), detrital minerals (quartz, feldspar, etc. The experimental data support provided by State Key Laboratory of Oil and Gas Reservoir Geology and Exploration is gratefully acknowledged. Pitfalls and limitations in gas adsorption data analysis, Microporous and Mesoporous Materials, vol. A Step-shaped water adsorption isotherm indicates that water can be uptake and released in a relatively small temperature and pressure difference, potentially leading to an energy-efficient ad-/desorption process. Unfortunately, the majority of adsorption equations are developed based on only one kind of adsorption mechanism, and they can be categorized into three aspects: monolayer adsorption, multilayer adsorption, and micropore filling. When relative pressure reaches initial capillary condensation pressure (usually around 0.4 ), adsorption-desorption curve forms hysteresis loop, which demonstrates that capillary condensation exists in the process of nitrogen adsorbed on shale. Near the saturated vapour pressure, capillary condensation occurs due to the size of the mesopores. Because the Langmuir equation describes adsorption on homogeneous surface, Gaussian energy distribution is used to adjust monolayer adsorption theory to heterogeneous surface [2022]. Focusing on the value of in shale adsorption isotherm and the shape of adsorption isotherm curve, we figure out that the curve becomes gradually convex as the value of increases, as shown in Figure 6(b). 103106, 1966. There seems to be a consensus that sorption-induced swelling in such nanoporous polymers governs sorption hysteresis. 53, no. Capillary condensation and adsorption of binary mixtures. Many researches have been done to find and modify adsorption equations suitable for describing methane adsorption. [3], Bell, L.N., and Labuza, T.P. () Variable in shale adsorption isotherm is related to shape of adsorption curve due to adsorption heat. Would you like email updates of new search results? Thus, must be larger than 0, and then we can obtain . E. Besedov, D. Bobok, and E. Besedov, Single-component and binary adsorption equilibrium of 1,2 dichloroethane and 1,2 dichloropropane on activated carbon, Petroleum & Coal, vol. activity was improved by increasing the reforming temperature from It can be seen from Fig. Thereafter, Langmuir adsorption isotherm is a case of BET adsorption isotherm, in which the pressure is much lower than saturated vapor pressure. 8 The starting point of the DD-model is the idea that primarily adsorbed water clusters A S around the functional group S partially detach according to the equilibrium A S A + A -S The capillary condensation, based on a. . 66096616, 2011. Moreover, heterogeneity of adsorbent surface has been taken into account, and an adsorption equation was built to express the relationship between equilibrium concentration and mass of adsorbate by combining Freundlich adsorption isotherm with Langmuir adsorption isotherm [42, 43]. In the aspect of pore size distribution analysis, the minimum pore volume is 0.0001cc/g (STP), and the pore size range is 0.35~400nm. Adsorption hysteresis is a term which is used when the desorption isotherm curve does not coincide with the adsorption isotherm curve, as shown in Fig. Condensation, melting and freezing of nitrogen in a powder of mesoporous silica grains (SBA-15) has been studied by combined volumetric sorption isotherm and scanning calorimetry measurements. 16, no. 16891705, 1997. Thus, set heat of adsorption between subsequent adsorbates as . The coefficient and exponent of relative pressure are variable fitting parameters in the new shale adsorption isotherm expressed as follows:A, B are undetermined coefficients; M, N, K are undetermined exponent. Laplace equation can provide the explanation. In terms of monolayer adsorption, Langmuir equation will be an appropriate choice. 4, pp. 22482256, 2016. Usually, Langmuir isotherm is a monolayer adsorption model for ideal interfaces; BET (Brunauer, Emmett, Teller) adsorption isotherm is a multilayer adsorption model based on specific assumptions; Freundlich isotherm is an empirical equation widely applied in liquid phase adsorption. 9, pp. 4 with j = 2 and q s,i = q s,j ) plus the Kelvin equation (Eq. This illustrates that the generated shale adsorption isotherm can express the difference of heat of adsorption released between different shale samples. powered by i 2 k Connect. According to the research by Kondou et al. All terms used in the equations are defined in the nomenclature section. 1526, 2015. This relationship between water activity and moisture content at a given temperature is called the moisture sorption isotherm. 