m—wvr~*-—~———‘— -_ I I RELATION BETWEEN PHOTOELASTIC PROPERTIES AND MOLECULAR BEHAVIOR IN CERTAIN PLASTICS Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY ‘ Tamma Venkata Kameswara Rao 1960 SHE‘SVS This is to certify that the thesis entitled RELATION BETWEEN PHO'I‘OELASTIC PROPERTIES AND W BEHAVICR IN CERTAIN PLASTICS presented by rm VENKATA KAHE$ARA RAO has been accepted towards fulfillment of the requirements for m 0? mom! degree in WHICS MO.W Major professor Dateww 1L“; ‘qta 0 ° 0 _ 0.169 LIBRARY Michigan State University Tamma Venkata Kameswara Rao Abstract The object of the present investigation was to find why materials are Iirefringent under stress. Polystyrene which has a very low photo- elastic effect. and Columbia Resin which has a high photoelastic effect were chosen as the experimental materials. These materials were rende- red into thin films by machining and polishing techniques and were later stressed using a specially designed and constructed straining unit. Ehe changes in the absorptions of an infrared beam by individual atomic groups were computed by first obtaining the infrared absorptionespeetra of Poly- styrene and OR - 39 under stress using a Perkin-liner Infrared Spectro- Phetemeter. It was found that the c - H aromatic does not contribute appreciably towards the change in absorption in Polystyrene and GB. - 39: also there is a somewhat greater absorption in Polystyrene due to c - H aliphatic group than in CR - 39. thus leading to the surmise that stress birefringence in Polystyrene might be due to the presence of a vibrating group like 6 - H aliphatic. further. the change in the absorption due to O - H wagging in the case of GB - 39 is remarkably high compared with that due to the same group in Polystyrene. It seemed probable that the O - H aliphatic influences the behavior of Polystyrene under stress and the 0 - H wagging is a deciding factor in on - 89. Ihe high photo- elastic behavior of GR - 39 compared with Polystyrene could be due to 1) lack of the presence of heavy groups like benzene rather too close to other relatively small groups lilo O - H and 2) the presence of additional groupslikeO-O. 020. 0-0, 0-0. MOW '_ - m... I'TI' =.- C’ i'wi ‘17 I MIG! mm PMOELASTIC rmmms AND HOLECUMR BIEWIOR II CERTAIN 21481103 By i'ma Yenkata I-eswara Res A IESIS Submitted to the School of Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfilment of the requirements for the degree of 100010! or PMS!!! Department of Applied Hechanics 1960 Amn'evocl M 0 ~ NW ,- fox) ’ 3 UV ‘54 0 l‘ i, i C‘ spy Table of Cont ente Statement of the problem Historical Sketch Background ‘i'heory a) optical Theory as applied to stress analysis b) Strains in the case of a Linear Chain molecule subjected to external load c) The theory of Infrared Spectra 6.) Molecular Structure and Mechanical behavior of a Polymer Experimental Procedure a) Description of the Photoelastic Apparatus b) Determination of Stress-optic coefficient of Polystyrene and C R - 39 o) no straining Unit for loading the films 4) Preparation of the film e) Description of the Infrared Spectrophotometer Observations and Results Discussion Conclusion Bibliography tclmowledgements Page No. 14 Statement ef the problem Else ebJeot ef the present investigation is to find why materials are birefringent under stress: in ether werds to find a relation between the behavior ef the molecules under stress and mechanical bi- refringenee. Historical Sketch An caerimcntal investigation of the optical properties of certain transparent solids in 1816 led David Brewsterl to the discovery that the forced deformation of a transparent solid alters its optical properties. is found that an optically isotropic trnsparent solid becomes optically anisotropic when subjected to external loads. and the degree of optical anisotropy is proportional to the deformation of the material. Polari- sed light transmitted through a piece of glass under stress exhibits a brilliant color pattern. Brewster suggested that these color patterns might serve for the measurement of stresses in engineering structures such as masonry bridges. a glass model being examined in polarised light under various loading conditions. fhis suggestion wont unheedod by engineers at the time. Comparisons of the color patterns with ma- lyticel solutions were made by the physicist llaxwellz. the suggestion was adopted much later by O. Wilson:5 in a study of the stresses in a beam with a concentrated load and by A. nssnagsr‘ in an investigation of arch bridges. his method was developed and extensively applied by :I. G. (kaiser5 who intrcdwod celluloid as the model material Brewster's discovery becam one of the useful subjects for investi- gation and development during the present century. no application of this optical property of transparent solids to experimental stress analysis has been given the name of Phetoolasticity. fodsy photo- olasticity has grown to the full stature of a powerful technical inst - rument for quantitative stress analysis which for two dimensions, at least, exceeds many other methods in reliability. scope and practicability. Ihore is hardly my method h which the cupleto exploration of principal stresses. let alone the stresses on free boundaries. can be determined with the same speed mid accuracy and at such a surprisingly shall cost as the photoelostic method. Nor is there a method which has the same visual appeal and covers the whole stress field with one pattern. A critical observation shows that the materials which exhibit phe- toolastic effect are essentially high polymers and are sometimes called plastics. 'e how. that there are a number of plastics in the market todq o.g. Bakelite, CR - 39. Catalin, Postcrite. Polystyrene, Cellulose acetate, Polymotlwl mothacrylate and so on: but only a few of them sa- ‘ tisfy the requirements of a good photoelastic material and hence could be used in the preparation of the models for stress analysis. can characteristics of an ideal photoelastic Interial could be summarised as follows: a) Optical trmsparency b) optical sensitivity to deformation c) Strict sdhsrsncs to boss's law d) Preedom from aging effects e) l'reodom from initial internal stress f) Elastic and optical isotropy and homgenoity g) llachinibility h) Constancy of properties during moderate changes in temperature mid treatment 1) Roascnable price loodless to say none of the materials thus far investigated meets all these requirements. In fact very few of the materials that are available for the construction of photoelaatic model no more than par- tially satisfactory. Ewe of the most satisfactory are l) a special type of Bakelite. desimted by the number Bf - 61 - 893 and 2) the Pittsburgh Plate Glass company product CD. - 39, now produced by the Bomalite Company of Wilmington. Del. more are several other mate- rials of a similar nature that are fairly satisfactory. Celluloid has been an old standby for years. In the following pages an attempt has been made to emlain wig materials are birefringent under stress; or, in other words. what is. the mechanism of artificial double refraction in materials under stress? Directly or indirectly this problem has been under investigation since about 1920. some of the research workers in the field being Kuhn and Gruns. Eroloarv. Budde, Gurneeg. and we'll? who tried to answer the why of artificial double refraction in materials under stress. in- optical anisotropy of a randomly linked chain. Pig. 1. has been thee- retically worked out by Kuhn and Grun. fhey arrived at the equation (d&' “7.) 7- ”"- @I " “23E "' 3£€|TE;:13 (l) where cg and 0(1 are the electronic polarisabilities. parallel ad perpendicular. respectively. to the individual lining 0(2 and 0(7‘.’ are the total electronic polarisabilities parallel and perpendicular, '-.-I- . -. , . . _ s . . 