13580
J. Phys. Chem. B 2004, 108, 13580-13585
ARTICLES r,r-Trehalose/Water Solutions. VII: An Elastic Incoherent Neutron Scattering Study on Fragility Salvatore Magazu` ,*,† Giacomo Maisano,† Federica Migliardo,† and Claudia Mondelli‡ Dipartimento di Fisica and INFM, UniVersita` di Messina, P.O. Box 55, I-98166 Messina, Italy, and INFM-OperatiVe Group Grenoble CRG IN13 and Institut Laue-LangeVin, 38042 Grenoble Cedex 9, France ReceiVed: July 9, 2003; In Final Form: May 13, 2004
The present neutron-scattering experimental findings concern with a study of fragility of trehalose, maltose, and sucrose/water mixtures. The fragility degree has been characterized by a new definition based on the correlation between viscosity and mean-square displacement as obtained by elastic incoherent neutron scattering. The fragility values obtained for the homologous disaccharides/water mixtures are compared with those obtained for other glass-forming systems of different “strength”. The less-fragile character of the trehalose/H2O mixture in respect to maltose and sucrose/H2O mixtures is finally linked to the better bioprotective capability.
I. Introduction Cryobiology is actually the study of living systems at any temperature below the standard physiological range.1 This includes, for example, hypothermia and hibernation, i.e., a physiological modification of sleep that allows the physiological temperature range to be stretched to include previously fatal temperatures. Some cryobiological topics involving temperatures below 0 °C are plants, insects, and vertebrate natural cold hardiness and sensitivity; freeze-drying; supercooling; cryosurgery; frostbite; and deliberate cryopreservation.1,2 It is well known that, at room temperature, water molecules are arranged randomly; when the water freezes, its molecules align themselves in a rigid structure. This means that when ice forms inside tissues, the ice squeezes vital ions and proteins out of the tissue, forcing them into shrinking pockets of residual unfrozen water.3 As cooling continues, more than eighty percent of tissue volume can become converted to ice, and the cells are crushed beyond recovery. Vitrification, stopping biological time without altering the natural order inside living cells, eliminates the formation of ice during cooling.4,5 During vitrification, ice formation is completely inhibited by cryoprotectants. As a result, liquid water molecules maintain their natural random arrangements during deep cooling.6,7 Once the cell is vitrified, “cryptobiosis” (“suspended animation”) is nearly achieved: all processes of metabolism and injury are slowed to almost zero. Freeze-drying as a future technology for storing some cells more conveniently than storage in liquid nitrogen gains some credibility from the existence of anhydrobiotic organisms.8,9 The tardigrades are perhaps the most famous creatures in this group, since they are highly complex, with heads, limbs, and internal body parts akin to those of many insects.10 Many studies are today focused to investigate the action of cryoprotectants on biostructures. Yoon et al.11 studied lipid* To whom correspondence may be addressed. E-mail: smagazu@ unime.it. Phone: +39 0906765025. Fax: +39 090395004. † Universita ` di Messina. ‡ INFM-Operative Group Grenoble CRG IN13 and Institut LaueLangevin.
