1 r r "1 Hi‘ H: 1‘ “;|ll‘ " I l!’ I My? [1 H I" H ’i H 11: Ill! \ } §TRENGW VAMAYEONS OF BtLATERALLY ORIENTED RUBEER HYDROCHLQREDE F ILM Thests for Hue Degree of M. 5. VuCLGA“ Sn; U‘MJEPSH Roiand Keith Lancaster 1957 1149515 LIBRARY Michigan Sta t6 University STRENGTH VARIATIONS OF BILATERALLY ORIENTED RUBBER HYDROCHLORIDE FILM By ROLAND KEITH LANCASTER AN ABSTRACT Submitted to the College of Agriculture Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Forest Products 1957 \( APRPOVedisnM w - 1101/ < W During preliminary investigation of the strength properties of bilaterally oriented rubber hydrochloride film considerable variation was found in breaking factor values for samples selected from different sections of the same film. The purpose of this paper is to present the methods used to isolate the areas of various strengths and on the basis of strength measurements to present a probable ex— planation of this variation based on the molecular structure and organization of the film. Because of the crystalline nature of rubber hydro- chloride and the transparency of the film used, optical ex- amination using polarized light proved most fruitful. By the use of the polariscope, it was possible not only to de- termine the principal direction of orientation but also to make a semi-quantitative estimate of the extent of orien- tation. On the basis of work carried out with similar polymeric materials an interpretation of the patterns of birefringent areas visible in the polariscope was made. It would be ex— pected that the strength measured with the direction of orientation would be greater than that measured across the direction of orientation. It would likewise be expected that the per cent difference between the ”with" and ”across" strength measurements would be greater for the highly oriented areas than the corresponding strength measurements for very slightly oriented areas. To confirm these observations samples were selected for strength measurements by polariscopic inspection. Breaking factor, thickness, and elongation measurements were then made on these samples. The results of these determinations indicated that the original interpretations of the polariscopic patterns were correct. The principal value of this study is that it pro- vides a foundation for further work with this film inasmuch as it furnishes a method for selecting homo- geneous samples. In addition the optical inspection procedure offers possibilities as a simple and rapid technique for evaluating the effect of changes in the orientation process. STRENGTH VERIATIONS OF BILATERALLY ORIENTED RUBBER HYDROCHLORIDE FILM By ROLAHD KEITH LANCASTER A T ESIS Submitted to the College of Agriculture fiichigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Forest Products 1957 / —. 7" €’_ I . ,0 - _:$ 13. '0- 0-2 :3 I) /'l ACKNOWLEDGMENTS The writer extends his sincere appreciation to Dr. J. W. Goff and Dr. H. J. Raphael of the Department of Forest Products for their guidance and help during the course of this investigation. Grateful acknowledgment is also made for the grad- uate research assistantship provided by the Tee—Pak Foun- dation during the past academic year. Sincere thanks are likewise extended to Tee-Pak, Incorporated, of Chicago, Illinois, for their generosity in supplying the film used in this study. ACKNOWLEDGMENTS LIST OF TABLES LIST OF FIGURES . . I. INTRODUCTION II. PREVIOUS III. IV. ANALYSIS OF DATA V. CONCLUSIONS AND DISCUSSION WORK .”. LITERATURE CITED . APPENDIX CONTENTS EXPERIMENTAL PROCEDURE iii Page ii iv 20 25 28 30 iv IJIST OF TF1 BIAES Table Page I. A Summary of Strength and Gauge Measurenents. . . 23 II. Per Cent Difference in Strength as Measured With and Across the Orientation Direction . . . . 24 Figure LIST OF FIGURES Page General Radio Company Type lSBA-A Polar- iscope with a DuMont Type 302 Oscillo- graphic Record Camera . . . . . . . . . . . . . 12 Polariscopic patterns obtained by placing samples of film D between crossed Polaroids . . 13 Testing Machines, Incorporated, Model 555 6 . 1 Motor Driven Micrometer . . . . . . . . . . . Schopper Tensile Testing Machine and Thwing Albert Model JDC 25 Sample Cutter . . . . . . . 