J. Phys. Chem. B 2005, 109, 16119-16126
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Molecular Mobility in Amorphous Maltose and Maltitol from Phosphorescence of Erythrosin B Sonali Shirke, Pavlo Takhistov, and Richard D. Ludescher* Department of Food Science, Rutgers, The State UniVersity of New Jersey, New Brunswick, New Jersey 08901-8520 ReceiVed: April 22, 2005; In Final Form: June 22, 2005
We have used phosphorescence from erythrosin B (tetraiodofluorescein) dispersed in amorphous thin films of maltose and maltitol at mole ratios of 0.8:104 dye:sugar to monitor the molecular mobility of these matrixes over the temperature range from -25 to over 110 °C. Analysis of the emission peak frequency and bandwidth (full width at half-maximum) and time-resolved intensity decay parameters provided information about thermally activated modes of matrix mobility that enhanced the rate of dipolar relaxation around the triplet state and the rate of intersystem crossing to the ground state (kTS0). Detectable dipolar relaxation began in the glassy state about 50 °C below Tg in both maltose and maltitol; the relaxation rate, however, while 3-4 orders of magnitude slower than literature values for the β relaxation determined from dielectric relaxation, had an activation energy only 2-fold smaller. Dipolar relaxation was further enhanced in the melt above Tg; the dipolar relaxation rates in the melt scaled nearly exactly with rates for the R relaxation determined from dielectric relaxation. Intensity decays were well fit using a stretched exponential decay function in which the lifetime (τ) and the stretching exponent (β) were the physically significant parameters. In maltose, the magnitude of kTS0 was essentially constant in the glass and increased dramatically at the Tg; in maltitol kTS0 increased moderately at Tg ) -50 °C and more dramatically in the melt at Tg ) +20 °C. The value of kTS0 in maltose: maltitol mixtures was significantly smaller than that seen in pure maltose and maltitol, suggesting that specific interactions decreased the mobility of the mixed sugar matrix; this phenomenon was comparable to the antiplasticization seen in mixtures of small molecule plasticizers with synthetic polymers and starch. The extent of inhomogeneous broadening and dynamic heterogeneity were essentially constant in the glass and increased dramatically in maltose and more gradually in maltitol at the glass transition.
The properties of amorphous solid biomaterials modulate the stability and shelf life of foods, feeds, and pharmaceuticals1-4 and the long-term viability of spores, seeds, and even whole organisms during anhydrobiosis.5-8 Biomolecules, and especially sugars, carbohydrates, and proteins, readily form amorphous solids at low temperature during cooling or at low moisture content during dehydration or freeze-concentration. Amorphous biomaterials maintain the long-range disorder of the liquid phase under all conditions yet undergo a dynamic transition to a hard, rigid, brittle glass at low temperature or low moisture content. The physical properties of amorphous sucrose, for example, make possible both the worldwide confection industry and the desiccation tolerance of plant anhydrobiotes. The amorphous solid forms in supercooled or supersaturated liquids when crystallization is frustrated9 by high viscosity such as occurs in sugar melts or solutions or by the stereochemical difficulty of nucleating crystals of complex macromolecules such as proteins.10 The resulting material is characterized by an absence of long-range molecular order as well as a complex hierarchy of molecular motions. Amorphous and especially polymeric materials typically exhibit a series of dynamic thermal transitions that reflect cooperative changes in distinct modes of molecular mobility.11 Two transitions are of special importance due to their widespread occurrence in both small molecules * Address correspondence to this author. Phone: 732-932-9611, ext 231. Telefax: 732-932-6776.
