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1 This article was downloaded by: [UQ Library] On: 11 February 215, At: 19: Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 7295 Registered office: Mortimer House, 37-1 Mortimer Street, London W1T 3JH, UK Click for updates Molecular Simulation Publication details, including instructions for authors and subscription information: On the phase transition in a monolayer adsorbed on graphite at temperatures below the 2D-critical temperature Poomiwat Phadungbut ab, Van T. Nguyen a, D.D. Do a, D. Nicholson a & Chaiyot Tangsathitkulchai b a School of Chemical Engineering, University of Queensland, St. Lucia, QLD 72, Australia b School of Chemical Engineering, Suranaree University of Technology, Nakhon Ratchasima 3, Thailand Published online: 2 Sep 2. To cite this article: Poomiwat Phadungbut, Van T. Nguyen, D.D. Do, D. Nicholson & Chaiyot Tangsathitkulchai (215) On the phase transition in a monolayer adsorbed on graphite at temperatures below the 2D-critical temperature, Molecular Simulation, 1:5-, -5, DOI:./ To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at

2 Molecular Simulation, 215 Vol. 1, Nos. 5, 5, CONFINED FLUIDS On the phase transition in a monolayer adsorbed on graphite at temperatures below the 2D-critical temperature Poomiwat Phadungbut a,b, Van T. Nguyen a, D.D. Do a *, D. Nicholson a and Chaiyot Tangsathitkulchai b a School of Chemical Engineering, University of Queensland, St. Lucia, QLD 72, Australia; b School of Chemical Engineering, Suranaree University of Technology, Nakhon Ratchasima 3, Thailand (Received 1 May 2; final version received August 2) Downloaded by [UQ Library] at 19: 11 February 215 Monte Carlo simulations in the grand ensemble and meso-canonical ensemble in which the adsorbent is connected to a finite reservoir have been used to study adsorption isotherms for monolayer argon adsorption on graphite at temperatures below the 2D-critical temperature in order to elucidate the microscopic details of the 2D-transitions: vapour solid, vapour liquid and liquid solid. An S-shaped van der Waals (vdw) loop was found when a small square surface was used; however, for large square surfaces and rectangular surfaces the isotherms exhibit a vdw-type loop with a vertical segment which indicates the coexistence of two phases separated by a boundary that changes its shape with the loading. This coexistence occurs at the same chemical potential as determined by the mid-density scheme, developed by Do and co-workers (Z. Liu, L. Herrera, V.T. Nguyen, D.D. Do, and D. Nicholson, A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition. Mol Simul. 37(11): , 211; Z. Liu, D.D. Do, and D. Nicholson, A thermodynamic study of the mid-density scheme to determine the equilibrium phase transition in cylindrical pores. Mol Simul. 3(3):19 199, 211). Keywords: argon; graphite; phase transition 1. Introduction Experimentally, the volumetric method is commonly used to obtain isotherms for gas adsorption in porous and nonporous materials.[1] An instrument for volumetric measurements of pure gas adsorption consists basically of a dosing reservoir and an adsorption cell housing solid adsorbent, connected together by an isolation valve. Initially, with the valve closed, a given amount of adsorptive gas is loaded into the dosing reservoir while the adsorption cell is cleaned of any impurities. Next, the valve is opened to allow the adsorptive to enter the adsorption cell and adsorb onto the solid sample; then sufficient time is allowed for the system to reach equilibrium. Therefore, adsorption measurements are carried out in a closed or canonical ensemble (NVT) system. However, many simulation studies of adsorption equilibrium are carried out in the grand canonical ensemble (equivalent to the assumption that the dosing reservoir is infinite and maintained at a constant chemical potential, m). This implies that any deviation from this chemical potential in the adsorption cell will be corrected in a dosing reservoir of infinite volume.[2,3] As a result of this infinite supply of adsorptive, isotherms calculated in the grand ensemble exhibit vertical sections in condensation and evaporation branches at temperatures less than the critical hysteresis temperature. The vertical transition in adsorption and desorption results directly from the large fluctuations (infinite dosing reservoir) that overcome the free energy barrier that separates the dense and rarefied phases. The grand ensemble, with an infinite dosing reservoir, does not therefore describe how the volumetric method is conducted experimentally. To rectify this, a method has been introduced in which the adsorbent cell is attached to a reservoir of finite volume,[,5] to simulate the operation of an actual volumetric experiment. The method is akin to the gauge cell Monte Carlo method proposed by Neimark and Vishnyakov [] and Jorge and Seaton [7]. The two methods have in common the use of a finite dosing reservoir, which suppresses fluctuations so that the van der Waals (vdw) loop in the isotherm can be traced at temperatures less than the critical hysteresis temperature. The importance of controlling fluctuations in the system by controlling the size of the gas reservoir has also been discussed by Neimark and Vishnyakov [], who used this technique as a method of tracing the vdw loop in their gauge cell method.