Investigating the Mechanisms of Polymer Crystallization by SAXS

Chapter 9

Investigating the Mechanisms of Polymer Crystallization by SAXS Experiments 1

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Downloaded by UNIV OF ARIZONA on July 17, 2015 | http://pubs.acs.org Publication Date: July 30, 1999 | doi: 10.1021/bk-2000-0739.ch009

G. Hauser , J. Schmidtke , G. Strobl , and T. Thurn-Albrecht 1

Fakultät für Physik der Albert-Ludwigs-Universität, 79104 Freiburg, Germany Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003 2

The importance of SAXS experiments for studies of the basic mechanisms of polymer crystallization and melting is demonstrated with four examples. (1) Time and temperature dependent measurements on s-PP during isothermal crystallization and melting yield the dependencies between crystallization temperature, crystal thickness, crystallization rate and melting point. Results show that the lamellar crystallites form in a two-step process. (2) Time dependent experiments on crystallizing PE enable the crystal thickening to be followed from the beginning and confirm the logarithmic law. (3) Temperature dependent studies on PE during cooling or heating prove that secondary crystallization here is based on a surface crystallization and melting mechanism. (4) The cross-hatching in i-PP has a characteristic signature in the SAXS-curve. Data evaluation yields the total length per unit volume of the edges along the intersections of the crystallites.

1

Introduction

Crystallization of polymers generally leads to the formation of layer-like crystallites with typical thicknesses in the range of 3-50 nm. Normally they are arranged in stacks, being separated by amorphous layers. Electron microscopy and small angle X-ray scattering are the primary tools used for studies of these nano-structures. Both in combination are required for a reliable structure determination. Electron microscopy directly shows the basic structural elements, and SAXS has to be employed for quantitative measurements, and in particular, when studying the changes with time, for example during a crystallization, or on cooling and heating. This contribution deals with some recent SAXS studies carried out 140

© 2000 American Chemical Society

In Scattering from Polymers; Cebe, P., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.

141 on isotactic and syndiotactic polypropylenes and polyethylene. They provided new insights into the kinetics and mechanisms of structure change. Here, we present the main results of the experiments in their context; the full description can be found elsewhere, as indicated in the text.

2

SAXS-data analysis


The majority of partially crystalline systems are set up of stacks of thin laterally extended crystallites. Here, the scattering intensity can be related to the onedimensional electron density correlation function K(z) defined as

It can be directly obtained by a Fourier transformation of the scattering intensity. If we use the scattering cross-section per unit volume Σ(q),Κ(z) follows as

q denotes the scattering vector, being related to the Bragg-scattering angle vB by

(r : classical electron radius) [1]. In the case of partially crystalline polymers, a trajectory along the surface normal passes through amorphous regions with an electron density ρ and crys tallites with a core density /9 , - As shown by Ruland [2], for such a layer system the second derivative of the correlation function, gives the distribution of distances between interfaces, in the form e

β)&

e

c

The expression between the brackets is set up of a series of distribution func tions, whereby the subscripts indicate which phases, amorphous and crystalline ones, are to be traversed while going from one interface to the other. Of main importance are the first three contributions. They give the distributions of the thickness of the amorphous and the crystalline layers respectively (h , h ) and of the sum of both (h ) which is identical with the long spacing L . Rather than by calculating the second derivative of the correlation function, K" (z) can also be deduced directly from the measuring data, by use of &

&c


c

142 If the boundaries between the crystalline and the amorphous regions are sharp within the resolution limit of SAXS experiments, the asymptotic behavior of in the limit of large scattering angles is given by Porod's law

Hereby Ρ denotes the Porod coefficient which is directly related to the specific in ternal surface O (the area per unit volume of the interface separating crystalline and amorphous regions), by


a c

3

Instrumentation

The SAXS experiments discussed in the following were conducted at a conven tional X-ray source with the aid of a Kratky camera, which was equipped with a temperature controlled sample holder. The changes of the structure during isothermal crystallization and the melting on heating were followed measuring the scattering curves with a position sensitive metal wire detector. A few min utes counting time were usually sufficient for a curve registration. Deconvolution of the slit-smeared data was achieved applying an algorithm developed in our group [3].

