# Correlation and Modeling of the Occurrence of Different Crystalline Forms of Isotactic Polypropylene as a Function of Cooling Rate and Uniaxial Stress in Thin and Thick Parts.

A study of structure development in thin melt spun isotactic polypropylene filaments is described, which is then applied to the
prediction of the behavior of thick parts. Conditions under which
different crystalline forms of polypropylene are obtained as a function
of cooling rate and spinline stress were investigated. Continuous
cooling transformation (CCT) curves are developed. This also allows us
to develop a map of crystalline form as a function of these variables.
We have applied the CCT curves and this map to predict the development
of cross-sectional variation structure in thick filaments and rods. This
is applied in particular to the quenching of a cylindrical rod and the
structural characterizations observed through the cross section are
compared with predictions from the CCT curves and solutions of
Fourier's transient heat conduction equation.

1. INTRODUCTION

Isotactic polypropylene was first described in papers by Natta and his co-workers [1-5] in 1955. They found the material to be crystalline with a melting point of 165[degrees]C. Isotactic polypropylene is today a very important commercial thermoplastic which is widely used in many applications. It is important to understand the structural variations and distribution of structures that this material may exhibit as a function of processing.

Early examinations by Natta et al. [4, 5] using wide-angle X-ray diffraction established polypropylene to exist in a monoclinic unit cell with dimensions a = 6.65 [dot{A}], b = 20.96 [dot{A}], c = 6.50 [dot{A}] (chain axis) and angle [beta] = 99[degrees] 20' corresponding to a density of 0.92. The strongest diffraction peaks were at 6.25 [dot{A}], 5.25 [dot{A}], 4.75 [dot{A}], 4.20 [dot{A}] and 4.05 [dot{A}] correspond to the 110, 040, 130, 111 and 131/041 crystallographic planes (see Table 1). It was shown that this unit cell corresponds to isotactic polypropylene in a 3/1 helix. Left handed and right handed helices are regularly disposed facing each other.

In 1959, Natta, Peraldo and Corradini [6] and Boye et al. [7], among others, called attention to a second form of polypropylene which arises in quenched and cold drawn films, and fibers. In this case fewer and broader X-ray diffraction peaks arise. Different infrared spectra and lower densities (d=0.88) were found. Natta et al. [6] described this form as "smectic". Two broad X-ray diffraction peaks were exhibited by this smectic structure. Natta et al. [6, 8] suggested the source of this form is a random arrangement of left and right handed helices in the unit cell.

In the same year, Keith et al. [9] presented X-ray diffraction evidence of the existence of a new crystallographic form in polypropylene. Using carefully quenched films they described a strong set of arcs in WAXS film patterns at 5.53 [dot{A}] and 4.173 [dot{A}]. They suggested that this corresponded to a hexagonal unit cell with basal parameter a = 12.74 [dot{A}] and an axial parameter of about 6.35 [dot{A}] with the inner arcs corresponding to a [200] reflection and the outer arcs to a [201] reflection (see Table 1). In a 1961 paper, Addink and Beintema [10] described samples containing Natta and Corradini's [1-4] monoclinic structure, from hereafter designated as [alpha] and Keith et al.'s [8] crystalline structure hereafter described as [beta]. They accepted Keith et al.'s proposal that the unit cell is hexagonal, but they argued the basal parameter is better taken as 6.38 [dot{A}], half of Keith et al.'s value. They suggest that crystallites consist of all right-handed or left handed helices. Addink and Beintema [10] also proposed a [gamma] crystalline form of isotactic polypropylene. Subsequent papers have both struggled over the nature of the unit cell of the [beta] form [11-13] or studied conditions under which the [beta], y, and smectic (now called pseudo-hexagonal) forms may be formed [14-21].

Studies of crystallization of polypropylene during processing, began with melt spinning/drawing investigations of Wyckoff [14] and Sheehan and Cole [15] in the early 1960s. Melt spinning investigations continued through the work of Katayama et al. [22], Kitao et al. [23], Fung et al. [24], Spruiell and White [25], Ishizuka and Koyama [26], Nadella et al. [27], Shimizu et al. [28], Jinan et al. [29] and the current authors [30] (see also Piccarolo et al. [31] and Martorana et al. [32]). It was clear that severe quenching of polymer melt filaments at low drawdown ratios led to smectic/pseudo-hexagonal structures [15, 25, 27]. Under a wide range of mild quench conditions including modest to high spinline stresses, uniaxially oriented [alpha]-monoclinic structures were found. High speed melt spinning at elevated temperatures has been found to lead to smectic/pseudo-hexagonal structures [29]. Studies of tubular film extrusion have generally found [alpha]-monoclinic structure [33]. Observations of the [beta] form seem limited through this structure has been found in injection molded parts [20, 34, 35] and in specially nucleated films [21]. Smectic structures are also produced by cold drawing monoclinic polypropylene filaments [14, 15].

It would seem logical that the type of crystalline form that occurs during solidification should depend upon the cooling rate, the level and character of the stress field and the applied pressure. These variables are all known to influence crystalline forms occurring in polymers. Stress seems pertinent rather than the kinematics of flow and deformation because the Rheo-Optical Law between birefringence and stress is obeyed [36, 37] by flexible chain polymer melts such as polypropylene. Birefringence is the anisotropy of the polarizability tensor [38, 39] and is well known to represent a second moment of the orientation distribution. This polymer chain orientation in the melt is controlled by the stress field. Further it is possible to quantitatively predict crystalline orientation in poly-olefins from applied stress fields [25, 27, 30].

It is our purpose in the present paper to explore the relationship of the crystalline form of isotactic polypropylene to cooling rate and applied uniaxial stress. We will develop a "map" of crystalline form as a function of these variables based on both our own experiments and results in the literature. We will also apply this map to quenched thick cylinders of polypropylene to interpret the structural variations across their cross section.

2. STRUCTURE DEVELOPMENT IN THIN FILAMENTS

2.1. Purpose

Our purpose in this section is to develop a correlation between quench rate, uniaxial stress, and the crystalline character of the solid phases formed. In our correlations we have used the experimental results of many different investigators on fibers and films including Natta et al. [6], Keith et al. [9], Addink and Beintema [10], Sheehan and Cole [15], Katayama et al. [22], Nadella et al. [27], Shimizu et al. [28, 29] as well as our own studies, which are reported below.

2.2. Materials

Various polypropylenes have been used by the authors whose data are here used. This is summarized in Table 2.

The isotactic polypropylene sample used by the authors was supplied by Quantum Chemical Corporation. Its melt index is 5.0 (g/10min.).

