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Analysis of Polystyrene-Toluene System Through ‘Dynamic’ Sorption Tests: Glass Transitions and Retrograde Vitrification Davide Pierleoni, Matteo Minelli, Giuseppe Scherillo, Giuseppe Mensitieri, Valerio Loianno, Francesco Bonavolontà, and Ferruccio Doghieri J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b08722 • Publication Date (Web): 06 Oct 2017 Downloaded from http://pubs.acs.org on October 8, 2017

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The Journal of Physical Chemistry

Analysis of Polystyrene-Toluene System through ‘Dynamic’ Sorption Tests: Glass Transitions and Retrograde Vitrification

Davide Pierleonia, Matteo Minellia, Giuseppe Scherillob, Giuseppe Mensitierib*, Valerio Loiannob, Francesco Bonavolontàc and Ferruccio Doghieria* a

Department of Civil, Chemical, Environmental and Materials Engineering (DICAM), ALMA MATER STUDIORUM University of Bologna, Italy b

Department of Chemical, Materials and Production Engineering (DICMAPI), University of Naples Federico II, Italy

c

Department of Electrical Engineering and Information Technology (DIETI), University of Naples Federico II, Italy

* Corresponding authors: Giuseppe Mensitieri, [email protected] Ferruccio Doghieri, [email protected]

Abstract Exposing a glassy polymer to a fluid phase (in gaseous or liquid state) containing a low molecular weight compound results in the sorption of the latter within the polymer inducing, among other effects, the plasticization of the material which also promotes a change in the glass transition temperature. The amount of sorbed penetrant is often related in a complex fashion to temperature and pressure of the fluid, thus determining that the locus of glass transition, when represented in pressure-temperature coordinates, may display as well rather complex patterns. This is an issue of particular importance in several applications of glassy polymers. In particular, we investigated the behavior of polystyrene in contact with toluene vapor by performing several modes of dynamic sorption experiments, in which the rate of change of the temperature of the system and/or of the pressure of the vapor phase are controlled with high accuracy, with the aim of creating a map of rubbery and glassy states of the polymer as a function of temperature and pressure of the toluene vapor. Isothermal tests were performed by changing the pressure at a controlled rate, isobaric tests were performed by changing the temperature at a controlled rate and isoactivity tests were performed by concurrently changing, in a proper way, both temperature and pressure. A relevant feature resulting from these experiments is the presence of a discontinuity in the slope of the mass of toluene sorbed within polystyrene reported as a function of temperature and/or pressure. This discontinuity has been interpreted as the indication of the occurrence of a glass transition. The elaboration of the 1 ACS Paragon Plus Environment


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experimental results allowed to identify of the pressure/temperature conditions at which rubbery or glassy states of the polymer mixture establish. Quite interestingly, the system displays the so- called‘retrograde vitrification’ phenomenon, which consists in the occurrence of a rubbery-to- glassy state transition as the temperature increases at a fixed pressure. The whole set of results has been successfully interpreted on the basis of thermodynamics of II order transitions accounting for the fact that experimental evidence of such transitions is significantly affected by the kinetics of polymer relaxation.

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1. INTRODUCTION Mass transport in glassy polymers is of relevance in a number of different applications, from membrane separation1,2 to drug delivery3, and it is of interest for the fundamental study in transport phenomena, as it is characterized by several anomalous behaviors, with respect to the case of diffusion in rubbery polymeric systems.4,5 In fact, both apparent vapor solubility and sorption kinetics in polymeric materials show significant changes in their essential features when temperature of the system is decreased below the glass transition point. While properties of rubbery solute-polymer mixtures are often satisfactorily described by relations from equilibrium thermodynamic, peculiar non-equilibrium characteristics are shown by solubility isotherms measured in glassy polymers.6 On the other hand, effective order of kinetic, n, in relationships for mass uptake over time, ∆m∝tn, in isothermal sorption experiments in which an initially glassy dry polymer is swollen up to a rubbery state, is typically higher than the 0.5 value predicted by Fick’s law. Several types of sorption kinetics have been actually named after data from integral sorption experiments of this kind, according to the effective order: “anomalous kinetics” (0.5 1).7 Moreover, different behaviors have been identified for the case of sorption processes induced by differential experiments in thin glassy polymer samples with non-negligible initial solute content, in which materials do not undergo to a glass-to-rubber transition.8 Several kinds of kinetics, from “two stage sorption” to “S” shaped and to “pseudo-Fickian” have been observed for the case of differential sorption experiment in glassy samples9,10 that are all manifestations of combined effect of diffusion and relaxation processes in glassy polymeric materials.11 This phenomenology is further complicated by the fact that presence of solute affects the glass transition point of the system itself, thus affecting the mass transport process. Gas or vapor solubility in non-equilibrium glassy polymers, formerly described by widely used empirical tools as the so called Dual-Mode-Sorption model6,12, have been more recently modeled by models making use of order parameters for the representation of out of equilibrium degree of the glassy polymeric structure13. These latter approaches could be ultimately applied to derive transport models for solute sorption/desorption in glassy polymeric materials, once suitable relations are defined for the time evolution of order parameters at assigned conditions for manipulated process variables. With reference to modelling efforts for sorption kinetics, remarkable attempts can be mentioned aiming at the representation of combined effects of stress, solute concentration and temperature histories14, which require detailed information for constitutive properties of materials, together with simplified approaches that make use of specific lumped parameters.15,16 The set up of either detailed or simplified models mentioned above requires specific experimental data for gas/vapor fugacity effect on polymer relaxation, which give also account of the effect of the history of process parameters. In this view, the first data required are pertinent to the variation of glass transition temperature, Tg, with solute content or, equivalently, of glass transition value for solute fugacity at assigned temperature. Exam 3 ACS Paragon Plus Environment


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of relaxation behavior induced by mass transport in glassy polymer is often pursued by means of sequences of differential sorption experiments in which solute pressure is raised at constant temperature. Changes in pertinent sorption kinetics for the various steps corresponds to different values of characteristic time for relaxation17. To the aim of retrieving constitutive relation for polymer relaxation as a function of process variables, however, the above characterization is unsatisfactory in several respects, as its results are largely dependent on the specific sequence of steps performed and on time needed to the completion of each sorption steps, which in turn cannot be anticipated in the experimental procedure. This work aims at the definition of alternative experimental protocols to retrieve unambiguous data useful to the evaluation of relaxation rate in polymer–solute systems. To this purpose, gravimetric measurements were considered, similar to those first collected by Doumenc et al. for the analysis of ageing phenomena in PMMAtoluene system.18 In this kind of tests, prescribed variations of one among the manipulated process variables are imposed to the polymeric sample, while keeping constant all the remaining variables in the same set. In particular, dynamic sorption or desorption processes induced in the polymeric system by varying the pressure of a vapor of a penetrant in contact with it, by varying the temperature or both, are followed by monitoring the change in mass of the sample. These experiments, performed here for the case of polystyrene (PS)-toluene pair, have been designed to specifically retrieve information about relaxation rate. Particular care was paid to ensure that effects of phenomena other than polymer relaxation, such as resistance to molecular diffusion, are negligible. It must be emphasized that the dynamic nature of sorption experiments here considered allows for the introduction of an arbitrary time scale for variation of boundary conditions in the test (e.g. rate of change of pressure of vapor of penetrant in contact with the polymer), by means of which specific relaxation times can be distinctly solicited in structural relaxation of the polymer-solute system under investigation. While analysis of the experimental data for the validation of relaxation laws is the long term goal of the research activity, in this report the attention is focused on the determination of conditions for rubber-to-glass transition identifying glass transition points on a temperature/solute pressure state diagram. Noteworthy, the rubber-toglass transition of interest is here identified by analyzing sorption/desorption processes. The transition points retrieved in this way should be kept distinct from other results obtained in polymer-solute systems by mean of different techniques, for example through differential scanning calorimetry measurements. Notwithstanding, similar to data from DSC experiments, they can be considered to highlight the nature of the transition, which is equally interpreted in the literature19 as a thermodynamic process (a second order phase transition, possibly affected by kinetics effects) and a purely kinetic process, only associated to an abrupt variation of relaxation time in the system. Experimental data for glass transition are analyzed in this work both on their dependence on process kinetics imposed by the rate of change of process variables and on the underlying second order phase change for which equilibrium solubility coefficient jumps at the transition point. 4 ACS Paragon Plus Environment

