J. Phys. Chem. C 2008, 112, 19055–19060
19055
Effect of Confinement on the Phase Transition of Benzene in Nanoporous Silica: A Positron Annihilation Study D. Dutta, P. K. Pujari,* K. Sudarshan, and S. K. Sharma Radiochemistry DiVision, Bhabha Atomic Research Centre, Mumbai 400 085, India ReceiVed: June 27, 2008; ReVised Manuscript ReceiVed: October 3, 2008
We report new results on the solid-liquid phase transition of benzene confined in nanopores of silica using positron annihilation spectroscopy. The pore sizes, ranging from 0.7 to 7.0 nm, were evaluated by positron lifetime and the Brunauer-Emmett-Teller (BET) techniques. Temperature dependent Doppler and lifetime measurements revealed discontinuities at temperatures below the bulk freezing temperature of benzene corresponding to the freezing of benzene confined in pores of different dimensions present in the silica samples. The temperatures corresponding to the freezing of confined liquids were assigned to the pore sizes on the basis of the well-known inverse correlation of depression in the freezing point with pore sizes. However, the magnitude of shift in the freezing point could not be explained on the basis of the classical Gibbs-Thomson relation. On the other hand, the data are seen to be consistent with the molecular cluster theory for microcrystal growth in confined region. I. Introduction The properties of freezing and melting of liquids confined in pores are known to be different from their bulk behavior. This is mainly due to the contribution of the surface free energy associated with the interface between the pore wall and liquid or solid. When a liquid is confined in a small pore, the surface area of the liquid becomes large compared to its volume, and hence the contribution of interfacial surface free energy becomes important in changing the freezing/melting temperature. At equilibrium, the relative values of interfacial free energies can be expressed as1
σLW ) σSW + σLS cos θ
(1)
where σLW, σSW, and σLS are the interfacial free energies per unit area for the liquid-wall, solid-wall, and liquid-solid interfaces respectively. The angle, θ, is the equilibrium contact angle between the liquid-solid and solid-wall interfaces. When the liquid solidifies in the pore, the change in free energy per unit length between solid and liquid is given as
∆FLfS ) ∆FVπr2 + 2πr(σLW - σSW) ) ∆FVπr2 + 2πrσLScos θ (2) where ∆FV is the volume free energy difference between the liquid and solid and r is the radius of the spherical pore. The shift in phase transition temperature ∆T of the liquid in a particular pore size can be obtained by minimizing ∆FLfS w.r.t. the radius of the pore and is given by
∆T ) Tpore-Tbulk )
σLSTbulk cos θ HFr
(3)
where the difference in volume free energy ∆FV ∼ HF∆T/Tbulk (H being the molar melting enthalpy of the solid and F being the molar density). It is assumed that the size of the solid formed in the pore is sufficiently large so that the material retains its bulk properties for H and F. The above equation shows that the * To whom correspondence should be addressed. E-mail: pujari@ barc.gov.in.
