transmem: Treatment of membrane-transport data.

Description

Treatment and visualization of membrane (selective) transport data. Transport profiles involving up to three species are produced as publication-ready plots and several membrane performance parameters (e.g. separation factors as defined in Koros et al. (1996) <doi:10.1351/pac199668071479> and non-linear regression parameters for the equations described in Rodriguez de San Miguel et al. (2014) <doi:10.1016/j.jhazmat.2014.03.052>) can be obtained. Many widely used experimental setups (e.g. membrane physical aging) can be easily studied through the package's graphical representations.

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

References

C. Paredes, E. Rodriguez de San Miguel, Polymer inclusion membrane for the recovery and concentration of lithium from seawater. Master thesis, Universidad Nacional Autónoma de México, México City, México, 2020.

Calculates regression curve for external standard calibration.

Description

Polinomial regression curves for external standard calibration are calculated to later convert signals into concentration values.

Usage

calibCurve(curve, order = 1, badpoint = NULL, intercept = TRUE, plot = TRUE)

Arguments

Details

A linear method (i.e lm()) is applied to obtain the regression curve.

Value

Model of the calibration curve.

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

See Also

calibPlane when using more than one explanatory variable.

Examples

  data(curvelithium)
  model1 <- calibCurve(curve = curvelithium, order = 1)
  model2 <- calibCurve(curve = curvelithium, order = 2)
  summary(model1)
  summary(model2)

Calculates regression plane for external standard calibration.

Description

A bivariated regression plane for external standard calibration is calculated to later convert signals into concentration values. It differs from calibCurve in the number of explanatory variables, 2 in this case. This function is useful when some interference effect is being considered such as the magnification of the interest species signal due to the presence of another (known) species in the same sample.

Usage

calibPlane(plane, badpoint = NULL, plot = TRUE, lines = 13, theta = -30,
  phi = 40, xlab = "Species 1", ylab = "Species 2", zlab = "Signal",
  pch = 18, cex = 2)

Arguments

Details

A linear method (i.e lm()) is applied to obtain the regression equation. The user must verify model assumptions such as normal distribution of residuals.

Value

Model of the calibration plane

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

Examples

  data(planelithium)
  planeModel <- calibPlane(plane = planelithium)
  summary(planeModel$model)

Creates a data frame as a complete self-contained transport data set

Description

The function transforms the data contained in concentration vectors of feed and strip phases to a data frame that contains the complete data of a transport process. This new data frame can be used by several functions inside the package. The output data frame may contain normalized fractions remaining in the feed and already transported to the strip phase, or the original data provided in concentration units.

Usage

conc2frac(feed, strip, time = NULL, correct.strip = FALSE, normalize = TRUE)

Arguments

Details

The change in concentration of species in the feed and strip phases as a function of time are the main magnitudes being measured in processes involving transport across membranes. The best form to deal with such data is inside a dataframe containing the information about the concentration of given species in both phases and the time transcurred.

Usually, this function is required after using signal2conc wich convert instrumental signals to concentrations.

Value

Data frame with the transport proccess information

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

Examples

  transData <- conc2frac(feed = c(0.200, 0.169, 0.152, 0.141, 0.138),
                         strip = c(0.000, 0.035, 0.045, 0.062, 0.069),
                         time = c(0, 2, 4, 6, 8))
  print(transData)

Lithium concentration results using a membrane

Description

A list of 5 datasets, each of one with the transport data of each cycle in a concentration experiment of lithium using a polymer inclusion membrane.

Usage

concentrationcycles

Format

A list of 5 data frames with 10 rows and 3 variables:

Time

Time in hours of each aliquot taken during the experiment

Phase

Phase of corresponding aliquot, Feed or Strip

Fraction

Remaining lithium concentration in the feed solution or transported lithium concentration to the strip solution

Source

Paredes, C. and Rodríguez de San Miguel, E., Selective lithium extraction and concentration from diluted alkaline aqueous media by a polymer inclusion membrane and application to seawater, Desalination, Volume 487, 2020, 114500, https://doi.org/10.1016/j.desal.2020.114500.

External standard calibration curve for lithium in water.

