2.5 Selection of compatible material combinations
3.3.2 Neat polymers
Isothermal crystallization
For isothermal measurements, B3S samples were fused at 250 °C and then cooled to several holding temperatures between 201 and 208 °C. Three samples were tested per holding temperature. The temperature was then held constant until the heat flow dropped to zero. C2000 samples were fused at 310 °C and cooled to hold-ing temperatures between 228 to 235 °C. The selected temperatures are within a narrow range. At lower temperatures the polymers started to crystallize already during cooling and disable the analysis of the isothermal crystallization behavior.
All measurements were found valid when the heat flow was 0 before the crystal-lization process started. Based on the DSC measurements, the relative degree of crystallinity X(t) was calculated according to the following equation:
X(t) =
where dH/dt expresses the rate of heat evolution, ΔHc(t) represents the heat flow produced at time t; and ΔHc,∞(t) is the total amount of heat created until the end of the isothermal crystallization process. This ratio can be also expressed as the crystallized mass fraction Wc.
The development of the relative degree of crystallinityX(t) is depicted in Figure 3-5 for neat B3S and C2000. Comparing both polymers, the maximumX(t) is obtained
0 500 1000 1500 2000 2500 0
Figure 3-5 Development of the relative degree of crystallinityX(t) for a) neat B3S and b) C2000.
more rapidly for C2000 than for B3S.X(t) determined by DSC represents the crys-tallized mass fraction (Wc). This data is to be converted into volume crystallinity (Vc) as follows to determine isothermal crystallization kinetic parameters:
Vc =
ρc and ρa refer to the density of the crystalline and amorphous polymer fractions.
For the analysis according to Avrami, Equation 3-1 is solved:
log−ln[1−Vc(t)]=nlogt+ logk. (3-9) Plotting log−ln[1−Vc(t)]against logtyields the Avrami plot with straight lines linearly fitted by using the least square method. The Avrami index n is obtained from the slope of the linear fit whereas the crystallization rate k is determined experimentally (kexp) from the intercept (Figure 3-6) for the linear fit. k can also be calculated by the following equation [97], based on the half-crystallization time t1/2:
kcalc = ln2
(t1/2)n. (3-10)
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
versus logt for the isothermal crystallization of a) B3S withρa = 1.08 g/cm3andρc = 1.24 g/cm3b) C2000, based onWcaccording to [98].
Table 3-2 summarizes the determined Avrami exponent n, the crystallization rate k, along with the time at maximum heat flow tmax, the half-crystallization time t1/2 and the crystallinity at tmax for B3S. The correlation coefficient of all linear fits for the Avrami plots (R2) was R2 > 0.99. The isotherms cannot be
super-Table 3-2Kinetic parameters for the isothermal crystallization of neat B3S.
Tc [ °C] 201 202 203 205 206 208 imposed by shifts along the logarithmic time axis. Nucleation mode is therefore thermal and indicates heterogeneous or homogeneous nucleation. Considering the calculated Avrami exponents, the time-dependance of the crystallization process is indicated by the decimal places (nn) and yield values smaller than 0.5 for four tem-peratures that refer to heterogeneous nucleation. With exception of nn at 205 °C and 206 °C, the results for nn indicate a heterogeneous nucleation mode. As B3S is pigmented with carbon black it is expected that the nucleation mode is heteroge-neous. The integerndyielded 2 for all measurements and refers to the formation of fibrils according to thermal nucleation. The crystallization rate constantkexp yields good agreement with kcalc and decreases with decreasing undercooling ΔT.
For neat C2000, the results from the analysis according to Avrami are summarized in Table 3-3. Interpretation of the yielded Avrami exponents for C2000 concludes
Table 3-3Kinetic parameters for the isothermal crystallization of neat C2000.
Tc [ °C] 228 229 230 232 233 235
n [-] 2.24 2.29 2.11 2.17 2.14 2.14
kexp[min−n] 0.71 0.69 0.41 0.25 0.14 0.05 kcalc[min−n] 0.60 0.58 0.41 0.24 0.13 0.05
tmax [min] 0.87 0.92 1.09 1.41 1.83 2.79
t1/2 [min] 1.07 1.08 1.29 1.63 2.17 3.48
X(tmax) [%] 23.35 22.16 21.82 19.34 16.89 16.38
athermal nucleation due to isotherms (Figure 3-6) that can be superimposed by shifting along the logarithmic time axis. Hence, the nucleation mode is heteroge-neous, indicated by athermal nucleation and decimal places for nd between 0.1 and 0.3, with growth of lamellae (nn = 2). In contrast to B3S, C2000 yields higher values for crystallization rate k. On the one hand this is contradictory to results from PA6T where terephthalic acid is known to inhibit crystallization [75]. How-ever, C2000 consist also of other monomers (indicated by affix ‘X’ in PA10T/X), not further specified by the manufacturer, that can act as a foreign nucleus. The strong heterogeneous nucleation behavior implied by the superimposable isotherms confirm this assumption. In this case, the crystallization-inhibiting nature of the terephthalic acid may be overruled by the dominating aliphatic regions with a considerable number of monomers acting as nucleating agent.