[] A reservoir of infinite size is equivalent to an open (grand canonical) system that places no limit on the number of particles exchanged; the canonical ensemble represents an opposite extreme where the number of particles is fixed. To describe a system where a limited number of particles can be exchanged with a reservoir of finite volume, they coined the term meso-canonical ensemble (MCE). Puibasset et al. [9] and Nguyen et al. [] have carried out simulations to study the effects of the size of the dosing *Corresponding author. d.d.do@uq.edu.au q 2 Taylor & Francis

3 Downloaded by [UQ Library] at 19: 11 February 215 reservoir, the surface dimension and the dosing increment on argon adsorption in slit pores at temperatures below the 3D-critical hysteresis temperature and observed a vdw loop for a sufficiently small size of the dosing reservoir, with a vertical segment in the unstable branch when the pore walls are rectangular in shape. 2D-transitions in the physically adsorbed simple gases on a graphite surface, at sufficiently low temperatures have been well studied.[ 2] For temperatures below the 2Dtriple point, a 2D-transition occurs between rarefied and dense phases on the surface. In the temperature range between the 2D triple point and the 2D critical temperature, there are 2D gas liquid and 2D liquid solid transitions, depending on the tangential pressure.[21,22] Above the 2D critical temperature, there is only a 2D hypercritical fluid solid transition, which is referred to as an ordering transition.[23 25] Experimentally, for argon adsorption on graphite, the triple point and critical temperatures in the first layer have been reported to be around 7.2 and 5 K, respectively.[19] The melting temperature has been obtained as 53.3 K using Gibbs ensemble Monte Carlo simulations.[2] Nguyen et al. [27] investigated the mechanism of 2D-condensation and the 2D-critical temperature, by analysing isosteric heat curves, and found that the spike at monolayer coverage disappears at temperatures below the 2D-critical temperature of approximately K. Furthermore, the 2D-vapour solid, vapour liquid and ordering transitions of adsorbed argon on graphite have been studied by the kinetic Monte Carlo [2] and Bin canonical Monte Carlo schemes.[2] In this work, as an extension of the study recently reported by Ustinov and Do [2], we used MCE and Grand Canonical Monte Carlo (GCMC) simulations to study the microscopic behaviour of argon adsorbed on a graphitic surface at temperatures below the 2D-critical temperature, by investigating the stable, metastable and unstable states. As in the previous investigations of the 3D-transition for capillary condensation, the effects of size of the dosing reservoir, the incremental dosing amount and the surface dimension are examined in detail. Molecular Simulation 7 2. Theory In order to obtain the adsorption isotherms and isosteric heats for argon adsorption on graphite, we employed the Monte Carlo scheme proposed by Nguyen et al. []. The size of simulation box perpendicular to the surface is 5 nm. The solid fluid interaction energy is calculated from the Steele --3 equation [29] with a surface density of 3.2 nm 22 and the fluid fluid interaction potential was calculated from the Lennard-Jones equation. The molecular parameters of a carbon atom in a graphene layer were s ss ¼.3 nm and 1 ss /k B ¼ 2 K, and those of argon are s ff ¼.35 nm and 1 ff /k B ¼ 119. K. The crosscollision diameter and well depth of the solid fluid interaction energy were calculated by the Lorentz Berthelot mixing rule. The cut-off radius was set as a half of the shortest simulation box length Concept of mass transfer lines In the volumetric method, a constant number of molecules, N, is introduced into the dosing reservoir. At t ¼ þ, the isolation valve is opened to connect it to the adsorption cell. Adsorption occurs until equilibrium is established, at which point we can write the following mass balance equation establishing the equilibrium between the gas and adsorbed phases: N 1 ¼ N 2 V 2 r 2 ; where N 1 is the number of molecules in the adsorbed phase, V 2 and r 2 are the volume and the density of the gas phase, respectively. A plot of N 1 versus r 2, therefore, represents an operating line relating N 1 to the gas density. The equilibrium point for the dosing amount N is, therefore, the intersection between this operating line and the isotherm as shown in Figure 1(a). Since the slope of the operating line is minus the volume of the dosing reservoir, its volume has a direct bearing on the determination of the equilibrium point in the unstable branch of the MCE isotherm which exhibits a vdw loop. As seen in Figure 1(a), ð1þ Figure 1. (Colour online) (a) Mass transfer lines for different sizes of the gas reservoir: (b) when V 2 is less than the critical value V 2,C and (c) when V 2 is greater than the critical value.

