A new ansatz for thermodynamics of confined systems Harald Morgner Wilhelm Ostwald Institute for Physical and Theoretical Chemistry Leipzig University, Linnéstrasse 2, D Leipzig, Introduction to the phenomenon of adsorption hysteresis Shortcomings of standard thermodynamics for confined systems New concept Applications: control of negative pressure (static, dynamic) molecular conformation, reaction rate, solvent properties, separation CompPhys10, Leipzig, Nov. 25, 2010

Adsorption Hysteresis in Porous Material R.Rockmann, PhD Thesis 2007, U Leipzig Introduction Theoretical Applications adsorption from vapor phase adsorption desorption

Introduction Theoretical Applications adsorption from vapor phase Adsorption Hysteresis in Porous Material H.Morgner J.Phys.Chem. C114 (2010)

Introduction Theoretical Applications computer simulation shape of pore isotherm of pores with two open ends crossing of grand potential curves gas reservoir adjusted gas density gas reservoir adjusted gas density treated explicitely in simulation pore wall

Simulation: adsorption in cylindrical pore of infinite length  EOS Introduction Theoretical Applications computer simulation

Simulation: adsorption in cylindrical pore of infinite length  EOS Introduction Theoretical Applications computer simulation

Introduction Theoretical Applications shortcomings of TD shape of pore isotherm of pores with two open ends crossing of grand potential curves observations: switching points decoupled from grand potential crossing switching points reproducibly stable in experiment and simulation „metastable“ states are stable in simulation and in experiment for any trial time (up to > 6 weeks) grand potential

Introduction Theoretical Applications shortcomings of TD Neimark&Vishnyakov J.Phys.Chem. B110 (2006) LJ-model for N 2 spherical pore with diameter 15.8  virtual interface to gas reservoir Monte Carlo simulation

Introduction Theoretical Applications shortcomings of TD Neimark&Vishnyakov J.Phys.Chem. B110 (2006) explanation by Neimark et al: both branches contain a set of microstates these sets are subsets of one common state (equilibrium). Thus, both branches form only one state in actual simulation (and experiment) only one subset of microstates is accessible depending on history (constraint equlibrium). thus, postulated equilibrium state does not show up in (computer) experiment true GCE isotherm „….the true GCE isotherm cannot be sampled in practical simulations….“

Introduction Theoretical Applications new concept, confined TD COS and concept of applying canonical boundary conditions COS allow to retrieve isotherm grand canonical boundary conditions canonical boundary conditions

Introduction Theoretical Applications new concept, confined TD COS(  ) two IF COS(  ) one IF curves of states (COS) rules of new concept: system is fully described by COS change within COS is always reversible switching between different COS is always irreversible, occurs only if required by boundary conditions all states of a system can be visited in simulation and experimentally

Introduction Theoretical Applications new concept, confined TD contr. chem. pot. contr. volume contr. amount curves of states (COS) COS(  ) two IF COS(  ) one IF Transitions between curves of states (COS)

Introduction Theoretical Applications new concept, confined TD Standard TD: one EOS exists states depend on actual boundary conditions, not on history rules involving TD potentials predict all equilibrium states hysteresis requires ad hoc assumptions Confined TD: one or more COS exist changing between states of same COS reversible change between COS irreversible TD potentials loose predictive power hysteresis natural consequence of concept

Introduction Theoretical Applications negative pressure negative pressure states expanded liquid: -140bar !

Introduction Theoretical Applications control of negative pressure negative pressure: exerts pull onto embedded molecule negative pressure is known for macroscopic systems, but metastable (e.g. A. R. Imre On the existence of negative pressure states, Phys. Stat. Sol. (b) 244 (2007) 893-9) in the nanoworld negative pressure states are stable and can be controlled, homogeneous negative pressure is taken on in volumes large enough to handle big (bio-)molecules for comparison: positive pressure of ~80bar turns CO 2 into polar solvent! what can -140bar do to influence molecular properties? molecular conformation reaction rate (large reaction volume) solvent properties separation of mixtures by inducing phase separation at neg. pressure Indirect methods to study liquid-liquid miscibility in binary liquids under negative pressure Imre, Attila R. et al. NATO Science Series, II: Mathematics, Physics and Chemistry (2007), 242 (Soft Matter under Exogenic Impacts),

Introduction Theoretical Applications negative pressure in stationary flow? for high throughput: continuous flow of solvent desirable can situation of negative pressure exist under stationary flow? the answer requires the ability to handle a velocity field

Introduction Theoretical Applications generalized diffusion Transport of Matter Common Treatment of Diffusion and Convection by generalized Diffusion single component: binary system: only one common driving force

Introduction Theoretical Applications negative pressure in stationary flow the answer: negative pressure can be held up under stationary flow! v=0.018cm/s => residence time in 100nm pore is ~500  s

Thank you ! comments or criticism welcome !!!

Introduction Theoretical Applications adsorption from vapor phase R.Rockmann PhD Thesis 2007 U Leipzig Adsorption Hysteresis in Porous Material SBA-15: silica pores with two open ends narrow pore size distribution

Introduction Theoretical Applications behavior of fluids in mesopores natural phenomena hydrology of ground water natural purification and pollution industrial activities oil extraction mixture separation, filtering catalysis sensor development basic research bioanalytics

Introduction Theoretical Applications new concept, confined TD Pore with bottom, narrow mouth curves of states (COS) homogeneous volume 3nm x31nm expanded liquid  neg. pressure, P< -100 bar

Introduction Theoretical Applications new concept, confined TD more complex pore shape five COS! if done correctly, full control over all states in all COS! large volume with neg. pressure P< -140bar in  13nm x 18nm

Adsorption in Porous Material adsorption R.Rockmann, PhD Thesis 2007, U Leipzig Introduction Theoretical Applications adsorption from vapor phase

Desorption in Porous Material desorption R.Rockmann, PhD Thesis 2007, U Leipzig Introduction Theoretical Applications adsorption from vapor phase