Mechanical Degradation of Thin Polystyrene Films BY ROBERT J. NASH AND DARRYL M. JACOBS Xerox Corporation, Rochester Research Center, Webster, New York 14580, USA Received 1 st June, 1972 Thin films of polystyrene drastically degrade, on a molecular scale, when subjected to mechanical forces. An examination, by gel permeation chromatography, of the molecular weight distributions of the degraded polymers shows that the polymer molecules do not undergo the random scissions or bisections that have been postulated in the many prior theoretical treatments of polymer degradation, but rather degrade via non-random multiple scissions. The mode of degradation is such that while medium molecular weight polystyrene molecules degrade directly to a limiting low molecular weight species, high molecular weight polystyrene degrades both indirectly through an intermediate species and directly to the limiting species.An analysis of the degradation data from a wide molecular weight distribution polystyrene sample yields a rate equation which is a decreasing function of molecular weight. A model is proposed which predicts the form of the degradation rate equation on the basis of molecular size : the mode of degradation is explained by the concept of polymer chain entanglement. Possible degradation pathways are differentiated using a computer simulation. The phenomenon of mechanical degradation of polymer molecules is well known. It is manifest in such diverse examples as the bond scission which can occur when polymer solutions are merely stirred or shaken,2 and in the more practical problem of molecular breakdown generated during the spinning or extrusion of polymer melts.Polymer degradation has been the subject of several and many experi- mental 6-25 and theoretical Unfortunately, a majority of the experi- mental studies have followed the degradation process through viscometric measure- ments which, by their nature, yield only limited information about the molecular weight distribution of the degraded species. This lack of distribution data has hindered theoretical developments, both in the formulation of models and in the testing of hypotheses. However, the recently developed experimental technique of gel permeation chr~matography,~~ which yields rapid measurements of molecular weight distributions, will alleviate this problem.To date, only a few studies of shear 22 and ultrasonic induced 21 degradation of polymer solutions have utilized this technique. The present study is the first systematic application of gel permeation chromatography to the process of mechanical degradation of thin, solid polymer films, and indeed appears to be the first mechanical degradation study on such films. EXPERIMENTAL MATERIALS Narrow distribution polystyrene samples having weight average molecular weights, M,, of 2~ lo5, 6 . 7 ~ lo5, and 8 . 6 ~ lo5, and molecular weight distributions, MWD, less than 1.2 were obtained from the Pressure Chemical Co. The National Bureau of Standards supplied a wide distribution polystyrene sample, NBS-706, having an Mw of N 3.6 x lo5 and a n MWD of -2.(For brevity, the samples will be further referred to as PSZOO, PS670, PS860 and NBS-706 respectively). 210R . J . NASH AND D . M. JACOBS 21 1 COATING A N D DEGRADATION PROCEDURES In a preliminary series of experiments, 2 pm films of polystyrene were solvent-cast onto the inner surface of glass jars. The addition of 2 mm diameter steel beads to the jars fol- lowed by rolling on a roll-mill served to mechanically degrade the films. However, this procedure gave poor results, partly because of non-uniformities in the films but chiefly because of the tendency of the films to flake from the glass substrate. While the flaking was reduced by etching the glass prior to coating, the method was abandoned because uniforrn films could not be reproducibly obtained.This problem was eliminated by casting the polystyrene films on the surface of spherical stainless steel shot (250 pm diameter, 9 x m2 g-' surface area; manufactured by the Nuclear Metals Division of the Whittaker Corporation). The coating vessel, a 0.25 1. stainless steel beaker, was screwed to the driving element of a vortex generator. Excellent coatings were obtained by the following steps : (a) warm the beaker plus shot, (b) add a toluene solution of polystyrene, (c) remove the solvent by evaporation combined with vigorous agitation, ( d ) remove residual solvent by heating the coated shot at 95°C in uacuo. The