4 P. Phadungbut et al. adsorbed phase per unit change in the excess amount, we used the following equation [31]: q st ¼ k B T þ u b 2 h U 1i2 U G ; ðþ N ex where u b is the molecular internal energy of the gas, U 1 is the energy of the adsorption system and U G is the energy of the gas space in the adsorption cell given by Figure 2. (Colour online) The path of mass transfer lines. U G ¼ V 1 hu 2 i; ð5þ V 2 Downloaded by [UQ Library] at 19: 11 February 215 there is a critical value for the volume of the dosing reservoir, V 2,C.IfV 2 is less than this critical value, the unstable branch can be traced (Figure 1(b)), but not when it is greater (Figure 1(c)). Only one equilibrium point has been determined for a given dosing amount; to trace the isotherm we increment the amount in the closed system by DN. This is shown graphically in Figure 2, where the blue line shows how the adsorbed amount varies with each increment. It is clear that the increment has to be small enough to trace the unstable branch even when V 2 is less than the critical value (for example, see the jump from Point A to B in Figure 1(b)) Analysis of simulation data We calculated the surface excess density as: G ex ¼ N ex S ¼ h N 1i2 r 2 V acc ; ð2þ S where N ex is the excess amount adsorbed, kn 1 l is the ensemble average of the number of molecules in the adsorption cell, r 2 is the gas density which is the same as that in the dosing cell, V acc is the accessible volume and S is the geometrical surface area of the solid. In the simulation, the excess chemical potential was calculated using the Widom method,[3,3] and the pressure by the virial equation. To measure the cohesiveness of the adsorbed phase, we calculated its compressibility for the adsorbed layer as: 1 N h N1 i 2 k i ¼ ; ð3þ k B Thr 1 i hn 1 i where k B is the Boltzmann constant, T is the operating temperature, kr 1 l is the ensemble average of the density of the adsorbate in the adsorption cell and kn 1 l is the ensemble average of the number of molecules. In order to calculate the isosteric heat of adsorption, which is defined as the change of the energy of the where U 2 is the energy of gas reservoir and V 1 is the volume of adsorption cell Mid-density scheme The mid-density scheme (MDS) developed by Liu et al. [32,33] to determine the equilibrium transition in the hysteresis loop of capillary condensation in mesoporous solids was applied to locate the 2D-transition of the adsorbed argon at temperatures less than the 2D-critical temperature. At a given chemical potential m* in the hysteresis loop, the two states on the hysteresis boundary are N A and N B. Molecules are removed randomly from the high-density configuration to give a state having (N A þ N B )/2 molecules (which is why the method is named the MDS). Simulation is then carried out at this mid-density in the canonical ensemble until the system is fully relaxed, followed by a simulation in the grand canonical ensemble at the same chemical potential m*. The state achieved at the end is taken to be the equilibrium state. 3. Results and discussion 3.1. Monolayer adsorption onto graphite We first investigated the effects of temperature on argon adsorption onto a square graphitic surface, 2s ff 2s ff, at temperatures above and below the 2D-critical temperature of the first layer, with GCMC and MCE ensembles Argon adsorption at 7.3 K The simulated adsorption isotherm and isosteric heat versus loading at 7.3 K obtained with grand and MCEs together with the experimental data are shown in Figure 3. For the MCE, we chose a cubic dosing volume having a linear dimension of nm and used a dosing increment of 2 molecules. The GCMC isotherm is the same as that reported by Nguyen et al. [27]. The MCE and GCMC isotherms are in excellent agreement; both describe the

5 Downloaded by [UQ Library] at 19: 11 February MCE GCMC Avgul and Kiselev data Isosteric heat (kj/mol) 1 experimental data qualitatively and they show no phase change or hysteresis because this temperature is well above the first-layer critical hysteresis temperature Phase transition below the 2D-critical temperature To show the evolution of the isotherm and heat from the 2D gas solid transition to the 2D gas liquid transition for temperatures below the 2D-critical temperature, we obtained the MCE isotherms at and 55 K, shown in Figure (a). The pressure is given on a logarithm scale because of the wide range spanned at and 55 K. With dosing reservoirs of linear dimension, nm for K and nm for 55 K, and a dosing increment of two molecules, vdw loops were observed for simulations carried out in this ensemble. The unstable states were Pressure (Pa) 2 Pace data Figure 3. (Colour online) Argon adsorption isotherms and isosteric heats for argon adsorbed on graphite at 7.3 K. The experimental curve for isotherm and isosteric heat are from Avgul and Kiselev [3] and Pace et al. [37], respectively. Molecular Simulation 9 traced, following the concept of mass transfer lines as described in Section 2.1. As further evidence of the state of the system, we show in Figure (b) the compressibility of the first layer for and 55 K. At K, there is one stage along the unstable branch as the system goes from the rarefied state to the solid state. However, at 55 K, there are two distinct transitions: vapour liquid and liquid solid. Some observations from an examination of Figure are as follows: 1. At K, there are two spinodal points: vapour-like (V) and solid-like (S), in Figure (a) and one-step in the compressibility curve. 