**High Biomass Productivity of Short-Rotation Willow Plantation in Boreal Hokkaido Achieved by Mulching and Cutback**

**Qingmin Han 1,\* ,**† **, Hisanori Harayama 1 , Akira Uemura 1,**† **, Eriko Ito 1 , Hajime Utsugi 2 , Mitsutoshi Kitao 1 and Yutaka Maruyama 3**

Received: 12 March 2020; Accepted: 27 April 2020; Published: 1 May 2020

**Abstract:** Weed control, which is commonly achieved by herbicides, is important in successfully establishing short-rotation coppice (SRC) of willow. In this study, we examined agricultural mulch film as a means of effective weed control and the influence of cutback practice (coppicing the first year's shoot growth in the winter following planting) on biomass production in boreal Hokkaido, Japan. One-year-old cuttings from two clones each of *Salix pet-susu* and *S. sachalinensis* were planted in double-rows at a density of 20,000 plants ha−1 . All plants were harvested three growing seasons after cutback. Average oven-dried biomass yield was 5.67 t ha−1 yr−1 with mulching, whereas it was 0.46 t ha−1 yr−1 in the unmulched control with a weed biomass of 4.13 t ha−1 yr−1 , indicating that mulching was an effective weed control. However, weeds grew vigorously on the ground between mulch sheets and their dry biomass amounted to 0.87 t ha−1 yr−1 . Further weeding between the mulch sheets enhanced the willow biomass yield to 10.70 t ha−1 yr−1 in the treatment with cutback. In contrast, cutback even reduced the willow yield when there were weeds between the mulch sheets. This negative effect of cutback on the willow yield resulted from nutrient competition with weeds; there was similar leaf nitrogen content and dry biomass per unit land area for the weeds and willows combined in the control and mulching treatments. These results suggest that growing SRC willow is feasible in boreal Hokkaido if combined with complete weed control and cutback, and is facilitated by using mulch film.

**Keywords:** cutback; mulch; *Salix*; short-rotation coppice; weed control; woody biomass

### **1. Introduction**

Woody biomass production is an economically viable and ecologically sound solution to address increasing energy demands; it also has positive effects on reducing global atmospheric CO2 and, consequently, the greenhouse effect. Willows (*Salix* spp.) are one of the best species for short-rotation coppice (SRC) in temperate climates because they are easily propagated vegetatively, they have a high yield potential in a few years, a broad genetic base, and they can re-sprout from their coppiced stools after harvesting [1]. However, despite their general plasticity, the adoption of willows as a bioenergy production system remains a challenge in respect to high yield [2]. In particular, weed control is of top priority in order to achieve a long-term high yielding SRC willow plantation [3–6]. It is

extremely important because weeds have a negative effect on the SRC willows as they compete for light, water, and nutrients, and they consequently reduce the survival rate of cuttings and biomass production [2,7]. Furthermore, the response to weed competition may differ between species and clones, as do growth patterns and competitive abilities, just as soil properties and climate differ between plantations [8]. To date, willow selection and breeding have focused on high biomass production under optimum conditions, and no commercial clone has been found to have high biomass productivity in the presence of competition from weeds [2,7,8]. Therefore, development of environmentally friendly, efficient, and cheap weed control measures might be the best way forward for the establishment of SRC willow plantations.

The application of mulches in agriculture and horticulture has increased dramatically in the last two decades throughout the world. This increase is due to benefits such as suppressed weed growth, soil moisture conservation, reducing certain insect pests, higher crop yield, earlier harvests, improved fruit quality, and more efficient use of soil nutrients [9–15]. The selection of an appropriate mulching material depends on crop type, crop management practices, and climatic conditions. Of the various materials being used as mulches, plastics are most commonly used in agriculture and horticulture. However, to our knowledge, there has been little research on the use of plastic mulch in plantations [16–18], whereas a report demonstrated that plastic mulch is an excellent way of promoting willow productivity by regulating water content in the soil and increasing soil temperature and controlling weeds on the poorly drained soil [17].

Coppicing the first year's shoot growth in the winter following planting, which is hereafter called cutback, is another common practice during the establishment of SRC willow plantations. This is mainly done to promote multiple stem sprouting and to facilitate fertilization and additional weeding during the second growth season [4–6,19,20]. However, recent studies indicate that this practice may reduce biomass productivity [8,20], and is no longer recommended in Sweden [21]. The factors and mechanisms determining the effect of cutback on biomass production are not fully understood. The reduced canopy due to cutback may provide weeds with new establishment opportunities and increase the need for further weed control during the years following establishment. Consequently, willow biomass production would decrease. Therefore, more studies are needed to determine whether cutback affects the ability of willows to compete with weeds, especially at the beginning of the second growing season, since some weed species may start to grow earlier than the willow. The interaction between cutback and weeds in relation to biomass production may be also be linked to resource limitation within plantations [22–24]. In this respect, information on nitrogen acquisition and allocation between willows and weeds would provide an insight into the effect of cutback practice on willow production [23,25,26].

Compared to European and North American countries, SRC willow cultivation is still a developing field in Japan [27–29]. The Feed-in Tariff Policy for renewable energy implemented in 2012 after the Fukushima Daiichi Nuclear Power Plant accident has become a driver, and the demand for wood resources has increased rapidly in recent years. Considering the above factors and their influence on the fast establishment of SRC willow plantations and long-term biomass productivity, we evaluated plastic mulch as a method of weed control. We further tested cutback and its interaction with weed control on the biomass production of *Salix pet-susu* and *S. sachalinensis* in the first harvest cycle, three growing seasons after cutback. There are no commercial willow cultivars in Japan, and these two species were selected because they are widely distributed in Northeastern region of Honshu and Hokkaido [30].

#### **2. Materials and Methods**

#### *2.1. Study Site and Experimental Design*

This study was carried out in a former grassland located near the Sanru river in Shimokawa town, Hokkaido (44◦250 N, 142◦420 E). The parent material of the soil is quaternary alluvial deposits with rounded or subrounded rock fragments covering the surface [31]. Soil nitrate nitrogen averaged from

surface to 40 cm depth was about 4.6 mg per kg soil [31]. During the period 1978–2016, mean annual precipitation was 918.4 mm, mean diurnal mean, maximum, and minimum temperatures were 5.1 ◦C, 10.3 ◦C, and −0.5 ◦C, respectively, obtained at a nearby meteorological station (44◦180 N, 142◦380 E, 143 m a.s.l.; Japanese Bureau of Meteorology). Average days with snow cover depth more than 3 cm at the same station amounted to 150 during the period 1984–2016. Further details about precipitation and temperature during the period 2013–2016 (the first harvest cycle) are presented in Figure S1.

To control weeds, plastic mulch film (150 cm width and 0.021 mm thickness; Sunshat, C.I. TAKIRON Corporation, Tokyo, Japan) was laid using an agricultural machine, following the crushing of surface rock fragments to 20 cm soil depth using a mechanical stone crusher in autumn of 2012 (Figure 1a). We selected this polyethylene mulch because of its excellent strength and weather resistance. In May 2013, one-year-old 20 cm long unrooted cuttings—the length most commonly recommended in most European and northern American countries [3–5,21,32,33]—were planted in a double-row arrangement (Figure 1a). The distances were 1.5 m between the double rows, 0.5 m between rows, and 0.5 m between cuttings within a row, resulting in a density of 20,000 cuttings per hectare. This system is used worldwide in order to facilitate the management of sites using farm machinery [3–5]. Each clone (either P81 and P82 from *S. pet-susu* or S27 and S67 from *S. sachalinensis*) was planted in separate mulched rows next to each other (Figure 1b). In addition, a row without mulch was included as a natural control to confirm the effect of weed competition on biomass productivity. An electric fence was installed around the site to protect the willows from predation by deer and rabbits.

**Figure 1.** Experimental design: (**a**) double row planting of 20 cm long cuttings through mulch films, (**b**) layout of cutback and weed control treatments of two clones of *Salix sachalinensis* (S27, S67) and *S. pet-susu* (P81, P82) within a block. Vertical lines represent cutback and grey columns represent non-cutback treatments. White areas between the mulched areas represent weed-control treatments and black cross-hatching represent non-weed-control treatments, respectively.

The cutback treatment was conducted over half of the site in order to examine its effect on biomass production of SRC willow. In the winter following planting (the end of 2013), the year's shoots were cut back using pruning shears in order to stimulate development of multiple stems on each plant in the next growing season. Although no weeds grew on soils covered by mulch, weeds grew vigorously on the ground between the mulch sheets in the first growing season. Therefore, half of this site was sprayed with herbicides (Roundup Maxload, Tokyo, Nissan Chemical Corporation) in May 2014 after weeds stated growing. A month later, we confirmed that all weeds had died.

Therefore, four treatments were established in a five-block design (Figure 1b) before the second growing season: with or without cutback and/or weed control. There were 20 cuttings in each treatment within a block.

#### *2.2. Allometric Equations*

Twelve sprouted stems from *S. sachalinensis* were cut down to 0.03 m above the ground in August 2015 to enable us to generate allometric equations based on the main-axis cutting method [34]. Immediately after felling, the total height (*H*) and basal diameter at 0.03 m (*D*0) of each stem were measured. *D*0 ranged from 13.85 to 41.15 mm, and *H* ranged from 221 to 445 cm. Each stem was sealed in a plastic bag and stored in an air-conditioned car until taken back to the laboratory. The main stems were divided into 0.50 m lengths. The length and basal diameter (*D*) of each stem section was measured and organs attached to the main stem were classified into leaves and branches. All samples were then oven-dried at 75 ◦C for 72 h and weighed. Allometric equations were estimated for biomass of stem, branch, and foliage of each stem in terms of *D*0, *H,* and *D* (Equations in Supplementary Material).

