Temperature and Molecular Weight Dependence of Mutual Diffusion

(15a) Consequently, a mutual diffusion coefficient of the c-hPS/c-dPS bilayer film is larger than the corresponding linear polystyrene/linear deuterat...
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Temperature and Molecular Weight Dependence of Mutual Diffusion Coefficient of Cyclic Polystyrene/Cyclic Deuterated Polystyrene Bilayer Films Daisuke Kawaguchi, Yutaka Ohta, Atsushi Takano, and Yushu Matsushita*

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Department of Applied Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

INTRODUCTION Physical properties of cyclic polymers have been paid a great attention as a counterpart of those of linear polymers. The difference between cyclic and linear polymers in terms of molecular structure is only the presence or the absence of chain ends. However, this small difference leads various kinds of different physical properties such as chain dimension in solution and bulk,1−6 glass transition temperatures,7−10 viscoelasticity,11−13 diffusion,14−17 microphase-separated structures,18 and crystallization19−21 etc. Hence, cyclic polymer is one of the ideal model polymers in attempt to understand an effect of topology on thermodynamics and molecular motion of polymers. The number of experimental reports on molecular motion of cyclic polymers is much less than that of computer simulation and theoretical studies22−35 because of the difficulty of synthesizing cyclic polymers, in particular, those having high molecular weight (Mw > 10k). Furthermore, an important technical problem was to determine the purity of cyclic polymers containing a linear precursor as an impurity. In later 1980s, some pioneering work on tracer diffusion and zero shear viscosity of cyclic polystyrenes were reported by Kramer et al.14 and McKenna et al.,11 respectively. The difference in the physical properties between cyclic and linear polystyrenes has been found in their reports whereas it was unclear how much amount of “linear contamination” was included in the samples at that time. Recently, a new high performance liquid chromatography named the liquid chromatography at the critical condition, LCCC, has been developed.36 This method enables us to evaluate the purity of cyclic polymers.37,38 Kapnistos et al. measured stress relaxation of cyclic polystyrenes with very high purity evaluated by LCCC measurement and reported that the cyclic polystyrenes with Mws of 198k and 161k, being much larger than the entanglement molecular weight, Me, for linear polystyrene, shows no obvious rubbery plateau but a power-law stress relaxation.12 They claim that entangled cyclic polymers exhibit completely different topological arrangement than their linear counterparts such as the lattice animal conformation.12,22,23 Prior to their report, we had investigated an interdiffusion of a bilayer film composed of cyclic polystyrene, c-hPS, and cyclic deuterated polystyrene, cdPS, whose molecular weights are 109k and 117k, respectively, and whose purities are over 95%, using secondary ion mass spectroscopy, DSIMS, in conjunction with neutron reflectivity.15a Consequently, a mutual diffusion coefficient of the c-hPS/ c-dPS bilayer film is larger than the corresponding linear polystyrene/linear deuterated polystyrene bilayer film. However, temperature and molecular weight dependence of the © 2012 American Chemical Society

diffusion coefficient is still an open question. In this note, therefore, we investigate temperature and molecular weight dependence of diffusion behavior of cyclic polystyrenes with high purity by DSIMS.

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EXPERIMENTS

Monodisperse cyclic and linear polystyrenes (c-hPS, l-hPS) and those deuterated counterparts (c-dPS, l-dPS) were used in this study. Table 1 shows characteristics of the samples used in this study. The details of

Table 1. Characteristics of Polystyrenes Used in This Study sample code

Mw

c-hPS-109k c-dPS-117k l-hPS-115k l-dPS-127k c-hPS-42k c-dPS-50k l-hPS-44k l-dPS-52k c-hPS-15k c-dPS-12k l-hPS-16k l-dPS-15k c-hPS-5k c-dPS-6k l-hPS-6k l-dPS-8k

109k 117k 115k 127k 41.7k 50.4k 44.2k 52.0k 15.0k 12.0k 16.0k 15.2k 4.8k 6.0k 6.0k 7.5k