2. At 55 K the system exists in three states: V, L and S, and four spinodal points can be identified in the canonical isotherm, and corresponding steps in the compressibility plot Argon adsorption at K To shed further light on argon adsorption at K, we studied the microscopic evolution of the adsorption along the MCE isotherm and the adsorption desorption isotherm obtained with GCMC, and determined the equilibrium phase coexistence with the MDS. The MCE isotherm in Figure 5(a) has a stepwise sigmoid behaviour, which is similar to that reported by Binder et al. [3] for adsorption of a pure fluid with a firstorder vapour solid transition. We show in Figure the 2D density contours of the first layer for the specific points marked in Figure 5(a). The vapour-like spinodal point A is characterised by a circular solid-like patch surrounded by a rarefied phase. As molecules are added into the system up to point B, this solid-like patch grows in size and changes its shape from circular to a strip spanning the full length of the graphite surface in one direction at Point C. This point represents the coexistence between the gas and solid Figure. (Colour online) (a) Meso-canonical argon adsorption isotherms and (b) compressibility for first layer argon adsorption at and 55 K. L1, liquid-like spinodal; L2, compressed liquid-like spinodal; S, solid-like spinodal and V, vapour-like spinodal.

6 5 P. Phadungbut et al. (a) (b) 1 2 1e- F E D C B MCE GCMC Mid density scheme A 1e-7 1e- 1e-5 2 Pressure (Pa) Isosteric heat (kj/mol) 1 MCE GCMC Figure 5. (Colour online) (a) Argon adsorption isotherms and (b) isosteric heats for argon adsorption on graphite at K. The points A F are from MCE simulations. Downloaded by [UQ Library] at 19: 11 February 215 phases whose areas are similar to each other. As more molecules are added to the system up to point D, the solid strip becomes larger at the expense of the rarefied phase. On further addition of molecules, the size of the rarefied phase diminishes, and it changes shape from a strip to circular at point E. This circular 2D-bubble then decreases in size and finally disappears at the solid-like spinodal point F. The GCMC isotherm, shown as filled circles in Figure 5(a), displays vertical adsorption desorption hysteresis loop boundaries because of the spontaneous condensation and evaporation, resulting from the large density fluctuations that the system needs in order to overcome the free energy barrier separating the two phases. Because of this thermal fluctuation the condensation occurs before the gas-like spinodal point A, and likewise evaporation occurs before the solid-like spinodal point F. At the condensation pressure, the rarefied phase in the first layer changes instantaneously to a 2D-solid-like phase. On desorption from a completely full first layer, the adsorbed density does not change (because of the cohesiveness of the solid-like first layer) until the chemical potential has passed the coexistence chemical potential; when the chemical potential approaches the solid-like spinodal point of the MCE isotherm (F) the first layer evaporates to a rarefied phase. The first-order vapour solid equilibrium transition determined by the MDS is shown as a dashed line in Figure 5(a), and coincides with the vertical section CD of the MCE isotherm. Since this vertical section is associated with the coexistence of the two phases in strip form, as discussed earlier, we can identify the equilibrium transition with the strip configuration of the two phases. This is the fundamental reason why the vertical section in the meso-canonical isotherm is more readily observed when rectangular surfaces are used in simulations. The isosteric heats obtained with MCE and grand canonical ensembles are shown in Figure 5(b). An estimate of the isosteric heat across the discontinuity in the isotherm cannot be made in GCMC simulations; but the MCE isosteric heat has a linear increase with loading over the very low pressure region, which is related to the linear increase in the number of nearest neighbour molecules as exemplified in Figure 5(b). Along the unstable branch of the MCE isotherm, the isosteric heat is constant (.1 kj/mol), which is in excellent agreement with the results obtained by Ustinov and Do [2] using the kinetic Monte Carlo method. A C E Strip solid Circular bubble Figure. (Colour online) 2D-density plots for argon adsorption at K on a square graphitic surface. The points A F are as indicated in Figure 5(a). B D F

