Ralph V. Chamberlin - The big world of nanothermodynamics

Ralph V. Chamberlin - The big world of nanothermodynamics
Small-system thermodynamics was originally developed by Terrell Hill to describe the properties of isolated
nanoparticles and individual molecules. Now we find that this “nanothermodynamics” is also crucial for
characterizing nanometer-sized fluctuations inside bulk materials. A key result is that if these fluctuations are
to obey the second law of thermodynamics, a nonlinear correction must be included in Boltzmann’s factor. I
will show that this correction improves agreement between standard models and the measured behavior of
liquids, glasses, polymers, and crystals. Indeed, the nonlinear correction provides a common explanation for
several empirical formulas including stretched-exponential relaxation, super-Arrhenius activation, non-classical
critical scaling, and 1/f noise. I will conclude with some thoughts regarding the life and legacy of Terrell Hill.
Anatoly B. Kolomeisky - How to Understand Molecular Transport through Channels: The Role of Interactions
The motion of molecules across channels and pores is critically important for understanding mechanisms of
many biological, chemical and physical processes. Here we investigate the role of different types of interactions
in the molecular transport through pores by analyzing exactly solvable discrete stochastic models. According to
this approach, the channel transport is a non-equilibrium process that can be viewed as a set of chemical
transitions between discrete spatially separated states. It provides a full dynamic description of the
translocation process. It is shown that the strength and the spatial distribution of molecule/channel
interactions can strongly modify the particle currents. Our analysis indicates that the most optimal transport is
achieved when the binding sites are near the entrance or near the exit of the pore depending on the sign of
interaction potential. These observations agree with single-molecule experiments on translocation of
polypeptides through biological channels. We also hypothesize that intermolecular interactions during the
channel transport might also significantly influence the translocation dynamics. Our explicit calculations show
that the increase in the flux can be observed for some optimal interaction strengths. The relevance of these
results for biological systems is discussed. The physical-chemical mechanisms of these phenomena are
discussed from the microscopic point of view.
Lionel Mercury - (Meta)Stability of water in micrometric and nanometric geometries: Is there a size effect?
The reducing geometries is very often evoked to explain experimental shifts of water properties occluded
inside small cavities. At nanometric level, the deviation of water properties can be modelled and measured and
both results agree that from 5 nm (10 nm at max.) to smaller confinement, the finite size effects play a growing
role to control the water thermodynamics. In the meantime, collecting large-scale evidences, like the phase
transitions and chemical saturations states observed/measured in natural aquifers, the threshold between
macroscopic and nanoscopic domains appears much more unclear, extending to 0.1 μm or more. The question
thus arises as for the existence of intermediate mesoscopic behaviors, between truly nanoscopic and truly
macroscopic domains.
Recently, we accumulated a large number of measurements (vibrational and X spectroscopies, phase
transitions) on water occluded in different types of cavities (closed cavities in quartz = fluid inclusions, open
nano-channels patterned inside silicon wafers, pores membranes, capillaries), and sometimes on the container.
These measurements tend to demonstrate that the properties of the water body can change as a function of
the distance to interfaces (over 1-3 micrometers !) and as a function of the confinement degree from around
35-40 nm.
These measurements open the discussion to the surface-to-volume competition in thermodynamics, especially
when addressing two-phases (or more) systems. Thermodynamics of small systems appears attractive to deal
with the evident size effect in confinement regime, though it is visible at sizes larger than usually defined.
Another challenge is to thermodynamically describe biphasic frontiers using surfacial formalism, possibly
requiring, in certain cases, the definition of an interfacial phase with finite width, instead of an abrupt interface
between two bulk phases. In both cases, the characteristic threshold between bulk and “others” behaviors
should be calculated and generalized on thermodynamic grounds.