and polymers; these are the R or glass transition (at temperature Tg), which reflects the onset of R relaxations (translational motions) linked to macroscopic flow, and the β transition within the glass (at Tβ), which reflects the activation of β relaxations that are more localized mode(s) of mobility. Whether the β relaxations are global properties of all molecules within the glass12 or regions of localized motion within the glass,13 and whether they reflect the mobility of whole molecules within the matrix14 or the mobility of specific groups,11,15 remains uncertain. Recent research has emphasized the importance of molecular relaxations in amorphous biomaterials in modulating the chemical and physical stability of foods16-18 and pharmaceuticals,19 in determining the long-term viability of seeds,7,20 and in desiccation tolerance in plants.6,8 These studies have used dielectric relaxation,15,21-23 mechanical spectroscopy,22 Fourier transforminfraredspectroscopy,24,25 nuclearmagneticresonance,26-28 electron spin resonance,20 and phosphorescence spectroscopy.12 We present here an investigation of the effect of temperature on the molecular mobility within amorphous maltose, its corresponding sugar alcohol maltitol, and their mixtures using phosphorescence emission and intensity decay from the triplet probe erythrosin B (tetraiodofluorescein) dispersed within the amorphous matrix. This study indicates that the mobility of these similar molecules displays distinct behavior within the glass and around the glass transition temperature and that interactions
10.1021/jp0521050 CCC: $30.25 © 2005 American Chemical Society Published on Web 07/30/2005
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between sugar and sugar alcohol actually lower the molecular mobility within the glassy state in mixtures. Materials and Methods Sample Preparation. Maltose and maltitol were purchased from Sigma-Aldrich (St. Louis, MO) with a minimum purity of 98%. These components were dissolved in deionized water at a concentration of 66-68 wt %. The free acid form of erythrosin B (Ery B) was dissolved in spectrophotometer grade dimethylformamide (DMF) to make a 10 mM solution; an aliquot from this solution was added to each of the sugar and sugar alcohol solutions to obtain a solution with a dye:sugar molar ratio of 0.8:104. Mixtures were prepared from 68 wt % samples of maltose and maltitol containing dye at a molar ratio of 0.8:104. To prepare a 70:30 mixture, for example, 70 parts of maltose solution was mixed with 30 parts of maltitol solution (weight basis); 50:50 and 30:70 mixtures were prepared similarly. To obtain glassy sugar films containing erythrosin B, 15 µL of dye-sugar solution was spread on a clean quartz slide 3 cm × 1.35 cm (NSG Precision Cells, Hicksville, NY), which was then dried for 5 min under a 1600 W hairdryer (Vidal Sassoon, NY). This method dried the films quickly without crystallization with a flow of ∼90 °C air and heated the slide to a maximum temperature of ∼88 °C (as measured by thermocouple probe). The thickness of the films was in the range of 10-40 µm as measured by micrometer (Mitutoyo Corp., Japan). The slides were stored in a desiccator containing P2O5 and Drie Rite for at least 4 days prior to any luminescence measurements. The slides were checked for crystallization under crossed polarizers using a Nikon Type 102 dissecting microscope (Nikon, Inc., Japan). The glass transition temperature (Tg) for maltose and maltitol was determined by averaging values from the literature: Tg was 93 ( 5 °C29-33 for maltose and 39 ( 1 °C29,34,35 for maltitol. The glass transition temperatures of blends of maltose and maltitol were calculated using the expression of Couchman and Karaz.36
Tg ) (x1Tg1 + κx2Tg2)/(x1 + κx2)
(1)
where x1 and x2 are the weight fraction of the components, κ is the ratio of heat capacity changes (∆Cp1/∆Cp2) at the glass transitions, and Tg1 and Tg2 are the Tg values of the individual components. The ∆Cp values were 0.61 and 0.56 J K-1 g-1 for maltose and maltitol, respectively.29 The calculated Tg values for binary mixtures calculated from this expression were 77, 67, and 56 °C for 70:30, 50:50, and 30:70 mixtures of maltose: maltitol. Luminescence Measurements and Data Analysis. All luminescence measurements were made using a Cary Eclipse fluorescence spectrophotometer (Varian Instruments, Walnut Creek, CA). A slide was fitted diagonally in a standard fluorescence cuvette, which was flushed with oxygen-free N2 gas for at least 15 min prior to making measurements (O2 will quench the triplet state). The temperature was controlled using a TLC 50 thermoelectric heating/cooling system (Quantum Northwest, Spokane, WA). For measurements below room temperature, the chamber surrounding the cuvette holder was flushed with dry air to eliminate moisture condensation. All the experimental measurements were conducted multiple times and average values were used for all data analyses and interpretations.
