Positron-annihilation-lifetime response and broadband dielectric relaxation spectroscopy: diethyl phthalate.

We report the results of a combined phenomenological analysis of the data from positron-annihilation-lifetime spectroscopy (PALS) and the relaxation data from broadband dielectric spectroscopy (BDS) on diethyl phthalate (DEP). The ortho-positronium (o-Ps) lifetime, tau3, as a function of temperature over a temperature range from 67 K up to 300 K is compared with the spectral features and the relaxation parameters of the BDS spectra decomposed into the primary alpha and the secondary beta processes in the temperature range from 140 K up to 380 K by using the Williams-Watts scheme. Phenomenological model-free analysis of the tau3-T plot provides the three characteristic PALS temperatures, where the two most pronounced ones at TgPALS=185 K and Tb2=245 K=1.32TgPALS are related to the glass-liquid transition and the onset of a quasiplateau region, respectively. In the case of a weaker bend effect at Tb1=210 K=1.14TgPALS, a number of new coincidences with changes in the dielectric beta process have been found. They concern the changes in width parameter of the distribution function for the beta relaxation time and the activation energy of the betaeff process, a crossover from the Arrhenius to the non-Arrhenius type of temperature dependence as well as with the onset of a short-time tail of the beta relaxation time distribution and finally, with changes in the relaxation strength of the alpha and betaeff processes. All these findings indicate a close connection of the o -Ps annihilation parameters and relaxation characteristics of BDS response for the DEP matrix.


I. INTRODUCTION
Structure-property relationships in condensed matter form continuing long-term topics of chemistry, physics, biology, and materials science. Traditionally, the former aspect of disordered materials is treated by means of diffraction methods by using x rays or neutron scattering techniques ͓1-4͔. However, the relevant structural quantities, i.e., the static structure factors and the related radial distribution functions or the density fluctuations are not easily related in a simple and quantitative way to physical properties of practical significance such as dynamics and transport.
On the other hand, it is generally accepted that the thermodynamic, dynamic, and transport properties of amorphous or partially crystalline materials are closely related to the structural and dynamical disorder of the matrix. In this respect, the free volume concept received a large extension because of its conceptual simplicity and physical plausibility in interpretation of the above-mentioned behavior ͓5,6͔. In spite of its large popularity, a sophisticated utilization of the free volume concept requires a firm establishing of some standard method for the free volume characterization. Here, positron-annihilation-lifetime spectroscopy ͑PALS͒ based on the annihilation of the bound system of positron and electron, the so-called ortho-positronium ͑o-Ps͒, is of great relevance. The o-Ps probe is a very sensitive indicator of the presence of local regions of the reduced electron density, such as vacancies in real crystals as well as free volume holes in amorphous materials ͓7-9͔. The basic o-Ps annihilation parameter, i.e., o-Ps lifetime, 3 , is interpreted in free volume terms and is a measure of the size of these local free volume hole regions. Semiempirical models are used to characterize the PALS data in terms of free volume hole characteristics such as mean free volume hole size ͓10͔ and free volume hole fraction ͓11,12͔. Subsequently, these free volume quantities are used in the correlation of various dynamics and transport phenomena ͓11-15͔.
As PALS experiment is carried out on a structurally and a dynamically fluctuating matrix with certain degrees of dynamical freedom determined by their chemical constitution and external variables such as temperature, T, and pressure, p, the PALS response is expected to be related to some parameters of the particle's mobility of glass-forming systems ͓16-20͔ ranging generally from picoseconds to seconds or even hours. Evidently, such a huge time scale of relaxation processes can be most effectively covered by broadband dielectric spectroscopy ͑BDS͒ ͓21-25͔.
