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devoted to the study of various pure glass-forming liquids, such as glycerol,2,6 .... single thermal mass i.e., geometry independent.18 The in- duced temperature ...

THE JOURNAL OF CHEMICAL PHYSICS 126, 094503 共2007兲

Induced thermal dynamics in the melt of glycerol and aerosil dispersions Dipti Sharma and Germano S. Iannacchione Department of Physics, Worcester Polytechnic Institute, Worcester, Massachusetts 01609

共Received 31 July 2006; accepted 16 January 2007; published online 7 March 2007兲 A high-resolution calorimetric spectroscopy study has been performed on pure glycerol and colloidal dispersions of an aerosil gel in glycerol covering a wide range of temperatures from 300 to 380 K, deep in the liquid phase of glycerol. The colloidal glycerol+ aerosil samples with 0.07, 0.14, and 0.32 g of silica per cm3 of glycerol reveal activated energy 共thermal兲 dynamics at temperatures well above the Tg of the pure glycerol. The onset of these dynamics appears to be due to the frustration or pinning imposed by the silica gel on the glycerol liquid and is apparently a long-range, cooperative phenomena. Since this behavior begins to manifest itself at relatively low silica densities 共large mean void length compared to the size of a glycerol molecule兲 and speeds up with increasing density, these induced dynamics are likely due to a coupling between the flexible aerosil gel and large groups of glycerol molecules mediated by mutual hydrogen bonding. This is supported by the lack of such thermal dynamics in pure aerosil gels, pure glycerol, or aerosil gels dispersed in a non-glass-forming, non-hydrogen-bonding, liquid crystal under nearly identical experimental conditions. The study of such frustrated colloids may provide a unique avenue for illuminating the physics of glasses. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2539000兴 I. INTRODUCTION

Glass-forming liquids are interesting materials for study and have continually drawn the attention of researchers because of their unusual physical properties.1–5 These materials show striking thermal and dynamical effects when they enter the glassy state. The glassy state is governed by the “static” disordered arrangement of the molecules when cooled to the glass-transition temperature 共Tg兲. This state is sometimes referred to as an amorphous solid. Much attention has been devoted to the study of various pure glass-forming liquids, such as glycerol,2,6,7 in order to understand this state of matter. However, it remains unclear whether the glass state is due to a particular molecular interaction or a collective phenomena of many molecules that rapidly increases the degeneracy of the ground state with decreasing temperature, which prevents crystallization and “freezes” the sample into an amorphous glass state. The latter mechanism represents an intrinsic frustration 共the so-called “stuck-states” view兲 and is the currently favored.8 One avenue pursued to illuminate this phenomena has been the study of mixtures of two or more glass-forming liquids or of a glass former with a solvent to isolate specific molecular interactions. However, only a few such studies have been performed to date, and these have not settled the central question.9 An extension of the method of mixtures approach would be to employ a random colloidal dispersion within a glassforming liquid to introduce frustration and alter the average physical properties 共i.e., viscosity兲. Such a gel system would introduce frustration, primarily structural, in a controlled way by increasing the density of the colloidal particles. In addition, this approach would have the advantage of introducing frustration with a characteristic length scale, the mean void size. The perturbations observed for a given mean void 0021-9606/2007/126共9兲/094503/6/$23.00

length could then be compared to a typical molecule size of the glass-forming liquid to determine the extent of the collective behavior. The colloidal gel could be obtained using dispersions of aerosil particles, a technique already used in the study of quenched random disorder on liquid crystal phase transitions.10 Further, it has been shown that the dynamics of the aerosil gel couples to the dynamics of the host fluid.11,12 A common calorimetric technique for studying phase transitions is differential scanning calorimetry 共DSC兲, which have been widely used in the study of glasses.13,14 However, the necessary fast scan rates for DSC severely distort the behavior of slowly relaxing systems. To measure the heat capacity directly over a wide range of temperatures and under near equilibrium conditions, an ac or modulation calorimetry 共MC兲 has proven to be of great benefit for thermodynamic studies.1,15–17 Also, in the MC technique measurements are made as a function of frequency, which permit a spectroscopic analysis of the thermodynamics. In this work, an MC technique is used as a function of frequency and temperature on a colloidal glass-forming liquid system to probe energy relaxations via calorimetric spectroscopy. This paper presents the results of a calorimetric spectroscopy study of colloidal dispersions of aerosil particles in glycerol at a number of aerosil densities. The addition of aerosil introduces thermal dynamics with relaxations on the order of a second beginning at a void length on the order of 100 nm and decreases by about a factor of 3 when the mean void length decreases by a factor of about 5. This indicates that the induced dynamics are due to a collective behavior of the glycerol molecules and the aerosil gel via mutual hydrogen bonding. Following this introduction, a theoretical re-