Delayed fluorescence and phosphorescence emission spectra used excitation at 500 nm (bandwidth 20 nm) and emission was collected from 520 to 750 nm (bandwidth 10 nm). The emission intensity was collected from a single lamp flash over a 3 ms gate following a delay time of 0.1 ms. Delayed fluorescence and phosphorescence spectra were analyzed to obtain the spectral width Γ (full width at half-maximum, fwhm) and peak frequency (νm) using a log-normal bandwidth function (I(ν)).37
I(ν) ) Io exp{-ln(2)[ln(1 + 2b(ν - νm)/∆)/b]2}
(2)
where Io, νm, b, and ∆ are the peak intensity, peak frequency, asymmetry parameter, and width parameter, respectively, for the emission band, and the bandwidth (Γ) of the emission band was related to the width and asymmetry parameters:
Γ ) ∆ sinh(b)/b
(3)
Luminescence spectra composed of both delayed fluorescence and phosphorescence bands were fit using a sum of two lognormal functions with independent fitting parameters.38 The dipolar relaxation time (φ) was calculated from the temperature dependence of the phosphorescence emission peak νP(T) by analyzing the relaxation function
∆ν ν(T) - νmax ) ∆νγ νmin - νmax
(4)
where ν(T) is the emission peak energy at temperature T, νmin is the peak energy at the lowest measured temperature, and νmax is the peak energy at the highest measured temperature. In a steady-state emission experiment, this relaxation function is the time average over the time-dependent relaxation of the matrix around the excited state, weighted by the phosphorescence intensity decay. Work by Richert and colleagues39 has indicated that the matrix relaxation is described by a stretched exponential function with time constant φ and stretching factor βe; our results indicate that the intensity decay also follows a stretched exponential with time constant τ and stretching factor βl (see below). The time average is thus given by the following integral:
〈 〉
∆ν ) ∆νr
∫0∞ exp[-(t/φ)β ] exp[-(t/τ)β ] dt ∫0∞ exp[-(t/τ)β ] dt e
l
(5)
l
Introducing a new variable R ) βl/βe, eq 5 can be rewritten as follows:
〈 〉
∆ν ) ∆νr
∫0∞ exp[-(t/φ)β(1+R)] dt ∫0∞ exp[-(t/φ)Rβ] dt
(6)
where βe ) β and βl ) Rβ. After integration of eq 6 over the time domain t ) [0, ∞] and several rearrangements, one obtains a solution for the emission relaxation function as a function of arbitrary βl, βe, φ, and τ:
〈 〉 ( ) ∆ν ) ∆νr
1 Rφ 1 1 ) βe τ 1 τ + Rφ 1 Γ Γ Rβ βl 1 + β φ
()
(7)
l
Equation 7 was solved for φ(T) using measured values of τ(T) and βl(T) for Ery B (Figure 6) and assuming that βe ) 0.5 based
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on work of Richert;39 the relaxation rate plotted in Figure 3 is the inverse of φ. To obtain intensity decays of Ery B in maltose and maltitol, the samples were excited at 530 nm (bandwidth 20 nm) and emission collected at 680 nm (bandwidth 20 nm) over the temperature range from -25 to 150 °C. Samples were equilibrated for 5 min at each temperature before collecting data. The intensity was collected as a function of time following the lamp flash over a window of 4 ms following a delay time of 0.1 ms and using a gate time of 0.02 ms; 10 cycles were summed to generate each decay transient. The intensity transients were analyzed using a stretch-exponential decay function:38,39
I(t) ) I(0) exp[-(t/τ)β] + constant
(8)
where I(0) is the initial intensity at time zero, τ is the Kohlrausch-Williams-Watts lifetime,40 and β is the stretching exponent. The appropriateness of this decay model is discussed at length elsewhere.38 Data analyses used the program NFIT (Island Products, Galveston, TX), which uses a nonlinear leastsquares algorithm that varies the adjustable parameters to minimize χ2. All fits gave R2 values in the range of 0.99 to 1.0 and modified residuals ((data - fit)/data1/2) plots that varied randomly about zero. Photophysical Analysis. Our analysis of the photophysics of Ery B follows that of Duchowicz et al.,41 using slightly different nomenclature. The measured emission rate for phosphorescence (kP ) 1/τ) is the sum of all possible deexcitation rates for the triplet state T1:
kP ) kRP + kTS0 + kTS1
(9)
where kRP is the rate of emission to the ground-state S0, kTS0 is the rate of intersystem crossing to S0 (rate of nonradiative quenching), and kTS1 is the rate of reverse intersystem crossing to the excited singlet S1. (Oxygen quenching is assumed negligible due to the elimination of oxygen.) The rate of radiative emission (kRP) is 41 s-1 and constant.41,42 The rate of reverse intersystem crossing to S1 (kTS1) is a thermally activated process:41
kTS1 ) kTS1° exp(-∆ETS/RT)
(10)
where kTS1° is the maximum rate of intersystem crossing from T1 to S1 at high temperature, ∆ETS is the energy gap between S1 and T1, R ) 8.314 J K-1 mol-1, and T is the temperature in Kelvin. The value of ∆ETS is calculated from the slope of a Van’t Hoff plot of the natural logarithm of the ratio of intensity of delayed fluorescence (IDF) to phosphorescence (IP) (ln(IDF/ IP) versus 1/T).38,41 The value of kTS1° ) 6.5 × 107 s-1 for Ery B in aqueous solution;41 however, this value was found to be too large for Ery B in amorphous sucrose38 and other sugars.43 We estimated that kTS1° ) 3.0 × 107 s-1 for Ery B in maltose. The measured phosphorescence intensity (IP) is proportional to the product of the quantum yield for formation of the triplet state (QT) and the probability of emission from the triplet state (qP). Assuming that QT is constant (in the absence of oxygen):
IP ∝ qP ) kRP/(kRP + kTS1 + kTS0)
(11)
1/IP ∝ (kRP + kTS1 + kTS0)/kRP
(12)
and
Since kRP is constant, this expression indicates that the decrease in intensity with temperature reflects an increase in
Figure 1. Delayed emission spectra of erythrosin B dispersed in amorphous maltose (a) and maltitol (b). Spectra collected from -20 to 120 °C by 10 °C increments in maltose (high to low intensity at 680 nm) and at -25 °C and from -10 to 80 °C by 10 °C increments in maltitol (high to low intensity at 680 nm).
