Maximum Crystal Growth Rate and Its Corresponding State in Polymeric Materials

Abstract

Abstract. The temperature dependence of crystal growth rate (G) shows a bell shape with the maximum growth rate G max. The activation energy for the molecular transport in G could be expressed in terms of equation of either Arrhenius or WLF. The G max showed remarkable molecular weight dependence. The plots of G/Gmax against T /Tcmax showed a single master curve without molecular weight dependence. The ratio of Go/Gmax gave a constant value for each polymer. Plots of ln(G/Gmax)/ ln(Go/Gmax) against T /Tcmax for various polymers showed the universal curve. The molecular weight dependence of Gmax was expressed as Gmax ∝ MW α , α was a constant but depending on the morphological features on the crystallization. The value of α was a function of the adsorption mechanism of polymer molecules on the crystal growth front and its diffusion mechanism. The ratio of T cmax/T o m was formulated. Tcmax was also correlated to many other thermodynamic transition temperatures. IntroductionAccording to a classical crystallization theory, a temperature dependence of linear crystal growth rate (G) can be expressed by two exponent factors, such as the molecular transport term (∆E) and the nucleation term (∆F ) [1][2][3]. These two terms have opposing temperature dependence thereby bring about a maximum growth rate (G max ). In fact, many polymeric materials show a bell shape temperature dependence of crystal growth rate, showing the maximum growth rate at T cmax [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. This equation has been applied frequently to data of spherulitic growth rate. Application to the polymer crystallization leads to that the molecular transport term is considerably important in the lower temperature ranges. The transport term can be expressed by either WLF or Arrhenius type. In analyzing the crystallization data in bulk polymers, the WLF expression has been used much familiar than the Arrhenius type, since it has been believed that the former expression fits the data better than the later one. However, the transport term could be sufficiently expressed by the Arrhenius type in polymer crystallization [18][19][20][21]. It is worth to recheck which transport term equation is better describing the temperature dependence of the linear crystal growth rate.On the basis of G max for many crystalline materials, a universal master curve of temperature dependence of crystal growth rate has been proposed by Magill et al. [22,23]. This universal curve comes from a phenomenological basis. The universal master curve is derived from the corresponding state in the growth rate

Non‐monotonic molecular weight dependence of crystallization rates of linear and cyclic poly(epsilon‐caprolactone)s in a wide temperature range

“…Similar trends of polymers with medium molecular weight having the highest crystallization rates is well known in the measurement of crystallization rates of many polymers, such as polyethylene, poly(ethylene oxide), poly(3,3‐diethyl oxetane), PCL and poly(ethylene succinate) . In general, higher molecular weights lead to slower crystallization rates because of the chain entanglement effect, but this trend reverses at lower molecular weights when the melting point effect becomes dominant.…”

“…Okui and Umemoto have proposed that for low molecular weight chains intermolecular crystal nucleation dominates crystal growth kinetics, while intramolecular crystal nucleation prevails for high molecular weight chains. 43 Note that the free energy barrier associated with intramolecular crystal nucleation has been found to be independent of chain length. 44 Certainly, such an independence does not occur any more for intermolecular crystal nucleation at low molecular weights.…”

“…In general, higher molecular weights lead to slower crystallization rates because of the chain entanglement effect, but this trend reverses at lower molecular weights when the melting point effect becomes dominant. Okui and Umemoto have proposed that for low molecular weight chains intermolecular crystal nucleation dominates crystal growth kinetics, while intramolecular crystal nucleation prevails for high molecular weight chains . Note that the free energy barrier associated with intramolecular crystal nucleation has been found to be independent of chain length .…”

“…Similar trends of polymers with medium molecular weight having the highest crystallization rates is well known in the measurement of crystallization rates of many polymers, such as polyethylene, 38,39 poly(ethylene oxide), 40 poly(3,3-diethyl oxetane), 41 PCL 42 and poly(ethylene succinate). 43 In general, higher molecular weights lead to slower crystallization rates because of the chain entanglement effect, but this trend reverses at lower molecular weights when the melting point effect becomes dominant. Okui and Umemoto have proposed that for low molecular weight chains intermolecular crystal nucleation dominates crystal growth kinetics, while intramolecular crystal nucleation prevails for high molecular weight chains.…”

The difference of equilibrium melting point between poly(l‐lactic acid) and poly(l‐lactic acid)/poly(d‐lactic acid) blends: cases with three molecular weights

“…[32][33][34] In addition, it was reported that the chains with lower M n prefer extended chain crystallization (ECC) while chains with higher M n prefer folded chain crystallization. 35,36 Considering the alternate arrangement of PLLA and PDLA chains in the lattice, SC is a typical example of intermolecular crystal nucleation and growth; 24 meanwhile, SC prefers the ECC model even with higher M n . Thus, for the PLA samples with higher M n , PLLA adopts the ECC model to a larger extent than the PLLA/PDLA blends.…”