Calculated Pore Size Research Articles

A fundamental model of water retention based on the theory of disjoining pressure of soil water

The article presents a new methodological approach to modeling the soil water retention curve (WRC), based entirely on the Deryagin phenomenon of wedging pressure of water films in relation to the soil physical system. It operates with a variable mass fraction of the liquid phase (soil solution) with the parameters of the concentration and charge of electrolyte ions, the specific surface area of the solid phase, as well as limitations by porosity and the standard potential of a conditionally zero water content in the soil. The new model, validated according to the author’s and independent literature data for soils of various genesis and granulometric composition from sands to clays, showed good agreement with experimental data and a more adequate description of water retention with normalized root-mean-square errors 5-10 times smaller compared with the most common empirical van Genuchten model for describing the WRC. Along with an adequate description of WRC in the entire range from the state of water saturation to conditionally zero water content, the new model makes it possible to analytically calculate pore size distributions, estimate the generalized Hammaker constant for interphase molecular interactions of liquid and solid phases of soil, the Debye thickness of the double electric layer and the specific surface area of the solid phase of soil, alternatively to the standard BET method.

Bifunctional luminescent conjugated microporous polymers containing BODIPY and tetraphenylethene units for highly efficient energy storage and enhanced sensing of Cu2+ ions

Here, using the Sonogashira coupling technique, a new fluorescent tetraphenylethene (TPE) and borondipyrromethene (BODIPY)-based CMP (TPE-BODIPY-CMP) was built and developed for usage in supercapacitors and Cu2+ ion detection. XPS, ssNMR, and FTIR techniques were used to validate the presence of the functional groups, aromatic carbons, and atoms [Si, B, C, N, O, and F] in the TPE-BODIPY-CMP framework. In the TPE-BODIPY-CMP, the calculated pore size, SBET, and carbon residue were 1.52–2.82 nm, 300 m2 g−1, and 67%, respectively. as per our electrochemical test, the capacitance stability [83.23% after 5000 cycles], and specific capacity of 176 F g−1 (0.5 A g−1) for TPE-BODIPY-CMP. We performed photoluminescence (PL) experiments on TPE-BODIPY-CMP to evaluate its capacity in cation detection [Cu2+, Pb2+, Al3+, Cr3+, Ni2+, Ce3+, Mg2+, Hg2+, Fe3+, Fe2+, Zn2+, and Ag+] and a limit of detection (LOD) of TPE-BODIPY-CMP toward Cu2+ ions was 2.5 × 10−7 M.

Information-Analytical Software for Developing Digital Models of Porous Structures’ Materials Using a Cellular Automata Approach

An information-analytical software has been developed for creating digital models of structures of porous materials. The information-analytical software allows you to select a model that accurately reproduces structures of porous materials—aerogels—creating a digital model by which you can predict their properties. In addition, the software contains models for calculating various properties of aerogels based on their structure, such as pore size distribution and mechanical properties. Models have been implemented that allow the description of various processes in porous structures—hydrodynamics of multicomponent systems, heat and mass transfer processes, dissolution, sorption and desorption. With the models implemented in this software, various digital models for different types of aerogels can be developed. As a comparison parameter, pore size distribution is chosen. Deviation of the calculated pore size distribution curves from the experimental ones does not exceed 15%, which indicates that the obtained digital model corresponds to the experimental sample. The software contains both the existing models that are used for porous structures modeling and the original models that were developed for different studied aerogels and processes, such as the dissolution of active pharmaceutical ingredients and mass transportation in porous media.