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© 2007 American Institute of Physics

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J. Chem. Phys. 126, 094503 共2007兲

D. Sharma and G. S. Iannacchione

view of calorimetric spectroscopy and the relevant glass dynamics is presented in Sec. II, and the experimental details are described in Sec. III. The results for temperature and frequency scans as well as an Arrhenius analysis are shown in Sec. IV, with discussion and conclusions drawn in Sec. V. II. THEORETICAL DESCRIPTION A. Complex heat capacity

In general, the source of a sample’s heat capacity 共C兲 are the fluctuations of the sample’s energy. Thus, it is natural to consider C as a dynamic quantity. However, for most materials the characteristic relaxation time of the energy fluctuations are too short to be sensed by traditional calorimetric techniques. Nevertheless, a complex heat capacity may be defined containing a real 共C⬘兲 and imaginary 共C⬙兲 component indicating the storage 共capacitance兲 and loss 共dispersion兲 of the energy in the sample analogous to a complex permittivity. Using a linear response approach, the relaxing enthalpy fluctuation 共at constant pressure兲 ␦HR defines an enthalpy correlation function as 具␦HR共0兲␦HR共t兲典. The complex heat capacity at a frequency ␻ is then given by C p共␻兲 = C⬘p共␻兲 − i





␻kB␤2具␦HR共0兲␦HR共t兲典dt,

共1兲

0

where ␤ = 共kBT兲−1 and the time integral is C⬙p. For energy dynamics characterized by a single frequency ␻m, the real part has two asymptotic limits, fast 共␻ Ⰷ ␻m, denoted by C⬁p 兲 and static 共␻ Ⰶ ␻m, denoted by C0p = C⬁p + kB␤2具␦HR2 典兲 compared to this mode. The imaginary part would exhibit a peak at ␻m that also marks the inflection point of the smooth roll over between the two frequency limits of C⬘p. B. Modulation calorimetry

Modulation calorimetry allows one to make frequency dependent C p measurements and so perform calorimetric spectroscopy. In modulation calorimetry, a small oscillating heating power P共t兲 = P0 exp共i␻t兲 is applied to the sample + cell and induces an rms temperature rise as well as small temperature oscillations. In what follows, the cell is considered to consist of the actual sample holder and the attached heater and thermometer. For a sample of finite thermal conductivity and a sample+ cell experimental arrangement of a thickness less than the thermal diffusion length, the heat flow equations may be set up considering the sample+ cell as a single thermal mass 共i.e., geometry independent兲.18 The induced temperature oscillation amplitude Tac is given, to second order, by Tac =



2Rs P0 1 + 共␻␶e兲−2 + ␻2␶2ii + ␻C 3Re



−1/2

,

共2兲

where P0 is the amplitude and ␻ is the angular frequency of the applied heating power, C = Cs + Cc is the total heat capacity of the sample+ cell, and Tac is the amplitude of the induced temperature oscillations. There are two important thermal relaxation time constants that are involved, the external ␶e = ReC and the internal ␶2ii = ␶s2 + ␶2c , which is the sum of

square internal time constants of the sample+ cell 共␶s = RsCs and ␶c = RcCc兲. Here, Rs is the sample’s thermal resistance and Re is the external thermal resistance to the bath. There is also a phase shift ⌽ between the applied heat and resulting temperature oscillations but it is more convenient to define a reduced phase shift ␾ = ⌽ + ␲ / 2 since for heating frequencies between 1 / ␶e and 1 / ␶ii, ⌽ ⬇ −␲ / 2. The reduced phase shift, to the same accuracy as Eq. 共2兲, is given by tan共␾兲 = 共␻␶e兲−1 − ␻␶i ,