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Occurrence of glass transition in a polymer-penetrant system is ruled by penetrant pressure and system temperature. In fact, a fluid can act both as a pressure-generating medium, thus promoting an increase of Tg at increasing pressure, and as an effective plasticizer, thus promoting a decrease of Tg. In particular, the plasticizing action depends in a complex fashion upon the combined effects of fluid pressure and temperature on fluid sorption within the polymer. Condo et al.20 theoeretically predicted the relevant features in terms of dependence of Tg value on fluid pressure using a consistent framework that combines Equation of State of mixtures to describe sorption equilibrium and the Gibbs-Di Marzio criterion for glass transition21,22 (i.e. the configurational mixture entropy is zero at the glass transition). They evidenced four fundamental types of behavior, ranging from type I to type IV.20 The so-called retrograde vitrification phenomenon is of particular relevance, consisting in a rubbery-to-glass transition for the polymer-penetrant mixture occurring at increasing temperature. In brief, in isobaric conditions, the increase in segmental motion occurring at increasing temperature is overcome by the decrease in the diluent concentration due to a decrease of its solubility within the polymer. In the present context, it is of particular interest the type IV behavior20, whose features are schematically illustrated in Figure 1, which reports a Tg behaviour as a function of pressure of penetrant in contact with polymer, displaying evidence of retrograde vitrification phenomenon.

Figure 1. Schematic representation of glass transition temperature vs fluid pressure envelope illustrating the type IV behavior (after Condo et al.20).

This issue has been addressed using several experimental approaches, including methods based on: in situ measurement of creep compliance23,24, gravimetric sorption measurements by identifying a discontinuity in the sorption isotherm that marks glass-to-rubber transition25,26, stepwise temperature-and pressure-scanning thermal analysis27, a minimum foaming temperature approach28, in situ spectroscopic ellipsometry29 or the detection of sharp increase in mutual diffusion coefficient in the polymer-penetrant system30. Notably, experimental evidence of retrograde vitrification has been provided only in a few cases, as for poly( methyl methacrylate) (PMMA) and 5 ACS Paragon Plus Environment


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poly( ethyl methacrylate) (PEMA) in contact with pressurized CO2 23,24,27,28,31, as well as for thin PS film-CO2 systems29 and for the PLLA-CO2system30. In this contribution, we present and discuss a thorough experimental analysis of the Tg – pressure map for the PS-toluene system, determining regions where glassy and rubbery states are observed for the mixture. The analysis is based on the results of dynamic sorption/desorption experiments carried out at isothermal, isobaric and isoactivity conditions. 2. EXPERIMENTAL 2.1 Material Samples in the form of self-standing thick films, or supported thin layers, were prepared from the same source of atactic polystyrene (weight average molecular weight Mw = 270000 kg/kmol; polydispersity index Mw/Mn = 1.1) kindly supplied by Versalis S.p.A., Mantua, Italy. Toluene, used either for sample preparation or for sorption/desorption tests, was used as provided by the supplier (HPLC grade, Sigma-Aldrich).Self-standing thickfilms (around 90 µm) were prepared by solvent casting a toluene-PS solution on a glass petri dish, after a suitable volume of solution has been dropped on it. Thin PS coatings (coating thickness lower than 1.0 µm) deposited on top of aluminum foils (thickness 17µm, ItalchimS.r.l., Bologna, Italy) were obtained by a spin coating process, starting from a PS-toluene solution (PS 7% by weight). By modifying the spinning rate, it was possible to obtain thin films with different thickness. Two series of coating films, 430 and 750 nm thick,were actually prepared and used for the sorption experiments. Disks with a diameter of 13 mm were cut from the PS spin coated aluminum foils, using a sharp cutting die. For all kind of samples, removal of residual traces of toluene was pursued by treating them at 120°C under vacuum for few hours followed by overnight cooling. Thickness of free standing PS film was measured by means of a mechanical micrometer, while the estimate of the average thickness of PS coating films was obtained after the evaluation of the mass of the coating. For the latter procedure, the weight of the coating film was calculated after the difference between the weight of coated disk and corresponding bare aluminum disk, as obtained after cleaning it by means of a solvent. A Mettler Toledo analytical balance, sensitivity 10-5g, was used for the evaluation of apparent weight of both coated and cleaned disks. The average thickness of the coating was finally estimated from its mass, based on the total area of the disk and on estimated room conditions value for mass density of polystyrene (1.04 g/cm3).

2.2 Apparatuses Different types of sorption/desorption experiments were performed in this work using two different apparatuses. A two-chambers pressure decay rig was used to perform pure component sorption steps from vapor phase into free standing thick polymer films.32. The apparatus, described in details in Supporting Information, allows for the vapor component to be transferred from pure gaseous phase to a polymer sample in a closed system in which 6 ACS Paragon Plus Environment

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temperature is set to a constant value, as well as the total volume. The pressure of the vapor phase is monitored during the process and the number of moles of vapor absorbed into the polymer sample are calculated at any time during the process based on the pressure value in gaseous phase. A gravimetric apparatus has been set up to monitor mass of toluene absorbed into samples of PS coated aluminum disks from pure component vapor phase. The apparatus allows to finely control temperature and pressure of toluene vapor inside the measuring chamber. In the apparatus, whose detailed description is provided in Supporting Information, the sample is hanged to the weighing arm of a CAHN-D200 electronic microbalance and hosted in a chamber in which temperature and pressure are regulated by two separate PID control systems. The temperature of the chamber is controlled by means of a thermostatic fluid circulating in a jacket surrounding the sample chamber, while the pressure of toluene vapor is controlled by means of a computer operated electric throttle valve connecting the apparatus to a vacuum pump and used to regulate the outflow of toluene vapor from sample chamber. The opening of a manual needle valve, connecting the vapor phase of a liquid toluene reservoir to the apparatus, is set to guarantee a constant proper inflow of toluene vapor in the sample chamber. A control LABVIEW software is used to drive electronic devices connected to the throttle valve and to the thermostatic bath and to acquire microbalance reading, temperature and pressure of toluene vapor. This computer control of the whole system allows to accurately change pressure and temperature of the sorption cell according to prescribed functions of time, within a relatively wide range of rates of change.

