Data for crystallisation of a homologous series of single and mixed n-alkanes (C16 – C23) from representative hydrocarbon fuel solvents

The data presented in this article relates to the crystallisation of 8 single n-alkanes, C16H34 – C23H48 in representative diesel solvents dodecane and toluene, as well as a mixture of these 8-alkanes with a composition representative of real diesel fuel in the same solvents. For the single alkane systems, the data was collected over a range of 5 concentrations ranging from 0.09 – 0.311xi, depending upon the system, and 4 concentrations for the 8-alkane mixture, 0.1 – 0.5xi. Raw average crystallisation and dissolution points as a function of cooling rate (q) from a polythermal methodology are presented. Along with the equilibrium crystallisation and dissolution temperatures, van't Hoff fitting parameters, relative critical undercooling (uc) values as a function of q as well as the calculated values of KG and αdet.


Specifications
Chemical Engineering Specific subject area Crystallisation and Fuels Type of data Tables  How the data were acquired Data was acquired from polythermal crystallisation experiments using the Technobis Crystal16, computationally using a dedicated systematic search algorithm, and thermodynamic data was collected using a Mettler Toledo DSC 1 with the polythermal method. Data format Raw & Analysed Description of data collection In all Crystal16 experiments solutions were homogenised above the dissolution point with agitation before crystallisation with each polythermal cycle being repeated 4 times. 7 cooling rates from 0.25 -5 °C/min were used, with dissolution and crystallisation points being obtained from a Boltzmann fitting of the turbidity/temperature data with dissolution taken when %T reached 99% and crystallisation taken when %T reached 90%. In all DSC experiments the samples were also homogenised above their melting point before crystallisation with each polythermal cycle being repeated 3 times at 2 °C/min.

Value of the Data
• Crystallisation of multicomponent n-alkane waxes in diesel fuels under cold weather conditions is a current technological problem, where the influence of the multicomponent nature of the fuel on the crystallisation behavior and its relation to additive effectiveness is not well understood. • Crystallisation of single n-alkanes, C 16 H 34 -C 23 H 48 , and model multicomponent mixtures of these compounds in both toluene and dodecane, provides and insight into the crystallisation behavior of these compounds in representative diesel solvents. • The data enables the nucleation mechanism to be determined as well as the calculation of key nucleation kinetic parameters, leading to a greater understanding of how crystallisation occurs in these systems and the impact of solute and solvent nature. • Future work on a more complete understanding of how the compositional nature of these fuels affects the nucleation mechanism, its kinetics and its impact on additive effectiveness, can be built from this founding work.

Objective
The crystallisation of n -alkanes in diesel fuels is a common problem facing the petrochemical industry. The multicomponent nature of these fuels and its influence on crystallisation, provides a complex challenge for additive manufactures in designing additives that combat this behaviour. In order to develop improved additives, it is vital to understand crystallisation in these systems. A recent article published by the authors investigated the crystallisation of single n -alkanes, C 16 H 34 -C 23 H 48 and model multicomponent mixtures of these, from representative fuel solvents, providing insight into the crystallisation behaviour of compounds representative of diesel. The information presented here expands upon the information in the referenced article, by providing a complete dataset of solubility and nucleation kinetic values for the n -alkanes C 16 H 34 -C 23 H 48 . This allows the published work to be used as a comprehensive reference for the crystallisation of these n -alkanes.

Solubility data
Average crystallisation (Tc) and dissolution (Td) temperatures for each single alkane solute and a mixture of the 8 alkanes representative of diesel fuel, at 7 cooling rates (q), 0.25, 0.5, 1, 2, 3.2, 4 and 5 °C/min, for each solution concentration are shown in Tables 1 and 2 for the solvents dodecane and toluene respectively. The temperature displayed is the average of 4 polythermal cycles, along with the calculated standard deviations. The data provided highlights the influence of solute composition, concentration and cooling rate upon the crystallisation and dissolution behaviour of single and multicomponent alkane solutions. The equilibrium values of crystallisation (Tc,l) and dissolution (Te) temperature for the single alkanes and an 8-alkane mixture, in both toluene and dodecane over the range of compositions used are shown in Table 3 along with their associated errors. Both were calculated from the intercept value of a linear fitting of the Tc or Td data with q. The data highlights solubility and MSZW of the alkanes and its dependence on solute composition, concentration and solvent. The parameters of the van't Hoff fitting of the equilibrium solubility data for the single alkanes and an 8-alkane mixture in toluene and dodecane and their associated errors are shown in Table 4 , along with the predicted solubility temperature at 0.165xi according to the model. This data highlights the difference in solubility normalised to the same concentration for all system as well as the applicability of the van't Hoff model. Table 1 Average crystallisation, T c , and dissolution, T d , temperatures with their associated errors from 4 repeats of a polythermal crystallisation and dissolution cycle for 8 single n-alkanes and a mixture of 8C n in dodecane at 7 cooling rates. Errors are the standard deviation from 4 repeat measurements of T c and T d at each cooling rate and concentration.    Table 2 Average crystallisation, T c , and dissolution, T d , temperatures with their associated errors from 4 repeats of a polythermal crystallisation and dissolution cycle for 8 single n-alkanes and a mixture of 8C n in toluene at 7 cooling rates. Errors are the standard deviation from 4 repeat measurements of T c and T d at each cooling rate and concentration.    Table 3 Equilibrium values of crystallisation, T c,l , and dissolution, T e , temperature for 8 single alkanes and a mixture of 8C n in toluene and dodecane determined for each concentration from the extrapolation to the 0 °c/min cooling rate linear fitting of T c and T d with cooling rate. Errors in T c,l and T e are the error in the intercept of these linear fits.