Description

A dataset containing the concentrations and emission signals of aqueous lithium standards measured by Flame Atomic Emission Spectrometry (FAES) at a Perkin-Elmer 3100 Atomic Absorption Spectrometer.

Usage

curvelithium

Format

A data frame with 8 rows and 2 variables:

Conc

lithium concentration in the standards, in mg/kg

Signal

emission signal of lithium at 670.8 nm, in arbitrary units

Source

Paredes, C. and Rodríguez de San Miguel, E., Selective lithium extraction and concentration from diluted alkaline aqueous media by a polymer inclusion membrane and application to seawater, Desalination, Volume 487, 2020, 114500, https://doi.org/10.1016/j.desal.2020.114500.

Plots transport profiles for processes involving several cycles

Description

Given the data (data frames) of a transport process that was carried in several cycles (e.g. membrane reuse or metal concentration studies), plots the transport profiles like in a continuous experiment indicating the end of each cycle

Usage

cyclesPlot(trans, xlab = "Time (h)", ylab = expression(Phi), xlim = NULL,
  ylim = NULL, xbreaks = NULL, ybreaks = NULL, size = 1.8,
  legend = FALSE)

Arguments

Details

If a concentration experiment has been made through the cycles, it is recommended the y-axis to be in concentration scale instead of fractions. To get the transport data frame in concentration units use conc2frac(..., normalize = FALSE). For more details see conc2frac.

Most transmem graphical representations are made using the package ggplot2 so the function returns a ggplot2 object that can be assigned to a variable for further modification.

Value

Plot of the transport process carried in several cycles

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

References

Wickham H (2016). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. ISBN 978-3-319-24277-4, https://ggplot2.tidyverse.org.

Interpolates secondary species concentration at missing time values

Description

If the secondary species concentration is determined in just a fraction of the aliquots and for some reason, the concentration in all the aliquots is required or desired, the function fits a polynomial trend line to the existing data and interpolates the concentration in missing aliquots.

Usage

fixSecondary(conc, time, compTime, order = 2)

Arguments

Value

Vector of interpolated concentrations at times provided in compTime.

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

Plots several single-phase transport profiles overlayed

Description

Given a list of several complete transport data, the function overlays the transport profiles in a defined phase. The function is useful in membrane reuse experiments as transport profile deterioration is easily visualized.

Usage

multiPlotSP(trans, phase = "strip", trend = NULL, legend = FALSE,
  xlab = "Time (h)", ylab = expression(Phi), xlim = NULL, ylim = NULL,
  xbreaks = NULL, ybreaks = NULL, size = 3, plot = TRUE, shape = 15,
  bw = FALSE, arw = FALSE, arw.pos = NULL, arw.txt = NULL,
  txt.pos = NULL, txt.size = NULL)

Arguments

Details

Most transmem graphical representations are made using the package ggplot2 so the function returns a ggplot2 object that can be assigned to a variable for further modification.

Value

Plot with the overlayed transport profiles for a single phase

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

Examples

  data(reusecycles)
  # First step is to get trend lines for each cycle:
  trend <- list()
  for (i in 1:length(reusecycles)) {
    trend[[i]] <- transTrend(trans = reusecycles[[i]])
  }
  # Default plot using colors:
  multiPlotSP(trans = reusecycles, trend = trend, legend = TRUE)

  # Black and white plot including an arrow:
  multiPlotSP(trans = reusecycles, trend = trend, legend = TRUE, bw = TRUE,
              arw = TRUE, arw.pos = c(6.1, 6.1, 0.8, 0.6),
              arw.txt = 'Cycle', txt.pos = c(6.15, 0.7))

Calculates permeability coefficients

Description

Permeability coefficients across a membrane as derived from integrated Fick's law can be obtained from transport data according to the equation

\ln{\Bigg(\frac{C}{C^0}\Bigg)}= -\frac{P~a}{V}t

where P is the permeability coefficient, a is the membrane exposed area, C and C^0 are the species concentrations at any time and at initial time in the feed phase, respectively, and V is solution volume.