weights of shot and polymer were chosen so as to give a nominally 2 pm coating thickness. A coating experiment typically yielded 150 g of coated shot, and this was a sufficient supply for all of the degradation experiments.For these experiments, 15 g of coated shot and 45 g of 2 mm diameter uncoated steel shot were placed in glass bottles (length = 9 cm, diam. = 4 cm) and rolled for various timed intervals at 275 r.p.m. on a roll mill at room temperature. A fresh jar and polymer sample was used for each degradation experiment. The large steel balls were added merely to accelerate the degradation process since excessive times were required when the coated shot was rolled alone. GEL PERMEATION CHROMATOGRAPHY After the required milling time, the polymer was recovered by the addition of tetrahydro- furan to the contents of the milling bottle. The resulting polymer solution was then analyzed using a Waters Associates Model 200 gel permeation chromatograph which had been pre- viously calibrated using standard polystyrene samples of known molecular weights.In brief, a gel permeation chromatograph separates polymer molecules on the basis of molecular size. The molecules elute from the column in order of decreasing size, and if (as in the present study) the effluent is monitored by a differential refractometer, the area of the chromatogram is proportional to the concentration of the injected polymer solution. The effluent is also measured by a syphon which places a tick mark-" elution count "-on the chromatogram for every passage of a fixed volume of carrier liquid. The elution volume (i.e., elution count number multiplied by syphon volume) can be related to the molecular weights of the eluting polymer molecules by the equation In (molecular weight) = a+ b (elution volume) where a and b are constants. RESULTS GEL PERMEATION CHROMATOGRAMS The various polystyrene samples were milled for a series of times up to 23 h.Since polymer degradation can be thermally induced,50 it was pertinent to check that the results obtained at extended milling times were not caused by possible milling- generated heating. As a test, therefore, a sample was milled for eight hours, the time being divided into alternate intervals of 30 min of milling and 30 min of resting. The result thus obtained matched that from a continuous eight hour milling experiment indicating an absence of any long-term thermal contributions to the degradation process. (The possibility still exists, however, that each violent impact of a milling ball causes local heating in the polymer film.) Fig.1,2 and 3 show the gel permeation chromatograms, for selected milling times,212 DEGRADATION OF POLYSTYRENE FILMS 0 9 2 12 5 FIG. 1.-NBS-706 gel permeation chromatograms for the degradation times noted (in hours). The ticks on the abscissa of each chromatogram mark, from left to right, the elution points for polystyrene molecules of molecular weights lo3, lo4, lo5 and lo6. 2 12 16 FIG. 2.-PS200 gel permeation chromatograms for the degradation times noted (in hours). The ticks on the abscissa of each chromatogram mark, from left to right, the elution points for polystyrene molecules of molecular weights lo3, lo4, lo5 and lo6.R . J . NASH A N D D.M. JACOBS 213 of the degradation experiments using the NBS-706, the PS200, and the PS860 poly- styrene samples : the PS670 sample gave results similar to those of the PS860 sample. In each case, the 23 h chromatogram closely resembled the 16 h chromatogram, the only apparent difference being a narrowing of the low molecular weight peak at the longer time. The chromatograms show that for each molecular weight sample examined, prolonged mechanical degradation produces the same limiting, low molecular weight species (M, z 8.4 x lo3). The generation of this latter species presumably accounts for the observed change in the polymer coating from a smooth to a powdery texture. 7 1 (d) 2 (b) 12 5 FIG. 3.