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A Study of Molecular Diffusion in Polymer Solutions by a Microinterferometric Method

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A Study of Molecular Diffusion in Polymer Solutions by a Microinterferometric Method Scholars' Mine Masters Theses Student Theses and Dissertations 1966 A study of molecular diffusion in polymer solutions by a microinterferometric method Girish T. Dalal Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Chemical Engineering Commons Department: Recommended Citation Dalal, Girish T., "A study of molecular diffusion in polymer solutions by a microinterferometric method" (1966). Masters Theses. 5757. https://scholarsmine.mst.edu/masters_theses/5757 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. ii ABSTRACT A microinterferometric method was used to study the effect of solute concentration on the diffusion coefficient in polymer solutions and also to d etermine the effect of polymer concentration on the dif­ fusion coefficient. The polyacrylonitrile-dimethylforruamide system was used as a means of dete rmining the accuracy of the experimental apparatus and procedure. The non-ionic, water soluble polymer, hydrox~thyl cellulose (commercially known as Na.trosol), was used to study this effect with urea and D-glucose as the solutes. The results obtained for the polyacrylonitrile-dimethylform­ amide s ystem were in close agreement with the results obtained by Secor, which meant that the experimental techniqu.e is accurate enou.gh to give r eproducible data. The differential diffusion coefficient in­ creased with the increase in solute concentration in all cases. The effect of solute concentration on the differential diffusion coefficient was found to be s imilar for various polymer concentrations and dif­ ferent solutes. The integral diffusion coefficient temained almost constant for the concentration range of the solutes used in this work. No effect of polymer concentration on the integral diffusion coefficient could be deduced from the experimental data. iii TABLE OF CONTENTS Page LIST OF FIGURES v LIST OF TABLES viii NOMENCLATURE ix I. INTRODUCTION 1 II. LITERATURE REVIEW 4 Theory Of Diffusion 4 Laws of Diffusion 5 Techniques for the Measurement of Diffusivity • 10 Steady State Diffusion. • • • •••• 1 1 Free Diffusion ..•••.•• 13 Restricted Diffusion . .••• . 17 Optical Techniques .. 17 Schlieren Methods ...•••• 17 Interferometric Methods ...•• . 19 The Optical Wedge Technique ••• 21 III. EXPERIMENTAL 25 Mate rials . ... 25 Expe rimental Apparatus ..... 2 5 Preparation Of Optical Wedge 28 Microscope ... ..... · . · · · · · · · · · 31 Concentration Measurement Apparatus . 31 Expe rimental Procedure. .. 34 Procedure For Obtaining Experimental Interference Pattern.• .. .. 34 Measurement Of Concentration .. .. .. .. 35 Computation Technique . .. 39 Evaluation Of The Integral . ... 40 Evaluation Of The Concentration Gradient 44 Data and Results . 46 IV. DISCUSSION . .. ... 48 Effect Of Solute Concentration .•. 48 Effect Of Polymer Concentration On Integral Diffusi vities • • •••.•• . ••••••..•.••• . 63 Experimental Equipment • •••••••••• • ••• 65 Prediction of Diffusi vity of a Solute in Very Dilute Solutions • • • • • • • • • • • • • • • • • • • • • • 6 7 iv Page v. CONCLUSIONS...••• . 68 VI. RECOMMENDATIONS . 70 VII. APPENDICES ....... 71 Appendix A - Derivation Of Formula For Diffusion Coefficient Appendix B - Materials .....•. 77 Appendix C - Data and Results •. 78 Appendix D - Computer Programs 92 Appendix E - Integration of Concentration­ distance Curves •••.•... 107 Appendix F - Evaluation Of Concentration Gradient ............. 112 Appendix G - Measurement of Interference Pattern ••. •.• .• 11 5 VIII. BIBLIOGRAPHY .•.• . 117 IX. ACKNOWLEDGMENT • . 119 X. VITA .•............ 120 v LIST OF FIGURES Figure Page 2. 1 Schematic Diffusion Cell for Steady-state Diffusion 12 2. 2 Free Diffusion. The Initial Arrangement of Solutions in the Cell at t = 0, and Concentration Gradie nt Curves at a later time , t1 14 2.3 Restricted Diffusion. Concentration Curve for a time, t2, after the concentrations have changed appreciably at the ends of the Cell 18 2.4 The Optical Wedge 22 3. 1 Schematic Drawing of Experimental Apparatus 27 Experimental Apparatus Assembly 29 3.3 Preparation of the Optical Wedge for Diffusion Measurements 30 3.4 Microscope used for the Experiment 32 3. 5 Abbe-Spencer Refrac tomete r use d for M easure­ ment of Refractive Inde x as a Function of Con centration 33 3. 6 Light-inte rference P atterns Observed During a D iffu sion Experiment 36 3 .7 Experimental Interference Patte rn at t = 11 seconds, for System 4. 37 3.8 Experimental Interference Patte rn at t = 15 seconds , fo r System 8. 38 3.9 Refractive Inde x (Sodium D-line ) of Solutions of Polyacrylonitrile in Dimethylformamid e at 25°C 41 3. 