#### *2.3. Growth Measurements and Harvesting*

In November 2016 after leaf senescence, three growing seasons after the cutback treatment, all stems of both *S. sachalinensis* and *S. pet-susu* were harvested. Fresh biomass of aboveground organs including branches and stems from each cutting were weighed immediately. Sub-samples of branches and stems were taken back to the laboratory for biomass production determination, expressed in oven-dried tonnes per hectare per year (t ha−1 yr−1 ). The ratio of dry biomass to fresh biomass was 0.5132, 0.5326, 0.5268, and 0.5474 for P81, P82, S27, and S67, respectively. Neither fertilization nor pesticide were applied during the first harvest cycle.

In order to examine the effect of cutback and weed control on the biomass increment process each year before harvesting, the *D*0 and *H* from each cutting of *S. sachalinensis* were measured in November 2014. All stems were revisited in November 2015 to measure *D*0 and *H*, as well as diameter at the height of the lowest branch (*D*). The number of sprouted stems from each cutting of *S. sachalinensis* was counted in November 2014.

#### *2.4. Nitrogen Analysis*

For nitrogen analysis, mature leaves from the aforementioned twelve sprouted stems used to develop the allometric equations were sampled. On the same occasion, weeds from the ground between mulches in treatments without weed control were harvested in three plots (50 cm × 70 cm) from each treatment.

All samples from leaves of both willow and weed were dried to constant mass at 75 ◦C and ground to a fine powder in a steel ball mill (MM400; Retsch, Haan, Germany). Total nitrogen concentration of the fine powder derived from each sample was measured after combustion in a CHN Analyzer (Vario Max CN, Elementar, Hanau, Germany).

#### *2.5. Statistical Analyses*

The effects of cutback, weeding, and species and their interactions on all dependent variables were analyzed by a two way or three way repeated-measures analysis of variance (ANOVA) using SigmaPlot 13.0 (Systat Software Inc., San Jose, CA, USA). We tested for normality and variance homogeneity at *p* < 0.05, and all variables were log-transformed when needed. The effect of the block on all variables was not significant at *p* < 0.05, and thus, these results are not shown. The Holm–Sidak method procedures were used for pairwise multiple comparison when significant treatment effects were revealed.

### **3. Results**

Mulch had a significant effect on biomass production in the first harvest cycle, three growing seasons after cutback (Table 1). Without mulch, weeds grew fast and its height could reach up to 120 cm in August, which resulted in 69% of unrooted cuttings of willow dying. Therefore, the average biomass production of willows was 0.46 t ha−1 yr−1 , which was even lower than weed production (4.13 t ha−1 yr−1 ). In contrast, willow biomass production increased to 5.67 t ha−1 yr−1 when mulches were used to control weeds, although weeds between the rows of willows growing in the ground not covered by mulch produced about 0.87 t ha−1 yr−1 . Both total plant biomass and leaf nitrogen content had similar values per unit land area in the control and mulched treatment.

land under natural conditions (no weed control) or plastic mulch. Values shown are mean ± SE. **Treatment Plant Type Biomass (t ha**−**1 yr**−**1) Leaf Nitrogen (%) Leaf Nitrogen (kg ha**−**1 yr**−**1)** Natural conditions Weeds 4.13 ± 0.15 1.36 ± 0.07 56.22 ± 0.16 Willow 0.46 ± 0.05 na na

Mulch Weeds 0.87 ± 0.11 1.84 ± 0.08 15.40 ± 1.27

Willow 5.67 ± 0.28 2.39 ± 0.10 57.29 ± 0.22

**Table 1.** Annual average biomass production and leaf nitrogen content of both weeds and willow in

With further weed control on the ground between mulches, willow biomass production increased to 11.43 and 8.84 t ha−1 yr−1 in the cutback treatment in *S. sachalinensis* and *S. pet-susu*, respectively (Figure 2). Without weed control, in contrast, cutback had no effect on biomass production in *S. pet-susu* and actually reduced yield by about 32% in *S. sachalinensis*. In addition, cutback and weed control had a significant interaction with respect to productivity (Figure 2, Table S1). Since the canopy of the willows closed during the second growing season after cutback, further weed control was not necessary.

**Figure 2.** Comparison of dry biomass production in the first harvest cycle after three growing seasons: C and nC represent with and without cutback; W and nW represent with and without weed control, respectively. The significance values of the factorial analysis are shown in Table S1. Different letters indicate significant differences in the corresponding values from the same species at *p* < 0.05. Values shown are mean ± SE from two clones of the same species.

Cutback practice even reduced biomass increase without weed control on the ground between the mulch sheets (Figure 3, Table S2). This negative effect was especially obvious in branches and stems when comparing pairs without weed control in the first growing season (Figure 3b,c). In the second growing season, the negative effect of cutback became insignificant in leaves and branches, but was still significant in stems. Stem biomass increase in the second growing season exhibited a three-fold increase compared to the first growing season in all treatments.

**Figure 3.** Annual biomass increments of (**a**) leaves, (**b**) branches, and (**c**) stems of *Salix sachalinensis* in the first and second growing seasons after cutback. C and nC represent with and without cutback; W and nW represent with and without weed control, respectively. The significance values of the factorial analysis are shown in Table S2. Different letters indicate significant differences in the corresponding values in a single year at *p* < 0.05. Values shown are mean ± SE from two clones of the same species.

Cutback promoted the formation of multiple stems (Figure 4, Table S1). Interestingly, a significant interaction between cutback and weed control was observed with respect to the number of stems per cutting, indicating that weed control is important for cutback to enhance productivity.

**Figure 4.** Number of stems sprouting from a single stool, counted after one season of growth since cutback in *Salix sachalinensis*. C and nC represent with and without cutback; W and nW represent with and without weed control, respectively. The significance values of the factorial analysis are shown in Table S1. Different letters indicate significant differences in the corresponding values at *p* < 0.05. Values shown are mean ± SE from two clones of the same species.

#### **4. Discussion**

Weed control is commonly achieved by one or two applications of herbicide during land preparation and planting for establishing an SRC willow plantation [3–6]. This study demonstrated that agricultural mulches are also an effective measure to control weeds in the boreal region studied, which has been less studied in forest plantations in comparison with agriculture and horticulture [16–18]. With complete weed suppression combined with cutback, annual average dry biomass production amounted to 10.70 t ha−1 yr−1 in the first harvest cycle, three growing seasons after cutback. However, cutback had no or even a negative effect on biomass production in the presence of weed competition, as found in previous studies [2,8]. These results suggest that cutback should only be conducted when weeds are absent.

#### *4.1. Weed Control by Agricultural Mulch Film*

In spite of mulching, weeds grew vigorously on the ground between mulch sheets. This adversely affected the growth of willows and as a result the biomass production in the first harvest cycle was reduced by 32% in *S. sachalinensis*. These results suggest that weeds on the ground between mulches also need to be controlled before cutback. In previous studies, the extent to which weeds influenced willow growth was reported to depend on both willow species and weed species [8,25]. In the present study, yield difference between *S. sachalinensis* and *S. pet-susu* provides further evidence for this conclusion. In addition, we found that total leaf nitrogen content per unit land area from weeds and willows combined was similar in the unweeded control and the mulched treatment. Thus, total biomass production per unit land area in the control was similar to that in the mulched treatment. These results suggest that competition for nutrients with weeds is the main cause of yield decrease at this site. Weed-related growth reduction may also differ depending on the plantation in terms of different soil nutrient limitation [2,35].

No weeds were observed in the second growing season after cutback because the willow canopy had closed, meaning that weed control conducted once during the establishment stage of a SRC plantation is sufficient. However, the negative effect of cutback on the biomass increment of stems remained as previously reported by Albertsson et al. [8], suggesting that weed control during the establishment year is extremely important in order to obtain a high yield SRC willow plantation [3–6]. Even though weed-related growth reduction decreases over time, the economic returns during the expected life cycle of a plantation will probably be much less if weeds are not controlled [8]. Yields over subsequent harvest cycles should be monitored, however, to validate this statement.

Mulches used in this study remained in good condition after the first harvest. Removal of the plastic is time-consuming (about 16 h/ha) [9]. In the long run, mulches are broken into pieces, some pieces being buried during soil preparation for a new crop and some remaining on the soil surface. The buried pieces are more difficult to decompose since they are less affected by light and high temperatures, creating serious soil problems whose environmental repercussion has not been fully evaluated. Considering that no weeds grow in the second growing season after cutback, biodegradable plastic mulch in organic production may be an environmentally friendly alternative to control weeds that deserves further research [9].

#### *4.2. Cutback*

When weeds between mulch sheets were not controlled, cutback had no effect on biomass production in *S. pet-susu* and actually reduced yield by about 32% in the first harvest cycle in *S. sachalinensis.* This negative effect has recently been reported in other willow species [8,20]. Therefore, the commonly recommended practice of cutback during establishment of a willow plantation should only be undertaken when there is sufficient weed control in place. A recent study showed that competition with weeds resulted in reduced willow growth at lower levels of fertilizer application compared to higher levels [7]. In this study, there was little difference in total leaf biomass and leaf nitrogen per land area between the unweeded control and the mulched treatment, indicating the same demand for nitrogen between weeds and willow. This limited nitrogen supply for willows in the presence of weeds resulted in lower leaf and branch increments in the cutback treatment and reduced biomass yield in the first harvest cycle.

*S. sachalinensis,* which had relatively higher growth reduction in the cutback and no weeding treatment compared to *S. pet-susu*, exhibited higher biomass production under optimum conditions (complete weed control). Similar results were reported previously for 10 commercial breeding clones in southern Sweden [8]. The relatively low biomass production even without weed competition may partly explain the low growth reduction with weed competition. In this respect, commercial breeding has been mainly aimed at the goal of high biomass production, and this is mostly considered under optimum environmental conditions. Willow species with high biomass productivity may have high nutrient demands and, thus, their productivity may decrease when exposed to competition from weeds. Therefore, further studies on physiological traits, such as nutrient and water acquisition and their use efficiency, canopy structure and development, and biomass allocation between aboveground organs and roots of different species and clones, are critical for the effective management of SRC plantations [22,25,36,37]. All these factors can be manipulated through genetic improvement and silvicultural practice [38].

