by first-principles method, which are consistent with those observed. Contrary to the other moganite phases known to date (i.e., SiO(2) and PON), moganite-AlPO(4) has a higher-pressure stability field than the corresponding quartz phase. This is the first moganite-type phase found in the ABX(4) system.     

Anisotropic NMR interaction tensors in the decamethylaluminocenium cation

Solid-state NMR experiments, analytical and numerical simulations of solid NMR powder patterns, ab initio self-consistent field and hybrid density functional theory calculations, and single-crystal X-ray diffraction are used to characterize the molecular structure and anisotropic NMR interaction tensors in the bis(pentamethylcyclopentadienyl)aluminum cation, [Cp(2)Al](+). This highly symmetric main group metallocene has a structure analogous to that of ferrocene and the cobaltocenium cation. The single-crystal X-ray diffraction structure is reported for [Cp(2)Al][AlCl(4)]. Solid-state (27)Al[(1)H] magic-angle spinning and static NMR experiments are used to study the aluminum chemical shielding and electric field gradient tensors, revealing axial symmetry in both cases with a large chemical shielding span of Omega = 83(3) ppm and a small nuclear quadrupole coupling constant, C(Q)((27)Al) = 0.86(10) MHz. Carbon-13 CPMAS NMR experiments in combination with ab initio calculations and simulations of the effects of chemical exchange on (13)C static powder patterns reveal dynamic rotation of rings and suggest a low internal rotational barrier for this process. Theoretical computations of interaction tensors using the Gaussian 98 and Amsterdam Density Functional software packages are in good agreement with experiment and lend insight into the molecular origin of these NMR interactions. Orientations of the NMR tensors determined from theory, the large chemical shielding span, and the very small value of C(Q)((27)Al) can all be rationalized in terms of the high molecular symmetry.     

Formation of small pore SAPO-44 type molecular sieve

The hydrothermal transformation of silico–aluminophosphate gel with cyclohexylamine to SAPO-44 has been examined. The hydrothermal crystallisation products of the SAPO have been investigated by X-ray diffraction, FTIR, nitrogen and water adsorption, thermogravimetric analysis, surface analysis and ²⁷Al, ³¹P, and ²⁹Si MAS NMR. Structural changes were observed in the silico–aluminophosphate gel with and without organic template and during the hydrothermal crystallisation. The silico–aluminophosphate gel converted to pure SAPO-CHA phase in 168 h at 473 K. The surface of SAPO-44 was silicon rich as compared with that of SAPO-34 and SAPO-18. The ²⁷Al MAS NMR signal of tetrahedrally coordinated Al observed in the silico–aluminophosphate gel without the organic template was changed to octa-, penta- and tetrahedrally coordinated aluminium upon the addition of the cyclohexylamine template to the SAPO gel. After 3 h of hydrothermal treatment at 473 K however, the ²⁷Al MAS NMR signals of the octahedral and pentacoordinated aluminium were removed. This was also confirmed by ³¹P and ²⁹Si MAS NMR. The tetrahedrally coordinated P and Si were detected within 3 h at 473 K. The sorption capacity and adsorption–desorption trends of the SAPO gels and the crystallisation products were found to be different. ²⁹Si MAS NMR results indicated that the percentage of Si (4Al) and its distribution were significantly affected by the crystallization period. SAPO-44 was thermally stable up to 973 K with phase change observed over the calcination temperature of 1193 K. The SAPO gels and the crystallisation products have also been investigated for their catalytic behaviour in n-hexane and ethanol conversion reactions.     

29Si NMR study of structural ordering in aluminosilicate geopolymer gels

A systematic series of aluminosilicate geopolymer gels was synthesized and then analyzed using 29Si magic-angle spinning nuclear magnetic resonance (MAS NMR) in combination with Gaussian peak deconvolution to characterize the short-range ordering in terms of T-O-T bonds (where T is Al or Si). The effect of nominal Na2O/(Na2O + K2O) and Si/Al ratios on short-range network ordering was quantified by deconvolution of the 29Si MAS NMR spectra into individual Gaussian peaks representing different Q4(mAl) silicon centers. The deconvolution procedure developed in this work is applicable to other aluminosilicate gel systems. The short-range ordering observed here indicates that Loewenstein's Rule of perfect aluminum avoidance may not apply strictly to geopolymeric gels, although further analyses are required to quantify the degree of aluminum avoidance. Potassium geopolymers appeared to exhibit a more random Si/Al distribution compared to that of mixed-alkali and sodium systems. This work provides a quantitative account of the silicon and aluminum ordering in geopolymers, which is essential for extending our understanding of the mechanical strength, chemical and thermal stability, and fundamental structure of these systems.     

