原文流動(dòng)誘導(dǎo)結(jié)晶的聚合物

1、Flow Induced Crystallization ofPolymersApplication to Injection MouldingChapter 1IntroductionThe final properties of a product, produced from semi-crystalline polymers, are to a great extend determined by the internal structure, which itself is established during processing of that product. For exam

2、ple, flow gradients act as a source for viscoelastic stresses, which can enhance nucleation and crystallization, not only accelerating the process, but also leading to different types of crystalline structures. A complete modeling, providing the means for pre- dicting the final product properties, i

3、s still not available. This study presents two important parts of that modeling; (i) a flow-induced crystallization model, based on the recoverable strain in the melt and, (ii) a new experimental technique to determine the specific volume of semi-crystalline polymers, and its relation to cooling rat

4、e dependent crystallization kinet- ics. Both are implemented in a computer code for the numerical simulation of the injection moulding process, and validated by comparing the predicted results with well defined experiments (partly from literature). Applications are found in predicting internal struc

5、tures (i) as resulting from the SCORIM process (which is a specific procedure (push -pull) to enhance mechanical properties like strength and stiffness), (ii) as present in a moulded strip (as a function of different processing conditions) and, finally, (iii) in their relation with long-term dimensi

6、onal stability.Crystallization of polymers is influenced by the thermo-mechanical history during pro- cessing. Dependent on the amount of strain experienced during flow, the number and type of the nuclei formed will be different, and so will be the final crystalline structure. For example, in the in

7、jection moulding process, the absence of shear in the center of a product results in a spherulitical structure, while in the highly strained regions at the cavity walls an oriented structure (in polyolefins often referred to as shish-kebabs) can be present (fig. 1.1). To clarify the role of the proc

8、essing conditions on the crystallization process (and, vice versa, the role of the growing crystal structure on processing behavior), a short overview will be presented concerning their mutual interactions.Crystallization of polymers related to processing: an overviewMolecular configuration, conform

9、ation and flowThe molecular configuration of polymer materials determines thematerials ability for order- ing. Three types of molecular structures are generally distinguished: isotactic, all side groups are present at one side of the backbone of the polymer chain; syndiotactic, with alternating side

10、 groups; and atactic, with randomly positioned side groups. Crystallization is possible 訐 the chain is symmetric or has only small side groups, which fit in a regularly packed confor-Fig. 1.1: A cross section of a product. After (44).mation; the polymer chain has to be linear and stereo specific. Th

11、erefore, isotactic polymers have the ability to crystallize; syndiotactic polymers might have this ability, depending on the side groups, while atactic polymers can not crystallize. The influence of isotacticity on the crystallization kinetics during quiescent crystallization has been studied by, fo

12、r example, Janimak (41).Polymer molecules, in general, show a random configuration without any orientation, when insolutions or melts. However, their state (conformation and orientation) can be altered by flow gradients, i.e. by stirring solutions or shearing melts. According to Keller (48) only two

13、stages of orientation exist; the fully random and the fully stretched chain, with no stable intermediate stages. The trans ition from one stage to the other is assumed to be sharp, showing a molecular weight dependent coil-stretch transformation at a critical strain rate and temperature. Thus, with

14、gradually increasing the elongational rate, first only s mall differences in the chain conformation will appear, but once a critical elongational rate has been reached, the chain will switch to the almost fully stretched stage of the conformation ( 1, with the deformation rate and 3 = 3(Mw, T, .) th

15、e relaxation time). Moreover, not only has the critical elongational rate to be reached, it must be maintained for a certain time as well ( 1, with t the deformation time). The structures observed in solutions or melts, all are the result of acombination of both these stages.Crystallization The crys

16、tallization behavior of polymers is determined by their ability to form ordered struc- tures; the configuration determines the conformation, which is influenced by the processing conditions. Crystallization under quiescent conditions is a phase transformation process, which is caused by a change in

17、the thermodynamic state of the system. This change can be a lowering of the temperature or a change in the hydrostatic pressure. In flow, chain extension can occur as explained in the preceding section. Thermodynamically, chain extension will increase the opportunity of crystal formation by increasi

18、ng the melting point, while kineti- cally the extended chain is closer to a crystal state than a random chain. By stretching the polymer chains, the rate of crystallization increases. Dependent on the conformation of thepolymer chain, two types of crystals can be formed; the random polymer chain wil

19、l lead to lamellar, chain folded crystals that finally form spherulites, while the fully extended chain will lead to extended chain crystals, finally resulting in shish-kebab structures (Keller ( 48). It has been shown, e.g. by Bashir ( 2) and Mackley (62), that the high end tail of the molecular we

20、ight distribution promotes the formation of extended chain crystals. Following Bashir (2), these high end tail molecules arestretched out while the rest remains practically unchanged; a stronger elongational rate results in a broader part of the molecular weight distribution to be extended. The elon