2.3 Methods 2.3.1 ‘Static’ sorption tests In order to provide a reference for the equilibrium solubility of toluene in the investigated polystyrene, conventional ‘static’ sorption tests of toluene vapor in PS were performed through the use of a pressure decay apparatus. In a typical procedure, free-standing thick PS films are placed in a sample holder and treated under high vacuum to remove any trace of volatiles from the polymer, then the samples are exposed to toluene vapor. The toluene vapor is first introduced in a pre-chamber, of known volume, where the temperature is set to a constant value and the value of pressure is monitored and acquired. After the attainment of a constant value of pressure, the gas is expanded into the sample chamber through a valve and the pressure decrease over time, due to toluene sorption within the samples, is monitored and acquired. Each sorption step of this “static” sorption experiments performed until a constant value of pressure (within the experimental accuracy) is recorded in the sample chamber for at least 24 hours. The corresponding (apparent) equilibrium amount of moles of toluene absorbed in PS is then evaluated through a mole balance. The calculation is based on the knowledge of the volumes of the pre-chamber and of the sample chamber, of the volume occupied by the PS samples and of the value of pressure in the chambers before and after sorption test, making use of a volumetric equation of state for 7 ACS Paragon Plus Environment


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the gaseous phase. Subsequent stepwise increases in penetrant pressure are then performed to characterize the sorption behavior at higher pressures. Integral ‘static’ sorption tests were performed in thin PS coating films in the gravimetric apparatus. This kind of test was always performed on thin films before each ‘dynamic’ sorption experiment to bring the polymer-toluene mixture in an equilibrium rubbery state, thus erasing any memory effect on the material resulting by previous treatments or sorption experiments. This integral ‘static’ sorption experiment procedure consists in first keeping a polymer sample under vacuum inside the measuring chamber of the microbalance long enough to completely dry it. At the end of the desorption stage, the chamber is rapidly filled with pure toluene vapor while the control system is set to maintain a constant value of both temperature and pressure. The level of toluene pressure in this kind of experiment is set to a value high enough to insure that the system reaches, after sorption is completed, an equilibrium rubbery state. Also in this case, the weight gain of the sample during the experiment is measured and recorded, to be then elaborated in order to derive the evolution of mass ratio (see section 2.3.2 for its definition) of toluene in PS sample over time.

2.3.2 Dynamic sorption/desorption test In this work, by ‘dynamic desorption/sorption test’is intended an experiment in which a vapor compound is adsorbed into/desorbed from a polymer sample as its chemical potential in the surrounding pure component gaseous phase is continuously modified at a prescribed rate over time. The gravimetric apparatus was used to perform different kinds of dynamic tests for toluene sorption/desorption in PS coated aluminum disks, according to the specific conditions imposed during the variation of toluene chemical potential: 1) isothermal, 2) isobaric and 3) isoactivity. To guarantee an adequate accuracy of the tests, around four hundred PS coated disks were hanged to the weighing arm of the microbalance, by piling them using a titanium thin wire. Before running any type of dynamic test, samples were preliminarily exposed to a sufficiently high toluene pressure through an integral static sorption experiment, described in the previous section, to insure the attainment of an equilibrium rubbery state, thus erasing any memory of previous treatment history on the sample. The dynamic experiment then proceeds following the prescriptions of each specific kind of test. In particular, in isothermal tests, first a decrease in pressure of toluene vapor in the balance chamber is imposed at a controlled rate promoting desorption of toluene, and bringing the polystyrene-toluene mixture into the glassy region; pressure is then raised at the same absolute rate, to determine the re-absorption of toluene, recovering the starting level of pressure. In the isobaric case, temperature of the balance chamber is changed in a loop while maintaining a constant pressure of toluene vapor. In fact, the isobaric test starts from rubbery state at low temperature proceeding then by heating the sample compartment, at a controlled rate, up to a temperature at which the sample is rubbery again (according to the observed type IV behavior) and then by cooling the sample 8 ACS Paragon Plus Environment

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compartment, at the same controlled rate, back to the initial value of temperature Finally, in the case of a dynamic isoactivity test, a path is followed along which temperature and pressure are both decreased at a controlled rate, in such a way that the toluene activity in the gaseous phase is kept at about a constant value for the entire duration of the experiment (see Supporting Information for further details). The obtained raw data in terms of sample weight change were elaborated to evaluate the ratio of mass of absorbed toluene to that of neat “dry” polymer, referred to in the following as ‘mass ratio’, Ω, or the toluene mass fraction, ω. Experimental conditions (in terms of rate of change of pressure and/or temperature) and sample thickness were properly selected to prevent any the influence on the observed behavior of kinetic effects related to toluene diffusion in the PS films. In fact, attention was paid to impose a sufficiently low rate of pressure decrease of toluene vapor and /or of temperature change to guarantee a rather uniform chemical potential within the polymer phase at any time. Experimental proof that this is actually the case will be also provided by showing the results obtained by imposing a standard pressure decreasing ramp on samples of different thickness and by performing consecutive decreasing/increasing pressure ramps on a sample. As a consequence, when the experiments are performed on the polymer mixture in a rubbery state, it is reasonable to assume that, at each time, a uniform toluene concentration is present within the PS film, in instantaneous equilibrium with the surrounding toluene vapor phase. In fact, in these conditions polymer relaxation is fast enough to let the polymer structure to accommodate rather instantaneously to the imposed changes of pressure and/or temperature. Conversely, when experiments are performed on the polymer mixture in a glassy state, one can still assume the uniformity of toluene chemical potential within the polymer, although the system does not attain instantaneously an equilibrium state, in view of the slower relaxation dynamics: in this case, an instantaneous pseudo-equilibrium is established between the polymer mixture and the toluene vapor phase.



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3. RESULTS AND DISCUSSION In this section the experimental results are presented and discussed, first reporting the outcomes of ‘static’ isothermal tests, performed at 40°C in the pressure decay apparatus, used to preliminary evaluate the range of glass transition for the toluene-PS mixture, and to collect equilibrium solubility data for the characterization of the thermodynamics for PS-toluene mixture in the rubbery sate. Then the results of ‘dynamic’ tests (isothermal tests at several temperatures, isobaric tests at a pressure equal to 36 mbar and isoactivity tests) performed on aluminum supported PS thin films are presented. As anticipated, for each test, samples were initially conditioned at a sufficiently high toluene pressure and a sufficiently long time to let the polymer mixture reach a rubbery state at equilibrium with the vapor phase, thus erasing any memory effect. As will be shown, these ‘dynamic’ sorption data display a discontinuity in the slope of the toluene mass ratio, within the polymer mixture phase, as a function of pressure of toluene vapor and/or temperature. These discontinuities are attributed to the occurrence of a rubber to glass transition of the polymer mixture. By reporting the coordinates of these discontinuities in a temperature vs pressure plot, a contour line is obtained separating the glassy from the rubbery domains of the polymer-toluene mixture. In the final part of this section we provide a proof that the observed discontinuities can be actually interpreted as a kinetically affected fingerprint of an underlying II order thermodynamic transition, in the framework of Ehrenfest33 phase transition theory. Since glass transition phenomenology, according to some theories, can be interpreted as a II order transition, these findings are used as a thermodynamics basis for attributing such discontinuities to the occurrence of a rubber-to-glass transition.