the sum kTS1 + kTS0; extensive curvature in a plot of ln(1/IP) versus 1/T must, however, reflect a change in kTS0 since kTS1 follows purely Arrhenius behavior. Results Temperature Dependence of Delayed Luminescence Spectra. Delayed emission spectra of the triplet xanthene probe Erythrosin B (tetraiodofluorescein; Ery B) dispersed in amorphous maltose and maltitol at a probe:sugar ratio of ∼0.8:104 were collected at temperatures ranging from -25 to 120 °C (Figure 1). We established in a previous study38 that Ery B molecules do not interact in amorphous sucrose at this concentration. Assuming a random distribution of Ery B molecules throughout the maltose and maltitol matrixes, each probe is surrounded by a solvent shell 11-12 sugar molecules thick. These probe molecules thus provide information about the dynamic properties of the unperturbed amorphous sugar matrix. The probe exhibits emission bands corresponding to both phosphorescence (emission peak at ∼680 nm) and delayed fluorescence (emission peak at ∼560 nm). The intensity of the delayed fluorescence, which reflects the effect of thermally stimulated reverse intersystem crossing from the excited triplet (T1) to the singlet (S1) state,44 increased with temperature with a corresponding decrease in the intensity of phosphorescence. Analysis of these delayed emission spectra using a sum of two log-normal bandwidth functions (eq 2, Materials and Methods) provides the peak intensity, the peak frequency, and the emission bandwidth (full-width at half-maximum) for both delayed fluorescence (IDF, νDF, ΓDF, respectively) and phosphorescence (IP, νP, ΓP, respectively). Van’t Hoff plots of ln(IDF/IP) versus 1/T were linear with R2 g 0.995 (data not shown); the slope provides a measure of the S1 r T1 energy gap (∆ETS). ∆ETS for Ery B was 32.7 ( 1.1 kJ
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Figure 3. Arrhenius plot of the effect of temperature on the rate of dipolar relaxation around the excited triplet state of Erythrosin B in maltose (9) and maltitol (0) (solid lines). The dipolar relaxation rate was calculated from the peak frequency data in Figure 2 using the method described in the Materials and Methods section. The dielectric relaxation rates for the R (dashed lines) and β (dotted lines) relaxation of maltose64 and maltitol22 are also plotted. The Tg values were 366 K for maltose and 312 K for maltitol. Figure 2. Variation of phosphorescence emission peak frequency νP (a) and bandwidth ΓP (b) with difference in temperature from glass transition (T - Tg) in maltose (9) and maltitol (0). Parameters determined from fit of spectra in Figure 1 to a log-normal function (see Materials and Methods). The Tg values were 93 °C for maltose and 39 °C for maltitol.
mol-1 in maltose and 34.2 ( 0.9 kJ mol-1 in maltitol. These values are significantly different from those for Ery B in amorphous sucrose (31.6 ( 0.4 kJ mol-1), in water (36.9 ( 0.6 kJ mol-1), in 66 wt % aqueous sucrose (36.9 ( 1.0 kJ mol-1),38 in ethanol (28.5 ( 2.5 kJ mol-1),41 and in poly(vinyl alcohol) (41.2 ( 0.4 kJ mol-1),42 suggesting that solvent (matrix) properties modulate the singlet-triplet energy gap. The phosphorescence emission peak frequency (νP) and bandwidth (ΓP) of Ery B varied systematically with temperature in both maltose and maltitol (Figure 2). (Due to complications inherent in the interpretation of relaxation events associated with the three-state S0 r S1 r T1 transition involved in delayed fluorescence, these data are not analyzed here.) These parameters are plotted versus the difference in temperature from the glass transition (∆T ) T - Tg) in order to highlight their dependence on the physical state of the amorphous sugar. The emission peak frequency was approximately constant at low temperature with nearly identical peak emission frequencies of 14 760 cm-1 in maltose and 14 720 cm-1 in maltitol, but decreased consistently in the glass at higher temperature in both sugars (Figure 2a). In maltose, the peak frequency began decreasing gradually with temperature above ∆T ≈ -90 °C and more significantly with temperature above Tg. In maltitol, the peak frequency decreased gradually and monotonically over the ∆T interval from -40 to +60 °C. The rate of dipolar relaxation around the excited triplet state was estimated from the temperature dependence of the peak emission energy as described in the Materials and Methods section (eq 7). Arrhenius plots of these relaxation rates (Figure 3) were clearly biphasic with break point temperatures (calculated from the intersection of linear fits to data at low and high temperature) of ∼363 K for maltose, essentially equal to the Tg of 366 K, and ∼344 K for maltitol, significantly above its Tg of 312 K. The activation energies calculated from the slopes at low and high temperature were 24.9 and 206 kJ mol-1, respectively, for maltose and 40.6 and 174 kJ mol-1, respectively, for maltitol. The Ery B bandwidth (ΓP, the full width at half-maximum) was nearly constant with temperature in the glass in both maltose and maltitol and increased at higher temperature in the melt
Figure 4. Arrhenius-type plot of the effect of temperature on the phosphorescence emission intensity IP of Erythrosin B in maltose (9) and maltitol (0). The value of IP was determined from a fit of the spectra in Figure 1 to a log-normal function (see Materials and Methods). The Tg values were 366 K for maltose and 312 K for maltitol.
