Polymer drying. V. Intramolecular-rotor fluorescence studies of evaporation from liquid-saturated poly(styrene-co-divinylbenzene)

The fluorescence intensity and residual weight of poly(styrene-co-divinylbenzene) saturated with a < 0.003M solution of a intramolecular-rotor-fluorescent probe-molecule in a volatile liquid were monitored simultaneously as the system evaporated at 23°C to virtual dryness. The “breakpoints” in the pattern for fluorescence increase coincided with the “breakpoints” in the kinetics of desorption with respect to the number, α_t of residual sorbed volatile molecules per phenyl group in the polymer, showing that both time-studies reflect the same physical changes in the system that occur reproducibly as α_t decreases monotonically through α′_s and α′_g the compositions that signal respectively incipient elimination of volatile molecules immobilized by adsorption to polymer, and incipient transition of the system from the rubbery state to the glassy state. The fluorescence intensity attained its asymptotic limit before α_t became equal to α_g the composition identified earlier to be that which marks completion of the transition to the glassy state.     

Polymer drying. VI. EPR spin-probe studies on swelled poly(styrene-co-divinylbenzene)

The electron paramagnetic resonance (EPR) signal and the residual number (α_t) of volatile molecules per phenyl group of poly(styrene-co-divinylbenzene) in samples that had been swelled to saturation in a dilute solution of a nitroxide spin-probe (TEMPO or 4-oxo-TEMPO), dissolved in a volatile liquid, were monitored simultaneously as the system containing excess liquid was allowed to evaporate to dryness. The results showed that the characteristic motionally narrowed three-line EPR spectrum began to change when α_t became equal to α_g (the number of sorbed molecules per phenyl group of polymer at liquid-saturation). The ratio of the intensity of the low-field and high-field hyperfine peaks relative to the middle peak decreased monotonically to an asymptotic limit that was attained when α_t became equal to α_g (the number of residual adsorbed molecules per phenyl group of polymer at completion of the transition from the rubbery state to the glassy state). The EPR hyperfine pattern, from which the rotational correlation times were estimated, changed most significantly as α_t decreased from α_G to α_g while exhibiting inflections at about α′_s and α′_g the compositions that mark, respectively, incipient desorption of adsorbed molecules and incipient transition from the rubbery state to the glassy state. The pattern between these inflections points, however, varied with the affinity of the solvent for the polymer.     

Polymer drying. VIII. Molecular interpretations of desorption from polystyrene–liquid systems

The results obtained in time studies that monitored evaporation from liquid-saturated poly(styrene-co-divinylbenzene) to virtual dryness at temperatures ranging from 20 to 80°C confirm those reported earlier for multireplicated time studies at 23 ± 1°C; i.e., when the residual composition (α_t, in sorbed molecules per phenyl group) attains the glassy state composition, the value of α_t thereafter is given by a linear combination of no more than six exponential decay functions. The logarithms of the rate constants (k_i) for decay of these populations at a given temperature decreased linearly with i, the population identification number in the order of decreasing decay rate. The Arrhenius activation energy (ΔE_i) for increase in k_i with temperature was characteristic of the sorbed species, but it was independent of i. The logarithms of the frequency factors (A_i) decreased linearly with i, the slope of which was numerically equal to that observed for the corresponding k_i relationships, signifying that the stepwise decrease of the latter at a given temperature is attributable primarily to a corresponding incremental decrease in entropy. It is suggested that this reflects discrete changes in the molecular structure of polymeric inclusion complexes formed during the transition from the rubbery to the glassy state, as discussed in the text. © 1993 John Wiley & Sons, Inc.     

Polymer drying. IV. A molecular interpretation of polymer drying

Further consideration of data already collected, in many time-studies that monitored gravimetrically evaporations of acetone, toluene, and chloroform from the corresponding liquid-saturated poly(styrene-co-divinylbenzene) samples, show that α_t, the residual number of sorbed molecules per phenyl group at a given level of desorption, is a linear function of α_s, the number of adsorbed molecules per accessible phenyl group in the polymer at thermodynamic equilibrium with excess test-liquid. Such linear relationships were noted at successive break-points in the kinetics of desorption (from gel-saturation to virtual dryness) that signaled sequentially (a) incipient elimination of adsorbed molecules from polymer in the rubbery state, (b) incipient transition from the rubbery state to the glassy state, (c) completion of this transition, and (d) successive depletions of five of the six populations of residual adsorbed molecules that were trapped in six different molecular environments by rigidification of the system during the transition. These results support the viewpoint that α_s is a parameter that reflects how well the molecular structure of the sorbed molecule can be accommodated by that of the monomer unit of the polymer.     