共3兲

where ␶i = ␶s + ␶c. The different internal relaxation times that enter in Eqs. 共2兲 and 共3兲 are related by ␶2ii = ␶2i − 2␶s␶c and must be taken into account in order to extract the complex heat capacity. Noting that 1 + tan2共␾兲 = cos−2共␾兲, Eq. 共3兲 can be substituted into Eq. 共2兲 to give C = C*



1 ␶i 2Rs − 2 ␶ c␶ s␻ 2 + 2 + 2 cos 共␾兲 ␶e 3Re



−1/2

共4兲

,

where C* ⬅ P0 / 共␻Tac兲. Factoring out cos共␾兲 gives C⬘ = C* cos共␾兲f共␻兲,

共5兲

where the total heat capacity is identified as the real part of the complex heat capacity. The function f共␻兲 is then given by

冋 冉

f共␻兲 = 1 + 2



␶i Rs + − ␶ ␶ ␻2 cos2共␾兲 ␶e 3Re c s



−1/2

,

共6兲

and may be regarded as a correction for a sample and cell having comparable finite thermal relaxation times. For most materials away from any phase transition, the imaginary part of the heat capacity is essentially zero at typical heating frequencies 共艋1 Hz兲. The imaginary part may be derived from Eq. 共3兲 by substituting the definitions for the relaxation times and for the heat capacity given by Eq. 共5兲. This yields C⬙ = C* sin共␾兲g共␻兲 − 共␻Re兲−1 ⬇ 0,

共7兲

where a frequency dependent correction function is introduced as



g共␻兲 = f共␻兲 1 +



␻␶i , tan共␾兲

共8兲

which also accounts for the comparable relaxation times of the sample and cell. Typically, the cell’s geometry and mass may be controlled and so its thermal relaxation time can be made much less than that of the sample, ␶c Ⰶ ␶s. In this case, the two internal relaxation times are approximately equal. Taking ␶ii = ␶i = RsCs, the correction function g共␻兲 does not change but the ␻2 term vanishes in f共␻兲. The frequency dependence for both correction functions enter through the reduced phase shift. At sufficiently low heating frequencies ␻ ⬍ ␶−1 e , ␾ approaches ␲ / 2 共⌽ approaches 0兲 and f共␻兲 ⯝ g共␻兲 ⬇ 1, which reduces the real and imaginary heat capacities in Eqs. 共5兲 and 共7兲 to

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C⬘ = C* cos共␾兲

共9兲

and C⬙ = C* sin共␾兲 − 共␻Re兲−1 ,

共10兲

where energy 共thermal兲 dynamics or dispersion in the sample will be indicated by a nonzero value of C⬙. Note that there will always be a dispersion peak in C⬙ at ⬇1 / ␶i, which represents the intrinsic 共internal兲 thermal relaxation mode of the sample+ cell package.

C. Brief review of glass dynamics

Glass-forming or supercooled liquids exhibit dynamics due to inhibited structural relaxations that diverge upon approaching the glass transition until the system falls from ergodicity 共equilibrium兲. Glass formers are characterized by a rapid increase in viscosity 共from 10−2 P above to 1015 P below the glass transition temperature兲 with decreasing temperature, which reflects the rapidly shifting time scale of structural relaxations of the liquid. The slow molecular motion, known as ␣ relaxation, has been well characterized on time scales between 100 ps and longer,19,20 and this stops completely below the glass transition temperature. The fast motion 共␤ relaxation兲 is predicted to exist at time scales between 1 and 100 ps,21 and persists even in the glassy state. However, ␤ relaxation is difficult to determine unambiguously by experiment and its physical meaning remains elusive. Qualitatively, ␣ relaxation can be thought of as the collective motion of many particles while ␤ relaxation is thought to be the motion of a single molecule rattling within a cage of nearest neighbors. Fundamentally, the primary issue in the understanding of glasses centers on whether the glassy behavior is due to stuck states of a collection of molecules or due to intrinsic molecular frustration preventing the crystallization of the material. Quantitatively, “glassy” dynamics typically obey a Vogel-Fulcher-Tammann 共or Arrhenius兲 behavior in that the dynamics are energetically activated.22,23 According to Arrhenius behavior, the relaxation time of glass-forming liquids can be given by