(Figure 2b). In maltose, ΓP increased dramatically at Tg, increasing from 1635 to 8260 cm-1 over the ∆T interval from -13 to +17 °C. The increase in maltitol was much less dramatic and occurred at higher temperature, increasing from 1640 to 2640 cm-1 over the ∆T interval from +32 to +62 °C. The inverse of the phosphorescence intensity (1/IP) is proportional to the sum of the rate constants for deexcitation of the excited triplet state (eq 12, Materials and Methods). Arrhenius plots of log(1/IP) versus the normalized temperature (Tg/T) for Ery B in both maltose and maltitol were nonlinear (Figure 4), displaying significant upward curvature at the maltose Tg ()93 °C) but significantly above the maltitol Tg ()39 °C). Break-point temperatures, estimated from the intersection of linear extrapolations to data points at low and high temperatures (not shown), were ∼90 °C for maltose and ∼70 °C for maltitol, essentially the same as the break point temperatures seen in the relaxation rate data (Figure 3). The significant increase in slope at high temperature suggests that additional modes of motion activated in the melt efficiently relax and quench the triplet state; these modes are activated near Tg in maltose but ∼30 °C above Tg in maltitol. Temperature Dependence of Phosphorescence Emission Intensity Decays. The phosphorescence emission intensity decay transients from Ery B in maltose and maltitol were collected as a function of temperature over the range from -25 to 140 °C for maltose and -25 to 100 °C for maltitol. All intensity decay transients were well fit using a stretched exponential decay model (eq 8, Materials and Methods) in which the Kohlrausch-Williams-Watts40 lifetime τ and the stretching
Molecular Mobility in Amorphous Maltose and Maltitol
Figure 5. Phosphorescence emission intensity decay transients (IP(t)) from Ery B in amorphous maltose (a) and maltitol (b) at -25 °C. Solid lines are calculated fits using τ ) 0.625 ms and β ) 0.927 for maltose, and τ ) 0.468 ms and β ) 0.941 for maltitol.
Figure 6. Effect of temperature on the lifetime τ (a) and stretching exponent β (b) from stretched exponential analyses (see Materials and Methods) of phosphorescence from Erythrosin B in amorphous maltose (9) and maltitol (0).
exponent45 β are the physically meaningful parameters. In this model, β reflects the width of an asymmetric lifetime distribution (with smaller values corresponding to increasing distribution width) while the lifetime essentially reflects the maximum value of the distribution.45 Such a model has proved effective in fitting decay data for Ery B dispersed in amorphous solid sucrose38 and amorphous gelatin films46,47 and has been widely used to describe kinetic processes within amorphous matrixes.48-51 Representative decay data at -25 °C in both maltose and maltitol are plotted in Figure 5 along with stretched exponential fits to these decay transients. The fit lifetimes (τ) and stretching exponents (β) from these analyses for pure maltose and maltitol are plotted versus temperature in Figure 6. The lifetime decreased with temperature from a maximum value of 0.66 and 0.55 ms at -25 °C in maltose and maltitol, respectively, to 0.07 ms in maltose at 140 °C (Figure 6a). The
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Figure 7. Variation of phosphorescence lifetime τ (a) and stretching exponent β (b) with difference in temperature from glass transition (T - Tg) in maltose (9), maltitol (0), and the 70:30 (2), 50:50 (b), and 30:70 (4) mixtures. Errors, not shown for the sake of clarity, are comparable to those plotted in Figure 6. The Tg values were 93 °C for maltose, 39 °C for maltitol, and 77 °C for the 70:30, 67 °C for the 50:50, and 56 °C for the 30:70 mixtures of maltose:maltitol.