Sorption and diffusion of carbon dioxide in single-phase polystyrene/poly(vinylmethylether) blends

The sorption and transport properties of CO₂ in miscible PS/PVME blends at 20°C are reported as a function of pressure from 1 to 15 atm. The complex shape of isotherms for glassy blends and the concentration-dependent diffusion coefficient for rubbery blends reveal a plasticization by sorbed CO₂. The significant depression in T_g has to be taken into account in the analysis of the sorption data. Diffusion coefficient for CO₂ passes through a minimum when plotted against the blend composition. Such a behavior can be quantitatively related to the negative volume mixing of the PS/PVME system in the framework of the theories based on unoccupied volume. © 1996 John Wiley & Sons, Inc.     

Infrared spectroscopic studies of CO2 sorbed in glassy and rubbery polymeric membranes

Infrared spectra of CO₂ sorbed in rubbery and glassy polymers were measured to examine the relationships between the spectroscopic data and physical properties of the polymeric membranes. The “V-shape” tendency in the plot of W₁ [i.e., half-width of CO₂ peak sorbed in the membranes] vs glass-transition temperature (T_g) is observed, and has exactly the same tendency that is widely known from the plot of log D (diffusion coefficient) vs T_g. It is suggested that the membranes having a wider W₁ give a faster diffusion coefficient, since W₁ is inversely related to the moment of inertia of CO₂ in the membranes. Two distinct peaks of CO₂ were not observed in the infrared spectra of CO₂ sorbed in the glassy polymers. This suggests that the states of CO₂ in the Henry mode and Langmuir mode in the glassy polymers are similar in the spectroscopic measurements. © 1994 John Wiley & Sons, Inc.     

Relaxations in thermosets. XIX. Dielectric effects during curing of diglycidyl ether of bisphenol-A with a catalyst and the properties of the thermoset

Changes in the dielectric permittivity ε′ and loss epsiv;″ during the curing of DGEBA catalyzed by 10 mole % dimethylbenzylamine have been studied from sol to gel to glass formation regions at different temperatures from 323 to 390 K. The ε′ monotonically decreases with time of cure, and ε″ initially decreases by several orders of magnitude and then increases to reach a peak value before finally decreasing to a low value characteristic of the glassy state. The features shift to shorter times and the peak vanishes as the curing temperature is increased. The decrease of ε″ at the initial stage of cure has been analyzed in terms of dc conductivity σ₀, which follows a power law, σ₀ ∝? (t_g–t)^x, as well as a new singularity equation, σ₀ ∝? exp[–B/(t₀–t)] where t_g, x, B, and t₀ are empirical constants that vary with the curing temperature; t_g is close to the time for gelation; and t₀ ≥ time for vitrification. The dielectric properties of the thermoset formed after different periods of cure have been studied from 77 to 325 K. Similar studies of the thermosets formed at different temperatures have been made. Increase in the curing period decreases the heights of both the γ-and α-relaxation peaks and increases their separation, while a β-relaxation peak emerges. Isothermal curing at high temperatures decreases the height of the γ peak to a vanishingly small value and increases that of the β peak from a vanishingly small value. In both the uncured and fully cured states, there is only one sub-T_g relaxation process named γ for the uncured and β for the cured state. These results are discussed in terms of our general physical concepts of local mode motions in an amorphous matrix. © 1993 John Wiley & Sons, Inc.     