Usage

permcoef(trans, vol, area, units = c("cm^3", "cm^2", "h"), conc0 = NULL,
  plot = FALSE)

Arguments

Details

Species concentration units may be arbitrary as long as the permeability coefficient is calculated using the change in concentration ratio which is, as most ratios, adimensional

Value

A numeric vector with the permeability coefficient and it's standard uncertainty from the regression. Units are meters per second.

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

Bivariated calibration plane for lithium in prescence of sodium.

Description

A dataset containing the concentrations of lithium and sodium combined standards and absorbance signals measured by Flame Atomic Absorption Spectrometry (FAAS) at a Perkin-Elmer 3100 Atomic Absorption Spectrometer.

Usage

planelithium

Format

A data frame with 40 rows and 3 variables:

Conc

lithium concentration in the standards, in mg/kg

Signal

absorbance signal of lithium at 670.8 nm, in absorbance units

Conc.S

sodium concentration in the standards, in mg/kg

Source

Paredes, C. and Rodríguez de San Miguel, E., Selective lithium extraction and concentration from diluted alkaline aqueous media by a polymer inclusion membrane and application to seawater, Desalination, Volume 487, 2020, 114500, https://doi.org/10.1016/j.desal.2020.114500.

Membrane reuse capability to transport lithium

Description

A list of 10 datasets, each of one with the transport data of each cycle in a reuse capability experiment of a polimeric inclusion membrane selective to lithium ions.

Usage

reusecycles

Format

A list of 10 data frames with 10 rows and 3 variables:

Time

Time in hours of each aliquot taken during the cycle

Phase

Phase of corresponding aliquot, Feed or Strip

Fraction

Remaining lithium fraction in the feed solution or transported lithium fraction to the strip solution

Source

Paredes, C. and Rodríguez de San Miguel, E., Selective lithium extraction and concentration from diluted alkaline aqueous media by a polymer inclusion membrane and application to seawater, Desalination, Volume 487, 2020, 114500, https://doi.org/10.1016/j.desal.2020.114500.

Lithium, sodium and potassium transport profiles across a membrane

Description

A list of 6 datasets containing by duplicate the transport profiles for lithium, sodium, and potassium from a synthetic simplified seawater matrix using a polymer inclusion membrane selective to lithium. Lithium samples were taken every 45 minutes during 4.5 hours while sodium and potassium determinations were made in samples taken every 1.5 hours.

Usage

seawaterLiNaK

Format

A list of 6 data frames (two for each lithium, sodium, and potassium) with 14 or 8 rows and 3 variables:

Time

Time in hours of each aliquot taken during the experiment

Phase

Phase of corresponding aliquot, Feed or Strip

Fraction

Remaining lithium concentration in the feed solution or transported lithium concentration to the strip solution

Source

Paredes, C. and Rodríguez de San Miguel, E., Selective lithium extraction and concentration from diluted alkaline aqueous media by a polymer inclusion membrane and application to seawater, Desalination, Volume 487, 2020, 114500, https://doi.org/10.1016/j.desal.2020.114500.

Calculates separation factors between two transported species

Description

Given the transport data frames of two species, the function calculates the separation factors of the main species A against a secondary species B for each sample taken. If the dataset of secondary species is smaller than that of the main species (e.g. if secondary species were determined in only half the aliquots), the transport profile is completed using fixSecondary function and a message will be printed.

Usage

sepfactor(main, secon, order = 2, mode = "batch", plot = TRUE)

Arguments

Details

Separation factor for batch systems at any time different from zero is defined as

SF_{A/B}(t)=\frac{C_a/C_b}{C_a^0/C_b^0}

where C_a and C_b are the concentrations of A and B, respectively, in the strip solution at a time t, and C_a^0 and C_b^0 are the concentrations of A and B, respectively, in the feed phase at t=0 (Chen et al., 2018).

For continuous or semicontinuous systems, the separation factor is calculated according to the equation

SF_{A/B}(t)\frac{C_{a,~s}/C_{b,~s}}{C_{a,~f}/C_{b,~f}}

where C_{a,~s}, C_{b,~s} are A and B concentrations in the strip phase at a time t and C_{a,~f}, C_{b,~f} are the concentrations of A and B in the feed solution at a time t (Koros and Shimidzu, 1996). Separation factor at t=0 equals 1 indicating that no species separation has occurred yet.