lifetime decreased linearly up to ∼60 °C in maltose and more dramatically above this temperature. In maltitol, on the other hand, the lifetime exhibited characteristic decreases at ca. -20 °C and at ca. 60 °C. The value of the stretching exponent β was in the range 0.90-0.95 and constant with temperature up to ∼70 °C in both maltose and maltitol (Figure 6b) and decreased at higher temperature to a minimum value of 0.6 in maltose at 140 °C. The values of the lifetimes (τ) and stretching exponents (β) for maltose and maltitol and for mixtures of maltose:maltitol of 70:30, 50:50, and 30:70 (w:w) are plotted versus T - Tg in Figure 7. The Tg values for the mixtures were calculated using the expression of Couchman and Karaz36 (eq 1, Materials and Methods). The Ery B lifetime was higher in maltose than in maltitol in the glass, but lower in maltose than maltitol in the melt above Tg. In the mixtures, the trends in the Ery B lifetime versus temperature in the 70:30 and 50:50 mixtures closely resembled that of pure maltose, while the trend in the 30:70 mixture closely resembled that of pure maltitol. Interestingly, the Ery B lifetimes were essentially identical (∼0.36 ms) in all samples at Tg. The value of β was constant at 0.90-0.95 in the glassy state for all samples and only began to decrease above the sample Tg. Within the melt, however, maltose and the 70:30 and 50:50 mixtures exhibited lower β values (and thus greater dynamic heterogeneity) than maltitol and the 30:70 mixture. This behavior was similar to that seen in the emission bandwidth (Figure 2b), where ΓP for maltose increased dramatically at Tg while the increase in maltitol was not only more gradual, but occurred at a temperature well above Tg. Calculation of Triplet State Photophysical Rate Constants. The Ery B phosphorescence emission rate kP ()1/τ) in the absence of oxygen is the sum of rates for radiative emission (kRP), reverse intersystem crossing to the excited singlet S1 (kTS1), and intersystem crossing to the ground singlet S0 (kTS0; eq 9, Materials and Methods).41 Since kRP is 41 s-1 and constant,41,42 the increase of kRP with temperature reflects increases in kTS1 and kTS0; the rate kTS1 follows Arrhenius kinetics (eq 10, Materials and Methods) while the rate kTS0 reflects the effect of temperature on the mobility of the amorphous matrix.38 We
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Figure 8. Effect of temperature on the rate constants for deexcitation of the triplet state of Erythrosin B in amorphous maltose (a) and maltitol (b); the rates plotted are kP (0, 9), kTS1 ([, ]), and kTS0 (2, 4) (see text for details).
Shirke et al. temperature,41 but essentially identical to the value in solid poly(vinyl alcohol) at room temperature (1460 s-1)42 and in amorphous sucrose at 5 °C (1600 cm-1).38 The value of kTS0 was approximately constant in the maltose glass well below Tg. In the temperature region near Tg/T ) 1.25 kTS0 ranged from 1420 s-1 in the 50:50 mixture to 1800 s-1 in pure maltitol (0: 100) with a rank order of 50:50 e 70:30 < 100:0 < 30:70 e 0:100, which persisted throughout the glassy state in all samples. The magnitude of kTS0 in maltose increased gradually within the glassy state before rising dramatically to 8740 s-1 in the melt above Tg (at Tg/T ) 0.96); no other sample exhibited such a large increase in kTS0 over this temperature interval. The behavior in maltitol was quite different as kTS0 was essentially identical with that in maltose in the glass at Tg/T ) 1.25, increased significantly over the next 20 °C, and then was constant through the glass transition before increasing to 4110 s-1 in the melt at Tg/T ) 0.85 (about 20 °C above the maltose Tg). Although the overall temperature dependence of kTS0 for the 70:30 and 50:50 maltose:maltitol mixtures resembled that of maltose, and that of the 30:70 mixture resembled maltitol, the dynamic behavior of these samples was not simply intermediate between that of the two pure components. In particular, kTS0 in the glass was lower in the 70:30 and 50:50 mixtures than in pure maltose or maltitol. Discussion
Figure 9. Arrhenius plot of the nonradiative decay rate (kTS0) for the triplet state of Erythrosin B in amorphous maltose (9), maltitol (0), and mixtures of maltose:maltitol of 70:30 (2), 50:50 (b), and 30:70 (4) as a function of normalized inverse temperature (Tg/T). The Tg values were 366 K for maltose, 312 K for maltitol, and 350 K for the 70:30, 340 K for the 50:50, and 329 K for the 30:70 mixtures of maltose:maltitol.
