Effect of ph on the Strength and Fatigue of Fused Silica Optical Fiber. A. T. Taylor and M. J. Matthewson

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1 Effect of ph on the Strength nd Ftigue of Fused Silic Opticl Fiber A. T. Tylor nd M. J. Mtthewson

2 EFFECT OF ph ON THE STRENGTH AND FATIGUE OF FUSED SILICA OPTICAL FIBER Andrew T. Tylor, M. John Mtthewson Rutgers University, Dept. of Cermic nd Mterils Eng., Pisctwy, New Jersey ABSTRACT The ftigue behvior of both bre nd polymer coted silic opticl fiber hs been determined in vrious buffered ph solutions. Bre nd polymer coted fibers were studied to distinguish ny coting effects. Numericl integrtion techniques were utilized to fit the dt to three kinetics models, nd the ftigue prmeters were clculted together with their corresponding confidence ellipses. The pprent rection order for the rection between the OH ion nd SiO between ph 4 nd ph 10 ws determined to be 0.3 nd this vlue is independent of the kinetics model used to fit to the dt. The reltionship between ftigue nd ph is nonliner; indicting different mechnisms t high, low, nd intermedite ph. INTRODUCTION The current industry ccepted model for strength nd relibility clcultions is combintion of n empiriclly derived rte lw for crck extension: 1, dc n c v AK dt I, (1) nd the well-known Griffith eqution: K Y c σ I, () where v is the slow crck growth velocity, A is constnt depending on the environment, σ is the pplied stress, K I is the stress intensity fctor, nd n is the stress corrosion susceptibility prmeter, which is often treted s constnt. Eq. 1 is mthemticlly simple to mnipulte nd ws useful in providing the initil bsis for the theory of subcriticl crck growth but hs outlived its usefulness nd now represents n obstcle to further progress. 3 Ko 4 determined tht A followed n Arrhenius temperture dependence nd tht the ctivtion energy depended on the pplied stress. For convenience, the power lw, designted model 1 here, my be rewritten s: 5 dc Model 1: A K n1 I 1, (3) dt K IC where K IC is the criticl stress intensity fctor. If, s is commonly ssumed, n 1 is mteril constnt, then ll the environmentl dependence of ftigue must be in A 1. Under these conditions A 1 is expected to depend on both n Arrhenius term nd the concentrtion of the chemicl species cusing the crck growth. While this species is normlly ssumed to be wter, here we will exmine only the dependence on the hydroxyl ion concentrtion. It is well known tht silic is weker nd ftigues fster in high ph. 4,6,7 We cn rewrite A 1 s: A x Q 1 ν [ OH ] exp (4) RT where ν is frequency fctor, x is the pprent rection order, Q is the ctivtion energy, nd R nd T hve their usul menings. One cn predict the time to filure, t f, under constnt pplied stress, σ, by combining Eqs. nd 3 nd integrting: t f K IC σ σ Y A ( n ) σ 1 1 i n 1, (5) 874 Interntionl Wire & Cble Symposium Proceedings 1998

