Ricardo
Medrano
,
M. Teresa R.
Laguna
,
Enrique
Saiz
and
M. Pilar
Tarazona
Departamento de Química Física, Universidad de Alcala, 28871 Alcalá de Henares, Spain. E-mail: enrique.saiz@uah.es; Fax: +34 91 8854763
First published on 26th November 2002
Size exclusion chromatography (SEC) with differential refractive index (RI), multiangle light scattering (MALS) and UV detectors has been used to obtain information about copolymers of styrene (S) and methyl methacrylate (MMA). Homopolymers PS and PMMA having broad molecular weight distributions, mixtures of PS and PMMA homopolymers, and copolymers containing different weight fractions of S and MMA units were studied. Molecular weight distributions, molecular dimensions and scaling laws are reported for these systems. The behavior of the random copolymers is very different from that exhibited by the heterogeneous mixtures of homopolymers. Thus, the results obtained for the copolymers can be explained by assuming that these molecules have homogeneous distributions of S and MMA units along their chains. On the contrary, the mixtures produce the results that would be expected from heterogeneous combinations of different molecules. The SEC technique offers the possibility of determining the composition of random copolymers and discriminating among random copolymers (having homogeneous distributions of units) and block copolymers.
The use of SEC with several detectors for providing quantitative information on copolymer composition and molecular weight distribution has been studied during the last decades.10–13 However, this use is complicated by the fact that the heterogeneity of the copolymer may influence the relationship of dimensions and molecular weight. In this sense, the light scattering detector which affords both dimensions and molecular weights simultaneously, seemed a promising technique and it has been studied intensively in recent years.14–18 Unfortunately, the heterogeneity in the chemical composition of the copolymer can also affect the value of the refractive index increment along the chromatogram and therefore may introduce errors in the magnitudes obtained with both differential refractive index and light scattering detectors.19
In this paper we describe a modification of the technique consisting in the addition of a new concentration sensitive detector, i.e. employing differential refractive index (RI), multiangle light scattering (MALS) and ultraviolet (UV) detectors. This combination allows the study of systems containing two different kinds of repeating units, such as copolymers with different sequences or mixtures of homopolymers, and provides magnitudes of interest from the physicochemical point of view such as molecular weight distributions and averages, chain shape and dimensions, scaling law coefficients, etc. for these systems. Three different kinds of systems have been studied, namely: (a) polystyrene (PS) and poly(methyl methacrylate) (PMMA) homopolymers with broad molecular weight distributions, (b) random styrene–methyl methacrylate copolymers containing different weight fractions of both monomers and (c) Mixtures of PS and PMMA homopolymers. Thus, the influence of the chemical homogeneity on the measured magnitudes can be studied since the mixtures of homopolymers are heterogeneous while the random copolymers are supposedly homogeneous. In fact, the copolymerization of styrene and methacrylate has been widely studied and it is used frequently as a model of free radical polymerization.20–23
Copolymers were prepared according to the following procedure: 20 mg of AIBN were added to four large Pyrex tubes capped with serum stoppers. The tubes were evacuated and flushed with dry nitrogen. The following monomer amounts were injected with a syringe: 4 ml MMA and 16 ml STY (Polymer A); 8 ml MMA and 12 ml STY (Polymer B); 12 ml MMA and 8 ml STY (Polymer C); 16 ml MMA and 4 ml STY (Polymer D). The tubes were shaken and placed in a constant temperature bath at 75°C for 2.5 h. Then the polymers were precipitated into methanol and dried in a vacuum oven. The reactivity ratios for radical copolymerization of styrene and methyl methacrylate are24rS
≈
0.48, rMMA
≈
0.46. Application of the copolymer equation with these values of r allows the evaluation of the composition of the copolymer formed at the first stages of the reaction (i.e. at low conversion) as function of the composition of the reaction mixtures. The composition calculated in this fashion for samples A through D are given as weight fraction of styrene in the second column of Table 1.
System | w S (Ec. copolymer) | w S (1H NMR) | (dn/dc)/ml g−1 | w S (eqn. (3)) | M i RI/MiUV (eqn. (14)) | w S (eqn. (18)) |
---|---|---|---|---|---|---|
A | 0.73 | 0.63 | 0.152 | 0.68 | 0.79 | 0.79![]() ![]() |
B | 0.57 | 0.51 | 0.145 | 0.61 | 0.63 | 0.56![]() ![]() |
C | 0.44 | 0.41 | 0.130 | 0.45 | 0.49 | 0.38![]() ![]() |
D | 0.38 | 0.35 | 0.124 | 0.39 | 0.36 | 0.26![]() ![]() |
PMMA | 0.087 | 0 | ||||
PS | 0.182 | 1 | ||||
M1 | 0.166 | 0.83 | ||||
M2 | 0.138 | 0.54 |
Two mixtures of PS and PMMA homopolymers were prepared from weighted amounts of PS and PMMA. Their weight fraction of styrene were wS=
0.83 (mixture M1) and wS
=
0.54 (mixture M2).