freezing and melting temperature of the liquid inside the pore either increases or decreases depending upon the value of the equilibrium contact angle. For smaller contact angle, i.e., when the liquid has attractive interaction with the pore wall, there is an elevation of the freezing point. Similarly larger contact angle or repulsive/weakly attractive interaction of liquid with pore wall leads to depression in freezing point. Equation 3 is analogous to the well-known Gibbs-Thomson equation for shift in freezing/melting temperature of confined liquids,2 which is given as
∆T ) Tpore-Tbulk ) -
2σLSTbulk HFr
(4)
In the limit of a small and highly inhomogeneous system, as the concept of surface tension (energy) is not well defined and the bulk value of melting enthalpy as well as bulk density of liquidremainsnolongervalid,adeviationfromtheGibbs-Thomson equation based on classical thermodynamics is expected. The behavior of liquids in small pores has potential applications in different areas including nanotribology, catalysis, lubrication, fabrication of nano particles, etc.3–6 To explore the effect of pore structure and interaction of pore wall with confined molecules on their freezing/melting behavior, a variety of experimental studies such as differential scanning calorimetry (DSC),2,7,8 nuclear magnetic resonance (NMR),2,9 dielectric spectroscopy,10–12 and neutron scattering13,14 have been carried out. All of these studies have focused on the structure as well as dynamics of confined liquids across the freezing/melting temperature. It is seen that the change in freezing temperature depends in a complex way on the measurement techniques, confined liquid and confining matrix with freezing temperature decreasing, increasing or remaining unchanged in some cases. Each of the experimental techniques measure a certain property, e.g., thermodynamic, structural, or dynamics (relaxations) as the case may be, giving different phase transition temperatures due primarily to the interference of the matrix and a small quantity of confined liquid.3,15 Some authors have simulated the free energy change of confined molecules by considering the
10.1021/jp805675y CCC: $40.75 2008 American Chemical Society Published on Web 11/07/2008
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fluid-wall interaction as a Lenard-Jones potential inside the small pores to study the shift in phase transition temperature of the confined system as a function of temperature.10,16,17 A large body of experimental data reveals an inverse correlation of freezing/melting temperature with pore size.3,15 However, an overall understanding of this phenomenon based on a range of observations is still missing. It is acknowledged that this area of research is experimentally and empirically driven and that the process of phase transition in confined liquids is not fully understood.15 Positron annihilation spectroscopy (PAS) is an in situ and nondestructive technique to study the microstructural properties of materials. Its utility in defect studies in metals/alloys, freevolume/pores in molecular solids is well documented.18–20 In the context of porous materials, a substantial fraction of thermalized positrons may form positronium (bound state of an electron and a positron) at the bulk-pore interface that diffuses and localizes in pores or regions of low ion density. Positronium (Ps) may exist in two states, viz., singlet para-positronium (pPs) and triplet ortho-positronium (o-Ps) with intrinsic lifetime of 125 ps and 142 ns, respectively. The latter primarily decays via three photon annihilation. However, in matter o-Ps can seek out electrons from the pore surface with opposite spin and decays via two-photon mode known as pick-off annihilation that reduces the triplet o-Ps lifetime to a few nanoseconds. The o-Ps trapped inside the pore has a probability of being found in and about the cavity given by the square modulus of its wave function ΨPs(r) with r measured from the center of the cavity. Thus the pick-off annihilation rate (lifetime) can be correlated to the pore size, i.e., the larger the size, the longer the o-Ps lifetime and vice versa. Several models are available in the literature to evaluate the pore size from o-Ps lifetime.21–26 We have used a simple relationship between the pick-off lifetime (τp) and micro cavity radius (R < 1 nm)
τp ) 18.8R - 5.07
(5)
nm.26
where τp is in ns and R is in For larger pores (pore radius R g 1 nm) the contribution of o-Ps intrinsic annihilation (three gamma) becomes significant along with o-Ps pick-off annihilation; hence, the lifetime becomes larger and the annihilation rate is given by
( R′δ ) + λ
λ ) λp + λ3γ ) ς
3γ
(6)
