Influence of chain architecture on the mechanochemical degradation of macromolecules

J. Biochem. Biophys. Methods 56 (2003) 117 – 139 www.elsevier.com/locate/jbbm

Influence of chain architecture on the mechanochemical degradation of macromolecules Andre´ M. Striegel * Solutia Inc., 730 Worcester Street, Springfield, MA 01151, USA

Abstract We detail here studies into the nature of mechanochemical degradation of macromolecules, effected by means of ultrasonic (US) irradiation. Specifically, we have investigated the effect of longchain branching (LCB), in the star configuration, on the degradation mechanism of polystyrene dissolved in DMAc/LiCl. The information obtained from size-exclusion chromatography with triple detection (refractometry, viscometry, multi-angle light scattering) shows that the degradation mechanism of stars is radically different from that of linear polymers. Whereas in the latter, from a macromolecular standpoint, it is merely necessary for the molar mass to be greater than some limiting value (Mlim), in the former both molar mass and structural factors affect ultrasonic degradation. We have examined the effects of arm number and of arm molar mass on star degradation, and propose the concept of a spanning molar mass (Mspan c 2Marm) such that, even in the event that Marm < Mlim for the stars, mechanochemical degradation may nonetheless proceed if Mspan>Mlim. This mechanism has been extended to other types of architecture (e.g., H-branched, dendritic), where it is proposed that a continuous path must exist with Mpath>Mlim for degradation to occur. Examination of the different radii afforded by viscometric and light-scattering detection gives insight into the solution thermodynamics and conformation of the stars with differing arm number and molar mass and of the effects of insonation on macromolecular structure. D 2003 Elsevier Science B.V. All rights reserved. Keywords: Mechanochemical degradation; Sonication; Polystyrene; Star polymers; Branching; DMAc/LiCl

1. Introduction In reviewing the ultrasonic (US) degradation of polymers in solution, Basedow and Ebert [1] stated ‘‘[t]he particular interest of ultrasonic degradation is the fact that, contrary * Tel.: +1-413-730-2560; fax: +1-413-730-2752. E-mail address: [email protected] (A.M. Striegel). 0165-022X/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0165-022X(03)00054-X

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to all chemical and thermal decomposition reactions, ultrasonic depolymerization is a nonrandom process that produces fragments of definite molecular size.’’ Cavitation, the formation and collapse of bubbles due to ultrasonic irradiation of a liquid, was said to provide ‘‘the most effective source of mechanical energy capable of causing the specific degradation of macromolecules.’’ This focusing of energy and specificity of chain scission has led to a large number of investigations into the effects of physicochemical factors such as ultrasonic intensity; analyte concentration; ionic strength, temperature, viscosity, and heat of vaporization of solvent; etc. on the ultrasonic degradation mechanism. Strangely absent from these studies appears to be the structured influence of polymer branching, in particular that of long-chain branching (LCB) [2]. To be certain, a number of US degradation studies have dealt with branched polymers. For dextran, which at high molar masses possesses both random LCB as well as shortchain branching (SCB), Lorimer et al. [3] determined that sonication reduces the molar mass and narrows the polydispersity, and Cote and Willett [4] determined that sonication depolymerized dextran more effectively than either twin-screw extrusion or high-pressure steam-jet cooking. Tayal and Khan [5] compared the US degradation of guar galactomannan, which has both random LCB and SCB, to enzymatic degradation and noted that US narrows the molar mass distribution (MMD) while enzymolysis broadens it. Sohn et al. [6] have studied the US degradation of high molar mass (Mv = 3.6
106 Da) xanthan gum. In addition to being a polyelectrolyte, xanthan has random LCB in which the branches possess both the a and h anomeric configurations and three different types of glycosidic linkages. Likewise, Zhang et al. [7] studied the sonic degradation of h(1 ! 3)-D-glucan with long h-(1 ! 6)-D-glucan branches. Studies of branched synthetic polymers have almost always dealt with poly(vinyl acetate), which has random LCB [8,9]. In their study, Schittenhelm and Kulicke [10] showed the combined influence of coil conformation and of random LCB in the US decomposition of derivatives of cellulose and starch. It should be obvious from the preceding paragraph that branching in all of the polymers mentioned was random in nature. This makes isolating the effects of chain architecture on US degradation quite difficult. To this end, we compare here the effects of insonation on the degradation of both linear and star polystyrenes of similar molar mass, utilizing size-exclusion chromatography with triple detection, refractometry, viscometry, and multi-angle light scattering. The degradation of stars is important in and of itself, as these macromolecules are used as rheological modifiers in various fluids, and may be viewed as hybrids between polymer-like entities and colloidal particles, establishing a link between these different domains of physics. Indeed, stars have been termed a new class of colloids, namely, ‘‘ultra-soft’’ colloids [11]. Beyond that, a comparison between linear and star polystyrenes allows study of the influence of branching on ultrasonic degradation for macromolecules with a controlled, well-defined architecture. We have examined the influence of arm length and number of arms for the polystyrene stars. Degradation rates are seen to depend as much on structure as on molar mass, with degradation mechanisms appearing to be substantially different for stars than they are for linear polymers. As a result of these experiments, a rethinking of the definition of the limiting molar mass (Mlim) to account for LCB in polymers seems appropriate.