Hong Qian - Hill's nanothermodynamics and stochastic thermodynamics
Two of the major contributions of T.L. Hill follow nicely Gibbs' two achievements: macroscopic chemical
thermodynamics and statistical mechanics of fluctuating ensembles. The latter has been significantly
superseded by the current theory of stochastic thermodynamics based on the notion of entropy production
along a trajectory, first noted by Hill and his coworker Y.-D. Chen in 1975! Stochastic thermodynamics has
found numerous applications in nonequilibrium chemistry of living cells. I shall give a brief overview of this in
the first half of my talk. A unification of nanothermodynamics and stochastic thermodynamics, thus, is in order.
Surpringly, there is a problem to establish a statistical foundation for Hill's theory, which requires the Gibbs
potential function G = E-TS+PV. We show that without the assumption of macroscopic limit, algebraic
Legendre transform and integral Legendre transform do not agree perfectly. Possible resolution to this
paradox will be discussed.
Guillaume Galliero - From local transport properties to shear induced swelling in nanopores
During this workshop we will give some examples of the impact of nanoporous slit on the dynamic behaviour of
confined fluids.
Using molecular dynamics simulation on simple systems, we will show how the local variations of the transport
properties of the confined fluid (diffusion [1], viscosity [2]), induced by density inhomogeneities, may be
described by a simple local average density model combined with a new weight function [3]. In addition, we
will discuss the couplings that occur between shear and swelling at the pore scale because of the fluid
confinement [4].
REFERENCES
1.
H. Hoang and G. Galliero, J. Chem. Phys. 136, art n° 184702 (2012).
2.
H. Hoang and G. Galliero, Phys. Rev. E. 86, art n° 021202 (2012).
3.
H. Hoang and G. Galliero, J. Phys. Cond. Matter 25, art n° 485001 (2013).
4.
H. Hoang and G. Galliero, Poromechnaics V, pp. 685-692 (2013).
Øivind Wilhelmsen - The Curvature Dependence of Heat and Mass Transfer through Interfaces
Heat and mass transfer through interfaces is central in nucleation, nanotechnology and many other fields of
research. Nanotechnology is rapidly developing, and demands knowledge of heat and mass transfer at the
nanoscale.[1-5]
We present a method to obtain the curvature dependence of interface resistivities, such as the Kapitza
resistance. The method combines the power of nonequilibrium molecular dynamics with the flexibility of
density functional theory. We use the method to, for the first time, obtain the terms in the curvature expansion
of the interface resistivities up to second order.[6]
Mass and heat transfer to bubbles and droplets occurs very differently. Fluctuations in the shape of the
bubble/droplet can enhance transport across the interface, leading to a highly heterogeneous initial growthphase in nucleation processes.[6]
References:
1] Keblinski P., Phillpot S.R., Choi S.U.S., Eastman J.A., Int. J. of Heat and Mass Transfer, 2002, 45, 855.
2] Patel H.E., Das S.K., Sundararajan T., Nair A.S., George B., Pradeep T.,Appl. Phys. Lett., 2003, 83, 2931.
3] Hu M., Poulikakos D., Grigoropoulos C.P, Pan H., J. Chem. Phys., 2010,132(16), 164504.
4] Bera C., Mingo N., Volz S., Phys. Rev. Lett., 2010, 104, 115502.
5] Wilhelmsen Ø., Bedeaux D., Kjelstrup S. Phys.
Sofia Calero - Molecular Simulations in Porous Materials: Environmental and Technological Applications
With the increasing demand for efficient, environmentally friendly, and energy saving procedures, porous
materials with tailored structures and tuneable surface properties are of wide spread use and this is only
expected to intensify in the future. Knowledge of the adsorption and diffusion behaviour as a function of
molecular composition and morphology is essential for an informed choice of material for a given application.