solute-water ternary systems at freezing temperatures and determined the distribution of solute and solvent between lamellar phases and a concentrated bulk solution phase in equilibrium with ice. They found that the disaccharides sucrose and trehalose (which have about twice the volume of the others) increased the hydration less than would be expected from their osmotic effects alone and that the disaccharides decreased the intramembrane stress more than the smaller solutes (DMSO and sorbitol).11 Another important cryobiological topic concerns crop resistance to water stress. In particular, harsh temperatures are likely to increase further as the range of environments in which crops are cultivated expands and the incidence of extreme weather conditions increases.12 Since the concept of optimal growth temperatures is a fundamental principle in biology, sugar accumulation, together with undercooling and vitrification, has been brought back into focus. The presence of trehalose in plants is at present a matter of discussion. It has recently been demonstrated13,14 that, in Arabidopsis thaliana, a small plant used worldwide as a model organism for basic and applied research in plant biology, the T6P component of the trehalose pathway is active and indispensable in plants by regulating carbohydrate utilization and growth. This central role of T6P may be more widely conserved than previously imagined,13 and it has been discovered that the synthesis of trehalose occurs in particular in a kind of plants, the so-called “resurrection" plants”, which as whole plants withstand the loss of cellular water and return to active metabolism and growth on rehydration.2 In this work, an elastic neutron scattering study on homologous disaccharides (trehalose, maltose, sucrose)/H2O mixtures as a function of temperature and concentration is presented, with the aim to connect the cryptoprotectant effectiveness of disaccharides and in particular of trehalose to their “fragility”. A new operative definition for the “fragility” degree is introduced and successfully applied to disaccharides/H2O mixtures and to a class of glass-forming systems. There are many definitions of “fragility”. As is well known, the behavioral properties of a glass-forming system can be
10.1021/jp035973a CCC: $27.50 © 2004 American Chemical Society Published on Web 08/13/2004
R,R-Trehalose/Water Solutions
J. Phys. Chem. B, Vol. 108, No. 36, 2004 13581
described in terms of the (3N + 1)-dimensional potential-energy hypersurface in the configurational space.15,16 The complexity of the energy landscape, explored by the system, can be correlated with the density of the minima of the hypersurface (degeneracy ∝ ∆Cp(Tg)) and with the distribution of the barrier heights between them ∆µ. These topological features of potential-energy hypersurfaces determine the structural sensitivity of a system to temperature changes in approaching the glass transition, namely, its “fragility” (∝[∆Cp(Tg)/∆µ]), which is operatively defined as
m)
d log η d(Tg/T)
|
(1)
T)Tg+
In the Angell’s classification of glass-forming systems,15,16 based on the choice of an invariant viscosity at the scaling temperature Tg (η(Tg) ) 1013 poise), the departure from the Arrhenius law is taken as a signature of the degree of fragility of the system. An Arrhenius behavior of viscosity in the Tg-scaled plot and a small heat capacity variation ∆Cp(Tg) characterize the strongest systems, whereas a large departure from Arrhenius law and a large heat capacity variation ∆Cp(Tg) characterize the most fragile ones. Between these two limiting cases, intermediate behaviors can be interpreted in terms of different kinetic (η) and thermodynamic contributions (∆Cp(Tg)): thermodynamically strong (small ∆Cp(Tg)) and kinetically fragile systems (nonArrhenius η behavior) are characterized by a low minima density of the potential-energy hypersurface and low energy barriers. Vice versa, thermodynamically fragile (large ∆Cp(Tg)) and kinetically strong systems (Arrhenius η behavior) are characterized by a high hypersurface configurational degeneracy and high barrier heights.14,15 On the other hand, Sokolov et al.,17,18 taking into account low-frequency Raman data, to characterize the fragility degree of glass-forming systems, introduced the ratio of the normalized Raman intensity In ) I/{ω[n(ω) + 1]} at the minimum, (In)min, to the intensity of the boson peak maximum, (In)max, R1 ) (Imin)/ (Imax). Through the evaluation of the R1(T) parameter at the glass transition, these authors have found a close correlation between the ratio of the relaxational to the vibrational contribution and the degree of fragility.17,18 For strong systems, the response to thermal perturbations is very slow and such systems are able to increase the resistance to temperature changes as occurs when trehalose is synthesized by living beings to survive in extreme