Dynamic measurements on polymer chain dimensions below the θ-temperature

Transcription

1 Dynamic measurements on polymer chain dimensions below the θtemperature R. Perzynski, M. Adam, M. Delsanti To cite this version: R. Perzynski, M. Adam, M. Delsanti. Dynamic measurements on polymer chain dimensions below the θtemperature. Journal de Physique, 1982, 43 (1), pp < /jphys: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1982 HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 61.40K 2014 Les 2014 (03B8 T / T)~M. Des To verify J. Physique 43 (1982) JANVIER 1982, 129 Classification Physics Abstracts Dynamic measurements on polymer chain dimensions below the 03B8temperature R. Perzynski, M. Adam and M. Delsanti (*) (**) Laboratoire Léon Brillouin, CEN Saclay, B.P. n 2, GifsurYvette, France (**) Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, USA (Reçu le 26 juin 1981, accepté le 21 septembre 1981) Résumé. expériences de diffusion de lumière quasiélastique et de viscosité sont réalisées en dessous de la température 03B8 pour observer la contraction d une chaine flexible. Les échantillons utilisés sont du polystyrène monodisperse dissous dans du cyclohexane (Mw 1,71 x 105; Mw 4,11 105; Mw 1,26 106). On observe que : facteurs d expansion hydrodynamique (03B1H et de viscosité (03B13~) s échellent selon la variable reduite 03B1H et 03B13~ par rapport à 03B8. ont un comportement linéaire dans un «domaine 03B8» (0 ~ 03B8 T / T ~M ~ 10) qui est symétrique Le «régime asymptotique collapsé» n est pas observé pour (03B8T T)~M~ 35. Abstract observe the contraction of a flexible chain, quasielastic light scattering and viscosity experiments were performed below the 03B8temperature. The systems used were monodisperse polystyrene (Mw 1.71 x 105, Mw , Mw ) dissolved in cyclohexane. It is observed that : 2014 Hydrodynamic and viscosity expansion factors, 03B1H and 03B13~, scale with the reduced variable (03B8T T)~M B1H and 03B13~ have a linear behaviour in a «03B8 domain» (0~ 03B8 T / T ~M ~ 10) which is symmetric with respect to the 03B8temperature There is no evidence of an asymptotic collapsed regime for (03B8T T)~M~ 35. Introduction. a flexible polymer chain at the theta temperature, the mean interaction between monomers vanishes and the chain has a Gaussian conformation. At temperature below the Flory theta temperature [2] (near the upper critical solution temperature) the attractive interactions between monomers become important. On cooling, the chain contracts and can reach a globular state. More often the contraction below the 0temperature is called the o coil globule transition». A large number of theoretical and experimental works have been devoted to this subject [112]. The different analyses lead to similar results presented in a simple way by Static and dynamic measurements have been performed on the «coil globule transition >> of a polystyrene chain dissolved in cyclohexane [510]. Unfortunately the data are sparse. instance, D. R. Bauer et al. [6] observed a small contraction of the chain and G. Swislow [9] et al. observed a sharp coil globule transition. Whatever the sharpness of the transition, the main point of the theory is that the expansion factor must de Gennes [1]. scale with the reduced variable T e M as suggest T, ed by the experiments of D. R. Bauer et al. [6]., Here our purpose is, to :.. whether the expansion factor scales as Article published online by EDP Sciences and available at

3 determine Let B8 the /U range of T T e M where the globular state regime is reached in the case of the well known system polystyrene cyclohexane. In order to measure the evolution of the size of the chain two complementary experiments are performed : quasielastic light scattering and viscosity measurements. Part 1 of this paper briefly recalls the theory of the coil globule transition, the experimental conditions are described in part 2, and the results obtained by the two techniques are presented and compared in part Theoretical background. 1.1 SINGLE CHAIN BEHAVIOUR. INFINITE DILUTION. us consider an isolated chain of N statistical units of length a. At 0temperature, its root mean square end to end distance R is Ro 2i a IN. In a mean field description, the chain expansion factor a Rlajk described with a modified Flory equation [14] : can be y is a steric coefficient and v is the excluded volume between monomers, which is proportional to the reduced temperature T In equation (1), the term (a) corresponds to excluded volume interactions. If T > 0, this term favours a swelling of the chain (v > 0); if T 0 these interactions become attractive (v 0) and favour a chain contraction. The term (b), due to the chain elasticity, prohibits large swelling and is mainly important when T > 0. The last term (c), a hard core repulsion, slows down the collapse of the chain, it becomes important for T 0. If y is a constant independent of T and N, equation (1) leads to an expansion factor which is a