18 I. INTRODUCTION This study represents the initial investigation in this laboratory of bilaterally oriented rubber hydrochloride film.1 ‘The original objective of this investigation was to measure any changes in strength properties which might occur when this film was subjected to controlled shrinkage at elevated temperatures. It was found, however, that there was a large variation in the breaking factor (2) values of samples se- lected from different sections of the same film, and for this reason it was deemed advisable to shift the emphasis of the project to a study of this variation in strength. The purpose of this paper is to present the methods used to isolate the areas of various strengths and, on the basis of strength measurements, to present a probable expla- nation of this variation based on the molecular structure and organization of the film. Because of the crystalline nature of rubber hydro- chloride and the transparency of the film used, optical ex- amination using polarized light proved most fruitful. By the use of the polarisc0pe, it was possible not only to de- termine the principal direction of orientation but also to make a semi-quantitative extimate of the extent of 1This film is available under the trade name of "Snug-Pak" from Tee-Pak, Inc., Chicago, Illinois. orientation. Breaking strength measurements which were made on samples selected by polariscopic inspection were used to confirm the optical observations. II. PREVIOUS WORK Crystallization and Orientation g£_High_Polymers Because of the general familiarity with inorganic crystalline materials, it is often inferred that for a substance to be classified as crystalline it must exhibit symmetrical plane boundaries. This property is in reality merely an external manifestation of a high degree of in- ternal geometrical organization. It is possible for a ma- terial to possess this high degree of internal organization without these external features. Such is the case with many high polymers; for, although they do not exhibit plane boundaries and sharp edges, they do show many properties of normal crystals such as well defined x-ray patterns, bi- refringence, and anisotrOpy of some mechanical and physio- chemical properties (3). In this study the birefringence and anisotropy of mechanical properties will be of par- ticular interest. Alfrey (1) defines a crystalline region as a section of matter in which the structural units are arranged in a far-reaching regular pattern. In the case of inorganic crystals the structural units are usually atoms or ions; however, this must be expanded to include repeating mo- lecular segments in the case of high polymers. It must also be recognized that even in nonpolymeric crystals the arrangement is never completely perfect, but the imperfections are almost always of a local nature. The significant point is that these small irregularities do not destroy the long range over-all regularity of arrangement. This distinction is especially important when dealing with polymeric crystals where local differences are common. The size of these polymeric crystals may range from 50 to 10,000 Angstrom units (8). However, Alfrey (1) points out that the essential requisite is that they be large enough to produce a distinct x-ray pattern. Mark (3) sums up his discussion of crystallites by defining them as small areas of somewhat indefinite size and shape inside of which the monomeric units are arranged in a three-dimensional periodic pattern. One of the most distinguishing characteristics of poly- meric crystalline materials is that they are never com- pletely crystalline. Regions of high geometric order, called crystallites or micelles, are separated by relatively amorphous regions (9) (10). Because of the large size of the polymer molecule and the fact that the crystallites are made up of regularly arranged molecular segments, one mole- cule usually extends through several phases. At various locations along its length one molecule may participate in several different crystalline and amorphous regions (10). Another factor to be considered is the orientation of the crystallites in the polymer. Usually these crystalline areas are randomly oriented; however, by subjecting the polymer to special treatment such as stretching, the crys- tallites may become aligned in one direction. Birefringence ig_High Polymeric Materials Refraction of light is best accounted for by realizing that light is an electromagnetic phenomenon and as such an interaction between its electric field and the field of the electrons in the material through which it passes is to be expected. The extent of this interaction is dependent upon the density and polarizability of the material, and the net result is a slowing down of the light through the material. This phenomenon is referred to as refraction. If a ma- terial presents a greater density in one direction than in another, two different refractive indices will result. This property of birefringence is characteristic of many crystalline materials. Both Houwink (7) and Alfrey (1) present a more rigid theoretical discussion of birefringence. The crystalline regions of polymers exhibit this property of birefringence; and, if sufficiently large crys- tallites are present, they may be conveniently studied with the polarizing