3 where σ i is the inert strength. In this model, the ctivtion energy is stress independent. Eq. 5 my be rewritten in simplified form: n 1 σ t fσ B1, (6) σ i where the so-clled B prmeter is: K IC B1 Y A ( n ). (7) 1 1 B 1 is considered constnt for ny mteril nd environment. In this form evlution of K IC nd Y is voided. One problem with this simplifiction is tht the vlue of B 1 is highly sensitive to the vlue ssumed for the inert strength. Other crck growth velocity models bsed on chemicl kinetics hve been proposed nd re designted model : 8 dc K I Model : A exp n, (8) dt K IC nd model 3: 9 Model 3: dc dt A K I exp n. (9) K IC 3 3 These three models hve been compred by Jkus, et l. 5 nd Bubel nd Mtthewson. 10 In model 1 bove, the ctivtion energy is independent of the pplied stress, despite experimentl evidence to the contrry. 4,11 In model, the stress ffects the ctivtion energy of the chemicl rection vi n ctivtion volume nd is liner with stress intensity. 8 In model 3, the ctivtion energy of the chemicl rection is by the strin energy density t the crck tip s chemicl potentil nd is qudrtic with stress intensity. 9 Predicted lifetimes re highly sensitive to the form of the stress dependence of the kinetics nd model 1 yields the most optimistic lifetime predictions. 5,1 Models nd 3 cnnot be explicitly integrted for dynmic ftigue nd therefore numericl techniques re necessry. Similr to model 1, the B-prmeters cn be defined for models nd 3 s: B K IC Y A ( n ), (10) K IC B3 Y A3( n3). (11) In generl, ftigue dt pper to give the best fit to model 1. 1,13 However, in ll three models the stress dependence is determined by the n i (i 1,, 3) while the environmentl dependence is contined within the A i. An lterntive mens of testing the ppropriteness of the kinetics model is to determine the trends in the ftigue prmeters with chnging environmentl conditions, such s humidity, 14,15 or ph. In this reserch, we hve determined the ftigue behvior of both bre nd polymer coted silic opticl fiber in vrious buffered ph solutions. For purposes of describing the dt it ws ssumed tht ftigue of silic involves the chemicl rection with OH ions only, s described by Eq. 4. Therefore, the slope of log A i vs. ph plot gives the pprent rection order x with respect to OH ions. EXPERIMENTAL PROCEDURE Dynmic ftigue experiments were performed using two-point bending technique on bre nd coted fused silic opticl fiber in temperture controlled 5±0. C stndrd ph buffer solutions (Fisher Scientific, Fir Lwn, NJ) in the rnge ph 1 to 1 from Fisher Scientific. In two-point bending, 16,17 the fiber is held between two fcepltes which re brought together t controlled rte by computer-controlled stepper motor until the fiber breks, s shown in figure 1. When the fiber breks the event is detected cousticlly by trnsducer. The filure strin, ε f, is clculted from the seprtion distnce t filure, D, s: d f ε f, (1) D d + d c g Interntionl Wire & Cble Symposium Proceedings

4 where d f is the fiber dimeter, d c is the dimeter of the fiber with coting, nd d g is the depth of the groove. d g Coted Fiber d f fiber d d c trnsducer fce pltes Bre Fiber fiber clmp pltes Figure 1. Two-point bending pprtus for bre nd coted opticl fiber. Bre fiber specimens were prepred by stripping the polymer coting by immersing in hot sulfuric cid (~ 00 C) for bout 30 s followed by rinsing with wter nd then cetone. This stripping method does not degrde the strength of the fiber. 18 After stripping, the bre fiber ws immersed in the ph environment for 30 s before breking. Coted fiber ws soked for t lest two weeks before breking to fully equilibrte with the test environment. A preliminry investigtion of the diffusion of ionic species through the polymer coted specimens ws done to substntite the forementioned soking time by monitoring strength s function of time fter immersion in the test environment. The dynmic ftigue dt for bre fiber ws for 1 specimens per rte, t four loding rtes spnning 1.5 decdes, while for the coted fiber 0 specimens per rte were used t nine loding rtes spnning 5 decdes. In this work, strin ws converted to stress, σ, using the following expression: 19 σ ε E 0 ( ε ), (13) f where the Young s modulus, E 0, is 7. GP. This eqution will not be vlid t high strins f d becuse the modulus will eventully decrese with strin since the tngent modulus (dσ/dε) must pproch zero t the theoreticl strength of the mteril. RESULTS AND DISCUSSION The effect of loding rte nd ph is seen in figure for bre fiber. These results loosely correlte with published dt for the ph dependence of the dissolution rte in queous solutions, s seen in figure 3. 0 We lso tested coted fused silic fiber nd found results similr to the bre fiber dt, s seen in figure 4. The error brs in figures nd 4 represent 95% confidence intervls. Typicl Weibull moduli were in the rnge of 70 to 90 for both bre nd coted fiber. Strength (MP) μm/s 316 μm/s 100 μm/s 31.6 μm/s Figure. Strength of bre fiber in two-point bending t 4 loding rtes in vrious 5 C ph buffer solutions. Numericl methods were utilized to find the ftigue prmeters from the dynmic ftigue dt. The observed trends in the clculted prmeters nd the size of the error brs mke it difficult to interpret the ftigue behvior. The error brs for the ftigue prmeters re lrge becuse these prmeters re correlted with one nother. For exmple, figure 5 shows the ellipses for the bre fiber in ph 7. The ellipses re ll nrrow nd the re of the normlized ellipses re mesure of the uncertinty, i.e., the smller the ellipses, the better the fit. In figure 5, model 1 hd the best fit while model 3 clerly hd the worst fit. Although model 1 fits 876 Interntionl Wire & Cble Symposium Proceedings 1998

