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Molecular motion in solid polymers detected by photon correlation spectroscopy
Volume 50.
CHEMICAL PHYSICS LETTERS
number 3
MOLECULAR DETECTED
MOTION BY PHOTON
15 September
1977
IN SOLID POLYMERS CORRELATION
SPECTROSCOPY
T.A. KING and M.F. TREADAWAY
Ph_vsics Department. Schuster Laboratory. Manchester Ml3 9PL. UK
University of Manchester,
Rcceivcd 10 Xl.~y IS77
Xloleculnr rclawtion in the lo-lo6 liz region in rl solid amorphous polymer PXIhlA has been detected by photon correlation spectroscopy. Relaxation times are found to depend strongly on sample annealing and sample temperature equilibration. The main relaxation frequencies. determined around the glass-rubber transition Tr are in good correspondence with values obtained by other methods.
1_ Introduction Molecular
relaxation
in a solid amorphous
polymer
detected by photon correlation spectroscopy is reported here. The observed relaxation times are in good correspondence with values obtained by dielectric and dynamical mechanical methods. A strong dependence on sample annealing and on temperature equilibration has been found. Light scattering is able to probe optical inhomogeneities and local structure in samples [ I] _ Isobaric and adiabatic density fluctuations lead to three components, respectively the central Rayleigh peak centred around the incident frequency and the Brillouin doublets. Rayleigh-Brillouin scattering derives contributions in addition to thermal density fluctuations from orientation fluctuations, structural relaxations and twocomponent and impurity concentration fluctuations. The coupling between structural relaxations and collective density fluctuation modes also produces a central component, the Mountain line. In a solid amorphous polymer this line is expected to have a sufflciently narrow frequency width to be mixed in with-the other central components_ We look here particularly at the light scattered spectrum of the central component derived from a solid amorphous polymer. Motion in solid polymers may be expected to be detectable by light scattering into the 494
central Rayleigh scattered component from thermal density fluctuations arising from brownian diffusion of polymer segments, by diffusion of small scale structural order, by large scale order (if it exists in the sample) or by diffusion of microcrystalline regions [2]. Also scattering into the central component may result from the diffusion and orientational fluctuations of parts of the chain having anisotropic polarizability. Elastic light scattering has been used previously to investigate static structure in solid polymers and dynamical information should be derived from measurements of the linewidth of this scattered light. There have now been several studies by photon correlation spectroscopy on concentrated polymer systems including solutions and networks and extension to bulk materials appears feasible even in the presence of intermolecular correlations. For solid polymers the linewidths are expected to fall within the frequency range which can be measured by light mixing techniques_ This possibility has been previously suggested by Jackson et al. [3] who studied scattered Iinewidths from solid polymethylmetbacrylate (PMMA). They found one temperature dependent and one temperature independent linewidth in the scattered light spectrum_ In that work most of the light scattered near the laser frequency was due to static inhomogeneities and the scattered intensity and linewidth were dependent on the region of the sample that was illuminated. The linewidths were observed using homodyne (alternatively
Volume 50, number 3
15 September 1977
CHEMICAL PHYSICS LETTERS
termed heterodyne) mixing in polarized scattering but not in depolarized scattered light. Ln addition to light scattering several other techniques are used to study molecular motion in solid polymers [4] including dynamical mechanical, dielectric, ultrasonic, nuclear magnetic resonance, neutron scattering, fluorescence and fluorescence/phosphorescence depolarization. Two main relaxations have been identified: the 01 and fi relaxations. The OLrelaxation observed above the glass transition temperature Tg is thought to correspond to segmental brownian motion of the polymer main chain. The fl relaxation has been attributed to brownian motion of the flexible side chains, however /3type relaxations are also found in po!ymers which do not contain a mobile side chain such as polyvinylchloride and in low molecular weight supercooled glasses [5] _ In solid polymers the (Y and /3 relaxations have characteristic frequencies in the range 10m2 to lo8 Hz depending on the temperature of the sample and at higher temperatures the OLand /3 relaxation frequencies merge.