-PS860 gel permeation chromatograms for the degradation times noted (in hours).The ticks on the abscissa of each chromatogram mark, from left to right, the elution points for polystyrene molecules of molecular weights lo3, lo4, lo5 and lo6. DISCUSSION PRIOR HYPOTHESES Even a superficial examination of fig. 1 , 2 and 3 reveals that many of the concepts of previous theoretical treatments of polymer degradation cannot apply to the present system. Thus, a commonly held hypothesis has been that polymer molecules, under mechanical stress, degrade by single scissions. The simplest view has the breakage point located at random along the polymer An alternative view has the break at the centre of the molecule,27 while a more refined treatment 30 holds that there is a range of possible positions, the probability for scission rising from zero near the ends of the molecule to a maximum at the centre.None of these views is in accord with the present data since, regardless of the location of the point of scission, single breaks will cause only a continuous shifting of the maximum in the molecular weight214 DEGRADATION OF POLYSTYRENE FILMS distribution to lower values. By contrast, fig. 1, 2 and 3 suggest that in fact mech- anical degradation occurs via concurrent multiple breakages. For example, in fig. 3, the molecular weights assignable to the three peak maxima in the chromatogram are in the approximate ratio of 70 : 7 : 1, and a traverse from fig. 3a to fig. 3fmust involve at least 10l8 bond breaks per gram of initial polymer. Considering the limited number of impacts possible during that time span, each impact must cause multiple scissions.That the chromatogram in fig. 3d is trimodal further implies a non- random distribution of scission sites. DEGRADATION MODEL BASED O N THE PRESENT DATA RATE OF DEGRADATION Possible parameters controlling the rate of degradation of thin polymer films include the time of degradation, the number and efficiency of impacts, the thickness of the film and the molecular weight of the polymer. In theory, a search for a possible molecular weight dependence would best be made using the data from the narrow distribution samples, PS860, PS670 and PS200. However, this approach is precluded by the variability in the coating thickness from sample to sample. The problem can be eliminated by use of the NBS-706 data since the molecular weight distribution of this sample must contain contributions from a wide spectrum of molecular species within a single film.As an initial step, consider fig. 4, which is a plot against degrad- ation time of the relative curve height (Nt/No where Nt and No are the curve heights at time t and time zero) at various elution counts (i.e., at various molecular weights). 0 : 0 4 degradation time/h FIG. 4.-NBS-706 degradation data for the elution counts noted. Since the heights are those taken directly from the chromatograms, they may contain contributions from instrumental effects and from overlapping neighbouring peaks : there is no ready method to correct for these contributions which, however, should be minor for the highest elution counts. WhiIe the plots for counts above 27 (equivalent to a molecular weight of M 1.4 x lo5) show a net increase with time caused by the arrival of fragments from the degradation of higher molecular weight species, the plots for counts below 27 apparently represent pure degradation.The relative peak heights at these latter counts decay exponentially with time, the rate decreasing withR. J . NASH AND D . M . JACOBS 215 decreasing molecular weight. At this point it will be helpful to develop a model to aid in the rate analysis. The model must explain the following observations : (a) The rate of degradation varies exponentially with time and is a decreasing function of molecular weight. (b) The number of bond scissions per impact is large. (c) The bond scissions per molecule are multiple and non-random. Since the same fixed coating weight was used for each of the various polystyrene films, the films of the largest molecular weight species will contain the fewest number of molecules.This fact alone is sufficient to cause the rate of degradation to be a decreasing function of molecular weight. Thus, consider a film of side lo and depth d. If each successful milling event is assumed to cause degradation within a zone having orthogonal dimensions b,, by, b,, then where P is the probability that a polymer molecule of size I will be at least partially within the degradation zone. The rate of degradation will be given by and hence dN/dt = -MPNt, Nt = No exp (-MPt), where M is the number of impacts per unit time having sufficient energy to cause degradation, No is the initial number of molecules and Nt is the number of molecules remaining at time t.Under the experimental conditions of the present study, the degradation zone appears to extend throughout the entire film depth, and thus the last term in eqn (1) can be taken as unity. If the zone dimension is assumed to be b in both the x and y directions then (2) Fig. 5 , the experimental data plotted according to eqn (2), yields (3) Nt = No exp [ - (Mt/Z~)(Z+b)2]. Nt = No exp [ -9.242 x 10-12t[(0.67M3) + 1920l2], 400 8 0 0 1200 (molecular weight)+ F I ~ . 