Cutback increased the number of stems produced by each stool in *S. sachalinensis*, in agreement with previous studies [20]. In our previous study, the number of sprouted stems of the same species produced in a nursery in Sapporo was higher than in this study [27]. This difference is probably related to differences in climatic conditions because the mean annual temperature in Sapporo is 2 ◦C higher than at the current site, indicating that local climatic factors should be taken into account when planning to establish an SRC willow plantation and considering biomass yield and economic return. The number of stems from the experimental willows in this study overlapped the lower end of commercial cultivars in other countries [4–6,17,20,33], indicating the importance of breeding for commercial cultivars to achieve the highest possible yields that are also competitive with weeds [38].

The average oven dry biomass production recorded for the two willows in this study falls within the range of European and North American countries, which is 7.0–18.0 t ha−1 yr−1 [2,20,21,39–41]. Yields depend on cultivars, site-specific conditions (soil fertility, climate), and type and intensity of management (fertilization, weeding, and protection from blight and insect). For example, fertilized willow SRC plantations had on average 38% higher yield than non-fertilized SRC plantations in Sweden [2]. In addition, it is generally found that yields are higher from the second harvest

cycle [19,39,40]. However, nutrient export in harvested biomass over multiple rotations will require soil nutrient amendments to maintain the SRC willow productivity that deserves further research [41,42].

### **5. Conclusions**

This study demonstrated that agricultural mulches are an effective measure for controlling weeds during the establishment of an SRC willow plantation. However, weeds between mulch sheets had negative effects on yield, especially in treatments with cutback, which was resulted from nutrient competition with weeds. Cutback practice should be used only when weeds are completely controlled. With complete weed control, 10.70 t dry biomass per hectare was achieved three years after cutback, indicating the feasibility of successfully establishing an SRC willow plantation in boreal Hokkaido, Japan.

**Supplementary Materials:** Supplementary Materials can be found online at http://www.mdpi.com/1999-4907/11/ 5/505/s1.

**Author Contributions:** Conceptualization, Q.H., H.H., A.U. and H.U.; Methodology, Q.H., H.H., A.U. and H.U.; Formal Analysis, Q.H.; Investigation, Q.H., H.H., A.U., E.I., M.K., Y.M. and H.U.; Writing—Original Draft Preparation, Q.H.; Writing—Review & Editing, Q.H., H.H., A.U., E.I., M.K., Y.M. and H.U.; Project Administration, Q.H., A.U. and H.U.; Funding Acquisition, Q.H. and H.U. All authors have read and agreed to the published version of the manuscript.

**Acknowledgments:** The authors thank Haruka Yamamoto for the biomass measurements, Yuji Takahashi of Shimokawa town for maintenance the experimental site, and Oji Holdings Co. for offering the willow cuttings. The authors thanks also the editor and the two anonymous reviewers for their valuable comments. This work was supported by an FFPRI Grant.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).


**1. Introduction**

Metals and their alloys have a crystalline structure, which is characterised by a regular arrangement of atomic cores. Technical metals obtained by conventional metallurgical methods have a polycrystalline structure [1,2]. This means that metals are made up of grains characterised by approximately the correct crystal structure. Polycrystalline materials consist of grains with various orientations. For many polycrystalline materials, the grain orientations are random before any working (deformation) of the material is undertaken. Therefore, even if the individual grains are anisotropic, the property differences tend to average out and, overall, the material is isotropic. When a material is formed, the grains are usually distorted and elongated in one or more directions which makes the material anisotropic [3].

In metals subjected to plastic working, the most important defects of the crystal lattice are dislocations and grain boundaries. Strain hardening—hardening of a material with deformation—results from interaction and multiplication of dislocations during plastic deformation. Grain boundaries have a much greater influence on the mechanical properties of metals than dislocations [4,5]. The high energy level of grain boundaries determines

**Citation:** Zaba, K.; Trzepieci ´ ˙ nski, T.; Rusz, S.; Puchlerska, S.; Balcerzak, M. Full-Field Temperature Measurement of Stainless Steel Specimens Subjected to Uniaxial Tensile Loading at Various Strain Rates. *Materials* **2021**, *14*, 5259. https://doi.org/10.3390/ma14185259

Academic Editors: Qing Liu and Jiangshan Zhang

Received: 28 June 2021 Accepted: 7 September 2021 Published: 13 September 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the occurrence of many phenomena, such as continuous mobility of boundaries leading to grain growth and lower corrosion resistance [6–8]. Grain boundaries also have a strong influence on the ductility of metals. The degree of strain hardening of materials by grain refining is described by the Hall–Petch relationship [9,10] according to which the yield strength of the material increases with the degree of grain refinement. On the one hand, grain boundaries inhibit the free movement of dislocations during grain deformation while participating in the process of material strengthening and in the formation of the deformation texture [1]. On the other hand, the grain boundaries are the main area of permanent deformation during creep or superplastic flow.

The deformation of the material (elastic or plastic) occurs under the influence of a load applied to it. Elastic deformation disappears when the load is removed. Plastic deformation remains after the material is unloaded. There are two main mechanisms of plastic deformation: the gliding motion of dislocations and deformation twinning [11,12]. The gliding motion does not occur simultaneously in all possible planes and directions of slip. Deformation occurs gradually, starting from the sliding planes and directions prioritised in relation to the direction of the applied load. During deformation, the number of active slip planes and free dislocations that are generated during deformation increases. Further plastic deformation requires the application of greater stress in order to initiate new dislocations [13–15]. The process by which stress increases with deformation is called work hardening. Plastic deformation is also accompanied by heat generation due to the internal resistance of the material, which can be detected at the microstructure scale when loading the material [16,17].

The investigation of heat generation and dissipation during plastic deformation was reflected in scientific research. Bodelot et al. [18] applied infrared (IR) coupled full-field measurements to observe the heterogeneities of kinematic and thermal data at the grain scale of austenitic stainless steel. Specimens were subjected to a cyclic loading. It was found that the temperature was significantly affected by diffusion and this observation tends to confirm that temperature may not be used as a damage indicator. Boulanger et al. [19] have focused on the determination of heat sources from a temperature field provided by an IR camera. They separately identified the dissipative and thermo-elastic heat sources. Thermal full-field measurements from infrared thermography were used to study the Portevin-Le Chatelier effect [20]. The temperature field provided insights into the dynamics of band formation and motion.

The non-contact optical methods for the measurement of temperature displacement include video extensometers [21], laser speckle correlation [22], interferometry methods [23–25] and temperature-calibrated CCD cameras [26]. In addition to IR thermography, the other technique that allows temperature changes to be coupled with strains is digital image correlation (DIC), in which digital images of an object before and after deformation are captured using a non-contact optic and material-independent measuring instrument, and then they are subject to correlation analysis [23,24,27]. High-speed DIC allows deformation and damage mechanisms to be analysed in a quantitative manner [28]. DIC was used to obtain strain fields and to investigate the propagation of the Lüders band in steel specimens subjected to the uniaxial tensile test [29]. The strain states associated with localised necking and diffuse strains are also investigated. Results show that the cross-section of a tensile specimen must be regarded as a structure, not as an elementary volume of material which is subjected to the uniform load. The results of investigations of Hung and Voloshin [30] indicated that for the uniform tension test, DIC is a very convenient and efficient tool for the measurement of in-plane strain measurement. Feng and Xue [31] applied infrared thermography tests and DIC tests for the display of the thermal field during mechanical tensile tests of 3D printed bolts. Cholewa et al. [32] developed the method of calibrated infrared thermal cameras with a stereo-vision DIC system applicable to scales of lengths both large and small. Zaba ˙ et al. [33] used DIC and IR thermography to find the relationship between yield stress and the Taylor–Quinney coefficient and their change with the strain rate during the stretching of nickel-based superalloys. A coupled thermography and DIC system was calibrated using a

series of one sided heat exposure experiments performed on loaded sandwich composites. Infrared thermography and DIC measurements are not applicable to experiments with low conductivity materials or discontinuous materials [33,34]. Maynadier, et al. [35] developed an infrared image correlation system equipped with a single IR camera to measure simultaneous thermal fields and deformation. The disadvantage of the proposed method is that this technique requires the use of a special coating for displacement measurement using the single camera. Chrysochoos et al. [34] proposed DIC and thermography measurements for the determination of the mechanical energy and heat sources involved at local scale during a heterogeneous tensile test. Thermodynamic analysis of the energy balance showed the influence of the dissipated mechanism on the stress–strain response.

Many of studies take place at a macroscopic scale with the measurement of the average temperature of the material [36,37]. Meanwhile, due to the grain structure of polycrystalline metals and the occurrence of various plastic deformation mechanisms, the temperature of the body subjected to loading is not uniform. The way to explain this phenomenon is to take full-field measurements. In this paper, the coupled IR and DIC measurements were conducted to assess the thermomechanical response of stainless steel strip samples subjected to tensile load at different strain rates. An analysis of variance (ANOVA) was used to gain information about the relationship between the strain hardening phenomenon, yield stress, sample orientation in respect of the sheet rolling direction, strain rate, and plastic strain of the specimen and temperature.

#### **2. Materials and Methods**

## *2.1. Material*

The research material was a titanium-stabilised austenitic stainless steel, 321 (AMS 5510). Steel 321 is a steel with good formability, weldability and resistance to intergranular corrosion that is mainly used in the chemical and aviation industries. The thickness of the sheets was 1 mm. The test samples were cut from the sheet in three directions: the rolling direction (RD), at an angle of 45◦ to the RD and perpendicular to the RD. The dimensions of test samples (Figure 1) were in accordance with the ASTM E8/E8M–11 standard [38]. The requirements for the chemical composition of the test steel are shown in Table 1 and are in accordance SAE AMS 5510 [39].

**Figure 1.** Dimensions (in mm) of the samples for the tensile test.

**Table 1.** Chemical composition of 321 steel (wt.%) [39].

#### *2.2. Uniaxial Tensile Test*

Dog-bone samples (Figure 1) were stretched in a uniaxial tensile test machine Zwick/Roell Z100 (Figure 2). Three different strain rates were used in the investigations: 4 × 10−3 s−1, 8 × 10−3 s−1 and 16 × 10−3 s−1. The tests were carried out at a temperature of 24 ◦C.

