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Reversible Wetting in Nanopores for Thermal Expansivity Control: From Extreme Dilatation to Unprecedented Negative Thermal Expansion Yaroslav Grosu,*,†,‡,§ Abdessamad Faik,§ Jean-Marie Nedelec,† and Jean-Pierre Grolier† †

Université Clermont Auvergne, CNRS, SIGMA Clermont, ICCF, F-63000 Clermont-Ferrand, France Laboratory of Thermomolecular Energetics, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Pr. Peremogy 37, 9 03056 Kyiv, Ukraine § CIC Energigune, Albert Einstein 48, Miñano, Á lava 01510, Spain ‡

S Supporting Information *

ABSTRACT: In this work a general thermodynamic grounds as well as experimental verification are given to demonstrate how a reversible wetting process of a liquid in nanopores provoked by a temperature variation can be used to develop systems with the necessary thermal expansion behavior. Thermal expansion coefficients of such nanoporous heterogeneous lyophobic systems can be controlled in the unprecedentedly wide range of both negative and positive values. Perspectives as well as challenges on the full potential use of the proposed mechanism are identified.

thermal expansion in reduced layered ruthenate was finally reported by Takenaka et al.11 In general, the most known materials with NTE are the cubic zirconium tungstate family ZrW2O8,3 some zeolites and zeolitelike materials,12 the family of AM2O7 compounds (where A = U, Th, Zr, Hf, Sn and M = P and V),13 Cd(CN)2, ReO3,14,15 and NaZn13-type La(Fe, Si, Co)13 compounds.16 For most of the known materials which demonstrate NTE, the value of the

1. INTRODUCTION Thermal expansion is a basic characteristic of a material or a system considered important not only in nearly every field of science and technology but also in other aspects of our life. It is very common in nature that a body expands/shrinks upon heating/cooling exhibiting positive thermal expansion (PTE).1 Such behavior can be useful as it represents the process of thermal to mechanical energy transformation but also can be undesirable when invariable dimensions within some temperature range are required. In the former case the rare phenomenon of negative thermal expansion (NTE)shrinking/expanding upon heating/cooling1−4becomes very useful to compensate for PTE and to reach zero thermal expansion, which is critical for applications like high-precision optics, electronics, photonics, mechanics, etc.4−6 In any of these cases, PTE or NTE, it is obviously important to be able to control the thermal expansion in terms of both its magnitude and its temperature range. In recent years the topic of NTE has generated increasing interest in the scientific and industrial communities.3,7−24 Numerous works are dedicated to the development of materials with pronounced NTE and its control in a required temperature range. In particular, in very recent works Engel et al. investigated organic systems demonstrating NTE.7 The feasibility of using multiwalled carbon nanotubes for the control of coefficients of thermal expansion of composite materials was evaluated in the work of Shirasu et al.8 Wang et al. fabricated a range of mechanical metamaterials with adjustable NTE.9 Ca3−xSrxMn2O7 perovskite was investigated in terms of NTE control by adjusting the composition.10 Colossal negative © 2017 American Chemical Society

isobaric thermal coefficient is ca. α ≡

1 V

( ∂∂VT )P ≈ −10−6 K−1.

However, for some materials, higher values were reported: α = −10−5 K−1 for ScF317 and α = −9 × 10−5 K−1 for Ca0.8La0.2Fe2As2.18 The apparent NTE value of α = −10−2 K−1 was reported for nanoporous fluorous metal organic framework (FMOF-1) due to sorption of N2 molecules during the cooling process.19 Takenaka reported α = −1.15 × 10−4 K−1 for reduced layered ruthenate.11 There are also some works on the negative coefficient of linear thermal expansion αi ≡

1 ∂L ,i L ∂T P −5

( )