7 Molecular Simulation 51 Downloaded by [UQ Library] at 19: 11 February MCE GCMC Mid density scheme Millot data C B D.1 Pressure (Pa) Figure 7. (Colour online) Argon adsorption isotherms on graphite at 55 K: Comparison between experimental data of Millot, MCE and GCMC simulations, and the equilibrium phase transition obtained by the MDS Argon adsorption at 55 K In Figure 7, we show the isotherms for argon adsorption at 55 K obtained from MCE and GCMC simulations which agree qualitatively with the experimental data of Millot [35] and the phase coexistence obtained with the MDS. We found that a cubic dosing reservoir with a linear dimension of nm and a dosing increment of two particles was sufficient to obtain the meso-canonical isotherm. A C E B D F A F E.1 Liquid droplet Figure. (Colour online) 2D-density plots for argon adsorption at 55 K on a square graphitic surface. The points A F are indicated in Figure 7. g(r) Distance (A) Figure 9. (Colour online) Radial distribution function of argon adsorption at 55 K. The dashed line at the distances.2 and 7. A. The lines are referred to Figure 7. Isosteric heat (kj/mol) 1 1 GCMC MCE 2 Figure. (Colour online) Isosteric heat of argon adsorption on graphite at 55 K. S stands for solid-like phase. In contrast to the results obtained at K, the MCE isotherm exhibits two vdw loops: the first associated with the vapour liquid transition and a second, smaller loop, for the liquid solid transition. The 2D density contours at specific points marked on the isotherm are shown in Figure. At the vapour spinodal point A, a liquid droplet nucleates and grows with loading up to point C. With further increase in the loading to point D, the first layer becomes covered with an unstructured 2D liquid which becomes progressively more structured as coverage approaches the spinodal point E, beyond which the second vdw loop corresponds to the transition from a 2D liquid to a 2D solid at point F. We also substantiated the transition from point E to point F with the radial distribution of argon particles in the first layer in Figure 9. It is seen that the position of the second peak decreases, resulting in a closer separation distance between neighbours, which indicates a phase change from a liquid-like state to a solid-like state. 2 S E F 25

8 52 P. Phadungbut et al. Figure 11. (Colour online) (a) Argon adsorption isotherms at 55 K on a graphite surface having different shapes. (b) 2D density plots along the vertical segment on the s ff s ff surface. Downloaded by [UQ Library] at 19: 11 February 215 In the GCMC isotherm, there are two hysteresis loops with vertical boundaries (Figure 7): the first corresponds to the vapour liquid transition and the second to the liquid solid transition. Initially, there is a rarefied gas-like state on the surface followed by a condensation to a 2D-liquid. As the chemical potential is increased, the 2D-liquid becomes more structured, and there is a transition from a compressed 2D liquid to a 2D solid monolayer. Upon desorption there are two distinct hysteresis loops, corresponding to the above-mentioned two transitions. The equilibrium transition obtained with the MDS was again found to coincide with the nearly vertical section of the MCE isotherm, confirming that the MDS correctly determines the equilibrium transition. The isosteric heats obtained at 55 K from simulations in the MCE and GE ensembles are shown in Figure. As before (at K), there is no GCMC isosteric heat through the discontinuity in the isotherm. The MCE isosteric heat has a linear increase with loading over the low-pressure region due to the linear increase in the number of nearest neighbour molecules as shown in the inset of Figure. The isosteric heat at the gas liquid transition is 11.7 kj/mol, which is around. kj/mol lower than the heat of the gas solid transition at K in qualitative agreement with Ustinov and Do [2] Effect of surface dimension on 2D-transition To show the effects of the shape of the graphite surface on the ease of forming a two-phase coexistence, we used a rectangular surface of s ff s ff in an MCE simulation at 55 K. This surface has the same area as the square surface in the previous section. The other parameters remain the same (the size of the dosing reservoir and the dosing increment). The MCE isotherm is shown in Figure 11(a) and exhibits a vdw loop with a clear vertical segment, corresponding to a phase co-existence, as confirmed by the 2D density contour plot in Figure 11(b) and by the equilibrium transition (dashed line) determined Figure. (Colour online) Effects of incremental dosing amount added into dosing cell on the meso-canonical isotherms for argon adsorbed on a square graphitic surface of 2s ff 2s ff at 55 K with a gas reservoir of size of nm. Figure 13. (Colour online) Effects of gas reservoir size on the MCE adsorption isotherms for argon at 55 K on a square graphitic surface of 2s ff 2s ff. with the MDS. This shows that the rectangular surface makes it easier for the two phases to form in the strip configuration.