4 , . . m . . I ' e . . . . . ‘ . a v D , . A x v . a . . y . . ( - . , . ‘ , . i s s - . , . - . . i . . . . - . . . ‘ u . ' ‘ O s a s I o s v i ' . / ' - . . . . ‘ . . . . ~ . , ‘ . . . . . . . — , . I i I, 1 (a) Random Chain (b) Zig-Zag Chain Fig. i. The Random and Zig-zag Chains. respectively, to the vector 'r' Pig. 1 (a); 'n' is the number of links in the chain: 'r' is the straight line distance between the ends of the chain; 'L' is the length of each link: and of,“ is the inverse Langevin function. ll'or a zigzag chain of 'n' links, a portion of which is shown in l'ig. 1 (b). it can be shown from standard optical theory that (acr- «a = n («i-«A [x— a sure] (2) In the derivation of this equation, the zigzag chain is assumed to have free rotation about the 'r' vector. this introduction of throe- limomsienal character is necessary in order to make a comparison bet- weon eqs. (1) and (2). It is also assumed that in any extension of this zigzag chain the bond angles all change in the same manner; eq. (2) may also be written as (dz' 0%) = eru-“QEG’S‘ 7%] freloar's work was on extension of Kuhn and Grun's theoretical studies. D plotted the relative polarisation anisotropy referred to the completely extended chain. (d a - Dig/n @rotqagainst the en- tension (r/nl.) for the random coil and the zigzag chain. Gurnoo attempted to put orientation on a quantitative basis. He started with the Ieronz-Ierentz equation mWLLN'L ' ll? 1' . e . . I I . . o ’ ’ o . ' L m ' . a J ' I 7 ‘ ‘ O . I. I ‘ , , ‘ ' —- . I ' . I ._ , " ‘ ' , I o . ‘ s O > ' . . I . . . _ . ‘ . I ., . . t O . ‘ . t I . t , 1 - I . \ n I ‘ I . ‘ r . - . r .1 . ‘ ‘ l / ‘ ‘ i l " .— l e ‘ d I . ‘ . . — . . . , , , I ‘ ‘ ’ . . . . ' ' s . _ ‘ ' l 21 . I . ‘ _ l ‘t v p. 1‘ i .- 'n‘a-I _MF:flNu “1-5-2 3 where n refractive index. ll molecular weight , at electronic polarizibility. I : svagadro's number. and f = density; rho relation between birefringence and polarization anisotropy which . Gurnee arrived at is as follows: (“1““) 7.___‘I_T_ NJ“ C“ +2) ..._..._._._ Fig. 2. Resolution of plane polarized light ray. 11 The magnitude of the resultant light ray emerging from the analyzer is R z: 00 sin]s sin (wtl-t-E.) cos I5 - 00 cosftein (wt2+é) . sin? or. R = (06/2) sin 2 55 sin (wtl-t-é ) - sin (wt2 *- E a (3a) where the tines t1 and t2 are the times taken by the components of the resultant light ray in passing through the material. In solids the velocity is dependent on the magnitude of the principal stresses. Equation (3a) indicates that there will be no light transmitted under the following two conditions: (1) When sin 2 I5 = 0. his condition is satisfied 1: the plane of polarization coincides with either of the planes containing the 0A or 03 vectors. A dark spot will appear in the material wherever this condition is satisfied and the locus of these points is called an 'iseclinic'. ror solids it has been well established that the inci- dent light rq is resolved into components the principal stress direc- tions and therefore the directions of the principal stresses can be determined from the isoclinics. (2) when sin (“14-6) :: sin (“2+6 ) (4) Ihie condition is satisfied if (“1+6 ) : (fl2+€+2n‘W) (5) where n is an integer. The relationship between t1 and t2 can be written as t1 = t2+ A t (6) and equation (6) reduces to wAt: 2n\ (7) 12 as the necessary condition for extinction. Since I: 2T/w -: l/c (8) lquation (7) can also be written as c A t = n 1 (9) The tom c at is the relative retardation between the component rays as they pass through the body. One of the fundamental theorems in solid photoelasticity is the relationship between the retardation and the principal stresses c At :Kd(sl-Sz) (10) Substitution of equation (10) into equation (9) gives Kd(81-82) :n ?\ (11) therefore when the difference in the principal stresses is such that equation (11) is satisfied extinction of the emergent light ray 'will be accomplished. If the incident light ray is Ionochrematic i.e.the wave—length.is a constant for each integral value of n, a series of black spots will be formed in the image of the specimen wherever equation (ll) is satisfied. The loci of these points are called “fringes". If the incident light ray is white light the stressed areas in the specimen, as viewed through the analyzer. will appear in colors as certain components of the white light are extinp guished. Upon proper calibration the colors can be related to the difference of the principal stresses. Each line of a single color is called an 'isochromat ic' . . i o . “h D a o . . s \ g . . . . v c . . . . , . o . . . \ ’ ‘ s A v . ' ‘ w ~ e ‘ - \ e . . . . — .a 9 13 It is apparent that a doubly refracting material when subjected to a stress will produce both isoclinics and isochronatics. How- ever, the isoclinics can be removed by using circularly polarized light. 14 Strains in the case of a Linear Chain molecule subjected to external load let a tensile force I be applied to a chain molecule parallel to its axis (11;. :5). there will result an elongation of the chain due to both stretch of the valence bonds and the opening of the valence angles. Ehese separate effects as they pertain to a single repeat- ing unit are: n) elongation of the Repeating Unit due to Stretching of valence Bonds: Let the bond length be L and the bond angle be at.‘ as shown in fig. 3. i Let A 1.1 be the elongation in the bond length due to a load 1‘ acting in the direction of the arrow shown in the figure. If we denote the interatomic force constant for the bond under consideration by k1, then A 1.1 -:. [1- cos ell/k1 New the contribution of each A L1 to the elongation along the axis of the chain will be CALQ’ -.: PC0159; JR: . CGSGL In order to facilitate the analysis a little bit let us treat the repeating distance along the chain as consisting of a number of seg- ments in series. each of the segments in turn consisting of a few valence bonds. Then the elongation of the 3th segment will be given by t ‘ 'l (Al-3* : Z; (ALA) : vii-1‘5: C05 9/1 Fig. 3. Definition of valence and axial angles. 16 and finally for the total elongation along the chain axis due to stretching only we have the expression I _. A L , b) Elongation of the Repeating Unit due to Opening of Valence Angles: 'l'he l'ig. 4 represents the geometry of the opening of the valence angles. As is apparent in the figure the opening. of the valence angles may be accomplished by the application of torques to the valence bonds in such a way as to decrease the angles 011. Such torques are supplied by the coqonents of r perpendicular to the particular valence bonds. i'he value of each such component is 1- sin 91. Inst d1 be the "angular" force constant, i.e.. the force per cm required to move a mobile atom in a direction perpendicular to the bond direction. as from A to B in fig. 4. It can be seen from l'ig. 5 thatAB = 1.14591 and dim =d1L1A01. where L1 is the internuclear bond distance. and A91 is the change in the angle 91. In equilibrium the resisting force for the atom in posit ion 3 is (11 1:10 91 - P sin 91 (1 sin 01)/d1 Referring to rigs. 4 and 5 the contribution of each displacement or, L1A91 to elongation along the chain axis will be ( ALQ" 3 LB sin 91 - (r einz 91)/d1 e e e - e - e . u e , . s s e e e e l l e p . e o a Axis Fig. 4. Geometry of opening of valence angles. ‘ h (ALQT \ l 0. I 1 \\x B Fig. 5. Contribution of angular displacement of an atom from A to B to the elongation along the chain axis. 19 Then for the 3th segnont the elongation will be M (“)3 : Z Qua-21> @737 9.11 91 A. t and finally, for the total elongation along the chain axis due to Opening of valence angles we can write the following equation: I. (AL)9 = 7% (AL), c) Total elongation of the repeating unit will be given by summing the elongations due to stretching of the bonds and opening of the valence angles. fhue the expression for the total elongation A L is (AL) (A Us + (“-39 \ $31.6. \ 1 —- w 313%? Cos Sid-2i do 1 20 !he Theory of Infra-red Spectra rho atoms of any molecule, when they are not at the absolute zero temperature, are in a state of constant oscillation about their equilibrium positions; and the auplitudes of these oscillations are of the order of 10"9 to 10'10 cm. their frequencies are high and are of the order of 10*1 3 to 1314 cycles per second. One could expect a direct relationship to exist between the vibrations of the atoms with- in a molecule and their effects on infrared beam incident upon them on account of the reason that these frequencies are of the same order of maglitude as those of infrared radiations. Actually these mole- cular vibrations which are accompanied by a change of dipole moment, so-called “infrared activs'l vibrations, absorb, by resonance, all or part of the incident radiation. provided the frequencies of the latter coincide exactly with those of the intramolecular vibrations. A concept of the dipole moment is given in the following lines. If a neutral molecule or atom is placed in an electric field, the charged particles in the molecule or atom are affected by the field. 