| Property Prediction |
Sections in this chapter
The specific example described in this section allows you to estimate the solubility parameter and the Young's modulus of an ethylene-propylene copolymer over a range of concentrations at room temperature. Note that the predictions of the Synthia module apply to an isotropic, atactic, amorphous polymer phase; the effects of ordering, tacticity, and crystallinity, in particular, are not taken into account. The results in this example thus apply to the amorphous regions of the copolymer.
This example is divided into sections:
A. Building the copolymer
C. Studying a range of concentrations
A. Building the copolymer
1. Starting Cerius2
Open a new UNIX shell and type:
> cerius2 |
| From the Visualizer panel, go to the POLYMER Deck and choose the SYNTHIA card. |
3. Load the monomer subunits and build the copolymer
| Select the Study/Copolymer item to bring up the Copolymer control panel. |
| In the box labeled Polymer enter co_eth_prop as a name for your new copolymer. |
| Click the arrow to the right of the first Monomer Name text field. Select polyolefin from the list of monomer types. |
| Click once again on the same arrow. |
You now see a list of monomers under the category polyolefin.
| Select PE from the list. |
You have now loaded the ethylene monomer.
| Now click the arrow to the right of the second Monomer Name text field. This time select polyolefin and then PP from the list. |
You have now loaded the propylene monomer. Note that the concentrations of the two monomers are each equal to 0.5. This is because neither concentration has been marked as fixed; the program automatically divides unassigned concentrations equally among unfixed monomers.
| Click the blue button labeled Add Copolymer to NEW Study. |
This loads your copolymer into Synthia. Note that the two monomers are loaded in as models and that the propylene monomer is displayed in the model window.
| Select the Study/Show item on the SYNTHIA card. |
This brings up a table displaying the name of your copolymer, the structures of each constituent monomer, their respective concentrations, and the default temperature and molecular weight for the study (298 K and 100000 respectively).
B. Predicting properties
1. Open the menu of properties
| Go to the SYNTHIA card and select the Properties/Select item. |
This brings up the Select Properties panel. The panel should display the Thermophysical category by default.
| Scroll through the list of properties on the panel and select Solubility Parameter (van Krevelen). |
3. Choose the mechanical properties
| Click the yellow popup labeled Thermophysical and select Mechanical. |
This displays a list of mechanical properties.
| Select Young's Modulus from the list. |
4. Predict the selected properties for the copolymer
| Now go to the Study Table and click the PREDICT button. |
The selected properties should be displayed in the table for the copolymer made up of ethylene and propylene in equal mole fractions. (Other mole fractions can be entered by checking the box marked Fixed (located to the right of the monomer name) for a monomer and then typing in a value into the box to its right.)
C. Studying a range of concentrations
1. Initiate a concentration study
|
Select the Study/Concentration Range item on the SYNTHIA card. |
| Click the yellow Range popup currently displaying the value None. |
You will see a list of allowed range monomers for co_eth_prop.
| Set the popup to PE. |
| Enter a Concentration Step of 0.2. |
3. Display the range in the study table
| Check the box labeled Display Range in Table. |
You should see six rows displayed in the table, one corresponding to each set of compositions in the range just defined. Note that both the Young's modulus and the solubility parameter increase monotonically with rising ethylene fraction.
|
Click the down arrow next to Over Range and select Solubility Parameter. |
| Click the Plot button. |
This graphically displays the variation of the copolymer solubility parameter with the mole fraction of ethylene.
Summary
In this short example, you:
For further practice with tutorials in Synthia or other polymer modules, please see the Cerius2 Tutorials--Materials Science book.