1, pp. Therefore, adsorption isotherms for homogeneous adsorbents and empirical isotherms may not apply to shale. 3342, 2017. . Pieiro, P. Brocos, A. Amigo, J. Gracia-Fadrique, and M. G. Lemus, Extended Langmuir isotherm for binary liquid mixtures, Langmuir, vol. K. Jessen, G.-Q. 341362, 2013. The value of is bigger, and the heat of adsorption is larger, which indicates that strength of interaction for adsorption is larger and adsorption curve increases more rapidly in low-pressure section shown in Figure 6(a). 13, pp. To extend BET equation to multicomponent adsorption, three kinds of n-component BET equations were proposed considering that adsorbed layers have evaporation-condensation characters for liquid mixture, supposing that the adsorbed layer of gas mixture is an ideal solution according to statistic thermodynamics and assuming gas mixture is immiscible liquid [2831]. This may take some time to load. 2, pp. U. Kuila and M. Prasad, Specific surface area and pore-size distribution in clays and shales, Geophysical Prospecting, vol. The absolute adsorption was calculated from the excess adsorption accordingly. 497507, 1931. 691704, 1959. F. Xiong, X. Wang, M. A. Amooie, M. R. Soltanian, Z. Jiang, and J. Moortgat, The shale gas sorption capacity of transitional shales in the Ordos Basin, NW China, Fuel, vol. Capillary condensation can be used in different applications. 45, no. 42614266, 2001. . 3, pp. D. M. Ruthven, Principles of adsorption and adsorption processes, John Wiley & Sons, 1984. Epub 2008 Nov 6. In this paper, for calculating the volume of capillary condensate and of adsorption films in a porous body, an approach based on the theory Examples: Adsorption of Benzene on Iron Oxide (Fe 2 O 3) at 50 0 C and adsorption of Benzene on silica gel at 50 0 C. At lower pressure region the graph is quite similar to Type II. DOI: 10.1039/C39930000724. Differences in adsorption and desorption pathways in capillary are caused by non-uniform pore geometries.From the Kelvin equation it can be seen that as Pv/Psat increases inside a capillary, a flatter interface can be created as the radius of the curvature increases. Adv Colloid Interface Sci. Type IV isotherms are observed on mesoporous surfaces. The adsorption isotherm was deconvoluted into those on the inner and external surfaces using the . Before This Paper. BET and Freundlich adsorption isotherms can be changed to functions which consider relative pressure as an independent variable. Micropore filling is also a common adsorption mechanism, which is introduced on the basis of Polanyi adsorption potential theory [32]. 266, no. Equation (15) can be converted to. The N2 adsorption isotherm of multiwall carbon nanotubes was measured at 77 K. A hump was observed near P/P0 = 0.4 in the adsorption isotherm. etry, adsorption system, operating conditions, heat and kinetic effects, and adsorption equilibrium relationships. Thus, an adsorption equation applicable to describe liquid adsorption is suitable for this adsorption stage. In this paper, for calculating the volume of capillary condensate and of adsorption films in a porous body, an approach based on the theory of surface forces is used. In cylindrical pores capillary condensation occurs due to capillary instability of curved wetting films on a capillary surface, when film thickness grows. On the contrary, it is hard to find an equation to depict low-pressure nitrogen adsorption because of the complicated adsorption mechanism. Firstly, a monolayer forms on the surface of the pores, followed by multilayer formation. Full PDF Package Download Full PDF Package. The capillary condensation theory provides a satisfactory explanation of the phenomenon of adsorption hysteresis, which is frequently observed for porous solids. 13691375, 1995. Fetching data from CrossRef. 5, no. S. Duan, M. Gu, X. In order to express adsorption capacity in same dimension, (5) is converted to, Under experimental conditions, saturated vapor pressure and density of adsorbate are constants. Commun., 1993, 724 BET theory (Brunauer-Emmett-Teller) provides a calculation to describe the physical adsorption of gas molecules on a solid surface. Wang, H.-L. Liu, W. Wei, and J.-H. Fang, Structure characteristics and accumulation significance of nanopores in Longmaxi shale gas reservoir in the southern Sichuan Basin, Journal of the China Coal Society, vol. Please enable it to take advantage of the complete set of features! The humidity control filter including a water-repellency coating having ventilation, a first adsorption layer of a porous . Adsorption and desorption data of shale measured by nitrogen at low temperature (77K) is a fundamental method to analyze pore structure of shale. 