Primary drainage and waterflood capillary pressures and fluid displacement in a mixed-wet microporous reservoir carbonate

A porous plate technique was developed to measure capillary pressure during both primary drainage and waterflooding in a reservoir carbonate rock sample. During primary drainage, a water-wet ceramic disc at the end of the sample allowed brine to be displaced but prevented the escape of oil while oil was injected at a sequence of increasing pressures. Saturation was measured using high-resolution three-dimensional X-ray imaging from the differences in greyscale (X-ray adsorption) between dry, partially-saturated and completely-saturated images. A two-step displacement process was observed, with the resolvable macro-pores displaced by oil followed by invasion into unresolved micro-porosity with a variation of two orders of magnitude in capillary pressure. The sample was then exposed to crude oil to render some of the solid surfaces oil-wet. A small amount of spontaneous imbibition (displacement at a positive capillary pressure) was observed in micro-porosity. Then an oil-wet porous plate was added to the outlet, so that water could be injected at a sequence of increasing pressures while only oil could escape. As expected, the oil-wet macro-porosity was displaced by brine at a low capillary pressure with a magnitude similar to that seen during drainage (but of opposite sign). Remarkably though the displacement of oil from micro-porosity occurred at a capillary pressure approximately an order of magnitude lower than in drainage, implying the existence of mixed-wettability with fluid menisci that are approximately minimal surfaces. The work demonstrates that in mixed-wet media displacement of oil from micro-porosity can occur at much lower capillary pressures that would be estimated from primary drainage results using the calculated pore size distribution.

Pore size distribution measurement with magnetic resonance [formula omitted] distributions outside the fast diffusion regime

Based on Brownstein-Tarr (BT) theory, a new method is proposed to determine the pore size distribution which is an important petrophysical property in studying fluid storage and fluid transport in reservoir rocks. For reservoir rocks with large pores, or high surface relaxivity, direct conversion from the magnetic resonance (MR) T2 distribution with the fast diffusion assumption may be unreliable. In this study, the ground mode lifetime T20 distribution was proposed to be utilized to estimate the pore size distribution. The T20 lifetime of large pores within a porous system can be determined directly through experiment. However, the T20 lifetimes of smaller pores may overlap with the first nonground mode T21 lifetimes of the larger pores, which collectively contribute to the MR signal with a shorter lifetime. To accurately determine the T20 lifetime of smaller pores, it is essential to remove the contribution to the distribution of the T21 lifetimes of the larger pores. The T21 distribution can be both experimentally observed and calculated through the proposed method. The proposed pore size distribution method is verified by calculation in the present work. Water-saturated glass bead packs were employed for initial experiments. The calculated pore size, and its distribution, match the geometric pore size. The proposed method was applied to determine the pore size distribution of a Berea sandstone. The results are in good agreement with SEM measurements.

Pyrene‐Based Polyimide Covalent Organic Framework with Temperature‐Dependent Fluorescence

AbstractThe synthesis of a fluorescent covalent organic framework (COF) using perylene and pyrene building blocks (PEPy‐COF), via a one‐pot condensation reaction is reported. PEPy‐COF is crystallized into 2D nanosheets with a cubic and prismatic crystalline morphology and demonstrates structural stability at temperatures up to 500 °C. The structural morphology is confirmed using X‐ray diffraction and atomic‐level simulations. These 2D porous polymer sheets form a tetragonal framework that is found to have a high specific surface area of 772 m2 g−1. Based on the definition of porous materials, the network is mesoporous with an observed pore size of 3.03 nm, which is in good agreement with the material's calculated pore size. The experimentally obtained HOMO‐LUMO band gap is 2.62 eV, confirming the semiconducting nature of PEPy‐COF. PEPy‐COF emits a shiny blue luminescence under UV and visible light. This luminescence intensity is temperature‐dependent in solvents with different polarities and dielectric constants demonstrating that the PEPy‐COF has potential use in a wide range of temperature‐sensing devices. The fluorescence intensity ratio is similar for different temperatures under ultra‐sound conditions and varying solvents.