#### **Figure 2.** Test stand.

#### *2.3. Digital Image Correlation Technique*

The digital image correlation Aramis system (GOM, Braunschweig, Germany) was used to determine the character of the deformation of the sample in a non-contact manner during the stretching process of samples. The measuring system consists of two essential components. The first is a scanner, consisting of two high-resolution digital cameras (Figure 2) positioned in relation to each other in such a way as to be able to build a spatial image. The second element of the set is a computer with special software for the numerical processing of images.

Proper surface preparation of the samples is necessary for DIC analysis. First, the samples are covered with white paint, and then a random pattern of contrasting black spots is applied. The selection of the size of the spots depends on the size of the test object and the optical properties of the measuring apparatus. The measurement process consists in taking a series of images of the sample by two cameras in successive stages of loading. Correlation of images from these cameras makes it possible to determine the position of each pixel by giving them coordinates in a three-dimensional coordinate system. Then the images are divided into so-called deformation grids, each of which contains a unique pattern of dots [40]. The initial setup becomes the reference step. Due to the deformation of the sheet surface, the spots in each element of the mesh change their position in relation to each other, which makes it possible to calculate the full field deformation in relation to the reference position. However, in order to make such an analysis possible, the system divides the measurement area into fields of a fixed size called facets. Local strains are obtained from the formula:

$$
\varepsilon\_{\text{eff}\%} = \left( \lim\_{l \to 0} \left( \frac{l\_{in} + \Delta l\_d}{l\_{in}} \right) - 1 \right) \cdot 100\% \tag{1}
$$

where *lin* is the initial dostance between two neighbouring facets and Δ*ld* is the distance increase during uniaxial tensile test.

The dimension of standard facet is 21 × 21 pixels. The second characteristic value is the distance between the centres of adjacent facets. The Aramis system offers many benefits, such as:

#### *2.4. Infrared (IR) Thermal Mapping*

The surface temperature of the samples during the stretching was measured using a high-sensitivity IR Flir T640 camera (Flir Systems AB, Antennvägen 6, 187 66 Täby, Sweden). The measurements of temperature were correlated with the measurement of strain using the A0Aramis system. Non-invasive distance measurement was performed with an accuracy of thermographic measurements in the range of +/− 2 ◦C. The principal parameters of the Flir T640 camera are listed in Table 2.

**Table 2.** Parameters of a Flir T640 camera.

#### *2.5. Analysis of Variance*

Quadratic multidimensional ANOVA was used to determine the relationship between material properties (strain hardening exponent, yield stress, sample orientation), process parameters (strain rate and percentage strain) and the maximum temperature appearing in the sample during the stretching process. The values of the strain hardening exponent were determined by approximating true stress-true strain curves using the well known Hollomon's power law.

ANOVA is a statistical method for examining observations that depend on one or more factors acting simultaneously. Due to the different numerical ranges of the data, they were normalised to the range [−1, +1] [41]. The *min*-*max* normalisation was applied by means of a linear function bringing the data to a new interval (Coded Low, Coded High).

Explanatory variables should be independent of each other. The input data were fitted with a polynomial, and the influence of individual variables on the quality of the model was checked using backward elimination. The minimum and maximum values of the input variables for samples made of 321 sheet are presented in Table 3. Intermediate values of input parameters were coded proportionally in the range [−1, +1].

**Table 3.** Factors and levels for analysis of variance (ANOVA) of stretching of specimens of 321 steel.

The regression models that were built were subjected to significance tests. The method of backward elimination of variables was used in the analysis. It is a variable selection procedure in which all the variables are entered into the regression equation and then removed sequentially. The variable with the lowest partial correlation with the dependent variable is considered for removal first. If it meets the elimination criteria, it is removed. The basis for removing or leaving a given variable in the model is the calculation of Fisher F statistics. The independent variable with the highest probability corresponding to the Fisher parameter F is removed from the model if the probability *p* is sufficiently high (typically *p* = 0.10). After the first variable is removed, the next one to be removed is the

one that has the smallest partial correlation with the dependent variable. The procedure exits when there are no other variables in the equation that meet the removal criteria. The significance of the regression model at a level of α = 0.05 is determined based on the variance due to the effect of a factor and the variance due to the error term.

#### **3. Results and Discussion**

#### *3.1. Experimental Investigations*

Figure 3 shows the evolution of the surface temperature of the samples cut along the sheet rolling direction of the 321 steel during its stretching with different strain rates. It is clearly visible that even within the range of proportional deformations the zone with the highest temperature is located approximately at the central point between the grippers of the testing machine. As a result of heat convection caused by internal friction of the material, an increase in the temperature of the samples was also observed in the part that is gripped where no plastic deformation occurs. Increasing the strain rate resulted in the intensification of heat generation. At the moment of the formation of a necking at the highest strain rate, the maximum sample temperature increased by more than 4 times compared to the initial temperature. Similar conclusions can be drawn for the samples cut at an angle of 45◦ with respect to RD and perpendicular to RD (Figure 4).

Only part of the mechanical energy is converted into heat in the deformation process. The remainder is stored in the microstructure of the material increasing the internal energy of the material. The total energy spent on deforming an elastic-plastic material is equal to the work undertaken on elastic (reversible) deformation and permanent (plastic) deformation. Moreover, the energy consumed on plastic deformation is divided into heat dissipated in the forming process and energy stored in the material [42–44]. The evolution of the microstructure during deformation depends on the type of material, the initial temperature and the loading situation [45,46]. Changing the deformation method usually leads to a partial or complete reconstruction of the dislocation systems formed in the previous stages of deformation and the formation of new systems [47,48]. The interaction of the lattice defects is related to the overlapping of their stress fields. If the overlap of stress fields caused by defects reduces the energy of the system, then with a specific activity of the respective slip systems, these defects will form configurations compliant with the principle of energy minimisation [49,50].

The plasticity margin measured as the difference between ultimate tensile stress and field stress is more pronounced in the case of 321 steel than for 17-4PH steel.

Figure 5 show the effect of percentage strain on the change in the maximum temperature of the specimens of 321 steel. These dependencies, determined by the determination coefficient R2, show a linear trend with a high correlation value R2 > 0.93. In the case of the sample made from 321 steel cut at an angle of 45◦ tested at a strain rate of 16 × 10−3 s−1, the last point corresponds to the advanced stage of sample necking. Therefore, the R2-value for that case is about 0.9484 (Figure 5c). In general, the higher the strain rate the steeper the trend lines. The samples made of 321 steel show anisotropic features, which are particularly visible at a strain rate of 8 × 10−3 s−1 (Figure 5b). Trend lines for samples cut at different angles are inclined at different angles with respect to the abscissa axis. True stress-strain curves for 321 steel determined at various strain rates are shown in Figure 6. True strain is defined as *εt*:

$$
\varepsilon\_l = \ln\left(\frac{l}{l\_0}\right) \tag{2}
$$

where *l* and *l*0 are the current and initial gauge lengths, respectively.

**Figure 3.** Infrared (IR) thermography images and digital image correlation charts for 321 steel samples cut along the sheet rolling direction, tested at the following strain rates: (**a**) 4 × 10−3 s−1, (**b**) 8 × 10−3 s−1 and (**c**) 16 × 10−3 s−1.

**Figure 4.** IR thermography images and digital image correlation charts for 321 steel samples cut perpendicular to the rolling direction (RD), tested at the following strain rates: (**a**) 4 × 10−3 s−1, (**b**) 8 × 10−3 s−1 and (**c**) 16 × 10−3 s−1.

**Figure 5.** Influence of strain on temperature for 321 steel samples tested at the following strain rates: (**a**) 4 × 10−3 s−1, (**b**) 8 × 10−3 s−1 and (**c**) 16 × 10−3 s−1.

**Figure 6.** True stress-true strain curves for 321 steel determined at the following strain rates: (**a**) 4 × 10−3 s−1, (**b**) 8 × 10−3 s−1 and (**c**) 16 × 10−3 s−1.

#### *3.2. Analysis of Variance (ANOVA) for 321 Steel Samples*

A quadratic model containing only statistically significant elements was chosen to fit the experimental data. The temperature response surface for the 321 steel specimens is given by:

$$\begin{array}{l} T = 76.71 - 18.56A - 10.02B - 4.19C + 4.71D + 48.61E - 4.97AB \\ \quad + 9.58AC + 8.27AD - 31.41AE - 12.99BC - 13.1BE \\ \quad - 21.35CE - 1.22DE + 13.36E^2 \end{array} \tag{3}$$

The significances of the influence of the individual material parameters as well as the conditions of the stretching process and their interaction in the regression model were determined on the basis of the ANOVA. The quality of fit of the model obtained to the values measured for a given research plan (Equation (3)) was then determined on the basis of the determination coefficients R2 and the F test. The significance of the model is confirmed by an F-value of 53.30 (Table 4). This model can, therefore, be used to predict temperature values based on material deformation. The probability that such a large F-value can result from data noise is only 0.01%.

**Table 4.** Results of analysis of variance for the regression model for 321 steel samples.

The probability values *p* for *E*, *AE*, *CE*, *E*2 that are less than 0.0500 prove that these factors are statistically significant. The parameters the removal of which will not reduce the quality of the model include, inter alia, *C*, *AB*, *BC*, *DE*. Due to the satisfactory value of the determination coefficient for the model equal to R2 = 0.9868 (Table 5), it was decided to leave these variables in the model. The predicted value of the coefficient of determination R2 = 0.8982 is in reasonable agreement with the adjusted coefficient of determination R2 = 0.9683 because the difference between their values is less than 0.2 [51]. The value of adequacy precision 27.6342 is greater than 4. The adequacy of model is, therefore, confirmed.