calculated the variation of kTS0 with temperature using eq 9, the measured value of kRP, and estimates of kTS1. The reported magnitudes of the preexponential factor (kTS1°) in kTS1 for Ery B range from 0.3 × 107 s-1 in ethanol and 6.5 × 107 s-1 in water41 to 111 × 107 s-1 in solid poly(vinyl alcohol),42 and thus provide little guidance. We have estimated maximum values for kTS1° of 3.0 × 107 s-1 for maltose and 6.5 × 107 s-1 for maltitol, as values larger than this led to physically unreasonable decreases in kTS0 with temperature. The temperature variation of kP ()1/τ) and estimated values for kTS1 and kTS0 for both maltose and maltitol are plotted in Figure 8. The calculated value for kTS0 represents the minimum possible value for the nonradiative quenching rate. A similar analysis provided minimum values for kTS0 for the maltose:maltitol mixtures. (Note that the estimated value of kTS1 is a significant (>20%) correction only at ∼80 °C and above for maltose and never for maltitol.) The kTS0 values for all samples are plotted as log(kTS0) versus Tg/T in Figure 9. In the glassy state at -25 °C, the lowest accessible temperature, kTS0 was 1580 s-1 in maltose (at Tg/T ) 1.475) and 1380 s-1 in the 50:50 mixture (at Tg/T ) 1.375); these values are larger than the value in ethanol (1000 s-1) and significantly smaller than that in water (3200 s-1) at room
The phosphorescence properties of Ery B in amorphous solids are consistent with the direct effect of two distinct modes of matrix molecular mobility: dipolar relaxation around the excited T1 state and molecular collision with the excited T1 state.38,47,52 Dipolar relaxation directly modulates the probe emission energy (frequency, νP) by stabilizing the excited triplet state and affects the bandwidth (ΓP) by influencing the extent of inhomogeneous broadening.39,53,54 Molecular collision modulates the intensity (IP) and decay kinetics (τ) by modulating the rate of intersystem crossing to the ground state.55-57 The details of these interactions are discussed here. The total decrease in emission peak frequency was moderate (∼300 cm-1) and weakly biphasic in maltose while the decrease in maltitol, albeit larger (∼500 cm-1), was approximately monophasic (linear) over a temperature interval of about 100 °C. The magnitudes of these frequency shifts are consistent with a dipolar relaxation mechanism.58 Dipolar relaxation reflects a thermally activated mode of mobility associated with reorientation of the sugar hydroxyl groups. One candidate for such mobility within the glass is the β relaxation seen in dielectric and mechanical relaxation.22,31 This relaxation has been assigned to internal motional modes of the sugar, either to side chain segmental motion15 and specifically to the rotation of the exocyclic hydroxyl group,33,59,60 or to motion about the glycosidic bond in disaccharides and higher sugar polymers;61,62 an alternative view assigns these motions to heterogeneity within the glass due to regions of loosely packed molecules.21,63 The activation energies of ∼25 kJ mol-1 in maltose and ∼41 kJ mol-1 in maltitol for the dipolar relaxation rate are comparable to but smaller than those seen in previous dielectric relaxation studies of maltose,62,64 45 and 49 kJ mol-1, and maltitol,22 61.3 kJ mol-1. However, the dipolar relaxation rates were significantly smaller than the β relaxation rates determined from dielectric relaxation measurements in these sugars. Over the temperature range below and near Tg the β relaxation rates reported in the literature for maltose62,64 and maltitol22 are 3-4 orders of magnitude larger than the calculated dipolar relaxation rates (Figure 3). The physical origin of the dipolar relaxation
Molecular Mobility in Amorphous Maltose and Maltitol within the sugar glasses is thus uncertain. Given the breadth of the β transition in these sugarssthe dielectric loss peak in maltose is >3 decades wide31,62sit is conceivable that only the slower dynamic components of the β relaxation contribute to dipolar relaxation around the triplet state of Ery B. If so, then the activation energy for these components is smaller than that characteristic of the ensemble of all β relaxations. On the other hand, given the near exact scaling between dipolar and dielectric R relaxation rates seen at T > Tg (Figure 3), dipolar relaxation within the melt clearly reflects the additional mobility associated with R relaxations activated near Tg. As we have noted in amorphous sucrose,38 the emission spectra of Ery B in amorphous maltose and maltitol actually blue shifts with time following excitation.43 It was thus not possible to measure the rate of dipolar relaxation around Ery B in these sugars by monitoring the red shift in emission energy as a function of time following excitation.39,58,65 This effect, which will be published elsewhere,66 reflects the presence of dynamic site heterogeneity in which probes in environments with blue-shifted emission spectra have longer lifetimes and probes in environments with red-shifted emission spectra have shorter lifetimes.38,47 The changing distribution of emission energy as the red-shifted, short lifetime probes decay away thus leads to a blue shift with time following excitation. The phosphorescence emission intensity (IP) and the lifetime (τ) are directly modulated by the rate of intersystem crossing kTS0; kTS0 in turn is modulated by the physical state of the amorphous matrix.38,46,56 The magnitude of kTS0 reflects both internal factors related to the manner in which the excited T1 state of Ery B is vibrational coupled to the S0 ground state as well as external factors apparently related to the manner in which the ground-state vibrational energy can dissipate from the excited probe into the surrounding matrix.57 Because