microscope. When such a berefringent ma- terial is placed between the crossed Nicol prisms of the microsc0pe, it resolves the plane polarized light produced by the polarizer into two perpendicular components prepagated at di'ferent velocities to produce a certain optical path difference. Only the components of these two perpendicular waves which are vibrating in the plane of the analyzer will be transmitted by it. At this point in— terference occurs because of the optical path difference (7). The extent of this interference is determined by the two different propagation velocities and, therefore, provides an index of the extent of crystallization. Another tY3€ of birefringence can occur in polymers and this is known as orientation birefringence. It is based on an assymetric arrangement of molecules not caused by crystallization. This type of birefringence occurs in polymers when chainlike molecules are elongated or stretched and become parallel thus producing an unequal distri— bution of density in different directions. According to Houwink (7) this type of birefringence provides a measure of the orientationand is not related to crystallization effects. Anisotropy g£_Mechanical Properties It is generally agreed that both crystallization and orientation produce a marked increase in the tensile strength of a polymeric material. This increase is always noted in the direction of alignment of the molecules (1)(7)(9). In the case of orientation of chainlike molecules they may become extended to the most favorable position for the exertion of maximum secondary valence forces between adiacent chains. Although the strength of a single sec- ondary bond is quite small, the combined strength of all the secondary bords along the entire chain length becomes a major factor in determining the strength of the material. From this Houwink (7) concludes that for a break to occur in an oriented nonplastic material many strong primary bonds must be broken. Crystallization which may result from such orien- tation produces an even greater increase in tensile strength because the relatively high crystal energies make sliding of the molecules past one another virtually impossible. A break may occur in this case only by the rupture of strong primary bonds. The question of the relative importance of orientation and crystallization in determining tensile strength has been investigated by several workers for the case of natu- ral rubber, and their results are summarized by Alfrey (1). They found that orientation was the most important single factor in determining tensile strength. Their study showed that oriented noncrystalline rubber was stronger than both crystallized nonoriented and noncrystallized nonoriented rubber. Oriented crystalline rubber proved to be the strongest of all. Crystallization and Orientation gi Rubber Hydrochloride Rubber hydrochloride is formed by the treatment of natural rubber with dry hydrogen chloride and according to Bunn (4) crystallizes spontaneously without a stretching treatment. Bunn (3) also states that upon stretching a fiber type x-ray diagram is produced which suggests that an orientation of the crystallites has taken place. From x-ray diagrams Bunn (4) has also worked out the size, shape, and cosposltion of the crystal unit cell. III. EKPERIIENTAL PROCEDURE Introduction Although there anpeared to be no published account of optical examination of rubber hydrochloride, the results obtained with thin rubber films suggested that such an ap- proach might yield information concerning the crystallinity and orientation of the film. Jxamination was therefore made using both tne polariscone and the polarizing micro- scope. The patterns which appeared when the film samples were placed between crossed Polaroid sheets indicated that the degree of birefringence varied markedly from one area to another. The problem then became one of trying to re— late the variations in birefringence to the variation in breaking strength. Film Tested The film used in this study is a commercial packag- ing film produced by stretching a rubber hydrochloride film approximately 100 per cent both longitudinally and across the web. This stretching process is carried out at temper- atures slightly below the melting point of rubber hydro- chloride. The film is cooled while in the stretched state, and it maintains these extended dimensions as long as the temperature of the film is kept below the point at which 10 flow begins to take place. Samples of the rubber hydrochloride film which had not been stretched were also examined. Optical Examination The principal ootical inspection was carried out using the General Radio Company polariscope shown in fig- ure 1. The polariscopic observations were made in a completely