2.3. Preparation of Thin Filaments

In our experiments the samples were melt spun from an Instron capillary rheometer using a capillary spinneret of diameter (D) 1.6 mm (1600 [mu]m) and length diameter ratio of 9.3. Melt spinning was carried out at various melt temperatures and take-up velocity ([V.sub.L]). Draw-down ratios up to 282 have been investigated. The diameter, d, of the melt spun filaments is given by the expression,

d = [[[frac{[[rho].sub.m]}{[[rho].sub.s]}] [frac{4Q}{[pi][D.sup.2]}]].sup.1/2]] [frac{D}{[sqrt{[V.sub.L]}]}] = [[[frac{[[rho].sub.m]}{[[rho].sub.s]}]].sup.1/2]] [[[frac{[V.sub.0]}{[V.sub.L]}]].sup.1/2]] D (1)

where [[rho].sub.m] is the melt density, [[rho].sub.s] is the solid fiber density, and Q is the melt volumetric flow rate. Here D is 1.6 mm. Filaments of thicknesses down to 100 [mu]m were produced in our studies.

The filaments were variously melt spun into ice water and through ambient air to a take-up device consisting of a polytetrafluorethylene roller. A Roth-schild Electronic Tensiometer was used to measure filament spinline tension. The distance of the capillary to the take-up in spinning through air was 600 mm. When a quench bath was used, it was placed 150 mm below the spinneret.

2.4. X-Ray Diffraction Investigations

The melt spun filaments in our experiments were characterized by wide angle X-ray diffraction using a General Electric X-ray generator (GE-XRD6) equipped with a copper target tube and graphite crystal mono-chrometer was used to obtain CuK[albha] radiation ([lambda] = 1.5418 [dot{A}]).

2.5. Results

Figure 1 shows from X-ray patterns of isotactic polypropylene at various temperature and draw-down ratio with both air (Fig. 1f) and ice-water quenching (Figs. 1a, b, c, d, e) obtained on our melt spun filaments. Figure 2 shows wide angle X-ray diffractometer scans as a function of Bragg angle. Figure 2 shows the 20 scan for high and low stress water quenched sam-pies at various melt temperatures.

For air quenched PP spun at 200[degrees]C, 230[degrees]C and 260[degrees]C, the samples had a well defined WAXS reflections at 6.42 [dot{A}], 5.37 [dot{A}], 4.82 [dot{A}], and 4.19 [dot{A}]. These correspond to the [alpha]-monoclinic unit cell (110), (040), (130), and (111) reflections [4, 5].

The 200[degrees]C, 230[degrees]C and 260[degrees]C melts spun into fibers and quenched in ice water had a less defined character. These may be identified as having a pseudo-hexagonal/smectic character. As draw-down ratio and spinline stress increased, the melt spun fiber's diffraction patterns became increasingly monoclinic in character. This was much less so for the 260[degrees]C melt.

None of the melt spun fibers was found to exhibit diffraction peaks corresponding to the [beta] crystalline form.

The earlier reported behavior of isotactic melt spun polypropylene filaments by other investigators [15, 19-21] are at least qualitatively similar to what we have reported above.

3. REPRESENTATION OF STRUCTURAL CHANGES

3.1. Isotropic Quiescent Crystallization

The experimental studies of the previous section and those of many other authors [1-5] have revealed that when quiescent polypropylene is cooled slowly from the melt that a monoclinic crystalline form designated [alpha] is formed. A more rapid cooling and quenching at 100-128[degrees]C [9, 19] produces a hexagonal form designated as [beta] together with [alpha]. A still more rapid quenching to 0[degrees]C produces the pseudo-hexagonal/ smectic form [6, 7, 15, 27, 30]. Thus it seems clear that

crystalline state =

F [rate of cooling [lgroup][frac{dT}{dt}][rgroup]. quench temp.] (2)

The above discussion suggests a diagram such as shown in Fig. 3 that indicates the crystalline states that form at different cooling rates. Such plots are well known to metallurgical engineers and were widely used together with isothermal transformation investigations for the characterization of quenching of steels [40-43]. They are called Continuous Cooling Transformation or CCT plots and were previously discussed by Spruiell and White [25] to represent crystallization of polyolefins. If we make an equivalence between steel and polypropylene, Austenite is equivalent to molten polypropylene, Ferrite and Cementite to [alpha]-monoclinic polypropylene, Martensite to the smectic form. For polypropylene with a [T.sub.g] of -15[degrees]C, the peak of the kinetic crystallizability curve should be about 90[degrees]C.

We draw lines in Fig. 3 on the plots corresponding to the heat treatment studies of Natta et al. [6], Keith et al. [7], and Turner Jones et al. [12]. This would seem to require that [beta] crystals occur near the nose of the CCT curve.

3.2. Influence of Uniaxial Applied Stresses

Uniaxial spinline tensile stress also influences structure development in the melt spinning of polypropylene. Melt spun fibers are observed to exhibit only [alpha]-monoclinic and smectic, but not [beta]. This is seen in our Figs. 1 and 2 and in the work of Spruiell and White [25], Nadella et al. [27], Jinan et al. [29] and the current authors [30]. Further uniaxial stresses are well known to significantly increase crystallization rate and thus to shift CCT curves towards shorter times.

We may express this by generalizing Eq 2 to

Crystalline state = F[[frac{dT}{dt}], [sigma]] (3a)

Rate of Crystallization = G[[frac{dT}{dt}], [sigma]] (3b)

where [sigma] is tensile stress. As stress is a second order tensor and the other variables in this equation are scalars. It would seem better to express [sigma] in terms of invariants such as

tr [sigma] tr [[sigma].sup.2] tr [[sigma].sup.3]

However, we do not have data from different stress states to allow investigating this. It does however indicate that applied pressure (equivalent to tr [sigma]) should be considered as well.

3.3. Estimation of Rate of Cooling, dT/dt

It is a problem to estimate rates of cooling at solidification and actual temperatures of solidification themselves. In the science of heat transfer, the heat flux q (Joule/sec) at a surface may be expressed in terms of Newton's Law of cooling (e.g., Ref. 44))

q = hA([T.sub.s] - [T.sub.surr]) (4)

where h is a heat transfer coefficient, A is a surface area, [T.sub.s] is the surface temperature and [T.sub.surr] is the temperature of the surroundings.

Consider the cooling of a descending filament in a thread line. The cooling rate may be expressed [45]

Gc [frac{dT}{dx}] = [rho]c[lgroup][frac{[pi][d.sup.2]}{4}][rgroup] [frac{dT}{d[t.sub.res]}] = -h[pi]d (T - [T.sub.surr]) (5)

where [t.sub.res] is residence time in the spinline, G is the mass flow, [rho] the density, c the heat capacity, h the heat transfer coefficient, and [T.sub.surr], the temperature of the surroundings, d is the filament diameter as defined in Eq 1.