The differential refractive index increments for the polymers in THF solution were measured with a Brice–Phoenix differential refractometer at 436 and 546 nm, at 25°C, and extrapolated to 632.8 nm using the Cauchy relationship.6
The 1H NMR spectra of the copolymers were obtained with a UNITY 300-MHz. The composition was determined in two ways. The molar fraction of styrene units can be obtained by multiplying the integral of aromatic protons by a factor of 8/5 and dividing this quantity by the sum of the integrals for all of the protons.20 Also, the molar fraction of styrene can be determined from the relationship between the aromatic protons of the styrene units and the methoxy protons of the methyl methacrylate units, which appear between δ values of 2.2 and 3.5 ppm.22 Both procedures gave the same results that are presented in the third column of Table 1 as weight fraction of styrene units.
Fig. 1 shows the raw signals from the detectors versus elution volume for both PS and PMMA homopolymers. In the case of PMMA only the RI signal is given because the UV detector does not see this polymer. These raw data were converted into true molecular weight distributions (MWD) by transforming detector signals into weight fractions and measuring molar masses at each elution volume with the MALS detector. The MWD of both polymers are shown in Fig. 2. The molecular weight averages obtained for PMMA are: Mn=
(3.4
±
0.2)
×
105, Mw
=
(6.3
±
0.2)
×
105 g mol−1, polydispersity ratio r
=
Mw/Mn
=
1.9.
![]() | ||
Fig. 1 Raw signal from the detectors as function of elution volume for PMMA (solid line: RI detector) and PS (dash line: UV and dot line: RI detectors) homopolymers. |
![]() | ||
Fig. 2 Molecular weight distributions for PMMA (solid line, obtained from RI detector) and PS (dash line from UV and dot line from RI) homopolymers. |
Both detectors see the PS, and the data obtained from UV are shown as dash lines in Figs. 1 and 2 while data from RI are represented by dot lines. The UV signal for a homopolymer solution having mass concentration c is given by:
SUV![]() ![]() | (1) |
![]() | (2) |
However, the normalization required to transform raw signals into weight fractions eliminates the k response factors of both detectors and the refractive index increment of the RI detector, so that both kinds of signals should provide the same MWD distribution, as the comparison of dot and dash lines of Fig. 2 indicates. Molecular weight averages obtained for the PS homopolymer from both detectors agree within experimental errors providing: Mn=
(8.1
±
0.5)105, Mw
=
(13.0
±
0.4)
×
105 g mol−1, r
=
Mw/Mn
=
1.6.
![]() | (3) |
![]() | (4) |
![]() | (5) |
When a light scattering detector is employed in SEC, the polymer concentration used is very small so that the 2A2c and higher terms are negligible and thus eqn. (4) can be expressed for slice i of the chromatogram as:
![]() | (6) |
The MALS detector measures simultaneously the excess Rayleigh ratio at different θ angles for each slice i which is assumed to be monodisperse both in composition and molecular weight.4,6 Thus, a plot of K′(dn/dc)2ici/(ΔRθ)iversus sin2(θ/2), affords to calculate the molecular weight Mi from the intercept and the radius of gyration, 〈s2〉i, from the slope for each slice of the chromatogram.
In the case of a copolymer the value of the refractive index increment of a given slice (dn/dc)i depends on chemical composition according to eqn. (3). This magnitude coincides with the mean refractive index increment of the whole sample dn/dc only if the chemical composition is homogeneous throughout the chromatogram. If the composition of eluted copolymer varies as a function of the volume of elution, the refractive index increment (dn/dc)i will change. When the refractive index increment of the whole sample is used instead the true (dn/dc)i for each slice, indeterminations are introduced and apparent molecular weights can be obtained.11,15,16
![]() | (7) |
When the SRIi signal is transformed into a mass concentration datum, a mean value dn/dc of the refractive index increment is employed to integrate the peak of the whole sample. The mass concentration ci thus obtained will be the true concentration if the (dn/dc)i coincides with the mean value dn/dc. If this condition is not fulfilled, an apparent concentration16 will be obtained:
![]() | (8) |
![]() | (9) |
Unlike RI, the response factor of the UV detector depends on the chemical nature of the sample. Thus, the signal produced by the ith slice of a chromatogram obtained from a sample containing different chemical species would be:
![]() | (10) |
In the present case, we have two different repeating units namely styrene and methyl methacrylate. However, at λ=
262 nm employed by the UV detector, (kUV)MMA
=
0 while (kUV)S
≠
0 so that eqn. (10) only contains the term corresponding to S units:
SUVi![]() ![]() ![]() ![]() | (11) |
The apparent molecular weight calculated with this SUVi using eqn. (6) with the value of dn/dc for the whole sample and extrapolated to zero angle will then be:
![]() | (12) |
![]() | (13) |
In the case of a perfectly homogeneous system, for instance a PS homopolymer, neither the composition (wi)S, nor refractive index increment do depend on molecular weight, so that local and mean values of these magnitude will coincide and eqn. (13) reduces to:
![]() | (14) |
The situation would be very similar for a perfectly homogeneous styrene–methyl methacrylate copolymer. Both the composition and the refractive index increment would again be independent of the slice studied and eqn. (14) will hold providing a constant value of wS, which of course would be smaller than unity, throughout the whole chromatogram.