An adsorption model for cylindrical pore and its method to calculate pore size distribution of coal by combining NMR

Coalbed methane (CBM) adsorption is closely related to pore size distribution in coal, the study of its adsorption state and pore characteristics of coal are of great significance to its exploitation and storage. In this paper, an extended simplified local density adsorption (SLD) model is proposed, which can be applied to cylindrical pores. Combining with the nuclear magnetic resonance (NMR) tests, the extended SLD model can predict the adsorption amount and pore size distribution of the whole sample without destroying its original pore structure. Three coal samples collected from different areas are selected for NMR test to measure T2 distribution and Magnetic Resonance Imaging (MRI) image. Then, the adsorption amount of the samples are obtained under constant temperature and different pressures. The fitting coefficients of the extend SLD model and experimental data of the three samples are all greater than 0.99, indicating that the proposed model matches the experimental results well. The two parameters obtained by fitting, transverse surface relaxivity (K) and the total number of pore (N), combined with T2, can get the radius and number of each pore in the sample. The inversion results show that the number summation of micropores and mesopores of the three samples are all exceeds 99%. However, due to the small pore size of micropores and mesopores, the pore volume summation of the three coal samples occupied by fractures and macropores are all over 27%. Further observation of cylindrical pore size and fluid molecular position shows that the distance between fluid-solid molecules is the main factor affecting the adsorption. The results of this paper are beneficial to predict and calculate the adsorption amount and pore size distribution of coal.

Pore Size Dependence of Permeability in Bicontinuous Nanoporous Media.

In this work, we employ many-body dissipative particle dynamics (mDPD) simulations to investigate the fluid flow process through bicontinuous nanoporous media, which are representative models for a broad class of nanoporous materials. The mDPD formulation includes attractive and repulsive interactions describing accurately fluid-fluid and fluid-solid interactions. As a mesoscale simulation method, mDPD can bridge the length and time scale gap between continuum and atomistic simulations. The bicontinuous nanoporous models are constructed considering a defined morphology, the porosity level, and varying pore sizes in the range from 3.41 to 13.63 nm. All models have a 0.65 porosity level and the same topology. The models provide a stochastic description of the morphology and pore size distribution and allow for a direct investigation of the dependence of permeability on the average pore size. The stationary nanoporous models are filled with fluid particles, and flow is induced by the action of confining pistons. Simulation results, obtained by imposing different pressure differences on the surfaces of the nanoporous media, indicate a linear pressure drop within the nanoporous model. Regardless of the complexities and different scales of the porous media considered, the steady-state fluid flow through the nanoporous models is proportional to the pressure gradient applied, in agreement with Darcy's law. The calculated pore size dependence of permeability is well described by the Hagen-Poiseuille law, considering a single shape correction factor that accounts for the flow resistance due to the complex nanoporous morphology. This work highlights the effect of the average pore size of a complex stochastic bicontinuous nanoporous medium on fluid properties. The results indicate rather a relatively simple dependence of permeability on the average pore size. The novel method we employ to generate the stochastic bicontinuous nanoporous structure allows the control of different geometric features that can be explored in future studies.

Study on Porosity in Zinc Oxide Ultrathin Films from Three-Step MLD Zn-Hybrid Polymers.

Deriving mesoporous ZnO from calcinated, molecular layer deposited (MLD) metal-organic hybrid thin films offers various advantages, e.g., tunable crystallinity and porosity, as well as great film conformality and thickness control. However, such methods have barely been investigated. In this contribution, zinc-organic hybrid layers were for the first time formed via a three-step MLD sequence, using diethylzinc, ethanolamine, and maleic anhydride. These zinc-organic hybrid films were then calcinated with the aim of enhancing the porosity of the obtained ZnO films. The saturation curves for the three-step MLD process were measured, showing a growth rate of 4.4 ± 0.2 Å/cycle. After initial degradation, the zinc-organic layers were found to be stable in ambient air. The transformation behavior of the zinc-organic layers, i.e., the evolution of the film thickness and refractive index as well as the pore formation upon heating to 400, 500, and 600 °C were investigated with the help of spectroscopic ellipsometry and ellipsometric porosimetry. The calculated pore size distribution showed open porosity values of 25%, for the sample calcinated at 400 °C. The corresponding expectation value for the pore radius obtained from this distribution was 2.8 nm.