'Ihe electrons are attracted to the positive side, and the positive particles are attracted to the negative side of the field. If the chem. centers can be displaced. then a dipole has been induced and th0 atom or molecule is said to have been polarized. In general. the ‘dgwa of polarization is preportional to the strength of the applied $1311 and preportionelity factor is dependent on the structure of the “Qua-1’ ' 21 Some molecules. by virtue of their structure, have a built-in displacement of charge. whereas some other molecules do not have their positive and negative charges displaced unless the molecules are sub- Jocted to an external electric field. 'i'he charge displacement that occurs without an external field is termed a permanent dipole. A molecule containing a permanent dipole is termed a polar molecule. rho product of the displaced charge and the distance of displacement is termed the dipole moment and is a vector quantity. Permanent dipole molecules, when subjected to an electric field. attempt to align them- selves parallel to the field. and the degree of alignment is a func- tion of the field strength and the temperature. Temperature acts to prevent aliglment by producing thermal motion. Permanent dipoles can be additionally polarized by the applied field, but the extent is small compared to the permanent displacement. If a sample of molecules of a single kind is irradiated in succes- sion w a series of monochromatic bands of infrared beam, and the per- centage of light transmitted is plotted as a function of either wave length or frequency. the resulting graph may be interpreted in terms of intremolecular vibrations. At the outset these atomic vibrations seem to be very complicated. but by detailed analysis it is possible to show that these motions happen to be the summations of a number of simple oscillations. Each of these simple vibrations is referred to as a 'fundamental' or I'normal'I mode of vibration. One could prove mathematically that a nonlinear molecule containing 'n' atoms possesses s , . n a r - t . A , b l e . . - e v ' ‘ ' L ‘ - . _ e - - - . , E . ~ e L r . e ' . r l e _ . 9 . . A - . . . . . . . . . e . , . ‘ V v a. . ' | ‘ ‘ ‘ ‘ 1 H ‘ g . ‘ n . l , . . , . e v e I ‘ A . ‘ , A ' l n . . . V . . . 4 v . - o . a . , u - . s ‘ - 22 3n - 6 such normal modes. whereas a linear molecule possesses 3n - 5. Carbon dioxide. 002. is an example of a linear molecule. On the other hand methane EH4 is a non-linear molecule. 002 and formal- detwde can be schematically represented as in rigs. 5(a) and 6(b). A normal mode of vibration is defined as a mode in which the center of gravity of the molecule does not move. and in which all of the atoms move with the same frequency and in phase. Each normal mode can occur without affecting the others. It is possible for all of the vibrations 3n - 6. or 3n - 5. as the case may be, to occur simul- taneously and yet for each one to retain its characteristic frequency. Infrared spectral studies therefore. constitute an analysis of the mechanics of the molecule. In order to get a picture of a normal vibration let us take the case of a mechanical model. A benzene molecule is conventionally represented as in Il'ig. 7. It can be constructed to bring out the mechanical analog by using weights in the ratio of 12 to l for the Carbon and Hydrogen atoms. respectively, these weights held in proper orientation by suitable springs. Suppose further that the carbon- hydrogen springs are now stretched slightly by moving each of the six pairs of weights so that the hydrogens are moved 12 times as far from the equilibrium positions as the carbons and in opposite directions. If . now. the weights are released simultaneously. a vibration will occur in which the weights mve back and forth along the connecting springs or bonds. i'he center of gravity of the whole model remains at rest and the weiglts move only along the line of the connecting Fig. 6 (a) Linear molecule of C02 (carbon dioxide). 0 O Q o H C H formaldehyde ( as in bakelite. for example ) H \C_____u ,,/ Fig. 6 (b) non-linear molecule of H a c c HC/\CH tic/\CH ——> uc\/tu Hc\/cu Conventional Schematic Fig. 7. Benzene molecule ( CG 86 ) 23 springs. since no original impetus was given to the weights in any other direction. This is a characteristic vibration of the model and it does not excite any other vibration in the model. l‘urther, the stretching motion is quite analogous to one of the m - 6, or, 30 normal modes of the benzene molecule. Another benzene vibration can be visualized readily by pulling the six carbon weights slightly above the plane of the model while the lwdrogen weights are pulled twelve times as far below and then releasing all twelve weights sim- ultneously. It is possible to demonstrate several other charac- teristic vibrations of the benzene molecule proceeding on similar lines. Let us imagine. for example. that the mechanical model is given a blow with a hmr. At first sight the weights seem to be per-- forming a complicated motion having no apparent relation to the indi- vidual modes of vibration referred to above. mwever. if this app- arently random motion is photographed with a stroboscOpic camera adjusted successively for each of the frequencies of the normal modes. each of these modes will be found to be faithfully performed by the weights. An infrared spectrometer plays the same role with respect to the actual benzene molecule as the stroboscopo does to the model. me, by measuring the frequencies of the infrared radiation absorbed by a substance the spectrometer determines the characteristic mechalical frequencies of its molecules. Since these molecular frequencies are functions of the atoms themselves. that is, the masses. the spatial arrangement. the valence forces. and to some extent the intermolecular 24 forces. the value of the infrared spectroscopic information is obvious. Apertinent question that comes to one's mind. at this stage. is whether there is any possibility of a mathematical calculation of the normal modes of vibration. Such a calculation. if successfully comleted. should make possible a unique determination of the struc- trure of the molecule in question. Ihe correct structure of the molecule would obviously be that whose calculated frequencies cor- respond exactly to those observed in the experimental spectrum. from a theoretical stand-Ipoint of view the expected frequencies can be calculated. provided the strengths of the individual interatomic forces are known: but. the complexity of such calculations would be aug- mented with increase in the number of atoms and their geometrical arrangement; When there is an increase in the complexity of the structure of a molecule a mathematical calculation might be considered to be almost an impossibility till recently. With the help of the electronic digital computers it might be possible ted” to handle such mathe- matical calculations. fhere aredso other methods that are used when the molecules are quite complex. in order to correlate the charac- teristics of an observed spectrum with the structure of the molecule. considerable success in this direction hassbeen achieved by a purely empirical approach. for the purpose of understanding the basis for such an emirical method. let us resort again to a discussion of mechanical molecular ".’ “ “'2'? . . o s . m l e v a , s , a r . . o . u 0 . . V. l v . ‘I O ’ . . . u s . . . . y a _ o , . s . . a . . e x . . a 0\ . . I . I l . . . .x a . o s . . . . A . . o _ _ X s o ib 25 models. Let the model of the molecules contain only one 0 - 3 bond as in the case of chloroform. 