1.Institute of Intelligent Flexible Mechatronics, Jiangsu University, Zhenjiang 212013, China 2.School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China 3.State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
Abstract:Graphene-based materials have aroused great interest for their potential applications in water desalination and purification membranes attributed to their ultrathin thickness, high mechanical strength, and anti-foiling properties. Reverse osmosis (RO) technology is currently the most progressive, energy-saving and efficient separation technology by membranes, therefore the new materials with high strength, strong pollution resistance and excellent performance are urgently needed. The ability of porous graphene to serve as a kind of novel advanced RO membrane is due to two major potential strengths of this atomically thin two-dimensional material, i.e., ultrahigh permeability and super selectivity. Thus, the reverse osmotic properties of the porous graphene membranes should be further investigated theoretically. In this paper, classical molecular dynamics method is used to investigate the reverse osmosis characteristics of brine in hydrogenated porous graphene reverse osmosis membrane. The results show that the water permeation rate increases with the driving force, pore size and temperature increasing, for the pore diameter larger than the hydration radius. The ion rejection rate decreases with the driving force and temperature increasing. Interestingly, as the porous graphene moves in the tangential direction to perform a shearing process, the interception rate of the salt ions can be effectively improved and the concentration difference polarization phenomenon can be reduced with the tangential velocity increasing, although the water flux decreases slightly. The influence mechanism of each parameter on permeability and on water flux are explored by analyzing the hydrogen bond distribution, the ionic hydration in feed solution, and the energy barrier of the water molecules in penetrating process. In order to further evaluate the effects of various parameter changes on the benefits of reverse osmosis membranes, both the selectivity and permeability are calculated to evaluate the tradeoff between permeability and selectivity, indicating that the increase of the pore diameter can obtain both high permeability and selectivity under the shearing circumstance of the membrane. The research results in this paper will provide a theoretical understanding of porous graphene-based desalination membrane and also may be helpful in designing the shearing graphene-based water filtration devices. Keywords:porous graphene/ reverse ssmosis/ hydrogen bond/ molecular dynamics
2.模型和模拟方法本文运用分子动力学方法对盐水在氢化多孔石墨烯中的反渗透特性进行了研究. 模拟体系包括氢化多孔石墨烯、盐水和两块石墨烯挡板, 如图1(a)所示. 左侧放置浓度为76.2 g/L的盐水, 右侧放置纯水, 总计2500个水分子、78个盐离子. 首先, 两侧石墨烯挡板都以1 MPa的压力挤压溶液, 弛豫0.5 ns, 使其体系相对稳定. 之后右侧挡板不施力, 左侧挡板施加200 MPa驱动力, 反渗透模拟过程持续4.2 ns. 在研究剪切运动对反渗透特性的影响时, 对反渗透膜施加一个恒定的沿着x方向的速度. 模拟体系总尺寸为3.4 nm × 3.4 nm × 24.0 nm. 图 1 (a) 压力驱动作用下以氢化多孔石墨烯为反渗透膜的反渗透分子动力学模型图 (其中灰色球为反渗透膜中的碳原子, 中间的红色、白色、紫色、绿色球分别代表盐水中的氧原子、氢原子、钠离子、氯离子, 左侧棕色球是用来提供驱动压力的单层石墨烯, 右侧粉色球是单层石墨烯挡板); (b) 氢化多孔石墨烯反渗透膜模型示意图(其中白色和黄色球分别表示带相同电量正电荷和负电荷的氢原子和碳原子, 其余灰色碳原子不带电) Figure1. (a) Molecular dynamics model for pressure-driven reverse osmosis by a hydrogenated porous graphene. The dark gray particles are carbon atoms of grapheme. The red, white, purple, and green spheres represent the oxygen atoms, hydrogen atoms, sodium ions, and chloride ions in the brine, respectively. The monolayer graphene at the left side is used to provide driving pressure, while the one at the right side is rigid boundary to confine the solvent. (b) A hydrogenated porous graphene reverse osmosis membrane model. The white and yellow particles are hydrogen and carbon atoms with the same positive and negative charges, respec-tively.
