In the Laboratory edited by
The Microscale Laboratory
R. David Crouch Dickinson College Carlisle, PA 17013-2896
Thermal Equilibrium in Plastic and Glass Microscale Containers
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Estela Curbelo, María F. Cerdá, and Eduardo Méndez* Laboratorio de Biomateriales, Instituto de Química Biológica, Facultad de Ciencias, Universidad de la República, Iguá 4225 casi Mataojo, 11400 Montevideo, Uruguay; *
[email protected] There is increasing interest in the use of microscale laboratory experiments owing to the reduction of pollution and laboratory-associated costs (1, 2). The implementation of microscale experiments frequently leads to the substitution of common medium-volume glass beakers (semi-microscale) by small-volume plastic or glass containers like vials and microcentrifuge or culture tubes. Although this represents an advantage in relation to breakage minimization, the relatively low value of the thermal conductivity for plastic materials (Table 1) introduces a new problem, particularly for physical chemistry experiments, where thermal equilibrium conditions are needed to carry out the measurements (3, 4). The extended thermal equilibration time should be taken into account in the design of new laboratory exercises in the framework of microscale experimentation. In this article, some examples that illustrate this fact are described, and a mathematical model is developed to account for the experimental observations. Experimental Results and Discussion The system under study consisted of a capped container made of a selected material with a known mass of water (solution) immersed in a controlled-temperature water bath set at TB. The thickness of the walls of the containers was 1.0 mm except for 1 mL glass container (2.1 mm). The temperature of the solution, TS, was monitored at selected time intervals with a digital thermometer (±0.1 ⬚C) inserted through the cap, until thermal equilibrium was achieved. The temperature ratio, TS兾TB, was calculated at each time. The solution temperature can be considered constant in the whole volume, since thermal conductivity of liquid water is noticeably larger than those of the plastics (Table 1). Different thermal profiles were obtained depending on the container’s material (Figure 1). For glass containers, an exponential temperature rise is obtained, while for plastic containers, a time delay is observed at the beginning of the heating process followed by an exponential temperature rise. For a given container’s material, the time needed to achieve Table 1. Thermal Conductivity of Different Materials and Liquid Water Material
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Thermal Conductivity/ (J s᎑1 m᎑1 K᎑1)
Glass (Pyrex)
1.05
Acrylic
0.2
Polyethylene
0.5
Polypropylene
0.5
Polyvinylchloride
0.19
Liquid water
0.61
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thermal equilibration of the solution increases with the quantity of solution, something intuitively expected. Comparison between Pyrex glass and polypropylene containers for a given quantity of solution and same wall thickness indicates that thermal equilibrium is achieved in plastics later (Figure 1B). The temperature ratio versus time profile can be modeled according to T U TS = 1 − 1 − 0 exp − t TB mS CP, S TB
(1)
or linearized as
ln
TB − T0 TB − TS
=
U t mS CP, S
(2)
where T0 corresponds to the temperature of the solution at the beginning of the heating process (at t = 0, TS = T0), and specific heat mS and CP,S are the mass and constant-pressure – capacity of the solution, respectively. U represents the mean heat transfer coefficient that takes into account the whole process under stationary conditions
1 = U
1 1 x + + M A hext h int kM
(3)
where A is the surface area through which heat is transferred, xM and kM are the thickness and the thermal conductivity coefficient of the container’s wall, respectively, and h is the convection coefficient at the interior and exterior wall of the container (see Supplementary MaterialW for a detailed deduction of these equations). Equations 1–3 contain the information needed to interpret the experimental data. Note that these equations are valid only under stationary conditions. Thermal equilibrium is achieved more rapidly as the quantity of solution (mS) decreases, as well – as for large values of the mean heat transfer coefficient (U ), both conditions– benefitting microscale experiments. The dependence of U on the material properties (eq 3) indicates that, for a given quantity of solution, thermal equilibrium is achieved more slowly for– plastic materi– als, because k plastic < k glass, and hence, U plastic < U glass. Additionally, for a given quantity of solution and container’s material, thermal equilibrium is achieved more slowly as the thickness of the container (xM) is increased. This can be clearly seen by noting that thermal equilibrium for 1 mL and 10 mL glass containers is achieved almost at the same time owing to the larger thickness of the walls of the glass vials (glass containers in Figures 1A and 1B). The accomplishment of stationary conditions can be better described by fitting data to eq 2 (Figures 1C and 1D).
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In the Laboratory
Figure 1. Thermal profiles fitted according to eqs 1 and 2 for 1 mL (A and C, respectively), and 10 mL (B and D, respectively) volume solution, in glass (Pyrex) (䉱) and plastic (polypropylene) (䊉) containers. The thickness of the walls of the containers employed was 1.0 mm except for 1 mL glass (2.1 mm).
For both types of materials, such conditions are observed for TS up to a value of 95% of the final temperature, TB. For glass containers, the stationary conditions are accomplished from t = 0, but for plastic containers, only after the time lag observed in the TS versus t profile. Hazards Containers filled with hot water should be handled with care.
Acknowledgment The authors wish to thank CSIC (Universidad de la República) for financial support.
Conclusions and Suggestions Heat transfer from a controlled-temperature bath to a solution through the container’s walls is highly dependent on the accumulation of energy by the container, which in turn depends on its thickness and type of material. Thermal equilibration of solutions take almost the same time in a common glass 10 mL semi-micro volumetric flask (xM = 1.0 mm) versus a 1 mL glass vial (xM = 2.1 mm), in this case due to the greater thickness of the latter. For 1 mL plastic container (xM = 1.0 mm), the wall is thinner but the material has a lower thermal conductivity; thus both effects cancel out and thermal equilibration takes approximately the same time as a 1 mL glass vial. For the same volume and thickness, thermal equilibrium is mainly dependent on the material of the container; thus, it takes a longer time (ca. 3 times) to achieve thermal equilibrium in a 10 mL plastic container versus a 10 mL glass container. Our findings can be summarized by a www.JCE.DivCHED.org
single statement: the same time is needed to achieve thermal equilibrium in a 50 mL glass container compared to a 1 mL plastic microcentrifuge tube with the same wall thickness. In conclusion, special attention should be given to the achievement of thermal equilibrium in the design of physical chemistry experiments. The usual consideration that microscale experimentation takes less time may be false depending on the material chosen.
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Supplemental Material
Derivations of the equations are available in this issue of JCE Online. Literature cited 1. Singh, M. M.; McGowan, C. B.; Szafran, Z.; Pike, R. M. J. Chem. Educ. 2000, 77, 625–626. 2. Singh, M. M.; Szafran, Z.; Pike, R. M. J. Chem. Educ. 1999, 76, 1684–1686. 3. Ragsdale, R. O.; Vanderhooft, J. C.; Zipp, A. P. J. Chem. Educ. 1998, 75, 215–216. 4. De Muro, J. C.; Margarian, H.; Mikhikian, A.; No, K. H.; Peterson, A. R. J. Chem. Educ. 1999, 76, 1113–1116.
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