1424, 2014. At the right hand side of equation, multiply both numerator and denominator by saturated vapor pressure as, The term can be written as . Variables in shale adsorption isotherm are related to shape of adsorption curve and parameter of heat of adsorption. 2, pp. The water molecules initially adsorb on the shale particle/pore surfaces at low. 1998 Jan 15;197(2):327-33. doi: 10.1006/jcis.1997.5292. The sharp slope increase and the hysteresis (type H1) are associated with capillary condensation and evaporation within the nanopores. . 3, pp. 12, pp. A New Method of Calculating Pore Size Distribution: Analysis of Adsorption Isotherms of N(2) and CCl(4) for a Series of MCM-41 Mesoporous Silicas. 117, 2003. R. Sakurovs, S. Day, S. Weir, and G. Duffy, Application of a modified Dubinin - Radushkevich equation to adsorption of gases by coals under supercritical conditions, Energy & Fuels, vol. 55, no. Capillary condensation will always occur when Pv0 and by increasing the vapor pressure in the given system, more condensation will occur. On the horizontal axis they provide relative humidity or water activity of the air presented to the material. 475499, 2007. By multiplying density of adsorbate () on both sides of (7) one gets. In the case of slit pores, coalescence of wetting films formed on opposite slit surfaces proceeds under the action of attractive dispersion forces. According to the new shale adsorption isotherm equation and the range of variables, we applied Matlab to perform curve fitting of relative pressure versus amount of adsorption for 80 shale samples. At higher pressures, capillary condensation typically occurs, as discussed in the next section. Samples were collected from Yanchang formation (Triassic, Ordos), Pingliang formation (Ordovician, Ordos), Wulalik formation (Ordovician, Ordos), Xujiahe formation (Triassic, Sichuan), Niutitang formation (Cambrian, Sichuan), and Doushantuo formation (Ediacaran, Sichuan). ADSORPTION EQUILIBRIUM The amount of a pure gas absorbed by a unit mass of a given adsorbent is a function of temperature and pressure alone, q f (P,T) where q is the amount of the gas (in cc at STP, grams or mols, etc) per unit amount of the absorbent. In adsorption breakthrough, by using a feed in the capillary condensation range of the isotherm on zeolite 13X, the breakthrough curve showed a shock wave in the low concentration and a proportionate pattern in the high concentration. 3, pp. The adsorption isotherms with ability to illustrate the process of monolayer adsorption, multilayer adsorption, and capillary condensation for 80 shale samples from Ordos Basin and Sichuan Basin are obtained. Occasionally, a set of isotherms are provided on one graph that shows each curve at a different temperature. contrary to the other works which are based on the results of isotherm adsorption. The results of curve fitting are highly accurate. 9338, pp. The evaluation of pore structure plays a critical role in exploring shale gas efficiently. O. Redlich and D. L. Peterson, A useful adsorption isotherm, The Journal of Physical Chemistry C, vol. F. Yang, Z. Ning, R. Zhang, H. Zhao, and B. M. Krooss, Investigations on the methane sorption capacity of marine shales from Sichuan Basin, China, International Journal of Coal Geology, vol. 24732479, 1986. L. Hong et al., Experimental study of mineral composition and brittle characteristics in longmaxi formation of lower silurian, southeast chongqing, Science Technology and Engineering, vol. Read more about how to correctly acknowledge RSC content. Adsorption Isotherm: Adsorption happens when a liquid or gas particle adheres to the surface of an adsorbent, resulting in the formation of an atomic layer on the adsorbate. R. M. Pollastro, D. M. Jarvie, R. J. Hill, and C. W. Adams, Geologic framework of the Mississippian Barnett Shale, Barnett-Paleozoic total petroleum system, Bend arch-Fort Worth Basin, Texas, AAPG Bulletin, vol. Isotherms of capillary condensation are often used to determine the vapor sorption capacity of porous adsorbents as well as the pore size distribution by radii. Furthermore, D-R (Dubinin-Radushkevich) equation, D-A (Dubinin-Astakhov) equation, and S-D-R (supercritical Dubinin-Radushkevich) equation are also used with consideration of methane adsorption as micropore filling [68]. D. M. Jarvie, R. J. Hill, T. E. Ruble, and R. M. Pollastro, Unconventional shale-gas systems: the Mississippian Barnett Shale of north-central Texas as one model for thermogenic shale-gas assessment, AAPG Bulletin, vol. Nitrogen adsorption experiment is one of the significant approaches to analyze pore size structure of shale. In this work, an adsorption isotherm is presented for H 2 O adsorption at 200-350 C and 0.05-4.5 bar partial pressure on molecular sieve (LTA) 3A. 89, no. The "liquid-phase capillary condensation" is defined as capillary phase separation. 