Relations between Stereoregularity and Melt Viscoelasticity of

Article pubs.acs.org/Macromolecules

Relations between Stereoregularity and Melt Viscoelasticity of Syndiotactic Polypropylene Naveed Ahmad,† Rocco Di Girolamo,‡ Finizia Auriemma,‡ Claudio De Rosa,‡ and Nino Grizzuti†,* †

Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli “Federico II”, Piazzale V. Tecchio, 80, 80125 Napoli, Italy ‡ Dipartimento di Scienze Chimiche, Università di Napoli “Federico II”, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy ABSTRACT: A set of syndiotactic polypropylene samples with tailored degree of stereoregularity and uniform distribution of stereodefects, obtained via organometallic catalysis, was used to study the relation between the syndiotactic pentad concentration and the viscoelastic plateau modulus in the melt state. The plateau modulus was found to increase with increasing the degree of stereoregularity, indicating that syndiotactic polypropylenes of different stereoregularity produce a different entanglement density of the amorphous phase. The change in plateau modulus was highly nonlinear for large values of syndiotactic pentad contents, suggesting that the presence of even a relatively small number of defects along the syndiotactic backbone significantly alters the space filling attitude of the polymer chain in the melt. This result, which confirms and extends those already obtained from experiments and numerical simulations, points out to the concept that the dynamics of macromolecular chains is largely controlled by the relative configuration of consecutive stereoisomeric centers along the chain, thus providing a link between chain dynamics and molecular architecture.

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where A is a constant of order unity. Typically, Vperv ≫ Veff. Equations 1−3 identify the volumetric properties of a single polymer chain. Quite surprisingly, however, they also define the interchain behavior in the melt. Indeed, the ratio between Vperv and Veff identifies the number of chains N occupying the pervaded volume. The molecular weight between entanglements, Me, is defined as the molecular weight such that N = 2, that is, when the test chain will be entangled with at most one other chain. From eqs 1-3 it follows that:

INTRODUCTION In the final decades of last century many efforts have been devoted to the determination of the relation between the microstructure of polymer melts and the equilibrium and dynamic macroscopic properties. In their fundamental review of 1994, Fetters et al.1 determined a full set of quantitative relationships relating molecular weight, density, chain dimensions and melt viscoelastic properties, with particular reference to the family of linear polyolefins. Their results can be summarized as follows. The linear chain is assumed to be Gaussian, with a mean square end-to-end radius ⟨R2⟩0 (or, alternatively, radius of gyration ⟨Rg2⟩0) given by: ⟨R2⟩0 = 6⟨R g 2⟩0 = C∞

M 2 l0 m0

3 m0 3 864 864 ⎛ M ⎞ Me = 2 = Me = 2 2 2 ⎜ 2 ⎟ A NA 2C∞3ρ2 l0 6 A NA ρ ⎝ ⟨R ⟩0 ⎠

Equation 4 shows that Me is an intrinsic, essentially Mindependent property of the polymer chain. At the same time, however, Me is directly related to the entangled polymer melt characteristics. In fact, the standard theory for the viscoelasticity of linear monodispersed, entangled polymer melts gives2

(1)

In eq 1 C∞ is the characteristic ratio, M the molecular weight, m0 the molecular weight per backbone bond, l0 the bond length. The space filling properties of the chain are described by two different “volumes”. On the one hand, the ef fective volume occupied by one chain (the test chain) is M 1 Veff = ∝M ρ NA

GN0 =

Vperv = A⟨R g 2⟩0

∝ M3/2 © XXXX American Chemical Society

ρkNAT Me

(5)

where G0N is the plateau modulus, k is the Boltzmann’s constant and T the absolute temperature. Notice that some authors prefer to use an alternative relation where the factor 4/

(2)

where ρ is the polymer density and NA the Avogadro’s number. On the other hand, the volume pervaded by one chain can be written as: 3/2

(4)