5.-NBS-706 degradation data.216 DEGRADATION OF POLYSTYRENE FILMS where M is the polymer molecular weight, t is the degradation time in seconds, and the factor 0.67 converts M3 to molecular dimensions in A.Thus, with the above assumptions, the degradation zone appears symmetrical since the film thickness is 2000A and the deduced zone size b is 1920A. Eqn (3) correctly predicts the rate of degradation not only for the selected components within the NBS-706 chromato- gram, but also for the PS860, PS670 and PS200 chromatograms. Fig. 6 shows the NBS-706 data and eqn (3) plotted so as to indicate the dependence of degradation on time and molecular size. -2.0 - -2.5 , 1 I 0 5 0 0 1000 1 5 0 0 (molecular weight)J FIG. 6.-The points are NBS-706 data ; the lines are those calculated using eqn (3), (see text). The numbers are the degradation times in hours. MODE OF DEGRADATION The chromatograms in fig. 1,2 and 3 show that selective bond scission must occur.Since bond breakage will occur at points least able to relieve the applied stresses, the data suggests that these “ weak ” points must be regularly distributed along the poly- mer molecule. A possible identification of these points can be made by noting that in an amorphous polymer film the molecules, being highly intertwined, will be most constrained in the regions of entanglement.” These regions have indeed been postulated as the sites for bond breakage in the shear-induced degradation of polymer While the mean distance between entanglements will not be a function of polymer molecular weight, the number of entanglements per molecule will increase with molecular weight. Thus, while large molecules will be able to relieve applied stresses by bond breakage at only a portion of the many regions of entanglement, smaller molecules under the same conditions will be forced to break at the majority of the regions.This view could account for the bimodal splitting of the degradation products from samples PS860 and PS670 and the single mode from PS200. An alternate, though complementary explanation can also be given from a probability standpoint. Thus, the probability for a molecule to be completely hit will be a function of the size of the molecule and of the impact zone. For the latter, the two extreme cases will be (a) the impact occurs at a point, (b) the impact zone greatly exceeds the dimensions of any of the impacted molecules. Case (a) will generateR . J . NASH AND D . M. JACOBS 217 large degradation fragments regardless of molecular size, while case (b) will cause all molecules to degrade directly to small fragments, provided that sufficient energy is available.Between these two cases there must be a zone size large enough com- pletely to degrade PS200, but small enough only partially to degrade PS860. Addi- tionally, since in any actual impact zone the stresses will vary from point to point, this variation will produce a range of modes of bond breakages. As molecular size decreases, the entanglements per molecule will diminish until, at some characteristic size, the molecules no longer drastically hinder one another. Molecules below this size will hence be expected to resist mechanical degradation provided that the applied stresses are not severe enough to produce bond breakage by some mechanism other than entanglement.The limiting molecular weight species observed in the present study may, therefore, be viewed as being in this sufficiently disentangled state, with the molecular weight distribution reflecting the distribution of inter-tangle spacings. It should be noted that many properties of polymers reflect the existence of molecular entanglement and the concept of a " critical entanglement molecular weight " is well established. COMPUTER SIMULATION By combining the results of the rate and mode examinations, an overall picture of the degradation process can be obtained. Fig. 7, a plot against time of the areas of the three component peaks in the chromatograms of sample PS860, suggests that degradation time/h weight peak 0 ; intermediate molecular weight A ; low molecular weight peak U.FIG. 7.