= a , b , c , along the

ith orientation. In particular, αC = −10 K−1 was reported for NaZn13-type La(Fe, Si, Co)13 compounds16 and for porous polyacrylamide polymer film with αC = −1.2 × 10−3 K−1.20 Some of the highest values of c-axial linear negative thermal expansion were also reported for pentamorphic organometallic martensite reaching values of αC = −7.9 × 10−5 K−1,21 for Ag3[Co(CN)6] with αC = −1.3 × 10−4 K−1,22,23 for FMOF-1 with αC = −1.7 × 10−4 K−1 under vacuum,19 and for (S,S)-octaReceived: March 20, 2017 Revised: May 5, 2017 Published: May 5, 2017 11499

DOI: 10.1021/acs.jpcc.7b02616 J. Phys. Chem. C 2017, 121, 11499−11507

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The Journal of Physical Chemistry C 3,5-diyn-2,7-diol with a maximum value of αC = −1.0 × 10−4 K−1,24 but due to the exceptionally large values of positive thermal expansion along the a and b axes, the overall (volumetric) thermal expansion of indicated materials is positive and very large. There are certainly less works on PTE, as this effect is classical and well known. Fabini et al. investigated positive thermal expansion in hybrid formamidinium lead iodide pervoskite.25 MZrF6 series (M = Ca, Mn, Fe, Co, Ni, and Zn) were explored in terms of thermal expansion control from positive to negative.26 The use of positive thermal expansion as an actuator still remains an explored topic.27 Tailoring the expansion of metal alloys was demonstrated in ref 28. Previously we demonstrated that a system consisting of a porous material and a nonwetting liquid (nanoporous heterogeneous lyophobic system (NHLS)) can exhibit both exceptional negative thermal expansion29,30 and extreme dilatation behaviors31 with orders of magnitude higher absolute values of the thermal coefficient compared to other materials and controlled temperature range. Such high values are reached due to the reversible intrusion−extrusion process of nonwetting liquid into porous material induced by temperature variation: since the liquid is nonwetting with respect to the porous solid, it does not penetrate inside the pores under ambient conditions; however, temperature variations can provoke intrusion or extrusion of a nonwetting liquid (depending on the NHLS) leading to pronounced volume variation. Due to such unconventional mechanism NHLS (which is typically in the form of a suspension) demonstrates orders of magnitude higher volume variation upon temperature change in comparison with solids. It is of high importance that both positive and negative thermal expansions of an NHLS can be easily controlled in terms of magnitude and temperature range by the pore size distribution of the solid and by the degree of nonwetting condition. In this work we generalize the theoretical basis for the mechanism responsible for different thermal expansion of an NHLS, demonstrating how it can be controlled in terms of magnitude, sign (positive or negative), and temperature range through the basic properties of the porous material and nonwetting liquid. Next, we validate the obtained conclusions with some experimental data.

temperature and volume. A detailed description of experimental setup is given elsewhere.67 The stability of the ZIF-8 samples before and after the intrusion−extrusion cycles was verified by XRD analysis using a Bruker D8 Advance X-ray diffractometer equipped with a LYNXEYE detector using Cu Kα1 radiation (λ = 1.5418 Å) and θ−2θ geometry. Data were collected at room temperature between 3° and 110° in 2θ with a step size of 0.02° and counting time of 8 s per step.

3. RESULTS AND DISCUSSION Thermodynamic Description of NHLS. Systems consisting of a porous material and a nonwetting liquid heterogeneous lyophobic systemshave been considered for energy applications and investigated extensively in recent years.32−79 The operational principle based on reversible forced intrusionspontaneous extrusion of nonwetting liquid into from the pores was considered promising for mechanical energy storage34,38,58,63,64 or dissipation35,41−57,79 due to several advantages compared to conventional working bodies, like system charge (intrusion)−discharge (extrusion) at constant pressure,33,34,38 absence of overheating upon operation even at high frequencies,35,39,40,79 and high energy density.37−39 In what follows we make an attempt to develop a general thermodynamic description of NHLS, with a particular focus on the isobaric conditions, which are explored very poorly in the literature at the moment. In our previous works it was demonstrated that a thermodynamical description of NHLS requires consideration of not only the bulk effects (determined by the properties of a porous solid and a nonwetting liquid) but also the interfacial effects (determined by liquid intrusion−extrusion process).29,30 Such basis allows writing the equation of state for NHLS f(P,V,T) = 0 in the general form as follows f (P , V , T ) = fi , e (P , ΔVi , e , T ) + fb (P , Vb , T ) = 0