Received: July 12, 2013 Revised: September 6, 2013

(3) A

dx.doi.org/10.1021/ma401469a | Macromolecules XXXX, XXX, XXX−XXX

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5 appears in the second member.3 Since this factor has no consequences on the results of this paper, we opted for the version without the 4/5 factor. Obviously, when comparing the results of the present work with those reported in the literature, the necessary conversions will be applied. Equations 4 and 5 where exploited to determine the relations between the microstructure and the macroscopic parameters of polymer melts by means of independent measurements of the mean square end-to-end radius (from small angle neutron scattering, SANS) and of the plateau modulus (from linear viscoelasticity).1,4−6 The analysis of a very large number of polymer species of different chemical structure indicated that the dimensionless constant A can be considered as a temperature independent, “universal constant”. The value A = 1.545 was found to provide an excellent agreement for a large number of polymers over a wide temperature window.3 It must be outlined that, in view of the high degree of correlation between the experimental measurements and the value of A obtained by data regression analysis, the complex (and both time-consuming and expensive) SANS measurements of ⟨R2⟩0 become in a way redundant. As a consequence, the much more affordable measure of the plateau modulus is in principle the only requirement to extract the information about the microstructure characteristics of a given polymer melt. Along with the molecular weight between entanglements, the so-called packing length is often used as a measure of the space filling ability of a polymer chain in the melt. The packing length, p, is defined as the ratio between the effective volume of the chain and its mean square end-to-end radius, and can be calculated as1 ⎛ A2 kT ⎞1/3 ⎟ p=⎜ 0 ⎝ 864GN ⎠

outstanding physical and mechanical properties, the most important one relying on the elastomeric behavior, notwithstanding the high crystallinity and the relatively high glass transition temperature.10 While sPP definitely shows interesting and unexpected elastic properties when compared to its isotactic (iPP) counterpart,10 one further striking difference comes from the peculiar behavior in terms of chain dimensions and rheological behavior in the melt state. The chain dimensions of sPP were measured for the first time by Jones et al.11 Their SANS data showed that, in spite of the identical monomer chemistry, sPP exhibit a (⟨R2⟩0)/(M) ratio considerably larger (about 1.5 times) than that of iPP. Conversely, previous measurements12 showed that the melt chain dimensions of isotactic and atactic PP were very similar. The difference between iPP and sPP dimensions in spite of their identical molecular weight per bond was also outlined by Fetters et al.5 As expected, in view of the equivalence stated by eqs 4 and 5, the above difference reflects also in the viscoelastic behavior of PPs of different stereoregularity. The plateau modulus of sPP was measured for the first time by Eckstein et al,13 who found that highly stereoregular sPPs have a plateau modulus significantly larger (about three times) than those, very similar to each other, of aPP and iPP. These results were confirmed by more recent measurements by Liu et al.14 Like the direct SANS measurements of the chain dimensions, the 3-fold enhancement of G0N for sPP confirms that its particular stereoregular architecture determines a more effective space filling in the melt state. The reason for this behavior is probably to be found in the fact that the chain conformation of sPP in the melt is dominated by trans conformations. This hypothesis, which was found to be compatible with earlier high resolution 13C NMR measurements,15 has been more recently confirmed by molecular dynamics simulations.16 The role of sPP stereoregularity in determining the chain dimensions of a polymer chain has been also considered for the case of (PE/sPP) copolymers, with sPP blocks having a high degree of stereoregularity.17 The measured increase in plateau modulus was the result of the larger unperturbed chain dimension of s-PP, compared to i-PP and a-PP, and its subsequent influence on the PE/sPP entanglement molecular weight. On the basis of the above considerations, the aim of this paper is to investigate the direct role of syndiotacticity on the viscoelastic plateau modulus and, as a consequence, on the chain dimension properties, on a sequence of sPPs characterized by a different syndiotacticity, obtained by metallocene catalysis. The structure of the paper is the following. After the above Introduction, which also motivates the objective of the present work, in the next section the materials, the experimental techniques, and the methods used to extract the plateau modulus from the experimental data are presented. Then, the results of the experimental viscoelastic measurements are reported and translated into microstructure polymer chain parameters. The discussion of the Experimental Results is followed by some concluding remarks.