where, λ3γ ()1/142 ns-1) is the intrinsic 3γ annihilation rate of o-Ps and ς includes the parameters such as Zeff as well as the density (F < 1) of the porous material, R′ is the size parameter for the large pore and δ is the diffusivity parameter at the surface of the mesopore.27 The total annihilation rate, however, does not depend on the geometric shape of the pore27,28 and the calibration evolved (λ ) 0.3/R′ +1/140) has worked well for silica and zeolite materials.27,29 In addition to the evaluation of pore size, positron annihilation technique is very sensitive to phase transitions that invariably involves alteration in the electron density/momentum distribution at the annihilation site. In the context of freezing/melting of liquids confined in nanopores, the pick-off rate of o-Ps is expected to vary with changes in density of liquid as well as free-volume following condensation of the liquid inside the pore. The momentum distribution is also expected to be sensitive to changes in density as well as free-volume originating from o-Ps as well as free positron states. Thus, localization of positron/Ps in the region of low ion density and their sensitivity to the change in electron density/momentum distribution make PAS technique an attrac-
tive nanoscopic probe to study the phase transition of confined liquids. There are not many reports on positron annihilation spectroscopic studies on the phase transition (freezing/melting) in confined geometry. The phase transition of CO2 and N2 gases in microporous materials has been studied by indexing the variation of three-to-two gamma ratio (3γ/2γ).30–34 Confinement induced change in free-volume and mobility of glycerol is reported in mesoporous silica glass.35 Recently, we have demonstrated that PAS technique is sensitive to phase transition of confined liquids in ZSM-5 zeolite.36 Distinct discontinuities in the annihilation parameters are seen corresponding to phase transition temperatures. In the present work, we have studied the phase transition behavior of benzene in nanoporous silica to (i) evaluate the positron/positronium response in the presence of pores of different sizes in the same sample and (ii) to determine the transition temperatures and examine the existing models on the shift in transition temperature vis-a`-vis pore size. II. Experimental Section Commercially available silica gel powder (Sigma Aldrich) having different pore sizes (silica 1 and 2) and analytical grade benzene were used. The samples were heated at 573 K under vacuum for 7-8 h to remove adsorbed air and moisture. They were cooled to room temperature, and a sufficient volume of benzene was injected using a syringe into the sample still in vacuum through a rubber septum so that the entire sample was covered with benzene. The liquid-sample mixture, a gel like structure, was kept overnight and heated at 323 K for homogeneous adsorption of liquid into the pores. The excess liquid /vapor at bulk surface of the sample was then removed by evacuating at room temperature through mechanical pumping for 10-15 min. During this time a clear transformation of brownish gel to white solid powder can be seen. FTIR measurements using a JASCO FTIR-610 instrument confirmed the incorporation of benzene similar to that reported elsewhere.36 The spectral features remain unaffected at least up to one hour of evacuation indicating that there is no escape of benzene from the micro and mesopores of silica. This arrangement was used for room temperature (298 K) positron lifetime measurements in benzene-loaded samples. The degree of pore filling is expected to be the maximum in vacuum following evacuation at elevated temperature but it has not been measured directly. It has been shown (DSC studies) that the degree of pore filling does not change the shift in freezing temperature.7 For low temperature measurements, the samples along with the source (∼3 × 105 Bq deposited on a thin nickel foil) were mounted on the cold head of an APD closed cycle helium refrigerator. The temperature variation was carried out in 1 K intervals with an accuracy of better than 0.1 K. Doppler broadened annihilation radiation measurements were carried out using a HPGe detector having resolution of 1.7 keV at the 1332 keV photo peak of 60Co. The shape parameter, namely, S-parameter defined as the normalized integrated counts in the energy range 511 ( 1 keV was evaluated. The reproducibility of the data was checked at several temperatures. A low temperature measurement on silica gel prior to incorporation of benzene (but similar heat treatment) has also been performed for comparison. In order to asses the extent of o-Ps yield in both the samples, 3γ/2γ ratios were measured in pure silica 1 and 2. It was found to be higher in silica-2 indicating higher Ps fraction as compared to silica-1. Positron annihilation lifetime measurements were carried out using BaF2 scintillators coupled to a fast-fast coincidence
Positron Annihilation Study
J. Phys. Chem. C, Vol. 112, No. 48, 2008 19057
TABLE 1: Pore Size Obtained Using Positron Annihilation Lifetime Data average pore radius (nm) (R)
τ (ns)
sample silica-1 benzene loaded silica-1 silica-2 benzene loaded silica-2
2.95 9.25 58.90 2.55 1.5 26.87 52.00 2.52