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2. Materials and methods 2.1. Materials Twenty-two kilodaltons linear polystyrene (PS) was purchased from Pressure Chemical (Pittsburgh, PA), 65 and 165 kDa linear PS and 400 kDa linear poly(methyl methacrylate) from Polymer Laboratories (Amherst, MA), all other polystyrenes from PSS Polymer Standards Service (Mainz, Germany). N,NV-dimethyl acetamide (DMAc) and LiCl were purchased from Fisher (Pittsburgh, PA). DMAc/0.5% LiCl was prepared by oven-drying the salt overnight at 150 jC and maintaining in a desiccator. After dissolving 5 g of dried LiCl in 1 l of DMAc at 100 jC, the solvent (DMAc/0.5% LiCl) was allowed to cool to less than 50 jC and then filtered through a 0.45-Am PTFE (Teflon) filter membrane (Phenomenex, Torrance, CA). Nomenclature of the samples is as follows. PS-L W refers to a linear PS where W=(Mw/ 1000). PS-StX Y/Z refers to a star PS with X number of arms, where Y=(Mn of arm/1000) and Z=(XY). For the linear PS, W were determined by SEC/MALS as described above. For the star polymers, X, Y, and Z are based on data supplied by the manufacturer. 2.2. Ultrasonic degradation For sonication experiments, 20 ml of DMAc/0.5%LiCl was added to 100 mg of sample in a scintillation vial; the solution was then mixed by gentle inversion and allowed to solvate overnight at room temperature. The next day, a few milliliters was removed for SEC analysis before sonication (see below), the rest of the solution sonicated for specified times in an ultrasonic bath (Branson 5200; Branson, Danbury, CT) operating at 47 kHz and 185 W. Room temperature ( f 20 – 25 jC) was maintained in the bath via a homemade water recirculation device. At the specified times (see tables and figures), a few millilitres of solution was removed for SEC analysis. 2.3. SEC/MALS Four hundred microliters of unfiltered solution was injected into a system consisting of a Waters 590 programmable HPLC pump (Waters, Milford, MA), a Shodex degassing unit (the mobile phase was also degassed by He-sparging in addition to vacuum degassing), a Waters 717+ autosampler, a Viscotek H502B differential viscometer (Viscotek, Houston, TX), a DAWN EOS multi-angle light-scattering photometer (Wyatt, Santa Barbara, CA), and an Optilab DSP interferometric differential refractive index detector (Wyatt). The detectors were connected in series with the refractometer last due to back-pressure considerations in this detector’s cell. The detectors were maintained at 35.0 F 0.1 jC. Separation occurred over a column bank consisting of four analytical SEC columns (three PSS GRALlinear 10 Am columns and one PSS GRAL10000 10 Am column) preceded by a guard column (PSS Polymer Standards Service). Column temperature was maintained at 35.0 F 0.1 jC with a Waters TCM column temperature system. Mobile phase was DMAc/ 0.5% LiCl at 1.0 ml/min. For all chromatographic determinations, results are averages of triplicate injections.

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The MALS detector was calibrated by the manufacturer using toluene. Normalization of the photodiodes was performed in-house using a small, monodisperse (Mw/Mn = 1.03), isotropic scatterer, linear polystyrene with Mp = 22 kDa. This PS was also used to determine the interdetector delays for SEC/MALS. Data acquisition and manipulation was performed using Wyatt’s ASTRA for Windows software (V. 4.73.04). 2.4. SEC3 The technique known as SEC3 combines the signals from the viscometer, the refractometer, and the 90j photodiode of the MALS detector [12]. It was used to determine intrinsic viscosities and viscometric radii of the samples. Interdetector delays and band-broadening parameters were calculated using a monodisperse (Mw/Mn = 1.02) linear PS standard (Mp = 165 kDa). The chromatographic set-up was the same as that for SEC/MALS, with data acquisition performed simultaneously by ASTRA for multi-angle light-scattering purposes and by the TriSEC GPC software (V. 3.0 Rev. B.05.15, Viscotek) for the purposes of SEC3. Minor variations in flow rate were corrected using the solvent/ air peak common to all refractometer traces, as related to the average value of the same peak in the chromatograms of the PS standard. 2.5. Specific refractive index increment determination The specific refractive index increment (Bn/Bc) was determined to be 0.146 ( F 0.001) ml/g for both the linear and star polystyrenes. This result is specific to solutions in DMAc/ 0.5% LiCl at 35 jC, and for experiments performed at 690 nm. Six dissolutions, ranging from 0.3 to 3.0 mg/ml, were injected into the Optilab DSP detector using a Rheodyne injector with 500 Al loop. Solvent and sample solutions were filtered through 0.22 Am PTFE syringe filters. Flow rate was 0.1 ml/min. The radiation from the light source of the refractometer is filtered to match the wavelength of the MALS detector (690 nm). Data acquisition and manipulation were conducted using Wyatt’s DNDC for Windows software (V 5.20 (build 28)).

3. Results and discussion 3.1. Star versus linear PS Molar mass and dilute solution data for the unsonicated polymers are given in the 0 min row of Tables 1 –5. No tabular or graphic information is provided for PS-L 65 nor for PS-St8 9.8/78. For the former, sonication for 240 min showed only an f 2% decrease in molar mass, an increase in polydispersity (Mw/Mn) from 1.000 to 1.004, and a decrease in the weight-average intrinsic viscosity, [g]w, from 0.22 to 0.21 dl/g, with all of these extremely minor changes occurring after 40 min of sonication time. For the star polystyrene, absolutely no changes were observed in molar mass averages or distribution, polydispersity, or intrinsic viscosity after being sonicated for 240 min.