5 best here, model lso hd good fit. At low ph, model hd the smllest ellipses while t high to moderte ph, model 1 hd the smllest ellipses. LOG 10 RATE OF DISSOLUTION Strength (MP) ph Figure 3. Dissolution rte vs. ph for fused silic μm/s 15.8 μm/s 5 μm/s 1.58 μm/s 0.5 μm/s μm/s 1581 μm/s 500 μm/s 158 μm/s Figure 4. Strength of coted fiber in two-point bending t 9 loding rtes in vrious 5 C ph buffers. Figures 6 nd 7 show the ftigue prmeters, n i, for bre nd coted fiber, respectively. By exmining these figures we see tht n i is not constnt with chnging environment. The trends in the dt re modest compred with the size of the error brs. It ws therefore decided to use the ssumption tht n i is constnt nd reexmine the dt. This ws ccomplished by clculting the weighted verge n i for ech model. Since n underlying ssumption of the models is tht ll the environmentl effect should be in A i, i.e., n i is constnt, this constrint on n i is resonble. The effect of constrining n i on the A i vlue is shown in figure 8. The error brs for the constrined fit re substntilly smller. Model shows the lest chnge in n i with ph. Only model showed the sme trends in A i with ph for constrined nd unconstrined n i. Normlized B i Figure 5. B i nd n i confidence ellipses clculted for bre fiber in ph 7 t 5 C nd normlized to the best fit vlues. Log n 3 Log n Log n Normlized Ftigue Prmeter, n i Figure 6. Fitted ftigue prmeter n i vs. ph for bre fiber. Interntionl Wire & Cble Symposium Proceedings

6 A simple chemicl kinetics model ws used tht ssumed tht the ftigue of silic involves the chemicl rection with OH ions, s written in Eq. 4. It is certin tht rection with moleculr wter is occurring simultneously. In the buffer solutions, the ctivity of wter is essentilly unity nd constnt. If the simple chemicl kinetics model were correct, the slope of log A i vs. ph plot would give the true rection order x with the OH ion. The pprent rection order between ph 4 nd ph 10 is 0.3, s seen in figure 8, nd this vlue is independent of the kinetics model used to fit to the dt. the behvior. Since predicted lifetimes re highly sensitive to the kinetic form of the stress dependence of ftigue nd model 1 is the most optimistic in lifetime predictions, one should use more conservtive nd logicl kinetic form, such s model. This model is bsed on physicl principls, rther thn model 1, which is empiricl in nture. Log A Unconstrined Constrined Log n 3 Log n Log A Log A 1-16 Unconstrined Constrined Unconstrined Constrined Log n Figure 7. Fitted ftigue prmeter n i vs. ph for coted fiber. CONCLUSIONS The vrious kinetic models were fitted to ftigue dt for both coted nd bre fiber. It ws found tht both the power lw, model 1, nd the exponentil, model, describe the stress dependence eqully well. Trends in the ftigue prmeters with ph fvors model, which therefore gives the best overll description of Figure 8. Log A i vs. ph for models 1,, nd 3 for bre fiber t 5 C showing both s fitted nd constrined vlues. The pprent rection order with respect to the OH ion between ph 4 nd ph 10 ws found to be 0.3 nd is pproximtely zero outside this rnge, i.e., ftigue is substntilly independent of ph t high nd low ph. It is likely tht the behvior between ph 4 nd 10 is more complex nd might show stronger [OH ] dependence over more limited rnge. ACKNOWLEDGEMENTS We thnk the Corning Foundtion for their support with Corning Foundtion Fellowship. 878 Interntionl Wire & Cble Symposium Proceedings 1998