0.43 0.76 3.05 0.35 1.00 2.48
TABLE 2: Parameters Derived from Nitrogen Gas Adsorption Isotherm sample
specific surface area (×104 cm2/g)
specific pore volume (cm3/g)
average pore radius (nm)
silica-1 silica-2
454.24 551.94
0.71 0.66
3.1 2.3
system. The resolving time (fwhm) measured with a 60Co source was 300 ps for the positron window settings. Measurements in benzene filled samples, as the case may be, were carried out with time dispersion of 25 ps per channel. For pure samples (without benzene) measurements were carried out with time dispersion of 50 and 500 ps (range of analysis 40 and 400 ns respectively) to evaluate shorter as well as longer lived components. Data analysis was carried out using both the PATFIT and MELT programs.37,38 A gist of the data analysis methodology is given in the following for silica-1. PATFIT analysis of 40 ns range with free and constraint analysis with 3 and 4 components reveal shorter components, e.g., 200-250 and 490-550 ps. Four component analysis gives a better fit in which a third component (2.9 ns) is clearly seen. The fourth component was seen to be around 12 ns that is apparently a mixture of two larger components. The 400 ns range fit with MELT gave four components 0.60, 2.95, 9.25, and 58.9 ns. The fit quality was checked on the basis of chi-square, maximum value of probability, and errors on intensities.38 Four component constraint free analysis (400 ns range) using PATFIT reproduces the longest component but fails to resolve the two shorter o-Ps components (2.95 and 9.25 ns). However, when the longest lived component is fixed the resolved life-times as obtained from MELT (0.60, 2.9 and 9.28 ns) are reproduced with variance of fit close to 1. The intensities of the o-Ps components thus obtained are 2.5%, 2% and 18.5% for 2.95, 9.25 and 58.9 ns components, respectively. Similarly, in silica-2 the intensities were 10.5%, 3.5%, and 15.3% for 1.5, 26.8, and 52 ns, respectively. It may be noted that higher Ps fraction in silica-2 is consistent with higher surface area (as measured using Brunauer-Emmett-Teller (BET), Table 2) and higher 3γ/2γ ratio. It may also be noted that the radius calculated from the longest life-times (dominant intensities) in either samples are closer to the average size determined from BET measurement. An attempt to extract a 140 ns (constrained analysis) component yielded very low intensity with large uncertainties. The specific pore surface as well as pore volume were measured by nitrogen gas adsorption using BET technique to evaluate the average pore size. III. Results and Discussions The positronium lifetime components in two silica gel powder samples (silica 1 and 2) before and after the incorporation of benzene are shown in Table 1. The distinct long-lived components in the pure samples correspond to o-Ps annihilation in
Figure 1. Temperature dependence of the S-parameter in silica-1 without benzene.
Figure 2. Temperature dependence of the S-parameter in silica-1 loaded with benzene.
micropores (pore size < 2 nm) and mesopores (pore size 2-50 nm). The specific pore surface area, specific pore volume and average pore radii of these two silica powder samples measured using BET gas adsorption method are shown in Table 2. The average pore radii are calculated using relation r ) 2V/S where V and S are measured pore volume and surface area, respectively. It is seen that the values of mesopore sizes calculated from positron life-times are close to these values. However, BET technique could not provide the information on other pore sizes (micropores) measured from Ps lifetime. When benzene molecules are incorporated into the matrices, they localize in these micro and mesopores and only one long-lived component of o-Ps is obtained which originates from this confined benzene. In order to observe the phase transition of benzene inside the pores, Doppler broadening measurements were carried out from 280 to 150 K. In addition, o-Ps pick-off lifetime (τ3) has been measured in the temperature range from 280 to 240 K.We have not observed any temperature dependence of the Sparameter for the pure silica sample (before incorporation of benzene) as shown in Figure 1. Figures 2-4 show the temperature dependence of S-parameter, o-Ps lifetime and intensity, respectively in benzene loaded silica-1. Figures 5-7 show the temperature dependence of S-parameter, o-Ps lifetime and intensity, respectively in silica-2. When benzene is incorporated, several discontinuities in the S-parameter are observed (Figures 2 and 5). The discontinuities observed in the Sparameter at different temperatures correspond to freezing of benzene confined in different pores. Similarly, discontinuities
19058 J. Phys. Chem. C, Vol. 112, No. 48, 2008
Figure 3. Temperature dependence of o-Ps lifetime in silica-1 loaded with benzene. Arrows indicate phase transition temperatures that coincide with discontinuities seen in the S-parameter as shown in Figure 2. The line drawn is to guide the eye.