(1)

where f i,e (P, ΔVi,e, T) represents the connection between pressure (P), temperature (T), and volume variation upon nonwetting liquid intrusion/extrusion into/from porous material (ΔVi,e), while f b(P, Vb, T) is the equation of state of the bulk phase of NHLS having volume Vb = Vl + Vm and consisting of liquid (Vl) and porous material (Vm). While f b(P, Vb, T) can be defined through known thermal coefficients of liquid and solid, f i,e (P, ΔVi,e, T) is more complex to express since it must reflect the pore size distribution of a solid, which directly influences the values of pressure and temperature under which intrusion/extrusion takes place. For example, in the case where the distribution of the pore radius r can be described by the

2. EXPERIMENTAL SECTION In this work two NHLSs were used based on microporous metal−organic framework ZIF-8 and mesoporous grafted silica gel HC18. ZIF-8 was purchased from Sigma-Aldrich as Basolite Z1200 (Zeolitic imidazolate framework); it consists of cage-like pores of ∼1.16 nm diameter connected by 6-ring windows of ∼0.34 nm and is characterized by a huge specific surface area of ca. 1800 m2/g. The porosity of the material was determined as 0.38 cm3/g by nitrogen gas sorption. HC18 stands for Hypersil 5u HS C18. It is a mesoporous silica grafted by linear chains of octylsilanes (C18H37) purchased from Hypersil. It has two-peak pore size distribution in the 3−11 nm range (Figure S1), surface of 140 m2/g, and pore volume of 0.4 cm3/g. Water was used as nonwetting liquid for these hydrophobic porous materials. A modified ST-7M transitiometer of the ST-7 model instrument (BGR-Tech) was used under isothermal conditions, with simultaneous recording of pressure and volume, and also under isobaric conditions, with simultaneous recording of

1

( )

Cauchy distribution function fr (r ) = π arctg

r − r0 80 Dr

with two

parameters (average radius r0 and its dispersion Dr), the equation of state for an NHLS may be written as f (P , V , T ) = V +

⎛ P − Pi , e(T ) ⎞ ⎟ arctg⎜ π D ⎠ ⎝

Vpore

+ fb (P , Vb , T ) + C = 0

(2a)

or 11500

DOI: 10.1021/acs.jpcc.7b02616 J. Phys. Chem. C 2017, 121, 11499−11507

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The Journal of Physical Chemistry C ΔV = −

⎛ ΔP − Pi , e(ΔT ) ⎞ ⎛ ∂V ⎞ ⎟ + ⎜ b ⎟ ΔP arctg⎜ D π ⎠ ⎝ ∂P ⎠T ⎝

Now by using the definition of the isobaric thermal expansion coefficient α and eq 2b, one can write for isobaric conditions

Vpore

⎛ ∂V ⎞ + ⎜ b ⎟ ΔT ⎝ ∂T ⎠ P

⎧ ⎪ ⎪ 1 ⎛ ∂V ⎞ ⎨α ≡ ⎜ ⎟ ⎝ ∂T ⎠ P V ⎪ ⎪ ⎩

(2b)

where Vpore is the volume of the pores in the system, Pi,e(T) is the temperature-dependent intrusion/extrusion pressure, D is the dispersion of the values of P i , e , and C=−

Vpore π

(

arctg

P0 − Pi , e(T0) D

)

equation at the initial pressure P0 and temperature T0. There are a large number of different distribution functions which can be used for that matter (Gaussian, LogNormal, Weibull, etc.)80 and perhaps will be more accurate than the Cauchy function; however, we consider the Cauchy distribution function as one of the most elegant mathematically-wise and easy to work functions for the purposes of demonstrating the proposed NHLS description. Therefore, we use it here for demonstration purposes, but any other function can be used depending on the best fit to real pore size distribution. The compressibility of the systems can be written using eq 2b as follows ⎧ ⎪ ⎪ 1 ⎛ ∂V ⎞ ⎨β ≡ ⎜ ⎟ ⎝ ∂P ⎠T V ⎪ ⎪ ⎩ Vpore =− · Vπ 1+