3.1 Static sorption tests Stepwise sorption tests (differential static sorption experiment) at 40°C on 90 µm thick free standing PS-films were performed in a pressure decay apparatus. During each sorption step, kinetics of toluene mass uptake was monitored and some relevant examples are reported in Figure 2 where are illustrated three different kinds of behavior detected for different steps in pressure of toluene vapor and, in turn, for different ranges of absorbed toluene concentration. A pseudo-Fickian sorption kinetics (Figure 2a) resulted for sorption data collected for the first step of the sequence of differential experiments (in the concentration range up to 0.03 toluene mass ratio), displaying an estimated average mutual diffusion coefficient of the order of 10-11 cm2/s. Conversely, high concentration (in the range from 0.11 to 0.13 of toluene mass ratio) sorption steps (Figure 2c) exhibit a typical Fickian sorption behavior, characterized by an average mutual diffusion coefficient for toluene/PS of the order of 10-8 cm2/s. In the intermediate toluene concentration range, a two-stage sorption kinetics was detected (Figure 2b), with a characteristic time of the diffusion stage that is intermediate between those recorded at lower and higher 10 ACS Paragon Plus Environment

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concentrations. In this pressure range, diffusion rate for PS-toluene mixture estimated for the initial diffusive stage, is consistent with the values retrieved by Krueger and Sadowski34 for the same system (and at the same temperature) near glass transition. The long term stage of the sorption process, which can be typically associated to relaxation phenomena in PS, is accompanied by a significant increase in toluene mass uptake in the polymer sample. The order parameters n, evaluated from the obtained sorption kinetics in differential sorption steps, indicated the toluene pressure at which glass-to-rubber transition occurs at 40°C is at about 28 mbar, as it is clearly marked by onset of clear Fickian type kinetics (order of kinetics n = 0.5) for sorption steps performed at a pressure of toluene vapor above this value.

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0 10 20 30 40 50 60 70 80 Square root of time [s1/2] (c) Figure 2. Examples of toluene step sorption curves acquired by the pressure decay technique in PS at 40°C. Curves show markedly different times to attain equilibrium as well as different kinetic behavior, moving from Non-Fickian to Fickian sorption at increasing pressure of toluene vapor. In the inset of each plot is reported the relative pressure step imposed. 11 ACS Paragon Plus Environment


Figure 3 reports the toluene sorption isotherm in PS, evaluated from apparent equilibrium toluene content attained at the end of each static differential sorption step in the sequence performed on thick free standing PS films at 40°C. It is possible to identify two different regions of the solubility isotherm separated by a transition zone from glassy to rubbery state, corresponding to a solute content of around 0.10 mass ratio.

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40°C

15 Glassy zone

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Rubbery zone

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10 15 20 25 30 35 40 45 Toluene pressure [mbar]

Figure 3. Toluene sorption isotherm in PS at 40°C obtained from pressure decay curves. The glass transition zone (shadowed in grey) is identified as the step with a Fickian-nonFickian transition

As discussed in section 2.3.1, static sorption tests were also performed on aluminum disks coated with thin PS films, prior to each dynamic sorption/desorption experiment, to bring the PS-toluene mixture in a rubbery state, thus erasing any memory effect related to previous treatments. Figures 4a,b report the toluene mass uptake results obtained in integral sorption experiments in a thin PS coating film (750 nm thick), corresponding to 40°C and 40 mbar and to 20°C and 33 mbar of pressure of toluene vapor, respectively. In view of the small value of volume-to-surface ratio of the sample, the characteristic time of the diffusion process is very small, and it can be roughly estimated to be shorter than 1 min. On the other hand, an equilibrium value for the toluene content in PS in the experiment is not reached earlier than one hour after the beginning of the sorption experiment. Opposite to differential sorption steps confined into the glassy region, the relaxation processes involved in integral sorption at time longer than the characteristic time for diffusion lead to a decrease of toluene content in the sample. The overall sorption kinetics indeed show a clear example of overshoot, for which a non-monotonous mass uptake over time is observed in a sorption process at constant boundary conditions. Due to its relevance in the interpretation of non-Fickian kinetics, the occurrence of overshoot phenomena in sorption kinetics has been discussed in the literature, with reference to its thermodynamic consistency and to its possible origin. Although 12 ACS Paragon Plus Environment

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this is not the first example of overshoot reported for vapor sorption in thermoplastic material (see, for example, the case of anomalous sorption in PMMA reported by Vrentas et al.35), it deserves to be noticed in view of clear evidence of the phenomenon given in this case. A deeper investigation of this specific aspect, however, is beyond the scope of this report and the detailed analysis of similar results obtained at different temperatures in integral sorption experiments performed as preliminary steps to dynamic sorption tests is left to a future work.

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6 (b)

Figure 4a,b. Examples of PS sample pretreatment in integral static sorption steps carried out at (a) 40°C and 40 mbar and (b) 20°C and 33 mbar. An overshoot occurs prior the attainment of a constant sorption value reached over long times. The overshoot amounts to a mass ratio of about 0.01 (see plot enlargement reported in the insets).