9 Molecular Simulation 53 Figure. (Colour online) Effects of gas reservoir size on the PNF in the adsorbed cell at 55 K on a square graphitic surface of 2s ff 2s ff. Downloaded by [UQ Library] at 19: 11 February Effects of incremental dosing amount The effects of dosing increment on the MCE isotherm for argon adsorption at 55 K on a square surface of 2s ff 2- s ff, with a cubic dosing volume having a linear dimension of nm, are shown in Figure. It is seen that the spinodal points, especially those associated with the liquid solid loop, could not be traced when these large dosing increments were used. 3.. Effect of gas reservoir volume Puibasset et al. [9] and Nguyen et al. [] investigated the effects of the dosing volume on argon adsorption in an infinite slit nanopore. Here, we have made a similar study for argon adsorption at 55 K on a square surface of 2s ff 2s ff using a dosing increment of two molecules for each equilibrium point. The adsorption isotherms for various dosing volumes are given in Figure 13, which shows that the second vdw loop is not found when a cubic dosing reservoir of linear dimension greater than nm is used. To understand better why larger dosing reservoirs do not yield the second vdw loop, we investigated the particle number fluctuation (PNF). The PNF in the adsorption cell can be calculated as: F ¼ f N; N hni ¼ N 2 2 hn 2 i N h i : ðþ The plots of F versus loading in Figure show that the fluctuations in the adsorption cell decrease with loading for the nm dosing reservoir sizes but are nonmonotonic for larger volumes. The pattern of the fluctuations, therefore, provides a criterion from which to judge whether the vdw loop will be produced correctly in an MCE isotherm.. Conclusions We have studied the microscopic behaviour of an argon monolayer adsorbed on a homogeneous graphite surface at temperatures below the 2D-critical temperature by analysing isotherms simulated in the MCE in which the adsorbent is connected to a reservoir of finite volume.[] On a square surface, the K isotherm has a single stage vapour solid transition, while the 55 K isotherm shows a continuous vdw-like loop during vapour liquid and liquid solid transitions. On a rectangular surface, two phases coexist in strip form and there is a vertical segment in the middle of the unstable branches of the loop. The equilibrium phase transition determined by the MDS [32,33] was found to coincide with the vertical segment of the vdw-like loops in the meso-canonical isotherms, adding further support to the validity of the MDS. Acknowledgements This research was supported by the Australian Research Council and Suranaree University of Technology whose support (to PP) is gratefully acknowledged. Funding This work was supported by the Thailand Research Fund (to PP and CT) through the Royal Golden Jubilee PhD programme [grant number 1.C.TS/53/A.1]. References [1] Sing KSW, Everett DH, Haul RAW, Moscou L, Pierotti RA, Rouquerol J, Siemieniewska T. Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity. Pure Appl Chem. 195;57():3 19. [2] Allen MP, Tildesley DJ. Computer simulation of liquids. Oxford: Clarendon; 197. [3] Frenkel D, Smit B. Understanding molecular simulation: from algorithms to applications. Vol. xviii. San Diego, CA: Academic Press; 199. p. 3.

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