function of only the reduced variable L IN. Thus for any temperature and any number of statistical units, the expansion factor can be represented by a single master curve a f (,r,/n). In the temperature range where attractive interactions dominate (T 0) a becomes smaller than 1. From formula (1) when a 1, that is in the asymptotic regime, a behaves like (T FN) 113. Then the chain is collapsed and its volume is proportional to N : R N 1,3 From a scaling point of view the expansion factor is a f(1:jn) where the function f is only known in the asymptotic regimes : f(s/) i 1 when sfl «1 (that is close to 0temperature) and f(t, (r:jnfl/3 when i N > 1 and T 0. In short : Gaussian. sjk «1, R R, N 1/2 the chain is i IN > 1, R N 1/3. Ll/3 the chain is a globule. Thus a mean field [3, 4] as well as a scaling description [1] lead to the same result : the expansion factor a is a function of the single reduced variable / N DILUTE SOLUTIONS. a given chain length, at finite concentration c and for T 0, demixing of a polymer solution takes place at a reduced temperature rd(c). The demixing curve, locus of the point TD(c), exhibits a maximum at a critical concentration cc 1 N,,IN I rature being Tc the corresponding critical tempe Using the coordinates T,IN, cjk, this diagram is universal [11, 14]. The temperature range of interest, where single chain behaviour can be observed, lies between the 0temperature and the demixing temperature. As c becomes smaller, the reduced temperature range becomes broader and the better are the conditions to observe a chain collapse EXPERIMENTAL EXPANSION FACTORS. The usual experiments do not measure the end to end expansion factor : Actually, using intensity light scattering, quasielastic light scattering or intrinsic viscosity experiments, one measures different expansion factors defined by : If the conformation of the chain is the same on all length scales the different mean values ag, ah, a11 are proportional to a. This condition is only realized at the 0 point and in the asymptotic regimes far from the theta point (I! IN > 1). Above the 0 point and for I T IN > 1, references [15, 16] consider the chain as a succession of blobs, the chain has Gaussian statistics inside the blobs (short distances) and excluded volume statistics outside the blobs. The expansion factors,. Rg D a Rg and H Rg(e) ah Ri$0) R40) are calculated in refe rence [16] using the blob model. A hydrodynamic

4 The average gives high weight at short distances, a static average gives the same weight everywhere. Thus the temperature crossover for ah is broader than for ag. Assuming an abrupt change from Gaussian to excluded volume statistics, it is found [16] that : where N, is the number of statistical units inside each blob and v is the excluded volume exponent v 3/5. Also where y is an adjustable parameter. T 0, by analogy to T > 0, we can imagine a symmetric description of the chain conformation, i.e. a chain with Gaussian statistics at short distances and globular statistics at long distances. Equation (3) for the expansion factor ah, with v 3, corresponds to such a description. It implies that the temperature crossover is broader for ah than for ag. Let us now consider the expansion factor a. Qualitatively the intrinsic viscosity is proportional to the volume of the polymer. Thus there exists a relation between LX?1 3, ag and ah. Some years ago it was proposed that [15,17] : If formula (4) is valid, from our two complementary experiments quasielastic light scattering and viscosity measurements, we can deduce the expansion factor of the radius of gyration. 2. Experimental conditions. LIGHT SCAT TERING MEASUREMENTS. incident light is provided by an argon ion laser A A. Spectral measurements of the Rayleigh light scattered by solutions are made with a light beating spectrometer. homodyne detection, it is necessary to have a clean scattering volume : the solutions are prepared one month in advance and their low viscosity allows any dust particles to fall on the bottom of the optic cell. The autocorrelation C(t) of the output of the photomultiplier is built up by a 24 channels real time Malvern correlator. ( more details see references [18, 19].) In order to observe the Brownian motion of the whole chain the scattering angles 0 are chosen in such a way that KRg momentum transfer : k/ 0.6. Where K is the n(t ) is the refractive index of the solution at the temperature T. In these conditions, we have : A and B are two adjustable parameters, 1:c 1 2 DK Z, where D is the diffusion coefficient of the chain.. The data are fitted to equation (6) by a least squares three parameters procedure. A single characteristic time Tc is determined whatever the sample time At : Tc 5 24 At 10 Tc. The good quality of the exponential fit and the precision (5 x 10 3) on the decay time measurements confirm the absence of stray light in the scattering volume. By a variation of a factor 10 on K 2, we verify that Tc is inversely