Phenomenological model-free analysis of the 3 -T dependences in a series of small molecular and polymeric glassformers revealed the existence of several characteristic PALS temperatures marked according to a unified notation ͓18͔ as T g PALS , T b1 and T b2 = T r ͓26͔ =T e ͓27͔ =T k ͓28͔ which are located at T b1 ϳ 1.2-1.3T g PALS and T b2 ϳ 1.4-1.7T g PALS ͓18͔. In order to utilize fully a potential of the PALS method for the characterization of any disordered system, the 3 vs T dependence and the origin of the PALS temperatures should be understood as completely as possible. Some progress has been achieved in this direction so far. Thus, it appears ͓13,16-20,29͔ that T b2 , marking the onset of quasiplateau region as temperature increases at relatively higher tempera-tures, coincides sometimes with the so-called Stickel's temperature T B ST ͓30͔ or/and the Schönhals temperature, T B SCH ͓31͔, at which significant changes in the relaxation parameters of the primary ␣ process from dielectric spectroscopy ͑DS͒ occur. Moreover, at T b2 , 3 , is often close to the mean relaxation time of the primary ␣ process, ␣ ͑T b2 ͒ as determined by standard peak analysis ͓16,18,29͔. Slighter change in the slope at T b1 more or less close to the glass transition is sometimes observed ͓16,18,29͔. It is also found that T b1 can be related to the temperature T ␣ ͑−6͒ at which the ␣ relaxation time from DS reaches 10 −6±1 s ͓18,20͔. Typically, the dielectric relaxation of usual glass-formers exhibits a broad spectrum with peak feature and a high frequency part from the so-called excess wing or/and secondary relaxation ͓21-24͔. The correlation T b1 ϳ T ␣ ͑−6͒ seems to suggest that the motion associated with the high-frequency part of the dielectric relaxation spectrum could be in some way related to the change in the slope of the 3 vs T plot just at around T b1 as it is demonstrated very recently by some of us for glycerol ͓32͔.
In addition to the above-mentioned phenomenological PALS vs DS comparisons, theoretical ͓20͔ as well as modeling ͓20͔ approaches are also of relevance. Recently, some of us tried to explain the T b1 in diethyl phthalate ͑DEP͒ by using an extended free volume ͑EFV͒ model ͓33,34͔. In this framework an agreement of the characteristic PALS temperature T b1 with the characteristic EFV temperature T 0 CG for the PALS data suggests that the change in free volume microstructure as seen by the o-Ps probe could be related to the dynamic crossover in the primary ␣ process from DS which occurs at T 0 CG ͑DS͒ХT 0 CG ͑PALS͒. The aim of this paper is to present empirical analysis of the PALS data by using the dynamic ones from BDS on DEP. It is found that a combination of both experimental techniques can provide further insight into the dynamic nature of the PALS response. It is shown that such a joint phenomenological approach can contribute to more detailed explanation of the PALS response of the condensed system and the related characteristic PALS temperatures and subsequently, to deeper understanding of the liquid and supercooled liquid states of condensed matter.

Material.
Diethyl phthalate ͑DEP͒ C 6 H 4 ͑O =C-O-CH 2 -CH 3 ͒ 2 from Aldrich Chemicals was used in both PALS and BDS studies. The glass transition temperature T g DSC = 183 K and melting transition temperature T m DSC = 273 K on the basis of the differential scanning calorimetry ͑DSC͒ study ͓35͔.

A. PALS
The positron-annihilation-lifetime spectra were obtained by the conventional fast-fast coincidence method using plastic scintillators coupled to Phillips XP2020 photomultipliers. The time resolution of prompt spectra was about 320 ps. The activity of 22 Na source was 4 MBq. The radioactive positron 22 Na source plus samples assembly was kept in a rotary pump vacuum. During the low temperature measurements from 67 K up to 300 K samples in a holder were fixed at the end of a cold finger of a closed-cycle helium gas refrigerator Leybold with automatic temperature regulation. The temperature stability was about 1 K ͓36͔.
The positron-lifetime spectra were analyzed using the well-known PATFIT-88 software package ͓37͔ in terms of three annihilation modes: a short-term component from para-positronium p-Ps, 1 , an intermediate one attributed to "free" positron 2 , and a long-term one, related to free volume microstructure: ortho-positronium o-Ps, 3 .
The DEP sample was measured in three cycles: one during relatively slow cooling cycle giving the amorphous sample, while the remaining two during slow heating, one after rapid cooling, before the annihilation data acquisition, provided the structurally transformed material. The time of acquisition per one temperature point was at least 2 hours.