61303 (Fig. 8). If the O - H spring is stretched and released. the carbon and hydrogen weights vibrate rapidly with a characteristic frequency. the chlorine weights. on the other hand. are so heavy they are almost totally unable to follow the vibrations. It is true. at least to a first approximation. that the observed stretching is a characteristic of the c - H spring (or bond) and the masses of these two atoms. and is practically indepen- dent of the rest of the molecules. Similarly. a bending or defor- mation can be studied by displacing the ludrogen weight in a direc- tion normal to the axis of molecular symmetry and then releasing it. Again the carbon and wdrogen weights will move characteristically with the remaining weights practically at re st. Il'rom the above ob- servations we arrive at the idea. that to the extent that atomic forces between a carbon and mdrogen atom are a fumdtion of these two atoms alone. the presence of G - H linkages in a molecule will cameo at least two infrared absorptions which are practically inde- pendent of the atomic constitution of the rest of the molecule. l'he truth of this has been well established experimentally. . 1 study of hundreds of molecules entaining O - H linkages has shown an absorp- tion at a frequency around 2900 cm'd' (0 - H stretching) and another around 1450 cm-1 (0 - H bending). One could find out with the help of a high resolution spectrometer that these 0 - H frequencies are influenced slightly by the relation of the O - H linkage to the mole- cules as a whole. Also the onset frequency value of these absorp- 4-13 '7" A ‘ my I . o . l 7 s . r V o Is . t e V , s. . o I . . L . . u. o - . o . J\\n1‘ c1 Fig. 8. Chloroform cl cl (CISCH). tion bands may be used to indicate the degree of saturation of the carbon atom to which the H is attached or whether the c - 3 occurs in a GB. 032. or CHzgroup. Although the mathematical approach has been of great value when @plied to single or highly symmetrical molecules. most of the infer- nation derived from infrared spectra is obtained by the application of the empirical method. It consists of comparing the spectrum of an unknom molecule with the spectra of several other molecules hav- inga a cannon atomic group. By a process of elimination it is often possible to find an absorption band whose frequency remains cmstant throughout the series. The presence of an absorption band. in an unblown molecule. at this frequency may reasonably form the basis for a guess that the particular atomic group is present. In this type of an empirical Qproach for identification ffom the spectral ' distribution curve. success is guaranteed only with constant application. It must not be assumed from this discussion that it is. or will be. possible to ascribe every observed absorption to a speci- fic group of atoms. Indeed. if this were true it would maloe more difficult the possibility of differentiating clearly between iso- meric compounds. In fact. one could correlate in this manner very few of the observed bands. Host of the observed bands arise from normal modes of vibration which are characteristic ofthe molecule as a whole. However. bheso general absorption bands are highly sensitive to structural changes. and hence furnish us with a "finger l . ,g I ‘ ‘ ‘ ~ I ' v ' . . . A . f A i ‘ 4 ~ ,— /‘s V, ‘ ' A ‘ I I ’ . l A ’ . . ' | . ‘ ’ . . ‘ I I r ’ ‘ r - - - ’ | b ‘ " > I - . l . I a a C . ‘ A , L .. 4 ~ " l r ~ 1 . . . . r I . I ‘ \ ‘ .. b . ' . . . ‘ . . ' r ' I! r ‘ N x ' l . . 0 . ‘ . p , ‘ v‘ . ‘ ‘ ' ’ ' . o . I . ‘ ‘ h 7 \ ‘ . . - I. v ‘1 L a ‘ ‘ o . . ' I . r ' . . r A t V I . » 1 , ’ ’ . I ' ‘ . l ‘ . . . . . ’ _ . . . - . . ' .' F ‘ m . . ~ I. ‘ '. ‘ L 7 ‘t . -‘ , f I I . . . ' 7‘ - ‘ 1 - , ' “ ‘ - . V l ' ' . . \ r ' " ' I“ . ‘ l ‘ . ‘ I . I , \ ' ‘ ' ‘ ‘ . D n- ' I ~ ‘ . . . v - 9 ‘ ‘ \ - ‘ ‘ . > s ' ‘ . no . . m ' ' ‘ (I . - o ' . . v 1- . ’ ‘.' ' ‘ r .‘ r‘ . r . ‘ ‘ . ' ‘ ‘ . . . ‘ V ‘ O . - . I . l ‘ e ' ‘ . ' 7’ ‘ . e V ‘ v - l 4 t ‘ ‘ ' ’ a .. 28 print' of the molecule. Only an account of this it is possible to carry on the analysis of isomeric mixtures and other closely related compounds. It is very important to remember. at this stage. that the normal modes of a molecule do not account for all of the absorp— tion bands observed in its infrared spectrum. tor example. in the far infrared there are absorptions caused by the slower rota- tions of the molecules or the massive lattice vibrations of cryb stale. Further. throughout the whole infrared region absorp- tions frequently occur at integral multiples (overtone bands) of the fundamentals. or at frequencies which are equal to the sum or difference (combination bands) of fundamentals. {these bands in general absorb very much less strongly than do the funda- mentals and consequently must be studied with thicker samples. Since they are so sensitive to the over-all molecular structure. they can sometimes be used more for successfully accurate fingerprint- ing of molecules and for the analysis of mixtures than the funda- mental absorptions. 29 Molecular Structure and Mechanical behavior of a Polymer Polymer is the name given toanumber of monomers bound together chemically. Monomer is the basic unit representing the molecule of a hydrocarbon. The gross chemical equation for the polymerization process is the rather simple one n (oz H4) —-—9 (02 H4),I where n represents the (average) degree of polymerization. The above hydrocarbon is called rolyetlwlene. Similarly the polymeri- sation relation in the case of Polystyrene can be represented as follows: n(OBHB) —-w- (G H) 8 e n fhere is a large diversity in the mechanical properties of high polymers. Different polymers have different atomic arrangements in the molecule and differences in the molecular architecture. law polymers are hard glassy solids; others are rubbery or Jelly-like or fibrous. i'he factors that govern the mechanical properties of these polymers can be listed as follows: 1. chemical composition of the polymer 2. Molecular architecture of the polymer chain 3. Extent of crystallization Chemical composition refers to the monomer that repeats itself to make up the polymer. Polystyrene 81d polyethylene. for example. can be represented as in rigs. 9(a) and 9(b). . (w J ‘u— - . ’ u r | e l \ ' . a . ~ a . . . < C . . ,- . _ . . . . . . m , . . . . e w ‘ ' . . , m A o s . . v . . v‘ , . ' e . A , o r ' ‘ . . . . , ‘ v ' _ ‘ I . ; . . ' . . , Fig. 9 (b) Polyeflylene H 31 further the benzene ring is replaced by the chlorine atom in the case of polyvinyl chloride as shown in 11g. 10. In the case of some of the polymers libs polyesters. polyamides. polysiloxanes etc.. atoms other than carbon are contained in the chain itself; fhe term molecular architecture refers to the molecular weight. molecular configuration. degree of cross-linking and so on. Il'or example polystyrene of molecular weight 50.000 and polystyrene of :melecular weight of 100.000 have different molecular architecture even though they hare the same chemical composition. the third structural feature refers to crystallinity: i.e. the ‘perfect regularity of the chain structure with exact repetition of the monomer units. In high polymers the phenomenon of crystallize» tion is somewhat different from.that observed with.lower molecular weight materials; the dimensions of the crystallites formed are much smaller than the chain length of the macromolecule. fhus. any one chain may thread its way through several.crystallites and several intervening amorphous regions. fhe result is always a.poly crystal- line mass. with the crystallites imbedded.in.an amorphous matrix. The crystallites may be randomly dispersed as in fig. 11(a) or parti- ally oriented as in Fig. 11(b) depending on the past history of the sample. It is also hown that in the case of tissue elasticity. since most animal tissues contain a high proportion of water. the water content also plays an important part in deciding the mechanical behavior. alley-qr“. .rtl. Fig. cl H 10. cl ‘/J\ I H 0—: *w * Polyvinyl chloride. H cl Cl Fig. 11 (a) Figs 11 (b) 33 Thus the difference in the plvsical preperties of the polymers can be attributed to the variations in one or all or even some of the factors mentioned above. It may be worth while here to consi- der the variations obtainable within a single chemical couposition with variation in molecular architecture and