Figure 4. Temperature dependence of o-Ps intensity in silica-1 loaded with benzene. Arrows indicate phase transition temperatures that coincide with discontinuities seen in the S-parameter as shown in Figure 2. The line drawn is to guide the eye.
Figure 5. Temperature dependence of the S-parameter in silica-2 loaded with benzene.
in the pick-off lifetime were seen at temperatures corresponding to the changes seen in the S-parameter (Figures 3 and 6). In the silica-1 sample, the measured S-parameter shows three distinct discontinuities (Figure 2) at ∼276, 269, and 265 K (the bulk freezing temperature of benzene is 278 K), which can be
Dutta et al.
Figure 6. Temperature dependence of o-Ps lifetime in silica-2 loaded with benzene. Arrows indicate phase transition temperatures that coincide with discontinuities seen in the S-parameter as shown in Figure 5. The line drawn is to guide the eye.
Figure 7. Temperature dependence of o-Ps intensity in silica-2 loaded with benzene. Arrows indicate phase transition temperatures that coincide with discontinuities seen in the S-parameter as shown in Figure 5. The line drawn is to guide the eye.
ascribed to three phase transitions of benzene corresponding to its confinement at three distinct regions (i.e., corresponding to pores with average radius ∼3.05, 0.76, and 0.43 nm respectively, as shown in Table 1). This assignment is based on the wellknown inverse relation of pore size with the depression of freezing point.3,7,15 The o-Ps pick-off lifetime (τ3) profile also shows discontinuities (like S-parameter) at these transition temperatures (Figure 3). Although the intensity variation over the entire temperature range studied is small, oscillatory behavior corresponding to phase transition temperatures are seen (Figure 4). The S-parameter profile indexes the p-Ps having a narrow momentum distribution. In the silica-1 sample, upon cooling, S-parameter decreases (Figure 2) at phase transition temperatures (276, 269, and 265 K). The physical reason for this decrease could be a reduction in o-Ps intensity due to the change in the properties of the liquid (density, surface tension etc). Decrease in τ3 is also consistent with the increase in density of benzene (Figure 3). Since the decrease in intensity is small corresponding to this temperature (Figure 4), the momentum distribution originating from free positron annihilation may also be contributing to the drop in the S-parameter. Smaller τ3 is
Positron Annihilation Study consistent with broader momentum distribution causing decrease in the S-parameter. On cooling below the respective freezing temperatures, S-parameter as well as τ3 are seen to increase giving nearly identical values seen prior to freezing. This is in contrast to the stepwise decrease in τ3 and I3 reported by Thosar et al.39 in bulk benzene. It has been argued30,36 that such increase in τ3 and the S-parameter below the freezing temperature could be due to creation of free-volume following condensation of the trapped liquid. However, it is not clear why the values of τ3/S-parameter should be almost equal to that prior to freezing of benzene. If we consider that the pores are completely filled with solid benzene then the Ps/positron will be detrapped and annihilate from a delocalized state. The smaller pores, where the benzene is still in liquid state, will facilitate Ps formation and the recovery of τ3/S-parameter could be explained. This explanation, however, can not satisfy the recovery seen below the lowest phase transition temperature (265 K). Therefore, the systematics, i.e., recovery below freezing point, may be linked to the dynamics of positron/Ps which is not fully understood. It is interesting to note that a recent report on glycerol confined in silica glass shows higher τ3 than bulk liquid at temperature below freezing point which has been ascribed to perturbation