Small Angle Light Scattering by Ordered Polymer SolutionsBY V. G. BARANOVU. S.S. R., LeningradInstitute of Macromolecular Compounds of the Academy of SciencesReceived 2nd January, 1970The niethod of sniall angle scattering of polarized light permits one to investigate fast processesof ordering of polymer solutions in the course of crystallization, and in particular, to study the kineticsof spherulite growth. The registration velocity of the scattering patterns was not lower than 2photos s-l, the exposure did not exceed 3 s, and the range of the size registered was from a fractionof a micron to several microns. This method was used for studying the temperature dependenceof the spherulite growth rate during isothermal crystallization of polypropylene solutions in decalinin the absence of the " kinetic memory " effect.The growth rate followed fairly closely the generalthermodynamic relationships. Crystallization of the polypropylene solution in decalin carried outwith stretching of the jet leads to the growth of spherulites flattened with respect to the stretchingdirection. When the take-up velocity grows, the flattening of the spherulites increases and theirradius decreases. A general formal explanation is given of the phenomenon of the flattening of thespherulites in the course of their growth in a mechanical field and of the peculiarities of the super-molecular order formation during molecular orientation.Investigation of ordering of polymer solutions during their isothermal or non-isothermal crystallization is of interest for at least two reasons.First, one mayobtain definite information on the structure and properties of the solutions themselvesand, when the concentration dependencies are studied, it provides information onthe melts or amorphous polymers. The latter problem is of fundamental importanceand is far from being solved. Secondly, morphological investigations of singlepolymer crystals obtained from solutions enable us to understand more profoundlythe structure and properties of the bulk polymer. Probably? it is no coincidencethat the scientific study of the structure of bulk crystallized polymers began with thediscovery and analysis of lamellar monocrystals of polymers grown from very diluteso1utions.l By increasing the polymer concentration it is possible to pass throughthe entire spectrum of the polymer morphology from single crystals to spherulite.Moreover, the solutions permit one to vary over a wide range the ordering of theprecrystalline phase by means of agitation, heating and change in concentration whilethe melt, in principle, probably cannot be greatly disordered since the energy ofdisordering should be comparable with the energy of breaking of a chemical bond.The usual methods of investigating the polymer morophology (X-ray diffractioninvestigations, electron and optical microscopy) are not always applicable to solutions,especially for kinetic and dynamic experiments involving fast processes.Con-sequently, our laboratory has developed a modified technique of small angle scatteringof polarized light specially applicable for kinetic studies.2EXPERIMENTALIn contrast t o the usual methods of polarized light scattering 3* we have used a broad(10-20 mm) incident light beam.This enabled us to attain a great increase in the scatteringvolume without changing the celI thickness (0.5-1 .O mm) and a corresponding decrease in13138 SMALL ANGLE LIGHT SCATTERINGthe exposure. This modification is described in detail in ref. (2), ( 5 ) and here we note onlythat it enabled us to register the scattering patterns at a velocity of not less than 2 photoss-I while the exposure did not exceed 3 s.The kinetics of the spherulite growth in solutions of polypropylene in decalin were studiedas follows. The solution in a sealed rectangular cell was placed in an air thermostat at atemperature T,>T;.After maintaining it at Tl for a certain time it was placed in an oilthermostat at a temperature T2tT;. The windows in the second thermostat permittedone to begin the registration of scattering patterns immediately. The precision of thermo-statting in the first thermostat was k2"C and in the second one it was fO.l"C.Besides carrying out experiments on the effect of Tl and T2 upon the kinetics of thespherulite growth, we have investigated the processes of ordering in solutions of polypropylenein decalin under non-isothermal conditions with simultaneous cooling and stretching of thesolution jet. The scheme of these experiments is given in fig. 1. In those cases when itwas impossible to observe the scattering patterns directly in the jet, the scattering patternof the " as-spun " filament was registered according to the method of V01kov.