darkened room so that the patterns would be more readily visible. Figure 2 shows some of the typical patterns which were observed when samples of the stretched film were placed between crossed Polaroids. On the basis of theoretical considerations the light areas were interpreted as being highly birefringent. Conversely the darker areas were con- sidered to be only very slightly birefringent. The striation effect shown was interpreted as giving an indication of the general direction of orientation of the assymetric units in the film responsible for the birefringence as well as in- dicating a nonhomogeneity of orientation. For example Figures 2-1 and 2-2 show highly oriented areas with the principal direction of orientation horizontal or normal to the machine direction, while Figures 2-3, 2-4, and 2-5 show highly oriented areas with the orientation direction vertical or parallel to the machine direction. Figures 2-6 and 2-7 show both horizontal and vertical orientation in 11 adjacent areas. In Figures 2-8, 2—9, and 2-10 several dark areas are visible which were typical of the very slightly oriented sections. Figure 2—11 shows an interesting anoma- lous checkered pattern. In all cases the machine direction is vertical. Although it is not readily apparent from the photographs shown in Figure 2, faint striations were also present in the dark areas which gave an indication of the direction of the slight amount of orientation which was present. When the film which had not been subjected to the stretching process was placed between the crossed Polar- oids, a completely dark field was produced indicating the absence of any birefringence in the film. This was true at all possible positions of rotation of the film in the field. Microscopic examination of the film was made using a Leitz petrographic microscope and an American Optical Spencer stereosconic polarizing microscope. The stretched film when magnified showed microscopic patterns which were very simi- lar to the macroscopic patterns which appeared in the polar- iscope. Although various areas could be isolated which appeared to be principally either birefringent or iso- tropic, striations were present which suggested that even on the microscopic scale the film was far from homogeneous. The nonstretched film was also examined using magnifications 12 . who as 288 oasaeamofiaouo «on on? 9323 a a»? omooeaaeaom 414m? 093. 5980 33 ~93ch .H Penman A -.___ ______,__——_- 13 Figure 2. Polariscopic patterns obtained by plac- ing samples of film D between crossed Polaroids. Note the one inch reference marks on 2J3 and 2-10. 1% of up to 360 diameters, and no indication of birefringence was noted. This would indicate that the crystallites which Bunn (h) states should be present were extremely small. In the case of natural rubber Smith and Saylor (11) were able to prepare crystals which were large enough to be plainly visible in the polarizing microscope using a magnification of 250 diameters. Selection 2£_Samples In the selection of samples to be used for strength measurements, four categories of orientation relationships were recognized; these were: (1) highly oriented areas with the principal direction of orientation parallel to the machine direction; (2) highly oriented areas with the principal direction of orientation normal to the machine direction; (3) slightly oriented areas with the principal direction of orientation parallel to the machine direction; and (A) slightly oriented areas with the principal direction of orientation normal to the machine direction. In each of these categories twelve samples were taken with the sample length parallel to the direction of orientation, and twelve samples were selected with the sample length normal to the direction of orientation. Sample length is used here as that direction in which the tension is applied during the breaking strength test. 15 The actual technique used in selecting the samples simply involved placing the film between crossed Polaroids and marking and coding the appropriate areas of the film with a wax marking pencil. One inch wide samples were then cut from the marked areas using a Thwing Albert Aodel JDC 25 Precision Sample Cutter. The thickness of each sample was measured using the Testing Machines, Incorporated, Model 555 Motor Driven Micrometer shown in Figure 3. Three thickness measurements were made across the one inch dimension of each sample. Since the anvils of the mLcrometer have a diameter of ap- proximately .6 of an inch, these measurements represent considerrble overlap. The length of sample actually sub- iected to tension in the testing machine was only one-half inch, thus the thickness measurements covered virtually the entire sample. Because these measurements