crystallinity. The molecular weight and the degree of branching can be independently controlled by the polymerization conditions. The degree of branch- ing in turn detemines the crystallinity; consequently polyethylene can be prepared with wide variations in crystallinity and molecular weight. with corresponding variations in physical properties. It is suggested that the chemical composition. and the tempera- ture either individually or both have a predominant effect on the resulting orientations and hence anisotropy of the molecules under stresses. Different materials under the same conditions of stress could exhibit different polarizabilities on account of their having different bond angles and bond forces. Secondly. in a particular chemical composition the flexibility of the atoms could be either increased or decreased byte introduction of an additional atom to either increase the stiffness or decrease it. hrthermore. these bond forces and bond angles are different between the different atoms of the same molecule. which would result in. under stresses. different orientations. low in order to be able to find out the effect of these orientations on the artificial double refraction of a certain polymer under stress it would be a more thorough investigation if one —---— . ‘ » . . . . . ' a I v I a ‘ s U . . ‘ . , v ‘ , . . ' . . . r . . . » . u. C v . I . A ‘ ' . . . . , . k ' N ' e . ~ . . ~ A. v e - v _ i a . , . . ‘ p , , \ . . , . t . . . e . . . . - . . - 3 . . ‘ - . . ' ' \ . ,— . . . . ' . , s I . s v v . u . , ‘ K . . , o s 7 . . ' i . . . ‘ _ - _ . . - g . ‘ O V O ' - s . ' . ' ' L ‘ ‘ v . ‘ w . C ' a n A . . - . . e ‘ ‘ ‘ . . A . A" u e I - . - , , , 34 could find out to what extent each atomic group has been deformed under the particular stress than speaking of the orientation of the molecule as such. the changes in the individual atomic groups could be studied by taking an infrared absorption spectrum of the particular polymer under stress. So one could hope to get a clear picture ofihe changes in the constituent atomic pairs which could later be related to the stress birefringence. 35 Description of the Photoelastic apparatus the apparatus for the Photoelastic Experiments consists essen- tially of the projection system. the Optical alignment guides. pola— rizer and analyzer combination. the straining frame and accessories. the projection system: It consists of a double convex lens of about 3.5 ft focal length mounted on a stand “ so as to enable the operator to adjust it on the guides at will. the lens projects the image on to a drawing board fixed to a wall. this would facilitate the visual observation as well as the plotting of isoclinics on a sheet of paper attached to the drawing board. the Optical Alignment guides and Accessories: A schematic diagrmn of the Optical parts in the photoelastic work is given in Fig. 11. the alignment guides are apair of mild steel rods 2;- ft long and 3/4” die. they are set parallel on awooden platform at a distance of 7.6”. At one end of the guides there is a dual lightsmource enabling the operator to choose white light or .mercury light at will. to protect the lamps from getting excessi- vely hot a fan is also provided close by. the polarizer and analy- zer are built in a cast iron fr-q in a crossed position. A condens- ing lens is also built into the same frame. A pair of quarter wave plates could be inserted between the polarizer and analyzer combination at will and they are held in position with the aid of flexible metal strips provided on the casting itself. mesa :eflooonoam moahaoc< coda o>cm savanna :oawooam umoh common 4 .3 .3... oao~a o>es savanna mommacuom neocodccu ounces waved < a a no a o [a a '7 38 I the Straining frame: the straining frame consists of a pair of alluminum annular rings set parallel with a separation of 3/4 inch and fixed to a steel tubing between the guides. A pair of bent alluminum plates are held in position on either side of the circular frame with the help of small pins. An alluminum frame whose shape is shown in fig. 13 could be inserted into the space between the circular rings and held in position with he help of slotted rod and pin. A long rectangular (23" x l' x 1") aluminum beam passes through a metal tubing held rigidly in position between the guides on to the plat- form by means of end flanges. One end of this been carries a hanger and is held by means of a screw support on the other end. At about half its length the beam is supported on a pin inside the metal tubing. the screw support referred to above could be used to set the beam horizontal initially. us 7: 40 Determination of Stress-Optic coefficient Iolystyrene A polystyrene boam 5 (5/8)" x (5/8)" x i" is cut out of a i" thick large polystyrene sheet. It on then.held in position roi- producing pure bending in the center portion as shown in fig. 14. A load of 9“' was added to the hangerand the appearance of a fringe on the screen.“ noted. We notice here that a load of as much as 90 17' was necessary to produce even one fringe on the screen on account of the fact that polystyrene is a poor photoelastic material. the monochromatic light used for obtaining the isochro- matic was mercury green 5461 A. the stress-optic coefficienti is calculated from the formula czt.fl .{u I where n is the fringe order. t is the thickness of the specimen. and Ifll is the stress on the boundary in which y is half the thichess of the beam. the stress-optic coefficient for polystyrene obtained in this experiment is 422 lbs. /in.2/fringe/ in. C B - 39 A CIR - 89 (Columbia Resin 39) been of the same dimensions as in the previous experiment he cut out of a large P thick sheet. the experiment was repeated in this case also for the purpose of finding the stress-Optic coefficient of 0 R - 39. A 60 1} load was found to —. 41 produce as many as 4 fringes. the value for 0 B - 39 obtained in 2 this experiment is 86.5 lbs./in. [fringe/in. the calculations are shown below: test specimen ........ Dolystyrene 5(5/8") x (ale-o x in 5461 A ’ ‘ 9°} 0:53K5ll6) t'x (5/8)’ x (1/12) (Lead for one fringe was 90 it) test Specimen . ....... Load Bonding moment ' w fringes per %" Stress-aptie coefficient 0 (t/an).(ny/I) 422 lbs/ ing] f rings] in. c a - 39 5(5/8') x (5/8“) x in so if ' so x (3/4) lb. ins. 4 c (t/zn).(My/I) l x (1/8) x so x (3/4) 1(5/16) x 12 x ' 1% x (5/8)8 35.5 lbs/inglfringe/in. ‘ 42 the Straining Unit for Loading the films A special type of straining unit has been designed and construc- ted in order to facilitate the loading of very thin films of about five thousandths inch thickness. A sketch of the unit is shown in 11.3. 1?. It consists of a steel base 3 6" x 1" x 1" and carries a vertical steel post Y 6" long and 1" square section on one end of the base. A clamping screw 0 from the side of the base ensures firm positioning of the vertical post. A rectangular strip of steel 1’. 6" x 4}" x 1/8'. is fixed on to the top of the vertical post by means of a screw 01. A thumb screw S passes through a hole in the hori- zontal steel plate at a distance of 1" from the center line of the vertical pillar. the bottom of the thumb screw rests on a flat bar 3 projecting from the vertical post and held in position by means of adamping screw 04 as shown in fig. 1‘. A long steel bolt D1 passes through a hole near the free end of the horizontal plats and is clamped on to it at any desired position of its length by means of clamping nuts 02 and 03. the steel bolt carries at one of its ends a: inverted U shown in the figure. A pair of steel flats AA 1'I x i- x 1/3". intended to: the purpose of gripping the test film. are held in the inside of the U by means of a l/8'I steel pin passing through the sides. Another vertical bolt L2 rising from the base carries a similar U at its top. A similar pair of steel grips as mentioned above are held in the inside of the U by means of a steel pin passing through the sides. (—5- k a II. _ _ _ u _\t_ _ m _ ._._ .— .II' I .|.._.\\1_| l (1 III _ _ Pi: _ [— .1.