(6)

Actually, p and Me are equivalent parameters. They offer, however, alternative physical views of the ability of polymer chains to “fill the space” in the melt state. On the one hand, Me indicates the (average) molecular weight between two entanglement points. Polymers with higher Me are “bulkier” than polymers with lower Me. Alternatively, one may think of the packing length in the following way. Take one polymer chain and confine it in a cylinder of radius ⟨R2⟩o1/2. Then, squeeze the cylinder to a “pie” until its volume equals the effective chain volume. The pie thickness, δ, is given by δ=

Veff 2

π ⟨R ⟩0

=

p π

(7)

The packing length, therefore, can be somewhat seen as a measure of the lateral size of the chain as compared to the longitudinal size. Using the words of Larson:7 “A large value of p means that the chain segments are short and fat, so that within the radius of gyration of the chain relatively less room is lef t to the other chains”. The discovery of single-center metallorganic catalysts for the polymerization of olefins has allowed for the synthesis of polyolefins with high control of the degree of stereoregularity, molecular mass and degree of incorporation of comonomers.8 One significant example within this class of polymers is given by syndiotactic polypropylene (sPP), whose scientific interest has grown only after the discovery of metallocene catalysts.8−13 The use of single-center organometallic catalysts made it possible to synthesize highly stereoregular sPP samples9 with

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EXPERIMENTAL SECTION Syndiotactic Polypropylenes. Samples of sPP with different degrees of syndiotacticity were selected from those studied in ref 18 and are listed in Table 1. They were prepared using the metallocene and half-metallocene catalysts of Chart 1.

B


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calorimeter performing scans in a flowing N2 atmosphere and a heating rate of 10 °C/min. Stereoregularity was determined by analysis of the 13C NMR spectra. Samples in Table 1 are ordered by decreasing rrrr abundance. The change in tacticity is mirrored by a corresponding decrease of the melting temperature. In the sample with the lowest [rrrr] the melting temperature could not be measured, indicating that the behavior is close to that of an atactic chain. As it will be shown later, the Mw ≫ Me relation is always obeyed, meaning that all samples in the melt state can be considered as well entangled. For the rheological tests, polymers were cast in films of about 0.5 mm thickness by compression molding at 423 K. Rheological Measurements. Small amplitude oscillatory shear measurements were carried out on an Advanced Rheometric Expansion System (ARES, TA Instruments). Because of the small sample quantities available, a parallel plate geometry with 8 mm plate diameter was always used. Polymer discs of the same diameter were punched out of the compression molded films. The gap thickness varied according to film size, but was always included between 0.45 and 0.55 mm. Temperature control was guaranteed by the ARES convective gas oven. In order to minimize possible thermal degradation effects, all test were performed using nitrogen as the heating gas. Before running the experiments, each freshly loaded sample was submitted to the same thermal history. In particular, samples were loaded in the rheometer at 473 K and there left for 10 min, in order to erase any crystalline memory. During this time, a time sweep oscillatory test at the frequency of 1 rad/s was run. After an initial decrease of the signal, due to melting, the moduli stabilized to a constant value, thus indicating the melt was complete, and also that no significant thermal degradation was occurring. After this thermal annealing, the sample was taken to the test temperature. When necessary, a gap compensation adjustment was applied, taking into account the thermal expansion of the instrument tools. Isothermal dynamic frequency sweep tests were generally performed within the frequency window 10−1−102 rad/s and the applied deformation was always kept below the linearity limit. In order to widen the frequency window, tests were performed at different temperatures and the time temperature superposition (TTS) principle was then applied to generate master curves at the reference temperature of 473 K. Both horizontal and vertical shift factors were used according to the procedure outlined by Ferry.23 In the latter case, the necessary temperature dependence of the melt polymer density was obtained by using the reduced variable correlation proposed by Rojo et al.24 The same density information was used for the calculation of Me from the plateau modulus data (see next section). The temperature window explored in the linear viscoelasticity measurements was different for each sample. The upper temperature limit was 473 K for all polymers, as a compromise with respect to thermal degradation (see above). The lower temperature limit was higher for the polymers with higher rrrr content, due to the higher crystallization temperature. This limited the accuracy in the determination of the plateau modulus for some samples, and required the adoption of different methods for the determination of the plateau modulus, as discussed below.

