Exceptionally Large and Controlled Effect of Negative Thermal

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Exceptionally Large and Controlled Effect of Negative Thermal Expansion in Porous Heterogeneous Lyophobic Systems Valentin A. Eroshenko, Yaroslav Grosu, Nikolay Tsyrin, Victor Stoudenets, Jean-Marie Nedelec, and Jean-Pierre E. Grolier J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b02112 • Publication Date (Web): 21 Apr 2015 Downloaded from http://pubs.acs.org on April 26, 2015

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The Journal of Physical Chemistry

Exceptionally Large and Controlled Effect of Negative Thermal Expansion in Porous Heterogeneous Lyophobic Systems Valentin Eroshenko,a,* Yaroslav Grosu,a,b,c Nikolay Tsyrin,a Victor Stoudenets,a Jean-Marie Nedelec,b,c Jean-Pierre E. Grolier b,c a

Laboratory of Thermomolecular Energetics, National Technical University of Ukraine “Kyiv

Polytechnic Institute”, Prospect Peremogy 37, 03056 Kyiv, Ukraine. b

Clermont University ENSCCF, Institute of Chemistry of Clermont-Ferrand, BP 10448, 63000

Clermont-Ferrand, France. c

CNRS, UMR 6296, ICCF, 24 av. des Landais, 63171 Aubière, France.

ABSTRACT Negative Thermal Expansion (NTE) is the process in which a system decreases its size upon heating and increases it upon cooling. NTE effect is unusual and useful for a great number of practical applications in the fields of electronics, medicine, mechanics, etc… In this work NTE effect is experimentally investigated for three porous Heterogeneous Lyophobic Systems (HLS), associating water and two grafted mesoporous silicas or the microporous metalorganic framework ZIF-8. Considerable NTE effect, more than one order of magnitude higher than best known materials, is observed for these systems. Additionally it is demonstrated that for

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HLS the temperature range in which NTE takes place is easily controlled by basic characteristics of the porous solid such as pore size distribution.

KEYWORDS: interface energy, liquid intrusion/extrusion, metal-organic framework, grafted silica Introduction Most of materials and systems expand upon temperature increase and shrink when decreasing their temperature 1. Reverse effect (when the size of the system is inversely proportional to its temperature) is called Negative Thermal Expansion (NTE) and is rarely observed 1–4. Associating NTE materials with regular positive thermal expansion materials opens the possibility of creating systems with controlled (for example zero) expansivity. Such opportunity is attractive in a wide range of practical applications in the fields of electronics, medicine, photonics 4, high-precision optics, mechanics 5,6, etc. Range of materials with NTE includes ZrW2O8 (cubic zirconium tungstate) family 3, some zeolites and zeolite-like materials 7, the family of AM2O7 compounds (where A =U, Th, Zr, Hf, Sn and M = P, V) 8, Cd(CN)2, ReO3 9,10, NaZn13-type La(Fe, Si, Co)13 compounds 11.

The value of NTE = and the temperature range (the possibility to set it) where NTE

is observed are naturally considered as the most important parameters of this phenomenon. For most of known materials the value of NTE is about ≈ −10 . Yet for some materials higher values were obtained and were fairly considered as huge: = −1 · 10 for ScF3 12 and = −9 · 10 for crystals of Ca0.8La0.2Fe2As2 13. The colossal value of = −1 · 10 registered for Fluorous Metal Organic Framework (FMOF-1) should be noted, even


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though it was obtained due to sorption of N2 molecules during the cooling process of the porous FMOF-1 and was claimed by the authors as “apparent NTE” 14.

Large negative coefficient of linear thermal expansion = , = , , along c

orientation of about ≈ −10 was reported for NaZn13-type La(Fe, Si, Co)13 compounds 11

and for porous polyacrylamide polymer film with ≈ −1.2 · 10 15. One of the highest

values of c-axial linear negative thermal expansion were also registered for pentamorphic organometallic martensite reaching values of ≈ −7.9 · 10 16, for Ag3[Co(CN)6] with ≈ −1.3 · 10# 17,18, for FMOF-1 with ≈ −1.7 · 10# under vacuum 14, for (S,S)octa-3,5-diyn-2,7-diol with maximum value of ≈ −2.0 · 10# 19, but due to exceptionally large values of positive thermal expansion along a and b axis overall (volumetric) thermal expansion of indicated materials is positive and is very large. In this paper we experimentally demonstrate that orders of magnitude larger effect of negative volumetric thermal expansion (values of ) may be achieved for porous heterogeneous lyophobic systems (HLS) in a temperature range which can be easily controlled by basic characteristics of HLS. A sound thermodynamic analysis is also provided to explain the observed results. Operational principles Porous Heterogeneous Lyophobic System (HLS) is an ensemble of porous solid with large specific surface area (400 – 2000 m2/g) and corresponding non-wetting liquid 20,21, which under certain conditions may have negative values of thermal expansion 22,23. The condition of lyophobicity (contact angle between solid material and corresponding liquid $ > 90°) does not