Non-isothermal crystallization
The non-isothermal measurements on neat polymers were conducted at the cooling rates 2, 5, 10, 20, 35 and 50 K/min. Three samples per cooling rate were investi-gated. The relative degree of crystallinity X(T) as a function of temperature was calculated as follows:
X(T) =
T
0 (dHc/dT)dT
∞
0 (dHc/dT)dT = ΔHc(T)
ΔHc,∞(T), (3-11) where ΔHc(T) is the enthalpy of crystallization at a certain temperature divided by ΔHc,∞(T), the enthalpy of crystallization when the crystallization process is completed. The mean relative degree of crystallinity X(T) is depicted in Figure 3-7 for neat B3S and C2000.
100 120 140 160 180 200 220
120 140 160 180 200 220 240 0
Figure 3-7 Development of the relative degree of crystallinity X(T) for a) neat B3S and b) C2000.
The analysis of the non-isothermal measurements was conducted according to the Ozawa method by solving Equation 3-3:
log−ln[1−X(T)]= logK(T)−mlogC. (3-12) Plotting log−ln[1−X(T)] against log C shall yield a set of straight lines at constant temperatures. The Ozawa exponent −m is obtained from the slope of the straight lines and the cooling function K(T) from the intercept of the initially linear region with the y-axis. Figure 3-8 shows the Ozawa plot for neat B3S and neat C2000 at constant temperatures. For the investigated cooling rates, the Ozawa
0.0 0.5 1.0 1.5 2.0
plots yield no straight lines at the majority and disallow the determination of m and K(T). This is a common problem in the analysis of non-isothermal crystal-lization data caused by the limited applicability of the Ozawa theory [99]. Ozawa
made the assumption that the dependance of the nucleation rate on the tempera-ture is not affected by the cooling rate. Thus, the analysis according to Ozawa is restricted to a narrow range of cooling rates leading to crystallization in resembling temperature ranges [87]. The Nakamura theory offers another possibility to analyze non-isothermal crystallization data and considers non-isothermal measurements as consecutive isothermal processes. This yields good results only for very slow cool-ing rates when the nucleation is unaffected by the coolcool-ing rate. Several authors introduced new approaches to handle non-isothermal crystallization data. Liu et al. [100] combined the Avrami (Eq. 3-1) and Ozawa equation (Eq. 3-3) to form a new kinetic equation:
logk+nlogt= logK(T)−mlogC (3-13) This method was also investigated for the present non-isothermal results but led to unsatisfactory results. Although this method is used by many researchers, the theo-ries according to Avrami and Ozawa require different assumptions: Avrami assumes the growth rate and Ozawa the cooling rate to be constant. Hence, combining the Avrami and Ozawa equation into one equation, possesses no theoretical substantia-tion. This also applies to other methods developed by Jeziorny or Kissinger yielding results without theoretically proven physical meaning [87].
Within this work, the non-isothermal measurements obtained from DSC are not analyzed further according to another method as the current procedures may be too simplified to properly account for complex crystallization behaviors. Never-theless, the results from the non-isothermal DSC data relating ΔHc, X(T), the peak temperature Tp during crystallization at the maximum rate of heat flow to different cooling rates (presented in Table 3-4) generates an understanding of the non-isothermal crystallization behavior.
Table 3-4 Effect of cooling rate on crystallization of neat B3S.
C [ °C/min] Tp [°C] ΔHc[J/g]
2 200.0 77.90±2.22
5 195.7 78.19±0.37
10 191.7 75.90±0.85
20 186.0 71.73±1.02
35 181.9 63.36±0.61
50 174.8 62.79±1.84
Specifically, Tp possesses practical importance since it refers to the maximum rate of crystallization as a function of the cooling rate [76]. This enables a better control of the final polymer properties during processing. The obtained values for ΔHc are
within the same range as reported by Fornes and Paul [86] for low to medium molecular weight nylons and found by Tjong and Bao [101].
Table 3-5 shows ΔHc,X(T) and the peak temperatureTp during crystallization at the maximum rate of heat flow in dependance of different cooling rates for C2000.
Table 3-5Effect of cooling rate on crystallization of neat C2000.
C [ °C/min] Tp [°C] ΔHc[J/g]
2 232.0 42.53±3.61
5 226.3 45.54±1.27
10 218.6 44.87±0.54
20 207.1 46.91±1.51
35 194.2 43.59±1.54
50 183.9 25.95±6.04
Figure 3-9 compares the enthalpy of crystallization ΔHcas a function of the cooling rate for B3S and C2000. The crystallization process proceeds most rapidly at a cooling rate of 2 °C/min for B3S. The maximum ΔHc for C2000 is obtained at a cooling rate of 20 °C/min.
0 10 20 30 40 50
20 30 40 50 60 70 80
90 B3S
Cubic fit C2000 Cubic fit
EnthalpyofCrystallizationΔHc[J/g]
Cooling rate [°C/min]
Figure 3-9 Plots of cooling rate versus enthalpy of crystallization ΔHc for B3S and C2000.