**Table 5.** Fit statistics of the regression model for 321 steel samples.

If the errors arising during the experimental tests are random, then the distribution of residuals in the form of deviations between the actual values and the expected values should be in accordance with the normal distribution. The distribution of residuals along a straight line (Figure 7a) shows that the studentised residuals have a normal distribution [52]. Figure 7b shows a comparison of the actual values and the predicted temperature values resulting from the introduction of independent variables to the regression model. The distribution of data around a straight line indicates that the regression model is of good quality [53,54].

**Figure 7.** (**a**) Normal % probability vs. externally studentised residuals and (**b**) predicted vs. actual values of temperature plots for 321 steel samples.

The relationship between the dependent and independent variables was analysed using 2D response surface plots. Figures 8 and 9 show the interactive effect of two selected parameters on the value of the maximum temperature in the sample during the stretching test when the other input parameters are constant [55–57]. Figure 8a indicates the synergistic role of the strain hardening exponent (SHE) and yield stress (YS). The heat is generated faster towards the low values of both the SHE and YS. Figure 8b indicates that the SHE plays a more significantly influential role in heat generation. However, the strain rate (SR) is a significant factor, but only when considering small values of SHE. For small values of SHE, the sample orientation in interaction with the SHE does not significantly affect the temperature value (Figure 8c). However, if the SHE increases then the difference between the temperature for 0◦ and 90◦ orientations increases to around 30 ◦C. For small values of SHE, starting from a plastic strain (PS) of about 80%, the regression model overestimates the temperature values (Figure 8d). However, the trend observed in the experimental

studies is maintained, i.e., with an increase in PS for a given SHE value, the temperature value increases.

**Figure 8.** Response surface plots presenting the interaction between the strain hardening exponent and (**a**) yield stress, (**b**) strain rate, (**c**) sample orientation and (**d**) plastic strain, affecting the value of the maximum temperature of the surface of the 321 steel sample.

The synergistic effect of both SR and YS is more complicated (Figure 9a). Similarly, in the case of sample orientation and YS (Figure 9b), it is only for the lowest value of YS that strain rate and orientation significantly affect the value of temperature. Figure 9c indicates that the orientation when testing samples with different SR values plays the following role: for orientation 0◦, the temperature is low and increases with change in the orientation to 45◦ and 90◦. The effect of PS and SR shown in Figure 9d is very similar to the effect of PS and SHE on temperature (Figure 8d). A strong correlation between PS and temperature is also confirmed in Figure 9e,f by the high isotherm concentration. Specimens cut at 90◦ heat faster during deformation than specimens cut at 0◦ (Figure 9e). The reverse effect is observed in Figure 9f: when the YS of specimens is small, the material heats up faster.

**Figure 9.** Response surface plots presenting the interaction between (**a**) strain rate (SR) and yield stress (YS), (**b**) sample orientation and YS, (**c**) sample orientation and SR, (**d**) plastic strain (PS) and SR, (**e**) PS and sample orientation and (**f**) PS and YS, affecting the value of maximum temperature of 321 steel sample surface.


**1. Introduction**

228 Neuroimaging – Cognitive and Clinical Neuroscience

Zimmermann M, Mattia JI (1999) Axis I diagnostic comorbidity and borderline personality

Zlotnick C, Johnson DM, Yen S, Battle CL, Sanislow CA, Skodol AE, Grilo CM, McGlashan

personality disorder. *Psychiatry Res* 154, 157-170.

disorders with PTSD. *J Nerv Ment Dis* 191, 706-713.

disorder. *Compr Psychiatr* 40, 245-252.

reduction and history of aggressive behaviour in patients with borderline

TH, Gunderson JG, Bender DS, Zanarini MC, Shea MT (2003) Clinical features and impairment in women with Borderline Personality Disorder (BPD) with Posttraumatic Stress Disorder (PTSD), BPD without PTSD, and other personality

> The aging human brain undergoes a variety of structural and metabolic changes, often coinciding with, or leading to, cognitive decline (Bullitt et al., 2009). Over the past decade, investigators have been searching for better methods to detect, treat, and prevent cognitive decline. This has lead to the development of a plethora of pharmaceutical approaches with limited success. Identifying non-pharmaceutical approaches for the prevention/treatment of cognitive decline is paramount. Because of its non-invasiveness, neuroimaging is fast becoming a preferred technology for evaluating brain structure and function. In addition, exercise is being recognized as a potential adjunct modality for preventing or reducing structural decline in the brain and perhaps attenuating corresponding cognitive decline. These two methodologies can work in tandem: first, for identification of subtle changes in the brain not detectable via standard cognitive testing and second, for application of appropriate exercise regimes shown to be associated with healthy brain aging. Taken together, disruptions in cognitive function may be delayed, or even halted, but only if intervention occurs "soon enough". The obvious questions to answer are: 1) What is "soon enough"? 2) What type of neuroimaging might be "best"? and, 3) What kind of exercise? Simple questions with no simple answers. This chapter will begin with common, often overlooked issues regarding the use of exercise as a research modality and then progress to incorporating exercise into neuroimaging studies.

#### **1.1 Sedentary and unhealthy**

A sedentary lifestyle, low aerobic fitness and obesity are associated with both cardiovascular and cerebrovascular diseases (Burns et al. 2008). Research over the last decade has shown that 6 months of aerobic exercise may reduce or prevent brain volume atrophy in the prefrontal brain region related to executive function and memory in the aged (Burns et al., 2008; Colcombe et al., 2006; Erickson et al.,2009). It has also been suggested that aerobic fitness and obesity may selectively impact brain regions as well as different hemispheres (Cronk et al., 2009; Gustafson et al., 2004, 2008; Marks et al., 2007, 2010; Raji et al., 2009; Soreca et al., 2009; Ward et al., 2005). For instance, greater aerobic fitness has been moderately associated with greater cerebral white matter integrity in the anterior and middle cingulum regions on the left side of the brain whereas a higher body mass index and higher abdominal girth have been significantly associated with lower cerebral white matter integrity in the posterior cingulum region on the right side of the brain (Marks et al., 2010).

MRI Techniques to Evaluate Exercise Impact on the Aging Human Brain 231

weight lifting. Thus, physical activity or exercise could mean participating in a marathon or dance class, lifting a 10 kg medicine ball, raking leaves, meditating while performing yoga,

Exercise scientists and physical educators continually find themselves clarifying the words that describe their work and this debate has raged for decades. For instance, the term *physical activity* is classically defined as any bodily movement that results in muscular contractions and increases energy expenditure above that which is used during rest (USDHHS/NHLBI, 2008). In contrast, the term *exercise* is defined as "*the regular or repeated use of a faculty or bodily orga*n" (Meriam Webster Free Dictionary, 2011). Thus, the term physical activity is often used due to its broader utility, but the term exercise should be used whenever the researcher's intent is to demonstrate the impact of *repeated exposure* to a *specific type* of physical activity. Therefore, exercise can be considered a structured sub-category of physical activity, with specific dosing parameters that result in health maintenance and/or improvement (Caspersen et al., 1985). The term *fitness,* in biological terms, simply means the ability of an organism to survive and reproduce. This generic term is most often used to connote one's health status and is expanded as needed (i.e., health fitness, physical fitness, aerobic fitness, brain fitness). The American College of Sports Medicine (1990) suggested the following definition be used for *physical fitness*: "fitness is the ability to perform moderate to vigorous levels of physical activity without undue fatigue and the capability of maintaining such ability throughout life." Obviously, this exercise science-based definition can be applied to the neurological system as well, suggesting that *brain fitness* can be defined as *the ability to perform daily cognitive tasks without undue mental fatigue or memory impairment and the*

Distinctions need to be made between the *acute* versus *chronic* impact of exercise on a physiological system, in this case, the brain. While it is important to know the short-term impact exercise has on physiological systems from a biological or safe participation standpoint, the establishment of long-term health benefits attributed to exercise exposures must account for the chronic adaptations due to historical (i.e., long-term) participation in an exercise regime. It is well-established that exercise is an acute stressor, thereby resulting in (relatively) immediate elevations in blood flow, heart rate, oxygen uptake, respiration, and increased circulation/uptake of most hormones and many metabolic substrates. However, the question remains, do any of these acute exercise responses, when experienced multiple times throughout the week, over several months to many years (i.e., chronic exposure), impact the brain in such a way as to become neuro-protective and prevent or attenuate neurological degeneration and cognitive decline commonly attributed to

Evaluating the brain at one point in time with a selection of a population is a cross-sectional study. One is able to infer relationships between brain structure/function and a host of variables, ranging from cognitive test scores to health fitness ratings. This is an excellent starting point and is where most of the exercise neurobiology literature is currently focused,

or simply walking around a shopping mall.

*capability to maintain cognitive abilities throughout life.*

**3. Acute versus chronic exercise participation**

**2.2 Working definitions**

unsuccessful brain aging?

**3.1 Cross-sectional or outcome study?**

This of course has implications beyond executive dysfunction; disruption of cerebral white matter integrity in the middle-posterior cingulum regions could impact motor movement, learning, and reading comprehension. Early transcranial doppler studies concluded that aerobic exercise may be beneficial for maintenance of cerebral blood flow (Marks et al., 2000; Orlandi and Murri, 1996). A decade later, cerebral blood vessel morphology studies suggested physically active older adults have younger-looking cerebral vasculature (Bullitt et al., 2009, 2010).

However, the retention and improvement of human brain plasticity via exercise is still not well understood. Despite animal studies demonstrating that exercise may promote neurogenesis, and human studies demonstrating a maintenance/increase in brain volume with exercise (Cotman et al., 2007; Ferris et al., 2007; van Praag et al., 1999), there is little information demonstrating the mechanism(s) for such changes. Furthermore, much of the evidence is equivocal as to whether these brain adaptations, presumably due to physical exercise, equates to improved cognitive function (Colcombe et al., 2003; Etnier and Nowell, 2006; Heyn et al., 2004; Kharti et al., 2001).