2, pp. Application of Langmuir isotherm to nitrogen adsorption isotherm for shale at low relative pressure section. 38, no. For each humidity value, a sorption isotherm indicates the corresponding water content value at a given, constant temperature. T. Li, H. Tian, J. Chen, and L. Cheng, Application of low pressure gas adsorption to the characterization of pore size distribution of shales: An example from Southeastern Chongqing area, China, Journal of Natural Gas Geoscience, vol. DOI: 10.1016/J.SEPPUR.2013.05.020 Corpus ID: 97024590; Water vapor adsorption isotherm expressions based on capillary condensation @article{Liu2013WaterVA, title={Water vapor adsorption isotherm expressions based on capillary condensation}, author={Xiang Jun Liu and Yunguang Shi and Mohammad Ali Kalbassi and Richard Paul Underwood and Ying Liu}, journal={Separation and Purification Technology . Y. S. Ho and G. McKay, Correlative biosorption equilibria model for a binary batch system, Chemical Engineering Science, vol. capillary condensation . A. V. Butler and C. Ockrent, Studies in electrocapillarity. 3739, Chemical Industry Press, Beijing, China, 2006. Acetone vapor adsorption results show NMR chemical-shift changes with time, suggesting initial adsorption into mesopores, followed by diffusion into micropores. 14, no. J Colloid Interface Sci. 8084, 1984. In particular, it demonstrates better performance on depicting nitrogen adsorption isotherm at low temperature. Especially, it has been real-ized that the shape of the equilibrium isotherm greatly influences adsorber dynamics. At equilibrium, the relationship between water content and equilibrium relative humidity of a material can be displayed graphically by a curve, the so-called moisture sorption isotherm. .The sorption isotherm shows the water content at each humidity value, and the water vapor is often expressed as the relative humidity. S. Chen, Y. Zhu, H. Wang, H. Liu, W. Wei, and J. Fang, Shale gas reservoir characterisation: a typical case in the southern Sichuan Basin of China, Energy, vol. According to BDDT (Brunauer-Deming-Deming-Teller) adsorption isotherm classification [50], nitrogen adsorption isotherms of shale belong to type IV (Figure 1), which indicates that adsorption on shale can be divided into three stages: monolayer adsorption, multilayer adsorption, and capillary condensation [5154]. Although capillary condensation theory has devoted to the determination of pore size distribution of mesopores, adsorption studies on regular mesoporous silica such as MCM-41 [1,2] or FSM [ 3,4] pointed that classical capillary condensation theory cannot explain the dependence of the adsorption hysteresis on the pore width. As the membrane is exposed to a certain vapor pressure gradient, adsorption, capillary condensation and surface flow phenomena occur at the same time, during the initial stages of the experiment . The physical and chemical meanings of parameters are figured out and ranges for each parameter are determined, which is used to restrict value of variables in the adsorption isotherm when doing regression analysis to match data from shale samples adsorption experiment. Figure 2. N. D. Hutson and R. T. Yang, Theoretical basis for the Dubinin-Radushkevitch (D-R) adsorption isotherm equation, Adsorption, vol. Because of the complexity of sorption processes, the isotherms cannot be determined explicitly by calculation, but must be recorded experimentally for each product. Accessibility As mentioned above, shale adsorption includes processes of monolayer adsorption, multilayer adsorption, and capillary condensation. Based on the Kelvin equation the flatter interface formed creates a larger pressure drop between the gas and liquid phase compared to the curved meniscus. The isotherm data are in good Expand 408 Save Alert A model to describe adsorption isotherms J. Adolphs, M. Setzer Chemistry 1996 Clipboard, Search History, and several other advanced features are temporarily unavailable. The .gov means its official. There are four stations of the experimental instrument. As a normal method to acquire surface area of shale, multipoint BET method testifies that BET equation can be applied to describe adsorption on shale at certain conditions (usually relative pressure below 0.4 ). Influence of Surface Wettability on Adsorption Isotherms of Water Vapor. Enter the email address you signed up with and we'll email you a reset link. and transmitted securely. capillary walls, which suppresses giant oscillatory behavior expected because of commensurability between atomic-scale confinement and molecule sizes. 