1

(

P − Pi , e(T ) D

· 2

)

V=−

⎛ P − Pi , e(T ) ⎞ ⎟ + Vb(T ) − C arctg⎜ D π ⎠ ⎝

Vpore

(5b)

∂Pi , e

( ) ∂T

defines the increase or decrease

P

(6a)

⎛ ∂Pi , e ⎞ 1 ⎛ ∂V ⎞ 1 ⎛ ∂Vb ⎞ ⎟ ⎜ ⎟ >0→ ⎜ ⎟ > ⎜ V ⎝ ∂T ⎠ P V ⎝ ∂T ⎠ P ⎝ ∂T ⎠ P

(6b)

⎛ ∂Pi , e ⎞ 1 ⎛ ∂V ⎞ 1 ⎛ ∂Vb ⎞ ⎟ ⎜ ⎟ =0→ ⎜ ⎟ = ⎜ ⎝ ⎠ V ∂T P V ⎝ ∂T ⎠ P ⎝ ∂T ⎠ P

(6c)

∂Pi , e

( ) ∂T

∈ [−0.2; 0.2], Vpore = 0.5 cm3/g, we explore

P

the behavior of the NHLS near intrusion/extrusion conditions (P − Pi,e(T)) ∈ [−1; 1] in Figure 1 for two different cases of pore size distribution broadness, reflected through intrusion− extrusion dispersion D. Figure 1a is for narrow distribution D = 0.2 MPa, and Figure 1b is for broad distribution D = 2 MPa. From Figure 1 one can see that depending on the intrusion/

(4)

where is the function describing the volume variation ΔV(k) i,e due to pressure or/and temperature provoked intrusion/ extrusion into/from the kth set of pores. In eqs 2a and 2b the parameters Pi,e(T) and D can be defined through the pore size distribution function of a solid. For example, in the simplest case intrusion/extrusion pressure is f (k) i,e

r0

)

⎛ ∂Pi , e ⎞ 1 ⎛ ∂V ⎞ 1 ⎛ ∂Vb ⎞ ⎟ ⎜ ⎟ 0, which according to eq 6b

means that such systems can be used to demonstrate extreme dilatation of the NHLS. While for the intrusion pressure the dependence is positive for {ZIF-8 + water} NHLS

Figure 1. Isobaric coefficient of thermal expansion of NHLS calculated using eqs 5a and 5b having, respectively, a (a) narrow pore size distribution and (b) broad pore size distribution.

it is negative for {HC18 + water} NHLS

∂Pi ∂T P

( )

∂Pi ∂T P

( )

> 0,

< 0. As we

previously demonstrated how an exceptionally large negative thermal expansion effect can be reached for an NHLS,29,30 we

Figure 2. PV isotherms of (a) {HC18 + water} NHLS at 275 K, (b) {HC18 + water} NHLS at 325 K, (c) {ZIF-8 + water} NHLS at 275 K, and (d) {ZIF-8 + water} NHLS at 325 K. 11502

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Figure 3. Relative volume change of (a) {HC18 + water} NHLS at atmospheric pressure upon heating and (b) {ZIF-8 + water} NHLS at a constant pressure of 23.8 MPa upon cooling.