21、gational rate, therefore, determines the amount of oriented molecules (extended chain crystals) present. These extended chain crystals themselves are inadequate to influence the material properties, given their limited number. However, they serve as nuclei for lamellar crystallization of the not ori

22、ented lower molecular bulk, which will show lamel- lar over-growth at a later stage, perpendicular to the central core (Bashir (2). The structure formed is called a shish-kebab. It has been shown by Petermann ( 67) that the number of core crystals, nucleated at a specific temperature, depends on the

23、 external strain. The core itself consists of a shish-kebab structure on a finer scale (Keller (48).A certain strain and strain rate have to be present for shear flow to induce (noticeable) crystallization. After a nucleus has been formed, continuous crystallization of polymers is kinetically contro

24、lled, the motion involved refers to the transport of molecules from the dis- ordered liquid phase to the ordered solid phase, and to the rotation and rearrangement of the molecules at the surface of the crystal, similar to quiescent crystallization. The crystallization process can thus be subdivided

25、 into three stages:Nuclea tion:Nucleation can have different causes like overall nucleation from a nucleation agent, pressure induced nucleation, strain induced nucleation and cooling. The nuclei formed act as starting points for polymer crystallization. There is no complete agreement on the physica

26、l background of the nucleation process. For example, Terrill et al. (81) considered, based on experimental evidence (WAXD and SAXS), the nucleation event during spinning of isotactic polypropylene to be the result of density fluctuations, although a repetition of old discussions on the true interpre

27、tation of combined WAXD and SAXS data1 question these re- sults. Even without considering the basic underlying physics precisely, in case of flow, nucleican be created by flow-induced ordering phenomena in the melt, while the nucleation process for a quiescent melt can be described by a Poisson poin

28、t process (Janeschitz-Kriegl ( 40). For polymers containing nucleation agents, also clustered point processes have some importance. Growth: The nuclei grow, dependent on the thermo-mechanical history which they experi- ence; if the nuclei are sufficiently strained they will grow into threads, otherw

29、ise they stay spherical and will further grow radially. In these, so called spherulites, the lamellae are present like twisted spokes in a sphere, while thread-like nuclei grow mainly perpendicular to the thread(fig.1.2)Perfection: Perfectioning is the process of improvement of the interior crystall

30、ine structure of the crystalline regions. This is also referred to as secondary crystallization.Fig. 1.2: A schematic outline of the concept of crystallization. After (48) and (55).ModelingHistorically, crystallization transformations are described by using a phase diagram assuming the transformatio

31、n to be in a quasi-equilibrium state, leading to a front model. An example of this approach is the description of the growth of the ice layer on the polar see (a Stefan- problem (78). It has been shown by Berger (5), that the front model is inadequate in describ- ing solidification,訐 the process is

32、governed by the kinetics of a phase change. For example, the occurrence of completely amorphous layers can never be understood using a front model. A zone model has to be used, were a phase change (crystallization) determines the solidification behavior. Crystallization in a moving zone takes place

33、when the characteristic time of heat diffusion is less than the characteristic time of crystallization. In the limiting case of very fast crystallization, compared with the process of heat conduction, the zone model shows a transition into the front model.Quiescent crystallization: Describing the gr

34、owth of the crystalline spherulites in case of quiescent crystallization has been done by representing the spherulites as spheres (Schultz ( 75). Spherulitical growth is then accounted for by enlarging the sphere radius. However, the crys- tallizing medium is limited by free surfaces or other bounda

35、ries that induce truncations of crystalline entities and locally modify the crystallization kinetics. Benard ( 4) formulated a mathematical description for the growth of already existing nuclei and concluded that the ki- netics clearly are the controlling factor in the systems investigated. A more c

36、omplete model for quiescent crystallization has been described by Janeschitz-Kriegl ( 39), which is based on the Kolmogoroff equation (Kolmogoroff ( 49), who formulated the crystallization kinetics in terms of time dependent (bulk) nucleation and crystal growth rate. This formulation has been extend

37、ed for the influence of confining surfaces and surface nucleation processes by Eder (15; 16). A Poisson point process with special intensity measures for the description of the nucleation process and a deterministic law for crystal growth forms the basis. Using the method proposed by Schneider (74),

38、 this generalized Kolmogoroffequation can be trans-formed in a set of differential equations (Schneider rate equations), which give a complete description of the crystalline structure. These rate equations are coupled with the energy equation by the source term, which takes into account the latent h

39、eat when the polymer crys- tallizes (Eder (17).Flow-induced crystallization: An onset for the description of flow-induced structures has been given by Eder et al. (19), who based their theory on the shear rate as the driving force for crystallization. Their model for flow-induced crystallization res

40、embles their model for quiescent crystallization. It is assumed that the influence of the deformation on crystal- lization, is due to the formation of thread-likenuclei (shish), on which lamellae grow mainly perpendicular (kebabs). This model is described in chapter 3 of this thesis. Jerschow (45) u

