RICERCA ITALIANA     

Vibrational dynamics and relaxation in densified glasses and confined disordered systems

Università degli Studi di Perugia

Abstract

The present project is promoting a research based on a collaboration between the Research Units (RU) of L’Aquila, Camerino, Messina, Perugia and Trento and it is devoted to the study of the vibrational dynamics, relaxation phenomena and structural characteristics in disordered systems. The aim of the research is to extract information on the correlation between dynamics and relaxation in glassy systems and in liquids/glasses in conditions where they are confined. This sort of activity is quite important for both the basic research and different technological applications. Indeed the disordered materials usually employed in many applied fields suffer the aging problem, that is the deterioration of even macroscopic properties which, in turn, are governed by microscopic/atomic mechanisms strongly related to dynamics and relaxation processes. In addition, the behaviour of confined disordered systems is becoming more and more important because it is relevant for understanding basic mechanisms related to reduced dimensionality, and it is important to develop applications which are becoming strategic for the use of nano-structured phases. In particular, we will study the characteristics of the acoustic waves which propagates at high frequency in the interval between GHz and THz and their relationship to the structural disorder and the to the interaction between propagating modes and relaxation processes. Also the correlation between the vibrational properties and those like, for instance, the effective viscosity at wavelength comparable to the interatomic distance, the glass transition and other correlated quantities, determined by diffusion and relaxation phenomena and the role of anharmonicity will be the key point of the present project. The experimental techniques will be based on the inelastic scattering of visible light, ultraviolet, x-ray and neutron, the diffraction of x-ray and neutron, DSC and low temperature calorimetry. An important role will be played also by the structural determination in the different systems which will be studied by the various RU of the project. The research groups involved in the project already represent a block of high qualification at the national and international level in the physics of disordered systems and they have already shown the capability of collaborating to perform investigations. In addition they have quite some capability of performing experiments employing the large scale infrastructures of Grenoble, ESRF and ILL, both as users and in the proposition and construction of new instruments. In addition, also many of the laboratory equipments available at the different units represent a rather unique support which is an important added value for the present project . Indeed at the RU of Alquila the only existing Brillouin spectrometer with two monochromators is installed which guarantees a very good contrasts against the elastic scattering, at the RU of Camerino sophisticated x-ray characterization lines are available which are dedicated to the study of the present systems, at the RU of Messina a low temperature calorimeter (down to 8 mK using the new refrigerator) is available which cannot be easily found in other laboratories, at the RU of Perugia a collaboration with the Deuteration Laboratory of Grenoble has been established to produce deuterated proteins and it is available an easy access to the CRG spectrometers in Grenoble, BRISP and IN13, which are unique tools in the world and finally at the RU of Trento a high level capability and instrumentation necessary to produce glasses is available. <<<

Principal Investigator

Francesco Sacchetti Università degli Studi di PERUGIA

Research Objectives

The objective of the present research project is a better understanding of the interaction mechanisms and the correlation which exists between the vibrational modes and the relaxation phenomena which are present in (either strong or fragile) glasses and in the correlated systems having a similar disordered structure, that is hydration water of biological molecules and ion exchange membranes. The interactions we mentioned appear relevant in different properties of these systems. On one hand, together with the structural disorder, they give rise to the attenuation of the propagating acoustic waves (density fluctuation modes), on the other hand they introduce a connection between the vibrational properties and those more related to atomic diffusion. The specific aims of the project are as follows:

1) We will perform an experimental study, by employing different techniques, of the frequency distribution and the attenuation of the propagating acoustic waves. The available data show that both the structural disorder and the relaxation phenomena contribute to the attenuation as a function of temperature and wave vector transfer Q. At high Q the structural contribution to the attenuation is generally more important, while the dynamic relaxation should be more important at low Q, while in the intermediate region the situation is less known. In addition the relevance of the microscopic and mesoscopic structure is still to be investigated. Therefore we would like to investigate also the intermediate Q region, by entering into it as much as possible, by performing studies using the inelastic scattering of ultraviolet radiation, x-ray and neutron, at different temperatures and on different systems within the categories we discussed above, by identifying the effects which are related to the density changes introduced by densification. The experiment will be performed at the laboratories of the RU’s, at the ELETTRA synchrotron and at the European infrastructures ILL and ESRF in Grenonble. In addition to the inelastic scattering measurements, accurate structural characterizations to be connected to the dynamic properties and calorimetric measurements as a function of temperature, down to very low temperature where the most exotic phenomena contributing to relaxation happen, will be performed. The systems we will consider are those indicated above, that is glasses of different level of fragility treated in different ways in order to give rise to some densification and hydration water of proteins and proton exchange membranes.

2) We will try to unify, as much as possible, the experimental observations in different systems in a unified view by connecting the experimental observations on the propagation of the density fluctuations to the characteristics of various systems. The connection to the polymorphic behaviour of many disordered systems can be invaluable in understanding the role of the structure on the dynamic properties. Indeed, it is important to mention that the present evidence on the polymorphic behaviour of even simple systems like germanium, silicon and their oxides, is practically limited to theoretical arguments or computer simulations, while the development of this project can produce new experimental data to be correlated to those on dynamics and relaxation. Finally the structural transformations, which are obtained through the progressive and appreciable increase of the density (increased atomic packing and higher connectivity of the glass network), produce a consistent reduction of the microscopic local mobility so that it is possible to study the effect on characteristic and somewhat anomalous (e.g. boson peak) aspects of the glassy systems and it is possible to identify the microscopic origin of the relaxation processes both due to thermal and tunnel activation. <<<