Instrumental aspects
Dielectric measurements on DEP above its T g were performed in a wide frequency range of 10 mHz-20 GHz using three different experimental setups depending upon the frequency range. In the frequency range of 10 −2 Hz-10 6 Hz dielectric measurements were made using a high-resolution Alpha dielectric analyzer supplied by Novocontrol, GmbH. For the frequency range of 10 6 Hz-10 9 Hz, an Agilent impedance analyzer HP4291B was used. For both setups, samples were prepared between two gold plated electrodes of 30 mm and 10 mm diameters, respectively. Teflon spacers of 0.1 mm thickness and negligible area were used to maintain the constant distance between the two electrodes. For both setups, isothermal frequency measurements were carried out on a series of temperatures with temperature stability better than 0.05 K. Measurements at and above room temperature were also carried out in the frequency range of 200 MHz-20 GHz using an integrated system of HP8361A vector network analyzer ͑VNA͒ and dielectric probe kit HP85070E with an open ended coaxial ͑OEC͒ probe. Complex permittivities were recorded using software supplied with a dielectric probe kit which controls the vector analyzer for dielectric measurements. More details about the setups, related accuracies, and calibration of the instruments can be found elsewhere ͓25͔. Below T g , measurements were made in the frequency range of 10 mHz-10 6 Hz using Alpha analyzer only.

Evaluation aspects
The treatment of the dielectric data is done assuming the picture originally developed by William and Watts ͓38͔. In this picture, one considers that the total dielectric relaxation is driven by two separate mechanisms. The fast one, usually, the ␤ relaxation, is attributed to the restricted motions in an otherwise rigid environment. This mechanism is the dominant one below glass transition temperature. However, only above T g where primary ͑␣͒ relaxation takes the dominant position, the total relaxation of the dipolar unit is achieved.
In this approach, the total correlation function can be written as where ␣ ͑t͒ and ␤ ͑t͒ are the two normalized relaxation functions corresponding to primary and secondary processes, respectively. In Eq. ͑1͒, ͑1− f ␣ ͒ is the fraction of the whole relaxation that is achievable by the secondary process. It can also be seen easily that when the two processes are well separated, i.e., when ␣ ͑t͒ decay is not significant until the ␤ ͑t͒ is complete ͑ ␣ ϳ 1 when ␤ ϳ 0͒, the above equation ͑1͒ can be approximated as the simple summation , which is a special case of Eq. ͑1͒, has been used extensively in literature to analyze the dielectric data by assuming simple superposition of the two relaxation processes. For the sake of clarity, in this paper, we will refer to Eq. ͑1͒ as William-Watts ansatz, while the second Eq. ͑2͒ will be called the additive ansatz as it is simple superposition of the two observed responses. In a typical dielectric experiment, the observed frequency dependent complex permittivity * ͑͒ can be expressed as where ⌽ * ͑͒ is the normalized relaxation function and 0 and ϱ are the two limiting values of a dielectric constant. As mentioned above, when the two processes are well separated, the WW ansatz turns into additive ansatz and ⌽ * ͑͒⌽ * can be written as where ⌽ ␣ * ͑͒ and ⌽ ␤ * ͑͒ are the normalized relaxation functions in the frequency domain corresponding to the primary and secondary relaxations, respectively. In this case, the total dielectric strength ⌬ is just the summation of individual dielectric strengths. Now, to describe the dielectric spectrum shape, it is well known that the dielectric shape of primary and secondary relaxation processes is non-Debye. However, this non-Debye shape can be accounted in terms of distribution functions of relaxation times, namely, g ␣ ͑log 10 ͒ and g ␤ ͑log 10 ͒, which are usually temperature dependent with characteristic relaxation times ␣ ͑T͒ and ␤ ͑T͒, respectively. Below the glass transition temperature, where secondary relaxation can be observed without the influence of primary relaxation, usually, ␤ ͑T͒ follows an Arrhenius-like temperature dependence as where E 0 represents an average activation energy of the ␤ process and k B is the Boltzmann's constant. Within this approach, the distribution of relaxation times can be interpreted in terms of a distribution of activation energies. Usually, a Gaussian distribution of energies provides a reasonable description of the secondary relaxation below T g . However, in a temperature range where the two relaxations start to overlap, the temperature dependence of ␤ can be different than the one that is extrapolated from low temperatures. This situation is in fact obtained using Eq. ͑1͒ which can be split in summation of the two terms as where the second term would correspond to the effective ␤ process, ␤ eff ͑t͒ = ␣ ͑t͒ ␤ ͑t͒. In our approach, ␤ and the shape of the ␣ process are fixed from the temperature regions where the respective parameters can be obtained from well separated processes. This approach has been applied to a number of different glass formers to describe the dynamics over broad range of temperatures ͓21,23,39-41͔. In addition this approach involves two parameters less than the additive ansatz approach ͓Eq. ͑2͔͒ and therefore, appears to be more appropriate to the current study, since the uncertainty of the parameters so obtained is significantly reduced.