10101013, 1963. The crystalline carbon nanotubes having mesopores that are open at one end, with pore width of 4 0.8 nm, were characterized by XRD, XPS, and HRTEM. 1 More Received 6 February 2005 MeSH 30993109, 2013. All three isotherms exhibit capillary condensation and adsorption hysteresis of Type H1, according to the IUPAC classification. 87125, 2008. M. A. Ahmadi and S. R. Shadizadeh, Experimental investigation of a natural surfactant adsorption on shale-sandstone reservoir rocks: Static and dynamic conditions, Fuel, vol. These predictions over the scanning behavior within capillary condensation hysteresis can be used to check whether real materials are made up of independent pores or not. This will happen till Pv is max. The authors also thank Dr. Christine Ehlig-Economides from University of Houston for her guidance and assistance. In this figure four different systems are shown in which Pv/Psat is increasing from left to right. 4b that N2 adsorption and desorption isotherms 225 to 325 C, in terms of the selectivity of C13-C20 hydrocarbons. K. Y. Foo and B. H. Hameed, Insights into the modeling of adsorption isotherm systems, Chemical Engineering Journal, vol. Synthetic applications such as sintering of materials are also highly dependent on bridging effects resulting from capillary condensation. Stencl J. Moisture Sorption Isotherms of Whey Powder Spray in the Temperature Range 10 C-40 C, Adsorption Science and Technology, Paper Number 128 r, (2002). For each humidity value, a sorption isotherm indicates the corresponding water content value at a given, constant temperature. Adv Colloid Interface Sci. For carbon dioxide adsorption, to take into account the monolayer adsorption property, both Langmuir equation and L-F equation are applied to depict variations of the adsorption capacity with pressure [911]. Capillary condensation occurs when the adsorption of a vapour in a capillary (any porous medium) forms drops and consequently a liquid surface with a very small radius of curvature. 4, pp. A generalization of thermodynamic Langmuir isotherm, the proposed model assumes competitive adsorption of multiple adsorbates on adsorbent surface for mixed-gas adsorption equilibria, and it . Tang, and A. R. Kovscek, Laboratory and simulation investigation of enhanced coalbed methane recovery by gas injection, Transport in Porous Media, vol. 992997, 2007. J Colloid Interface Sci. Adsorption isotherms of cyclopentane and nitrogen on a new porous crystalline aluminosilicate from the family MCM-41 are characterized by the volume filling of channels by capillary condensation without hysteresis, which commences in the region prior to the lower closure point at the hysteresis loop. 6, pp. The isotherm has been developed on the basis of experimental data obtained from a thermogravimetric analysis and integrated breakthrough curves. 11, pp. He found that Type II and Type III isotherms require highly porous materials or desiccants, with first monolayer adsorption, followed by multilayer adsorption and finally leading to capillary condensation, explaining these materials high moisture capacity at high relative humidity.[2]. The separated phase is counted as "adsorbed" amount on porous materials. Toggle navigation 2). Shale gas has attracted much attention in United States, China, Canada, and so forth, because of the gas storage mechanism and recovery potential of shale gas reservoirs [1, 2]. Considering methane adsorption as monolayer adsorption, Langmuir equation, L-F (Langmuir-Freundlich) equation, and M-L (modified Langmuir) equation are successfully applied to evaluate methane adsorption [35]. Copyright Clearance Center request page. M. M. Dubinin and V. A. Astakhov, Description of Adsorption Equilibria of Vapors on Zeolites over Wide Ranges of Temperature and Pressure, in Molecular Sieve Zeolites-II, vol. G. L. Aranovich and M. D. Donohue, A New Approach to Analysis of Multilayer Adsorption, Journal of Colloid and Interface Science, vol. Disclaimer, National Library of Medicine 2, pp. As shown in Figure 4, Freundlich isotherm fits the medium-high relative pressure section of nitrogen adsorption on shale, especially relative pressure section after occurrence of capillary condensation. 