were closely exponential. Because of the long structural relaxation times near Tg the sample was left for several hours at each set temperature to equilibrate. Results were taken over a wide range of correlation times and computer fitted to a single exponential and a background term. Some data was found not to produce a reasonable computer fit which may indicate the presence of more than one significant contribution to the linewidth. Improvements in the samples and experimental technique will then warrant a more precise analytic method extending the single exponential routines. The experimental linewidth r (hwhm) of the intensity fluctuation spectrum is related to the relaxation frequency fas, r = 4nf. Observing times for an individual correlation function were in the range of 10 to 60 minutes and depended on the temperature and time scale being used.
3. Results The observed temperature dependences of r are shown in fig. I_ A large number of measurements were
2. Techniques For this study the sample of “conventional” PMMA was supplied by I.C.I. Ltd. and was cut and polished into a rectangular block. To reduce static inhomogeneities the sample was initially annealed at 125°C for 48 hours. The intensity of light scattered from the sample dropped dramatically on annealing by about 5 times although there would still be residual scattering from dirt contamination. The Tg of the sample was measured by differential scanning calorimetry to be 38 1 -+ 1 K. Polarized photon correlation spectroscopy measurements were made using a single mode argon ion laser at a power of 100 mW at 488.0 mn, a fast photomultiplier detector (Mullard 56 AVP) selected for low intrinsic correlations and electronically shuttered and the signal was analysed by a 48 channel digital autocorrelator (Malvern Instruments type K 7023) with single channel clipping. After annealing the intensity of the dynamically scattered signal was sufficiently large to allow self-beating intensity fluctuation (or alternatively homodyne) mixing within one coherence area. Measurements were made as a function of temperature from 290 to A00 K and over a range of correlation time scales and the autocorrelation decay functions
1 22 I
25
3
35
l
‘4 JcIO’(K’I
I
450
400
350
300 T( KI
1. ?he temperature dependence of the intensity fluctuation linewidths (0) for solid PhIMA compared with dielectric
495
Volume 50, number 3
CHEMICAL PHYSICS LETTERS
taken at each stabilised temperature. The temperature range over which measurements could be made were restricted by experimental difficulties in determining the linewidth. The first important observation is that the analysed frequencies divide into two sets which are in approximate agreement with dielectric and dynamical mechanical QIand fl relaxation measurements, for example, as collected in McCrum et al. [4]. This indicates that photon correl.ation spectroscopy can observe structural fluctuations in polymers similar to those observed by these other techniques and confirms the one other report [3] of linewidths detected by this method. By variation of the correlation time scale the Q and p relaxations were detectable as they were well separated in frequency_ There is a systematic discrepancy on the Q! and, to a certain extent, the 0 frequencies which may mean that the light scattering technique detects a slightly different motion. From the single exponential fitting procedure there will be a contribution from the p process in the 01data which would tend to increase the apparent linewidth in line with the observations. Activation energies (in kJ mol-l) derived from the (Y and /3 frequencies are Ea =406*40and.IZfl=63*8. These values are similar to those from other techniques [4] of E, = 418460 for dielectric and &, = 334 for mechanical and ED = 79-96 for dielectric and EC,= 71-125 for mechanical measurements. Using the present experimental techniques there is some evidence for the presence of more than one component in the central peak. Further refinement in the samples and technique may enable the separation of other components to be made.