N 1.05 1.04 1.11 1.13 4.01 4.50 4.25 4.64 1.01 1.07 1.43 1.36 4.6 5.4 5.8 6.7

× × × × × × × × × × × × × × × ×

Ne 103 103 103 103 102 102 103 102 102 102 102 102 101 101 101 101

8.2 8.2 8.6 8.9 3.1 3.5 3.3 3.6 1.1 8.4 1.2 1.1 3.6 4.2 4.5 5.2

× 10−1

× × × ×

10−1 10−1 10−1 10−1

Mw/Mn

Tg/K

1.02 1.02 1.04 1.04 1.02 1.02 1.03 1.04 1.02 1.02 1.03 1.04 1.02 1.02 1.04 1.05

376.0 373.6 376.0 378.9 370.6 372.8 375.6 374.5 377.0 371.0 371.7 365.3 377.1 375.1 365.9 364.8

syntheses and characterization of c-PSs were described elsewhere.38 Cyclic structure of c-hPS-109k was directly confirmed by atomic force microscopic observation39 and the purity of c-PSs is confirmed to be higher than 95% based on LCCC measurements.38 Weight-average molecular weights, Mws, were evaluated by multi angle laser light scattering. N and Ne listed in Table 1 are degree of polymerization and a number of entanglement segments, respectively. The Nes are calculated by Mw/Me where Me for hPS is 13.3k40 (Me for dPS is simply estimated to be a factor of 1.08 (=112/104, weight ratio of monomeric unit of styrene-d8/styrene-h8)). Glass transition temperatures, Tgs, of c-hPS, c-dPS, l-hPS, and l-dPS were measured by differential scanning calorimetry. The Tgs of c-hPS and c-dPS are basically constant independent of Mw although the values are somewhat dispersed. l-hPS/l-dPS and c-hPS/c-dPS bilayer films were prepared by floating technique.41 The bottom dPS layer for the bilayer was prepared from a toluene solution onto a silicon wafer Received: April 3, 2012 Revised: July 19, 2012 Published: July 31, 2012 6748

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by spin-coating. The thickness of this layer was ca. 200 nm. The dPS films were annealed at 393 K for 48 h under vacuum to remove the residual solvent and the strain imposed by the film preparation process. The top hPS film with the nearly same thickness was independently prepared by a similar manner. The perimeter of the hPS films were scored with a blade and the films were successively floated off onto the water surface. Then, the hPS film was picked up onto the dPS film. The bilayers were annealed above Tgs under nitrogen atmosphere for sufficiently long times and successively immersed into liquid nitrogen to quench the interdiffusion. Table 2 is the bilayer films

Table 2. Bilayer Films Used in This Study sample code

top layer

bottom layer

C-bilayer-1 L-bilayer-1 C-bilayer-2 L-bilayer-2 C-bilayer-3 L-bilayer-3 C-bilayer-4 L-bilayer-4

c-hPS-109k l-hPS-115k c-hPS-42k l-hPS-44k c-hPS-15k l-hPS-16k c-hPS-5k l-hPS-6k

c-dPS-117k l-dPS-127k c-dPS-50k l-dPS-52k c-dPS-12k l-dPS-15k c-dPS-6k l-dPS-8k

Figure 1. Temperature dependence of mutual diffusion coefficients, D, of C-bilayer-1 and L-bilayer-1. Open and filled circles denote the experimental D values for C-bilayer-1 and L-bilayer-1, respectively. The broken line is the calculated D values of l-PS with Mw of 121k (eq 4). The solid line denotes the calculated values for c-PS (eq 6).

samples. By substituting these values into eqs 2 and 3, temperature dependence of l-PS of 121k can be described as follows, DL = 1.43 × 10−9 × T × 10(−B /(T − TV ))

used in this study. The Mws of the bilayers are approximately the same with largest difference being 20%. The Ne values of the second lowest Mw samples, i.e. the components of C-bilayer-3 and L-bilayer-3, are around unity. The concentration profiles near the interfaces were examined on the basis of DSIMS (SIMS 4000, Seiko Instruments Inc., Atomika Analysetechnik GmbH). The incident beam of oxygen ions with 4k eV and ca. 30 nA was focused onto a 200 μm × 200 μm area of the specimen surface. The incident angle was 45°. Gold layer of 20 nm thick was sputter-coated on the specimen surface to avoid a charging of the specimen during the DSIMS measurement. Depth profiles of normalized D− ion intensity were analyzed by the following equation derived from Fick’s second law,15a,41,42

⎡ ⎛ z C(z) = 0.5⎢1 − erf⎜⎜ 2 ⎢⎣ ⎝ a + 4Dt

⎞⎤ ⎟⎟⎥ ⎠⎥⎦

(for l − PS with M w of 121k)