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Table 1 Effects of sonication on molar mass and dilute solution parameters of PS-L 257 Sonication time (min)

Mn (
105 Da)

Mw (
105 Da)

Mz (
105 Da)

Mw/Mn

[g]w (dl/g)

RG (nm)

Rg (nm)

Rg/RG

0 5 10 20 40 120 240 360

2.568 2.565 2.505 2.396 2.184 1.636 1.141 1.013

2.570 2.567 2.514 2.436 2.303 1.942 1.440 1.294

2.572 2.569 2.522 2.470 2.422 2.196 1.756 1.601

1.001 1.001 1.004 1.016 1.055 1.187 1.262 1.277

0.57 0.57 0.56 0.54 0.51 0.45 0.36 0.35

17.5 17.4 17.3 17.0 16.8 16.1 14.2 13.6

13.2 13.0 12.8 12.5 11.9 10.9 9.2 8.9

0.76 0.75 0.74 0.73 0.71 0.68 0.65 0.72

Historically, one feature that became evident during early studies of the ultrasonic degradation of polymers was the appearance of the so-called ‘‘limiting molecular weight’’ or ‘‘limiting molar mass,’’ Mlim. This concept refers to a molar mass beyond which degradation of the polymer chains is not possible. It has been described as corresponding to the critical molecular length that can diffuse the loaded mechanical stress without a breakage of covalent bonds [13]. Isolating the effects of varying a number of physicochemical parameters on the resultant limiting molar mass, as well as on the mechanochemical degradation rate, has proven difficult. This is witnessed by the fact that for linear PS, by far the most widely studied polymer in US degradation experiments, Mlim values have been reported ranging from 15 kDa [1] to 320 kDa [14]. In our study, it would appear that the 65-kDa linear PS is very close to Mlim for the experimental conditions employed. We interject here a brief sidebar concerning the term ‘‘mechanochemical degradation’’ in referring to the ultrasonic depolymerization of macromolecules. Degradation in US is caused by mechanical forces that arise in liquids due to the propagation of acoustic energy through them as a result of the cavitation process mentioned in the Introduction. A consequence of the mechanical rupture of polymer chains is the formation of free valences at the ends of the chain fragments. The depolymerization reactions may thus proceed by homolytic cleavage (formation of two free macroradicals), heterolytic cleavage (formation of two macromolecular ions with opposite charges), or intramolecular disproportionation (formation of two stable macromolecular fragments) [1]. Hence, the nature of the mechanochemical term. Table 2 Effects of sonication on molar mass and dilute solution parameters of PS-St3 85/255 Sonication time (min)

Mn (
105 Da)

Mw (
105 Da)

Mz (
105 Da)

Mw/Mn

[g]w (dl/g)

RG (nm)

Rg (nm)

Rg/RG

0 5 10 20 40 120 240

2.390 2.374 2.358 2.299 1.876 1.494 1.019

2.523 2.526 2.494 2.462 2.155 1.846 1.347

2.672 2.696 2.644 2.636 2.414 2.177 1.724

1.056 1.064 1.057 1.071 1.148 1.236 1.322

0.48 0.47 0.47 0.46 0.42 0.39 0.33

15.7 15.6 15.7 16.0 15.2 14.5 13.0

12.4 12.3 12.3 12.1 11.1 10.2 8.6

0.79 0.79 0.78 0.76 0.73 0.70 0.66

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Table 3 Effects of sonication on molar mass and dilute solution parameters of PS-St8 25.3/202 Sonication time (min)

Mn (
105 Da)

Mw (
105 Da)

Mz (
105 Da)

Mw/Mn

[g]w (dl/g)

RG (nm)

Rg (nm)

Rg/RG

0 5 10 20 40 120 240

1.808 1.802 1.789 1.770 1.746 1.646 1.472

1.932 1.926 1.910 1.903 1.880 1.790 1.674

2.037 2.030 2.012 2.008 1.989 1.902 1.818

1.068 1.068 1.068 1.075 1.077 1.088 1.137

0.22 0.22 0.22 0.22 0.22 0.21 0.20

9.8 9.6 9.7 9.8 9.8 9.6 9.4

8.5 8.5 8.5 8.4 8.4 9.1 7.1

0.87 0.88 0.87 0.85 0.86 0.85 0.83

The effects of insonation on the remainder of the samples are shown numerically in Tables 1 – 5. RG, as defined here, corresponds to the z-average root-mean-square radius of the polymers obtained from SEC/MALS experiments. Rg, the viscometric radius determined using SEC3, is defined via Eq. (1):