523533, 2007. From (1) and (2), the coefficient and exponent of pressure in Langmuir and BET adsorption isotherm () correspond to physical and chemical parameters of monolayer and multilayer adsorption. W. F. L. Brown, The joule-thermal effect and the equation of state of gases with non-polar molecules, Russian Journal of Physical Chemistry, vol. 24632479, 1973. D. J. K. Ross and R. M. Bustin, Characterizing the shale gas resource potential of Devonian-Mississippian strata in the Western Canada sedimentary basin: application of an integrated formation evaluation, AAPG Bulletin, vol. T. Guo, Evaluation of highly thermally mature shale-gas reservoirs in complex structural parts of the Sichuan Basin, Journal of Earth Science, vol. For multilayer adsorption, BET adsorption isotherm is a representation of multilayer adsorption model generated by Brunauer, Emmett, and Teller, which assumes the interaction between adsorbate and adsorbent surface is much larger than that between neighboring molecules. 22212295, 1916. S. Kondou, T. Ishikawa, and I. Abe, Adsorption Science (Chinese version), p. 42, Chemical Industry Press, Beijing, China, 2006. Chen, Y.-M. Zhu, H.-Y. The adsorption isotherms, for all samples and the two different analytes used, are of type IV, see for example gure 3(c). 236246, 2017. . O. Franke, G. Schulz-Ekloff, J. Rathousk, J. Strek and A. Zukal, Unable to load your collection due to an error, Unable to load your delegates due to an error. The results of 6 samples are selected randomly and displayed in Figure 5, and the other fitting results are shown in Table 1. 57, Article ID 385471, pp. 11, pp. In fact, most adsorbents are heterogeneous porous media. For outgassing, the pulverized samples were dried and vacuumized at 80C for 12 hours. Such a set of adsorption isotherms is provided in Figure 3 as measured by Dini on a Type V silica gel. Application of BET isotherm to nitrogen adsorption isotherm for shale before capillary condensation. Shale is extremely heterogeneous due to component diversity and structure complexity. 123, pp. In this study, a new nitrogen adsorption isotherm is applied to simultaneously depict monolayer adsorption, multilayer adsorption, and capillary condensation, which provides more real and accurate representation of nitrogen adsorption on shale. A steep capillary condensation step indicates uniform mesopores - narrow pore size distribution. To request permission to reproduce material from this article, please go to the *e-mail: [email protected] Study on the Adsorption of Heavy Metal Ions from Aqueous Solution on Modied SBA-15 Liliana Giraldo a , Juan Carlos Moreno-Pirajn b * a Facultad de Ciencias, Universidad Nacional de Colombia, Bogot, Colombia b Grupo de Investigacin en Slidos Porosos y Calorimetra, Facultad de Ciencias, Universidad Nacional de Colombia, Bogot, Colombia Received: April 23 . 2, pp. Bookshelf "Practical Aspects of Moisture Sorption Isotherm Measurement and Use". Absorption is a phenomenon of filling the pores of a solid with liquid water; it occurs by capillary condensation. J. Toth, State equation of the solid-gas interface layers, Acta Chimica Academiae Scientiarum Hungaricae, vol. We probe a molecular-scale study of adsorbate adsorption via nuclear magnetic resonance (NMR). . 62, no. 490495, 1948. This pore needs to be ignored when using the desorption of N2 isotherm at 77 K because this is not related to the pore condensation on the . On the basis of BDDT (Brunauer-Deming-Deming-Teller) adsorption isotherm classification, nitrogen adsorption belongs to type IV, which indicates that it includes three processes: monolayer adsorption, multilayer adsorption, and capillary condensation. 17, no. Modeling secondary and higher-order isotherms: (a) adsorption isotherm and (b) desorption isotherm. The theory is appropriate for adsorption on solid surfaces with homogeneous chemical properties, which is frequently applied to calculate specific surface area for porous media. 22, pp. 2.1. 6, p. 1024, 1959. Capillary Condensation Adsorption Isotherm for the Gas Molecules Adsorbed on the Porous Adsorbent Composed of 1 Group of Sites Let us assume that the porous adsorbent is composed of a num-ber of capillaries, they are formed of two flat walls, the adsorption occurs both on the free surface and among the capillary walls, and An effect of external capillary condensation onto the felt of compounds with high surface tension was demonstrated for VOC concentrations above 1500 mg m(-3).
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