A method was developed to determine the specific heat capacity and thermal conductivity of leaf tissue by non-invasive, contact-free near infrared laser probing, which requires less than 1 min per sample.
Plants can produce valuable substances such as secondary metabolites and recombinant proteins. The purification of the latter from plant biomass can be streamlined by heat treatment (blanching). A blanching apparatus can be designed more precisely if the thermal properties of the leaves are known in detail, i.e., the specific heat capacity and thermal conductivity. The measurement of these properties is time consuming and labor intensive, and usually requires invasive methods that contact the sample directly. This can reduce the product yield and may be incompatible with containment requirements, e.g., in the context of good manufacturing practice. To address these issues, a non-invasive, contact-free method was developed that determines the specific heat capacity and thermal conductivity of an intact plant leaf in about one minute. The method involves the application of a short laser pulse of defined length and intensity to a small area of the leaf sample, causing a temperature increase that is measured using a near infrared sensor. The temperature increase is combined with known leaf properties (thickness and density) to determine the specific heat capacity. The thermal conductivity is then calculated based on the profile of the subsequent temperature decline, taking thermal radiation and convective heat transfer into account. The associated calculations and critical aspects of sample handling are discussed.
The large-scale processing of biological materials often requires heat-treatment steps such as pasteurization. The equipment for such processes can be designed more precisely if the thermal properties of the biological materials are well characterized, including the specific heat capacity (cp,s) and thermal conductivity (λ). These parameters can be determined easily for liquids, suspensions and homogenates by calorimetry 1. However, measuring such parameters in solid samples can be labor intensive, and often requires direct contact with the sample or even its destruction 2. For example, photothermal techniques require direct contact between the sample and detector 3. Such limitations are acceptable during food processing, but are incompatible with highly regulated processes such as the production of biopharmaceutical proteins in plants in the context of good manufacturing practice 4. In such a context, repeated (e.g., weekly) monitoring of thermal properties may be required during a seven-week growth period for individual plants as a quality control tool. If such a monitoring would require and consume a leaf for each measurement, there would be no biomass left to process at the time of harvest.
Additionally, using only leaf parts instead would cause wounding to the plant and increase the risk of necrosis or pathogen infection, again diminishing the process yield. The likelihood of pathogen infection may also increase if a method with direct contact to the sample would be used, inducing the risk that an entire batch of plants can be infected through contact with a contaminated sensor device. Similar aspects have to be considered for the monitoring of plant stresses like drought, e.g., in an ecophysiological context. For example, water loss is often monitored by a change in the fresh biomass, which requires an invasive treatment of the plants under investigation 5, e.g., dissecting a leaf. Instead, determining the specific heat capacity, which depends on the water content of a sample, in a non-invasive manner as describe here, can be used as a surrogate parameter for the hydration status of plants. In both scenarios (pharmaceutical production and ecophysiology), artificial stresses induced by destructive or invasive measurement techniques would be deleterious as they can distort the experimental data. Therefore, previously reported flash methods 6 or the placement of samples between silver plates 7 are unsuitable for such processes and experiments because they either require direct contact to the sample or are destructive. The parameters cp,s and λ must be determined in order to design the process equipment for a blanching step that can simplify product purification and thus reduce manufacturing costs 8-10. Both cp,s and λ can now be rapidly determined by contact-free non-destructive near infrared (NIR) laser probing in a consistent and reproducible manner 11 and this new method will be explained in detail below. The results obtained with this method were successfully used to simulate heat transfer in tobacco leaves 12, allowing the design of appropriate processing equipment and the selection of corresponding parameters such as the blanching temperature.
The method is easy to set up (Figure 1) and has two phases, measurement and analysis, each of which comprises two major steps. In the measurement phase, a leaf sample is first locally heated by a short laser pulse and the maximum sample temperature is recorded. The temperature profile of the sample is then recorded for a duration of 50 s. In the analysis phase, leaf properties such as density (easily and accurately determined by pycnometric measurement) are combined with the maximum sample temperature to calculate cp,s. In the second step, the leaf temperature profile is used as the input for an energy balance equation, taking conduction, convection and radiation into account, to calculate λ.
Detailed step-by-step instructions are provided in the protocol section, expanding on the contents of the accompanying video. Typical measurements are then shown in the results section. Finally, the benefits and limitations of the method are highlighted in the discussion section along with potential improvements and further applications.