Table 1. Main Properties of the sPP Polymers sample

catalyst

[rrrr] (%)

Tm (K)

sPP-1 sPP-2 sPP-3 sPP-4 sPP-5 sPP-6

1 2 3 4 5 6

93 91.5 70.6 60.1 46.9 26.5

422 418 373 350 321 −

Mw (g/mol) 213 766 297 241 886 1 190

000 000 000 000 000 000

Mw/Mna 2.4 4.5 2.3 2.2 2.5 2.4

a

Determined by GPC analysis at 408 K with 1,2 dichlorobenzene, using monodisperse fractions as a standard.

Chart 1. Structure of Zirconocene and Titanocene Complexes Used as Syndiospecific Catalysts of Propene Polymerization

The highly stereoregular sample sPP-1, with a fully syndiotactic pentad concentration, [rrrr], of 93 mol %, has been prepared using the single-center Cs-symmetric metallocene catalyst 1 isopropylidene(cyclopentadienyl)(9-fluorenyl)zirconium dichloride (Me2C(Cp)(9-Flu)ZrCl2, Me = methyl, Cp = cyclopentadienyl, Flu = fluorenyl), activated with methylaluminoxane (MAO),9 as described in ref 19. The highly stereoregular sample sPP-2 with higher molecular mass and larger polydispersity has been prepared with the Ti complex 2 (Ph2C(Cp)(3,6-t-Bu2Flu)ZrCl2, Ph = phenyl, t-Bu = tert-butyl), activated with MAO, at polymerization temperatures of 40 °C.20 Samples of medium stereoregularity, sPP-3 and sPP-4, have been prepared with the constrained geometry Ti complexes 3 [Me2Si(2,7-t-Bu2Flu)(t-BuN)]-TiCl220b and 4 [Me2Si(3,6-tBu2Flu)(t-BuN)]TiCl2), respectively activated with MAO.15 A poorly syndiotactic sample with [rrrr] = 46.9 mol % (sample sPP-5), has been prepared with the catalyst 5, a silyl-bridged indenyl-tert-butylamido complex of titanium activated with MAO, in which the indenyl ligand has a heterocycle condensed onto the cyclopentadienyl moiety.21 Finally, a fully amorphous polypropylene sample (sPP-6, [rrrr] = 26%) of high molecular mass has been prepared with the catalyst 6 dimethylsilyl (tetramethyl cyclopentadienyl) (tert-butylamido) TiCl2.22 Also this catalyst has been activated with MAO. The peak melting temperature, the concentration of the fully syndiotactic rrrr pentads, and the average molecular mass of all analyzed samples are reported in Table 1. Melting temperatures were obtained with a Perkin-Elmer DSC-7 differential scanning C


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Plateau Modulus Determination. Within the limits of tube models, where eq 5 holds, several semiempirical methods for the determination of the plateau modulus can be used. The most relevant ones were reviewed by Liu et al.25 It is common opinion that the most reliable method is to obtain the plateau modulus as the value of the elastic modulus corresponding to the minimum of the loss modulus:3,24 GN0 = G′(ω)G

(8)

GN0 = G′(ω)tan δ→ min

(9)

melting temperature, the induction time for the onset of crystallization at 408 K was still sufficiently long to allow for performing the test on a truly molten sample. In spite of that, the mechanical limit imposed to the maximum experimental frequency (which could be possibly increased only by using the very new piezoelectric technique27) was still too low to reveal the plateau region. As a consequence, measurements could not be performed at temperatures sufficiently low to disclose the plateau region. The data in Figure 1 extend to frequencies that are still far away from the region where either G″ or tan δ attain their minimum. Furthermore, the loss modulus is almost reaching a maximum, which however cannot be well appreciated. This situation is better understood when the loss modulus is plotted as a function of frequency on a linear−log scale in Figure 2.

″ → min Equation 6 requires an experimental data set sufficiently extended at high frequencies, where the minimum in G″ usually appears. Even so, in some cases (for example, for highly polydispersed polymers) only a minimum in tan δ (G″/G′) is detected. In this case, it is usually assumed that:

When the experimental data do not offer a sufficiently extended plateau region, but the maximum in loss modulus (marking the onset of the plateau region) is present, the socalled integral method is used:24 GN0 =

2 π

+∞

∫−∞

G″(ω) d[ln(ω)]

(10)

In order to be applied, eq 10 typically requires a somewhat arbitrary data extrapolation procedure at high frequencies.12,23Finally, when the available experimental frequency window is so narrow that only the crossover point can be measured, more empirical methods must be used. A successful method is the one proposed by Wu:26

Figure 2. Loss modulus of sPP-1 on a linear−log scale. The reference temperature is 473 K.