Molecular Simulations are ideally suited to identify improved structures for adsorption applications and to
guide the design of new materials. Efficient simulation methodology and accurate force field potentials are
essential to reach this goal. Much progress has been made in the search of fast and efficient simulation and
screening methods, but the development of good, transferable force fields, and accurate models for flexible
structures is still a formidable challenge. We perform molecular simulations to study the adsorption and
diffusion behaviour of a variety of molecules on metal-organic frameworks. These are a relative new class of
porous materials with potential applications in molecular adsorption, gas separation, and storage/release
applications due to their good stability, large void volumes, and well-defined cavities of uniform size. As an
example we can study structural deformation upon adsorption, identify the preferential adsorption sites as a
function of pressure, temperature and humidity, study the effect of functionalization of open metal site find
non accessible places by comparing our results with experimental data, analyse molecular diffusion inside the
pores, or study the framework composition and the mechanisms behind the instability of MOFs in humid
environments.
Cees van Rijn - Liquid Threads: a case study of non-equilibrium fluid mechanics
In many liquid thread and droplet formation processes a general pattern is observed: droplets appear and
coupled liquid threads quickly disappear, just watch liquid droplets detaching from a slowly running tap or
emanating from a water surface. Fluid threads seem to be intrinsically instable and under influence of the
interfacial tension force they tend to be readily transformed into droplets. This poses an interesting question:
Under which conditions will a liquid thread with a finite viscosity appear to be stable? We show that the shape
of a stable liquid thread is concave, can be accurately described, and that an upper bound on the length of the
liquid thread can be predicted before breakup sets in.
Sondre Schnell - Small Systems Thermodynamics to Determine Kirkwood-Buff Coefficients From Equilibrium
Molecular Dynamics Simulations
For systems far from the thermodynamic limit, properties like the total energy U, the enthalpy H, and Gibbs
free energy G, are no longer extensive. Such systems cannot be described using classical thermodynamics. Hill
proposed an extension to the classical thermodynamics, based on finite systems with so few particles, the
system will be far from the thermodynamic limit. This approach describes the thermodynamics of small
systems, or nanothermodynamics. Using equilibrium molecular simulations, we demonstrate how Kirkwood-Bu
(KB) coefficients can be determined directly from small systems. This is done using both density fluctuations, as
well correcting the pair correlation functions. By extrapolating to the thermodynamic limit, this method gives
the KB-coefficients for an open system. Without this approach grandcanonical simulations would be required,
simulations both time-consuming and computationally difficult for dense systems. Since the method sampled
directly in the grand-canonical ensemble, it can be used to determine KB-coefficients for systems with charge4
as well as for chemical reactions.
Elif Genceli Guner - Non-Equilibrium Thermodynamics of Water-Ice Interface
In crystallization from an aqueous solution on a cold surface, during phase transition it is frequently assumed
that all of the heat of crystallization is transferred into the cold side (i.e. to the crystal side) and the
temperature values of both sides (crystal side and the liquid side) of the interface are equal.
To understand the crystallization phenomena better, this work aims to investigate the crystal growth from an
aqueous solution on a cooled surface theoretically and experimentally in terms of irreversible thermodynamics
aspect for (i) estimating the magnitude of the temperature jump at the crystal - liquid interface, (ii) quantifying
the effect of the coupling of heat and mass transport and (iii) showing the error one may do using this
assumption.
Thus, ice formation from pure water is taken as an example case. A quartz growth cell is designed and
constructed for this crystallization experiment. The cell underneath surface is cooled via a heat exchanger. Data
is collected during crystallization on the heat exchanger surface. Thermo Liquid Crystal is used to detect the
temperature profile at a micro scale both in the solution and under the ice crystals.
To define the fluxes and forces of the system, the excess entropy production rate for heat and mass transport
into, out of and across the interface (between ice surface and liquid) is used. The method describes the
interface as a separate (two-dimensional) phase in local equilibrium. Coupled heat and mass flux equations
from non-equilibrium thermodynamics are defined for crystal growth and solved taking the advantage of the
Onsager equations. A temperature jump at the ice-water interfaces is detected up to 1.7 °C. This observation is
the experimental proof for the existence of an interfacial temperature jump during liquid-solid phase
transition.Coupling coefficients and all transfer resistivities at the interface of a growing ice on a cooled surface
is defined.
This knowledge can improve film- or fugacity models for the interface, change current modelling of phase
transitions and eventually help the prevention of crystal growth at unwanted locations (such as scale layer
formation on heat exchanger surfaces) in process industry saving considerable capital and operational costs.