The temperature-residence time gradient is:

[frac{dT}{d[t.sub.res]}] = - [frac{4h}{rcd}] (T - [T.sub.surr]) (6)

Heat transfer coefficients during melt spinning of fibers through air have been correlated notably by Kase and Matsuo [45] through expressions of form

[frac{hd}{[k.sub.a]}] = 0.42 [[lgroup][frac{dv[[rho].sub.a]}{[[eta].sub.a]}][rgroup].sub.1/3] (7)

where d is the fiber diameter, [k.sub.a] is the thermal conductivity of air, [[rho].sub.a] is the density of air, and [[eta].sub.a] is the viscosity of air. Equation 7 suggests that heat transfer coefficients are below 500w/[m.sup.2]k when the diameter of the fiber is of order hundreds of microns.

Quenching descending fibers into cold water should involve boiling phenomena. Heat transfer coefficients for boiling heat transfer have been investigated by Piling and Lynch [46], Jakob and Fritz [47], Nukiyama [48], and Rohsenow [49]. Generally these heat transfer coefficients are much higher than those for convective heat transfer. In the nucleate pool boiling region, the most widely accepted correlation is that of Rohsenow [49] who expresses the heat transfer coefficient h

h =

[[eta].sub.1][Delta][H.sub.v][[frac{g([[rho].sub.1] - [[rho].sub.v])}{[gamma]}].sub.1/2] [[lgroup][frac{[c.sub.p1]}{[C.sub.sf][Delta][H.sub.v]P[[r.sup.1.0].su b.1]}][rgroup].sup.3] [([T.sub.s] - [T.sub.sat]).sup.2] (8)

where [[rho].sub.1] is the density of the saturated liquid, [[rho].sub.v] is the density of the saturated vapor, [[eta].sub.1] is the liquid viscosity, [Delta][H.sub.v] is the heat of vaporization per unit mass, g is the local gravitational acceleration, [gamma] is the surface tension, [c.sub.p1] is the specific heat of the saturated liquid, [C.sub.sf] is the surface-fluid constant ([approx] 0.01), P[r.sub.1] is the Prandtl number of the saturated liquid ([c.sub.p1] [[eta].sub.1]/[k.sub.1]), and [T.sub.s]-[T.sub.sat] is the excess temperature of the surface temperature over the boiling temperature. These suggest heat transfer coefficients orders of magnitude higher than for air quenching. The value of h is of order 30,000w/[m.sup.2]K when the diameter of the fiber is of order hundreds of microns.

From Eq 6 at a temperature of 90[degrees]C where isotactic polypropylene might be considered to crystallize based upon earlier investigators of melt spinning [22, 27], values of dT/d[t.sub.res] computed for spinning through air are of order 500[degrees]C/sec while for boiling heat transfer through ice-water the value of dT/d[t.sub.res] is 45.000[degrees]C/sec. The diameter of the fiber is taken as 100 [mu]m in these calculations.

3.4. Structural Map

We have sought to correlate the cooling rate at the inception of crystallization together with applied stress to indicate the position where different crystalline structures occur. Using our experimental data and those of other investigations [9, 25, 27, 29, 30] for the crystalline character of melt spun fibers, together with calculations of dT/dt, we have constructed Fig. 4. It can be seen that at low cooling rates and high stresses, generally monoclinic structures are formed. At high cooling rates and low stresses there is a large pseudo-hexagonal/smectic region. The situation with the [beta]-form is much more difficult. The behavior is much less reproducible from sample to sample and seems very susceptible to nucleating agents (e.g. Ref. 21). [beta] has not as indicated earlier been seen in melt spun fibers but has been claimed [20] as a stress favored form based in molding experiments [20, 34, 35]. [beta] would seem to be suppressed by uniaxial tensile but apparently not by shear stresses. We suggest as a beginning the small region shown in Fig. 4 as where [beta] might be expected to form. This is based by the experiments of Keith et al. [9] and Turner Jones et al. [12]. This region should change in size depending upon nucleating impurities.

3.5. CCT Curves With Uniaxial Stress Effects

It is possible to use the results of Fig. 4 with the solutions of Eq 6 to 8 to construct CCT curves for polypropylene as shown in Fig. 5. This includes zero stress behavior forming [alpha], [beta] and smectic structures based on the experiments of Natta et al. [1-6, 8] and Keith et al [9]. Dashed lines represent high stress data from our own results and those of Katayama et al. [22], Nadella et al. [27], and Shimizu et al. [28, 29]. One obtains a series of curves associated with different uniaxial stress levels.

The effect of uniaxial stress is that the nose of [alpha]-monoclinic polypropylene moves to the left and hovers over what was the smectic region in the quiescent state. The effect of uniaxial stress is analogous to the influence of certain alloying elements such as cobalt in the transformation of Austenite. The implication that only [alpha] forms at high uniaxial stresses at moderate cooling rates requires additional critical discussion.

4. QUENCHING OF THICK RODS

4.1. General

It should be possible to predict the crystalline forms occurring in a quenched thick cross section from knowing the cooling rate and the stress-field if we can predict the transient temperatures during cooling. We should be able to use Figs. 3 to 5 to accomplish this.

In this section we will describe an experimental study of quenching a thick rod and then determining the structural variations through the cross section. We will experimentally determine the structural character through the cross section and then seek to predict it from first principles. Kang and White [50] have previously done this for the orientation birefringence through a thick melt spun filaments of polycarbonate.

4.2. Experimental

Samples of rods of diameter 12 mm were molded in the barrel of an Instron capillary rheometer. These were subsequently extruded out and quenched in ice-water.

The quenched samples were cut into several parts represently different radii. These sections were 1.5 mm thick. WAXS patterns were obtained using a General Electric X-ray generator (GE-XRD6) and used to determine crystalline character.

X-ray diffractometer scans from samples cut from different positions are shown in Fig. 6a, b, c, d, and e. We have sought to estimate the amounts of monoclinic [alpha], hexagonal [beta], and pseudohexagonal smectic throughout the cross-section. In the 1.5 mm thick section including the outer surface, we detect primarily [beta], but not the smectic form, as might be expected. The detection of the [beta] from is based upon the (100) reflection at 5.5 [dot{A}]. As one moves into the core, the portion of crystallized polypropylene with monoclinic structure increases.

We have experimentally determined the relative amounts of the a and [beta] phases by quantitative evaluation of the areas under WAXS peak and comparing them to what would be expected for pure [alpha] and [beta]. Specifically we used (110), (040), and (130) for [alpha] and (100) for [beta]. Figure 7 shows the calculated distribution of relative amounts of [alpha] and [beta] as a function of radial position.