␶ = ␶o exp共␤⌬E兲,

共11兲

where ␶ is the relaxation time of some 共usually structural兲 fluctuation, ␶0 is the high-temperature limit of this fluctuation, ⌬E is the activation energy, and ␤ = 共kBT兲−1 as usual. This activated relaxation mode can become very long and complicates the interpretation of thermodynamic measurements. Glycerol has been a particularly well studied example of such glass-forming liquids that exhibit all of the above characteristics.1,2,9 However, although the ␣ relaxation as described above is presumably a cooperative mode, it is not likely directly connected to the induced thermal relaxations in these colloidal dispersion. For pure glycerol, the ␣-mode frequency at ⬇240 K is ⬃50 kHz,24–26 which can be extrapolated, using Eq. 共11兲, to near and above room temperature to the order of 100 MHz.

FIG. 1. Cartoon depicting the fractal gel formed by the diffusion-limited aggregation 共hydrogen bonding兲 of aerosil nanoparticles in an organic solvent. However, in glycerol H bonding between the glycerol and aerosil is also possible and may change the “pearl-necklace” nature of the aerosil dispersion. In any case, the distribution of aerosil should remain relatively random.

III. EXPERIMENT

The pure glycerol obtained from Aldrich was used after carefully degassing at 323 K for ⲏ2 h because of its hydroscopic nature. The pure glycerol has a molecular weight of M w = 92.09 g mol−1, a density of ␳g = 1.26 g cm−3, and a nominal glass transition temperature of Tg ⯝ 195 K. The hydrophilic type-300 aerosil silica nanoparticles obtained from Degussa27 were thoroughly dried at ⬃573 K under vacuum for ⬃2 h prior to use. The specific surface area of the aerosils measured by the manufacturer via Brunner-EmmettTeller nitrogen isotherms is a = 300 m2 g−1 and each aerosil sphere is roughly 7 nm in diameter. However, small-angle x-ray scattering studies have shown that the basic aerosil unit consists of a few of these spheres fused together during the manufacturing process.11 The hydrophilic nature of the aerosils arises from the hydroxyl groups covering the surface and allows the aerosil particles to hydrogen bond to each other. This type of bond is weak and can be easily broken and reformed leading to the thixotropic nature of these gels. The aerosil gelation in an organic solvent occurs via a reactionlimited aggregation process resulting in a fractal dimension of d f ⯝ 2.15.28 See Fig. 1 for a conceptual illustration. However, pure glycerol is a hydrogen-bonding liquid that may alter the distribution of aerosil gel from that shown in Fig. 1. Each glycerol+ sil colloidal dispersion sample was created by mixing appropriate quantities of aerosil and glycerol together with spectroscopic grade 共low-water content兲 acetone solvent that was subsequently evaporated away. The resulting solvent depleted mixtures were then annealed and degassed at 323 K for 1 h. The final samples appear by visual inspection to be uniform. These colloidal samples may be characterized by the conjugate density ␳S, defined as the mass of aerosil per open 共glycerol兲 volume, and allows one to determine the mean void length l0 = 2 / a␳S.12 The characterization of the aerosil by ␳S and l0 depends only on the random nature of the aerosil gel structure. It is likely that the aerosil gel remains random in glycerol despite the likely hydrogen bonding between the glycerol and aerosil surface. See Table I for a summary of these parameters. In addition to the

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J. Chem. Phys. 126, 094503 共2007兲

D. Sharma and G. S. Iannacchione

TABLE I. Summary of the calorimetric results for the glycerol+ aerosil samples. Shown are the silica mass fraction x = M sil / M Total, conjugate density ␳S 共in g of aerosil per cm3 of glycerol兲, mean void length l0 共in nm兲, integrated dispersion peak ⌬C⬙p 共in J K−1 mole−1兲, the high-temperature the activation energy ⌬E 共in kJ mole−1兲, and the high-temperature relaxation time ␶0 共in seconds兲 obtained by an Arrhenius analysis using Eq. 共11兲. x