Table 1 lists the properties that you can calculate with Synthia, together with references to the expressions in Bicerano (1993) that are evaluated when performing these calculations, and an estimate of the standard deviation in the predicted values. In many cases, the standard deviations are values of standard deviations in the mean that are taken directly from the correlations performed in Bicerano (1993). For some properties, correlations in Bicerano (1993) were performed against values computed from group contributions. In these cases, the values of standard deviation listed in Table 1 are a combination of uncertainties in the correlations performed in Bicerano (1993) and uncertainties in the original group contribution approach (the latter usually being the major contributor). The standard deviations listed in Table 1 are only intended to serve as a guide for you to assess the relative merit of the large range of properties that may be computed by the Synthia module.
Scope and limitations
The correlations implemented in the Synthia module were developed for isotropic (unoriented) amorphous atactic homopolymers and alternating and random copolymers constructed from the following nine elements: carbon, nitrogen, oxygen, silicon, sulfur, fluorine, chlorine, and bromine. They are also applicable to the amorphous phase of semi-crystalline polymers. Consequently, the following predictions are beyond the scope of Synthia: effects of tacticity, ordering (crystallinity and liquid crystallinity), and orientation of polymers; predictions for cross-linked, ladder, and biological polymers, for block copolymers, and for polymeric systems containing additives and impurities that have a significant effect on the properties of the polymer. Also, Synthia does not predict the dependence of most properties on molecular weight; the estimates correspond to typical high molecular weight polymers (the only current exception is zero-shear viscosity as defined in chapter 13 of Bicerano (1993).
Computing repeat unit length
The repeat unit length is used in correlations for many of the mechanical properties. To compute this distance appropriately, you should set all repeat units to their fully extended all-trans conformations and energy minimize these structures before you submit them to Synthia. For most polymer repeat units, you can adequately perform this minimization using the Run item on the MINIMIZER card in the OFF Methods deck. 
are measured. The repeat unit length 
is then computed as:
Eq. 1
Energy minimization of repeat units
It is advised that you energy minimize all repeat units before submitting them to the Synthia module. The fact that minimization may affect the repeat unit length determined by Synthia has been mentioned in the previous section. In turn, this length affects several other aspects of geometry used to compute polymer properties. To achieve adequate minimization of structures it is usually sufficient to follow these steps:1. Set repeat units to their all-trans conformation.
2. Set all parameters to their default values.
3. Select the Run item from the MINIMIZER card in the OFF
METHODS deck.
Values of cohesive energy and solubility parameter used in correlations for other properties
Two independent values are computed for the cohesive energy of a polymer, and subsequently two corresponding values are calculated for the solubility parameter. These two sets of values result from correlations to cohesive energies predicted by group contributions developed by Fedors (1974a and b) and van Krevelen (1990). Consequently, they are termed Fedors-like and van Krevelen-like values, and are listed this way in the output file.
Representation of amide groups
It is recommended that you build amide and similar functional groups with the following structure:
Units of permeability
The units for the permeability values that are given in the Synthia output file are: cm3 mil (day 100 inches2 atm)-1, which are often referred to as "Dow Units" (DU). Here, mil denotes one thousandth of an inch.
Developing correlations with QSAR
The Synthia module allows you to develop your own correlations for properties if you also have access to the QSAR module, with which Synthia is integrated. The Correlate item on the SYNTHIA card automatically brings up a QSAR table. In addition to the structural descriptors used internally by Synthia, all the properties available for prediction in Synthia at 298 K and for a molecular weight of 100000 are available for use as descriptors in QSAR studies.
Performing polymer properties calculations
The method for performing polymer properties calculations involves the following steps:1. Build or edit monomers by selecting the Build/3D-Sketch item
from the top menu bar of the Visualizer panel. Alternatively,
you can select monomers from the monomer library: these are
accessible directly within Synthia during homopolymer and
copolymer calculations.
| Step 2 is not necessary for structures in the monomer library, since they have predefined head and tail atoms. |
4. Add the homopolymer to the study by pushing the Add Homopolymer to Study button.
6. To choose which properties to predict for your polymer, go to the SYNTHIA card and select the Properties/Select item to open the Select Properties panel. Choose the category of properties you are interested in from the yellow popup above the property list. Then click on properties within the list displayed to add them to the set of properties to compute in your study.