conditions. Obviously “strong system” is not synonymous with “bioprotectant system”; this can be one of the reasons that makes a system so effective. Another important reason is the strong interaction with water. The interaction between disaccharides and water has been characterized in previous works.19-25 Ultrasonic measurements25 showed that, in respect to the other disaccharides, the trehalose/ water system is characterized, in all the investigated concentration range, by both the highest value of the interaction strength and of the hydration number. This circumstance indicates that trehalose has a more marked preference for water in comparison with maltose and sucrose, this feature being a key to understand the physical mechanisms that make disaccharides, and trehalose in particular, so extraordinary as cryo- and cryptoprotectants. II. Experimental Section Trehalose, maltose, and sucrose have the same chemical formula (C12H22O11) (molecular weight Mw ) 342.3) but different structures. More precisely, R,R-trehalose is a disaccharide of glucose (R-D-glucopyranosil R-D-glucopyranoside)
constituted by two pyranose (six-membered) rings in the same R configuration linked by a glycosidic bond between the chiral carbon atoms C1 of the two rings. Maltose (4-O-R-D-glucopyranosil-D-glucose) is also constituted by two pyranose rings of glucose in the R configuration, but the oxygen bridge links the two carbon atoms C1 and C4 of the two rings. Maltose is a reducing sugar because the anomeric carbons on the right-hand sugar are part of a hemiacetal. Sucrose (R-D-glucopyranosil β-D-fructofuranoside) is constituted by a glucose ring (pyranose) in the R configuration and a fructose ring (furanose) in the β configuration; the R and β structures of the same monosaccharide differ only in the orientation of the OH groups at some carbon atom in the ring itself. Sucrose is a disaccharide that yields to formation of glucose and fructose on acidic hydrolysis. Unlike most other disaccharides, sucrose is not a reducing sugar and does not exhibit mutarotation. These facts imply that sucrose has no hemiacetal linkages and that glucose and fructose must both be glycosides. This can happen only if the two sugars are joined by a glycoside link between C1 of glucose and C2 of fructose. Ultrapure powdered trehalose, maltose, and sucrose, D2O, and H2O, purchased by Aldrich-Chemie, were used to prepare solutions at a weight fraction corresponding to 6 and 19 water (D2O and H2O) molecules for each disaccharide molecule. The backscattering spectrometer IN13 at the Institute Laue Langevin (Grenoble, France) is characterized by a relatively high energy of the incident neutrons (16 meV), which makes it possible to span a wide range of momentum transfer Q (e5.5 Å-1) with a very good energy resolution (∼8 µeV). Therefore, neutron-scattering experiments on IN1326,27 provide information on the motions of the sample hydrogens in a space-time window of 1 Å and 0.1 ns given by its scattering vector modulus, Q, range, and energy resolution and allow the characterization of both flexibility (obtained from the fluctuation amplitudes) and rigidity (obtained from how fluctuations vary with temperature and expressed as a mean environmental force constant). Measurements were carried out across the glass transition temperatures in a temperature range of 20-310 K. The incident wavelength was 2.23 Å; the Q range was 0.28-4.27 Å-1; the elastic energy resolution (full width at half maximum) was 8 µeV. Raw data were corrected for cell scattering and detector response and normalized to unity at Q ) 0 Å-1. Neutron scattering is particularly suited to the study of thermal molecular motions which have been shown to be correlated with the ability of a protein to undergo functional conformational changes,27-29 because neutrons of 1-Å wavelength have an energy close to 1 kcal/mol. Depending on the energy resolution of the spectrometer, neutron scattering can be used to observe (1) elastic scattering, from which mean-square fluctuations in a given time scale can be calculated,27 (2) quasielastic scattering, from which correlation times of diffusion motions can be calculated,28 and (3) inelastic scattering, arising from vibrational modes.29 On backscattering spectrometers, a time scale up to ∼0.1 ns can be achieved (matching well with thermal motions) and a standard analysis as a function of scattering vector Q yields values for the mean-square displacements, dominated by hydrogen-atom motions in the sample because their incoherent cross section is an order of magnitude larger than that of other atoms. In the case of low hydrated biological ternary systems in the time scale examined, H atoms reflect the global thermal behavior because they move with the larger chemical groups, such as amino acid side chains, to which they are bound.28,30
13582 J. Phys. Chem. B, Vol. 108, No. 36, 2004
Magazu` et al.