M

2.63 log Mw ⎛ G0 ⎞ N n log⎜ ⎟ = 0.38 + M ⎝ Gco ⎠ 1 + 2.45 log Mw n

In view of the limited window of experimental data, in this case the plateau modulus could be calculated only from the crossover method, eq 11. Figures 3 and 4 show the same results for sample sPP-2. In this case, the lower melting temperature allowed to extend the

(11)

where Gco is the crossover modulus and the polydispersity index Mw/Mn should be less than three. In this work, eqs 8−11 have been used for the determination of G0N, depending on the available data.

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EXPERIMENTAL RESULTS Figure 1 shows the frequency response master curve for sample sPP-1 at the reference temperature of 473 K. sPP-1 is the polymer with the highest rrrr pentad content and, therefore, with the highest melting temperature. The lowest temperature at which frequency sweep experiments could be performed was 408 K. Although this temperature was well below the polymer

Figure 3. Viscoelastic response of sPP-2 at the reference temperature of 473 K. Symbols as in Figure 1.

measurements over a wider temperature range. While the minimum in G″ or tan δ could not be observed also in this case, the possibility to explore lower temperatures, coupled to the higher molecular weight of sPP-2, makes it possible to observe a well-defined maximum in the loss modulus curve (Figure 3). This is made clearer in the linear−log plot of G″(see Figure 4). As a consequence, for sPP-2 the more reliable integral method, eq 10, could be used. In particular, the frequency region of the

Figure 1. Viscoelastic response of sPP-1. Key: (▲) elastic modulus; (○) loss modulus; (□) tan δ. The reference temperature is 473 K. D


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values obtained from different methods is found. The only exception is for sample sPP-2, where the plateau modulus calculated by the crossover method, eq 11, is much larger than that obtained from the integral method, eq 10. It must be reminded, however, that the crossover method is considered as reliable only when Mw/Mn < 3,25,26 whereas for sPP-2 (see Table 1) Mw/Mn = 4.5. For this reason, the plateau modulus for sPP-2 calculated by the crossover method is considered as unreliable and will not be considered in the subsequent data analysis.

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DISCUSSION On the basis of the plateau modulus data, the molecular weight between entanglements and the packing length calculated from eqs 5 and 6 are reported in Table 2. With the exception of sPP2 (see above), whenever possible Me has been calculated by averaging the values obtained with the different methods. The data reported in Table 2 clearly show that the sPP plateau modulus is an increasing function of the rrrr pentad content. As an obvious consequence of eqs 5 and 6, both the molecular weight between entanglements and the packing length are decreasing functions of [rrrr]. This means that, in spite of the identical molecular weight and chemical structure of each monomer, upon increasing [rrrr] the unperturbed chain dimension of sPP becomes larger or, alternatively, the average lateral size of the chain becomes smaller. The above-described dependence of chain dimensions upon [rrrr] is not unexpected, especially when the data reported in Table 2 are compared with the already available evidence in the literature. Figure 6 shows the behavior of Me as a function of

Figure 4. Loss modulus of sPP-2 on a linear−log scale. The reference temperature is 473 K.

loss modulus data after the maximum was sufficiently extended to allow for a robust extrapolation at higher frequencies and, therefore, for a reliable evaluation of the integral in eq 10. The experimental results for samples sPP-3 and sPP-4 are qualitatively very similar to those of sample sPP-2, and for this reason are not explicitly shown. On the contrary, for the samples with the lowest content of rrrr pentads, that is, sPP-5 and sPP-6, the possibility to measure the viscoelastic response at much lower temperatures allowed for the determination of the “complete” frequency response curve. This is shown in Figure 5 for sample sPP-5 (data for sPP-6 are not shown here