7. Display the study table by selecting the Study/Show item.
a. Check the Selected Models box on the Predict panel
a. Select a copolymer for the study from the Polymer list
c. Pick initial and final concentrations and a concentration step
for the range monomer.
To circumvent this limitation, the method implemented in the
No attempt is made here to discuss or explain the details of all of the correlations that are used within the Synthia module. For this information, refer to Jozef Bicerano's research monograph (Bicerano 1993). The description of the theory underlying this module is restricted in this document to a brief outline summarized from Bicerano's work. A complete description is given, however, of all assumptions and modifications made to the original approach (Bicerano 1993) in the course of implementing this computer program.
Graphical theoretical treatment of molecular properties starts by construction of the hydrogen-suppressed graph of the molecule. To represent a repeat unit, special considerations are required to take into account chain continuation in a consistent manner, and not introduce truncation errors. The procedure is illustrated here by considering the repeat unit of poly(vinyl fluoride) (PVF). This repeat unit is shown in Figure 2, together with the hydrogen-suppressed graph that will be utilized.
|
The next step is to define two atomic indices (
and 
), that describe the bonding and electronic environment of each non-hydrogen atom. The first is the simple connectivity index, 
, which equals the number of non-hydrogen atoms to which an atom is bonded. The latter atomic index, 
, contains electronic configuration information for the atom and is given by:
Eq. 2
where 
is the number of valence electrons of the atom, 
is the number of hydrogens bonded to it, and 
is its atomic number.
and 
can also be defined in terms of the atomic indices. These are defined by:
Eq. 3
and:
Eq. 4
The values of the atomic and bond indices that are obtained for the PVF repeat unit are shown in Figure 3. In this figure the connectivity indices 
and 
are shown in Figure 3(a), and the valence indices 
and 
are shown in Figure 3(b).
|
Connectivity indices of polymer chains
The connectivity indices for the polymer chain can now be defined. It is these chain connectivity indices that are later used in the correlations with polymer properties.
and 
for the polymer molecule are defined in terms of the summations:
Eq. 5
and:
Eq. 6
over the vertices of the hydrogen-suppressed graph.
and 
for the polymer molecule are defined in terms of the summations:
Eq. 7
and:
Eq. 8
over the edges of the hydrogen-suppressed graph.
Eq. 9
Eq. 10
Eq. 11
Eq. 12
Note that the 
and 
values outside of the square brackets in Figure 3 are not included in the summations. They are included in the figure to take the chain connectivity into account, and to allow the correct assignment of the 
and 
values for all of the atoms and bonds within the brackets.
General forms of the correlations in terms of connectivity indices
Extensive properties depend upon the size of the system, and their values increase in direct proportion to the amount of material present. Examples of such properties include: molar volume, molar heat capacity, and cohesive energy. Such properties are correlated directly with the values of 
.
scaled by the number of non-hydrogen atoms in the system N. These scaled values are denoted by the Greek letter 
, with all the usual superscripts and subscripts that are used with the corresponding 
.
Eq. 13
Eq. 14
Here, a and b are sets of linear regression coefficients. There is no additive constant term in the correlation for an extensive property because the value of constant does not change as a function of the amount of material present. The structural parameters are combinations of connectivity indices and geometrical parameters that are used in correlations for certain properties. The atomic and group correction terms are terms that are dependent upon the number of certain types of atoms or groups that may be present. 
Backbone and side group connectivity indices
In correlations to predict certain properties, it is necessary to separate the contributions of atoms in the backbone and those in side chains into two sets of 
s. This is not discussed further here--for additional information please see Bicerano (1993).
Actual correlations for various properties and validation against experimental data
All the correlations used in the Synthia module are fully documented in Bicerano (1993), in addition to their validation against extensive experimental data.
Bicerano, J. Prediction of Polymer Properties, Marcel Dekker, Inc.: New York (1993).
References