A. PALS results
As mentioned in Sec. II, the DEP sample was measured in both cooling and heating cycles. Figure 1 shows the o-Ps lifetime, 3 , as a function of temperature for DEP from 67 K up to 300 K as measured in these various cycles. The o-Ps FIG. 1. Ortho-positronium lifetime, 3 , as a function of temperature as obtained in cooling ͑black squares͒ and two heating cycles ͑empty squares and crosses͒ with different heating rates. The first measurement was performed in a heating cycle from the low temperature region up to room temperature after rapid cooling of the sample which provided the structurally transformed material ͑empty squares͒. The next measurement was carried out during a relatively slow cooling cycle from room temperature down to low temperature giving the amorphous sample ͑solid squares͒. Finally, the cooled sample was measured in another heating cycle with different temperature steps as previously which provided the structurally transformed material again ͑crosses͒. The characteristic PALS temperatures T g PALS , T b1 , and T b2 from the best linear regression analyses are marked. The error bars are given and in most cases are smaller than the data points. data are practically independent of the cycle type from glassy state up to 210 K. Above this temperature, the two slow heating cycles indicate certain structural change which is attributed to the transformation from supercooled liquid to a crystalline solid state as supported by comparison with the DSC data from the literature ͓35͔. Therefore, the PALS results are discussed in two separate ways. The PALS response regarding the amorphous type sample is analyzed in detail here. The PALS one concerning the structurally transforming material will be discussed later.
Phenomenological, i.e., microscopic model-free, analysis of the 3 -T dependence by using the best linear regression fitting ͓16,18-20,29͔ indicates the presence of four regions of different thermal behavior. These regions can be approximated by the following linear expressions, where r is a regression coefficient: Region I from 67 K up to 180 K, 3 = ͑2.67 ± 0.44͒ ϫ 10 −3 T + ͑0.92 ± 0.06͒, r = 0.925;

͑9͒
Finally, in region IV above 245 K up to 300 K, the average value of the o-Ps lifetime is quasiconstant and reaches ͑2.50+ / −0.09͒ ns. The intersection points of these linear expressions define the characteristic PALS temperatures, T g PALS = 185 K, T b1 = 210 K, and finally, T b2 = 245 K ͓33͔.

B. BDS results
Figures 2͑a͒-2͑h͒ display the representative BDS spectra of DEP over a very wide frequency range covering the whole temperature range from 140 K up to 298 K together with the results of their phenomenological spectral analyses. In general, the BDS spectra of DEP exhibit the typical features known for many small molecular and polymer glass formers ͓24͔. Starting from below, at 150 K, lying below the T g PALS = 185 K ϳ T g DSC = 183 K, the BDS spectrum consists of the small dielectric loss peak which is attributed to the secondary ␤ process. This rather symmetric peak can be approximated by the log-normal distribution function G͑log 10 ␤ ͒ implying the Gaussian distribution of activation energies G͑E ␤ ͒ as described in the data evaluation section above. On crossing the T g PALS , a strong main peak feature with the so-called highfrequency wing comes into the dielectric frequency window used. The BDS spectra above T g can be considered as being composed of both the primary ␣ relaxation and the secondary ␤ process. Subsequently, for more detailed spectral analysis the Williams-Watts ͑WW͒ ansatz can be applied. The results of such analysis are also presented in Figs. 2͑b͒-2͑g͒. Example of the BDS spectra at around T g PALS and that for a deeply supercooled liquid DEP at 195 K lying in between T g PALS and T b1 are given in Figs. 2͑b͒ and 2͑c͒, where the ␣ process dominates over the weaker ␤ eff one. On increasing the