PorE: A code for deterministic and systematic analyses of porosities.

Accurate numerical calculations of porosities and related properties are of importance when analyzing metal-organic frameworks (MOFs). We present porE, an open-source, general-purpose implementation to compute such properties and discuss all results regarding their sensitivity to numerical parameters. Our code combines the numerical efficiency of Fortran with the user-friendliness of Python. Three different approaches to calculate porosities are implemented in porE, and their advantages and drawbacks are discussed. In contrast to commonly used implementations, our approaches are entirely deterministic and do not require any stochastic averaging. In addition to the calculation of porosities, porE can calculate pore size distributions and offers the possibility to analyze pore windows. The underlying approaches are outlined, and pore windows are discussed concerning their impact on the analyzed porosities. Comparisons with reference values aim for a clear differentiation between void and accessible porosities, which we provide for a small benchmark set consisting of eight MOFs. In addition, our approaches are used for a bigger benchmark set containing 370 MOFs, where we determine linear relationships within our approaches as well as to reference values. We show how these relationships can be used to derive corrections to a give porosity approach, minimizing its mean error. As a highlight we show how complex workflows can be designed with a few lines of Python code using porE.

Experimental Research on Durability of Fly Ash Pavement Concrete and Mix Proportion Optimization

This paper focused on the optimization of the C40 fly ash concrete pavement, which was considered as a measure to accelerate the consumption of industrial solid wastes such as fly ash, committing to the goal of zero waste. By comparing with three groups of ordinary mix proportion, the performances (e.g., mechanical properties, durability, and brittle property) of the optimized mix proportion were evaluated via multiple mechanical and physical tests. Their air voids’ structure was characterized by the BJH method (a method to calculate pore size described by Barrett, Joyner, and Halenda), and the results were combined with the road performances of concrete to analyze the formation mechanism of high durability of optimized fly ash pavement concrete. As for the experimental results for the optimized, its 28 d compressive strength peaked at 50.8 MPa together with corresponding 28 d flexural strength at 8.2 MPa, which indicated a favorable mechanical performance for wide application in pavement construction. Except for the mechanical properties, the better durability indicators obtained after optimization also provided a more compact pore structure for the optimized. The raw materials and construction technology of the two kinds of pavements were compared. Promoting the use of optimized fly ash pavement concrete can break the situation of the asphalt pavement monopolizing heavy‐haul highway and greatly reduce the industrial wastes which can be used as raw materials in the production of cement, such as blast furnace slag and fly ash. It was proved that the optimized fly ash concrete pavement can be used to replace the asphalt pavement under the premise of achieving the same working performances.

Insights into the estimation of capacitance for carbon-based supercapacitors.

Carbon-based materials are broadly used as the active component of electric double layer capacitors (EDLCs) in energy storage systems with a high power density. Most of the reported computational studies have investigated the electrochemical properties under equilibrium conditions, limiting the direct and practical use of the results to design electrochemical energy systems. In the present study, for the first time, the experimental data from more than 300 published papers have been extracted and then analyzed through an optimized support vector machine (SVM) by a grey wolf optimization (GWO) algorithm to obtain a correlation between carbon-based structural features and EDLC performance. Several structural features, including calculated pore size, specific surface area, N-doping level, ID/IG ratio, and applied potential window were selected as the input variables to determine their impact on the respective capacitances. Sensitivity analysis, which has only been performed in this study for approximating the EDLC capacitance, indicated that the specific surface area of the carbon-based supercapacitors is of the greatest effect on the corresponding capacitance. The proposed SVM-GWO, with an R2 value of 0.92, showed more accuracy than all the other proposed machine learning (ML) models employed for this purpose.