the efficiency of this vibration coupling is related to the overall mobility of the matrix,55 the magnitude of kTS0 provides a direct measure of matrix mobility. In amorphous sucrose, kTS0 is essentially constant in the glass and increases dramatically at the glass transition,38 indicating that the R relaxations activated at Tg provide an efficient mechanism to dissipate probe vibrational energy into the matrix. The behavior of kTS0 in maltose is quantitatively similar to that seen in sucrose; kTS0 was essentially constant in the glass and increased dramatically at the maltose Tg (Figure 9). The behavior in maltitol was quite different, however, as kTS0 increased in the glass at Tg/T g 1.25 (about 50 °C below Tg) and was constant through the glass transition before increasing significantly about 20 °C above Tg. The magnitude of kTS0 in maltitol thus appeared to be modulated by a thermally activated change in the mobility in the glass; again, the most likely candidate involves the β relaxations activated well below Tg. This specificity may reflect the intensity of the dielectrically detected β relaxation, which is more intense in sugar alcohols than in sugars33,60 and in maltitol than maltose.22 The increase in kTS0, like the increase in dipolar relaxation rate, occurred at higher temperature in maltitol than in maltose, also reflecting the activation of R relaxations at higher temperature in the sugar alcohol (Figure 3). It is worth noting that the sensitivity of the probe in maltitol to β relaxations at low doping ratios of 0.8:104 supports a model that assigns these relaxations to a global, rather than a local, mode of mobility that is uniform throughout the glass.12 The emission bandwidth and the stretching exponent provide alternative measures of the heterogeneity of the amorphous matrix. The bandwidth provides a direct measure of the extent
J. Phys. Chem. B, Vol. 109, No. 33, 2005 16125 of inhomogeneous broadening due to a distribution of energetic environments within the matrix;39,67 this distribution of energetic interactions may in turn reflect a distribution of dipolar relaxation rates.68 The stretching exponent (β) provides an indirect measure of the width of the distribution of lifetimes required to adequately fit the intensity decay, smaller values of β corresponding to an increase in the width of the lifetime distribution required to fit the decay.45 Given that the lifetime is largely determined by the magnitude of kTS0, lower values of β thus indicate an increasing width in the distribution of kTS0 values, and thus an increasing width in the distribution of dynamic environments. Although a quantitative comparison is not possible, it is clear that in maltose both the energetic and the dynamic heterogeneity increase dramatically at Tg, while in maltitol the increase in energetic and dynamic heterogeneity increases more gradually at Tg. The dynamic behavior of the maltose:maltitol mixtures provides an indication of dynamic synergy in these sugar matrixes. Although the thermal response of the maltitol-rich 30: 70 mixture generally resembled that of pure maltitol and the thermal response of the 50:50 and 70:30 mixtures resembled that of pure maltose, the mobility of the mixtures was not intermediate between that of the pure components; kTS0 in the 50:50 and 70:30 mixtures was significantly lower than that of either pure maltose or pure maltitol throughout the glass and into the melt (Figure 9). Specific interactions between maltose and maltitol thus decreased the ability of the matrix to vibrationally dissipate the triplet state energy of Ery B by decreasing the mobility of the amorphous matrix. This lower mobility in the mixtures may be compared to the well-known phenomenon of antiplasticization seen in amorphous synthetic polymers69,70 where the presence of a small molecule plasticizer, while lowering the glass transition temperature, also decreases mobility within the glass to generate a more rigid, less elastic, or less permeable matrix. Recently, such antiplasticization behavior has been reported in starch-glycerol71 and starchsorbitol72,73 films, and in freeze-dried amorphous powders of polyvinyl pyrolidone, dextran, or ficoll with added small molecule plasticizers;74 in addition, Seow et al.75 have argued that many physical and chemical studies of stability in food matrixes in the presence of low amounts of water or other small molecule plasticizers are understandable in terms of the phenomenon of antiplasticization. In both synthetic polymers76 and in carbohydrates77,78 antiplasticization has been related to negative volume changes on mixing which result in a decrease in free volume and a corresponding decrease in the molecular mobility. Studies of both synthetic polymers79 and carbohydrates, including starch73 and maltose,80 suggest that the effect may be due to a suppression of β relaxations within the glass. Although reports of antiplasticization behavior have been largely confined to mixtures of molecules of dissimilar sizes (and glass transition temperatures), our results suggest that such behavior also occurs in mixtures of molecules of nearly identical mass and similar structures. Since a similar decrease in mobility has been detected in mixtures of lactose and lactitol,43 also based on erythrosin phosphorescence lifetimes, this phenomenon may be a general feature of sugar-sugar alcohol and other carbohydrate mixtures and thus worthy of additional study. Acknowledgment. This research was supported by a grant from the National Research Initiative of the United States Department of Agriculture (No. 2002-01585). Ms. Shirke also gratefully acknowledges the support of the Mid-Atlantic Consortium and the W. K. Kellogg Foundation.
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