Nucleation kinetics data
The natural log of the cooling rate (K/sec) and the natural log of the relative critical undercooling (u c ) for each concentration for each alkane solute and an 8-alkane mixture, are shown in Tables 11 and 12 in dodecane and toluene respectively. The linear fitting of this data determines the nucleation mechanism according to the rule of 3 from the KBHR approach. The calculated values of the detectable fraction of crystallised volume ( α det ) and the growth rate constant (K G ) for each concentration of alkane and 8-alkane mixture in dodecane and toluene are shown in Tables 13 and 14 respectively. This data is used in the calculation of the nucleation kinetic parameters for the instantaneous case according to the KBHR approach.    Growth rate constant, K G (m/s), and detectable fraction of crystallised volume, α det , calculated for each concentration of 8 alkanes and a mixture of 8 alkanes in dodecane for the KBHR approach instantaneous nucleation case.
Alkanes in Dodecane C 16 C 17 C 18 The growth rate constant K G was calculated using the equation below derived from the spiral growth case from Kashchiev [1] ; The sticking coefficient ε was assumed to be 1, the diameter of a solute molecule, d, was calculated from d = 3 6 × ν/π where ν is the solute molecular volume, the solute diffusion coefficient D ef , was assumed to be 10 9 nm 2 /s [2] , C was the concentration in mol nm −3 . The crystallite growth shape factor, k v , was taken as 4H 0 for a square plate crystal, m was taken as 1 for growth by diffusion of solute through a stagnant layer around the crystallite, as m = ½ applied to the case where growth was controlled by undisturbed diffusion of solute and each solution was magnetically agitated. The dimensionality of crystallite growth, d, was taken as 2 for disks or plates. n was calculated from the linear fit of ln q = ln q 0 + ( n + 1 ) ln u c .
The detectable fraction of crystallised volume was calculated using:  Table 15 shows the composition of a model fuels composed of 8 alkanes C 16 H 34 -C 23 H 48 in dodecane and toluene as well as a reference diesel fuel. Table 16 shows the provenance of the chemicals used in this study.

Materials
n -Alkanes, representative of the major constituents of diesel fuels, were chosen for this study, C 16 H 34 -C 23 -H 48 . Toluene and dodecane were chosen as representative for both the aromatic and aliphatic solvent components of diesel fuels. A model 8-alkane mixture was constructed where the relative composition of C 16 H 34 -C 23 H 48 matched that of a real diesel fuel. Table 15 shows the relative composition of the 8-alkane mixture in mole fraction, Table 16 shows the summary of the raw materials used in this research.

Equipment
The polythermal crystallisation experiments were conducted using a Technobis Crystal16 [3] crystallisation screening platform. This is a multicell crystalliser consisting of 16 individual cells which can take a 1.5mL vial of solution. 4 cells are grouped into a block, resulting in 4 blocks which can be individually temperature controlled via a Peltier heat exchanger linked to a refrigerated recirculating bath. The system can cool to ca. -15 °C and heat to an upper limit of 100 °C at a range of cooling rates from 0.1 -10 °C/min. A dry air purging system prevents condensation when cooling below sub-ambient temperatures. Each cell holds 1mL of solution in which crystallisation and dissolution can be followed as a function of temperature and time by turbidity via a transmission turbidity red laser source/detector, with each cell being magnetically agitated with a 2 × 7mm stirrer bar.
Polythermal crystallisation experiments were also carried out on a Mettler Toledo DSC 1 with cryogenic cooler, for the purpose of determining the thermodynamic parameters of an 8-alkane mixture. Samples were prepared around 10mg in mass in a sealed standard aluminium crucible.

Solution preparation
All solutions were prepared on a 5mL scale, as this was a sufficient volume to provide solution to fill 4 Crystal16 cells at once to provide a full run of cooling rates. For each alkane 5 concentrations were prepared, which were unique for each alkane but ranged overall from 0.09 -0.311 x i . Solutes were weighed out using a balance of ±0.01mg accuracy. 5mL of solvent was added using a Sartorius 50 0-50 0 0μL mechanical pipette.
Mixtures were heated on a hotplate with a magnetic stirrer to a temperature high enough that the solution completely dissolved and were left to homogenise at this temperature for 1 hour. A Sartorius 1-10 0 0μL mechanical pipette was used to transfer 1mL of solution to a 1.5mL glass GC vial, in which a 2 × 7mm PTFE stirrer bar had been placed. 16 vials were filled with 4 concentrations in 4 vials each, providing an almost complete set of concentrations to run at 7 cooling rates on the Crystal16 In the case of the 8-alkane mixture pre-determined amounts of each alkane were weighed into a large dish. This mixture was then completely melted over a water-bath, with an inverted watch-glass placed over the mixture so that any condensation formed drained away from the mixture. After homogenising for 1 hour above its melting point, the mixture was weighed into vials and dissolved as described above.

