Thermophysical Properties Analysis Panel

Analyze the density of a solid as a function of temperature to determine the coefficient of thermal expansion and the glass transition temperature. The densities are obtained from MD simulations at a set of temperatures in the NPT ensemble, and the uncertainties in the results due to the simulations can also be estimated.

To open this panel, click the Tasks button and browse to Materials → Classical Mechanics → Thermophysical Properties → Thermophysical Properties Results.
To open this panel from the entry group for the results of a thermophysical properties job, and load the results, use the Workflow Action Menu .

The following licenses are required to use this panel: MS Maestro

Using
Features
Additional Resources

Using the Thermophysical Properties Analysis Panel

To obtain the thermochemical properties, two methods are available:

A bilinear fit, in which a linear regression is performed on the low temperature (glassy) region and the high temperature (rubbery) region of the plot of density against temperature.
A hyperbola fit, in which a single hyperbolic curve is fitted to all points of the plot of density against temperature.

The coefficient of thermal expansion is the slope of the fitted line when you do a bilinear fit. The glass transition temperature is the temperature at which the two regression lines or the two asymptotes meet. If you want both properties, but want to do the hyperbola fit for T_g, do the bilinear fit first and save the properties, then do the hyperbola fit and save, to overwrite the T_g from the bilinear fit.

Bilinear fit

The points initially included in each linear regression are adjusted so that the sum of the R² values is maximized, with all points included in the fit.

You can adjust the sets of points that are included in the fits by dragging the vertical boundaries of the two colored areas so that they include more or fewer points. These regions do not need to include all the points—for example, you might want to leave out points in the middle that are not clearly in either region. The regressions are redone when the number of points changes. You can also exclude points from the fit (such as outliers) by selecting the points and then clicking Remove Selected Points from Fits. By these means you can adjust the fits to maximize the R² values. The coefficient of thermal expansion and the glass transition temperature values are also updated when you adjust the sets of points.

When you have finished adjusting the points in the fit, you can save the computed coefficient of thermal expansion and glass transition temperature to the structure in the project, by clicking Store CTE and Tg.

Hyperbola fit

The equation of the hyperbola is

ρ = ρ₀ + 2at + b[t + √(t² + e^c) ]

where t = (T − T₀)/2; ρ is the density and T is the temperature; ρ₀ and T₀ are the density and temperature at the glass transition. The parameters of the fit are a, b, c, ρ₀, and T₀. The parameter c determines how close the hyperbola comes to the intersection of the asymptotes. The asymptotes are the two lines obtained for c = −∞:

ρ_lo = ρ₀ + a (T − T₀)
ρ_hi = ρ₀ + (a+b) (T − T₀)

where lo and hi refer to the glassy (low-temperature) and rubbery (high-temperature) regions.

The non-asymptotic region is defined by a parameter P, the "asymptotic convergence threshold". This region is defined as the temperature range from T-h to T+h, where

h = e^−c/2 (2P-1) [P(1-P)]^−1/2

The asymptotes are regarded as defined if there are temperature points that lie outside this region on both sides. The useful range of P is 0.5 to 1.0, which yields values of h from 0 to ∞.

This method is described more fully in Patrone et al. [18] (available online here).

Uncertainty Analysis

As the MD simulation has various sources of noise (or error) such as finite size, finite simulation time, time steps, and so on, the effect of noise in the simulation can be estimated by creating synthetic data sets in which random noise is added to the residuals of the density fit (i.e. the differences between the values from the simulation and the values obtained from the fit). From a large number of synthetic data sets, a probability distribution is obtained for T_g which yields a mean, standard deviation, and RMSD. This process estimates the uncertainty in the simulation (the "within-simulation" noise); it does not estimate the uncertainty that would arise from a set of independent simulations on a system of the same size or of differing sizes. The details are given in section 5.1 of the paper by Patrone et al. [18].

Thermophysical Properties Analysis Panel Features

Load Data from Workspace button
Generate Report button
Fit tab
Uncertainty tab
Reset button

Load Data from Workspace button

Load the data from the Workspace structure for analysis. The structure displayed in the Workspace must be the output from a thermophysical properties calculation.

Generate Report button

Generate a report based on the panel contents. A dialog box opens, in which you can set a file base name to be used as the first part of the file name, and choose the type of report:

PDF Report—generate a PDF file that contains descriptive text and equations, panel figures, and all panel settings as tables.
Plots—generate images of the plots in the panel.
Data—write out the raw Tg data in CSV format.

The figures are generated with the current data and settings, so they should be exactly like the figures in the panel when you generate the report. When you have chosen the type, a file browser opens so you can navigate to a directory for the report.

Fit tab

Plot area

This area displays the plot of the density against the temperature, and displays the lines or curves that are used to determine the coefficient of thermal expansion and the glass transition temperature. The toolbar is a standard toolbar with controls for managing the plot, and is described in the Plot Toolbar topic.

Points can be selected in the plot area and removed from the fits by clicking Remove Selected Points from Fits.