10 Expe rimental Concentration Profile for Poly­ acrylonitrile-Dimethylformamide System at t = 90 seconds 42 vi Figure Page c 3. 11 Evaluation of .Jo(' x dC 45 3. 12 Experimental Concentration Gradient as a Function of Distance for Polyacrylonitrile­ Dimethylformarnide System at t = 90 Seconds 47 4. 1 Effect of Concentration on the Diffusion Coefficient for Solutions of Polyacrylonitrile in Dimethyl­ formamide at 77°F, with t = 90 seconds 49 4. 2 Diffu~ivity versus concentration for 0. 8% Natrosol in Water with Urea as Solute, at 77°F, with t = 12 seconds. 51 4. 3 Diffusivity versus Concentration for 0. 8% Natrosol in Water with D-Glucose as Solute, at 770F, with t = 15 seconds. 52 4.4 Diffusivity versus Concentration for 1. 0% Natrosol in Wa ter with Urea as Solute, at 77°F, with t = 15 54 4.5 Diffusivity versus Concentration for 1. 0% Natrosol in wate r with D-Glucose as Solute, at 77°F, with t = 15 s e conds 55 4. 6 Diffusivity versus Concentration for 1. 88% Natrosol in Wate r with Urea as Solute, at 77°F, with t = 10 seconds 56 4.7 Diffusivity versus Concentration for 1. 88% Natrosol in Water with D-G1uc ose as Solute , at 77°F, with t = 30 seconds 57 4.8 Diffusivity versus Concentration for 2. 5% Natrosol in Water with Urea as Solute, at 77°F, with t = 11 Seconds 58 4.9 Diffusivity versus Concentration for 2. 5% Natrosol in Wa t e r with D-Glucose as Solute, at 77°F, with t = 1 7 S e conds 59 4. 10 Diffusivity versus Concentration for 3 . 51% Natrosol in Water with Urea as Solute, at 77°F, with t = 10 seconds 60 vii Figure Page 4. 11 Diffusivity versus Concentration for 3. 51% Natrosol in Water with D-Glucose as Solute, at 77°F, with t = 16 seconds. 61 4. lZ Integral Diffusivity as a Function of Polymer Concentration for Natrosol-Water Systems. 63 E. 1 Evaluation of De from a Concentration-distance Curve Using Equation (Z. ZZ). 109 E. Z Evaluation of the .Jor.~ X dC. 110 F. 1 Concentration Profile for System 3, at t = 16 Seconds. 114b G. 1 A Sketch of Experimental Interference Pattern, showing how to measure the Fringe Pattern. 116 viii LIST OF TABLES Table Page 3. 1 Polymeric Systems Used for the Study. 26 c. 1 Polymeric Systems Used for the Study. 79 c. 2 Data and Results for System 1. 80 c. 3 Data and Results for System 2. 81 C.4 Data and Results for System 3. 82 c. 5 Data and Results for System 4 . 83 c. 6 Data and Results for System 5. 84 c. 7 Data and Results for System 6. 85 c . 8 Data and Results for System 7. 86 c. 9 Data and Results for System 8. 87 c. 10 Data and Results for System 9. 88 c. 11 Data and Results for System 10. 89 c. 12 Data and Resulty for System 11. 90 c. 13 Values of Integrated Diffusivities, D, for the Systems Studied. 91 F. 1 Comparison of Concentration Gradients Obtained by Two Different Methods. 114 F. 2 Average Absolute Percentage Deviation of Observed Concentrations from Those Predicted by Gompertz Equation and Davis' Method. 114a ix NOMENCLATURE A = area under the curve of concentration versus distance, (gm./100 cc. soln. )em. a = intercept of straight line that results when (x - x 1 ) / § is plotted against x. a' = cross-sectional area, sq. em. a 1, a 2 , a 3 = constants in Gompertz equation. b = slope of straight line that results when (x - x 1 )/ § is plotted against x . C = concentration of solute, gm. Icc. C 0 = initial concentration of solute, gm. Icc. c' = concentration of solute at original interface, gm. Icc. c = concentration of solute, gm./100 cc. D = molecular diffusion coefficient of a solute, sq. em. /sec. D = integral {average) diffusion coefficient of a solute, sq. em. I sec. Dnn = diffusion coefficient of a solute in a non-Ne wtonian fluid, sq. cm. / sec. d = distance between adjacent bright fringes, em. h = h eight, em. M = molecular weight. N = diffusion flux, gm. I sq. em. sec. -' N = diffusion flux in vector notation, gm. /sq. em. sec. n = refractive index of solution. no = refractive index of solvent. X r = x/2 ~~ Boltzmann's variable, ern. I (sec. ) 112 T = absolute temperature, °K. t = time, seconds. V = volume, cu. ern. w = weight fraction of solute. X = fractional area occupied, sq. ern. x = coordinate, corresponds to distance, ern. y = coordinate, corresponds to concentr ation of solute, gm. / c c . y I = small angle of deflection, rad. z = coordinate, corresponds to depth of the medium, em. Subscripts A = solute A. A' = rese r vo1r. A ' . B = solvent B. B ' = reservo1r. B' . c = at some concentration C. Co = at initial concentration C 0 • cp = prope rties or parameters of the continuous phase portion of the non-Newtonian fluid. i = i th sol ute. t = at time t. x = direction x. y = direction y. xi z = direction z. 1, 2 = positions 1 and 2 in a system. Greek Letters and Other Symbols a = intercept, Gompertz equation. A = change in property.- 9 = wedge angle, minutes or rad. ~ = wave length, mi.J.
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