Value

Data frame with two variables: Time in the same units as provided data and SF with the separation factors at each time.

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

References

Q. B. Chen, Z. Y. Ji, J. Liu, Y. Y. Zhao, S. Z. Wang, J. S. Yuan, Development of recovering lithium from brines by selective-electrodialysis: Effect of coexisting cations on the migration of lithium, Journal of Membrane Science 548 (2018) 408-420. doi:10.1016/j.memsci.2017.11.040.505

J. Koros, H. Ma, T. Shimidzu, Terminology for membranes and membrane processes (iupac recommendations 1996), Pure and Applied Chemistry 68 (7) (1996) 1479-1489. doi:10.1351/pac199668071479.

Examples

  data(seawaterLiNaK)
  sepfactor(main = seawaterLiNaK$Lithium.1,
            secon = seawaterLiNaK$Sodium.1)
  sepfactor(main = seawaterLiNaK$Lithium.1,
            secon = seawaterLiNaK$Potassium.1)

Converts signals into concentration by using given model.

Description

After a calibration model is established (either by using calibCurve or calibPlane), the function interpolates the signals of samples to get the associated concentrations.

Usage

signal2conc(signal, model, dilution = NULL, planar = FALSE, Conc.S = NULL)

Arguments

Value

Numeric vector of species concentrations.

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

Examples

  # A regression model is needed:
  data(curvelithium)
  model <- calibCurve(curve = curvelithium, order = 2)

  signal <- c(0.395, 0.259, 0.188, 0.141, 0.110, 0.095, 0.084)
  (conc <- signal2conc(signal = signal, model = model))

Plots transport profiles of single run experiments

Description

Given the transport complete information of the interest species and, optionally, secondary and tertiary species, the function plots transport profiles including (if given) non-linear regression models that can be obtained using transTrend.

Usage

transPlot(trans, trend = NULL, secondary = NULL, tertiary = NULL,
  sec.trend = "spline", lin.secon = FALSE, span = 0.75, legend = FALSE,
  xlab = "Time (h)", ylab = expression(Phi), xlim = NULL, ylim = NULL,
  xbreaks = NULL, ybreaks = NULL, size = 2.8, bw = FALSE, srs = NULL,
  plot = TRUE)

Arguments

Details

Most transmem graphical representations are made using the package ggplot2 so the function returns a ggplot2 object that can be assigned to a variable for further modification.

This function has a version that uses replicated experiments and may be useful to illustrate repeateability. For more information see transPlotWR.

Value

Plot of the transport profile considering all provided species.

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

References

Wickham H (2016). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. ISBN 978-3-319-24277-4, https://ggplot2.tidyverse.org.

Examples

  data(seawaterLiNaK)
  trend <- transTrend(trans = seawaterLiNaK$Lithium.1, model = 'paredes')
  transPlot(trans = seawaterLiNaK$Lithium.1, trend = trend,
            secondary = seawaterLiNaK$Sodium.1,
            tertiary = seawaterLiNaK$Potassium.1)
  transPlot(trans = seawaterLiNaK$Lithium.1, trend = trend,
            secondary = seawaterLiNaK$Sodium.1,
            tertiary = seawaterLiNaK$Potassium.1, bw = TRUE)

Plots transport profiles of replicated experiments

Description

The function works the same way as transPlot but requires several experimental data sets that must be concatenated in lists. This allows the process reproducibility to be evaluated in the analysis of the results.

Usage

transPlotWR(trans, trend = NULL, secondary = NULL, tertiary = NULL,
  legend = FALSE, xlab = "Time (h)", ylab = expression(Phi),
  xlim = NULL, ylim = NULL, xbreaks = NULL, ybreaks = NULL,
  lin.secon = FALSE, sec.trend = "spline", span = 0.75,
  explicit = FALSE, size = 3, plot = TRUE, bw = FALSE, srs = NULL)

Arguments

Details

Most transmem graphical representations are made using the package ggplot2 so the function returns a ggplot2 object that can be assigned to a variable for further modification.

Value

Plot of replicated transport profiles including all provided species

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

References

Wickham H (2016). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. ISBN 978-3-319-24277-4, https://ggplot2.tidyverse.org.