Figure 5. Viscoelastic response of sPP-5 at the reference temperature of 473 K. Symbols as in Figure 1. Figure 6. The molecular weight between entanglements as a function of the rrrr pentad relative abundance at 473 K. Key: (○) this work; (■) Eckstein et al.;13 (−) Liu et al.;14 (⬢) Liu et al.14 calculated using eq 11; (◆) Fetters et al.4 (atactic and isotactic polypropylene).

for brevity). The minimum in G″ and tan δ is now clearly appreciated, and makes it possible to apply eq 8 to determine the plateau modulus. The plateau moduli calculated from the experimental data are reported in Table 2. It can be immediately noticed that, when more than one method is used, good agreement between the

the rrrr pentad content. Me reaches a horizontal plateau for low values of [rrrr], which can be considered as the atactic limit. Conversely, at high values of pentad content, Me decreases as [rrrr] increases, the variation becoming steeper for higher values of [rrrr]. Figure 6 shows also the experimental values of Me from viscoelastic measurements already available in the literature. Eckstein et al.13 measured Me of three differently stereoregular polypropylenes. In Figure 6, their syndiotactic sample is the black square in the bottom right part of the plot. Unfortunately, the authors do not provide stereoregularity information in terms of pentad content, but only as triad relative abundance ([rr] = 93%). Therefore, their value is not directly comparable with our data. It must be added, as pointed

Table 2. Plateau Modulus of the sPP Polymers at 473 K G0N(Pa) sample

crossover

sPP-1 sPP-2 sPP-3 sPP-4 sPP-5 sPP-6

792 000 985 000 514 000 477 000 447 000 437 000

G″ integral 644 530 491 458 411

000 000 000 000 000

G″min

Me (g/mol)

p (Å)

477 000 439 000

3810 4700 5760 6220 6530 7010

2.83 3.04 3.26 3.34 3.39 3.48 E


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out by Liu et al.,14 that this extremely low value of Me might be due to the calculation methods used, as well as by the presence of some chain branching (as suggested by the shape of the viscoelastic moduli, see Figure 4 of ref 13). Conversely, the value of Me reported by the same authors for an atactic sample ([rr] = 17% Me = 7050 g/mol, black square in the upper left part of the plot) is in good agreement with the value measured in the present work for the sPP with the lowest pentad content ([rrrr] = 26.5%, Me = 7010 g/mol). The results obtained at very low values of [rrrr] agree well also with the Me values reported by Fetters et al.6 for atactic and isotactic polypropylenes (Me = 7010 g/mol for aPP and Me = 6850 g/mol for iPP). The two practically coincident values are merged into the single black diamond point in the upper left part of Figure 6. The results by Eckstein et al.13 for the high tacticity sPP, and in particular the apparent underestimate of Me, were discussed by Liu et al.,14 who measured an average Me = 3370 g/mol for three sPP samples having [rrrr] in the range 76.5 to 81.2% (thick black segment in the bottom right part of Figure 6). As a general comment to the results at high amounts of rrrr pentad contents, it must be said that all measurements, included those presented in this paper, have been obtained in conditions which are somewhat critical for a robust determination of the plateau modulus. This can be understood by comparing Figure 1 and 2 of the present work, Figure 6 of Eckstein et al.13 and Figure 2 of Liu et al.14 In all cases, due to the high melting temperature, the data are limited to frequencies where the decreasing part of the G″ curve following the maximum is very small (or practically absent, in our data), thus making the integral method calculation either impossible or very much dependent upon the extrapolation procedure used to evaluate the integral in eq 10. The dependence of Me upon the calculation method is confirmed when the data of Liu et al.14 are treated by the crossover method, eq 11, and plotted as black exagons in Figure 6. In spite of all the just discussed discrepancies, the experimental results definitely indicate that the highly syndiotactic polypropylenes show values of Me significantly lower than those characterized by lower syndiotacticity. The results summarized in Figure 6 unambiguously show that the polypropylene chain dimensions in the melt gradually change upon increasing the amount of rrrr syndiotactic pentads along the backbone. More particularly, the change in Me and p, as detected by the plateau modulus data, become more relevant in the region of high values of [rrrr]. This results, at first sight not necessarily expected, can be supported and explained by several consideration. As mentioned in the Introduction, molecular dynamics simulations on fully syndiotactic PP melts,16 indicate that a more expanded chain dimension with respect to the iso- and atactic architectures is due to the dominance of trans-conformer in the chain. It is therefore reasonable to expect that even a small increase of defects in the syndiotactic sequence randomly dispersed along the chain, which in turn determines a decrease of the rrrr pentad content, can determine local trans−gauche transitions leading to a decrease of the overall chain dimensions. Following a completely different approach based on the rotational isomeric state (RIS) model, the conformation of stereoregular PP chains in the melt is expected to exhibit short sequences of helices of opposite chirality separated by joints at low cost of conformational energy. Low energy conformations including such joints have been proposed in ref 28 both for