\\_ N4 \ < Illvl .m.mlu a _ _ c _ u a. > a $111111 . m . o W m a. aw“ _\i \L . h _ \, FIIH «U m can: mcncanncm one .ca .eru 44 seen grip has a set of three holes 1/8" diameter drilled sym- metrically in it; the center hole is intended to take in the steel pin passing through the sides of the U. and the two outer holes to take in small brass screws and nuts for clamping the test film tightly in between the grips. the load measuring device includes four ER - 4 strain gages mounted on the horizontal steel plate. they are connected to a strain indicator which is later calibrated. the four gages are intended not only to augment the output but also provide the noose- sary temperature compensation. the straining unit was designed to be used with a maximum load of 5 lbs. Calibration of the Straining Unit An SB - 4 strain indicator was connected to the strain gages. the upper portion of the gripping unit was set in position along with small steel grips AA held inside the U by means of the steel pin. the strain indicator is adjusted to zero (i.e. null deflec- tion in the galvanometer after choosing the proper scale and gage factor). In the present experiment the gage factor of the gages was 1.97. A load of 4% lb was added to the upper gripping device and the deflection in the strain indicator was noted. the bridge was balanced for null deflection and another élb load was added agadm.’ this experiment was done up to a 4 lb load and each time _ m. Alt-'3 "3‘5 34-4"?- . . . . ; , , , . _ e . , o c . . . e V e A . . o r v . . .. a s - l w o a . . K . ' I . e a L . - a 45 the strain indicator reading is noted. It was observed that a lead of % lb produced an output of 30 micro-inches per inch on the strain indicator. While working with the straining unit every care was taken to see that the strain gages are protected safely. the strain indicator was calibrated for different leads and the readings are shown in table I. A graph ias drawn showing the re- lation between the load and the strain indicator output. table 1. Strain Indicator Calibration Reading of the indicator Strain indicator output for 5 lb Iead leading unloading 0 1320 1:520 4; n 1290 1290 1 lb 1250 1260 1% I 12:50 1230 2 I 1200 1200 2% I 1170 1170 3 I 1140 1140 3% I 1110 1110 4 I 1080 1080 30 micro—inches per inch 0 m m m m menu mom monocuoaowa ca «omens aoaeoaucn Load in pounds 46 treparation of the film the preparation of the test film for taking the infrared absorp- tion spectra seemed to be the most difficult part of the experiment. It has to be very thin. of the order of about 2 to 3 thousandths inch thick. there are two methods of obtaining such a thin film for infra- red work. One is to dissolve the given polymer in a suitable sol- vent and pour it in thin layers on a flat glass piece and let the polymer dry up. But this method of preparation has the draw back that the heat of polymer (as some heat is required to melt the pla- stic) during the process of cooling could affect the polymerization besides inducing thermal stresses. Of course the latter can be removed by annealing but the changes in polymerisation are to be guarded against. the second method of obtaining the polymer film is to tales a piece of the given plastic from a thick sheet fI thick and attempt to thin it down to the required extent. this is not so easy as it is mentioned here; and it also makes one think if it is not a rather an odd procedure. It is well known to the photo- elasticians in the engineering field that a in thickness 1e good size for photoelastic work. In the presentQinvestigation as it is desired to correlate the photoelastic effect with the infrared absorptions it is but obvious that one chooses a *- thick piece for photoelastic studies. rnrther. to make onto that the directional properties of the plastic do not have any effect in the experi- 47 mentation one has to use a similar piece cut in the same direction from the original thick plastic sheet for the purpose of machining: and it is a successful machining that could ensure a satisfactory infra- red resolution spectrum. A piece of the plastic sI x 1I x iI was cut from the large iI thick sheet in the same direction as the pieces for photoelasticwork were cut. this piece was then fixed on the bed of the milling ma- chine with the help of scotch tape. In using this scotch tape for fixing the specimen on the bed of the milling machine the following procedure was adapted. the adhesive side of the tape is first attached to the plastic piece and then the top layer of the non- adhesive side of the tape is carefully peeled off so that one could get another adhesive side of the tape. the bed of the machine is carefully cleaned with a piece of clean cotton cloth and then the plastic was set on it flat. the adhesive side of the tape would stick to the bed ad would facilitate the firm fixing of the speci- men. In the case of polystyrene a 5/16“ double flute end mill driven at 2450 rpm tas used and the machining job was done using the automatic drive. In the case of Columbia Resin which is a rather brittle material it was found that specially ground 1" fly cutter could yield better results. the speed was the same as before. No coolant was found to be necessary in either case but an occasional cleaning up of the surface being machined with a small paint brush 48 using a. little oil would ensure a better machined surface. It was found that it is not a good practice to start large cuts from the begining, as it would result in excessive heat in the pla- stic and would melt besides sticking to the cutting edge. The following scheme was used in the process of machining. A twenty thousandths inch thick lmr was removed each time for five times: then a 10 thousandths layer was removed for another 10 tins; lastly a layer of 2 thousandths thick was removed each time till the desired thickness of‘lhe film was obtained. Extreme care was taken in re- moving the film from the bed of the machine. A blunt razor blade carefully advanced longitudinally underneath the surface of the film was found to be satisfactory for the particular Job. i'he specimen was then fixed on a narrow portion on all the four sides on apiece of flat of cold rolled steel using scotch tqe. The surface was then polished with what is commercially known as plexi glass polish. Ihe polishing business seemed to be a special technique in itself which should be mastered with constant practice. On the whole the preparation of the film for the infrared spectral studies seemed to be a machinist's cum artist's Job. It is only with a constant practice on this Job that a reasonably satisfactory film could be produced. 49 Description of the Infrared Spectrophotometer A brief description of the rerkin-Illmr Infrared Spectrophoto- meter used in the present investigation is given below. fhe basic instrument consists of a single unit, 40" long, 20" wide and 23" high. A separate external amplifier is also provided. The main instrument consists of two separate mountings with a 6" clearance in between intended for accomodating the samlos and refe- rences. The source and source focussing mirrors are under the right hand cover and the photometer unit, monochronator md detector are provided on he left hand side. rho recording drum and the wave- length drive are mounted on top of the monochmmator cover. the main control knobs are provided on the cover on the right hand side with additional controls on the front side of the base or chasis. Ihe counters reading wavelength and slit width directly in microns are visible through windows in the cover on the left side. An opaque shutter for each beam is pivoted on the side of the small cover on the right. he aptical system of the Infrared Spectrophotometer is shown in fig. 1‘. Two beams of light from the same source so are brought to two separate foci by two pairs of mirrors, K1 3: H3. and 1428: M4, one beam 8. passing through the sample 0, and the other 3, through a reference 1. rho” two beams are then combined by a rotating sector mirror. M7. that transmits one beam and reflects the other into the 50 same direction as the transmitted beam. The composite beam passes through a monochromator to a detector. If the two beams are equal in intensity no output is observed from the detector. If the beams have unequal intensities a pulsating voltage appears pro- portional to the difference in intensity. fhis off balance vol- tage after necessary amlification is used through an intermediate pgwer stage to actuate a pen servo motor. Actually when the two beams are balanced, the detector sees no change in the radiation incident upon it. the moment an unbalance occurs between the sample beam and reference beam, a 13 cycle alternating voltage is developed which is amplified by the preamplifier. The first-stage transformer in the preamplifier steps up the voltage approximately 300 times and from thence the signal is amlified until a high enough voltage is attained so that the signal can be separated from its 13 cycle car- rier. At this stage. the phase and amplitude of the signal are determined and this signal is filtered and fed into the 60 cycle modu- lator and power stage. the signal form which actuates the pen servo motor. m Iornst (5th source In the Perkin—llmer instrument a Hornet glower is used as the source .80, of infrared radiation. It is mounted on an easily re- movable base between two ceramic posts that are wound with platinum wire for preheating and starting. the two pairs of concave mirrors. “1 and it . M and H . form two identical images. I and 12. of the 3 2 4 1 w..