First Results

As explained above, despite remarkably increased by the constant improvement of experimental techniques in the last decade, our knowledge of dynamics and correlated processes (e.g. relaxations) in glasses and undercooled liquids is still confined to a phase where large amounts of data are collected and interpreted on the base of phenomenological and empirical models. Indeed, the wide variety of existing disordered systems makes the acquisition of new information very difficult, as even very different samples, in terms of chemical or structural properties, display similar behaviours and it is therefore difficult to predict in advance which category (e.g. in terms of rigidity) a new material will belong to. In the present project, the possibility of changing the sample properties without modifying its chemical composition and/or the experimental conditions of study, is considered very useful. In particular, when applicable, permanent densification appears as a promising way to change the characteristics of the studied system without affecting its chemical properties and thus performing a set of experiments all in similar conditions. The main targets of this project concern, first of all, the possibility of producing in a controlled way a set of new and well-characterised samples, having different properties with respect to the initial prototypes. The production processes must be defined in detail and the samples must be produced in amounts which have to be well suitable for the kind of desired experimental studies. In particular, for experimental investigations by means of inelastic neutron scattering, samples with masses of the order of about 10 g and of adequate purity are needed. Besides considerable amounts of sample, high-quality inelastic neutron scattering experiments often require a precise control of the isotopic composition as well. For instance, B2O3 samples have to be produced with a negligible content of isotope 10 of the B atom, as the latter has such a large neutron absorption cross section that would make the experiments definitely impossible to carry out. The use of samples containing isotope 11 of the B atom allows instead the fulfilment of experiments in optimal conditions. MBP samples will have to be both completely deuterium-substituted, and produced in the usual hydrogenated form. By carrying out four experiments (deuterated protein with deuterated water, deuterated protein with hydrogenated water, hydrogenated protein with deuterated water, hydrogenated protein with hydrogenated water), this kind of sample preparation provides the possibility of determining all the three involved correlation functions: protein-protein, protein-water and water-water. The latter correlation function is of major interest, due to the properties of undercooled liquid displayed by hydration water, which is known to undergo a glass transition at low temperature and whose properties are known to depend on the protein hydration level, that is on the level and kind of protein-water interactions. It will be therefore very important for the present project to develop the ability of producing MBP samples to a controlled hydration level, in both deuterated and hydrogenated form. For the contribution of hydration water to be visible in an experiment of inelastic neutron scattering, the samples must have masses of at least 1 g, as in this kind of samples the mass of hydration water is in general similar or slightly less than that of the protein. Smaller samples will also be employed for inelastic X-ray scattering. In this case, a comparison between dry and hydrated protein samples will be necessary to obtain some information about the dynamics of hydration water. Nevertheless, thanks to the complete coherence of the X-ray cross-section, such piece of information will be a precious support for the interpretation of the neutron scattering data. The collected structural and thermodynamical data of all the investigated systems, besides being important in terms of fundamental information, will have a great interest per se. Indeed, structural studies allow an accurate determination of phase diagrams, in particular as concerns systems displaying properties of polymorphism. Structural changes have a fundamental role in defining the average interactions which determine the propagation speed of density fluctuations, whereas, local ordering is definitely important in determining attenuation processes in the range of short wavelengths. Because of the need of performing delicate experiments in well controlled temperature and pressure conditions, an important target of this project is the production of sample holders capable of operating at high temperatures (up to 1000 K and beyond), without introducing excessive background scattering that would spoil the measurement. For light-, neutron- and X-ray-scattering experiments, the choice of the sample holder has an important role and represents the first step to a successful experiment. The project proposers have a wide experience in this field. Nonetheless, the introduction of new materials and production techniques for innovative sample holders will be an important and useful step forward for future research as well. Even sample holders of proteins can be a delicate issue when high hydration levels are employed, because of the possible chemical aggression of the sample holder walls. The development of new methods for protecting the material constituting the sample holder (usually an aluminium alloy) will be very important. Finally, the development of the very low-temperature calorimeter, which will allow to single out thermodynamic process unexplored up to now, will be of great relevance. In conclusion, the present project will provide new information about the behaviour of some model and confined systems, investigated upon changing the sample preparation conditions and the measuring conditions. Despite the proposed research project does not have direct connections with technological developments, the investigated systems are very important for several technological applications. Understanding boron structures in normal and permanently densified glasses is of fundamental importance in condensed matter physics, because (i) B2O3 is a primary component of a wide range of optical materials and glass-ceramics and, mostly, (ii) small amounts of B2O3 in magmatic melts could regulate the transport properties and the dynamics of magmas in the Earth’s interior. Even classical glasses like SiO2 can find extremely high-level applications and cannot be substituted with any other material nowadays. For example, the mechanical suspensions of the experiment VIRGO, the 5km interferometer developed for the search of gravitational waves, are made of SiO2. In high-technology applications, like the one cited above, relaxation processes produce an intrinsic noise that has to be minimised. A better knowledge of such processes is essential for improving the production methods and attain the development of new materials. On the other hand, a deeper knowledge of the behaviour of complex materials, such as nafion, has a direct impact on problems connected to the improvement of fuel cells performances. Indeed, nafion is the most common ionic-exchange based membrane presently employed. Hydration and transport processes, essential to the functioning of fuel cells, are also the first cause of deterioration of the membrane itself, and therefore the first cause of limitation of the fuel cells lifetime. Protein deuteration is an essential step for a better understanding of the processes biomolecules are involved in. Hydration water is the essential environment for their functional activity, and in turn water density fluctuations are thought to drive the conformational changes which allow such activity. <<<