3.2 Dynamic desorption/sorption tests 13 ACS Paragon Plus Environment


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Several different factors and related characteristic times may affect mass uptake kinetics in dynamic sorption tests described in section 2: rate of change of boundary conditions, relaxation process in polymeric material and resistance to mass transport in the solid sample. Unlike the case of the other factors, the characteristic time of mass transport in polymer sample is affected by the volume-to-surface ratio of the specimen. Because of that, the kinetic of diffusion process can be manipulated by adjusting the thickness of the solid sample, without affecting the rate of any other phenomenon. The thickness of PS coating films prepared for dynamic sorption tests was designed to accelerate toluene transport to such an extent that sorption kinetics is mainly ruled by relaxation behavior of polymer mixture in the range of interest for the rate of change of boundary conditions. The mutual diffusion coefficient, D, in polymer-solute system is very sensitive to solute content and, indeed, a large variation in characteristic time for diffusion was observed in static sorption experiments in the same free standing film from dry to fully plasticized conditions. When an intermediate value D (10-10 cm2/s) is considered, a characteristic time for diffusion process lower than 1 min can be estimated for the case of film thickness lower than 1 µm. Based on that, the glass-to-rubbery transition zone at 40°C can be crossed in a dynamic sorption test at a rate as high as 0.16 mbar/min (that is the maximum value adopted in this investigation) keeping as low as few percent the relative variation of apparent equilibrium solubility within the characteristic time for diffusion. According to the above consideration, the difference between minimum and maximum solute concentration in the polymer sample due to diffusion kinetics is limited to at the most 1% of the average value, even within the glassy region, for the rate of pressure variation mentioned above. In order to verify the reliability of these estimates for the cases of both rubbery and glassy state of the polymeric mixture, preliminary tests were performed to ensure that the diffusion resistance in a dynamic sorption test is actually negligible for the rate of pressure change of interest in this work. A first test was run on PS coating film 750 nm thick, performing isothermal dynamic sorption experiments at 40°C in which toluene pressure is changed in a cyclic fashion, confined into the rubbery region. Under those conditions, the relaxation time is low enough to allow for the phenomenon to be ignored, and difference observed for the mass ratio measured at the same toluene pressure between sorption/desorption branches can only be attributed to diffusion resistance in the solid. Results from this kind of experiments are reported in Figure 5 for the case of two different values of the rate of change for toluene pressure. As one can see, the uncertainty in solute content due to diffusion resistance is lower than 1%, even for the case of the highest rate used (0.16 mbar/min). The same kind of test cannot be considered to verify that diffusive resistance is negligible in the glassy polymer mixture, as the significant effect of the slow relaxation phenomena would invariably affect the result of a cyclic process, performed below the glass transition. A different test was thus designed, simply comparing the result for toluene mass ratio as function of toluene pressure in the gaseous phase for dynamic desorption test run at the same pressure change rate in PS samples of different thickness. In case desorption kinetics was affected by diffusive resistance, different mass ratios would result at the same values of toluene pressure for samples of 14 ACS Paragon Plus Environment

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different thickness. Experimental data were obtained at 40°C by the same isothermal dynamic desorption test performed on 750 nm and 430 nm thick PS coating film, bringing both samples from rubbery conditions down below the glass transition zone, as identified from static sorption experiments. No significant difference was observed between data retrieved for the two samples (Figure 6), thus confirming that the diffusion resistance does not affect appreciably the dynamic sorption/desorption tests considered in this work even when the polymer mixture is in the glassy state. Only one value for thickness was finally considered for samples used in this work and, in fact, all results for dynamic experiments reported in the next sections refer to the case of toluene sorption/desorption in thin PS coating films with thickness equal to 750 nm.

24 Mass ratio x 100

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22

0.16 mbar/min 0.04 mbar/min Rubbery zone 40°C

20

18.4

18.3

18.2

18 16 36

on i t orp s de

on i t rp so

18.1

18.0 38.5

38

38.6

38.7

38.8

40 42 44 46 Toluene pressure [mbar]

38.9

48

39.0

50

Figure 5. Results of sorption/desorption tests in PS performed by cycling the pressure of toluene vapor at a controlled rate. In the inset is reported an enlargement of the results for the case of a rate of change of pressure equal to 0.16 mbar/min. A good overlap between sorption and desorption ramp confirms the limited effect of diffusive phenomena on the rate of change of toluene mass ratio in the PS-toluene mixture.



12 Mass ratio x 100

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thick thin

11 10

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T = 40°C 0.04 mbar/min

9 8 10

15 20 25 Toluene pressure [mbar]

30

Figure 6. . Dynamic sorption tests at 40°C with toluene in two PS samples of different thickness; desorbing isotherms at constant rates are thickness-independent.

3.2.1 ‘Dynamic’ isothermal tests Different kinds of toluene sorption/desorption tests in thin PS coating films were performed in this work according to the “dynamic” protocol. Results for a 40°C isothermal sorption-desorption cycle, spanning both above and below the glass transition zone already identified, are reported in Figure 7. Following a preliminary integral sorption experiment at a toluene pressure of 40 mbar, solute desorption was allowed by continuously decreasing the pressure of toluene vapor at a constant controlled rate of 0.16 mbar/min down to 10 mbar. After completing the pressure decrease stage, pressure of toluene vapor is increased back to 40 mbar, at the same rate of 0.16 mbar/min. A hysteretic behavior for the desorption/sorption cycle is evident from data reported in Figure 7 in the region of low pressures. In fact, in this region, desorption and subsequent sorption branches do not overlap. Several relevant features of solute mass ratio, Ω, obtained from the sorption/desorption cycle in Figure 7 deserve to be highlighted, as they are evidenced in all similar tests performed at different temperature or rate of change for pressure: -

a discontinuity in the value of the slope of the toluene mass ratio as a function of pressure is evident, pointed out by the arrow in Figure 7. In fact a remarkable difference is evident, along the desorption stage, in the values of the isothermal solubility coefficient (i.e. the derivative of toluene mass ratio as a function of pressure, dΩ/dp) above and below a transition region, the coefficient being higher at toluene pressure values above those marking the transition. The pressure value at which the transition is located is referred to as Pg. This discontinuity, as we will better discuss later, is assumed to identify a rubber-to 16 ACS Paragon Plus Environment

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glass transition of the PS-toluene system. The exact location of the discontinuity was evaluated by using a mathematical procedure illustrated in detail in the Supporting Information; -

in the low pressure range of the cycle, the solubility coefficient is higher along the desorption branch (decreasing pressure) as compared to the sorption branch (increasing pressure);

-

the sorption branch recovers the mass ratio values of the desorption branch at pressure values significantly higher than those at which the transition occurs along the desorption stage;

-

a small, although not negligible, difference is measured at highest values of pressure between the solubility isotherm measured along the initial desorption path and the corresponding curve registered during the subsequent sorption run.

It is worth noting that a similar behavior was also observed by Doumenc for toluene in PMMA10. While all features in the above list could be the subject of specific analysis relevant to the study of relaxation behavior in polymer-solute system, in the present context we focus our attention only on the features displayed by the desorption branch. In what follows, the observed transition from rubber-like to glassy-like state in dynamic desorption tests is analyzed in detail, evaluating the variation of Pg with temperature and depressurization rate.

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18

T = 40°C dp/dt = 0.16 mbar/min

16 14 12 10 pg

8 6

10

15 20 25 30 35 Toluene pressure [mbar]

40

Figure 7. Example of experimental results of a dynamic isothermal desorption/sorption test at 40°C of toluene in PS: a constant rate of 0.16 mbar/min has been applied both along the decreasing and of increasing pressure branches. Rubbery to glassy state transition is evidenced by an arrow. Isothermal experiments were performed at 40°C at different values of the rate of pressure decrease, from 40 mbar down to 10 mbar and results are collectively presented in a log-log plot in Figure 8 along with the results of ‘static’ sorption tests carried out with the pressure decay apparatus, in terms of toluene mass fraction as a function of pressure of toluene vapor. It is evident that the results obtained from ‘dynamic’ tests are quite 17 ACS Paragon Plus Environment