proportional to K 2. The optical cell is set in a copper jacket [20]. The temperature is regulated within ± 0.01 OC by an ATNE monitor. Lowest temperatures, down to 14 OC, are obtained with a cold water circulation. The temperature measurement is made with two thermocouples in contact with the cell. These procedures allow us to determine the diffusion coefficient D(T) within an accuracy of ± 1 % against temperature T determined within oc VISCOSITY MEASUREMENTS. The viscosity q of polystyrene solution (M,, 4.11 x 105) is measured with a capillary viscometer : CannonUbbelohde fourbulb shear dilution (type ). The viscometer is immersed in a regulated temperature water bath, the temperature being controlled within ± OC. The flow times (proportional to the viscosity) are measured at five concentrations (c 5 x 10 3 g/cm3) as a function of temperature. The reproductibility of the flow times measurements is better than ± 0.5 ; o. The measurements are done at shear rate ranging from 160 s 1 to 500 s 1; within the accuracy of the measurements no shear rate effects are detected SAMPLES. The polydispersity has a drastic influence on the shape of the demixing curve. a polydisperse sample, as T is lowered, the highest molecular weight chains demix first. Thus the average molecular weight of the solution and its average concentration evolve as the temperature decreases. So in our experiments we used the best monodisperse polystyrene available (MW/Mn 1.1). In order to determine the region where the contraction of a polystyrene chain dissolved in cyclohexane can be observed, a preliminary study of the demixing curves was performed. Even with our low polydispersity samples, these curves do not superpose in t N, c Jk coordinates [21] (in agreement with the observation of Caroline [7]). a given value of cj M, the higher is the molecular weight the larger is 1:DJM [22]. instance at cjm roo.; 4 x 102, we find :

5 I Linear all(t) aji) Loglog 132 We did not measure the 0temperature of the polysty. renecyclohexane system. We choose 0 35 C, the temperature at which the second virial coefficients becomes equal to zero [23]. Light scattering experiments were performed on samples with the following characteristics : Viscosity measurements where done on : 3. Experimental results and discussions. 3.1 DIFFUSION COEFFICIENT. The diffusion coefficient D was measured by light scattering at different temperatures for each sample. We made a temperature interpolation of the measurements and a linear extrapolation [22] of D to zero concentration. Thus we obtained the diffusion coefficient of a single chain at a given temperature T : Do(T). The hydrodynamic radius is obtained from : mical expansion factor ah RHI RH(O) is plotted against the reduced variable i.jm. ah scales on a single curve [6] for our two different molecular weight samples (MW 1.71 x 105 and MW 1.26 x 106) and shows various regimes of behaviour : is a linear function of reduced temperature in the «0 domain» (0 K ) I c,,,rm I ;: 10) [27]. Figure 1 shows that this linear behaviour is obeyed in a temperature range symmetric with respect to 0. departs from its linear behaviour when I r J M > 10. On figure 3, the experimental data obtained for T 0 are set in a loglog plot The effective exponent defined as varies continuously from 0 down to 0.2. The hydrodynamic radius is far from its asymptotic regime where the temperature exponent would be equal to a constant value 1/3, following section 1. The similarity in behaviour of ah on both sides of 0 suggests that, even for T 0, there is a strong influence of the spatial crossover on hydrodynamic properties [15]. Thus in figure 2 we have plotted the transposed calculation of blob model (Eq. (2) with y 10 2 and v 1/3). We have normalized the ns being the solvent viscosity [24]. The experimental measurements at the 0 temperature (see Fig.1 and appendix II) are in agreement with previous values [6, 7, 20, 25, 26] RH(O) 2, 0.23 M0.5 A and the theoretical predictions. In figure 1 the dyna Fig. 2. plot of ah versus 0 T T IM. The notation is the same as in figure 1. The dotted line is create. f(r M) (see text). The solid line has the 3 slope. Fig. 1. plot of the hydrodynamic expansion factor for different molecular weights: Mw X 105, + M,, 1.26 x 106 and 0 MW 1.71 x 105 from reference [20]. The arrows bound the 0 domain. curve at the edge of the 0 domain (T,/ M ;:t 10 and RH ~ RH(O)). Such an agreement between the calculated and the experimental behaviour is quite surprising. We recall that in this model, the hydrodynamic temperature drossover must be broader than the static one. This point has to be verified. To our knowledge, the static experiments [5, 8, 10] are in disagreement among themselves. Anyway the main problem of this model is still the symmetrization with respect to 0 (i.e. the existence of a Gaussian blob for lowest temperatures) which is implicitly assumed in the calculation without any strong justification.