III. Theoretical Background Hydrogen atoms in a system move in a potential V(r), where r(t) denotes the position vector of the particle at time t.26,29 The function describing the scattering process is the incoherent N xR 〈exp[iQrR(t)] intermediate scattering function I(Q,t) ) ∑R)1 N exp[-iQrR(0)]〉, where xR(∑R)1 xR ) 1) is the fraction of dynamically equivalent particles in the potential V∝(r) and brackets denote the ensemble average over many trajectories for particles initially at thermal equilibrium. In the Gaussian approximation, an orientational average can be performed
[
N
I(Q,t) =
∑ R)1
xR exp -
Q2 6
〈[rR(t) - rR(0)]2〉
]
(2)
Because of the polydispersity in particle dynamics, the meansquare displacement can be written as 〈[rR(t) - rR(0)]2〉 ) 2〈rR2〉[1 - CR(t)], where 〈rR2〉 is the equilibrium mean-square displacement and CR(t) is the stationary position relaxation function. The mean-square displacement reduces to the equilibrium value for times long enough such that CR(t) f 0.26,29 The incoherent dynamic structure factor Sincoh(Q,ω) is the Fourier transform of I(Q,t), and it is composed by two contributions, an elastic contribution Selincoh(Q) ) I(Q,∞)δ(ω) = I(Q,τ) (τ being the experimental resolution time) and a quasielastic contribution that involves energies pω > 0. Selincoh(Q) is related to the normalized elastic intensity by
[
N
Selincoh(Q) = I(Q,t) )
∑ R)1
xR exp -
Q2 3
〈rR2〉[1 - CR(t)]
]
(3)
Selincoh(Q) relaxes to I(Q,∞) when the resolution time is long enough such that CR(t) f 0. The mean-square displacement, 〈u2〉, which takes into account fluctuations of all particles in the investigated system, is given by
〈u 〉 ) -3 2
|
d{ln[Selincoh(Q)]} dQ
2
Q)0
N
)
xR〈rR2〉[1 - CR(τ)] ∑ R)1 (4)
For a given experiment, CR(t) is a constant that rescales the observed mean-square displacement and therefore CR(t) ) 0 can be assumed. Furthermore, for simplicity in the present analysis, the assumption that all particles are dynamically equivalent can be made, therefore xR ) 1 can be assumed.26,29 The mean-square displacement of a set of quantized harmonic oscillators for T < (h〈ν〉/2KB ((h〈ν〉)/(KB) being the Debye temperature, KB being the Boltzmann constant, and 〈ν〉 being the average frequency of a set of oscillators considered as an Einstein solid) is almost a constant equal to the zero-point fluctuations (h〈ν〉)/2Kforce (where Kforce is the average force field constant of a set of oscillators considered as an Einstein solid), whereas it linearly increases with the temperature for T > (h〈ν〉)/ 2KB.25,28 The mean-square displacements originating from harmonic vibrational motions can be expressed by
〈∆u2(T)〉 )
[ ] (
h〈ν〉 h〈ν〉 coth -1 2Kforce 2KBT
)
(5)
Because a force constant is not defined for anharmonic motions, an operational approach in which the “resilience” of an anharmonic environment is quantified by a pseudo force constant
Figure 1. Intensity surfaces vs exchanged wave vectors and temperatures for trehalose, maltose, and sucrose/H2O mixtures.
〈k〉 calculated from the derivative of the scan at T according to 〈k〉 ) 0.00138/(du2〉/dT) has been suggested.26,29 IV. Results and Discussion Figure 1 shows, as an example, the intensity surfaces vs Q and temperature for trehalose, maltose, and sucrose/H2O mixtures at a weight fraction corresponding 19 H2O molecules for each disaccharide molecule. In Figure 2 and its insert, the elastically scattered intensity profiles of trehalose and sucrose/ H2O and D2O mixtures as a function of temperature for different concentration values are shown. By an inspection of Figures 1 and 2, we observe a dynamical transition for all the investigated
R,R-Trehalose/Water Solutions
J. Phys. Chem. B, Vol. 108, No. 36, 2004 13583
Figure 2. Comparison of elastically scattered intensity profiles of trehalose and sucrose/H2O and D2O mixtures as a function of temperature for different concentration values.