4.3. Interpretation of Structural Cross-Sectional Distributions in Thick Quenched Samples

We have sought to analyze the problem of quenching of a thick rod. The temperature-time-position profile through a thick quenched cylindrical sample may be obtained from Fourier's law of heat conduction [51]. We take this for slow crystallization to be of form

[rho]c [frac{[partial]T}{[partial]t}] = k [frac{1}{r}] [frac{[partial]}{[partial]r}] [lgroup]r[frac{[partial]T}{[partial]r}][rgroup] + [rho][Delta]H [frac{dX}{dt}] (9)

where

T(r,0) = [T.sub.0] (10a)

- k [frac{[partial]T}{[partial]r}] (R, [x.sub.1]) = h([T.sub.s] - [T.sub.surr]) (10b)

[frac{[partial]T}{[partial]r}] (0, [x.sub.1]) = 0 (10c)

where [T.sub.s] is the temperature at surface of thick rod and [T.sub.surr] is the surrounding temperature. Here [Delta]H is the heat of crystallization per unit mass and [partial]X/[partial]t the rate of crystallization.

It should be noted that Eqs 9 and 10 differ from the classical Stefan analysis [45] of heat conduction during solidification. This procedure was developed to interpret the melting of ice and freezing of water. It represents a very high crystallization rate asymptote and is not appropriate for polypropylene. We instead follow the approach of Berger and Schneider [52], which was developed for analyzing the slow crystallization of thermoplastics.

Let us first consider the case where [Delta]H is zero. The solution of Eq 9 yields the temperature profile across the cross section as function of time. It has the form [51]

[frac{T(r, t) - [T.sub.surr]}{[T.sub.0] - [T.sub.surr]}] =

2 [[[sum].sup.[infty]].sub.n=1] [frac{1}{[[gamma].sub.n]}] [frac{[J.sub.1]([[gamma].sub.n])[J.sub.0][[[gamma].sub.n](r/R)]}{[[[J .sup.2].sub.0] ([[gamma].sub.n]) + [[J.sup.2].sub.1] ([[gamma].sub.n])]}] [e.sup.-[[[gamma].sup.2].sub.n][alpha]t/[R.sup.2]] (11)

where [[gamma].sub.n] is [[lambda].sub.n]R and [[lambda].sub.n] represents the eigenvalues. [J.sub.0]([[gamma].sub.n]) and [J.sub.1]([[gamma].sub.n]) are Bessel functions.

We now consider the full problem where [Delta]H is not zero. It is also readily possible to solve Eq 9 analytically if the source term, i.e. [rho][Delta]H([partial]X/[partial]t), is independent of temperature and time. However, this is not the case, and we must instead solve Eq 9 numerically. In doing this we must represent the crystallization rate of polypropylene as a function of temperature and time as

[frac{dX}{dt}] = 0 (T [greater than] [T.sub.2])

[frac{dX}{dt}] = [alpha] (T,t) (1 - X) ([T.sub.2] [greater than] T [greater tan] [T.sub.1]) (12a,b,c)

[frac{dX}{dt}] = 0 ([T.sub.1] [greater than] T)

To proceed we introduce a finite difference scheme. We know the point where crystallization starts from Fig. 8. Dividing the rod into M radial slices, we obtain from Eq 9,

[rho]c [frac{T(r,t + [Delta]t) - T(r,t)}{[Delta]t}] = k [lgroup][frac{T(r + [Delta]r,t) + T(r - [Delta]r,t) - 2T(r,t)}{[([Delta]r).sup.2] + [frac{1}{m[Delta]r}] [frac{T(r + [Delta]r,t) - T(r - [Delta]r,t)}{2[Delta]r}][rgroup] + [rho][Delta]H[frac{dX}{dt}] (r,t) (13)

where m = 0 at core and m = M at surface of the thick rod.

4.4. Comparison of Experiment with Predictions

We first applied the solution of Eq 11, which represents a zero heat of crystallization for a thick sample. Here [rho] is taken as 910kg/[m.sup.3], c is 1.81 x [10.sup.3]J/kg-K, h is 30,000W/[m.sup.2]-K, k is 0.138W/m-K and [T.sub.surr] is 0[degrees]C. The temperature profile is shown as a function of radius in Fig. 8. Comparing this solution to Fig. 3 leads to the prediction that the outer layer of the 80% of the rod should be smectic and the remainder [alpha] and [beta]. This is not what is found.

We now apply our solution with [Delta]H [neq] 0 to this problem. Values of [Delta]H for polypropylene in the range 84 to 238kJ/kg have been cited in the literature. We chose [Delta]H = 238kJ/kg, which is taken from Janeschitz-Kriegl and Eder's paper [53]. The value of [alpha](T, t) of Eq 12b was taken from the work of Malkin et al. [54] on the quiescent crystallization of polypropylene to be 0.056[s.sup.-1] for the case of the crystallization temperature being 110[degrees]C and the crystallinity 50%. We used the finite-difference conduction equation of cylinder for numerically solving Eq 9 and Eq 13. We did the numerical calculations by using the MATLAB program.

The numerical solution of Eq 9 leads to the temperature profile shown in Fig. 9. Plateaus appear in the temperature profile which are not seen in Fig. 8 where [Delta]H was taken to be zero. There are due the evolution of heat during crystallization. The effect of [Delta]H is to make the crystallization process slower.

We have sought to use the calculated crystallization rates of Fig. 9 to predict the distribution of crystallization phase through the cross section shown in Fig. 7. We now do not predict the smectic unit cell in the outer portions of the rod. We predict instead that there is the mixture of the [alpha] -monoclinic and [beta]-hexagonal unit cell structures which become increasingly monocilnic as we move to the core of the rod. This is what is observed. If we vary [Delta]H downward from 238 to 84kJ/kg there is not much effect on these results.

5. CONCLUSIONS

Using thin sample (fiber and film) experimental data, we can predict the relationship of crystalline form of isotactic polypropylene to cooling rate and applied this to predict the crystalline structure variation through a thick rod by modeling the crystallizing kinetics together with the transient Fourier heat conduction equation.

CHEOL-HO CHOI and JAMES L. WHITE

Institute of Polymer Engineering

University of Akron

Akron, Ohio 44325

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1. INTRODUCTION

Isotactic polypropylene was first described in papers by Natta and his co-workers [1-5] in 1955. They found the material to be crystalline with a melting point of 165[degrees]C. Isotactic polypropylene is today a very important commercial thermoplastic which is widely used in many applications. It is important to understand the structural variations and distribution of structures that this material may exhibit as a function of processing.