Fernando Bresme - Non-equilibrium simulations at the nanoscale
Non-equilibrium molecular simulations offer a powerful tool to interrogate the non-equilibrium response of
materials at the nanoscale using a microscopic approach. It provides a route to visualize transient processes
and uncover novel non-equilibrium behaviour, hence complementing the predicting power of theoretical
approaches and providing a powerful tool to rationalize experimental observations
I will discuss recent work performed in our lab that focuses on computational studies of heat and mass
transport in nanomaterials, manipulation of nanoparticles with external fields and the investigation of tunable
friction in nanopores.
Thuat Trinh - Thermodynamics of CO2 adsorbed on a Graphite Surface from Molecular Dynamics Simulation
and Small System Method
A method to calculate thermodynamic properties of macroscopic systems by extrapolating properties of
systems of molecular dimensions was recently developed (Small System Method)1 Here we apply the method
for a graphite surface system with CO2 gas adsorbed2,3 in two distinct layers (Figure 1). From Equilibrium
Molecular Dynamics simulation data, we predicted the chemical potential and activity coefficient of the surface
in various temperature and pressure conditions.3 We will present a recent implementation of the method into
a popular simulation package LAMMPS. An extension to experimental data of CO2 and CH4 adsorbed on
activated carbon material will be discussed.
Markus Hutter - Effect of nanoscopic confinement on the viscoelasticity of filled elastomers
This paper deals with the viscoelastic effects in hard-particle filled elastomer nanocomposites. Since the fillers
are hard and the matrix is purely elastic, the emergence of rate-dependent behavior (viscous-like) is of
particular interest. It is discussed that this behavior originates from the immobilization of network chainsegments close to the filler particles, which effectively results in a locally increased glass-transition
temperature. We discuss how such aspects can be built into a concurrent two-scale model for the macroscopic
viscoelastic behavior of such nanocomposites, using nonequilibrium thermo-dynamics.
Jan van Eijkel - Nanothermodynamics in nanochannels, sensors and actuators: experiments and
interpretation
The first part of this talk concerns acid/base chemistry in small confinements.
It is standard textbook theory to predict the response of a potentiometric sensor to its potential determining
ion by a thermodynamic description of the solid/solution interface. Such a description can also be used to
predict the surface potential of an oxide to the solution pH. In this talk we will further expand the use of this
theory to explain transient pH changes observed in glass nanochannels filling with aqueous solutions. We will
subsequently show how this knowledge can be used to make a electrochemical proton actuator.
The second part of this talk concerns water behavior in small confinement.
Here we will show how thermodynamics can be used to qualitatively predict the surprisingly high drying speed
of nanochannels
David Lopez - Nanothermodynamics of nucleation
Phase transitions such as condensation, cavitation, or crystallization are omnipresent phenomena in nature.
The mechanism triggering most of them is the formation of a rare embryo or nucleus of the new phase by
random fluctuations.
This initiating mechanism is known as nucleation and its understanding and control is of utmost interest in a
wide range of scientific and technological disciplines. However, despite intense investigations for more than a
century, nucleation is still an unsolved problem. One of the main reasons for that is the fact that these nuclei
are non-equilibrium entities consisting on just a few molecules, whose properties are difficult to characterize
and predict.
In this talk, we will discuss our investigations on the nucleation of nanodroplets and nanobubbles, combining
theory with simulations. We will see how, remarkably, the properties of these nanosized entities can be
precisely described in the context of nanothermodynamics, and how the results of these studies provide useful
insight to control and predict accurately the occurrence of this important phenomenon.
Ivan Latella - Hill's method for systems with long-range interactions
Systems with long-range interactions are characterized by an interaction potential whose range is of the order
of the size of the system. The energy due to interactions between different parts of the system cannot be
neglected if these interactions are long-ranged, causing the system to be intrinsically nonadditive. Although
the system may contain a large number of particles, since the range of the interactions is of the order of its
size, the system itself can be regarded as small, in a thermodynamic sense. Thus, the nonadditivity in these
systems persists even in the limit of large number of particles.