systems, in particular for the trehalose mixtures the transition temperature is higher that for the sucrose mixtures. Below the onset temperature, the elastic intensity has the Gaussian form expected for a harmonic solid. The decrease in the elastic intensity above the dynamical transition temperature can be attributed to the excitation of new degrees of freedom, especially at low Q, and, as suggested by Figures 1 and 2, is very less marked in the case of trehalose/water mixtures than for the sucrose/water mixtures. This circumstance clearly indicates that trehalose shows a larger structural resistance to temperature changes as it occurs in “stronger” systems and presents a higher “rigidity” in comparison with the sucrose/H2O mixture. As the deviation from Gaussian behavior increases with temperature, the motion involves the jumping of hydrogens to distinct sites of different energy,25,27 the expression of the integrated intensity as a function of Q being27,29
[
(
Iel(Q) ) A exp(-Q2〈u2〉) 1 - 2p1p2
)]
sin(Qd) Qd
(6)
where p1 and p2 are the probabilities to find the scattering particles on the ground state and the excited state, respectively, and d is the distance between the two potential minima. By fitting the elastic intensity of trehalose and sucrose/H2O and D2O mixtures as a function of Q2, we obtain the result that p1_trehalose > p1_sucrose, and d ≈ 1 Å for all investigated temperature values, indicating that in the case of trehalose/H2O mixtures we have more hindered dynamical processes with respect to the sucrose/H2O mixtures and hence more rigid structures on a nanoscopic scale. Figure 3 shows the temperature dependence of the derived mean-square displacements for trehalose and sucrose/H2O mixtures, respectively. In the insert, the same plot for trehalose and sucrose/D2O mixtures is shown. By fitting according to eq 5, we obtain the values of Kforce ) 0.40 N/m and Kforce ) 0.22 N/m for the average force-field constant for trehalose and sucrose mixtures, respectively, indicating the trehalose/H2O system as the strongest system. The following procedure, aimed to link the bioprotectant effectiveness of disaccharide/water mixtures to the “fragility degree” of these systems, provides a new operative definition for fragility, based on the evaluation by neutron scattering of the temperature dependence of the mean-square displacements. The new definition, different from many other phenomenological parameters as, e.g., resilience introduced in the literature,26
Figure 3. Temperature dependence of the derived mean-square displacements for trehalose and sucrose/H2O mixtures. In the insert, the same plot for trehalose and sucrose/D2O mixtures is shown.
allows us to connect a transport quantity, i.e., viscosity, with an atomic quantity, the nanoscopic mean-square displacement. Starting from the works on selenium by Migliardo et al.31 and Magazu` et al.,32 the following picture for the elementary flow process (the R relaxation) is suggested: a given atom is jumping back and forth in the fast processes (β-relaxation motions). Its probability distribution in that fast motion is a Gaussian with the mean-square amplitude 〈u2〉loc defined as the difference between the mean-square displacement of the ordered (amorphous and liquid) and the ordered phase (crystalline)33
〈u2〉loc ) 〈u2〉disord - 〈u2〉ord
(7)
If the amplitude of that fast motion exceeds by chance a critical displacement u0, a local structural reconfiguration (the R relaxation) takes place. Assuming the time scale of the fast motion to be independent of temperature, the waiting time for the occurrence of an R process at a given atom is proportional to the probability of finding the atom outside of the sphere with radius u0. Defining in this way 〈u2〉loc, a linear relation is observed between the logarithm of viscosity and the inverse of 〈u2〉loc. The same relation can be obtained from the liquid data on the basis of 〈u2〉loc ) 〈u2〉liq - 〈u2〉hard where 〈u2〉liq is the meansquare displacement for motion faster than the resolution limit and 〈u2〉hard takes into account only the typical lattice vibrational frequencies. This linear relation includes both the region below the glass-transition temperature and above the melting temperature. Within this picture, one can express viscosity with the following expression
η ) η0 exp[u02/〈u2〉loc]
(8)
Equation 8 allows fitting the experimental data for selenium of Migliardo et al.31 and Magazu` et al.32 better than the VogelFulcher law. Taking into account eqs 1, 7, and 8, we now introduce a new operative definition to characterize the “fragility” degree by elastic neutron scattering as follows
M)
d(u02/〈u2〉loc) d(Tg/T)
|
T)Tg+
(9)
13584 J. Phys. Chem. B, Vol. 108, No. 36, 2004
Magazu` et al. and of 295, respectively, whereas for the trehalose + 6H2O and sucrose + 6H2O mixtures, we obtain for the fragility parameter M the values of 241 and of 244, respectively. In Figure 5, the fragility parameter values obtained at two different experimental resolutions, specifically at 8 µeV by IN1335-37 and at 150-200 µeV by IN6,33,34 are reported. The reported values indicate that the present operative definition for fragility furnishes an excellent direct proportionality between M and m. This means that the obtained proportionality law linking M and m can be very useful when the value of Tg is far from the temperature values of the measured viscosity, and therefore m must be calculated by extrapolating the value of viscosity at Tg with a large indeterminacy. From this analysis, it clearly emerges that the trehalose/water mixtures are characterized in respect to the sucrose/water mixtures by a lower fragility, namely, by a higher resistance to local structural changes when temperature decreases toward the glass-transition value.