in the structure of liquid due to confinement.35 A careful look at their data (Figure 1 in ref 35) shows a recovery of τ3 below freezing temperature similar to observation made by us. Similar discontinuities in the S-parameter are seen in silica-2 at ∼274, 266, and 258 K corresponding to liquid confined in ∼4.96, 2.0, and 0.7 nm pores, respectively (Figure 5). These discontinuities coincide with the temperatures where change in slope of τ3 are observed (Figure 6). The intensity profile as a function of temperature shows discontinuities at temperatures corresponding to phase transition (Figure 7). We have not observed any other phase transitions at least up to 150 K from Doppler broadened annihilation radiation measurement. Also, no remarkable difference in the heating and cooling cycle is seen and hence not shown in figure similar to our observation in ZSM-5.36 Similar studies using other techniques have not mentioned the occurrence of hysteresis.3,15 However, hysteresis was seen in the condensation of carbon dioxide in vycor glass.30 The phase transition temperature of benzene confined in the pores can be obtained using equation 4 taking the bulk values of melting enthalpy, surface energy (σLS/H ) 0.33/mol)7 and density of benzene. However, the calculated values of phase transition temperature or the shift in the freezing temperature are seen to be different from our observation as shown in Figure 8. This is indicative of the fact that the parameters used in equation 4 may have a dependence on the pore size, e.g., enthalpy, surface energy, and density, may be different for different pore size. A substantial discussion on the dependence of these parameters on pore size has been presented by Jackson et al.7 The pore surface anisotropy that determines the strength of fluid-wall interaction in nano pores and the effect of inhomogeneity of solid benzene structure in the confined space are important in determining the shift in freezing point. The structure of confined benzene below the transition temperatures is expected to have inhomogeneous phases with partial crystalline domain, as reported by Radhakrishnan et al. and Bartkowiak et al. using Monte Carlo simulation method.17,10 Numerical simulation work by Wales et al. points to the formation of small molecular cluster in pores that interact with the pore wall via Van der Waals potential.40 The variation of S-parameter at the freezing/melting point also indicates the agglomeration of benzene molecules in the pores.36 If the solid benzene molecules are agglomerated to form small benzene
J. Phys. Chem. C, Vol. 112, No. 48, 2008 19059
Figure 8. Shift in freezing point vs inverse of pore radius. The dotted line shows the calculated shift in freezing point using Gibbs-Thomson equation. The solid circles are obtained experimentally and the solid line is the fit to the experimental data using molecular cluster theory for microcrystal growth (eq 7).
clusters in the pores, then the melting temperature will be directly related to the number of atoms in the cluster and the depression of freezing/melting point is expressed as ∆T ) AN-1/3 - BN-2/3, where A and B are constants and N is the number of atoms in the cluster.7 If this equation is derived for the spherical cavity with the assumption R (cavity radius) ∝ N1/3, then the leading term has the same inverse radius dependence as predicted by equation 4. However, for very small pores with large surface to volume ratio, the N-2/3 (surface effect) term becomes significant and the above equation can be represented as
∆T A′ B′ ) Tbulk R R2
(7)
