The field of enthalpy relaxation is reviewed. Current phenomenologies for dealing with the non-linear and non-exponential character of enthalpy relaxation are presented, and their successes and shortcomings are discussed. Qualitative experimental data and quantitative parameterizations are summarized, and some directions for future research are suggested.

Enthalpy relaxation and recovery in amorphous materials

A method was developed to determine the kinetic parameters controlling structural relaxation in the glass transition region from data acquired during continuous heating or cooling. The nonexponential character of the relaxation is accounted for by assuming an equilibrium isothermal relaxation function of the form exp [−(t/Toe)s], where Toe is a relaxation time and 0<β1. The data are linearized using the method of Narayanaswamy, and the continuous temperature variation during heating or cooling is dealt with by invoking the superposition principle. The analysis yields the kinetic parameters A, the relaxation-time preexponential term; Δh★, the relaxation-time activation enthalpy; x, a term describing the relative effects of temperature and structure on the rate of relaxation; and β. The method was applied to analysis of the variation of the enthalpy of vitreous B2O3 during rate heating through the transition region following rate cooling through the same region at a variety of rates.

Analysis of Structural Relaxation in Glass Using Rate Heating Data

Der Einflus einer Temperung auf den Zustand von technischem Polyvinylchlorid wird zunachst durch kalorimetrische Messungen untersucht. Eine Temperung unterhalb der Glastemperatur fuhrt infolge von Enthalpie-Relaxation zu Zustandsanderungen, die nicht eine Erhohung der Ordnung der amorphen Bereiche im Sinne zunehmender Kristallinitat bedeuten, sondern durch eine Verringerung der Leerstellen-Konzentration bedingt sind. Die Enthalpie-Relaxation ausert sich bei kalorimetrischen Untersuchungen darin, das je nach dem Verhaltnis von Aufheiz- und Abkuhlgeschwindigkeit der cp-Stufe bei der Glastemperatur ein endothermes Maximum („Uberhitzungs-Maximum”) unmittelbar uberlagert ist oder das bei scharf abgeschreckten Proben am unteren Ende des Glasubergangs-Bereiches der Stufe ein Maximum oder Minimum vorgelagert ist. Die Uberhitzungsenthalpie, die ein quantitatives Mas fur die bei der Temperung abgelaufenen Zustandsanderungen ist, ist stark von der angewandten Aufheizgeschwindigkeit abhangig. Der Glas-Ubergang beginnt bei um so tieferen Temperaturen, je scharfer Polyvinylchlorid von oberhalb der Glastemperatur abgeschreckt wird. Den gleichen Befund erhalt man aus dynamisch-mechanischen Untersuchungen.



Das untersuchte Polyvinylchlorid ist partiell kristallin. Die beim langsamen Abkuhlen aus der Schmelze gebildeten Kristalle schmelzen beim Aufheizen im Temperaturbereich zwischen 115 und 205°C. Die Schmelzwarme betragt ca. 2 cal/g. Durch scharfes Abschrecken last sich die Kristallinitat verringern. Beim nachfolgenden Aufheizen findet in diesem Fall eine Nachkristallisation statt. Eine nachtragliche Temperung oberhalb der Glastemperatur fuhrt auch bei langsam aus der Schmelze kristallisiertem Polyvinylchlorid zu einer Nachkristallisation. Die bei dieser Nachkristallisation gebildeten Kristalle ergeben beim Aufheizen ein endothermes Schmelzmaximum, dessen Flache (Schmelzwarme) von der Heizgeschwindigkeit unabhangig ist und das immer oberhalb der Glastemperatur-Stufe, und zwar ca. 25°C oberhalb der jeweiligen Tempertemperatur (Temperzeit 1–2 Stdn.), liegt. Es steht in keinem ursachlichen Zusammenhang mit dem durch Temperung unterhalb der Glastemperatur hervorgerufenen Uberhitzungs-Maximum.



Die Diffusion von Flussigkeiten und die Permeation von Gasen hangen stark von der thermischen Vorgeschichte ab. Durch Temperung sowohl oberhalb als auch unterhalb der Glastemperatur steigt die im Zugversuch ermittelte Streck-Spannung an, und die Bruchdehnung fallt stark ab. Die oberhalb und unterhalb der Glastemperatur erzielten Veranderungen beruhen jedoch auf zwei verschiedenen Ursachen.



The influence of annealing upon the physical state of polyvinylchloride is investigated by calorimetric measurements. As a consequence of enthalpy relaxation an annealing below the glass transition temperature results in changes of state, which can not be interpreted by an increase of crystallinity or order, but by a decrease of the hole concentration of the amorphous regions. Depending upon the relation between heating and cooling rate either an endothermal peak („super-heating peak”) is superimposed on the cp-step at the glass transition temperature, or a peak or minimum is found below Tg. The super-heating enthalpy, which quantitatively measures the changes of state during annealing strongly depends on the heating rate. With increasing quenching rate the beginning of the glass transition range is shifted to lower temperature. The same result is obtained by dynamic mechanical measurements.



