LABORATORY “2”
Gel Permeation Chromatography (GPC)
of Polystyrene
Mohammed Alzayer
Chris Clay
Xinhang Shen
Mat E 453
Lab Section 2
September 16, 2014
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ABSTRACT
In polymer science, polydispersity index (PDI) is an important measure of the sizes of
molecules present in a given polymer. In order to get an estimate of this number, there are
several size separation techniques used that allow PDI to be determined indirectly. Those
size exclusion methods include gel permeation chromatography (GPC). In this lab, a
sample of polystyrene (PS) was analyzed to determine the molecular weight averages,
PDI, and degree of polymerization.
1. INTRODUCTION
1.1 GPC Background
Gel permeation chromatography (GPC) is a separation
technique that helps determine the molecular weight
distribution of polymeric materials. The
chromatographic method works by placing rigid gel
beads, also known as the stationary phase, in a column
(Figure 1). Even though the term GPC is commonly
used by researchers, “size exclusion chromatography”
Figure 1. Gel Permeation
Chromatography columns. [1]
is the more accurate term to describe the technique
since the stationary phase is usually not a gel.
These beads are non-ionic and contain pores in variety of sizes; they are usually made of
highly cross-linked polystyrene
or glass (Figure 2)[2].
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The polymeric sample, dissolved in an
appropriate solvent, flows through the column
along with the beads. The polymer molecules
diffuse into the bead’s pores. The larger the
molecule, the fewer pores it can enter and the
Figure 2. Beads used for GPC [3]
less time it takes to elute. The time a molecule
spends inside the column is referred to as the elution time. Therefore, in GPC, elution
time is the parameter that indirectly measures the molecular weight distribution of a
polymer since it distinguishes the sizes of molecules in a given sample [2].
The elution time is easily recorded by a detector after the molecules are separated and
eluted from the column. One of the most common detectors used is the differential
refractive index detector (RI), which compares the refractive index of the sample solution
to that of a reference solution. The difference in refractive index will be proportional to
the concentration of eluent. Another common detector measures the absorption of UV
radiation at a specific wavelength. The amount of radiation absorbed is proportional to
the concentration of eluent. Light scattering detectors make use of the fact that the
amount of light scatter by a polymer is proportional to the mass of the polymer squared.
1.2 Solvent Selection
The stationary phase size falls between 3 to 20µm while its pores are in the order of 50Å
to 100 nm. The number of pores in the beads, just like their sizes, is random [4]. In order
to test a polymer using GPC, the sample must be in a diluted form in order to be able to
get inside the pores of the stationary phase. The solvent used in the polymer solution
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must be selected carefully depending on the type of the polymer molecules. There are
several types of solvents. Polar protic solvents include water and alcohols while dipolar
aprotic solvents include other solvents such as DMF, DMSO, and acetone. Finally, there
are nonpolar solvents such as THF and benzene [4]. Following the ‘like dissolves like’
rule, a nonpolar polymer would dissolve in a nonpolar solvent. For example, in this lab, a
nonpolar solvent (chloroform) was used to dissolve polystyrene. There are other factors
that contribute to the process of solvent selection. Other than the ability to dissolve the
sample, the solvent must be inert to the material used in the column. It must also be able
to withstand the operating temperature range. Another important factor is the solvent’s
ability to easily separate from solute [4].
1.3 Molecular Weight Distribution
There are number of parameters that can be used to characterize the size of a polymer
chain. These include the number average molecular weight (Mn), the weight average
molecular weight (Mw), polydispersity index (PDI), and the average degree of
̅̅̅̅ ).
polymerization (𝐷𝑃
The number average molecular weight is the total weight of a sample divided by the
number of molecules within the sample and is given by Equation 1:
𝑀𝑛 =
∑𝑖 𝑁𝑖 𝑀𝑖
∑𝑖 𝑁𝑖
,
(1)
where
Mn : number average molecular weight,
Ni : number of polymeric chains,
Mi : the molecular weight of chains Ni .