Figure 4. Isobaric thermal expansion coefficient α of (a) {HC18 + water} NHLS at atmospheric pressure upon heating and (b) {ZIF-8 + water} NHLS at a constant pressure of 23.8 MPa upon cooling.

demonstrates one peak of α (one-step intrusion) while {HC18 + water} NHLS demonstrates two peaks of α (two-step extrusion). This is due to the differences in the pore size distributions of two systems. While ZIF-8 is known to have one statistical peak of pore size due to its defined crystalline structure, amorphous silica gel HC18 has two as can be seen from gas sorption analysis (Figure S1) as well as from the water intrusion experiment, particularly if one plots the compressibility of the system as a function of pressure (Figure 5). We now use the {HC18 + water} NHLS to confront the proposed model with experiment, as this system demonstrates more complex behavior and allows one to use an equation of state in its general form (eq 4) for HLSs based on porous

focus on the extreme dilatation behavior in this work, demonstrating that it can be reached by both intrusion and extrusion processes following the theoretical basis described above. In particular, for {HC18 + water} NHLS the transformation from bumper to shock-absorber behavior in the 275−325 K temperature range suggests that extrusion of water may be induced by the temperature increase from 275 to 325 K under atmospheric pressure. This process is demonstrated in Figure 3. After compression of the {HC18 + water} NHLS at 275 K (Figure 2) water remains inside the pores even after the pressure is lowered to atmospheric pressure. Once the temperature of the system is increased, extrusion takes place, generating a huge volume increase (dilatation) of nearly 50% of its initial volume V0. The experimental thermal expansion coefficient of such system is shown in Figure 4, reaching the maximum value α = 2 × 10−2 (K−1). It is orders of magnitude larger compared to known materials with pronounced dilatation. For the {ZIF-8 + water} NHLS due to its high value of intrusion pressure in order to reach the effect of extreme dilatation experiments were performed under controlled isobaric condition of P = 23.8 MPa. Taking advantage of its positive dependence of intrusion pressure (eq 6b) we were able to provoke intrusion of the water into the pores by cooling the system at constant pressure (Figure 3b). The obtained thermal expansion behavior for this NHLS is similar to the {HC18 + water} NHLS in terms of the magnitude as both systems have similar pore volume and extrusion pressure temperature dependence. The evident difference of the isobaric thermal expansion coefficient for the two NHLSs is that {ZIF-8 + water} NHLS

Figure 5. Adjustment of the parameters of eqs 3a and 3b using experimental compressibility of {HC18 + water} NHLS. 11503

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expansion behavior compared to known systems in terms of the control of both the magnitude and the temperature range. However, in order to be able to use the full potential of the proposed mechanism there are two highly desirable properties which must be reached. (1) Negligible intrusion−extrusion hysteresis. The presence of pressure hysteresis in the isothermal compression− decompression cycle (Figure 2) results in a temperature hysteresis in the isobaric heating−cooling cycle, which is certainly a nondesirable phenomenon. In particular, this does not allow us to obtain the heating−cooling cycle at the same pressure for studied NHLSs, as such hysteresis leads to very large intrusion and extrusion temperatures difference, increasing the necessary temperature range for the cycle beyond the characteristics of our equipment and/or beyond the temperature range where water is in the liquid state. We recently reported a new NHLS based on Cu2(tebpz) MOF, which exhibits negligible hysteresis (molecular spring).76 We further focus our work on reaching the reversible heating−cooling cycle for such NHLSs. (2) Acceptable intrusion/extrusion pressure. It seems that in most cases taking advantage of the prominent thermal expansion of NHLSs is more preferable at atmospheric pressure. However, among the great variety of reported NHLSs there is clear evidence of a deficit of the ones having an intrusion−extrusion cycle near atmospheric conditions. This is due to the fact that such systems were considered for mechanical energy storage/dissipation applications, where relatively high operational pressures are required to reach an attractive energy capacity. With this regard deep understanding of the mechanism behind intrusion−-extrusion pressure hysteresis is definitely required along with the development of NHLSs with desirable intrusion−extrusion pressures.