Furthermore, the nonadditive character, manifested in the nonextensivity of thermodynamic quantities, is also
a remarkable property of systems with a small number of particles and it constitutes the basis on which Hill's
approach is built. We will exploit this connection to show that the formalism of nanothermodynamics can also
be applied to large systems with long-range interactions.
Niels Tas - Capillarity in Silicon Based Nanochannels
Elasto-capillary deformation of thin capped nanochannels can be used to measure the pressure in isolated
confined liquid plugs. These measurements confirm the existence of capillary negative pressure, in accordance
with the Young-Laplace equation. Despite the tension in the liquid, plugs are stable on a time-scale of minutes.
The role of the confinement in the (meta)stability will be discussed.
Dynamic capillarity measurements, following the model of Washburn, reveal the existence of (apparent)
viscosity effects in water flowing in sub-100 nm nanochannels. The ionic content of the water plays a crucial
role in understanding these effects.
Christophe Labbez - Chemical potential of charged species at solid/liquid interfaces
In this talk I will discuss and criticize the concept of “surface pH”. This concept was introduced early in the last
century by J. Danielli to explain the change in interfacial tension of interfacial films formed by long chain
aliphatic acids in conjunction with their degree of dissociation. Today it has spread to a large scientific
community including analytical chemistry, electrochemistry and colloid and surface chemistry to rationalize
surface charge formation, adsorption and transport of charge species, corrosion, particle growth and so forth.
Using simple thermodynamic arguments I will show that the notion of “surface pH” is simply wrong as long as
systems are at equilibrium. This will be further illustrated with the application of fluctuation theory on a model
charged plate immersed in a chloride acid solution. Finally, I will conclude with the potential application of
fluctuation theory to the detection of traces of charged species (proteins, heavy metals, nanoparticles …) in
aqueous solutions.
Giancarlo Franzese - Thermodynamics of nanoconfined water and for water at biological interfaces
We study, by simulations and analytic approach, the behavior of water in hydrophobic nanoconfinement or at
the interface of proteins [1,2]. We analyze the metastability of supercooled liquid water, between hydrophobic
walls, with respect to ice formation and clarify how the interplay between breaking of hydrogen bonds (HB)
and cooperative rearranging regions of 1-nm size gives rise to diffusion extrema and offers a possible
explanation for the ultrafast transport of water in sub-nanometer channels [3,4]. We discuss the relevance at
low temperature of two isobaric loci of increasing fluctuations and of two associated dynamic crossovers due
to the HB dynamics, consistent with experiments for hydrated proteins [5,6,7]. We study the fluctuations at
cryopreservation temperatures and for confinement in disordered nanochannels we find a dramatic decrease
of the average compressibility, relevant for the preservation of food and organic materials [8].
However, detailed studies of anomalous liquids, including water, confined in disordered nanoporous matrices
show a large inclrease of local compressibility near hydrophobic interfaces [9]. Furthermore, we observe that in
a slit-pore geometry, depending on how strong is the confinement, the fluctuations increase from 2D-like to
3D-like, something unexpected based on studies for simple liquids. We ascribe this result to the strong
cooperativity and the low coordination number of the HB network [10]. If the time will allows us, we will
discuss the relevance of these results for the protein folding, superdiffusion in nanoconfinement [11] and for
nanomedicine [12]
REFERENCES
[1] G. Franzese, V. Bianco, S. Iskrov, Food Biophysics 6 ,186 (2011).
[2] G. Franzese, and V. Bianco, Food Biophysics, 8, 153 (2013).
[3] F. de los Santos, and G. Franzese, J. Phys. Chem. B 115, 14311 (2011).
[4] F. de los Santos, and G. Franzese, Phys. Rev. E 85, 010602(R) (2012).
[5] K. Stokely, M. G. Mazza, H. E. Stanley, and G. Franzese, Proc. Natl.Acad. Sci. USA 107, 1301-1306 (2010).