其中, α = 0.5是渗透性加权值, ${J_{{{\rm{w}}_{\max }}}}$是当前条件下水通量的最大值. 在压力驱动下盐水区的水分子不断通过反渗透膜, 但离子被滞留下来, 导致盐水区渗透膜附近离子浓度不断增加产生浓差极化现象[27]. 在膜附近不断提高的盐浓度会与其他区域溶液产生浓度差, 使局部渗透压和流体阻力增加, 而促使水通量不断减少. 当膜表面浓度增加到饱和度后, 可能会产生结晶和沉积, 造成纳米孔堵塞反渗透膜报废等危害. 如上所述, 离子可能倾向于阻塞膜壁上的孔, 这在海水淡化反渗透中被称为结垢问题. 工业上, 一般通过提高高浓度水的流速和原溶液温度去降低浓差极化, 从而提高反渗透效益和反渗透膜寿命. Li等[28]制作的反渗透脱盐纳米离心机, 利用原溶液和渗透膜的相对运动使之具有防污功能, 对反渗透膜防污去垢具有启发意义. 在本模型中, 为了削弱浓差极化现象预防结垢, 分别模拟了升高体系温度和在反渗透膜上施加剪切速度产生溶液与膜的相对运动对反渗透特性的影响. 如图3(a)、图4(a)和图4(b)所示, 统计了反渗透过程中在膜1 nm范围内盐水区的盐离子占总盐离子的占比和反渗透膜端口盐水区水分子和氢键状态. 在剪切速度为0—400 m/s时, 盐离子的占比随速度的增加而减少, 端口处的水分子随之增加. 所以对于氢化多孔石墨烯作反渗透膜施加剪切作用, 可以有效削弱浓差极化现象. 而随着温度的增加端口的水分子数减小, 所以温度的升高并不能削弱浓差极化现象. 但是从图2可知, 在保持200 MPa的驱动力和控制温度在298 K的条件下, 水通量随着剪切速度的增加而减少. 结合图4(a)中盐水原溶液每个水分子平均氢键数随速度的增加而增加, 氢键对水分子运动起阻碍作用, 这也就解释了水通量的减少. 根据图3(b)盐水区z向氢键和速度呈负相关, 氢键在距膜1.5 nm范围内波动较大, 且对速度的增加起到阻碍作用. 反渗透主要发生在氢化多孔石墨烯的纳米孔处, 此处水分子运动将更为集中和剧烈, 所以研究水分子通过纳米孔周围的氢键状态是十分有意义的. 在盐水区, 以纳米孔的中心为球心、半径为1.5 nm 的半球区域记为端口, 并统计端口内每个水分子所含氢键数. 通过图4(a)和图4(b)可知, 相比盐水溶液的氢键数, 氢化多孔石墨烯孔端口处的水分子的氢键较小, 端口处的水分子较为活跃, 有利于水渗透. 另一方面, 通过表2中速度为100 m/s的效益好于无剪切作用下的效益, 可以得知剪切作用还可以提升反渗透效益. 图 3 在盐水区距离石墨烯膜1 nm范围内盐离子占总盐离子的占比随速度的变化; (b) 当剪切速度为400 m/s时, 盐水区氢键和速度的z向分布 Figure3. (a) Proportion ratio of salt ions in the brine zone to the total salt ion in the range of 1 nm of the membrane; (b) the z-directional distribution of hydrogen bonds (HB) and velocity in brine zone when the shearing speed is 400 m/s.
图 4 盐水区平均每个水分子氢键数和端口水分子数及其氢键平均数的z向分布关系图 (a) 在不同剪切速度下; (b) 在不同温度下 Figure4. The z-directional distribution relationship between the number of hydrogen bonds per water molecule and the number of port water molecules and their hydrogen bond average in the feed solution: (a) Different shearing speeds; (b) different temperatures.