Twinkling fractal theory of the glass transition

In this paper we propose a solution to an unsolved problem in solid state physics, namely, the nature and structure of the glass transition in amorphous materials. The development of dynamic percolating fractal structures near T_g is the main element of the Twinkling Fractal Theory (TFT) presented herein and the percolating fractal twinkles with a frequency spectrum F(ω) ∼ ω^df–1 exp −|ΔE|/kT as solid and liquid clusters interchange with frequency ω. The Orbach vibrational density of states for a fractal is g(ω) ∼ ω^df–1, where d_f = 4/3 and the temperature dependent activation energy behaves as ΔE ∼ (T² − T). The key concept of the TFT derives from the Boltzmann population of excited states in the anharmonic intermolecular potential between atoms, coupled with percolating solid fractal structures near T_g. The twinkling fractal spectrum F(ω) at T_g predicts the correct dynamic heterogeneity behavior via the spatio-temporal thermal fluctuation autocorrelation relaxation function C(t). This function behaves as C(t) ∼ t^−1/3 (short times), C(t) ∼ t^−4/3 (long times) and C(t) ∼ t⁻² (ω < ω_c), which were found to be in excellent agreement with published nanoscale AFM dielectric force fluctuation experiments on a glassy polymer near T_g. Using the Morse potential, the TFT predicts that T_g = 2D_o/9k, where D_o is the interatomic bonding energy ∼ 2–5 kcal/mol and is comparable to the heat of fusion ΔH_f. Because anharmonicity controls both the thermal expansion coefficient α_L and T_g, the TFT uniquely predicts that α_L×T_g ≈ 0.03, which is found to be universal for a broad range of glassy materials from Pyrex to polymers to glycerol. Below T_g, the glassy structure attains a frustrated nonequilibrium state by getting constrained on the fractal structure and the thermal expansion in the glass is reduced by the percolation threshold p_c as α_g ≈ p_cα_L. The change in heat capacity ΔC_p = C_pL–C_pg at T_g was found to be related to the change in dimensionality from D_f to 3 in the Debye approximation as the ratio C_pL/C_pg = 3/D_f, where D_f is the fractal dimension of the glass. For polymers, the TFT describes the molecular weight dependence of T_g, the role of crosslinks on T_g, the Flory-Fox rule of mixtures and the WLF relation for the time-temperature shift factor a_T, which are traditionally viewed in terms of Free-Volume theory. The TFT offers new insight into the behavior of nano-confined glassy materials and the dynamics of physical aging. It also predicts the relation between the melting point T_m and T_g as T_m/T_g = 1/[1−p_c] ≈ 2. The TFT is universal to all glass forming liquids. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2765–2778, 2008     

Kinetics of the solvolysis of the trans-chloroazidobis(diaminoethane)cobalt (III) ion in water + t-Butyl Alcohol Mixtures

The kinetics of the solvolysis of the ion trans-[Coen₂N₃Cl]⁺ have been investigated at several temperatures in mixtures of water with t-butyl alcohol with concentrations of the latter ranging up to 50 vol% or a mol fraction of 0.16. Values for the enthalpy and entropy of activation show sharp changes with changing solvent composition which can be correlated with extrema in the physical properties of the mixture concerned with sharp changes in solvent structure. Plots of log(rate constant) against the reciprocal of the dielectric constant and against the Grunwald-Winstein Y factor are both curved. The application of a free energy cycle shows that the effect of changes in solvent structure on the solvolysis dominates on the cobalt(III) cation in the transition state over that on the cation in the initial state.     

Bisphenol-A polycarbonate–diluent interactions

The effect of low-molecular-weight miscible additives on the sub-T_g (β) relaxation process in bisphenol-A polycarbonate (BPAPC) was studied using high-resolution carbon-13 solid-state NMR. The trend of the spin-lattice relaxation times T₁ at 50 MHz suggests that strong intermolecular interactions occur upon mixing when BPAPC is physically stiffened by the antiplasticizing diluent, diphenylphthalate. The values of ¹³C T₁ at 15 MHz in d-chloroform solutions for similar BPAPC-diluent mixtures suggest that diluent effects on the megahertz mobility of the polymer occur exclusively in the solid state. These results are explained using equilibrium thermodynamics, in the Ehrenfest sense, at the second-order glass transition temperature T_g. Theory predicts that the temperature dependence of the Flory–Huggins interaction parameter ?χ/?T changes abruptly as the polymer-diluent blends are cooled below T_g from the molten state. The difference between ?χ/?T in the liquid and glassy states is the major factor which determines the diluent concentration dependence of T_g. A method is developed to estimate the relative magnitudes of χ for polymerdiluent blends in the glassy state.     

A relationship between macroradical decay kinetics and α-segmental dynamics in glassy amorphous polymers

For a series of five amorphous polymers with a broad range of T_g values the kinetics of macroradical decay was measured by ESR technique and evaluated by the second-order kinetic model. It was found that the temperature T_tr of the transition between two regions of different reactivity in free radical decay reaction agrees quite well with the temperature parameter T₀ of the Vogel-Fulcher-Tamman-Hesse (VFTH) equation for α-segmental dynamics. This parameter represents the onset of α-segmental mobility in glassy state below T_g. A nontraditional way of the estimation of T₀ values for α-segmental dynamics through study of the macroradical decay in glassy state of amorphous polymers has been suggested. © 1996 John Wiley & Sons, Inc.     