Formation of single-walled aluminosilicate nanotubes from molecular precursors and curved nanoscale intermediates

We report the identification and elucidation of the mechanistic role of molecular precursors and nanoscale (1-3 nm) intermediates with intrinsic curvature in the formation of single-walled aluminosilicate nanotubes. We characterize the structural and compositional evolution of molecular and nanoscale species over a length scale of 0.1-100 nm by electrospray ionization mass spectrometry, nuclear magnetic resonance spectroscopy ((27)Al liquid-state, (27)Al and (29)Si solid-state MAS), and dynamic light scattering. Together with structural optimization of key experimentally identified species by solvated density functional theory calculations, this study reveals the existence of intermediates with bonding environments, as well as intrinsic curvature, similar to the structure of the final nanotube product. We show that "proto-nanotube-like" intermediates with inherent curvature form in aqueous synthesis solutions immediately after initial hydrolysis of reactants, disappear from the solution upon heating to 95 °C due to condensation accompanied by an abrupt pH decrease, and finally form ordered single-walled aluminosilicate nanotubes. Detailed quantitative analysis of NMR and ESI-MS spectra from the relevant aluminosilicate, aluminate, and silicate solutions reveals the presence of a variety of monomeric and polymeric aluminate and aluminosilicate species (Al(1)Si(x)-Al(13)Si(x)), such as Keggin ions [AlO(4)Al(12)(OH)(24)(H(2)O)(12)](7+) and polynuclear species with a six-membered Al oxide ring unit. Our study also directly reveals the complexation of aluminate and aluminosilicate species with perchlorate species that most likely inhibit the formation of larger condensates or nontubular structures. Integration of all of our results leads to the construction of the first molecular-level mechanism of single-walled metal oxide nanotube formation, incorporating the role of monomeric and polymeric aluminosilicate species as well as larger nanoparticles.     

Methane dehydrogenation and aromatization in the absence of oxygen on Mo/HZSM-5: A study on the interaction between Mo species and HZSM-5 by using Al and Si MAS NMR

By using a high-resolution solid state nuclear magnetic resonance spectrometer with ²⁷Al and ²⁹Si probes, the interaction between Mo species and HZSM-5 of frsol|Mo/HZSM-5 catalysts has been studied. The results show that there is a strong interaction between Mo species and HZSM-5 zeolite. The framework aluminum in the zeolite can be easily extracted by the introduction of Mo species. The extractability of framework aluminum by Mo species increases with increasing Mo loading and the calcination temperature. The extraction process leads to the formation of non-framework Al at first and then a new crystalline phase of Al₂(MoO₄)₃. The dealumination of the catalyst having a Mo loading of 15% and had been calcined at 973 K is so severe that all the aluminum in the framework are extracted and no framework Al could be detected by ²⁷Al MAS NMR. The catalyst, therefore, lost its catalytic activity for methane dehydrogenation and aromatization in the absence of oxygen. The Si/Al ratio measured from ²⁹Si MAS NMR further confirms the dealumination process observed by ²⁷Al MAS NMR. The MAS NMR results give us an evidence that Al₂(MoO₄)₃ crystallites are much less active for the reaction.     

直接法合成ZSM—5型分子筛的物理化学表征

用高分辨~(29)Si、~(27)Al和~(23)Na NMR对直接法合成的不同硅铝比ZSM-5型分子筛局域结构作了表征,用~(29)Si和~(27)Al魔角旋转核磁共振研究了经不同温度水蒸气处理ZSM-5型分子筛的骨架脱铝,对不同条件下ZSM-5型分子筛中发生的正交-单斜晶型变化进行了系统的X射线衍射实验研究。     

焙烧对HZSM－5分子筛结构的影响

运用魔角自转固态核磁共振谱（ＭＡＳ－ＮＭＲ），研究了焙烧对ＨＺＳＭ－５分子筛结构的影响．结果表明，高温焙烧将引起ＨＺＳＭ－５分子筛骨架的脱铝，当焙烧温度从５００℃增加到７００℃时，ＨＺＳＭ－５的骨架Ｓｉ／Ａｌ比由１６．７增加至２２．７；而当焙烧温度由７００℃到８００℃时，骨架Ｓｉ／Ａｌ比则由２２．７增加到了４８．５．２７Ａｌ－ＭＡＳＮＭＲ结果表明，从骨架上脱下来的铝，部分地形成了ＮＭＲ不可见的无定形态．随着焙烧温度的升高，ＮＭＲ不可见铝增多