materials with a complex pore size distribution (more than one statistical peak). and For that matter first we determine intrusion P(k) i extrusion P(k) pressures as well as their dispersion D(k). It is e easier to do by fitting the theoretical compressibility (eq 3a) to experimental one (Figure 5). From such fitting one gets V(1) pore = 3 (1) 0.015 cm3/g, V(2) pore = 0.29 cm /g, Pi (T = 300 K) = 13.7 MPa, (1) P(2) i (T = 300 K) = 16.8 MPa, Pe (T = 300 K) = 1.9 MPa, (2) (1) Pe (T = 300 K) = 2.0 MPa, D = 0.4 MPa, and D(2) = 2.1 MPa. Using these parameters in eq 2b we obtain rather good agreement between the theoretical and the experimental curves of the PV isotherms (Figure 2b), suggesting that the Cauchy function is a judicious choice for this system. Next, by introducing the obtained parameters of {HC18 + water} NHLS in eqs 5a and 5b one may compare the obtained model curve with experiment for volume variation upon temperature change (Figure 3a) as well as for isobaric thermal expansion coefficient α (Figure 4a). The temperature coefficient of the extrusion pressure

∂Pe ∂T P

( )

= 0.04 MPa/K

was used from experimental data at different temperatures (Figure 2a and 2b). However, in principle such coefficient may be calculated using the bubble nucleation approach, which was described in detail in previous works,42,55,79 and it is out of the scope of this article. From Figure 4 it can be seen that α can be predicted by using the proposed approach. Perhaps a more complex distribution function than the Cauchy one can be used to improve the agreement between experiment and model. However, such improvement is purely mathematical and more cumbersome with respect to the thermodynamical approach demonstration, which is the main goal of this work. There could be of course some physical assumptions, which might decrease the predictive aim, like, for example, the temperature and/or pressure dependence of the pore size distribution. Retrospective and Perspective. At this point it seems that only one application based on pronounced dilatation of NHLS can be found in the early works of Eroshenko.81 It was shown that previously melted metal alloy intruded inside the pores results in its extrusion upon liquefaction and as a result in pronounced dilatation. Such mechanism was used to create a thermal actuator called a “thermal key”,81 which reached an application level as an autonomic emergency actuator at a nuclear power plant.82 The advantage of the thermal key is the considerable amount of stored mechanical energy released in a smooth (nonexplosive) way upon heating it above the metal alloy melting point due to a relatively high extrusion pressure. The mechanism of thermal expansion control proposed in this work has a different nature (reversible wetting) and has several advantages compared to the thermal key: (1) ability to work in continuous heating−cooling cycles, while the thermal key after each discharge (extrusion) must be recharged by means of compression of the NHLS above the intrusion pressure under temperature higher than the melting point of the metal alloy; (2) ability to reach an effect of negative thermal expansion, while the thermal key can exhibit only dilatation; (3) the intrusion−extrusion cycle in the proposed mechanism is not destructive for a porous material, while in thermal key crystallization melting of an alloy inside the pores may have a negative (destructive) effect on the structure of a porous material due to a pronounced volume variation inside the nanoconfinement. From the results presented in this and previous works29−31 it clearly appears that NHLSs have unprecedented thermal



CONCLUSIONS The exceptional variability of the thermal expansion behavior of nanoporous heterogeneous lyophobic systems (NHLSs) was demonstrated theoretically and experimentally. The thermal expansion coefficient of an NHLS not only can reach orders of magnitude higher values compared to best known materials but its sign (positive or negative) and temperature range can be tuned by the basic characteristics of the NHLS. Such behavior is due to the unconventional mechanism occurring in a NHLS, i.e., reversible wetting of a liquid in nanoporous material induced by temperature variation. Due to the strong orientation of previous works on the use of NHLSs for mechanical energy storage/dissipation applications, the lack of systems with negligible intrusion−extrusion pressure hysteresis operating under close to atmospheric pressure is observed. Development of NHLSs with such characteristics would be very beneficial in terms of the potential applications, particularly in the area of negative thermal expansion materials.



ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b02616. Figures of gas sorption isotherms, XRD patterns and pore size distribution (PDF) 11504

DOI: 10.1021/acs.jpcc.7b02616 J. Phys. Chem. C 2017, 121, 11499−11507

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yaroslav Grosu: 0000-0001-6523-1780 Jean-Pierre Grolier: 0000-0002-6524-8731 Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS The help of Cristina Luengo with gas sorption measurements is appreciated.



REFERENCES

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