Polymer drying. III. Comparison of molecular desorption from poly(styrene-co-divinylbenzene) in the gel-state and in the glass-state

The results observed in 44 time-studies that monitored evaporation from liquid-saturated poly(Sty-co-DVB) particles enmeshed in poly(tetrafluoroethylene) microfibers under conditions that precluded decrease in area of the microporous composite film sample verified that after the enmeshed particles undergo transition from the gel-state to the glass-state, the number of residual adsorbed molecules per phenyl group of polymer is given by a linear combination of n < 7 exponential decay functions, the first order rate constants of which are related to one another by the equation: log k_i = log k₀ ? mi, where m is characteristic of the polymer, and k₀ is characteristic of the sorbed liquid such that k₁ is about 10⁵ times faster than k₆. The results also show that k₁ of the set of nk_i for desorption from poly(Sty-co-DVB) in the glass-state is equal to k_gel, the first-order rate constant for desorption of the test-liquid from that polymer in the gel-state. These results are interpreted to mean that i, the identification number of the ith population, reflects the number of phenyl groups in the “host” polymer with which the “guest” volatile molecule is associated simultaneously as discussed in the text.     

Specific surface of two hydrated cements differing in strength

Specific surface, S, of CSH-gel particles of disordered layered structure, was studied by water sorption/retention in two cement pastes differing in strength, i.e. C-33 (weaker) and C-43 (stronger), w/c=0.4. Hydration time in liquid phase was t _h=1 and 6 months, followed by hydration in water vapour either on increasing stepwise the relative humidity, RH=0.5→0.95→1.0 (WS) or on its lowering in an inverse order (WR). Specific surface was estimated from evaporable (sorbed) water content, EV (110°C), assuming a bi- and three-molecular sorbed water layer at RH=0.5 or 0.95, respectively (WS). On WR it was three- and three- to four-molecular (50 to 75%), respectively, causing a hysteresis of sorption isotherm. At RH=0.5 the S increased with cement strength from 146 m² g^-1 (C-33, 1 m) to 166 m² g^-1 (C-43, 1 m) and with hydration time to 163 (C-33, 6 m) and to 204 m² g^-1 (C-43, 6 m). At RH=1.0 (and 0.95), higher S-value were measured but these differences were smaller: S amounted to 190-200 m² g^-1 in C-33 (1 and 6 m) and 198-210 m² g-1 in C-43 (1 and 6 m). Thus no collapse occurred on air drying of paste C-43 (6 m). This revised version was published online in July 2006 with corrections to the Cover Date.     

Polymer drying. II. Replicated time-studies of molecular desorption from liquid swollen poly(styrene-co-divinylbenzene) before and after transition from the gel-state to the glass-state

A total of 90 time-studies were monitored gravimetrically in order to establish the parameters that affect the reproducibility of the kinetic changes that occur sequentially when liquid-saturated poly(styrene-co-divinylbenzene) [poly(Sty-co-DVB)] particles, enmeshed in a matrix of polytetrafluroethylene (PTFE) microfibers, are allowed to evaporate to apparent dryness at constant temperature. The test liquids were toluene, chloroform, and acetone. The absorbent samples were made from six different compositions of polymer particles, the DVB mode fractions, x, of which increased from 0.01 to 0.11. The weight, W_g, of residual sorbed molecules per gram of polymer at the glass-transition composition was constant despite the large differences in x. Thereafter the weight of residual sorbed molecules was given by a linear combination of up to six exponential decay functions, which indicated that these molecules were “locked” into six different types of molecular environments (i.e., populations) created by the change from the gel-state to the glass-state. The fractions of W_g in the populations with the fastest (k₁) and the slowest (k_n) decay rates were usually less than those with intermediate decay rates. The logarithm of k_i in a given time study was a linear function of i, the numerical sequence of decreasing k.     