The polyvinylchloride samples are partially crystalline. The crystals, grown during cooling, melt within a broad temperature range between 115 and 205°C. The heat of fusion is about 2 cal/g. By sharp quenching the crystallinity is reduced. An exothermal crystallisation process is observed if the quenched samples are re-heated in the calorimeter. During annealing even the slowly cooled samples undergo a further crystallization, if the annealing is performed above the glass transition temperature. The melting of the crystals grown during annealing yields an endothermal melting peak above Tg and that about 25°C above the annealing temperature. The corresponding heat of fusion is independent of heating rate. There is no fundamental relation between the super-heating peaks and these melting peaks.



The diffusion of liquids and the permeation of gases are found t o be strongly dependent on thermal history. The relations between thermal history and the ultimate properties are discussed. Annealing above and below the glass transition results in increasing tensile yield strength and strongly decreasing ultimate elongation. The changes above and below Tg are due to different mechanisms.

Einfluß der thermischen vorgeschichte auf die eigenschaften von polyvinylchlorid

Glass transition and structural relaxation in semi-crystalline poly(ethylene terephthalate): a DSC study

Isothermal curing of a DGEBA epoxy resin with a hardener derived from phtalic anhydride was performed at temperatures T c between 30 and 130°C. The structural relaxation process was found to begin at higher curing times (t c ) when T c decreases because the vitrification of the systems starts later. Both the enthalpy recovery and the temperature of the endothermic peak increase with the annealing time, calculated as the difference between t c and the time in which vitrification occurs, and tend tohave a limiting value.

Vitrification and further structural relaxation in the isothermal curing of an epoxy resin

A difference has been observed in the DTA and DSC curves for the glass transition of both PVC homopolymer and acetate copolymer, depending on the rate of quenching or annealing below the glass transition temperature. The difference has the appearance of an endothermal peak added to the glass transition curve and is attributed to an alignment of stereoregular chain segments of adjacent polymer molecules. The lengths of chain segments are assumed to be so short that no x-ray evidence of crystallinity was obtained. The orientation process involved has an activation energy of 47.8 kcal./mole in the homopolymer and 43.6 kcal./mole in the copolymer. The measured rate of the process agrees with the principle of time–temperature superposition, the rates becoming equal for homopolymer and copolymer at equal temperatures below their glass transition temperatures.

DTA evidence for physical orientation (crystallinity) in PVC

Poly(vinyl chloride) displays a normal DSC or DTA curve for the glass transition when quenched from above its T g . However if cooled slowly or annealed near the glass-transition temperature, a peak appears on the DSC or DTA curve at the T g . In this article quantitative studies of the time and temperature effects on the production of this endothermal peak during the annealing of PVC homopolymer and an acetate copolymer are presented. This phenomenon conforms to the Williams, Landell, and Ferry equation for the relaxation of polymer chains, the rate of the peak formation becoming negligible at more than 50°C below T g . The energy difference between the quenched and annealed forms is small. For a PVC homopolymer annealed 2 hr at 68°C, which is T g -10°C, the difference is 0.25 cal/g. For a 13per thousand acetate copolymer of PVC similarly annealed, the difference is 0. 36 cal/g. The measured rates of the process give a calculated activation energy of 13-14 kcal/mole for PVC homopolymer and copolymer. This appearance of a peak on the T* lg*s curve for a polymer when annealed near the glass temperature appears to be a general phenomenon.

Quantitative study of the annealing of poly(vinyl chloride) near the glass transition

Correlations between processing characteristics and measurable physical properties were investigated for 16 commercial poly(vinyl chloride) polymers and acetate copolymers. Processing was evaluated with the Brabender Plasti-Corder. The glass transition temperature and dry blending procedure were examined by differential thermal analysis. The polymers included high and low molecular weight materials and examples of suspension, emulsion, and solution methods of polymerization. Effects due to the amount of plasticizer, stabilizers, and other additives were measured and are discussed.

Processing of poly(vinyl chloride) polymers correlated with composition, glass transition, and viscosity

Differential thermal analysis has been used to examine the process of dry blending of plasticizer and PVC. The rate of transformation of the glass transition from that of the polymer initially in the cold mix to the glass transition of the blend (blend Tg) has been examined at various temperatures from room temperature to above the polymer Tg. The dependence on temperature of this rate of transformation of the observed Tg is similar to the temperature dependence of the diffusion of plasticizer into PVC. It is concluded that diffusion of plasticizer into polymer particles is the rate-determining step in the dry blending of PVC. It also appears that a single mechanism of diffusion is involved both below and above the glass transition of the polymer.

Plasticizer diffusion as the rate-determining step in dry blending of poly(vinyl chloride)†

Consistent data are available from several authors to provide equations for the calculation of number-average and weight-average molecular weights of commercial poly(vinyl chloride) polymers from determinations of intrinsic viscosity in cyclohexanone solution at 30°C. Reasonable approximations of the molecular weights can be calculated quickly by use of the following simple equations: Mn = ½[η] × 105; Mw = 0.9[η] × 105.

Calculation of number‐average and weight‐average molecular weight of poly(vinyl chloride) polymers from intrinsic viscosity measurements

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