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The weight average molecular weight uses the weight fraction of weight range and
divides by the total weight of the sample. Mw is typically bigger than Mn. Mw can be
calculated using Equation 2:
𝑀𝑤 =
∑𝑖 𝑁𝑖 𝑀𝑖 2
∑𝑖 𝑁𝑖 𝑀𝑖
=
∑𝑖 𝑤𝑖 𝑀𝑖
∑𝑖 𝑤𝑖
,
(2)
where
𝑀𝑤 : weight average molecular weight,
𝑁𝑖 : number of polymeric chains,
𝑀𝑖 : the molecular weight of chains 𝑁𝑖 .
𝑤𝑖 : Weight of chains 𝑁𝑖 which equals 𝑁𝑖 𝑀𝑖 .
The PDI gives information about how the molecular weight varies and is calculated by
taking the ratio of the Mw and Mn (Equation 3):
𝑃𝐷𝐼 =
𝑀𝑤
𝑀𝑛
,
(3)
where
𝑃𝐷𝐼: polydispersity index,
𝑀𝑤 : weight average molecular weight,
𝑀𝑛 : number average molecular weight.
The degree of polymerization tells how many monomers are present in the average
polymer and can be calculated using Equation 4:
̅̅̅̅ = 𝑀 ,
𝐷𝑃
𝑀
(4)
0
where
̅̅̅̅
𝐷𝑃 : average degree of polymerization,
𝑀: molecular weight of polymer (can be either 𝑀𝑤 or 𝑀𝑛 ),
𝑀0 : number average molecular weight.
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2. EXPERIMENTAL PROCEDURES
2.1 Materials
Rubber gloves, goggles, electric balance, extraction needle, measuring glass, beakers,
GPC column, intensity detector, and computer.
2.2 Sample Preparation
1. 25 mg of polystyrene from the previous lab was added to 5 mL of HPLC
grade chloroform to make a 5 mg/mL solution.
2. Five mL of solution were drawn into a 5 mL syringe and filtered with
0.45 µL filter. (Figure 3).
3. 1.5 mL of solution were placed in a 2 mL vial.
4. The carousel for the GPC was pulled out, and the vial was placed inside.
Note the position of the vial (number slot).
5. Sample location and name were entered in the “Sample Queue”
Figure 3. Filtering the
polystyrene solution. [1]
spreadsheet in the computer software.
6. The “Inject Broad Samples” function was used with the method of “201202013_PS”.
7. A Run Time of 30 minutes was used.
8. The Inj. Vol. used was 25 µL.
9. The number of injections was set to 1, with 1 minute being allowed per injection.
10. The method was run for 30 minutes. Data was collected in real time and saved.
11. The sample vial was removed from the carousel.
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3. RESULTS
3.1 Raw Data
The raw data from the GPC came in the format of a spreadsheet with time and intensity
columns. These can be plotted to obtain Figure 4:
GPC Curve
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21
Intensity
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6
1
-4
1
6
11
16
21
26
-9
-14
Elution Time (min)
Figure 4. Entire GPC curve for PS sample (400 mg
BPO)
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As the relevant data occurs in the 15 to 27 minute range, a separate plot can be generated
for this range so the details can be seen more clearly (Figure 5).
GPC Curve for Analysis
2.5
Intensity
2
1.5
1
0.5
0
15
17
19
21
23
25
27
29
Elution Time (min)
Figure 5. Zoomed in GPC curve for PS sample (400
BPO) (15.8 to 27 mins)
3.2 Calibration Curve
Based on the elution time and molecular weight data for a polystyrene monodispersed
standard (Appendix, Table 1,) a log MW vs elution time curve was plotted (Figure 6). A
linear function was fit to this data, allowing the molecular weight of any polystyrene
sample to be calculated from the elution time. For example, if the elution time of a PS
segment is 15.8, its log molecular weight should be - 0.2859(15.8) + 9.8625= 5.35 and
taking the inverse of log yields a molecular weight of 221452 g/mol.