involved read- ings which approached the limit of accuracy of the micro- meter, the zero point of the instrument was checked care- fully both before and after each reading. The thickness value was rejected if the zero point had drifted more than .00002 of an inch. The micrometer was adjusted so that the anvils exerted a pressure of eight pounds per square inch on the sample. neasurement g£_Tensile Properties In so far as possible these tests were carried out 16 .uosoaouou: dosage nose: mmm Hose: .eoueaomaoooa Jagged: magmas .n enemas 17 according to the "Tentative Methods of Tests for Tensile Properties of Thin Plastic Sheets and Films" of the American Society for Testing Materials (2). The Schopper type testing machine shown in Figure 4 was used in ac- cordance with Method B of the above procedure with two exceptions. First, the maximum rate of motion of the powered grips of this testing machine was twelve inches per minute as Opposed to the recommended twenty inches per minute. Second, the recommended initial grip separation was two inches; however, because of the limit of the size of some of the oriented areas, it was necessary to use an initial grip separation of one—half inch. To avoid sample slippage in the jaws each jaw face was covered with a coarse cloth backed pressure sensitive tape. The testing machine used also provided a direct meas- ure of the elongation of each sample at break. The calibration of the testing machine was checked initially and several times during the tests. This was carried out by attaching weights of known value to the upper jaws and checking the value indicated by the pendu— lum. The values corresponded within the limits of possible error of reading the instrument. The results of these strength measurements were expressed as breaking factors. The breaking factor is 18 Figure h. Schopper Tensile Testing Machine and Thwing Albert Model JDC 25 Sample Cutter. 19 defined as the breaking load divided by the original width of the test specimen (2). Because of the design of the testing machine, the breaking factor is based on the max- imum strength which is not necessarily the strength at break. All tests in this study were carried out in the standard laboratory atmosphere of 73.4 t 20 Fahrenheit and 50 t 2 per cent relative humidity (2). Three types of film were included in this study. They are coded B, D, and E. Film B is the nonstretched Pliofilm of type N2 which is described by the producer (6) as a "standard all-purpose, low water-vapor-gas transmission packaging film." Film D is produced by laminating two sheets of 80 gauge2 N2 Pliofilm and then subjecting it to the orientation process. Film E is formed in a similar manner from one sheet of 80 gauge and one sheet of 120 gauge N2 Pliofilm. _ 2A method of indicating the thickness of a film in which the numerical prefix is the last figures of the S-digit decimal fraction of the thickness in inches, thus: 90 gauge = .00030 inches. This method of expressing thickness is used for most packaging films except Cellophane. 20 IV. AwALYSIS OF DATA The original observations of the gauge, breaking factor, and elongation for all three films are recorded in Tables I through IX of the appendix. Tables X through XVII of the appendix summarize the statiStical analyses of these data. In this connection it should be pointed out that the significance of differences between mean breaking factors and mean thicknesses was determined by the use of the "least significant difference between means" technique described by Snedecor (12). The LSD values listed in these tables are the smallest differences between any two means which may exist if the two means are to be interpreted as being significantly different at the specified level. Since the existence of equality of variance is one of the assumptions of the analysis of variance technique, it is necessary to check this assumption for each set of observations (7). This is carried out in Tables XIV through XVII of the appendix by a method discussed by Snedecor (12). The significance of the difference between the mean breaking factors of film B is shown in Table IX of the appendix. In this case it was necessary to modify the num- ber of degrees of freedom available for the ”t" test since the variances of the "with" and "across" strengths were not 21 the same. The technique used is presented by Dixon and Massey (5). Table I below summarizes the breaking factor and gauge measurements with respect to orientation and machine di- rection. In all cases except observations (7) and (Q) of film D the breaking factor measured with the direction of orientation was significantly larger than the breaking factor measured across the direction of orientation at a level of at least 5 per