3½gM Rg u 10pNA

1=3 ð1Þ

where NA is Avogadro’s number. The linear polymers are seen to be essentially monodisperse in nature, whereas the stars, while certainly possessing an extremely narrow polydispersity, have slightly higher values of Mw/Mn due to small amounts of unreacted arm material (and, possibly, to the presence of a small amount of stars with + 1 and  1 arms than expected, though the present chromatographic conditions do not allow for such highly tailored resolution). We note that a small amount of unreacted arm material was observed in the chromatograms and distributions of all of the unsonicated stars. Following we examine the effects of molar mass and of number of arms on the ultrasonic degradation of PS. We first compare PS-L 257, PS-St3 85/255, and PS-St8 25.3/202. All three of these polymers have similar molar masses. The effects of sonication time on the differential MMD of these PSs can be seen in Figs. 1A, 2A, and 3A. It becomes immediately evident that the degradation mechanism of the stars is quite different from that of the linear

Table 4 Effects of sonication on molar mass and dilute solution parameters of PS-L 447 Sonication time (min)

Mn (
105 Da)

Mw (
105 Da)

Mz (
105 Da)

Mw/Mn

[g]w (dl/g)

RG (nm)

Rg (nm)

Rg/RG

0 5 10 20 40 120 240

4.452 4.268 3.809 2.920 2.387 1.046 0.725

4.468 4.325 4.048 3.478 3.074 1.335 0.878

4.484 4.378 4.241 3.942 3.709 1.647 1.037

1.004 1.013 1.063 1.191 1.288 1.276 1.210

0.76 0.73 0.70 0.62 0.56 0.32 0.26

23.4 22.8 22.2 21.6 20.7 13.4 11.3

16.7 16.4 16.1 14.8 13.6 8.7 7.1

0.72 0.72 0.73 0.69 0.66 0.65 0.63

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Table 5 Effects of sonication on molar mass and dilute solution parameters of PS-St8 45.5/364 Sonication time (min)

Mn (
105 Da)

Mw (
105 Da)

Mz (
105 Da)

Mw/Mn

[g]w (dl/g)

RG (nm)

Rg (nm)

Rg/RG

0 5 10 20 40 120 240 360 480 600 720

3.552 3.254 2.882 2.184 1.982 1.322 0.927 0.647 0.542 0.475 0.442

3.812 3.583 3.396 2.973 2.837 2.238 1.664 1.114 0.917 0.731 0.609

4.054 3.862 3.802 3.568 3.504 3.075 2.267 1.950 1.644 1.259 0.925

1.073 1.101 1.178 1.362 1.431 1.692 1.692 1.723 1.692 1.539 1.378

0.38 0.36 0.36 0.34 0.33 0.31 0.27 0.24 0.23 0.22 0.21

14.6 14.4 14.4 14.0 13.8 13.3 12.5 12.1 11.2 10.6 10.4

13.0 12.6 12.3 11.5 11.1 9.9 8.4 7.2 6.6 6.2 5.7

0.89 0.88 0.86 0.82 0.80 0.74 0.67 0.59 0.60 0.59 0.55

polymer. Moreover, differences between the degradation mechanisms of the two stars are also observed. For the linear PS, the MMD is seen to broaden continuously as a function of sonication time. While some bimodality in the distribution exists at 120 min, it stands in stark contrast to the MMDs of the stars. The three-arm PS degrades rather quickly (a discussion of degradation rates is given below) via loss of arm(s) while the eight-arm PS, of similar molar mass, shows almost no arm loss nor any other form of degradation. The effects of sonication on the size of the polymers is evidenced graphically in the differential distributions of the root-mean-square radii (RG), Figs. 1B, 2B, and 3B and, numerically, in Tables 1 –3. Polydispersities are seen to increase and intrinsic viscosities to decrease, both substantially, as a function of sonication time, for the linear and three-arm star, while changes for the eight-arm material are much more modest (virtually imperceptible, in the case of [g]w). Trends analogous to the intrinsic viscosity changes are also observed for the two radii being measured, RG and Rg. In comparing the US degradation of PS-L 447 and PS-St8 45.5/364, we see once again clear evidence of a difference in degradation mechanisms in Figs. 4A and 5A. PS-L 447 degrades in a similar manner to PS-L 257. The degradation of PS-St 8 45.5/364, however, proceeds in a manner akin to that of the lower molar mass three-arm star, not to that of the lower molar mass eight-arm star. The degradation of the highest molar mass linear and star polymers may also be followed through the cumulative molar mass distribution plots, Figs. 4B and 5B. Examination of these plot is quite instructive, as they show an initial broadening followed by a narrowing of the MMD of both polymers, more drastically so for the star. This effect can be quantified by the equivalent trend in the polydispersities, as seen in Tables 4 and 5. This initial increase in polydispersity followed by a decrease has been previously reported for narrow polydispersity PS [14] and poly(methyl methacrylate) [15] among others, and is a direct consequence of the limiting molar mass concept described above. While the longer chains continue to degrade with increasing sonication time, those chains that have reached the limiting degree of polymerization will not do so, thereby creating a lower limit in the MMD. It should be noted that sonication of broad polydispersity polymers leads only to a narrowing of the polydispersity without the initial broadening [14,15].

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A

40

Differential weight fraction

PS-L 257 0 min 5 min 10 min 20 min 40 min 120 min 240 min 360 min

30

20

10

0 104

2.5x104

5x1047.5x104105

2.5x105

5x105

Molar mass (g/mol)

B

Differential weight fraction

80

PS-L 257 0 min 5 min 10 min 20 min 40 min 120 min 240 min 360 min

60

40

20

0 5

10

15

20

25

R.M.S. Radius (nm) Fig. 1. Effect of sonication time on the (A) differential molar mass distribution (MMD) and (B) differential rootmean-square (R.M.S.) radius distribution (RGD) of PS-L 257.