Figure 1: Apparatus used to determine leaf thermal properties. A. Photograph of the measurement apparatus used to determine the specific heat capacity and thermal conductivity of leaves. The peripheral devices (computers, oscilloscope) are not shown. B. Schematic representation of the measurement apparatus. The laser and connected equipment are highlighted in red, the NIR detector for temperature measurement is shown in purple, the leaf sample is green and the photodiode power sensor is blue. C. Drawing of the elements of the measurement setup with the same color code as in B. The size bar indicates 0.1 m. D. Screenshot illustrating the typical elements of the laser control software. Please click here to view a larger version of this figure.
1. Plant Cultivation and Sample Preparation
2. Determine Leaf Thickness and Density
3. Determine the Spectral Transmission and Reflection of Leaves
4. Set up the Measurement Apparatus
5. Prepare the Leaf Samples
6. Take the Temperature Measurements
Figure 2: Measuring leaf transmission using a photodiode power sensor. A. Typical voltage profile for a reference experiment without a leaf sample visualized using an oscilloscope. B. Voltage profile with a leaf sample mounted in the apparatus. In both cases, the transmitted laser power is proportional to each of the two flanks. Please click here to view a larger version of this figure.
7. Calculate the Specific Heat Capacity of the Leaf Sample
8. Prepare the Temperature Profile Data for Thermal Conductivity Calculations
Figure 3: Data processing scheme for the calculation of λ. A. After data reduction, the temperature profiles are normalized to the ambient temperature. B. Next, all data points before the maximum sample temperature (Tmax) are removed. C. Measurement artifacts (shown in the "inconsistent" data set) are identified based on temperature shifts larger than three times the baseline noise and removed from the dataset prior to fitting to an exponential function. D. The Celsius temperature scale is converted into the Kelvin scale. E. For each time interval, λ is calculated based on the temperature profile. F. A window of 20 s is defined in which a relevant temperature change can be observed. G. Based on the selected time window, the average and standard deviation are calculated for λ. H. Representative results for two different N. tabacum leaf samples. Orange arrows and lines indicate the effect of the corresponding processing step on the presented data. Please click here to view a larger version of this figure.
9. Calculation of the Thermal Conductivity of the Leaf Sample
Measurement of Leaf Properties
Using the above microscopic method, a leaf thickness of 0.22-0.29 × 10−3 m was determined for both N. tabacum (0.25±0.04 × 10−3 m, n=33) and N. benthamiana (0.26±0.02 × 10−3 m, n=24), which is well within the 0.20-0.33 × 10−3 m range previously reported for the leaves of various plant species 3. Determining the thickness with a dial-gauge yielded values of ~0.28 × 10−3 m (n=10), which was within one standard deviation of the results from the microscopic measurement. Thus, the dial-gauge measurement may be preferred over the microscopic method for thickness determination in routine applications as it was easier to apply and the results for cp,s and ʎ deviated less than 10% from the more labor intensive technique. The density of N. tabacum and N. benthamiana leaves was 750±10 kg m−3 (n=20), which matches the 631-918 kg m−3 range previously reported for leaves in other species 3.
Calculation of the Specific Heat Capacity
Temperature profiles collected for Nicotiana species showed a rapid increase over the time of the laser pulse until the maximum temperature (Tmax) was reached within less than 1 s. After the pulse, the temperature decreased exponentially until it reached ambient temperature (T0) (Figure 3A−E). The specific heat capacity (cp,s) was calculated according to Equation 8 yielding values of 3661 ± 323 J kg-1 K-1 for N. tabacum and 2,252 ± 285 J kg-1 K-1 for N. benthamiana. Two cultivation settings and durations were used for each species (see section 1.2) but this did not affect cp,s (Figure 4). However, the cp,s values decreased linearly from the old (bottom) to young (top) leaves (R2 = 0.85) in the case of N. tabacum (Figure 4A), which correlated to the water content [g g-1 biomass] that had been determined as the difference of wet biomass at the time of harvest and the mass after 72 h incubation at 60 °C 11. This correlation between water content and specific heat capacity was in agreement with previous observations by other authors 13. An inverse correlation was observed for N. benthamiana (R2 = 0.79), where the difference between the specific heat capacities of leaves of different degrees of maturity (bottom = old; top = young) were only 13% compared to 21% for N. tabacum. This difference may originate in the fact that the water content in leaves of N. benthamiana is almost constant over the different degrees of leaf maturation 11. A sensitivity analysis revealed that differences in cp,s were proportional to fluctuations in the measurement parameters in Equation 8. The effect of the reflected and transmitted laser power was sub-proportional, because these parameters were not individual factors in Equation 7. Accordingly, the effect of errors in these two parameters was smaller than those caused by fluctuations in the laser power or ambient temperature. In general, the measurement was considered to be robust because all parameters involved in the calculation of cp,s had a coefficient variation of less than 10% (Figure 4C and D).