综上, 本模型通过施加切向作用可以减弱浓差极化现象. 对于一个恒温系统, 计算分子自由能是统计其能量消耗的重要手段. 本文通过反渗透发生前后自由能之差和轴向分布密度来计算能障(potential of mean force, PMF)[29], 来解释粒子通过纳米孔的难易程度. 所采用的自由能差值计算公式和能障计算公式为
统计计算得到图5(a)和图5(b), 膜入口附近的能障随着温度的增加和剪切速度的降低而减小, 水分子的通过性提高, 这也就解释了为什么温度的增加和剪切速度的降低能提高水通量. 盐离子在水溶剂中, 水分子以氢键相连围绕着盐离子为中心形成两个水合层, 而离子水合壳的直径与孔径的大小关系决定了离子截留率. 从不同温度、驱动力条件下离子与水分子径向分布函数图(图6(a)和图6(b))可以得到, 离子与水分子可以形成非常稳固的两层以离子为核心的水合壳. 并且, 驱动力温度对这种水合壳半径影响不大, 故以距离子2—3.3 ?为Na+第一水合层, 3.3—6 ?为Na+第二水合层, 对离子水合层进行分析, 统计出Na+两个水合层内的水分子数和氢键. 以Na+为研究对象, 对水合壳每一层内的水分子和氢键进行统计. 如图7(a)和图7(b)水合状态图, 可以清楚地描述水合作用的强度. 随着温度的升高, 每一水合层的水分子和每个水分子氢键的平均数降低, 而速度的提高与之相反. 每个水合层的水分子越多、氢键数越大, 离子周围水分子联系越紧固, 水合作用越强. 离子水合作用越强, 离子周围水分子通过氢键结合得越紧密, 水合层越难被削弱, 离子也就越难通过纳米孔, 离子截留率也相应提高. 这也就解释了图2中温度越低、剪切速度越大, 水合作用的增强导致离子截留率越高. 图 5 (a) 驱动力为200 MPa无剪切作用时, 水分子沿z轴方向转移的能障随温度的变化; (b) 驱动力为200 MPa时, 水分子沿z轴方向转移的能障随剪切速度的变化 Figure5. (a) The PMF of water molecules along the z-axis at different temperatures for the membrane without shearing; (b) the PMF of water molecules along the z-axis for different shear speeds. The driving pressure in feed solution is 200 MPa.
图 6 (a) 不同驱动压力下, 水分子和盐离子径向分布函数G(r); (b) 不同温度下, 水分子和盐离子径向分布函数G(r) Figure6. (a) Radial distribution function G(r) of water molecules and salt ions under different driving pressures; (b) radial distri-bution function G(r) of water molecules and salt ions at different temperatures.
图 7 (a)不同温度和(b)不同剪切速度下的水合状态图, 其中包含第一水合层水分子平均数(黑色)、第一水合层水分子氢键平均数(红色)、第二水合层水分子平均数(蓝色)和第二水合层(紫色)水分子氢键平均数 Figure7. (a) Hydration state diagram at different temperatures; (b) hydration state diagram at different shear velocities. Black square: The number of water molecules in first hydration shell. Red square: HB in first hydration shell. Blue square: The number of water molecules in second hydration shell. Purple square: HB in second hydration shell.
表3孔径为1.6 nm下选择性和渗透性效益权衡 Table3.Trade-offs between selectivity and permeability with pore diameter of 1.6 nm.
图 8 (a) 不同驱动力、温度、速度条件下, 孔径为1.6 nm的氢化多孔石墨烯盐离子截留率和水通量的关系; (b) 在温度为298 K、剪切速度为0的条件下, 孔径为0.82 nm的不同驱动力的水通量 Figure8. (a) Salt rejection versus water permeability for pore diameter of 1.6 nm under different conditions of pressure, temperature and speed; (b) water permeability as a function of driving pressure for the pore diameter of 0.82 nm at the temperature of 298 K and the shearing speed of 0.