Monte Carlo simulation method for calculating pore size distributions from high-pressure CO2 adsorption in Micro-Mesoporous Carbons

An original methodology is suggested for evaluating the pore size distribution in carbons in the wide range of micro- and mesopores from 0.385 to 10 nm from a single isotherm of high-pressure adsorption of CO2 at 273 K. The proposed method is based on the reference theoretical isotherms calculated by Monte Carlo simulations in model pores of slit and cylindrical geometry. The relationship between the pore size and the pore filling pressure is established. Special attention is given to predicting of the capillary condensation transitions in mesopores by using the meso-canonical ensemble (gauge cell) Monte Carlo simulations. The proposed technique is demonstrated and verified against the conventional N2 and Ar low temperature adsorption methods drawing on the example of micro-mesoporous carbons of the CMK family. Advantages and limitations of CO2 adsorption characterization of nanoporous materials are discussed and further improvements are proposed.

Applications of mercury intrusion capillary pressure for pore structures: A review

The shape, size, and connectivity of porous structures control the overall storage capacity and flow in oil and gas reservoirs. The mercury intrusion capillary pressure (MICP) technique is widely utilized to measure capillary pressure and calculate pore size distribution of core samples in the geo-energy industry. Combining the MICP capillary pressure data with parameters from other experimental methods (such as scanning electron microscopy, and nuclear magnetic resonance) or theoretical approaches (such as fractal theory) can more accurately describe the pore structure of reservoirs. In this paper, the latest advances on the application of primary drainage MICP curves from reservoir porous structures are reviewed in three main aspects: The measurement and calculation of MICP capillary pressure, estimation of pore size distributions making use of fractal characteristics, and determination of permeability. Experimental measurements and numerical simulation methods of MICP capillary pressure with its influencing factors are also discussed. MICP capillary pressure combined with other methods are argued to be one of the main directions for future research on reservoir pore structures. Cited as: Jiao, L., Andersen, P.Ø., Zhou, J., Cai, J. Applications of mercury intrusion capillary pressure for pore structures: A review. Capillarity, 2020, 3(4): 62-74, doi: 10.46690/capi.2020.04.02

Effect of ZO Protein Knockdown on Leak Pathway Pore Size in MDCK Renal Epithelial Cell Populations

The tight junction is the primary barrier to the paracellular movement of water and solutes across epithelial cells (paracellular permeability). Paracellular permeability is divided into two pathways: the Pore Pathway (small solute size, high capacity, charge‐selective) and the Leak Pathway (large solute size, low capacity, charge‐nonselective). Much has been learned about the molecular basis, properties, and regulation of the Pore Pathway. The Leak Pathway is much less well understood. Two basic questions about the Leak Pathway that remain controversial are: 1) does the Leak Pathway have a size limit; and 2) if so, how is the Leak Pathway size limit affected by manipulating specific tight junction proteins. We have initiated an investigation of these two questions by measuring the paracellular permeability of a size range of fluorescein dextrans (4 kDa to 70 kDa) and calculating pore size using the mathematical model, the Renkin sieving equation. In this mathematical model, calculation of pore size is independent of total flux rate, which is also affected by the pore volume fraction and pore length. We first used this approach to examine Leak Pathway permeability in the wild type MDCK renal epithelial cell line. The paracellular movement of all fluorescein dextrans across MDCK cell monolayers was linear with time. The apparent permeability (Papp) decreased with increasing solute Stokes radius. Using the Renkin sieving equation, the Leak Pathway pore size in wild type MDCK cell monolayers was calculated to be ~423 Angstroms. We then examined the effect of knockdown of either of the tight junction‐associated cytoplasmic proteins, ZO‐1 or ZO‐2, on pore size. The paracellular flux rates for all fluorescein dextrans were higher across ZO‐1 knockdown MDCK (ZO‐1 KD) cell populations than across either wild type MDCK cell populations or ZO‐2 knockdown MDCK (ZO‐2 KD) cell populations, which were similar. The paracellular flux of each fluorescein dextran was linear with time across populations of either ZO‐1 KD cells or ZO‐2 KD cells. Papp decreased with increasing Stokes radius for both knockdown cell lines. The calculated pore size for ZO‐2 KD cell populations was similar to that calculated for wild type MDCK cell populations. In contrast, the pore size for ZO‐1 KD cell populations was substantially smaller (~171 Angstroms) than was calculated for wild type MDCK cell populations despite the fact that the total flux rate for all fluorescein dextrans was significantly higher across ZO‐1 KD cell populations. These results indicate that knockdown of ZO‐1 in MDCK cells decreases the Leak Pathway pore size, whereas, knockdown of ZO‐2 does not alter Leak Pathway pore size. In addition, since the flux rate across ZO‐1 KD cell monolayers is higher than across monolayers of the other two cell lines, these results suggest ZO‐1 KD cell populations exhibit either a greater pore volume fraction and/or a shorter pore length than do either wild type MDCK cell populations or ZO‐2 KD cell populations.Support or Funding InformationNYITCOM internal funds