isotactic and syndiotactic PP. As shown in Figure 7 they consist of conformational sequences of the type [← right-handed →

Figure 7. Minimum energy conformations of isotactic (A, A′) and syndiotactic (B,B′) chains in the liquid state (melt and solution), including short portions of chains in helical conformation of opposite handedness, connected by joints that can move along the backbone with a low energy barrier. The values of dihedral angles along the backbone are specified and correspond to (TG)n sequences for isotactic polypropylene, (TTGG)n sequences for syndiotactic polypropylene, with T, G+, and G− standing for dihedral angles deviating from 180, +60, and −60°, respectively by ±30°. In A′, X and Y indicate dihedral angles close to T and/or ±120°.28

joint ← left-handed →] and [← left-handed → joint ← righthanded →] that are always present in pairs along the chains and are joined together at low cost of internal energy by couples of consecutive dihedral angles in the trans or ±120° state in the case of isotactic chains (Figure 7A,A′) and long sequences of consecutive bonds in the trans state (≥4) in the case of syndiotactic chains. The energy barriers required to move a joint along the backbone to the next adjacent monomeric unit are quite low and very similar for iso- and syndiotactic PP. Therefore, also in agreement with experimental solution NMR results,29 the mobility of the joints connecting helices of opposite chirality in iPP and sPP are expected to be similar. Such a mobility strongly affects the dynamical behavior of the random coil thus playing an important role in determining the viscoelastic properties of the polymeric materials. This means that the differences in plateau modulus between sPP and iPP are not related to the differences in segmental mobility, but rather to the major frequency of sequences of dihedral angles in trans-conformation. As a consequence, by increasing the concentration of stereodefects in sPP the concentration and length of trans bonds sequences is expected to decrease, thus determining the observed decrease of the plateau modulus.

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CONCLUSIONS The possibility to access syndiotactic polypropylenes (sPP) of different stereoregularity, expressed in terms of rrrr pentad content, and the measurement of their viscoelastic properties has allowed for a quantitative evaluation of the melt chain dimension properties, in terms of either molecular weight between entanglements, Me, or packing length, p. Two main results have been obtained. On the one hand, Me (and, correspondingly, p) are a decreasing function of the rrrr pentad relative abundance. This F


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result, while confirming previous, relatively sparse measurements performed at the two extremes of the [rrrr] window (highly syndiotactic and highly atactic stereoregularity), also indicates that the sPP chain dimensions gradually change upon changing [rrrr]. On the other hand, the results clearly indicate that the space filling parameters Me and p dramatically change only when [rrrr] attains sufficiently high values (exceeding about 70%). These findings can be explained by the presence (confirmed by RIS calculations) of low energy conformations of the stereoregular chain including joints between ordered stereoregular sequences.28 They are also supported by molecular dynamics simulations,16 which indicate that the larger chain dimensions of sPP is due to the dominance of trans-conformers in the chain. If the static average properties of the random coil state of vinyl polymer chains have been well established in relation to their molecular structure, less is known about the influence that intramolecular interactions exert on the dynamical behavior of these polymers, i.e., on their internal viscosity.30 Therefore, the present study provides a relevant result toward linking the chain dynamics to the molecular architecture.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (N.G.) [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors greatly appreciate the financial support of the Italian Ministry of the Education, University and Research (MIUR), under Project PRIN No. 20085LE7AZ.

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REFERENCES

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Relations between Stereoregularity and Melt Viscoelasticity of

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