4

Kinetics of primary crystallization

4.1

The s-PP scenario

Experiments were carried out on a syndiotactic polypropylene [4] and two sam ples of syndiotactic poly(propene-eo-octene) [5], synthesized by S. Jungling in the Institute of Macromolecular Chemistry of our university using a metallocene catalyst. The chemical properties of the two samples are given in Table 1 (co-unit contents were determined by NMR spectroscopy).

Table 1: s-Polypropylene and s-poly(propene-co-octene). Properties of samples.

sample s-PP s-P(P-co-0)4 s-P(P-eo-0)15

octene-units % (weight) %(mole) 0 0 4 1.7 15 6.4

meso-diads

M

n

M /M w

% 3 (3) (3)

104.000 73.000 94.000

1.7 2.1 1.7


n


143

Figure 1: Functions Κ" (ζ) giving the distribution of crystal thicknesses, ob tained by time- and temperature-dependent SAXS experiments: Changes during isothermal crystallization of s-P(P-co-0)4 at 116 °C (top left) and of s-P(P-co0)15 at 70 °C (bottom left) and during the subsequent melting processes (right hand sides).

The crystallite formation during isothermal crystallization was studied in time-dependent SAXS experiments. Subsequent to the isothermal crystallization the melting was monitored in temperature dependent SAXS measurements up to the melting point. Fig. 1 displays as an example the curves K"(z) for s-P(Peo-0)4 and s-P(P-co-0)15 during and subsequent to isothermal crystallization processes. The formation and melting of the crystallites shows up in the changing height of the ridge dominating K (z). The location of the ridge gives the crystal thick ness. As is observed, this thickness remains constant through both the time of isothermal crystallization and the subsequent melting. Curves indicate thick nesses of 5.7 nm and 3.5 nm for s-P(P-co-0)4 and s-P(P-co-0)15 respectively. Observations were similar for s-PP and all crystallization temperatures; always the thickness remained constant until melting. From the measurements we ob tained for the three samples the dependencies of the crystallite thickness (d ), the (Avrami-) time of crystallization (r) and the melting peak (Tf) on the crys tallization temperature (T ). The relationships are displayed in Fig. 3, showing τ as a function of T and Fig. 2, which depicts the relations between T , d and Tf in the form suggested by the Gibbs-Thomson relation, Tf and T versus d~ . n

c

c

c

c

c


c

l


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Figure 2: s-PP and s-P(P-co-O): Relations between the inverse crystallite thick ness, the crystallization temperature and the melting peak. The dashed line represents the Tf (d~ )~dependence of a perfect s-PP as obtained by an extrapo lation procedure. The arrows indicate the limiting temperatures with zero growth rate. 1

10 7

Ί

10 i

s-P(P-co-0)15 s-P(P-co-0)4 s-PP

6

s

1

· A

•

1

•

1

«

,

,

1

1

1

1

Γ

10 4

2

io -i 10

1

10

ϋ

j

40

60

,

J

80

,

100 r [°C]

,

120

,

,

140

,

1——

160

c

Figure 3: s-PP and s-P(P-co-O): Avrami times of crystallization in dependence on the crystallization temperature.



145

Ο

10

20

30

40

50

z/nm

Figure 4: P E : Interface distribution function at the beginning and the end of an isothermal crystallization at 121 °C.