Figure 4: Specific heat capacity and thermal conductivity values determined for N. tabacum and N. benthamiana. A. Specific heat capacity and thermal conductivity of N. tabacum leaves according to the leaf position on the plant (bottom = old leaves; middle = mature leaves; top = young leaves). Stars and triangles indicate plants that were 49 and 56 days old, respectively. B. Specific heat capacity and thermal conductivity of N. benthamiana leaves according to the leaf position on the plant. Stars and triangles indicate plants that were cultivated in a phytotron or greenhouse, respectively. C. Sensitivity of specific heat capacity values to changes in the input parameters. Triangles show specific heat capacity values resulting from a 10% increase (red, upward) or decrease (blue, downward) in single model parameters. D. Sensitivity of thermal conductivity values to changes in the input parameters. Triangles mark shoe thermal conductivity values resulting from a 10% increase (red, upward) or decrease (blue, downward) in single model parameters. Error bars in A and B indicate the standard deviation (n≥3), while in C and D they represent the complete range of values obtained during 10% variation sensitivity analysis. Please click here to view a larger version of this figure.
Calculation of the Thermal Conductivity
The thermal conductivity (ʎ) was calculated from the temperature profiles by exponential fitting (Figure 3) combined with equations for conductive and convective heat transfer as well as thermal radiation. Equation 15 yielded average values of 0.49 ± 0.13 J m−1 s−1 K−1 (n = 19) for N. tabacum and 0.41 ± 0.20 J m−1 s−1 K−1 (n = 25) for N. benthamiana. There was no correlation between ʎ and plant age or cultivation setting, although a correlation between the leaf age and ʎ was observed for N. benthamiana (Figure 4B), agreeing with previously reported age-dependent differences in other plant species 14. As discussed above, the water content was an unlikely reason for this difference as it was found to be homogenous across leaves of varying maturity for N. benthamiana. Instead, we speculate that changes in the leaf tissue, e.g., the cell wall composition, were responsible for this observation by altering the heat transfer properties of the leaves and thus affecting the value of ʎ. The determination of ʎ was sensitive to changes in the ambient temperature. A sensitivity analysis revealed that fluctuations of ±2.3 K altered the value of ʎ by 64-125%. According to Equation 15, the ambient temperature has an effect by the power of four on the thermal radiation and thus directly affects the value of ʎ.
Evaluation of the Measurement Apparatus
It was possible to set up the measurement assembly within 3 h. Once this was complete, the start-up time of the system was approximately 15 min per measurement series. Single measurements took less than 3 min, including sample preparation and the entire measurement cycle. Analysis of the laser exposure time revealed that a heating time of 0.5 s resulted in a temperature increase of 19.9±4.3 °C (n=55) was the best compromise between the high ΔT (achieved by long laser pulses) required for a good signal-to-noise ratio (SNR) and the low ΔT (achieved by short laser pulses) required to avoid tissue damage. Pulse durations longer than 0.5 s resulted in the loss of mass from the sample, probably reflecting the evaporation of water and/or damage to the leaf tissue as the sample temperature reached up to 70 °C, whereas only 42.9±4.2 °C (n=55) were observed for 0.5 s laser pulses. For durations of less than 0.5 s, the temperature noise of ±0.31 K (standard deviation, n = 25) accounted for more than 5% of ΔT and was thus a significant part of ΔT. In contrast, at 0.5 s the noise accounted only for 2.5% of the signal and was thus regarded as insignificant. Additionally, the samples did not heat up to more than ~45 °C, which is a temperature that tobacco plants can also be exposed to in the natural tropic to sub-tropic habitat and which is only detrimental to plant species found in tundra habitats 15. The power density of the laser was 170 kW m-2, whereas natural solar radiation is typically in the range of 1.0-1.4 kW m-2 16,17. However, due to the very short time of the pulse, this higher energy dose did probably not damage the leaf tissue as indicated by a recently published microscopic analysis 11. The temperature data used to calculate ʎ were restricted to the initial 20 s after the laser pulse because only during this period did the noise (±0.31 K) account for less than 5% of the sample's temperature signal and was thus regarded as insignificant. When temperature data from beyond the 20 s time frame were used, the values calculated for ʎ declined (Figure 3F). A possible explanation was that some of the assumptions made for the calculation of ʎ did not apply for low values of ΔT. Especially, the term describing thermal radiation in Equation 15 might have been affected as it is affected by the forth power of temperature. Also, the leaf area surrounding the sample spot exposed to the laser might have heated up slightly and thus might not have been the ideal heat sink assumed in the model reducing the effective ΔTx and ultimately the calculated ʎ.