On the contrary, an heterogeneous sample such a mixture of PS and PMMA homopolymers or a block copolymer of those two units would show molecular weight dependence on both the composition and refractive index increment and therefore the ratio MRIi/MUVi will be different from one slice to another.
Thus, the ratio between the apparent molecular weights obtained with these two detectors offers a simple way of analyzing random copolymers of S and MMA units allowing the determination of the composition and, what may be more interesting, deciding whether or not the distribution of monomer units along the copolymer chain is really random.
On the other hand, the ratio of responses of UV and RI detectors at the same elution volume can yield information about the composition of the copolymer.10 This ratio can be expressed combining eqns. (11), (7) and (3) as:
![]() | (15) |
That can be solved for the styrene weight fraction at elution point i:
![]() | (16) |
Application of eqns. (1) and (2) to the PS homopolymer and division among them allows the evaluation of the ratio kUVS/kRI between the response factors of the detectors as function of the ratio RSi among the signals obtained for PS:
![]() | (17) |
Substitution of eqn. (17) into eqn. (16) gives:
![]() | (18) |
This equation holds only if the UV response factor of styrene units, through the absorption coefficient, is the same independently of their position in the homopolymer, copolymers, and mixtures. However, assuming that this condition is fulfilled, eqn. (18) provides another way of determining the composition of the copolymer and deciding whether or not this composition is homogeneous along the chains.
![]() | ||
Fig. 3 Chromatogram for polystyrene showing the RI signal (solid line) UV signal (dashed line) and the MALS signal at 90° (dotted line). Solid circles are the values of RSi used in eqns. (17) and (18). |
Fig. 4 shows the molecular weight of all the systems studied, calculated from the scattered light, plotted versus the elution volume. The signals from the differential refractive index detector have also been plotted in the same figure. The plots of molecular weight versusve are linear and the uncertainties in the tails or heads of the molecular weight distributions are much easily discernable from the scattering in data points of the calibration curve than from the raw chromatograms. For the homopolymers PS and PMMA, these plots are their respective absolute calibration curves for SEC whereas for the copolymers and mixtures the molecular weight can be an apparent molecular weight if the (dn/dc)i of each slice is different than the dn/dc of the whole sample according to eqn. (6). Since the values of the Mark–Houwink parameters in THF for both PS and PMMA are comparable,29 the values of the absolute calibration curves for all polymers are very similar. The data for copolymers, A through D, is more scattered than that of homopolymers, PS and PMMA, and mixtures, M1 and M2. This is because the molecular weights of the copolymers are considerably lower than the other polymers and are thus susceptible to higher experimental errors. Although the solution properties of a random copolymer are not strictly the weighted averaged of the homopolymer properties, it has been shown that the average approximation is valid for the calibration curve for random copolymers of styrene and methyl methacrylate in THF.20 This result is in agreement with the fact that their calibration curves are alike as explained above.
![]() | ||
Fig. 4 Logarithm of molecular weight versus elution volume for all the systems studied. The corresponding RI signals are also shown. |
The first difference between the copolymers (samples A, B, C and D) and the mixtures (samples M1 and M2) can be qualitatively observed in Fig. 4. The RI signals of the different copolymers have almost identical shape and the main differences are displacements along the volume axis due to their distinct molecular weight produced because of the differences in the polymerization process. However, in the mixtures, the signal for M1, that has a larger MMA content, becomes noticeably higher that that of M1 at elution volumes beyond 11.5 ml. Moreover, the slope of the calibration curve is larger for M2 than for M1. These facts support the previous assumptions about the different homogeneity of copolymers and mixtures. If copolymers A through D are random, then they should be much more homogeneous than the prepared mixtures that are completely heterogeneous. These qualitative arguments will be supported by further quantitative results presented below.