Examples

  data(seawaterLiNaK)
  # Transport data frames and transport NLS regresions must be in lists
  lithium   <- list(seawaterLiNaK$Lithium.1, seawaterLiNaK$Lithium.2)
  sodium    <- list(seawaterLiNaK$Sodium.1, seawaterLiNaK$Sodium.2)
  potassium <- list(seawaterLiNaK$Potassium.1, seawaterLiNaK$Potassium.2)
  trend     <- list(transTrend(trans = seawaterLiNaK$Lithium.1),
                    transTrend(trans = seawaterLiNaK$Lithium.2))

  transPlotWR(trans = lithium, trend = trend, secondary = sodium,
              tertiary = potassium, bw = TRUE)

Fits trend equations that model transport profiles

Description

Given a transport profile dataset, the results may be studied and compared in terms of empirical functions that describe the transport process in terms of regression parameters that can be asociated with the performance of the membrane system. The parameters are obtained by non-linear regression and are independent for each solution at both sides of the membrane. This is particularly useful when performing system optimizations since the parameters can be used as response variables depending on the optimization goal.

Usage

transTrend(trans, model = "paredes", eccen = 1)

Arguments

Details

Two empirical equations have been implemented in the function. In the 'rodriguez' model (Rodriguez de San Miguel et al., 2014), the fractions (\Phi) in feed or strip phases as a function of time (t) are fitted to

\Phi(t)=Ae^{-t/d}+y_0

where A, d and y_0 are the parameters to be found. In this model, parameter d determines the steepness of the species concentration change in time, y_0 reflects the limiting value to which the profiles tend to at long pertraction times and A is not supposed to play an important role in the transport description. The parameters of each phase are summarized in the functions G_{feed} and G_{strip} for the feed and strip phases:

G_{feed}=\frac{1}{y_0d},\qquad G_{strip}=\frac{y_0}{d}

The bigger each G function, the better the transport process.

In the 'paredes' model (Paredes and Rodriguez de San Miguel, 2020), the transported fractions to the strip solution and from the feed solution are adjusted to the equations:

\Phi_s(t)=\frac{\alpha_s t^\gamma}{\beta_s^{-1}+t^\gamma}

\Phi_f(t)=1-\frac{\alpha_f t^\gamma}{\beta_f^{-1}+t^\gamma}

respectively. In those equations, adjustable parameters \alpha and \beta relates the maximum fraction transported at long pertraction times and the steepness of the concentration change, respectively. \gamma is an excentricity factor to improve the adjustment and does not need to be changed for systems under similar conditions. The subscripts s and f means strip and feed phases, respectively.

The later model has the disadvantage over the former that the equation to use depends on the phase to be modeled but has the great advantage that if no significant accumulation is presented in the membrane, the parameters \alpha and \beta should be quite similar for both phases and a consensus value can be obtained in various simple ways, while the other model yields quite diferent parameters for each phase. Paredes parameters are combined by using meta-analysis tools that consider the associated uncertainty of each one due to lack of fit to get summarized, lower-uncertainty results. Besides, once the \gamma parameter has been chosen, the later model uses only two parameters and while comparing models with similar performance, the simpler the better.

Value

A list of 4 or 5 components (depending on the model chosen) with the regression information for each phase, the eccentricity factor (only in Paredes model), the name of the model used, and the sumarized results of the regression: G_{feed} and G_{strip} values for the Rodriguez model or summarized \alpha and \beta parameters with asocciated uncertainty for the Paredes model.

Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Eduardo Rodriguez de San Miguel, erdsmg@unam.mx

References

E. Rodriguez de San Miguel, X. Vital, J. de Gyves, Cr(vi) transport via a sup ported ionic liquid membrane containing cyphos il101 as carrier: System analysis and optimization through experimental design strategies, Journal of Hazardous Materials 273 (2014) 253 - 262.
doi:10.1016/j.jhazmat.2014.03.052.

C. Paredes, E. Rodriguez de San Miguel, Polymer inclusion membrane for the recovery and concentration of lithium from seawater. Master thesis, Universidad Nacional Autónoma de México, México City, México, 2020.