Early examinations by Natta et al. [4, 5] using wide-angle X-ray diffraction established polypropylene to exist in a monoclinic unit cell with dimensions a = 6.65 [dot{A}], b = 20.96 [dot{A}], c = 6.50 [dot{A}] (chain axis) and angle [beta] = 99[degrees] 20' corresponding to a density of 0.92. The strongest diffraction peaks were at 6.25 [dot{A}], 5.25 [dot{A}], 4.75 [dot{A}], 4.20 [dot{A}] and 4.05 [dot{A}] correspond to the 110, 040, 130, 111 and 131/041 crystallographic planes (see Table 1). It was shown that this unit cell corresponds to isotactic polypropylene in a 3/1 helix. Left handed and right handed helices are regularly disposed facing each other.

In 1959, Natta, Peraldo and Corradini [6] and Boye et al. [7], among others, called attention to a second form of polypropylene which arises in quenched and cold drawn films, and fibers. In this case fewer and broader X-ray diffraction peaks arise. Different infrared spectra and lower densities (d=0.88) were found. Natta et al. [6] described this form as "smectic". Two broad X-ray diffraction peaks were exhibited by this smectic structure. Natta et al. [6, 8] suggested the source of this form is a random arrangement of left and right handed helices in the unit cell.

In the same year, Keith et al. [9] presented X-ray diffraction evidence of the existence of a new crystallographic form in polypropylene. Using carefully quenched films they described a strong set of arcs in WAXS film patterns at 5.53 [dot{A}] and 4.173 [dot{A}]. They suggested that this corresponded to a hexagonal unit cell with basal parameter a = 12.74 [dot{A}] and an axial parameter of about 6.35 [dot{A}] with the inner arcs corresponding to a [200] reflection and the outer arcs to a [201] reflection (see Table 1). In a 1961 paper, Addink and Beintema [10] described samples containing Natta and Corradini's [1-4] monoclinic structure, from hereafter designated as [alpha] and Keith et al.'s [8] crystalline structure hereafter described as [beta]. They accepted Keith et al.'s proposal that the unit cell is hexagonal, but they argued the basal parameter is better taken as 6.38 [dot{A}], half of Keith et al.'s value. They suggest that crystallites consist of all right-handed or left handed helices. Addink and Beintema [10] also proposed a [gamma] crystalline form of isotactic polypropylene. Subsequent papers have both struggled over the nature of the unit cell of the [beta] form [11-13] or studied conditions under which the [beta], y, and smectic (now called pseudo-hexagonal) forms may be formed [14-21].

Studies of crystallization of polypropylene during processing, began with melt spinning/drawing investigations of Wyckoff [14] and Sheehan and Cole [15] in the early 1960s. Melt spinning investigations continued through the work of Katayama et al. [22], Kitao et al. [23], Fung et al. [24], Spruiell and White [25], Ishizuka and Koyama [26], Nadella et al. [27], Shimizu et al. [28], Jinan et al. [29] and the current authors [30] (see also Piccarolo et al. [31] and Martorana et al. [32]). It was clear that severe quenching of polymer melt filaments at low drawdown ratios led to smectic/pseudo-hexagonal structures [15, 25, 27]. Under a wide range of mild quench conditions including modest to high spinline stresses, uniaxially oriented [alpha]-monoclinic structures were found. High speed melt spinning at elevated temperatures has been found to lead to smectic/pseudo-hexagonal structures [29]. Studies of tubular film extrusion have generally found [alpha]-monoclinic structure [33]. Observations of the [beta] form seem limited through this structure has been found in injection molded parts [20, 34, 35] and in specially nucleated films [21]. Smectic structures are also produced by cold drawing monoclinic polypropylene filaments [14, 15].

It would seem logical that the type of crystalline form that occurs during solidification should depend upon the cooling rate, the level and character of the stress field and the applied pressure. These variables are all known to influence crystalline forms occurring in polymers. Stress seems pertinent rather than the kinematics of flow and deformation because the Rheo-Optical Law between birefringence and stress is obeyed [36, 37] by flexible chain polymer melts such as polypropylene. Birefringence is the anisotropy of the polarizability tensor [38, 39] and is well known to represent a second moment of the orientation distribution. This polymer chain orientation in the melt is controlled by the stress field. Further it is possible to quantitatively predict crystalline orientation in poly-olefins from applied stress fields [25, 27, 30].

It is our purpose in the present paper to explore the relationship of the crystalline form of isotactic polypropylene to cooling rate and applied uniaxial stress. We will develop a "map" of crystalline form as a function of these variables based on both our own experiments and results in the literature. We will also apply this map to quenched thick cylinders of polypropylene to interpret the structural variations across their cross section.

2. STRUCTURE DEVELOPMENT IN THIN FILAMENTS

2.1. Purpose

Our purpose in this section is to develop a correlation between quench rate, uniaxial stress, and the crystalline character of the solid phases formed. In our correlations we have used the experimental results of many different investigators on fibers and films including Natta et al. [6], Keith et al. [9], Addink and Beintema [10], Sheehan and Cole [15], Katayama et al. [22], Nadella et al. [27], Shimizu et al. [28, 29] as well as our own studies, which are reported below.

2.2. Materials

Various polypropylenes have been used by the authors whose data are here used. This is summarized in Table 2.

The isotactic polypropylene sample used by the authors was supplied by Quantum Chemical Corporation. Its melt index is 5.0 (g/10min.).

2.3. Preparation of Thin Filaments

In our experiments the samples were melt spun from an Instron capillary rheometer using a capillary spinneret of diameter (D) 1.6 mm (1600 [mu]m) and length diameter ratio of 9.3. Melt spinning was carried out at various melt temperatures and take-up velocity ([V.sub.L]). Draw-down ratios up to 282 have been investigated. The diameter, d, of the melt spun filaments is given by the expression,

d = [[[frac{[[rho].sub.m]}{[[rho].sub.s]}] [frac{4Q}{[pi][D.sup.2]}]].sup.1/2]] [frac{D}{[sqrt{[V.sub.L]}]}] = [[[frac{[[rho].sub.m]}{[[rho].sub.s]}]].sup.1/2]] [[[frac{[V.sub.0]}{[V.sub.L]}]].sup.1/2]] D (1)

where [[rho].sub.m] is the melt density, [[rho].sub.s] is the solid fiber density, and Q is the melt volumetric flow rate. Here D is 1.6 mm. Filaments of thicknesses down to 100 [mu]m were produced in our studies.

The filaments were variously melt spun into ice water and through ambient air to a take-up device consisting of a polytetrafluorethylene roller. A Roth-schild Electronic Tensiometer was used to measure filament spinline tension. The distance of the capillary to the take-up in spinning through air was 600 mm. When a quench bath was used, it was placed 150 mm below the spinneret.

2.4. X-Ray Diffraction Investigations

The melt spun filaments in our experiments were characterized by wide angle X-ray diffraction using a General Electric X-ray generator (GE-XRD6) equipped with a copper target tube and graphite crystal mono-chrometer was used to obtain CuK[albha] radiation ([lambda] = 1.5418 [dot{A}]).