4. Discussion An explanation of the temperature independent linewidths observed by Jackson et al. [3] but not observed here may be that frozen-in excess free volume causes additional relaxation times until temperatures approaching Tg are reached. Then such frozen-in stresses
15 September 1977
This and earlier work [3] demonstrates that photon correlation spectroscopy is a new technique to observe relaxation in solid polymers andealso, as mentioned earlier, in concentrated systems. An advantage of this light scattering method is that the sample is observed with little perturbation. A number of questions are raised by this work; one of these is the precise nature of the scattering mechanism and the relative importance of thermal density fluctuations, chain diffusion into free volume and regions occupied by unreacted monomer, diffusion of short range and long range regions of order and intramolecular diffusion. Other points of interest are the range of applicability of the technique and whether new relaxations may be observed, for example, in polymeric solids. There have been several modeis proposed for the polymeric arnorphous state. These range from the polymer having a conformation as in the unperturbed state to a conformation including a large degree of local order. Observations on amorphous polymers by new techniques should provide fresh information on this subject as, for example, has neutron scattering and photon correlation spectroscopy may be a new and useful probe in this study.
Acknowledgement We are grateful to Dr. P. Lamb and Dr. F.M. Willmouth of I.C.I. Ltd., Plastics Division, for providing the PMMA sample and to Dr. G. Howard of the Department of Polymer and Fibre Science, UMIST, for the measurement of Tg. We thank the Science Research Council for a postdoctoral fellowship for MFT and for equipment support.
References P.A. Fleury and J.P. Boon, Advan. Chem. Phys. 24 (1973) 1. R-S. hlitchell and J.E. Guillet, J. Pol. Sot. 12 (1974) 713. D.A. Jackson, E.P. Pike, J.G. Powles and J.M. Vaughan,
would disappear. Also relaxation to equilibrium after altering the sample temperature may contribute a low
J. Phys. C 6 (1973) L55. N.G. McCrum, B.E. Read and G. Williams, Anelastic and
frequency relaxation. It is known that the scattered intensity of EMMA depends on its thermal history [2,6] _ The lengthy annealing time and the long time allowed for equilibration at each set temperature in this study should minimise these effects.
dielectric effects on polymeric solids Wiley. New York, 1967). G.P. Johari and M. Goldstein, J. Chem. Phys. 53 (1970) 2372. M. Dettenmaier and E.W. Fischer, KolIoid Z. Z. Pal. 251 (1973) 922.
496
CHEMICAL PHYSICS LETTERS
number 3
MOLECULAR DETECTED
MOTION BY PHOTON
15 September
1977
IN SOLID POLYMERS CORRELATION
SPECTROSCOPY
T.A. KING and M.F. TREADAWAY
Ph_vsics Department. Schuster Laboratory. Manchester Ml3 9PL. UK
University of Manchester,
Rcceivcd 10 Xl.~y IS77
Xloleculnr rclawtion in the lo-lo6 liz region in rl solid amorphous polymer PXIhlA has been detected by photon correlation spectroscopy. Relaxation times are found to depend strongly on sample annealing and sample temperature equilibration. The main relaxation frequencies. determined around the glass-rubber transition Tr are in good correspondence with values obtained by other methods.