␳S

l0

⌬C⬙p

⌬E

␶0

0 0.05 0.10 0.20

0.00 0.07 0.14 0.32

⬁ 101 48 21

1.32 1.90 2.37 4.13

0.00 1.12 2.27 4.17

1.92 1.36 0.92 0.49

pure glycerol sample, three glycerol+ sil samples were prepared with ␳S of 0.07, 0.14, and 0.32 g cm−3 共the units are dropped hereafter兲. High-resolution ac calorimetry was performed using a home-built calorimeter. The sample+ cell arrangement consisted of a silver crimp-sealed cup+ lid with dimensions of ⬃12 mm diameter and ⬃0.5 mm thickness, closely matching the dimensions of the heater. The average mass of the silver cell was 0.135 g and the sample 共glycerol+ aerosil兲 was 36 mg. The total mass of cell+ sample did not deviate by more than ⬃35 mg between all sample cells. After the sample was introduced into a cell and crimp sealed at atmospheric pressure, a 120 ⍀ strain-gauge heater and 1 M⍀ carbon-flake thermistor were attached. The cell was then mounted in the calorimeter, the details of which have been described elsewhere.29 Because the internal thermal relaxations depend on the sample+ cell geometry, all cells studied in this work closely matched each other in dimension and mass to better than 5%, in order to better isolate effects introduced by the aerosil. Three experiments were performed: temperature, time, and frequency scans with the following protocols. For temperature scans, measurements were made on a freshly mounted sample at a constant modulation frequency of 15 mHz as the cell is first heated then immediately cooled between 300 and 380 K using a constant rate of ±2 K hr−1. After the cell had cooled to the initial temperature of 300 K, a time scan was preformed to monitor the heat capacity as it relaxed back to the initial value. Frequency scans were then performed at fixed temperatures from 300 to 380 K in 20 K intervals over the frequency range from 1 to 2000 mHz 共i.e., ␻ from 0.0063 to 12.6 s−1兲. IV. RESULTS A. Temperature and time scans

Heating and cooling scans for the pure glycerol and the ␳S = 0.32 glycerol+ sil samples are shown in Fig. 2. From the C p data, clear indications of hysteresis are observed for the pure glycerol in that the values of C p on cooling, though parallel over most of the temperature range, do not reproduce the values observed on the heating scan of a freshly loaded sample. For the glycerol+ sil samples, this hysteresis decreases with increasing aerosil content to that shown for the highest silica content sample in Fig. 2. This behavior is in contrast to that of the reduced phase shift. For pure glycerol,

FIG. 2. Total heat capacity 共a兲 and phase shift 共b兲 observed in temperature scans for pure glycerol 共solid line兲 and ␳S = 0.32 glycerol+ sil 共dashed line兲 samples. Arrows indicate the direction of the scan, all at a rate of 2 K h−1, with the cooling scan immediately following the heating. All scans were performed using a modulation frequency of 15 mHz. Note that the apparent hysteresis in C p progressively decreases with increasing silica content while that for ␾ is reversed.

␾ reproduces itself between heating and cooling. However, for the glycerol+ sil samples, ␾ displays an increasing hysteresis, like that described for C p, but with increasing aerosil content. After returning to the starting temperature of 300 K, measurements made as a function of time, not shown here, revealed a very slow, nearly linear, evolution back to the initial C p values. For the pure glycerol, this was observed to take 2 – 3 days; while for the ␳S = 0.20 sample, approximately 6 days were required for the sample to recover its initial C p and ␾ values. Temperature scan experiments were repeated under partial vacuum conditions. Despite the increase in measurement noise, the observed hysteresis in C p was minimized while the results for ␾ appeared unaffected. This is understandable in that C p is extensive and proportional to the total mass while ␾ is dominated by the internal thermal relaxation time, which is governed by the sample+ cell geometry. The variation of C p indicate desorption and absorption of mass while the variation of ␾ indicates a real change in the internal thermal dynamics. Given these results and the observation that the deviations on heating for C p occur very close to 373 K, it is likely that the source of this behavior is absorbed water in the sample. As the sample is heated and approaches water’s boiling point, it desorbs and passes through the crimped cell into the small chamber containing the sample + cell. Upon cooling, the water vapor would then very slowly diffuse back into the cell and be absorbed by the hygroscopic glycerol+ sil. Although an artifact of the experiment, this behavior has important implications as to the role of the aerosil in the colloidal sample. B. Frequency scans