2.5. Results

Figure 1 shows from X-ray patterns of isotactic polypropylene at various temperature and draw-down ratio with both air (Fig. 1f) and ice-water quenching (Figs. 1a, b, c, d, e) obtained on our melt spun filaments. Figure 2 shows wide angle X-ray diffractometer scans as a function of Bragg angle. Figure 2 shows the 20 scan for high and low stress water quenched sam-pies at various melt temperatures.

For air quenched PP spun at 200[degrees]C, 230[degrees]C and 260[degrees]C, the samples had a well defined WAXS reflections at 6.42 [dot{A}], 5.37 [dot{A}], 4.82 [dot{A}], and 4.19 [dot{A}]. These correspond to the [alpha]-monoclinic unit cell (110), (040), (130), and (111) reflections [4, 5].

The 200[degrees]C, 230[degrees]C and 260[degrees]C melts spun into fibers and quenched in ice water had a less defined character. These may be identified as having a pseudo-hexagonal/smectic character. As draw-down ratio and spinline stress increased, the melt spun fiber's diffraction patterns became increasingly monoclinic in character. This was much less so for the 260[degrees]C melt.

None of the melt spun fibers was found to exhibit diffraction peaks corresponding to the [beta] crystalline form.

The earlier reported behavior of isotactic melt spun polypropylene filaments by other investigators [15, 19-21] are at least qualitatively similar to what we have reported above.

3. REPRESENTATION OF STRUCTURAL CHANGES

3.1. Isotropic Quiescent Crystallization

The experimental studies of the previous section and those of many other authors [1-5] have revealed that when quiescent polypropylene is cooled slowly from the melt that a monoclinic crystalline form designated [alpha] is formed. A more rapid cooling and quenching at 100-128[degrees]C [9, 19] produces a hexagonal form designated as [beta] together with [alpha]. A still more rapid quenching to 0[degrees]C produces the pseudo-hexagonal/ smectic form [6, 7, 15, 27, 30]. Thus it seems clear that

crystalline state =

F [rate of cooling [lgroup][frac{dT}{dt}][rgroup]. quench temp.] (2)

The above discussion suggests a diagram such as shown in Fig. 3 that indicates the crystalline states that form at different cooling rates. Such plots are well known to metallurgical engineers and were widely used together with isothermal transformation investigations for the characterization of quenching of steels [40-43]. They are called Continuous Cooling Transformation or CCT plots and were previously discussed by Spruiell and White [25] to represent crystallization of polyolefins. If we make an equivalence between steel and polypropylene, Austenite is equivalent to molten polypropylene, Ferrite and Cementite to [alpha]-monoclinic polypropylene, Martensite to the smectic form. For polypropylene with a [T.sub.g] of -15[degrees]C, the peak of the kinetic crystallizability curve should be about 90[degrees]C.

We draw lines in Fig. 3 on the plots corresponding to the heat treatment studies of Natta et al. [6], Keith et al. [7], and Turner Jones et al. [12]. This would seem to require that [beta] crystals occur near the nose of the CCT curve.

3.2. Influence of Uniaxial Applied Stresses

Uniaxial spinline tensile stress also influences structure development in the melt spinning of polypropylene. Melt spun fibers are observed to exhibit only [alpha]-monoclinic and smectic, but not [beta]. This is seen in our Figs. 1 and 2 and in the work of Spruiell and White [25], Nadella et al. [27], Jinan et al. [29] and the current authors [30]. Further uniaxial stresses are well known to significantly increase crystallization rate and thus to shift CCT curves towards shorter times.

We may express this by generalizing Eq 2 to

Crystalline state = F[[frac{dT}{dt}], [sigma]] (3a)

Rate of Crystallization = G[[frac{dT}{dt}], [sigma]] (3b)

where [sigma] is tensile stress. As stress is a second order tensor and the other variables in this equation are scalars. It would seem better to express [sigma] in terms of invariants such as

tr [sigma] tr [[sigma].sup.2] tr [[sigma].sup.3]

However, we do not have data from different stress states to allow investigating this. It does however indicate that applied pressure (equivalent to tr [sigma]) should be considered as well.

3.3. Estimation of Rate of Cooling, dT/dt

It is a problem to estimate rates of cooling at solidification and actual temperatures of solidification themselves. In the science of heat transfer, the heat flux q (Joule/sec) at a surface may be expressed in terms of Newton's Law of cooling (e.g., Ref. 44))

q = hA([T.sub.s] - [T.sub.surr]) (4)

where h is a heat transfer coefficient, A is a surface area, [T.sub.s] is the surface temperature and [T.sub.surr] is the temperature of the surroundings.

Consider the cooling of a descending filament in a thread line. The cooling rate may be expressed [45]

Gc [frac{dT}{dx}] = [rho]c[lgroup][frac{[pi][d.sup.2]}{4}][rgroup] [frac{dT}{d[t.sub.res]}] = -h[pi]d (T - [T.sub.surr]) (5)

where [t.sub.res] is residence time in the spinline, G is the mass flow, [rho] the density, c the heat capacity, h the heat transfer coefficient, and [T.sub.surr], the temperature of the surroundings, d is the filament diameter as defined in Eq 1.

The temperature-residence time gradient is:

[frac{dT}{d[t.sub.res]}] = - [frac{4h}{rcd}] (T - [T.sub.surr]) (6)

Heat transfer coefficients during melt spinning of fibers through air have been correlated notably by Kase and Matsuo [45] through expressions of form

[frac{hd}{[k.sub.a]}] = 0.42 [[lgroup][frac{dv[[rho].sub.a]}{[[eta].sub.a]}][rgroup].sub.1/3] (7)

where d is the fiber diameter, [k.sub.a] is the thermal conductivity of air, [[rho].sub.a] is the density of air, and [[eta].sub.a] is the viscosity of air. Equation 7 suggests that heat transfer coefficients are below 500w/[m.sup.2]k when the diameter of the fiber is of order hundreds of microns.