— W,‘ Is 52 source. each magnified to twice its original size. The first two M1 and 112 are placed close together to permit taking light from the same part of the source for the reference and sample beams. They also help to make the instrument more compact and increase the amount of free space available for samples. fwo solid shutters on the outside ofte source housing permit closing off either or both beams independently. Hornet glower has several important proper- ties, like long life. high operating temperature. good black body characteristics. etc.. which make it useful as a source of infrared radiation. The rhotometer Section The images formed by the first two pairs of concave mirrors are inside the main spectrometer cover. At the image I in the re- 2. ference beam. there is a moving multiple wedge type of diaphragmnl. that rolls in and out of the optical path to change the amount of light transmitted. A separate control provided in front of the base of the instrument would enable this. wedge to be moved so as to enable the operator to adjust the percentage of light transmitted thus con- trolling the position of the pen on the drum. After passing through the two apertm'es the two divergent beams are reflected by plane 5 M7. The sample beam is reflected from the sector mirror and the re- mirrors, )1 , H6. and 14 . to opposite sides of a rotating sector mirror 8 ference beam transmitted by it. fhe concave mirror H9 is calculated 53 to be free from astigmatism at 8° off axis and 1:1 magnification in order to avoid blurring of the image. A flat mirror N10, throws the image of 11 and 12 on the entrance slit 8 of the monochromator. l The two field lenses L1 and L2 are made of potassium bromide. They throw images of M3 and 314 on H9 and also serve as windows in the monochromator cover. Pr. (Fig. 1‘) is a rock: salt prism mounted on removable table. This prism nrves asme monochromator. The small mirror. I13. behind the prism compensates the- wavelength scale for change of refractive index due to temperature variation. The collimator, “11' is a concave mirror 80 mm in diameter. 27 cm in focal length. parabolized 18° off axis. It is corrected to about a quarter wavelength of sodium light. giving a visual resolving power of better than 6A at the D lines with two traversals ofm light flint prism. Its mounting has screw adjustments for focus and for the horizontal and vertical angle adjustment. The Bocorder The Recorder in the Perkin-Elmer spectrohotometer is designed to have the following properties: 1. Coupling of the scanning system and recorder such that the recor- der is unaffected by changes in scanning speed, 2. High reproducibility of recording. 3. Standard size sheet charts to simplify filing procedures. 4. Allowance for wide range of scanning speeds. 54 5. Allowance for adjusting the abscissa to spread out spectra. 6. Compact construction. The recording drum turns upward in front so that a good length of spectrum is clearly visible to the operator immdiately after it is recorded. The recording chart is held on the drum by two pairs of spring-loaded clips which clamp the ends of the paper in position. The zero transmission point recorded by the pen may be aijusted to coincide with the zero on the recorder paper by unclamping the pen from its drive cable and moving it. On the left of the recorder are located the scanning motor, scanning pulley system, and the scale change gears. The motor speed is controlled by a knob on the main control panel. Large reductions in scanning spped can be accomp- lished by changing (l) the pulley belts (2) the change gear and (3) by varying the PEN SPEED control. A separate wheel provided at the lift side of the recorder called as the ”inching wheel ' permits the operator to move the scanning system a small amount without dri- ving the system electrically. The observations and results for Polystyrene and Columbia Resin at zero,2 #’and 4 a} load are shown below in tables 2 to 5. The tables are computed using the infrared absorption graphs at the above mentioned loads. These graphs are obtained with a Terkin-Elmer Infrared Spectr0photometer. ”W L 55 Results: Table 2 Material . . . . . . . . . . Polystyrene Phase .......... Solid Sample size 2(5/15)- x (3/4)- x 0.003u Reference . . . . . . . . " " x 0.005“ frequency Vibrating group in percentage absorbanoe per 0.003" microns thickness zero psi. 333 psi. 666 psi. 0 - H aromatic 3.35 29 28.5 28 0 - E aliphatic 3.5 31 29 29 0 - H wagging 6.85 40 39 39 0 — H aromatic out of plane vibrati one 13. 5 13 . 5 13. 5 13. 5 ”v raw—- 56 Polystyrene (contd.) Sample . . ... ... 0.008I thick Reference ........ 0.005“ " Table 3 frequency Vibrating group in percentage abso rbence per 0.001“ microns thickness seleopsi. 333 psi. 666 psi. 0 - H aromatic 3.35 24.4 23.9 23.5 0 - E aliphatic 3.5 m 24.4 24.4 c " 3 “Sins 6.85 33.6 32.8 32.8 C - H aromatic out of plane vibrations 13 . 5 ll . 3 ll . 3 10. 5 0.0 "' Polystyrene Absorbance 0'7‘ Legend: 0-8- Solid line ——————— zero load. Dashed line ------ 2 3 1.00 Dotted line ...... 4 # Wavelength in Microns ———~——> OJ 0 9 ' 3 f ‘ 1 = : t , .J (1 7 g 9 10 I]. If) 1 Material ........ 58 Table 4 rm. eeeeeeee 80116» cal-“big BO.“ 0 B " 39. Sample 1(5/e)- x (3/4” x 0.007. Reference .... " " x 0.005” frequency Vibrating group in percentage absorbanoe per 0.002" microns thickness mere psi. 380 psi. 760 psi. 0 H 2.86 35 35 3'7 0 - B aromatic 3.35 2'7 26 26 0 - H aliphatic 3.65 30 30 30.2 c =' 0 5.55 43 42 4e 0 - 0 5.9 35 39 38 0 = 0 6.2 45.5 45.5 48 O - C aromatic 6.4 45.5 45.5 48 g - g wagging 6.8 to 12.0 vat-lulu fromlO te4o 0 - 2 out of plane iibrations 12.45 27.5 30 28.5 Benzene out of plus vibrations 13.2 30 32 31.5 59 Table 5 G R - 39 (contd.) Sample . . . . . . . 0.007“ thick Reference ..... 0.005“ " frequency Vibrating group in percentage absorbanoe per 0.001“ microns thickness zero psi. 380 psi. 760 psi. 9 H 2.86 31.5 31.5 35 O - H aromatic 3.35 24.3 23.4 23.4 c - E aliphatic 3.65 27 27 27.18 0 a 0 5.55 38.7 37.8 37.8 0 «- O 5.9 31.5 35.1 34.2 G 3 0 6.2 40.9 40.9 43.2 0 -'- 0 aromatic 6.4 40.9 40.9 43.2 0 - n wagging 6.8 to 12.0 variable from 9 B 30.. c - 0 " c - H out of plane vibrations 12.45 24.8 27 $.6 Benzene out of plane vibrations 13.2 27 28.8 28.4 O .0. it ' bmmbancc 4'4 ,_ ___...— . -<'*..--- . Ce lumhia Resin (CR ., 39) .V " .(V I r i" I. g)” ‘1’ / / ’ ; . ' / / f w ' 4’ « . i - e f ’ / . ./ ,/ ‘ l X . ,. w ‘ ~ .‘ a \ i l . r / .‘1 ..‘f . / J ' ’2‘ 1 r: / .u \ Legend: bolvid line zero lead Dashed line ~ ~-~-— Z: 7,: IUcld {1‘ # H Dotted line. . , . . . " fiavelemgth in Microns —————.