cent. In all cases except observations (5) and (6) of film B it was found that there was no sig- nificant difference between the gauge measurements of the "with" and "across" samples. Table II presents the results of a calculation of the per cent difference in breaking factors as measured with and across the direction of orientation. These figures were calculated by dividing the difference between the "with” and the "across" by the "with” and expressing the result as a percentage. Tables XVIII and XIX of the appendix represent strength values of samples of films B and E which were measured on a Baldwin Emery Model SR4 Testing Machine. These values are included because with this testing machine it is possible to measure both the strength at yield and break. There was no difference between the yield and break values noted 22 for film E. A significant difference between the break and yield strengths was apparent for film B. These data are not directly comparable to that reported in Tables I through IX of the appendix since with this testing machine it was necessary to employ Method A as recommended by the American Society for Testing Materials (2). These tables are included merely to indicate the difference in strength at yield and break for the nonstretched film. 23 omefl mmfi 5N an 04 233.8 mama an s d 5:. 332B m 0.3 $4 a: 0.8 8."... a 38% cognate «.3 8d 5 swan min A his 3333 dun ww.~ as Tom Jaws Am madman] a La 9.235 :.on was :3 93 $5 3 a»? ages“ can «as A8 his saw as 483 3335 TH SJ «5 can Hod 3 n3: 333.8 ism on .uaw 3 w :3 no .N 4w 383. n 89:38 as... dad 5 Nd: saws 3 n3: aflefi dis“: damn? uoaosm hogan owes magnum .25: haggafioum .39 .wafiaaum 333820 Iqa sweets 323: 3 33083 838: 3 no 9.33. ads 1932 qoaoquoano HoHHdusm dogmas—3.5 HO do.“ #02 HQ H Ends msgadflz Hang a: maczaam ho g 4 24 TABLE II PER CENT DIFFERENCE IN STRENGTH AS MEASURED WITH AND.ACROSS THE ORIENTATION DIRECTION —----- W 311m Extent of Orientation Parallel Orientation Normal Orientation to Machine Direction to Machine Direction Highly Oriented 37’70 i 37°73 % E Slightly 18.15 $ 11.52 1 Oriented HiSle an 2 Oriented '35 $ 39.7 % D .__. Slightly Oriented 17'26 % 9.h5 % Slightly B Oriented 9'02 $ 25 V. CONCLUSIONS AND DISCUSSION The most obvious conclusion which might be drawn from an examination of the data of Table I is that the strength measured with the direction of orientation is greater than that measured across the direction of orientation. This conclusion has value in that it tends to confirm the origi- nal hypothesis that the patterns observed in the polariscope are produced by an orientation phenomenon. From the work of Bunn (h) it seems likely that this consists of an orien- tation of crystallites. Another indication of the validity of the assumptions concerning the patterns observed in the polariscope may be found in Table II. If the areas selected as being highly and slightly oriented are actually oriented to the degree indicated, then it would be expected that the per cent dif- ference in strength between the "with" and "across" directions for a highly oriented area would be significantly larger than the corresponding difference for a slightly oriented area. This was found to be the case as shown in Table II. It should be noted that a slight anisotropy of strength was found in the nonstretched sample also. It is possible ‘that this likewise was caused by an orientation of crystal- JLites, but that the aggregates of crystallites were too~ 26 small to exhibit a visible optical effect. If it is assumed that this anisotrOpy of strength of the nonstretched film is actually caused by an orientation in the machine di- rection, then the per cent difference in strength measured in the "with" and the "across” directions for the non- stretched film is approximately the sane as the per cent difference found for the very slightly oriented areas of the stretched film. The original question concerning the source of the strength variability of the stretched film remains to be answered. The results of this study indicate that it is influenced by both thickness and orientation. For example, in film E, if sanples parallel to the nachine direction had been selected without the aid of the polariscope, ob— servations (l), (a), (5), and (3) would have been typical values (see Table I). Of these, observations (4), (3), and (q) are essentially the sane thickness. The strength dif- fTrences noted could logically be assigned to orientation effects. Similarly, since observations (2), (6),2(4), and (8) of film E represent samples selected across the orien- tation direction, it would be expected that their strength values would exhibit no orientation effects. This is true ‘when comparisons are made between (2) and (6) and