Quenching descending fibers into cold water should involve boiling phenomena. Heat transfer coefficients for boiling heat transfer have been investigated by Piling and Lynch [46], Jakob and Fritz [47], Nukiyama [48], and Rohsenow [49]. Generally these heat transfer coefficients are much higher than those for convective heat transfer. In the nucleate pool boiling region, the most widely accepted correlation is that of Rohsenow [49] who expresses the heat transfer coefficient h

h =

[[eta].sub.1][Delta][H.sub.v][[frac{g([[rho].sub.1] - [[rho].sub.v])}{[gamma]}].sub.1/2] [[lgroup][frac{[c.sub.p1]}{[C.sub.sf][Delta][H.sub.v]P[[r.sup.1.0].su b.1]}][rgroup].sup.3] [([T.sub.s] - [T.sub.sat]).sup.2] (8)

where [[rho].sub.1] is the density of the saturated liquid, [[rho].sub.v] is the density of the saturated vapor, [[eta].sub.1] is the liquid viscosity, [Delta][H.sub.v] is the heat of vaporization per unit mass, g is the local gravitational acceleration, [gamma] is the surface tension, [c.sub.p1] is the specific heat of the saturated liquid, [C.sub.sf] is the surface-fluid constant ([approx] 0.01), P[r.sub.1] is the Prandtl number of the saturated liquid ([c.sub.p1] [[eta].sub.1]/[k.sub.1]), and [T.sub.s]-[T.sub.sat] is the excess temperature of the surface temperature over the boiling temperature. These suggest heat transfer coefficients orders of magnitude higher than for air quenching. The value of h is of order 30,000w/[m.sup.2]K when the diameter of the fiber is of order hundreds of microns.

From Eq 6 at a temperature of 90[degrees]C where isotactic polypropylene might be considered to crystallize based upon earlier investigators of melt spinning [22, 27], values of dT/d[t.sub.res] computed for spinning through air are of order 500[degrees]C/sec while for boiling heat transfer through ice-water the value of dT/d[t.sub.res] is 45.000[degrees]C/sec. The diameter of the fiber is taken as 100 [mu]m in these calculations.

3.4. Structural Map

We have sought to correlate the cooling rate at the inception of crystallization together with applied stress to indicate the position where different crystalline structures occur. Using our experimental data and those of other investigations [9, 25, 27, 29, 30] for the crystalline character of melt spun fibers, together with calculations of dT/dt, we have constructed Fig. 4. It can be seen that at low cooling rates and high stresses, generally monoclinic structures are formed. At high cooling rates and low stresses there is a large pseudo-hexagonal/smectic region. The situation with the [beta]-form is much more difficult. The behavior is much less reproducible from sample to sample and seems very susceptible to nucleating agents (e.g. Ref. 21). [beta] has not as indicated earlier been seen in melt spun fibers but has been claimed [20] as a stress favored form based in molding experiments [20, 34, 35]. [beta] would seem to be suppressed by uniaxial tensile but apparently not by shear stresses. We suggest as a beginning the small region shown in Fig. 4 as where [beta] might be expected to form. This is based by the experiments of Keith et al. [9] and Turner Jones et al. [12]. This region should change in size depending upon nucleating impurities.

3.5. CCT Curves With Uniaxial Stress Effects

It is possible to use the results of Fig. 4 with the solutions of Eq 6 to 8 to construct CCT curves for polypropylene as shown in Fig. 5. This includes zero stress behavior forming [alpha], [beta] and smectic structures based on the experiments of Natta et al. [1-6, 8] and Keith et al [9]. Dashed lines represent high stress data from our own results and those of Katayama et al. [22], Nadella et al. [27], and Shimizu et al. [28, 29]. One obtains a series of curves associated with different uniaxial stress levels.

The effect of uniaxial stress is that the nose of [alpha]-monoclinic polypropylene moves to the left and hovers over what was the smectic region in the quiescent state. The effect of uniaxial stress is analogous to the influence of certain alloying elements such as cobalt in the transformation of Austenite. The implication that only [alpha] forms at high uniaxial stresses at moderate cooling rates requires additional critical discussion.

4. QUENCHING OF THICK RODS

4.1. General

It should be possible to predict the crystalline forms occurring in a quenched thick cross section from knowing the cooling rate and the stress-field if we can predict the transient temperatures during cooling. We should be able to use Figs. 3 to 5 to accomplish this.

In this section we will describe an experimental study of quenching a thick rod and then determining the structural variations through the cross section. We will experimentally determine the structural character through the cross section and then seek to predict it from first principles. Kang and White [50] have previously done this for the orientation birefringence through a thick melt spun filaments of polycarbonate.

4.2. Experimental

Samples of rods of diameter 12 mm were molded in the barrel of an Instron capillary rheometer. These were subsequently extruded out and quenched in ice-water.

The quenched samples were cut into several parts represently different radii. These sections were 1.5 mm thick. WAXS patterns were obtained using a General Electric X-ray generator (GE-XRD6) and used to determine crystalline character.

X-ray diffractometer scans from samples cut from different positions are shown in Fig. 6a, b, c, d, and e. We have sought to estimate the amounts of monoclinic [alpha], hexagonal [beta], and pseudohexagonal smectic throughout the cross-section. In the 1.5 mm thick section including the outer surface, we detect primarily [beta], but not the smectic form, as might be expected. The detection of the [beta] from is based upon the (100) reflection at 5.5 [dot{A}]. As one moves into the core, the portion of crystallized polypropylene with monoclinic structure increases.

We have experimentally determined the relative amounts of the a and [beta] phases by quantitative evaluation of the areas under WAXS peak and comparing them to what would be expected for pure [alpha] and [beta]. Specifically we used (110), (040), and (130) for [alpha] and (100) for [beta]. Figure 7 shows the calculated distribution of relative amounts of [alpha] and [beta] as a function of radial position.

4.3. Interpretation of Structural Cross-Sectional Distributions in Thick Quenched Samples

We have sought to analyze the problem of quenching of a thick rod. The temperature-time-position profile through a thick quenched cylindrical sample may be obtained from Fourier's law of heat conduction [51]. We take this for slow crystallization to be of form

[rho]c [frac{[partial]T}{[partial]t}] = k [frac{1}{r}] [frac{[partial]}{[partial]r}] [lgroup]r[frac{[partial]T}{[partial]r}][rgroup] + [rho][Delta]H [frac{dX}{dt}] (9)

where

T(r,0) = [T.sub.0] (10a)

- k [frac{[partial]T}{[partial]r}] (R, [x.sub.1]) = h([T.sub.s] - [T.sub.surr]) (10b)

[frac{[partial]T}{[partial]r}] (0, [x.sub.1]) = 0 (10c)

where [T.sub.s] is the temperature at surface of thick rod and [T.sub.surr] is the surrounding temperature. Here [Delta]H is the heat of crystallization per unit mass and [partial]X/[partial]t the rate of crystallization.

It should be noted that Eqs 9 and 10 differ from the classical Stefan analysis [45] of heat conduction during solidification. This procedure was developed to interpret the melting of ice and freezing of water. It represents a very high crystallization rate asymptote and is not appropriate for polypropylene. We instead follow the approach of Berger and Schneider [52], which was developed for analyzing the slow crystallization of thermoplastics.