These aforementioned discrepancies may be due, at least in part, to the state of flux with research in this area. Numerous neuroimaging techniques are being used and the technology itself is rapidly changing. Cognitive tests commonly used for those with known cognitive deficits may not be sensitive enough to detect subtle cognitive changes in presumed healthy community dwelling elderly. Furthermore, researchers are using a variety of exercise paradigms, some of which are not reproducible due to lack of reporting standard exercise prescription procedures. Other factors such as age, gender, training status, and diet, known to be potential confounders in exercise and aging studies, are often overlooked. Finally, there is confusion in which term to use to simply identify the exercise paradigm itself. All of these factors make comparisons across studies difficult and the ability to draw definitive conclusions impossible (American College of Sports Medicine, 2010; Leasure and Jones, 2008; Lommatzsch et al., 2005).

Therefore, the aims of this chapter are threefold: 1) Clarify the use of exercise, physical activity and related terms as profiling variables versus intervention modalities, 2) Review neuroimaging techniques currently being used to study the impact of exercise and physical activity on the aging human brain structure, and 3) Highlight the pros and cons for use of such methods with exercise paradigms.


**8. Conclusions**

Intensive animal farming has both positive and negative impact on the environment and biodiversity depending upon the agricultural production. Intensive animal farming has provided society with marketable goods which can also be exported to foreign countries. The farming output uses market values which are limited because positive and negative outwardness are created along with the product goods and services in the agricultural activities. Therefore, the integrated/comprehensive approach covering market and nonmarket farming system output is required.


*Article* **Evaluation of the Macro- and Micro-Economic Factors Affecting the Financial Energy of Households**

**Tomasz Korol**

Faculty of Management and Economics, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland<EMAIL_ADDRESS>
**Abstract:** This paper is an evaluation of the common macro-economic, micro-economic, and social factors affecting households' financial situations. Moreover, the author's objective was to develop a fuzzy logic model for forecasting fluctuations in the number of nonperforming consumer loans in a country using the example of Poland. This study represents one of the first attempts in the global literature to develop such a forecasting model based on macro-economic factors. The findings confirm the usefulness of the proposed innovative approach to forecasting the volume of household insolvencies in a country.

**Keywords:** economics of family; personal finance; financial energy; forecasting; bankruptcy of households; financial health; consumer finance; consequences of COVID-19


*2.3. Dynamic DEA*

Traditional DEA models do not consider the interdependencies between consecutive periods. This can be a problem in the case of electricity generation because the level of installed capacity available for a country is determined by the installed capacity in the immediately preceding period, which modifies the efficiency assessment [28]. Static DEA models assume that the inputs in period *t* are mixed with the technology of period *t* to produce the outputs of period *t*.

Färe and Grosskopf [29] were the first to incorporate variables that connect consecutive periods, called link flows, from carry-over equations into the DEA approach, allowing inputs to be stored by modeling "savings" in period *t* to be used in period *t* + 1. Later, Tone and Tsutsui [30] identified different kinds of carry-over activities and proposed a dynamic slack-based model.


*Communication* **Study of Relative Humidity Vertical Distribution Characteristics before Precipitation by Microwave Radiometer Data over Southeast China**

**Yongjiang Yu 1,2,\*, Yan Zou 3 and Weihua Pan 1,2**

**Abstract:** We investigated the relative humidity (RH) vertical distribution characteristics before precipitation using microwave radiometer measurements over southeast China in 2021. The superposed epoch method is used to analyze the profile and vertical statistical characteristics and evolution of RH during precipitation events. There is a shallow, high-humidity area on the ground, with a thickness of about 0.1–0.2 Km, from 12 to 8 h before precipitation. An obvious dry layer appears in the lower layer near the ground 8–0 h before precipitation, with a thickness of about 1 km and humidity of less than 80%, which continues until the appearance of precipitation. The water vapor content in the air begins to accumulate and the humidity increases before the occurrence of LRs, MRs, and HRs, classified by total rainfall. The SDPs, MDPs, and LDPs, which are classified by precipitation duration, showed more obvious and significant characteristics of humidity increase. The statistical analysis of the 44 precipitation cases shows that the relative humidity on the ground and in the air increases significantly before precipitation, and the vertical distribution of the relative humidity and the increase in the water vapor content in the air have a more direct and obvious impact on the precipitation duration. The deep and high-humidity area of 2–4 km is conducive to maintaining the precipitation process for a long time.

**Keywords:** relative humidity; microwave radiometer data; total rainfall; precipitation duration; vertical distribution

### **1. Introduction**

Moisture plays an important role in many weather processes, especially in continuous precipitation process. The root cause of abnormally heavy precipitation is closely related to the water vapor supply and transportation under the background of large-scale circulation [1,2]. Atmospheric water vapor content and vertical distribution are crucial meteorological parameters for understanding atmospheric thermodynamic processes [3]. On the one hand, the water vapor content directly influences the global hydrological cycle, which is closely related to atmospheric energy transmission, radiation budget balance, cloud and rain formation, and climate change [4–6]. On the other hand, the microphysical features of precipitation, which can be reflected by its vertical structure, are helpful in understanding the thermodynamic and dynamic properties of precipitation systems.

The influence of water vapor at different heights on surface precipitation is different [7,8]. The sensitivity of the structure and strength of a squall line in the initial and early development stages to initial low-level humidity and environment vertical wind shear are investigated in a two-dimensional idealized squall line simulation using the WRF model. The results of the sensitivity test of low-level humidity indicate that increasing low-level humidity is favorable for convective triggering and stronger convective systems [9]. The radar reflectivity and precipitation rate from the Precipitation Radar onboard

**Citation:** Yu, Y.; Zou, Y.; Pan, W. Study of Relative Humidity Vertical Distribution Characteristics before Precipitation by Microwave Radiometer Data over Southeast China. *Atmosphere* **2023**, *14*, 513. https://doi.org/10.3390/ atmos14030513

Academic Editors: Duanyang Liu, Hongbin Wang and Shoupeng Zhu

Received: 5 February 2023 Revised: 26 February 2023 Accepted: 1 March 2023 Published: 7 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Tropical Rainfall Measuring Mission satellite are obtained over the global tropical regions (35◦ S–35◦ N) during the period from 2007 to 2012, combined with coincident vertical velocity at 400 hPa, relative humidity at 850 hPa, and lower tropospheric stability from European Centre for Medium-Range Weather Forecasts reanalysis. The results imply that coincident vertical velocity at 400 hPa and relative humidity at 850 hPa are most likely to play a dominant role in dictating the vertical development of convection [10]. The analysis of cyclone heavy rain processes with different low-level humidity conditions in Qingdao indicated that the relative humidity at 850 hPa before the heavy rain was higher and the duration of rainfall was longer [11].

The traditional method of detecting atmospheric water vapor and temperature profiles is based on the radiosonde (RS) carried by a sounding balloon. It has the advantages of high accuracy and reliability, low power consumption, light weight, and small size. However, it is influenced by limits of equipment and manpower costs, the launch frequency of RS is relatively low [3]. Additionally, the motion path of the sounding balloon can vary, largely due to the horizontal advection and variable ascent rate [12], which will cause measured drift in the atmospheric profile. The microwave radiometer (MWR) is a passive remote sensing instrument that provides vertical profiles of atmospheric temperature and water vapor content by measuring the thermal radiation emitted by the atmosphere. Compared with the RS, it has applicability due to the advantages of high temporal resolution, reasonable vertical resolution, and ability to automatically measure under almost all-weather conditions [13–15]. In addition, the MWR can also provide other atmospheric parameters, such as cloud base height, integrated water vapor (IWV), and liquid water path (LWP), which are important for evaluating cloud water resources, climate change, and precipitation [16–18]. Performance of MWR was also estimated by comparing with the RS data. The temperature profile measured by the microwave radiometer was better under cloudy conditions, while the RH profile had higher accuracy under cloud-free conditions [19–21]. The comparison of temperature and vapor density obtained from MWR and RS observations during the Integrative Monsoon Frontal Rainfall Experiment Show that: for all sky conditions, the temperature of MWR has a good agreement with that of RS. The vapor density from two measurements also shows reasonable agreement [22–24].

In the past, research on microwave radiometer retrieval data mainly focused on the evolution characteristics of the total accumulated water vapor and cloud liquid water in the whole layer before the beginning of precipitation. There are few studies on the distribution and evolution characteristics of the vertical profile of water vapor and relative humidity, and the analysis of the contribution of moisture to precipitation duration is also less involved.

Jian'ou city is located to the south of Wuyi Mountains. Subtropical monsoon climate prevailing at this city brings significant seasonal differences in temperature and rainfall. Jian'ou has abundant rainfall, with an average annual precipitation of 1753.7 mm, and the disasters caused by precipitation in this city are very serious. In this study, Jian'ou is adopted as a representative city for the southeast China to investigate the vertical structure characteristics of humidity in different rainfall regimes using continuous MWR observations in 2021.

The remainder of this paper is organized as follows. Section 2 introduces the dataset and method used in this study. Our analyses of RH variation and its vertical distribution before precipitation are presented and discussed in Section 3, and conclusions are given in Section 4.

### **2. Materials and Methods**

The observation station selected in this study is located at Jian'ou National Reference Climate Station (118◦19 23 E, 27◦03 10 N, UTC +8, 150 m above sea level) in southeast China from Jan to Dec 2021 to explore the humidity properties of the atmosphere before different rainfall regimes (Figure 1).

**Figure 1.** Geographical map of study area ((**a**) is Fujian Province, (**b**) is Jian'ou Station).

### *2.1. Instruments*

The MWR is a QFW6000 unit independently manufactured by China Research Institute of Radiowave Propagation. It observes brightness temperature in 48 channels, including 24 K bands (22–32 GHz) and 24 V bands (51–59 GHz). Combined with ambient temperature, pressure, and relative humidity from the meteorological sensors attached to MWR, atmospheric profiles (temperature, vapor density, and relative humidity) are retrieved from these brightness temperatures. Atmospheric profiles derived from MWR have a temporal resolution of ∼3 min and vertical resolutions of 50 m from the surface to 0.5 km, 100 m from 0.5 to 2.0 km, and 250 m from 2.0 to 10.0 km.