temperature, the secondary ␤ eff process intensifies as it can be seen at the first characteristic PALS temperature T b1 = 210 K and T b1 Ͻ T = 220 K Ͻ T b2 in Figs. 2͑d͒ and 2͑e͒, respectively. At T = 233 K lying still below T b2 the ␤ eff process becomes more effective in the dielectric relaxation- Fig. 2͑f͒. At still higher temperature, e.g., 245 K only one peak feature is present in the BDS spectra which is even more evident at very high temperatures, e.g., T = 298 K- Fig. 2͑h͒. Figure 3 shows the relaxation map of the relaxation times vs inverse of the temperature for all the motional processes observed in DEP in our BDS study. The primary ␣ relaxation has been measured over a wide temperature range in the liquid state above T g DSC = 183 K up to 380 K. At relatively lower temperatures up to ca. 270 K the relaxation times exhibit the non-Arrhenius character which is followed by an approximately linear course above 270 K suggesting a crossover to the Arrhenius-type dependence in the relatively high temperature region. The secondary process detected over the temperature range from 140 K up to ca. 245 K shows also a complicated course reflecting a change in the character of the local scale mobility with temperature. At low temperatures, below T g PALS = 185 K the usual Arrhenius-type temperature dependence of the ␤-relaxation times is evident as it is observed very often for glass formers. On crossing the T g PALS , the Arrhenius character persists up to T cr ϳ 215 K. Above 215 K a clear crossover from the Arrhenius type to the non-Arrhenius-type dependence occurs. Note, however, that in the fitting procedure it was assumed that the Arrhenius T dependence of the ␤ relaxation remains the same as at low temperatures whereas the crossover to the non-Arrhenius behavior of the effective ␤ process is properly captured by the WW ansatz. Similar crossover behaviors have been found for both small molecules ͓39,40͔ as well as polymer ͓21,23,41͔ glass-forming systems. Finally, on further increasing the temperature the apparent dominance of the ␤ eff process over the ␣ relaxation appears at around 245 K. Figure 4 shows the relaxation strengths of the ␣ process, ⌬ ␣ , and the ␤ eff relaxation, ⌬ ␤eff , as well as that of the total relaxation process, ⌬. The change in temperature dependence of ⌬ ␣ and ⌬ ␤eff occurs above T cr = 215 K. On further increasing the temperature the ␤ eff contribution becomes the most effective in the dielectric relaxation process. Note that already at these temperatures the two relaxation components ␣ and ␤ eff are looking very much similar in all the characteristics ͓see Fig. 2͑f͔͒: shapes, intensity, and peak position. This makes any separation procedure rather uncertain. Finally, above ϳ245 K the total relaxation is fully dominated by a single process.
The so-called Schönhals plot ͓31͔ for the total relaxation strength as a function of the logarithm of relaxation frequency is presented in Fig. 5. Three regions of different behavior can be seen whose linear representations determine the intersection points which define the characteristic BDS temperatures: T B1 SCH = 212 K and T B2 SCH = 235 K. These temperatures reveal uncompensated changes in ␣ and/or ⌬.
FIG. 2. ͑Color online͒ Dielectric loss spectra of DEP decomposed by using the WW ansatz into the ␣-͑---͒ and ␤ eff -͑-·-·-͒ relaxation component at selected temperatures: ͑a͒ in supercooled glassy state at 150 K; ͑b͒ at T ϳ T g ; ͑c͒ in strongly supercooled liquid state at T g Ͻ 195 K Ͻ T b1 ; ͑d͒ at T b1 = 210 K; ͑e͒ in weakly supercooled liquid at T b1 Ͻ 220 K or ͑f͒ 233 K Ͻ T b2 , respectively; ͑g͒ at T b2 = 245 K and finally, ͑h͒ in normal liquid state at 298 K. The arrows mark the equivalent frequencies, f 3 , related to the o-Ps lifetimes via f 3 ͑T͒ =1/2 3 ͑T͒ ͓32͔ which indicate how the secondary ␤and primary ␣-relaxation processes reach the ns scale of the PALS method-see text.