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different from those of ‘static’ tests. In fact, at pressure values above the transition region, results from static sorption and those from dynamic desorption are almost equal, since an equilibrium rubbery state for the PStoluene mixture in contact with the toluene vapor phase is expected to be attained in both cases. Actually, a small difference in the solubility coefficient, which indeed looks a bit higher in the case of calculated static sorption tests, can be appreciated in the rubbery region. Moreover, the amount of absorbed toluene is higher in the case of dynamic desorption tests. Most likely, these features can be attributed to residual relaxation processes in the rubbery state that occurs during the long static sorption tests. On the other hand, the mechanical constraint experienced by supported film used in desorption runs, as opposed to the case of free standing films used in static sorption tests, can also be responsible for the difference in apparent solubility. It should be finally kept in mind that two apparatuses, with manometric and gravimetric detection of mass uptake, respectively, were used for static sorption and dynamic desorption tests and it is likely that different small systematic errors characterize the two distinct measurement techniques. Conversely, at pressure values smaller than those of the transition region, data collected in case of dynamic desorption tests markedly departed from those obtained in the case of static sorption experiments. In view of the non-equilibrium nature of the glassy state and of its history dependent behavior, this feature can be attributed to the different history of the sample in a dynamic desorption test with respect to static sorption conditions. The effect of sample history and of non-equilibrium nature of polymer-toluene mixture can be also recognized in the different apparent solubility measured in the glassy region for desorption runs managed at different depressurization rate. As we are able to rule out the effect of diffusive resistance on apparent solubility measured in dynamic desorption test, we can now discuss the results in Figure 8 only in terms of ratio between imposed time for variation of boundary conditions and characteristic time for relaxation phenomena in the polymer. Indeed, the characteristic time for change of boundary conditions is kept constant in each dynamic desorption test and its value increases as the rate of change of toluene pressure decreases. As opposed, characteristic time of relaxation can be assumed to be roughly independent on the rate of pressure decrease, but it dramatically increases as the toluene concentration decreases in the system. At relatively high pressure of toluene vapor the relaxation time is much smaller than the characteristic time of variation of boundary conditions and the apparent solubility measured at an assigned toluene pressure in a dynamic desorption test is ultimately very close to the thermodynamic equilibrium value, independently of the rate of decrease of pressure. On the other hand, the apparent solubility departs from the equilibrium value when the relaxation time increases above the characteristic time of variation in boundary conditions, which occurs across the transition zone. More specifically, departure from equilibrium conditions occurs at lower toluene concentration for the case of slower depressurization experiments, because lower toluene concentration need to be reached for the characteristic relaxation time to match the corresponding time for variation of boundary conditions in these cases. Consequently, the location of the rubber-to-glass transition occurs at lower values of Pg the lower is the rate of pressure decrease. 18 ACS Paragon Plus Environment

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Figure 8. Log-log plot reporting experimental results of ‘dynamic’ isothermal desorption tests performed at several pressure decreasing rate at a temperature of 40°C. For the sake of comparison is also reported the sorption isotherm obtained by static experiments carried out with the pressure decay (PD) apparatus. This behavior has remarkable analogies with the case of a pure polymer submitted to a temperature decrease at constant pressure. In such a case, the glass transition temperature, Tg, is marked by a clear discontinuity in the the slope of the specific volume vs temperature. If one considers the glass transition as a II order thermodynamic transition, Tg value should be independent on the rate of temperature decrease. However, the experimental evidence of the underlying thermodynamic transition is affected by kinetic factors. In fact, the experimentally accessible glass transition occurs at temperatures located above the purely thermodynamic glass transition, where, due to the reduction of the macromolecular mobility, the polymer structure is no more able to attain an equilibrium rubbery state. Then, the higher is the cooling rate, the higher is the experimentally observed glass transition temperature36-38. In summary, the apparent solubility isotherm retrieved from a single isothermal dynamic desorption test displays two distinct values for the solubility coefficient (slope of the apparent solubility isotherm in Figure 8) for equilibrium and non-equilibrium branches, the two branches merging at a (glass) transition zone. Indeed, linear dependences of solute content from solute pressure can be distinctly recognized above and below the transition 19 ACS Paragon Plus Environment


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region, with clearly higher sensitivity for the upper branch with respect to the lower one. As already mentioned, the location of the transition, in terms of Pg value, has been evaluated by following a calculation procedure reported in Supporting Information. Different values of glass transition pressure, Pg, retrieved at different values of the rate of pressure decrease, are reported in Table 1 along with the value of ω at which the glass transition occurs at 40°C, ωg.

Pressure decrease rate

0.16

0.04

0.01

0.004

28.7

28.3

27.7

26.5

0.113

0.101

0.099

0.099

[mbar/min] Pg [mbar] ωg

Table 1. Values of glass transition pressure and of mass fraction of toluene at the transition, obtained at 40°C and different pressure decreasing ratio in dynamic desorption tests.

Together with solute concentration, characteristic time for relaxation also depends on temperature and results for departure from equilibrium for apparent solubility from dynamic desorption experiments are expected to considerably change when tests are run at different temperatures. Thermodynamic equilibrium solubility isotherms as a function of penetrant pressure are also expected to be different at different temperature, however the equilibrium solute content within the polymer at assigned solute activity typically shows rather limited sensitivity to temperature, and toluene–PS system is not an exception in this regard.39 For this reason, when comparing dynamic desorption results at different temperatures, it is useful to refer to plots for apparent solubility as function of solute activity, as illustrated in Figure 9, being the toluene activity calculated as the ratio between actual pressure in the experiment and toluene vapor pressure at the corresponding temperature. Data are reported in Figure 9 for apparent solubility in isothermal dynamic desorption runs performed in a temperature range from 20 to 90°C, obtained at the same depressurization rate of 0.16 mbar/min. It can be observed that, while at high toluene activity, very similar solute content are indeed exhibited by dynamic experiments run at different temperature, rather diverse apparent solubility are evidenced in desorption runs in the low activity region. More specifically, the positive departure of apparent solubility from common equilibrium solubility trend is limited to lower activity range for the case of higher temperature experiments. This feature can be easily explained considering the time associated to change in boundary conditions is the same for all experiments in focus, while characteristic time for relaxation as function of toluene content significantly varies with temperature and the same value of the latter is reached at lower solute contents for the case of higher temperatures. These data were analyzed to determine the value of Pg at each temperature, by adopting the same mathematical 20 ACS Paragon Plus Environment

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procedure used in the case of isothermal tests performed at 40°C (see Supporting Information for details). The values of Pg determined for each isothermal dynamic desorption test, all at a depressurization rate of 0.16 mbar/min, are reported in Table 2 along with the corresponding toluene mass fraction, ωg.

Figure 9. Experimental results of isothermal dynamic desorption experiments performed at different temperatures. Values of toluene mass fraction within the polymer mixture reported as a

function of solvent activity evaluated as the ratio between toluene pressure and the vapor pressure at each temperature.

Temperature [ºC] 20 30 40 50 60 70 85

Pg[mbar] 15.0 ±2 22.0 ±2 30.1 ±2 35.7 ±2 40.2 ±2 39.1 ±2 30.55 ±2

ωg 0.159 0.135 0.113 0.081 0.060 0.039 0.018

Table 2. Values of Pg and corresponding ωg determined from dynamic desorption tests carried out at different temperatures and at a deoressurization rate of 0.16 mbar/min.