1_ Introduction Molecular
relaxation
in a solid amorphous
polymer
detected by photon correlation spectroscopy is reported here. The observed relaxation times are in good correspondence with values obtained by dielectric and dynamical mechanical methods. A strong dependence on sample annealing and on temperature equilibration has been found. Light scattering is able to probe optical inhomogeneities and local structure in samples [ I] _ Isobaric and adiabatic density fluctuations lead to three components, respectively the central Rayleigh peak centred around the incident frequency and the Brillouin doublets. Rayleigh-Brillouin scattering derives contributions in addition to thermal density fluctuations from orientation fluctuations, structural relaxations and twocomponent and impurity concentration fluctuations. The coupling between structural relaxations and collective density fluctuation modes also produces a central component, the Mountain line. In a solid amorphous polymer this line is expected to have a sufflciently narrow frequency width to be mixed in with-the other central components_ We look here particularly at the light scattered spectrum of the central component derived from a solid amorphous polymer. Motion in solid polymers may be expected to be detectable by light scattering into the 494
central Rayleigh scattered component from thermal density fluctuations arising from brownian diffusion of polymer segments, by diffusion of small scale structural order, by large scale order (if it exists in the sample) or by diffusion of microcrystalline regions [2]. Also scattering into the central component may result from the diffusion and orientational fluctuations of parts of the chain having anisotropic polarizability. Elastic light scattering has been used previously to investigate static structure in solid polymers and dynamical information should be derived from measurements of the linewidth of this scattered light. There have now been several studies by photon correlation spectroscopy on concentrated polymer systems including solutions and networks and extension to bulk materials appears feasible even in the presence of intermolecular correlations. For solid polymers the linewidths are expected to fall within the frequency range which can be measured by light mixing techniques_ This possibility has been previously suggested by Jackson et al. [3] who studied scattered Iinewidths from solid polymethylmetbacrylate (PMMA). They found one temperature dependent and one temperature independent linewidth in the scattered light spectrum_ In that work most of the light scattered near the laser frequency was due to static inhomogeneities and the scattered intensity and linewidth were dependent on the region of the sample that was illuminated. The linewidths were observed using homodyne (alternatively
Volume 50, number 3
15 September 1977
CHEMICAL PHYSICS LETTERS
termed heterodyne) mixing in polarized scattering but not in depolarized scattered light. Ln addition to light scattering several other techniques are used to study molecular motion in solid polymers [4] including dynamical mechanical, dielectric, ultrasonic, nuclear magnetic resonance, neutron scattering, fluorescence and fluorescence/phosphorescence depolarization. Two main relaxations have been identified: the 01 and fi relaxations. The OLrelaxation observed above the glass transition temperature Tg is thought to correspond to segmental brownian motion of the polymer main chain. The fl relaxation has been attributed to brownian motion of the flexible side chains, however /3type relaxations are also found in po!ymers which do not contain a mobile side chain such as polyvinylchloride and in low molecular weight supercooled glasses [5] _ In solid polymers the (Y and /3 relaxations have characteristic frequencies in the range 10m2 to lo8 Hz depending on the temperature of the sample and at higher temperatures the OLand /3 relaxation frequencies merge.
were closely exponential. Because of the long structural relaxation times near Tg the sample was left for several hours at each set temperature to equilibrate. Results were taken over a wide range of correlation times and computer fitted to a single exponential and a background term. Some data was found not to produce a reasonable computer fit which may indicate the presence of more than one significant contribution to the linewidth. Improvements in the samples and experimental technique will then warrant a more precise analytic method extending the single exponential routines. The experimental linewidth r (hwhm) of the intensity fluctuation spectrum is related to the relaxation frequency fas, r = 4nf. Observing times for an individual correlation function were in the range of 10 to 60 minutes and depended on the temperature and time scale being used.
3. Results The observed temperature dependences of r are shown in fig. I_ A large number of measurements were