[6] M. G. Mazza, K. Stokely, S. E. Pagnotta, F. Bruni, H. E. Stanley, and G. Franzese, Proc. Natl. Acad. Sci. USA
108, 19873 (2011).
[7] V. Bianco, M. G. Mazza, K. Stokely, F. Bruni, H. E. Stanley, and G.Franzese, in “Fragility of Glass-forming
Liquids”, A. L. Greer, K. F.Kelton and S. Sastry Eds. (Hindustan Book Agency, New Delhi, 2014), pag.183-189.
[8] E. G. Strekalova, M. G. Mazza, H. E. Stanley, and G. Franzese, Phys.Rev. Lett. 106, 145701 (2011).
[9] E. G. Strekalova, J. Luo, H. E. Stanley, G. Franzese, S. V.Buldyrev, Phys. Rev. Lett. 109, 105701 (2012).
[10] V. Bianco and G. Franzese, Nature Sci. Rep. 4, 4440;DOI:10.1038/srep04440 (2014).
[11] Fabio Leoni and G. Franzese, J. Chem. Phys. 141, 174501(2014)
[12] P. Vilaseca, K. A. Dawson, and G. Franzese, Soft Matter 9,6978 (2013).
Jean-Marc Simon - Application of Hill’s thermodynamics of small system: The Small System Method
Before reaching the thermodynamic limit, different intensive thermodynamic properties change with the
system size. This is particularly the case for molar quantities like the molar enthalpy or molar internal energy.
This effect is mainly due to the fact that the system has a finite volume so it exhibits a surface, virtual or not,
that affects the values of the properties. For molar quantities, it can also be seen like an effect of the volume of
the particles on the limited volume. The thermodynamics of small system of T. L. Hill [1] gives a general
background to systematically express these thermodynamic properties in terms of system size [2, 3].
Alternatively to Hill’s approach similar size effects were obtained using the Kirkwood-Buff’s formalism based on
pair correlation functions [4, 5]. We applied these size properties on molecular simulations to calculate at the
thermodynamic limit the thermodynamic factor, i.e. the derivative of the chemical potential with the
concentration, in open systems [2, 3, 4, 5, 6]. Following the same approach, we also computed partial molar
enthalpy and partial internal energy. This was done on systems were other methods fail to compute such
thermodynamics properties. We call this new approach the small system method (SSM).
REFERENCES
[1] T. L. Hill. Thermodynamics of small systems. Part 1, Benjamin, New York, 1963.
[2] Thermodynamics of small systems embedded in a reservoir: a detailed analysis of finite size effects S. K.
Schnell, T. J. H. Vlugt, J.-M. Simon, D. Bedeaux, S. Kjelstrup, Mol. Phys. 110, 1069 (2012)
[3] Thermodynamics of a small system in a mT reservoir, S. K. Schnell, T. J. H. Vlugt, J.-M. Simon, D. Bedeaux, S.
Kjelstrup, Chem. Phys. Let. 504, 199 (2011)
[4] Kirkwood-Buff Integrals for Finite Volumes, P. Kruger, S. K. Schnell, D. Bedeaux, S. Kjelstrup, T. J. H. Vlugt, J.M. Simon, J. Phys. Chem. Lett., 4, 235 (2013)
[5] How to apply Kirkwood-buff theory of individual species in salt solutions, S. K. Schnell, P. Englebienne, J.-M.
Simon, P. Kruger, S. P. Balayi, S. Kjelstrup, D. Bedeaux, A. Bardow, T. J. H. Vlugt, Chemical Physics Letters 582,
154 (2013).
[6] Fick diffusion coefficients of liquid mixtures directly obtained from equilibrium molecular dynamics, X. Liu, S.
K. Schnell, J.-M. Simon, D. Bedeaux, S. Kjelstrup, A. Bardow, T. J. H. Vlugt, J. Phys. Chem. B, 115, 12921 (2011) +
Correction J. Phys. Chem. B, 116, 6070 (2012)
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