RS is usually used as a standard criterion to evaluate other measurements because it detects atmospheric parameters directly with various correction methods for improving its accuracy. Atmospheric temperature, water vapor density, and relative humidity profiles retrieved from the MWR were verified using radiosonde soundings.

Comparison of temperature and relative humidity obtained from MWR and RS were operated at Fu'zhou station during December 2016, which have the same climate with Jian'ou in the north of Fujian Province. For all sky conditions, the temperature of MWR has good agreement with that of RS and a correlation coefficient (R) of 0.995, with a root mean square error of 0.3–0.22 ◦C. The relative humidity from two measurements also shows reasonable agreement, with an R of 0.743 and a root mean square error of 2.5–12.55%. The relative humidity data obtained from MWR at Jian'ou station was filtered strictly by removing missing data and singular value number during 2021. So, the atmospheric profiles data used in this paper were successive, stable, and credible.

### *2.2. Data and Methods*

 The MWR dataset has the temporal resolution of 3 min. Since the time step of the data is not an integer, in order to facilitate the analysis and maintain the data accuracy as much as possible, before the individual statistics, this paper takes the average value of the physical quantity in a total of 5 min before and after a certain time as the physical quantity value at that time, and it is reasonable to set the temporal resolution as 5 min.

Therefore, select and classify rainfall samples according to the following criteria:

1. Investigate the hourly precipitation data of Jian'ou Station from 1 January to 31 December 2021, and continuous precipitation as a sample.

The occurrence time of precipitation is set as the 0-hour time, and the 1 h before precipitation is set as −1 h while the 1 h after precipitation is set as +1 h. If no precipitation occurs during the 12 h before 0-hour time, and the accumulated precipitation within 1 h after 0 time is more than 1 mm or the precipitation duration is greater than 6 h, then the case is picked. Using this principle, 44 samples were selected to investigate the temporal variation in relative humidity (see Table 1). According to the total rainfall, there are 12 LRs, 13 MRs, and 19 HRs. According to the precipitation duration, there are 23 SDPs, 13 MDPs, and 8 LDPs.

**Table 1.** Cases information of precipitation at Jian'ou station during 2021.

**Table 1.** *Cont.*

**Table 1.** *Cont.*

In order to study the change characteristics of relative humidity and its vertical structure before the beginning of different types of precipitation, temporal variations in the relative humidity were analyzed with superposed epoch method, which highlights the effect of the factor in the key time periods while weakening the effects of other factors [25].

The superposed epoch is a row–column array in which the "response" index values filling any row are data pertaining to a single key event. Thus, the number of rows is the sample size of such events. The columns line up the index values in fixed time relation to the key times; column averages comprise the "superposed epoch analysis." By this averaging method, any fluctuations in the response index that are locked in time relative to the key time column are preserved in the average, whereas fluctuations shifting in time from row to row are averaged out [26].

### **3. Results and Discussion**

Because the RH can provide information about hydrometeors in the atmosphere, it is a key parameter used in numerical models and precipitation forecast. We analyzed the variation in the RH before and after precipitation using the superposed epoch method. This section first presents statistical characteristics of RH from MWR before precipitation. Moreover, retrieval applications of MWR in rainy environments are further studied to support nowcasting and precipitation duration estimation.

### *3.1. Variation in RH before and after Precipitation Classify by Total Rainfall*

Figure 2 shows statistical characteristics of relative humidity from 12 precipitation cases of LR. The relative humidity on the ground and in the air began to increase 12–6 h before the start of precipitation, and the relative humidity increased in the near ground layer (below 0.2 km) and the middle and low layer (1–3 km), but the humidity of these two layers did not reach saturation (exceeded 80%). There is an obvious dry layer (humidity is lower than 70%) between the two layers of accumulated water vapor growth, and the thickness of the dry layer is about 0.8 km; 6–0 h before the start of precipitation, the wet layer near the ground began to rise, and a dry layer with a thickness of 1 km appeared near the ground until the occurrence of precipitation. The humidity continues to increase between 1–3 km during −6 to 0 h, forming a high-humidity area.

**Figure 2.** Vertical distributions of relative humidity during 12 h before and 6 h after the start of LRs in 2021.

The statistical analysis results of 13 precipitation cases of MR are shown in Figure 3. It can be seen that the ground and air humidity increased 12–8 h before the precipitation, especially the water vapor content near the ground increased significantly, the thickness of the high-humidity area on the ground reached 0.2 km, and the relative humidity exceeded 90%. After −8 h, the humidity in the lower layer decreased, an obvious dry layer appeared below 2 km, and the water vapor began to accumulate in the high humidity area around 3 km in the middle layer, and the wet layer thickened and became nearly saturated, until the appearance of precipitation.

Figure 4 illustrates the vertical distributions of relative humidity during 12 h before and 6 h after the start of 19 HR cases. From 12 to 8 h before the beginning of precipitation, there is a process of significant humidity increase on the ground, with humidity exceeding 80% and thickness only about 0.1 km, and then the humidity near the ground decreases, and a dry layer with humidity less than 70% appears below 1 km. From 12 h before the precipitation, the process of external water vapor transport and humidity increase in the middle and lower layers (1–4 km) began to occur, and the wet layer was thick.

**Figure 3.** Vertical distributions of relative humidity during 12 h before and 6 h after the start of MRs in 2021.

**Figure 4.** Vertical distributions of relative humidity during 12 h before and 6 h after the start of HRs in 2021.

#### *3.2. Variation in RH before and after Precipitation Classify by Duration*

Precipitation is when water vapor in the atmosphere condenses and becomes heavy enough to fall to the ground. Clouds are made of water vapor under different conditions, including variations in relative humidity and air pressure, the vapor particles can begin to combine and form much larger droplets. The increase in relative humidity, which in turn leads to the accumulation of water vapor, is a necessary condition for the formation of

precipitation. It not only affects the total rainfall in the rainfall regimes, but also helps to maintain the rainfall regimes for a long time.

Figure 5 presents the mean RH profile from 0 to 10 km during 12 h before and 6 h after the occurrence of 23 SDP cases at Jian'ou station. It is shown that the ground relative humidity began to increase significantly 12–8 h before the start of precipitation, and average relative humidity exceeds 80%, but the high humidity area near the ground is shallow, about 0.2 km thick. From −8 to 0 h before the beginning of precipitation, with the increase in water vapor, the relative humidity on the ground decreases, and a dry layer appears near the ground. From −4 to 0 h before the precipitation, the water vapor in the air began to increase gradually, and the humidity layer at the height of 1–4 km began to thicken. Within 2 h before the precipitation, the humidity increased rapidly and approached saturation, with the average humidity layer thickness reaching 3 km.

**Figure 5.** Vertical distributions of relative humidity during 12 h before and 6 h after the start of SDPs in 2021.

The temporally averaged RH profiles during 12 h before and 6 h after the occurrence time of the 13 MDP events are presented in Figure 6. It is shown that the ground relative humidity began to increase significantly 12 h before the beginning of precipitation, and a shallow and discontinuous high humidity layer appeared, with the average relative humidity reaching more than 80%. Continuous and deep wet areas appear, with average humidity of more than 80% and average thickness of 2.2 Km, between 1.8–4 Km in the air. There is an obvious dry layer between the high humidity layer on the ground and in the air, with a thickness of about 1.5 km. With the further transportation of water vapor within 2 h before the precipitation, the dry layer between the ground and the air disappears, the thickness of the humidity layer reaches 5–6 Km, and the average humidity exceeds 90%, which is close to saturation.

Figure 7 presents the statistical characteristics of the relative humidity profile during the 8 LDP cases at Jian'ou station before precipitation. It can be seen that 12–8 h before the start of precipitation, along with the water vapor transport, a deep moisture layer begins to appear in the middle and low layers, with a thickness of 5–6 Km and an average humidity of more than 80%; the layer between 2 and 4 km is the water vapor concentration zone, which air close to saturation and humidity is more than 90%. From −8 to −1 h before precipitation, the bottom atmospheric humidity began to decrease. The atmospheric

moisture content is low within 1 km above the ground, and the humidity is less than 80%. The moisture is mainly concentrated in the middle and upper layers of 1.5–5.5 km, the relative humidity is more than 80%, and the local humidity exceeds 90%.

**Figure 6.** Vertical distributions of relative humidity during 12 h before and 6 h after the start of MDPs in 2021.

**Figure 7.** Vertical distributions of relative humidity during 12 h before and 6 h after the start of LDPs in 2021.

### **4. Summary and Conclusions**

The main objective of this study was to investigate the variation and vertical distributions of RH before precipitation. We used the superposed epoch method to analyze the profile of RH during precipitation events.

There is a shallow high humidity area on the ground, with a thickness of about 0.1–0.2 km, from 12 to 8 h before precipitation. An obvious dry layer appears in the lower layer near the ground 8–0 h before precipitation, with a thickness of about 1 km and humidity of less than 80%, which continues until the appearance of precipitation.

The water vapor content in the air began to accumulate and the humidity increased before the occurrence of LRs, MRs, and HRs, which is classified by total rainfall. The increase in air humidity continues from 12 h before precipitation to the beginning of precipitation. The wet layer thickness of LRs is the thinnest, and the height of wet layer is also low. Before precipitation of MRs and HRs, the characteristics of water vapor accumulation in the atmosphere are similar. High humidity areas with relative humidity greater than 80% are continuous and deep. Before the start of HRs, the thickness of the humidity layer (RH > 80%) can reach 4 km and the height can reach 6 km.

The SDPs, MDPs, and LDPs, which are classified by precipitation duration, also showed statistical characteristics of significant increase in humidity. There is a high humidity area in the middle and low layers until 2 h before SDPs. The 12–0 h before the occurrence of MDPs, a continuous and deep humidity layer appeared between 1.8 and 4 Km on the ground, with an average thickness of 2.2 Km. The humidity layer became thicker as the precipitation approached. The 12–6 h before LDPs, water vapor content below 6 km is very rich, and the thickness of high humidity area reaches 5–6 Km. After that, the humidity layer rises, and the high humidity layer between 1.5 and 5.5 km is maintained until the appearance of precipitation.