Phenomenological analysis of PALS and BDS data
In order to reveal further the nature of the PALS response and the physical meaning of the characteristic PALS temperatures, we discuss the PALS data by using the detailed BDS results. At first glance, the PALS response exhibits roughly a quasisigmoid form which is the typical feature of most of the glass-forming systems when measured over a very wide temperature range from a glassy state through a supercooled liquid state up to a normal liquid ͓7-9,18,26-29͔. Approximate linear-type regression analysis of 3 -T dependence suggests the three characteristic PALS temperatures in the temperature range from 67 K up to 295 K with the following values of o-Ps lifetime: 3 ͑T g PALS ͒ = 1.41 ns, 3 ͑T b1 ͒ = 1.77 ns, and finally, 3 ͑T b2 ͒ϳ2.50 ns. The last two values are shown also in Fig. 3 and they can be compared with the temperature dependences of the corresponding relaxation times for all the relaxation processes. Starting from above, we can see that at T b2 = 245 K the plateau value of o-Ps lifetime is comparable with the relaxation time from the single relaxation- Fig. 2͑g͒. This finding for DEP is fully compatible with those for several other systems from our recent combined PALS and DS investigations on small molecular ͓16,18-20,32͔ as well as polymer ͓18͔ glass formers suggesting the approximate equality of the plateau o-Ps lifetime with the ␣ relaxation time at this temperature. Note that these previous findings 3 ͑T b2 ͒Х ␣ ͑T b2 ͒ have been based on comparisons of the plateau 3 value with the peak relaxation time from standard peak analyses being attributed to the ␣ process or to the so-called unified ␣␤ process without any detailed spectral analysis. One interesting difference within the class of crystallizing small molecular glass formers such as glycerol ͑GL͒ ͓15͔ and orthoterphenyl ͑OTP͒ ͓42͔ and DEP can be mentioned. In GL, which is of the intermediate fragility, the plateau effect occurs at T b2 which is commensurate with the corresponding melting point, T m ͓19͔. In contrast, for fragile DEP the 3 ͑T b2 ͒Х single ͑T b2 ͒ equality is reached already at about 30 K below the corresponding T m DSC = 273 K. As similar situation has been found for further fragile OTP systems but this finding has not been discussed ͓42͔.
On decreasing the temperature, the o-Ps lifetime values remain within the nanosecond range, while the relaxation times become considerably higher due to a dramatic slowing down of the main relaxation process. At T b1 , the ␣ relaxation time reaches the value ␣ ͑T b1 ͒ =10 −5.1 s which is consistent with our very recent empirical finding, ␣ ͑T b1 ͒ =10 −͑6±1͒ s ͓18,20͔. Thus, some universal feature of the main loss process seems to be related to a weaker bend effect in the PALS response. Likely, because of the three orders of magnitude difference between 3 and ␣ this feature could be related to the high-frequency part of the dielectric process which in framework of the WW analysis belongs to the secondary ␤ eff relaxation- Fig. 2. Indeed, as it follows from comparison of Fig. 1 with Figs. 3 and 4 the characteristic PALS temperature T b1 lies quite close to the crossover temperature, T cr , at which both the time and relaxation strength parameters of the secondary ␤ eff process exhibit the significant variations. In particular, the relaxation time of the ␤ eff process changes its character from the Arrhenius type in the glassy state with a continuation over ϳ25 K into the deeply supercooled liquid one to the non-Arrhenius one in the slightly supercooled liquid state at T cr ϳ 215 K. At the same time, the relaxation strength of the ␣ process starts to reduce and that of the ␤ eff contribution becomes more effective in the dielectric relaxation. However, at higher temperatures ͑T Ͼ 240 K͒ the separation of the two relaxation components is questionable because both exhibit similar characteristics. Thus, above the total relaxation can be considered as a single process.
In spite of the existence of the above-mentioned temperature matching between the changes in the o-Ps lifetime and the crossovers in the ␤ eff relaxation time and the ␤ eff relaxation strength, the two-order difference between the time scales for the o-Ps annihilation lifetime and the mean ␤ eff process still does exist. In particular, at T b1 3 = 1.8ϫ 10 −9 s Ͻ ␤ eff = 2.4ϫ 10 −7 s. This fact calls for a more detailed inspection of both the primary ␣ and especially, of the secondary ␤ process as presented in Figs. 2, 6, and 7. Figure 2͑b͒ shows that the high-frequency tail of the secondary ␤ peak reaches the ns scale of PALS method just at around T g PALS . This finding correlates with increasing trend in the o-Ps life-time, 3 , above T g PALS in Fig. 1. On increasing the temperature, the fraction of ␤ peak overcoming the ns scale increases and in between 210 K and 220 K also a short time tail of the ␣ relaxation peak reaches the ns level. Further, regarding the secondary ␤ process contribution, Figure 6 shows both the width parameters of the Gaussian distribution function for the ␤ relaxation as obtained from the spectral analysis by using the WW approach as a function of temperature over the whole T range of the existence of the ␤ eff process ͓23͔. A pronounced change in the width of the activation energy distribution, E ␤ , and the corresponding width of the ␤ relaxation time distribution, log ␤ , at around 210 K is evident. In Fig. 7 the distribution functions of the secondary relaxation times G͑log 10 ␤ ͒ vs log 10 ␤ for the ␤ process at several selected temperatures are displayed. As it can be seen, at 140 K, i.e., in the deep glassy state, the ␤ relaxation time distribution is characterized by overall longer times compared to the PALS method in full consistency with Fig. 2. On increasing the temperature, G͑log 10 ␤ ͒ shifts to lower values and a very short time tail of the relaxation time distribution approaches the relevant PALS time scale already at around T g PALS . On further increasing the temperature, at T b1 a certain fraction of the ␤ eff relaxation time distribution becomes shorter than the ns level as depicted by the arrows at the characteristic temperatures. These findings in Figs. 2, 6, and 7 correlate with the fact that the 3 vs T dependence increases more steeply with temperature above T b1 .