-PS860 degradation data : variation of component peak areas with time. High molecular the degradation process can be represented as a series of consecutive, irreversible reactions. If the high, intermediate and low molecular weight peaks are labelled A, B, and C, then two possible pathways appear possible : (a) A+B+C (b) A+B C w For each pathway, expressions for the concentration of each species as a function of218 DEGRADATION OF POLYSTYRENE FILMS time can be derived by an application of Laplace-Carlson transforms to the compon- ent rate equations.52 Unfortunately, by an appropriate choice of rate constants, the experimental results can be correctly described by both pathways. Therefore, a kinetic analysis based on the degradation data of one molecular species alone cannot reveal which is the correct pathway.However, if the rates calculated using eqn (3) are inserted into the kinetic analysis, then (b) emerges as the likely mode. To illus- trate this point, the following computer simulation of the gel permeation chromato- grams was made for both pathways. For the simulation of the PS860 data, peaks A, B and C are approximated by three Gaussian curves of fixed base widths in the proportion 5 : 8 : 8. Peak C is assumed to be comprised of non-degradable molecules : the small amount of degradation observed experimentally is simulated by a gradual shift in the peak maxima to lower values as time progresses. To calculate the amount of degradation occurring for peaks A and B, eqn (3) was rewritten in the following form : f= 1 -exp [-9.242 x 10-12[(0.67M9)+ 1920l2] (4) wherefis the fraction of molecules of molecular weight M which degrade in unit time.Rather than calculate the extent of degradation for selected values of M within peaks A and B, only the value of M at the peak maximum was considered, the 16 FIG. 8.-Computer simulation, using pathway (a), (see text), of PS860 degradation chromatograms for the times noted (in hours). The ticks on the abscissa of each chromatogram mark, from left to right, the elution points for polystyrene molecules of molecular weights lo3, lo4, lo5 and lo6. entire distribution being calculated on the basis of the behaviour of this single value. This tacitly assumes that the molecules within a distribution all degrade similarly : the experimental results suggest that this is a reasonable assumption.219 At each pass through the program, (simulating one hour of degradation), the previous height values for peaks A and B are multiplied by the required values off.For peak B, the resulting " fragment " is added to peak C ; for peak A, the " frag- ment " is divided, after scaling to allow for the differences in peak base widths (the sum of the peak areas, being proportional to polymer concentration, must be main- tained constant to simulate mass balance), between peaks B and C according to a ratio Y. Experimentally, the area under the total chromatogram decreases slightly with time ( z 5 % loss after 23 h of degradation) prcsumably because of production of fragments below the resolution of the chromatograph (i.e., < 1000 molecular weight). To simulate this loss, a small amount of the " fragment " from A is removed from the computed chromatogram.Following each degradation step, the program calculates the curve envelope for the sum of the three component peaks. The program was run in a time-shared interactive mode on a Xerox Sigma 7 computer, the results being displayed on a Hewlett-Packard 7200A graphic plotter R . J . NASH AND D. M. JACOBS 2 FIG. 9.-Computer simulation, using pathway (b), (see text), of PS860 degradation chromatograms for the times noted (in hours). The ticks on the abscissa of each chromatogram mark, from left to right, the elution points for polystyrene molecules of molecular weights lo3, lo4, lo5 and lo6.driven by an ASR-33 Teletype. In this way, the effect of various values of Y could be readily visualized. To simulate pathway (a), Y was taken as zero. The computed chromatograms, fig. 8, using this value do not match the experimental chromatograms, in particular the computed peak B grows too rapidly. This occurs because eqn (4) predicts that the rate of degradation of peak A will exceed that of peak B. The closest simulation, fig. 9, was achieved using pathway (b) with the degradation products being distributed 65 % to peak B, 31.5 % to peak C and 3.5 % as non-detectable fragments. The simulation thus suggests that fragmentation of the PS860 polystyrene mole- cules occur via two parallel, consecutive paths, one involving on the average w7220 DEGRADATION OF POLYSTYRENE FILMS breaks per molecule, the other ~ 7 0 