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Fig. 2. Effect of sonication time on the (A) MMD and (B) RGD of PS-St3 85/255.

125

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Fig. 3. Effect of sonication time on the (A) MMD and (B) RGD of PS-St8 25.3/202.

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127

Fig. 4. Effect of sonication time on the (A) MMD and (B) cumulative molar mass distribution (CMD) of PS-L 447.

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Fig. 5. Effect of sonication time on the (A) MMD and (B) CMD of PS-St8 45.5/364.

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129

Fig. 6 is an overlay of the elution chromatograms, as monitored by the differential refractive index (DRI) detector, for PS-St8 45.5/364 at three different sonication times. The ‘‘piston-like’’ variation in the peaks of the star (retention time of f 24 min) and arm (retention time of f 28.5 min) shows the respective and simultaneous diminution and growth of these two species. Fig. 6 is less ambiguous in this regard than the MMD (Fig. 5A), where the weighting of the two species in solution serves to elevate the average molar mass of one (the arm) while lowering that of the other (the star). One can also observe in Fig. 6, at 0 min of sonication time, the small amount of unreacted arm material present and alluded to earlier. Finally, shoulders may be observed at sonication times of 120 and 720 min in between the regions corresponding to the free arm and to the eight-arm star. Quite likely, these are due to stars which have lost an integer number of arms though, as mentioned previously, the resolution of the current method impedes us from determining this unambiguously. Discussion of the peaks at retention time of f 38 min is left for Section 3.5. To quantitatively compare the trends observed, we have attempted to assign values to the degradation rates (k) of the various polymers. Most methods of calculating the US rate of degradation require a value for Mlim which, as mentioned previously, is not a welldefined quantity for PS (nor for other polymers). We have thus opted to apply the method of Malhotra, previously used to calculate k for a variety of poly(alkyl methacrylates) [16]

Fig. 6. Overlay of differential refractometer (DRI) traces for PS-St8 45.5/364 at three different sonication times, 0, 120, and 720 min.

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as well as for native dextran [3], and which is independent of a formal value for Mlim. This method relies on relationships (2) and (3): 1 1 ¼ þ kVt Mn;t Mn;0 kV¼

k Mo

ð2Þ

ð3Þ

where Mn,t is the number-average molar mass at sonication time t, Mn,0 is the numberaverage molar mass of the unsonicated sample (i.e., at t = 0), and Mo is the molar mass of the repeat unit of the polymer (for PS, Mo = 104 Da). Thus, a plot of 1/Mn,t versus t will give kVand, consequently, k. The degradation rates of the polystyrene samples are given in Table 6. We first examine the linear polymers and observe an increase in k as a function of molar mass. This is in accordance with all other experimental investigations on ultrasonic degradation of polymers [1]. The degradation constant of (linear) PS in tetrahydrofuran has been found to depend on the 1.25 power of M [17]. In the present experiments, k f M1.31 for the linear PS samples, in good agreement with previous observations. In combining the information from Table 6 with that previously presented numerically and graphically, we conclude that the stars appear to follow a two-step degradation mechanism, consisting of (1) loss of arm(s), followed by (2) simultaneous degradation of stars with depleted number of arms and degradation of separated arms, where the latter will occur only if Marm>Mlim. Thus, in comparing PS-St3 85/255 to PS-St8 45.5/364, we see that k1bk2 for the three-arm sample and k1>k2 for the eight-arm material. The three-arm star possesses a trimethylbenzene core, such that arm loss in this star requires breaking a CUC bond (with a bond dissociation energy of 608 F 21 kJ/mol at 298 K [18]), while the core of the eight-arm star is

Table 6 Effect of molar mass and chain architecture on the ultrasonic degradation rate constants of linear and star PS Sample

k (
10 6 min 1)a

PS-L 65 PS-St8 9.8/78 PS-L 257 PS-St3 85/255

0.22 (0.00)b,c NDd 2.12 (0.04) k1 = 0.87 (0.11)e k2 = 2.36 (0.26)e 0.54 (0.02) 5.21 (0.30) k1 = 6.11 (1.07)f k2 = 3.24 (0.19)f

PS-St8 25.3/202 PS-L 447 PS-St8 45.5/364 a

Calculated using Eqs. (2) and (3) from text [16]. Values in parentheses correspond to standard deviations. c Determined for 40 V t V 240 min. d ND = No degradation observed. e k1 determined for 0 V t V 20 min, k2 determined for 40 V t V 240 min. f k1 determined for 0 V t V 40 min, k2 determined for 120 V t V 480 min. b