Our experimental DL values are shown by the filled circles and are consistent with the calculated ones shown by the broken line. Taking a slight difference in molecular weights of linear and cyclic molecules into account, temperature dependence of DL value with Mw of 113k can be expressed as, DL = 1.65 × 10−9 × T × 10(−B /(T − TV )) (for l − PS with M w of 113k)

(5)

To analyze the data for c-PS, the solid line was obtained by fitting process using a prefactor as only a fitting parameter with keeping B and TV values the same as the l-PSs’ ones. In other words, the fitting analysis was conducted by using eq 5 maintaining the contour shape of the curve and shifting it vertically. The solid line is in good agreement with the experimental values for c-PS shown in open circles and can be expressed by the eq 6.

(1)

where z, a, D, and t are the distance from the interface, an instrument function (=ca. 10 nm), a diffusion coefficient and time, respectively. D values were extracted from each depth profile by fitting analysis with eq 1. The analytical methods were described in our previous paper in detail.14a

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DC = 3.30 × 10−9 × T × 10(−B /(T − TV ))

RESULTS AND DISCUSSION Temperature Dependence of Interdiffusion of Cyclic Polystyrenes. Figure 1 compares temperature dependence of D values for c-PS and l-PS, DC and DL. Open and filled circles denote the DC and DL values with Mw of 113k and 121k, respectively. The broken line is the calculated DL values reported by Kramer et al.43 According to their paper, the DL value can be calculated based on the empirical equations as follows, D B log =A− T T − TV (2) ⎛ Mw ⎞ ⎟ A = −9.49 − 2 log⎜ ⎝ 255000 ⎠

(4)

(for c − PS with M w of 113k)

(6)

It is apparent from eqs 5 and 6 that the absolute DC value is ca. 2-fold larger than that for the corresponding l-PS at all the temperatures employed. Hence, the mutual diffusion data prove that the segmental friction coefficients of l-PS and c-PS are the same. Molecular Weight Dependence of Interdiffusion of Cyclic Polystyrenes. Figure 2a shows a double logarithmic plot of D versus Mw at 393 K for C-bilayers and L-bilayers, respectively, where filled and open circles denote the DC and DL values. The error bars are the standard deviation of the D values obtained by multiple independent experiments. Here, the slope of the double logarithmic plot is defined as ν. We will discuss the ν values of our data separated in two regimes: Mw ≤ Me and Mw > Me, being recognized as “unentangled ring” and “entangled ring” regimes, respectively. The ν values for the L-bilayers are −2.0 for Mw > Me and −2.6 for Mw ≤ Me, respectively. The ν value for Mw > Me strongly suggests that the chains in the L-bilayers move based

(3)

where T is an absolute temperature, TV is Vogel temperature (= 322 K), B is an activation temperature (=710 (K) log(cm2 /s K)), and Mw is the molecular weight of the sample. For the linear case in Figure 1, the Mw value for linear polystyrene is calculated to be 121k by arithmetic average of Mws of the 6749

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Figure 2. (a) Double−logarithmic plots of D versus Mw of C-bilayers and L-bilayers (a) at 393 K and (b) at iso-free volume state (T = T − Tg = 20 K). Open and filled circles denote the D values of C-bilayers and L-bilayers, respectively. The solid and broken lines are the best-fit calculated ones and the numbers are the exponent values of the double logarithmic plots.