Solid lines in Figs. 5 and 6 present the absolute molecular weight distributions of the copolymers (Fig. 5) and the mixtures (Fig. 6) calculated from the combined measurements of molecular weight (MALS detector) and concentration (RI detector). The dots on these figures show the styrene weight fractions (wi)S calculated using eqn. (18), for each slice of the central part of the chromatogram. At the head and tail parts of the chromatograms the values of the styrene weight fraction are very disperse due to the errors in the ratio of the signals of UV and RI and are no represented in the figure. The differences in the values of (wi)S for copolymers and mixtures due to the different heterogeneity of the sample are clearly appreciable in both figures. Thus, the calculated values of (wi)S for copolymers are constant within experimental error whereas (wi)S for mixtures increases as the molecular weight grows (elution volume diminishes). This is a consequence of the different molecular weights of the two homopolymers used to prepare the samples. Thus, as the top panel on Fig. 4 shows, PS chains are, in average, larger than PMMA's. Consequently, when the mixture elutes through the column, the first portions (i.e. low elution volume and high molecular weight) will be richer in PS than the last ones. Thus, the behavior of (wi)S through the chromatogram provides information about the heterogeneity of the system allowing discrimination between homogeneous and heterogeneous copolymers. The average values of wS obtained for the copolymers A through D are presented in the seventh column of Table 1. The agreement of these values of wS and those obtained by dn/dc (fifth column) or NMR (third column) is qualitatively good and the quantitative differences can be attributed to several features. First, errors in the analysis of the chromatograms, especially in the determination of the base lines, can significantly affect the value of the ratio of the UV/RI signals ratio for PS, RSi and thus, the final results.22 Second, in the deduction of eqn. (18), it has been assumed that the UV response factor of styrene does not depend on the micro heterogeneity of the polymer.
![]() | ||
Fig. 5 Molecular weight distributions for copolymers A through D calculated from MALS and RI detector (solid lines) or MALS and UV detector (broken line). Solid circles represent the values of styrene weight fraction calculated according to eqn. (18). |
![]() | ||
Fig. 6 Apparent molecular weight distributions and styrene weight fraction for each slice of mixtures M1 and M2. See legend of Fig. 3. |
Broken lines in Figs. 5 and 6 represent the MWDs calculated with concentrations obtained by the UV detector instead of the RI detector. It is interesting to compare the apparent MWD of each sample (copolymer or mixture) obtained using RI or UV as the concentration detectors. According to eqn. (8), the concentration seen by the RI detector will be an apparent concentration if the (dn/dc)i does not coincide with the dn/dc of the whole sample. On the other hand, the concentration that sees the UV detector is proportional to the concentration of the styrene units (eqn. (11)) of the copolymer. As can be seen in Fig. 5, the MWDs obtained with both detectors for each copolymer are similar in form although they are displaced along the molecular weight axe. The similarity in the form supports the random composition of the copolymers A through D, whereas the displacement is a consequence of the differences in the molecular weights calculated according eqns. (9) and (12). On the contrary, the MWDs of each mixture (Fig. 6) obtained using RI and UV detectors are different since they are heterogeneous samples. The sixth column on Table 1 presents the averaged values of the ratio MRIi/MUVi for copolymers A through D. According to eqn. (14), this ratio is the polymer composition expressed as weight fraction of styrene units.
![]() | ||
Fig. 7 Log–log plot of root mean squared radius of gyration versus molecular weight for the polymers. |
Polymer | 10−5Mn | 10−5Mw | 103Q | q |
---|---|---|---|---|
PS | 8.1![]() ![]() |
13.0![]() ![]() |
12.4![]() ![]() |
0.59![]() ![]() |
PMMA | 3.4![]() ![]() |
6.3![]() ![]() |
7.2![]() ![]() |
0.61![]() ![]() |
A | 1.43![]() ![]() |
2.8![]() ![]() |
5![]() ![]() |
0.65![]() ![]() |
B | 1.32![]() ![]() |
2.9![]() ![]() |
12![]() ![]() |
0.60![]() ![]() |
C | 1.1![]() ![]() |
2.3![]() ![]() |
20![]() ![]() |
0.57![]() ![]() |
D | 1.04![]() ![]() |
2.2![]() ![]() |
16![]() ![]() |
0.58![]() ![]() |
M1 | 7.7![]() ![]() |
15.3![]() ![]() |
12.6![]() ![]() |
0.59![]() ![]() |
M2 | 4.5![]() ![]() |
14.1![]() ![]() |
11.0![]() ![]() |
0.59![]() ![]() |
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