7 REFERENCES 1. W. Griffioen, Evlution of opticl fiber lifetime models bsed on the power lw, Opt. Eng., F. P. Kpron nd C. R. Kurkjin, Relibility nd stndrds in photonics, Proc. XVIII Int. Cong. Glss, C I. Scnln, The constnts ssocited with the process of crck growth in silic in wter s function of stress nd temperture, unpublished work. 4. C. K. Ko, Opticl fibre nd cbles in Opticl fibre communictions, eds. M.J. Howes nd D.V. Morgn, Wiley, K. Jkus, J. E. Ritter, Jr. nd J. M. Sullivn, Dependency of ftigue predictions on the form of the crck velocity eqution, J. Am. Cerm. Soc., 64 [6] S. M. Wiederhorn, A chemicl interprettion of sttic ftigue, J. Am. Cerm. Soc., 55 [] G. S. White, S. W. Freimn, S. M. Wiederhorn nd T. D. Coyle, Effects of counterions on crck growth in vitreous silic, J. Am. Cerm. Soc., 70 [1] S. M. Wiederhorn nd L. H. Bolz, Stress corrosion nd sttic ftigue of glss, J. Am. Cerm. Soc., 53 [10] B. R. Lwn, An tomistic model of kinetic crck growth in brittle solids, J. Mt. Sci., G. M. Bubel nd M. J. Mtthewson, Opticl fiber relibility implictions of uncertinty in the ftigue crck growth model, Opt. Eng., 30 [6] Y. S. Shiue, Strength degrdtion of silic opticl fibers: chemicl kinetics nd coting effects, M. J. Mtthewson, Fiber lifetime predictions, Proc. Soc. Photo-Opt. Instrum. Eng., M. J. Mtthewson, Chemicl kinetics models for the ftigue behvior of fused silic opticl fiber, MRS Proc. Spring Meeting, in press. 14. J. L. Armstrong, M. J. Mtthewson, C. R. Kurkjin nd C. Y. Chou, Kinetics models for ftigue of high-strength fused silic opticl fiber, J. L. Armstrong, M. J. Mtthewson nd C. R. Kurkjin, The humidity dependence of highstrength fused silic lightguides, J. Am. Cerm. Soc. submitted. 16. P. W. Frnce, M. J. Prdine, M. H. Reeve nd G. R. Newns, Liquid nitrogen strengths of coted opticl glss fibres, J. Mt. Sci., M. J. Mtthewson, C. R. Kurkjin nd S. T. Gulti, Strength mesurement of opticl fibers by bending, J. Am. Cerm. Soc., 69 [11] M. J. Mtthewson, C. R. Kurkjin nd J. R. Hmblin, Acid stripping of fused silic opticl fibers without strength degrdtion, J. Lightwve Tech., 15 [3] W. Griffioen, Effect of nonliner elsticity on mesured ftigue dt nd lifetime estimtions of opticl fibers, J. Am. Cerm. Soc., 75 [10] H. Bumnn in The chemistry of silic," R. K. Iler, p. 65, Wiley, New York, Interntionl Wire & Cble Symposium Proceedings

He ws wrded the Corning Foundtion Fellowship t Rutgers University from 1995-1997.

8 Andrew Thoms Tylor Rutgers University Dept. of Cermic nd Mterils Eng. 607 Tylor Rod Pisctwy, New Jersey Andrew Tylor received his BS nd MS in Cermic nd Mterils Engineering from Rutgers University in 1993 nd 1995, respectively. He ws wrded the Corning Foundtion Fellowship t Rutgers University from He is currently pursuing his PhD in the Fiber Optic Mterils Reserch Progrm t Rutgers University investigting the strength nd relibility of opticl fibers. Dr. M. John Mtthewson Rutgers University Dept. of Cermic nd Mterils Eng. 607 Tylor Rod Pisctwy, New Jersey mjohnm@frcture.rutgers.edu John Mtthewson received his BA degree in Theoreticl Physics in 1975 nd his MA nd PhD degrees in Physics in 1978, ll from Cmbridge University. Since then he hs worked in the Cmbridge University Computer Lbortory, AT&T Bell Lbortories nd IBM Almden Reserch Center. He is now n Associte Professor in the Fiber Optic Mterils Reserch Progrm t Rutgers University where his reserch group is concerned with strength nd ftigue of opticl mterils in generl nd oxide nd non-oxide fibers in prticulr. 880 Interntionl Wire & Cble Symposium Proceedings 1998

CHM Physical Chemistry I Chapter 1 - Supplementary Material

CHM Physical Chemistry I Chapter 1 - Supplementary Material CHM 3410 - Physicl Chemistry I Chpter 1 - Supplementry Mteril For review of some bsic concepts in mth, see Atkins "Mthemticl Bckground 1 (pp 59-6), nd "Mthemticl Bckground " (pp 109-111). 1. Derivtion