Supplementary information for Adsorption Induced Transitions in Soft Porous Crystals: An Osmotic Potential Approach to Multistability and Intermediate Structures D. Bousquet, F.-X. Coudert, A. G. J. Fossati, A. V. Neimark, A. H. Fuchs, A. Boutin α L Figure S1: Snapshot of a unit cell of our simplified MIL-53 model. i
h Figure S2: Snapshot of a unit cell of our slit pore model. fluid-fluid 3.5 Å 150 K host-fluid 3.4 Å 140 K Figure S3: Lennard Jones parameters for the fluid-fluid and host fluid interactions in the MIL53 model and in the slit pore model. ii
K H (bar -1 ) 1 10 0 5 10 h (Å) Figure S4: Henry s constant (in logarithmic scale) of the slit pore as a function of slit pore height h. Black dots: numerical results from Grand Canonical Monte Carlo simulations; red curve: analytical fit using Eq. 3. 5 10 15 N max (molecules/u.c.) Figure S5: 1 1.2 1.4 1.6 α/α MCS Profile of saturation uptake (N max )asafunctionofporeopening for our simple MIL-53 model. Black dots: data obtained from Grand Canonical Monte Carlo simulations; red line: linear approximation N max = A + B, with B =0.216 and A = 4.85 iii
K (bar -1 ) 0.1 1 H 10 100 1 1.2 1.4 1.6 α/α MCS Figure S6: Henry s constant (in logarithmic scale) of adsorption in the simple MIL-53 model. Black dots: numerical results from Grand Canonical Monte Carlo simulations; red curve: analytical fit using Eq. 3, resulting in the parameters KH 0 =5.9 10 8 bar 1, 1 =23.57 and 2 =15.52. PHbarL 10 1 10-1 10-2 0.9 1.0 1.1 1.2 ê 0 Figure S7: 2D surface of the osmotic potential as a function of pore opening and external gas pressure P in the case of a large adsorbate ( MCS =1.2 0 ). The color scale ranges from 50 (purle) to 30 kj/mol (red). iv
0 20 40 60 F host (kj.mol -1 ) F host (kj.mol -1 ) 0 20 40 60 Figure S8: Profile of the host free energy, F host, of the simplified MIL-53 model in case A(top) and case B(bottom) as a function of pore opening v
α( ) 35 40 45 50 3.2 3.4 3.6 σ(å) Figure S9: Evolution of the order parameter MCS as a function of the LJ parameter of the adsorbate Dependance of maximum loading and Henry s constant as a function of particle size Henry s constant and maximum loading profile as a function of the order parameter have been computed for a reference particle size (with LJ parameter ref and ref ). The single particle most comfortable state order parameter has been computed for a set of particle with increase size. The evolution of MCS appears to be roughly linear as a function of the Lennard Jones parameter (see Fig.S9). MCS ( )=18.0782 18.2117 Furthermore, the maximum loading for a particle with LJ parameters ref and extrapolated following : has been N max (, )=N max (, ref ref 3 ) vi
0-50 -100-150 -200-250 Figure S10: Profile of osmotic potential upon adsorption for a bistable material, as a function of the channel opening, for different values of external gas pressure, in case A1 0-50 -100 Figure S11: Profile of osmotic potential upon adsorption for a bistable material, as a function of the channel opening, for different values of external gas pressure, in case A2 vii
0-50 Figure S12: Profile of osmotic potential upon adsorption for a bistable material, as a function of the channel opening, for different values of external gas pressure, in case A3 0-100 -200 Figure S13: Profile of osmotic potential upon adsorption for a bistable material, as a function of the channel opening, for different values of external gas pressure, in case B1 viii
0-100 Figure S14: Profile of osmotic potential upon adsorption for a bistable material, as a function of the channel opening, for different values of external gas pressure, in case B2 0-50 -100 Figure S15: Profile of osmotic potential upon adsorption for a bistable material, as a function of the channel opening, for different values of external gas pressure, in case B3 ix
N ads (molecules/u.c.) 0 2 4 6 8 10 1.21.41.61.8 2 0.1 1 10 100 P(bar) Figure S16: Behavior of a bistable material upon gas adsorption, in case B2 (see Section III A). Top: evolution of host pore opening as a function of external gas pressure; bottom: adsorption isotherm. N max (molecules/u.c.) 0 50 100 150 200 Figure S17: 5 10 15 h(å) Profile of saturation uptake (N max )foraslitpore,asafunctionoftheslit pore height h. Black dots: data obtained from Grand Canonical Monte Carlo simulations; the red line is a guide for the eyes. x
N max (molecules/u.c.) 0 2 4 6 8 10 Figure S18: 0.8 1 1.2 1.4 1.6 1.8 α/α MCS Profile of saturation uptake (N max )asafunctionofporeopening for our simple MIL-53 model, in which we have introduced an artificial step at / 0 =1.3 to demonstrate the influence of packing effects on adsorption-induced transitions. xi