The contact-free, non-destructive measurement method described above can be used to determine cp,s and ʎ in a simultaneous and reproducible manner. The calculation of ʎ in particular depends on several parameters that are sensitive to errors. Nevertheless, the impact of these errors was either linear or sub-proportional, and the coefficient of variation for all parameters was found to be less than 10%. Even though the method can thus be regarded as robust, some technical improvements can be made to reduce the remaining sources of error.
Mounting the sample into the assembly was technically challenging because a flat leaf surface is preferable for measurement but the sample naturally has an undulating surface. This problem could be overcome by designing a dedicated sample holder with geometries precisely adjusted to the leaf sample, e.g., leaf thickness and width, clamping the sample in the preferable orientation. This approach would make the measurements more reproducible, but would compromise the contact-free nature of the measurement because firm contact between the sample and holder would be required to pull the leaf surface flat. The benefits of using this kind of holder would therefore depend on the context of the measurement, i.e., whether the precision or contact-free nature of the measurement is most important. In contrast, such considerations may not be necessary at all for leaves with an inherently flat surface, e.g., rice and related species.
Convective heat transfer due to air movement in the environment of the sample should be kept to a minimum during measurements because this strongly affects the calculation of both cp,s and ʎ18. The apparatus should therefore be located away from air streams generated by air conditioning systems, radiators or other equipment, such as computer with integral cooling fans. This is also important because changes in the relative water content of the leaves 19 that might occur before or during the measurement due to evaporation, which can be increased by air movements 20, were not accounted for in the model. Thus, measurements, especially with detached leaves, should be carried out rapidly as described in the protocol section to avoid errors during data acquisition. In the future, the effects of evaporation on the measurement may be reduced or avoided if the measurement is conducted in an at least partially enclosed measurement chamber with an implemented humidity control.
The accuracy of cp,s and ʎ values can be increased by measuring the parameters used in the corresponding equations more precisely. In the case of cp,s these parameters are the laser power, maximum and ambient temperature and sample volume, i.e., the product of laser spot area and thickness, and sample density (Equation 8). The latter two parameters must be determined in experiments accompanying the actual measurement and their reliability can be improved if several representative biological replicates are tested. However, even when a simple dial-gauge measurement was used, the difference in leaf thickness compared to a microscopic analysis was only 11%, which affected the values calculated for cp,s and ʎ by the same degree. In contrast, temperatures and laser power can be monitored throughout the measurement. The accuracy of cp,s can be improved if these online data are used instead of fixed values for laser power and ambient temperature, and the data are collected using well-calibrated sensors. These considerations also apply to ʎ, but the ambient and sample temperatures are the most important parameters because both affect the calculated value by the power of four.
The current calculation of ʎ was based on several assumptions regarding convective heat transfer and thermal radiation. For example, the emissivity (ε) and convective heat transfer coefficient (h) were not measured or calculated explicitly in the method presented above, but were derived from previous publications 18,21. The accuracy of ʎ could therefore be improved by determining these two parameters under the actual measurement conditions. However, using the literature data for calculations nevertheless yielded ʎ values that were within the range experimentally determined for other plant species for which similar properties can be expected due to their phylogeny to Nicotiana species and their physiology, i.e., herbaceous plants 3. Even if the values for ε and h were varied over the entire range previously reported for these values in plants, e.g., 0.93-0.98 for ε 21, their effect on the final value of ʎ was <10% and thus within the natural variation observed here.
The method presented above was not only able to determine the thermal properties of intact unharmed leaves and detached leaves, but it also correctly identified different types of more severe damage introduced intentionally before measurement. Therefore, different types of leaf samples can be readily distinguished, providing a tool to remove, prior to analysis, any poor samples that would yield low-quality data. This feature could be used for quality control when monitoring biological materials, e.g., samples failing to meet specifications in terms of cp,s and ʎ could be excluded from further processing. This would be an asset in the context of a highly regulated processes such as molecular farming 4.