The outcome can be summarized as follows. With increasing content of noncry stallizable units (octene-units or meso-diads) one observes, as expected, a systematic shift of the melting points to lower temperatures and similar shifts of the crystallization time versus temperature curves, but surprisingly, no effect at all on the crystal thickness. The thicknesses of all three samples show a common temperature dependence, being inversely proportional to the supercooling below the equilibrium melting point of perfect syndiotactic polypropylene. The latter is located at 196 °C, as determined by an extrapolation based on measured melting points. Crystal thicknesses (being unaffected by the presence of non-cry stallizable units) and growth rates (being strongly affected) are independent properties. Results may be understood as indicating that crystallization from the melt takes place in two steps. The first step is the formation of 'native' crystallites which, as shown by the slope of the 'crystallization' line T versus d " , have a high surface free energy. They change into the final form by structural relaxation processes associated with the surfaces only (the line starts from the equilibrium melting point!). The difference between the temperatures of crystallization and melting is due to this stabilization process, which leaves the crystallite thickness unchanged. There is a further conclusion: Data demonstrate that the popu lar Hoffman-Weeks plot when applied to random copolymers does not yield the respective equilibrium melting points; it can only be used for perfect homopolymers. 1

c


146 OJr 0.8

•

•

0.7 0.6 0.5 o.o* O'O

0.4 0.3


0.2

•

ο.-' °αο·"

T»121*C e

• Porod constant Ρ Ο Lamellar thicknee* d

04

°4r

10*

10» Vmin

Q

I T

Figure 5: Evolution with time of the crystal thickness and the inner surface.

4.2

PE: Kinetics of crystal thickening

Different from s-PP, crystallites of polyethylene thicken with time. This was clearly demonstrated by time-dependent SAXS experiments carried out during an isothermal crystallization [6]. Fig. 4 shows a typical result, in a comparison of the interface distribution function K"(z) obtained at the beginning and the final stage of the crystallization process. At the beginning K (z) is dominated by the crystallite contribution (d ), which is indicative for isolated crystallites. During further development the con tribution associated with the amorphous layers (d ) grows and finally reaches the same amplitude as that of the crystallites. Simultaneously the latter is shifted to higher values of z. Observations thus show the change from individual lamellae to the final stack which occurs together with a crystal thickening. For the thick ening we found, as expected, a logarithmic time dependence. Data are given in Fig. 5, together with the time dependence of the Porod coefficient Ρ On

c

a

ac

5 5.1

Mechanisms of secondary crystallization PE: Evidence for surface crystallization and melting

Cooling a sample after completion of an isothermal crystallization at elevated temperatures generally results in a further increase of the crystallinity. In the


147


25r

Ό

5

10

15

20 z/nm

25

30

35

40

Figure 6: P E : Interface distribution functions obtained after an isothermal crys tallization at 124 °C and a subsequent cooling to 78 °C.



148

-δ Ο

10

20

30

40

50

z/nm Figure 8: ΡΕ: Interface distribution functions at T- 88 °C obtained for samples crystallized at different temperatures.

discussion of the physical processes contributing to this 'secondary crystallization' two mechanisms are considered. First, it can be connected with the formation of new crystallites, being inserted into the intervening spaces, and second, a reversible thickening of the existing lamellae can be envisaged. Carrying out SAXS experiments, a discrimination is possible. Fig. 6 shows a result which is typical for linear polyethylene [7]. Interface distribution functions were obtained after an isothermal crystalliza tion at 124 °C and a subsequent cooling to 78 °C. The peak at low ζ is due to the amorphous layers, the other one relates to the crystallites. Cooling leads to a shift of the amorphous and crystalline contribution to lower and higher values respectively. This behaviour is indicative for a surface crystallization, here asso ciated with a decrease of d from 10 to 5nm and a corresponding increase of d . Fig. 7 depicts the dependence of d on temperature. Further experiments demonstrated that this dependence is a unique one, d (T) being independent of the thermal history. Fig. 8 demonstrates this fact. The interface distribution functions of three samples, crystallized at different T 's and subsequently cooled to 88 °C, show clearly different long periods and different thicknesses of the crystalline layer, whereas the contributions of the amorphous layers are identical. The dependence d (T) can be quantitatively explained by a model which accounts for the entanglements in the amorphous phase and the change in their a

c

a

a

c

a



149

A

Figure 9: i-PP: Scattering curves I(s)s (s = q/4n) measured at 153 °C and 31 °C.