Facile pore size tuning and characterization of nanoporous ceramic membranes for the purification of polysaccharide

Developing nanoporous ceramic membranes with tunable pore structure offers a new paradigm to the precise separation and purification of functional polysaccharides. Here, a facile in-situ chemical deposition method was applied to obtain nanoporous ZrO2 membranes with controllable pore size. A modified rejection curve method based on Poiseuille flow, Ferry's equation, and log-normal distribution was proposed to calculate pore size distribution of membrane. The results showed that with the increase of precursor content from 0 to 20 wt%, the geometric mean diameter of ceramic membranes decreased from 5.9 nm to 3.1 nm, corresponding to a significant decrease of molecular weight cut-off from 15.0 kDa to 3.3 kDa. Still, the pure water permeability was maintained at a high level of about 42 L m−2 h−1·bar−1. Meanwhile, the geometric standard deviation decreased from 1.20 to 1.16, indicating a narrower pore size distribution. The obtained nanoporous ZrO2 membrane performed a high rejection of dextran, while the fructose can be effectively and efficiently separated with a separation factor as high as 11.5, therefore enlarging our choices removing fructose from dextran.

Nuclear magnetic resonance surface relaxivity and its advanced application in calculating pore size distributions

Abstract Both laboratory and downhole nuclear magnetic resonance (NMR) measurements are commonly used to calculate the pore size distribution (PSD) that is important in determining the reservoir storage capacity and evaluating producibility, etc. The surface relaxivity is a key parameter to calculate the PSD using NMR transversal relaxation time (T2) distributions. Accurate surface relaxivity value would result in a reasonable PSD. In order to comprehensively study surface relaxivity, the conventional sandstone, tight sandstone, and shale samples are selected to perform experiments including porosity, permeability, NMR, mercury injection capillary pressure (MICP) and low temperature nitrogen adsorption (LTNA), etc. Three approaches, including LTNA, MICP, and Kozeny's equation, are used to determine the surface relaxivity. We find that for all samples, the surface relaxivity determined with Kozeny's equation is greater than that using LTNA and MICP data, indicating that surface relaxivity of smaller pores is less than that of bigger pores. It is also observed that the surface relaxivity of conventional sandstone is greater than that of tight sandstone and shales. The surface relaxivity of sandstone and shale samples are both affected by clay content. For shale samples, the surface relaxivity ranges from 3.41 μm/s to 9.79 μm/s and is influenced by organic matter contents as well. An equation for predicting surface relaxivity of shale is established. Finally, we propose an advanced method for calculating reasonable PSDs of sandstone and shale formation by the combination of two surface relaxivities, which could be applied to laboratory and field wells.