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allow for the liquid to spontaneously penetrate into the pores of the solid under ambient conditions (pressure and temperature). Forced intrusion of the liquid into the pores (say due to the increase of the pressure to some critical value '() ) decreases the volume of the HLS by the value of the pores volume of the lyophobic solid ∆+() = −+,-./0 . So the work that the system stores upon the intrusion process may be written as: 1() = −'() ∆+() = '() +,-./0 (1) The presence of non-wetting liquid inside the lyophobic pores is energetically unfavorable (capillary forces tend to expulse it), so the process of liquid extrusion from the pores is spontaneous and occurs when the pressure is decreased to some critical value '/4) . If liquid is fully expulsed from the pores, the HLS returns to its initial state ∆+/4) = +,-./0 . The work associated with the extrusion process which the system restores may be written as: 1/4) = −'/4) ∆+/4) = −'/4) +,-./0 (2) From eqs. (1) and (2) it can be seen that specific mechanical energy which the HLS stores (5() = 1() ⁄+66 ) and restores (5/4) = 1/4) ⁄+66 ) is proportional to the porosity of the matrix 8=

9:;>

and to the intrusion/extrusion pressures '(),/4) . Although extreme values of this

parameter have obvious technical limitations. Here +66 is initial volume of HLS. In many cases '() and '/4) can be identified with Laplace capillary pressures: '(),/4) = −

?@A$B,C (3) DE6


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Where the advancing contact angle $B is used for the intrusion pressure '() and the receding contact angle $C is used for the extrusion pressure '/4) ; ? is the surface tension of the liquid and D is a geometry parameter (D = 0.5 for cilinders and D = 0.33 for spheres), E6 is an average pore radius. Due to the non-wetting condition G$B,C > 90°H @A$B,C < 0. Although it should be noted that direct application of equation (3) is often questionable for a HLS due to the small size of its pores: for microporous materials, where the diameter of the pore is only of few molecular layers 21,24–27, such macroscopic parameter as the contact angle $ does not exist. On the other hand for a mesoporous HLS the extrusion pressure is additionally determined by the condition of critical bubble nucleation inside the pores 28,29 and for both intrusion and extrusion pressures the effect of the line tension on the values of $B,C should be taken into account 29,30. Reversible intrusion/extrusion process is followed by the development/reduction of a large ‘solid – liquid’ interface Ω development as: ∆+(),/4) = −DE∆Ω (4) Hence if eq. (3) is applicable, the mechanical energy that HLS stores/restores during intrusion/extrusion process is determined by the Gibbs work of interface development/reduction: L1(),/4) = −?@A$B,C MN (5) Such development/reduction of the interface Ω is followed by an endothermal/exothermal effect (breakage/recovery of intermolecular bonds of the liquid), so during compression/decompression a HLS also stores/restores thermal energy in the form of Gibbs heat of interface development/reduction:


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LO(),/4) = P

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MG?@A$B,C H MN (6) MP

For a real HLS as described above the surface effects (which are dominant for a HLS) are always accompanied by classical bulk effects of the liquid and of the porous matrix. So the overall work and heat for HLS is defined as: L1R,S = L1(),/4) + L16 = −?@A$B,C MN + 'M+6 (7) LOR,S = LO(),/4) + LO6 = P

MG?@A$B,C H MN + LO6 (8) MP

Where indexes “c” and “d” stand for compression and decompression respectively, “0” indicates the bulk phase (liquid and matrix), M+6 = M+ + M+V determines change of the volume of the liquid + and of the matrix +V due to pressure or temperature change. Total volume change for HLS may be written as: M+R,S = M+(),/4) + M+6 (9) In the general case the volume of HLS is a function of pressure ' and temperature P, hence the total differential of +R,S may be written: X+(),/4) X+(),/4) M+R,S (', P) = W Y M' + W Y MP − +66 Z 6 M' + +66 6 MP (10), X' XP

where Z 6 = − > > >

,[

is the isothermal compressibility and 6 = > > >

,[

is the isobaric

coefficient of thermal expansion of components of the HLS (liquid and matrix) when interface effects do not take place (i. e. Ω = @^A_).


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Negative thermal expansion of porous heterogeneous lyophobic systems The form of the first term of eq. (10) is determined by the pores size distribution function of the matrix:

9:;

Exceptionally Large and Controlled Effect of Negative Thermal

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