Synthesis of polystyrene-polysiloxane side-chain liquid crystalline block copolymers

The synthesis of a new liquid crystalline block copolymer consisting of a polystyrene block and a side-chain liquid crystalline siloxane block is reported. The synthetic approach described is based on the anionic polymerization of styrene and cyclic trimethyltrivinyltrisiloxane monomers, followed by functionalization of the siloxane block with side chain mesogens. The siloxane block has a T_g well below 25°C and is designed to exhibit a chiral smectic C^* phase at room temperature. These block copolymers are the first side-chain liquid crystalline block copolymers which contain both a high T_g glassy block and a low T_g liquid crystalline block.     

Frequency spectra of disordered metals: especially liquid Rb

The phonon frequency spectrum g(ω) of a crystal, such as body centred cubic (bcc) Rb, is known to be characterized by the Van Hove singularities at ω?≠?0. However, for a liquid metal like Rb, g(ω) has a single, hydrodynamic-like singularity, namely a cusp ∝ ω ^(1/2), at ω?=?0. Here, we note first that computer simulation on liquid Rb near freezing has revealed a rather well-defined Debye frequency ω_D. Therefore, we propose here a zeroth-order model g ₀ (ω ) of g(ω) for Rb, which combines the Debye model with the ‘hydrodynamic’ ω ^(1/2) cusp. The corresponding velocity autocorrelation function 〈 v (t)·v (0)〉 has correctly a long-time tail ∝ t ^-(3/2). The terms from g ₀ (ω ) involving ω_D are then damped by weak exponential factors exp (-α _i t), and the resulting first-order approximation, g ₁ (ω ) say, to the frequency spectrum is found to have features in common with the molecular dynamics (MD) simulation form. Thus ω_D is fixed, as well as transport coefficients for the known thermodynamic state. The article concludes with a more qualitative discussion on supercooled liquids, and on metallic glasses such as Fe, for which MD simulations exist.     

Polyisobutylene-containing block polymers by sequential monomer addition. IV. New triblock thermoplastic elastomers comprising high Tg styrenic glassy segments: Synthesis,characterization and physical properties

New linear triblock thermoplastic elastomers (TPEs) comprising a rubbery polyisobutylene (PIB) midblock flanked by two glassy endblocks of various styrenic polymers have been synthesized by living carbocationic polymerization by sequential monomer addition. First isobutylene (IB) was polymerized by a bifunctional tert-ether (dicumyl methyl ether) initiator in conjunction with TiCl₄ coinitiator in CH₃Cl/methylcyclohexane (MeCHx) (40/60 v/v) solvent mixtures at ?80°C. After the living narrow molecular weight distribution PIB midblock ( = 1.1–1.2) has reached the desired molecular weight, the styrenic monomers together with an electron pair donor (ED) and a proton trap (di-tert-butylpyridine, DtBP) were added to start the blocking of the glassy segments from the living ⊕PIB⊕ chain ends. While p-methylstyrene (pMeSt), p-t-butylstyrene (ptBuSt) and indene (In) gave essentially 100% blocking to the corresponding glassy endblocks, the blocking of 2,4,6-trimethylstyrene (TMeSt) and α-methylstyrene (αMeSt) were ineffective. Uncontrolled initiation by protic impurities was prevented by the use of DtBP. In the simultaneous presence of DtBP and the strong ED N,N-dimethylacetamide (DMA), TPEs with good mechanical properties (10–20 MPa tensile strength, 300–600% elongation) were prepared. The products exhibit a low and a high temperature T_g characteristic of phase separated rubbery and glassy domains. The service temperature of these new TPEs exceeds that of PSt–PIB–PSt triblock copolymers due to the higher T_gs (PpMeSt = 108, PptBuSt = 142 and PIn = 220–240°C) of the outer blocks. The T_g of the glassy blocks can be regulated by copolymerizing two styrene derivatives; a triblock copolymer with outer blocks of poly(pt-butylstyrene-co-indene) showed a single glassy transition T_g = +165°C, i.e., in between that of PptBuSt and PIn. Virgin TPEs have been repeatedly compression molded without deterioration of physical properties. The high melt flow index obtained with a TPE containing PptBuSt endblocks suggests superior processability relative to those with PSt end-blocks. The tensile strength retention at 60°C of the former TPE is far superior to that of a PSt–PIB–PSt triblock of similar composition.     