Artificial neural network enabled capacitance prediction for carbon-based supercapacitors

Carbon is the most widely used electrode for the supercapacitors. This work applies the artificial neural network (ANN) technology to predict the capacitance of carbon-based supercapacitors. For training the ANN model, we extracted data from hundreds of published papers. Moreover, five features were selected to figure out their impact on capacitance, including specific surface area, calculated pore size, ID/IG ratio, N-doping level and voltage window. Then, several carbon-based samples were chosen to evaluate the performance of ANN. As the result, comparing to other machine learning methods, such as linear regression and Lasso, ANN exhibits the best accuracy and adaptability in the capacitance predication.

Determining the Volume-size Pore Space Parameters in the Grinding Wheels

In forming structural and mechanical properties and performance criteria of a grinding wheel, pores are a key player. They are stochastically distributed in the shard of the wheel, have a random size and shape in the limited volume of the wheel shard, which makes it difficult to determine the volume-size parameters of the pore space in the grinding wheel.Experimental and analytical studies of the wheels on the ceramic bond allowed authors to reveal a porosity and pore size dependence on the size of grain, hardness, and structure of wheels, taking into account the type and the quality index of abrasives and also the method of tool modification. It was found that the tool porosity increases with increasing its structure number and decreasing hardness and size of grain.On the basis of obtained experimental data, an equation was compiled that reflects the power relationship between the porosity of a serial standard tool and its structural characteristics. By varying the structural characteristics of wheels, it is possible to determine the optimal porosity required for the grinding process in each concrete case.A comparison of experimental and calculated data on determining porosity of tools with different structural characteristics has shown that the difference in the values of porosity is within the range of 5 ÷ 8 %.Mathematical and statistical processing of experimental data, taking into account the dependence of the pore diameter on structural characteristics of the abrasive tool, allowed us to define a dependence of the pore size on the size of grain and porosity. The pore size grows with increasing size of grains and structure number and decreases with increasing hardness of the abrasive tool. The calculated pore size values differ from those experimentally obtained in the range of 5 – 12% with a confidence probability of 95 %.The presented calculation dependences and experimental data allowed authors to determine the porosity and the pore size of the tool through its GOST-normalized structural characteristics, as well as to make a rational choice of the tool for specified grinding modes and conditions.

Determination of Isosteric Heat of Adsorption by Quenched Solid Density Functional Theory

The heat of adsorption is one of the most important parameters characterizing energetic heterogeneity of the adsorbent surface. Heats of adsorption are either determined directly by calorimetry or calculated from adsorption isotherms measured at different temperatures using the thermodynamic Clausius-Clapeyron equation. Here, we present a method for calculating the isosteric heat of adsorption that requires as input only a single adsorption isotherm measured at one temperature. The proposed method is implemented with either nonlocal (NLDFT) or quenched solid (QSDFT) density functional theory models of adsorption that are currently widely used for calculating pore size distributions in various micro- and mesoporous solids. The pore size distribution determined from the same experimental isotherm is used for predicting the isosteric heat. The QSDFT method has advantages of taking into account two factors contributing to the structural heterogeneity of adsorbents: the molecular level roughness of the surface and the pore size distribution. The method is illustrated with examples of low temperature nitrogen and argon adsorption on selected samples of carbons of different degree of graphitization and MCM-41 mesoporous silicas of different pore size. The isosteric heat predictions from the NLDFT and QSDFT methods are compared against relevant experiments and the results of Monte Carlo (MC) simulations, with good agreement found in the cases where the surface model adequately reflects the pore surface roughness. Analyses with the QSDFT method show that the isosteric heat of adsorption significantly depends of the molecular level roughness of the adsorbent surface, which is ignored in NLDFT and MC models. The proposed QSDFT method with further verification can be used for calculating the isosteric heat as an additional parameter characterizing the adsorbent surface in parallel with routine calculations of the pore size distribution from a single adsorption isotherm.