~-v2 i13 2FIG.1.-Registration scheme of light scattering by stretched jet. 1, hot solution; 2, take-upapparatus ; 3, laser with polarizer ; 4, analyzer and registering apparatus.We used the isotactic polypropylene manufactured in Czechoslovakia, Brno, with adegree of isotacticity greater than 97 % and a viscosity-average mol. wt cu. 100 000; thedecalin was of C.P. grade.RESULTSThe following change in scattering pattern occurs during isothermal crystallizationfrom solution : the distance between discrete reflexes is reduced and their intensityincreases (fig.2). The position of the maximum of the scattering intensity 0, permitsone to find the spherulite radius R from the equationwhere A' is the wavelength of incident light in the medium. Thus, it is possible tofind the change in R with time (fig. 3) and to determine the rate G of the spherulitegrowth at the given temperature T,.R = 2A'(7~ sin en,)-1, (1V. G . BARANOV 139t 6)FIG. 3.-Change in the spherulite radius with time. TI = 155"C, T2 = 25"C, C = 10 %.For a preceding study in our lab~ratory,~ we have reported some results on thedependence of G on T I , T2 and some other parameters. The most interesting resultwas the so-called effect of " kinetic memory ". When the solution was heated toTI = const, which only slightly exceeded T,, and the melting-crystallization cyclesat T2 = const were repeated, the spherulite growth rate increases appreciably withthe growth in the number of cycles.Melting of a sample at TI which greatly exceedT, does not produce this effect. Since we were interested in the dependence of Gon T2, the results in fig. 4 were obtained under conditions that excluded the effectof kinetic memory.When the crystallization in solution occurs during stretching, the small anglescattering pattern of polarized light has the form shown in fig. 5. Jt is possible toobtain from this figure both the mean radius of the spherulite from eqn (I) and thedeviation of its shape from the spherical one from the equationit, = tan !in#,43nr( bE,"2Z JX uI000000120 40 60T2 "CFIG.4.-G as a function of Tz , TI = 15S0C, C = 10 %140 SMALL ANGLE LIGHT SCATTERINGwhere A1 is the ratio of the maximum size of the spherulite to its minimum size andpm is the azimuthal direction of maximum scattering in the plane of the pattern. Fig.5 shows that the largest spherulite size is normal to the direction of the jet axis.Fig. 6 gives R and R1 as a function of the take-up velocity V2. (We could not measuredirectly the stresses occurring during stretching but according to some data thestresses are proportional to V2.) In all the cases under investigation, R decreasesand A1 increases with increasing V2.86nW 244201,YI I I 1 I? 4 A 8 !r3FIG. 6.-R and hl as functions of the take-up velocity.v 2 x 10 (rn s-1)DISCUSSIONIt is usually assumed lo that the secondary nucleation on the surface of the growingspherulite is the elementary act of the spherulite growth and the molecular chains ofthe new crystals are as a rule l1 tangential (or almost tangential) to the spheruliteradius. The spherulite growth rate is determined by the following general equation l2G = N exp (- E,,/RT- AF*/RT), (3)where N is either constant or inversely proportional to T ; ED is the energy of chaintransfer to the crystallizing surface and AF* is the free energy of the formation of anucleus having a critical size and R is the gas constant.Usually ED is identifiedwith the activation energy of viscous flow and the relationships of ED with tempera-ture may be expressed by the equation of Williams-Landell-Ferry.13 In this workwe assume that the contribution of the first term of the exponent is negligible. Whenthe nucleation of a cylindrical nuclei is three-dirnensional,l2AF* = 8no,pi/(A fu)2, (44AF* = 4a,ou/Afu, (4b)and when it is two-dimensional,where 0, and a; are the free energies of the end and the lateral surfaces, respectively,and AL is the free energy of fusion per monomer unit ; it can be written asAh = AH,-TAS,,.( 5 V. G. BARANOV 141Usually it is assumed l 2 that AH, and ASu are equal to their equilibrium values,hence(6)According to the above approximations, during crystallization of the unperturbedstate, log G should be linearly dependent on Tm/T(AT), or on T i / T ( A T ) 2 accordingto the type of nucleation.12 As a rule the inadequate precision of the experimentaldata l4 does not permit one to distinguish between these two cases; however, thedependence of log G on T,/T(AT) and T,2/(AQ2T is nearly always linear.14 Fig.7shows that for crystallization from solution both dependences are also practicallyA h = AHu(Tm-T)/Tm = AH,AT/T,.linear.