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trimethylsilane, where losing an arm requires breaking of the weaker CUSi bond (bond dissociation energy of 451.5 kJ/mol at 298 K [18]). We expect k1 for the eight-arm star to be greater than k1 for the three-arm star, as observed. After arm loss in the three-arm star, what remains in the solution is two-arm star (essentially, linear PS with a trimethylbenzene group in the middle of the chain) and arm material with Marm>Mlim, that is, two degradation mechanisms occurring simultaneously and, hence, the much larger value for k2 as compared to k1. In the case of the PS-St8 45.5/364, though, Marm V Mlim, so that in the second part of the mechanism the degradation rates of the star species with 7, 6, 5. . .arms are weighted down by the slow or non-degradation of the free arm material and k2 < k1 for this star. What about the two other eight-arm stars? PS-St8 9.8/78 has M z Mlim, but shows not evidence of degradation. PS-St8 25.3/202 obviously has MHMlim, but k for this star is approximately one order of magnitude smaller than for PS-L 257, which has similar molar mass. As seen in Table 2 and Fig. 2A,B, degradation of PS-St8 25.3/202 barely occurs. It appears that when long-chain branching is present in polymers, at least in the star configuration, the concept of Mlim needs to be reconsidered. Is Marm>Mlim a necessary condition for star degradation to occur? This is quite clearly not the case, based on the degradation data for PS-St8 45.5/364, for which Marm V Mlim but which readily degrades. We propose here the concept of a ‘‘spanning molar mass,’’ Mspan, defined as: Mspan ¼ 2Marm þ Mcore

ð4Þ

where Mcore is the molar mass of the core material (Fig. 7B). Because, in the majority of cases, MarmHMcore, Eq. (4) reduces to Eq. (5): Mspan c2Marm

ð5Þ

This is similar to regarding the stars as a group of linear polymers entangled at the chain centers. Ultrasound-induced bond scission arises from large shear gradients generated during the collapse of cavitation bubbles, in analogy with transient elongational flow degradation [19], where the latter is also a nonrandom process that occurs near the chain midpoint [20,21]. From the point-of-view of the traveling shock wave released by the collapsing bubble, ‘‘free’’ chains (i.e., linear polymers) and chains ‘‘tied together’’ at their midpoint (i.e., stars) should appear virtually identical, as the configurational relaxation times of macromolecules are on the order of 10 3 s, many orders of magnitude (regardless of architecture) greater than the time required for a shock wave to travel across a polymer coil, which is normally on the order of 10 10 s [1]. Thus, for a star polymer, US degradation is expected to occur if either of the following is met: (1) Marm>Mlim, (2) Mspan>Mlim. Obviously, if the first is true, so will be the second (modus ponens); if the second is not true, neither will be the first (modus tollens). For linear polymers, degradation will occur, as traditionally expected, if M>Mlim. It would be interesting to examine two (or more) stars with different numbers of arms, but with Marm>Mlim for both, and thus elucidate the effect of arm number on this region of the mechanism, specially if the molar mass of an individual arm is the same for the stars being studied. Also of interest should be the study of miktoarm stars (stars containing

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Fig. 7. Structures of various polymer architectures: (A) H-polymer, (B) Star, (C) Random LCB, and (D) Dendrimer.

chemically different arms) as well as of stars where the arms are composed of block copolymers. Unfortunately, all of these materials are presently unavailable to us. 3.2. Consequences of proposed mechanism for other architectures Extending this mechanism to other types of macromolecular architectures, we examine first the so-called ‘‘H-polymers,’’ of the type shown in Fig. 7A. Named because of their structure, H-polymers have found extensive application as models in the rheological study of long-chain polymer branching [22]. They may be considered to be formed of a bridge segment (‘‘bridge’’) tying together two sets of arms. For the sake of the present discussion, all arms are considered to have identical molar mass, though Marm is not necessarily equal to Mbridge. From here, we would expect US degradation of an H-polymer if any of the following minimal conditions is met: (1) Mbridge>Mlim, (2) Marm>Mlim, (3) (Marm + Mbridge)>Mlim, (4) 2Marm>Mlim, (5) (2Marm + Mbridge)>Mlim. What this boils down to is that it is necessary for a path to exist, the molar mass of which (Mpath) is greater than Mlim. We may describe said path as that traced upon the backbone of the polymer without ever having to double back on or onto the trace. An example is shown in Fig. 7D for a dendritically branched polymer, upon which we have traced one possible path with a thick line. This proposition can be extended to randomly branched (Fig. 7C) [2] and hyperbranched polymers [23,24], as well. The creation of a path in the molecule, increasing in length as the degree of polymerization increases, at a given point possessing Mpath>Mlim and, therefore, the polymer being able to degrade ultrasonically at this point, is a problem

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that should be amenable to analysis by percolation theory [25]. The critical path length necessary for degradation to occur would thus correspond to the percolation cluster; structures such as dendrimers [23,26] can be transposed quite conveniently onto the wellknown Bethe lattice for this type of study. At the moment, we leave this to others to explore. The proposed theory should have interesting consequences when comparing a star with a large number of arms which, consequently, is close to the hard-sphere limit (see Section 3.4), to a dendrimer of equivalent molar mass (also resembling a hard sphere as generation number increases). US degradation of the star is possible if either Marm or Mspan>Mlim. Even though its molar mass is equal to that of the star, however, degradation of the dendrimer may not occur if a path does not exist such that Mpath>Mlim. These properties may be of great interest in the field of rheological modifiers. The recent synthesis of star branched polymers with dendritic cores adds a fascinating element to this problem [27]. 3.3. Choice of solvent It should be noted that the mechanism proposed in the previous sections is based solely on molar masses of the polymers and/or their various subsections as well as on architectural characteristics. No allowance has been made for such factors as solvent/ solution viscosity, enthalpy of vaporization of solvent, conformation of analyte in solution (i.e., ‘‘goodness’’ of solvent), etc. These factors have been discussed elsewhere in the literature for linear polymers [1,9,13,14,28 – 30]. For these studies, we chose DMAc/LiCl as the solvent based on its versatility as solvent, mobile phase, and derivatization medium for a large number of natural and synthetic polymers [31 – 37]. We note that linear PS may be expected to adopt an extended, random coil conformation in DMAc/LiCl at the temperature of these experiments based on the value of the exponent a in the Mark-Houwink Equation (6): ½g ¼ KM a