6 . hexane, Interpolations From 133 From references [9, 10] the collapse of PS in cyclowas observed on a sample of MW 2.6 x 10 and high polydispersity (MW/Mn ~ 1.3). It would be interesting to check whether, in this range of high molecular weights i$k a representation is still universal. 3.2 INTRINSIC VISCOSITY. between measurements made at different temperatures, allow us to have at a given temperature, the variation of the viscosity with the monomer concentration. Intrinsic yiscosity [ tl(7)] is obtained by extrapolation of c q,,p(t) where qsp(t) is the specific viscosity the molecular weight MW 4.11 x 105, the intrinsic viscosity at the.0 temperature [q(0)] is equal to 53 ± 3 cm3/g, in agreement with values reviewed in reference [28]. a3(t) is obtained in two different ways by using equation (2) and an lim qsp(t, c)1 i7sp(o, c). Within co experimental accuracy both treatments lead to the same value. reduced variable M, in a loglog plot. We also report an values deduced from references [29, 30] on molecular weights Mw 7.56 x 105 and Mw 3.2 x 106. Whatever the molecular weight all the points lie on the same master curve (in agreement with the scaling description [11]). The curve departs from a linear approximation when i jk > 10. Thus the 8 domain has the same extension for diffusion coefficient, intrinsic viscosity and radius of gyration measured by neutron scattering [5]. We see that for 10 t/m, 25 the factor an cannot be described by a simple power law a z1. Following equation (4) from our two kinds of experiments, we can deduce the expansion factor of the radius of gyration ag (LX3/aH)1/2. In figure 4, we compare our ag with the ag obtained from neutron scattering experiment [5] in the same range of TI/M. We found that : for 1: JX1 ;$ 10, ag coincides with but for T/m Z 10, ag is larger than ag g ag. Fig. 4. Comparison between the expansion factors : Xn, ag and X /2 ag 2013L The symbols are the same as in figures 1, 2, 3 and ah /2013 M,,, 2.9 x 10 from reference [5]. 03B8T M 10 the dotted line represents the linear behaviour of ah. 0T > to the lines have the same meaning as in figure 2. In fact, equation (4) is only an approximation (see appendix I). We have : Fig T T M on Variation of the viscosity expansion factor an versus a loglog scale. The dotted line represents a linear behaviour and the full line a power law with slope 1. o MW 4.11 l x 105 present work, x MW 7.56 x 105 from reference [29] and V Mv 3:2 x 106 from reference [30]. On figure 3 we give the variation of an versus the where fl is a numerical factor depending on temperature and chain statistics. By normalization fl 1 at the 0 point and fl 1.7 in the globular state. It seems reasonable to assume that fl has a monotonic variation between the two asymptotic regimes. So, from the numerical evaluations, # increases when the temperature decreases which could explain that experimentally ag is larger than ag. 4. Conclusion. this set of experiments it appears that hydrodynamic and viscosity expansion factors, ah and att respectively, scale in a representation which is in agreement with theory [1, 3, 4]. This confirms the hypothesis that the steric