- 6- 8(TmITAT)X lo2i 2 3 4I I I I[T2/T(AT)2] x 10FIG.7.-Log G as a function of T:/T(AT)” and TmITAT for data in fig. 4.As already mentioned, the elementary act of the spherulite growth is the foldingof the macromolecular chain. When the macromolecular chain is oriented, itsfolding and crystallization in the direction of orientation are favourable for the freeenergy of the formation of a nucleus of critical size.In contrast, its folding andcrystallization in the direction perpendicular to the orientation require additionalenergy AFII. Hence, the growth rates in these two directions will be different andmay be formally written asGI = Nexp [-ED/RT-(AF*-AFl)/RT], (74GI] = N exp [ -ED/RT-(AF* + AFII)/RT]. (74In A1 = (AF, +AFII)/RTConsequently, according to the scheme in fig. 8, In A1 under the condition that thegrowth in linear (Gl/GllzRl/Rll = &) is given byAt present, the physical meaning of the values AFl and AF,, is not sufficiently clear,but most probably they are associated with the changes in the entropy of the solutionwhen a mechanical field is present, and both these values grow with increase in theelongation of the jet.Thus, the growth rate of the spherulite or of its relic formincreases infinitely in the direction normal to the direction of jet stretching, while inthe direction of the stretching it drops to values negligible in comparison with the(8142 SMALL ANGLE LIGHT SCATTERINGfirst rate. In fact, crystalline aggregations obtained by crystallization of the solutionin the gap between two rotating coaxial cylinders have the shape of flat lamellaethreaded on a single filament.15 The largest size of the lamellae is normal to thedirection of the force stretching the macromolecules. These structures were calledthe shish-kebab structures.16. The above considerations may provide the mostlikely explanation of the appearance of these structures which should be consideredas degenerate forms of the spherulite morphology under the condition GI, / < GI.tpFIG.S.-Schenie of the spherulite flattening mechanism.One other process of crystallization in the polymer systems undergoing stretchingis possible. This is the orientational crystallization in the course of which the mole-cules become completely or partially extended in the stretching direction and arecrystallized without folding. Experimentally this morphology was not observed forsolutions ; nevertheless there are some indications of its possible existence. l’.0P (N m-2)FIG. 9.-Relationship of morphology and stress during crystallization and stretchingV. G . BARANOV 143Thus, the general picture of the effect of stretching on the morphology and crystal-lization kinetics of the polymer systems may be shown in the scheme in fig.9. Inthis figure the ordinate gives the parameter connected with the overall crystallizationkinetics and the abscissa gives the stresses developing during stretching. The firstzone corresponds to the growthof flattened spherulites, the second one to the structuresof the shislz-kebab type, and the third one to purely orientational crystallization.In addition to a change in the overall rate of crystallization, onemayexpect changesin the geometry and in the type of nucleation. At present, this suggestion is confirmedonly by the experiments of Kim and Mande1kern.l' They have found that a changein the elongation of natural rubber undergoing crystallization changes the Avramiconstant from ca.4 to 1 ; i.e., the nucleation becomes unidimensional and not three-dimensional.The author is indebted to Prof. S . Ya. Frenkel for his valuable suggestions anddiscussions and to Mr. A. V. Kenarov for the preparation and testing of samples ofthe polypropylene solutions.' P. H. Geil, Polymer Single Crystals (Wiley & Sons, 1963), chap. 2.A. V. Kenarov, V. G. Baranov and S. Ya. Frenkel, Vysokomolekul. Soedin. A, 1969, 11, 1725.M. B. Rhodes and R. S. Stein, J. Polymer. Sci., 1965,45,531.S . Ya. Frenkel, V. G. Baranov and T. I. Volkov, J. Polymer Sci. C, 1967, 16,1655.V. G. Baranov, A. V. Kenarov and T. I. Volkov, J. Polymer Sci., in press.T . I. Volkov, Vysokomolekul. Soedin. A, 1967, 9,2734. ' T. I. Volkov, G. S. Farshyan, V. G. Baranov and S. Ya. Frenkel, Vysokomolekul. 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