Figure 4. Linear dependence of the logarithm of the viscosity on 1/〈u2〉loc for the trehalose + 19H2O mixture. In the insert, the logarithm of the viscosity as a function of 1/〈u2〉loc for the trehalose + 6H2O mixture is shown. The solid lines indicate the best fit of the experimental data.
V. Conclusions The present elastic neutron scattering findings furnish useful information on the different nature of the involved dynamical processes in bioprotection that can justify the higher trehalose “cryptobiotic” effectiveness. In this work, a new operative definition for the “fragility” degree of glass-forming systems is furnished. The better cryptoprotectant effectiveness of trehalose is ascribed to the lower flexibility and fragile character of the matrix in which biostructures are immersed, i.e., of the trehalose/water mixture. This circumstance implies a better attitude to encapsulate biostructures in more rigid and more temperature insensitive structures in respect to sucrose/water mixtures. Acknowledgment. The authors gratefully acknowledge the Institut Laue-Langevin (Grenoble, France) for dedicated runs on the IN13 spectrometer. They also acknowledge the Universita` Italo-Francese for the Galileo Project 2003 funding. References and Notes
Figure 5. Fragility parameter M, as obtained in the present work by elastic incoherent neutron scattering experiments, vs the fragility parameter m, as obtained by viscosity measurements. The black points are experimental data obtained by using the IN13 spectrometer at an instrumental elastic energy resolution of 8 µeV; the gray points are experimental data obtained by using the IN6 spectrometer at a instrumental elastic energy resolution of 150-200 µeV. The solid black and gray lines indicate the best fits.
Such a definition implies a fragility parameter depending on the instrumental resolution, which determines the observation time scale. However, we are interested on a comparison of the fragility degree which is meaningful when an identical experimental setup for IN13 is employed. We shall show in fact that coherent results are obtained also for other glass-forming systems, such as B2O3,34 glycerol,35 PB,36 o-terphenyl,37 and selenium.33 Figure 4 shows, as an example, log η as a function of 1/〈u2〉loc for trehalose + 19H2O mixtures. In the insert, the logarithm of the viscosity as a function of 1/〈u2〉loc for the trehalose + 6H2O mixture is shown. As it can be seen, the linear behavior is very well observed in a wide temperature range. From eq 9, we evaluate a fragility parameter M of 302 for the trehalose + 19H2O mixture and of 355 for the sucrose + 19H2O mixture, respectively; for trehalose + 19D2O and sucrose + 19D2O mixtures, we obtain a fragility parameter M of 272