Timescale

24 months

National and international background

The disordered systems give rise to a large extent of phenomena over a wide range of temperature and characteristic times. Surprisingly, the dynamics and thermodynamics of this wide and heterogeneous class of systems show similarities and universal trends which are independent of the specific structure and chemical bonding. This observation suggests that behind the experimental observations there are common and universal origins. At present there are several approaches which try to manage the intrinsic complexity of these systems, however there exist a quite general concept which is very useful for discussing the possible universal mechanisms. This is the idea of “Energy Landscape” (EL) of an interacting atomic system in the many dimension configuration space[1]. This surface is characterized by a large number of local minima, usually proportional to exp(N), N being the number of atoms in the system. In particular, there exists a distribution of energy minima and is possible to jump from a minimum to another one by crossing saddle points to overcome energy barriers of variable height. Each single minimum defines a possible (meta)stable configuration of the ensemble of N atoms. In liquid state, thermal energy is high enough to allow the system to overcome most of the barriers between different minima. If the liquid is cooled-down quickly enough, the system can be trapped in one of the local minima, usually corresponding to a configuration without symmetry properties: the lack of translational symmetry in an extended system gives rise to a glass, while a system which consists of a finite number of atoms generates asymmetric molecules with a variety of morphology. Even a system with only 10 atoms, results in around 3000 possible minima [2]. Most of these configurations, especially for large N, correspond to local rearrangements of a finite number of atoms and the system can pass quite easily from one configuration to the other one by overcoming rather low energetic barriers. These kind of configurations are grouped within a basin. More in detail, the EL has a hierarchical structure, arranged in a number of tiers,
with different tiers having widely separated average barrier heights. When the temperature is rather low, the system is confined within a minimum, and the atoms can only oscillate around their equilibrium position, but diffusion is hindered. Therefore, the EL geometrical features, i.e. curvatures, of minima determine the vibrational properties of the system. On the contrary, diffusive and relaxation phenomena correspond to barrier crossing, thus depending on their height, and on the morphology and the location of the saddle points. The barrier crossing, which can be activated thermally at a finite temperature, or through quantum mechanisms (tunnel effect), can takes place in a characteristic time varying from picoseconds to hours or more. Within this picture, “all” the dynamical and thermodynamical properties of the system (vibrations, glass transition, relaxation (and then aging), tunnel effect, diffusion (and then viscosity), formation of complex molecules, etc.) are determined from the EL, even if they are characterised by extremely different timescales and originates from different regions of the EL, i.e. minima for vibrational features, sable point and barriers for diffusive and relaxation properties.
On these grounds we propose to face two open problems of the dynamics of disordered systems:

(1) The propagation of the density fluctuations as affected by processes such as the densification and the interaction with the local environment
(2) Analysis of the mechanisms through which acoustic waves are attenuated in relationship to the point (1)