All these empirical correlations between the effects on PALS response and the relaxation dynamics can be explained by using the general free volume idea that the o-Ps probe-"senses" a part of the whole free volume distribution under FIG. 6. Width parameters of the Gaussian distribution function for activation energy, E ␤ , and the corresponding log-normal distribution for the ␤-relaxation time log 10 ␤ as a function of temperature. Pronounced changes above T x = 210 K close to the characteristic PALS temperature T b1 are evident. appropriate free space and time conditions ͓7-10͔. The former condition means that the o-Ps probe can sample local free volumes larger than the o-Ps probe size and the latter one means that the life of local free volume entities must be longer then the o-Ps lifetime. Thus, a part of the whole free volume distribution can be eliminated or blocked for detection by the o-Ps probe due to some motion which occurs on the appropriate time and amplitude scale. In other words, all the motions with the shorter time scale having the sufficient large displacements can contribute to the so-called "closing" part of the whole free volume distribution which thus becomes ineffective for the o-Ps probe sampling. Thus, in our case, the correlations between the PALS and BDS data in Figs. 2, 6, and 7 provide the evidence in favor of the blocking hypothesis of the PALS response in DEP. The highfrequency part of the distribution of the local ␤ eff process as well as of the high-frequency tail of the ␣ process occur on the shorter time scale compared to the observed o-Ps lifetime. Accordingly, the small size fraction of the free volume distribution becomes inaccessible for o-Ps localization due to these rapid motions of the sufficiently high frequency and amplitude. Consequently, the o-Ps probe has more chance to be localized and annihilated from the larger free volume holes resulting into the longer o-Ps lifetimes and the observed change of slope in the 3 -T plot. Thus, the PALS method is able to measure the effective free volume situation in the condensed matter.
Finally, an interesting finding can be seen from comparison of the PALS response recorded in heating scans and the crossover phenomena in the parameters characterizing the ␤ eff and ␣ processes in Figs. 3-6. Decrease in the 3 value just above 210 K down to a level lower than that for the glassy state and the following drastic increase above 270 K approaching the plateau level of the normal liquid are observed in this case. As the latter effect occurs very close to the melting temperature of the crystal form of DEP T m DSC = 273 K ͓35͔ it can be concluded that the structural transformation from deeply supercooled liquid to crystalline phase takes place, being responsible for the former effect. Then, although it is quite generally believed that the crystallization is controlled by the primary process, this finding seems to suggest that also the secondary process might be of relevance in the observed phase change in DEP, at least.
In summary, all these empirical facts point to a very close relationship between the PALS response and the dynamical features of the matrix, especially those of the high-frequency character, which at low temperatures are associated in majority with the secondary ␤ eff process and in minority with the high-frequency part of the primary ␣ relaxation. Thus, in PALS experiment we observe the effective PALS response of a system which is given by a close interplay of the corresponding time scales of the relevant annihilation and dynamic phenomena. The validity of this finding on a typical small molecular glass-forming compound should be further verified for other types of glass-forming systems including polymer ones. The works in this direction are in progress.

V. CONCLUSIONS
A combined analysis of the PALS and BDS databases on a small molecular glass-former system of diethyl phthalate has been performed. Comparison at phenomenological level revealed a number of coincidences between the various effects on the PALS response and various parameters of the dielectric response. In particular, the numerous changes in time and strength relaxation parameters of the secondary ␤ eff process appear to coincide with the bend effects on the PALS response at T b1 and T b2 , respectively. These findings point to the effective nature of the PALS response being influenced in majority by the local ␤ eff process and in minority also by the high-frequency tail of the ␣ process.
It also confirms that PALS is able to sense the dynamics of glass-forming systems.