Polythermal analysis
Each block was set to follow a specific temperature program of heating and cooling at prescribed rates so that each concentration would be run at 0.25, 0.5, 1, 2, 3.2, 4 and 5 °C/min. 4 blocks allowed 4 cooling rates to be run simultaneously on 4 different solution concentrations. Each temperature program would begin with heating to 40 °C, with this temperature being held for 30 minutes to ensure complete dissolution. The sample was then cooled at the specified rate to -15 °C, before being held at this temperature for 30 minutes to ensure the system stabilised, before heating back up at the same rate to 40 °C. This cycle was repeated 4 times. From this the crystallisation temperature and dissolution temperature were determined, by fitting a Boltzmann [4] curve to the transition %T vs. temperature data and determining the temperature at 99%T for T diss and 90%T for T cryst from the equation of the fit.
This data was then calibrated based on the linear response of the temperature of a thermocouple inside a cell containing only solvent, and the Crystal16 measured temperature for each block. With the correct block's calibration being applied to the data that was collected on that block and with that solvent.
This data was then analysed using the polythermal method of plotting T c and T d vs cooling rate to determine the equilibrium values at q = 0 °C/min, T c,l and T e . The solubility was modelled with the Van't Hoff equation along with the solute's ideal solubility. The nucleation mechanism and associated kinetic parameters were determined using the KBHR approach [5][6][7] , a complete walk through of this approach can be found here [8] .
The nucleation mechanism was determined from the KBHR approach using the "rule of 3". For a plot of ln( q ) vs. ln( u c ), where q is the cooling rate (Ks -1 ) and u c is the relative critical undercooling as defined by; The gradient of a linear fitting of this plot, known as the nucleation mechanism parameter ω, determines the mechanism. When ω > 3 the mechanism in progressive and when ω < 3 the mechanism is instantaneous. For the progressive case the critical cluster radius r * , number of molecules in the critical cluster i * , and the effective interfacial tension γ eff can be determined by fitting Eq. 4 to a graph of ln( q ) vs. ln( u c ).
The parameters a 1 , a 2 and q 0 are given by.
Where V is the solution volume, K J is the nucleation rate constant and N det is the number of crystallites at the detection point. From the parameter a 2 γ eff can be determined through. b = k n v 2 0 γ 3 e f f kT e λ 2 (8) k n is the nucleus shape factor and v 0 is the volume occupied by a solute molecule in the crystal. r * and i * can then be calculated using.
1 /md a n K G T e (12) Where k v is the crystallite growth shape factor 4 π 3 for spheres, 8 for cubes, π H 0 for disks, 4H 0 for square plates (H 0 is the fixed disk or plate thickness), and 2A 0 for needles (A 0 is the fixed needle cross-sectional area). K G is the growth rate constant. d is the dimensionality of crystallite growth, 3 for spheres or cubes, 2 for disks or plates and 1 for needles. a is the dimensionless molecular latent heat of crystallization and is defined in Eq. 13 as: Where λ is the latent heat of crystallization and k is the Boltzmann constant. α det is the detectable fraction of crystallized volume.

Computational methods
Intermolecular interactions were determined using dedicated software [9][10][11] that uses gridbased modelling with a systematic search algorithm to investigate the intermolecular interactions between a target and probe molecule by calculating the interaction energy between the two at each point on a user defined grid. The molecules were constructed and optimised using the Forcite module of Materials Studio [12] before being run in the grid search.
For both solvents the optimal grid was determined by establishing the number and energy of interactions found as a function of grid size. Ideally a grid with infinitely high resolution would be used however software and hardware limited the total number of grid points to less than ≈10 0 0. As a result, the optimal spacing of these grid points was determined to find the strongest interactions. In the case of Toluene this was a 30-30-30 Å (XYZ) size grid with 8-11-8 (UVW) and 972 grid points, for dodecane this was 20-20-30 Å (XYZ) Å size grid with 7-11-8 (UVW) grid lines. The Euler angles in all cases were 30 °at all grid points. XYZ represents the physical size of the grid in angstroms, UVW represents the number of grid lines in a specific direction, XYZ, from the origin.
The interaction energy at each of the individual grid points and Euler angles from these optimised grids, was calculated for each n -alkane target and solvent probe pair. From the interaction energies of all interactions for a given probe/target pair, the strength of the strongest interaction was determined, as well as the total number of interactions with values above a threshold value e.g., -1.0kCal/mole, and the total sum of energies of all the interactions above these threshold values.