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log MW vs Elution Time
6.5
6
5.5
y = -0.2859x + 9.8625
R² = 0.9832
log MW
5
4.5
4
3.5
3
2.5
2
13
15
17
19
21
23
25
Elution Time (min)
Figure 6. Standard plot log Mw vs elution time
3.3 Polydipersivity Index and Degree of Polymerization
As explained in section 3.2, the molecular weights of the sample segments were
calculated using the equation obtained from the standard monodispersed PS. Hence, it
was possible to calculate N, the number of polymeric chains, by multiplying the
molecular weight by the peak intensity. Only the peak between 15.8 min and 27 min was
analyzed.
Using the equations listed in section 1.2, it was possible to get an estimate of both the
polydispersity index and the average degree of polymerization. To get an estimate of the
PDI, 𝑀𝑛 and 𝑀𝑤 must be determined first. Having both M and N calculated as stated
above, “N×M” and “N× 𝑀2 ” were calculated as well. In order to calculate 𝑀𝑛 , the
numbers in the N column were summed up. The numbers in N×M column were summed
up as well. 𝑀𝑛 was finally calculated by dividing the sum of N×M by the sum of N. This
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is shown in equation (1). 𝑀𝑤 was calculated in similar fashion using equation (2).
Furthermore, the degree of polymerization using both the number average molecular
weight and the weight average molecular weight were calculated. The table below
summarizes the results of this lab.
Table 1. Summary of results obtained from GPC analysis.
Parameter
𝑀𝑛 (g/mol)
𝑀𝑤 (g/mol)
𝑃𝐷𝐼
𝑀0 (g/mol)
𝑋𝑛
𝑋𝑤
Value
55,418
89,950
1.62313
104.15
532.10
863.66
4. DISCUSSION
4.1 GPC Curve Peaks
Figure 4 shows the entire intensity vs elution time curve including parts that are
insignificant to the analysis of PS distribution. The flat line at the beginning of the curve
indicates that no polymer had eluted from the column yet. The peak between 15.8 and 27
minutes was the peak we analyzed. In the significant GPC curve between 15.8 and 27
min (Figure 5), there are more than one peak. There are two major peaks at 20.5 min and
26 min. The peaks indicate that there are more than one size distribution of molecular
weight in the polymer. The segments with the molecular weights of 10036 g/mol and 269
g/mol are the most common in the polymer mixture (calculated by log Mw = - 0.2859 t +
9.8625) using the elution time of the major peaks.
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The sharp positive peak after 27 minutes indicates the presence of a large amount of very
low molecular weight polystyrene. This could be the result of unreacted monomer of low
weight polystyrene radicals combining with each other, preventing further growth. The
negative peak at the end of the GPC curve might be a result of the solution running out of
solvent, so a smaller refractive index would be measured.
4.2 Effect of Initiator Concentration
From the “polymer synthesis” experiment, the 400 mg BPO sample is expected to have
the lowest molecular weight compared to the 100 mg and 250 mg samples. Increasing the
amount of benzoyl peroxide relative to styrene shortens the polymeric chains and hence
results in a lower molecular weight. However, since only the 400 mg sample was tested
in GPC, no quantitative data of how much higher the molecular weights of the other
samples are can be provided.
5. CONCLUSIONS
1. GPC is a useful technique to gain information about the size and dispersivity of a
polymer sample.
2. If a larger concentration of radical initiator is used, the resulting polymer chains are
expected to have a lower molecular weight.
3. Average molecular weight on the order of 104 – 105 g/mol were obtained, which are
typical for polymers.
4. The 1.6 PDI of the polystyrene sample in this experiment falls in the range expected
for free radical polymerization (1.5<PDI<2.0).
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6. ACKNOWLEDGMENTS
The data was taken from a Mat E 453 group from the previous year.
7. REFERENCES
1. Gel Permeation Chromatography. Iowa State Polymer Composites Research Group,
15 Jan. 2013. Web.
2. Mendoza, J. D., Lab 2: GPC, Iowa State University.
3. Size Exclusion Chromatography (SEC). Phenomenex, 7 May 2014. Web.
4. Mendoza, J. D., Mat E 453 Lecture, Iowa State University.
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Appendix
Table 1. Data used for generation of calibration curve.
Table 2. Example of spreadsheet used for calculations. Entire spreadsheet is not shown
for brevity.
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