7 Is INTRINSIC The Experimental 134 coefficient y in equation (1) is temperature independent. Hydrodynamic radius data, above and below the 0temperature, show that a «0 domain» exists, symmetric with respect to 0. In this «0 domain» the chain is essentially Gaussian and the variation of the expansion factor can be expressed by a linear approximation. Whatever the measurement, the 0 domain corresponds to renecyclohexane system. In the present dynamic measurements up to I 1 a crossover regime is observed but no collapsed asymptotic behaviour. It would be interesting to make new experiments to clear two main points : T 0, is there a different temperature crossover for static and dynamic magnitudes? the scaling in T,/m respected even for high molecular weight monodisperse samples? Or is there a high molecular weight effect related to self entanglements, playing an important role and inducing the sharp collapse of the chain observed by Tanaka? Equations (A. 1), (A. 3) lead to : in the globular state. values of RH (A) Appendix H. deduced from light scattering measurements (accuracy of 1 %) and viscosity expansion factor from intrinsic viscosity measurements, at different temperatures. Acknowledgments. authors thank J. Lebo P. Cotton for stimulating discussions. witz and J. One of us M. D. thanks H. Yu and J. D. Ferry for their hospitality. Appendix I. VISCOSITY AT THE 0 POINT. Following the formula (86, 97b) of Zimm s paper [31] for the case of large hydrodynamic interactions, we have : RH is defined in section 3.1 and Rg RI,16 if R is the root mean square end to end distance. NA is the Avogadro number and M is the molecular weight of the polymer. INTRINSIC VISCOSITY IN THE GLOBULAR STATE AND RELATION BETWEEN THE DIFFERENT EXPANSION FACTORS. Following Einstein formula and Stokes law [32]; we have : a globule

8 135 References and notes [1] DE GENNES, P. G., J. Physique Lett. 36 (1975) L55. [2] FLORY, P. J., Principles of Polymer Chemistry (Cornell University Press, Ithaca and London) PTITSYN, O. B., KRON, A. K. and EIZNER, Yu. Ye., J. Polym. Sci. Part C 16 (1968) [3] LIFSHITZ, I. M., GROSBERG, A. Yu., KHOKHLOV, A. R., Rev. Mod. Phys. 50 (1978) 683. [4] SANCHEZ, I. C., Macromolecules 12 (1979) 980. [5] NIERLICH, M., COTTON, J. P., FARNOUX, B., J. Chem. Phys. 69 (1978) [6] BAUER, D. R., ULLMAN, R., Macromolecules 13 (1980) 392. [7] PRITCHARD, M. J., CAROLINE, D., Macromolecules 13 (1980) 957. [8] NOSE, T., CHU, B., Macromolecules 12 (1979) [9] SWISLOW, G., SUN, S. T., NISHIO, I., TANAKA, T., Phys. Rev. Lett. 44 (1980) 796. [10] SUN, S. T., NISHIO, I., SWISLOW, G., TANAKA, T., J. Chem. Phys. 73 (1980) [11] DAOUD, M. and JANNINK, G., J. Physique 37 (1976) 973. [12] WEBMAN, I., LEBOWITZ, J. L. and KALOS, M. H., to be published. [13] convenience we use a 03C4 definition of the opposite sign of the usual one. [14] COTTON, J. P., NIERLICH, M., BOUÉ, F., DAOUD, M., FARNOUX, B., JANNINK, G., DUPLESSIX, R., PICOT, C., J. Chem. Phys. 65 (1976) 110. [15] WEILL, G., DES CLOIZEAUX, J., J. Physique 40 (1979) 99. [16] AKCASU, A. Z., HAN, C. C., Macromolecules 12 (1979) 276. [17] HAN, C. C., Polymer 20 (1979) [18] DELSANTI, M., Thesis, Université de ParisSud (1978). [19] ADAM, M., DELSANTI, M., Macromolecules 10 (1977) [20] ADAM, M., DELSANTI, M., J. Physique 41 (1980) 713. [21] The number of statistical units N in the chain is proportional to the molecular weight Mw of the polymer. Then 03C4 ~N ~ ~Mw. 03C4 [22] Our preliminary results will be published later. [23] STRAZIELLE, C., BENOIT, H., Macromolecules 8 (1975) 203. [24] The ~s(t) temperature dependence is taken into account as in reference [19]. [25] KING, T. A., KNOX, A., LEE, W. I., MACADAM, J. D. G., Polymer 14 (1973) 151. [26] HAN, C. C., Polymer 20 (1979) 259. [27] 03C4 ~M ~ 10 is equivalent to 03C4 ~03C4* in reference [19]. [28] EINAGA, Y., MIYAKI, Y., FUJITA, H., J. Polym. Sci. 17 (1979) [29] YAMAMOTO, A., FUJII, M., TANAKA, G., YAMAKAWA, H., Polymer J. 2 (1971) 79. [30] KRIGBAUM, W. R., CARPENTER, D. K., J. Phys. Chem. 59 (1955) [31] ZIMM, B. H., J. Chem. Phys. 24 (1956) 269. [32] See for instance YAMAKAWA, H., Modern theory of polymer solutions (Harper and Row publishers, N.Y.) 1971, p. 353.