To probe the slow energy dynamics of the pure glycerol and colloidal samples, frequency scans were performed from 1 to 2000 mHz. The pure glycerol frequency scans exhibited a peak in the imaginary heat capacity at a frequency 共␻ p兲

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Induced thermal dynamics

J. Chem. Phys. 126, 094503 共2007兲

FIG. 5. Semilog plot of relaxation time ␶ = 1 / ␻ p 共taken from the frequency of the peak in C⬙p兲 vs inverse temperature for each sample studied. The legend indicates the ␳S for each sample. The slope is taken between 1000/ T = 2.6 and 3.0 provides the activation energy ⌬E and the intercept at 1000/ T = 0 provides the high-temperature relaxation time ␶0 of the samples following Eq. 共11兲. FIG. 3. Real 共a兲 and imaginary 共b兲 heat capacity as a function of heating frequency for the ␳S = 0.14 sample upon heating a fresh sample to selected temperatures from 300 to 380 K. The lines are guides to the eye and inset denotes the different temperatures in kelvin.

coincident with the inflection point of the real heat capacity roll-off. This dispersion peak remained stationary at ␻ p ⯝ 0.5 s−1 as the temperature progressively increased from 300 to 380 K and is associated with the intrinsic 共internal兲 thermal relaxation of the sample+ cell. In contrast, the dispersion peak for the glycerol+ sil samples, also coincident with the inflection point of C⬘p, clearly shifts to higher frequency with increasing temperature. An example of the resulting real and imaginary heat capacities, after all calibrations and internal corrections, is shown in Fig. 3 for the ␳S = 0.10 sample at five temperatures. As the temperature increases progressively to 380 K, this dispersion peak shifts towards higher frequencies, more strongly with increasing ␳ S. The evolution of the C⬙p / ␻ peak at 300 K as a function of frequency for the three ␳S samples is given in Fig. 4. The dispersion peak increases in height and shifts to lower frequencies with increasing amounts of aerosil. The integration of C⬙p / ␻ over the range of frequency covered in this study yields the total imaginary heat capacity of this relaxation

FIG. 4. Dispersion peak scaled by the frequency for all samples at 300 K. The integration of this peak yields the total dispersion 共or loss兲 heat capacity ⌬C⬙p. The legend indicates the ␳S for each sample.

mode 共⌬C⬙p兲. The values of ⌬C⬙p are recorded in Table I and appear to linearly increase with aerosil concentration. The frequency at which the imaginary heat capacity exhibits a peak ␻ p determines a characteristic relaxation time ␶r = 1 / ␻ p for this particular “thermal” mode. A semilog plot of ␶r vs 1000/ T reveal a linear region indicating that these relaxations appear to be energetically activated. See Fig. 5. The slope of the linear region in Fig. 5 is directly related to the activation energy ⌬E as given in Eq. 共11兲. The pure glycerol does not exhibit activated dynamics 共zero slope兲 as expected for the isotropic nature of the pure glycerol at high temperature. However, the thermal relaxations for the glycerol+ sil samples become activated at progressively lower temperatures representing the onset of an Arrheniustype behavior. It is clear that as the aerosil content increases, the activation energy of the glycerol+ sil system continuously increases while the high-temperature internal thermal relaxation time continuously decreases. Table I summarizes the results of an Arrhenius analysis for all samples studied. V. DISCUSSION AND CONCLUSIONS