——————~p- .5. . - - ; I I | = l ' 3 4 'v‘ (I 7 a 9 w 1: l2 61 Discussion of results rolystyreme is a thermoplastic. Its chemical formula is (0833):? fig. 15 shows a representative portion of a polystyrene chain. It consists of linear chain molecules with 032 - Oh in the chain length and the bonus ring at right angles to the length of chain. In the int literature it has been established that there are characteristic high absorptions for infrared beam for some of the vibrating maps. Thus. for example, 0 - H aromatic has been mtudied and it alqu seemed to have a high absorption peak due to stretching at 3.3 microns. which is called an I'infrared active" vibration resulting in a change of dipole moment. Hg. 18 shows a representative portion of a c n - 39 molecule. It consists of a bonzene ring with symmetrically placed parallel chains of G - 0 - 082 - 0 m 032. Its chemical name is dialyll pthallate. and is a thermosotting resin. Resin is the name given to‘a polymer either thermoplastic or thermoset. A thermoplastic melts on heating but a thermoset starts melting first but on contin- ued heating it sets itself and. becomes rigid with an additional chau- racteristic of forming innumerable numer of cross-links. There are some comon groups. however, between polystyrene and 03 - 39. namely, 0 - H aromatic. G - H aliphatic, c - Hwagging. and G - H in the benzene ring. The additional vibrating groups in 0 B. - 39 are 0 = 0, 0 - 0, 0 '-'- 0, O - C. The tabular statements given on pages 58 and H c \. \ c c c —— 0 cu H CH on C on on n on cs cu cu , on c CH fl Fig. 16. Representative portion of polystyrene chain. CH 0 cu ///////'\\\\\\\\ea c ,0 c "2—-~c““" on H ' 2 CH \/CH C 0 32 C -—-— CH2 Cl 0 H Fig. 17. Molecular structure of C R - 39. (Dialyll Phthaliate) 62 59 show numerically the differences in percentage absorptions of the infrared beam. 0 - H aromatic in polystyrene contributes an amount of 0.5 per cent towards the chmge in absorption at 333 psi. and 0.9 percent towards the change in absorption at 666 psi. 9n the other hand C - H aromatic in 0 B - $9 contributes an amount of 1.1 per cent townds the change in absorption at 380 psi and also at 760 psi. Considering next C - H aliphatic vibrating group it contributes 1.6 per cent to the change in absorption in polystyrene and a saximum change of 0.18 per cent at 760 psi in C R - 39. This might mean that the vibrating group C - H aliphatic undergoes greater change in dipole mommt in polystyrene with consequent increase in the absorp- tion of incident beam. However. the changes in C - E aromatic 0.9 and 1.1 in polystyrene and C R - 39 ,respoctively'do not differ much thus leading to surmise that they do not undergo appreciable varia- tion with stress. In other words me change in the intro-molecular activity with stress in polystyrene aid 0 R - 39 due to the C - H aromatic group is negligible; also the change in the intro-molecular activity due to 0 - H aliphatic in polystyrene which is 1.6 per cent in terms of absorption might mean that any phenomenon associated with stress in polystyrene could be pro due to the presence of a C - H aliphatic group. Turning now to the 0 - H wagging in polystyrene we notice that there is a chnge in absorption of only 0.8 per cent at both 333psi and 666 psi in polystyrene, whereas there is a change in absorption of9 to 36per cent intho case ofCR- 39. This changeobviously 63 is quite a bit and it seens that there is huge intra-vmolecular activity due to O - H wagging in Columbia Rosin resulting in a large absorption of the incident infrared been with increase in stress. Lastly we have the out of plane deformations of the benzene ring at about 13.5 microns. 'l'he change in percentage absorption in the case ef polystyrene is zero at 333 psi and 0.8 at 666 psi. he changes in C 3 - 39 aree1.8 at 380 psi and 1.4 at 760 psi. Actually there is a:; greater absorption oi the incident bean in the case of 0 l - 39 than in the case of polystyrene. Besides there are other groups liloe C = 0, 0 - 0, = C, C - C in C B - 39. !he tabular statement On page 59 shows that the changes in the intensities of the incident infrared bean are not much in celparison with those of C - H waging in C n - 39. Actually there is a decrease in absorption of 0.9 at both 380 psi and 760 psi for C I 0 and In increase in absorption of 3.6 at 380 psi and 2.? at 750psi forthe vibratinggroup 0-0. me groups 08 C andC- C practically contribute the same change in absorption with lead, i.e. about 2.3 per cent increase in absorption 760 psi. 64 Conclusion Il'rom the previous discussion we conclude that the C - H are-- matic does not contribute appreciably towards the change in absorp- tion in polystyrene and CB - 39; and there is also a fairly greater absorption in polystyrene due to C - H aliphatic group than in 03 «- 39 thus leading to a surmise that stress birefringence in polysty- rene might be due to the presence of a vibrating group like 0 - H aliphatic. However, the change in the percent absorption due to C - H wagging in the case of CB - 39 is remarkably high compared with that due to the same group in polystyrene. faking now a look at l'ig. 16 showing the structure of polystyrene and also l'ig. 17 showing that of CR - 39 it seems probable that the CE aliphatic group influences the behavior of polystyrene under stress; and also the fact that the absorption of the CH aliphatic is very little (1.6 per cent) could be due to the presence of a heavy benzene ring. Presumably, if the C - H bond is ttretched and released, the carbon and hydrogen seems vibrate rapidly with a characteristic frequency and the amplitude is influenced by the presence of a heavy benzene ring close to it. But on account of the lack of such a heavy ring near the CH group in C3 - 39 a greater amplitude of vibration could be possible which is revealed in the C - H wagging resulting in a greater dipole moment change and thus giving rise to relatively large absorptions of incident infrared beam for CH wagging. 65 Also the presence of the additional groups like 0 - 0. C - C contribute slightly towards the absorptions with stress in CR - 39. This could be possibly due to the fact that these groups are rela- tively smaller compared with the benzene ring and hence could follow the vibration much better. 'i‘he discussion given in the previous pages with the concluding remarks above based on the marked difference in'me infrared spectrum of CB - 39 for different loads from the spectrum of polystyrene leads one to the surmise that the high photoelastic behavior of CR - 39 compared with polystyrene could be due to 1) lack of the presence of heavy groups like benzene rather too close to other relatively small groups like CH, and 2) the presence of additional groupslikae0=0, 030, 0-0, C—C. 10. 66 Bibliography D. Brewster, Trans. Boy. Soc. (London), 1816, p.156. J. Clerk Harwell. Sci. Papers, vol. 1, p. 30. C. Wilson. Phil. Mag.. vol. 32. p. 481, 1891. A. Mesnager, Ann. ponts et chaussees, 4° Trimestre, p. 129, 1901, and 9" Series, vol. 16, p. 135. 1913. The numerous publications of rrof. Coker are compiled in his papers: Gen. Elec. Rev; vol. 23. p. 870, 1920, and J. Franklin Inst., vol. 199, p. 289. 1925; also the book "Photoelasticity' by E. G. Coker and L. N. G. Filon, (Cambridge University Press. 1931). W. Kuhn and F. Grun, Kolloid - Z. 101. 348 (1942). L. R. 0. Treloar, Trans. Faraday Soc. 4'3. 277 (1947). J. 1'. mdd, Journal of Applied Physics, vol. 29. No. 10, Oct. 1958. I. 1‘. Gurnee, Journal of Applied physics. vol. 25. Ho. 10. 1232 - 1240, Oct. 1954. 3. D. Andrews, Journal of applied Physics. vol. 29. No. 10, 1421 - 1428, Oct. 1956. 67 Acknowledgements The author takes this Opportunity to express his sincere appreciation to Dr. Charles 0. Harris. Professor and mad of the Department of Applied Mechanics. for his keen interest and gui- dance during this investigation. Dr. Earris's continued encouragement and advice were invaluable. The author wishes to acknowledge with gratitude the financial assistance given by Mr. Hoffman of the lngineering Experiment Star- P, 3. K. Bvenaert. tion and also the help received from the Faculty members Prof. T. Triffett, Prof. W. Bradley. Prof. C. A. Tatro, and Prof. H. Larcher. The author is highly thankful to the authorities of the High- ways department and also to Messr. E. l‘inney, M. H. Jansen, and R. Cook, for the help received during the use of the Infrared Spectrophotometer. Il'inally, the author wishes to thank most sincerely his wife Mrs. T. Satyavati whose patience and understanding made possible the completion of this work. r Weir. r -1‘m%x.war.z 1. ,4 A..-“ {ESE {ii-ELY “a“!!! h L-.- .-~- .‘ ._¥A-_ . ll muummm' 175 8026 31293 03 H H H H " Tlllll N“ A” u ”