Relaxations in thermosets. IX. Ionic conductivity and gelation of DGEBA-based thermosets cured with pure and mixed amines

The results obtained during the isothermal curing of diglycidyl ether of bisphenol-A-based thermosets cross-linked with pure diaminodiphenyl methane and pure diaminodiphenyl sulfone and with their mixtures have been analyzed to determine how the dc conductivity changes with time during the conversion of its liquid to a gel. The complex permittivity data are first analyzed to show that ac measurements can be used to obtain the ionic conductivity over a considerable period of the curing process. The procedure allows one to obtain the dc conductivity without having data as a function of frequency. The shape of the complex plane plots of the electrical modulus are semicircles, but with small deviations that appear at long times during the curing process. The dielectric consequences of the chemical changes with time during the cross-linking of the thermoset are analogous to the frequency dependence of the complex permittivity of a liquid. The analysis shows that the dc conductivity σ_o of a thermoset during its cure follows a power law, σ_o∝ (t_g—t)^x, where t is the curing time (t < t_g). The results can also be described equally well by a new equation, σ_o ∝ exp[—B/(t_o—t)], where x, t_g, B, and t_o are empirical constants all of which vary with the temperature of the cure. t_g is close to the time for gelation known from independent studies and t_o is close to but longer than the time for vitrification. These conclusions are discussed in terms of scaling concepts for the gelation phenomenon.     

Nonlinear viscoelasticity of polystyrene solutions. I. Strain-dependent relaxation modulus

Strain-dependent relaxation moduli G(t,s) were measured for polystyrene solutions in diethyl phthalate with a relaxometer of the cone-and-plate type. Ranges of molecular weight M and concentration c were from 1.23 × 10⁶ to 7.62 × 10⁶ and 0.112 to 0.329 g/cm³. Measurements were performed at various magnitudes of shear s ranging from 0.055 to 27.2. The relaxation modulus G(t,s) always decreased with increasing s and the relative amount of decrease (i.e.,–log[G(t,s)/G(t,0)]) increased as t increased. However, the detailed strain dependences of G(t,s) could be classified into two types according to the M and c of the solution. When cM < 10⁶, the plot of log G(t,s) versus log t varied from a convex curve to an S-shaped curve with increasing s. For solutions of cM > 10⁶, the curves were still convex and S-shaped at very small and large s, respectively, but in a certain range of s (approximately 3 < s < 7) log G(t,s) decreased rapidly at short times and then very slowly; a peculiar inflection and a plateau appeared on the plot of log G(t,s) versus log t. The strain-dependent relaxation spectrum exhibited a trough at times corresponding to the plateau of log G(t,s). The longest relaxation time τ₁(s) and the corresponding relaxation strength G₁(s) were evaluated through the “Procedure X” of Tobolsky and Murakami. The relaxation time τ₁(s) was independent of s for all the solutions studied while G₁(s) decreased with s. The reduced relaxation strength G₁(s)/G₁(0) was a simple function of s (The plot of log G₁(s)/G₁(0) against log s was a convex curve) and was approximately independent of M and c in the range of cM <10⁶. This behavior of G₁(s)/G₁(0) was in agreement with that observed for a polyisobutylene solution and seems to have wide applicability to many polymeric systems. On the other hand, log G₁(s)/G₁(0) as a function of log s decreased in two steps and decreased more rapidly when M or c was higher. It was suggested that in the range of cM < 10⁶, a kind of geometrical factor might be responsible for a large part of the nonlinear behavior, while in the range of cM > 10⁶, some “intrinsic” nonlinearity of the entanglement network system might be important.     

Diffusion with discontinuous swelling. V. Type II diffusion into sheets and spheres

Type II diffusion into uniform spheres (radius R) and sheets (thickness 2l) is calculated under the assumption that the glass-gel boundary proceeds at a constant velocity v from the surface towards the interior of the sample, that the diffusion coefficient D_g in the glass is constant and that the diffusion coefficient D_r of the rubbery gel is so much higher than vR or vl that practically no sorbate gradient is needed for the transport through the gel of the sorbate. The diffusion process is completed when this boundary reaches the center of the sample. The concentration profile of the sorbate in the glassy matrix in front of the boundary varies with time and velocity v. It does not, however, influence the boundary propagation velocity. Hence the often observed increase of the rate of the weight gain just at the end of the diffusion process is not considered at all. The relative weight gain of the sample W(t)/W_∞ as a function of time is the only quantity usually measured. From the ordinate intercept A and the initial slope B of the plot of W(t)/t^1/2W_∞ vs. t^1/2, one can calculate the characteristic transport properties, i.e., the diffusion coefficient D_g of the glass and the velocity v of the glass–gel boundary.