ð6Þ

where K and a are empirically determined constants. At theta (h) conditions, a will adopt a value of 0.5, while the value for a linear random coil in a good solvent is normally in the range 0.6 –0.8. Studies in our laboratory with broad MMD linear PSs have yielded a value for a = 0.64 under the present solvent/temperature conditions. 3.4. The ratio Rg/RG Much has been published on the information, both structural and thermodynamic, that can be derived from the ratio of the root-mean-square radius (RG) to the hydrodynamic (Stokes) radius (Rh) [38,39]. The former, as mentioned earlier, is determined from multiangle (or variable angle) static light-scattering experiments, the latter via dynamic (quasielastic) light scattering. The lack of dynamic light scattering capability in our laboratory has prevented us from pursuing this avenue of investigation and, as such, it is not discussed further here. Utilizing the on-line viscometer, we have been able to measure the viscometric radii (Rg) of the linear and star polymers, as defined in Eq. (1). The ratio of this radius to that

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determined from static light scattering (i.e., to RG) is given in the last column of Tables 1– 5. The change of Rg/RG with sonication time is plotted in Fig. 8A for the linear polymers and in Fig. 8B for the stars. No data is given for PS-St8 9.8/78, as the size of this polymer is too small to be determined accurately by static light scattering due to a virtual lack of angular dissymmetry. Several observations can be made from the tables and figures. First, the ratio Rg/RG is very similar for all the linear PSs and changes little with sonication time. This is not surprising, as degradation of the linear polymers is merely increasing the polydispersity, not changing the structure. Second, the ratio for the non-sonicated threearm star is 0.79. This is similar to the value of 0.84 reported by Bauer et al. [40] for threearm star PS under good solvent conditions. pffiffiffiffiffiffiffiffi Third, for star polymers, the ratio is expected to increase as the hard sphere limit ( 5=3) is approached, that is, as the number of arms increases [41]. This is observed in Fig. 8B, as the ratios for the eight-arm stars are larger than that of the three-arm star (all before sonication). Fourth, the ratio is expected to be molar mass-independent, depending only on the number of arms [41]. This is also observed in Fig. 8B in which the two eight-arm stars, widely differing in molar mass of the arms, have virtually identical values of Rg/RG (0.87 and 0.89 before sonication). Fifth, the ratio is observed to decrease quickly with sonication time for the three-arm star and for the highest molar mass eight-arm star, while little change occurs for PS-St8 25.3/202. As noted previously, much structural change is occurring in the former two cases as a result of the sonication process while in the last case, the structure of the analyte remains virtually invariant. As more free arm material is produced in the stars that degrade ultrasonically, the ratio of the radii approaches that of the linear polymers. 3.5. An X-file? As observed in Fig. 6, the DRI chromatogram overlay for PS-St8 45.5/364, as sonication time increases, a small peak appears at retention time of 37.8 min and continues to increase (slowly) as a function of sonication time (see Fig. 6 and inset). The retention time of this peak corresponds to that of oligomeric PS of only a few repeat units (i.e., it is a very low molar mass species). Moreover, it is observed for all of the polymers, both linear and star, regardless of molar mass or number of arms. The retention time is highly reproducible, averaging 37.8 F 0.1 min over all of the runs of all of the samples, and it is not observed in any of the unsonicated polymers. The retention time of the peak does not change as a function of sonication time, indicating that whatever species is being produced, only its quantity is increasing with time, not its size. It is even seen in the chromatograms of PS-St8 9.8/78, for which no other form of degradation is evident. As noted previously, mechanochemical degradation resembles elongational flow degradation, both processes being nonrandom and occurring near the chain midpoint. It thus appears highly unlikely that the low molar mass fragment is due to ultrasonic degradation of the polymers. Having ruled out the effects of structure, we concentrated on the chemistry of the polymers. Experiments with a 400-kDa linear PMMA also showed the same peak subsequent (but not prior) to sonication. Could the peak be the result of a minor, secondary degradation mechanism? Sonication of DMAc/0.5% LiCl (without any added polymer) also showed the 37.8-min peak, which was not present in the unsonicated

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Fig. 8. Effect of sonication time on Rg/RG for (A) linear PSs and (B) star PSs.