The points used for the two fits in the bilinear fit are indicated by the two colored regions: green for the low-temperature (glassy) region and blue for the high-temperature (rubbery) region. You can drag the boundaries of these regions to change the sets of points included in each fit. The data for the fits are updated in the panel when you make the changes.

The non-asymptotic region in the hyperbola fit is indicated by a yellow colored region (it may be very narrow, depending on the data). Changing the asymptotic convergence threshold changes the size of this region.

Remove Selected Points from Fits button

Click this button after selecting one or more points on the plot to remove them from the fits for the properties. The number of points fitted and the total number of points are reported to the right of this button.

Restore All Points button

Restore all points to the plot to be used for fitting.

Fitting section

Fit the data in the plot with a chosen method.

Choose fitting method options

Select the method for fitting the data:

Hyperbola fit—Fit all points to a hyperbola. The curve is displayed as a red solid line, and the two asymptotes are displayed as blue dashed lines. The glass transition temperature is taken as the temperature at which the two asymptotes intersect.
Bilinear fit—Perform separate linear regressions on the low temperature (glassy) region and the high temperature (rubbery) region. The coefficient of thermal expansion is determined from the slope of the fit in the glassy region. The glass transition temperature is taken as the temperature at which the two lines intersect.

Asymptotic convergence threshold box

This parameter determines the size of the non-asymptotic region for a hyperbola fit. A value of 1 makes the size infinite; a value of 0.5 makes the size zero. The fit is considered to have converged if there are points outside the non-asymptotic region on both sides. The convergence is indicated by a mark next to the left of the Store CTE and Tg button. If convergence is not obtained, you can change this value to ensure that there are points in the asymptotic region.

This text box is only available if you choose Hyperbola fit.

Equation and R² boxes

These boxes display the equations of the asymptotes for the hyperbola fit, or the equation of the lines of best fit and the squared correlation coefficient R² for the glassy (low T) and rubbery (high T) regions for the bilinear fit. The values are updated as you remove or restore points in the plot.

Tg box

This box displays the glass transition temperature derived from the fit, in K. The value is updated as you remove or restore points in the plot. If the value of T_g is outside the data range, a message to this effect is shown instead of the value.

Store CTE and Tg button Store Tg button

Save the glass transition temperature, and the coefficient of thermal expansion from a bilinear fit, to the structure that was loaded. This button allows you to save the properties when you are satisfied with the fit to the data: it is not done automatically. The button text changes when you change the fitting method, to indicate which values are saved. T_g is not stored if it is outside the data range, and it is removed from button label.

Thermal expansion coefficient at T K boxes

The text boxes below the label show coefficients of thermal expansion, with a text box to specify the temperature at which they are evaluated. The values are updated as you remove points from the plot or restore points to the plot, or change the temperature. The boxes show the volumetric thermal expansion coefficient; the linear thermal expansion coefficient (if you used an isotropic barostat, as it is the same in all three directions) or the linear thermal expansion coefficients in each crystal direction (if you used an anisotropic barostat).

These boxes are only present if you chose to use a bilinear fit.

Uncertainty tab

Estimate the uncertainty in T_g due to the simulation. This is done by creating synthetic data from the simulation data by adding random Gaussian noise, and fitting the results to give a distribution of T_g values from which a mean and standard deviation are derived.

Plot area

This area displays a histogram plot of the probability of the predicted T_g value occurring in the synthetic data against the predicted T_g. The toolbar is a standard toolbar with controls for managing the plot, and is described in the Plot Toolbar topic.

Sampling section

Set parameters for the synthetic data.

Choose fitting method options: Choose the type of fit for T_g for which to run the uncertainty analysis, from Hyperbola fit and Bilinear fit. See above.
Random seed text box: Specify the random seed for generating the Gaussian noise.
Sample size text box: Set the number of synthetic data sets to be used in estimating the uncertainty.
Create button: Create and analyze the synthetic data sets and display the results in the plot area.

Viewing section

Make settings for display of the synthetic data used for uncertainty analysis.

Number of bins text box: Number of bins for the partitioning of the T_g predictions from the synthetic data for the histogram plot.
Normal fit option: Display the Gaussian fit to the T_g predictions, and calculate the mean, standard deviation, and RMSD.
mean, standard deviation, RMSD text boxes: Show the mean, standard deviation, and RMSD from the Gaussian fit to the T_g predictions.

Status bar

Use the Reset button to reset the panel to its default settings and clear any data from the panel. If the panel has a Job toolbar, you can also reset the panel from the Settings button menu.

If you can submit a job from the panel, the status bar displays information about the current job settings and status for the panel. The settings include the job name, task name and task settings (if any), number of subjobs (if any) and the host name and job incorporation setting. The job status can include messages about job start, job completion and incorporation.

The status bar also contains the Help button , which opens an option menu with choices to open the help topic for the panel (Documentation), launch Maestro Assistant, or if available, choose from an option menu of Tutorials. If the panel is used by one or more tutorials, hover over the Tutorials option to display a list of tutorials. Choosing a tutorial opens the tutorial topic.

Tutorials