which fits our experimental data as shown in Figure 8. The obtained values of the coefficients A′ and B′ from the fitting are 0.03 nm and 0.0025 nm2, respectively. The origin of these two parameters should depend on the degrees of anisotropy of the liquid and pore surface, the strength of the pore-wall interaction energy as well as the enthalpy of phase transition of benzene in the nano pores. Needless to say, our data cannot be fitted to the Gibbs-Thomson equation (eq 4). Even if we try to fit our data to a straight line, the slope is seen to be different from the expected value of 2σLS/HF, where these values correspond to bulk values of benzene.7 This implies that the parameters used in Gibbs-Thomson equation changes with change in the number of confined molecules or the size of the pore. It has been reported that the density of liquid increases when trapped in nano pores.41 In addition to the change in the bulk properties of trapped liquid, the presence of a liquid layer that effectively reduces the size of the pore can also influence a deviation from Gibbs-Thomson equation.7 Celestini et al. took an approach to account for the surface melting of nanospherical particle or the molecular cluster inside the pore based on the density functional formalism, through a phenomenological description of solid-liquid and liquid-matrix interaction.42,43 According to this model the predicted shift in freezing temperature is given by
2γsl ∆T ξ ) 1+ Tbulk FHr r - 2ξ
(
)
(8)
where ξ is the correlation length of short-range intermolecular interaction. Though the surface effect is taken into account in
19060 J. Phys. Chem. C, Vol. 112, No. 48, 2008 this model, it suffers from the same limitation as of eq 4 because it uses the bulk value of the parameters. However, the correlation obtained by us, considering the formation of small benzene molecular cluster in the pore, can serve as an empirical relation between the shift in freezing/melting point of benzene and size of the nano pore. IV. Conclusion Positron annihilation spectroscopic technique is seen to be a sensitive probe for study of phase transition in confined liquids. Phase transition of benzene confined in nanopores of different dimensions present in the same sample is sensitively manifested in Ps lifetime and S-parameter. From this quasi-thermodynamic measurement phase transition temperatures corresponding to different pore sizes are evaluated. Although a depression in freezing temperature is seen in all cases, the magnitude of shift from the bulk freezing temperature cannot be explained by classical Gibbs-Thomson equation. A correlation between the nano pore size and the shift in freezing/melting point of benzene is obtained by taking into consideration the surface contribution of small pores. This correlation seems to be consistent with molecular cluster theory for microcrystal growth in confined region. The contribution of structural imperfection and hence the heterogeneity of interfacial energy of benzene and pore wall is discussed qualitatively. Further studies are required to explore these contributions in nanoscopic scale more quantitatively. Acknowledgment. The authors are thankful to Dr. K. T. Pillai of Fuel Chemistry Division, BARC, Mumbai for providing help in BET measurements. References and Notes (1) Jackson, K. A.; Chalmers, B. J. Appl. Phys. 1958, 29, 1178. (2) Dosseh, G.; Xia, Y.; Alba-Simionesco, C. J. Phys. Chem. B 2003, 107, 6445. (3) Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. J. Phys: Condens. Matter 2006, 18, R15. (4) Murase, N.; Gonda, K.; Watanabe, T. J. Phys. Chem. 1986, 90, 5420. (5) Feldman, R. F.; Cheng-yi, H. Cem. Concr. Res. 1985, 15, 765. (6) Eyraud, C.; Quinson, J. F.; Brun, M. In Characterization of Porous Solids; Unger, K.; Rouquerol, J.; Singh, K. S. W.; Kral, H., Eds.; Elsevier: Amsterdam, 1988; p 307. (7) Jackson, C. L.; McKenna, G. B. J. Chem. Phys. 1990, 93, 9002. and the references therein. (8) Zheng, W.; Sindee, L. S. J. Chem. Phys. 2007, 127, 194501. (9) Kimmich, R. Chem. Phys. 2002, 284, 253. (10) Sliwinska-Bartkowiak, M.; Dudziak, G.; Sikorski, R.; Gras, R.; Radhakrishnan, R.; Gubbins, K. E. J. Chem. Phys. 2001, 114, 950.