on the reptation theory44,45 whereas the ν value for Mw ≤ Me is unreasonable value of −2.6 probably due to the decrease in the Tgs at the molecular weight region. On the other hand, the ν values for the C-bilayers are −1.9 at Mw > Me and −2.2 at Mw ≤ Me. The DC values are larger than the DL ones at Mw > Me and vice versa at Mw ≤ Me, resulting in showing the crossover of DC and DL values around 30k. This behavior is in good agreement with Monte Carlo simulations of cyclic and linear alkenes.26 To discuss the relation between D and Mw at an iso-free volume condition, the DL values of L-bilayer-3 and L-bilayer-4 were recalculated. Since the temperature dependence of segmental frictional coefficient for c-PS is the same as that for l-PS as proved in the former section, the DL values were estimated using temperature dependence of D values. Since the Tgs of l-hPS-16k and l-dPS-15k are ca. 5 K lower than the other l- and c-PSs with Mw > Me, the DL value for L-bilayer-3 at 388 K was estimated taking this Tg difference into account. Similarly, the DL value for L-bilayer-4 at 383 K was also estimated. The DC values were not recalculated because the Tgs of cyclic polystyrenes can be regarded as constant independent of Mw. Figure 2b shows double logarithmic plots of DC and DL values versus Mw at iso-free volume condition, where T − Tg = ca. 20 K is the same as those of all the C-bilayers and L-bilayers. At the iso-free volume condition, the DC value is larger than DL for all the molecular weights. The ν values for DL are −2.0 at Mw > Me and −0.9 at Mw ≤ Me, which are consistent with the reptation and Rouse models, respectively. Moreover, a previous experimental report on diffusion of polybutadiene revealed that the ν value is −2.3 for sufficiently large Mw.46 In either case, the result of linear polystyrenes is quite reasonable because the critical entanglement molecular weight of l-PS is ca. 30k. For cyclic polymers at Mw > Me, the theory based on the lattice-animal conformation predicted that DC is proportional to N−2.0.23 A recent molecular dynamics simulation of cyclic polyethylenes done by Hur and co-workers revealed that the ν value is −1.9 if the Mw is sufficiently large.28b They claimed that the ring diffusion coefficients exhibit a broad crossover regime from unentangled to entangled dynamics and that DC is proportional to N−1.2 for small rings and to N−1.9 for large rings.28b Our result of ν = −1.9 well corresponds to the molecular dynamics simulation28b as well as the theory based on the lattice-animal picture.12,22,23 This result clearly indicates that entangled cyclic polystyrenes exhibit completely different topological arrangement from their linear counterparts such as the lattice animal conformation.12,22,23 On the other hand, molecular dynamic simulation exhibits ν = −1.0 for M < Me and ν = −1.2 around the transition from

unentangled to the entangled states.28 Experimental results of unentangled cyclic poly(oxyethylene)s with Mw ranging from 400 to 1500 shows that D is proportional to N−1.12 on the basis of NMR spin−spin relaxation technique.16b Both groups concluded that the diffusion of unentangled rings can be explained in terms of Rouse model. However, our data exhibit ν = −2.2, being inconsistent with the previous results. The possible reasons for the deviation of our results might be related to the purity, the difference in Tgs among the samples for the smallest ring. The effect of small amounts of linear contaminants on the diffusion of cyclic molecules might be more significant in low molecular weight regime than in high molecular weight one because the Tg of the linear molecules is lower than that of the corresponding cyclic one at this regime. Hence, the linear contaminants can diffuse much faster than the cyclic molecules at a same annealing temperature. Another effect of linear contaminants may be the surface segregation at the original surface which is the bilayer interface owing to the low surface energy of chain end moiety (diphenyl ethylene). If these two effects act, cyclic molecules including small amount of linear contaminants would diffuse evidently faster than ideal pure cyclic molecules in low molecular weight regime.

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CONCLUSIONS Interdiffusion of c-hPS/c-dPS and l-hPS/l-dPS bilayer films which are symmetric in terms of both molecular weight and topology was investigated by DSIMS measurements as a function of temperature and molecular weight. For Mw of 113k being larger than the critical entanglement molecular weight for l-PS, the DC value is twice as large as the DL one at all the temperature employed. The DC value is larger than the DL one for all the molecular weights at an iso-free volume condition, whereas a crossover of the DC and DL values was observed around Mw of 30k at 393 K due to the Tg reduction of l-PS. The double logarithmic plots of DC vs Mw exhibit no explicit transition such as that from unentangled to entangled rings. For cyclic polystyrenes at Mw > Me, the exponent of the plot is −1.9, corresponding to the recent molecular dynamics simulation and the theory based on the lattice-animal picture for entangled rings. At Mw ≤ Me, the exponent of the cyclic polystyrenes is −2.2, being inconsistent with the previous results.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 6750

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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was in part supported by the Grant-in-Aids for young scientist (A)(No.22685013) and scientific research (A) (No.22245038), the Global COE program “Elucidation and Design of Materials Molecular Functions”, and “Nanotechnology Support Project” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. D.K. thanks Prof. Keiji Tanaka and Mr. Kazuhiro Koguchi in Kyushu University for helping DSIMS and DSC measurements and fruitful discussion.

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