150 density with d . Surface crystallization and melting can be understood as being driven by the changing entropy of the subchains between the entanglement points. a

5.2

i-PP: Formation of the cross-hatched structure


Secondary crystallization in isotactic polypropylene occurs in a peculiar way. On cooling additional crystallites are formed, however, many of them are oriented oblique to the primary lamellae rather than parallel as is normally observed. As explained by Lotz and Wittmann [8], this 'cross-hatching' is caused by an epitaxial growth mechanism. If cross-hatching occurs the one-dimensional model used so far in the analysis of SAXS data becomes invalid. There is a simple check which shows the deviations. For a stack of crystallites one expects K"(z) = 0 since

0 = /i (0) = h (0) = h (0) etc. a

c

AC

(compare Eq.(4)) and therefore, according to Eq.(5) oo 4

4

0 = / [ l i m q I(q)-q I(q)]dq 0

(8)

4

Hence, I(q)q must fluctuate about the average given by the limiting value lim(g -> oo)q I(q). This is indeed observed for P E and s-PP at all temperatures. For i-PP the condition is fulfilled during the primary isothermal crystallization, but then, on cooling, it is violated. Fig. 9 shows the result of a measurement [9], Cross-hatching produces 'edges' along the lines where the oblique secondary lamellae touch the primary crystallites. Exactly these edges can be directly re lated to the observed deviation. A theoretical analysis gives the following result A

oo 4

2

f[ lim q*I(q) - q I(q)]dq = 2nL Ap w{a) J q-*oo ο

(9)

8

Here, the parameter L denotes the total length per unit volume of edges at the boundaries of the inner surfaces, i.e. the 'specific inner edge length'; w(a) is a function depending on the angle a enclosed by the two surfaces. Evaluation of the SAXS data obtained for i-PP during cooling yielded the temperature depen dence of L w(a) displayed in Fig. 10. Obviously secondary crystallization here is associated with a growing number of edges, simultaneous with the increases of the crystallinity and the specific inner surface. For the given cross-hatched structure it is no longer possible to employ the one-dimensional electron density correlation function and interface distance dis tribution function. Still applicable, because generally valid for two-phase systems, are the Porod-law (eq.(6)) and the equation for the 'invariant' s

s

oo

Φ„{ΐ - ΦΜ

=

4τΛΐ /

47r

« ziiïb 2


( ) 10


151

Figure 10: i-PP: Temperature dependence of the specific length of edges.

where φ describes the crystallinity. They yield the specific inner surface 0 and c, provided that the electron density difference Ap% or the overall electron density decrease Ape is known. A dilatometric measurement can give these lacking quantities. 0

8

c

References [1] G. Strobl. The Physics of Polymers, page 408. Springer, 1997. [2] W. Ruland. Colloid Polym.Sci., 255:417, 1977. [3] G. Strobl. Acta Crystallogr., A26:367, 1970. [4] J. Schmidtke, G. Strobl, and T. Thurn-Albrecht. Macromolecules, 30:5804, 1997. [5] G. Hauser, J. Schmidtke, and G. Strobl. Macromolecules, 31:6250, 1998. [6] T. Albrecht and G.R. Strobl. Macromolecules, 29:783, 1996. [7] T. Albrecht and G.R. Strobl. Macromolecules, 28:5827, 1995. [8] B. Lotz and J.C. Wittmann. J.Polym.Sci., Polym.Phys.Ed., 24:1541, 1986. [9] T. Albrecht and G. Strobl. Macromolecules, 28:5267, 1995.


Investigating the Mechanisms of Polymer Crystallization by SAXS

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