41、sed this model in analyzing the structure distribution found in isotactic polypropylene, after fast short term shear at low degrees of super-cooling. Besides a flow-induced (shish-kebab) structure at the surface and a spherulitical structure in the center, in between both layers a fine grained layer

42、 has been observed. It has been suggested that this layer consists of thread-like structures perpendicular to the flow direction. A model based on the conformation of the molecules in the melt has been proposed by Bushman ( 8) and Doufas (12), which includes a conformation tensor (the driving force,

43、 calculated using a viscoelastic model), an orienta- tion tensor and the degree of crystallinity. No description is available, however, of the final structure (size of structures, etc.). Other models have been proposed by Ito ( 37), based on the strain present in the melt, and by Vferhoyen ( 86), ba

44、sed on the Cauchy stress. An iso-kinetic approach is used in models based on the Nakamura equations (Nakamura (66) byIsayev (35) and Guo (29). The (dis)advantages of all these models are discussed in chapter 3.Relation with other material propertiesThe evolution of structure (spherulites and shish-k

45、ebabs) will influence the material proper- ties. The most severe effects are observed in the viscosity and the specific volume. Effects in other properties like the thermal conductivity and thermal capacity will not be discussed here.Viscosity: The coupling between the crystal structure and the visc

46、osity of a polymer melt, is not fully clarified yet. For example, in startup flow experiments, it has been observed by Lagasse (52) that a sudden rise in the viscosity correlates with the appearance of crystal s in the sheared melt. Experiments by Vleeshouwers ( 87) showed the same kind of behavior.

47、 Initially, the melt still shows an amorphous behavior, since the amount of crystalline material (or the number of crystals) is very low. With increasing amount (or number) the influence on the viscosity will increase. Guo et al. (27) assumed that the melt loses its fluidity upon the occurrence of c

48、rystallization, i.e. a step-like change in the viscosity. They do not give a physical explanation although; one could assume that a network occurs in this stage. Another possibility could be, that the crystals form a separate phase in the amorphous melt. The rhe- ology will then be changed like is k

49、nown from dispersion rheology (see for example Ito ( 36) and Verhoyen (85).Specific volume: In polymer processing, the specific volume is influenced by process- ing characteristics like temperature, pressure and flow history, and it determines shrinkage which expresses itself by dimensional (in)stab

50、ility. For amorphous polymers, the pressure and temperature history determine the specific volume and (frozen in) molecular orientation determines the anisotropic dimensional instability via (slow) relaxation processes below the glass transition temperature (Meijer (65). For semi-crystalline polymer

51、s, however, the spe- cific volume is also influenced by the crystalline structure. This structure itself is influenced by the pressure and the temperature history, by the configuration of the polymer chains and flow induced ordering phenomena as well. Consequently, for semi-crystalline polymers the

52、specific volume has to be related to pressure, temperature, cooling rate and the crystalline state (Zuidema ( 94). For a correct modeling of the injection moulding of semi-crystalline polymers, accurate measurements and modeling of the specific volume have to be achieved not only in relation to the

53、pressure and temperature, but al so to the cooling rate and ordered state of the molecules. This conclusion is subscribed by Fleischmann ( 22), regarding the influence of the processing conditions on the specific volume. The specific volume will be discussed in more detail in chapter 4.ProcessingFor

54、 polymer melts it has been observed (V an der Vegt (83) that the flow through a capillary die can become blocked by crystal formation, induced by the elongational flow at the con- striction. Bashir (2; 3) and Keller (48) explored these findings somewhat further and observed a macroscopical rheologic

55、al effect in capillary flow of high molecular weight polyethylenes; a reduced flow resistance coupled with the absence of extrudate distortions when extruding a polymer melt in a specific processing window. Experiments by T as ( 80) showed that, dur- ing film blowing of LDPE films, the viscoelastic

56、stresses at the freeze line determine the majority of the mechanical properties by directing the crystallization. Saiu ( 71) performed an experimental study on the influence of injection moulding conditions on product proper- ties for an isotactic polypropylene. Chiang (11) studied shrinkage, warpag

57、e and sink marks resulting from the injection moulding process, using semi-crystalline polymers. The effect of crystallization on the mechanical and physical properties has been studied, for isotactic polypropylenes with different molar masses. It has been observed (Guo ( 28) that increasing the inj

58、ection speed or the melt injection temperature leads to a decrease in the thickness of the flow-induced layer. The complicated thermo-mechanical history, in all these examples, requires a numerical analysis. The effect of processing conditions will be discussed in more detail in chapter 5.Mechanical

59、 propertiesThe resulting morphology of the product is, together with the molecular composition, the factor determining the mechanical and dimensional properties. Because the solidification be- havior of amorphous polymers is quite well understood, prediction of warpage and shrinkage from ejection up

60、 to the complete life cycle of a product can be done (Caspers ( 9), Meijer (65). This knowledge allows one to reduce shrinkage and warpage by choosing a different polymer(with different relaxation time/molecular weight (distribution) by adjusting the processing conditions, or by improving the mould