The advantages of this new method compared to others in the literature include the rapid sample handling, minimal preparation, contact-free and non-destructive simultaneous measurement of cp,s and ʎ, and the use of common equipment that can be found in many optical laboratories. This will facilitate broader applications of the method compared to those requiring specialized and expensive devices such as differential scanning calorimeters. Furthermore, calorimetry requires direct contact with the sample22 so there is a risk of damage, and the method is usually limited to the measurement of specific heat capacity 22. In contrast, whereas thermal imaging can detect necrosis or physical changes in leaves or entire plants in a contact-free manner 23, it also requires complex image analysis and dedicated specialized devices 24 which might be overcome in the future by cheaper and more powerful IR cameras and accompanying peripheral devices. Spectral analysis is another contact-free method for the analysis of water content and chlorophyll levels 25, but it has not yet been used to determine specific heat capacity and/or thermal conductivity.
The measurement approach reported herein is a robust method to determine the thermal properties of plant leaves with low investment costs and short measurement times. It was successfully used to determine cp,s and ʎ in N. tabacum and N. benthamiana, two species that are relevant in the area of molecular farming 4. The values calculated for both parameters based on leaf temperature profiles were in good agreement with those previously reported for other plant species 3. The method is non-destructive, contact-free, and does not require complex sample preparation, providing advantages over all current alternative methods for the analysis of thermal properties. The simple design may also facilitate the development of hand-held devices to increase flexibility.
The authors have nothing to disclose.
The authors are grateful to Dr. Thomas Rademacher and Ibrahim Al Amedi for cultivating the plants used in this study. We would like to thank Dr. Richard M. Twyman for his assistance with editing the manuscript. This work was in part funded by the European Research Council Advanced Grant “Future-Pharma”, proposal number 269110, the Fraunhofer Zukunftsstiftung (Future Foundation), the Fraunhofer-Gesellschaft Internal Programs under Grant No. Attract 125-600164.
1" tube | Thorlabs | SM1L10E | Tube for fiber holder |
Agarose | Sigma Aldrich | A0701 | Agarose |
Bi-Convex lense f=25.4 | Thorlabs | LB1761 | Lense |
Digital Handheld Optical Power and Energy Meter Console | Thorlabs | PM100D | Console for thermal surface absorber sensor |
Digital Phosphor Oscilloscope | Tektronix | DPO7104 | Oscilloscope |
DMR light microscope | Leica | n.a. | Light microscope |
Falcon 50mL Conical Centrifuge Tubes | Fisher Scientific | 14-432-2 | Pycnometer |
Ferty 2 Mega | Kammlott | 5.220072 | Fertilizer |
Fiber holder | Thorlabs | Fiber holder | |
Forma -86C ULT freezer | ThermoFisher | 88400 | Freezer |
Greenhouse | n.a. | n.a. | For plant cultivation |
Grodan Rockwool Cubes 10x10cm | Grodan | 102446 | Rockwool block |
Infrared Detector Optris CT | Optris | OPTCTLT15 | Infrared detector |
Infrared Detector Software Compact Connect | Optris | n.a. | Control software for infrared detector |
Lambda 1050 UV/Vis spectrophotometer | PerkinElmer | L1050 | UV/VIS Spectrophotometer |
Laser 400μm, 1550nm Conduction Cooled Single Bar Fiber Coupled Module | DILAS | M1F-SS2.1 | Laser |
Laser cover | Amtron | LM200 | Laser Cover |
Laser Driver | Amtron | CS 408 | Laser Driver |
Osram cool white 36 W | Osram | 4930440 | Light source |
Photodiode sensor | Thorlabs | PDA20H-EC | Power sensor for transmission measurements |
Precision weight Ohaus Analytical Plus | Ohaus | 80251552 | Precision weight |
Sample frame | Fraunhofer ILT | n.a. | Fixation of the leaf sample |
Software Pyro Control | Amtron | n.a. | Laser Power Control Software |
Stainless-steel-holder | n.a. | n.a. | Holder for measurement set-up |
Teflon plates 2cm | Fraunhofer ILT | n.a. | Teflon attenuation |
Thermal surface absorber Power sensor | Thorlabs | S314C | Sensor for laser power measurements |
Vibratome | Leica | 1491200S001 | Vibratome |
Zoc/Pro 6.51 | EmTec Innovative Software | n.a. | Laser Control Software |