(1) Bryant, G.; Wolfe, J. Cryo-Lett. 1992, 13, 23. (2) Hirsh, A. Cryobiology 1987, 24, 214. (3) Wolfe, J.; Bryant, G. NATO ASI Ser. 1992, 64, 205. (4) Fahy, G. M. Prog. Clin. Biol. Res. 1986, 224, 305. (5) Crowe, J. H.; Carpenter, J. F.; Crowe, L. M. Annu. ReV. Physiol. 1998, 60, 73. (6) Crowe, J. H.; Crowe, L. M.; Carpenter, J. F.; Rudolph, A. S.; Wistrom, C. A.; Spargo, B. J.; Anchordoguy, T. J. Biochim. Biophys. Acta 1988, 947, 367. (7) Koster K. L.; Webb, M. S.; Bryant, G.; Lynch, D. V. Biochim. Biophys. Acta 1994, 1193, 143. (8) Crowe, J. H.; Crowe, L. M.; Chapman, D. Science 1984, 223, 701. (9) Storey, K. B.; Storey, J. M. Annu. ReV. Physiol. 1992, 54, 619. (10) Crowe, J. H.; Crowe, L. M. Methods Enzymol. 1986, 127, 696. (11) Yoon, Y. H.; Pope, J.; Wolfe, J. Biophys. J. 1998, 74, 1949. (12) Dowgert, M. F.; Wolfe, J.; Steponkus, P. L. Plant Physiol. 1987, 83, 1001. (13) Uemura, M.; Joseph, R. A.; Steponkus, P. L. Plant Physiol. 1995, 109, 15. (14) Schluepmann, H.; Pellny, T.; Van Dijken, A.; Smeekens, S.; Paul, M. Proc. Natl. Acad. Sci., U.S.A. 2003, 100, 6849. (15) Angell, C. A.; Poole, P. H.; Shao, J. NuoVo Cimento D 1994, 16, 993. (16) Angell, C. A. Prog. Theor. Phys. 1997, 126, 1. (17) Sokolov, A. P.; Kisliuk, A.; Quitmann, D.; Duval, E. Phys. ReV. B 1993, 48, 7692. (18) Sokolov, A. P.; Kisliuk, A.; Quitmann, D.; Kudlik, A.; Ro¨ssler, E. J. Non-Cryst. Solids 1994, 172, 138. (19) Branca, C.; Magazu`, S.; Maisano, G.; Migliardo, P. J. Chem. Phys. 1999, 111, 281. (20) Branca, C.; Magazu`, S.; Maisano, G.; Migliardo, P. J. Phys. Chem. 1999, 103, 1347.
R,R-Trehalose/Water Solutions (21) Branca, C.; Magazu`, S.; Maisano, G.; Migliardo, F.; Soper, A. K. Appl. Phys. A 2002, 74, 450. (22) Magazu`, S.; Villari, V.; Migliardo, P.; Maisano, G.; Telling, M. T. F. J. Phys. Chem. 2001, 105, 1851. (23) Branca, C.; Magazu`, S.; Maisano, G.; Migliardo, F.; Romeo, G. J. Phys. Chem. B 2001, 105, 10140. (24) Branca, C.; Magazu`, S.; Maisano, G.; Migliardo, F. Phys. ReV. B 2001, 64, 224204. (25) Magazu`, S.; Migliardo, P.; Musolino, A. M.; Sciortino, M. T. J. Phys. Chem. 1997, 101, 2348. (26) Zaccai, G. Science 2000, 288, 1604. (27) Doster, W.; Cusack, S.; Petry, W. Nature 1989, 337, 754. (28) Smith, J. C. Q. ReV. Biophys. 1991, 24, 227. (29) Bicout, D. J.; Zaccai, G. Biophys. J. 2001, 80, 1115.
J. Phys. Chem. B, Vol. 108, No. 36, 2004 13585 (30) Re´at, V.; Patzelt, H.; Ferrand, M.; Pfister, C.; Oesterhelt, D.; Zaccai, G. Proc. Natl. Acad. Sci., U.S.A. 1998, 95, 4970. (31) Galli, G.; Migliardo, P.; Bellissent, R.; Reichardt, W. Solid State Commun. 1986, 57, 195. (32) Burattini, E.; Federico, M.; Galli, G.; Magazu`, S.; Majolino, D. NuoVo Cimento D 1988, 10, 425. (33) Buchenau, U.; Zorn, R. Europhys. Lett. 1992, 18, 523. (34) Engberg, D.; Wischnewski, A.; Buchenau, U.; Bo¨rjesson, L.; Dianoux, A. J.; Sokolov, A. P.; Torell, L. M. Phys. ReV. B 1998, 58, 9087. (35) Wuttke, J.; Petry, W.; Coddens, G.; Fujara, F. Phys. ReV. E 1995, 52, 4026. (36) Frick, B.; Richter, D. Science 1995, 267, 1939. (37) To¨lle, A.; Zimmermann, H.; Fujara, F.; Petry, W.; Schmidt, W.; Schober, H.; Wuttke, J. Eur. Phys. J. B 2000, 16, 73.