This kind of study, beyond a fundamental interest for basic science, can contribute significantly to the material science. Most of application oriented solid state devices are realised with non crystalline materials, such as ceramics, polymers, plastic, etc. For instance, the mechanical properties of polymeric materials are ruled by viscosity. Thus the dependence of such a quantity from external parameters, like pressure and temperature, determines both the exploitation range and the kind of application of those materials. The functionality of several biological systems is tightly bound to the conformation and the dynamics of hydration water, which shows properties similar to those of glassy systems, with states resembling the polymorphic phases of ice [2]. To unravel the relationship between the relaxation and the vibrational dynamics in these disordered systems is thus crucial to deeply understand most of the mechanisms which appear “universal” even if in remarkably different fields and materials.
(1) Concerning the first aspect, we observe that on applying high pressures one gives rise to the “densification” of the system, with the following structural modifications, sensible alteration of the coordination number [3] and of the existing intermediate length scale order [4]. Noticeable changes can be also observed on other physical properties, such as specific heat at low temperature [5], Gruneisen parameter [6], and the sound velocity [7]. In addition, densification leads to the increase of both the thermal conductivity plateau [8] and the Boson peak frequency [9]. Some modifications of densified systems persist even when high pressure is removed, while in general, for applied pressures below 12 GPa initial thermodynamic conditions can be restored with thermal treatments at temperatures above Tg [10]. In this case pressure induces transitions among different metastable states. Conversely, when a hydrostatic pressure above 12 GPa is applied, permanent structural changes occur, due to irreversible densification processes. Permanent densification opens new scenarios, as it happens for the case of amorphous ice [11,12], where polymorphism has been discovered for a long time. Permanent densification allows one to study physical properties which are difficult to measure, such as thermodynamic quantities. In addition, permanent densification is the only way to observe physical properties in altered conditions, when in-situ experiments are very difficult or impossible, as in the case of inelastic neutron scattering measurements. In this context, it is worth to note that by applying high pressures one may profoundly change the microscopic interactions in condensed phase, and even provoke unusual morphologic transformations or transitions between structural phases with different density. Recently, prototypical glassy oxides, such as SiO2, GeO2 and B2O3, have been reversibly [13] and permanently [14] densified. Polyamorphism phenomena have been observed, consisting in transitions between two amorphous phases of different densities, together with a gradual increase of the coordination in the network-forming ion (NFI) and significant changes in the short- and intermediate- range order (respectively SRO and IRO). In fact, the structure of densified glasses results from a non-equilibrium state and the formation of additional local constraints is a possible mechanism through which the structure reacts to pressure changes. Little is known about the effect of densification on the propagation of density fluctuations, but obviously the structural changes involved in this phenomenon may give precious information to understand these mechanisms.
Quite interestingly, very similar conditions occur also in confined or interfacial systems, such as hydration water of proteins and proton exchange membranes. It is useful to investigate as well the propagation of density fluctuations in such kind of systems, for basic and applied science reasons. Indeed, the well-known ice polymorphism [11,12], is probably related to dynamical effects on these confined systems [2]. An additional aspect which deserves attention is the result that there exists a relationship among the microscopic properties that characterise the propagation of the density fluctuations, the fragility (following the definition of Angell [15], by which the fragility is a measure of the departure of shear viscosity from the Arrhenius thermal activated behaviour), and the temperature dependence of the so-called non-ergodicity factor (which is a quantity determined by the harmonic low-temperature vibrational properties of the solid). This results has been obtained by comparing the elastic and the inelastic contributions of X-ray spectra. With other words, it is possible to predict the fragility (i.e. the shear viscosity temperature variation near the glass transition), on the basis of the low-temperature vibrational spectra properties. In terms of EL, this witnesses the correlation between the properties near the minima and those determined by transitions among different basins. These results are crucial for phenomena such as densification and/or variation of the “vicinal” environment confined or interfacial systems.

(2) – Concerning the second aspect, i.e. the relationship between the attenuation of the acoustic waves and the macroscopic densification or the effects of the local environment, the present knowledge is still quite limited. In fact, all the correlations emphasised between the propagation of the density fluctuations and the features of various systems have a phenomenological character, and only numerical simulations give some information on the microscopic mechanisms [17]. The available experimental results suggest that in the prototypical strong glass SiO2 the low-momentum transfer (&lt;0.1 nm^-1) attenuation of longitudinal collective modes increases like Q^2 [18,19], but this behaviour is disconnected with the high-Q (&gt;1 nm^-1) trend [20]. In the intermediate region there should be a different intermediate mechanism. Thus, the key still open points deal with the microscopic mechanisms underlying to both the propagation and attenuation of density fluctuations. On a qualitative point of view, it is obvious from above, that the interaction between collective modes and diffusive/relaxation is mainly responsible for the attenuation in liquids. On the other hand, diffusion can not affect attenuation in glasses, even if no evident alternative microscopic process has been found to account for this phenomenon. In addition, when temperature decreases, the situation is even more complex, as tunnelling effects give rise to clear evidences [21,22]. The widening of the present understanding requires new experiments to extend the range of observable parameters. For such a goal new instrumentation and new systems are necessary.

