Physical aging and its effects on the dynamics

in this work and will be discussed in detail later in this thesis.

2.3 Physical aging and its effects on the dynamics

Physical aging is a structural relaxation process in the non-equilibrium glassy state below T_g towards the equilibrium liquid state. This process incorporates significant changes in prac-tically all physical quantities like volume, enthalpy, entropy etc. and influences mechanical properties like modulus, damping or creep and stress relaxation rates. In last decades, this phenomenon is extensively studied and reviewed by many authors. [59, 110–114]

Volume

Temperature

Glassy State

Liquid

T

Equilibrium Line t_e

10 t_e

100 t_e 10 t_e

t_e

1000 t_e

T

T

Figure 2.3: Schematic volume vs temperature plot showing the effects of isothermal physical aging under isobaric conditions. Teand teare the annealing temperatures and times respectively.

A classical method to study physical aging is to investigate tiny changes in volume or den-sity during isothermal annealing for long times below Tg. Physical aging effects could be visualized in a volume vs. temperature plot as shown in figure 2.3. Consider a sample which is cooled at a rate Q and falls out of the equilibrium at temperature Tg where it becomes glassy. If the sample is then annealed below Tg, at an annealing temperature Tefor a certain

time t_e, volume will decrease to reach its equilibrium value. Enthalpy and entropy will also follow similar trends. Due to densification, new metastable states are formed as long as the equilibrium density is not reached.

Figure 2.4: Normalized volume as a function of aging time for different temperatures Teafter the quenches from 210^◦C to different aging temperatures as given in the legend for polyetherimide (Tg=207.5^◦C). Taken from [115]

Experimentally, many authors have studied physical aging in amorphous polymeric glasses using volume dilatometry. [59, 111, 115, 116] Data from isothermal physical aging experi-ments on polyetherimide are shown as an example in Figure 2.4. [115] Normalized volume (δ_v^∗ = [(vt − v∞)/(vo − v∞)], where v(t) is the time dependent specific volume, vo the initial specific volume at the aging temperature and v∞ is the specific volume at equilib-rium), decreases linearly with logte until the equilibrium is approached for long annealing times and δ_v^∗becomes nearly zero. The densification is faster below T_g since the mobility of the glass is higher at that temperatures. Equilibration should finalize on time scales which are proportional to the equilibrium α relaxation time τ_α at T_e. Otherwise, the driving force V_glass − V_liquid in Figure 2.3 is larger far below T_g and the total changes due to physical aging are more pronounced. Many more complicated aging experiments are performed and different models have been proposed to understand the linear range where δ^∗_v ∝ logte. A final molecular understanding is still missing like in case of glass transition. Details will not be discussed here since density is not measured for our samples and quantitative analysis of aging effects can not be done for the nanophase separated side chain polymers studied in this

2.3 Physical aging and its effects on the dynamics 17

work. Readers are referred to the literature. [110, 111]

Figure 2.5: Tensile creep compliance vs creep time for polyvinyl chloride (PVC) (Tg= 80^◦C). Samples were quenched from 90^◦C to 20^◦C and aged at 20^◦C for .03 to 1000 days. After 1000 days sample was re-quenched to 20^◦C and measured after 1 day of annealing at 20^◦C. Taken from [59, 114]

Apart from dilatometry, linear response techniques can also be used to detect physical ag-ing since the α relaxation is strongly influenced by non-equilibrium below Tg. In particular, physical aging significantly changes the mechanical properties. This can be systematically studied by linear response methods like creep etc. (see section 4.1.2) This approach was pioneered by Struik. [59] Struik measured the creep compliance for isothermally aged sam-ples after different annealing times from 0.03 days to 1000 days. Representative results for polyvinyl chloride are presented in Figure 2.5 showing small-strain creep compliance vs creep time after different aging times t_e. It is clearly seen that creep curves with the in-creasing annealing time at T_e = 20^◦C shifts systematically to longer creep times without significant change of the curve shape. This equilibration process continues even after ex-tremely long annealing times of 3 years. This can be explained on the basis of a decrease in the free volume (Vf) as well as configurational entropy (Sc) resulting in longer α relaxation times. Obviously, the shape of the creep curve (non-exponential behavior) and Kohlrausch parameter βKW W remains similar for all the aging times and hence an empirical formula has been proposed to quantify changes due to physical aging in relaxation curves which is

logτ = logτ_o+ µlogt_e (2.10)

where τ is the average relaxation time after the isothermal annealing step, teis the isothermal annealing time, τ0 is the average relaxation time before annealing and µ is the Struik factor

describing the shift. It can be seen in Figure 2.5 that if master curve is constructed accord-ing to this empirical equation all the curve collapse on the curve after 1000 days of agaccord-ing.

However, it should be noted that µ is system specific and varies in the range 0.8 ≤ µ ≤ 1.

Note that, reversibility of the physical aging phenomenon is also shown in Figure 2.5. The aged PVC sample was reheated to 90^◦C above Tg and annealed at room temperature for 1 day. Crossed points is the creep compliance obtained afterwards which is in good agreement with the initially obtained result after 1 day of physical aging.

Note that localized motions seen as Johari-Goldstein β relaxation in glasses are only weakly influenced by physical aging. Reduction of the β intensity and small frequency shifts have been reported. [117]

Figure 2.6: DSC heating scans for polymethylmethacrylate (Tg ≈ 105^◦C) performed after annealing at Te= 90^◦C for different annealing times indicated. The heating rate is 10K/min. Taken from [111]

Another large number of physical aging experiments often called structural relaxation exper-iments have been performed using calorimetry. Aim is to follow up the decrease of enthalpy and entropy as the system tends to achieve equilibrium during physical aging below T_g. Such effects could be probed by conventional differential scanning calorimetry. The decrease of enthalpy during annealing at Tehas to recover and shows up as an endotherm following the glass transition step in subsequent DSC heating scans, often stated as structural relaxation or enthalpy relaxation peak. Figure 2.6 data for polymethylmethacrylate as a typical exam-ple. [111] Heating scan following the annealing at Te = 90^◦C for varied annealing times are