between (4) and (Q). These two comparisons are not complicated by clifferences in thickness. Towever, when (2) and (4) are 27 compared and (6) and (Q) are compared, the significant differences noted can be accounted for only by the dif- ferences in thickness. Similar relationships were found for film D. Although further study would be necessary to clarify the relationshio between the degree of orientation and the thickness, these data suggest that within limits they may be considered to be independent variables. The principal value of this study is that it pro- vides a foundation for further experimentation. For example, it would now be possible to proceed with the original objective which was to measure strength changes upon heat shrinkage. It would be possible now to select uniform samples for such a study. In addition the optical inspection procedure offers possibilities as a simple and rapid technique for evaluating the effect of changes in the orientation process. (l) (2) (3) (4) (5) (6) (7) (9) (10) (ll) 28 LITERATURE CITED Alfrey, Turner. Hechanical Behavior of High Polymers. Vol. VI of High Polymers. New York: Interscience Publishers, Inc., l9h3. American Society for Testing Materials. ASTM Standards 22 Plastics. Philadelphia: American Society for Testing Materials, 1957. Bunn, C.W. The Study gbeubberlike Substances By X-Ray Difraction Methods. ("Advances in Colloid Science: Scientific Progress in the Field of Rubber and Synthetic Elastomers," Vol. II.) New York: Interscience Publishers, Tnc., 1946. Bunn, c.w. "The Crystal Structure of Rubber Hydro- chloride," Journal g£_the Chemical Society (London), 1942, 65k. Dixon, T.J. and Massey, F.J. Introduction 33 Statistical Analysis. New York: McGraw-Hill Book Co.,Inc., 1951. Goodyear Tire and Rubber Company. "Pliofilm End Use Chart." Akron, Ohio: Goodyear Tire and Rubber Co., 1955. Houwink, R. Elastomers and Plastoners: Their Chemistry, Physics, and Technology. (Elscvier's Polymer Series, Vol. I.) New York: Elsevier Publishirg Co., Inc., 1950. Mark, H. The Investigation 3: High Polymers with X-Rays. ("Frontiers in Chemistry: The Chemistry of Large Mol- ecules, Vol. I, Edited by R.E. Burk and O. Grummitt.) New York: Interscience Publishers, Inc., 1943. Mark, H. and Tobolsky, A.V. Ph sical Chemistry 3; Hi h Polymeric Systems. Vol. II of High Polymers. New Yor : ' Interscience Publishers, Inc., 1950. Meyer, K.H. Natural and Synthetic High Polymers. Vol. IV of High Polymers. New York: Interscience Publishers, Inc., 1950 Smith, H.W. and Saylor, C.P. "Optical and Dimensional Changes Which Accompany the Freezing and Melting of Hevea Rubber," Journal 23 Research g£_the National Bureau of Standards, XXI (September 1933) 257. (12) Snedecor, G.W. Statistical Methods. Ames, Iowa: The Iowa State College Press, 19 . 29 APPENDIX 31 use. Hm.~ m.om Has. Hm.a o.ms use: 0mm. Ns.m n.na :a.om.~a «an. mm.m n.3n mm.an.em sen. am.~ a.»m os.mm.mm can. oo.s n.as om.ma.sa one. am.~ m.mm mm.sm.sm man. oo.a n.~m ~m.mm.mm can. sm.~ n.ms ms.om.om son. an.“ a.sa ms.aa.m: man. as.~ o.nm nm.~n.an «as. «s.: n.os H:.om.ms com. n~.~ m.ms om.om.ms «as. om.s a.~m am.am.om can. no.~ o.Hs n:.aa.mn mam. mm.: a.ma o:.:m.nm cow. om.~ o.as om.ss.ms mas. mm.m m.o: as.sm.aa own. 3:... 5.3 3.3.3 as. win an? $.36“ own. wa.~ 5.:3 ms.:s.ma new. om.: o.on as.om.nm mos. ms.~ a.sm mm.ow.~m «on. m~.: s.mm ow.~s.mm «mm. m~.~ m.a: n:.mn.s: com. os.: a.nm sn.on.mn .qd .nn .mpa .aa "maw.upa nod» nopodm amuse omsoo nod» Heaven amass amuse usmdoan mndxuonm omega» _ aamsoan wuaxsonm ommuohd couscouan aoauepqouuo «moped noses moansdm noapoauan noapasqoauo new: gonna moaaaum onsoann finHmodz oa AHAqdm4mflona H.548 39 $.n u $33813» ooa u 2 8 u 9: u «a 38:3: nmn.H ma.m o.p~a “no.~ :m.m m.-~ nae: oom.~ mm.“ u.on~ oma.~ma.oma mom.~ m~.o n.H~H Hma.o~H.n~H :ao.H om.m m.-a nma.n-.mua saw.” mH.o n.mHH maa.waa.m~a mo~.a :m.m m.ma~ -H.¢HH.5HH ooo.~ om.o o.o~H mHH.m~H.maa mmo.m mm.“ s.o~a n-.~ma.nma -o.a m:.o 5.:ma mma.-a.n~a 0mm. om.“ o.ona oma.ona.ona omH.~ ~:.m n.o~H ama.maa.oma own.H om.m o.:- m~H.-H.n- com.” ~:.m m.o~a -H.H~H.¢HH Now. mm.m o.H~H mmfl.mad.naa nam.n am.o o.n~H -H.B~H.oma mam.H om.m u.m~fl ona.omfl.nma cum.” o~.o m.H~H mma.uafl.amfl mm~.H oo.o o.:~H HNH.¢~H.HMH m5~.~ om.o m.m- wma.¢ma.:~a omm.fl o~.o n.n:a om~.mafi.mma mmm.~ -.o o.H~H wHH.m~H.:~H m-.m oH.w o.onH mma.om~.mua mmo.~ m:;o “.mma aaa.mma.ona omm.H mo.o 5.:ma ona.-~.-a ~ mam. m:.m o.HmH HnH.onH.~nH .§ 3.134 1mm afifimfl nod» uoaodh owdaw owquc noaa hapoufi amuse omquu Lamaoan wqaxdoum oManopq lowdoan MdfiMdOhm onuohd noapoouan magnum: noouo< nexus moamauw qofiaomuan nudged: neat dogma moamadm :AHH afluoaamammoz m quh NH flqm< Mawxcoum cwwuop« dodauoaan caanocz 666004 amuse moamacm mdfimd QHBZHHMO Hnmuam H :AHh HHHbN Hnm