Data in Table 2 show that, differently from solute concentration, glass transition pressure in PS-toluene system changes with temperature in a non-monotonous way, a maximum being shown around 60°C. This behavior is the result of combined effects of temperature and pressure on sorption and on associated plasticization effect. Based on the above evidence, it can be anticipated that at toluene pressures below the above mentioned maximum value 21 ACS Paragon Plus Environment


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a finite temperature range exists in which the system is in glassy state, while rubbery conditions are recognized both below a lower limit temperature or above an upper one. This also means that when exposing a PS sample at a fixed toluene pressure, a rubbery to glassy transition could occur either lowering the temperature below the upper limit or raising it above the lower limit of the corresponding temperature range in which glassy state can be observed. The latter condition is referred to as “retrograde vitrification”20,31 and it is the result of the reduction in solute concentration/plasticization effect occurring when the temperature is increased at constant solute pressure. Opposite to what happens in high temperature/low concentration range, solute induced plasticization prevails on temperature effect per se in the low temperature/high concentration range. A confirmation of this behavior has been looked for in this work by performing isobaric dynamic sorption/desorption processes, as described in next section.

3.2.2 Dynamic isobaric tests In addition to the isothermal experiments described in the previous section, one dynamic isobaric test was performed maintaining a constant pressure of 36 mbar, by first increasing the temperature from 30°C to 92°C, at a constant rate of temperature change, , of 2°C/hour, and then decreasing it back to 30°C, at the same absolute rate. The apparent solubility data obtained are reported in Figure 10. As it refers to experimental data at lower and higher temperatures in the range explored, sorption and desorption runs show similar solubility coefficient, consistent with the interpretation that the measured solute contents in those regions represent different part of the same equilibrium solubility isobaric curve. At intermediate temperature, on the other hand, higher solute content is shown for the case desorption (heating) runs with respect to that of sorption (cooling), thus confirming the existence of a non-equilibrium region at the assigned toluene pressure. The observed behavior can be interpreted as follows. At the starting conditions (low temperature), the PS-toluene mixture is in a rubbery state then, as temperature is increased a rubber-to-glass transition occurs, promoted by the decrease in solubility accompanying heating of the system. Further increase in temperature promotes a glass-to-rubber transition. When temperature is decreased, the mixture again displays a rubber-to-glass transition and further cooling then promotes again a glass-to-rubber transition. Different from the case of isothermal paths, the non-equilibrium glassy region along isobaric lines is confined and its limited extension does not allow for a characteristic value of glassy solubility coefficient to be retrieved. Under these circumstances, the procedure used to identify glass transition point after experimental data from isothermal experiments (see Supporting Information) cannot be directly extended to the case of isobaric test. To circumvent this difficulty, a different approach has been adopted in this case to estimate the two rubber-to-glass transition points (one along the heating path, the other along the cooling path), as detailed in what follows. An equilibrium thermodynamic approach based on a non-random compressible lattice fluid theory (Non Random 22 ACS Paragon Plus Environment

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Hydrogen Bonding, NRHB), developed by Panayiotou et al.40,41, was used to model the phase equilibrium between the polymer-toluene mixture in the rubbery state and the toluene vapor phase. It is important to note here that, since the system at hand is not endowed with specific self- and cross- hydrogen bonding (HB) interactions, the terms of NRHB model associated with formation HBs have been consistently set to be equal to zero. An excellent fitting was obtained considering only sorption (desorption) data in the lowest and highest temperature regions, where the polymer mixture is expected to be in a rubbery state (see continuous red line in figure 10). Small but significant deviations are instead observed for experimental data from model prediction in the intermediate temperature region, where the system is expected to be in the glassy state. In fact, NRHB model has been developed for equilibrium rubbery system and it is not expected to properly describe the thermodynamics of a system at glassy state. The rubber-to-glass transition has been then assumed to occur at that point in isobaric curve for solute content where the difference between experimental data and equilibrium results obtained by using the NRHB model becomes significant. The exact location of this point has been taken as that where the departure becomes higher than 1% of the value of the experimental mass ratio. Obviously, this procedure is affected by a higher error when compared to the case of the procedure adopted for isothermal tests.

. Figure 10. Isobaric experiment at a toluene pressure of 36 mbar carried out between TMIN = 30°C and TMAX = 92°C. Red continuous line represents NRHB fitting of data in the rubbery regions. Dashed-dotted blu lines represent experimental data obtained with the CAHN D-200 microbalance.



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In Table 3, values are reported for temperature, Tg, and toluene mass fraction, ωg, estimated at rubber-to-glass transition points as evaluated from isobaric test. As anticipated, two different rubber-to-glass transition points have been identified, along cooling and heating paths of the experiment, corresponding to higher and lower temperature limits for the glassy region at the assigned toluene pressure. Interestingly, the recovery of rubbery condition from the glassy state (glass-to rubber transitions) for both cooling and heating runs in isobaric experiments (see Figure 10) occurs at temperatures well beyond the transition points indicated in Table 3, parallel to what shown for the same kind of recovery by isothermal experiments in sorption runs with respect to transition point retrieved after data form desorption runs.

Heating path Cooling path

Tg [K] 319 ±8 343 ±8

ωg 0.105 0.036

Table 3. Values of Tg and corresponding toluene mass fraction determined from dynamic isobaric tests carried out at 36 mbar in the 30-92 °C range.

3.2.3 Dynamic isoactivity tests A third kind of dynamic experiments was performed in this work for the PS-toluene system, in which temperature was decreased at a prescribed rate, while toluene activity, a, was kept at an approximately constant value, by properly changing its pressure in vapor phase. In details, different isoactivity tests were performed by decreasing system temperature at the rate of 2°C/hour and concurrently changing the pressure to maintain a constant value of the ratio between actual pressure in gaseous phase and vapor pressure of toluene (p/p0). Indeed, as discussed in the Supporting Information, the latter condition corresponds to a quite constant value of the toluene vapor activity, approximately equal to the ratio p/p0. Results for three different isoactivity tests corresponding to the case a = 0.11, 0.20 and 0.30 were collected in this work. Figure 11 reports the results obtained in the case of toluene activity equal to 0.30. Similarly to the case of isothermal tests, in isoactivity experiments there is evidence of a clear change for the sensitivity of apparent solubility to the potential variable modulated in the test, as the latter is moved from higher to lower values. Indeed, the solubility coefficient in this case, dΩ/dT, increases as temperature decreases in a relatively narrow temperature interval (see arrows in Figure 11) from negligible value registered at high temperature to a maximum value that appears to be substantially constant in the lower temperature range. The results are consistent with the assumption of one rubber-to-glass transition in the temperature range explored within the isoactivity experiment performed. In view of the features exhibited, results from these tests can be elaborated similarly to the case of isothermal experiments (see Supporting Information for details) to identify glass transition value for temperature (pressure) and solute 24 ACS Paragon Plus Environment

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content (see arrows in Figure 11). Results from the mentioned analysis after data retrieved in isoactivity experiments are reported in Table 4, in terms of temperature, pressure, and toluene mass fraction at which rubber-to-glass transition occurs.

Figure 11. Experimental results of dynamic isoactivity tests performed at a constant toluene activity equal to 0.3. Evolution of toluene mass ratio as a function of temperature (left) and of pressure (right).