breaks.Presumably, the ratio of medium to small fragments is related to the dimensions of the impacted molecule and the impact zone, and the stress distribution within the zone. The present results are not compre- hensive enough to reveal the form of such a relationship : experiments on polymer films of various thicknesses or different chemical constitution might offer a way to explore this point. Throughout this work, the polymer samples have been referred to as “thin films ”, however, a better description would be “ thin coatings ”. As such they are doubtless influenced by the physical properties of the substrate : pre- sumably a change of substrate could cause a change in the degradation process.From a practical point of view it should be noted that solids are often given protective coatings of thin polymer films. The present study shows that the deterioration of such coatings by mild mechanical forces can occur not only by macroscopic but also by molecular degradation. R. S. Porter, M. J. R. Cantow and J. F. Johnson, J. Polymer Sci. C, 1967, 16, 1. R. M. Thomas, J. C. Zimmer, L. B. Turner, R. Rosen and P. K. Frolich, Znd. Eng. Chem., 1940, 32, 299. N. K. Baramboim, Mechanochemistry of Polymers (Maclaren and Sons Ltd., London, 1964). H. H. G. Jellinek, Degradation of Vinyl Polymers (Academic Press, New York, 1955). N. Grassie, Chemistry of High Polymer Degradation Processes (Interscience Publishers, New York, 1956). N. K. Baramboim, Zhur.Fiz. Khim., 1958,32, 806. H. W. W. Brett and H. H. G. Jellinek, J. Polymer Sci., 1956, 21, 535. R. J. Ceresa and W. F. Watson, J. Appl. Polymer Sci., 1959, 1, 101. G. Gooberman and J. Lamb, J. Polymer Sci., 1960, 42, 35. lo H. Grohn, K. Bischof, M. Loesche and K. Moeckel, PIaste Kautschuk, 1961, 8, 593. l 1 H. Grohn and K. Bischof, Wiss. Z. Tech. Hochsch. Chem. Leuna-Merseburg, 196112, 4, 153. l2 H. H. G. Jellinek and G. White, J. Polymer Sci., 1951, 6, 757. l3 H. H. G. Jellinek and G. White, J. Polymer Sci., 1951, 7, 21. l4 H. H. G. Jellinek and G. White, J. Polymer Sci., 1951, 7, 33. l 5 W. R. Johnson and C. C. Price, J. Polymer Sci., 1960, 45, 217. l 6 K. Mackenzie and A. E. Jemmett, Wear, 1971, 17, 389. M. A. K. Mostafa, J. Polymer Sci., 1958, 28, 499.A. Nakano and Y. Minoura, J. Appl. Polymer Sci., 1971, 15,927. l9 R. S. Porter, M. J. R. Cantow and J. F. Johnson, J. Appl. Phys., 1964, 35, 15. 2o R. S. Porter and J. F. Johnson, J. Appl. Phys., 1964, 35, 3149. 21 R. S. Porter, M. J. R. Cantow and J. F. Johnson, J. Appl. Polymer Sci., 1967, 11, 335. 22 R. S. Porter, M. J. R. Cantow and J. F. Johnson, J. Polymer Sci. C, 1967, 16, 1. 23 R. S. Porter, M. J. R. Cantow and J. F. Johnson, Polymer, 1967, 8, 87. 24 H. Staudinger and W. Heuer, Ber., 1934, 67, 1159. 25 H. Staudinger and E. Dreher, Ber., 1936, 69, 1091. 26 P. E. M. Allen, G. M. Burnett, G. W. Hastings, H. W. Melville and D. W. OvenaI1, J. Polymer 27 F. Bueche, J. Appl. Polymer Sci., 1960, 4, 101. 2 8 G. Gooberman, J. Polymer Sci., 1960, 42,25. G. Gooberman, J. Polymer Sci., 1960, 47, 229. 30 G. J. Heymach and D. E. Jost, .I. Polymer Sci. C, 1958, 25, 145. 31 H. H. G. Jellinek and G. White, J. Polymer Sci., 1951, 6, 745. 32 H. H. G. Jellinek, J. Polymer Sci., 1956, 22, 149. 33 H. H. G. Jellinek, J. Polymer Sci., 1959, 37, 485. 34 H. H. G. Jellinek, J. Polymer Sci., 1962, 62, 281. 35 J. Malac, J. Polymer Sci. C, 1971, 33, 223. 36 M. A. K. Mostafa, J. Polymer Sci., 1956, 22, 535. 37 M. A. K. Mostafa, J. Polymer Sci., 1958, 27, 473. 38 M. A. K. Mostafa, J. Polymer Sci., 1958, 28, 499. 39 M. A. K. Mostafa, J. Polymer Sci., 1958, 28, 519. 40 M. A. K. Mostafa, J. Polymer Sci., 1958, 33, 295. 41 M. A. K. Mostafa, J. Polymer Sci., 1958, 33, 311. 42 M. A. K. Mostafa, J. Polymer Sci., 1958, 33, 323. Sci., 1958, 33, 213.R . J . N A S H A N D D . M . JACOBS 22 1 43 M. Okkuama and T. Hirose, J. Appl. Polymer Sci., 1963, 7, 591. 44 D. W. Ovenhall, G. W. Hastings and P. E. M. Allen, J. Polymer Sci., 1958, 33, 207. 45 D. W. Ovenhall, J. Polymer Sci., 1960, 42, 455. 46 N. Sata and M. Okuyama, 2. Elektrochem., 1954,58, 196. 47 G. Schmid and 0. Rommel, 2. phys. Chem., l939,185A, 97. 48 G. Schmid and 0. Rommel, 2. Elektrochem., 1939,45,659. 49 H. Determann, Gel Chromatography (Springer-Verlag, New York, 1969). 5 0 H. H. G. Jellinek, J. Polymer Sci., 1948, 3, 850. 51 R. S. Porter and J. F. Johnson, Chem. Rev., 1966, 66, 1. s2 N. M. Rodiguin and E. N. Rodiguina, Consecutive Chemical Reactions (D. Van Nostrand Company, Inc., Princeton, 1964).