Let us first consider the case where [Delta]H is zero. The solution of Eq 9 yields the temperature profile across the cross section as function of time. It has the form [51]

[frac{T(r, t) - [T.sub.surr]}{[T.sub.0] - [T.sub.surr]}] =

2 [[[sum].sup.[infty]].sub.n=1] [frac{1}{[[gamma].sub.n]}] [frac{[J.sub.1]([[gamma].sub.n])[J.sub.0][[[gamma].sub.n](r/R)]}{[[[J .sup.2].sub.0] ([[gamma].sub.n]) + [[J.sup.2].sub.1] ([[gamma].sub.n])]}] [e.sup.-[[[gamma].sup.2].sub.n][alpha]t/[R.sup.2]] (11)

where [[gamma].sub.n] is [[lambda].sub.n]R and [[lambda].sub.n] represents the eigenvalues. [J.sub.0]([[gamma].sub.n]) and [J.sub.1]([[gamma].sub.n]) are Bessel functions.

We now consider the full problem where [Delta]H is not zero. It is also readily possible to solve Eq 9 analytically if the source term, i.e. [rho][Delta]H([partial]X/[partial]t), is independent of temperature and time. However, this is not the case, and we must instead solve Eq 9 numerically. In doing this we must represent the crystallization rate of polypropylene as a function of temperature and time as

[frac{dX}{dt}] = 0 (T [greater than] [T.sub.2])

[frac{dX}{dt}] = [alpha] (T,t) (1 - X) ([T.sub.2] [greater than] T [greater tan] [T.sub.1]) (12a,b,c)

[frac{dX}{dt}] = 0 ([T.sub.1] [greater than] T)

To proceed we introduce a finite difference scheme. We know the point where crystallization starts from Fig. 8. Dividing the rod into M radial slices, we obtain from Eq 9,

[rho]c [frac{T(r,t + [Delta]t) - T(r,t)}{[Delta]t}] = k [lgroup][frac{T(r + [Delta]r,t) + T(r - [Delta]r,t) - 2T(r,t)}{[([Delta]r).sup.2] + [frac{1}{m[Delta]r}] [frac{T(r + [Delta]r,t) - T(r - [Delta]r,t)}{2[Delta]r}][rgroup] + [rho][Delta]H[frac{dX}{dt}] (r,t) (13)

where m = 0 at core and m = M at surface of the thick rod.

4.4. Comparison of Experiment with Predictions

We first applied the solution of Eq 11, which represents a zero heat of crystallization for a thick sample. Here [rho] is taken as 910kg/[m.sup.3], c is 1.81 x [10.sup.3]J/kg-K, h is 30,000W/[m.sup.2]-K, k is 0.138W/m-K and [T.sub.surr] is 0[degrees]C. The temperature profile is shown as a function of radius in Fig. 8. Comparing this solution to Fig. 3 leads to the prediction that the outer layer of the 80% of the rod should be smectic and the remainder [alpha] and [beta]. This is not what is found.

We now apply our solution with [Delta]H [neq] 0 to this problem. Values of [Delta]H for polypropylene in the range 84 to 238kJ/kg have been cited in the literature. We chose [Delta]H = 238kJ/kg, which is taken from Janeschitz-Kriegl and Eder's paper [53]. The value of [alpha](T, t) of Eq 12b was taken from the work of Malkin et al. [54] on the quiescent crystallization of polypropylene to be 0.056[s.sup.-1] for the case of the crystallization temperature being 110[degrees]C and the crystallinity 50%. We used the finite-difference conduction equation of cylinder for numerically solving Eq 9 and Eq 13. We did the numerical calculations by using the MATLAB program.

The numerical solution of Eq 9 leads to the temperature profile shown in Fig. 9. Plateaus appear in the temperature profile which are not seen in Fig. 8 where [Delta]H was taken to be zero. There are due the evolution of heat during crystallization. The effect of [Delta]H is to make the crystallization process slower.

We have sought to use the calculated crystallization rates of Fig. 9 to predict the distribution of crystallization phase through the cross section shown in Fig. 7. We now do not predict the smectic unit cell in the outer portions of the rod. We predict instead that there is the mixture of the [alpha] -monoclinic and [beta]-hexagonal unit cell structures which become increasingly monocilnic as we move to the core of the rod. This is what is observed. If we vary [Delta]H downward from 238 to 84kJ/kg there is not much effect on these results.

5. CONCLUSIONS

Using thin sample (fiber and film) experimental data, we can predict the relationship of crystalline form of isotactic polypropylene to cooling rate and applied this to predict the crystalline structure variation through a thick rod by modeling the crystallizing kinetics together with the transient Fourier heat conduction equation.

CHEOL-HO CHOI and JAMES L. WHITE

Institute of Polymer Engineering

University of Akron

Akron, Ohio 44325

REFERENCES

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Strong WAXS Reflections Occurring in Crystalline Isotactic Polypropylene. d spacings ([dot{A}]) Natta and Natta et al. (6) Keith et al. (9) Corradini (1-5) Interpretation Interpretation Observation Interpretation 6.25 [alpha]-110 -- -- 5 85 (broad) -- smectic -- 5.5[sim]5.53 -- -- [beta]-200 5.25 [alpha]-040 -- -- 4.75 [alpha]-130 -- -- 4.173[sim]4.20 [alpha]-1ll -- [beta]-201 4.05 [alpha]-13 1/041 -- -- d spacings ([dot{A}]) Addink and Beintema (10) Interpretation 6.25 [alpha]-110 5 85 (broad) -- 5.5[sim]5.53 [beta]-100 5.25 [alpha]-040 4.75 [alpha]-130 4.173[sim]4.20 [alpha]-111/[beta]-101 4.05 -- Various Author's PP Melt samples. Authors Supplier and Grade Characterization Observed Unit Cell Keith et al. Hercules Profax Film [alpha]-monoclinic, [9, 10] Mw = 500,00 [beta]-hexagonal Nadella et al. Hercules Profax 6423 Fiber [alpha]-monoclinic, [27] MI = 6.6, smectic Mw = 277,000 Kikutani et al. Ube Industries Ltd. Fiber [alpha]-monoclinic, [29] PP-S 115M pseudohexagonal MI =15, Mv = 185,000 Sheehan and Hercules Profax Fiber [alpha]-monoclinic, Coie [15] MI = 0.61, 2.71, 3.58, smectic 7.89, and 9.37 Mw = 680,000,540,000, 450,000,400,000,and 320,000. Choi and White Quantum Chemial Co. Fiber [alpha]-monoclinic, [30] PP 8000-GK smectic MI = 5.0

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Author: | CHOI, CHEOL-HO; WHITE, JAMES L. |
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Publication: | Polymer Engineering and Science |

Date: | Mar 1, 2000 |

Words: | 5579 |

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