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solvent, indicating that our mystery species is not a sample degradation product. As with previous experiments, the area of the peak increased as a function of sonication time, but the retention time remained invariant. The inside of the caps of the scintillation vials that were used for the sonication experiments were coated with PTFE. We also sonicated DMAc/LiCl solutions in vials using caps with polypropylene interiors. The same peak was observed once again. The peak was also observed, though in smaller quantity, when unsonicated solutions of DMAc/LiCl were heated at 100 jC for several hours and subsequently analyzed by SEC. Solutions of DMAc/LiCl that had been sonicated for several hours (and in which the peak in question had been observed) were heated to 100+ jC for 2 h and subsequently re-analyzed. The peak had neither disappeared nor changed substantially in size. It was not observed when solutions of neat DMAc (i.e., sans LiCl) were analyzed subsequent to either sonication or heating. We note that gas chromatography/mass spectrometry (GC/MS) analysis of the sonicated (up to 9.5 h of sonication time) and unsonicated DMAc/LiCl solutions showed no difference between the samples, indicating that whatever species was created by sonication was either non-volatile or was weak enough to degrade in the GC inlet (e.g., a non-covalently bound species). Previous work has taken advantage of the extremely soft ionization characteristics of electrospray ionization mass spectrometry (ESI-MS) to study the lithiation of DMAc and of other homologous amides [42], as well as the lithiation of natural polymers in the oligomeric region [31]. ESI-MS analysis of the same samples as examined by GC/MS indicated the possibility that the peak may correspond to either acetic acid or to the ion pair (CH3)COO(CH3)2NH2+ (both observed as lithiated ions in the mass spectrum). Resolution in our SEC system is insufficient to separate acetic acid from dimethylamine, such that, if the gas-phase species observed with ESI-MS correspond to species in solution, the ‘‘37.8min’’ peak could be due to either acetic acid, to dimethylamine, or to both. The experiments just described show that the peak in question is indisputably not due to polymer degradation. As such, we have decided not to pursue the matter further at this time (though we feel fairly certain it is not of extraterrestrial origin). We have found no other reports in the US polymer degradation literature that allude to this type of solvent phenomenon, which may simply be due to localized heating of the solvent during the sonication process.

4. Conclusions The influence of polymer architecture on the mechanochemical degradation of macromolecules has been studied via the comparison of two model systems, linear and star polystyrene, using size-exclusion chromatography with triple detection (RI, MALS, viscometry). Results from extended sonication experiments show that long-chain polymer branching has a large effect on the mechanism through which this type of degradation proceeds. For linear polymers, the traditional concept of the molar mass of the polymer having to exceed some limiting value for degradation to occur continues to apply. For star-branched polymers, however, structural as well as molar mass factors need be considered simultaneously when attempting to predict whether degradation will occur or not, as well as when

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trying to predict the relative rates of the various stages of the degradation process. We have proposed here the concept of a spanning molar mass (Mspan) for star polymers to reconcile the molar mass and architectural data with the observations from the ultrasonic degradation experiments. We examined the implications of this approach for other types of structures such as dendrimers, H-polymers, etc. and proposed further that a continuous path is necessary in branched polymers, with Mpath>Mlim, for US degradation to occur. (For linear polymers, M = Mspan = Mpath.) A wealth of information is obtained from a triple-detector SEC experiment, not only with respect to molar mass and dilute solution data, but also to shape, conformation, and solution thermodynamics. Information from the different types of radii obtained from viscometry and multi-angle light scattering has been combined to show how the stars approach the hard-sphere limit as the number of arms increases, independent of molar mass of the arms, and how the shape of the three-arm star is in accordance with previously observed behavior in a thermodynamically good solvent. The results presented here should have direct bearing on investigations of the mechanisms of mechanochemical polymer degradation, as well as in the field of rheological modifiers, where stars and other highly branched polymers have found application. They should also be of interest to those working in the relatively new field of extrusion sonication, that is, using extruders with an ultrasonic die attachment. The latter have been used in the devulcanization of carbon black-filled natural rubber vulcanizates [43], as well as to improve the rheological behavior of polystyrene [44]. Acknowledgements The author is most grateful to Dr. David B. Alward (UCB) for many helpful discussions and suggestions at all stages of this project, as well as for reviewing an early draft of the manuscript. I also thank Dr. William A. Dupont (UCB) and Ms. Susan V. Greene for helpful discussions and Drs. Frederick D. Hileman and Hugh A. Taylor (UCB) for the ESIMS and GC/MS analyses, respectively. References [1] Basedow AM, Ebert KH. Ultrasonic degradation of polymers in solution. Adv Polym Sci 1977;22:83 – 148. [2] Striegel AM. Long-chain polymer branching: determination by GPC-SEC. In: Cazes J, editor. Encyclopedia of chromatography. New York: Marcel Dekker; 2001. p. 497 – 500. [3] Lorimer JP, Mason TJ, Cuthbert TC, Brookfield EA. Effect of ultrasound on the degradation of aqueous native dextran. Ultrason Sonochem 1995;2:S55 – 7. [4] Cote GL, Willett JL. Thermomechanical depolymerization of dextran. Carbohydr Polym 1999;39:119 – 26. [5] Tayal A, Khan SA. Degradation of a water-soluble polymer: molecular weight changes and chain scission characteristics. Macromolecules 2000;33:9488 – 93. [6] Sohn J-I, Kim CA, Choi HJ, Jhon MS. Drag-reduction effectiveness of xanthan gum in a rotating disk apparatus. Carbohydr Polym 2001;45:61 – 8. [7] Zhang L, Zhang X, Zhou Q, Zhang M, Li X. Triple helix of b-D-glucan from Lentinus edodes in 0.5 M NaCl aqueous solution characterized by light scattering. Polymer J 2001;33:317 – 21. [8] Madras G, Kumar S, Chattopadhyay S. Continuous distribution kinetics for ultrasonic degradation of polymers. Polym Degrad Stab 2000;69:73 – 8.

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