Dutta et al. (11) Barut, G.; Pissis, P.; Plester, R.; Nimtz, G. Phys. ReV. Lett. 1998, 80, 3543. (12) Gorbatschow, W.; Arndt, M.; Stannarius, R.; Kremer, F. Europhys. Lett. 1996, 35, 719. (13) Schonhals, A.; Goering, H.; Schick, C.; Frick, B.; Zorn, R. Eur. Phys. J. E 2003, 12, 173. (14) Alba-Simionesco, C.; Dosseh, G.; Dumont, E.; Geil, B.; Morineau, D.; Frick, B; Teboul, V.; Xia, Y. Eur. Phys. J. E 2003, 12, 19. (15) Alcoutlabi, M.; McKenna, G. B. J. Phys: Condens. Matter 2005, 17, R461. (16) Miyahara, M.; Gubbins, K. J. Chem. Phys. 1997, 106, 2865. (17) Radhakrishnan, R.; Gubbins, K. E.; Sliwinska-Bartkowiak, M. J. Chem. Phys. 2000, 112, 11048. (18) Positron Solid-state Physics; Proceedings of the international school of Physics; Brandt, W.; Dupasquier, A., Eds.; North Holland Publishing Company: Amsterdam, 1983. (19) Nakanishi, H.; Jean, Y. C. Positron and Positronium Chemistry; Schrader, D. M.; Jean, Y. C., Eds.; Elsevier: Amsterdam, 1988. (20) Gidley, D. W.; Peng, H. G.; Vallery, R. S. Ann. ReV. Mater. Res. 2006, 36, 49–79. (21) Tao, S. J. J. Chem. Phys. 1972, 56, 5499. (22) Eldrup, M.; Lightbody, D.; Sherwood, J. N. Chem. Phys. 1981, 63, 51. (23) Nakanishi, H.; Ujihira, Y. J. Phys. Chem. 1982, 86, 4446. (24) Goworek, T.; Ciesielski, K.; Jasinska, B.; Wawryszczuk, J. Chem. Phys. 1998, 230, 305. (25) Ito, K.; Nakanishi, H.; Ujihira, Y. J. Phys. Chem. B 1999, 103, 4555. (26) Dutta, D.; Ganguly, B.; Gangopadhyay, D.; Mukherjee, T.; DuttaRoy, B. J. Phys: Condens. Matter 2002, 14, 7539. (27) Dutta, D.; Ganguly, B.; Gangopadhyay, D.; Mukherjee, T.; DuttaRoy, B. J. Phys. Chem. B 2004, 108, 8947. (28) Dull, T. D.; Frieze, W. E.; Gidley, D. W.; Sun, J. N.; Yee, A. F. J. Phys. Chem. B 2001, 105, 4657. (29) Dutta, D.; Chatterjee, S.; Ganguly, B.; Pillai, K. T. J. Appl. Phys. 2005, 98, 033509. (30) Duffy, J. A.; Alam, M. A. Langmuir 2000, 16, 9513. (31) Duffy, J. A.; Wilkinson, N. J.; Fretwell, H. M.; Alam, M. A. J. Phys: Condens. Matter 1995, 7, L27. (32) Duffy, J. A.; Wilkinson, N. J.; Fretwell, H. M.; Alam, M. A.; Evans, R. J. Phys: Condens. Matter 1995, 7, L713. (33) Alam, M. A.; Clarke, A. P.; Duffy, J. A. Langmuir 2000, 16, 7551. (34) Wilkinson, N. J.; Alam, M. A.; Clayton, J. M.; Evans, R.; Fretwell, H. M.; Usmar, S. G. Phys. ReV. Lett. 1992, 24, 3535. (35) Kilburn, D.; Sokol, P. E.; Alam, M. A. Appl. Phys. Lett. 2008, 92, 033109. (36) Dutta, D.; Sachdeva, A.; Pujari, P. K. Chem. Phys. Lett. 2006, 432, 116. (37) Kirkegaard, P.; Pedersen, N. J.; Eldrup, M. PATFIT-88, Risø-M2740; Roskilde: Denmark, 1989. (38) Shukla, A.; Peter, M.; Hoffmann, L. Nucl. Instrum. Meth. A 1993, 335, 310. (39) Thosar, B. V.; Lagu, R. G.; Kulkarni, V. G.; Chandra, G. Phys. Status Solidi 1973, 55, 415. (40) Wales, D. J.; Berry, R. S. J. Chem. Phys. 1990, 92, 4283. (41) Turnbull, D. J. Appl. Phys. 1950, 21, 1022. (42) Celestini, F.; Pelleng, R. J. M.; Bordarier, P.; Rousseau, B. Z. Physik. D 1996, 37, 49. (43) Bosch, A.; Celestini, F. Z. Physik. D 1993, 28, 293.
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