[1] Stillinger, F.H. Science 267, 1935-1939 (1995). Sastry, S., Debenedetti, P. G. &amp; Stillinger, F.H. Nature 393, 554-557 (1998). Scala, A., Starr, F. W., La Nave, E., Sciortino, F. &amp; Stanley, H. E., Nature 406, 166-169 (2000). Sastry, S., Nature 409, 164-167 (2001).
[2] Low Frequency Vibrational Dynamics of Protein Hydration Water. Comparison with Hexagonal and Amorphous Ice. A. Paciaroni, A. Orecchini, E. Cornicchi, M. Marconi, C. Petrillo, F. Sacchetti, M. Hartlein, M. Moulin, and M. Tarek, to be published.
[3] C. Meade, R. J. Hemley, and H. K. Mao, Phys. Rev. Lett. 69, 1387 (1992)
[4] S. Susman, K. J. Volin, D. L. Price, M. Grimsditch, J. P. Rino, R. K. Kalia, and P. Vashishta, Phys. Rev. B 43, 1194 (1991).
[5] Y. Inamura, M. Arai, O. Yamamuro, A. Inaba, N. Kitamura, T. Otomo, T. Matsuo, S. M. Bennington, A.C. Hannon, Physica B 263-264, 299 (1999)
[6] C. Z. Tan, J. Arndt, Physica B 229 (1997) 217
[7] E. Rat, M. Foret, G. Massiera, R. Vialla, M. Arai, R. Vacher, and E. Courtens, Phys. Rev. B 72, 214204 (2005).
[8] D. Zhu and H. Weng, J. Non Cryst. Solids 185, 262 (1995)
[9] A. Monaco, A. I. Chumakov, G. Monaco, W. A. Crichton, A. Meyer, L. Comez, D. Fioretto, J. Korecki, and R. Rüff, Phys. Rev. Lett. 97, 135501 (2006).
[10] A. Polian and M. Grimsditch, Phys. Rev. B 41, 6086 (1990).
[11] Debenedetti P G and Stanley H E Phys. Today 56 (6), 40 (2003).
[12] Koza M M, Schober H, Geil B, Lorenzen M, and Requardt H, Phys. Rev. B 69, 024204 (2004).
[13] J. Nicholas, S. Sinogeikin, J. Kieffer, J. Bass, Phys. Rev. Lett. 92, 215701 (2004).
[14] S. Sampath, C. J. Benmore, K. M. Lantzky, J. Neuefeind, K. Leinenweber, D. L. Price, and J. L. Yarger, Phys. Rev. Lett. 90, 115502 (2003).
[15] C.A. Angell, J. Non-Cryst. Solids, 131-133, 13 (1991); Science, 267, 1924 (1995).
[16] T. Scopigno, G. Ruocco, F. Sette, G. Monaco, Science 302, 849 (2003).
[17] P. Bordat, F. Affouard, M. Descamps, K.L. Ngai, Phys. Rev. Lett. 93, 105502 (2004).
[18] C. Masciovecchio, A. Gessini, S. Di Fonzo, L. Comez, S.C. Santucci, D. Fioretto, Phys. Rev. Lett. 92, 247401 (2004)
[19] P. Benassi, S. Caponi, R. Eramo, A. Fontana, A. Giugni, M. Nardone, M. Sampoli, G. Viliani, Phys. Rev. B 71, 172201 (2005).
[20] P. Benassi, M. Krisch, C. Masciovecchio, V. Mazzacurati, G. Monaco, G. Ruocco, F. Sette, and R. Verbeni, Phys. Rev. Lett. 77, 3835 (1996).
[21] G. Carini Jr, G. Carini, G. D’Angelo, G. Tripodo, A. Bartolotta, G. Salvato, Phys. Rev. B 72 14201 (2005).
[22] G. Carini Jr, G. Carini, G. Tripodo, A. Bartolotta, G. Di Marco, J. Phys. Cond. Matter 18 3251 (2006); G. Carini Jr, G. Carini, G. D’Angelo, G. Tripodo, A. Bartolotta, G. Di Marco, J. Phys. Cond. Matter 18, 10915 (2006). <<<