Toluene vapor activity 0.11 0.20 0.30

Tg [K]

Pg [mbar]

ωg

349.0 ±4 337.9 ±4 319.0 ±4

37.1 ±2 40.1 ±2 33.1 ±2

0.029 0.054 0.083

Table 4. Values of Tg, Pg and corresponding toluene mass fraction determined from dynamic isoactivity tests.

3.3 Theoretical interpretation of observed discontinuities and state diagram The entire set of data of rubber-to-glass transition points for manipulated process variables (T and p), as derived from the analysis of isothermal, isobaric and isoactivity tests, is shown in the state diagram pictured in Figure 12. It is important to stress here that points represented in the plot have been identified based only on desorption (isothermal tests and isobaric heating test) or on sorption (isobaric cooling test and isoactivity tests) processes for which a continuous variation of process variable was imposed in order to induce a state change from equilibrium (rubbery) to non-equilibrium (glassy) conditions. Data have been retrieved from the analysis of results described above, essentially counting on the evidence of changes in the solubility coefficient in each experiment, defined as sensitivity of solute mass ratio to the manipulated process variable. Mentioned discontinuities for solubility 25 ACS Paragon Plus Environment


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coefficient are indeed consistent with the interpretation of transition in focus as a thermodynamic second order phase changes according to definition given by Ehrenfest.33 Under the hypothesis of the existence of an underlying phase change of this kind, the occurrence of discontinuity in the slope of the plot of toluene mass ratio as a function of manipulated variable in dynamic sorption/desorption experiments, can be justified on the basis of thermodynamics arguments reported De Bruyn Ouboter and Beenakker.42 In fact, it is demonstrated there that ‘it appears to be a general property that the first order equilibrium curves for liquid binary mixtures show a singularity at the junction with the second order lambda curve as can be seen on the basis of pure thermodynamic consideration’. In particular, these authors derived mathematical expressions highlighting that there is a discontinuity in the slope of the first order equilibrium curve (boiling curve), i.e. in the values of ⁄ and ⁄ ,where Xi is the mole fraction of component ‘i’, at the junction with the second order line. In the case of the system under investigation, the liquid mixture displaying the II order transition corresponds to the polymer mixture phase in equilibrium with the external vapor phase. It has been shown in previous sections that the exact location of transition point slightly depends on the rate at which process variable is changed in the test and we should talk in terms of transition region rather than boundary. It is explicitly noted here that the transitions observed experimentally need to be interpreted as the experimentally accessible, kinetically affected, manifestations of the underlying II order thermodynamic transitions. In the Supporting Information we provide some calculations, based on the approach proposed by De Bruyn Ouboter and Beenakker42, specifically focused on our experimental results, to further prove that the observed singularities are indeed consistent with the presence of a second order transition, most likely of glassy nature as meant in established literature. Data for low-pressure glass transition temperature of dry polystyrene, corresponding to the case of null value of toluene pressure, has been added in Figure 12 to results from dynamic sorption/desorption experiments to represent the whole glassy region in the same diagram. It is noted (Figure 12) that results from isobaric and isoactivity experiments are qualitatively consistent with those retrieved from isothermal experiments, although a non-negligible quantitative discrepancy is evident, that is likely due to the different procedure used to retrieve the transition points from isobaric experiment data as compared to isothermal and isoactivity tests. Most notably, plot in Figure 12 confirms that the PS-toluene system is characterized by the so-called “type IV” behavior20,31 and retrograde vitrification is apparent for toluene pressure and system temperature lower than 40 mbar and 60°C, respectively. The diagram defines in detail the boundary of glassy region around maximum toluene pressure consistent with glassy conditions for polystyrene and indicates that interval of toluene pressure for retrograde vitrification extends below 15 mbar. Furthermore, the state diagram in Figure 12 illustrates number and nature of transitions the system experiences in different kind of experiments. Typical paths for isothermal, isobaric and isoactivity dynamic experiments performed are schematized in Figure 13 for the specific case of a system displaying type IV behavior. 26 ACS Paragon Plus Environment

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It should be finally clarified that recovery of rubbery condition from glassy states through the same kind of mass transport process (e.g, isothermal and isobaric sorption tests in this work) exhibits a different behavior - since it depends on the history of the process in non-equilibrium state - for which the non-equilibrium conditions can be observed for pairs of process variables outside the glassy domain in Figure 12 and a transition point cannot be actually identified in the same term as for rubber-to-glass transition.

Figure 12. Plot of rubber-to-glass transition points as determined from isothermal, isobaric and isoactivity experiments. For isothermal experiments results refer to tests performed at a pressure decrease rate equal to 0.16 mbar/min. For isobaric and isoactivity experiments results refer to experiments performed at rate of temperature change equal to 2 °C/hour. Dotted curve is a guide to the eye.



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Figure 13. Schematic plot illustrating the experimental paths followed in typical dynamic isothermal, isobaric and isoactivity sorption/desorptiontests, for the case of a polymerpenetrant system displaying a ‘type IV’ behavior.


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4. Conclusions An experimental procedure to characterize relaxation phenomena in polymeric systems has been considered extending to vapor sorption processes scanning techniques typically applied to calorimetric analysis in the same systems. The only precedent of the same kind of measurement is provided by Doumenc et al.18 for toluene induced aging of PMMA, although similar scanning experiments for solute fugacity were used by Alcoutlabi et al. 43 to monitor physical aging of resins by measuring volume change in the system. The technique has been here used for the PS-toluene system to highlight the effect of scanning rate of the controlled variable and examples have been provided following three different kinds of experiment, differing for the type of manipulated variable. This experimental procedure provides valuable information for the solvent induced polymer relaxation that, combined with thermodynamic model for non-equilibrium solubility and diffusivity, can ultimately results in a modelling tool of several non-Fickian features exhibited by sorption kinetics in glassy polymers, that is left to future work. A detailed analysis has been performed on the glass transition in PS-toluene system, in large temperature and activity ranges, based on the results from dynamical toluene sorption/desorption experiments performed by modifying in a controlled way presuure and/or temperature in isothermal, isobaric and isoactivity tests. In each case, discontinuities have been detected in the first derivative of the curve reporting the mass ratio of toluene within the polymer as a function of temperature and/or pressure. These discontinuities have been ascribed to the occurrence of rubber-to-glass transition of the polymer-solute system and have been used to construct a contour plot defining the regions, in the temperature-pressure space, where the PS-toluene mixture is a glassy or rubbery state. Evidence of ‘retrograde vitrification’ was found, i.e. the system is capable to undergo a transition from rubbery to glassy state by increasing the temperature at constant pressure. To the authors knowledge, this is the first time that such a phenomenon is reported for the PS-toluene system. The experimental results have been rationalized interpreting the glass transition as a II order thermodynamic phase transition, whose experimental evidence is significantly affected by the kinetics of polymer relaxation.



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5. Supporting Information Supporting Information is available containing details on experimental apparatuses, on the procedure adopted for calculating the location of discontinuities and on the thermodynamic interpretation of the discontinuity occurring at the transition.


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Retrograde vitrification in polystyrene/toluene system 254x190mm (96 x 96 DPI)

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