The statistical analysis of the filtered 44 precipitation cases shows that the relative humidity on the ground and in the air increases significantly before precipitation, and the vertical distribution of the relative humidity and the increase of the water vapor content in the air have a more direct and obvious impact on the precipitation duration. The deep and high humidity area of 2–4 km is conducive to maintaining the precipitation process for a long time.

A large number of numerical model simulations and reanalysis data analysis show that the physical quantities that affect the atmospheric thermal and dynamic environment during precipitation mainly include rising speed, relative humidity, temperature, and vertical wind shear. The transportation of warm and humid air leads to the increase in the convective available potential energy over the precipitation area. The increase in low-level humidity is favorable for convective triggering and stronger convective systems. The increased convective intensity and upward movement make it easier for new convective cells to form at the leading edge of the cold poll. The increased low-level humidity also leads to more precipitation, which raises the intensity of cold poor. Coincident vertical velocity at 400 hPa and relative humidity at 850 hPa most likely play a dominant role in dictating the vertical development of convection. The important causes of longer duration and the larger accumulated of precipitation was the higher relative humidity conditions and long-lasting upward motion, as well as continuous water vapor transport. Therefore, it is of great significance to strengthen the analysis of the of low-level jet and relative humidity vertical distribution by microwave radiometer data for the prediction of precipitation.

**Author Contributions:** Conceptualization, Y.Y.; Y.Z.; W.P.; methodology, Y.Y.; Y.Z.; software, Y.Y.; validation, Y.Z.; formal analysis, Y.Y.; Y.Z.; investigation, Y.Y.; Y.Z.; resources, Y.Y.; data curation, Y.Y.; writing—original draft preparation, Y.Y.; writing—review and editing, Y.Y.; visualization, W.P.; supervision, Y.Y.; project administration, Y.Y.; funding acquisition, Y.Y.; Y.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Open Research Fund of Fujian Provincial Meteorological Bureau (2021KX02), the National Key Research and Development Program of China (2019YFC1510303).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data were observed by Fujian Provincial Meteorological Bureau. If you want to obtain it, please apply through email (fjqxyyj@163.com).

**Acknowledgments:** The authors acknowledge the free use of the microwave radiometer data provided by Fujian Provincial Meteorological Bureau. We also appreciate the anonymous reviewers for their constructive comments and thoughtful suggestions.

**Conflicts of Interest:** The authors declare that they have no conflict of interest.

### **References**

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**1. Introduction**

Zeolites are excellent catalysts due to the presence of acid sites on the framework. These catalyze a number of reactions such as hydrocarbon isomerization, hydrocarbon cracking or transformation. In recent times, there have been considerable increase in investigations pertaining to various aspects of zeolites [1–13]. There have been several studies aimed at clarifying the mechanism involved in the reactions catalyzed by zeolites. Boronat and Corma have discussed the changes in energy on proton exchange between zeolite and an adsorbate. They attempt to compute the contribution due to the van der Waals interaction between the zeolite and the adsorbate, which can be significant when the molecules are of size similar to the pore [1]. Davis and coworkers have attempted synthesis of enantiomerically enriched molecular sieve. Recently they succeeded in such a synthesis and this has been discussed in a recent article [11, 13]. Corma and coworkers have discussed various novel approaches to the synthesis of zeolites [3]. Dusselier and Davis have discussed at length the synthesis and the use in catalysis of small pore zeolites [12]. Corma and coworkers have discussed the synthesis of a new all-silica polymorph ITQ-55, which is highly efficient in the separation of ethane and ethylene with a high selectivity of 100 [4]. Prashant Kumar et al. [9] have pointed out the novel synthesis of MFI nanosheets with sandwiched MEL. Zeolite can be used for separation of xylene isomers with a high degree of separation [8]. From these it is evident that many new and novel aspects of zeolites are still being discovered and zeolites continues to be an exciting field of research with a bounty of surprises.

argon in NaCaA is higher than xenon in NaY, further investigations were carried out to find the reasons for this. To start with the energy barrier at the bottleneck was computed. This is shown in **Figure 1** [27]. From the figure it is seen that the energy barrier for xenon at the window in Y is positive while the barrier at the window is negative for argon in A zeolite. This explains why the diffusivity of argon in A zeolite is higher than xenon in Y zeolite. The trends seen in the observed barrier appears to be due to the strong interaction of argon with the oxygens of the 8-ring window. As argon is about the same diameter as the window, its strength of interaction with the oxygens is optimum being close to ϵ, which occurs at a distance at which the Lennard-Jones curve is minimum in energy. This is not the case for xenon in zeolite Y where xenon can be close to only some of the oxygens of the 12-ring window. This is the first indication that nongeometrical factors can

*Anomalous Diffusivity in Porous Solids: Levitation Effect*

*DOI: http://dx.doi.org/10.5772/intechopen.92685*

influence the diffusivity. This study shows that sorbate-zeolite interaction plays an

This study suggests that an understanding of diffusivity as a function of the diameter of the guest species might show something interesting. Such a study was carried out and the results were indeed found to be interesting [28]. A molecular dynamics study of monatomic guest molecules confined to zeolite NaY and NaCaA were carried out in which the diameter of the guest molecule was varied. The diffusivities of the guest species was computed from the time evolution of the mean square displacements. A plot of diffusivity as a function of the reciprocal of square of the guest diameter is shown in **Figure 2** for guests in both zeolites Y and A [28]. It is seen that the diffusivities decrease linearly with increase in the reciprocal of the square of the diameter of the guest molecule for small diameters. This is referred to as the linear regime (LR). As the diameter increases, it is seen that the diffusivity suddenly increases and later decreases sharply exhibiting a maximum in diffusivity. This is referred to as the anomalous regime (AR). This increase followed by a decrease in diffusivity was surprising and needed further investigations.

As can be seen the location of the guest diameter at which the maximum occurs is different in both zeolite Y and A (see **Figure 3** [28]). In order to understand the reasons for the maximum in diffusivity we have tried to search in literature any report that refers to such an observation. Derouane and coworkers have reported a finding arrived at through a theoretical analysis. They showed that the nesting

*Potential energy landscape of (a) xenon in zeolite NaY at 190 K and (b) argon in zeolite NaCaA at 140 K. the*

*energy landscapes are computed from molecular dynamics simulations.*

important role.

**Figure 1.**

**55**

Zeolites are porous aluminosilicates capable of accommodating molecules within the pores. They are well known for their catalytic, ion-exchange, and separation properties. They are widely used in petrochemical industries for processing hydrocarbons. Hydrocarbon cracking, transformation, isomerization, etc. are achieved with the help of zeolites [14, 15]. Zeolites are also used in separating hydrocarbon molecules of various sizes [16]. Larger hydrocarbons such as C15 and with still higher number of carbon atoms diffuse slowly through the pores and hence reach the bottom of a zeolite column last. Small molecules such as C1-C5 diffuse fast and exit from the column first [17, 18]. Other molecules of intermediate size have values of diffusivity in between those of C15 and C1-C5 and exit at intermediate times. Thus the various fractions from crude can be separated. This separation is much more energy efficient as compared to separation by distillation.

Another application of zeolites is its use for ion-exchange and water softening [19, 20]. Ions such as Ca2+ can be exchanged with Na+ already present in the zeolites, thus removing these ions from water. Zeolites are therefore used in detergents for washing clothes.

Apart from the use of zeolite for separation based on the size of the molecule, it is also of considerable use for separations based on the shape of the molecules. This property of zeolites is often referred to as shape selectivity [21]. The pore dimensions of zeolites, which are not always of regular shape, make this possible. An oft quoted example is the separation of xylenes (p-, m-, and o-xylenes) using silicate or ZSM-5 [22, 23]. At sufficiently high temperatures, o-xylene will convert to p-xylene and ZSM-5 also acts as a catalyst.

Zeolites and other host materials also exhibit interesting properties. They exhibit window effect, single file diffusion, and levitation effect [24–26]. Here we will focus on the levitation effect, which refers to the dependence of diffusivity on the guest or diffusant diameter.


**3.1. Introduction**

4 4 4 4

*CfT*

is fixed to 1/4, as in [5], which gives a good approximation for ambient

4 4

*M*

*M*

h

h

(26)

(27)

*M a*

*C f T*

h

Compared to Carnot efficiency engine the Müser engine efficiency, even when *C* is maximal,

(1 )(1 ) 1 1 4(1 )

In the assumption of *Ta*=289.23*K* the maximum efficiency without concentration, i.e. the solar cell sees the sun through a solid angle *ωs* is 12.79% which is better than the predicted value of Würfel [7] but still very low, as shown in figure 8. For concentration equal to 10, 100 and *CMAX*,

**Figure 7.** The maximum solar efficiency using Müser engine for different concentration rates (*C*=1, 10, 100 and *Cmax*)

*C f*

é ù - -- = + ê ú - ë û

*M s*

(1 )(1 ) 1 1 (1 )

é ù - -- = + ê ú - ë û

h

*S M*

*S M*

h h

the efficiency reaches 33.9, 54.71 and 85.7% respectively.

with Carnot Efficiency limit as a function of ambient temperature.

h h

remains low.

If the ratio *Ta*

4 / *f Ts* 4

58 Solar Cells - New Approaches and Reviews

temperature, *Ta*=289.23*K*, with *Ts*=6000*K*.

Hence, the corresponding *ηS* becomes:

In a quantum converter the semiconductor energy band-gap, of which the cell is made, is the most important and critical factor controlling efficiency losses. Although what seems to be fundamental in a solar cell is the existence of two distinct levels and two selective contacts allowing the collection of photo-generated carriers [2].

Incident photons with energy higher than the energy gap can be absorbed, creating electronhole pairs, while those with lower energy are not absorbed, either reflected or transmitted. The excess energy of the absorbed energy greater than the energy gap is dissipated in the process of electrons thermalisation, resulting in further loss of the absorbed energy. Besides, only the free energy (the Helmholtz potential) that is not associated with entropy can be extracted from the device, which is determined by the second law of thermodynamics.