Because the sample+ cell configuration are nearly identical for all the samples studied, the differences observed with the introduction of aerosil is particularly significant. The artifact of hysteresis in C p shown in Fig. 2, provides evidence that the aerosil particles participates strongly in the hydrogen bonding of glycerol since, as the aerosil content increases, the absorption and desorption of water is reduced. This is not surprising given the hydrophilic nature of the type-300 aerosil. This observation further indicates that the aerosil surface is likely coated by a bound layer of glycerol. This would strongly couple the dynamics between the aerosil gel and the glycerol fluid, the two components of this colloid. It should be noted that this hysteresis relaxes on the order of days while the observed internal thermal dynamics relaxes on the order of seconds for the pure glycerol or the glycerol+ sil samples. However, the behavior of ␾ cannot be explained by the absorbtion/desorbtion of water. The temperature dependent hysteresis of ␾ is essentially zero for the pure glycerol and largest for the highest ␳S glycerol+ sil

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094503-6

J. Chem. Phys. 126, 094503 共2007兲

D. Sharma and G. S. Iannacchione

FIG. 6. Silica mass fraction dependence of the thermal energy dynamics in glycerol+ sil colloids. Shown are the total dispersion heat capacity ⌬C⬙p 共open circles, left axis兲 and activation energy ⌬E 共filled squares, right axis兲 of samples containing 0%, 5%, 10%, and 20% silica by mass.

sample. The temperature dependent behavior of C p, an extensive quantity, would indicate that the “breathing” of water in these colloidal samples is greatest for the pure glycerol sample. Thus, the two phenomena of a temperature dependent hysteresis in C p and the frequency dependent thermal dynamics do not appear to be closely related. Since the thermal conductivity of the silica is greater than the glycerol, increasing its content should, in principle, reduce the internal thermal resistance of the sample and so, decrease the internal thermal time constant. This is confirmed at high temperature 共lowest values of 1000/ T兲 for the samples studied here as seen in Fig. 5. However, this mechanism alone would result in a frequency independent shift of the internal thermal time constant in these glycerol+ sil samples that are not observed. In addition, calorimetric spectroscopy measurements on pure 共dry兲 aerosil as well as colloidal dispersions of an aerosil gel in a non-hydrogenbonding liquid crystal10,11 under nearly identical experimental conditions are similar to the pure glycerol results shown here and do not reveal dynamics. The observed onset of a frequency dependent thermal time constant clearly indicates the aerosil induced activated dynamics of the thermal properties for these colloids. As the silica density increases, the effective viscosity of the colloidal mixture increases commensurate with an increase in the activation energy. It is tempting to conclude that the dynamics of the “thickened” glycerol+ sil at high temperatures is equivalent to the pure glycerol at low temperatures and so, related to an induced glassy behavior. However, it is not clear at this point how the thermal transport properties relate to any specific structural frustration expected for an induced glassy state. In any case, the observed dynamics may be likely due to the aerosil gel imposed frustration over large length scales within the colloidal dispersion and involve a large collection of glycerol molecules. This is illustrated by considering an estimated size of a glycerol molecule from the specific volume as ⬃1 nm in comparison to a mean void length of ⬃100 nm for the ␳S = 0.07 sample. A summary of the thermodynamic results are given in Fig. 6 and Table I. Finally, there is clearly a strong correlation between the ac-

tivation energy ⌬E and the total heat capacity loss ⌬C⬙p, both increasing linearly with aerosil content. This correlation indicates the self-consistency of these results. The energy 共thermal兲 dynamics of glycerol containing a colloidal dispersion of aerosil silica nanoparticles has been studied by high-resolution modulation calorimetry. This work has demonstrated a temperature, low-frequency, and silica density dependent complex heat capacity for this system. The results obtained highlight the potential of using frustrated glass-forming liquids, via colloidal gel dispersions whose gel properties may be varied, as a novel experimental system for gaining insight into the glass state. Clearly other experiments are called for to shed light on this phenomena and establish a connection between the observed thermal dynamics and a structural property of the mixture. Dielectric spectroscopy studies of the molecular dynamics of the glycerol as well as x-ray analysis of the aerosil gel structure in these colloids would be of particular interest. ACKNOWLEDGMENTS

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