2. Techniques For this study the sample of “conventional” PMMA was supplied by I.C.I. Ltd. and was cut and polished into a rectangular block. To reduce static inhomogeneities the sample was initially annealed at 125°C for 48 hours. The intensity of light scattered from the sample dropped dramatically on annealing by about 5 times although there would still be residual scattering from dirt contamination. The Tg of the sample was measured by differential scanning calorimetry to be 38 1 -+ 1 K. Polarized photon correlation spectroscopy measurements were made using a single mode argon ion laser at a power of 100 mW at 488.0 mn, a fast photomultiplier detector (Mullard 56 AVP) selected for low intrinsic correlations and electronically shuttered and the signal was analysed by a 48 channel digital autocorrelator (Malvern Instruments type K 7023) with single channel clipping. After annealing the intensity of the dynamically scattered signal was sufficiently large to allow self-beating intensity fluctuation (or alternatively homodyne) mixing within one coherence area. Measurements were made as a function of temperature from 290 to A00 K and over a range of correlation time scales and the autocorrelation decay functions
1 22 I
25
3
35
l
‘4 JcIO’(K’I
I
450
400
350
300 T( KI
1. ?he temperature dependence of the intensity fluctuation linewidths (0) for solid PhIMA compared with dielectric
495
Volume 50, number 3
CHEMICAL PHYSICS LETTERS
taken at each stabilised temperature. The temperature range over which measurements could be made were restricted by experimental difficulties in determining the linewidth. The first important observation is that the analysed frequencies divide into two sets which are in approximate agreement with dielectric and dynamical mechanical QIand fl relaxation measurements, for example, as collected in McCrum et al. [4]. This indicates that photon correl.ation spectroscopy can observe structural fluctuations in polymers similar to those observed by these other techniques and confirms the one other report [3] of linewidths detected by this method. By variation of the correlation time scale the Q and p relaxations were detectable as they were well separated in frequency_ There is a systematic discrepancy on the Q! and, to a certain extent, the 0 frequencies which may mean that the light scattering technique detects a slightly different motion. From the single exponential fitting procedure there will be a contribution from the p process in the 01data which would tend to increase the apparent linewidth in line with the observations. Activation energies (in kJ mol-l) derived from the (Y and /3 frequencies are Ea =406*40and.IZfl=63*8. These values are similar to those from other techniques [4] of E, = 418460 for dielectric and &, = 334 for mechanical and ED = 79-96 for dielectric and EC,= 71-125 for mechanical measurements. Using the present experimental techniques there is some evidence for the presence of more than one component in the central peak. Further refinement in the samples and technique may enable the separation of other components to be made.
4. Discussion An explanation of the temperature independent linewidths observed by Jackson et al. [3] but not observed here may be that frozen-in excess free volume causes additional relaxation times until temperatures approaching Tg are reached. Then such frozen-in stresses
15 September 1977
This and earlier work [3] demonstrates that photon correlation spectroscopy is a new technique to observe relaxation in solid polymers andealso, as mentioned earlier, in concentrated systems. An advantage of this light scattering method is that the sample is observed with little perturbation. A number of questions are raised by this work; one of these is the precise nature of the scattering mechanism and the relative importance of thermal density fluctuations, chain diffusion into free volume and regions occupied by unreacted monomer, diffusion of short range and long range regions of order and intramolecular diffusion. Other points of interest are the range of applicability of the technique and whether new relaxations may be observed, for example, in polymeric solids. There have been several modeis proposed for the polymeric arnorphous state. These range from the polymer having a conformation as in the unperturbed state to a conformation including a large degree of local order. Observations on amorphous polymers by new techniques should provide fresh information on this subject as, for example, has neutron scattering and photon correlation spectroscopy may be a new and useful probe in this study.
Acknowledgement We are grateful to Dr. P. Lamb and Dr. F.M. Willmouth of I.C.I. Ltd., Plastics Division, for providing the PMMA sample and to Dr. G. Howard of the Department of Polymer and Fibre Science, UMIST, for the measurement of Tg. We thank the Science Research Council for a postdoctoral fellowship for MFT and for equipment support.
References P.A. Fleury and J.P. Boon, Advan. Chem. Phys. 24 (1973) 1. R-S. hlitchell and J.E. Guillet, J. Pol. Sot. 12 (1974) 713. D.A. Jackson, E.P. Pike, J.G. Powles and J.M. Vaughan,
would disappear. Also relaxation to equilibrium after altering the sample temperature may contribute a low
J. Phys. C 6 (1973) L55. N.G. McCrum, B.E. Read and G. Williams, Anelastic and
frequency relaxation. It is known that the scattered intensity of EMMA depends on its thermal history [2,6] _ The lengthy annealing time and the long time allowed for equilibration at each set temperature in this study should minimise these effects.
dielectric effects on polymeric solids Wiley. New York, 1967). G.P. Johari and M. Goldstein, J. Chem. Phys. 53 (1970) 2372. M. Dettenmaier and E.W. Fischer, KolIoid Z. Z. Pal. 251 (1973) 922.
496